Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,4,Mod(1,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1850.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.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: | \(109.153533511\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1850.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 5.00000 | 0.962250 | 0.481125 | − | 0.876652i | \(-0.340228\pi\) | ||||
0.481125 | + | 0.876652i | \(0.340228\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −10.0000 | −0.680414 | ||||||||
\(7\) | 19.0000 | 1.02590 | 0.512952 | − | 0.858417i | \(-0.328552\pi\) | ||||
0.512952 | + | 0.858417i | \(0.328552\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.00000 | 0.137051 | 0.0685253 | − | 0.997649i | \(-0.478171\pi\) | ||||
0.0685253 | + | 0.997649i | \(0.478171\pi\) | |||||||
\(12\) | 20.0000 | 0.481125 | ||||||||
\(13\) | −6.00000 | −0.128008 | −0.0640039 | − | 0.997950i | \(-0.520387\pi\) | ||||
−0.0640039 | + | 0.997950i | \(0.520387\pi\) | |||||||
\(14\) | −38.0000 | −0.725423 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 72.0000 | 1.02721 | 0.513605 | − | 0.858027i | \(-0.328310\pi\) | ||||
0.513605 | + | 0.858027i | \(0.328310\pi\) | |||||||
\(18\) | 4.00000 | 0.0523783 | ||||||||
\(19\) | −44.0000 | −0.531279 | −0.265639 | − | 0.964072i | \(-0.585583\pi\) | ||||
−0.265639 | + | 0.964072i | \(0.585583\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 95.0000 | 0.987176 | ||||||||
\(22\) | −10.0000 | −0.0969094 | ||||||||
\(23\) | −182.000 | −1.64998 | −0.824992 | − | 0.565145i | \(-0.808820\pi\) | ||||
−0.824992 | + | 0.565145i | \(0.808820\pi\) | |||||||
\(24\) | −40.0000 | −0.340207 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.0000 | 0.0905151 | ||||||||
\(27\) | −145.000 | −1.03353 | ||||||||
\(28\) | 76.0000 | 0.512952 | ||||||||
\(29\) | 10.0000 | 0.0640329 | 0.0320164 | − | 0.999487i | \(-0.489807\pi\) | ||||
0.0320164 | + | 0.999487i | \(0.489807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −244.000 | −1.41367 | −0.706834 | − | 0.707380i | \(-0.749877\pi\) | ||||
−0.706834 | + | 0.707380i | \(0.749877\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 25.0000 | 0.131877 | ||||||||
\(34\) | −144.000 | −0.726347 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.00000 | −0.0370370 | ||||||||
\(37\) | 37.0000 | 0.164399 | ||||||||
\(38\) | 88.0000 | 0.375671 | ||||||||
\(39\) | −30.0000 | −0.123176 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −225.000 | −0.857051 | −0.428526 | − | 0.903530i | \(-0.640967\pi\) | ||||
−0.428526 | + | 0.903530i | \(0.640967\pi\) | |||||||
\(42\) | −190.000 | −0.698039 | ||||||||
\(43\) | 2.00000 | 0.00709296 | 0.00354648 | − | 0.999994i | \(-0.498871\pi\) | ||||
0.00354648 | + | 0.999994i | \(0.498871\pi\) | |||||||
\(44\) | 20.0000 | 0.0685253 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 364.000 | 1.16671 | ||||||||
\(47\) | −221.000 | −0.685876 | −0.342938 | − | 0.939358i | \(-0.611422\pi\) | ||||
−0.342938 | + | 0.939358i | \(0.611422\pi\) | |||||||
\(48\) | 80.0000 | 0.240563 | ||||||||
\(49\) | 18.0000 | 0.0524781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 360.000 | 0.988433 | ||||||||
\(52\) | −24.0000 | −0.0640039 | ||||||||
\(53\) | 659.000 | 1.70794 | 0.853968 | − | 0.520325i | \(-0.174189\pi\) | ||||
0.853968 | + | 0.520325i | \(0.174189\pi\) | |||||||
\(54\) | 290.000 | 0.730815 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −152.000 | −0.362712 | ||||||||
\(57\) | −220.000 | −0.511223 | ||||||||
\(58\) | −20.0000 | −0.0452781 | ||||||||
\(59\) | 156.000 | 0.344228 | 0.172114 | − | 0.985077i | \(-0.444940\pi\) | ||||
0.172114 | + | 0.985077i | \(0.444940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −620.000 | −1.30136 | −0.650679 | − | 0.759353i | \(-0.725516\pi\) | ||||
−0.650679 | + | 0.759353i | \(0.725516\pi\) | |||||||
\(62\) | 488.000 | 0.999614 | ||||||||
\(63\) | −38.0000 | −0.0759929 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −50.0000 | −0.0932511 | ||||||||
\(67\) | −416.000 | −0.758545 | −0.379272 | − | 0.925285i | \(-0.623826\pi\) | ||||
−0.379272 | + | 0.925285i | \(0.623826\pi\) | |||||||
\(68\) | 288.000 | 0.513605 | ||||||||
\(69\) | −910.000 | −1.58770 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1125.00 | −1.88046 | −0.940232 | − | 0.340535i | \(-0.889392\pi\) | ||||
−0.940232 | + | 0.340535i | \(0.889392\pi\) | |||||||
\(72\) | 16.0000 | 0.0261891 | ||||||||
\(73\) | 641.000 | 1.02772 | 0.513859 | − | 0.857875i | \(-0.328216\pi\) | ||||
0.513859 | + | 0.857875i | \(0.328216\pi\) | |||||||
\(74\) | −74.0000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −176.000 | −0.265639 | ||||||||
\(77\) | 95.0000 | 0.140601 | ||||||||
\(78\) | 60.0000 | 0.0870982 | ||||||||
\(79\) | −484.000 | −0.689294 | −0.344647 | − | 0.938732i | \(-0.612001\pi\) | ||||
−0.344647 | + | 0.938732i | \(0.612001\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | 450.000 | 0.606027 | ||||||||
\(83\) | −1239.00 | −1.63853 | −0.819265 | − | 0.573416i | \(-0.805618\pi\) | ||||
−0.819265 | + | 0.573416i | \(0.805618\pi\) | |||||||
\(84\) | 380.000 | 0.493588 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | −0.00501548 | ||||||||
\(87\) | 50.0000 | 0.0616157 | ||||||||
\(88\) | −40.0000 | −0.0484547 | ||||||||
\(89\) | 1304.00 | 1.55308 | 0.776538 | − | 0.630071i | \(-0.216974\pi\) | ||||
0.776538 | + | 0.630071i | \(0.216974\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −114.000 | −0.131324 | ||||||||
\(92\) | −728.000 | −0.824992 | ||||||||
\(93\) | −1220.00 | −1.36030 | ||||||||
\(94\) | 442.000 | 0.484987 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −160.000 | −0.170103 | ||||||||
\(97\) | 560.000 | 0.586179 | 0.293090 | − | 0.956085i | \(-0.405317\pi\) | ||||
0.293090 | + | 0.956085i | \(0.405317\pi\) | |||||||
\(98\) | −36.0000 | −0.0371076 | ||||||||
\(99\) | −10.0000 | −0.0101519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 735.000 | 0.724111 | 0.362056 | − | 0.932156i | \(-0.382075\pi\) | ||||
0.362056 | + | 0.932156i | \(0.382075\pi\) | |||||||
\(102\) | −720.000 | −0.698928 | ||||||||
\(103\) | 650.000 | 0.621810 | 0.310905 | − | 0.950441i | \(-0.399368\pi\) | ||||
0.310905 | + | 0.950441i | \(0.399368\pi\) | |||||||
\(104\) | 48.0000 | 0.0452576 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1318.00 | −1.20769 | ||||||||
\(107\) | −1956.00 | −1.76723 | −0.883615 | − | 0.468214i | \(-0.844898\pi\) | ||||
−0.883615 | + | 0.468214i | \(0.844898\pi\) | |||||||
\(108\) | −580.000 | −0.516764 | ||||||||
\(109\) | 1620.00 | 1.42356 | 0.711779 | − | 0.702403i | \(-0.247890\pi\) | ||||
0.711779 | + | 0.702403i | \(0.247890\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 185.000 | 0.158193 | ||||||||
\(112\) | 304.000 | 0.256476 | ||||||||
\(113\) | 934.000 | 0.777552 | 0.388776 | − | 0.921332i | \(-0.372898\pi\) | ||||
0.388776 | + | 0.921332i | \(0.372898\pi\) | |||||||
\(114\) | 440.000 | 0.361489 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 40.0000 | 0.0320164 | ||||||||
\(117\) | 12.0000 | 0.00948205 | ||||||||
\(118\) | −312.000 | −0.243406 | ||||||||
\(119\) | 1368.00 | 1.05382 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1306.00 | −0.981217 | ||||||||
\(122\) | 1240.00 | 0.920199 | ||||||||
\(123\) | −1125.00 | −0.824698 | ||||||||
\(124\) | −976.000 | −0.706834 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 76.0000 | 0.0537351 | ||||||||
\(127\) | −1899.00 | −1.32684 | −0.663421 | − | 0.748246i | \(-0.730896\pi\) | ||||
−0.663421 | + | 0.748246i | \(0.730896\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 10.0000 | 0.00682520 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −236.000 | −0.157400 | −0.0787001 | − | 0.996898i | \(-0.525077\pi\) | ||||
−0.0787001 | + | 0.996898i | \(0.525077\pi\) | |||||||
\(132\) | 100.000 | 0.0659385 | ||||||||
\(133\) | −836.000 | −0.545041 | ||||||||
\(134\) | 832.000 | 0.536372 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −576.000 | −0.363173 | ||||||||
\(137\) | −1610.00 | −1.00403 | −0.502013 | − | 0.864860i | \(-0.667407\pi\) | ||||
−0.502013 | + | 0.864860i | \(0.667407\pi\) | |||||||
\(138\) | 1820.00 | 1.12267 | ||||||||
\(139\) | −500.000 | −0.305104 | −0.152552 | − | 0.988295i | \(-0.548749\pi\) | ||||
−0.152552 | + | 0.988295i | \(0.548749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1105.00 | −0.659984 | ||||||||
\(142\) | 2250.00 | 1.32969 | ||||||||
\(143\) | −30.0000 | −0.0175435 | ||||||||
\(144\) | −32.0000 | −0.0185185 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1282.00 | −0.726706 | ||||||||
\(147\) | 90.0000 | 0.0504971 | ||||||||
\(148\) | 148.000 | 0.0821995 | ||||||||
\(149\) | 1751.00 | 0.962735 | 0.481367 | − | 0.876519i | \(-0.340140\pi\) | ||||
0.481367 | + | 0.876519i | \(0.340140\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2704.00 | −1.45727 | −0.728637 | − | 0.684900i | \(-0.759846\pi\) | ||||
−0.728637 | + | 0.684900i | \(0.759846\pi\) | |||||||
\(152\) | 352.000 | 0.187835 | ||||||||
\(153\) | −144.000 | −0.0760896 | ||||||||
\(154\) | −190.000 | −0.0994197 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −120.000 | −0.0615878 | ||||||||
\(157\) | 2661.00 | 1.35268 | 0.676341 | − | 0.736589i | \(-0.263565\pi\) | ||||
0.676341 | + | 0.736589i | \(0.263565\pi\) | |||||||
\(158\) | 968.000 | 0.487405 | ||||||||
\(159\) | 3295.00 | 1.64346 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3458.00 | −1.69272 | ||||||||
\(162\) | 1342.00 | 0.650849 | ||||||||
\(163\) | −1854.00 | −0.890899 | −0.445449 | − | 0.895307i | \(-0.646956\pi\) | ||||
−0.445449 | + | 0.895307i | \(0.646956\pi\) | |||||||
\(164\) | −900.000 | −0.428526 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2478.00 | 1.15862 | ||||||||
\(167\) | 1808.00 | 0.837768 | 0.418884 | − | 0.908040i | \(-0.362421\pi\) | ||||
0.418884 | + | 0.908040i | \(0.362421\pi\) | |||||||
\(168\) | −760.000 | −0.349019 | ||||||||
\(169\) | −2161.00 | −0.983614 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 88.0000 | 0.0393540 | ||||||||
\(172\) | 8.00000 | 0.00354648 | ||||||||
\(173\) | 3619.00 | 1.59045 | 0.795224 | − | 0.606316i | \(-0.207353\pi\) | ||||
0.795224 | + | 0.606316i | \(0.207353\pi\) | |||||||
\(174\) | −100.000 | −0.0435689 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 80.0000 | 0.0342627 | ||||||||
\(177\) | 780.000 | 0.331234 | ||||||||
\(178\) | −2608.00 | −1.09819 | ||||||||
\(179\) | 34.0000 | 0.0141971 | 0.00709855 | − | 0.999975i | \(-0.497740\pi\) | ||||
0.00709855 | + | 0.999975i | \(0.497740\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 737.000 | 0.302656 | 0.151328 | − | 0.988484i | \(-0.451645\pi\) | ||||
0.151328 | + | 0.988484i | \(0.451645\pi\) | |||||||
\(182\) | 228.000 | 0.0928598 | ||||||||
\(183\) | −3100.00 | −1.25223 | ||||||||
\(184\) | 1456.00 | 0.583357 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2440.00 | 0.961879 | ||||||||
\(187\) | 360.000 | 0.140780 | ||||||||
\(188\) | −884.000 | −0.342938 | ||||||||
\(189\) | −2755.00 | −1.06030 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1704.00 | 0.645535 | 0.322767 | − | 0.946478i | \(-0.395387\pi\) | ||||
0.322767 | + | 0.946478i | \(0.395387\pi\) | |||||||
\(192\) | 320.000 | 0.120281 | ||||||||
\(193\) | −690.000 | −0.257343 | −0.128672 | − | 0.991687i | \(-0.541071\pi\) | ||||
−0.128672 | + | 0.991687i | \(0.541071\pi\) | |||||||
\(194\) | −1120.00 | −0.414491 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 72.0000 | 0.0262391 | ||||||||
\(197\) | −175.000 | −0.0632905 | −0.0316453 | − | 0.999499i | \(-0.510075\pi\) | ||||
−0.0316453 | + | 0.999499i | \(0.510075\pi\) | |||||||
\(198\) | 20.0000 | 0.00717848 | ||||||||
\(199\) | −3590.00 | −1.27884 | −0.639418 | − | 0.768859i | \(-0.720825\pi\) | ||||
−0.639418 | + | 0.768859i | \(0.720825\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2080.00 | −0.729910 | ||||||||
\(202\) | −1470.00 | −0.512024 | ||||||||
\(203\) | 190.000 | 0.0656916 | ||||||||
\(204\) | 1440.00 | 0.494217 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1300.00 | −0.439686 | ||||||||
\(207\) | 364.000 | 0.122221 | ||||||||
\(208\) | −96.0000 | −0.0320019 | ||||||||
\(209\) | −220.000 | −0.0728120 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1011.00 | −0.329858 | −0.164929 | − | 0.986305i | \(-0.552740\pi\) | ||||
−0.164929 | + | 0.986305i | \(0.552740\pi\) | |||||||
\(212\) | 2636.00 | 0.853968 | ||||||||
\(213\) | −5625.00 | −1.80948 | ||||||||
\(214\) | 3912.00 | 1.24962 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1160.00 | 0.365407 | ||||||||
\(217\) | −4636.00 | −1.45029 | ||||||||
\(218\) | −3240.00 | −1.00661 | ||||||||
\(219\) | 3205.00 | 0.988922 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −432.000 | −0.131491 | ||||||||
\(222\) | −370.000 | −0.111859 | ||||||||
\(223\) | 3243.00 | 0.973845 | 0.486922 | − | 0.873445i | \(-0.338119\pi\) | ||||
0.486922 | + | 0.873445i | \(0.338119\pi\) | |||||||
\(224\) | −608.000 | −0.181356 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1868.00 | −0.549812 | ||||||||
\(227\) | 5480.00 | 1.60229 | 0.801146 | − | 0.598469i | \(-0.204224\pi\) | ||||
0.801146 | + | 0.598469i | \(0.204224\pi\) | |||||||
\(228\) | −880.000 | −0.255612 | ||||||||
\(229\) | 2203.00 | 0.635713 | 0.317857 | − | 0.948139i | \(-0.397037\pi\) | ||||
0.317857 | + | 0.948139i | \(0.397037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 475.000 | 0.135293 | ||||||||
\(232\) | −80.0000 | −0.0226390 | ||||||||
\(233\) | −3718.00 | −1.04538 | −0.522692 | − | 0.852522i | \(-0.675072\pi\) | ||||
−0.522692 | + | 0.852522i | \(0.675072\pi\) | |||||||
\(234\) | −24.0000 | −0.00670483 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 624.000 | 0.172114 | ||||||||
\(237\) | −2420.00 | −0.663274 | ||||||||
\(238\) | −2736.00 | −0.745162 | ||||||||
\(239\) | −1038.00 | −0.280932 | −0.140466 | − | 0.990086i | \(-0.544860\pi\) | ||||
−0.140466 | + | 0.990086i | \(0.544860\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2050.00 | 0.547934 | 0.273967 | − | 0.961739i | \(-0.411664\pi\) | ||||
0.273967 | + | 0.961739i | \(0.411664\pi\) | |||||||
\(242\) | 2612.00 | 0.693825 | ||||||||
\(243\) | 560.000 | 0.147835 | ||||||||
\(244\) | −2480.00 | −0.650679 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2250.00 | 0.583149 | ||||||||
\(247\) | 264.000 | 0.0680078 | ||||||||
\(248\) | 1952.00 | 0.499807 | ||||||||
\(249\) | −6195.00 | −1.57668 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 702.000 | 0.176533 | 0.0882666 | − | 0.996097i | \(-0.471867\pi\) | ||||
0.0882666 | + | 0.996097i | \(0.471867\pi\) | |||||||
\(252\) | −152.000 | −0.0379964 | ||||||||
\(253\) | −910.000 | −0.226131 | ||||||||
\(254\) | 3798.00 | 0.938219 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5340.00 | −1.29611 | −0.648055 | − | 0.761594i | \(-0.724417\pi\) | ||||
−0.648055 | + | 0.761594i | \(0.724417\pi\) | |||||||
\(258\) | −20.0000 | −0.00482615 | ||||||||
\(259\) | 703.000 | 0.168658 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.0000 | −0.00474318 | ||||||||
\(262\) | 472.000 | 0.111299 | ||||||||
\(263\) | 4791.00 | 1.12329 | 0.561646 | − | 0.827378i | \(-0.310168\pi\) | ||||
0.561646 | + | 0.827378i | \(0.310168\pi\) | |||||||
\(264\) | −200.000 | −0.0466256 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1672.00 | 0.385402 | ||||||||
\(267\) | 6520.00 | 1.49445 | ||||||||
\(268\) | −1664.00 | −0.379272 | ||||||||
\(269\) | −6030.00 | −1.36675 | −0.683375 | − | 0.730068i | \(-0.739488\pi\) | ||||
−0.683375 | + | 0.730068i | \(0.739488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2173.00 | −0.487086 | −0.243543 | − | 0.969890i | \(-0.578310\pi\) | ||||
−0.243543 | + | 0.969890i | \(0.578310\pi\) | |||||||
\(272\) | 1152.00 | 0.256802 | ||||||||
\(273\) | −570.000 | −0.126366 | ||||||||
\(274\) | 3220.00 | 0.709954 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3640.00 | −0.793849 | ||||||||
\(277\) | 5996.00 | 1.30059 | 0.650297 | − | 0.759680i | \(-0.274644\pi\) | ||||
0.650297 | + | 0.759680i | \(0.274644\pi\) | |||||||
\(278\) | 1000.00 | 0.215741 | ||||||||
\(279\) | 488.000 | 0.104716 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3636.00 | 0.771906 | 0.385953 | − | 0.922518i | \(-0.373873\pi\) | ||||
0.385953 | + | 0.922518i | \(0.373873\pi\) | |||||||
\(282\) | 2210.00 | 0.466679 | ||||||||
\(283\) | 2616.00 | 0.549488 | 0.274744 | − | 0.961517i | \(-0.411407\pi\) | ||||
0.274744 | + | 0.961517i | \(0.411407\pi\) | |||||||
\(284\) | −4500.00 | −0.940232 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 60.0000 | 0.0124052 | ||||||||
\(287\) | −4275.00 | −0.879252 | ||||||||
\(288\) | 64.0000 | 0.0130946 | ||||||||
\(289\) | 271.000 | 0.0551598 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2800.00 | 0.564051 | ||||||||
\(292\) | 2564.00 | 0.513859 | ||||||||
\(293\) | −8238.00 | −1.64256 | −0.821278 | − | 0.570528i | \(-0.806739\pi\) | ||||
−0.821278 | + | 0.570528i | \(0.806739\pi\) | |||||||
\(294\) | −180.000 | −0.0357068 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −296.000 | −0.0581238 | ||||||||
\(297\) | −725.000 | −0.141646 | ||||||||
\(298\) | −3502.00 | −0.680756 | ||||||||
\(299\) | 1092.00 | 0.211211 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.0000 | 0.00727669 | ||||||||
\(302\) | 5408.00 | 1.03045 | ||||||||
\(303\) | 3675.00 | 0.696776 | ||||||||
\(304\) | −704.000 | −0.132820 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 288.000 | 0.0538035 | ||||||||
\(307\) | −8633.00 | −1.60492 | −0.802461 | − | 0.596704i | \(-0.796477\pi\) | ||||
−0.802461 | + | 0.596704i | \(0.796477\pi\) | |||||||
\(308\) | 380.000 | 0.0703004 | ||||||||
\(309\) | 3250.00 | 0.598337 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1180.00 | −0.215150 | −0.107575 | − | 0.994197i | \(-0.534309\pi\) | ||||
−0.107575 | + | 0.994197i | \(0.534309\pi\) | |||||||
\(312\) | 240.000 | 0.0435491 | ||||||||
\(313\) | −238.000 | −0.0429794 | −0.0214897 | − | 0.999769i | \(-0.506841\pi\) | ||||
−0.0214897 | + | 0.999769i | \(0.506841\pi\) | |||||||
\(314\) | −5322.00 | −0.956490 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1936.00 | −0.344647 | ||||||||
\(317\) | 7482.00 | 1.32565 | 0.662825 | − | 0.748774i | \(-0.269357\pi\) | ||||
0.662825 | + | 0.748774i | \(0.269357\pi\) | |||||||
\(318\) | −6590.00 | −1.16210 | ||||||||
\(319\) | 50.0000 | 0.00877574 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9780.00 | −1.70052 | ||||||||
\(322\) | 6916.00 | 1.19694 | ||||||||
\(323\) | −3168.00 | −0.545734 | ||||||||
\(324\) | −2684.00 | −0.460219 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3708.00 | 0.629961 | ||||||||
\(327\) | 8100.00 | 1.36982 | ||||||||
\(328\) | 1800.00 | 0.303013 | ||||||||
\(329\) | −4199.00 | −0.703642 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2894.00 | −0.480570 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(332\) | −4956.00 | −0.819265 | ||||||||
\(333\) | −74.0000 | −0.0121777 | ||||||||
\(334\) | −3616.00 | −0.592391 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1520.00 | 0.246794 | ||||||||
\(337\) | −7631.00 | −1.23349 | −0.616746 | − | 0.787162i | \(-0.711550\pi\) | ||||
−0.616746 | + | 0.787162i | \(0.711550\pi\) | |||||||
\(338\) | 4322.00 | 0.695520 | ||||||||
\(339\) | 4670.00 | 0.748199 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1220.00 | −0.193744 | ||||||||
\(342\) | −176.000 | −0.0278275 | ||||||||
\(343\) | −6175.00 | −0.972066 | ||||||||
\(344\) | −16.0000 | −0.00250774 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7238.00 | −1.12462 | ||||||||
\(347\) | 9858.00 | 1.52509 | 0.762543 | − | 0.646937i | \(-0.223950\pi\) | ||||
0.762543 | + | 0.646937i | \(0.223950\pi\) | |||||||
\(348\) | 200.000 | 0.0308078 | ||||||||
\(349\) | −1290.00 | −0.197857 | −0.0989285 | − | 0.995095i | \(-0.531542\pi\) | ||||
−0.0989285 | + | 0.995095i | \(0.531542\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 870.000 | 0.132300 | ||||||||
\(352\) | −160.000 | −0.0242274 | ||||||||
\(353\) | 5384.00 | 0.811789 | 0.405894 | − | 0.913920i | \(-0.366960\pi\) | ||||
0.405894 | + | 0.913920i | \(0.366960\pi\) | |||||||
\(354\) | −1560.00 | −0.234218 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5216.00 | 0.776538 | ||||||||
\(357\) | 6840.00 | 1.01404 | ||||||||
\(358\) | −68.0000 | −0.0100389 | ||||||||
\(359\) | −4197.00 | −0.617017 | −0.308509 | − | 0.951222i | \(-0.599830\pi\) | ||||
−0.308509 | + | 0.951222i | \(0.599830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4923.00 | −0.717743 | ||||||||
\(362\) | −1474.00 | −0.214010 | ||||||||
\(363\) | −6530.00 | −0.944177 | ||||||||
\(364\) | −456.000 | −0.0656618 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6200.00 | 0.885462 | ||||||||
\(367\) | −10848.0 | −1.54295 | −0.771473 | − | 0.636262i | \(-0.780480\pi\) | ||||
−0.771473 | + | 0.636262i | \(0.780480\pi\) | |||||||
\(368\) | −2912.00 | −0.412496 | ||||||||
\(369\) | 450.000 | 0.0634853 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12521.0 | 1.75218 | ||||||||
\(372\) | −4880.00 | −0.680151 | ||||||||
\(373\) | −6833.00 | −0.948524 | −0.474262 | − | 0.880384i | \(-0.657285\pi\) | ||||
−0.474262 | + | 0.880384i | \(0.657285\pi\) | |||||||
\(374\) | −720.000 | −0.0995463 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1768.00 | 0.242494 | ||||||||
\(377\) | −60.0000 | −0.00819670 | ||||||||
\(378\) | 5510.00 | 0.749746 | ||||||||
\(379\) | 12553.0 | 1.70133 | 0.850665 | − | 0.525708i | \(-0.176199\pi\) | ||||
0.850665 | + | 0.525708i | \(0.176199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9495.00 | −1.27675 | ||||||||
\(382\) | −3408.00 | −0.456462 | ||||||||
\(383\) | −4476.00 | −0.597162 | −0.298581 | − | 0.954384i | \(-0.596513\pi\) | ||||
−0.298581 | + | 0.954384i | \(0.596513\pi\) | |||||||
\(384\) | −640.000 | −0.0850517 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1380.00 | 0.181969 | ||||||||
\(387\) | −4.00000 | −0.000525404 0 | ||||||||
\(388\) | 2240.00 | 0.293090 | ||||||||
\(389\) | −11244.0 | −1.46554 | −0.732768 | − | 0.680479i | \(-0.761772\pi\) | ||||
−0.732768 | + | 0.680479i | \(0.761772\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13104.0 | −1.69488 | ||||||||
\(392\) | −144.000 | −0.0185538 | ||||||||
\(393\) | −1180.00 | −0.151458 | ||||||||
\(394\) | 350.000 | 0.0447532 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −40.0000 | −0.00507595 | ||||||||
\(397\) | −14359.0 | −1.81526 | −0.907629 | − | 0.419773i | \(-0.862110\pi\) | ||||
−0.907629 | + | 0.419773i | \(0.862110\pi\) | |||||||
\(398\) | 7180.00 | 0.904274 | ||||||||
\(399\) | −4180.00 | −0.524466 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8702.00 | −1.08368 | −0.541842 | − | 0.840480i | \(-0.682273\pi\) | ||||
−0.541842 | + | 0.840480i | \(0.682273\pi\) | |||||||
\(402\) | 4160.00 | 0.516124 | ||||||||
\(403\) | 1464.00 | 0.180960 | ||||||||
\(404\) | 2940.00 | 0.362056 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −380.000 | −0.0464509 | ||||||||
\(407\) | 185.000 | 0.0225310 | ||||||||
\(408\) | −2880.00 | −0.349464 | ||||||||
\(409\) | 3376.00 | 0.408148 | 0.204074 | − | 0.978955i | \(-0.434582\pi\) | ||||
0.204074 | + | 0.978955i | \(0.434582\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8050.00 | −0.966125 | ||||||||
\(412\) | 2600.00 | 0.310905 | ||||||||
\(413\) | 2964.00 | 0.353145 | ||||||||
\(414\) | −728.000 | −0.0864233 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 192.000 | 0.0226288 | ||||||||
\(417\) | −2500.00 | −0.293586 | ||||||||
\(418\) | 440.000 | 0.0514859 | ||||||||
\(419\) | −6295.00 | −0.733964 | −0.366982 | − | 0.930228i | \(-0.619609\pi\) | ||||
−0.366982 | + | 0.930228i | \(0.619609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13884.0 | −1.60728 | −0.803640 | − | 0.595116i | \(-0.797106\pi\) | ||||
−0.803640 | + | 0.595116i | \(0.797106\pi\) | |||||||
\(422\) | 2022.00 | 0.233245 | ||||||||
\(423\) | 442.000 | 0.0508056 | ||||||||
\(424\) | −5272.00 | −0.603847 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11250.0 | 1.27949 | ||||||||
\(427\) | −11780.0 | −1.33507 | ||||||||
\(428\) | −7824.00 | −0.883615 | ||||||||
\(429\) | −150.000 | −0.0168813 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8130.00 | −0.908604 | −0.454302 | − | 0.890848i | \(-0.650111\pi\) | ||||
−0.454302 | + | 0.890848i | \(0.650111\pi\) | |||||||
\(432\) | −2320.00 | −0.258382 | ||||||||
\(433\) | 5983.00 | 0.664029 | 0.332015 | − | 0.943274i | \(-0.392272\pi\) | ||||
0.332015 | + | 0.943274i | \(0.392272\pi\) | |||||||
\(434\) | 9272.00 | 1.02551 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6480.00 | 0.711779 | ||||||||
\(437\) | 8008.00 | 0.876601 | ||||||||
\(438\) | −6410.00 | −0.699273 | ||||||||
\(439\) | −7664.00 | −0.833218 | −0.416609 | − | 0.909086i | \(-0.636782\pi\) | ||||
−0.416609 | + | 0.909086i | \(0.636782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.0000 | −0.00388727 | ||||||||
\(442\) | 864.000 | 0.0929780 | ||||||||
\(443\) | 2577.00 | 0.276381 | 0.138191 | − | 0.990406i | \(-0.455871\pi\) | ||||
0.138191 | + | 0.990406i | \(0.455871\pi\) | |||||||
\(444\) | 740.000 | 0.0790965 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6486.00 | −0.688612 | ||||||||
\(447\) | 8755.00 | 0.926392 | ||||||||
\(448\) | 1216.00 | 0.128238 | ||||||||
\(449\) | 12080.0 | 1.26969 | 0.634845 | − | 0.772640i | \(-0.281064\pi\) | ||||
0.634845 | + | 0.772640i | \(0.281064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1125.00 | −0.117459 | ||||||||
\(452\) | 3736.00 | 0.388776 | ||||||||
\(453\) | −13520.0 | −1.40226 | ||||||||
\(454\) | −10960.0 | −1.13299 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1760.00 | 0.180745 | ||||||||
\(457\) | 10490.0 | 1.07375 | 0.536873 | − | 0.843663i | \(-0.319606\pi\) | ||||
0.536873 | + | 0.843663i | \(0.319606\pi\) | |||||||
\(458\) | −4406.00 | −0.449517 | ||||||||
\(459\) | −10440.0 | −1.06165 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14810.0 | −1.49625 | −0.748124 | − | 0.663559i | \(-0.769045\pi\) | ||||
−0.748124 | + | 0.663559i | \(0.769045\pi\) | |||||||
\(462\) | −950.000 | −0.0956667 | ||||||||
\(463\) | −15578.0 | −1.56365 | −0.781826 | − | 0.623496i | \(-0.785712\pi\) | ||||
−0.781826 | + | 0.623496i | \(0.785712\pi\) | |||||||
\(464\) | 160.000 | 0.0160082 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7436.00 | 0.739198 | ||||||||
\(467\) | 2062.00 | 0.204321 | 0.102161 | − | 0.994768i | \(-0.467424\pi\) | ||||
0.102161 | + | 0.994768i | \(0.467424\pi\) | |||||||
\(468\) | 48.0000 | 0.00474103 | ||||||||
\(469\) | −7904.00 | −0.778194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13305.0 | 1.30162 | ||||||||
\(472\) | −1248.00 | −0.121703 | ||||||||
\(473\) | 10.0000 | 0.000972094 0 | ||||||||
\(474\) | 4840.00 | 0.469005 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5472.00 | 0.526909 | ||||||||
\(477\) | −1318.00 | −0.126514 | ||||||||
\(478\) | 2076.00 | 0.198649 | ||||||||
\(479\) | 3438.00 | 0.327946 | 0.163973 | − | 0.986465i | \(-0.447569\pi\) | ||||
0.163973 | + | 0.986465i | \(0.447569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −222.000 | −0.0210443 | ||||||||
\(482\) | −4100.00 | −0.387448 | ||||||||
\(483\) | −17290.0 | −1.62882 | ||||||||
\(484\) | −5224.00 | −0.490609 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1120.00 | −0.104535 | ||||||||
\(487\) | 19592.0 | 1.82299 | 0.911497 | − | 0.411306i | \(-0.134927\pi\) | ||||
0.911497 | + | 0.411306i | \(0.134927\pi\) | |||||||
\(488\) | 4960.00 | 0.460100 | ||||||||
\(489\) | −9270.00 | −0.857268 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4444.00 | 0.408462 | 0.204231 | − | 0.978923i | \(-0.434531\pi\) | ||||
0.204231 | + | 0.978923i | \(0.434531\pi\) | |||||||
\(492\) | −4500.00 | −0.412349 | ||||||||
\(493\) | 720.000 | 0.0657752 | ||||||||
\(494\) | −528.000 | −0.0480888 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3904.00 | −0.353417 | ||||||||
\(497\) | −21375.0 | −1.92917 | ||||||||
\(498\) | 12390.0 | 1.11488 | ||||||||
\(499\) | −1140.00 | −0.102271 | −0.0511357 | − | 0.998692i | \(-0.516284\pi\) | ||||
−0.0511357 | + | 0.998692i | \(0.516284\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9040.00 | 0.806143 | ||||||||
\(502\) | −1404.00 | −0.124828 | ||||||||
\(503\) | 3180.00 | 0.281887 | 0.140944 | − | 0.990018i | \(-0.454986\pi\) | ||||
0.140944 | + | 0.990018i | \(0.454986\pi\) | |||||||
\(504\) | 304.000 | 0.0268675 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1820.00 | 0.159899 | ||||||||
\(507\) | −10805.0 | −0.946483 | ||||||||
\(508\) | −7596.00 | −0.663421 | ||||||||
\(509\) | 15213.0 | 1.32476 | 0.662382 | − | 0.749167i | \(-0.269546\pi\) | ||||
0.662382 | + | 0.749167i | \(0.269546\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12179.0 | 1.05434 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 6380.00 | 0.549091 | ||||||||
\(514\) | 10680.0 | 0.916488 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 40.0000 | 0.00341260 | ||||||||
\(517\) | −1105.00 | −0.0939997 | ||||||||
\(518\) | −1406.00 | −0.119259 | ||||||||
\(519\) | 18095.0 | 1.53041 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16271.0 | 1.36823 | 0.684113 | − | 0.729376i | \(-0.260190\pi\) | ||||
0.684113 | + | 0.729376i | \(0.260190\pi\) | |||||||
\(522\) | 40.0000 | 0.00335393 | ||||||||
\(523\) | −16322.0 | −1.36465 | −0.682324 | − | 0.731050i | \(-0.739031\pi\) | ||||
−0.682324 | + | 0.731050i | \(0.739031\pi\) | |||||||
\(524\) | −944.000 | −0.0787001 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9582.00 | −0.794287 | ||||||||
\(527\) | −17568.0 | −1.45213 | ||||||||
\(528\) | 400.000 | 0.0329693 | ||||||||
\(529\) | 20957.0 | 1.72245 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −312.000 | −0.0254984 | ||||||||
\(532\) | −3344.00 | −0.272520 | ||||||||
\(533\) | 1350.00 | 0.109709 | ||||||||
\(534\) | −13040.0 | −1.05673 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3328.00 | 0.268186 | ||||||||
\(537\) | 170.000 | 0.0136612 | ||||||||
\(538\) | 12060.0 | 0.966438 | ||||||||
\(539\) | 90.0000 | 0.00719216 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11876.0 | −0.943788 | −0.471894 | − | 0.881655i | \(-0.656429\pi\) | ||||
−0.471894 | + | 0.881655i | \(0.656429\pi\) | |||||||
\(542\) | 4346.00 | 0.344422 | ||||||||
\(543\) | 3685.00 | 0.291231 | ||||||||
\(544\) | −2304.00 | −0.181587 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1140.00 | 0.0893544 | ||||||||
\(547\) | −3824.00 | −0.298908 | −0.149454 | − | 0.988769i | \(-0.547752\pi\) | ||||
−0.149454 | + | 0.988769i | \(0.547752\pi\) | |||||||
\(548\) | −6440.00 | −0.502013 | ||||||||
\(549\) | 1240.00 | 0.0963969 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −440.000 | −0.0340193 | ||||||||
\(552\) | 7280.00 | 0.561336 | ||||||||
\(553\) | −9196.00 | −0.707150 | ||||||||
\(554\) | −11992.0 | −0.919659 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2000.00 | −0.152552 | ||||||||
\(557\) | 16410.0 | 1.24832 | 0.624160 | − | 0.781297i | \(-0.285441\pi\) | ||||
0.624160 | + | 0.781297i | \(0.285441\pi\) | |||||||
\(558\) | −976.000 | −0.0740455 | ||||||||
\(559\) | −12.0000 | −0.000907953 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1800.00 | 0.135465 | ||||||||
\(562\) | −7272.00 | −0.545820 | ||||||||
\(563\) | −12798.0 | −0.958031 | −0.479015 | − | 0.877806i | \(-0.659006\pi\) | ||||
−0.479015 | + | 0.877806i | \(0.659006\pi\) | |||||||
\(564\) | −4420.00 | −0.329992 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5232.00 | −0.388547 | ||||||||
\(567\) | −12749.0 | −0.944282 | ||||||||
\(568\) | 9000.00 | 0.664844 | ||||||||
\(569\) | −22716.0 | −1.67365 | −0.836823 | − | 0.547474i | \(-0.815590\pi\) | ||||
−0.836823 | + | 0.547474i | \(0.815590\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3151.00 | −0.230937 | −0.115469 | − | 0.993311i | \(-0.536837\pi\) | ||||
−0.115469 | + | 0.993311i | \(0.536837\pi\) | |||||||
\(572\) | −120.000 | −0.00877177 | ||||||||
\(573\) | 8520.00 | 0.621166 | ||||||||
\(574\) | 8550.00 | 0.621725 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −128.000 | −0.00925926 | ||||||||
\(577\) | 3556.00 | 0.256565 | 0.128283 | − | 0.991738i | \(-0.459054\pi\) | ||||
0.128283 | + | 0.991738i | \(0.459054\pi\) | |||||||
\(578\) | −542.000 | −0.0390039 | ||||||||
\(579\) | −3450.00 | −0.247629 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23541.0 | −1.68097 | ||||||||
\(582\) | −5600.00 | −0.398844 | ||||||||
\(583\) | 3295.00 | 0.234074 | ||||||||
\(584\) | −5128.00 | −0.363353 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16476.0 | 1.16146 | ||||||||
\(587\) | −13564.0 | −0.953741 | −0.476871 | − | 0.878973i | \(-0.658229\pi\) | ||||
−0.476871 | + | 0.878973i | \(0.658229\pi\) | |||||||
\(588\) | 360.000 | 0.0252486 | ||||||||
\(589\) | 10736.0 | 0.751051 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −875.000 | −0.0609013 | ||||||||
\(592\) | 592.000 | 0.0410997 | ||||||||
\(593\) | −427.000 | −0.0295696 | −0.0147848 | − | 0.999891i | \(-0.504706\pi\) | ||||
−0.0147848 | + | 0.999891i | \(0.504706\pi\) | |||||||
\(594\) | 1450.00 | 0.100159 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7004.00 | 0.481367 | ||||||||
\(597\) | −17950.0 | −1.23056 | ||||||||
\(598\) | −2184.00 | −0.149348 | ||||||||
\(599\) | 18603.0 | 1.26894 | 0.634472 | − | 0.772945i | \(-0.281217\pi\) | ||||
0.634472 | + | 0.772945i | \(0.281217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20406.0 | −1.38499 | −0.692494 | − | 0.721423i | \(-0.743488\pi\) | ||||
−0.692494 | + | 0.721423i | \(0.743488\pi\) | |||||||
\(602\) | −76.0000 | −0.00514540 | ||||||||
\(603\) | 832.000 | 0.0561885 | ||||||||
\(604\) | −10816.0 | −0.728637 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7350.00 | −0.492695 | ||||||||
\(607\) | −1028.00 | −0.0687401 | −0.0343700 | − | 0.999409i | \(-0.510942\pi\) | ||||
−0.0343700 | + | 0.999409i | \(0.510942\pi\) | |||||||
\(608\) | 1408.00 | 0.0939177 | ||||||||
\(609\) | 950.000 | 0.0632117 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1326.00 | 0.0877974 | ||||||||
\(612\) | −576.000 | −0.0380448 | ||||||||
\(613\) | −21875.0 | −1.44131 | −0.720655 | − | 0.693294i | \(-0.756159\pi\) | ||||
−0.720655 | + | 0.693294i | \(0.756159\pi\) | |||||||
\(614\) | 17266.0 | 1.13485 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −760.000 | −0.0497099 | ||||||||
\(617\) | 8431.00 | 0.550112 | 0.275056 | − | 0.961428i | \(-0.411304\pi\) | ||||
0.275056 | + | 0.961428i | \(0.411304\pi\) | |||||||
\(618\) | −6500.00 | −0.423088 | ||||||||
\(619\) | 1217.00 | 0.0790232 | 0.0395116 | − | 0.999219i | \(-0.487420\pi\) | ||||
0.0395116 | + | 0.999219i | \(0.487420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26390.0 | 1.70530 | ||||||||
\(622\) | 2360.00 | 0.152134 | ||||||||
\(623\) | 24776.0 | 1.59331 | ||||||||
\(624\) | −480.000 | −0.0307939 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 476.000 | 0.0303910 | ||||||||
\(627\) | −1100.00 | −0.0700634 | ||||||||
\(628\) | 10644.0 | 0.676341 | ||||||||
\(629\) | 2664.00 | 0.168872 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7408.00 | −0.467366 | −0.233683 | − | 0.972313i | \(-0.575078\pi\) | ||||
−0.233683 | + | 0.972313i | \(0.575078\pi\) | |||||||
\(632\) | 3872.00 | 0.243702 | ||||||||
\(633\) | −5055.00 | −0.317406 | ||||||||
\(634\) | −14964.0 | −0.937376 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13180.0 | 0.821731 | ||||||||
\(637\) | −108.000 | −0.00671761 | ||||||||
\(638\) | −100.000 | −0.00620539 | ||||||||
\(639\) | 2250.00 | 0.139294 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14559.0 | 0.897108 | 0.448554 | − | 0.893756i | \(-0.351939\pi\) | ||||
0.448554 | + | 0.893756i | \(0.351939\pi\) | |||||||
\(642\) | 19560.0 | 1.20245 | ||||||||
\(643\) | 12122.0 | 0.743460 | 0.371730 | − | 0.928341i | \(-0.378765\pi\) | ||||
0.371730 | + | 0.928341i | \(0.378765\pi\) | |||||||
\(644\) | −13832.0 | −0.846362 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6336.00 | 0.385893 | ||||||||
\(647\) | −22648.0 | −1.37617 | −0.688087 | − | 0.725628i | \(-0.741549\pi\) | ||||
−0.688087 | + | 0.725628i | \(0.741549\pi\) | |||||||
\(648\) | 5368.00 | 0.325424 | ||||||||
\(649\) | 780.000 | 0.0471767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23180.0 | −1.39554 | ||||||||
\(652\) | −7416.00 | −0.445449 | ||||||||
\(653\) | 18368.0 | 1.10076 | 0.550379 | − | 0.834915i | \(-0.314483\pi\) | ||||
0.550379 | + | 0.834915i | \(0.314483\pi\) | |||||||
\(654\) | −16200.0 | −0.968609 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3600.00 | −0.214263 | ||||||||
\(657\) | −1282.00 | −0.0761272 | ||||||||
\(658\) | 8398.00 | 0.497550 | ||||||||
\(659\) | 1327.00 | 0.0784409 | 0.0392205 | − | 0.999231i | \(-0.487513\pi\) | ||||
0.0392205 | + | 0.999231i | \(0.487513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13768.0 | −0.810156 | −0.405078 | − | 0.914282i | \(-0.632756\pi\) | ||||
−0.405078 | + | 0.914282i | \(0.632756\pi\) | |||||||
\(662\) | 5788.00 | 0.339814 | ||||||||
\(663\) | −2160.00 | −0.126527 | ||||||||
\(664\) | 9912.00 | 0.579308 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 148.000 | 0.00861094 | ||||||||
\(667\) | −1820.00 | −0.105653 | ||||||||
\(668\) | 7232.00 | 0.418884 | ||||||||
\(669\) | 16215.0 | 0.937082 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3100.00 | −0.178352 | ||||||||
\(672\) | −3040.00 | −0.174510 | ||||||||
\(673\) | 12773.0 | 0.731594 | 0.365797 | − | 0.930695i | \(-0.380796\pi\) | ||||
0.365797 | + | 0.930695i | \(0.380796\pi\) | |||||||
\(674\) | 15262.0 | 0.872211 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8644.00 | −0.491807 | ||||||||
\(677\) | 22575.0 | 1.28158 | 0.640789 | − | 0.767717i | \(-0.278608\pi\) | ||||
0.640789 | + | 0.767717i | \(0.278608\pi\) | |||||||
\(678\) | −9340.00 | −0.529057 | ||||||||
\(679\) | 10640.0 | 0.601363 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27400.0 | 1.54181 | ||||||||
\(682\) | 2440.00 | 0.136998 | ||||||||
\(683\) | 11770.0 | 0.659395 | 0.329697 | − | 0.944087i | \(-0.393053\pi\) | ||||
0.329697 | + | 0.944087i | \(0.393053\pi\) | |||||||
\(684\) | 352.000 | 0.0196770 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12350.0 | 0.687355 | ||||||||
\(687\) | 11015.0 | 0.611715 | ||||||||
\(688\) | 32.0000 | 0.00177324 | ||||||||
\(689\) | −3954.00 | −0.218629 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21404.0 | 1.17836 | 0.589180 | − | 0.808002i | \(-0.299451\pi\) | ||||
0.589180 | + | 0.808002i | \(0.299451\pi\) | |||||||
\(692\) | 14476.0 | 0.795224 | ||||||||
\(693\) | −190.000 | −0.0104149 | ||||||||
\(694\) | −19716.0 | −1.07840 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −400.000 | −0.0217844 | ||||||||
\(697\) | −16200.0 | −0.880371 | ||||||||
\(698\) | 2580.00 | 0.139906 | ||||||||
\(699\) | −18590.0 | −1.00592 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 416.000 | 0.0224138 | 0.0112069 | − | 0.999937i | \(-0.496433\pi\) | ||||
0.0112069 | + | 0.999937i | \(0.496433\pi\) | |||||||
\(702\) | −1740.00 | −0.0935500 | ||||||||
\(703\) | −1628.00 | −0.0873417 | ||||||||
\(704\) | 320.000 | 0.0171313 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10768.0 | −0.574021 | ||||||||
\(707\) | 13965.0 | 0.742868 | ||||||||
\(708\) | 3120.00 | 0.165617 | ||||||||
\(709\) | 14960.0 | 0.792432 | 0.396216 | − | 0.918157i | \(-0.370323\pi\) | ||||
0.396216 | + | 0.918157i | \(0.370323\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 968.000 | 0.0510588 | ||||||||
\(712\) | −10432.0 | −0.549095 | ||||||||
\(713\) | 44408.0 | 2.33253 | ||||||||
\(714\) | −13680.0 | −0.717032 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 136.000 | 0.00709855 | ||||||||
\(717\) | −5190.00 | −0.270327 | ||||||||
\(718\) | 8394.00 | 0.436297 | ||||||||
\(719\) | 22501.0 | 1.16710 | 0.583551 | − | 0.812077i | \(-0.301663\pi\) | ||||
0.583551 | + | 0.812077i | \(0.301663\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12350.0 | 0.637917 | ||||||||
\(722\) | 9846.00 | 0.507521 | ||||||||
\(723\) | 10250.0 | 0.527250 | ||||||||
\(724\) | 2948.00 | 0.151328 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 13060.0 | 0.667634 | ||||||||
\(727\) | −4616.00 | −0.235486 | −0.117743 | − | 0.993044i | \(-0.537566\pi\) | ||||
−0.117743 | + | 0.993044i | \(0.537566\pi\) | |||||||
\(728\) | 912.000 | 0.0464299 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 144.000 | 0.00728595 | ||||||||
\(732\) | −12400.0 | −0.626116 | ||||||||
\(733\) | −3251.00 | −0.163818 | −0.0819089 | − | 0.996640i | \(-0.526102\pi\) | ||||
−0.0819089 | + | 0.996640i | \(0.526102\pi\) | |||||||
\(734\) | 21696.0 | 1.09103 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5824.00 | 0.291679 | ||||||||
\(737\) | −2080.00 | −0.103959 | ||||||||
\(738\) | −900.000 | −0.0448909 | ||||||||
\(739\) | −7319.00 | −0.364322 | −0.182161 | − | 0.983269i | \(-0.558309\pi\) | ||||
−0.182161 | + | 0.983269i | \(0.558309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1320.00 | 0.0654405 | ||||||||
\(742\) | −25042.0 | −1.23898 | ||||||||
\(743\) | 19177.0 | 0.946885 | 0.473443 | − | 0.880825i | \(-0.343011\pi\) | ||||
0.473443 | + | 0.880825i | \(0.343011\pi\) | |||||||
\(744\) | 9760.00 | 0.480939 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13666.0 | 0.670708 | ||||||||
\(747\) | 2478.00 | 0.121373 | ||||||||
\(748\) | 1440.00 | 0.0703899 | ||||||||
\(749\) | −37164.0 | −1.81301 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21203.0 | 1.03024 | 0.515119 | − | 0.857119i | \(-0.327748\pi\) | ||||
0.515119 | + | 0.857119i | \(0.327748\pi\) | |||||||
\(752\) | −3536.00 | −0.171469 | ||||||||
\(753\) | 3510.00 | 0.169869 | ||||||||
\(754\) | 120.000 | 0.00579594 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11020.0 | −0.530150 | ||||||||
\(757\) | −7938.00 | −0.381125 | −0.190562 | − | 0.981675i | \(-0.561031\pi\) | ||||
−0.190562 | + | 0.981675i | \(0.561031\pi\) | |||||||
\(758\) | −25106.0 | −1.20302 | ||||||||
\(759\) | −4550.00 | −0.217595 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17811.0 | −0.848421 | −0.424210 | − | 0.905564i | \(-0.639448\pi\) | ||||
−0.424210 | + | 0.905564i | \(0.639448\pi\) | |||||||
\(762\) | 18990.0 | 0.902802 | ||||||||
\(763\) | 30780.0 | 1.46043 | ||||||||
\(764\) | 6816.00 | 0.322767 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8952.00 | 0.422257 | ||||||||
\(767\) | −936.000 | −0.0440639 | ||||||||
\(768\) | 1280.00 | 0.0601407 | ||||||||
\(769\) | 40790.0 | 1.91278 | 0.956388 | − | 0.292099i | \(-0.0943536\pi\) | ||||
0.956388 | + | 0.292099i | \(0.0943536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26700.0 | −1.24718 | ||||||||
\(772\) | −2760.00 | −0.128672 | ||||||||
\(773\) | −3123.00 | −0.145312 | −0.0726562 | − | 0.997357i | \(-0.523148\pi\) | ||||
−0.0726562 | + | 0.997357i | \(0.523148\pi\) | |||||||
\(774\) | 8.00000 | 0.000371517 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4480.00 | −0.207246 | ||||||||
\(777\) | 3515.00 | 0.162291 | ||||||||
\(778\) | 22488.0 | 1.03629 | ||||||||
\(779\) | 9900.00 | 0.455333 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5625.00 | −0.257719 | ||||||||
\(782\) | 26208.0 | 1.19846 | ||||||||
\(783\) | −1450.00 | −0.0661798 | ||||||||
\(784\) | 288.000 | 0.0131195 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2360.00 | 0.107097 | ||||||||
\(787\) | −4685.00 | −0.212201 | −0.106101 | − | 0.994355i | \(-0.533837\pi\) | ||||
−0.106101 | + | 0.994355i | \(0.533837\pi\) | |||||||
\(788\) | −700.000 | −0.0316453 | ||||||||
\(789\) | 23955.0 | 1.08089 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17746.0 | 0.797693 | ||||||||
\(792\) | 80.0000 | 0.00358924 | ||||||||
\(793\) | 3720.00 | 0.166584 | ||||||||
\(794\) | 28718.0 | 1.28358 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14360.0 | −0.639418 | ||||||||
\(797\) | 36848.0 | 1.63767 | 0.818835 | − | 0.574029i | \(-0.194620\pi\) | ||||
0.818835 | + | 0.574029i | \(0.194620\pi\) | |||||||
\(798\) | 8360.00 | 0.370853 | ||||||||
\(799\) | −15912.0 | −0.704538 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2608.00 | −0.115043 | ||||||||
\(802\) | 17404.0 | 0.766280 | ||||||||
\(803\) | 3205.00 | 0.140849 | ||||||||
\(804\) | −8320.00 | −0.364955 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2928.00 | −0.127958 | ||||||||
\(807\) | −30150.0 | −1.31516 | ||||||||
\(808\) | −5880.00 | −0.256012 | ||||||||
\(809\) | 12946.0 | 0.562617 | 0.281308 | − | 0.959617i | \(-0.409232\pi\) | ||||
0.281308 | + | 0.959617i | \(0.409232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31489.0 | 1.36341 | 0.681707 | − | 0.731626i | \(-0.261238\pi\) | ||||
0.681707 | + | 0.731626i | \(0.261238\pi\) | |||||||
\(812\) | 760.000 | 0.0328458 | ||||||||
\(813\) | −10865.0 | −0.468699 | ||||||||
\(814\) | −370.000 | −0.0159318 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5760.00 | 0.247108 | ||||||||
\(817\) | −88.0000 | −0.00376834 | ||||||||
\(818\) | −6752.00 | −0.288604 | ||||||||
\(819\) | 228.000 | 0.00972767 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11835.0 | −0.503099 | −0.251550 | − | 0.967844i | \(-0.580940\pi\) | ||||
−0.251550 | + | 0.967844i | \(0.580940\pi\) | |||||||
\(822\) | 16100.0 | 0.683153 | ||||||||
\(823\) | 19728.0 | 0.835571 | 0.417785 | − | 0.908546i | \(-0.362806\pi\) | ||||
0.417785 | + | 0.908546i | \(0.362806\pi\) | |||||||
\(824\) | −5200.00 | −0.219843 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5928.00 | −0.249711 | ||||||||
\(827\) | −22642.0 | −0.952043 | −0.476021 | − | 0.879434i | \(-0.657922\pi\) | ||||
−0.476021 | + | 0.879434i | \(0.657922\pi\) | |||||||
\(828\) | 1456.00 | 0.0611105 | ||||||||
\(829\) | 24280.0 | 1.01722 | 0.508612 | − | 0.860996i | \(-0.330159\pi\) | ||||
0.508612 | + | 0.860996i | \(0.330159\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29980.0 | 1.25150 | ||||||||
\(832\) | −384.000 | −0.0160010 | ||||||||
\(833\) | 1296.00 | 0.0539060 | ||||||||
\(834\) | 5000.00 | 0.207597 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −880.000 | −0.0364060 | ||||||||
\(837\) | 35380.0 | 1.46107 | ||||||||
\(838\) | 12590.0 | 0.518991 | ||||||||
\(839\) | 16508.0 | 0.679284 | 0.339642 | − | 0.940555i | \(-0.389694\pi\) | ||||
0.339642 | + | 0.940555i | \(0.389694\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24289.0 | −0.995900 | ||||||||
\(842\) | 27768.0 | 1.13652 | ||||||||
\(843\) | 18180.0 | 0.742767 | ||||||||
\(844\) | −4044.00 | −0.164929 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −884.000 | −0.0359250 | ||||||||
\(847\) | −24814.0 | −1.00663 | ||||||||
\(848\) | 10544.0 | 0.426984 | ||||||||
\(849\) | 13080.0 | 0.528745 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6734.00 | −0.271256 | ||||||||
\(852\) | −22500.0 | −0.904739 | ||||||||
\(853\) | 19990.0 | 0.802397 | 0.401198 | − | 0.915991i | \(-0.368594\pi\) | ||||
0.401198 | + | 0.915991i | \(0.368594\pi\) | |||||||
\(854\) | 23560.0 | 0.944036 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15648.0 | 0.624810 | ||||||||
\(857\) | 3744.00 | 0.149233 | 0.0746165 | − | 0.997212i | \(-0.476227\pi\) | ||||
0.0746165 | + | 0.997212i | \(0.476227\pi\) | |||||||
\(858\) | 300.000 | 0.0119369 | ||||||||
\(859\) | −3140.00 | −0.124721 | −0.0623605 | − | 0.998054i | \(-0.519863\pi\) | ||||
−0.0623605 | + | 0.998054i | \(0.519863\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21375.0 | −0.846060 | ||||||||
\(862\) | 16260.0 | 0.642480 | ||||||||
\(863\) | 13168.0 | 0.519402 | 0.259701 | − | 0.965689i | \(-0.416376\pi\) | ||||
0.259701 | + | 0.965689i | \(0.416376\pi\) | |||||||
\(864\) | 4640.00 | 0.182704 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11966.0 | −0.469540 | ||||||||
\(867\) | 1355.00 | 0.0530775 | ||||||||
\(868\) | −18544.0 | −0.725143 | ||||||||
\(869\) | −2420.00 | −0.0944682 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2496.00 | 0.0970996 | ||||||||
\(872\) | −12960.0 | −0.503304 | ||||||||
\(873\) | −1120.00 | −0.0434207 | ||||||||
\(874\) | −16016.0 | −0.619850 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12820.0 | 0.494461 | ||||||||
\(877\) | −35002.0 | −1.34770 | −0.673850 | − | 0.738868i | \(-0.735361\pi\) | ||||
−0.673850 | + | 0.738868i | \(0.735361\pi\) | |||||||
\(878\) | 15328.0 | 0.589174 | ||||||||
\(879\) | −41190.0 | −1.58055 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17142.0 | −0.655538 | −0.327769 | − | 0.944758i | \(-0.606297\pi\) | ||||
−0.327769 | + | 0.944758i | \(0.606297\pi\) | |||||||
\(882\) | 72.0000 | 0.00274871 | ||||||||
\(883\) | 22340.0 | 0.851417 | 0.425708 | − | 0.904860i | \(-0.360025\pi\) | ||||
0.425708 | + | 0.904860i | \(0.360025\pi\) | |||||||
\(884\) | −1728.00 | −0.0657454 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5154.00 | −0.195431 | ||||||||
\(887\) | 22605.0 | 0.855695 | 0.427848 | − | 0.903851i | \(-0.359272\pi\) | ||||
0.427848 | + | 0.903851i | \(0.359272\pi\) | |||||||
\(888\) | −1480.00 | −0.0559297 | ||||||||
\(889\) | −36081.0 | −1.36121 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3355.00 | −0.126147 | ||||||||
\(892\) | 12972.0 | 0.486922 | ||||||||
\(893\) | 9724.00 | 0.364391 | ||||||||
\(894\) | −17510.0 | −0.655058 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2432.00 | −0.0906779 | ||||||||
\(897\) | 5460.00 | 0.203238 | ||||||||
\(898\) | −24160.0 | −0.897806 | ||||||||
\(899\) | −2440.00 | −0.0905212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47448.0 | 1.75441 | ||||||||
\(902\) | 2250.00 | 0.0830563 | ||||||||
\(903\) | 190.000 | 0.00700200 | ||||||||
\(904\) | −7472.00 | −0.274906 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 27040.0 | 0.991549 | ||||||||
\(907\) | 13880.0 | 0.508134 | 0.254067 | − | 0.967187i | \(-0.418232\pi\) | ||||
0.254067 | + | 0.967187i | \(0.418232\pi\) | |||||||
\(908\) | 21920.0 | 0.801146 | ||||||||
\(909\) | −1470.00 | −0.0536379 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52582.0 | 1.91232 | 0.956158 | − | 0.292852i | \(-0.0946044\pi\) | ||||
0.956158 | + | 0.292852i | \(0.0946044\pi\) | |||||||
\(912\) | −3520.00 | −0.127806 | ||||||||
\(913\) | −6195.00 | −0.224561 | ||||||||
\(914\) | −20980.0 | −0.759252 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8812.00 | 0.317857 | ||||||||
\(917\) | −4484.00 | −0.161477 | ||||||||
\(918\) | 20880.0 | 0.750700 | ||||||||
\(919\) | −19298.0 | −0.692690 | −0.346345 | − | 0.938107i | \(-0.612577\pi\) | ||||
−0.346345 | + | 0.938107i | \(0.612577\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43165.0 | −1.54434 | ||||||||
\(922\) | 29620.0 | 1.05801 | ||||||||
\(923\) | 6750.00 | 0.240714 | ||||||||
\(924\) | 1900.00 | 0.0676465 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31156.0 | 1.10567 | ||||||||
\(927\) | −1300.00 | −0.0460600 | ||||||||
\(928\) | −320.000 | −0.0113195 | ||||||||
\(929\) | 8658.00 | 0.305769 | 0.152885 | − | 0.988244i | \(-0.451144\pi\) | ||||
0.152885 | + | 0.988244i | \(0.451144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −792.000 | −0.0278805 | ||||||||
\(932\) | −14872.0 | −0.522692 | ||||||||
\(933\) | −5900.00 | −0.207028 | ||||||||
\(934\) | −4124.00 | −0.144477 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −96.0000 | −0.00335241 | ||||||||
\(937\) | 22427.0 | 0.781919 | 0.390960 | − | 0.920408i | \(-0.372143\pi\) | ||||
0.390960 | + | 0.920408i | \(0.372143\pi\) | |||||||
\(938\) | 15808.0 | 0.550266 | ||||||||
\(939\) | −1190.00 | −0.0413570 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48158.0 | 1.66834 | 0.834169 | − | 0.551509i | \(-0.185948\pi\) | ||||
0.834169 | + | 0.551509i | \(0.185948\pi\) | |||||||
\(942\) | −26610.0 | −0.920383 | ||||||||
\(943\) | 40950.0 | 1.41412 | ||||||||
\(944\) | 2496.00 | 0.0860571 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20.0000 | −0.000687374 0 | ||||||||
\(947\) | −13696.0 | −0.469969 | −0.234984 | − | 0.971999i | \(-0.575504\pi\) | ||||
−0.234984 | + | 0.971999i | \(0.575504\pi\) | |||||||
\(948\) | −9680.00 | −0.331637 | ||||||||
\(949\) | −3846.00 | −0.131556 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37410.0 | 1.27561 | ||||||||
\(952\) | −10944.0 | −0.372581 | ||||||||
\(953\) | −33293.0 | −1.13165 | −0.565827 | − | 0.824524i | \(-0.691443\pi\) | ||||
−0.565827 | + | 0.824524i | \(0.691443\pi\) | |||||||
\(954\) | 2636.00 | 0.0894588 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −4152.00 | −0.140466 | ||||||||
\(957\) | 250.000 | 0.00844446 | ||||||||
\(958\) | −6876.00 | −0.231893 | ||||||||
\(959\) | −30590.0 | −1.03003 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29745.0 | 0.998456 | ||||||||
\(962\) | 444.000 | 0.0148806 | ||||||||
\(963\) | 3912.00 | 0.130906 | ||||||||
\(964\) | 8200.00 | 0.273967 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 34580.0 | 1.15175 | ||||||||
\(967\) | −1194.00 | −0.0397068 | −0.0198534 | − | 0.999803i | \(-0.506320\pi\) | ||||
−0.0198534 | + | 0.999803i | \(0.506320\pi\) | |||||||
\(968\) | 10448.0 | 0.346913 | ||||||||
\(969\) | −15840.0 | −0.525133 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30912.0 | 1.02164 | 0.510820 | − | 0.859687i | \(-0.329342\pi\) | ||||
0.510820 | + | 0.859687i | \(0.329342\pi\) | |||||||
\(972\) | 2240.00 | 0.0739177 | ||||||||
\(973\) | −9500.00 | −0.313007 | ||||||||
\(974\) | −39184.0 | −1.28905 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9920.00 | −0.325340 | ||||||||
\(977\) | 31404.0 | 1.02836 | 0.514178 | − | 0.857684i | \(-0.328097\pi\) | ||||
0.514178 | + | 0.857684i | \(0.328097\pi\) | |||||||
\(978\) | 18540.0 | 0.606180 | ||||||||
\(979\) | 6520.00 | 0.212850 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3240.00 | −0.105449 | ||||||||
\(982\) | −8888.00 | −0.288826 | ||||||||
\(983\) | −40411.0 | −1.31120 | −0.655601 | − | 0.755108i | \(-0.727584\pi\) | ||||
−0.655601 | + | 0.755108i | \(0.727584\pi\) | |||||||
\(984\) | 9000.00 | 0.291575 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1440.00 | −0.0465101 | ||||||||
\(987\) | −20995.0 | −0.677080 | ||||||||
\(988\) | 1056.00 | 0.0340039 | ||||||||
\(989\) | −364.000 | −0.0117033 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11002.0 | −0.352664 | −0.176332 | − | 0.984331i | \(-0.556423\pi\) | ||||
−0.176332 | + | 0.984331i | \(0.556423\pi\) | |||||||
\(992\) | 7808.00 | 0.249903 | ||||||||
\(993\) | −14470.0 | −0.462429 | ||||||||
\(994\) | 42750.0 | 1.36413 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −24780.0 | −0.788338 | ||||||||
\(997\) | −6618.00 | −0.210225 | −0.105112 | − | 0.994460i | \(-0.533520\pi\) | ||||
−0.105112 | + | 0.994460i | \(0.533520\pi\) | |||||||
\(998\) | 2280.00 | 0.0723168 | ||||||||
\(999\) | −5365.00 | −0.169911 |
(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 | 1850.4.a.d.1.1 | 1 | ||
5.4 | even | 2 | 74.4.a.b.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 666.4.a.c.1.1 | 1 | |||
20.19 | odd | 2 | 592.4.a.a.1.1 | 1 | |||
40.19 | odd | 2 | 2368.4.a.b.1.1 | 1 | |||
40.29 | even | 2 | 2368.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.4.a.b.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
592.4.a.a.1.1 | 1 | 20.19 | odd | 2 | |||
666.4.a.c.1.1 | 1 | 15.14 | odd | 2 | |||
1850.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2368.4.a.b.1.1 | 1 | 40.19 | odd | 2 | |||
2368.4.a.d.1.1 | 1 | 40.29 | even | 2 |