Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 18x^{5} - 8x^{4} + 51x^{3} + 47x^{2} - 2x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1338) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.01737\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.79108 | −1.69542 | −0.847711 | − | 0.530459i | \(-0.822020\pi\) | ||||
−0.847711 | + | 0.530459i | \(0.822020\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.04653 | −0.773515 | −0.386758 | − | 0.922181i | \(-0.626405\pi\) | ||||
−0.386758 | + | 0.922181i | \(0.626405\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.79108 | 1.19884 | ||||||||
\(11\) | 3.58410 | 1.08065 | 0.540324 | − | 0.841457i | \(-0.318302\pi\) | ||||
0.540324 | + | 0.841457i | \(0.318302\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.68304 | −0.466791 | −0.233396 | − | 0.972382i | \(-0.574984\pi\) | ||||
−0.233396 | + | 0.972382i | \(0.574984\pi\) | |||||||
\(14\) | 2.04653 | 0.546958 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.06098 | −1.71254 | −0.856270 | − | 0.516528i | \(-0.827224\pi\) | ||||
−0.856270 | + | 0.516528i | \(0.827224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.27006 | 1.43845 | 0.719225 | − | 0.694777i | \(-0.244497\pi\) | ||||
0.719225 | + | 0.694777i | \(0.244497\pi\) | |||||||
\(20\) | −3.79108 | −0.847711 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.58410 | −0.764133 | ||||||||
\(23\) | −5.91836 | −1.23406 | −0.617032 | − | 0.786938i | \(-0.711665\pi\) | ||||
−0.617032 | + | 0.786938i | \(0.711665\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.37227 | 1.87445 | ||||||||
\(26\) | 1.68304 | 0.330071 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.04653 | −0.386758 | ||||||||
\(29\) | −1.71227 | −0.317961 | −0.158981 | − | 0.987282i | \(-0.550821\pi\) | ||||
−0.158981 | + | 0.987282i | \(0.550821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.59661 | −1.18479 | −0.592393 | − | 0.805649i | \(-0.701817\pi\) | ||||
−0.592393 | + | 0.805649i | \(0.701817\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.06098 | 1.21095 | ||||||||
\(35\) | 7.75855 | 1.31143 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.84027 | −1.12453 | −0.562267 | − | 0.826956i | \(-0.690071\pi\) | ||||
−0.562267 | + | 0.826956i | \(0.690071\pi\) | |||||||
\(38\) | −6.27006 | −1.01714 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.79108 | 0.599422 | ||||||||
\(41\) | −7.17153 | −1.12001 | −0.560003 | − | 0.828491i | \(-0.689200\pi\) | ||||
−0.560003 | + | 0.828491i | \(0.689200\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.20919 | 1.25189 | 0.625945 | − | 0.779868i | \(-0.284714\pi\) | ||||
0.625945 | + | 0.779868i | \(0.284714\pi\) | |||||||
\(44\) | 3.58410 | 0.540324 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.91836 | 0.872614 | ||||||||
\(47\) | −4.20034 | −0.612682 | −0.306341 | − | 0.951922i | \(-0.599105\pi\) | ||||
−0.306341 | + | 0.951922i | \(0.599105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.81172 | −0.401674 | ||||||||
\(50\) | −9.37227 | −1.32544 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.68304 | −0.233396 | ||||||||
\(53\) | −2.24115 | −0.307845 | −0.153923 | − | 0.988083i | \(-0.549191\pi\) | ||||
−0.153923 | + | 0.988083i | \(0.549191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.5876 | −1.83215 | ||||||||
\(56\) | 2.04653 | 0.273479 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.71227 | 0.224832 | ||||||||
\(59\) | 11.2120 | 1.45968 | 0.729841 | − | 0.683617i | \(-0.239594\pi\) | ||||
0.729841 | + | 0.683617i | \(0.239594\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.28773 | 0.292913 | 0.146457 | − | 0.989217i | \(-0.453213\pi\) | ||||
0.146457 | + | 0.989217i | \(0.453213\pi\) | |||||||
\(62\) | 6.59661 | 0.837770 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.38054 | 0.791408 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.15716 | −1.11872 | −0.559362 | − | 0.828923i | \(-0.688954\pi\) | ||||
−0.559362 | + | 0.828923i | \(0.688954\pi\) | |||||||
\(68\) | −7.06098 | −0.856270 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.75855 | −0.927324 | ||||||||
\(71\) | −10.1516 | −1.20477 | −0.602384 | − | 0.798207i | \(-0.705782\pi\) | ||||
−0.602384 | + | 0.798207i | \(0.705782\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.168150 | 0.0196804 | 0.00984022 | − | 0.999952i | \(-0.496868\pi\) | ||||
0.00984022 | + | 0.999952i | \(0.496868\pi\) | |||||||
\(74\) | 6.84027 | 0.795165 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.27006 | 0.719225 | ||||||||
\(77\) | −7.33497 | −0.835898 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.46545 | 0.502402 | 0.251201 | − | 0.967935i | \(-0.419174\pi\) | ||||
0.251201 | + | 0.967935i | \(0.419174\pi\) | |||||||
\(80\) | −3.79108 | −0.423855 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.17153 | 0.791964 | ||||||||
\(83\) | 17.1161 | 1.87873 | 0.939367 | − | 0.342913i | \(-0.111414\pi\) | ||||
0.939367 | + | 0.342913i | \(0.111414\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 26.7687 | 2.90348 | ||||||||
\(86\) | −8.20919 | −0.885219 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.58410 | −0.382067 | ||||||||
\(89\) | −8.00626 | −0.848662 | −0.424331 | − | 0.905507i | \(-0.639491\pi\) | ||||
−0.424331 | + | 0.905507i | \(0.639491\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.44439 | 0.361070 | ||||||||
\(92\) | −5.91836 | −0.617032 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.20034 | 0.433232 | ||||||||
\(95\) | −23.7703 | −2.43878 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.4161 | −1.76834 | −0.884171 | − | 0.467164i | \(-0.845276\pi\) | ||||
−0.884171 | + | 0.467164i | \(0.845276\pi\) | |||||||
\(98\) | 2.81172 | 0.284026 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.37227 | 0.937227 | ||||||||
\(101\) | −6.54042 | −0.650796 | −0.325398 | − | 0.945577i | \(-0.605498\pi\) | ||||
−0.325398 | + | 0.945577i | \(0.605498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.14277 | −0.211134 | −0.105567 | − | 0.994412i | \(-0.533666\pi\) | ||||
−0.105567 | + | 0.994412i | \(0.533666\pi\) | |||||||
\(104\) | 1.68304 | 0.165036 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.24115 | 0.217679 | ||||||||
\(107\) | 3.51417 | 0.339728 | 0.169864 | − | 0.985468i | \(-0.445667\pi\) | ||||
0.169864 | + | 0.985468i | \(0.445667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.51709 | 0.145311 | 0.0726554 | − | 0.997357i | \(-0.476853\pi\) | ||||
0.0726554 | + | 0.997357i | \(0.476853\pi\) | |||||||
\(110\) | 13.5876 | 1.29553 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.04653 | −0.193379 | ||||||||
\(113\) | −7.71445 | −0.725714 | −0.362857 | − | 0.931845i | \(-0.618199\pi\) | ||||
−0.362857 | + | 0.931845i | \(0.618199\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.4370 | 2.09226 | ||||||||
\(116\) | −1.71227 | −0.158981 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.2120 | −1.03215 | ||||||||
\(119\) | 14.4505 | 1.32468 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.84579 | 0.167799 | ||||||||
\(122\) | −2.28773 | −0.207121 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.59661 | −0.592393 | ||||||||
\(125\) | −16.5756 | −1.48257 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.13695 | 0.367095 | 0.183548 | − | 0.983011i | \(-0.441242\pi\) | ||||
0.183548 | + | 0.983011i | \(0.441242\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.38054 | −0.559610 | ||||||||
\(131\) | 18.2131 | 1.59129 | 0.795644 | − | 0.605765i | \(-0.207133\pi\) | ||||
0.795644 | + | 0.605765i | \(0.207133\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.8319 | −1.11266 | ||||||||
\(134\) | 9.15716 | 0.791058 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.06098 | 0.605474 | ||||||||
\(137\) | −2.56030 | −0.218741 | −0.109370 | − | 0.994001i | \(-0.534883\pi\) | ||||
−0.109370 | + | 0.994001i | \(0.534883\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.5289 | 1.14750 | 0.573752 | − | 0.819029i | \(-0.305487\pi\) | ||||
0.573752 | + | 0.819029i | \(0.305487\pi\) | |||||||
\(140\) | 7.75855 | 0.655717 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.1516 | 0.851899 | ||||||||
\(143\) | −6.03219 | −0.504437 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.49136 | 0.539078 | ||||||||
\(146\) | −0.168150 | −0.0139162 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.84027 | −0.562267 | ||||||||
\(149\) | 16.9096 | 1.38529 | 0.692646 | − | 0.721278i | \(-0.256445\pi\) | ||||
0.692646 | + | 0.721278i | \(0.256445\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.75657 | 0.631220 | 0.315610 | − | 0.948889i | \(-0.397791\pi\) | ||||
0.315610 | + | 0.948889i | \(0.397791\pi\) | |||||||
\(152\) | −6.27006 | −0.508569 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.33497 | 0.591069 | ||||||||
\(155\) | 25.0083 | 2.00871 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7828 | 0.860565 | 0.430283 | − | 0.902694i | \(-0.358414\pi\) | ||||
0.430283 | + | 0.902694i | \(0.358414\pi\) | |||||||
\(158\) | −4.46545 | −0.355252 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.79108 | 0.299711 | ||||||||
\(161\) | 12.1121 | 0.954567 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0330 | 0.864173 | 0.432087 | − | 0.901832i | \(-0.357777\pi\) | ||||
0.432087 | + | 0.901832i | \(0.357777\pi\) | |||||||
\(164\) | −7.17153 | −0.560003 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.1161 | −1.32847 | ||||||||
\(167\) | 24.3706 | 1.88585 | 0.942926 | − | 0.333002i | \(-0.108062\pi\) | ||||
0.942926 | + | 0.333002i | \(0.108062\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1674 | −0.782106 | ||||||||
\(170\) | −26.7687 | −2.05307 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.20919 | 0.625945 | ||||||||
\(173\) | 12.3663 | 0.940193 | 0.470096 | − | 0.882615i | \(-0.344219\pi\) | ||||
0.470096 | + | 0.882615i | \(0.344219\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.1806 | −1.44992 | ||||||||
\(176\) | 3.58410 | 0.270162 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.00626 | 0.600095 | ||||||||
\(179\) | 10.6717 | 0.797639 | 0.398819 | − | 0.917030i | \(-0.369420\pi\) | ||||
0.398819 | + | 0.917030i | \(0.369420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.07663 | −0.303013 | −0.151507 | − | 0.988456i | \(-0.548412\pi\) | ||||
−0.151507 | + | 0.988456i | \(0.548412\pi\) | |||||||
\(182\) | −3.44439 | −0.255315 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.91836 | 0.436307 | ||||||||
\(185\) | 25.9320 | 1.90656 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.3073 | −1.85065 | ||||||||
\(188\) | −4.20034 | −0.306341 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 23.7703 | 1.72448 | ||||||||
\(191\) | 19.2883 | 1.39566 | 0.697828 | − | 0.716265i | \(-0.254150\pi\) | ||||
0.697828 | + | 0.716265i | \(0.254150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.82656 | 0.563368 | 0.281684 | − | 0.959507i | \(-0.409107\pi\) | ||||
0.281684 | + | 0.959507i | \(0.409107\pi\) | |||||||
\(194\) | 17.4161 | 1.25041 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.81172 | −0.200837 | ||||||||
\(197\) | −17.9536 | −1.27914 | −0.639569 | − | 0.768734i | \(-0.720887\pi\) | ||||
−0.639569 | + | 0.768734i | \(0.720887\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.34926 | 0.379199 | 0.189600 | − | 0.981862i | \(-0.439281\pi\) | ||||
0.189600 | + | 0.981862i | \(0.439281\pi\) | |||||||
\(200\) | −9.37227 | −0.662719 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.54042 | 0.460182 | ||||||||
\(203\) | 3.50422 | 0.245948 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.1878 | 1.89888 | ||||||||
\(206\) | 2.14277 | 0.149294 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.68304 | −0.116698 | ||||||||
\(209\) | 22.4725 | 1.55446 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.8871 | −0.818344 | −0.409172 | − | 0.912457i | \(-0.634182\pi\) | ||||
−0.409172 | + | 0.912457i | \(0.634182\pi\) | |||||||
\(212\) | −2.24115 | −0.153923 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.51417 | −0.240224 | ||||||||
\(215\) | −31.1217 | −2.12248 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.5002 | 0.916450 | ||||||||
\(218\) | −1.51709 | −0.102750 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.5876 | −0.916076 | ||||||||
\(221\) | 11.8839 | 0.799399 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | 2.04653 | 0.136740 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.71445 | 0.513157 | ||||||||
\(227\) | −6.81249 | −0.452161 | −0.226080 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226080 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.2778 | −1.14175 | −0.570874 | − | 0.821037i | \(-0.693396\pi\) | ||||
−0.570874 | + | 0.821037i | \(0.693396\pi\) | |||||||
\(230\) | −22.4370 | −1.47945 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.71227 | 0.112416 | ||||||||
\(233\) | 25.8848 | 1.69577 | 0.847886 | − | 0.530179i | \(-0.177875\pi\) | ||||
0.847886 | + | 0.530179i | \(0.177875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.9238 | 1.03875 | ||||||||
\(236\) | 11.2120 | 0.729841 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.4505 | −0.936688 | ||||||||
\(239\) | 26.1645 | 1.69244 | 0.846219 | − | 0.532835i | \(-0.178873\pi\) | ||||
0.846219 | + | 0.532835i | \(0.178873\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.73250 | 0.626926 | 0.313463 | − | 0.949600i | \(-0.398511\pi\) | ||||
0.313463 | + | 0.949600i | \(0.398511\pi\) | |||||||
\(242\) | −1.84579 | −0.118652 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.28773 | 0.146457 | ||||||||
\(245\) | 10.6594 | 0.681006 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.5528 | −0.671456 | ||||||||
\(248\) | 6.59661 | 0.418885 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.5756 | 1.04833 | ||||||||
\(251\) | −5.46503 | −0.344950 | −0.172475 | − | 0.985014i | \(-0.555176\pi\) | ||||
−0.172475 | + | 0.985014i | \(0.555176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.2120 | −1.33359 | ||||||||
\(254\) | −4.13695 | −0.259576 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.0155642 | 0.000970868 0 | 0.000485434 | − | 1.00000i | \(-0.499845\pi\) | ||||
0.000485434 | 1.00000i | \(0.499845\pi\) | ||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.9988 | 0.869844 | ||||||||
\(260\) | 6.38054 | 0.395704 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.2131 | −1.12521 | ||||||||
\(263\) | −21.7779 | −1.34288 | −0.671442 | − | 0.741057i | \(-0.734325\pi\) | ||||
−0.671442 | + | 0.741057i | \(0.734325\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.49636 | 0.521927 | ||||||||
\(266\) | 12.8319 | 0.786772 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.15716 | −0.559362 | ||||||||
\(269\) | −19.9425 | −1.21592 | −0.607959 | − | 0.793969i | \(-0.708011\pi\) | ||||
−0.607959 | + | 0.793969i | \(0.708011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.6300 | −0.949452 | −0.474726 | − | 0.880134i | \(-0.657453\pi\) | ||||
−0.474726 | + | 0.880134i | \(0.657453\pi\) | |||||||
\(272\) | −7.06098 | −0.428135 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.56030 | 0.154673 | ||||||||
\(275\) | 33.5912 | 2.02562 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.1815 | −1.57309 | −0.786547 | − | 0.617531i | \(-0.788133\pi\) | ||||
−0.786547 | + | 0.617531i | \(0.788133\pi\) | |||||||
\(278\) | −13.5289 | −0.811407 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.75855 | −0.463662 | ||||||||
\(281\) | 32.8035 | 1.95689 | 0.978446 | − | 0.206505i | \(-0.0662089\pi\) | ||||
0.978446 | + | 0.206505i | \(0.0662089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.8724 | 0.646294 | 0.323147 | − | 0.946349i | \(-0.395259\pi\) | ||||
0.323147 | + | 0.946349i | \(0.395259\pi\) | |||||||
\(284\) | −10.1516 | −0.602384 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.03219 | 0.356691 | ||||||||
\(287\) | 14.6768 | 0.866342 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.8575 | 1.93279 | ||||||||
\(290\) | −6.49136 | −0.381186 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.168150 | 0.00984022 | ||||||||
\(293\) | 20.3692 | 1.18998 | 0.594990 | − | 0.803733i | \(-0.297156\pi\) | ||||
0.594990 | + | 0.803733i | \(0.297156\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −42.5057 | −2.47478 | ||||||||
\(296\) | 6.84027 | 0.397583 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.9096 | −0.979549 | ||||||||
\(299\) | 9.96084 | 0.576050 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.8003 | −0.968356 | ||||||||
\(302\) | −7.75657 | −0.446340 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.27006 | 0.359612 | ||||||||
\(305\) | −8.67295 | −0.496612 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.7120 | 1.06795 | 0.533975 | − | 0.845500i | \(-0.320698\pi\) | ||||
0.533975 | + | 0.845500i | \(0.320698\pi\) | |||||||
\(308\) | −7.33497 | −0.417949 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −25.0083 | −1.42037 | ||||||||
\(311\) | −0.0834666 | −0.00473296 | −0.00236648 | − | 0.999997i | \(-0.500753\pi\) | ||||
−0.00236648 | + | 0.999997i | \(0.500753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.4273 | −1.26766 | −0.633832 | − | 0.773471i | \(-0.718519\pi\) | ||||
−0.633832 | + | 0.773471i | \(0.718519\pi\) | |||||||
\(314\) | −10.7828 | −0.608511 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.46545 | 0.251201 | ||||||||
\(317\) | 6.63887 | 0.372876 | 0.186438 | − | 0.982467i | \(-0.440306\pi\) | ||||
0.186438 | + | 0.982467i | \(0.440306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.13696 | −0.343604 | ||||||||
\(320\) | −3.79108 | −0.211928 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.1121 | −0.674981 | ||||||||
\(323\) | −44.2728 | −2.46340 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.7739 | −0.874979 | ||||||||
\(326\) | −11.0330 | −0.611063 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.17153 | 0.395982 | ||||||||
\(329\) | 8.59612 | 0.473919 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.4184 | −0.627614 | −0.313807 | − | 0.949487i | \(-0.601605\pi\) | ||||
−0.313807 | + | 0.949487i | \(0.601605\pi\) | |||||||
\(332\) | 17.1161 | 0.939367 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.3706 | −1.33350 | ||||||||
\(335\) | 34.7155 | 1.89671 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.45042 | −0.133483 | −0.0667414 | − | 0.997770i | \(-0.521260\pi\) | ||||
−0.0667414 | + | 0.997770i | \(0.521260\pi\) | |||||||
\(338\) | 10.1674 | 0.553032 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 26.7687 | 1.45174 | ||||||||
\(341\) | −23.6429 | −1.28034 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0800 | 1.08422 | ||||||||
\(344\) | −8.20919 | −0.442610 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.3663 | −0.664817 | ||||||||
\(347\) | −23.4542 | −1.25909 | −0.629543 | − | 0.776965i | \(-0.716758\pi\) | ||||
−0.629543 | + | 0.776965i | \(0.716758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.6132 | −0.621642 | −0.310821 | − | 0.950469i | \(-0.600604\pi\) | ||||
−0.310821 | + | 0.950469i | \(0.600604\pi\) | |||||||
\(350\) | 19.1806 | 1.02525 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.58410 | −0.191033 | ||||||||
\(353\) | −29.0016 | −1.54360 | −0.771800 | − | 0.635866i | \(-0.780643\pi\) | ||||
−0.771800 | + | 0.635866i | \(0.780643\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 38.4853 | 2.04259 | ||||||||
\(356\) | −8.00626 | −0.424331 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.6717 | −0.564016 | ||||||||
\(359\) | 5.42796 | 0.286477 | 0.143238 | − | 0.989688i | \(-0.454248\pi\) | ||||
0.143238 | + | 0.989688i | \(0.454248\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.3136 | 1.06914 | ||||||||
\(362\) | 4.07663 | 0.214263 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.44439 | 0.180535 | ||||||||
\(365\) | −0.637468 | −0.0333666 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.5582 | 1.80392 | 0.901961 | − | 0.431817i | \(-0.142127\pi\) | ||||
0.901961 | + | 0.431817i | \(0.142127\pi\) | |||||||
\(368\) | −5.91836 | −0.308516 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −25.9320 | −1.34814 | ||||||||
\(371\) | 4.58657 | 0.238123 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.9829 | 0.827563 | 0.413781 | − | 0.910376i | \(-0.364208\pi\) | ||||
0.413781 | + | 0.910376i | \(0.364208\pi\) | |||||||
\(374\) | 25.3073 | 1.30861 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.20034 | 0.216616 | ||||||||
\(377\) | 2.88182 | 0.148421 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.69996 | 0.190054 | 0.0950272 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950272 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(380\) | −23.7703 | −1.21939 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.2883 | −0.986878 | ||||||||
\(383\) | −5.53886 | −0.283023 | −0.141511 | − | 0.989937i | \(-0.545196\pi\) | ||||
−0.141511 | + | 0.989937i | \(0.545196\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.8074 | 1.41720 | ||||||||
\(386\) | −7.82656 | −0.398361 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.4161 | −0.884171 | ||||||||
\(389\) | −10.0091 | −0.507480 | −0.253740 | − | 0.967273i | \(-0.581661\pi\) | ||||
−0.253740 | + | 0.967273i | \(0.581661\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.7894 | 2.11338 | ||||||||
\(392\) | 2.81172 | 0.142013 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.9536 | 0.904487 | ||||||||
\(395\) | −16.9289 | −0.851783 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.11076 | −0.256501 | −0.128251 | − | 0.991742i | \(-0.540936\pi\) | ||||
−0.128251 | + | 0.991742i | \(0.540936\pi\) | |||||||
\(398\) | −5.34926 | −0.268134 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.37227 | 0.468613 | ||||||||
\(401\) | 10.8760 | 0.543122 | 0.271561 | − | 0.962421i | \(-0.412460\pi\) | ||||
0.271561 | + | 0.962421i | \(0.412460\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.1024 | 0.553048 | ||||||||
\(404\) | −6.54042 | −0.325398 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.50422 | −0.173911 | ||||||||
\(407\) | −24.5162 | −1.21522 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.1322 | −1.73718 | −0.868588 | − | 0.495535i | \(-0.834972\pi\) | ||||
−0.868588 | + | 0.495535i | \(0.834972\pi\) | |||||||
\(410\) | −27.1878 | −1.34271 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.14277 | −0.105567 | ||||||||
\(413\) | −22.9457 | −1.12909 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −64.8884 | −3.18525 | ||||||||
\(416\) | 1.68304 | 0.0825178 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.4725 | −1.09917 | ||||||||
\(419\) | −28.4444 | −1.38960 | −0.694800 | − | 0.719203i | \(-0.744507\pi\) | ||||
−0.694800 | + | 0.719203i | \(0.744507\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.6070 | 1.44296 | 0.721478 | − | 0.692437i | \(-0.243463\pi\) | ||||
0.721478 | + | 0.692437i | \(0.243463\pi\) | |||||||
\(422\) | 11.8871 | 0.578656 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.24115 | 0.108840 | ||||||||
\(425\) | −66.1774 | −3.21008 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.68190 | −0.226573 | ||||||||
\(428\) | 3.51417 | 0.169864 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 31.1217 | 1.50082 | ||||||||
\(431\) | 24.5257 | 1.18136 | 0.590682 | − | 0.806905i | \(-0.298859\pi\) | ||||
0.590682 | + | 0.806905i | \(0.298859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.31750 | −0.207486 | −0.103743 | − | 0.994604i | \(-0.533082\pi\) | ||||
−0.103743 | + | 0.994604i | \(0.533082\pi\) | |||||||
\(434\) | −13.5002 | −0.648028 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.51709 | 0.0726554 | ||||||||
\(437\) | −37.1084 | −1.77514 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1308 | 0.483517 | 0.241759 | − | 0.970336i | \(-0.422276\pi\) | ||||
0.241759 | + | 0.970336i | \(0.422276\pi\) | |||||||
\(440\) | 13.5876 | 0.647764 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.8839 | −0.565260 | ||||||||
\(443\) | 38.9310 | 1.84967 | 0.924834 | − | 0.380370i | \(-0.124203\pi\) | ||||
0.924834 | + | 0.380370i | \(0.124203\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.3524 | 1.43884 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.04653 | −0.0966894 | ||||||||
\(449\) | 29.2856 | 1.38207 | 0.691037 | − | 0.722820i | \(-0.257154\pi\) | ||||
0.691037 | + | 0.722820i | \(0.257154\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.7035 | −1.21033 | ||||||||
\(452\) | −7.71445 | −0.362857 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.81249 | 0.319726 | ||||||||
\(455\) | −13.0580 | −0.612166 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.9698 | 0.513148 | 0.256574 | − | 0.966525i | \(-0.417406\pi\) | ||||
0.256574 | + | 0.966525i | \(0.417406\pi\) | |||||||
\(458\) | 17.2778 | 0.807338 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 22.4370 | 1.04613 | ||||||||
\(461\) | 19.4524 | 0.905989 | 0.452994 | − | 0.891513i | \(-0.350356\pi\) | ||||
0.452994 | + | 0.891513i | \(0.350356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.6650 | 1.09980 | 0.549902 | − | 0.835229i | \(-0.314665\pi\) | ||||
0.549902 | + | 0.835229i | \(0.314665\pi\) | |||||||
\(464\) | −1.71227 | −0.0794903 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.8848 | −1.19909 | ||||||||
\(467\) | 7.36165 | 0.340656 | 0.170328 | − | 0.985387i | \(-0.445517\pi\) | ||||
0.170328 | + | 0.985387i | \(0.445517\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.7404 | 0.865351 | ||||||||
\(470\) | −15.9238 | −0.734510 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −11.2120 | −0.516075 | ||||||||
\(473\) | 29.4226 | 1.35285 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 58.7646 | 2.69631 | ||||||||
\(476\) | 14.4505 | 0.662338 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −26.1645 | −1.19673 | ||||||||
\(479\) | −13.0356 | −0.595611 | −0.297805 | − | 0.954627i | \(-0.596255\pi\) | ||||
−0.297805 | + | 0.954627i | \(0.596255\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.5124 | 0.524922 | ||||||||
\(482\) | −9.73250 | −0.443303 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.84579 | 0.0838996 | ||||||||
\(485\) | 66.0259 | 2.99808 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.1666 | 1.18572 | 0.592860 | − | 0.805305i | \(-0.297999\pi\) | ||||
0.592860 | + | 0.805305i | \(0.297999\pi\) | |||||||
\(488\) | −2.28773 | −0.103561 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.6594 | −0.481544 | ||||||||
\(491\) | 14.1175 | 0.637112 | 0.318556 | − | 0.947904i | \(-0.396802\pi\) | ||||
0.318556 | + | 0.947904i | \(0.396802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0903 | 0.544521 | ||||||||
\(494\) | 10.5528 | 0.474791 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.59661 | −0.296196 | ||||||||
\(497\) | 20.7754 | 0.931906 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8191 | −0.752929 | −0.376464 | − | 0.926431i | \(-0.622860\pi\) | ||||
−0.376464 | + | 0.926431i | \(0.622860\pi\) | |||||||
\(500\) | −16.5756 | −0.741283 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.46503 | 0.243916 | ||||||||
\(503\) | −35.2287 | −1.57077 | −0.785385 | − | 0.619008i | \(-0.787535\pi\) | ||||
−0.785385 | + | 0.619008i | \(0.787535\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.7952 | 1.10337 | ||||||||
\(506\) | 21.2120 | 0.942989 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.13695 | 0.183548 | ||||||||
\(509\) | 19.5271 | 0.865522 | 0.432761 | − | 0.901509i | \(-0.357539\pi\) | ||||
0.432761 | + | 0.901509i | \(0.357539\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.344123 | −0.0152231 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.0155642 | −0.000686507 0 | ||||||||
\(515\) | 8.12342 | 0.357961 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0544 | −0.662094 | ||||||||
\(518\) | −13.9988 | −0.615073 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.38054 | −0.279805 | ||||||||
\(521\) | −5.15078 | −0.225660 | −0.112830 | − | 0.993614i | \(-0.535991\pi\) | ||||
−0.112830 | + | 0.993614i | \(0.535991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.9064 | −1.39517 | −0.697585 | − | 0.716502i | \(-0.745742\pi\) | ||||
−0.697585 | + | 0.716502i | \(0.745742\pi\) | |||||||
\(524\) | 18.2131 | 0.795644 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.7779 | 0.949563 | ||||||||
\(527\) | 46.5786 | 2.02899 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.0270 | 0.522912 | ||||||||
\(530\) | −8.49636 | −0.369058 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.8319 | −0.556332 | ||||||||
\(533\) | 12.0700 | 0.522809 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.3225 | −0.575981 | ||||||||
\(536\) | 9.15716 | 0.395529 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.9425 | 0.859784 | ||||||||
\(539\) | −10.0775 | −0.434068 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.2955 | 1.47448 | 0.737239 | − | 0.675632i | \(-0.236129\pi\) | ||||
0.737239 | + | 0.675632i | \(0.236129\pi\) | |||||||
\(542\) | 15.6300 | 0.671364 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.06098 | 0.302737 | ||||||||
\(545\) | −5.75140 | −0.246363 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.1609 | 0.990288 | 0.495144 | − | 0.868811i | \(-0.335115\pi\) | ||||
0.495144 | + | 0.868811i | \(0.335115\pi\) | |||||||
\(548\) | −2.56030 | −0.109370 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −33.5912 | −1.43233 | ||||||||
\(551\) | −10.7360 | −0.457371 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.13867 | −0.388616 | ||||||||
\(554\) | 26.1815 | 1.11234 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.5289 | 0.573752 | ||||||||
\(557\) | −25.1057 | −1.06376 | −0.531881 | − | 0.846819i | \(-0.678515\pi\) | ||||
−0.531881 | + | 0.846819i | \(0.678515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.8164 | −0.584371 | ||||||||
\(560\) | 7.75855 | 0.327859 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −32.8035 | −1.38373 | ||||||||
\(563\) | −12.9346 | −0.545130 | −0.272565 | − | 0.962137i | \(-0.587872\pi\) | ||||
−0.272565 | + | 0.962137i | \(0.587872\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.2461 | 1.23039 | ||||||||
\(566\) | −10.8724 | −0.456999 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.1516 | 0.425950 | ||||||||
\(569\) | 24.2386 | 1.01613 | 0.508067 | − | 0.861318i | \(-0.330360\pi\) | ||||
0.508067 | + | 0.861318i | \(0.330360\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.1667 | −1.13689 | −0.568446 | − | 0.822720i | \(-0.692455\pi\) | ||||
−0.568446 | + | 0.822720i | \(0.692455\pi\) | |||||||
\(572\) | −6.03219 | −0.252218 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −14.6768 | −0.612596 | ||||||||
\(575\) | −55.4684 | −2.31319 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.3175 | 0.512786 | 0.256393 | − | 0.966573i | \(-0.417466\pi\) | ||||
0.256393 | + | 0.966573i | \(0.417466\pi\) | |||||||
\(578\) | −32.8575 | −1.36669 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.49136 | 0.269539 | ||||||||
\(581\) | −35.0286 | −1.45323 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.03250 | −0.332672 | ||||||||
\(584\) | −0.168150 | −0.00695808 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.3692 | −0.841443 | ||||||||
\(587\) | −30.0582 | −1.24064 | −0.620318 | − | 0.784350i | \(-0.712997\pi\) | ||||
−0.620318 | + | 0.784350i | \(0.712997\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41.3611 | −1.70425 | ||||||||
\(590\) | 42.5057 | 1.74993 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.84027 | −0.281133 | ||||||||
\(593\) | −21.2323 | −0.871907 | −0.435953 | − | 0.899969i | \(-0.643589\pi\) | ||||
−0.435953 | + | 0.899969i | \(0.643589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −54.7830 | −2.24588 | ||||||||
\(596\) | 16.9096 | 0.692646 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.96084 | −0.407329 | ||||||||
\(599\) | 22.3975 | 0.915136 | 0.457568 | − | 0.889175i | \(-0.348721\pi\) | ||||
0.457568 | + | 0.889175i | \(0.348721\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.0705 | −0.533156 | −0.266578 | − | 0.963813i | \(-0.585893\pi\) | ||||
−0.266578 | + | 0.963813i | \(0.585893\pi\) | |||||||
\(602\) | 16.8003 | 0.684731 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.75657 | 0.315610 | ||||||||
\(605\) | −6.99753 | −0.284490 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.0034 | 0.974270 | 0.487135 | − | 0.873327i | \(-0.338042\pi\) | ||||
0.487135 | + | 0.873327i | \(0.338042\pi\) | |||||||
\(608\) | −6.27006 | −0.254284 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.67295 | 0.351158 | ||||||||
\(611\) | 7.06934 | 0.285995 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.2075 | −0.977731 | −0.488866 | − | 0.872359i | \(-0.662589\pi\) | ||||
−0.488866 | + | 0.872359i | \(0.662589\pi\) | |||||||
\(614\) | −18.7120 | −0.755155 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.33497 | 0.295534 | ||||||||
\(617\) | 9.48916 | 0.382019 | 0.191010 | − | 0.981588i | \(-0.438824\pi\) | ||||
0.191010 | + | 0.981588i | \(0.438824\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.2784 | 0.614093 | 0.307046 | − | 0.951695i | \(-0.400659\pi\) | ||||
0.307046 | + | 0.951695i | \(0.400659\pi\) | |||||||
\(620\) | 25.0083 | 1.00436 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.0834666 | 0.00334670 | ||||||||
\(623\) | 16.3851 | 0.656453 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.9780 | 0.639121 | ||||||||
\(626\) | 22.4273 | 0.896374 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.7828 | 0.430283 | ||||||||
\(629\) | 48.2990 | 1.92581 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.4001 | −1.36945 | −0.684724 | − | 0.728803i | \(-0.740077\pi\) | ||||
−0.684724 | + | 0.728803i | \(0.740077\pi\) | |||||||
\(632\) | −4.46545 | −0.177626 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.63887 | −0.263663 | ||||||||
\(635\) | −15.6835 | −0.622381 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.73223 | 0.187498 | ||||||||
\(638\) | 6.13696 | 0.242965 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.79108 | 0.149855 | ||||||||
\(641\) | −14.9350 | −0.589897 | −0.294948 | − | 0.955513i | \(-0.595302\pi\) | ||||
−0.294948 | + | 0.955513i | \(0.595302\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.53019 | 0.336398 | 0.168199 | − | 0.985753i | \(-0.446205\pi\) | ||||
0.168199 | + | 0.985753i | \(0.446205\pi\) | |||||||
\(644\) | 12.1121 | 0.477283 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 44.2728 | 1.74189 | ||||||||
\(647\) | 7.45426 | 0.293057 | 0.146529 | − | 0.989206i | \(-0.453190\pi\) | ||||
0.146529 | + | 0.989206i | \(0.453190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.1851 | 1.57740 | ||||||||
\(650\) | 15.7739 | 0.618703 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.0330 | 0.432087 | ||||||||
\(653\) | −27.5619 | −1.07858 | −0.539291 | − | 0.842120i | \(-0.681308\pi\) | ||||
−0.539291 | + | 0.842120i | \(0.681308\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −69.0473 | −2.69790 | ||||||||
\(656\) | −7.17153 | −0.280001 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.59612 | −0.335112 | ||||||||
\(659\) | 38.8035 | 1.51157 | 0.755786 | − | 0.654819i | \(-0.227255\pi\) | ||||
0.755786 | + | 0.654819i | \(0.227255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.27956 | −0.127560 | −0.0637800 | − | 0.997964i | \(-0.520316\pi\) | ||||
−0.0637800 | + | 0.997964i | \(0.520316\pi\) | |||||||
\(662\) | 11.4184 | 0.443790 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.1161 | −0.664233 | ||||||||
\(665\) | 48.6466 | 1.88643 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.1338 | 0.392384 | ||||||||
\(668\) | 24.3706 | 0.942926 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −34.7155 | −1.34118 | ||||||||
\(671\) | 8.19945 | 0.316536 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6978 | 0.952030 | 0.476015 | − | 0.879437i | \(-0.342081\pi\) | ||||
0.476015 | + | 0.879437i | \(0.342081\pi\) | |||||||
\(674\) | 2.45042 | 0.0943866 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.1674 | −0.391053 | ||||||||
\(677\) | 25.6722 | 0.986664 | 0.493332 | − | 0.869841i | \(-0.335779\pi\) | ||||
0.493332 | + | 0.869841i | \(0.335779\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.6427 | 1.36784 | ||||||||
\(680\) | −26.7687 | −1.02653 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 23.6429 | 0.905334 | ||||||||
\(683\) | 2.96766 | 0.113554 | 0.0567772 | − | 0.998387i | \(-0.481918\pi\) | ||||
0.0567772 | + | 0.998387i | \(0.481918\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.70629 | 0.370858 | ||||||||
\(686\) | −20.0800 | −0.766657 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.20919 | 0.312972 | ||||||||
\(689\) | 3.77194 | 0.143700 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.4367 | −0.549198 | −0.274599 | − | 0.961559i | \(-0.588545\pi\) | ||||
−0.274599 | + | 0.961559i | \(0.588545\pi\) | |||||||
\(692\) | 12.3663 | 0.470096 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.4542 | 0.890309 | ||||||||
\(695\) | −51.2890 | −1.94550 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.6381 | 1.91805 | ||||||||
\(698\) | 11.6132 | 0.439567 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −19.1806 | −0.724959 | ||||||||
\(701\) | 10.1930 | 0.384986 | 0.192493 | − | 0.981298i | \(-0.438343\pi\) | ||||
0.192493 | + | 0.981298i | \(0.438343\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −42.8889 | −1.61758 | ||||||||
\(704\) | 3.58410 | 0.135081 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.0016 | 1.09149 | ||||||||
\(707\) | 13.3852 | 0.503400 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.53923 | −0.0578069 | −0.0289034 | − | 0.999582i | \(-0.509202\pi\) | ||||
−0.0289034 | + | 0.999582i | \(0.509202\pi\) | |||||||
\(710\) | −38.4853 | −1.44433 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.00626 | 0.300047 | ||||||||
\(713\) | 39.0411 | 1.46210 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.8685 | 0.855233 | ||||||||
\(716\) | 10.6717 | 0.398819 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.42796 | −0.202570 | ||||||||
\(719\) | −25.2733 | −0.942535 | −0.471267 | − | 0.881990i | \(-0.656203\pi\) | ||||
−0.471267 | + | 0.881990i | \(0.656203\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.38525 | 0.163315 | ||||||||
\(722\) | −20.3136 | −0.755994 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.07663 | −0.151507 | ||||||||
\(725\) | −16.0479 | −0.596003 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.8379 | 1.32915 | 0.664576 | − | 0.747220i | \(-0.268612\pi\) | ||||
0.664576 | + | 0.747220i | \(0.268612\pi\) | |||||||
\(728\) | −3.44439 | −0.127658 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.637468 | 0.0235938 | ||||||||
\(731\) | −57.9649 | −2.14391 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.5067 | −1.86551 | −0.932754 | − | 0.360514i | \(-0.882601\pi\) | ||||
−0.932754 | + | 0.360514i | \(0.882601\pi\) | |||||||
\(734\) | −34.5582 | −1.27557 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.91836 | 0.218154 | ||||||||
\(737\) | −32.8202 | −1.20895 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.7084 | 1.09284 | 0.546420 | − | 0.837511i | \(-0.315990\pi\) | ||||
0.546420 | + | 0.837511i | \(0.315990\pi\) | |||||||
\(740\) | 25.9320 | 0.953279 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.58657 | −0.168378 | ||||||||
\(743\) | −20.6363 | −0.757071 | −0.378535 | − | 0.925587i | \(-0.623572\pi\) | ||||
−0.378535 | + | 0.925587i | \(0.623572\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −64.1057 | −2.34865 | ||||||||
\(746\) | −15.9829 | −0.585175 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −25.3073 | −0.925326 | ||||||||
\(749\) | −7.19185 | −0.262784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.8799 | 0.579466 | 0.289733 | − | 0.957108i | \(-0.406434\pi\) | ||||
0.289733 | + | 0.957108i | \(0.406434\pi\) | |||||||
\(752\) | −4.20034 | −0.153171 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.88182 | −0.104950 | ||||||||
\(755\) | −29.4057 | −1.07018 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.4774 | 1.68925 | 0.844624 | − | 0.535359i | \(-0.179824\pi\) | ||||
0.844624 | + | 0.535359i | \(0.179824\pi\) | |||||||
\(758\) | −3.69996 | −0.134389 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 23.7703 | 0.862238 | ||||||||
\(761\) | −27.1864 | −0.985507 | −0.492754 | − | 0.870169i | \(-0.664010\pi\) | ||||
−0.492754 | + | 0.870169i | \(0.664010\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.10477 | −0.112400 | ||||||||
\(764\) | 19.2883 | 0.697828 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.53886 | 0.200127 | ||||||||
\(767\) | −18.8703 | −0.681367 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.9323 | −1.18757 | −0.593784 | − | 0.804625i | \(-0.702367\pi\) | ||||
−0.593784 | + | 0.804625i | \(0.702367\pi\) | |||||||
\(770\) | −27.8074 | −1.00211 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.82656 | 0.281684 | ||||||||
\(773\) | 45.5182 | 1.63718 | 0.818588 | − | 0.574382i | \(-0.194758\pi\) | ||||
0.818588 | + | 0.574382i | \(0.194758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −61.8252 | −2.22083 | ||||||||
\(776\) | 17.4161 | 0.625203 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0091 | 0.358842 | ||||||||
\(779\) | −44.9659 | −1.61107 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.3842 | −1.30193 | ||||||||
\(782\) | −41.7894 | −1.49439 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.81172 | −0.100418 | ||||||||
\(785\) | −40.8786 | −1.45902 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.1542 | −0.468898 | −0.234449 | − | 0.972128i | \(-0.575329\pi\) | ||||
−0.234449 | + | 0.972128i | \(0.575329\pi\) | |||||||
\(788\) | −17.9536 | −0.639569 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.9289 | 0.602302 | ||||||||
\(791\) | 15.7878 | 0.561351 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.85034 | −0.136729 | ||||||||
\(794\) | 5.11076 | 0.181374 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.34926 | 0.189600 | ||||||||
\(797\) | 4.81033 | 0.170391 | 0.0851953 | − | 0.996364i | \(-0.472849\pi\) | ||||
0.0851953 | + | 0.996364i | \(0.472849\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.6585 | 1.04924 | ||||||||
\(800\) | −9.37227 | −0.331360 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.8760 | −0.384045 | ||||||||
\(803\) | 0.602666 | 0.0212676 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45.9179 | −1.61839 | ||||||||
\(806\) | −11.1024 | −0.391064 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.54042 | 0.230091 | ||||||||
\(809\) | −31.7294 | −1.11554 | −0.557772 | − | 0.829994i | \(-0.688344\pi\) | ||||
−0.557772 | + | 0.829994i | \(0.688344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.5222 | −1.59850 | −0.799251 | − | 0.600997i | \(-0.794770\pi\) | ||||
−0.799251 | + | 0.600997i | \(0.794770\pi\) | |||||||
\(812\) | 3.50422 | 0.122974 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 24.5162 | 0.859293 | ||||||||
\(815\) | −41.8270 | −1.46514 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.4721 | 1.80078 | ||||||||
\(818\) | 35.1322 | 1.22837 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 27.1878 | 0.949441 | ||||||||
\(821\) | 5.66307 | 0.197643 | 0.0988213 | − | 0.995105i | \(-0.468493\pi\) | ||||
0.0988213 | + | 0.995105i | \(0.468493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.9183 | −1.70519 | −0.852593 | − | 0.522576i | \(-0.824971\pi\) | ||||
−0.852593 | + | 0.522576i | \(0.824971\pi\) | |||||||
\(824\) | 2.14277 | 0.0746471 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22.9457 | 0.798385 | ||||||||
\(827\) | −46.4492 | −1.61520 | −0.807599 | − | 0.589733i | \(-0.799233\pi\) | ||||
−0.807599 | + | 0.589733i | \(0.799233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.9868 | −1.24987 | −0.624936 | − | 0.780676i | \(-0.714875\pi\) | ||||
−0.624936 | + | 0.780676i | \(0.714875\pi\) | |||||||
\(830\) | 64.8884 | 2.25231 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.68304 | −0.0583489 | ||||||||
\(833\) | 19.8535 | 0.687883 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −92.3908 | −3.19731 | ||||||||
\(836\) | 22.4725 | 0.777229 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28.4444 | 0.982595 | ||||||||
\(839\) | −29.6956 | −1.02521 | −0.512604 | − | 0.858625i | \(-0.671319\pi\) | ||||
−0.512604 | + | 0.858625i | \(0.671319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0681 | −0.898901 | ||||||||
\(842\) | −29.6070 | −1.02032 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.8871 | −0.409172 | ||||||||
\(845\) | 38.5453 | 1.32600 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.77746 | −0.129795 | ||||||||
\(848\) | −2.24115 | −0.0769613 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 66.1774 | 2.26987 | ||||||||
\(851\) | 40.4832 | 1.38775 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.7681 | −0.574130 | −0.287065 | − | 0.957911i | \(-0.592680\pi\) | ||||
−0.287065 | + | 0.957911i | \(0.592680\pi\) | |||||||
\(854\) | 4.68190 | 0.160211 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.51417 | −0.120112 | ||||||||
\(857\) | 25.2913 | 0.863934 | 0.431967 | − | 0.901889i | \(-0.357820\pi\) | ||||
0.431967 | + | 0.901889i | \(0.357820\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.6717 | 1.35358 | 0.676790 | − | 0.736176i | \(-0.263370\pi\) | ||||
0.676790 | + | 0.736176i | \(0.263370\pi\) | |||||||
\(860\) | −31.1217 | −1.06124 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.5257 | −0.835350 | ||||||||
\(863\) | −2.95874 | −0.100717 | −0.0503583 | − | 0.998731i | \(-0.516036\pi\) | ||||
−0.0503583 | + | 0.998731i | \(0.516036\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −46.8816 | −1.59402 | ||||||||
\(866\) | 4.31750 | 0.146715 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.5002 | 0.458225 | ||||||||
\(869\) | 16.0046 | 0.542920 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.4119 | 0.522211 | ||||||||
\(872\) | −1.51709 | −0.0513751 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 37.1084 | 1.25521 | ||||||||
\(875\) | 33.9224 | 1.14679 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.0556 | 1.58896 | 0.794478 | − | 0.607293i | \(-0.207745\pi\) | ||||
0.794478 | + | 0.607293i | \(0.207745\pi\) | |||||||
\(878\) | −10.1308 | −0.341899 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.5876 | −0.458038 | ||||||||
\(881\) | −56.0650 | −1.88888 | −0.944439 | − | 0.328686i | \(-0.893394\pi\) | ||||
−0.944439 | + | 0.328686i | \(0.893394\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.9775 | 1.27805 | 0.639023 | − | 0.769188i | \(-0.279339\pi\) | ||||
0.639023 | + | 0.769188i | \(0.279339\pi\) | |||||||
\(884\) | 11.8839 | 0.399700 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.9310 | −1.30791 | ||||||||
\(887\) | −39.0844 | −1.31233 | −0.656163 | − | 0.754619i | \(-0.727822\pi\) | ||||
−0.656163 | + | 0.754619i | \(0.727822\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.46640 | −0.283954 | ||||||||
\(890\) | −30.3524 | −1.01741 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | −26.3364 | −0.881313 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.4572 | −1.35233 | ||||||||
\(896\) | 2.04653 | 0.0683698 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.2856 | −0.977273 | ||||||||
\(899\) | 11.2952 | 0.376716 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.8247 | 0.527197 | ||||||||
\(902\) | 25.7035 | 0.855833 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.71445 | 0.256579 | ||||||||
\(905\) | 15.4548 | 0.513735 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.4930 | −1.04571 | −0.522854 | − | 0.852422i | \(-0.675133\pi\) | ||||
−0.522854 | + | 0.852422i | \(0.675133\pi\) | |||||||
\(908\) | −6.81249 | −0.226080 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.0580 | 0.432867 | ||||||||
\(911\) | 27.7005 | 0.917759 | 0.458880 | − | 0.888498i | \(-0.348251\pi\) | ||||
0.458880 | + | 0.888498i | \(0.348251\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 61.3458 | 2.03025 | ||||||||
\(914\) | −10.9698 | −0.362850 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.2778 | −0.570874 | ||||||||
\(917\) | −37.2737 | −1.23089 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.5430 | −0.776612 | −0.388306 | − | 0.921531i | \(-0.626940\pi\) | ||||
−0.388306 | + | 0.921531i | \(0.626940\pi\) | |||||||
\(920\) | −22.4370 | −0.739725 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.4524 | −0.640631 | ||||||||
\(923\) | 17.0855 | 0.562375 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −64.1088 | −2.10789 | ||||||||
\(926\) | −23.6650 | −0.777679 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.71227 | 0.0562081 | ||||||||
\(929\) | −60.0063 | −1.96874 | −0.984372 | − | 0.176102i | \(-0.943651\pi\) | ||||
−0.984372 | + | 0.176102i | \(0.943651\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.6296 | −0.577788 | ||||||||
\(932\) | 25.8848 | 0.847886 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.36165 | −0.240880 | ||||||||
\(935\) | 95.9419 | 3.13764 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.7590 | 1.88690 | 0.943452 | − | 0.331511i | \(-0.107558\pi\) | ||||
0.943452 | + | 0.331511i | \(0.107558\pi\) | |||||||
\(938\) | −18.7404 | −0.611896 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 15.9238 | 0.519377 | ||||||||
\(941\) | −14.4905 | −0.472378 | −0.236189 | − | 0.971707i | \(-0.575898\pi\) | ||||
−0.236189 | + | 0.971707i | \(0.575898\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 42.4437 | 1.38216 | ||||||||
\(944\) | 11.2120 | 0.364920 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.4226 | −0.956610 | ||||||||
\(947\) | 49.5458 | 1.61002 | 0.805012 | − | 0.593259i | \(-0.202159\pi\) | ||||
0.805012 | + | 0.593259i | \(0.202159\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.283003 | −0.00918666 | ||||||||
\(950\) | −58.7646 | −1.90658 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.4505 | −0.468344 | ||||||||
\(953\) | −15.2950 | −0.495452 | −0.247726 | − | 0.968830i | \(-0.579683\pi\) | ||||
−0.247726 | + | 0.968830i | \(0.579683\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −73.1236 | −2.36622 | ||||||||
\(956\) | 26.1645 | 0.846219 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.0356 | 0.421161 | ||||||||
\(959\) | 5.23972 | 0.169200 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.5153 | 0.403718 | ||||||||
\(962\) | −11.5124 | −0.371176 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.73250 | 0.313463 | ||||||||
\(965\) | −29.6711 | −0.955146 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.2994 | 0.974364 | 0.487182 | − | 0.873300i | \(-0.338025\pi\) | ||||
0.487182 | + | 0.873300i | \(0.338025\pi\) | |||||||
\(968\) | −1.84579 | −0.0593260 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −66.0259 | −2.11997 | ||||||||
\(971\) | 33.9790 | 1.09044 | 0.545219 | − | 0.838294i | \(-0.316446\pi\) | ||||
0.545219 | + | 0.838294i | \(0.316446\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.6872 | −0.887612 | ||||||||
\(974\) | −26.1666 | −0.838431 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.28773 | 0.0732284 | ||||||||
\(977\) | 5.13359 | 0.164238 | 0.0821191 | − | 0.996623i | \(-0.473831\pi\) | ||||
0.0821191 | + | 0.996623i | \(0.473831\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.6953 | −0.917105 | ||||||||
\(980\) | 10.6594 | 0.340503 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.1175 | −0.450506 | ||||||||
\(983\) | 23.1353 | 0.737901 | 0.368950 | − | 0.929449i | \(-0.379717\pi\) | ||||
0.368950 | + | 0.929449i | \(0.379717\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68.0633 | 2.16868 | ||||||||
\(986\) | −12.0903 | −0.385035 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.5528 | −0.335728 | ||||||||
\(989\) | −48.5849 | −1.54491 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.4476 | 0.649540 | 0.324770 | − | 0.945793i | \(-0.394713\pi\) | ||||
0.324770 | + | 0.945793i | \(0.394713\pi\) | |||||||
\(992\) | 6.59661 | 0.209443 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20.7754 | −0.658957 | ||||||||
\(995\) | −20.2795 | −0.642902 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.5682 | 0.524721 | 0.262360 | − | 0.964970i | \(-0.415499\pi\) | ||||
0.262360 | + | 0.964970i | \(0.415499\pi\) | |||||||
\(998\) | 16.8191 | 0.532401 | ||||||||
\(999\) | 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 | 4014.2.a.v.1.1 | 7 | ||
3.2 | odd | 2 | 1338.2.a.j.1.7 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1338.2.a.j.1.7 | ✓ | 7 | 3.2 | odd | 2 | ||
4014.2.a.v.1.1 | 7 | 1.1 | even | 1 | trivial |