Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + 3375594921 x^{11} + 115310342333 x^{10} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(6.43791\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.43791 | −0.657425 | −0.328712 | − | 0.944430i | \(-0.606615\pi\) | ||||
−0.328712 | + | 0.944430i | \(0.606615\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −72.6775 | −0.567793 | ||||||||
\(5\) | −171.827 | −0.614747 | −0.307374 | − | 0.951589i | \(-0.599450\pi\) | ||||
−0.307374 | + | 0.951589i | \(0.599450\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1529.87 | 1.68582 | 0.842909 | − | 0.538056i | \(-0.180841\pi\) | ||||
0.842909 | + | 0.538056i | \(0.180841\pi\) | |||||||
\(8\) | 1492.62 | 1.03071 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1278.03 | 0.404150 | ||||||||
\(11\) | 1638.92 | 0.371263 | 0.185632 | − | 0.982619i | \(-0.440567\pi\) | ||||
0.185632 | + | 0.982619i | \(0.440567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7315.98 | −0.923572 | −0.461786 | − | 0.886991i | \(-0.652791\pi\) | ||||
−0.461786 | + | 0.886991i | \(0.652791\pi\) | |||||||
\(14\) | −11379.0 | −1.10830 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1799.27 | −0.109818 | ||||||||
\(17\) | −33214.7 | −1.63968 | −0.819841 | − | 0.572592i | \(-0.805938\pi\) | ||||
−0.819841 | + | 0.572592i | \(0.805938\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 55570.3 | 1.85868 | 0.929342 | − | 0.369221i | \(-0.120375\pi\) | ||||
0.929342 | + | 0.369221i | \(0.120375\pi\) | |||||||
\(20\) | 12488.0 | 0.349049 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −12190.1 | −0.244078 | ||||||||
\(23\) | 51886.9 | 0.889222 | 0.444611 | − | 0.895724i | \(-0.353342\pi\) | ||||
0.444611 | + | 0.895724i | \(0.353342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −48600.5 | −0.622086 | ||||||||
\(26\) | 54415.6 | 0.607179 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −111187. | −0.957196 | ||||||||
\(29\) | −10383.5 | −0.0790591 | −0.0395296 | − | 0.999218i | \(-0.512586\pi\) | ||||
−0.0395296 | + | 0.999218i | \(0.512586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 92770.0 | 0.559296 | 0.279648 | − | 0.960103i | \(-0.409782\pi\) | ||||
0.279648 | + | 0.960103i | \(0.409782\pi\) | |||||||
\(32\) | −177673. | −0.958508 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 247048. | 1.07797 | ||||||||
\(35\) | −262873. | −1.03635 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −504232. | −1.63653 | −0.818266 | − | 0.574840i | \(-0.805064\pi\) | ||||
−0.818266 | + | 0.574840i | \(0.805064\pi\) | |||||||
\(38\) | −413327. | −1.22194 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −256473. | −0.633623 | ||||||||
\(41\) | −635489. | −1.44001 | −0.720003 | − | 0.693971i | \(-0.755860\pi\) | ||||
−0.720003 | + | 0.693971i | \(0.755860\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 101770. | 0.195200 | 0.0976002 | − | 0.995226i | \(-0.468883\pi\) | ||||
0.0976002 | + | 0.995226i | \(0.468883\pi\) | |||||||
\(44\) | −119112. | −0.210801 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −385930. | −0.584597 | ||||||||
\(47\) | 72413.1 | 0.101736 | 0.0508680 | − | 0.998705i | \(-0.483801\pi\) | ||||
0.0508680 | + | 0.998705i | \(0.483801\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.51695e6 | 1.84198 | ||||||||
\(50\) | 361486. | 0.408975 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 531707. | 0.524397 | ||||||||
\(53\) | −1.67234e6 | −1.54297 | −0.771487 | − | 0.636245i | \(-0.780487\pi\) | ||||
−0.771487 | + | 0.636245i | \(0.780487\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −281610. | −0.228233 | ||||||||
\(56\) | 2.28351e6 | 1.73758 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 77231.8 | 0.0519754 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 727353. | 0.410290 | 0.205145 | − | 0.978732i | \(-0.434233\pi\) | ||||
0.205145 | + | 0.978732i | \(0.434233\pi\) | |||||||
\(62\) | −690015. | −0.367695 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.55182e6 | 0.739965 | ||||||||
\(65\) | 1.25708e6 | 0.567763 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.81505e6 | 1.14347 | 0.571735 | − | 0.820439i | \(-0.306271\pi\) | ||||
0.571735 | + | 0.820439i | \(0.306271\pi\) | |||||||
\(68\) | 2.41396e6 | 0.930999 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.95522e6 | 0.681323 | ||||||||
\(71\) | 850222. | 0.281921 | 0.140961 | − | 0.990015i | \(-0.454981\pi\) | ||||
0.140961 | + | 0.990015i | \(0.454981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.84245e6 | 1.75778 | 0.878891 | − | 0.477023i | \(-0.158284\pi\) | ||||
0.878891 | + | 0.477023i | \(0.158284\pi\) | |||||||
\(74\) | 3.75043e6 | 1.07590 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.03871e6 | −1.05535 | ||||||||
\(77\) | 2.50732e6 | 0.625883 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.74755e6 | 0.626977 | 0.313488 | − | 0.949592i | \(-0.398502\pi\) | ||||
0.313488 | + | 0.949592i | \(0.398502\pi\) | |||||||
\(80\) | 309162. | 0.0675106 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.72671e6 | 0.946695 | ||||||||
\(83\) | −2.78632e6 | −0.534882 | −0.267441 | − | 0.963574i | \(-0.586178\pi\) | ||||
−0.267441 | + | 0.963574i | \(0.586178\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.70719e6 | 1.00799 | ||||||||
\(86\) | −756957. | −0.128330 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.44628e6 | 0.382663 | ||||||||
\(89\) | 6.16092e6 | 0.926361 | 0.463181 | − | 0.886264i | \(-0.346708\pi\) | ||||
0.463181 | + | 0.886264i | \(0.346708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.11925e7 | −1.55697 | ||||||||
\(92\) | −3.77101e6 | −0.504894 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −538602. | −0.0668838 | ||||||||
\(95\) | −9.54849e6 | −1.14262 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.67686e7 | −1.86550 | −0.932751 | − | 0.360521i | \(-0.882599\pi\) | ||||
−0.932751 | + | 0.360521i | \(0.882599\pi\) | |||||||
\(98\) | −1.12830e7 | −1.21097 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.53216e6 | 0.353216 | ||||||||
\(101\) | −7.93944e6 | −0.766770 | −0.383385 | − | 0.923589i | \(-0.625242\pi\) | ||||
−0.383385 | + | 0.923589i | \(0.625242\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.76750e7 | 1.59378 | 0.796889 | − | 0.604125i | \(-0.206477\pi\) | ||||
0.796889 | + | 0.604125i | \(0.206477\pi\) | |||||||
\(104\) | −1.09200e7 | −0.951931 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.24387e7 | 1.01439 | ||||||||
\(107\) | 9.16951e6 | 0.723607 | 0.361803 | − | 0.932254i | \(-0.382161\pi\) | ||||
0.361803 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.32228e7 | 0.977982 | 0.488991 | − | 0.872289i | \(-0.337365\pi\) | ||||
0.488991 | + | 0.872289i | \(0.337365\pi\) | |||||||
\(110\) | 2.09459e6 | 0.150046 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.75264e6 | −0.185134 | ||||||||
\(113\) | 2.66031e7 | 1.73443 | 0.867216 | − | 0.497932i | \(-0.165907\pi\) | ||||
0.867216 | + | 0.497932i | \(0.165907\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.91557e6 | −0.546647 | ||||||||
\(116\) | 754649. | 0.0448892 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.52759e6 | 0.0855894 | ||||||||
\(119\) | −5.08142e7 | −2.76421 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.68011e7 | −0.862163 | ||||||||
\(122\) | −5.40999e6 | −0.269735 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.74229e6 | −0.317564 | ||||||||
\(125\) | 2.17749e7 | 0.997173 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.04342e7 | −0.885209 | −0.442604 | − | 0.896717i | \(-0.645945\pi\) | ||||
−0.442604 | + | 0.896717i | \(0.645945\pi\) | |||||||
\(128\) | 1.11998e7 | 0.472037 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.35007e6 | −0.373261 | ||||||||
\(131\) | 4.18739e7 | 1.62740 | 0.813699 | − | 0.581286i | \(-0.197450\pi\) | ||||
0.813699 | + | 0.581286i | \(0.197450\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.50153e7 | 3.13340 | ||||||||
\(134\) | −2.09381e7 | −0.751745 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.95770e7 | −1.69003 | ||||||||
\(137\) | −5.60709e7 | −1.86301 | −0.931506 | − | 0.363725i | \(-0.881505\pi\) | ||||
−0.931506 | + | 0.363725i | \(0.881505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.90420e7 | −1.23305 | −0.616524 | − | 0.787336i | \(-0.711460\pi\) | ||||
−0.616524 | + | 0.787336i | \(0.711460\pi\) | |||||||
\(140\) | 1.91049e7 | 0.588433 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.32387e6 | −0.185342 | ||||||||
\(143\) | −1.19903e7 | −0.342888 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.78417e6 | 0.0486014 | ||||||||
\(146\) | −4.34556e7 | −1.15561 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.66463e7 | 0.929211 | ||||||||
\(149\) | −5.58520e7 | −1.38320 | −0.691602 | − | 0.722278i | \(-0.743095\pi\) | ||||
−0.691602 | + | 0.722278i | \(0.743095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.78120e7 | −1.60283 | −0.801414 | − | 0.598110i | \(-0.795919\pi\) | ||||
−0.801414 | + | 0.598110i | \(0.795919\pi\) | |||||||
\(152\) | 8.29455e7 | 1.91576 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.86493e7 | −0.411471 | ||||||||
\(155\) | −1.59404e7 | −0.343826 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.45770e7 | 0.919310 | 0.459655 | − | 0.888098i | \(-0.347973\pi\) | ||||
0.459655 | + | 0.888098i | \(0.347973\pi\) | |||||||
\(158\) | −2.04361e7 | −0.412190 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.05290e7 | 0.589240 | ||||||||
\(161\) | 7.93801e7 | 1.49907 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.62679e7 | −1.74111 | −0.870553 | − | 0.492075i | \(-0.836238\pi\) | ||||
−0.870553 | + | 0.492075i | \(0.836238\pi\) | |||||||
\(164\) | 4.61857e7 | 0.817625 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.07244e7 | 0.351645 | ||||||||
\(167\) | 3.06157e7 | 0.508671 | 0.254335 | − | 0.967116i | \(-0.418143\pi\) | ||||
0.254335 | + | 0.967116i | \(0.418143\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.22500e6 | −0.147015 | ||||||||
\(170\) | −4.24496e7 | −0.662677 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.39640e6 | −0.110833 | ||||||||
\(173\) | 1.60370e7 | 0.235484 | 0.117742 | − | 0.993044i | \(-0.462434\pi\) | ||||
0.117742 | + | 0.993044i | \(0.462434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.43523e7 | −1.04872 | ||||||||
\(176\) | −2.94884e6 | −0.0407716 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.58244e7 | −0.609013 | ||||||||
\(179\) | 2.33939e7 | 0.304872 | 0.152436 | − | 0.988313i | \(-0.451288\pi\) | ||||
0.152436 | + | 0.988313i | \(0.451288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.84290e7 | −1.23381 | −0.616904 | − | 0.787038i | \(-0.711614\pi\) | ||||
−0.616904 | + | 0.787038i | \(0.711614\pi\) | |||||||
\(182\) | 8.32487e7 | 1.02359 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.74475e7 | 0.916527 | ||||||||
\(185\) | 8.66407e7 | 1.00605 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.44361e7 | −0.608754 | ||||||||
\(188\) | −5.26280e6 | −0.0577650 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.10208e7 | 0.751187 | ||||||||
\(191\) | −3.21552e7 | −0.333914 | −0.166957 | − | 0.985964i | \(-0.553394\pi\) | ||||
−0.166957 | + | 0.985964i | \(0.553394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.59381e7 | 0.259709 | 0.129854 | − | 0.991533i | \(-0.458549\pi\) | ||||
0.129854 | + | 0.991533i | \(0.458549\pi\) | |||||||
\(194\) | 1.24723e8 | 1.22643 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.10248e8 | −1.04587 | ||||||||
\(197\) | 1.60676e7 | 0.149733 | 0.0748666 | − | 0.997194i | \(-0.476147\pi\) | ||||
0.0748666 | + | 0.997194i | \(0.476147\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.47444e7 | 0.582394 | 0.291197 | − | 0.956663i | \(-0.405947\pi\) | ||||
0.291197 | + | 0.956663i | \(0.405947\pi\) | |||||||
\(200\) | −7.25421e7 | −0.641187 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.90529e7 | 0.504094 | ||||||||
\(203\) | −1.58854e7 | −0.133279 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.09194e8 | 0.885240 | ||||||||
\(206\) | −1.31465e8 | −1.04779 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.31634e7 | 0.101425 | ||||||||
\(209\) | 9.10751e7 | 0.690061 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.05485e7 | −0.297157 | −0.148578 | − | 0.988901i | \(-0.547470\pi\) | ||||
−0.148578 | + | 0.988901i | \(0.547470\pi\) | |||||||
\(212\) | 1.21541e8 | 0.876090 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.82020e7 | −0.475717 | ||||||||
\(215\) | −1.74869e7 | −0.119999 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.41926e8 | 0.942872 | ||||||||
\(218\) | −9.83501e7 | −0.642950 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.04667e7 | 0.129589 | ||||||||
\(221\) | 2.42998e8 | 1.51436 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.68937e7 | −0.403941 | −0.201971 | − | 0.979392i | \(-0.564735\pi\) | ||||
−0.201971 | + | 0.979392i | \(0.564735\pi\) | |||||||
\(224\) | −2.71816e8 | −1.61587 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.97871e8 | −1.14026 | ||||||||
\(227\) | −1.22298e8 | −0.693949 | −0.346975 | − | 0.937875i | \(-0.612791\pi\) | ||||
−0.346975 | + | 0.937875i | \(0.612791\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.32389e8 | −1.27876 | −0.639382 | − | 0.768889i | \(-0.720810\pi\) | ||||
−0.639382 | + | 0.768889i | \(0.720810\pi\) | |||||||
\(230\) | 6.63132e7 | 0.359379 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.54987e7 | −0.0814867 | ||||||||
\(233\) | −7.69697e7 | −0.398634 | −0.199317 | − | 0.979935i | \(-0.563872\pi\) | ||||
−0.199317 | + | 0.979935i | \(0.563872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.24425e7 | −0.0625419 | ||||||||
\(236\) | 1.49264e7 | 0.0739203 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.77951e8 | 1.81726 | ||||||||
\(239\) | 1.06849e7 | 0.0506264 | 0.0253132 | − | 0.999680i | \(-0.491942\pi\) | ||||
0.0253132 | + | 0.999680i | \(0.491942\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.74132e8 | −1.72173 | −0.860866 | − | 0.508831i | \(-0.830078\pi\) | ||||
−0.860866 | + | 0.508831i | \(0.830078\pi\) | |||||||
\(242\) | 1.24965e8 | 0.566808 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.28622e7 | −0.232960 | ||||||||
\(245\) | −2.60654e8 | −1.13235 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.06551e8 | −1.71663 | ||||||||
\(248\) | 1.38470e8 | 0.576470 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.61959e8 | −0.655566 | ||||||||
\(251\) | −2.63434e8 | −1.05151 | −0.525755 | − | 0.850636i | \(-0.676217\pi\) | ||||
−0.525755 | + | 0.850636i | \(0.676217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.50383e7 | 0.330136 | ||||||||
\(254\) | 1.51988e8 | 0.581958 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.81936e8 | −1.05029 | ||||||||
\(257\) | 3.92808e8 | 1.44349 | 0.721746 | − | 0.692158i | \(-0.243340\pi\) | ||||
0.721746 | + | 0.692158i | \(0.243340\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.71409e8 | −2.75890 | ||||||||
\(260\) | −9.13616e7 | −0.322372 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.11454e8 | −1.06989 | ||||||||
\(263\) | 2.41410e8 | 0.818297 | 0.409148 | − | 0.912468i | \(-0.365826\pi\) | ||||
0.409148 | + | 0.912468i | \(0.365826\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.87353e8 | 0.948539 | ||||||||
\(266\) | −6.32336e8 | −2.05998 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.04591e8 | −0.649254 | ||||||||
\(269\) | −2.35755e8 | −0.738463 | −0.369231 | − | 0.929337i | \(-0.620379\pi\) | ||||
−0.369231 | + | 0.929337i | \(0.620379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.49957e8 | −0.457692 | −0.228846 | − | 0.973463i | \(-0.573495\pi\) | ||||
−0.228846 | + | 0.973463i | \(0.573495\pi\) | |||||||
\(272\) | 5.97621e7 | 0.180067 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.17051e8 | 1.22479 | ||||||||
\(275\) | −7.96521e7 | −0.230958 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.52984e7 | −0.269406 | −0.134703 | − | 0.990886i | \(-0.543008\pi\) | ||||
−0.134703 | + | 0.990886i | \(0.543008\pi\) | |||||||
\(278\) | 2.90391e8 | 0.810637 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.92369e8 | −1.06817 | ||||||||
\(281\) | 7.30263e7 | 0.196339 | 0.0981696 | − | 0.995170i | \(-0.468701\pi\) | ||||
0.0981696 | + | 0.995170i | \(0.468701\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.79740e8 | 0.471404 | 0.235702 | − | 0.971825i | \(-0.424261\pi\) | ||||
0.235702 | + | 0.971825i | \(0.424261\pi\) | |||||||
\(284\) | −6.17920e7 | −0.160073 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.91825e7 | 0.225423 | ||||||||
\(287\) | −9.72214e8 | −2.42759 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.92880e8 | 1.68856 | ||||||||
\(290\) | −1.32705e7 | −0.0319517 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.24614e8 | −0.998056 | ||||||||
\(293\) | −8.12673e8 | −1.88747 | −0.943733 | − | 0.330709i | \(-0.892712\pi\) | ||||
−0.943733 | + | 0.330709i | \(0.892712\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.52897e7 | 0.0800333 | ||||||||
\(296\) | −7.52628e8 | −1.68678 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.15422e8 | 0.909353 | ||||||||
\(299\) | −3.79603e8 | −0.821261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.55695e8 | 0.329073 | ||||||||
\(302\) | 5.04379e8 | 1.05374 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.99858e7 | −0.204118 | ||||||||
\(305\) | −1.24979e8 | −0.252225 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.93647e8 | −0.381968 | −0.190984 | − | 0.981593i | \(-0.561168\pi\) | ||||
−0.190984 | + | 0.981593i | \(0.561168\pi\) | |||||||
\(308\) | −1.82226e8 | −0.355372 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.18563e8 | 0.226039 | ||||||||
\(311\) | −1.76764e8 | −0.333220 | −0.166610 | − | 0.986023i | \(-0.553282\pi\) | ||||
−0.166610 | + | 0.986023i | \(0.553282\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.36535e8 | 0.251675 | 0.125837 | − | 0.992051i | \(-0.459838\pi\) | ||||
0.125837 | + | 0.992051i | \(0.459838\pi\) | |||||||
\(314\) | −3.31560e8 | −0.604377 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.99685e8 | −0.355993 | ||||||||
\(317\) | 1.67078e8 | 0.294586 | 0.147293 | − | 0.989093i | \(-0.452944\pi\) | ||||
0.147293 | + | 0.989093i | \(0.452944\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.70177e7 | −0.0293518 | ||||||||
\(320\) | −2.66645e8 | −0.454892 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.90422e8 | −0.985524 | ||||||||
\(323\) | −1.84575e9 | −3.04765 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.55560e8 | 0.574541 | ||||||||
\(326\) | 7.16032e8 | 1.14465 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.48544e8 | −1.48422 | ||||||||
\(329\) | 1.10783e8 | 0.171508 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.82887e8 | 0.580327 | 0.290163 | − | 0.956977i | \(-0.406290\pi\) | ||||
0.290163 | + | 0.956977i | \(0.406290\pi\) | |||||||
\(332\) | 2.02503e8 | 0.303702 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.27717e8 | −0.334413 | ||||||||
\(335\) | −4.83702e8 | −0.702944 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.71340e8 | 1.09785 | 0.548923 | − | 0.835873i | \(-0.315038\pi\) | ||||
0.548923 | + | 0.835873i | \(0.315038\pi\) | |||||||
\(338\) | 6.86147e7 | 0.0966515 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.14784e8 | −0.572329 | ||||||||
\(341\) | 1.52042e8 | 0.207646 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.06083e9 | 1.41943 | ||||||||
\(344\) | 1.51904e8 | 0.201194 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.19281e8 | −0.154813 | ||||||||
\(347\) | 1.31263e9 | 1.68651 | 0.843257 | − | 0.537511i | \(-0.180635\pi\) | ||||
0.843257 | + | 0.537511i | \(0.180635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.67291e8 | −0.714360 | −0.357180 | − | 0.934036i | \(-0.616262\pi\) | ||||
−0.357180 | + | 0.934036i | \(0.616262\pi\) | |||||||
\(350\) | 5.53026e8 | 0.689457 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.91191e8 | −0.355859 | ||||||||
\(353\) | −1.79304e8 | −0.216959 | −0.108480 | − | 0.994099i | \(-0.534598\pi\) | ||||
−0.108480 | + | 0.994099i | \(0.534598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.46091e8 | −0.173310 | ||||||||
\(356\) | −4.47760e8 | −0.525981 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.74002e8 | −0.200430 | ||||||||
\(359\) | 1.28294e9 | 1.46344 | 0.731722 | − | 0.681603i | \(-0.238717\pi\) | ||||
0.731722 | + | 0.681603i | \(0.238717\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.19419e9 | 2.45470 | ||||||||
\(362\) | 7.32106e8 | 0.811136 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.13441e8 | 0.884039 | ||||||||
\(365\) | −1.00389e9 | −1.08059 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.71884e7 | 0.0181512 | 0.00907560 | − | 0.999959i | \(-0.497111\pi\) | ||||
0.00907560 | + | 0.999959i | \(0.497111\pi\) | |||||||
\(368\) | −9.33583e7 | −0.0976530 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.44426e8 | −0.661404 | ||||||||
\(371\) | −2.55846e9 | −2.60118 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.02127e8 | −0.800318 | −0.400159 | − | 0.916446i | \(-0.631045\pi\) | ||||
−0.400159 | + | 0.916446i | \(0.631045\pi\) | |||||||
\(374\) | 4.04891e8 | 0.400210 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.08085e8 | 0.104860 | ||||||||
\(377\) | 7.59657e7 | 0.0730168 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.63664e6 | 0.00909261 | 0.00454630 | − | 0.999990i | \(-0.498553\pi\) | ||||
0.00454630 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(380\) | 6.93960e8 | 0.648772 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.39168e8 | 0.219523 | ||||||||
\(383\) | −8.26495e8 | −0.751700 | −0.375850 | − | 0.926681i | \(-0.622649\pi\) | ||||
−0.375850 | + | 0.926681i | \(0.622649\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.30826e8 | −0.384760 | ||||||||
\(386\) | −1.92925e8 | −0.170739 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.21870e9 | 1.05922 | ||||||||
\(389\) | −7.27469e8 | −0.626601 | −0.313300 | − | 0.949654i | \(-0.601435\pi\) | ||||
−0.313300 | + | 0.949654i | \(0.601435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.72341e9 | −1.45804 | ||||||||
\(392\) | 2.26424e9 | 1.89854 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.19509e8 | −0.0984383 | ||||||||
\(395\) | −4.72104e8 | −0.385432 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.15679e9 | −0.927871 | −0.463936 | − | 0.885869i | \(-0.653563\pi\) | ||||
−0.463936 | + | 0.885869i | \(0.653563\pi\) | |||||||
\(398\) | −4.81563e8 | −0.382880 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.74451e7 | 0.0683165 | ||||||||
\(401\) | −9.57807e7 | −0.0741776 | −0.0370888 | − | 0.999312i | \(-0.511808\pi\) | ||||
−0.0370888 | + | 0.999312i | \(0.511808\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.78703e8 | −0.516550 | ||||||||
\(404\) | 5.77019e8 | 0.435367 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.18154e8 | 0.0876211 | ||||||||
\(407\) | −8.26394e8 | −0.607585 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.12641e9 | −0.814079 | −0.407040 | − | 0.913410i | \(-0.633439\pi\) | ||||
−0.407040 | + | 0.913410i | \(0.633439\pi\) | |||||||
\(410\) | −8.12176e8 | −0.581978 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.28457e9 | −0.904936 | ||||||||
\(413\) | −3.14203e8 | −0.219475 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.78766e8 | 0.328817 | ||||||||
\(416\) | 1.29985e9 | 0.885251 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.77408e8 | −0.453663 | ||||||||
\(419\) | 2.46333e9 | 1.63596 | 0.817981 | − | 0.575245i | \(-0.195093\pi\) | ||||
0.817981 | + | 0.575245i | \(0.195093\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.02698e8 | 0.393652 | 0.196826 | − | 0.980438i | \(-0.436937\pi\) | ||||
0.196826 | + | 0.980438i | \(0.436937\pi\) | |||||||
\(422\) | 3.01596e8 | 0.195358 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.49617e9 | −1.59035 | ||||||||
\(425\) | 1.61425e9 | 1.02002 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.11275e9 | 0.691674 | ||||||||
\(428\) | −6.66417e8 | −0.410859 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.30066e8 | 0.0788902 | ||||||||
\(431\) | −1.69548e9 | −1.02005 | −0.510027 | − | 0.860159i | \(-0.670364\pi\) | ||||
−0.510027 | + | 0.860159i | \(0.670364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.31537e8 | −0.314649 | −0.157324 | − | 0.987547i | \(-0.550287\pi\) | ||||
−0.157324 | + | 0.987547i | \(0.550287\pi\) | |||||||
\(434\) | −1.05563e9 | −0.619867 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.61000e8 | −0.555291 | ||||||||
\(437\) | 2.88337e9 | 1.65278 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.39663e9 | −1.35200 | −0.675998 | − | 0.736904i | \(-0.736287\pi\) | ||||
−0.675998 | + | 0.736904i | \(0.736287\pi\) | |||||||
\(440\) | −4.20337e8 | −0.235241 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.80740e9 | −0.995580 | ||||||||
\(443\) | 2.03310e9 | 1.11108 | 0.555542 | − | 0.831489i | \(-0.312511\pi\) | ||||
0.555542 | + | 0.831489i | \(0.312511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.05861e9 | −0.569478 | ||||||||
\(446\) | 4.97550e8 | 0.265561 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.37408e9 | 1.24745 | ||||||||
\(449\) | −3.46417e9 | −1.80608 | −0.903040 | − | 0.429557i | \(-0.858670\pi\) | ||||
−0.903040 | + | 0.429557i | \(0.858670\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.04151e9 | −0.534622 | ||||||||
\(452\) | −1.93344e9 | −0.984798 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.09639e8 | 0.456219 | ||||||||
\(455\) | 1.92317e9 | 0.957146 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.70035e8 | −0.132347 | −0.0661735 | − | 0.997808i | \(-0.521079\pi\) | ||||
−0.0661735 | + | 0.997808i | \(0.521079\pi\) | |||||||
\(458\) | 1.72849e9 | 0.840692 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.47962e8 | 0.310382 | ||||||||
\(461\) | 1.94305e9 | 0.923698 | 0.461849 | − | 0.886959i | \(-0.347186\pi\) | ||||
0.461849 | + | 0.886959i | \(0.347186\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.57266e8 | −0.0736378 | −0.0368189 | − | 0.999322i | \(-0.511722\pi\) | ||||
−0.0368189 | + | 0.999322i | \(0.511722\pi\) | |||||||
\(464\) | 1.86827e7 | 0.00868215 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.72494e8 | 0.262072 | ||||||||
\(467\) | 1.00777e9 | 0.457881 | 0.228941 | − | 0.973440i | \(-0.426474\pi\) | ||||
0.228941 | + | 0.973440i | \(0.426474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.30666e9 | 1.92768 | ||||||||
\(470\) | 9.25465e7 | 0.0411166 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.06553e8 | −0.134186 | ||||||||
\(473\) | 1.66793e8 | 0.0724708 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.70074e9 | −1.15626 | ||||||||
\(476\) | 3.69305e9 | 1.56950 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.94732e7 | −0.0332830 | ||||||||
\(479\) | −1.14824e9 | −0.477372 | −0.238686 | − | 0.971097i | \(-0.576717\pi\) | ||||
−0.238686 | + | 0.971097i | \(0.576717\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.68895e9 | 1.51145 | ||||||||
\(482\) | 2.78276e9 | 1.13191 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.22106e9 | 0.489530 | ||||||||
\(485\) | 2.88130e9 | 1.14681 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.65456e9 | 1.04146 | 0.520729 | − | 0.853722i | \(-0.325660\pi\) | ||||
0.520729 | + | 0.853722i | \(0.325660\pi\) | |||||||
\(488\) | 1.08566e9 | 0.422888 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.93872e9 | 0.744438 | ||||||||
\(491\) | 2.25039e9 | 0.857971 | 0.428986 | − | 0.903311i | \(-0.358871\pi\) | ||||
0.428986 | + | 0.903311i | \(0.358871\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.44886e8 | 0.129632 | ||||||||
\(494\) | 3.02389e9 | 1.12855 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.66918e8 | −0.0614210 | ||||||||
\(497\) | 1.30073e9 | 0.475268 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.47962e8 | 0.269481 | 0.134740 | − | 0.990881i | \(-0.456980\pi\) | ||||
0.134740 | + | 0.990881i | \(0.456980\pi\) | |||||||
\(500\) | −1.58254e9 | −0.566188 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.95940e9 | 0.691288 | ||||||||
\(503\) | −5.29706e9 | −1.85587 | −0.927933 | − | 0.372746i | \(-0.878416\pi\) | ||||
−0.927933 | + | 0.372746i | \(0.878416\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.36421e9 | 0.471370 | ||||||||
\(506\) | −6.32507e8 | −0.217039 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.48511e9 | 0.502615 | ||||||||
\(509\) | −2.52094e9 | −0.847327 | −0.423663 | − | 0.905820i | \(-0.639256\pi\) | ||||
−0.423663 | + | 0.905820i | \(0.639256\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.93818e9 | 2.96330 | ||||||||
\(512\) | 6.63440e8 | 0.218452 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.92167e9 | −0.948988 | ||||||||
\(515\) | −3.03703e9 | −0.979771 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.18679e8 | 0.0377709 | ||||||||
\(518\) | 5.73767e9 | 1.81377 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.87635e9 | 0.585197 | ||||||||
\(521\) | −6.27028e9 | −1.94247 | −0.971236 | − | 0.238118i | \(-0.923470\pi\) | ||||
−0.971236 | + | 0.238118i | \(0.923470\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.45997e8 | −0.197458 | −0.0987289 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987289 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(524\) | −3.04329e9 | −0.924025 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.79559e9 | −0.537969 | ||||||||
\(527\) | −3.08133e9 | −0.917067 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.12574e8 | −0.209284 | ||||||||
\(530\) | −2.13731e9 | −0.623593 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.17870e9 | −1.77912 | ||||||||
\(533\) | 4.64922e9 | 1.32995 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.57557e9 | −0.444835 | ||||||||
\(536\) | 4.20181e9 | 1.17858 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.75353e9 | 0.485484 | ||||||||
\(539\) | 2.48616e9 | 0.683861 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.10398e9 | −0.842807 | −0.421404 | − | 0.906873i | \(-0.638462\pi\) | ||||
−0.421404 | + | 0.906873i | \(0.638462\pi\) | |||||||
\(542\) | 1.11536e9 | 0.300898 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.90135e9 | 1.57165 | ||||||||
\(545\) | −2.27204e9 | −0.601212 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.73990e9 | −0.715779 | −0.357890 | − | 0.933764i | \(-0.616504\pi\) | ||||
−0.357890 | + | 0.933764i | \(0.616504\pi\) | |||||||
\(548\) | 4.07509e9 | 1.05781 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.92445e8 | 0.151837 | ||||||||
\(551\) | −5.77016e8 | −0.146946 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.20339e9 | 1.05697 | ||||||||
\(554\) | 7.08821e8 | 0.177114 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.83747e9 | 0.700116 | ||||||||
\(557\) | −2.13952e9 | −0.524595 | −0.262297 | − | 0.964987i | \(-0.584480\pi\) | ||||
−0.262297 | + | 0.964987i | \(0.584480\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.44548e8 | −0.180282 | ||||||||
\(560\) | 4.72978e8 | 0.113811 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.43163e8 | −0.129078 | ||||||||
\(563\) | 2.85723e9 | 0.674786 | 0.337393 | − | 0.941364i | \(-0.390455\pi\) | ||||
0.337393 | + | 0.941364i | \(0.390455\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.57113e9 | −1.06624 | ||||||||
\(566\) | −1.33689e9 | −0.309912 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.26906e9 | 0.290578 | ||||||||
\(569\) | 3.13031e9 | 0.712352 | 0.356176 | − | 0.934419i | \(-0.384080\pi\) | ||||
0.356176 | + | 0.934419i | \(0.384080\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.57416e9 | −1.02822 | −0.514109 | − | 0.857725i | \(-0.671877\pi\) | ||||
−0.514109 | + | 0.857725i | \(0.671877\pi\) | |||||||
\(572\) | 8.71422e8 | 0.194690 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.23124e9 | 1.59596 | ||||||||
\(575\) | −2.52173e9 | −0.553173 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.19496e9 | −1.12581 | −0.562907 | − | 0.826520i | \(-0.690317\pi\) | ||||
−0.562907 | + | 0.826520i | \(0.690317\pi\) | |||||||
\(578\) | −5.15358e9 | −1.11010 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.29669e8 | −0.0275955 | ||||||||
\(581\) | −4.26271e9 | −0.901714 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.74082e9 | −0.572850 | ||||||||
\(584\) | 8.72056e9 | 1.81176 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.04459e9 | 1.24087 | ||||||||
\(587\) | −2.60032e9 | −0.530632 | −0.265316 | − | 0.964162i | \(-0.585476\pi\) | ||||
−0.265316 | + | 0.964162i | \(0.585476\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.15526e9 | 1.03955 | ||||||||
\(590\) | −2.62481e8 | −0.0526158 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.07248e8 | 0.179721 | ||||||||
\(593\) | −7.30947e9 | −1.43944 | −0.719721 | − | 0.694263i | \(-0.755731\pi\) | ||||
−0.719721 | + | 0.694263i | \(0.755731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.73125e9 | 1.69929 | ||||||||
\(596\) | 4.05918e9 | 0.785374 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.82346e9 | 0.539917 | ||||||||
\(599\) | −1.02859e9 | −0.195545 | −0.0977725 | − | 0.995209i | \(-0.531172\pi\) | ||||
−0.0977725 | + | 0.995209i | \(0.531172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.84013e9 | −0.533676 | −0.266838 | − | 0.963741i | \(-0.585979\pi\) | ||||
−0.266838 | + | 0.963741i | \(0.585979\pi\) | |||||||
\(602\) | −1.15804e9 | −0.216340 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.92840e9 | 0.910074 | ||||||||
\(605\) | 2.88689e9 | 0.530013 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.39067e9 | 1.52278 | 0.761388 | − | 0.648296i | \(-0.224518\pi\) | ||||
0.761388 | + | 0.648296i | \(0.224518\pi\) | |||||||
\(608\) | −9.87333e9 | −1.78156 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.29582e8 | 0.165819 | ||||||||
\(611\) | −5.29773e8 | −0.0939605 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.69978e9 | −0.473388 | −0.236694 | − | 0.971584i | \(-0.576064\pi\) | ||||
−0.236694 | + | 0.971584i | \(0.576064\pi\) | |||||||
\(614\) | 1.44033e9 | 0.251115 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.74249e9 | 0.645101 | ||||||||
\(617\) | −3.54215e9 | −0.607112 | −0.303556 | − | 0.952814i | \(-0.598174\pi\) | ||||
−0.303556 | + | 0.952814i | \(0.598174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.53401e9 | −1.27676 | −0.638380 | − | 0.769721i | \(-0.720395\pi\) | ||||
−0.638380 | + | 0.769721i | \(0.720395\pi\) | |||||||
\(620\) | 1.15851e9 | 0.195222 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.31475e9 | 0.219067 | ||||||||
\(623\) | 9.42539e9 | 1.56168 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.54007e7 | 0.00907685 | ||||||||
\(626\) | −1.01554e9 | −0.165457 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.23974e9 | −0.521978 | ||||||||
\(629\) | 1.67479e10 | 2.68339 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.21541e10 | 1.92584 | 0.962920 | − | 0.269787i | \(-0.0869533\pi\) | ||||
0.962920 | + | 0.269787i | \(0.0869533\pi\) | |||||||
\(632\) | 4.10106e9 | 0.646228 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.24271e9 | −0.193668 | ||||||||
\(635\) | 3.51116e9 | 0.544179 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.10980e10 | −1.70120 | ||||||||
\(638\) | 1.26576e8 | 0.0192966 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.92443e9 | −0.290183 | ||||||||
\(641\) | −6.74739e9 | −1.01189 | −0.505944 | − | 0.862566i | \(-0.668856\pi\) | ||||
−0.505944 | + | 0.862566i | \(0.668856\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.85998e9 | −1.31430 | −0.657150 | − | 0.753760i | \(-0.728238\pi\) | ||||
−0.657150 | + | 0.753760i | \(0.728238\pi\) | |||||||
\(644\) | −5.76915e9 | −0.851160 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.37286e10 | 2.00360 | ||||||||
\(647\) | 5.90409e9 | 0.857015 | 0.428507 | − | 0.903538i | \(-0.359040\pi\) | ||||
0.428507 | + | 0.903538i | \(0.359040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.36599e8 | −0.0483344 | ||||||||
\(650\) | −2.64462e9 | −0.377717 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.99651e9 | 0.988587 | ||||||||
\(653\) | 8.95278e9 | 1.25823 | 0.629117 | − | 0.777310i | \(-0.283416\pi\) | ||||
0.629117 | + | 0.777310i | \(0.283416\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.19507e9 | −1.00044 | ||||||||
\(656\) | 1.14341e9 | 0.158139 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.23991e8 | −0.112754 | ||||||||
\(659\) | −1.19309e10 | −1.62396 | −0.811979 | − | 0.583687i | \(-0.801609\pi\) | ||||
−0.811979 | + | 0.583687i | \(0.801609\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.52536e9 | −0.474786 | −0.237393 | − | 0.971414i | \(-0.576293\pi\) | ||||
−0.237393 | + | 0.971414i | \(0.576293\pi\) | |||||||
\(662\) | −2.84788e9 | −0.381521 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.15892e9 | −0.551306 | ||||||||
\(665\) | −1.46079e10 | −1.92625 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.38769e8 | −0.0703011 | ||||||||
\(668\) | −2.22507e9 | −0.288820 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.59773e9 | 0.462133 | ||||||||
\(671\) | 1.19207e9 | 0.152326 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.13472e9 | 0.269953 | 0.134976 | − | 0.990849i | \(-0.456904\pi\) | ||||
0.134976 | + | 0.990849i | \(0.456904\pi\) | |||||||
\(674\) | −5.73716e9 | −0.721751 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.70450e8 | 0.0834743 | ||||||||
\(677\) | −1.03034e10 | −1.27621 | −0.638103 | − | 0.769951i | \(-0.720281\pi\) | ||||
−0.638103 | + | 0.769951i | \(0.720281\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.56537e10 | −3.14490 | ||||||||
\(680\) | 8.51867e9 | 1.03894 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.13088e9 | −0.136512 | ||||||||
\(683\) | −4.34566e9 | −0.521895 | −0.260947 | − | 0.965353i | \(-0.584035\pi\) | ||||
−0.260947 | + | 0.965353i | \(0.584035\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.63450e9 | 1.14528 | ||||||||
\(686\) | −7.89033e9 | −0.933170 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.83112e8 | −0.0214366 | ||||||||
\(689\) | 1.22348e10 | 1.42505 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.26968e9 | 0.146393 | 0.0731965 | − | 0.997318i | \(-0.476680\pi\) | ||||
0.0731965 | + | 0.997318i | \(0.476680\pi\) | |||||||
\(692\) | −1.16553e9 | −0.133706 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.76324e9 | −1.10876 | ||||||||
\(695\) | 6.70847e9 | 0.758013 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.11076e10 | 2.36115 | ||||||||
\(698\) | 4.21946e9 | 0.469638 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.40374e9 | 0.595458 | ||||||||
\(701\) | 1.71178e9 | 0.187687 | 0.0938435 | − | 0.995587i | \(-0.470085\pi\) | ||||
0.0938435 | + | 0.995587i | \(0.470085\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.80204e10 | −3.04180 | ||||||||
\(704\) | 2.54330e9 | 0.274722 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.33365e9 | 0.142634 | ||||||||
\(707\) | −1.21463e10 | −1.29264 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.22235e10 | 1.28805 | 0.644025 | − | 0.765004i | \(-0.277263\pi\) | ||||
0.644025 | + | 0.765004i | \(0.277263\pi\) | |||||||
\(710\) | 1.08661e9 | 0.113938 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.19592e9 | 0.954806 | ||||||||
\(713\) | 4.81355e9 | 0.497338 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.06025e9 | 0.210790 | ||||||||
\(716\) | −1.70021e9 | −0.173104 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.54240e9 | −0.962104 | ||||||||
\(719\) | 5.76282e8 | 0.0578207 | 0.0289104 | − | 0.999582i | \(-0.490796\pi\) | ||||
0.0289104 | + | 0.999582i | \(0.490796\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.70403e10 | 2.68682 | ||||||||
\(722\) | −1.63202e10 | −1.61378 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.15357e9 | 0.700548 | ||||||||
\(725\) | 5.04644e8 | 0.0491816 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.68604e9 | 0.355787 | 0.177894 | − | 0.984050i | \(-0.443072\pi\) | ||||
0.177894 | + | 0.984050i | \(0.443072\pi\) | |||||||
\(728\) | −1.67061e10 | −1.60478 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.46685e9 | 0.710407 | ||||||||
\(731\) | −3.38027e9 | −0.320067 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.75370e9 | −0.539614 | −0.269807 | − | 0.962914i | \(-0.586960\pi\) | ||||
−0.269807 | + | 0.962914i | \(0.586960\pi\) | |||||||
\(734\) | −1.27846e8 | −0.0119331 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.21889e9 | −0.852327 | ||||||||
\(737\) | 4.61363e9 | 0.424528 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.57514e9 | −0.690455 | −0.345227 | − | 0.938519i | \(-0.612198\pi\) | ||||
−0.345227 | + | 0.938519i | \(0.612198\pi\) | |||||||
\(740\) | −6.29683e9 | −0.571230 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.90296e10 | 1.71008 | ||||||||
\(743\) | −9.30976e9 | −0.832679 | −0.416340 | − | 0.909209i | \(-0.636687\pi\) | ||||
−0.416340 | + | 0.909209i | \(0.636687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.59688e9 | 0.850321 | ||||||||
\(746\) | 5.96615e9 | 0.526149 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.95628e9 | 0.345646 | ||||||||
\(749\) | 1.40281e10 | 1.21987 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.04130e10 | 0.897091 | 0.448546 | − | 0.893760i | \(-0.351942\pi\) | ||||
0.448546 | + | 0.893760i | \(0.351942\pi\) | |||||||
\(752\) | −1.30290e8 | −0.0111725 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.65026e8 | −0.0480030 | ||||||||
\(755\) | 1.16519e10 | 0.985334 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.37115e9 | −0.450020 | −0.225010 | − | 0.974356i | \(-0.572241\pi\) | ||||
−0.225010 | + | 0.974356i | \(0.572241\pi\) | |||||||
\(758\) | −7.16765e7 | −0.00597771 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.42523e10 | −1.17771 | ||||||||
\(761\) | 2.00035e10 | 1.64535 | 0.822677 | − | 0.568509i | \(-0.192479\pi\) | ||||
0.822677 | + | 0.568509i | \(0.192479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.02292e10 | 1.64870 | ||||||||
\(764\) | 2.33696e9 | 0.189594 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.14740e9 | 0.494186 | ||||||||
\(767\) | 1.50255e9 | 0.120239 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.99672e10 | −1.58334 | −0.791670 | − | 0.610949i | \(-0.790788\pi\) | ||||
−0.791670 | + | 0.610949i | \(0.790788\pi\) | |||||||
\(770\) | 3.20445e9 | 0.252950 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.88511e9 | −0.147461 | ||||||||
\(773\) | 1.32942e10 | 1.03522 | 0.517611 | − | 0.855616i | \(-0.326821\pi\) | ||||
0.517611 | + | 0.855616i | \(0.326821\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.50867e9 | −0.347930 | ||||||||
\(776\) | −2.50292e10 | −1.92278 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.41085e9 | 0.411943 | ||||||||
\(779\) | −3.53143e10 | −2.67652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.39344e9 | 0.104667 | ||||||||
\(782\) | 1.28186e10 | 0.958552 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.72940e9 | −0.202284 | ||||||||
\(785\) | −7.65954e9 | −0.565143 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.67731e10 | −1.22659 | −0.613297 | − | 0.789853i | \(-0.710157\pi\) | ||||
−0.613297 | + | 0.789853i | \(0.710157\pi\) | |||||||
\(788\) | −1.16775e9 | −0.0850174 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.51147e9 | 0.253393 | ||||||||
\(791\) | 4.06992e10 | 2.92394 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.32130e9 | −0.378932 | ||||||||
\(794\) | 8.60410e9 | 0.610005 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.70546e9 | −0.330679 | ||||||||
\(797\) | 1.36721e10 | 0.956603 | 0.478301 | − | 0.878196i | \(-0.341253\pi\) | ||||
0.478301 | + | 0.878196i | \(0.341253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.40518e9 | −0.166815 | ||||||||
\(800\) | 8.63498e9 | 0.596275 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.12408e8 | 0.0487662 | ||||||||
\(803\) | 9.57528e9 | 0.652600 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.36397e10 | −0.921548 | ||||||||
\(806\) | 5.04813e9 | 0.339593 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.18506e10 | −0.790314 | ||||||||
\(809\) | −2.47296e10 | −1.64209 | −0.821046 | − | 0.570862i | \(-0.806609\pi\) | ||||
−0.821046 | + | 0.570862i | \(0.806609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.97641e9 | −0.393430 | −0.196715 | − | 0.980461i | \(-0.563027\pi\) | ||||
−0.196715 | + | 0.980461i | \(0.563027\pi\) | |||||||
\(812\) | 1.15451e9 | 0.0756751 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.14664e9 | 0.399441 | ||||||||
\(815\) | 1.65414e10 | 1.07034 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.65540e9 | 0.362816 | ||||||||
\(818\) | 8.37817e9 | 0.535196 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.93596e9 | −0.502633 | ||||||||
\(821\) | −6.86651e9 | −0.433047 | −0.216523 | − | 0.976277i | \(-0.569472\pi\) | ||||
−0.216523 | + | 0.976277i | \(0.569472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.06812e10 | −0.667916 | −0.333958 | − | 0.942588i | \(-0.608384\pi\) | ||||
−0.333958 | + | 0.942588i | \(0.608384\pi\) | |||||||
\(824\) | 2.63820e10 | 1.64272 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.33701e9 | 0.144288 | ||||||||
\(827\) | −1.28871e10 | −0.792291 | −0.396146 | − | 0.918188i | \(-0.629652\pi\) | ||||
−0.396146 | + | 0.918188i | \(0.629652\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.54525e10 | 1.55164 | 0.775819 | − | 0.630956i | \(-0.217337\pi\) | ||||
0.775819 | + | 0.630956i | \(0.217337\pi\) | |||||||
\(830\) | −3.56102e9 | −0.216173 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.13531e10 | −0.683411 | ||||||||
\(833\) | −5.03852e10 | −3.02027 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.26061e9 | −0.312704 | ||||||||
\(836\) | −6.61911e9 | −0.391812 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.83220e10 | −1.07552 | ||||||||
\(839\) | −1.16543e10 | −0.681269 | −0.340635 | − | 0.940196i | \(-0.610642\pi\) | ||||
−0.340635 | + | 0.940196i | \(0.610642\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.71421e10 | −0.993750 | ||||||||
\(842\) | −4.48282e9 | −0.258797 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.94696e9 | 0.168724 | ||||||||
\(845\) | 1.58510e9 | 0.0903773 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.57035e10 | −1.45345 | ||||||||
\(848\) | 3.00898e9 | 0.169447 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.20067e10 | −0.670588 | ||||||||
\(851\) | −2.61631e10 | −1.45524 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.84397e9 | −0.487894 | −0.243947 | − | 0.969789i | \(-0.578442\pi\) | ||||
−0.243947 | + | 0.969789i | \(0.578442\pi\) | |||||||
\(854\) | −8.27657e9 | −0.454724 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.36866e10 | 0.745826 | ||||||||
\(857\) | 9.53214e9 | 0.517318 | 0.258659 | − | 0.965969i | \(-0.416719\pi\) | ||||
0.258659 | + | 0.965969i | \(0.416719\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.01239e10 | −0.544971 | −0.272485 | − | 0.962160i | \(-0.587846\pi\) | ||||
−0.272485 | + | 0.962160i | \(0.587846\pi\) | |||||||
\(860\) | 1.27090e9 | 0.0681345 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.26108e10 | 0.670608 | ||||||||
\(863\) | −3.34111e9 | −0.176951 | −0.0884755 | − | 0.996078i | \(-0.528199\pi\) | ||||
−0.0884755 | + | 0.996078i | \(0.528199\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.75558e9 | −0.144763 | ||||||||
\(866\) | 3.95353e9 | 0.206858 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.03148e10 | −0.535356 | ||||||||
\(869\) | 4.50301e9 | 0.232773 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.05948e10 | −1.05608 | ||||||||
\(872\) | 1.97366e10 | 1.00801 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.14463e10 | −1.08658 | ||||||||
\(875\) | 3.33127e10 | 1.68105 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.70327e10 | −0.852679 | −0.426339 | − | 0.904563i | \(-0.640197\pi\) | ||||
−0.426339 | + | 0.904563i | \(0.640197\pi\) | |||||||
\(878\) | 1.78259e10 | 0.888835 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.06691e8 | 0.0250642 | ||||||||
\(881\) | 6.92335e9 | 0.341115 | 0.170558 | − | 0.985348i | \(-0.445443\pi\) | ||||
0.170558 | + | 0.985348i | \(0.445443\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.45719e9 | −0.120109 | −0.0600547 | − | 0.998195i | \(-0.519128\pi\) | ||||
−0.0600547 | + | 0.998195i | \(0.519128\pi\) | |||||||
\(884\) | −1.76605e10 | −0.859845 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.51220e10 | −0.730453 | ||||||||
\(887\) | −1.99592e10 | −0.960307 | −0.480154 | − | 0.877184i | \(-0.659419\pi\) | ||||
−0.480154 | + | 0.877184i | \(0.659419\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.12617e10 | −1.49230 | ||||||||
\(890\) | 7.87387e9 | 0.374389 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.86167e9 | 0.229355 | ||||||||
\(893\) | 4.02402e9 | 0.189095 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.01971e9 | −0.187419 | ||||||||
\(896\) | 1.71342e10 | 0.795768 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.57662e10 | 1.18736 | ||||||||
\(899\) | −9.63280e8 | −0.0442174 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.55463e10 | 2.52999 | ||||||||
\(902\) | 7.74667e9 | 0.351473 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.97083e10 | 1.78769 | ||||||||
\(905\) | 1.69128e10 | 0.758481 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.22070e10 | 0.543227 | 0.271614 | − | 0.962406i | \(-0.412443\pi\) | ||||
0.271614 | + | 0.962406i | \(0.412443\pi\) | |||||||
\(908\) | 8.88829e9 | 0.394019 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.43044e10 | −0.629251 | ||||||||
\(911\) | −1.78824e10 | −0.783629 | −0.391815 | − | 0.920044i | \(-0.628153\pi\) | ||||
−0.391815 | + | 0.920044i | \(0.628153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.56655e9 | −0.198582 | ||||||||
\(914\) | 2.00850e9 | 0.0870081 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.68894e10 | 0.726074 | ||||||||
\(917\) | 6.40616e10 | 2.74350 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.01138e10 | −0.429843 | −0.214921 | − | 0.976631i | \(-0.568949\pi\) | ||||
−0.214921 | + | 0.976631i | \(0.568949\pi\) | |||||||
\(920\) | −1.33076e10 | −0.563432 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.44522e10 | −0.607262 | ||||||||
\(923\) | −6.22020e9 | −0.260375 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.45059e10 | 1.01806 | ||||||||
\(926\) | 1.16973e9 | 0.0484113 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.84487e9 | 0.0757788 | ||||||||
\(929\) | −7.28094e9 | −0.297942 | −0.148971 | − | 0.988842i | \(-0.547596\pi\) | ||||
−0.148971 | + | 0.988842i | \(0.547596\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.42976e10 | 3.42367 | ||||||||
\(932\) | 5.59397e9 | 0.226342 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.49571e9 | −0.301022 | ||||||||
\(935\) | 9.35360e9 | 0.374230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.64374e10 | −1.04986 | −0.524928 | − | 0.851147i | \(-0.675908\pi\) | ||||
−0.524928 | + | 0.851147i | \(0.675908\pi\) | |||||||
\(938\) | −3.20325e10 | −1.26731 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.04292e8 | 0.0355109 | ||||||||
\(941\) | 7.30500e9 | 0.285796 | 0.142898 | − | 0.989737i | \(-0.454358\pi\) | ||||
0.142898 | + | 0.989737i | \(0.454358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.29735e10 | −1.28049 | ||||||||
\(944\) | 3.69531e8 | 0.0142971 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.24059e9 | −0.0476441 | ||||||||
\(947\) | −6.35717e9 | −0.243242 | −0.121621 | − | 0.992577i | \(-0.538809\pi\) | ||||
−0.121621 | + | 0.992577i | \(0.538809\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.27432e10 | −1.62344 | ||||||||
\(950\) | 2.00879e10 | 0.760154 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.58463e10 | −2.84908 | ||||||||
\(953\) | 6.22176e9 | 0.232856 | 0.116428 | − | 0.993199i | \(-0.462856\pi\) | ||||
0.116428 | + | 0.993199i | \(0.462856\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.52514e9 | 0.205273 | ||||||||
\(956\) | −7.76550e8 | −0.0287453 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.54047e9 | 0.313836 | ||||||||
\(959\) | −8.57811e10 | −3.14070 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.89063e10 | −0.687188 | ||||||||
\(962\) | −2.74381e10 | −0.993668 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.71910e10 | 0.977587 | ||||||||
\(965\) | −4.45686e9 | −0.159655 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.37902e10 | −1.20171 | −0.600853 | − | 0.799360i | \(-0.705172\pi\) | ||||
−0.600853 | + | 0.799360i | \(0.705172\pi\) | |||||||
\(968\) | −2.50777e10 | −0.888637 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.14308e10 | −0.753943 | ||||||||
\(971\) | 4.96021e10 | 1.73873 | 0.869366 | − | 0.494169i | \(-0.164528\pi\) | ||||
0.869366 | + | 0.494169i | \(0.164528\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.97291e10 | −2.07870 | ||||||||
\(974\) | −1.97444e10 | −0.684680 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.30870e9 | −0.0450574 | ||||||||
\(977\) | 3.46137e10 | 1.18745 | 0.593727 | − | 0.804667i | \(-0.297656\pi\) | ||||
0.593727 | + | 0.804667i | \(0.297656\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.00972e10 | 0.343924 | ||||||||
\(980\) | 1.89437e10 | 0.642943 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.67382e10 | −0.564052 | ||||||||
\(983\) | 9.52456e9 | 0.319822 | 0.159911 | − | 0.987131i | \(-0.448879\pi\) | ||||
0.159911 | + | 0.987131i | \(0.448879\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.76084e9 | −0.0920480 | ||||||||
\(986\) | −2.56523e9 | −0.0852231 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.95471e10 | 0.974689 | ||||||||
\(989\) | 5.28054e9 | 0.173577 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.31860e10 | 1.40956 | 0.704782 | − | 0.709424i | \(-0.251045\pi\) | ||||
0.704782 | + | 0.709424i | \(0.251045\pi\) | |||||||
\(992\) | −1.64827e10 | −0.536090 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.67469e9 | −0.312453 | ||||||||
\(995\) | −1.11248e10 | −0.358025 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.74177e9 | 0.183490 | 0.0917451 | − | 0.995783i | \(-0.470755\pi\) | ||||
0.0917451 | + | 0.995783i | \(0.470755\pi\) | |||||||
\(998\) | −5.56327e9 | −0.177163 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.8.a.e.1.8 | 18 | ||
3.2 | odd | 2 | 177.8.a.d.1.11 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.11 | ✓ | 18 | 3.2 | odd | 2 | ||
531.8.a.e.1.8 | 18 | 1.1 | even | 1 | trivial |