Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8670,2,Mod(1,8670)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8670, 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("8670.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8670.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: | \(69.2302985525\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.20417871872.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} - 8x^{5} + 38x^{4} + 40x^{3} - 20x^{2} - 24x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 510) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.792510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8670.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.80701 | 1.81688 | 0.908440 | − | 0.418015i | \(-0.137274\pi\) | ||||
0.908440 | + | 0.418015i | \(0.137274\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −2.65672 | −0.801030 | −0.400515 | − | 0.916290i | \(-0.631169\pi\) | ||||
−0.400515 | + | 0.916290i | \(0.631169\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 4.55356 | 1.26293 | 0.631465 | − | 0.775405i | \(-0.282454\pi\) | ||||
0.631465 | + | 0.775405i | \(0.282454\pi\) | |||||||
\(14\) | −4.80701 | −1.28473 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.04449 | 1.38670 | 0.693350 | − | 0.720601i | \(-0.256134\pi\) | ||||
0.693350 | + | 0.720601i | \(0.256134\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 4.80701 | 1.04898 | ||||||||
\(22\) | 2.65672 | 0.566414 | ||||||||
\(23\) | −4.32010 | −0.900804 | −0.450402 | − | 0.892826i | \(-0.648719\pi\) | ||||
−0.450402 | + | 0.892826i | \(0.648719\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.55356 | −0.893026 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.80701 | 0.908440 | ||||||||
\(29\) | 4.06491 | 0.754834 | 0.377417 | − | 0.926043i | \(-0.376812\pi\) | ||||
0.377417 | + | 0.926043i | \(0.376812\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −3.93892 | −0.707451 | −0.353725 | − | 0.935349i | \(-0.615085\pi\) | ||||
−0.353725 | + | 0.935349i | \(0.615085\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.65672 | −0.462475 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.80701 | 0.812533 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.53073 | 0.909247 | 0.454624 | − | 0.890684i | \(-0.349774\pi\) | ||||
0.454624 | + | 0.890684i | \(0.349774\pi\) | |||||||
\(38\) | −6.04449 | −0.980546 | ||||||||
\(39\) | 4.55356 | 0.729153 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −11.3393 | −1.77091 | −0.885453 | − | 0.464728i | \(-0.846152\pi\) | ||||
−0.885453 | + | 0.464728i | \(0.846152\pi\) | |||||||
\(42\) | −4.80701 | −0.741738 | ||||||||
\(43\) | −7.80625 | −1.19044 | −0.595221 | − | 0.803562i | \(-0.702935\pi\) | ||||
−0.595221 | + | 0.803562i | \(0.702935\pi\) | |||||||
\(44\) | −2.65672 | −0.400515 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 4.32010 | 0.636964 | ||||||||
\(47\) | 1.83866 | 0.268196 | 0.134098 | − | 0.990968i | \(-0.457186\pi\) | ||||
0.134098 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 16.1074 | 2.30105 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.55356 | 0.631465 | ||||||||
\(53\) | 5.88254 | 0.808029 | 0.404014 | − | 0.914753i | \(-0.367615\pi\) | ||||
0.404014 | + | 0.914753i | \(0.367615\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −2.65672 | −0.358231 | ||||||||
\(56\) | −4.80701 | −0.642364 | ||||||||
\(57\) | 6.04449 | 0.800612 | ||||||||
\(58\) | −4.06491 | −0.533748 | ||||||||
\(59\) | 3.50381 | 0.456157 | 0.228078 | − | 0.973643i | \(-0.426756\pi\) | ||||
0.228078 | + | 0.973643i | \(0.426756\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 7.66447 | 0.981334 | 0.490667 | − | 0.871347i | \(-0.336753\pi\) | ||||
0.490667 | + | 0.871347i | \(0.336753\pi\) | |||||||
\(62\) | 3.93892 | 0.500243 | ||||||||
\(63\) | 4.80701 | 0.605627 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.55356 | 0.564799 | ||||||||
\(66\) | 2.65672 | 0.327019 | ||||||||
\(67\) | 13.8487 | 1.69189 | 0.845946 | − | 0.533268i | \(-0.179036\pi\) | ||||
0.845946 | + | 0.533268i | \(0.179036\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.32010 | −0.520079 | ||||||||
\(70\) | −4.80701 | −0.574548 | ||||||||
\(71\) | 4.86663 | 0.577563 | 0.288781 | − | 0.957395i | \(-0.406750\pi\) | ||||
0.288781 | + | 0.957395i | \(0.406750\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 8.43486 | 0.987226 | 0.493613 | − | 0.869682i | \(-0.335676\pi\) | ||||
0.493613 | + | 0.869682i | \(0.335676\pi\) | |||||||
\(74\) | −5.53073 | −0.642935 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 6.04449 | 0.693350 | ||||||||
\(77\) | −12.7709 | −1.45537 | ||||||||
\(78\) | −4.55356 | −0.515589 | ||||||||
\(79\) | −13.1363 | −1.47795 | −0.738975 | − | 0.673733i | \(-0.764690\pi\) | ||||
−0.738975 | + | 0.673733i | \(0.764690\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.3393 | 1.25222 | ||||||||
\(83\) | −17.6812 | −1.94077 | −0.970385 | − | 0.241565i | \(-0.922339\pi\) | ||||
−0.970385 | + | 0.241565i | \(0.922339\pi\) | |||||||
\(84\) | 4.80701 | 0.524488 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.80625 | 0.841769 | ||||||||
\(87\) | 4.06491 | 0.435804 | ||||||||
\(88\) | 2.65672 | 0.283207 | ||||||||
\(89\) | 15.5491 | 1.64820 | 0.824101 | − | 0.566443i | \(-0.191681\pi\) | ||||
0.824101 | + | 0.566443i | \(0.191681\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 21.8890 | 2.29459 | ||||||||
\(92\) | −4.32010 | −0.450402 | ||||||||
\(93\) | −3.93892 | −0.408447 | ||||||||
\(94\) | −1.83866 | −0.189643 | ||||||||
\(95\) | 6.04449 | 0.620152 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −17.1612 | −1.74246 | −0.871229 | − | 0.490876i | \(-0.836677\pi\) | ||||
−0.871229 | + | 0.490876i | \(0.836677\pi\) | |||||||
\(98\) | −16.1074 | −1.62709 | ||||||||
\(99\) | −2.65672 | −0.267010 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.08472 | −0.605452 | −0.302726 | − | 0.953078i | \(-0.597897\pi\) | ||||
−0.302726 | + | 0.953078i | \(0.597897\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.35517 | −0.133529 | −0.0667645 | − | 0.997769i | \(-0.521268\pi\) | ||||
−0.0667645 | + | 0.997769i | \(0.521268\pi\) | |||||||
\(104\) | −4.55356 | −0.446513 | ||||||||
\(105\) | 4.80701 | 0.469116 | ||||||||
\(106\) | −5.88254 | −0.571362 | ||||||||
\(107\) | 3.10006 | 0.299694 | 0.149847 | − | 0.988709i | \(-0.452122\pi\) | ||||
0.149847 | + | 0.988709i | \(0.452122\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 15.4449 | 1.47935 | 0.739676 | − | 0.672964i | \(-0.234979\pi\) | ||||
0.739676 | + | 0.672964i | \(0.234979\pi\) | |||||||
\(110\) | 2.65672 | 0.253308 | ||||||||
\(111\) | 5.53073 | 0.524954 | ||||||||
\(112\) | 4.80701 | 0.454220 | ||||||||
\(113\) | −4.15242 | −0.390627 | −0.195313 | − | 0.980741i | \(-0.562572\pi\) | ||||
−0.195313 | + | 0.980741i | \(0.562572\pi\) | |||||||
\(114\) | −6.04449 | −0.566118 | ||||||||
\(115\) | −4.32010 | −0.402852 | ||||||||
\(116\) | 4.06491 | 0.377417 | ||||||||
\(117\) | 4.55356 | 0.420977 | ||||||||
\(118\) | −3.50381 | −0.322551 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −3.94187 | −0.358351 | ||||||||
\(122\) | −7.66447 | −0.693908 | ||||||||
\(123\) | −11.3393 | −1.02243 | ||||||||
\(124\) | −3.93892 | −0.353725 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.80701 | −0.428243 | ||||||||
\(127\) | −13.0929 | −1.16181 | −0.580903 | − | 0.813973i | \(-0.697301\pi\) | ||||
−0.580903 | + | 0.813973i | \(0.697301\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.80625 | −0.687302 | ||||||||
\(130\) | −4.55356 | −0.399373 | ||||||||
\(131\) | 5.41965 | 0.473517 | 0.236758 | − | 0.971569i | \(-0.423915\pi\) | ||||
0.236758 | + | 0.971569i | \(0.423915\pi\) | |||||||
\(132\) | −2.65672 | −0.231237 | ||||||||
\(133\) | 29.0559 | 2.51947 | ||||||||
\(134\) | −13.8487 | −1.19635 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.13674 | 0.609733 | 0.304866 | − | 0.952395i | \(-0.401388\pi\) | ||||
0.304866 | + | 0.952395i | \(0.401388\pi\) | |||||||
\(138\) | 4.32010 | 0.367751 | ||||||||
\(139\) | 7.28029 | 0.617506 | 0.308753 | − | 0.951142i | \(-0.400088\pi\) | ||||
0.308753 | + | 0.951142i | \(0.400088\pi\) | |||||||
\(140\) | 4.80701 | 0.406267 | ||||||||
\(141\) | 1.83866 | 0.154843 | ||||||||
\(142\) | −4.86663 | −0.408398 | ||||||||
\(143\) | −12.0975 | −1.01164 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.06491 | 0.337572 | ||||||||
\(146\) | −8.43486 | −0.698074 | ||||||||
\(147\) | 16.1074 | 1.32851 | ||||||||
\(148\) | 5.53073 | 0.454624 | ||||||||
\(149\) | 0.266600 | 0.0218407 | 0.0109204 | − | 0.999940i | \(-0.496524\pi\) | ||||
0.0109204 | + | 0.999940i | \(0.496524\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −13.1064 | −1.06659 | −0.533293 | − | 0.845931i | \(-0.679046\pi\) | ||||
−0.533293 | + | 0.845931i | \(0.679046\pi\) | |||||||
\(152\) | −6.04449 | −0.490273 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.7709 | 1.02911 | ||||||||
\(155\) | −3.93892 | −0.316382 | ||||||||
\(156\) | 4.55356 | 0.364576 | ||||||||
\(157\) | 2.93377 | 0.234140 | 0.117070 | − | 0.993124i | \(-0.462650\pi\) | ||||
0.117070 | + | 0.993124i | \(0.462650\pi\) | |||||||
\(158\) | 13.1363 | 1.04507 | ||||||||
\(159\) | 5.88254 | 0.466516 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −20.7668 | −1.63665 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −9.13905 | −0.715825 | −0.357913 | − | 0.933755i | \(-0.616511\pi\) | ||||
−0.357913 | + | 0.933755i | \(0.616511\pi\) | |||||||
\(164\) | −11.3393 | −0.885453 | ||||||||
\(165\) | −2.65672 | −0.206825 | ||||||||
\(166\) | 17.6812 | 1.37233 | ||||||||
\(167\) | 19.0664 | 1.47540 | 0.737700 | − | 0.675128i | \(-0.235912\pi\) | ||||
0.737700 | + | 0.675128i | \(0.235912\pi\) | |||||||
\(168\) | −4.80701 | −0.370869 | ||||||||
\(169\) | 7.73489 | 0.594991 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.04449 | 0.462234 | ||||||||
\(172\) | −7.80625 | −0.595221 | ||||||||
\(173\) | 5.19673 | 0.395100 | 0.197550 | − | 0.980293i | \(-0.436701\pi\) | ||||
0.197550 | + | 0.980293i | \(0.436701\pi\) | |||||||
\(174\) | −4.06491 | −0.308160 | ||||||||
\(175\) | 4.80701 | 0.363376 | ||||||||
\(176\) | −2.65672 | −0.200257 | ||||||||
\(177\) | 3.50381 | 0.263362 | ||||||||
\(178\) | −15.5491 | −1.16545 | ||||||||
\(179\) | 0.209059 | 0.0156258 | 0.00781292 | − | 0.999969i | \(-0.497513\pi\) | ||||
0.00781292 | + | 0.999969i | \(0.497513\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 14.4208 | 1.07189 | 0.535945 | − | 0.844253i | \(-0.319956\pi\) | ||||
0.535945 | + | 0.844253i | \(0.319956\pi\) | |||||||
\(182\) | −21.8890 | −1.62252 | ||||||||
\(183\) | 7.66447 | 0.566574 | ||||||||
\(184\) | 4.32010 | 0.318482 | ||||||||
\(185\) | 5.53073 | 0.406628 | ||||||||
\(186\) | 3.93892 | 0.288816 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.83866 | 0.134098 | ||||||||
\(189\) | 4.80701 | 0.349659 | ||||||||
\(190\) | −6.04449 | −0.438513 | ||||||||
\(191\) | 12.3810 | 0.895857 | 0.447928 | − | 0.894069i | \(-0.352162\pi\) | ||||
0.447928 | + | 0.894069i | \(0.352162\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 3.59378 | 0.258686 | 0.129343 | − | 0.991600i | \(-0.458713\pi\) | ||||
0.129343 | + | 0.991600i | \(0.458713\pi\) | |||||||
\(194\) | 17.1612 | 1.23210 | ||||||||
\(195\) | 4.55356 | 0.326087 | ||||||||
\(196\) | 16.1074 | 1.15053 | ||||||||
\(197\) | −4.80943 | −0.342658 | −0.171329 | − | 0.985214i | \(-0.554806\pi\) | ||||
−0.171329 | + | 0.985214i | \(0.554806\pi\) | |||||||
\(198\) | 2.65672 | 0.188805 | ||||||||
\(199\) | 4.44449 | 0.315062 | 0.157531 | − | 0.987514i | \(-0.449647\pi\) | ||||
0.157531 | + | 0.987514i | \(0.449647\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 13.8487 | 0.976814 | ||||||||
\(202\) | 6.08472 | 0.428119 | ||||||||
\(203\) | 19.5401 | 1.37144 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.3393 | −0.791974 | ||||||||
\(206\) | 1.35517 | 0.0944193 | ||||||||
\(207\) | −4.32010 | −0.300268 | ||||||||
\(208\) | 4.55356 | 0.315732 | ||||||||
\(209\) | −16.0585 | −1.11079 | ||||||||
\(210\) | −4.80701 | −0.331715 | ||||||||
\(211\) | −15.5928 | −1.07346 | −0.536728 | − | 0.843755i | \(-0.680340\pi\) | ||||
−0.536728 | + | 0.843755i | \(0.680340\pi\) | |||||||
\(212\) | 5.88254 | 0.404014 | ||||||||
\(213\) | 4.86663 | 0.333456 | ||||||||
\(214\) | −3.10006 | −0.211916 | ||||||||
\(215\) | −7.80625 | −0.532382 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −18.9344 | −1.28535 | ||||||||
\(218\) | −15.4449 | −1.04606 | ||||||||
\(219\) | 8.43486 | 0.569975 | ||||||||
\(220\) | −2.65672 | −0.179116 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −5.53073 | −0.371199 | ||||||||
\(223\) | −0.246992 | −0.0165398 | −0.00826992 | − | 0.999966i | \(-0.502632\pi\) | ||||
−0.00826992 | + | 0.999966i | \(0.502632\pi\) | |||||||
\(224\) | −4.80701 | −0.321182 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 4.15242 | 0.276215 | ||||||||
\(227\) | 0.206352 | 0.0136961 | 0.00684804 | − | 0.999977i | \(-0.497820\pi\) | ||||
0.00684804 | + | 0.999977i | \(0.497820\pi\) | |||||||
\(228\) | 6.04449 | 0.400306 | ||||||||
\(229\) | 12.8458 | 0.848875 | 0.424438 | − | 0.905457i | \(-0.360472\pi\) | ||||
0.424438 | + | 0.905457i | \(0.360472\pi\) | |||||||
\(230\) | 4.32010 | 0.284859 | ||||||||
\(231\) | −12.7709 | −0.840261 | ||||||||
\(232\) | −4.06491 | −0.266874 | ||||||||
\(233\) | −0.165078 | −0.0108146 | −0.00540732 | − | 0.999985i | \(-0.501721\pi\) | ||||
−0.00540732 | + | 0.999985i | \(0.501721\pi\) | |||||||
\(234\) | −4.55356 | −0.297675 | ||||||||
\(235\) | 1.83866 | 0.119941 | ||||||||
\(236\) | 3.50381 | 0.228078 | ||||||||
\(237\) | −13.1363 | −0.853294 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.2098 | 1.24258 | 0.621288 | − | 0.783582i | \(-0.286610\pi\) | ||||
0.621288 | + | 0.783582i | \(0.286610\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 4.55105 | 0.293159 | 0.146579 | − | 0.989199i | \(-0.453174\pi\) | ||||
0.146579 | + | 0.989199i | \(0.453174\pi\) | |||||||
\(242\) | 3.94187 | 0.253393 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.66447 | 0.490667 | ||||||||
\(245\) | 16.1074 | 1.02906 | ||||||||
\(246\) | 11.3393 | 0.722970 | ||||||||
\(247\) | 27.5239 | 1.75131 | ||||||||
\(248\) | 3.93892 | 0.250122 | ||||||||
\(249\) | −17.6812 | −1.12050 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −12.6713 | −0.799805 | −0.399903 | − | 0.916558i | \(-0.630956\pi\) | ||||
−0.399903 | + | 0.916558i | \(0.630956\pi\) | |||||||
\(252\) | 4.80701 | 0.302813 | ||||||||
\(253\) | 11.4773 | 0.721570 | ||||||||
\(254\) | 13.0929 | 0.821521 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.7579 | 0.671061 | 0.335531 | − | 0.942029i | \(-0.391084\pi\) | ||||
0.335531 | + | 0.942029i | \(0.391084\pi\) | |||||||
\(258\) | 7.80625 | 0.485996 | ||||||||
\(259\) | 26.5863 | 1.65199 | ||||||||
\(260\) | 4.55356 | 0.282400 | ||||||||
\(261\) | 4.06491 | 0.251611 | ||||||||
\(262\) | −5.41965 | −0.334827 | ||||||||
\(263\) | −8.77699 | −0.541212 | −0.270606 | − | 0.962690i | \(-0.587224\pi\) | ||||
−0.270606 | + | 0.962690i | \(0.587224\pi\) | |||||||
\(264\) | 2.65672 | 0.163510 | ||||||||
\(265\) | 5.88254 | 0.361361 | ||||||||
\(266\) | −29.0559 | −1.78153 | ||||||||
\(267\) | 15.5491 | 0.951590 | ||||||||
\(268\) | 13.8487 | 0.845946 | ||||||||
\(269\) | −17.3898 | −1.06027 | −0.530136 | − | 0.847913i | \(-0.677859\pi\) | ||||
−0.530136 | + | 0.847913i | \(0.677859\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −17.9138 | −1.08819 | −0.544093 | − | 0.839025i | \(-0.683126\pi\) | ||||
−0.544093 | + | 0.839025i | \(0.683126\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.8890 | 1.32478 | ||||||||
\(274\) | −7.13674 | −0.431146 | ||||||||
\(275\) | −2.65672 | −0.160206 | ||||||||
\(276\) | −4.32010 | −0.260040 | ||||||||
\(277\) | −26.2658 | −1.57816 | −0.789080 | − | 0.614290i | \(-0.789442\pi\) | ||||
−0.789080 | + | 0.614290i | \(0.789442\pi\) | |||||||
\(278\) | −7.28029 | −0.436642 | ||||||||
\(279\) | −3.93892 | −0.235817 | ||||||||
\(280\) | −4.80701 | −0.287274 | ||||||||
\(281\) | 28.5009 | 1.70022 | 0.850111 | − | 0.526603i | \(-0.176535\pi\) | ||||
0.850111 | + | 0.526603i | \(0.176535\pi\) | |||||||
\(282\) | −1.83866 | −0.109490 | ||||||||
\(283\) | −3.66103 | −0.217625 | −0.108813 | − | 0.994062i | \(-0.534705\pi\) | ||||
−0.108813 | + | 0.994062i | \(0.534705\pi\) | |||||||
\(284\) | 4.86663 | 0.288781 | ||||||||
\(285\) | 6.04449 | 0.358045 | ||||||||
\(286\) | 12.0975 | 0.715340 | ||||||||
\(287\) | −54.5083 | −3.21752 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −4.06491 | −0.238700 | ||||||||
\(291\) | −17.1612 | −1.00601 | ||||||||
\(292\) | 8.43486 | 0.493613 | ||||||||
\(293\) | 15.6314 | 0.913197 | 0.456598 | − | 0.889673i | \(-0.349068\pi\) | ||||
0.456598 | + | 0.889673i | \(0.349068\pi\) | |||||||
\(294\) | −16.1074 | −0.939401 | ||||||||
\(295\) | 3.50381 | 0.203999 | ||||||||
\(296\) | −5.53073 | −0.321467 | ||||||||
\(297\) | −2.65672 | −0.154158 | ||||||||
\(298\) | −0.266600 | −0.0154437 | ||||||||
\(299\) | −19.6718 | −1.13765 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −37.5247 | −2.16289 | ||||||||
\(302\) | 13.1064 | 0.754190 | ||||||||
\(303\) | −6.08472 | −0.349558 | ||||||||
\(304\) | 6.04449 | 0.346675 | ||||||||
\(305\) | 7.66447 | 0.438866 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.39589 | −0.0796676 | −0.0398338 | − | 0.999206i | \(-0.512683\pi\) | ||||
−0.0398338 | + | 0.999206i | \(0.512683\pi\) | |||||||
\(308\) | −12.7709 | −0.727687 | ||||||||
\(309\) | −1.35517 | −0.0770930 | ||||||||
\(310\) | 3.93892 | 0.223716 | ||||||||
\(311\) | −3.49665 | −0.198277 | −0.0991385 | − | 0.995074i | \(-0.531609\pi\) | ||||
−0.0991385 | + | 0.995074i | \(0.531609\pi\) | |||||||
\(312\) | −4.55356 | −0.257794 | ||||||||
\(313\) | −23.2668 | −1.31512 | −0.657558 | − | 0.753404i | \(-0.728411\pi\) | ||||
−0.657558 | + | 0.753404i | \(0.728411\pi\) | |||||||
\(314\) | −2.93377 | −0.165562 | ||||||||
\(315\) | 4.80701 | 0.270844 | ||||||||
\(316\) | −13.1363 | −0.738975 | ||||||||
\(317\) | −15.1546 | −0.851168 | −0.425584 | − | 0.904919i | \(-0.639931\pi\) | ||||
−0.425584 | + | 0.904919i | \(0.639931\pi\) | |||||||
\(318\) | −5.88254 | −0.329876 | ||||||||
\(319\) | −10.7993 | −0.604645 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 3.10006 | 0.173028 | ||||||||
\(322\) | 20.7668 | 1.15729 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.55356 | 0.252586 | ||||||||
\(326\) | 9.13905 | 0.506165 | ||||||||
\(327\) | 15.4449 | 0.854104 | ||||||||
\(328\) | 11.3393 | 0.626110 | ||||||||
\(329\) | 8.83844 | 0.487279 | ||||||||
\(330\) | 2.65672 | 0.146247 | ||||||||
\(331\) | −24.0083 | −1.31961 | −0.659807 | − | 0.751435i | \(-0.729362\pi\) | ||||
−0.659807 | + | 0.751435i | \(0.729362\pi\) | |||||||
\(332\) | −17.6812 | −0.970385 | ||||||||
\(333\) | 5.53073 | 0.303082 | ||||||||
\(334\) | −19.0664 | −1.04327 | ||||||||
\(335\) | 13.8487 | 0.756637 | ||||||||
\(336\) | 4.80701 | 0.262244 | ||||||||
\(337\) | −26.8726 | −1.46384 | −0.731922 | − | 0.681388i | \(-0.761377\pi\) | ||||
−0.731922 | + | 0.681388i | \(0.761377\pi\) | |||||||
\(338\) | −7.73489 | −0.420722 | ||||||||
\(339\) | −4.15242 | −0.225529 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4646 | 0.566689 | ||||||||
\(342\) | −6.04449 | −0.326849 | ||||||||
\(343\) | 43.7792 | 2.36386 | ||||||||
\(344\) | 7.80625 | 0.420885 | ||||||||
\(345\) | −4.32010 | −0.232586 | ||||||||
\(346\) | −5.19673 | −0.279378 | ||||||||
\(347\) | 7.98128 | 0.428457 | 0.214229 | − | 0.976784i | \(-0.431276\pi\) | ||||
0.214229 | + | 0.976784i | \(0.431276\pi\) | |||||||
\(348\) | 4.06491 | 0.217902 | ||||||||
\(349\) | −13.3176 | −0.712874 | −0.356437 | − | 0.934319i | \(-0.616009\pi\) | ||||
−0.356437 | + | 0.934319i | \(0.616009\pi\) | |||||||
\(350\) | −4.80701 | −0.256946 | ||||||||
\(351\) | 4.55356 | 0.243051 | ||||||||
\(352\) | 2.65672 | 0.141603 | ||||||||
\(353\) | −16.9293 | −0.901054 | −0.450527 | − | 0.892763i | \(-0.648764\pi\) | ||||
−0.450527 | + | 0.892763i | \(0.648764\pi\) | |||||||
\(354\) | −3.50381 | −0.186225 | ||||||||
\(355\) | 4.86663 | 0.258294 | ||||||||
\(356\) | 15.5491 | 0.824101 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.209059 | −0.0110491 | ||||||||
\(359\) | 20.8739 | 1.10168 | 0.550842 | − | 0.834609i | \(-0.314307\pi\) | ||||
0.550842 | + | 0.834609i | \(0.314307\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 17.5358 | 0.922939 | ||||||||
\(362\) | −14.4208 | −0.757940 | ||||||||
\(363\) | −3.94187 | −0.206894 | ||||||||
\(364\) | 21.8890 | 1.14730 | ||||||||
\(365\) | 8.43486 | 0.441501 | ||||||||
\(366\) | −7.66447 | −0.400628 | ||||||||
\(367\) | −9.48837 | −0.495289 | −0.247645 | − | 0.968851i | \(-0.579656\pi\) | ||||
−0.247645 | + | 0.968851i | \(0.579656\pi\) | |||||||
\(368\) | −4.32010 | −0.225201 | ||||||||
\(369\) | −11.3393 | −0.590302 | ||||||||
\(370\) | −5.53073 | −0.287529 | ||||||||
\(371\) | 28.2774 | 1.46809 | ||||||||
\(372\) | −3.93892 | −0.204223 | ||||||||
\(373\) | −8.88776 | −0.460191 | −0.230095 | − | 0.973168i | \(-0.573904\pi\) | ||||
−0.230095 | + | 0.973168i | \(0.573904\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −1.83866 | −0.0948214 | ||||||||
\(377\) | 18.5098 | 0.953302 | ||||||||
\(378\) | −4.80701 | −0.247246 | ||||||||
\(379\) | −20.5944 | −1.05786 | −0.528931 | − | 0.848665i | \(-0.677407\pi\) | ||||
−0.528931 | + | 0.848665i | \(0.677407\pi\) | |||||||
\(380\) | 6.04449 | 0.310076 | ||||||||
\(381\) | −13.0929 | −0.670769 | ||||||||
\(382\) | −12.3810 | −0.633467 | ||||||||
\(383\) | −32.6635 | −1.66903 | −0.834513 | − | 0.550989i | \(-0.814251\pi\) | ||||
−0.834513 | + | 0.550989i | \(0.814251\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −12.7709 | −0.650863 | ||||||||
\(386\) | −3.59378 | −0.182919 | ||||||||
\(387\) | −7.80625 | −0.396814 | ||||||||
\(388\) | −17.1612 | −0.871229 | ||||||||
\(389\) | 26.9553 | 1.36669 | 0.683344 | − | 0.730097i | \(-0.260525\pi\) | ||||
0.683344 | + | 0.730097i | \(0.260525\pi\) | |||||||
\(390\) | −4.55356 | −0.230578 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −16.1074 | −0.813545 | ||||||||
\(393\) | 5.41965 | 0.273385 | ||||||||
\(394\) | 4.80943 | 0.242296 | ||||||||
\(395\) | −13.1363 | −0.660959 | ||||||||
\(396\) | −2.65672 | −0.133505 | ||||||||
\(397\) | 30.6356 | 1.53755 | 0.768777 | − | 0.639517i | \(-0.220866\pi\) | ||||
0.768777 | + | 0.639517i | \(0.220866\pi\) | |||||||
\(398\) | −4.44449 | −0.222782 | ||||||||
\(399\) | 29.0559 | 1.45462 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −28.4374 | −1.42010 | −0.710048 | − | 0.704153i | \(-0.751327\pi\) | ||||
−0.710048 | + | 0.704153i | \(0.751327\pi\) | |||||||
\(402\) | −13.8487 | −0.690712 | ||||||||
\(403\) | −17.9361 | −0.893461 | ||||||||
\(404\) | −6.08472 | −0.302726 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −19.5401 | −0.969757 | ||||||||
\(407\) | −14.6936 | −0.728334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.3744 | −1.50192 | −0.750960 | − | 0.660348i | \(-0.770409\pi\) | ||||
−0.750960 | + | 0.660348i | \(0.770409\pi\) | |||||||
\(410\) | 11.3393 | 0.560010 | ||||||||
\(411\) | 7.13674 | 0.352029 | ||||||||
\(412\) | −1.35517 | −0.0667645 | ||||||||
\(413\) | 16.8428 | 0.828782 | ||||||||
\(414\) | 4.32010 | 0.212321 | ||||||||
\(415\) | −17.6812 | −0.867938 | ||||||||
\(416\) | −4.55356 | −0.223257 | ||||||||
\(417\) | 7.28029 | 0.356517 | ||||||||
\(418\) | 16.0585 | 0.785446 | ||||||||
\(419\) | −22.0797 | −1.07866 | −0.539332 | − | 0.842093i | \(-0.681323\pi\) | ||||
−0.539332 | + | 0.842093i | \(0.681323\pi\) | |||||||
\(420\) | 4.80701 | 0.234558 | ||||||||
\(421\) | −2.61967 | −0.127675 | −0.0638374 | − | 0.997960i | \(-0.520334\pi\) | ||||
−0.0638374 | + | 0.997960i | \(0.520334\pi\) | |||||||
\(422\) | 15.5928 | 0.759048 | ||||||||
\(423\) | 1.83866 | 0.0893985 | ||||||||
\(424\) | −5.88254 | −0.285681 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.86663 | −0.235789 | ||||||||
\(427\) | 36.8432 | 1.78297 | ||||||||
\(428\) | 3.10006 | 0.149847 | ||||||||
\(429\) | −12.0975 | −0.584073 | ||||||||
\(430\) | 7.80625 | 0.376451 | ||||||||
\(431\) | 13.3377 | 0.642456 | 0.321228 | − | 0.947002i | \(-0.395904\pi\) | ||||
0.321228 | + | 0.947002i | \(0.395904\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −11.1422 | −0.535461 | −0.267730 | − | 0.963494i | \(-0.586274\pi\) | ||||
−0.267730 | + | 0.963494i | \(0.586274\pi\) | |||||||
\(434\) | 18.9344 | 0.908882 | ||||||||
\(435\) | 4.06491 | 0.194897 | ||||||||
\(436\) | 15.4449 | 0.739676 | ||||||||
\(437\) | −26.1128 | −1.24915 | ||||||||
\(438\) | −8.43486 | −0.403033 | ||||||||
\(439\) | 30.1107 | 1.43711 | 0.718554 | − | 0.695471i | \(-0.244804\pi\) | ||||
0.718554 | + | 0.695471i | \(0.244804\pi\) | |||||||
\(440\) | 2.65672 | 0.126654 | ||||||||
\(441\) | 16.1074 | 0.767017 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.4432 | 1.35138 | 0.675689 | − | 0.737187i | \(-0.263846\pi\) | ||||
0.675689 | + | 0.737187i | \(0.263846\pi\) | |||||||
\(444\) | 5.53073 | 0.262477 | ||||||||
\(445\) | 15.5491 | 0.737098 | ||||||||
\(446\) | 0.246992 | 0.0116954 | ||||||||
\(447\) | 0.266600 | 0.0126097 | ||||||||
\(448\) | 4.80701 | 0.227110 | ||||||||
\(449\) | −32.6308 | −1.53994 | −0.769971 | − | 0.638079i | \(-0.779729\pi\) | ||||
−0.769971 | + | 0.638079i | \(0.779729\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 30.1254 | 1.41855 | ||||||||
\(452\) | −4.15242 | −0.195313 | ||||||||
\(453\) | −13.1064 | −0.615794 | ||||||||
\(454\) | −0.206352 | −0.00968458 | ||||||||
\(455\) | 21.8890 | 1.02617 | ||||||||
\(456\) | −6.04449 | −0.283059 | ||||||||
\(457\) | 0.770239 | 0.0360302 | 0.0180151 | − | 0.999838i | \(-0.494265\pi\) | ||||
0.0180151 | + | 0.999838i | \(0.494265\pi\) | |||||||
\(458\) | −12.8458 | −0.600246 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.32010 | −0.201426 | ||||||||
\(461\) | 21.3672 | 0.995169 | 0.497584 | − | 0.867416i | \(-0.334220\pi\) | ||||
0.497584 | + | 0.867416i | \(0.334220\pi\) | |||||||
\(462\) | 12.7709 | 0.594154 | ||||||||
\(463\) | −5.59618 | −0.260076 | −0.130038 | − | 0.991509i | \(-0.541510\pi\) | ||||
−0.130038 | + | 0.991509i | \(0.541510\pi\) | |||||||
\(464\) | 4.06491 | 0.188709 | ||||||||
\(465\) | −3.93892 | −0.182663 | ||||||||
\(466\) | 0.165078 | 0.00764711 | ||||||||
\(467\) | 17.4394 | 0.806998 | 0.403499 | − | 0.914980i | \(-0.367794\pi\) | ||||
0.403499 | + | 0.914980i | \(0.367794\pi\) | |||||||
\(468\) | 4.55356 | 0.210488 | ||||||||
\(469\) | 66.5710 | 3.07397 | ||||||||
\(470\) | −1.83866 | −0.0848109 | ||||||||
\(471\) | 2.93377 | 0.135181 | ||||||||
\(472\) | −3.50381 | −0.161276 | ||||||||
\(473\) | 20.7390 | 0.953579 | ||||||||
\(474\) | 13.1363 | 0.603370 | ||||||||
\(475\) | 6.04449 | 0.277340 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.88254 | 0.269343 | ||||||||
\(478\) | −19.2098 | −0.878635 | ||||||||
\(479\) | −26.6130 | −1.21598 | −0.607990 | − | 0.793945i | \(-0.708024\pi\) | ||||
−0.607990 | + | 0.793945i | \(0.708024\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 25.1845 | 1.14832 | ||||||||
\(482\) | −4.55105 | −0.207294 | ||||||||
\(483\) | −20.7668 | −0.944921 | ||||||||
\(484\) | −3.94187 | −0.179176 | ||||||||
\(485\) | −17.1612 | −0.779251 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −9.44787 | −0.428124 | −0.214062 | − | 0.976820i | \(-0.568669\pi\) | ||||
−0.214062 | + | 0.976820i | \(0.568669\pi\) | |||||||
\(488\) | −7.66447 | −0.346954 | ||||||||
\(489\) | −9.13905 | −0.413282 | ||||||||
\(490\) | −16.1074 | −0.727657 | ||||||||
\(491\) | 11.4423 | 0.516383 | 0.258192 | − | 0.966094i | \(-0.416873\pi\) | ||||
0.258192 | + | 0.966094i | \(0.416873\pi\) | |||||||
\(492\) | −11.3393 | −0.511217 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −27.5239 | −1.23836 | ||||||||
\(495\) | −2.65672 | −0.119410 | ||||||||
\(496\) | −3.93892 | −0.176863 | ||||||||
\(497\) | 23.3939 | 1.04936 | ||||||||
\(498\) | 17.6812 | 0.792316 | ||||||||
\(499\) | −13.8201 | −0.618672 | −0.309336 | − | 0.950953i | \(-0.600107\pi\) | ||||
−0.309336 | + | 0.950953i | \(0.600107\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 19.0664 | 0.851823 | ||||||||
\(502\) | 12.6713 | 0.565548 | ||||||||
\(503\) | 3.80954 | 0.169859 | 0.0849295 | − | 0.996387i | \(-0.472933\pi\) | ||||
0.0849295 | + | 0.996387i | \(0.472933\pi\) | |||||||
\(504\) | −4.80701 | −0.214121 | ||||||||
\(505\) | −6.08472 | −0.270766 | ||||||||
\(506\) | −11.4773 | −0.510227 | ||||||||
\(507\) | 7.73489 | 0.343518 | ||||||||
\(508\) | −13.0929 | −0.580903 | ||||||||
\(509\) | 27.4822 | 1.21813 | 0.609064 | − | 0.793121i | \(-0.291545\pi\) | ||||
0.609064 | + | 0.793121i | \(0.291545\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.5465 | 1.79367 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.04449 | 0.266871 | ||||||||
\(514\) | −10.7579 | −0.474512 | ||||||||
\(515\) | −1.35517 | −0.0597160 | ||||||||
\(516\) | −7.80625 | −0.343651 | ||||||||
\(517\) | −4.88478 | −0.214833 | ||||||||
\(518\) | −26.5863 | −1.16814 | ||||||||
\(519\) | 5.19673 | 0.228111 | ||||||||
\(520\) | −4.55356 | −0.199687 | ||||||||
\(521\) | 9.33363 | 0.408914 | 0.204457 | − | 0.978876i | \(-0.434457\pi\) | ||||
0.204457 | + | 0.978876i | \(0.434457\pi\) | |||||||
\(522\) | −4.06491 | −0.177916 | ||||||||
\(523\) | −29.1806 | −1.27598 | −0.637990 | − | 0.770045i | \(-0.720234\pi\) | ||||
−0.637990 | + | 0.770045i | \(0.720234\pi\) | |||||||
\(524\) | 5.41965 | 0.236758 | ||||||||
\(525\) | 4.80701 | 0.209795 | ||||||||
\(526\) | 8.77699 | 0.382695 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.65672 | −0.115619 | ||||||||
\(529\) | −4.33672 | −0.188553 | ||||||||
\(530\) | −5.88254 | −0.255521 | ||||||||
\(531\) | 3.50381 | 0.152052 | ||||||||
\(532\) | 29.0559 | 1.25973 | ||||||||
\(533\) | −51.6343 | −2.23653 | ||||||||
\(534\) | −15.5491 | −0.672876 | ||||||||
\(535\) | 3.10006 | 0.134027 | ||||||||
\(536\) | −13.8487 | −0.598174 | ||||||||
\(537\) | 0.209059 | 0.00902158 | ||||||||
\(538\) | 17.3898 | 0.749725 | ||||||||
\(539\) | −42.7927 | −1.84321 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −26.1951 | −1.12621 | −0.563107 | − | 0.826384i | \(-0.690394\pi\) | ||||
−0.563107 | + | 0.826384i | \(0.690394\pi\) | |||||||
\(542\) | 17.9138 | 0.769464 | ||||||||
\(543\) | 14.4208 | 0.618856 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.4449 | 0.661586 | ||||||||
\(546\) | −21.8890 | −0.936763 | ||||||||
\(547\) | 27.0508 | 1.15661 | 0.578304 | − | 0.815821i | \(-0.303715\pi\) | ||||
0.578304 | + | 0.815821i | \(0.303715\pi\) | |||||||
\(548\) | 7.13674 | 0.304866 | ||||||||
\(549\) | 7.66447 | 0.327111 | ||||||||
\(550\) | 2.65672 | 0.113283 | ||||||||
\(551\) | 24.5703 | 1.04673 | ||||||||
\(552\) | 4.32010 | 0.183876 | ||||||||
\(553\) | −63.1464 | −2.68526 | ||||||||
\(554\) | 26.2658 | 1.11593 | ||||||||
\(555\) | 5.53073 | 0.234767 | ||||||||
\(556\) | 7.28029 | 0.308753 | ||||||||
\(557\) | −6.91753 | −0.293105 | −0.146552 | − | 0.989203i | \(-0.546818\pi\) | ||||
−0.146552 | + | 0.989203i | \(0.546818\pi\) | |||||||
\(558\) | 3.93892 | 0.166748 | ||||||||
\(559\) | −35.5462 | −1.50344 | ||||||||
\(560\) | 4.80701 | 0.203133 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.5009 | −1.20224 | ||||||||
\(563\) | 34.1322 | 1.43850 | 0.719251 | − | 0.694750i | \(-0.244485\pi\) | ||||
0.719251 | + | 0.694750i | \(0.244485\pi\) | |||||||
\(564\) | 1.83866 | 0.0774214 | ||||||||
\(565\) | −4.15242 | −0.174694 | ||||||||
\(566\) | 3.66103 | 0.153884 | ||||||||
\(567\) | 4.80701 | 0.201876 | ||||||||
\(568\) | −4.86663 | −0.204199 | ||||||||
\(569\) | −27.7102 | −1.16167 | −0.580836 | − | 0.814021i | \(-0.697274\pi\) | ||||
−0.580836 | + | 0.814021i | \(0.697274\pi\) | |||||||
\(570\) | −6.04449 | −0.253176 | ||||||||
\(571\) | 23.2801 | 0.974243 | 0.487122 | − | 0.873334i | \(-0.338047\pi\) | ||||
0.487122 | + | 0.873334i | \(0.338047\pi\) | |||||||
\(572\) | −12.0975 | −0.505822 | ||||||||
\(573\) | 12.3810 | 0.517223 | ||||||||
\(574\) | 54.5083 | 2.27513 | ||||||||
\(575\) | −4.32010 | −0.180161 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −5.51048 | −0.229404 | −0.114702 | − | 0.993400i | \(-0.536591\pi\) | ||||
−0.114702 | + | 0.993400i | \(0.536591\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.59378 | 0.149353 | ||||||||
\(580\) | 4.06491 | 0.168786 | ||||||||
\(581\) | −84.9940 | −3.52614 | ||||||||
\(582\) | 17.1612 | 0.711356 | ||||||||
\(583\) | −15.6282 | −0.647255 | ||||||||
\(584\) | −8.43486 | −0.349037 | ||||||||
\(585\) | 4.55356 | 0.188266 | ||||||||
\(586\) | −15.6314 | −0.645728 | ||||||||
\(587\) | 1.39173 | 0.0574427 | 0.0287214 | − | 0.999587i | \(-0.490856\pi\) | ||||
0.0287214 | + | 0.999587i | \(0.490856\pi\) | |||||||
\(588\) | 16.1074 | 0.664257 | ||||||||
\(589\) | −23.8088 | −0.981023 | ||||||||
\(590\) | −3.50381 | −0.144249 | ||||||||
\(591\) | −4.80943 | −0.197834 | ||||||||
\(592\) | 5.53073 | 0.227312 | ||||||||
\(593\) | 46.3361 | 1.90280 | 0.951399 | − | 0.307962i | \(-0.0996470\pi\) | ||||
0.951399 | + | 0.307962i | \(0.0996470\pi\) | |||||||
\(594\) | 2.65672 | 0.109006 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.266600 | 0.0109204 | ||||||||
\(597\) | 4.44449 | 0.181901 | ||||||||
\(598\) | 19.6718 | 0.804441 | ||||||||
\(599\) | −41.5318 | −1.69694 | −0.848472 | − | 0.529240i | \(-0.822477\pi\) | ||||
−0.848472 | + | 0.529240i | \(0.822477\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −21.6941 | −0.884921 | −0.442461 | − | 0.896788i | \(-0.645894\pi\) | ||||
−0.442461 | + | 0.896788i | \(0.645894\pi\) | |||||||
\(602\) | 37.5247 | 1.52939 | ||||||||
\(603\) | 13.8487 | 0.563964 | ||||||||
\(604\) | −13.1064 | −0.533293 | ||||||||
\(605\) | −3.94187 | −0.160260 | ||||||||
\(606\) | 6.08472 | 0.247175 | ||||||||
\(607\) | 2.93865 | 0.119276 | 0.0596381 | − | 0.998220i | \(-0.481005\pi\) | ||||
0.0596381 | + | 0.998220i | \(0.481005\pi\) | |||||||
\(608\) | −6.04449 | −0.245136 | ||||||||
\(609\) | 19.5401 | 0.791803 | ||||||||
\(610\) | −7.66447 | −0.310325 | ||||||||
\(611\) | 8.37243 | 0.338712 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.6455 | 1.03581 | 0.517906 | − | 0.855438i | \(-0.326712\pi\) | ||||
0.517906 | + | 0.855438i | \(0.326712\pi\) | |||||||
\(614\) | 1.39589 | 0.0563335 | ||||||||
\(615\) | −11.3393 | −0.457246 | ||||||||
\(616\) | 12.7709 | 0.514553 | ||||||||
\(617\) | 2.65698 | 0.106966 | 0.0534829 | − | 0.998569i | \(-0.482968\pi\) | ||||
0.0534829 | + | 0.998569i | \(0.482968\pi\) | |||||||
\(618\) | 1.35517 | 0.0545130 | ||||||||
\(619\) | 8.27530 | 0.332612 | 0.166306 | − | 0.986074i | \(-0.446816\pi\) | ||||
0.166306 | + | 0.986074i | \(0.446816\pi\) | |||||||
\(620\) | −3.93892 | −0.158191 | ||||||||
\(621\) | −4.32010 | −0.173360 | ||||||||
\(622\) | 3.49665 | 0.140203 | ||||||||
\(623\) | 74.7447 | 2.99458 | ||||||||
\(624\) | 4.55356 | 0.182288 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.2668 | 0.929928 | ||||||||
\(627\) | −16.0585 | −0.641314 | ||||||||
\(628\) | 2.93377 | 0.117070 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −4.80701 | −0.191516 | ||||||||
\(631\) | 15.7145 | 0.625583 | 0.312791 | − | 0.949822i | \(-0.398736\pi\) | ||||
0.312791 | + | 0.949822i | \(0.398736\pi\) | |||||||
\(632\) | 13.1363 | 0.522534 | ||||||||
\(633\) | −15.5928 | −0.619760 | ||||||||
\(634\) | 15.1546 | 0.601867 | ||||||||
\(635\) | −13.0929 | −0.519576 | ||||||||
\(636\) | 5.88254 | 0.233258 | ||||||||
\(637\) | 73.3458 | 2.90607 | ||||||||
\(638\) | 10.7993 | 0.427548 | ||||||||
\(639\) | 4.86663 | 0.192521 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −21.1603 | −0.835780 | −0.417890 | − | 0.908498i | \(-0.637230\pi\) | ||||
−0.417890 | + | 0.908498i | \(0.637230\pi\) | |||||||
\(642\) | −3.10006 | −0.122349 | ||||||||
\(643\) | 22.0202 | 0.868392 | 0.434196 | − | 0.900818i | \(-0.357032\pi\) | ||||
0.434196 | + | 0.900818i | \(0.357032\pi\) | |||||||
\(644\) | −20.7668 | −0.818326 | ||||||||
\(645\) | −7.80625 | −0.307371 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 38.7558 | 1.52365 | 0.761824 | − | 0.647784i | \(-0.224304\pi\) | ||||
0.761824 | + | 0.647784i | \(0.224304\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −9.30861 | −0.365395 | ||||||||
\(650\) | −4.55356 | −0.178605 | ||||||||
\(651\) | −18.9344 | −0.742099 | ||||||||
\(652\) | −9.13905 | −0.357913 | ||||||||
\(653\) | −11.7703 | −0.460608 | −0.230304 | − | 0.973119i | \(-0.573972\pi\) | ||||
−0.230304 | + | 0.973119i | \(0.573972\pi\) | |||||||
\(654\) | −15.4449 | −0.603943 | ||||||||
\(655\) | 5.41965 | 0.211763 | ||||||||
\(656\) | −11.3393 | −0.442727 | ||||||||
\(657\) | 8.43486 | 0.329075 | ||||||||
\(658\) | −8.83844 | −0.344558 | ||||||||
\(659\) | −39.9393 | −1.55581 | −0.777906 | − | 0.628380i | \(-0.783718\pi\) | ||||
−0.777906 | + | 0.628380i | \(0.783718\pi\) | |||||||
\(660\) | −2.65672 | −0.103412 | ||||||||
\(661\) | 4.91728 | 0.191260 | 0.0956301 | − | 0.995417i | \(-0.469513\pi\) | ||||
0.0956301 | + | 0.995417i | \(0.469513\pi\) | |||||||
\(662\) | 24.0083 | 0.933108 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.6812 | 0.686166 | ||||||||
\(665\) | 29.0559 | 1.12674 | ||||||||
\(666\) | −5.53073 | −0.214312 | ||||||||
\(667\) | −17.5608 | −0.679957 | ||||||||
\(668\) | 19.0664 | 0.737700 | ||||||||
\(669\) | −0.246992 | −0.00954928 | ||||||||
\(670\) | −13.8487 | −0.535023 | ||||||||
\(671\) | −20.3623 | −0.786078 | ||||||||
\(672\) | −4.80701 | −0.185435 | ||||||||
\(673\) | 37.1460 | 1.43187 | 0.715936 | − | 0.698166i | \(-0.246000\pi\) | ||||
0.715936 | + | 0.698166i | \(0.246000\pi\) | |||||||
\(674\) | 26.8726 | 1.03509 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 7.73489 | 0.297496 | ||||||||
\(677\) | 4.15436 | 0.159665 | 0.0798325 | − | 0.996808i | \(-0.474561\pi\) | ||||
0.0798325 | + | 0.996808i | \(0.474561\pi\) | |||||||
\(678\) | 4.15242 | 0.159473 | ||||||||
\(679\) | −82.4942 | −3.16584 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.206352 | 0.00790743 | ||||||||
\(682\) | −10.4646 | −0.400710 | ||||||||
\(683\) | 36.1292 | 1.38245 | 0.691223 | − | 0.722642i | \(-0.257072\pi\) | ||||
0.691223 | + | 0.722642i | \(0.257072\pi\) | |||||||
\(684\) | 6.04449 | 0.231117 | ||||||||
\(685\) | 7.13674 | 0.272681 | ||||||||
\(686\) | −43.7792 | −1.67150 | ||||||||
\(687\) | 12.8458 | 0.490098 | ||||||||
\(688\) | −7.80625 | −0.297610 | ||||||||
\(689\) | 26.7865 | 1.02048 | ||||||||
\(690\) | 4.32010 | 0.164463 | ||||||||
\(691\) | −20.2855 | −0.771697 | −0.385849 | − | 0.922562i | \(-0.626091\pi\) | ||||
−0.385849 | + | 0.922562i | \(0.626091\pi\) | |||||||
\(692\) | 5.19673 | 0.197550 | ||||||||
\(693\) | −12.7709 | −0.485125 | ||||||||
\(694\) | −7.98128 | −0.302965 | ||||||||
\(695\) | 7.28029 | 0.276157 | ||||||||
\(696\) | −4.06491 | −0.154080 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 13.3176 | 0.504078 | ||||||||
\(699\) | −0.165078 | −0.00624384 | ||||||||
\(700\) | 4.80701 | 0.181688 | ||||||||
\(701\) | 15.9377 | 0.601958 | 0.300979 | − | 0.953631i | \(-0.402687\pi\) | ||||
0.300979 | + | 0.953631i | \(0.402687\pi\) | |||||||
\(702\) | −4.55356 | −0.171863 | ||||||||
\(703\) | 33.4305 | 1.26085 | ||||||||
\(704\) | −2.65672 | −0.100129 | ||||||||
\(705\) | 1.83866 | 0.0692478 | ||||||||
\(706\) | 16.9293 | 0.637141 | ||||||||
\(707\) | −29.2493 | −1.10003 | ||||||||
\(708\) | 3.50381 | 0.131681 | ||||||||
\(709\) | 43.9963 | 1.65231 | 0.826157 | − | 0.563439i | \(-0.190522\pi\) | ||||
0.826157 | + | 0.563439i | \(0.190522\pi\) | |||||||
\(710\) | −4.86663 | −0.182641 | ||||||||
\(711\) | −13.1363 | −0.492650 | ||||||||
\(712\) | −15.5491 | −0.582727 | ||||||||
\(713\) | 17.0165 | 0.637274 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0975 | −0.452421 | ||||||||
\(716\) | 0.209059 | 0.00781292 | ||||||||
\(717\) | 19.2098 | 0.717402 | ||||||||
\(718\) | −20.8739 | −0.779009 | ||||||||
\(719\) | −21.3486 | −0.796169 | −0.398084 | − | 0.917349i | \(-0.630325\pi\) | ||||
−0.398084 | + | 0.917349i | \(0.630325\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −6.51433 | −0.242606 | ||||||||
\(722\) | −17.5358 | −0.652617 | ||||||||
\(723\) | 4.55105 | 0.169255 | ||||||||
\(724\) | 14.4208 | 0.535945 | ||||||||
\(725\) | 4.06491 | 0.150967 | ||||||||
\(726\) | 3.94187 | 0.146296 | ||||||||
\(727\) | −3.91209 | −0.145091 | −0.0725457 | − | 0.997365i | \(-0.523112\pi\) | ||||
−0.0725457 | + | 0.997365i | \(0.523112\pi\) | |||||||
\(728\) | −21.8890 | −0.811261 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.43486 | −0.312188 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 7.66447 | 0.283287 | ||||||||
\(733\) | 6.92135 | 0.255646 | 0.127823 | − | 0.991797i | \(-0.459201\pi\) | ||||
0.127823 | + | 0.991797i | \(0.459201\pi\) | |||||||
\(734\) | 9.48837 | 0.350222 | ||||||||
\(735\) | 16.1074 | 0.594129 | ||||||||
\(736\) | 4.32010 | 0.159241 | ||||||||
\(737\) | −36.7921 | −1.35526 | ||||||||
\(738\) | 11.3393 | 0.417407 | ||||||||
\(739\) | −2.94473 | −0.108324 | −0.0541619 | − | 0.998532i | \(-0.517249\pi\) | ||||
−0.0541619 | + | 0.998532i | \(0.517249\pi\) | |||||||
\(740\) | 5.53073 | 0.203314 | ||||||||
\(741\) | 27.5239 | 1.01112 | ||||||||
\(742\) | −28.2774 | −1.03810 | ||||||||
\(743\) | −39.4041 | −1.44560 | −0.722798 | − | 0.691059i | \(-0.757144\pi\) | ||||
−0.722798 | + | 0.691059i | \(0.757144\pi\) | |||||||
\(744\) | 3.93892 | 0.144408 | ||||||||
\(745\) | 0.266600 | 0.00976746 | ||||||||
\(746\) | 8.88776 | 0.325404 | ||||||||
\(747\) | −17.6812 | −0.646923 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.9020 | 0.544508 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 33.2917 | 1.21483 | 0.607416 | − | 0.794384i | \(-0.292206\pi\) | ||||
0.607416 | + | 0.794384i | \(0.292206\pi\) | |||||||
\(752\) | 1.83866 | 0.0670489 | ||||||||
\(753\) | −12.6713 | −0.461768 | ||||||||
\(754\) | −18.5098 | −0.674087 | ||||||||
\(755\) | −13.1064 | −0.476992 | ||||||||
\(756\) | 4.80701 | 0.174829 | ||||||||
\(757\) | 46.6744 | 1.69641 | 0.848206 | − | 0.529667i | \(-0.177683\pi\) | ||||
0.848206 | + | 0.529667i | \(0.177683\pi\) | |||||||
\(758\) | 20.5944 | 0.748022 | ||||||||
\(759\) | 11.4773 | 0.416599 | ||||||||
\(760\) | −6.04449 | −0.219257 | ||||||||
\(761\) | −7.34541 | −0.266271 | −0.133135 | − | 0.991098i | \(-0.542505\pi\) | ||||
−0.133135 | + | 0.991098i | \(0.542505\pi\) | |||||||
\(762\) | 13.0929 | 0.474305 | ||||||||
\(763\) | 74.2437 | 2.68780 | ||||||||
\(764\) | 12.3810 | 0.447928 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.6635 | 1.18018 | ||||||||
\(767\) | 15.9548 | 0.576094 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 39.8949 | 1.43865 | 0.719324 | − | 0.694675i | \(-0.244452\pi\) | ||||
0.719324 | + | 0.694675i | \(0.244452\pi\) | |||||||
\(770\) | 12.7709 | 0.460230 | ||||||||
\(771\) | 10.7579 | 0.387437 | ||||||||
\(772\) | 3.59378 | 0.129343 | ||||||||
\(773\) | 37.0561 | 1.33281 | 0.666407 | − | 0.745588i | \(-0.267831\pi\) | ||||
0.666407 | + | 0.745588i | \(0.267831\pi\) | |||||||
\(774\) | 7.80625 | 0.280590 | ||||||||
\(775\) | −3.93892 | −0.141490 | ||||||||
\(776\) | 17.1612 | 0.616052 | ||||||||
\(777\) | 26.5863 | 0.953778 | ||||||||
\(778\) | −26.9553 | −0.966394 | ||||||||
\(779\) | −68.5405 | −2.45572 | ||||||||
\(780\) | 4.55356 | 0.163044 | ||||||||
\(781\) | −12.9292 | −0.462645 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.06491 | 0.145268 | ||||||||
\(784\) | 16.1074 | 0.575263 | ||||||||
\(785\) | 2.93377 | 0.104711 | ||||||||
\(786\) | −5.41965 | −0.193312 | ||||||||
\(787\) | 38.9395 | 1.38804 | 0.694021 | − | 0.719954i | \(-0.255837\pi\) | ||||
0.694021 | + | 0.719954i | \(0.255837\pi\) | |||||||
\(788\) | −4.80943 | −0.171329 | ||||||||
\(789\) | −8.77699 | −0.312469 | ||||||||
\(790\) | 13.1363 | 0.467369 | ||||||||
\(791\) | −19.9607 | −0.709722 | ||||||||
\(792\) | 2.65672 | 0.0944023 | ||||||||
\(793\) | 34.9006 | 1.23936 | ||||||||
\(794\) | −30.6356 | −1.08722 | ||||||||
\(795\) | 5.88254 | 0.208632 | ||||||||
\(796\) | 4.44449 | 0.157531 | ||||||||
\(797\) | 19.9096 | 0.705235 | 0.352617 | − | 0.935768i | \(-0.385292\pi\) | ||||
0.352617 | + | 0.935768i | \(0.385292\pi\) | |||||||
\(798\) | −29.0559 | −1.02857 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 15.5491 | 0.549401 | ||||||||
\(802\) | 28.4374 | 1.00416 | ||||||||
\(803\) | −22.4090 | −0.790797 | ||||||||
\(804\) | 13.8487 | 0.488407 | ||||||||
\(805\) | −20.7668 | −0.731933 | ||||||||
\(806\) | 17.9361 | 0.631772 | ||||||||
\(807\) | −17.3898 | −0.612148 | ||||||||
\(808\) | 6.08472 | 0.214060 | ||||||||
\(809\) | −47.0466 | −1.65407 | −0.827036 | − | 0.562149i | \(-0.809975\pi\) | ||||
−0.827036 | + | 0.562149i | \(0.809975\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −28.1042 | −0.986873 | −0.493436 | − | 0.869782i | \(-0.664259\pi\) | ||||
−0.493436 | + | 0.869782i | \(0.664259\pi\) | |||||||
\(812\) | 19.5401 | 0.685722 | ||||||||
\(813\) | −17.9138 | −0.628265 | ||||||||
\(814\) | 14.6936 | 0.515010 | ||||||||
\(815\) | −9.13905 | −0.320127 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.1848 | −1.65079 | ||||||||
\(818\) | 30.3744 | 1.06202 | ||||||||
\(819\) | 21.8890 | 0.764864 | ||||||||
\(820\) | −11.3393 | −0.395987 | ||||||||
\(821\) | 10.3014 | 0.359521 | 0.179760 | − | 0.983710i | \(-0.442468\pi\) | ||||
0.179760 | + | 0.983710i | \(0.442468\pi\) | |||||||
\(822\) | −7.13674 | −0.248922 | ||||||||
\(823\) | 38.9160 | 1.35653 | 0.678263 | − | 0.734819i | \(-0.262733\pi\) | ||||
0.678263 | + | 0.734819i | \(0.262733\pi\) | |||||||
\(824\) | 1.35517 | 0.0472097 | ||||||||
\(825\) | −2.65672 | −0.0924949 | ||||||||
\(826\) | −16.8428 | −0.586037 | ||||||||
\(827\) | 37.3497 | 1.29878 | 0.649388 | − | 0.760457i | \(-0.275025\pi\) | ||||
0.649388 | + | 0.760457i | \(0.275025\pi\) | |||||||
\(828\) | −4.32010 | −0.150134 | ||||||||
\(829\) | 39.3644 | 1.36718 | 0.683590 | − | 0.729866i | \(-0.260418\pi\) | ||||
0.683590 | + | 0.729866i | \(0.260418\pi\) | |||||||
\(830\) | 17.6812 | 0.613725 | ||||||||
\(831\) | −26.2658 | −0.911151 | ||||||||
\(832\) | 4.55356 | 0.157866 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.28029 | −0.252096 | ||||||||
\(835\) | 19.0664 | 0.659819 | ||||||||
\(836\) | −16.0585 | −0.555394 | ||||||||
\(837\) | −3.93892 | −0.136149 | ||||||||
\(838\) | 22.0797 | 0.762731 | ||||||||
\(839\) | 42.8275 | 1.47857 | 0.739285 | − | 0.673392i | \(-0.235163\pi\) | ||||
0.739285 | + | 0.673392i | \(0.235163\pi\) | |||||||
\(840\) | −4.80701 | −0.165858 | ||||||||
\(841\) | −12.4765 | −0.430225 | ||||||||
\(842\) | 2.61967 | 0.0902797 | ||||||||
\(843\) | 28.5009 | 0.981624 | ||||||||
\(844\) | −15.5928 | −0.536728 | ||||||||
\(845\) | 7.73489 | 0.266088 | ||||||||
\(846\) | −1.83866 | −0.0632143 | ||||||||
\(847\) | −18.9486 | −0.651081 | ||||||||
\(848\) | 5.88254 | 0.202007 | ||||||||
\(849\) | −3.66103 | −0.125646 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.8933 | −0.819053 | ||||||||
\(852\) | 4.86663 | 0.166728 | ||||||||
\(853\) | −11.3847 | −0.389804 | −0.194902 | − | 0.980823i | \(-0.562439\pi\) | ||||
−0.194902 | + | 0.980823i | \(0.562439\pi\) | |||||||
\(854\) | −36.8432 | −1.26075 | ||||||||
\(855\) | 6.04449 | 0.206717 | ||||||||
\(856\) | −3.10006 | −0.105958 | ||||||||
\(857\) | 14.5298 | 0.496327 | 0.248164 | − | 0.968718i | \(-0.420173\pi\) | ||||
0.248164 | + | 0.968718i | \(0.420173\pi\) | |||||||
\(858\) | 12.0975 | 0.413002 | ||||||||
\(859\) | −18.8024 | −0.641530 | −0.320765 | − | 0.947159i | \(-0.603940\pi\) | ||||
−0.320765 | + | 0.947159i | \(0.603940\pi\) | |||||||
\(860\) | −7.80625 | −0.266191 | ||||||||
\(861\) | −54.5083 | −1.85764 | ||||||||
\(862\) | −13.3377 | −0.454285 | ||||||||
\(863\) | −3.91801 | −0.133371 | −0.0666853 | − | 0.997774i | \(-0.521242\pi\) | ||||
−0.0666853 | + | 0.997774i | \(0.521242\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 5.19673 | 0.176694 | ||||||||
\(866\) | 11.1422 | 0.378628 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18.9344 | −0.642677 | ||||||||
\(869\) | 34.8994 | 1.18388 | ||||||||
\(870\) | −4.06491 | −0.137813 | ||||||||
\(871\) | 63.0610 | 2.13674 | ||||||||
\(872\) | −15.4449 | −0.523030 | ||||||||
\(873\) | −17.1612 | −0.580820 | ||||||||
\(874\) | 26.1128 | 0.883279 | ||||||||
\(875\) | 4.80701 | 0.162507 | ||||||||
\(876\) | 8.43486 | 0.284988 | ||||||||
\(877\) | 10.7928 | 0.364449 | 0.182224 | − | 0.983257i | \(-0.441670\pi\) | ||||
0.182224 | + | 0.983257i | \(0.441670\pi\) | |||||||
\(878\) | −30.1107 | −1.01619 | ||||||||
\(879\) | 15.6314 | 0.527235 | ||||||||
\(880\) | −2.65672 | −0.0895578 | ||||||||
\(881\) | −30.3602 | −1.02286 | −0.511430 | − | 0.859325i | \(-0.670884\pi\) | ||||
−0.511430 | + | 0.859325i | \(0.670884\pi\) | |||||||
\(882\) | −16.1074 | −0.542363 | ||||||||
\(883\) | 38.7408 | 1.30373 | 0.651866 | − | 0.758334i | \(-0.273986\pi\) | ||||
0.651866 | + | 0.758334i | \(0.273986\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.50381 | 0.117779 | ||||||||
\(886\) | −28.4432 | −0.955569 | ||||||||
\(887\) | −55.1041 | −1.85021 | −0.925107 | − | 0.379706i | \(-0.876025\pi\) | ||||
−0.925107 | + | 0.379706i | \(0.876025\pi\) | |||||||
\(888\) | −5.53073 | −0.185599 | ||||||||
\(889\) | −62.9377 | −2.11086 | ||||||||
\(890\) | −15.5491 | −0.521207 | ||||||||
\(891\) | −2.65672 | −0.0890033 | ||||||||
\(892\) | −0.246992 | −0.00826992 | ||||||||
\(893\) | 11.1137 | 0.371907 | ||||||||
\(894\) | −0.266600 | −0.00891643 | ||||||||
\(895\) | 0.209059 | 0.00698809 | ||||||||
\(896\) | −4.80701 | −0.160591 | ||||||||
\(897\) | −19.6718 | −0.656823 | ||||||||
\(898\) | 32.6308 | 1.08890 | ||||||||
\(899\) | −16.0113 | −0.534008 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −30.1254 | −1.00307 | ||||||||
\(903\) | −37.5247 | −1.24874 | ||||||||
\(904\) | 4.15242 | 0.138107 | ||||||||
\(905\) | 14.4208 | 0.479364 | ||||||||
\(906\) | 13.1064 | 0.435432 | ||||||||
\(907\) | −29.6139 | −0.983315 | −0.491657 | − | 0.870789i | \(-0.663609\pi\) | ||||
−0.491657 | + | 0.870789i | \(0.663609\pi\) | |||||||
\(908\) | 0.206352 | 0.00684804 | ||||||||
\(909\) | −6.08472 | −0.201817 | ||||||||
\(910\) | −21.8890 | −0.725614 | ||||||||
\(911\) | 2.96899 | 0.0983669 | 0.0491835 | − | 0.998790i | \(-0.484338\pi\) | ||||
0.0491835 | + | 0.998790i | \(0.484338\pi\) | |||||||
\(912\) | 6.04449 | 0.200153 | ||||||||
\(913\) | 46.9740 | 1.55461 | ||||||||
\(914\) | −0.770239 | −0.0254772 | ||||||||
\(915\) | 7.66447 | 0.253379 | ||||||||
\(916\) | 12.8458 | 0.424438 | ||||||||
\(917\) | 26.0523 | 0.860323 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.58747 | −0.0523659 | −0.0261830 | − | 0.999657i | \(-0.508335\pi\) | ||||
−0.0261830 | + | 0.999657i | \(0.508335\pi\) | |||||||
\(920\) | 4.32010 | 0.142430 | ||||||||
\(921\) | −1.39589 | −0.0459961 | ||||||||
\(922\) | −21.3672 | −0.703691 | ||||||||
\(923\) | 22.1605 | 0.729421 | ||||||||
\(924\) | −12.7709 | −0.420131 | ||||||||
\(925\) | 5.53073 | 0.181849 | ||||||||
\(926\) | 5.59618 | 0.183902 | ||||||||
\(927\) | −1.35517 | −0.0445097 | ||||||||
\(928\) | −4.06491 | −0.133437 | ||||||||
\(929\) | −27.4847 | −0.901744 | −0.450872 | − | 0.892589i | \(-0.648887\pi\) | ||||
−0.450872 | + | 0.892589i | \(0.648887\pi\) | |||||||
\(930\) | 3.93892 | 0.129162 | ||||||||
\(931\) | 97.3608 | 3.19087 | ||||||||
\(932\) | −0.165078 | −0.00540732 | ||||||||
\(933\) | −3.49665 | −0.114475 | ||||||||
\(934\) | −17.4394 | −0.570634 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.55356 | −0.148838 | ||||||||
\(937\) | −43.8053 | −1.43106 | −0.715529 | − | 0.698583i | \(-0.753814\pi\) | ||||
−0.715529 | + | 0.698583i | \(0.753814\pi\) | |||||||
\(938\) | −66.5710 | −2.17362 | ||||||||
\(939\) | −23.2668 | −0.759283 | ||||||||
\(940\) | 1.83866 | 0.0599703 | ||||||||
\(941\) | 31.1296 | 1.01479 | 0.507397 | − | 0.861712i | \(-0.330608\pi\) | ||||
0.507397 | + | 0.861712i | \(0.330608\pi\) | |||||||
\(942\) | −2.93377 | −0.0955872 | ||||||||
\(943\) | 48.9871 | 1.59524 | ||||||||
\(944\) | 3.50381 | 0.114039 | ||||||||
\(945\) | 4.80701 | 0.156372 | ||||||||
\(946\) | −20.7390 | −0.674282 | ||||||||
\(947\) | −5.39288 | −0.175245 | −0.0876225 | − | 0.996154i | \(-0.527927\pi\) | ||||
−0.0876225 | + | 0.996154i | \(0.527927\pi\) | |||||||
\(948\) | −13.1363 | −0.426647 | ||||||||
\(949\) | 38.4086 | 1.24680 | ||||||||
\(950\) | −6.04449 | −0.196109 | ||||||||
\(951\) | −15.1546 | −0.491422 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.3834 | −0.984215 | −0.492107 | − | 0.870535i | \(-0.663773\pi\) | ||||
−0.492107 | + | 0.870535i | \(0.663773\pi\) | |||||||
\(954\) | −5.88254 | −0.190454 | ||||||||
\(955\) | 12.3810 | 0.400639 | ||||||||
\(956\) | 19.2098 | 0.621288 | ||||||||
\(957\) | −10.7993 | −0.349092 | ||||||||
\(958\) | 26.6130 | 0.859827 | ||||||||
\(959\) | 34.3064 | 1.10781 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −15.4849 | −0.499513 | ||||||||
\(962\) | −25.1845 | −0.811981 | ||||||||
\(963\) | 3.10006 | 0.0998979 | ||||||||
\(964\) | 4.55105 | 0.146579 | ||||||||
\(965\) | 3.59378 | 0.115688 | ||||||||
\(966\) | 20.7668 | 0.668160 | ||||||||
\(967\) | 18.8257 | 0.605395 | 0.302698 | − | 0.953087i | \(-0.402113\pi\) | ||||
0.302698 | + | 0.953087i | \(0.402113\pi\) | |||||||
\(968\) | 3.94187 | 0.126696 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 17.1612 | 0.551014 | ||||||||
\(971\) | −34.5809 | −1.10975 | −0.554876 | − | 0.831933i | \(-0.687234\pi\) | ||||
−0.554876 | + | 0.831933i | \(0.687234\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 34.9964 | 1.12193 | ||||||||
\(974\) | 9.44787 | 0.302729 | ||||||||
\(975\) | 4.55356 | 0.145831 | ||||||||
\(976\) | 7.66447 | 0.245334 | ||||||||
\(977\) | 8.43629 | 0.269901 | 0.134950 | − | 0.990852i | \(-0.456912\pi\) | ||||
0.134950 | + | 0.990852i | \(0.456912\pi\) | |||||||
\(978\) | 9.13905 | 0.292234 | ||||||||
\(979\) | −41.3095 | −1.32026 | ||||||||
\(980\) | 16.1074 | 0.514531 | ||||||||
\(981\) | 15.4449 | 0.493117 | ||||||||
\(982\) | −11.4423 | −0.365138 | ||||||||
\(983\) | −26.8259 | −0.855614 | −0.427807 | − | 0.903870i | \(-0.640714\pi\) | ||||
−0.427807 | + | 0.903870i | \(0.640714\pi\) | |||||||
\(984\) | 11.3393 | 0.361485 | ||||||||
\(985\) | −4.80943 | −0.153241 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.83844 | 0.281331 | ||||||||
\(988\) | 27.5239 | 0.875653 | ||||||||
\(989\) | 33.7238 | 1.07235 | ||||||||
\(990\) | 2.65672 | 0.0844359 | ||||||||
\(991\) | −8.83209 | −0.280561 | −0.140280 | − | 0.990112i | \(-0.544800\pi\) | ||||
−0.140280 | + | 0.990112i | \(0.544800\pi\) | |||||||
\(992\) | 3.93892 | 0.125061 | ||||||||
\(993\) | −24.0083 | −0.761879 | ||||||||
\(994\) | −23.3939 | −0.742011 | ||||||||
\(995\) | 4.44449 | 0.140900 | ||||||||
\(996\) | −17.6812 | −0.560252 | ||||||||
\(997\) | −42.7597 | −1.35421 | −0.677107 | − | 0.735885i | \(-0.736767\pi\) | ||||
−0.677107 | + | 0.735885i | \(0.736767\pi\) | |||||||
\(998\) | 13.8201 | 0.437467 | ||||||||
\(999\) | 5.53073 | 0.174985 |
(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 | 8670.2.a.ck.1.7 | 8 | ||
17.10 | odd | 16 | 510.2.u.c.151.4 | ✓ | 16 | ||
17.12 | odd | 16 | 510.2.u.c.331.4 | yes | 16 | ||
17.16 | even | 2 | 8670.2.a.cj.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
510.2.u.c.151.4 | ✓ | 16 | 17.10 | odd | 16 | ||
510.2.u.c.331.4 | yes | 16 | 17.12 | odd | 16 | ||
8670.2.a.cj.1.2 | 8 | 17.16 | even | 2 | |||
8670.2.a.ck.1.7 | 8 | 1.1 | even | 1 | trivial |