Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, 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("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{130}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 130 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-11.4018\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −29.8035 | −1.91190 | −0.955948 | − | 0.293536i | \(-0.905168\pi\) | ||||
−0.955948 | + | 0.293536i | \(0.905168\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 21.0000 | 0.375659 | 0.187830 | − | 0.982202i | \(-0.439855\pi\) | ||||
0.187830 | + | 0.982202i | \(0.439855\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 645.249 | 2.65535 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −331.874 | −0.826973 | −0.413486 | − | 0.910510i | \(-0.635689\pi\) | ||||
−0.413486 | + | 0.910510i | \(0.635689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −66.8211 | −0.109662 | −0.0548308 | − | 0.998496i | \(-0.517462\pi\) | ||||
−0.0548308 | + | 0.998496i | \(0.517462\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −625.874 | −0.718222 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −240.537 | −0.201864 | −0.100932 | − | 0.994893i | \(-0.532182\pi\) | ||||
−0.100932 | + | 0.994893i | \(0.532182\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 441.979 | 0.280878 | 0.140439 | − | 0.990089i | \(-0.455149\pi\) | ||||
0.140439 | + | 0.990089i | \(0.455149\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1071.37 | 0.422298 | 0.211149 | − | 0.977454i | \(-0.432279\pi\) | ||||
0.211149 | + | 0.977454i | \(0.432279\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2684.00 | −0.858880 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11988.4 | −3.16485 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1791.75 | 0.395623 | 0.197812 | − | 0.980240i | \(-0.436617\pi\) | ||||
0.197812 | + | 0.980240i | \(0.436617\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5688.74 | −1.06319 | −0.531596 | − | 0.846998i | \(-0.678407\pi\) | ||||
−0.531596 | + | 0.846998i | \(0.678407\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 9891.00 | 1.58109 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11210.7 | 1.34626 | 0.673131 | − | 0.739523i | \(-0.264949\pi\) | ||||
0.673131 | + | 0.739523i | \(0.264949\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1991.50 | 0.209662 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12077.9 | −1.12210 | −0.561048 | − | 0.827783i | \(-0.689602\pi\) | ||||
−0.561048 | + | 0.827783i | \(0.689602\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9921.98 | 0.818328 | 0.409164 | − | 0.912461i | \(-0.365820\pi\) | ||||
0.409164 | + | 0.912461i | \(0.365820\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 13550.2 | 0.997506 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −16869.2 | −1.11391 | −0.556956 | − | 0.830542i | \(-0.688031\pi\) | ||||
−0.556956 | + | 0.830542i | \(0.688031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7168.84 | 0.385943 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5298.77 | 0.259111 | 0.129555 | − | 0.991572i | \(-0.458645\pi\) | ||||
0.129555 | + | 0.991572i | \(0.458645\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6969.35 | −0.310660 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13172.5 | −0.537009 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 41384.8 | 1.54778 | 0.773892 | − | 0.633317i | \(-0.218307\pi\) | ||||
0.773892 | + | 0.633317i | \(0.218307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 21523.3 | 0.740601 | 0.370300 | − | 0.928912i | \(-0.379255\pi\) | ||||
0.370300 | + | 0.928912i | \(0.379255\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1403.24 | −0.0411954 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 26618.8 | 0.724437 | 0.362219 | − | 0.932093i | \(-0.382019\pi\) | ||||
0.362219 | + | 0.932093i | \(0.382019\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −31930.5 | −0.807390 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 58096.5 | 1.36774 | 0.683870 | − | 0.729603i | \(-0.260295\pi\) | ||||
0.683870 | + | 0.729603i | \(0.260295\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 39987.5 | 0.878248 | 0.439124 | − | 0.898426i | \(-0.355289\pi\) | ||||
0.439124 | + | 0.898426i | \(0.355289\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 79992.6 | 1.64209 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 43949.8 | 0.792299 | 0.396150 | − | 0.918186i | \(-0.370346\pi\) | ||||
0.396150 | + | 0.918186i | \(0.370346\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 200502. | 3.39552 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 22421.4 | 0.357246 | 0.178623 | − | 0.983918i | \(-0.442836\pi\) | ||||
0.178623 | + | 0.983918i | \(0.442836\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5051.27 | −0.0758322 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −53400.4 | −0.756390 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −24062.0 | −0.322001 | −0.161001 | − | 0.986954i | \(-0.551472\pi\) | ||||
−0.161001 | + | 0.986954i | \(0.551472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 169544. | 2.03271 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9281.56 | 0.105514 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −71896.4 | −0.775850 | −0.387925 | − | 0.921691i | \(-0.626808\pi\) | ||||
−0.387925 | + | 0.921691i | \(0.626808\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −214141. | −2.19590 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15865.5 | 0.154757 | 0.0773783 | − | 0.997002i | \(-0.475345\pi\) | ||||
0.0773783 | + | 0.997002i | \(0.475345\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −160574. | −1.49135 | −0.745677 | − | 0.666307i | \(-0.767874\pi\) | ||||
−0.745677 | + | 0.666307i | \(0.767874\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 205047. | 1.73139 | 0.865693 | − | 0.500575i | \(-0.166878\pi\) | ||||
0.865693 | + | 0.500575i | \(0.166878\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −112544. | −0.907313 | −0.453657 | − | 0.891177i | \(-0.649881\pi\) | ||||
−0.453657 | + | 0.891177i | \(0.649881\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −334119. | −2.57391 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −118332. | −0.871782 | −0.435891 | − | 0.900000i | \(-0.643567\pi\) | ||||
−0.435891 | + | 0.900000i | \(0.643567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22498.7 | 0.158640 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −43116.2 | −0.291190 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −50910.9 | −0.316116 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 359962. | 2.14533 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −121989. | −0.698306 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 245195. | 1.34897 | 0.674485 | − | 0.738289i | \(-0.264366\pi\) | ||||
0.674485 | + | 0.738289i | \(0.264366\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −295710. | −1.56456 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 69993.7 | 0.356353 | 0.178177 | − | 0.983999i | \(-0.442980\pi\) | ||||
0.178177 | + | 0.983999i | \(0.442980\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −251757. | −1.18891 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −187664. | −0.854239 | −0.427119 | − | 0.904195i | \(-0.640472\pi\) | ||||
−0.427119 | + | 0.904195i | \(0.640472\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −78272.7 | −0.343616 | −0.171808 | − | 0.985130i | \(-0.554961\pi\) | ||||
−0.171808 | + | 0.985130i | \(0.554961\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 502763. | 2.12968 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22176.1 | 0.0906872 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 37626.7 | 0.148620 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −92166.4 | −0.340100 | −0.170050 | − | 0.985435i | \(-0.554393\pi\) | ||||
−0.170050 | + | 0.985435i | \(0.554393\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −53416.0 | −0.190646 | −0.0953232 | − | 0.995446i | \(-0.530388\pi\) | ||||
−0.0953232 | + | 0.995446i | \(0.530388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −155206. | −0.536019 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −119463. | −0.399398 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 280501. | 0.908206 | 0.454103 | − | 0.890949i | \(-0.349960\pi\) | ||||
0.454103 | + | 0.890949i | \(0.349960\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −157922. | −0.495393 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −626810. | −1.84785 | −0.923925 | − | 0.382574i | \(-0.875038\pi\) | ||||
−0.923925 | + | 0.382574i | \(0.875038\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 207711. | 0.593950 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 293997. | 0.815741 | 0.407870 | − | 0.913040i | \(-0.366272\pi\) | ||||
0.407870 | + | 0.913040i | \(0.366272\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −366828. | −0.987974 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 285187. | 0.745828 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −714187. | −1.81425 | −0.907124 | − | 0.420864i | \(-0.861727\pi\) | ||||
−0.907124 | + | 0.420864i | \(0.861727\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.23341e6 | −2.95920 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −580050. | −1.35311 | −0.676554 | − | 0.736393i | \(-0.736528\pi\) | ||||
−0.676554 | + | 0.736393i | \(0.736528\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 308046. | 0.698907 | 0.349454 | − | 0.936954i | \(-0.386367\pi\) | ||||
0.349454 | + | 0.936954i | \(0.386367\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −641470. | −1.41595 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 235425. | 0.505736 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 79827.8 | 0.166936 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 202789. | 0.402218 | 0.201109 | − | 0.979569i | \(-0.435545\pi\) | ||||
0.201109 | + | 0.979569i | \(0.435545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 605988. | 1.17104 | 0.585519 | − | 0.810659i | \(-0.300891\pi\) | ||||
0.585519 | + | 0.810659i | \(0.300891\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 41821.5 | 0.0787614 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −310.819 | −0.000570614 0 | −0.000285307 | − | 1.00000i | \(-0.500091\pi\) | ||||
−0.000285307 | 1.00000i | \(0.500091\pi\) | ||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −409666. | −0.733327 | −0.366664 | − | 0.930354i | \(-0.619500\pi\) | ||||
−0.366664 | + | 0.930354i | \(0.619500\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −793332. | −1.38505 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −253635. | −0.421526 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 691300. | 1.12135 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −146681. | −0.232278 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 441339. | 0.682442 | 0.341221 | − | 0.939983i | \(-0.389160\pi\) | ||||
0.341221 | + | 0.939983i | \(0.389160\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.73148e6 | −2.61498 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 208362. | 0.307412 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.19177e6 | −1.67912 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16072.9 | 0.0221368 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 265133. | 0.357028 | 0.178514 | − | 0.983937i | \(-0.442871\pi\) | ||||
0.178514 | + | 0.983937i | \(0.442871\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.73185e6 | −2.28062 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.43044e6 | −1.84249 | −0.921244 | − | 0.388985i | \(-0.872826\pi\) | ||||
−0.921244 | + | 0.388985i | \(0.872826\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.25805e6 | 1.58529 | 0.792646 | − | 0.609682i | \(-0.208703\pi\) | ||||
0.792646 | + | 0.609682i | \(0.208703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 224723. | 0.271180 | 0.135590 | − | 0.990765i | \(-0.456707\pi\) | ||||
0.135590 | + | 0.990765i | \(0.456707\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −354254. | −0.418452 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.30986e6 | −1.51479 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.28193e6 | −1.45167 | −0.725837 | − | 0.687867i | \(-0.758547\pi\) | ||||
−0.725837 | + | 0.687867i | \(0.758547\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 576125. | 0.638961 | 0.319480 | − | 0.947593i | \(-0.396492\pi\) | ||||
0.319480 | + | 0.947593i | \(0.396492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.06247e6 | −3.32703 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29533.5 | −0.0308015 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −668236. | −0.683017 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −609040. | −0.610185 | −0.305092 | − | 0.952323i | \(-0.598687\pi\) | ||||
−0.305092 | + | 0.952323i | \(0.598687\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −355559. | −0.349229 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 150546. | 0.144983 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.03067e6 | −0.973389 | −0.486695 | − | 0.873572i | \(-0.661798\pi\) | ||||
−0.486695 | + | 0.873572i | \(0.661798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.15612e6 | 1.05052 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 910585. | 0.811767 | 0.405883 | − | 0.913925i | \(-0.366964\pi\) | ||||
0.405883 | + | 0.913925i | \(0.366964\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 111274. | 0.0973374 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 717133. | 0.615633 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.42100e6 | −1.19733 | −0.598663 | − | 0.801001i | \(-0.704301\pi\) | ||||
−0.598663 | + | 0.801001i | \(0.704301\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −297530. | −0.246097 | −0.123049 | − | 0.992401i | \(-0.539267\pi\) | ||||
−0.123049 | + | 0.992401i | \(0.539267\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 890749. | 0.710270 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 849612. | 0.665305 | 0.332653 | − | 0.943049i | \(-0.392056\pi\) | ||||
0.332653 | + | 0.943049i | \(0.392056\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.67065e6 | −2.82314 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7680.49 | −0.00580261 | −0.00290130 | − | 0.999996i | \(-0.500924\pi\) | ||||
−0.00290130 | + | 0.999996i | \(0.500924\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −985368. | −0.731362 | −0.365681 | − | 0.930740i | \(-0.619164\pi\) | ||||
−0.365681 | + | 0.930740i | \(0.619164\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −276623. | −0.201733 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.36200e6 | −0.959251 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.14277e6 | 1.48335 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.16934e6 | 1.47625 | 0.738124 | − | 0.674665i | \(-0.235712\pi\) | ||||
0.738124 | + | 0.674665i | \(0.235712\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 869080. | 0.581440 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.97865e6 | 2.61724 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −71590.0 | −0.0463099 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −472846. | −0.295879 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 451989. | 0.278214 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.39093e6 | −0.842287 | −0.421143 | − | 0.906994i | \(-0.638371\pi\) | ||||
−0.421143 | + | 0.906994i | \(0.638371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.78566e6 | 2.85132 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.03794e6 | 1.19479 | 0.597394 | − | 0.801948i | \(-0.296203\pi\) | ||||
0.597394 | + | 0.801948i | \(0.296203\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.16958e6 | 0.674789 | 0.337395 | − | 0.941363i | \(-0.390454\pi\) | ||||
0.337395 | + | 0.941363i | \(0.390454\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 801137. | 0.447774 | 0.223887 | − | 0.974615i | \(-0.428125\pi\) | ||||
0.223887 | + | 0.974615i | \(0.428125\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −594634. | −0.327170 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.11112e6 | −3.31023 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −106312. | −0.0566992 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 179348. | 0.0941862 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.35421e6 | 1.73469 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.64951e6 | −1.32922 | −0.664608 | − | 0.747192i | \(-0.731402\pi\) | ||||
−0.664608 | + | 0.747192i | \(0.731402\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.23371e6 | 3.57479 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 558994. | 0.272142 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.40056e6 | −1.63108 | −0.815541 | − | 0.578699i | \(-0.803560\pi\) | ||||
−0.815541 | + | 0.578699i | \(0.803560\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.52672e6 | 1.66676 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.88794e6 | 0.879230 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −670541. | −0.303304 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 617709. | 0.275398 | 0.137699 | − | 0.990474i | \(-0.456029\pi\) | ||||
0.137699 | + | 0.990474i | \(0.456029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.70539e6 | −1.18896 | −0.594479 | − | 0.804111i | \(-0.702642\pi\) | ||||
−0.594479 | + | 0.804111i | \(0.702642\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 801080. | 0.347063 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.18064e6 | 1.35856 | 0.679279 | − | 0.733880i | \(-0.262293\pi\) | ||||
0.679279 | + | 0.733880i | \(0.262293\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.22003e6 | 0.513805 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.45970e6 | 1.82629 | 0.913145 | − | 0.407635i | \(-0.133646\pi\) | ||||
0.913145 | + | 0.407635i | \(0.133646\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.28075e6 | −0.921108 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.51732e6 | 0.604382 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 839738. | 0.329922 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 461247. | 0.178759 | 0.0893795 | − | 0.995998i | \(-0.471512\pi\) | ||||
0.0893795 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.79322e6 | −2.97955 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.41954e6 | 1.27261 | 0.636305 | − | 0.771437i | \(-0.280462\pi\) | ||||
0.636305 | + | 0.771437i | \(0.280462\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.63570e6 | 1.33509 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −119726. | −0.0433847 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16355.6 | −0.00584882 | −0.00292441 | − | 0.999996i | \(-0.500931\pi\) | ||||
−0.00292441 | + | 0.999996i | \(0.500931\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.30767e6 | −2.57909 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.43643e6 | −1.19705 | −0.598523 | − | 0.801105i | \(-0.704246\pi\) | ||||
−0.598523 | + | 0.801105i | \(0.704246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.40215e6 | 2.17294 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.81052e6 | −1.61183 | −0.805914 | − | 0.592033i | \(-0.798325\pi\) | ||||
−0.805914 | + | 0.592033i | \(0.798325\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −257704. | −0.0852469 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.08606e6 | −0.681310 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 922946. | 0.297635 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.29848e6 | 1.05036 | 0.525180 | − | 0.850991i | \(-0.323998\pi\) | ||||
0.525180 | + | 0.850991i | \(0.323998\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 136164. | 0.0422865 | 0.0211432 | − | 0.999776i | \(-0.493269\pi\) | ||||
0.0211432 | + | 0.999776i | \(0.493269\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 380127. | 0.116591 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.21054e6 | 1.27556 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.72054e6 | −1.11332 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.74869e6 | −0.812490 | −0.406245 | − | 0.913764i | \(-0.633162\pi\) | ||||
−0.406245 | + | 0.913764i | \(0.633162\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.59304e6 | 1.63322 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 470849. | 0.134203 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.33280e6 | 0.656958 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.87219e6 | −0.520973 | −0.260486 | − | 0.965478i | \(-0.583883\pi\) | ||||
−0.260486 | + | 0.965478i | \(0.583883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 655225. | 0.180171 | 0.0900856 | − | 0.995934i | \(-0.471286\pi\) | ||||
0.0900856 | + | 0.995934i | \(0.471286\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.08849e7 | −2.95782 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 645601. | 0.173377 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −660927. | −0.173385 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.37690e6 | −1.65355 | −0.826773 | − | 0.562535i | \(-0.809826\pi\) | ||||
−0.826773 | + | 0.562535i | \(0.809826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.80003e6 | −1.23034 | −0.615168 | − | 0.788396i | \(-0.710912\pi\) | ||||
−0.615168 | + | 0.788396i | \(0.710912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.12141e6 | −0.284145 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 473522. | 0.118614 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.59508e6 | −1.38562 | −0.692811 | − | 0.721119i | \(-0.743628\pi\) | ||||
−0.692811 | + | 0.721119i | \(0.743628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.14010e6 | −1.00231 | −0.501154 | − | 0.865358i | \(-0.667091\pi\) | ||||
−0.501154 | + | 0.865358i | \(0.667091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −505303. | −0.120963 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.74688e6 | 0.650237 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −305966. | −0.0716239 | −0.0358119 | − | 0.999359i | \(-0.511402\pi\) | ||||
−0.0358119 | + | 0.999359i | \(0.511402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00832e6 | 0.927943 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.59198e6 | 0.364496 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 892608. | 0.199926 | 0.0999632 | − | 0.994991i | \(-0.468127\pi\) | ||||
0.0999632 | + | 0.994991i | \(0.468127\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.88366e6 | 0.638870 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.01465e6 | 0.660670 | 0.330335 | − | 0.943864i | \(-0.392838\pi\) | ||||
0.330335 | + | 0.943864i | \(0.392838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.45497e6 | −0.749017 | −0.374508 | − | 0.927224i | \(-0.622188\pi\) | ||||
−0.374508 | + | 0.927224i | \(0.622188\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.56043e6 | 0.763607 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.83776e6 | 0.602120 | 0.301060 | − | 0.953605i | \(-0.402660\pi\) | ||||
0.301060 | + | 0.953605i | \(0.402660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.35990e6 | −1.73640 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.29284e6 | −0.676734 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.18627e6 | −0.241240 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.41903e6 | 0.688028 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.70442e6 | −0.936845 | −0.468422 | − | 0.883505i | \(-0.655177\pi\) | ||||
−0.468422 | + | 0.883505i | \(0.655177\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −749113. | −0.147633 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.50982e6 | −0.291455 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.16634e6 | −0.796036 | −0.398018 | − | 0.917378i | \(-0.630302\pi\) | ||||
−0.398018 | + | 0.917378i | \(0.630302\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.86811e7 | 3.53290 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.57876e6 | −0.295537 | −0.147768 | − | 0.989022i | \(-0.547209\pi\) | ||||
−0.147768 | + | 0.989022i | \(0.547209\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −430981. | −0.0798622 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.49697e6 | −0.824910 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.55712e6 | −0.279943 | −0.139972 | − | 0.990156i | \(-0.544701\pi\) | ||||
−0.139972 | + | 0.990156i | \(0.544701\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.76215e6 | −1.55961 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.19459e6 | −0.210523 | −0.105261 | − | 0.994445i | \(-0.533568\pi\) | ||||
−0.105261 | + | 0.994445i | \(0.533568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 333175. | 0.0581358 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.09328e7 | 1.88890 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.16857e6 | −0.542087 | −0.271043 | − | 0.962567i | \(-0.587369\pi\) | ||||
−0.271043 | + | 0.962567i | \(0.587369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.29864e6 | −0.888936 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.37204e6 | −0.560241 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.59846e6 | 0.921175 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.12853e7 | 3.46865 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.00658e6 | 0.162462 | 0.0812312 | − | 0.996695i | \(-0.474115\pi\) | ||||
0.0812312 | + | 0.996695i | \(0.474115\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.78985e6 | 1.40517 | 0.702583 | − | 0.711602i | \(-0.252030\pi\) | ||||
0.702583 | + | 0.711602i | \(0.252030\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.36835e6 | 0.214620 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.28851e6 | −0.821664 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.67035e7 | 4.10990 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 807055. | 0.123051 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.30599e6 | 0.650412 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.72875e7 | 2.58700 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.54864e6 | −0.521277 | −0.260639 | − | 0.965436i | \(-0.583933\pi\) | ||||
−0.260639 | + | 0.965436i | \(0.583933\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.18086e6 | −1.33624 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.36343e6 | −0.340841 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.68179e6 | −0.669027 | −0.334513 | − | 0.942391i | \(-0.608572\pi\) | ||||
−0.334513 | + | 0.942391i | \(0.608572\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.38879e7 | 1.96655 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 791915. | 0.111122 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.01650e6 | −0.966914 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.79507e6 | 0.791445 | 0.395723 | − | 0.918370i | \(-0.370494\pi\) | ||||
0.395723 | + | 0.918370i | \(0.370494\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −662997. | −0.0897392 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.37915e6 | −0.319165 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.59703e6 | −1.01012 | −0.505060 | − | 0.863084i | \(-0.668530\pi\) | ||||
−0.505060 | + | 0.863084i | \(0.668530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.48498e6 | −0.327493 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.81699e6 | −1.27115 | −0.635576 | − | 0.772038i | \(-0.719237\pi\) | ||||
−0.635576 | + | 0.772038i | \(0.719237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.25888e6 | −0.674999 | −0.337499 | − | 0.941326i | \(-0.609581\pi\) | ||||
−0.337499 | + | 0.941326i | \(0.609581\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.04384e6 | −0.769000 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.87555e6 | −0.362703 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.63468e6 | −1.07971 | −0.539855 | − | 0.841758i | \(-0.681521\pi\) | ||||
−0.539855 | + | 0.841758i | \(0.681521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.80606e7 | −2.23890 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.75852e6 | −0.214277 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −905441. | −0.109388 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.32014e6 | −0.397705 | −0.198852 | − | 0.980029i | \(-0.563721\pi\) | ||||
−0.198852 | + | 0.980029i | \(0.563721\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.51430e6 | −0.298627 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9263.50 | 0.00109095 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.40001e6 | 0.747384 | 0.373692 | − | 0.927553i | \(-0.378092\pi\) | ||||
0.373692 | + | 0.927553i | \(0.378092\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.22095e7 | 1.40204 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.49862e6 | −0.853915 | −0.426957 | − | 0.904272i | \(-0.640415\pi\) | ||||
−0.426957 | + | 0.904272i | \(0.640415\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 227052. | 0.0256412 | 0.0128206 | − | 0.999918i | \(-0.495919\pi\) | ||||
0.0128206 | + | 0.999918i | \(0.495919\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.71757e7 | 1.92363 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.06913e6 | −0.118752 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.63037e7 | 1.79603 | 0.898015 | − | 0.439965i | \(-0.145009\pi\) | ||||
0.898015 | + | 0.439965i | \(0.145009\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.12722e6 | 0.122153 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.04062e7 | −1.11852 | −0.559259 | − | 0.828993i | \(-0.688914\pi\) | ||||
−0.559259 | + | 0.828993i | \(0.688914\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.55921e6 | 0.805914 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.74140e6 | 0.501411 | 0.250705 | − | 0.968063i | \(-0.419337\pi\) | ||||
0.250705 | + | 0.968063i | \(0.419337\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.08534e7 | −1.13851 | −0.569256 | − | 0.822160i | \(-0.692769\pi\) | ||||
−0.569256 | + | 0.822160i | \(0.692769\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.28440e7 | −1.33651 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.82573e6 | 0.596555 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.37161e6 | 0.444092 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.69659e6 | −0.271762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.58978e7 | −1.58951 | −0.794757 | − | 0.606928i | \(-0.792402\pi\) | ||||
−0.794757 | + | 0.606928i | \(0.792402\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.31534e7 | −1.30476 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.14909e6 | 0.506753 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.74867e7 | 3.63183 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.11828e7 | 1.07499 | 0.537496 | − | 0.843267i | \(-0.319371\pi\) | ||||
0.537496 | + | 0.843267i | \(0.319371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.55983e6 | 0.148782 | 0.0743909 | − | 0.997229i | \(-0.476299\pi\) | ||||
0.0743909 | + | 0.997229i | \(0.476299\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.20991e6 | −0.587741 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.54824e7 | −1.45404 | −0.727020 | − | 0.686616i | \(-0.759095\pi\) | ||||
−0.727020 | + | 0.686616i | \(0.759095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.37345e7 | −1.27998 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 614752. | 0.0564179 | 0.0282090 | − | 0.999602i | \(-0.491020\pi\) | ||||
0.0282090 | + | 0.999602i | \(0.491020\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.46987e6 | 0.133867 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.58019e7 | 2.33205 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.32697e7 | 1.19028 | 0.595139 | − | 0.803623i | \(-0.297097\pi\) | ||||
0.595139 | + | 0.803623i | \(0.297097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.03584e6 | −0.448299 | −0.224150 | − | 0.974555i | \(-0.571960\pi\) | ||||
−0.224150 | + | 0.974555i | \(0.571960\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −479030. | −0.0423232 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.91962e6 | 0.167071 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.90190e6 | −0.682600 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.14301e6 | −0.612457 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.28068e6 | 0.704739 | 0.352369 | − | 0.935861i | \(-0.385376\pi\) | ||||
0.352369 | + | 0.935861i | \(0.385376\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.21770e7 | 2.71823 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.52513e7 | 1.27889 | 0.639446 | − | 0.768836i | \(-0.279164\pi\) | ||||
0.639446 | + | 0.768836i | \(0.279164\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.26321e7 | 3.52265 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.88673e6 | −0.646912 | −0.323456 | − | 0.946243i | \(-0.604845\pi\) | ||||
−0.323456 | + | 0.946243i | \(0.604845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.94094e6 | −0.320903 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.74943e7 | −3.03091 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −354069. | −0.0284145 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.66190e6 | −0.132407 | −0.0662033 | − | 0.997806i | \(-0.521089\pi\) | ||||
−0.0662033 | + | 0.997806i | \(0.521089\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.64373e6 | −0.129083 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.90517e6 | 0.226511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.69754e6 | −0.518469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.39364e7 | −1.07117 | −0.535583 | − | 0.844483i | \(-0.679908\pi\) | ||||
−0.535583 | + | 0.844483i | \(0.679908\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.95490e6 | 0.378135 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.05580e7 | 0.800036 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.01874e7 | −0.761108 | −0.380554 | − | 0.924759i | \(-0.624267\pi\) | ||||
−0.380554 | + | 0.924759i | \(0.624267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.83586e7 | 2.10383 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.09473e6 | −0.448984 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 465699. | 0.0340675 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.82060e7 | 2.77545 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.39169e7 | 1.00397 | 0.501983 | − | 0.864877i | \(-0.332604\pi\) | ||||
0.501983 | + | 0.864877i | \(0.332604\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.71705e7 | −1.22163 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.80905e6 | −0.339793 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.42063e6 | 0.240033 | 0.120016 | − | 0.992772i | \(-0.461705\pi\) | ||||
0.120016 | + | 0.992772i | \(0.461705\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.25504e7 | 2.96541 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.38660e6 | −0.165191 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.03162e7 | 0.709186 | 0.354593 | − | 0.935021i | \(-0.384619\pi\) | ||||
0.354593 | + | 0.935021i | \(0.384619\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.83406e6 | −0.599090 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.03890e7 | 0.699779 | 0.349889 | − | 0.936791i | \(-0.386219\pi\) | ||||
0.349889 | + | 0.936791i | \(0.386219\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 880202. | 0.0588893 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.04738e7 | 0.696035 | 0.348018 | − | 0.937488i | \(-0.386855\pi\) | ||||
0.348018 | + | 0.937488i | \(0.386855\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.93550e6 | −0.127762 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.44674e7 | 0.948612 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.40445e6 | 0.608462 | 0.304231 | − | 0.952598i | \(-0.401600\pi\) | ||||
0.304231 | + | 0.952598i | \(0.401600\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.81515e7 | 1.16661 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.12174e6 | −0.0716181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.33677e7 | −0.847848 | −0.423924 | − | 0.905698i | \(-0.639348\pi\) | ||||
−0.423924 | + | 0.905698i | \(0.639348\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.05969e7 | 0.667690 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.22623e7 | 1.39350 | 0.696752 | − | 0.717312i | \(-0.254628\pi\) | ||||
0.696752 | + | 0.717312i | \(0.254628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.25933e6 | −0.201361 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.76537e6 | −0.169733 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.65833e6 | −0.588961 | −0.294480 | − | 0.955658i | \(-0.595147\pi\) | ||||
−0.294480 | + | 0.955658i | \(0.595147\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.07176e7 | 1.86102 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.10951e6 | 0.307561 | 0.153780 | − | 0.988105i | \(-0.450855\pi\) | ||||
0.153780 | + | 0.988105i | \(0.450855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.52686e7 | 0.913154 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.33816e6 | −0.315172 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.92807e7 | −1.13108 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.14802e7 | −1.25209 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.89051e6 | 0.341176 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.51592e7 | 1.44797 | 0.723984 | − | 0.689816i | \(-0.242309\pi\) | ||||
0.723984 | + | 0.689816i | \(0.242309\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.71386e7 | −1.55201 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.43821e6 | −0.0812155 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.31636e6 | −0.186099 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.35976e6 | 0.187354 | 0.0936768 | − | 0.995603i | \(-0.470138\pi\) | ||||
0.0936768 | + | 0.995603i | \(0.470138\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.05767e6 | 0.224859 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.55260e7 | −0.855024 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.32708e7 | −0.726287 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.23507e7 | 2.28916 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.97050e7 | −1.59572 | −0.797862 | − | 0.602840i | \(-0.794036\pi\) | ||||
−0.797862 | + | 0.602840i | \(0.794036\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.26386e7 | 0.674757 | 0.337379 | − | 0.941369i | \(-0.390460\pi\) | ||||
0.337379 | + | 0.941369i | \(0.390460\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.86743e6 | 0.470513 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.31630e7 | −0.694162 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.38531e6 | 0.229850 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.61760e7 | −1.35533 | −0.677666 | − | 0.735370i | \(-0.737008\pi\) | ||||
−0.677666 | + | 0.735370i | \(0.737008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.29843e6 | 0.375604 | 0.187802 | − | 0.982207i | \(-0.439864\pi\) | ||||
0.187802 | + | 0.982207i | \(0.439864\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.65474e7 | −1.35796 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.18681e7 | −0.603418 | −0.301709 | − | 0.953400i | \(-0.597557\pi\) | ||||
−0.301709 | + | 0.953400i | \(0.597557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.04338e7 | 0.527298 | 0.263649 | − | 0.964619i | \(-0.415074\pi\) | ||||
0.263649 | + | 0.964619i | \(0.415074\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.53214e7 | −1.27199 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.17394e6 | 0.306441 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.81991e7 | 3.36484 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.91444e7 | −1.42939 | −0.714695 | − | 0.699436i | \(-0.753435\pi\) | ||||
−0.714695 | + | 0.699436i | \(0.753435\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.73008e7 | −0.843482 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 228906. | 0.0110940 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.70339e6 | −0.371142 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.93674e7 | 1.39829 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.20108e7 | 0.568524 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.63032e7 | −1.23776 | −0.618879 | − | 0.785487i | \(-0.712413\pi\) | ||||
−0.618879 | + | 0.785487i | \(0.712413\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.98892e6 | 0.280177 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.43598e6 | −0.159808 | −0.0799040 | − | 0.996803i | \(-0.525461\pi\) | ||||
−0.0799040 | + | 0.996803i | \(0.525461\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.09139e7 | 0.504659 | 0.252329 | − | 0.967641i | \(-0.418803\pi\) | ||||
0.252329 | + | 0.967641i | \(0.418803\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.19058e7 | −1.00123 | −0.500614 | − | 0.865671i | \(-0.666892\pi\) | ||||
−0.500614 | + | 0.865671i | \(0.666892\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.49979e7 | −0.681539 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.05923e7 | 1.83399 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.45858e7 | −0.655210 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.77869e6 | −0.0794430 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.63911e7 | −2.06015 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.46927e6 | 0.284025 | 0.142012 | − | 0.989865i | \(-0.454643\pi\) | ||||
0.142012 | + | 0.989865i | \(0.454643\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.46540e7 | −2.82243 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.03983e7 | −0.885430 | −0.442715 | − | 0.896662i | \(-0.645985\pi\) | ||||
−0.442715 | + | 0.896662i | \(0.645985\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.62381e7 | −0.700862 | −0.350431 | − | 0.936589i | \(-0.613965\pi\) | ||||
−0.350431 | + | 0.936589i | \(0.613965\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.59016e7 | −1.11165 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.79027e6 | −0.289786 | −0.144893 | − | 0.989447i | \(-0.546284\pi\) | ||||
−0.144893 | + | 0.989447i | \(0.546284\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.65413e7 | −2.80800 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.45585e6 | −0.312873 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.21810e7 | −0.508308 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.13363e6 | 0.0885398 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.01928e7 | −0.420623 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.27455e6 | −0.0523052 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.46897e6 | 0.262551 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.42142e7 | −1.38098 | −0.690492 | − | 0.723340i | \(-0.742606\pi\) | ||||
−0.690492 | + | 0.723340i | \(0.742606\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.02372e7 | 0.410932 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.47390e6 | 0.178604 | 0.0893019 | − | 0.996005i | \(-0.471536\pi\) | ||||
0.0893019 | + | 0.996005i | \(0.471536\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.44107e6 | −0.295433 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.34709e7 | −0.531916 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 537900. | 0.0210094 | 0.0105047 | − | 0.999945i | \(-0.496656\pi\) | ||||
0.0105047 | + | 0.999945i | \(0.496656\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.14547e7 | 1.61036 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.88207e6 | −0.149989 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00896e7 | −1.15628 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.03610e8 | −3.96006 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.77241e7 | 0.673792 | 0.336896 | − | 0.941542i | \(-0.390623\pi\) | ||||
0.336896 | + | 0.941542i | \(0.390623\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.07379e7 | −2.28431 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.67638e6 | 0.0627111 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.32444e7 | 1.23700 | 0.618499 | − | 0.785786i | \(-0.287741\pi\) | ||||
0.618499 | + | 0.785786i | \(0.287741\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.48575e7 | −1.29013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.78480e7 | −1.02523 | −0.512613 | − | 0.858620i | \(-0.671322\pi\) | ||||
−0.512613 | + | 0.858620i | \(0.671322\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.29398e7 | −0.473859 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.30569e7 | 0.835459 | 0.417729 | − | 0.908571i | \(-0.362826\pi\) | ||||
0.417729 | + | 0.908571i | \(0.362826\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.67201e6 | −0.0963102 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.38767e7 | −0.856097 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.85536e7 | 1.01843 | 0.509213 | − | 0.860641i | \(-0.329937\pi\) | ||||
0.509213 | + | 0.860641i | \(0.329937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.25858e6 | 0.151097 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.77222e7 | 0.625514 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.73258e6 | 0.130377 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.32306e8 | 4.59743 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.27257e7 | 0.439911 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.45310e7 | 1.18753 | 0.593763 | − | 0.804640i | \(-0.297642\pi\) | ||||
0.593763 | + | 0.804640i | \(0.297642\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.16848e6 | 0.108403 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.24933e7 | 0.425236 | 0.212618 | − | 0.977135i | \(-0.431801\pi\) | ||||
0.212618 | + | 0.977135i | \(0.431801\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.34519e6 | −0.180074 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.89440e7 | −1.30528 | −0.652641 | − | 0.757667i | \(-0.726339\pi\) | ||||
−0.652641 | + | 0.757667i | \(0.726339\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.98556e6 | 0.266286 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.26191e7 | −2.40923 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 279901. | 0.00923889 | 0.00461945 | − | 0.999989i | \(-0.498530\pi\) | ||||
0.00461945 | + | 0.999989i | \(0.498530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6527.20 | −0.000214356 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.06301e7 | 0.345578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.96343e7 | −0.635084 | −0.317542 | − | 0.948244i | \(-0.602858\pi\) | ||||
−0.317542 | + | 0.948244i | \(0.602858\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.89647e7 | 2.54132 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.60299e6 | −0.275481 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.73374e7 | 1.18961 | 0.594807 | − | 0.803868i | \(-0.297228\pi\) | ||||
0.594807 | + | 0.803868i | \(0.297228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.34399e8 | −4.26072 |
(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 | 784.6.a.r.1.1 | 2 | ||
4.3 | odd | 2 | 98.6.a.f.1.2 | 2 | |||
7.3 | odd | 6 | 112.6.i.b.65.1 | 4 | |||
7.5 | odd | 6 | 112.6.i.b.81.1 | 4 | |||
7.6 | odd | 2 | 784.6.a.bc.1.2 | 2 | |||
12.11 | even | 2 | 882.6.a.bl.1.1 | 2 | |||
28.3 | even | 6 | 14.6.c.b.9.2 | ✓ | 4 | ||
28.11 | odd | 6 | 98.6.c.f.79.1 | 4 | |||
28.19 | even | 6 | 14.6.c.b.11.2 | yes | 4 | ||
28.23 | odd | 6 | 98.6.c.f.67.1 | 4 | |||
28.27 | even | 2 | 98.6.a.c.1.1 | 2 | |||
84.47 | odd | 6 | 126.6.g.e.109.1 | 4 | |||
84.59 | odd | 6 | 126.6.g.e.37.1 | 4 | |||
84.83 | odd | 2 | 882.6.a.bt.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.c.b.9.2 | ✓ | 4 | 28.3 | even | 6 | ||
14.6.c.b.11.2 | yes | 4 | 28.19 | even | 6 | ||
98.6.a.c.1.1 | 2 | 28.27 | even | 2 | |||
98.6.a.f.1.2 | 2 | 4.3 | odd | 2 | |||
98.6.c.f.67.1 | 4 | 28.23 | odd | 6 | |||
98.6.c.f.79.1 | 4 | 28.11 | odd | 6 | |||
112.6.i.b.65.1 | 4 | 7.3 | odd | 6 | |||
112.6.i.b.81.1 | 4 | 7.5 | odd | 6 | |||
126.6.g.e.37.1 | 4 | 84.59 | odd | 6 | |||
126.6.g.e.109.1 | 4 | 84.47 | odd | 6 | |||
784.6.a.r.1.1 | 2 | 1.1 | even | 1 | trivial | ||
784.6.a.bc.1.2 | 2 | 7.6 | odd | 2 | |||
882.6.a.bl.1.1 | 2 | 12.11 | even | 2 | |||
882.6.a.bt.1.1 | 2 | 84.83 | odd | 2 |