Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8022,2,Mod(1,8022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8022.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: | \(64.0559925015\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 17x^{7} - 12x^{6} + 72x^{5} + 81x^{4} - 67x^{3} - 105x^{2} - 17x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.17782\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8022.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.12019 | 0.948177 | 0.474088 | − | 0.880477i | \(-0.342778\pi\) | ||||
0.474088 | + | 0.880477i | \(0.342778\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.12019 | 0.670462 | ||||||||
\(11\) | −5.65813 | −1.70599 | −0.852995 | − | 0.521918i | \(-0.825217\pi\) | ||||
−0.852995 | + | 0.521918i | \(0.825217\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.41673 | −0.947631 | −0.473815 | − | 0.880624i | \(-0.657124\pi\) | ||||
−0.473815 | + | 0.880624i | \(0.657124\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −2.12019 | −0.547430 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.62524 | 0.879250 | 0.439625 | − | 0.898181i | \(-0.355111\pi\) | ||||
0.439625 | + | 0.898181i | \(0.355111\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.530988 | −0.121817 | −0.0609085 | − | 0.998143i | \(-0.519400\pi\) | ||||
−0.0609085 | + | 0.998143i | \(0.519400\pi\) | |||||||
\(20\) | 2.12019 | 0.474088 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −5.65813 | −1.20632 | ||||||||
\(23\) | −1.83642 | −0.382921 | −0.191460 | − | 0.981500i | \(-0.561322\pi\) | ||||
−0.191460 | + | 0.981500i | \(0.561322\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −0.504804 | −0.100961 | ||||||||
\(26\) | −3.41673 | −0.670076 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 7.73144 | 1.43569 | 0.717847 | − | 0.696201i | \(-0.245128\pi\) | ||||
0.717847 | + | 0.696201i | \(0.245128\pi\) | |||||||
\(30\) | −2.12019 | −0.387092 | ||||||||
\(31\) | −8.59340 | −1.54342 | −0.771711 | − | 0.635974i | \(-0.780599\pi\) | ||||
−0.771711 | + | 0.635974i | \(0.780599\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.65813 | 0.984954 | ||||||||
\(34\) | 3.62524 | 0.621724 | ||||||||
\(35\) | 2.12019 | 0.358377 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −11.6878 | −1.92146 | −0.960732 | − | 0.277479i | \(-0.910501\pi\) | ||||
−0.960732 | + | 0.277479i | \(0.910501\pi\) | |||||||
\(38\) | −0.530988 | −0.0861377 | ||||||||
\(39\) | 3.41673 | 0.547115 | ||||||||
\(40\) | 2.12019 | 0.335231 | ||||||||
\(41\) | 12.4762 | 1.94846 | 0.974229 | − | 0.225560i | \(-0.0724212\pi\) | ||||
0.974229 | + | 0.225560i | \(0.0724212\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −6.43569 | −0.981433 | −0.490717 | − | 0.871319i | \(-0.663265\pi\) | ||||
−0.490717 | + | 0.871319i | \(0.663265\pi\) | |||||||
\(44\) | −5.65813 | −0.852995 | ||||||||
\(45\) | 2.12019 | 0.316059 | ||||||||
\(46\) | −1.83642 | −0.270766 | ||||||||
\(47\) | −8.05558 | −1.17503 | −0.587514 | − | 0.809214i | \(-0.699893\pi\) | ||||
−0.587514 | + | 0.809214i | \(0.699893\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.504804 | −0.0713901 | ||||||||
\(51\) | −3.62524 | −0.507635 | ||||||||
\(52\) | −3.41673 | −0.473815 | ||||||||
\(53\) | 5.25315 | 0.721576 | 0.360788 | − | 0.932648i | \(-0.382508\pi\) | ||||
0.360788 | + | 0.932648i | \(0.382508\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −11.9963 | −1.61758 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0.530988 | 0.0703311 | ||||||||
\(58\) | 7.73144 | 1.01519 | ||||||||
\(59\) | 5.97094 | 0.777350 | 0.388675 | − | 0.921375i | \(-0.372933\pi\) | ||||
0.388675 | + | 0.921375i | \(0.372933\pi\) | |||||||
\(60\) | −2.12019 | −0.273715 | ||||||||
\(61\) | 12.0771 | 1.54631 | 0.773157 | − | 0.634215i | \(-0.218676\pi\) | ||||
0.773157 | + | 0.634215i | \(0.218676\pi\) | |||||||
\(62\) | −8.59340 | −1.09136 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.24411 | −0.898521 | ||||||||
\(66\) | 5.65813 | 0.696468 | ||||||||
\(67\) | −0.347898 | −0.0425025 | −0.0212513 | − | 0.999774i | \(-0.506765\pi\) | ||||
−0.0212513 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(68\) | 3.62524 | 0.439625 | ||||||||
\(69\) | 1.83642 | 0.221079 | ||||||||
\(70\) | 2.12019 | 0.253411 | ||||||||
\(71\) | −5.14641 | −0.610767 | −0.305383 | − | 0.952229i | \(-0.598785\pi\) | ||||
−0.305383 | + | 0.952229i | \(0.598785\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −12.9220 | −1.51241 | −0.756205 | − | 0.654334i | \(-0.772949\pi\) | ||||
−0.756205 | + | 0.654334i | \(0.772949\pi\) | |||||||
\(74\) | −11.6878 | −1.35868 | ||||||||
\(75\) | 0.504804 | 0.0582898 | ||||||||
\(76\) | −0.530988 | −0.0609085 | ||||||||
\(77\) | −5.65813 | −0.644804 | ||||||||
\(78\) | 3.41673 | 0.386869 | ||||||||
\(79\) | −15.6065 | −1.75587 | −0.877934 | − | 0.478781i | \(-0.841079\pi\) | ||||
−0.877934 | + | 0.478781i | \(0.841079\pi\) | |||||||
\(80\) | 2.12019 | 0.237044 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.4762 | 1.37777 | ||||||||
\(83\) | −13.4142 | −1.47240 | −0.736200 | − | 0.676764i | \(-0.763382\pi\) | ||||
−0.736200 | + | 0.676764i | \(0.763382\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 7.68619 | 0.833685 | ||||||||
\(86\) | −6.43569 | −0.693978 | ||||||||
\(87\) | −7.73144 | −0.828898 | ||||||||
\(88\) | −5.65813 | −0.603159 | ||||||||
\(89\) | 15.3853 | 1.63084 | 0.815420 | − | 0.578870i | \(-0.196506\pi\) | ||||
0.815420 | + | 0.578870i | \(0.196506\pi\) | |||||||
\(90\) | 2.12019 | 0.223487 | ||||||||
\(91\) | −3.41673 | −0.358171 | ||||||||
\(92\) | −1.83642 | −0.191460 | ||||||||
\(93\) | 8.59340 | 0.891095 | ||||||||
\(94\) | −8.05558 | −0.830870 | ||||||||
\(95\) | −1.12579 | −0.115504 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −16.3823 | −1.66337 | −0.831685 | − | 0.555247i | \(-0.812624\pi\) | ||||
−0.831685 | + | 0.555247i | \(0.812624\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −5.65813 | −0.568664 | ||||||||
\(100\) | −0.504804 | −0.0504804 | ||||||||
\(101\) | −10.9489 | −1.08946 | −0.544729 | − | 0.838612i | \(-0.683368\pi\) | ||||
−0.544729 | + | 0.838612i | \(0.683368\pi\) | |||||||
\(102\) | −3.62524 | −0.358952 | ||||||||
\(103\) | −9.79451 | −0.965082 | −0.482541 | − | 0.875873i | \(-0.660286\pi\) | ||||
−0.482541 | + | 0.875873i | \(0.660286\pi\) | |||||||
\(104\) | −3.41673 | −0.335038 | ||||||||
\(105\) | −2.12019 | −0.206909 | ||||||||
\(106\) | 5.25315 | 0.510231 | ||||||||
\(107\) | −0.795378 | −0.0768921 | −0.0384461 | − | 0.999261i | \(-0.512241\pi\) | ||||
−0.0384461 | + | 0.999261i | \(0.512241\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 14.3889 | 1.37821 | 0.689104 | − | 0.724663i | \(-0.258004\pi\) | ||||
0.689104 | + | 0.724663i | \(0.258004\pi\) | |||||||
\(110\) | −11.9963 | −1.14380 | ||||||||
\(111\) | 11.6878 | 1.10936 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −8.17372 | −0.768919 | −0.384459 | − | 0.923142i | \(-0.625612\pi\) | ||||
−0.384459 | + | 0.923142i | \(0.625612\pi\) | |||||||
\(114\) | 0.530988 | 0.0497316 | ||||||||
\(115\) | −3.89356 | −0.363076 | ||||||||
\(116\) | 7.73144 | 0.717847 | ||||||||
\(117\) | −3.41673 | −0.315877 | ||||||||
\(118\) | 5.97094 | 0.549669 | ||||||||
\(119\) | 3.62524 | 0.332325 | ||||||||
\(120\) | −2.12019 | −0.193546 | ||||||||
\(121\) | 21.0145 | 1.91041 | ||||||||
\(122\) | 12.0771 | 1.09341 | ||||||||
\(123\) | −12.4762 | −1.12494 | ||||||||
\(124\) | −8.59340 | −0.771711 | ||||||||
\(125\) | −11.6712 | −1.04391 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −15.4919 | −1.37468 | −0.687341 | − | 0.726335i | \(-0.741222\pi\) | ||||
−0.687341 | + | 0.726335i | \(0.741222\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.43569 | 0.566631 | ||||||||
\(130\) | −7.24411 | −0.635351 | ||||||||
\(131\) | −17.5231 | −1.53100 | −0.765499 | − | 0.643437i | \(-0.777508\pi\) | ||||
−0.765499 | + | 0.643437i | \(0.777508\pi\) | |||||||
\(132\) | 5.65813 | 0.492477 | ||||||||
\(133\) | −0.530988 | −0.0460425 | ||||||||
\(134\) | −0.347898 | −0.0300538 | ||||||||
\(135\) | −2.12019 | −0.182477 | ||||||||
\(136\) | 3.62524 | 0.310862 | ||||||||
\(137\) | −10.7313 | −0.916836 | −0.458418 | − | 0.888737i | \(-0.651584\pi\) | ||||
−0.458418 | + | 0.888737i | \(0.651584\pi\) | |||||||
\(138\) | 1.83642 | 0.156327 | ||||||||
\(139\) | 19.8459 | 1.68330 | 0.841652 | − | 0.540020i | \(-0.181583\pi\) | ||||
0.841652 | + | 0.540020i | \(0.181583\pi\) | |||||||
\(140\) | 2.12019 | 0.179189 | ||||||||
\(141\) | 8.05558 | 0.678402 | ||||||||
\(142\) | −5.14641 | −0.431877 | ||||||||
\(143\) | 19.3323 | 1.61665 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 16.3921 | 1.36129 | ||||||||
\(146\) | −12.9220 | −1.06944 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −11.6878 | −0.960732 | ||||||||
\(149\) | −12.2987 | −1.00754 | −0.503772 | − | 0.863836i | \(-0.668055\pi\) | ||||
−0.503772 | + | 0.863836i | \(0.668055\pi\) | |||||||
\(150\) | 0.504804 | 0.0412171 | ||||||||
\(151\) | 17.6647 | 1.43753 | 0.718766 | − | 0.695252i | \(-0.244707\pi\) | ||||
0.718766 | + | 0.695252i | \(0.244707\pi\) | |||||||
\(152\) | −0.530988 | −0.0430688 | ||||||||
\(153\) | 3.62524 | 0.293083 | ||||||||
\(154\) | −5.65813 | −0.455945 | ||||||||
\(155\) | −18.2196 | −1.46344 | ||||||||
\(156\) | 3.41673 | 0.273557 | ||||||||
\(157\) | −18.2820 | −1.45906 | −0.729532 | − | 0.683947i | \(-0.760262\pi\) | ||||
−0.729532 | + | 0.683947i | \(0.760262\pi\) | |||||||
\(158\) | −15.6065 | −1.24159 | ||||||||
\(159\) | −5.25315 | −0.416602 | ||||||||
\(160\) | 2.12019 | 0.167616 | ||||||||
\(161\) | −1.83642 | −0.144730 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 8.89726 | 0.696888 | 0.348444 | − | 0.937330i | \(-0.386710\pi\) | ||||
0.348444 | + | 0.937330i | \(0.386710\pi\) | |||||||
\(164\) | 12.4762 | 0.974229 | ||||||||
\(165\) | 11.9963 | 0.933911 | ||||||||
\(166\) | −13.4142 | −1.04114 | ||||||||
\(167\) | 19.7895 | 1.53136 | 0.765680 | − | 0.643222i | \(-0.222403\pi\) | ||||
0.765680 | + | 0.643222i | \(0.222403\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −1.32595 | −0.101996 | ||||||||
\(170\) | 7.68619 | 0.589504 | ||||||||
\(171\) | −0.530988 | −0.0406057 | ||||||||
\(172\) | −6.43569 | −0.490717 | ||||||||
\(173\) | −11.2793 | −0.857546 | −0.428773 | − | 0.903412i | \(-0.641054\pi\) | ||||
−0.428773 | + | 0.903412i | \(0.641054\pi\) | |||||||
\(174\) | −7.73144 | −0.586119 | ||||||||
\(175\) | −0.504804 | −0.0381596 | ||||||||
\(176\) | −5.65813 | −0.426498 | ||||||||
\(177\) | −5.97094 | −0.448803 | ||||||||
\(178\) | 15.3853 | 1.15318 | ||||||||
\(179\) | −3.64668 | −0.272565 | −0.136283 | − | 0.990670i | \(-0.543516\pi\) | ||||
−0.136283 | + | 0.990670i | \(0.543516\pi\) | |||||||
\(180\) | 2.12019 | 0.158029 | ||||||||
\(181\) | −1.91630 | −0.142437 | −0.0712186 | − | 0.997461i | \(-0.522689\pi\) | ||||
−0.0712186 | + | 0.997461i | \(0.522689\pi\) | |||||||
\(182\) | −3.41673 | −0.253265 | ||||||||
\(183\) | −12.0771 | −0.892765 | ||||||||
\(184\) | −1.83642 | −0.135383 | ||||||||
\(185\) | −24.7803 | −1.82189 | ||||||||
\(186\) | 8.59340 | 0.630099 | ||||||||
\(187\) | −20.5121 | −1.49999 | ||||||||
\(188\) | −8.05558 | −0.587514 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −1.12579 | −0.0816737 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 0.0643161 | 0.00462957 | 0.00231479 | − | 0.999997i | \(-0.499263\pi\) | ||||
0.00231479 | + | 0.999997i | \(0.499263\pi\) | |||||||
\(194\) | −16.3823 | −1.17618 | ||||||||
\(195\) | 7.24411 | 0.518762 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.31491 | 0.449919 | 0.224959 | − | 0.974368i | \(-0.427775\pi\) | ||||
0.224959 | + | 0.974368i | \(0.427775\pi\) | |||||||
\(198\) | −5.65813 | −0.402106 | ||||||||
\(199\) | 9.61618 | 0.681673 | 0.340836 | − | 0.940123i | \(-0.389290\pi\) | ||||
0.340836 | + | 0.940123i | \(0.389290\pi\) | |||||||
\(200\) | −0.504804 | −0.0356951 | ||||||||
\(201\) | 0.347898 | 0.0245388 | ||||||||
\(202\) | −10.9489 | −0.770364 | ||||||||
\(203\) | 7.73144 | 0.542641 | ||||||||
\(204\) | −3.62524 | −0.253818 | ||||||||
\(205\) | 26.4519 | 1.84748 | ||||||||
\(206\) | −9.79451 | −0.682416 | ||||||||
\(207\) | −1.83642 | −0.127640 | ||||||||
\(208\) | −3.41673 | −0.236908 | ||||||||
\(209\) | 3.00440 | 0.207819 | ||||||||
\(210\) | −2.12019 | −0.146307 | ||||||||
\(211\) | 16.0386 | 1.10414 | 0.552072 | − | 0.833796i | \(-0.313837\pi\) | ||||
0.552072 | + | 0.833796i | \(0.313837\pi\) | |||||||
\(212\) | 5.25315 | 0.360788 | ||||||||
\(213\) | 5.14641 | 0.352626 | ||||||||
\(214\) | −0.795378 | −0.0543709 | ||||||||
\(215\) | −13.6449 | −0.930572 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −8.59340 | −0.583358 | ||||||||
\(218\) | 14.3889 | 0.974540 | ||||||||
\(219\) | 12.9220 | 0.873191 | ||||||||
\(220\) | −11.9963 | −0.808790 | ||||||||
\(221\) | −12.3865 | −0.833205 | ||||||||
\(222\) | 11.6878 | 0.784434 | ||||||||
\(223\) | 19.9769 | 1.33775 | 0.668875 | − | 0.743375i | \(-0.266776\pi\) | ||||
0.668875 | + | 0.743375i | \(0.266776\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −0.504804 | −0.0336536 | ||||||||
\(226\) | −8.17372 | −0.543708 | ||||||||
\(227\) | 3.10798 | 0.206284 | 0.103142 | − | 0.994667i | \(-0.467110\pi\) | ||||
0.103142 | + | 0.994667i | \(0.467110\pi\) | |||||||
\(228\) | 0.530988 | 0.0351656 | ||||||||
\(229\) | 18.5609 | 1.22654 | 0.613268 | − | 0.789875i | \(-0.289854\pi\) | ||||
0.613268 | + | 0.789875i | \(0.289854\pi\) | |||||||
\(230\) | −3.89356 | −0.256734 | ||||||||
\(231\) | 5.65813 | 0.372278 | ||||||||
\(232\) | 7.73144 | 0.507594 | ||||||||
\(233\) | 7.66569 | 0.502196 | 0.251098 | − | 0.967962i | \(-0.419208\pi\) | ||||
0.251098 | + | 0.967962i | \(0.419208\pi\) | |||||||
\(234\) | −3.41673 | −0.223359 | ||||||||
\(235\) | −17.0793 | −1.11413 | ||||||||
\(236\) | 5.97094 | 0.388675 | ||||||||
\(237\) | 15.6065 | 1.01375 | ||||||||
\(238\) | 3.62524 | 0.234990 | ||||||||
\(239\) | −4.31275 | −0.278969 | −0.139484 | − | 0.990224i | \(-0.544545\pi\) | ||||
−0.139484 | + | 0.990224i | \(0.544545\pi\) | |||||||
\(240\) | −2.12019 | −0.136858 | ||||||||
\(241\) | −28.8232 | −1.85667 | −0.928334 | − | 0.371748i | \(-0.878759\pi\) | ||||
−0.928334 | + | 0.371748i | \(0.878759\pi\) | |||||||
\(242\) | 21.0145 | 1.35086 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 12.0771 | 0.773157 | ||||||||
\(245\) | 2.12019 | 0.135454 | ||||||||
\(246\) | −12.4762 | −0.795455 | ||||||||
\(247\) | 1.81424 | 0.115438 | ||||||||
\(248\) | −8.59340 | −0.545682 | ||||||||
\(249\) | 13.4142 | 0.850091 | ||||||||
\(250\) | −11.6712 | −0.738153 | ||||||||
\(251\) | 8.56547 | 0.540648 | 0.270324 | − | 0.962769i | \(-0.412869\pi\) | ||||
0.270324 | + | 0.962769i | \(0.412869\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 10.3907 | 0.653259 | ||||||||
\(254\) | −15.4919 | −0.972047 | ||||||||
\(255\) | −7.68619 | −0.481328 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.0282 | −1.62359 | −0.811796 | − | 0.583941i | \(-0.801510\pi\) | ||||
−0.811796 | + | 0.583941i | \(0.801510\pi\) | |||||||
\(258\) | 6.43569 | 0.400668 | ||||||||
\(259\) | −11.6878 | −0.726245 | ||||||||
\(260\) | −7.24411 | −0.449261 | ||||||||
\(261\) | 7.73144 | 0.478564 | ||||||||
\(262\) | −17.5231 | −1.08258 | ||||||||
\(263\) | −6.37183 | −0.392904 | −0.196452 | − | 0.980513i | \(-0.562942\pi\) | ||||
−0.196452 | + | 0.980513i | \(0.562942\pi\) | |||||||
\(264\) | 5.65813 | 0.348234 | ||||||||
\(265\) | 11.1377 | 0.684182 | ||||||||
\(266\) | −0.530988 | −0.0325570 | ||||||||
\(267\) | −15.3853 | −0.941566 | ||||||||
\(268\) | −0.347898 | −0.0212513 | ||||||||
\(269\) | −16.0331 | −0.977555 | −0.488777 | − | 0.872409i | \(-0.662557\pi\) | ||||
−0.488777 | + | 0.872409i | \(0.662557\pi\) | |||||||
\(270\) | −2.12019 | −0.129031 | ||||||||
\(271\) | 22.3891 | 1.36004 | 0.680020 | − | 0.733194i | \(-0.261971\pi\) | ||||
0.680020 | + | 0.733194i | \(0.261971\pi\) | |||||||
\(272\) | 3.62524 | 0.219813 | ||||||||
\(273\) | 3.41673 | 0.206790 | ||||||||
\(274\) | −10.7313 | −0.648301 | ||||||||
\(275\) | 2.85625 | 0.172238 | ||||||||
\(276\) | 1.83642 | 0.110540 | ||||||||
\(277\) | 1.87730 | 0.112796 | 0.0563980 | − | 0.998408i | \(-0.482038\pi\) | ||||
0.0563980 | + | 0.998408i | \(0.482038\pi\) | |||||||
\(278\) | 19.8459 | 1.19028 | ||||||||
\(279\) | −8.59340 | −0.514474 | ||||||||
\(280\) | 2.12019 | 0.126705 | ||||||||
\(281\) | −1.54137 | −0.0919502 | −0.0459751 | − | 0.998943i | \(-0.514639\pi\) | ||||
−0.0459751 | + | 0.998943i | \(0.514639\pi\) | |||||||
\(282\) | 8.05558 | 0.479703 | ||||||||
\(283\) | −15.7354 | −0.935373 | −0.467687 | − | 0.883894i | \(-0.654912\pi\) | ||||
−0.467687 | + | 0.883894i | \(0.654912\pi\) | |||||||
\(284\) | −5.14641 | −0.305383 | ||||||||
\(285\) | 1.12579 | 0.0666863 | ||||||||
\(286\) | 19.3323 | 1.14314 | ||||||||
\(287\) | 12.4762 | 0.736448 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −3.85762 | −0.226919 | ||||||||
\(290\) | 16.3921 | 0.962578 | ||||||||
\(291\) | 16.3823 | 0.960348 | ||||||||
\(292\) | −12.9220 | −0.756205 | ||||||||
\(293\) | −3.70401 | −0.216391 | −0.108195 | − | 0.994130i | \(-0.534507\pi\) | ||||
−0.108195 | + | 0.994130i | \(0.534507\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 12.6595 | 0.737065 | ||||||||
\(296\) | −11.6878 | −0.679340 | ||||||||
\(297\) | 5.65813 | 0.328318 | ||||||||
\(298\) | −12.2987 | −0.712442 | ||||||||
\(299\) | 6.27456 | 0.362867 | ||||||||
\(300\) | 0.504804 | 0.0291449 | ||||||||
\(301\) | −6.43569 | −0.370947 | ||||||||
\(302\) | 17.6647 | 1.01649 | ||||||||
\(303\) | 10.9489 | 0.628999 | ||||||||
\(304\) | −0.530988 | −0.0304543 | ||||||||
\(305\) | 25.6057 | 1.46618 | ||||||||
\(306\) | 3.62524 | 0.207241 | ||||||||
\(307\) | −18.3234 | −1.04577 | −0.522886 | − | 0.852403i | \(-0.675145\pi\) | ||||
−0.522886 | + | 0.852403i | \(0.675145\pi\) | |||||||
\(308\) | −5.65813 | −0.322402 | ||||||||
\(309\) | 9.79451 | 0.557190 | ||||||||
\(310\) | −18.2196 | −1.03481 | ||||||||
\(311\) | −19.4591 | −1.10343 | −0.551713 | − | 0.834034i | \(-0.686026\pi\) | ||||
−0.551713 | + | 0.834034i | \(0.686026\pi\) | |||||||
\(312\) | 3.41673 | 0.193434 | ||||||||
\(313\) | 7.82362 | 0.442217 | 0.221108 | − | 0.975249i | \(-0.429033\pi\) | ||||
0.221108 | + | 0.975249i | \(0.429033\pi\) | |||||||
\(314\) | −18.2820 | −1.03171 | ||||||||
\(315\) | 2.12019 | 0.119459 | ||||||||
\(316\) | −15.6065 | −0.877934 | ||||||||
\(317\) | −1.62203 | −0.0911021 | −0.0455510 | − | 0.998962i | \(-0.514504\pi\) | ||||
−0.0455510 | + | 0.998962i | \(0.514504\pi\) | |||||||
\(318\) | −5.25315 | −0.294582 | ||||||||
\(319\) | −43.7455 | −2.44928 | ||||||||
\(320\) | 2.12019 | 0.118522 | ||||||||
\(321\) | 0.795378 | 0.0443937 | ||||||||
\(322\) | −1.83642 | −0.102340 | ||||||||
\(323\) | −1.92496 | −0.107108 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.72478 | 0.0956736 | ||||||||
\(326\) | 8.89726 | 0.492774 | ||||||||
\(327\) | −14.3889 | −0.795709 | ||||||||
\(328\) | 12.4762 | 0.688884 | ||||||||
\(329\) | −8.05558 | −0.444119 | ||||||||
\(330\) | 11.9963 | 0.660375 | ||||||||
\(331\) | 5.80972 | 0.319331 | 0.159665 | − | 0.987171i | \(-0.448958\pi\) | ||||
0.159665 | + | 0.987171i | \(0.448958\pi\) | |||||||
\(332\) | −13.4142 | −0.736200 | ||||||||
\(333\) | −11.6878 | −0.640488 | ||||||||
\(334\) | 19.7895 | 1.08283 | ||||||||
\(335\) | −0.737609 | −0.0402999 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 34.2577 | 1.86613 | 0.933067 | − | 0.359702i | \(-0.117122\pi\) | ||||
0.933067 | + | 0.359702i | \(0.117122\pi\) | |||||||
\(338\) | −1.32595 | −0.0721219 | ||||||||
\(339\) | 8.17372 | 0.443936 | ||||||||
\(340\) | 7.68619 | 0.416842 | ||||||||
\(341\) | 48.6226 | 2.63306 | ||||||||
\(342\) | −0.530988 | −0.0287126 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −6.43569 | −0.346989 | ||||||||
\(345\) | 3.89356 | 0.209622 | ||||||||
\(346\) | −11.2793 | −0.606376 | ||||||||
\(347\) | 0.654394 | 0.0351297 | 0.0175649 | − | 0.999846i | \(-0.494409\pi\) | ||||
0.0175649 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(348\) | −7.73144 | −0.414449 | ||||||||
\(349\) | 20.2461 | 1.08375 | 0.541874 | − | 0.840459i | \(-0.317715\pi\) | ||||
0.541874 | + | 0.840459i | \(0.317715\pi\) | |||||||
\(350\) | −0.504804 | −0.0269829 | ||||||||
\(351\) | 3.41673 | 0.182372 | ||||||||
\(352\) | −5.65813 | −0.301579 | ||||||||
\(353\) | −11.9714 | −0.637172 | −0.318586 | − | 0.947894i | \(-0.603208\pi\) | ||||
−0.318586 | + | 0.947894i | \(0.603208\pi\) | |||||||
\(354\) | −5.97094 | −0.317352 | ||||||||
\(355\) | −10.9114 | −0.579115 | ||||||||
\(356\) | 15.3853 | 0.815420 | ||||||||
\(357\) | −3.62524 | −0.191868 | ||||||||
\(358\) | −3.64668 | −0.192733 | ||||||||
\(359\) | 24.6520 | 1.30108 | 0.650542 | − | 0.759470i | \(-0.274542\pi\) | ||||
0.650542 | + | 0.759470i | \(0.274542\pi\) | |||||||
\(360\) | 2.12019 | 0.111744 | ||||||||
\(361\) | −18.7181 | −0.985161 | ||||||||
\(362\) | −1.91630 | −0.100718 | ||||||||
\(363\) | −21.0145 | −1.10297 | ||||||||
\(364\) | −3.41673 | −0.179085 | ||||||||
\(365\) | −27.3972 | −1.43403 | ||||||||
\(366\) | −12.0771 | −0.631280 | ||||||||
\(367\) | −25.7416 | −1.34370 | −0.671850 | − | 0.740687i | \(-0.734500\pi\) | ||||
−0.671850 | + | 0.740687i | \(0.734500\pi\) | |||||||
\(368\) | −1.83642 | −0.0957302 | ||||||||
\(369\) | 12.4762 | 0.649486 | ||||||||
\(370\) | −24.7803 | −1.28827 | ||||||||
\(371\) | 5.25315 | 0.272730 | ||||||||
\(372\) | 8.59340 | 0.445547 | ||||||||
\(373\) | 14.3450 | 0.742755 | 0.371378 | − | 0.928482i | \(-0.378886\pi\) | ||||
0.371378 | + | 0.928482i | \(0.378886\pi\) | |||||||
\(374\) | −20.5121 | −1.06066 | ||||||||
\(375\) | 11.6712 | 0.602699 | ||||||||
\(376\) | −8.05558 | −0.415435 | ||||||||
\(377\) | −26.4163 | −1.36051 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −6.54180 | −0.336030 | −0.168015 | − | 0.985784i | \(-0.553736\pi\) | ||||
−0.168015 | + | 0.985784i | \(0.553736\pi\) | |||||||
\(380\) | −1.12579 | −0.0577521 | ||||||||
\(381\) | 15.4919 | 0.793673 | ||||||||
\(382\) | −1.00000 | −0.0511645 | ||||||||
\(383\) | −1.70210 | −0.0869734 | −0.0434867 | − | 0.999054i | \(-0.513847\pi\) | ||||
−0.0434867 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −11.9963 | −0.611388 | ||||||||
\(386\) | 0.0643161 | 0.00327360 | ||||||||
\(387\) | −6.43569 | −0.327144 | ||||||||
\(388\) | −16.3823 | −0.831685 | ||||||||
\(389\) | −13.5361 | −0.686307 | −0.343153 | − | 0.939279i | \(-0.611495\pi\) | ||||
−0.343153 | + | 0.939279i | \(0.611495\pi\) | |||||||
\(390\) | 7.24411 | 0.366820 | ||||||||
\(391\) | −6.65748 | −0.336683 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 17.5231 | 0.883922 | ||||||||
\(394\) | 6.31491 | 0.318141 | ||||||||
\(395\) | −33.0887 | −1.66487 | ||||||||
\(396\) | −5.65813 | −0.284332 | ||||||||
\(397\) | −8.64242 | −0.433751 | −0.216875 | − | 0.976199i | \(-0.569586\pi\) | ||||
−0.216875 | + | 0.976199i | \(0.569586\pi\) | |||||||
\(398\) | 9.61618 | 0.482015 | ||||||||
\(399\) | 0.530988 | 0.0265827 | ||||||||
\(400\) | −0.504804 | −0.0252402 | ||||||||
\(401\) | 6.08530 | 0.303885 | 0.151943 | − | 0.988389i | \(-0.451447\pi\) | ||||
0.151943 | + | 0.988389i | \(0.451447\pi\) | |||||||
\(402\) | 0.347898 | 0.0173516 | ||||||||
\(403\) | 29.3614 | 1.46259 | ||||||||
\(404\) | −10.9489 | −0.544729 | ||||||||
\(405\) | 2.12019 | 0.105353 | ||||||||
\(406\) | 7.73144 | 0.383705 | ||||||||
\(407\) | 66.1311 | 3.27800 | ||||||||
\(408\) | −3.62524 | −0.179476 | ||||||||
\(409\) | −28.2163 | −1.39520 | −0.697602 | − | 0.716485i | \(-0.745750\pi\) | ||||
−0.697602 | + | 0.716485i | \(0.745750\pi\) | |||||||
\(410\) | 26.4519 | 1.30637 | ||||||||
\(411\) | 10.7313 | 0.529335 | ||||||||
\(412\) | −9.79451 | −0.482541 | ||||||||
\(413\) | 5.97094 | 0.293811 | ||||||||
\(414\) | −1.83642 | −0.0902553 | ||||||||
\(415\) | −28.4406 | −1.39610 | ||||||||
\(416\) | −3.41673 | −0.167519 | ||||||||
\(417\) | −19.8459 | −0.971856 | ||||||||
\(418\) | 3.00440 | 0.146950 | ||||||||
\(419\) | 28.2638 | 1.38078 | 0.690390 | − | 0.723438i | \(-0.257439\pi\) | ||||
0.690390 | + | 0.723438i | \(0.257439\pi\) | |||||||
\(420\) | −2.12019 | −0.103455 | ||||||||
\(421\) | 8.29174 | 0.404115 | 0.202057 | − | 0.979374i | \(-0.435237\pi\) | ||||
0.202057 | + | 0.979374i | \(0.435237\pi\) | |||||||
\(422\) | 16.0386 | 0.780748 | ||||||||
\(423\) | −8.05558 | −0.391676 | ||||||||
\(424\) | 5.25315 | 0.255116 | ||||||||
\(425\) | −1.83004 | −0.0887699 | ||||||||
\(426\) | 5.14641 | 0.249344 | ||||||||
\(427\) | 12.0771 | 0.584452 | ||||||||
\(428\) | −0.795378 | −0.0384461 | ||||||||
\(429\) | −19.3323 | −0.933373 | ||||||||
\(430\) | −13.6449 | −0.658014 | ||||||||
\(431\) | −6.44130 | −0.310266 | −0.155133 | − | 0.987894i | \(-0.549581\pi\) | ||||
−0.155133 | + | 0.987894i | \(0.549581\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 25.3953 | 1.22042 | 0.610211 | − | 0.792239i | \(-0.291085\pi\) | ||||
0.610211 | + | 0.792239i | \(0.291085\pi\) | |||||||
\(434\) | −8.59340 | −0.412497 | ||||||||
\(435\) | −16.3921 | −0.785942 | ||||||||
\(436\) | 14.3889 | 0.689104 | ||||||||
\(437\) | 0.975119 | 0.0466463 | ||||||||
\(438\) | 12.9220 | 0.617439 | ||||||||
\(439\) | −14.9239 | −0.712278 | −0.356139 | − | 0.934433i | \(-0.615907\pi\) | ||||
−0.356139 | + | 0.934433i | \(0.615907\pi\) | |||||||
\(440\) | −11.9963 | −0.571901 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −12.3865 | −0.589165 | ||||||||
\(443\) | 25.1056 | 1.19280 | 0.596402 | − | 0.802686i | \(-0.296596\pi\) | ||||
0.596402 | + | 0.802686i | \(0.296596\pi\) | |||||||
\(444\) | 11.6878 | 0.554679 | ||||||||
\(445\) | 32.6198 | 1.54632 | ||||||||
\(446\) | 19.9769 | 0.945932 | ||||||||
\(447\) | 12.2987 | 0.581706 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −37.7012 | −1.77923 | −0.889615 | − | 0.456712i | \(-0.849027\pi\) | ||||
−0.889615 | + | 0.456712i | \(0.849027\pi\) | |||||||
\(450\) | −0.504804 | −0.0237967 | ||||||||
\(451\) | −70.5921 | −3.32405 | ||||||||
\(452\) | −8.17372 | −0.384459 | ||||||||
\(453\) | −17.6647 | −0.829959 | ||||||||
\(454\) | 3.10798 | 0.145865 | ||||||||
\(455\) | −7.24411 | −0.339609 | ||||||||
\(456\) | 0.530988 | 0.0248658 | ||||||||
\(457\) | 3.99000 | 0.186644 | 0.0933221 | − | 0.995636i | \(-0.470251\pi\) | ||||
0.0933221 | + | 0.995636i | \(0.470251\pi\) | |||||||
\(458\) | 18.5609 | 0.867292 | ||||||||
\(459\) | −3.62524 | −0.169212 | ||||||||
\(460\) | −3.89356 | −0.181538 | ||||||||
\(461\) | 30.6319 | 1.42667 | 0.713336 | − | 0.700823i | \(-0.247184\pi\) | ||||
0.713336 | + | 0.700823i | \(0.247184\pi\) | |||||||
\(462\) | 5.65813 | 0.263240 | ||||||||
\(463\) | 17.6524 | 0.820377 | 0.410188 | − | 0.912001i | \(-0.365463\pi\) | ||||
0.410188 | + | 0.912001i | \(0.365463\pi\) | |||||||
\(464\) | 7.73144 | 0.358923 | ||||||||
\(465\) | 18.2196 | 0.844915 | ||||||||
\(466\) | 7.66569 | 0.355106 | ||||||||
\(467\) | −11.4024 | −0.527641 | −0.263820 | − | 0.964572i | \(-0.584983\pi\) | ||||
−0.263820 | + | 0.964572i | \(0.584983\pi\) | |||||||
\(468\) | −3.41673 | −0.157938 | ||||||||
\(469\) | −0.347898 | −0.0160644 | ||||||||
\(470\) | −17.0793 | −0.787811 | ||||||||
\(471\) | 18.2820 | 0.842391 | ||||||||
\(472\) | 5.97094 | 0.274835 | ||||||||
\(473\) | 36.4140 | 1.67432 | ||||||||
\(474\) | 15.6065 | 0.716830 | ||||||||
\(475\) | 0.268045 | 0.0122988 | ||||||||
\(476\) | 3.62524 | 0.166163 | ||||||||
\(477\) | 5.25315 | 0.240525 | ||||||||
\(478\) | −4.31275 | −0.197261 | ||||||||
\(479\) | −9.83500 | −0.449373 | −0.224686 | − | 0.974431i | \(-0.572136\pi\) | ||||
−0.224686 | + | 0.974431i | \(0.572136\pi\) | |||||||
\(480\) | −2.12019 | −0.0967729 | ||||||||
\(481\) | 39.9341 | 1.82084 | ||||||||
\(482\) | −28.8232 | −1.31286 | ||||||||
\(483\) | 1.83642 | 0.0835601 | ||||||||
\(484\) | 21.0145 | 0.955203 | ||||||||
\(485\) | −34.7336 | −1.57717 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 17.9436 | 0.813102 | 0.406551 | − | 0.913628i | \(-0.366731\pi\) | ||||
0.406551 | + | 0.913628i | \(0.366731\pi\) | |||||||
\(488\) | 12.0771 | 0.546705 | ||||||||
\(489\) | −8.89726 | −0.402348 | ||||||||
\(490\) | 2.12019 | 0.0957803 | ||||||||
\(491\) | 4.97688 | 0.224603 | 0.112302 | − | 0.993674i | \(-0.464178\pi\) | ||||
0.112302 | + | 0.993674i | \(0.464178\pi\) | |||||||
\(492\) | −12.4762 | −0.562472 | ||||||||
\(493\) | 28.0284 | 1.26233 | ||||||||
\(494\) | 1.81424 | 0.0816267 | ||||||||
\(495\) | −11.9963 | −0.539194 | ||||||||
\(496\) | −8.59340 | −0.385855 | ||||||||
\(497\) | −5.14641 | −0.230848 | ||||||||
\(498\) | 13.4142 | 0.601105 | ||||||||
\(499\) | −14.3583 | −0.642765 | −0.321382 | − | 0.946950i | \(-0.604147\pi\) | ||||
−0.321382 | + | 0.946950i | \(0.604147\pi\) | |||||||
\(500\) | −11.6712 | −0.521953 | ||||||||
\(501\) | −19.7895 | −0.884131 | ||||||||
\(502\) | 8.56547 | 0.382296 | ||||||||
\(503\) | 3.64411 | 0.162483 | 0.0812414 | − | 0.996694i | \(-0.474112\pi\) | ||||
0.0812414 | + | 0.996694i | \(0.474112\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −23.2138 | −1.03300 | ||||||||
\(506\) | 10.3907 | 0.461924 | ||||||||
\(507\) | 1.32595 | 0.0588873 | ||||||||
\(508\) | −15.4919 | −0.687341 | ||||||||
\(509\) | −20.6190 | −0.913919 | −0.456960 | − | 0.889487i | \(-0.651062\pi\) | ||||
−0.456960 | + | 0.889487i | \(0.651062\pi\) | |||||||
\(510\) | −7.68619 | −0.340350 | ||||||||
\(511\) | −12.9220 | −0.571638 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.530988 | 0.0234437 | ||||||||
\(514\) | −26.0282 | −1.14805 | ||||||||
\(515\) | −20.7662 | −0.915068 | ||||||||
\(516\) | 6.43569 | 0.283315 | ||||||||
\(517\) | 45.5795 | 2.00459 | ||||||||
\(518\) | −11.6878 | −0.513533 | ||||||||
\(519\) | 11.2793 | 0.495104 | ||||||||
\(520\) | −7.24411 | −0.317675 | ||||||||
\(521\) | 16.5313 | 0.724248 | 0.362124 | − | 0.932130i | \(-0.382052\pi\) | ||||
0.362124 | + | 0.932130i | \(0.382052\pi\) | |||||||
\(522\) | 7.73144 | 0.338396 | ||||||||
\(523\) | 20.6771 | 0.904147 | 0.452073 | − | 0.891981i | \(-0.350685\pi\) | ||||
0.452073 | + | 0.891981i | \(0.350685\pi\) | |||||||
\(524\) | −17.5231 | −0.765499 | ||||||||
\(525\) | 0.504804 | 0.0220315 | ||||||||
\(526\) | −6.37183 | −0.277825 | ||||||||
\(527\) | −31.1532 | −1.35705 | ||||||||
\(528\) | 5.65813 | 0.246239 | ||||||||
\(529\) | −19.6276 | −0.853372 | ||||||||
\(530\) | 11.1377 | 0.483790 | ||||||||
\(531\) | 5.97094 | 0.259117 | ||||||||
\(532\) | −0.530988 | −0.0230213 | ||||||||
\(533\) | −42.6279 | −1.84642 | ||||||||
\(534\) | −15.3853 | −0.665788 | ||||||||
\(535\) | −1.68635 | −0.0729073 | ||||||||
\(536\) | −0.347898 | −0.0150269 | ||||||||
\(537\) | 3.64668 | 0.157366 | ||||||||
\(538\) | −16.0331 | −0.691235 | ||||||||
\(539\) | −5.65813 | −0.243713 | ||||||||
\(540\) | −2.12019 | −0.0912383 | ||||||||
\(541\) | −11.7578 | −0.505507 | −0.252753 | − | 0.967531i | \(-0.581336\pi\) | ||||
−0.252753 | + | 0.967531i | \(0.581336\pi\) | |||||||
\(542\) | 22.3891 | 0.961693 | ||||||||
\(543\) | 1.91630 | 0.0822362 | ||||||||
\(544\) | 3.62524 | 0.155431 | ||||||||
\(545\) | 30.5072 | 1.30678 | ||||||||
\(546\) | 3.41673 | 0.146223 | ||||||||
\(547\) | 15.4976 | 0.662631 | 0.331316 | − | 0.943520i | \(-0.392507\pi\) | ||||
0.331316 | + | 0.943520i | \(0.392507\pi\) | |||||||
\(548\) | −10.7313 | −0.458418 | ||||||||
\(549\) | 12.0771 | 0.515438 | ||||||||
\(550\) | 2.85625 | 0.121791 | ||||||||
\(551\) | −4.10531 | −0.174892 | ||||||||
\(552\) | 1.83642 | 0.0781634 | ||||||||
\(553\) | −15.6065 | −0.663656 | ||||||||
\(554\) | 1.87730 | 0.0797588 | ||||||||
\(555\) | 24.7803 | 1.05187 | ||||||||
\(556\) | 19.8459 | 0.841652 | ||||||||
\(557\) | 5.34896 | 0.226643 | 0.113321 | − | 0.993558i | \(-0.463851\pi\) | ||||
0.113321 | + | 0.993558i | \(0.463851\pi\) | |||||||
\(558\) | −8.59340 | −0.363788 | ||||||||
\(559\) | 21.9890 | 0.930036 | ||||||||
\(560\) | 2.12019 | 0.0895943 | ||||||||
\(561\) | 20.5121 | 0.866022 | ||||||||
\(562\) | −1.54137 | −0.0650186 | ||||||||
\(563\) | 8.04695 | 0.339138 | 0.169569 | − | 0.985518i | \(-0.445762\pi\) | ||||
0.169569 | + | 0.985518i | \(0.445762\pi\) | |||||||
\(564\) | 8.05558 | 0.339201 | ||||||||
\(565\) | −17.3298 | −0.729071 | ||||||||
\(566\) | −15.7354 | −0.661409 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −5.14641 | −0.215939 | ||||||||
\(569\) | −13.5562 | −0.568304 | −0.284152 | − | 0.958779i | \(-0.591712\pi\) | ||||
−0.284152 | + | 0.958779i | \(0.591712\pi\) | |||||||
\(570\) | 1.12579 | 0.0471544 | ||||||||
\(571\) | 8.19030 | 0.342754 | 0.171377 | − | 0.985206i | \(-0.445178\pi\) | ||||
0.171377 | + | 0.985206i | \(0.445178\pi\) | |||||||
\(572\) | 19.3323 | 0.808325 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | 12.4762 | 0.520747 | ||||||||
\(575\) | 0.927035 | 0.0386600 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −29.8019 | −1.24067 | −0.620335 | − | 0.784337i | \(-0.713003\pi\) | ||||
−0.620335 | + | 0.784337i | \(0.713003\pi\) | |||||||
\(578\) | −3.85762 | −0.160456 | ||||||||
\(579\) | −0.0643161 | −0.00267288 | ||||||||
\(580\) | 16.3921 | 0.680645 | ||||||||
\(581\) | −13.4142 | −0.556515 | ||||||||
\(582\) | 16.3823 | 0.679068 | ||||||||
\(583\) | −29.7230 | −1.23100 | ||||||||
\(584\) | −12.9220 | −0.534718 | ||||||||
\(585\) | −7.24411 | −0.299507 | ||||||||
\(586\) | −3.70401 | −0.153011 | ||||||||
\(587\) | 2.15875 | 0.0891010 | 0.0445505 | − | 0.999007i | \(-0.485814\pi\) | ||||
0.0445505 | + | 0.999007i | \(0.485814\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 4.56300 | 0.188015 | ||||||||
\(590\) | 12.6595 | 0.521184 | ||||||||
\(591\) | −6.31491 | −0.259761 | ||||||||
\(592\) | −11.6878 | −0.480366 | ||||||||
\(593\) | −14.4005 | −0.591356 | −0.295678 | − | 0.955288i | \(-0.595546\pi\) | ||||
−0.295678 | + | 0.955288i | \(0.595546\pi\) | |||||||
\(594\) | 5.65813 | 0.232156 | ||||||||
\(595\) | 7.68619 | 0.315103 | ||||||||
\(596\) | −12.2987 | −0.503772 | ||||||||
\(597\) | −9.61618 | −0.393564 | ||||||||
\(598\) | 6.27456 | 0.256586 | ||||||||
\(599\) | −8.37404 | −0.342154 | −0.171077 | − | 0.985258i | \(-0.554725\pi\) | ||||
−0.171077 | + | 0.985258i | \(0.554725\pi\) | |||||||
\(600\) | 0.504804 | 0.0206086 | ||||||||
\(601\) | 21.3849 | 0.872309 | 0.436155 | − | 0.899872i | \(-0.356340\pi\) | ||||
0.436155 | + | 0.899872i | \(0.356340\pi\) | |||||||
\(602\) | −6.43569 | −0.262299 | ||||||||
\(603\) | −0.347898 | −0.0141675 | ||||||||
\(604\) | 17.6647 | 0.718766 | ||||||||
\(605\) | 44.5546 | 1.81140 | ||||||||
\(606\) | 10.9489 | 0.444770 | ||||||||
\(607\) | −22.7477 | −0.923301 | −0.461651 | − | 0.887062i | \(-0.652743\pi\) | ||||
−0.461651 | + | 0.887062i | \(0.652743\pi\) | |||||||
\(608\) | −0.530988 | −0.0215344 | ||||||||
\(609\) | −7.73144 | −0.313294 | ||||||||
\(610\) | 25.6057 | 1.03674 | ||||||||
\(611\) | 27.5238 | 1.11349 | ||||||||
\(612\) | 3.62524 | 0.146542 | ||||||||
\(613\) | 8.38344 | 0.338604 | 0.169302 | − | 0.985564i | \(-0.445849\pi\) | ||||
0.169302 | + | 0.985564i | \(0.445849\pi\) | |||||||
\(614\) | −18.3234 | −0.739472 | ||||||||
\(615\) | −26.4519 | −1.06664 | ||||||||
\(616\) | −5.65813 | −0.227973 | ||||||||
\(617\) | −30.0978 | −1.21169 | −0.605847 | − | 0.795581i | \(-0.707166\pi\) | ||||
−0.605847 | + | 0.795581i | \(0.707166\pi\) | |||||||
\(618\) | 9.79451 | 0.393993 | ||||||||
\(619\) | −18.8535 | −0.757785 | −0.378892 | − | 0.925441i | \(-0.623695\pi\) | ||||
−0.378892 | + | 0.925441i | \(0.623695\pi\) | |||||||
\(620\) | −18.2196 | −0.731718 | ||||||||
\(621\) | 1.83642 | 0.0736931 | ||||||||
\(622\) | −19.4591 | −0.780240 | ||||||||
\(623\) | 15.3853 | 0.616400 | ||||||||
\(624\) | 3.41673 | 0.136779 | ||||||||
\(625\) | −22.2212 | −0.888846 | ||||||||
\(626\) | 7.82362 | 0.312695 | ||||||||
\(627\) | −3.00440 | −0.119984 | ||||||||
\(628\) | −18.2820 | −0.729532 | ||||||||
\(629\) | −42.3711 | −1.68945 | ||||||||
\(630\) | 2.12019 | 0.0844703 | ||||||||
\(631\) | 4.80622 | 0.191332 | 0.0956662 | − | 0.995413i | \(-0.469502\pi\) | ||||
0.0956662 | + | 0.995413i | \(0.469502\pi\) | |||||||
\(632\) | −15.6065 | −0.620793 | ||||||||
\(633\) | −16.0386 | −0.637478 | ||||||||
\(634\) | −1.62203 | −0.0644189 | ||||||||
\(635\) | −32.8457 | −1.30344 | ||||||||
\(636\) | −5.25315 | −0.208301 | ||||||||
\(637\) | −3.41673 | −0.135376 | ||||||||
\(638\) | −43.7455 | −1.73190 | ||||||||
\(639\) | −5.14641 | −0.203589 | ||||||||
\(640\) | 2.12019 | 0.0838078 | ||||||||
\(641\) | −15.0629 | −0.594950 | −0.297475 | − | 0.954730i | \(-0.596144\pi\) | ||||
−0.297475 | + | 0.954730i | \(0.596144\pi\) | |||||||
\(642\) | 0.795378 | 0.0313911 | ||||||||
\(643\) | −48.3680 | −1.90745 | −0.953723 | − | 0.300686i | \(-0.902784\pi\) | ||||
−0.953723 | + | 0.300686i | \(0.902784\pi\) | |||||||
\(644\) | −1.83642 | −0.0723652 | ||||||||
\(645\) | 13.6449 | 0.537266 | ||||||||
\(646\) | −1.92496 | −0.0757366 | ||||||||
\(647\) | −8.55762 | −0.336435 | −0.168217 | − | 0.985750i | \(-0.553801\pi\) | ||||
−0.168217 | + | 0.985750i | \(0.553801\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −33.7843 | −1.32615 | ||||||||
\(650\) | 1.72478 | 0.0676515 | ||||||||
\(651\) | 8.59340 | 0.336802 | ||||||||
\(652\) | 8.89726 | 0.348444 | ||||||||
\(653\) | 8.98741 | 0.351705 | 0.175852 | − | 0.984417i | \(-0.443732\pi\) | ||||
0.175852 | + | 0.984417i | \(0.443732\pi\) | |||||||
\(654\) | −14.3889 | −0.562651 | ||||||||
\(655\) | −37.1522 | −1.45166 | ||||||||
\(656\) | 12.4762 | 0.487115 | ||||||||
\(657\) | −12.9220 | −0.504137 | ||||||||
\(658\) | −8.05558 | −0.314039 | ||||||||
\(659\) | −21.4718 | −0.836421 | −0.418210 | − | 0.908350i | \(-0.637343\pi\) | ||||
−0.418210 | + | 0.908350i | \(0.637343\pi\) | |||||||
\(660\) | 11.9963 | 0.466955 | ||||||||
\(661\) | 31.8319 | 1.23812 | 0.619060 | − | 0.785344i | \(-0.287514\pi\) | ||||
0.619060 | + | 0.785344i | \(0.287514\pi\) | |||||||
\(662\) | 5.80972 | 0.225801 | ||||||||
\(663\) | 12.3865 | 0.481051 | ||||||||
\(664\) | −13.4142 | −0.520572 | ||||||||
\(665\) | −1.12579 | −0.0436565 | ||||||||
\(666\) | −11.6878 | −0.452893 | ||||||||
\(667\) | −14.1982 | −0.549757 | ||||||||
\(668\) | 19.7895 | 0.765680 | ||||||||
\(669\) | −19.9769 | −0.772350 | ||||||||
\(670\) | −0.737609 | −0.0284963 | ||||||||
\(671\) | −68.3338 | −2.63800 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 9.52768 | 0.367265 | 0.183633 | − | 0.982995i | \(-0.441214\pi\) | ||||
0.183633 | + | 0.982995i | \(0.441214\pi\) | |||||||
\(674\) | 34.2577 | 1.31956 | ||||||||
\(675\) | 0.504804 | 0.0194299 | ||||||||
\(676\) | −1.32595 | −0.0509979 | ||||||||
\(677\) | −1.47448 | −0.0566690 | −0.0283345 | − | 0.999598i | \(-0.509020\pi\) | ||||
−0.0283345 | + | 0.999598i | \(0.509020\pi\) | |||||||
\(678\) | 8.17372 | 0.313910 | ||||||||
\(679\) | −16.3823 | −0.628695 | ||||||||
\(680\) | 7.68619 | 0.294752 | ||||||||
\(681\) | −3.10798 | −0.119098 | ||||||||
\(682\) | 48.6226 | 1.86186 | ||||||||
\(683\) | −18.4990 | −0.707843 | −0.353921 | − | 0.935275i | \(-0.615152\pi\) | ||||
−0.353921 | + | 0.935275i | \(0.615152\pi\) | |||||||
\(684\) | −0.530988 | −0.0203028 | ||||||||
\(685\) | −22.7523 | −0.869322 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −18.5609 | −0.708141 | ||||||||
\(688\) | −6.43569 | −0.245358 | ||||||||
\(689\) | −17.9486 | −0.683788 | ||||||||
\(690\) | 3.89356 | 0.148225 | ||||||||
\(691\) | −40.3726 | −1.53584 | −0.767922 | − | 0.640543i | \(-0.778709\pi\) | ||||
−0.767922 | + | 0.640543i | \(0.778709\pi\) | |||||||
\(692\) | −11.2793 | −0.428773 | ||||||||
\(693\) | −5.65813 | −0.214935 | ||||||||
\(694\) | 0.654394 | 0.0248405 | ||||||||
\(695\) | 42.0770 | 1.59607 | ||||||||
\(696\) | −7.73144 | −0.293060 | ||||||||
\(697\) | 45.2293 | 1.71318 | ||||||||
\(698\) | 20.2461 | 0.766326 | ||||||||
\(699\) | −7.66569 | −0.289943 | ||||||||
\(700\) | −0.504804 | −0.0190798 | ||||||||
\(701\) | 17.1461 | 0.647600 | 0.323800 | − | 0.946126i | \(-0.395040\pi\) | ||||
0.323800 | + | 0.946126i | \(0.395040\pi\) | |||||||
\(702\) | 3.41673 | 0.128956 | ||||||||
\(703\) | 6.20609 | 0.234067 | ||||||||
\(704\) | −5.65813 | −0.213249 | ||||||||
\(705\) | 17.0793 | 0.643245 | ||||||||
\(706\) | −11.9714 | −0.450549 | ||||||||
\(707\) | −10.9489 | −0.411777 | ||||||||
\(708\) | −5.97094 | −0.224402 | ||||||||
\(709\) | 28.5871 | 1.07361 | 0.536806 | − | 0.843706i | \(-0.319631\pi\) | ||||
0.536806 | + | 0.843706i | \(0.319631\pi\) | |||||||
\(710\) | −10.9114 | −0.409496 | ||||||||
\(711\) | −15.6065 | −0.585289 | ||||||||
\(712\) | 15.3853 | 0.576589 | ||||||||
\(713\) | 15.7811 | 0.591008 | ||||||||
\(714\) | −3.62524 | −0.135671 | ||||||||
\(715\) | 40.9881 | 1.53287 | ||||||||
\(716\) | −3.64668 | −0.136283 | ||||||||
\(717\) | 4.31275 | 0.161063 | ||||||||
\(718\) | 24.6520 | 0.920005 | ||||||||
\(719\) | 36.8258 | 1.37337 | 0.686685 | − | 0.726955i | \(-0.259065\pi\) | ||||
0.686685 | + | 0.726955i | \(0.259065\pi\) | |||||||
\(720\) | 2.12019 | 0.0790147 | ||||||||
\(721\) | −9.79451 | −0.364767 | ||||||||
\(722\) | −18.7181 | −0.696614 | ||||||||
\(723\) | 28.8232 | 1.07195 | ||||||||
\(724\) | −1.91630 | −0.0712186 | ||||||||
\(725\) | −3.90287 | −0.144949 | ||||||||
\(726\) | −21.0145 | −0.779920 | ||||||||
\(727\) | −36.5052 | −1.35390 | −0.676951 | − | 0.736028i | \(-0.736699\pi\) | ||||
−0.676951 | + | 0.736028i | \(0.736699\pi\) | |||||||
\(728\) | −3.41673 | −0.126632 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.3972 | −1.01401 | ||||||||
\(731\) | −23.3309 | −0.862925 | ||||||||
\(732\) | −12.0771 | −0.446382 | ||||||||
\(733\) | −4.78136 | −0.176604 | −0.0883019 | − | 0.996094i | \(-0.528144\pi\) | ||||
−0.0883019 | + | 0.996094i | \(0.528144\pi\) | |||||||
\(734\) | −25.7416 | −0.950140 | ||||||||
\(735\) | −2.12019 | −0.0782043 | ||||||||
\(736\) | −1.83642 | −0.0676915 | ||||||||
\(737\) | 1.96845 | 0.0725089 | ||||||||
\(738\) | 12.4762 | 0.459256 | ||||||||
\(739\) | 2.78479 | 0.102440 | 0.0512201 | − | 0.998687i | \(-0.483689\pi\) | ||||
0.0512201 | + | 0.998687i | \(0.483689\pi\) | |||||||
\(740\) | −24.7803 | −0.910943 | ||||||||
\(741\) | −1.81424 | −0.0666479 | ||||||||
\(742\) | 5.25315 | 0.192849 | ||||||||
\(743\) | −19.0883 | −0.700282 | −0.350141 | − | 0.936697i | \(-0.613866\pi\) | ||||
−0.350141 | + | 0.936697i | \(0.613866\pi\) | |||||||
\(744\) | 8.59340 | 0.315049 | ||||||||
\(745\) | −26.0755 | −0.955331 | ||||||||
\(746\) | 14.3450 | 0.525207 | ||||||||
\(747\) | −13.4142 | −0.490800 | ||||||||
\(748\) | −20.5121 | −0.749997 | ||||||||
\(749\) | −0.795378 | −0.0290625 | ||||||||
\(750\) | 11.6712 | 0.426173 | ||||||||
\(751\) | −11.6462 | −0.424976 | −0.212488 | − | 0.977164i | \(-0.568157\pi\) | ||||
−0.212488 | + | 0.977164i | \(0.568157\pi\) | |||||||
\(752\) | −8.05558 | −0.293757 | ||||||||
\(753\) | −8.56547 | −0.312143 | ||||||||
\(754\) | −26.4163 | −0.962024 | ||||||||
\(755\) | 37.4524 | 1.36303 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 4.55068 | 0.165397 | 0.0826986 | − | 0.996575i | \(-0.473646\pi\) | ||||
0.0826986 | + | 0.996575i | \(0.473646\pi\) | |||||||
\(758\) | −6.54180 | −0.237609 | ||||||||
\(759\) | −10.3907 | −0.377159 | ||||||||
\(760\) | −1.12579 | −0.0408369 | ||||||||
\(761\) | 51.8367 | 1.87908 | 0.939539 | − | 0.342443i | \(-0.111254\pi\) | ||||
0.939539 | + | 0.342443i | \(0.111254\pi\) | |||||||
\(762\) | 15.4919 | 0.561212 | ||||||||
\(763\) | 14.3889 | 0.520914 | ||||||||
\(764\) | −1.00000 | −0.0361787 | ||||||||
\(765\) | 7.68619 | 0.277895 | ||||||||
\(766\) | −1.70210 | −0.0614995 | ||||||||
\(767\) | −20.4011 | −0.736641 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −35.7537 | −1.28931 | −0.644655 | − | 0.764474i | \(-0.722999\pi\) | ||||
−0.644655 | + | 0.764474i | \(0.722999\pi\) | |||||||
\(770\) | −11.9963 | −0.432317 | ||||||||
\(771\) | 26.0282 | 0.937381 | ||||||||
\(772\) | 0.0643161 | 0.00231479 | ||||||||
\(773\) | −2.01138 | −0.0723442 | −0.0361721 | − | 0.999346i | \(-0.511516\pi\) | ||||
−0.0361721 | + | 0.999346i | \(0.511516\pi\) | |||||||
\(774\) | −6.43569 | −0.231326 | ||||||||
\(775\) | 4.33799 | 0.155825 | ||||||||
\(776\) | −16.3823 | −0.588090 | ||||||||
\(777\) | 11.6878 | 0.419298 | ||||||||
\(778\) | −13.5361 | −0.485292 | ||||||||
\(779\) | −6.62473 | −0.237356 | ||||||||
\(780\) | 7.24411 | 0.259381 | ||||||||
\(781\) | 29.1191 | 1.04196 | ||||||||
\(782\) | −6.65748 | −0.238071 | ||||||||
\(783\) | −7.73144 | −0.276299 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −38.7613 | −1.38345 | ||||||||
\(786\) | 17.5231 | 0.625028 | ||||||||
\(787\) | 7.92134 | 0.282365 | 0.141183 | − | 0.989984i | \(-0.454910\pi\) | ||||
0.141183 | + | 0.989984i | \(0.454910\pi\) | |||||||
\(788\) | 6.31491 | 0.224959 | ||||||||
\(789\) | 6.37183 | 0.226843 | ||||||||
\(790\) | −33.0887 | −1.17724 | ||||||||
\(791\) | −8.17372 | −0.290624 | ||||||||
\(792\) | −5.65813 | −0.201053 | ||||||||
\(793\) | −41.2642 | −1.46533 | ||||||||
\(794\) | −8.64242 | −0.306708 | ||||||||
\(795\) | −11.1377 | −0.395013 | ||||||||
\(796\) | 9.61618 | 0.340836 | ||||||||
\(797\) | 10.9960 | 0.389499 | 0.194749 | − | 0.980853i | \(-0.437611\pi\) | ||||
0.194749 | + | 0.980853i | \(0.437611\pi\) | |||||||
\(798\) | 0.530988 | 0.0187968 | ||||||||
\(799\) | −29.2034 | −1.03314 | ||||||||
\(800\) | −0.504804 | −0.0178475 | ||||||||
\(801\) | 15.3853 | 0.543613 | ||||||||
\(802\) | 6.08530 | 0.214879 | ||||||||
\(803\) | 73.1146 | 2.58016 | ||||||||
\(804\) | 0.347898 | 0.0122694 | ||||||||
\(805\) | −3.89356 | −0.137230 | ||||||||
\(806\) | 29.3614 | 1.03421 | ||||||||
\(807\) | 16.0331 | 0.564391 | ||||||||
\(808\) | −10.9489 | −0.385182 | ||||||||
\(809\) | 49.8017 | 1.75093 | 0.875467 | − | 0.483278i | \(-0.160554\pi\) | ||||
0.875467 | + | 0.483278i | \(0.160554\pi\) | |||||||
\(810\) | 2.12019 | 0.0744958 | ||||||||
\(811\) | 10.8964 | 0.382626 | 0.191313 | − | 0.981529i | \(-0.438725\pi\) | ||||
0.191313 | + | 0.981529i | \(0.438725\pi\) | |||||||
\(812\) | 7.73144 | 0.271321 | ||||||||
\(813\) | −22.3891 | −0.785219 | ||||||||
\(814\) | 66.1311 | 2.31790 | ||||||||
\(815\) | 18.8639 | 0.660773 | ||||||||
\(816\) | −3.62524 | −0.126909 | ||||||||
\(817\) | 3.41727 | 0.119555 | ||||||||
\(818\) | −28.2163 | −0.986558 | ||||||||
\(819\) | −3.41673 | −0.119390 | ||||||||
\(820\) | 26.4519 | 0.923742 | ||||||||
\(821\) | 45.3251 | 1.58186 | 0.790929 | − | 0.611908i | \(-0.209598\pi\) | ||||
0.790929 | + | 0.611908i | \(0.209598\pi\) | |||||||
\(822\) | 10.7313 | 0.374297 | ||||||||
\(823\) | 18.2341 | 0.635599 | 0.317800 | − | 0.948158i | \(-0.397056\pi\) | ||||
0.317800 | + | 0.948158i | \(0.397056\pi\) | |||||||
\(824\) | −9.79451 | −0.341208 | ||||||||
\(825\) | −2.85625 | −0.0994419 | ||||||||
\(826\) | 5.97094 | 0.207755 | ||||||||
\(827\) | 57.3076 | 1.99278 | 0.996391 | − | 0.0848816i | \(-0.0270512\pi\) | ||||
0.996391 | + | 0.0848816i | \(0.0270512\pi\) | |||||||
\(828\) | −1.83642 | −0.0638201 | ||||||||
\(829\) | −2.15392 | −0.0748087 | −0.0374043 | − | 0.999300i | \(-0.511909\pi\) | ||||
−0.0374043 | + | 0.999300i | \(0.511909\pi\) | |||||||
\(830\) | −28.4406 | −0.987189 | ||||||||
\(831\) | −1.87730 | −0.0651228 | ||||||||
\(832\) | −3.41673 | −0.118454 | ||||||||
\(833\) | 3.62524 | 0.125607 | ||||||||
\(834\) | −19.8459 | −0.687206 | ||||||||
\(835\) | 41.9575 | 1.45200 | ||||||||
\(836\) | 3.00440 | 0.103909 | ||||||||
\(837\) | 8.59340 | 0.297032 | ||||||||
\(838\) | 28.2638 | 0.976358 | ||||||||
\(839\) | 15.7268 | 0.542948 | 0.271474 | − | 0.962446i | \(-0.412489\pi\) | ||||
0.271474 | + | 0.962446i | \(0.412489\pi\) | |||||||
\(840\) | −2.12019 | −0.0731534 | ||||||||
\(841\) | 30.7752 | 1.06121 | ||||||||
\(842\) | 8.29174 | 0.285752 | ||||||||
\(843\) | 1.54137 | 0.0530875 | ||||||||
\(844\) | 16.0386 | 0.552072 | ||||||||
\(845\) | −2.81125 | −0.0967101 | ||||||||
\(846\) | −8.05558 | −0.276957 | ||||||||
\(847\) | 21.0145 | 0.722065 | ||||||||
\(848\) | 5.25315 | 0.180394 | ||||||||
\(849\) | 15.7354 | 0.540038 | ||||||||
\(850\) | −1.83004 | −0.0627698 | ||||||||
\(851\) | 21.4638 | 0.735768 | ||||||||
\(852\) | 5.14641 | 0.176313 | ||||||||
\(853\) | −1.58582 | −0.0542976 | −0.0271488 | − | 0.999631i | \(-0.508643\pi\) | ||||
−0.0271488 | + | 0.999631i | \(0.508643\pi\) | |||||||
\(854\) | 12.0771 | 0.413270 | ||||||||
\(855\) | −1.12579 | −0.0385014 | ||||||||
\(856\) | −0.795378 | −0.0271855 | ||||||||
\(857\) | −9.13838 | −0.312161 | −0.156081 | − | 0.987744i | \(-0.549886\pi\) | ||||
−0.156081 | + | 0.987744i | \(0.549886\pi\) | |||||||
\(858\) | −19.3323 | −0.659994 | ||||||||
\(859\) | 12.4840 | 0.425948 | 0.212974 | − | 0.977058i | \(-0.431685\pi\) | ||||
0.212974 | + | 0.977058i | \(0.431685\pi\) | |||||||
\(860\) | −13.6449 | −0.465286 | ||||||||
\(861\) | −12.4762 | −0.425189 | ||||||||
\(862\) | −6.44130 | −0.219391 | ||||||||
\(863\) | −30.9644 | −1.05404 | −0.527020 | − | 0.849853i | \(-0.676691\pi\) | ||||
−0.527020 | + | 0.849853i | \(0.676691\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −23.9141 | −0.813105 | ||||||||
\(866\) | 25.3953 | 0.862969 | ||||||||
\(867\) | 3.85762 | 0.131012 | ||||||||
\(868\) | −8.59340 | −0.291679 | ||||||||
\(869\) | 88.3036 | 2.99550 | ||||||||
\(870\) | −16.3921 | −0.555745 | ||||||||
\(871\) | 1.18867 | 0.0402767 | ||||||||
\(872\) | 14.3889 | 0.487270 | ||||||||
\(873\) | −16.3823 | −0.554457 | ||||||||
\(874\) | 0.975119 | 0.0329839 | ||||||||
\(875\) | −11.6712 | −0.394559 | ||||||||
\(876\) | 12.9220 | 0.436595 | ||||||||
\(877\) | 13.4456 | 0.454025 | 0.227012 | − | 0.973892i | \(-0.427104\pi\) | ||||
0.227012 | + | 0.973892i | \(0.427104\pi\) | |||||||
\(878\) | −14.9239 | −0.503657 | ||||||||
\(879\) | 3.70401 | 0.124933 | ||||||||
\(880\) | −11.9963 | −0.404395 | ||||||||
\(881\) | −51.6111 | −1.73882 | −0.869412 | − | 0.494089i | \(-0.835502\pi\) | ||||
−0.869412 | + | 0.494089i | \(0.835502\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 20.3553 | 0.685009 | 0.342504 | − | 0.939516i | \(-0.388725\pi\) | ||||
0.342504 | + | 0.939516i | \(0.388725\pi\) | |||||||
\(884\) | −12.3865 | −0.416602 | ||||||||
\(885\) | −12.6595 | −0.425545 | ||||||||
\(886\) | 25.1056 | 0.843440 | ||||||||
\(887\) | −11.6889 | −0.392475 | −0.196238 | − | 0.980556i | \(-0.562872\pi\) | ||||
−0.196238 | + | 0.980556i | \(0.562872\pi\) | |||||||
\(888\) | 11.6878 | 0.392217 | ||||||||
\(889\) | −15.4919 | −0.519581 | ||||||||
\(890\) | 32.6198 | 1.09342 | ||||||||
\(891\) | −5.65813 | −0.189555 | ||||||||
\(892\) | 19.9769 | 0.668875 | ||||||||
\(893\) | 4.27742 | 0.143138 | ||||||||
\(894\) | 12.2987 | 0.411328 | ||||||||
\(895\) | −7.73164 | −0.258440 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −6.27456 | −0.209502 | ||||||||
\(898\) | −37.7012 | −1.25811 | ||||||||
\(899\) | −66.4394 | −2.21588 | ||||||||
\(900\) | −0.504804 | −0.0168268 | ||||||||
\(901\) | 19.0440 | 0.634446 | ||||||||
\(902\) | −70.5921 | −2.35046 | ||||||||
\(903\) | 6.43569 | 0.214166 | ||||||||
\(904\) | −8.17372 | −0.271854 | ||||||||
\(905\) | −4.06291 | −0.135056 | ||||||||
\(906\) | −17.6647 | −0.586870 | ||||||||
\(907\) | 40.3018 | 1.33820 | 0.669100 | − | 0.743172i | \(-0.266680\pi\) | ||||
0.669100 | + | 0.743172i | \(0.266680\pi\) | |||||||
\(908\) | 3.10798 | 0.103142 | ||||||||
\(909\) | −10.9489 | −0.363153 | ||||||||
\(910\) | −7.24411 | −0.240140 | ||||||||
\(911\) | −44.8871 | −1.48718 | −0.743588 | − | 0.668638i | \(-0.766877\pi\) | ||||
−0.743588 | + | 0.668638i | \(0.766877\pi\) | |||||||
\(912\) | 0.530988 | 0.0175828 | ||||||||
\(913\) | 75.8993 | 2.51190 | ||||||||
\(914\) | 3.99000 | 0.131977 | ||||||||
\(915\) | −25.6057 | −0.846499 | ||||||||
\(916\) | 18.5609 | 0.613268 | ||||||||
\(917\) | −17.5231 | −0.578663 | ||||||||
\(918\) | −3.62524 | −0.119651 | ||||||||
\(919\) | −40.0817 | −1.32217 | −0.661087 | − | 0.750309i | \(-0.729905\pi\) | ||||
−0.661087 | + | 0.750309i | \(0.729905\pi\) | |||||||
\(920\) | −3.89356 | −0.128367 | ||||||||
\(921\) | 18.3234 | 0.603776 | ||||||||
\(922\) | 30.6319 | 1.00881 | ||||||||
\(923\) | 17.5839 | 0.578781 | ||||||||
\(924\) | 5.65813 | 0.186139 | ||||||||
\(925\) | 5.90006 | 0.193993 | ||||||||
\(926\) | 17.6524 | 0.580094 | ||||||||
\(927\) | −9.79451 | −0.321694 | ||||||||
\(928\) | 7.73144 | 0.253797 | ||||||||
\(929\) | 34.4310 | 1.12964 | 0.564822 | − | 0.825213i | \(-0.308945\pi\) | ||||
0.564822 | + | 0.825213i | \(0.308945\pi\) | |||||||
\(930\) | 18.2196 | 0.597445 | ||||||||
\(931\) | −0.530988 | −0.0174024 | ||||||||
\(932\) | 7.66569 | 0.251098 | ||||||||
\(933\) | 19.4591 | 0.637063 | ||||||||
\(934\) | −11.4024 | −0.373098 | ||||||||
\(935\) | −43.4895 | −1.42226 | ||||||||
\(936\) | −3.41673 | −0.111679 | ||||||||
\(937\) | −29.4960 | −0.963593 | −0.481797 | − | 0.876283i | \(-0.660016\pi\) | ||||
−0.481797 | + | 0.876283i | \(0.660016\pi\) | |||||||
\(938\) | −0.347898 | −0.0113593 | ||||||||
\(939\) | −7.82362 | −0.255314 | ||||||||
\(940\) | −17.0793 | −0.557067 | ||||||||
\(941\) | 35.0316 | 1.14200 | 0.570998 | − | 0.820951i | \(-0.306556\pi\) | ||||
0.570998 | + | 0.820951i | \(0.306556\pi\) | |||||||
\(942\) | 18.2820 | 0.595661 | ||||||||
\(943\) | −22.9116 | −0.746105 | ||||||||
\(944\) | 5.97094 | 0.194337 | ||||||||
\(945\) | −2.12019 | −0.0689697 | ||||||||
\(946\) | 36.4140 | 1.18392 | ||||||||
\(947\) | 3.67687 | 0.119482 | 0.0597410 | − | 0.998214i | \(-0.480973\pi\) | ||||
0.0597410 | + | 0.998214i | \(0.480973\pi\) | |||||||
\(948\) | 15.6065 | 0.506876 | ||||||||
\(949\) | 44.1512 | 1.43321 | ||||||||
\(950\) | 0.268045 | 0.00869654 | ||||||||
\(951\) | 1.62203 | 0.0525978 | ||||||||
\(952\) | 3.62524 | 0.117495 | ||||||||
\(953\) | −49.4895 | −1.60312 | −0.801561 | − | 0.597913i | \(-0.795997\pi\) | ||||
−0.801561 | + | 0.597913i | \(0.795997\pi\) | |||||||
\(954\) | 5.25315 | 0.170077 | ||||||||
\(955\) | −2.12019 | −0.0686077 | ||||||||
\(956\) | −4.31275 | −0.139484 | ||||||||
\(957\) | 43.7455 | 1.41409 | ||||||||
\(958\) | −9.83500 | −0.317755 | ||||||||
\(959\) | −10.7313 | −0.346531 | ||||||||
\(960\) | −2.12019 | −0.0684288 | ||||||||
\(961\) | 42.8466 | 1.38215 | ||||||||
\(962\) | 39.9341 | 1.28753 | ||||||||
\(963\) | −0.795378 | −0.0256307 | ||||||||
\(964\) | −28.8232 | −0.928334 | ||||||||
\(965\) | 0.136362 | 0.00438965 | ||||||||
\(966\) | 1.83642 | 0.0590859 | ||||||||
\(967\) | 45.2145 | 1.45400 | 0.727001 | − | 0.686637i | \(-0.240914\pi\) | ||||
0.727001 | + | 0.686637i | \(0.240914\pi\) | |||||||
\(968\) | 21.0145 | 0.675430 | ||||||||
\(969\) | 1.92496 | 0.0618387 | ||||||||
\(970\) | −34.7336 | −1.11523 | ||||||||
\(971\) | 4.84691 | 0.155545 | 0.0777723 | − | 0.996971i | \(-0.475219\pi\) | ||||
0.0777723 | + | 0.996971i | \(0.475219\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 19.8459 | 0.636229 | ||||||||
\(974\) | 17.9436 | 0.574950 | ||||||||
\(975\) | −1.72478 | −0.0552372 | ||||||||
\(976\) | 12.0771 | 0.386578 | ||||||||
\(977\) | 7.92023 | 0.253391 | 0.126695 | − | 0.991942i | \(-0.459563\pi\) | ||||
0.126695 | + | 0.991942i | \(0.459563\pi\) | |||||||
\(978\) | −8.89726 | −0.284503 | ||||||||
\(979\) | −87.0521 | −2.78220 | ||||||||
\(980\) | 2.12019 | 0.0677269 | ||||||||
\(981\) | 14.3889 | 0.459403 | ||||||||
\(982\) | 4.97688 | 0.158819 | ||||||||
\(983\) | −56.4428 | −1.80025 | −0.900123 | − | 0.435637i | \(-0.856523\pi\) | ||||
−0.900123 | + | 0.435637i | \(0.856523\pi\) | |||||||
\(984\) | −12.4762 | −0.397727 | ||||||||
\(985\) | 13.3888 | 0.426603 | ||||||||
\(986\) | 28.0284 | 0.892605 | ||||||||
\(987\) | 8.05558 | 0.256412 | ||||||||
\(988\) | 1.81424 | 0.0577188 | ||||||||
\(989\) | 11.8186 | 0.375811 | ||||||||
\(990\) | −11.9963 | −0.381267 | ||||||||
\(991\) | −19.0966 | −0.606624 | −0.303312 | − | 0.952891i | \(-0.598093\pi\) | ||||
−0.303312 | + | 0.952891i | \(0.598093\pi\) | |||||||
\(992\) | −8.59340 | −0.272841 | ||||||||
\(993\) | −5.80972 | −0.184366 | ||||||||
\(994\) | −5.14641 | −0.163234 | ||||||||
\(995\) | 20.3881 | 0.646346 | ||||||||
\(996\) | 13.4142 | 0.425045 | ||||||||
\(997\) | −6.66164 | −0.210976 | −0.105488 | − | 0.994421i | \(-0.533640\pi\) | ||||
−0.105488 | + | 0.994421i | \(0.533640\pi\) | |||||||
\(998\) | −14.3583 | −0.454503 | ||||||||
\(999\) | 11.6878 | 0.369786 |
(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 | 8022.2.a.p.1.8 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8022.2.a.p.1.8 | ✓ | 9 | 1.1 | even | 1 | trivial |