Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,12,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(7.68343180560\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1969}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 492 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(22.6867\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 32.0000 | 0.707107 | ||||||||
\(3\) | −141.734 | −0.336750 | −0.168375 | − | 0.985723i | \(-0.553852\pi\) | ||||
−0.168375 | + | 0.985723i | \(0.553852\pi\) | |||||||
\(4\) | 1024.00 | 0.500000 | ||||||||
\(5\) | 3125.00 | 0.447214 | ||||||||
\(6\) | −4535.49 | −0.238118 | ||||||||
\(7\) | 85586.9 | 1.92472 | 0.962362 | − | 0.271772i | \(-0.0876097\pi\) | ||||
0.962362 | + | 0.271772i | \(0.0876097\pi\) | |||||||
\(8\) | 32768.0 | 0.353553 | ||||||||
\(9\) | −157058. | −0.886599 | ||||||||
\(10\) | 100000. | 0.316228 | ||||||||
\(11\) | 767235. | 1.43638 | 0.718188 | − | 0.695849i | \(-0.244972\pi\) | ||||
0.718188 | + | 0.695849i | \(0.244972\pi\) | |||||||
\(12\) | −145136. | −0.168375 | ||||||||
\(13\) | 220960. | 0.165054 | 0.0825268 | − | 0.996589i | \(-0.473701\pi\) | ||||
0.0825268 | + | 0.996589i | \(0.473701\pi\) | |||||||
\(14\) | 2.73878e6 | 1.36098 | ||||||||
\(15\) | −442919. | −0.150599 | ||||||||
\(16\) | 1.04858e6 | 0.250000 | ||||||||
\(17\) | −930719. | −0.158983 | −0.0794913 | − | 0.996836i | \(-0.525330\pi\) | ||||
−0.0794913 | + | 0.996836i | \(0.525330\pi\) | |||||||
\(18\) | −5.02587e6 | −0.626920 | ||||||||
\(19\) | −1.77341e7 | −1.64310 | −0.821551 | − | 0.570135i | \(-0.806891\pi\) | ||||
−0.821551 | + | 0.570135i | \(0.806891\pi\) | |||||||
\(20\) | 3.20000e6 | 0.223607 | ||||||||
\(21\) | −1.21306e7 | −0.648151 | ||||||||
\(22\) | 2.45515e7 | 1.01567 | ||||||||
\(23\) | −3.99596e7 | −1.29455 | −0.647274 | − | 0.762257i | \(-0.724091\pi\) | ||||
−0.647274 | + | 0.762257i | \(0.724091\pi\) | |||||||
\(24\) | −4.64434e6 | −0.119059 | ||||||||
\(25\) | 9.76562e6 | 0.200000 | ||||||||
\(26\) | 7.07072e6 | 0.116711 | ||||||||
\(27\) | 4.73683e7 | 0.635312 | ||||||||
\(28\) | 8.76410e7 | 0.962362 | ||||||||
\(29\) | 7.68554e7 | 0.695801 | 0.347901 | − | 0.937531i | \(-0.386895\pi\) | ||||
0.347901 | + | 0.937531i | \(0.386895\pi\) | |||||||
\(30\) | −1.41734e7 | −0.106490 | ||||||||
\(31\) | −2.96314e7 | −0.185893 | −0.0929465 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929465 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(32\) | 3.35544e7 | 0.176777 | ||||||||
\(33\) | −1.08743e8 | −0.483700 | ||||||||
\(34\) | −2.97830e7 | −0.112418 | ||||||||
\(35\) | 2.67459e8 | 0.860762 | ||||||||
\(36\) | −1.60828e8 | −0.443300 | ||||||||
\(37\) | 5.40911e7 | 0.128238 | 0.0641189 | − | 0.997942i | \(-0.479576\pi\) | ||||
0.0641189 | + | 0.997942i | \(0.479576\pi\) | |||||||
\(38\) | −5.67491e8 | −1.16185 | ||||||||
\(39\) | −3.13176e7 | −0.0555818 | ||||||||
\(40\) | 1.02400e8 | 0.158114 | ||||||||
\(41\) | 1.26006e8 | 0.169856 | 0.0849280 | − | 0.996387i | \(-0.472934\pi\) | ||||
0.0849280 | + | 0.996387i | \(0.472934\pi\) | |||||||
\(42\) | −3.88179e8 | −0.458312 | ||||||||
\(43\) | −2.88676e8 | −0.299457 | −0.149728 | − | 0.988727i | \(-0.547840\pi\) | ||||
−0.149728 | + | 0.988727i | \(0.547840\pi\) | |||||||
\(44\) | 7.85648e8 | 0.718188 | ||||||||
\(45\) | −4.90808e8 | −0.396499 | ||||||||
\(46\) | −1.27871e9 | −0.915384 | ||||||||
\(47\) | −1.57008e9 | −0.998579 | −0.499290 | − | 0.866435i | \(-0.666406\pi\) | ||||
−0.499290 | + | 0.866435i | \(0.666406\pi\) | |||||||
\(48\) | −1.48619e8 | −0.0841875 | ||||||||
\(49\) | 5.34780e9 | 2.70456 | ||||||||
\(50\) | 3.12500e8 | 0.141421 | ||||||||
\(51\) | 1.31915e8 | 0.0535374 | ||||||||
\(52\) | 2.26263e8 | 0.0825268 | ||||||||
\(53\) | −4.09006e9 | −1.34342 | −0.671711 | − | 0.740813i | \(-0.734440\pi\) | ||||
−0.671711 | + | 0.740813i | \(0.734440\pi\) | |||||||
\(54\) | 1.51579e9 | 0.449234 | ||||||||
\(55\) | 2.39761e9 | 0.642367 | ||||||||
\(56\) | 2.80451e9 | 0.680492 | ||||||||
\(57\) | 2.51353e9 | 0.553315 | ||||||||
\(58\) | 2.45937e9 | 0.492006 | ||||||||
\(59\) | 3.77882e9 | 0.688129 | 0.344065 | − | 0.938946i | \(-0.388196\pi\) | ||||
0.344065 | + | 0.938946i | \(0.388196\pi\) | |||||||
\(60\) | −4.53549e8 | −0.0752996 | ||||||||
\(61\) | −9.64103e9 | −1.46154 | −0.730768 | − | 0.682626i | \(-0.760838\pi\) | ||||
−0.730768 | + | 0.682626i | \(0.760838\pi\) | |||||||
\(62\) | −9.48205e8 | −0.131446 | ||||||||
\(63\) | −1.34422e10 | −1.70646 | ||||||||
\(64\) | 1.07374e9 | 0.125000 | ||||||||
\(65\) | 6.90500e8 | 0.0738143 | ||||||||
\(66\) | −3.47979e9 | −0.342028 | ||||||||
\(67\) | −1.63819e10 | −1.48236 | −0.741178 | − | 0.671308i | \(-0.765733\pi\) | ||||
−0.741178 | + | 0.671308i | \(0.765733\pi\) | |||||||
\(68\) | −9.53056e8 | −0.0794913 | ||||||||
\(69\) | 5.66364e9 | 0.435939 | ||||||||
\(70\) | 8.55869e9 | 0.608651 | ||||||||
\(71\) | 1.03471e10 | 0.680609 | 0.340304 | − | 0.940315i | \(-0.389470\pi\) | ||||
0.340304 | + | 0.940315i | \(0.389470\pi\) | |||||||
\(72\) | −5.14649e9 | −0.313460 | ||||||||
\(73\) | 4.27149e9 | 0.241159 | 0.120580 | − | 0.992704i | \(-0.461525\pi\) | ||||
0.120580 | + | 0.992704i | \(0.461525\pi\) | |||||||
\(74\) | 1.73091e9 | 0.0906778 | ||||||||
\(75\) | −1.38412e9 | −0.0673500 | ||||||||
\(76\) | −1.81597e10 | −0.821551 | ||||||||
\(77\) | 6.56653e10 | 2.76463 | ||||||||
\(78\) | −1.00216e9 | −0.0393023 | ||||||||
\(79\) | −1.96636e10 | −0.718977 | −0.359489 | − | 0.933149i | \(-0.617049\pi\) | ||||
−0.359489 | + | 0.933149i | \(0.617049\pi\) | |||||||
\(80\) | 3.27680e9 | 0.111803 | ||||||||
\(81\) | 2.11087e10 | 0.672658 | ||||||||
\(82\) | 4.03220e9 | 0.120106 | ||||||||
\(83\) | −1.35791e10 | −0.378391 | −0.189196 | − | 0.981939i | \(-0.560588\pi\) | ||||
−0.189196 | + | 0.981939i | \(0.560588\pi\) | |||||||
\(84\) | −1.24217e10 | −0.324075 | ||||||||
\(85\) | −2.90850e9 | −0.0710991 | ||||||||
\(86\) | −9.23762e9 | −0.211748 | ||||||||
\(87\) | −1.08930e10 | −0.234311 | ||||||||
\(88\) | 2.51407e10 | 0.507836 | ||||||||
\(89\) | 2.25058e10 | 0.427218 | 0.213609 | − | 0.976919i | \(-0.431478\pi\) | ||||
0.213609 | + | 0.976919i | \(0.431478\pi\) | |||||||
\(90\) | −1.57058e10 | −0.280367 | ||||||||
\(91\) | 1.89113e10 | 0.317683 | ||||||||
\(92\) | −4.09186e10 | −0.647274 | ||||||||
\(93\) | 4.19978e9 | 0.0625994 | ||||||||
\(94\) | −5.02424e10 | −0.706102 | ||||||||
\(95\) | −5.54191e10 | −0.734818 | ||||||||
\(96\) | −4.75581e9 | −0.0595296 | ||||||||
\(97\) | −1.08976e11 | −1.28851 | −0.644255 | − | 0.764811i | \(-0.722832\pi\) | ||||
−0.644255 | + | 0.764811i | \(0.722832\pi\) | |||||||
\(98\) | 1.71130e11 | 1.91241 | ||||||||
\(99\) | −1.20501e11 | −1.27349 | ||||||||
\(100\) | 1.00000e10 | 0.100000 | ||||||||
\(101\) | 1.63516e11 | 1.54807 | 0.774037 | − | 0.633140i | \(-0.218234\pi\) | ||||
0.774037 | + | 0.633140i | \(0.218234\pi\) | |||||||
\(102\) | 4.22127e9 | 0.0378566 | ||||||||
\(103\) | −7.69876e10 | −0.654359 | −0.327180 | − | 0.944962i | \(-0.606098\pi\) | ||||
−0.327180 | + | 0.944962i | \(0.606098\pi\) | |||||||
\(104\) | 7.24042e9 | 0.0583553 | ||||||||
\(105\) | −3.79081e10 | −0.289862 | ||||||||
\(106\) | −1.30882e11 | −0.949943 | ||||||||
\(107\) | 1.19891e11 | 0.826376 | 0.413188 | − | 0.910646i | \(-0.364415\pi\) | ||||
0.413188 | + | 0.910646i | \(0.364415\pi\) | |||||||
\(108\) | 4.85052e10 | 0.317656 | ||||||||
\(109\) | −7.33426e10 | −0.456573 | −0.228287 | − | 0.973594i | \(-0.573312\pi\) | ||||
−0.228287 | + | 0.973594i | \(0.573312\pi\) | |||||||
\(110\) | 7.67235e10 | 0.454222 | ||||||||
\(111\) | −7.66655e9 | −0.0431841 | ||||||||
\(112\) | 8.97444e10 | 0.481181 | ||||||||
\(113\) | 2.18835e11 | 1.11734 | 0.558669 | − | 0.829391i | \(-0.311312\pi\) | ||||
0.558669 | + | 0.829391i | \(0.311312\pi\) | |||||||
\(114\) | 8.04329e10 | 0.391253 | ||||||||
\(115\) | −1.24874e11 | −0.578939 | ||||||||
\(116\) | 7.86999e10 | 0.347901 | ||||||||
\(117\) | −3.47036e10 | −0.146337 | ||||||||
\(118\) | 1.20922e11 | 0.486581 | ||||||||
\(119\) | −7.96574e10 | −0.305997 | ||||||||
\(120\) | −1.45136e10 | −0.0532449 | ||||||||
\(121\) | 3.03337e11 | 1.06318 | ||||||||
\(122\) | −3.08513e11 | −1.03346 | ||||||||
\(123\) | −1.78594e10 | −0.0571990 | ||||||||
\(124\) | −3.03426e10 | −0.0929465 | ||||||||
\(125\) | 3.05176e10 | 0.0894427 | ||||||||
\(126\) | −4.30149e11 | −1.20665 | ||||||||
\(127\) | 3.93053e11 | 1.05568 | 0.527838 | − | 0.849345i | \(-0.323003\pi\) | ||||
0.527838 | + | 0.849345i | \(0.323003\pi\) | |||||||
\(128\) | 3.43597e10 | 0.0883883 | ||||||||
\(129\) | 4.09152e10 | 0.100842 | ||||||||
\(130\) | 2.20960e10 | 0.0521946 | ||||||||
\(131\) | −2.63175e11 | −0.596008 | −0.298004 | − | 0.954565i | \(-0.596321\pi\) | ||||
−0.298004 | + | 0.954565i | \(0.596321\pi\) | |||||||
\(132\) | −1.11353e11 | −0.241850 | ||||||||
\(133\) | −1.51781e12 | −3.16252 | ||||||||
\(134\) | −5.24220e11 | −1.04818 | ||||||||
\(135\) | 1.48026e11 | 0.284120 | ||||||||
\(136\) | −3.04978e10 | −0.0562088 | ||||||||
\(137\) | 5.20521e11 | 0.921457 | 0.460728 | − | 0.887541i | \(-0.347588\pi\) | ||||
0.460728 | + | 0.887541i | \(0.347588\pi\) | |||||||
\(138\) | 1.81237e11 | 0.308255 | ||||||||
\(139\) | 6.82675e11 | 1.11592 | 0.557960 | − | 0.829868i | \(-0.311584\pi\) | ||||
0.557960 | + | 0.829868i | \(0.311584\pi\) | |||||||
\(140\) | 2.73878e11 | 0.430381 | ||||||||
\(141\) | 2.22533e11 | 0.336272 | ||||||||
\(142\) | 3.31107e11 | 0.481263 | ||||||||
\(143\) | 1.69528e11 | 0.237079 | ||||||||
\(144\) | −1.64688e11 | −0.221650 | ||||||||
\(145\) | 2.40173e11 | 0.311172 | ||||||||
\(146\) | 1.36688e11 | 0.170525 | ||||||||
\(147\) | −7.57966e11 | −0.910761 | ||||||||
\(148\) | 5.53893e10 | 0.0641189 | ||||||||
\(149\) | 1.01566e12 | 1.13299 | 0.566493 | − | 0.824066i | \(-0.308300\pi\) | ||||
0.566493 | + | 0.824066i | \(0.308300\pi\) | |||||||
\(150\) | −4.42919e10 | −0.0476236 | ||||||||
\(151\) | 5.34040e11 | 0.553605 | 0.276803 | − | 0.960927i | \(-0.410725\pi\) | ||||
0.276803 | + | 0.960927i | \(0.410725\pi\) | |||||||
\(152\) | −5.81111e11 | −0.580924 | ||||||||
\(153\) | 1.46177e11 | 0.140954 | ||||||||
\(154\) | 2.10129e12 | 1.95489 | ||||||||
\(155\) | −9.25981e10 | −0.0831338 | ||||||||
\(156\) | −3.20692e10 | −0.0277909 | ||||||||
\(157\) | −7.29675e11 | −0.610494 | −0.305247 | − | 0.952273i | \(-0.598739\pi\) | ||||
−0.305247 | + | 0.952273i | \(0.598739\pi\) | |||||||
\(158\) | −6.29237e11 | −0.508394 | ||||||||
\(159\) | 5.79701e11 | 0.452397 | ||||||||
\(160\) | 1.04858e11 | 0.0790569 | ||||||||
\(161\) | −3.42002e12 | −2.49165 | ||||||||
\(162\) | 6.75479e11 | 0.475641 | ||||||||
\(163\) | −2.12171e11 | −0.144429 | −0.0722143 | − | 0.997389i | \(-0.523007\pi\) | ||||
−0.0722143 | + | 0.997389i | \(0.523007\pi\) | |||||||
\(164\) | 1.29030e11 | 0.0849280 | ||||||||
\(165\) | −3.39823e11 | −0.216317 | ||||||||
\(166\) | −4.34531e11 | −0.267563 | ||||||||
\(167\) | −2.36613e11 | −0.140961 | −0.0704804 | − | 0.997513i | \(-0.522453\pi\) | ||||
−0.0704804 | + | 0.997513i | \(0.522453\pi\) | |||||||
\(168\) | −3.97495e11 | −0.229156 | ||||||||
\(169\) | −1.74334e12 | −0.972757 | ||||||||
\(170\) | −9.30719e10 | −0.0502747 | ||||||||
\(171\) | 2.78529e12 | 1.45677 | ||||||||
\(172\) | −2.95604e11 | −0.149728 | ||||||||
\(173\) | −7.36983e11 | −0.361579 | −0.180790 | − | 0.983522i | \(-0.557865\pi\) | ||||
−0.180790 | + | 0.983522i | \(0.557865\pi\) | |||||||
\(174\) | −3.48577e11 | −0.165683 | ||||||||
\(175\) | 8.35810e11 | 0.384945 | ||||||||
\(176\) | 8.04504e11 | 0.359094 | ||||||||
\(177\) | −5.35588e11 | −0.231727 | ||||||||
\(178\) | 7.20185e11 | 0.302089 | ||||||||
\(179\) | 1.35344e11 | 0.0550487 | 0.0275244 | − | 0.999621i | \(-0.491238\pi\) | ||||
0.0275244 | + | 0.999621i | \(0.491238\pi\) | |||||||
\(180\) | −5.02587e11 | −0.198250 | ||||||||
\(181\) | −1.35881e12 | −0.519907 | −0.259953 | − | 0.965621i | \(-0.583707\pi\) | ||||
−0.259953 | + | 0.965621i | \(0.583707\pi\) | |||||||
\(182\) | 6.05161e11 | 0.224636 | ||||||||
\(183\) | 1.36646e12 | 0.492172 | ||||||||
\(184\) | −1.30940e12 | −0.457692 | ||||||||
\(185\) | 1.69035e11 | 0.0573497 | ||||||||
\(186\) | 1.34393e11 | 0.0442645 | ||||||||
\(187\) | −7.14080e11 | −0.228359 | ||||||||
\(188\) | −1.60776e12 | −0.499290 | ||||||||
\(189\) | 4.05411e12 | 1.22280 | ||||||||
\(190\) | −1.77341e12 | −0.519594 | ||||||||
\(191\) | 1.10648e12 | 0.314964 | 0.157482 | − | 0.987522i | \(-0.449662\pi\) | ||||
0.157482 | + | 0.987522i | \(0.449662\pi\) | |||||||
\(192\) | −1.52186e11 | −0.0420938 | ||||||||
\(193\) | 6.17025e12 | 1.65858 | 0.829292 | − | 0.558816i | \(-0.188744\pi\) | ||||
0.829292 | + | 0.558816i | \(0.188744\pi\) | |||||||
\(194\) | −3.48724e12 | −0.911114 | ||||||||
\(195\) | −9.78674e10 | −0.0248570 | ||||||||
\(196\) | 5.47615e12 | 1.35228 | ||||||||
\(197\) | 2.00333e12 | 0.481047 | 0.240523 | − | 0.970643i | \(-0.422681\pi\) | ||||
0.240523 | + | 0.970643i | \(0.422681\pi\) | |||||||
\(198\) | −3.85602e12 | −0.900494 | ||||||||
\(199\) | −7.73897e12 | −1.75789 | −0.878944 | − | 0.476925i | \(-0.841751\pi\) | ||||
−0.878944 | + | 0.476925i | \(0.841751\pi\) | |||||||
\(200\) | 3.20000e11 | 0.0707107 | ||||||||
\(201\) | 2.32187e12 | 0.499183 | ||||||||
\(202\) | 5.23250e12 | 1.09465 | ||||||||
\(203\) | 6.57782e12 | 1.33922 | ||||||||
\(204\) | 1.35081e11 | 0.0267687 | ||||||||
\(205\) | 3.93770e11 | 0.0759619 | ||||||||
\(206\) | −2.46360e12 | −0.462702 | ||||||||
\(207\) | 6.27599e12 | 1.14775 | ||||||||
\(208\) | 2.31693e11 | 0.0412634 | ||||||||
\(209\) | −1.36062e13 | −2.36011 | ||||||||
\(210\) | −1.21306e12 | −0.204963 | ||||||||
\(211\) | −9.01879e12 | −1.48455 | −0.742275 | − | 0.670096i | \(-0.766253\pi\) | ||||
−0.742275 | + | 0.670096i | \(0.766253\pi\) | |||||||
\(212\) | −4.18822e12 | −0.671711 | ||||||||
\(213\) | −1.46654e12 | −0.229195 | ||||||||
\(214\) | 3.83653e12 | 0.584336 | ||||||||
\(215\) | −9.02112e11 | −0.133921 | ||||||||
\(216\) | 1.55217e12 | 0.224617 | ||||||||
\(217\) | −2.53606e12 | −0.357792 | ||||||||
\(218\) | −2.34696e12 | −0.322846 | ||||||||
\(219\) | −6.05416e11 | −0.0812103 | ||||||||
\(220\) | 2.45515e12 | 0.321184 | ||||||||
\(221\) | −2.05652e11 | −0.0262407 | ||||||||
\(222\) | −2.45330e11 | −0.0305358 | ||||||||
\(223\) | 2.06620e12 | 0.250897 | 0.125448 | − | 0.992100i | \(-0.459963\pi\) | ||||
0.125448 | + | 0.992100i | \(0.459963\pi\) | |||||||
\(224\) | 2.87182e12 | 0.340246 | ||||||||
\(225\) | −1.53377e12 | −0.177320 | ||||||||
\(226\) | 7.00271e12 | 0.790077 | ||||||||
\(227\) | −1.56806e13 | −1.72672 | −0.863359 | − | 0.504591i | \(-0.831643\pi\) | ||||
−0.863359 | + | 0.504591i | \(0.831643\pi\) | |||||||
\(228\) | 2.57385e12 | 0.276657 | ||||||||
\(229\) | 6.02309e12 | 0.632010 | 0.316005 | − | 0.948758i | \(-0.397658\pi\) | ||||
0.316005 | + | 0.948758i | \(0.397658\pi\) | |||||||
\(230\) | −3.99596e12 | −0.409372 | ||||||||
\(231\) | −9.30701e12 | −0.930989 | ||||||||
\(232\) | 2.51840e12 | 0.246003 | ||||||||
\(233\) | 1.43129e13 | 1.36544 | 0.682718 | − | 0.730682i | \(-0.260798\pi\) | ||||
0.682718 | + | 0.730682i | \(0.260798\pi\) | |||||||
\(234\) | −1.11052e12 | −0.103476 | ||||||||
\(235\) | −4.90649e12 | −0.446578 | ||||||||
\(236\) | 3.86951e12 | 0.344065 | ||||||||
\(237\) | 2.78701e12 | 0.242116 | ||||||||
\(238\) | −2.54904e12 | −0.216373 | ||||||||
\(239\) | 2.22886e13 | 1.84881 | 0.924407 | − | 0.381407i | \(-0.124560\pi\) | ||||
0.924407 | + | 0.381407i | \(0.124560\pi\) | |||||||
\(240\) | −4.64434e11 | −0.0376498 | ||||||||
\(241\) | 2.06638e13 | 1.63726 | 0.818629 | − | 0.574323i | \(-0.194735\pi\) | ||||
0.818629 | + | 0.574323i | \(0.194735\pi\) | |||||||
\(242\) | 9.70679e12 | 0.751781 | ||||||||
\(243\) | −1.13830e13 | −0.861830 | ||||||||
\(244\) | −9.87241e12 | −0.730768 | ||||||||
\(245\) | 1.67119e13 | 1.20952 | ||||||||
\(246\) | −5.71501e11 | −0.0404458 | ||||||||
\(247\) | −3.91853e12 | −0.271200 | ||||||||
\(248\) | −9.70962e11 | −0.0657231 | ||||||||
\(249\) | 1.92462e12 | 0.127423 | ||||||||
\(250\) | 9.76562e11 | 0.0632456 | ||||||||
\(251\) | −1.23384e13 | −0.781721 | −0.390861 | − | 0.920450i | \(-0.627823\pi\) | ||||
−0.390861 | + | 0.920450i | \(0.627823\pi\) | |||||||
\(252\) | −1.37648e13 | −0.853229 | ||||||||
\(253\) | −3.06584e13 | −1.85946 | ||||||||
\(254\) | 1.25777e13 | 0.746475 | ||||||||
\(255\) | 4.12233e11 | 0.0239426 | ||||||||
\(256\) | 1.09951e12 | 0.0625000 | ||||||||
\(257\) | 1.19160e13 | 0.662975 | 0.331487 | − | 0.943460i | \(-0.392450\pi\) | ||||
0.331487 | + | 0.943460i | \(0.392450\pi\) | |||||||
\(258\) | 1.30929e12 | 0.0713061 | ||||||||
\(259\) | 4.62949e12 | 0.246822 | ||||||||
\(260\) | 7.07072e11 | 0.0369071 | ||||||||
\(261\) | −1.20708e13 | −0.616897 | ||||||||
\(262\) | −8.42159e12 | −0.421441 | ||||||||
\(263\) | 1.54645e12 | 0.0757845 | 0.0378923 | − | 0.999282i | \(-0.487936\pi\) | ||||
0.0378923 | + | 0.999282i | \(0.487936\pi\) | |||||||
\(264\) | −3.56330e12 | −0.171014 | ||||||||
\(265\) | −1.27814e13 | −0.600797 | ||||||||
\(266\) | −4.85699e13 | −2.23624 | ||||||||
\(267\) | −3.18984e12 | −0.143866 | ||||||||
\(268\) | −1.67751e13 | −0.741178 | ||||||||
\(269\) | 1.43195e13 | 0.619855 | 0.309927 | − | 0.950760i | \(-0.399695\pi\) | ||||
0.309927 | + | 0.950760i | \(0.399695\pi\) | |||||||
\(270\) | 4.73683e12 | 0.200903 | ||||||||
\(271\) | 2.26776e13 | 0.942468 | 0.471234 | − | 0.882008i | \(-0.343809\pi\) | ||||
0.471234 | + | 0.882008i | \(0.343809\pi\) | |||||||
\(272\) | −9.75929e11 | −0.0397456 | ||||||||
\(273\) | −2.68038e12 | −0.106980 | ||||||||
\(274\) | 1.66567e13 | 0.651568 | ||||||||
\(275\) | 7.49253e12 | 0.287275 | ||||||||
\(276\) | 5.79957e12 | 0.217970 | ||||||||
\(277\) | 9.25283e12 | 0.340907 | 0.170454 | − | 0.985366i | \(-0.445477\pi\) | ||||
0.170454 | + | 0.985366i | \(0.445477\pi\) | |||||||
\(278\) | 2.18456e13 | 0.789074 | ||||||||
\(279\) | 4.65386e12 | 0.164813 | ||||||||
\(280\) | 8.76410e12 | 0.304325 | ||||||||
\(281\) | −2.26511e12 | −0.0771265 | −0.0385633 | − | 0.999256i | \(-0.512278\pi\) | ||||
−0.0385633 | + | 0.999256i | \(0.512278\pi\) | |||||||
\(282\) | 7.12107e12 | 0.237780 | ||||||||
\(283\) | −3.60409e13 | −1.18024 | −0.590121 | − | 0.807315i | \(-0.700920\pi\) | ||||
−0.590121 | + | 0.807315i | \(0.700920\pi\) | |||||||
\(284\) | 1.05954e13 | 0.340304 | ||||||||
\(285\) | 7.85478e12 | 0.247450 | ||||||||
\(286\) | 5.42490e12 | 0.167640 | ||||||||
\(287\) | 1.07845e13 | 0.326926 | ||||||||
\(288\) | −5.27001e12 | −0.156730 | ||||||||
\(289\) | −3.34057e13 | −0.974725 | ||||||||
\(290\) | 7.68554e12 | 0.220032 | ||||||||
\(291\) | 1.54457e13 | 0.433905 | ||||||||
\(292\) | 4.37401e12 | 0.120580 | ||||||||
\(293\) | 1.63348e13 | 0.441918 | 0.220959 | − | 0.975283i | \(-0.429081\pi\) | ||||
0.220959 | + | 0.975283i | \(0.429081\pi\) | |||||||
\(294\) | −2.42549e13 | −0.644005 | ||||||||
\(295\) | 1.18088e13 | 0.307741 | ||||||||
\(296\) | 1.77246e12 | 0.0453389 | ||||||||
\(297\) | 3.63426e13 | 0.912548 | ||||||||
\(298\) | 3.25012e13 | 0.801142 | ||||||||
\(299\) | −8.82948e12 | −0.213670 | ||||||||
\(300\) | −1.41734e12 | −0.0336750 | ||||||||
\(301\) | −2.47069e13 | −0.576371 | ||||||||
\(302\) | 1.70893e13 | 0.391458 | ||||||||
\(303\) | −2.31758e13 | −0.521314 | ||||||||
\(304\) | −1.85956e13 | −0.410776 | ||||||||
\(305\) | −3.01282e13 | −0.653618 | ||||||||
\(306\) | 4.67767e12 | 0.0996694 | ||||||||
\(307\) | −5.61322e13 | −1.17476 | −0.587382 | − | 0.809310i | \(-0.699842\pi\) | ||||
−0.587382 | + | 0.809310i | \(0.699842\pi\) | |||||||
\(308\) | 6.72412e13 | 1.38231 | ||||||||
\(309\) | 1.09118e13 | 0.220355 | ||||||||
\(310\) | −2.96314e12 | −0.0587845 | ||||||||
\(311\) | 6.92340e13 | 1.34939 | 0.674694 | − | 0.738097i | \(-0.264275\pi\) | ||||
0.674694 | + | 0.738097i | \(0.264275\pi\) | |||||||
\(312\) | −1.02621e12 | −0.0196511 | ||||||||
\(313\) | −3.23822e13 | −0.609273 | −0.304637 | − | 0.952469i | \(-0.598535\pi\) | ||||
−0.304637 | + | 0.952469i | \(0.598535\pi\) | |||||||
\(314\) | −2.33496e13 | −0.431684 | ||||||||
\(315\) | −4.20067e13 | −0.763151 | ||||||||
\(316\) | −2.01356e13 | −0.359489 | ||||||||
\(317\) | −1.84023e13 | −0.322885 | −0.161442 | − | 0.986882i | \(-0.551615\pi\) | ||||
−0.161442 | + | 0.986882i | \(0.551615\pi\) | |||||||
\(318\) | 1.85504e13 | 0.319893 | ||||||||
\(319\) | 5.89661e13 | 0.999433 | ||||||||
\(320\) | 3.35544e12 | 0.0559017 | ||||||||
\(321\) | −1.69927e13 | −0.278282 | ||||||||
\(322\) | −1.09441e14 | −1.76186 | ||||||||
\(323\) | 1.65055e13 | 0.261224 | ||||||||
\(324\) | 2.16153e13 | 0.336329 | ||||||||
\(325\) | 2.15781e12 | 0.0330107 | ||||||||
\(326\) | −6.78946e12 | −0.102126 | ||||||||
\(327\) | 1.03951e13 | 0.153751 | ||||||||
\(328\) | 4.12897e12 | 0.0600532 | ||||||||
\(329\) | −1.34378e14 | −1.92199 | ||||||||
\(330\) | −1.08743e13 | −0.152959 | ||||||||
\(331\) | 6.74629e13 | 0.933277 | 0.466639 | − | 0.884448i | \(-0.345465\pi\) | ||||
0.466639 | + | 0.884448i | \(0.345465\pi\) | |||||||
\(332\) | −1.39050e13 | −0.189196 | ||||||||
\(333\) | −8.49546e12 | −0.113696 | ||||||||
\(334\) | −7.57163e12 | −0.0996744 | ||||||||
\(335\) | −5.11934e13 | −0.662930 | ||||||||
\(336\) | −1.27198e13 | −0.162038 | ||||||||
\(337\) | 1.07897e14 | 1.35222 | 0.676109 | − | 0.736802i | \(-0.263665\pi\) | ||||
0.676109 | + | 0.736802i | \(0.263665\pi\) | |||||||
\(338\) | −5.57868e13 | −0.687843 | ||||||||
\(339\) | −3.10163e13 | −0.376264 | ||||||||
\(340\) | −2.97830e12 | −0.0355496 | ||||||||
\(341\) | −2.27342e13 | −0.267012 | ||||||||
\(342\) | 8.91293e13 | 1.03009 | ||||||||
\(343\) | 2.88468e14 | 3.28081 | ||||||||
\(344\) | −9.45933e12 | −0.105874 | ||||||||
\(345\) | 1.76989e13 | 0.194958 | ||||||||
\(346\) | −2.35834e13 | −0.255675 | ||||||||
\(347\) | −1.29756e13 | −0.138458 | −0.0692288 | − | 0.997601i | \(-0.522054\pi\) | ||||
−0.0692288 | + | 0.997601i | \(0.522054\pi\) | |||||||
\(348\) | −1.11545e13 | −0.117156 | ||||||||
\(349\) | −7.76358e13 | −0.802643 | −0.401321 | − | 0.915937i | \(-0.631449\pi\) | ||||
−0.401321 | + | 0.915937i | \(0.631449\pi\) | |||||||
\(350\) | 2.67459e13 | 0.272197 | ||||||||
\(351\) | 1.04665e13 | 0.104861 | ||||||||
\(352\) | 2.57441e13 | 0.253918 | ||||||||
\(353\) | −4.21031e13 | −0.408839 | −0.204420 | − | 0.978883i | \(-0.565531\pi\) | ||||
−0.204420 | + | 0.978883i | \(0.565531\pi\) | |||||||
\(354\) | −1.71388e13 | −0.163856 | ||||||||
\(355\) | 3.23347e13 | 0.304377 | ||||||||
\(356\) | 2.30459e13 | 0.213609 | ||||||||
\(357\) | 1.12902e13 | 0.103045 | ||||||||
\(358\) | 4.33101e12 | 0.0389253 | ||||||||
\(359\) | 1.84963e14 | 1.63707 | 0.818533 | − | 0.574460i | \(-0.194788\pi\) | ||||
0.818533 | + | 0.574460i | \(0.194788\pi\) | |||||||
\(360\) | −1.60828e13 | −0.140184 | ||||||||
\(361\) | 1.98008e14 | 1.69978 | ||||||||
\(362\) | −4.34818e13 | −0.367630 | ||||||||
\(363\) | −4.29933e13 | −0.358025 | ||||||||
\(364\) | 1.93652e13 | 0.158841 | ||||||||
\(365\) | 1.33484e13 | 0.107850 | ||||||||
\(366\) | 4.37268e13 | 0.348018 | ||||||||
\(367\) | −1.68959e14 | −1.32470 | −0.662351 | − | 0.749194i | \(-0.730441\pi\) | ||||
−0.662351 | + | 0.749194i | \(0.730441\pi\) | |||||||
\(368\) | −4.19007e13 | −0.323637 | ||||||||
\(369\) | −1.97903e13 | −0.150594 | ||||||||
\(370\) | 5.40911e12 | 0.0405524 | ||||||||
\(371\) | −3.50056e14 | −2.58572 | ||||||||
\(372\) | 4.30058e12 | 0.0312997 | ||||||||
\(373\) | −1.87187e14 | −1.34238 | −0.671191 | − | 0.741284i | \(-0.734217\pi\) | ||||
−0.671191 | + | 0.741284i | \(0.734217\pi\) | |||||||
\(374\) | −2.28505e13 | −0.161474 | ||||||||
\(375\) | −4.32538e12 | −0.0301198 | ||||||||
\(376\) | −5.14483e13 | −0.353051 | ||||||||
\(377\) | 1.69820e13 | 0.114845 | ||||||||
\(378\) | 1.29732e14 | 0.864651 | ||||||||
\(379\) | −7.47613e13 | −0.491090 | −0.245545 | − | 0.969385i | \(-0.578967\pi\) | ||||
−0.245545 | + | 0.969385i | \(0.578967\pi\) | |||||||
\(380\) | −5.67491e13 | −0.367409 | ||||||||
\(381\) | −5.57090e13 | −0.355499 | ||||||||
\(382\) | 3.54074e13 | 0.222713 | ||||||||
\(383\) | −1.55521e14 | −0.964264 | −0.482132 | − | 0.876099i | \(-0.660137\pi\) | ||||
−0.482132 | + | 0.876099i | \(0.660137\pi\) | |||||||
\(384\) | −4.86995e12 | −0.0297648 | ||||||||
\(385\) | 2.05204e14 | 1.23638 | ||||||||
\(386\) | 1.97448e14 | 1.17280 | ||||||||
\(387\) | 4.53390e13 | 0.265498 | ||||||||
\(388\) | −1.11592e14 | −0.644255 | ||||||||
\(389\) | −8.76448e13 | −0.498889 | −0.249444 | − | 0.968389i | \(-0.580248\pi\) | ||||
−0.249444 | + | 0.968389i | \(0.580248\pi\) | |||||||
\(390\) | −3.13176e12 | −0.0175765 | ||||||||
\(391\) | 3.71912e13 | 0.205811 | ||||||||
\(392\) | 1.75237e14 | 0.956206 | ||||||||
\(393\) | 3.73009e13 | 0.200706 | ||||||||
\(394\) | 6.41064e13 | 0.340151 | ||||||||
\(395\) | −6.14489e13 | −0.321536 | ||||||||
\(396\) | −1.23393e14 | −0.636745 | ||||||||
\(397\) | 5.19767e13 | 0.264521 | 0.132261 | − | 0.991215i | \(-0.457776\pi\) | ||||
0.132261 | + | 0.991215i | \(0.457776\pi\) | |||||||
\(398\) | −2.47647e14 | −1.24301 | ||||||||
\(399\) | 2.15125e14 | 1.06498 | ||||||||
\(400\) | 1.02400e13 | 0.0500000 | ||||||||
\(401\) | −3.40753e14 | −1.64114 | −0.820570 | − | 0.571546i | \(-0.806344\pi\) | ||||
−0.820570 | + | 0.571546i | \(0.806344\pi\) | |||||||
\(402\) | 7.42999e13 | 0.352976 | ||||||||
\(403\) | −6.54735e12 | −0.0306823 | ||||||||
\(404\) | 1.67440e14 | 0.774037 | ||||||||
\(405\) | 6.59648e13 | 0.300822 | ||||||||
\(406\) | 2.10490e14 | 0.946975 | ||||||||
\(407\) | 4.15005e13 | 0.184198 | ||||||||
\(408\) | 4.32258e12 | 0.0189283 | ||||||||
\(409\) | 3.34635e14 | 1.44575 | 0.722875 | − | 0.690979i | \(-0.242820\pi\) | ||||
0.722875 | + | 0.690979i | \(0.242820\pi\) | |||||||
\(410\) | 1.26006e13 | 0.0537132 | ||||||||
\(411\) | −7.37756e13 | −0.310301 | ||||||||
\(412\) | −7.88353e13 | −0.327180 | ||||||||
\(413\) | 3.23417e14 | 1.32446 | ||||||||
\(414\) | 2.00832e14 | 0.811579 | ||||||||
\(415\) | −4.24347e13 | −0.169222 | ||||||||
\(416\) | 7.41419e12 | 0.0291776 | ||||||||
\(417\) | −9.67584e13 | −0.375786 | ||||||||
\(418\) | −4.35399e14 | −1.66885 | ||||||||
\(419\) | 1.37830e14 | 0.521396 | 0.260698 | − | 0.965420i | \(-0.416047\pi\) | ||||
0.260698 | + | 0.965420i | \(0.416047\pi\) | |||||||
\(420\) | −3.88179e13 | −0.144931 | ||||||||
\(421\) | 4.35453e14 | 1.60468 | 0.802342 | − | 0.596864i | \(-0.203587\pi\) | ||||
0.802342 | + | 0.596864i | \(0.203587\pi\) | |||||||
\(422\) | −2.88601e14 | −1.04974 | ||||||||
\(423\) | 2.46594e14 | 0.885340 | ||||||||
\(424\) | −1.34023e14 | −0.474972 | ||||||||
\(425\) | −9.08905e12 | −0.0317965 | ||||||||
\(426\) | −4.69292e13 | −0.162065 | ||||||||
\(427\) | −8.25146e14 | −2.81305 | ||||||||
\(428\) | 1.22769e14 | 0.413188 | ||||||||
\(429\) | −2.40279e13 | −0.0798365 | ||||||||
\(430\) | −2.88676e13 | −0.0946965 | ||||||||
\(431\) | 1.51185e14 | 0.489647 | 0.244824 | − | 0.969568i | \(-0.421270\pi\) | ||||
0.244824 | + | 0.969568i | \(0.421270\pi\) | |||||||
\(432\) | 4.96693e13 | 0.158828 | ||||||||
\(433\) | −3.75044e13 | −0.118413 | −0.0592065 | − | 0.998246i | \(-0.518857\pi\) | ||||
−0.0592065 | + | 0.998246i | \(0.518857\pi\) | |||||||
\(434\) | −8.11539e13 | −0.252997 | ||||||||
\(435\) | −3.40407e13 | −0.104787 | ||||||||
\(436\) | −7.51028e13 | −0.228287 | ||||||||
\(437\) | 7.08648e14 | 2.12707 | ||||||||
\(438\) | −1.93733e13 | −0.0574244 | ||||||||
\(439\) | −1.61934e14 | −0.474004 | −0.237002 | − | 0.971509i | \(-0.576165\pi\) | ||||
−0.237002 | + | 0.971509i | \(0.576165\pi\) | |||||||
\(440\) | 7.85648e13 | 0.227111 | ||||||||
\(441\) | −8.39917e14 | −2.39786 | ||||||||
\(442\) | −6.58085e12 | −0.0185549 | ||||||||
\(443\) | −1.29342e14 | −0.360179 | −0.180090 | − | 0.983650i | \(-0.557639\pi\) | ||||
−0.180090 | + | 0.983650i | \(0.557639\pi\) | |||||||
\(444\) | −7.85055e12 | −0.0215920 | ||||||||
\(445\) | 7.03306e13 | 0.191058 | ||||||||
\(446\) | 6.61183e13 | 0.177411 | ||||||||
\(447\) | −1.43954e14 | −0.381533 | ||||||||
\(448\) | 9.18983e13 | 0.240590 | ||||||||
\(449\) | 1.30255e13 | 0.0336852 | 0.0168426 | − | 0.999858i | \(-0.494639\pi\) | ||||
0.0168426 | + | 0.999858i | \(0.494639\pi\) | |||||||
\(450\) | −4.90808e13 | −0.125384 | ||||||||
\(451\) | 9.66764e13 | 0.243977 | ||||||||
\(452\) | 2.24087e14 | 0.558669 | ||||||||
\(453\) | −7.56916e13 | −0.186427 | ||||||||
\(454\) | −5.01780e14 | −1.22097 | ||||||||
\(455\) | 5.90978e13 | 0.142072 | ||||||||
\(456\) | 8.23633e13 | 0.195626 | ||||||||
\(457\) | 3.45724e14 | 0.811318 | 0.405659 | − | 0.914025i | \(-0.367042\pi\) | ||||
0.405659 | + | 0.914025i | \(0.367042\pi\) | |||||||
\(458\) | 1.92739e14 | 0.446899 | ||||||||
\(459\) | −4.40866e13 | −0.101004 | ||||||||
\(460\) | −1.27871e14 | −0.289470 | ||||||||
\(461\) | 2.96945e14 | 0.664234 | 0.332117 | − | 0.943238i | \(-0.392237\pi\) | ||||
0.332117 | + | 0.943238i | \(0.392237\pi\) | |||||||
\(462\) | −2.97824e14 | −0.658308 | ||||||||
\(463\) | 4.55258e14 | 0.994402 | 0.497201 | − | 0.867635i | \(-0.334361\pi\) | ||||
0.497201 | + | 0.867635i | \(0.334361\pi\) | |||||||
\(464\) | 8.05887e13 | 0.173950 | ||||||||
\(465\) | 1.31243e13 | 0.0279953 | ||||||||
\(466\) | 4.58014e14 | 0.965509 | ||||||||
\(467\) | −3.66499e14 | −0.763537 | −0.381768 | − | 0.924258i | \(-0.624685\pi\) | ||||
−0.381768 | + | 0.924258i | \(0.624685\pi\) | |||||||
\(468\) | −3.55365e13 | −0.0731683 | ||||||||
\(469\) | −1.40208e15 | −2.85313 | ||||||||
\(470\) | −1.57008e14 | −0.315778 | ||||||||
\(471\) | 1.03420e14 | 0.205584 | ||||||||
\(472\) | 1.23824e14 | 0.243290 | ||||||||
\(473\) | −2.21482e14 | −0.430132 | ||||||||
\(474\) | 8.91843e13 | 0.171202 | ||||||||
\(475\) | −1.73185e14 | −0.328620 | ||||||||
\(476\) | −8.15691e13 | −0.152999 | ||||||||
\(477\) | 6.42379e14 | 1.19108 | ||||||||
\(478\) | 7.13234e14 | 1.30731 | ||||||||
\(479\) | 5.78377e14 | 1.04801 | 0.524005 | − | 0.851715i | \(-0.324437\pi\) | ||||
0.524005 | + | 0.851715i | \(0.324437\pi\) | |||||||
\(480\) | −1.48619e13 | −0.0266224 | ||||||||
\(481\) | 1.19520e13 | 0.0211661 | ||||||||
\(482\) | 6.61242e14 | 1.15772 | ||||||||
\(483\) | 4.84734e14 | 0.839062 | ||||||||
\(484\) | 3.10617e14 | 0.531589 | ||||||||
\(485\) | −3.40551e14 | −0.576239 | ||||||||
\(486\) | −3.64255e14 | −0.609406 | ||||||||
\(487\) | −4.75203e14 | −0.786086 | −0.393043 | − | 0.919520i | \(-0.628578\pi\) | ||||
−0.393043 | + | 0.919520i | \(0.628578\pi\) | |||||||
\(488\) | −3.15917e14 | −0.516731 | ||||||||
\(489\) | 3.00718e13 | 0.0486363 | ||||||||
\(490\) | 5.34780e14 | 0.855257 | ||||||||
\(491\) | 7.59641e14 | 1.20132 | 0.600662 | − | 0.799503i | \(-0.294904\pi\) | ||||
0.600662 | + | 0.799503i | \(0.294904\pi\) | |||||||
\(492\) | −1.82880e13 | −0.0285995 | ||||||||
\(493\) | −7.15307e13 | −0.110620 | ||||||||
\(494\) | −1.25393e14 | −0.191767 | ||||||||
\(495\) | −3.76565e14 | −0.569522 | ||||||||
\(496\) | −3.10708e13 | −0.0464732 | ||||||||
\(497\) | 8.85576e14 | 1.30998 | ||||||||
\(498\) | 6.15879e13 | 0.0901019 | ||||||||
\(499\) | −4.91039e14 | −0.710499 | −0.355249 | − | 0.934772i | \(-0.615604\pi\) | ||||
−0.355249 | + | 0.934772i | \(0.615604\pi\) | |||||||
\(500\) | 3.12500e13 | 0.0447214 | ||||||||
\(501\) | 3.35362e13 | 0.0474686 | ||||||||
\(502\) | −3.94828e14 | −0.552760 | ||||||||
\(503\) | −4.25544e14 | −0.589278 | −0.294639 | − | 0.955609i | \(-0.595199\pi\) | ||||
−0.294639 | + | 0.955609i | \(0.595199\pi\) | |||||||
\(504\) | −4.40472e14 | −0.603324 | ||||||||
\(505\) | 5.10987e14 | 0.692320 | ||||||||
\(506\) | −9.81069e14 | −1.31484 | ||||||||
\(507\) | 2.47090e14 | 0.327576 | ||||||||
\(508\) | 4.02486e14 | 0.527838 | ||||||||
\(509\) | −1.41466e15 | −1.83529 | −0.917644 | − | 0.397404i | \(-0.869911\pi\) | ||||
−0.917644 | + | 0.397404i | \(0.869911\pi\) | |||||||
\(510\) | 1.31915e13 | 0.0169300 | ||||||||
\(511\) | 3.65584e14 | 0.464165 | ||||||||
\(512\) | 3.51844e13 | 0.0441942 | ||||||||
\(513\) | −8.40035e14 | −1.04388 | ||||||||
\(514\) | 3.81311e14 | 0.468794 | ||||||||
\(515\) | −2.40586e14 | −0.292638 | ||||||||
\(516\) | 4.18972e13 | 0.0504210 | ||||||||
\(517\) | −1.20462e15 | −1.43434 | ||||||||
\(518\) | 1.48144e14 | 0.174530 | ||||||||
\(519\) | 1.04456e14 | 0.121762 | ||||||||
\(520\) | 2.26263e13 | 0.0260973 | ||||||||
\(521\) | 6.27267e14 | 0.715888 | 0.357944 | − | 0.933743i | \(-0.383478\pi\) | ||||
0.357944 | + | 0.933743i | \(0.383478\pi\) | |||||||
\(522\) | −3.86265e14 | −0.436212 | ||||||||
\(523\) | 2.23774e14 | 0.250063 | 0.125032 | − | 0.992153i | \(-0.460097\pi\) | ||||
0.125032 | + | 0.992153i | \(0.460097\pi\) | |||||||
\(524\) | −2.69491e14 | −0.298004 | ||||||||
\(525\) | −1.18463e14 | −0.129630 | ||||||||
\(526\) | 4.94865e13 | 0.0535877 | ||||||||
\(527\) | 2.75785e13 | 0.0295537 | ||||||||
\(528\) | −1.14026e14 | −0.120925 | ||||||||
\(529\) | 6.43961e14 | 0.675855 | ||||||||
\(530\) | −4.09006e14 | −0.424827 | ||||||||
\(531\) | −5.93495e14 | −0.610095 | ||||||||
\(532\) | −1.55424e15 | −1.58126 | ||||||||
\(533\) | 2.78424e13 | 0.0280354 | ||||||||
\(534\) | −1.02075e14 | −0.101728 | ||||||||
\(535\) | 3.74661e14 | 0.369566 | ||||||||
\(536\) | −5.36802e14 | −0.524092 | ||||||||
\(537\) | −1.91829e13 | −0.0185377 | ||||||||
\(538\) | 4.58224e14 | 0.438303 | ||||||||
\(539\) | 4.10302e15 | 3.88477 | ||||||||
\(540\) | 1.51579e14 | 0.142060 | ||||||||
\(541\) | 5.47756e14 | 0.508162 | 0.254081 | − | 0.967183i | \(-0.418227\pi\) | ||||
0.254081 | + | 0.967183i | \(0.418227\pi\) | |||||||
\(542\) | 7.25684e14 | 0.666425 | ||||||||
\(543\) | 1.92589e14 | 0.175079 | ||||||||
\(544\) | −3.12297e13 | −0.0281044 | ||||||||
\(545\) | −2.29196e14 | −0.204186 | ||||||||
\(546\) | −8.57720e13 | −0.0756460 | ||||||||
\(547\) | 4.33518e14 | 0.378509 | 0.189255 | − | 0.981928i | \(-0.439393\pi\) | ||||
0.189255 | + | 0.981928i | \(0.439393\pi\) | |||||||
\(548\) | 5.33013e14 | 0.460728 | ||||||||
\(549\) | 1.51420e15 | 1.29580 | ||||||||
\(550\) | 2.39761e14 | 0.203134 | ||||||||
\(551\) | −1.36296e15 | −1.14327 | ||||||||
\(552\) | 1.85586e14 | 0.154128 | ||||||||
\(553\) | −1.68295e15 | −1.38383 | ||||||||
\(554\) | 2.96091e14 | 0.241058 | ||||||||
\(555\) | −2.39580e13 | −0.0193125 | ||||||||
\(556\) | 6.99060e14 | 0.557960 | ||||||||
\(557\) | −7.36061e14 | −0.581715 | −0.290857 | − | 0.956766i | \(-0.593941\pi\) | ||||
−0.290857 | + | 0.956766i | \(0.593941\pi\) | |||||||
\(558\) | 1.48924e14 | 0.116540 | ||||||||
\(559\) | −6.37858e13 | −0.0494264 | ||||||||
\(560\) | 2.80451e14 | 0.215191 | ||||||||
\(561\) | 1.01209e14 | 0.0768998 | ||||||||
\(562\) | −7.24834e13 | −0.0545367 | ||||||||
\(563\) | −9.03199e14 | −0.672957 | −0.336478 | − | 0.941691i | \(-0.609236\pi\) | ||||
−0.336478 | + | 0.941691i | \(0.609236\pi\) | |||||||
\(564\) | 2.27874e14 | 0.168136 | ||||||||
\(565\) | 6.83858e14 | 0.499689 | ||||||||
\(566\) | −1.15331e15 | −0.834557 | ||||||||
\(567\) | 1.80663e15 | 1.29468 | ||||||||
\(568\) | 3.39054e14 | 0.240632 | ||||||||
\(569\) | −2.25786e15 | −1.58701 | −0.793503 | − | 0.608566i | \(-0.791745\pi\) | ||||
−0.793503 | + | 0.608566i | \(0.791745\pi\) | |||||||
\(570\) | 2.51353e14 | 0.174973 | ||||||||
\(571\) | 9.15100e14 | 0.630913 | 0.315457 | − | 0.948940i | \(-0.397842\pi\) | ||||
0.315457 | + | 0.948940i | \(0.397842\pi\) | |||||||
\(572\) | 1.73597e14 | 0.118540 | ||||||||
\(573\) | −1.56826e14 | −0.106064 | ||||||||
\(574\) | 3.45104e14 | 0.231172 | ||||||||
\(575\) | −3.90231e14 | −0.258910 | ||||||||
\(576\) | −1.68640e14 | −0.110825 | ||||||||
\(577\) | 2.84484e14 | 0.185179 | 0.0925893 | − | 0.995704i | \(-0.470486\pi\) | ||||
0.0925893 | + | 0.995704i | \(0.470486\pi\) | |||||||
\(578\) | −1.06898e15 | −0.689234 | ||||||||
\(579\) | −8.74535e14 | −0.558528 | ||||||||
\(580\) | 2.45937e14 | 0.155586 | ||||||||
\(581\) | −1.16219e15 | −0.728299 | ||||||||
\(582\) | 4.94261e14 | 0.306817 | ||||||||
\(583\) | −3.13804e15 | −1.92966 | ||||||||
\(584\) | 1.39968e14 | 0.0852626 | ||||||||
\(585\) | −1.08449e14 | −0.0654437 | ||||||||
\(586\) | 5.22714e14 | 0.312484 | ||||||||
\(587\) | −1.99879e15 | −1.18374 | −0.591871 | − | 0.806032i | \(-0.701611\pi\) | ||||
−0.591871 | + | 0.806032i | \(0.701611\pi\) | |||||||
\(588\) | −7.76157e14 | −0.455380 | ||||||||
\(589\) | 5.25486e14 | 0.305441 | ||||||||
\(590\) | 3.77882e14 | 0.217606 | ||||||||
\(591\) | −2.83940e14 | −0.161992 | ||||||||
\(592\) | 5.67186e13 | 0.0320595 | ||||||||
\(593\) | 8.52303e14 | 0.477302 | 0.238651 | − | 0.971105i | \(-0.423295\pi\) | ||||
0.238651 | + | 0.971105i | \(0.423295\pi\) | |||||||
\(594\) | 1.16296e15 | 0.645269 | ||||||||
\(595\) | −2.48929e14 | −0.136846 | ||||||||
\(596\) | 1.04004e15 | 0.566493 | ||||||||
\(597\) | 1.09688e15 | 0.591969 | ||||||||
\(598\) | −2.82543e14 | −0.151087 | ||||||||
\(599\) | 1.08984e14 | 0.0577449 | 0.0288725 | − | 0.999583i | \(-0.490808\pi\) | ||||
0.0288725 | + | 0.999583i | \(0.490808\pi\) | |||||||
\(600\) | −4.53549e13 | −0.0238118 | ||||||||
\(601\) | 3.21315e14 | 0.167156 | 0.0835778 | − | 0.996501i | \(-0.473365\pi\) | ||||
0.0835778 | + | 0.996501i | \(0.473365\pi\) | |||||||
\(602\) | −7.90620e14 | −0.407556 | ||||||||
\(603\) | 2.57291e15 | 1.31426 | ||||||||
\(604\) | 5.46856e14 | 0.276803 | ||||||||
\(605\) | 9.47929e14 | 0.475468 | ||||||||
\(606\) | −7.41624e14 | −0.368625 | ||||||||
\(607\) | −3.08680e15 | −1.52044 | −0.760222 | − | 0.649664i | \(-0.774910\pi\) | ||||
−0.760222 | + | 0.649664i | \(0.774910\pi\) | |||||||
\(608\) | −5.95058e14 | −0.290462 | ||||||||
\(609\) | −9.32301e14 | −0.450984 | ||||||||
\(610\) | −9.64103e14 | −0.462178 | ||||||||
\(611\) | −3.46924e14 | −0.164819 | ||||||||
\(612\) | 1.49685e14 | 0.0704769 | ||||||||
\(613\) | 8.70867e14 | 0.406368 | 0.203184 | − | 0.979141i | \(-0.434871\pi\) | ||||
0.203184 | + | 0.979141i | \(0.434871\pi\) | |||||||
\(614\) | −1.79623e15 | −0.830684 | ||||||||
\(615\) | −5.58106e13 | −0.0255802 | ||||||||
\(616\) | 2.15172e15 | 0.977444 | ||||||||
\(617\) | 3.06108e15 | 1.37818 | 0.689091 | − | 0.724675i | \(-0.258010\pi\) | ||||
0.689091 | + | 0.724675i | \(0.258010\pi\) | |||||||
\(618\) | 3.49177e14 | 0.155815 | ||||||||
\(619\) | −1.21317e15 | −0.536566 | −0.268283 | − | 0.963340i | \(-0.586456\pi\) | ||||
−0.268283 | + | 0.963340i | \(0.586456\pi\) | |||||||
\(620\) | −9.48205e13 | −0.0415669 | ||||||||
\(621\) | −1.89282e15 | −0.822442 | ||||||||
\(622\) | 2.21549e15 | 0.954162 | ||||||||
\(623\) | 1.92620e15 | 0.822276 | ||||||||
\(624\) | −3.28389e13 | −0.0138955 | ||||||||
\(625\) | 9.53674e13 | 0.0400000 | ||||||||
\(626\) | −1.03623e15 | −0.430821 | ||||||||
\(627\) | 1.92847e15 | 0.794768 | ||||||||
\(628\) | −7.47187e14 | −0.305247 | ||||||||
\(629\) | −5.03436e13 | −0.0203876 | ||||||||
\(630\) | −1.34422e15 | −0.539630 | ||||||||
\(631\) | 2.95354e15 | 1.17539 | 0.587693 | − | 0.809084i | \(-0.300036\pi\) | ||||
0.587693 | + | 0.809084i | \(0.300036\pi\) | |||||||
\(632\) | −6.44338e14 | −0.254197 | ||||||||
\(633\) | 1.27827e15 | 0.499922 | ||||||||
\(634\) | −5.88875e14 | −0.228314 | ||||||||
\(635\) | 1.22829e15 | 0.472112 | ||||||||
\(636\) | 5.93614e14 | 0.226199 | ||||||||
\(637\) | 1.18165e15 | 0.446398 | ||||||||
\(638\) | 1.88691e15 | 0.706706 | ||||||||
\(639\) | −1.62510e15 | −0.603427 | ||||||||
\(640\) | 1.07374e14 | 0.0395285 | ||||||||
\(641\) | −1.24519e15 | −0.454483 | −0.227241 | − | 0.973838i | \(-0.572971\pi\) | ||||
−0.227241 | + | 0.973838i | \(0.572971\pi\) | |||||||
\(642\) | −5.43767e14 | −0.196775 | ||||||||
\(643\) | 2.82493e14 | 0.101356 | 0.0506778 | − | 0.998715i | \(-0.483862\pi\) | ||||
0.0506778 | + | 0.998715i | \(0.483862\pi\) | |||||||
\(644\) | −3.50210e15 | −1.24582 | ||||||||
\(645\) | 1.27860e14 | 0.0450979 | ||||||||
\(646\) | 5.28175e14 | 0.184714 | ||||||||
\(647\) | −3.45042e15 | −1.19646 | −0.598230 | − | 0.801324i | \(-0.704129\pi\) | ||||
−0.598230 | + | 0.801324i | \(0.704129\pi\) | |||||||
\(648\) | 6.91691e14 | 0.237821 | ||||||||
\(649\) | 2.89924e15 | 0.988413 | ||||||||
\(650\) | 6.90500e13 | 0.0233421 | ||||||||
\(651\) | 3.59446e14 | 0.120487 | ||||||||
\(652\) | −2.17263e14 | −0.0722143 | ||||||||
\(653\) | 3.55303e15 | 1.17105 | 0.585527 | − | 0.810653i | \(-0.300888\pi\) | ||||
0.585527 | + | 0.810653i | \(0.300888\pi\) | |||||||
\(654\) | 3.32645e14 | 0.108718 | ||||||||
\(655\) | −8.22421e14 | −0.266543 | ||||||||
\(656\) | 1.32127e14 | 0.0424640 | ||||||||
\(657\) | −6.70874e14 | −0.213812 | ||||||||
\(658\) | −4.30010e15 | −1.35905 | ||||||||
\(659\) | 1.76602e14 | 0.0553511 | 0.0276756 | − | 0.999617i | \(-0.491189\pi\) | ||||
0.0276756 | + | 0.999617i | \(0.491189\pi\) | |||||||
\(660\) | −3.47979e14 | −0.108159 | ||||||||
\(661\) | 3.46137e15 | 1.06694 | 0.533470 | − | 0.845819i | \(-0.320888\pi\) | ||||
0.533470 | + | 0.845819i | \(0.320888\pi\) | |||||||
\(662\) | 2.15881e15 | 0.659927 | ||||||||
\(663\) | 2.91479e13 | 0.00883654 | ||||||||
\(664\) | −4.44960e14 | −0.133782 | ||||||||
\(665\) | −4.74315e15 | −1.41432 | ||||||||
\(666\) | −2.71855e14 | −0.0803949 | ||||||||
\(667\) | −3.07111e15 | −0.900748 | ||||||||
\(668\) | −2.42292e14 | −0.0704804 | ||||||||
\(669\) | −2.92851e14 | −0.0844895 | ||||||||
\(670\) | −1.63819e15 | −0.468762 | ||||||||
\(671\) | −7.39693e15 | −2.09932 | ||||||||
\(672\) | −4.07035e14 | −0.114578 | ||||||||
\(673\) | 6.92295e15 | 1.93290 | 0.966448 | − | 0.256864i | \(-0.0826893\pi\) | ||||
0.966448 | + | 0.256864i | \(0.0826893\pi\) | |||||||
\(674\) | 3.45272e15 | 0.956162 | ||||||||
\(675\) | 4.62581e14 | 0.127062 | ||||||||
\(676\) | −1.78518e15 | −0.486379 | ||||||||
\(677\) | −3.89173e15 | −1.05173 | −0.525865 | − | 0.850568i | \(-0.676258\pi\) | ||||
−0.525865 | + | 0.850568i | \(0.676258\pi\) | |||||||
\(678\) | −9.92523e14 | −0.266058 | ||||||||
\(679\) | −9.32695e15 | −2.48002 | ||||||||
\(680\) | −9.53056e13 | −0.0251373 | ||||||||
\(681\) | 2.22248e15 | 0.581472 | ||||||||
\(682\) | −7.27496e14 | −0.188806 | ||||||||
\(683\) | 4.79007e15 | 1.23318 | 0.616592 | − | 0.787283i | \(-0.288513\pi\) | ||||
0.616592 | + | 0.787283i | \(0.288513\pi\) | |||||||
\(684\) | 2.85214e15 | 0.728387 | ||||||||
\(685\) | 1.62663e15 | 0.412088 | ||||||||
\(686\) | 9.23099e15 | 2.31988 | ||||||||
\(687\) | −8.53677e14 | −0.212829 | ||||||||
\(688\) | −3.02698e14 | −0.0748641 | ||||||||
\(689\) | −9.03740e14 | −0.221737 | ||||||||
\(690\) | 5.66364e14 | 0.137856 | ||||||||
\(691\) | 1.60990e15 | 0.388749 | 0.194374 | − | 0.980927i | \(-0.437732\pi\) | ||||
0.194374 | + | 0.980927i | \(0.437732\pi\) | |||||||
\(692\) | −7.54670e14 | −0.180790 | ||||||||
\(693\) | −1.03133e16 | −2.45112 | ||||||||
\(694\) | −4.15220e14 | −0.0979043 | ||||||||
\(695\) | 2.13336e15 | 0.499054 | ||||||||
\(696\) | −3.56943e14 | −0.0828415 | ||||||||
\(697\) | −1.17276e14 | −0.0270041 | ||||||||
\(698\) | −2.48435e15 | −0.567554 | ||||||||
\(699\) | −2.02863e15 | −0.459810 | ||||||||
\(700\) | 8.55869e14 | 0.192472 | ||||||||
\(701\) | −2.46356e15 | −0.549686 | −0.274843 | − | 0.961489i | \(-0.588626\pi\) | ||||
−0.274843 | + | 0.961489i | \(0.588626\pi\) | |||||||
\(702\) | 3.34928e14 | 0.0741477 | ||||||||
\(703\) | −9.59257e14 | −0.210708 | ||||||||
\(704\) | 8.23812e14 | 0.179547 | ||||||||
\(705\) | 6.95417e14 | 0.150385 | ||||||||
\(706\) | −1.34730e15 | −0.289093 | ||||||||
\(707\) | 1.39948e16 | 2.97962 | ||||||||
\(708\) | −5.48442e14 | −0.115864 | ||||||||
\(709\) | 6.21323e15 | 1.30246 | 0.651228 | − | 0.758882i | \(-0.274254\pi\) | ||||
0.651228 | + | 0.758882i | \(0.274254\pi\) | |||||||
\(710\) | 1.03471e15 | 0.215227 | ||||||||
\(711\) | 3.08834e15 | 0.637445 | ||||||||
\(712\) | 7.37470e14 | 0.151044 | ||||||||
\(713\) | 1.18406e15 | 0.240647 | ||||||||
\(714\) | 3.61285e14 | 0.0728635 | ||||||||
\(715\) | 5.29776e14 | 0.106025 | ||||||||
\(716\) | 1.38592e14 | 0.0275244 | ||||||||
\(717\) | −3.15905e15 | −0.622588 | ||||||||
\(718\) | 5.91883e15 | 1.15758 | ||||||||
\(719\) | 7.12825e15 | 1.38348 | 0.691742 | − | 0.722145i | \(-0.256844\pi\) | ||||
0.691742 | + | 0.722145i | \(0.256844\pi\) | |||||||
\(720\) | −5.14649e14 | −0.0991248 | ||||||||
\(721\) | −6.58914e15 | −1.25946 | ||||||||
\(722\) | 6.33627e15 | 1.20193 | ||||||||
\(723\) | −2.92877e15 | −0.551346 | ||||||||
\(724\) | −1.39142e15 | −0.259953 | ||||||||
\(725\) | 7.50541e14 | 0.139160 | ||||||||
\(726\) | −1.37578e15 | −0.253162 | ||||||||
\(727\) | 5.59273e15 | 1.02137 | 0.510686 | − | 0.859767i | \(-0.329391\pi\) | ||||
0.510686 | + | 0.859767i | \(0.329391\pi\) | |||||||
\(728\) | 6.19685e14 | 0.112318 | ||||||||
\(729\) | −2.12599e15 | −0.382437 | ||||||||
\(730\) | 4.27149e14 | 0.0762612 | ||||||||
\(731\) | 2.68676e14 | 0.0476084 | ||||||||
\(732\) | 1.39926e15 | 0.246086 | ||||||||
\(733\) | −2.75558e15 | −0.480995 | −0.240498 | − | 0.970650i | \(-0.577311\pi\) | ||||
−0.240498 | + | 0.970650i | \(0.577311\pi\) | |||||||
\(734\) | −5.40669e15 | −0.936705 | ||||||||
\(735\) | −2.36864e15 | −0.407304 | ||||||||
\(736\) | −1.34082e15 | −0.228846 | ||||||||
\(737\) | −1.25688e16 | −2.12922 | ||||||||
\(738\) | −6.33291e14 | −0.106486 | ||||||||
\(739\) | 1.99004e15 | 0.332138 | 0.166069 | − | 0.986114i | \(-0.446893\pi\) | ||||
0.166069 | + | 0.986114i | \(0.446893\pi\) | |||||||
\(740\) | 1.73091e14 | 0.0286749 | ||||||||
\(741\) | 5.55389e14 | 0.0913266 | ||||||||
\(742\) | −1.12018e16 | −1.82838 | ||||||||
\(743\) | −7.01045e15 | −1.13581 | −0.567907 | − | 0.823093i | \(-0.692247\pi\) | ||||
−0.567907 | + | 0.823093i | \(0.692247\pi\) | |||||||
\(744\) | 1.37618e14 | 0.0221322 | ||||||||
\(745\) | 3.17394e15 | 0.506687 | ||||||||
\(746\) | −5.98997e15 | −0.949208 | ||||||||
\(747\) | 2.13271e15 | 0.335481 | ||||||||
\(748\) | −7.31218e14 | −0.114179 | ||||||||
\(749\) | 1.02611e16 | 1.59054 | ||||||||
\(750\) | −1.38412e14 | −0.0212979 | ||||||||
\(751\) | −9.37589e15 | −1.43216 | −0.716082 | − | 0.698016i | \(-0.754066\pi\) | ||||
−0.716082 | + | 0.698016i | \(0.754066\pi\) | |||||||
\(752\) | −1.64634e15 | −0.249645 | ||||||||
\(753\) | 1.74877e15 | 0.263245 | ||||||||
\(754\) | 5.43423e14 | 0.0812074 | ||||||||
\(755\) | 1.66887e15 | 0.247580 | ||||||||
\(756\) | 4.15141e15 | 0.611400 | ||||||||
\(757\) | 1.88289e15 | 0.275294 | 0.137647 | − | 0.990481i | \(-0.456046\pi\) | ||||
0.137647 | + | 0.990481i | \(0.456046\pi\) | |||||||
\(758\) | −2.39236e15 | −0.347253 | ||||||||
\(759\) | 4.34534e15 | 0.626173 | ||||||||
\(760\) | −1.81597e15 | −0.259797 | ||||||||
\(761\) | 6.71695e15 | 0.954018 | 0.477009 | − | 0.878898i | \(-0.341721\pi\) | ||||
0.477009 | + | 0.878898i | \(0.341721\pi\) | |||||||
\(762\) | −1.78269e15 | −0.251375 | ||||||||
\(763\) | −6.27717e15 | −0.878777 | ||||||||
\(764\) | 1.13304e15 | 0.157482 | ||||||||
\(765\) | 4.56804e14 | 0.0630365 | ||||||||
\(766\) | −4.97667e15 | −0.681837 | ||||||||
\(767\) | 8.34968e14 | 0.113578 | ||||||||
\(768\) | −1.55838e14 | −0.0210469 | ||||||||
\(769\) | −5.72271e15 | −0.767374 | −0.383687 | − | 0.923463i | \(-0.625346\pi\) | ||||
−0.383687 | + | 0.923463i | \(0.625346\pi\) | |||||||
\(770\) | 6.56653e15 | 0.874252 | ||||||||
\(771\) | −1.68890e15 | −0.223257 | ||||||||
\(772\) | 6.31833e15 | 0.829292 | ||||||||
\(773\) | −3.24936e15 | −0.423458 | −0.211729 | − | 0.977328i | \(-0.567909\pi\) | ||||
−0.211729 | + | 0.977328i | \(0.567909\pi\) | |||||||
\(774\) | 1.45085e15 | 0.187735 | ||||||||
\(775\) | −2.89369e14 | −0.0371786 | ||||||||
\(776\) | −3.57094e15 | −0.455557 | ||||||||
\(777\) | −6.56157e14 | −0.0831174 | ||||||||
\(778\) | −2.80463e15 | −0.352767 | ||||||||
\(779\) | −2.23461e15 | −0.279091 | ||||||||
\(780\) | −1.00216e14 | −0.0124285 | ||||||||
\(781\) | 7.93865e15 | 0.977611 | ||||||||
\(782\) | 1.19012e15 | 0.145530 | ||||||||
\(783\) | 3.64051e15 | 0.442051 | ||||||||
\(784\) | 5.60757e15 | 0.676140 | ||||||||
\(785\) | −2.28023e15 | −0.273021 | ||||||||
\(786\) | 1.19363e15 | 0.141920 | ||||||||
\(787\) | 1.29754e16 | 1.53201 | 0.766003 | − | 0.642838i | \(-0.222243\pi\) | ||||
0.766003 | + | 0.642838i | \(0.222243\pi\) | |||||||
\(788\) | 2.05140e15 | 0.240523 | ||||||||
\(789\) | −2.19185e14 | −0.0255204 | ||||||||
\(790\) | −1.96636e15 | −0.227361 | ||||||||
\(791\) | 1.87294e16 | 2.15057 | ||||||||
\(792\) | −3.94857e15 | −0.450247 | ||||||||
\(793\) | −2.13028e15 | −0.241232 | ||||||||
\(794\) | 1.66325e15 | 0.187045 | ||||||||
\(795\) | 1.81157e15 | 0.202318 | ||||||||
\(796\) | −7.92470e15 | −0.878944 | ||||||||
\(797\) | −1.21467e16 | −1.33795 | −0.668974 | − | 0.743286i | \(-0.733266\pi\) | ||||
−0.668974 | + | 0.743286i | \(0.733266\pi\) | |||||||
\(798\) | 6.88401e15 | 0.753053 | ||||||||
\(799\) | 1.46130e15 | 0.158757 | ||||||||
\(800\) | 3.27680e14 | 0.0353553 | ||||||||
\(801\) | −3.53473e15 | −0.378771 | ||||||||
\(802\) | −1.09041e16 | −1.16046 | ||||||||
\(803\) | 3.27724e15 | 0.346395 | ||||||||
\(804\) | 2.37760e15 | 0.249592 | ||||||||
\(805\) | −1.06876e16 | −1.11430 | ||||||||
\(806\) | −2.09515e14 | −0.0216957 | ||||||||
\(807\) | −2.02956e15 | −0.208736 | ||||||||
\(808\) | 5.35808e15 | 0.547327 | ||||||||
\(809\) | 3.06008e15 | 0.310468 | 0.155234 | − | 0.987878i | \(-0.450387\pi\) | ||||
0.155234 | + | 0.987878i | \(0.450387\pi\) | |||||||
\(810\) | 2.11087e15 | 0.212713 | ||||||||
\(811\) | 1.63765e15 | 0.163910 | 0.0819552 | − | 0.996636i | \(-0.473884\pi\) | ||||
0.0819552 | + | 0.996636i | \(0.473884\pi\) | |||||||
\(812\) | 6.73568e15 | 0.669612 | ||||||||
\(813\) | −3.21419e15 | −0.317376 | ||||||||
\(814\) | 1.32802e15 | 0.130248 | ||||||||
\(815\) | −6.63033e14 | −0.0645904 | ||||||||
\(816\) | 1.38323e14 | 0.0133843 | ||||||||
\(817\) | 5.11941e15 | 0.492038 | ||||||||
\(818\) | 1.07083e16 | 1.02230 | ||||||||
\(819\) | −2.97018e15 | −0.281657 | ||||||||
\(820\) | 4.03220e14 | 0.0379810 | ||||||||
\(821\) | 1.07044e15 | 0.100156 | 0.0500778 | − | 0.998745i | \(-0.484053\pi\) | ||||
0.0500778 | + | 0.998745i | \(0.484053\pi\) | |||||||
\(822\) | −2.36082e15 | −0.219416 | ||||||||
\(823\) | −3.24575e15 | −0.299651 | −0.149825 | − | 0.988712i | \(-0.547871\pi\) | ||||
−0.149825 | + | 0.988712i | \(0.547871\pi\) | |||||||
\(824\) | −2.52273e15 | −0.231351 | ||||||||
\(825\) | −1.06195e15 | −0.0967400 | ||||||||
\(826\) | 1.03494e16 | 0.936533 | ||||||||
\(827\) | −2.05440e16 | −1.84674 | −0.923369 | − | 0.383913i | \(-0.874576\pi\) | ||||
−0.923369 | + | 0.383913i | \(0.874576\pi\) | |||||||
\(828\) | 6.42662e15 | 0.573873 | ||||||||
\(829\) | 5.85872e15 | 0.519700 | 0.259850 | − | 0.965649i | \(-0.416327\pi\) | ||||
0.259850 | + | 0.965649i | \(0.416327\pi\) | |||||||
\(830\) | −1.35791e15 | −0.119658 | ||||||||
\(831\) | −1.31144e15 | −0.114800 | ||||||||
\(832\) | 2.37254e14 | 0.0206317 | ||||||||
\(833\) | −4.97730e15 | −0.429978 | ||||||||
\(834\) | −3.09627e15 | −0.265721 | ||||||||
\(835\) | −7.39417e14 | −0.0630396 | ||||||||
\(836\) | −1.39328e16 | −1.18006 | ||||||||
\(837\) | −1.40359e15 | −0.118100 | ||||||||
\(838\) | 4.41057e15 | 0.368683 | ||||||||
\(839\) | −2.25383e16 | −1.87168 | −0.935838 | − | 0.352430i | \(-0.885355\pi\) | ||||
−0.935838 | + | 0.352430i | \(0.885355\pi\) | |||||||
\(840\) | −1.24217e15 | −0.102482 | ||||||||
\(841\) | −6.29376e15 | −0.515861 | ||||||||
\(842\) | 1.39345e16 | 1.13468 | ||||||||
\(843\) | 3.21043e14 | 0.0259724 | ||||||||
\(844\) | −9.23524e15 | −0.742275 | ||||||||
\(845\) | −5.44793e15 | −0.435030 | ||||||||
\(846\) | 7.89100e15 | 0.626030 | ||||||||
\(847\) | 2.59617e16 | 2.04632 | ||||||||
\(848\) | −4.28874e15 | −0.335856 | ||||||||
\(849\) | 5.10823e15 | 0.397446 | ||||||||
\(850\) | −2.90850e14 | −0.0224835 | ||||||||
\(851\) | −2.16146e15 | −0.166010 | ||||||||
\(852\) | −1.50173e15 | −0.114597 | ||||||||
\(853\) | 1.84471e16 | 1.39865 | 0.699326 | − | 0.714803i | \(-0.253484\pi\) | ||||
0.699326 | + | 0.714803i | \(0.253484\pi\) | |||||||
\(854\) | −2.64047e16 | −1.98913 | ||||||||
\(855\) | 8.70403e15 | 0.651489 | ||||||||
\(856\) | 3.92860e15 | 0.292168 | ||||||||
\(857\) | −1.53957e15 | −0.113764 | −0.0568820 | − | 0.998381i | \(-0.518116\pi\) | ||||
−0.0568820 | + | 0.998381i | \(0.518116\pi\) | |||||||
\(858\) | −7.68894e14 | −0.0564529 | ||||||||
\(859\) | −2.14973e16 | −1.56827 | −0.784136 | − | 0.620589i | \(-0.786893\pi\) | ||||
−0.784136 | + | 0.620589i | \(0.786893\pi\) | |||||||
\(860\) | −9.23762e14 | −0.0669605 | ||||||||
\(861\) | −1.52853e15 | −0.110092 | ||||||||
\(862\) | 4.83792e15 | 0.346233 | ||||||||
\(863\) | −1.16923e16 | −0.831462 | −0.415731 | − | 0.909488i | \(-0.636474\pi\) | ||||
−0.415731 | + | 0.909488i | \(0.636474\pi\) | |||||||
\(864\) | 1.58942e15 | 0.112308 | ||||||||
\(865\) | −2.30307e15 | −0.161703 | ||||||||
\(866\) | −1.20014e15 | −0.0837306 | ||||||||
\(867\) | 4.73472e15 | 0.328239 | ||||||||
\(868\) | −2.59693e15 | −0.178896 | ||||||||
\(869\) | −1.50866e16 | −1.03272 | ||||||||
\(870\) | −1.08930e15 | −0.0740957 | ||||||||
\(871\) | −3.61974e15 | −0.244668 | ||||||||
\(872\) | −2.40329e15 | −0.161423 | ||||||||
\(873\) | 1.71156e16 | 1.14239 | ||||||||
\(874\) | 2.26767e16 | 1.50407 | ||||||||
\(875\) | 2.61191e15 | 0.172152 | ||||||||
\(876\) | −6.19946e14 | −0.0406052 | ||||||||
\(877\) | 1.13573e16 | 0.739225 | 0.369613 | − | 0.929186i | \(-0.379490\pi\) | ||||
0.369613 | + | 0.929186i | \(0.379490\pi\) | |||||||
\(878\) | −5.18188e15 | −0.335172 | ||||||||
\(879\) | −2.31520e15 | −0.148816 | ||||||||
\(880\) | 2.51407e15 | 0.160592 | ||||||||
\(881\) | 1.12847e16 | 0.716346 | 0.358173 | − | 0.933655i | \(-0.383400\pi\) | ||||
0.358173 | + | 0.933655i | \(0.383400\pi\) | |||||||
\(882\) | −2.68773e16 | −1.69554 | ||||||||
\(883\) | −5.36286e15 | −0.336211 | −0.168106 | − | 0.985769i | \(-0.553765\pi\) | ||||
−0.168106 | + | 0.985769i | \(0.553765\pi\) | |||||||
\(884\) | −2.10587e14 | −0.0131203 | ||||||||
\(885\) | −1.67371e15 | −0.103632 | ||||||||
\(886\) | −4.13894e15 | −0.254685 | ||||||||
\(887\) | 8.12685e15 | 0.496984 | 0.248492 | − | 0.968634i | \(-0.420065\pi\) | ||||
0.248492 | + | 0.968634i | \(0.420065\pi\) | |||||||
\(888\) | −2.51218e14 | −0.0152679 | ||||||||
\(889\) | 3.36402e16 | 2.03188 | ||||||||
\(890\) | 2.25058e15 | 0.135098 | ||||||||
\(891\) | 1.61953e16 | 0.966190 | ||||||||
\(892\) | 2.11579e15 | 0.125448 | ||||||||
\(893\) | 2.78439e16 | 1.64077 | ||||||||
\(894\) | −4.60653e15 | −0.269785 | ||||||||
\(895\) | 4.22950e14 | 0.0246185 | ||||||||
\(896\) | 2.94075e15 | 0.170123 | ||||||||
\(897\) | 1.25144e15 | 0.0719534 | ||||||||
\(898\) | 4.16815e14 | 0.0238190 | ||||||||
\(899\) | −2.27733e15 | −0.129345 | ||||||||
\(900\) | −1.57058e15 | −0.0886599 | ||||||||
\(901\) | 3.80670e15 | 0.213581 | ||||||||
\(902\) | 3.09364e15 | 0.172518 | ||||||||
\(903\) | 3.50181e15 | 0.194093 | ||||||||
\(904\) | 7.17077e15 | 0.395039 | ||||||||
\(905\) | −4.24627e15 | −0.232509 | ||||||||
\(906\) | −2.42213e15 | −0.131823 | ||||||||
\(907\) | −1.18191e16 | −0.639361 | −0.319680 | − | 0.947525i | \(-0.603576\pi\) | ||||
−0.319680 | + | 0.947525i | \(0.603576\pi\) | |||||||
\(908\) | −1.60570e16 | −0.863359 | ||||||||
\(909\) | −2.56815e16 | −1.37252 | ||||||||
\(910\) | 1.89113e15 | 0.100460 | ||||||||
\(911\) | 1.50443e16 | 0.794366 | 0.397183 | − | 0.917739i | \(-0.369988\pi\) | ||||
0.397183 | + | 0.917739i | \(0.369988\pi\) | |||||||
\(912\) | 2.63563e15 | 0.138329 | ||||||||
\(913\) | −1.04183e16 | −0.543513 | ||||||||
\(914\) | 1.10632e16 | 0.573688 | ||||||||
\(915\) | 4.27020e15 | 0.220106 | ||||||||
\(916\) | 6.16764e15 | 0.316005 | ||||||||
\(917\) | −2.25243e16 | −1.14715 | ||||||||
\(918\) | −1.41077e15 | −0.0714203 | ||||||||
\(919\) | −3.98208e15 | −0.200389 | −0.100195 | − | 0.994968i | \(-0.531947\pi\) | ||||
−0.100195 | + | 0.994968i | \(0.531947\pi\) | |||||||
\(920\) | −4.09186e15 | −0.204686 | ||||||||
\(921\) | 7.95585e15 | 0.395602 | ||||||||
\(922\) | 9.50225e15 | 0.469685 | ||||||||
\(923\) | 2.28629e15 | 0.112337 | ||||||||
\(924\) | −9.53038e15 | −0.465494 | ||||||||
\(925\) | 5.28233e14 | 0.0256476 | ||||||||
\(926\) | 1.45682e16 | 0.703148 | ||||||||
\(927\) | 1.20916e16 | 0.580154 | ||||||||
\(928\) | 2.57884e15 | 0.123001 | ||||||||
\(929\) | 4.06546e16 | 1.92763 | 0.963814 | − | 0.266575i | \(-0.0858919\pi\) | ||||
0.963814 | + | 0.266575i | \(0.0858919\pi\) | |||||||
\(930\) | 4.19978e14 | 0.0197957 | ||||||||
\(931\) | −9.48384e16 | −4.44387 | ||||||||
\(932\) | 1.46564e16 | 0.682718 | ||||||||
\(933\) | −9.81282e15 | −0.454407 | ||||||||
\(934\) | −1.17280e16 | −0.539902 | ||||||||
\(935\) | −2.23150e15 | −0.102125 | ||||||||
\(936\) | −1.13717e15 | −0.0517378 | ||||||||
\(937\) | −1.18458e15 | −0.0535792 | −0.0267896 | − | 0.999641i | \(-0.508528\pi\) | ||||
−0.0267896 | + | 0.999641i | \(0.508528\pi\) | |||||||
\(938\) | −4.48664e16 | −2.01746 | ||||||||
\(939\) | 4.58966e15 | 0.205173 | ||||||||
\(940\) | −5.02424e15 | −0.223289 | ||||||||
\(941\) | −1.02223e16 | −0.451652 | −0.225826 | − | 0.974168i | \(-0.572508\pi\) | ||||
−0.225826 | + | 0.974168i | \(0.572508\pi\) | |||||||
\(942\) | 3.30944e15 | 0.145370 | ||||||||
\(943\) | −5.03516e15 | −0.219887 | ||||||||
\(944\) | 3.96238e15 | 0.172032 | ||||||||
\(945\) | 1.26691e16 | 0.546853 | ||||||||
\(946\) | −7.08743e15 | −0.304150 | ||||||||
\(947\) | −1.68932e16 | −0.720755 | −0.360378 | − | 0.932807i | \(-0.617352\pi\) | ||||
−0.360378 | + | 0.932807i | \(0.617352\pi\) | |||||||
\(948\) | 2.85390e15 | 0.121058 | ||||||||
\(949\) | 9.43829e14 | 0.0398042 | ||||||||
\(950\) | −5.54191e15 | −0.232370 | ||||||||
\(951\) | 2.60824e15 | 0.108731 | ||||||||
\(952\) | −2.61021e15 | −0.108186 | ||||||||
\(953\) | −3.76078e16 | −1.54977 | −0.774884 | − | 0.632103i | \(-0.782192\pi\) | ||||
−0.774884 | + | 0.632103i | \(0.782192\pi\) | |||||||
\(954\) | 2.05561e16 | 0.842219 | ||||||||
\(955\) | 3.45775e15 | 0.140856 | ||||||||
\(956\) | 2.28235e16 | 0.924407 | ||||||||
\(957\) | −8.35751e15 | −0.336559 | ||||||||
\(958\) | 1.85081e16 | 0.741055 | ||||||||
\(959\) | 4.45498e16 | 1.77355 | ||||||||
\(960\) | −4.75581e14 | −0.0188249 | ||||||||
\(961\) | −2.45305e16 | −0.965444 | ||||||||
\(962\) | 3.82463e14 | 0.0149667 | ||||||||
\(963\) | −1.88300e16 | −0.732664 | ||||||||
\(964\) | 2.11598e16 | 0.818629 | ||||||||
\(965\) | 1.92820e16 | 0.741741 | ||||||||
\(966\) | 1.55115e16 | 0.593306 | ||||||||
\(967\) | −3.52262e16 | −1.33974 | −0.669869 | − | 0.742479i | \(-0.733650\pi\) | ||||
−0.669869 | + | 0.742479i | \(0.733650\pi\) | |||||||
\(968\) | 9.93976e15 | 0.375890 | ||||||||
\(969\) | −2.33939e15 | −0.0879674 | ||||||||
\(970\) | −1.08976e16 | −0.407462 | ||||||||
\(971\) | 3.56726e16 | 1.32626 | 0.663131 | − | 0.748504i | \(-0.269227\pi\) | ||||
0.663131 | + | 0.748504i | \(0.269227\pi\) | |||||||
\(972\) | −1.16562e16 | −0.430915 | ||||||||
\(973\) | 5.84281e16 | 2.14784 | ||||||||
\(974\) | −1.52065e16 | −0.555847 | ||||||||
\(975\) | −3.05836e14 | −0.0111164 | ||||||||
\(976\) | −1.01094e16 | −0.365384 | ||||||||
\(977\) | −4.79343e16 | −1.72277 | −0.861383 | − | 0.507957i | \(-0.830401\pi\) | ||||
−0.861383 | + | 0.507957i | \(0.830401\pi\) | |||||||
\(978\) | 9.62298e14 | 0.0343911 | ||||||||
\(979\) | 1.72672e16 | 0.613646 | ||||||||
\(980\) | 1.71130e16 | 0.604758 | ||||||||
\(981\) | 1.15191e16 | 0.404798 | ||||||||
\(982\) | 2.43085e16 | 0.849464 | ||||||||
\(983\) | 2.05131e16 | 0.712833 | 0.356416 | − | 0.934327i | \(-0.383998\pi\) | ||||
0.356416 | + | 0.934327i | \(0.383998\pi\) | |||||||
\(984\) | −5.85217e14 | −0.0202229 | ||||||||
\(985\) | 6.26039e15 | 0.215131 | ||||||||
\(986\) | −2.28898e15 | −0.0782203 | ||||||||
\(987\) | 1.90460e16 | 0.647230 | ||||||||
\(988\) | −4.01257e15 | −0.135600 | ||||||||
\(989\) | 1.15354e16 | 0.387661 | ||||||||
\(990\) | −1.20501e16 | −0.402713 | ||||||||
\(991\) | −2.11314e16 | −0.702301 | −0.351150 | − | 0.936319i | \(-0.614209\pi\) | ||||
−0.351150 | + | 0.936319i | \(0.614209\pi\) | |||||||
\(992\) | −9.94265e14 | −0.0328615 | ||||||||
\(993\) | −9.56179e15 | −0.314281 | ||||||||
\(994\) | 2.83384e16 | 0.926298 | ||||||||
\(995\) | −2.41843e16 | −0.786151 | ||||||||
\(996\) | 1.97081e15 | 0.0637116 | ||||||||
\(997\) | 4.57566e16 | 1.47106 | 0.735531 | − | 0.677491i | \(-0.236933\pi\) | ||||
0.735531 | + | 0.677491i | \(0.236933\pi\) | |||||||
\(998\) | −1.57133e16 | −0.502398 | ||||||||
\(999\) | 2.56220e15 | 0.0814711 |
(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 | 10.12.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 90.12.a.l.1.2 | 2 | |||
4.3 | odd | 2 | 80.12.a.g.1.2 | 2 | |||
5.2 | odd | 4 | 50.12.b.f.49.4 | 4 | |||
5.3 | odd | 4 | 50.12.b.f.49.1 | 4 | |||
5.4 | even | 2 | 50.12.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.12.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.12.a.f.1.2 | 2 | 5.4 | even | 2 | |||
50.12.b.f.49.1 | 4 | 5.3 | odd | 4 | |||
50.12.b.f.49.4 | 4 | 5.2 | odd | 4 | |||
80.12.a.g.1.2 | 2 | 4.3 | odd | 2 | |||
90.12.a.l.1.2 | 2 | 3.2 | odd | 2 |