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: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 12x^{6} + 46x^{5} + 54x^{4} - 148x^{3} - 98x^{2} + 126x + 69 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 446) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.34519\) 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 | ||||||||
\(5\) | −2.47654 | −1.10754 | −0.553771 | − | 0.832669i | \(-0.686812\pi\) | ||||
−0.553771 | + | 0.832669i | \(0.686812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.22714 | 1.59771 | 0.798854 | − | 0.601526i | \(-0.205440\pi\) | ||||
0.798854 | + | 0.601526i | \(0.205440\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.47654 | −0.783150 | ||||||||
\(11\) | 5.26393 | 1.58713 | 0.793567 | − | 0.608483i | \(-0.208221\pi\) | ||||
0.793567 | + | 0.608483i | \(0.208221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.397464 | −0.110237 | −0.0551183 | − | 0.998480i | \(-0.517554\pi\) | ||||
−0.0551183 | + | 0.998480i | \(0.517554\pi\) | |||||||
\(14\) | 4.22714 | 1.12975 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.36962 | −0.817252 | −0.408626 | − | 0.912702i | \(-0.633992\pi\) | ||||
−0.408626 | + | 0.912702i | \(0.633992\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.28228 | 1.44125 | 0.720627 | − | 0.693323i | \(-0.243854\pi\) | ||||
0.720627 | + | 0.693323i | \(0.243854\pi\) | |||||||
\(20\) | −2.47654 | −0.553771 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.26393 | 1.12227 | ||||||||
\(23\) | 5.61872 | 1.17159 | 0.585793 | − | 0.810461i | \(-0.300783\pi\) | ||||
0.585793 | + | 0.810461i | \(0.300783\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.13324 | 0.226648 | ||||||||
\(26\) | −0.397464 | −0.0779490 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.22714 | 0.798854 | ||||||||
\(29\) | −6.69038 | −1.24237 | −0.621186 | − | 0.783663i | \(-0.713349\pi\) | ||||
−0.621186 | + | 0.783663i | \(0.713349\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.70413 | 0.306071 | 0.153036 | − | 0.988221i | \(-0.451095\pi\) | ||||
0.153036 | + | 0.988221i | \(0.451095\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.36962 | −0.577885 | ||||||||
\(35\) | −10.4687 | −1.76953 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0571 | 1.65337 | 0.826685 | − | 0.562665i | \(-0.190224\pi\) | ||||
0.826685 | + | 0.562665i | \(0.190224\pi\) | |||||||
\(38\) | 6.28228 | 1.01912 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.47654 | −0.391575 | ||||||||
\(41\) | −7.86868 | −1.22888 | −0.614440 | − | 0.788963i | \(-0.710618\pi\) | ||||
−0.614440 | + | 0.788963i | \(0.710618\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.70616 | −1.48017 | −0.740087 | − | 0.672511i | \(-0.765216\pi\) | ||||
−0.740087 | + | 0.672511i | \(0.765216\pi\) | |||||||
\(44\) | 5.26393 | 0.793567 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.61872 | 0.828436 | ||||||||
\(47\) | −5.92396 | −0.864098 | −0.432049 | − | 0.901850i | \(-0.642209\pi\) | ||||
−0.432049 | + | 0.901850i | \(0.642209\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.8687 | 1.55267 | ||||||||
\(50\) | 1.13324 | 0.160264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.397464 | −0.0551183 | ||||||||
\(53\) | 9.23536 | 1.26857 | 0.634287 | − | 0.773098i | \(-0.281294\pi\) | ||||
0.634287 | + | 0.773098i | \(0.281294\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.0363 | −1.75782 | ||||||||
\(56\) | 4.22714 | 0.564875 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.69038 | −0.878490 | ||||||||
\(59\) | −1.14009 | −0.148427 | −0.0742137 | − | 0.997242i | \(-0.523645\pi\) | ||||
−0.0742137 | + | 0.997242i | \(0.523645\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.68915 | 0.216273 | 0.108136 | − | 0.994136i | \(-0.465512\pi\) | ||||
0.108136 | + | 0.994136i | \(0.465512\pi\) | |||||||
\(62\) | 1.70413 | 0.216425 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.984334 | 0.122092 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.20836 | −1.00281 | −0.501405 | − | 0.865213i | \(-0.667183\pi\) | ||||
−0.501405 | + | 0.865213i | \(0.667183\pi\) | |||||||
\(68\) | −3.36962 | −0.408626 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.4687 | −1.25124 | ||||||||
\(71\) | −13.5176 | −1.60425 | −0.802124 | − | 0.597157i | \(-0.796297\pi\) | ||||
−0.802124 | + | 0.597157i | \(0.796297\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.5832 | 1.35571 | 0.677853 | − | 0.735197i | \(-0.262910\pi\) | ||||
0.677853 | + | 0.735197i | \(0.262910\pi\) | |||||||
\(74\) | 10.0571 | 1.16911 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.28228 | 0.720627 | ||||||||
\(77\) | 22.2513 | 2.53578 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1922 | 1.37173 | 0.685866 | − | 0.727728i | \(-0.259424\pi\) | ||||
0.685866 | + | 0.727728i | \(0.259424\pi\) | |||||||
\(80\) | −2.47654 | −0.276885 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.86868 | −0.868950 | ||||||||
\(83\) | 11.5699 | 1.26996 | 0.634979 | − | 0.772529i | \(-0.281009\pi\) | ||||
0.634979 | + | 0.772529i | \(0.281009\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.34499 | 0.905141 | ||||||||
\(86\) | −9.70616 | −1.04664 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.26393 | 0.561137 | ||||||||
\(89\) | 2.22335 | 0.235675 | 0.117837 | − | 0.993033i | \(-0.462404\pi\) | ||||
0.117837 | + | 0.993033i | \(0.462404\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.68013 | −0.176126 | ||||||||
\(92\) | 5.61872 | 0.585793 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.92396 | −0.611009 | ||||||||
\(95\) | −15.5583 | −1.59625 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.70312 | 0.477530 | 0.238765 | − | 0.971077i | \(-0.423257\pi\) | ||||
0.238765 | + | 0.971077i | \(0.423257\pi\) | |||||||
\(98\) | 10.8687 | 1.09790 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.13324 | 0.113324 | ||||||||
\(101\) | −7.51418 | −0.747689 | −0.373844 | − | 0.927491i | \(-0.621961\pi\) | ||||
−0.373844 | + | 0.927491i | \(0.621961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.47096 | −0.342004 | −0.171002 | − | 0.985271i | \(-0.554700\pi\) | ||||
−0.171002 | + | 0.985271i | \(0.554700\pi\) | |||||||
\(104\) | −0.397464 | −0.0389745 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.23536 | 0.897017 | ||||||||
\(107\) | 3.40486 | 0.329160 | 0.164580 | − | 0.986364i | \(-0.447373\pi\) | ||||
0.164580 | + | 0.986364i | \(0.447373\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.16765 | 0.303406 | 0.151703 | − | 0.988426i | \(-0.451524\pi\) | ||||
0.151703 | + | 0.988426i | \(0.451524\pi\) | |||||||
\(110\) | −13.0363 | −1.24296 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.22714 | 0.399427 | ||||||||
\(113\) | 13.8478 | 1.30269 | 0.651345 | − | 0.758782i | \(-0.274205\pi\) | ||||
0.651345 | + | 0.758782i | \(0.274205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.9150 | −1.29758 | ||||||||
\(116\) | −6.69038 | −0.621186 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.14009 | −0.104954 | ||||||||
\(119\) | −14.2438 | −1.30573 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.7090 | 1.51900 | ||||||||
\(122\) | 1.68915 | 0.152928 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.70413 | 0.153036 | ||||||||
\(125\) | 9.57618 | 0.856519 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3827 | 1.27626 | 0.638129 | − | 0.769930i | \(-0.279709\pi\) | ||||
0.638129 | + | 0.769930i | \(0.279709\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.984334 | 0.0863318 | ||||||||
\(131\) | 11.4275 | 0.998427 | 0.499214 | − | 0.866479i | \(-0.333622\pi\) | ||||
0.499214 | + | 0.866479i | \(0.333622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.5560 | 2.30270 | ||||||||
\(134\) | −8.20836 | −0.709094 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.36962 | −0.288942 | ||||||||
\(137\) | 12.4673 | 1.06515 | 0.532575 | − | 0.846383i | \(-0.321225\pi\) | ||||
0.532575 | + | 0.846383i | \(0.321225\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.9523 | −1.35306 | −0.676529 | − | 0.736416i | \(-0.736517\pi\) | ||||
−0.676529 | + | 0.736416i | \(0.736517\pi\) | |||||||
\(140\) | −10.4687 | −0.884763 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.5176 | −1.13437 | ||||||||
\(143\) | −2.09222 | −0.174960 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.5690 | 1.37598 | ||||||||
\(146\) | 11.5832 | 0.958630 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.0571 | 0.826685 | ||||||||
\(149\) | −10.1232 | −0.829322 | −0.414661 | − | 0.909976i | \(-0.636100\pi\) | ||||
−0.414661 | + | 0.909976i | \(0.636100\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.60791 | −0.537744 | −0.268872 | − | 0.963176i | \(-0.586651\pi\) | ||||
−0.268872 | + | 0.963176i | \(0.586651\pi\) | |||||||
\(152\) | 6.28228 | 0.509560 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 22.2513 | 1.79306 | ||||||||
\(155\) | −4.22035 | −0.338986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.2131 | −1.53337 | −0.766687 | − | 0.642021i | \(-0.778096\pi\) | ||||
−0.766687 | + | 0.642021i | \(0.778096\pi\) | |||||||
\(158\) | 12.1922 | 0.969961 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.47654 | −0.195788 | ||||||||
\(161\) | 23.7511 | 1.87185 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.03067 | −0.159054 | −0.0795271 | − | 0.996833i | \(-0.525341\pi\) | ||||
−0.0795271 | + | 0.996833i | \(0.525341\pi\) | |||||||
\(164\) | −7.86868 | −0.614440 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.5699 | 0.897996 | ||||||||
\(167\) | −6.69006 | −0.517692 | −0.258846 | − | 0.965919i | \(-0.583342\pi\) | ||||
−0.258846 | + | 0.965919i | \(0.583342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8420 | −0.987848 | ||||||||
\(170\) | 8.34499 | 0.640031 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.70616 | −0.740087 | ||||||||
\(173\) | −9.35263 | −0.711067 | −0.355534 | − | 0.934663i | \(-0.615701\pi\) | ||||
−0.355534 | + | 0.934663i | \(0.615701\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.79036 | 0.362117 | ||||||||
\(176\) | 5.26393 | 0.396784 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.22335 | 0.166647 | ||||||||
\(179\) | 14.3762 | 1.07453 | 0.537265 | − | 0.843414i | \(-0.319458\pi\) | ||||
0.537265 | + | 0.843414i | \(0.319458\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.31275 | −0.617882 | −0.308941 | − | 0.951081i | \(-0.599975\pi\) | ||||
−0.308941 | + | 0.951081i | \(0.599975\pi\) | |||||||
\(182\) | −1.68013 | −0.124540 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.61872 | 0.414218 | ||||||||
\(185\) | −24.9067 | −1.83118 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.7374 | −1.29709 | ||||||||
\(188\) | −5.92396 | −0.432049 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.5583 | −1.12872 | ||||||||
\(191\) | 4.28743 | 0.310227 | 0.155114 | − | 0.987897i | \(-0.450426\pi\) | ||||
0.155114 | + | 0.987897i | \(0.450426\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0794 | −0.869493 | −0.434746 | − | 0.900553i | \(-0.643162\pi\) | ||||
−0.434746 | + | 0.900553i | \(0.643162\pi\) | |||||||
\(194\) | 4.70312 | 0.337665 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.8687 | 0.776334 | ||||||||
\(197\) | 9.02457 | 0.642974 | 0.321487 | − | 0.946914i | \(-0.395817\pi\) | ||||
0.321487 | + | 0.946914i | \(0.395817\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.68635 | 0.403094 | 0.201547 | − | 0.979479i | \(-0.435403\pi\) | ||||
0.201547 | + | 0.979479i | \(0.435403\pi\) | |||||||
\(200\) | 1.13324 | 0.0801322 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.51418 | −0.528696 | ||||||||
\(203\) | −28.2812 | −1.98495 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.4871 | 1.36104 | ||||||||
\(206\) | −3.47096 | −0.241833 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.397464 | −0.0275591 | ||||||||
\(209\) | 33.0695 | 2.28746 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.0768 | 0.969086 | 0.484543 | − | 0.874768i | \(-0.338986\pi\) | ||||
0.484543 | + | 0.874768i | \(0.338986\pi\) | |||||||
\(212\) | 9.23536 | 0.634287 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.40486 | 0.232751 | ||||||||
\(215\) | 24.0377 | 1.63936 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.20360 | 0.489012 | ||||||||
\(218\) | 3.16765 | 0.214540 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −13.0363 | −0.878909 | ||||||||
\(221\) | 1.33930 | 0.0900911 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | 0.0669650 | ||||||||
\(224\) | 4.22714 | 0.282437 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.8478 | 0.921140 | ||||||||
\(227\) | −18.5581 | −1.23175 | −0.615874 | − | 0.787845i | \(-0.711197\pi\) | ||||
−0.615874 | + | 0.787845i | \(0.711197\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.97505 | −0.460924 | −0.230462 | − | 0.973081i | \(-0.574024\pi\) | ||||
−0.230462 | + | 0.973081i | \(0.574024\pi\) | |||||||
\(230\) | −13.9150 | −0.917527 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.69038 | −0.439245 | ||||||||
\(233\) | 20.7728 | 1.36087 | 0.680437 | − | 0.732806i | \(-0.261790\pi\) | ||||
0.680437 | + | 0.732806i | \(0.261790\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.6709 | 0.957024 | ||||||||
\(236\) | −1.14009 | −0.0742137 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.2438 | −0.923291 | ||||||||
\(239\) | 6.29587 | 0.407246 | 0.203623 | − | 0.979049i | \(-0.434728\pi\) | ||||
0.203623 | + | 0.979049i | \(0.434728\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.597940 | 0.0385167 | 0.0192583 | − | 0.999815i | \(-0.493870\pi\) | ||||
0.0192583 | + | 0.999815i | \(0.493870\pi\) | |||||||
\(242\) | 16.7090 | 1.07409 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.68915 | 0.108136 | ||||||||
\(245\) | −26.9167 | −1.71964 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.49698 | −0.158879 | ||||||||
\(248\) | 1.70413 | 0.108212 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.57618 | 0.605651 | ||||||||
\(251\) | 20.8104 | 1.31354 | 0.656770 | − | 0.754091i | \(-0.271922\pi\) | ||||
0.656770 | + | 0.754091i | \(0.271922\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.5766 | 1.85946 | ||||||||
\(254\) | 14.3827 | 0.902450 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.4454 | 0.901079 | 0.450540 | − | 0.892756i | \(-0.351232\pi\) | ||||
0.450540 | + | 0.892756i | \(0.351232\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 42.5126 | 2.64160 | ||||||||
\(260\) | 0.984334 | 0.0610458 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.4275 | 0.705995 | ||||||||
\(263\) | −19.6267 | −1.21023 | −0.605116 | − | 0.796137i | \(-0.706873\pi\) | ||||
−0.605116 | + | 0.796137i | \(0.706873\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.8717 | −1.40500 | ||||||||
\(266\) | 26.5560 | 1.62826 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.20836 | −0.501405 | ||||||||
\(269\) | 18.6877 | 1.13941 | 0.569705 | − | 0.821849i | \(-0.307057\pi\) | ||||
0.569705 | + | 0.821849i | \(0.307057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.8614 | 0.842022 | 0.421011 | − | 0.907055i | \(-0.361675\pi\) | ||||
0.421011 | + | 0.907055i | \(0.361675\pi\) | |||||||
\(272\) | −3.36962 | −0.204313 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.4673 | 0.753174 | ||||||||
\(275\) | 5.96530 | 0.359721 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.45827 | −0.0876192 | −0.0438096 | − | 0.999040i | \(-0.513949\pi\) | ||||
−0.0438096 | + | 0.999040i | \(0.513949\pi\) | |||||||
\(278\) | −15.9523 | −0.956757 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.4687 | −0.625622 | ||||||||
\(281\) | −29.8921 | −1.78321 | −0.891606 | − | 0.452812i | \(-0.850421\pi\) | ||||
−0.891606 | + | 0.452812i | \(0.850421\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9064 | −0.826649 | −0.413325 | − | 0.910584i | \(-0.635633\pi\) | ||||
−0.413325 | + | 0.910584i | \(0.635633\pi\) | |||||||
\(284\) | −13.5176 | −0.802124 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.09222 | −0.123716 | ||||||||
\(287\) | −33.2620 | −1.96339 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.64567 | −0.332098 | ||||||||
\(290\) | 16.5690 | 0.972964 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.5832 | 0.677853 | ||||||||
\(293\) | 9.40146 | 0.549239 | 0.274620 | − | 0.961553i | \(-0.411448\pi\) | ||||
0.274620 | + | 0.961553i | \(0.411448\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.82348 | 0.164390 | ||||||||
\(296\) | 10.0571 | 0.584555 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.1232 | −0.586419 | ||||||||
\(299\) | −2.23324 | −0.129151 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.0292 | −2.36489 | ||||||||
\(302\) | −6.60791 | −0.380243 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.28228 | 0.360313 | ||||||||
\(305\) | −4.18323 | −0.239531 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.68510 | −0.153247 | −0.0766233 | − | 0.997060i | \(-0.524414\pi\) | ||||
−0.0766233 | + | 0.997060i | \(0.524414\pi\) | |||||||
\(308\) | 22.2513 | 1.26789 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.22035 | −0.239700 | ||||||||
\(311\) | −5.58052 | −0.316442 | −0.158221 | − | 0.987404i | \(-0.550576\pi\) | ||||
−0.158221 | + | 0.987404i | \(0.550576\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.58610 | −0.372268 | −0.186134 | − | 0.982524i | \(-0.559596\pi\) | ||||
−0.186134 | + | 0.982524i | \(0.559596\pi\) | |||||||
\(314\) | −19.2131 | −1.08426 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.1922 | 0.685866 | ||||||||
\(317\) | 2.39147 | 0.134318 | 0.0671592 | − | 0.997742i | \(-0.478606\pi\) | ||||
0.0671592 | + | 0.997742i | \(0.478606\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −35.2177 | −1.97181 | ||||||||
\(320\) | −2.47654 | −0.138443 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 23.7511 | 1.32360 | ||||||||
\(323\) | −21.1689 | −1.17787 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.450422 | −0.0249849 | ||||||||
\(326\) | −2.03067 | −0.112468 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.86868 | −0.434475 | ||||||||
\(329\) | −25.0414 | −1.38058 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.1305 | 1.60116 | 0.800578 | − | 0.599229i | \(-0.204526\pi\) | ||||
0.800578 | + | 0.599229i | \(0.204526\pi\) | |||||||
\(332\) | 11.5699 | 0.634979 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.69006 | −0.366064 | ||||||||
\(335\) | 20.3283 | 1.11065 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.8500 | −1.24472 | −0.622360 | − | 0.782731i | \(-0.713826\pi\) | ||||
−0.622360 | + | 0.782731i | \(0.713826\pi\) | |||||||
\(338\) | −12.8420 | −0.698514 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.34499 | 0.452571 | ||||||||
\(341\) | 8.97043 | 0.485776 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.3534 | 0.883002 | ||||||||
\(344\) | −9.70616 | −0.523321 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.35263 | −0.502801 | ||||||||
\(347\) | 21.2023 | 1.13820 | 0.569100 | − | 0.822269i | \(-0.307292\pi\) | ||||
0.569100 | + | 0.822269i | \(0.307292\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.60228 | −0.0857683 | −0.0428842 | − | 0.999080i | \(-0.513655\pi\) | ||||
−0.0428842 | + | 0.999080i | \(0.513655\pi\) | |||||||
\(350\) | 4.79036 | 0.256056 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.26393 | 0.280568 | ||||||||
\(353\) | −33.2158 | −1.76790 | −0.883949 | − | 0.467583i | \(-0.845125\pi\) | ||||
−0.883949 | + | 0.467583i | \(0.845125\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.4769 | 1.77677 | ||||||||
\(356\) | 2.22335 | 0.117837 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.3762 | 0.759807 | ||||||||
\(359\) | 14.4807 | 0.764264 | 0.382132 | − | 0.924108i | \(-0.375190\pi\) | ||||
0.382132 | + | 0.924108i | \(0.375190\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.4670 | 1.07721 | ||||||||
\(362\) | −8.31275 | −0.436909 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.68013 | −0.0880629 | ||||||||
\(365\) | −28.6861 | −1.50150 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.75467 | −0.0915933 | −0.0457966 | − | 0.998951i | \(-0.514583\pi\) | ||||
−0.0457966 | + | 0.998951i | \(0.514583\pi\) | |||||||
\(368\) | 5.61872 | 0.292896 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24.9067 | −1.29484 | ||||||||
\(371\) | 39.0391 | 2.02681 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.25682 | −0.220410 | −0.110205 | − | 0.993909i | \(-0.535151\pi\) | ||||
−0.110205 | + | 0.993909i | \(0.535151\pi\) | |||||||
\(374\) | −17.7374 | −0.917181 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.92396 | −0.305505 | ||||||||
\(377\) | 2.65918 | 0.136955 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.9544 | −0.614057 | −0.307029 | − | 0.951700i | \(-0.599335\pi\) | ||||
−0.307029 | + | 0.951700i | \(0.599335\pi\) | |||||||
\(380\) | −15.5583 | −0.798124 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.28743 | 0.219364 | ||||||||
\(383\) | 8.95992 | 0.457830 | 0.228915 | − | 0.973446i | \(-0.426482\pi\) | ||||
0.228915 | + | 0.973446i | \(0.426482\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −55.1063 | −2.80848 | ||||||||
\(386\) | −12.0794 | −0.614824 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.70312 | 0.238765 | ||||||||
\(389\) | −28.9842 | −1.46956 | −0.734779 | − | 0.678306i | \(-0.762714\pi\) | ||||
−0.734779 | + | 0.678306i | \(0.762714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.9330 | −0.957481 | ||||||||
\(392\) | 10.8687 | 0.548951 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.02457 | 0.454651 | ||||||||
\(395\) | −30.1945 | −1.51925 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.7072 | 1.89247 | 0.946235 | − | 0.323480i | \(-0.104853\pi\) | ||||
0.946235 | + | 0.323480i | \(0.104853\pi\) | |||||||
\(398\) | 5.68635 | 0.285031 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.13324 | 0.0566620 | ||||||||
\(401\) | 12.0873 | 0.603609 | 0.301804 | − | 0.953370i | \(-0.402411\pi\) | ||||
0.301804 | + | 0.953370i | \(0.402411\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.677330 | −0.0337402 | ||||||||
\(404\) | −7.51418 | −0.373844 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −28.2812 | −1.40357 | ||||||||
\(407\) | 52.9397 | 2.62412 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.4033 | −1.55280 | −0.776398 | − | 0.630243i | \(-0.782955\pi\) | ||||
−0.776398 | + | 0.630243i | \(0.782955\pi\) | |||||||
\(410\) | 19.4871 | 0.962398 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.47096 | −0.171002 | ||||||||
\(413\) | −4.81933 | −0.237144 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.6532 | −1.40653 | ||||||||
\(416\) | −0.397464 | −0.0194873 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 33.0695 | 1.61748 | ||||||||
\(419\) | 2.07737 | 0.101486 | 0.0507432 | − | 0.998712i | \(-0.483841\pi\) | ||||
0.0507432 | + | 0.998712i | \(0.483841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.49258 | −0.218955 | −0.109477 | − | 0.993989i | \(-0.534918\pi\) | ||||
−0.109477 | + | 0.993989i | \(0.534918\pi\) | |||||||
\(422\) | 14.0768 | 0.685247 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.23536 | 0.448509 | ||||||||
\(425\) | −3.81859 | −0.185229 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.14025 | 0.345541 | ||||||||
\(428\) | 3.40486 | 0.164580 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.0377 | 1.15920 | ||||||||
\(431\) | −20.9570 | −1.00947 | −0.504733 | − | 0.863276i | \(-0.668409\pi\) | ||||
−0.504733 | + | 0.863276i | \(0.668409\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.8960 | −1.67700 | −0.838499 | − | 0.544904i | \(-0.816566\pi\) | ||||
−0.838499 | + | 0.544904i | \(0.816566\pi\) | |||||||
\(434\) | 7.20360 | 0.345784 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.16765 | 0.151703 | ||||||||
\(437\) | 35.2984 | 1.68855 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.0750 | −1.43540 | −0.717700 | − | 0.696352i | \(-0.754805\pi\) | ||||
−0.717700 | + | 0.696352i | \(0.754805\pi\) | |||||||
\(440\) | −13.0363 | −0.621482 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.33930 | 0.0637040 | ||||||||
\(443\) | 13.1760 | 0.626011 | 0.313006 | − | 0.949751i | \(-0.398664\pi\) | ||||
0.313006 | + | 0.949751i | \(0.398664\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.50621 | −0.261020 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.22714 | 0.199713 | ||||||||
\(449\) | 8.67959 | 0.409615 | 0.204808 | − | 0.978802i | \(-0.434343\pi\) | ||||
0.204808 | + | 0.978802i | \(0.434343\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.4202 | −1.95040 | ||||||||
\(452\) | 13.8478 | 0.651345 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.5581 | −0.870977 | ||||||||
\(455\) | 4.16091 | 0.195067 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.35788 | −0.297409 | −0.148705 | − | 0.988882i | \(-0.547510\pi\) | ||||
−0.148705 | + | 0.988882i | \(0.547510\pi\) | |||||||
\(458\) | −6.97505 | −0.325923 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.9150 | −0.648790 | ||||||||
\(461\) | 4.87973 | 0.227272 | 0.113636 | − | 0.993522i | \(-0.463750\pi\) | ||||
0.113636 | + | 0.993522i | \(0.463750\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.0302 | −1.07031 | −0.535153 | − | 0.844755i | \(-0.679746\pi\) | ||||
−0.535153 | + | 0.844755i | \(0.679746\pi\) | |||||||
\(464\) | −6.69038 | −0.310593 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.7728 | 0.962284 | ||||||||
\(467\) | −38.8138 | −1.79609 | −0.898045 | − | 0.439904i | \(-0.855012\pi\) | ||||
−0.898045 | + | 0.439904i | \(0.855012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.6978 | −1.60220 | ||||||||
\(470\) | 14.6709 | 0.676718 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.14009 | −0.0524770 | ||||||||
\(473\) | −51.0925 | −2.34924 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.11933 | 0.326657 | ||||||||
\(476\) | −14.2438 | −0.652865 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.29587 | 0.287966 | ||||||||
\(479\) | −23.9684 | −1.09514 | −0.547571 | − | 0.836759i | \(-0.684447\pi\) | ||||
−0.547571 | + | 0.836759i | \(0.684447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.99731 | −0.182262 | ||||||||
\(482\) | 0.597940 | 0.0272354 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.7090 | 0.759498 | ||||||||
\(485\) | −11.6475 | −0.528884 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0747 | 1.09093 | 0.545464 | − | 0.838134i | \(-0.316353\pi\) | ||||
0.545464 | + | 0.838134i | \(0.316353\pi\) | |||||||
\(488\) | 1.68915 | 0.0764641 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −26.9167 | −1.21597 | ||||||||
\(491\) | −18.3355 | −0.827470 | −0.413735 | − | 0.910397i | \(-0.635776\pi\) | ||||
−0.413735 | + | 0.910397i | \(0.635776\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.5440 | 1.01533 | ||||||||
\(494\) | −2.49698 | −0.112344 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.70413 | 0.0765178 | ||||||||
\(497\) | −57.1409 | −2.56312 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.3146 | 0.819873 | 0.409937 | − | 0.912114i | \(-0.365551\pi\) | ||||
0.409937 | + | 0.912114i | \(0.365551\pi\) | |||||||
\(500\) | 9.57618 | 0.428260 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.8104 | 0.928813 | ||||||||
\(503\) | −17.3936 | −0.775544 | −0.387772 | − | 0.921755i | \(-0.626755\pi\) | ||||
−0.387772 | + | 0.921755i | \(0.626755\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.6091 | 0.828096 | ||||||||
\(506\) | 29.5766 | 1.31484 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.3827 | 0.638129 | ||||||||
\(509\) | −2.10219 | −0.0931779 | −0.0465890 | − | 0.998914i | \(-0.514835\pi\) | ||||
−0.0465890 | + | 0.998914i | \(0.514835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.9636 | 2.16602 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.4454 | 0.637159 | ||||||||
\(515\) | 8.59597 | 0.378784 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.1833 | −1.37144 | ||||||||
\(518\) | 42.5126 | 1.86789 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.984334 | 0.0431659 | ||||||||
\(521\) | 16.6037 | 0.727423 | 0.363711 | − | 0.931512i | \(-0.381509\pi\) | ||||
0.363711 | + | 0.931512i | \(0.381509\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.9631 | −1.22274 | −0.611370 | − | 0.791345i | \(-0.709381\pi\) | ||||
−0.611370 | + | 0.791345i | \(0.709381\pi\) | |||||||
\(524\) | 11.4275 | 0.499214 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.6267 | −0.855763 | ||||||||
\(527\) | −5.74227 | −0.250137 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.57006 | 0.372611 | ||||||||
\(530\) | −22.8717 | −0.993484 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.5560 | 1.15135 | ||||||||
\(533\) | 3.12751 | 0.135468 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.43226 | −0.364558 | ||||||||
\(536\) | −8.20836 | −0.354547 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.6877 | 0.805685 | ||||||||
\(539\) | 57.2120 | 2.46429 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.8764 | 0.639586 | 0.319793 | − | 0.947487i | \(-0.396387\pi\) | ||||
0.319793 | + | 0.947487i | \(0.396387\pi\) | |||||||
\(542\) | 13.8614 | 0.595400 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.36962 | −0.144471 | ||||||||
\(545\) | −7.84480 | −0.336034 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.8124 | −1.23193 | −0.615965 | − | 0.787774i | \(-0.711234\pi\) | ||||
−0.615965 | + | 0.787774i | \(0.711234\pi\) | |||||||
\(548\) | 12.4673 | 0.532575 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.96530 | 0.254361 | ||||||||
\(551\) | −42.0308 | −1.79057 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 51.5382 | 2.19163 | ||||||||
\(554\) | −1.45827 | −0.0619562 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.9523 | −0.676529 | ||||||||
\(557\) | −6.71043 | −0.284330 | −0.142165 | − | 0.989843i | \(-0.545406\pi\) | ||||
−0.142165 | + | 0.989843i | \(0.545406\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.85784 | 0.163169 | ||||||||
\(560\) | −10.4687 | −0.442382 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.8921 | −1.26092 | ||||||||
\(563\) | −39.9362 | −1.68311 | −0.841556 | − | 0.540171i | \(-0.818360\pi\) | ||||
−0.841556 | + | 0.540171i | \(0.818360\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.2945 | −1.44278 | ||||||||
\(566\) | −13.9064 | −0.584529 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.5176 | −0.567187 | ||||||||
\(569\) | 43.0174 | 1.80338 | 0.901691 | − | 0.432381i | \(-0.142326\pi\) | ||||
0.901691 | + | 0.432381i | \(0.142326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5809 | −0.610190 | −0.305095 | − | 0.952322i | \(-0.598688\pi\) | ||||
−0.305095 | + | 0.952322i | \(0.598688\pi\) | |||||||
\(572\) | −2.09222 | −0.0874801 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −33.2620 | −1.38833 | ||||||||
\(575\) | 6.36737 | 0.265538 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.7450 | −0.488949 | −0.244475 | − | 0.969656i | \(-0.578615\pi\) | ||||
−0.244475 | + | 0.969656i | \(0.578615\pi\) | |||||||
\(578\) | −5.64567 | −0.234829 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.5690 | 0.687990 | ||||||||
\(581\) | 48.9074 | 2.02902 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.6143 | 2.01340 | ||||||||
\(584\) | 11.5832 | 0.479315 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.40146 | 0.388371 | ||||||||
\(587\) | −12.8126 | −0.528834 | −0.264417 | − | 0.964408i | \(-0.585179\pi\) | ||||
−0.264417 | + | 0.964408i | \(0.585179\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.7058 | 0.441126 | ||||||||
\(590\) | 2.82348 | 0.116241 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.0571 | 0.413343 | ||||||||
\(593\) | −10.9227 | −0.448540 | −0.224270 | − | 0.974527i | \(-0.572000\pi\) | ||||
−0.224270 | + | 0.974527i | \(0.572000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.2754 | 1.44615 | ||||||||
\(596\) | −10.1232 | −0.414661 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.23324 | −0.0913239 | ||||||||
\(599\) | −8.51940 | −0.348093 | −0.174047 | − | 0.984737i | \(-0.555684\pi\) | ||||
−0.174047 | + | 0.984737i | \(0.555684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.0294566 | −0.00120156 | −0.000600780 | − | 1.00000i | \(-0.500191\pi\) | ||||
−0.000600780 | 1.00000i | \(0.500191\pi\) | ||||||||
\(602\) | −41.0292 | −1.67223 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.60791 | −0.268872 | ||||||||
\(605\) | −41.3804 | −1.68235 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.1334 | −1.71014 | −0.855072 | − | 0.518510i | \(-0.826487\pi\) | ||||
−0.855072 | + | 0.518510i | \(0.826487\pi\) | |||||||
\(608\) | 6.28228 | 0.254780 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.18323 | −0.169374 | ||||||||
\(611\) | 2.35456 | 0.0952552 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.6271 | 1.15624 | 0.578119 | − | 0.815953i | \(-0.303787\pi\) | ||||
0.578119 | + | 0.815953i | \(0.303787\pi\) | |||||||
\(614\) | −2.68510 | −0.108362 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.2513 | 0.896532 | ||||||||
\(617\) | −46.9913 | −1.89180 | −0.945899 | − | 0.324461i | \(-0.894817\pi\) | ||||
−0.945899 | + | 0.324461i | \(0.894817\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.13666 | −0.367233 | −0.183617 | − | 0.982998i | \(-0.558781\pi\) | ||||
−0.183617 | + | 0.982998i | \(0.558781\pi\) | |||||||
\(620\) | −4.22035 | −0.169493 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.58052 | −0.223758 | ||||||||
\(623\) | 9.39841 | 0.376539 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.3820 | −1.17528 | ||||||||
\(626\) | −6.58610 | −0.263233 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.2131 | −0.766687 | ||||||||
\(629\) | −33.8885 | −1.35122 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.8501 | 1.70583 | 0.852917 | − | 0.522046i | \(-0.174831\pi\) | ||||
0.852917 | + | 0.522046i | \(0.174831\pi\) | |||||||
\(632\) | 12.1922 | 0.484980 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.39147 | 0.0949774 | ||||||||
\(635\) | −35.6193 | −1.41351 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.31990 | −0.171161 | ||||||||
\(638\) | −35.2177 | −1.39428 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.47654 | −0.0978938 | ||||||||
\(641\) | 0.754636 | 0.0298063 | 0.0149032 | − | 0.999889i | \(-0.495256\pi\) | ||||
0.0149032 | + | 0.999889i | \(0.495256\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.69430 | 0.263997 | 0.131999 | − | 0.991250i | \(-0.457861\pi\) | ||||
0.131999 | + | 0.991250i | \(0.457861\pi\) | |||||||
\(644\) | 23.7511 | 0.935925 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.1689 | −0.832879 | ||||||||
\(647\) | −11.0067 | −0.432718 | −0.216359 | − | 0.976314i | \(-0.569418\pi\) | ||||
−0.216359 | + | 0.976314i | \(0.569418\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00137 | −0.235574 | ||||||||
\(650\) | −0.450422 | −0.0176670 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.03067 | −0.0795271 | ||||||||
\(653\) | 21.2361 | 0.831032 | 0.415516 | − | 0.909586i | \(-0.363601\pi\) | ||||
0.415516 | + | 0.909586i | \(0.363601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.3007 | −1.10580 | ||||||||
\(656\) | −7.86868 | −0.307220 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −25.0414 | −0.976214 | ||||||||
\(659\) | −17.7235 | −0.690408 | −0.345204 | − | 0.938528i | \(-0.612190\pi\) | ||||
−0.345204 | + | 0.938528i | \(0.612190\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.3253 | 1.45179 | 0.725893 | − | 0.687808i | \(-0.241427\pi\) | ||||
0.725893 | + | 0.687808i | \(0.241427\pi\) | |||||||
\(662\) | 29.1305 | 1.13219 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.5699 | 0.448998 | ||||||||
\(665\) | −65.7671 | −2.55034 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.5914 | −1.45555 | ||||||||
\(668\) | −6.69006 | −0.258846 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.3283 | 0.785351 | ||||||||
\(671\) | 8.89155 | 0.343254 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.1625 | −0.661566 | −0.330783 | − | 0.943707i | \(-0.607313\pi\) | ||||
−0.330783 | + | 0.943707i | \(0.607313\pi\) | |||||||
\(674\) | −22.8500 | −0.880150 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.8420 | −0.493924 | ||||||||
\(677\) | 34.3533 | 1.32031 | 0.660153 | − | 0.751131i | \(-0.270491\pi\) | ||||
0.660153 | + | 0.751131i | \(0.270491\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.8807 | 0.762953 | ||||||||
\(680\) | 8.34499 | 0.320016 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.97043 | 0.343496 | ||||||||
\(683\) | 32.1375 | 1.22971 | 0.614854 | − | 0.788641i | \(-0.289215\pi\) | ||||
0.614854 | + | 0.788641i | \(0.289215\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.8756 | −1.17970 | ||||||||
\(686\) | 16.3534 | 0.624377 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.70616 | −0.370044 | ||||||||
\(689\) | −3.67072 | −0.139843 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.8160 | −1.85705 | −0.928523 | − | 0.371274i | \(-0.878921\pi\) | ||||
−0.928523 | + | 0.371274i | \(0.878921\pi\) | |||||||
\(692\) | −9.35263 | −0.355534 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.2023 | 0.804828 | ||||||||
\(695\) | 39.5065 | 1.49857 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.5144 | 1.00431 | ||||||||
\(698\) | −1.60228 | −0.0606474 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.79036 | 0.181059 | ||||||||
\(701\) | 7.98889 | 0.301736 | 0.150868 | − | 0.988554i | \(-0.451793\pi\) | ||||
0.150868 | + | 0.988554i | \(0.451793\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 63.1813 | 2.38293 | ||||||||
\(704\) | 5.26393 | 0.198392 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.2158 | −1.25009 | ||||||||
\(707\) | −31.7635 | −1.19459 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.0293 | 0.752215 | 0.376108 | − | 0.926576i | \(-0.377262\pi\) | ||||
0.376108 | + | 0.926576i | \(0.377262\pi\) | |||||||
\(710\) | 33.4769 | 1.25637 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.22335 | 0.0833236 | ||||||||
\(713\) | 9.57505 | 0.358588 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.18146 | 0.193776 | ||||||||
\(716\) | 14.3762 | 0.537265 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.4807 | 0.540416 | ||||||||
\(719\) | −39.8402 | −1.48579 | −0.742894 | − | 0.669409i | \(-0.766547\pi\) | ||||
−0.742894 | + | 0.669409i | \(0.766547\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.6722 | −0.546422 | ||||||||
\(722\) | 20.4670 | 0.761704 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.31275 | −0.308941 | ||||||||
\(725\) | −7.58181 | −0.281581 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9681 | −0.963105 | −0.481552 | − | 0.876417i | \(-0.659927\pi\) | ||||
−0.481552 | + | 0.876417i | \(0.659927\pi\) | |||||||
\(728\) | −1.68013 | −0.0622698 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −28.6861 | −1.06172 | ||||||||
\(731\) | 32.7060 | 1.20968 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.10226 | −0.225392 | −0.112696 | − | 0.993630i | \(-0.535949\pi\) | ||||
−0.112696 | + | 0.993630i | \(0.535949\pi\) | |||||||
\(734\) | −1.75467 | −0.0647662 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.61872 | 0.207109 | ||||||||
\(737\) | −43.2082 | −1.59160 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.1254 | −0.740325 | −0.370163 | − | 0.928967i | \(-0.620698\pi\) | ||||
−0.370163 | + | 0.928967i | \(0.620698\pi\) | |||||||
\(740\) | −24.9067 | −0.915588 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 39.0391 | 1.43317 | ||||||||
\(743\) | 40.5766 | 1.48861 | 0.744306 | − | 0.667838i | \(-0.232780\pi\) | ||||
0.744306 | + | 0.667838i | \(0.232780\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.0704 | 0.918508 | ||||||||
\(746\) | −4.25682 | −0.155853 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.7374 | −0.648545 | ||||||||
\(749\) | 14.3928 | 0.525901 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.1752 | 1.79443 | 0.897215 | − | 0.441595i | \(-0.145587\pi\) | ||||
0.897215 | + | 0.441595i | \(0.145587\pi\) | |||||||
\(752\) | −5.92396 | −0.216024 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.65918 | 0.0968417 | ||||||||
\(755\) | 16.3647 | 0.595574 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.4273 | −0.742443 | −0.371221 | − | 0.928544i | \(-0.621061\pi\) | ||||
−0.371221 | + | 0.928544i | \(0.621061\pi\) | |||||||
\(758\) | −11.9544 | −0.434204 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.5583 | −0.564359 | ||||||||
\(761\) | 9.34786 | 0.338860 | 0.169430 | − | 0.985542i | \(-0.445807\pi\) | ||||
0.169430 | + | 0.985542i | \(0.445807\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.3901 | 0.484753 | ||||||||
\(764\) | 4.28743 | 0.155114 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.95992 | 0.323735 | ||||||||
\(767\) | 0.453146 | 0.0163621 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.4214 | −0.988840 | −0.494420 | − | 0.869223i | \(-0.664619\pi\) | ||||
−0.494420 | + | 0.869223i | \(0.664619\pi\) | |||||||
\(770\) | −55.1063 | −1.98589 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.0794 | −0.434746 | ||||||||
\(773\) | −24.2376 | −0.871766 | −0.435883 | − | 0.900003i | \(-0.643564\pi\) | ||||
−0.435883 | + | 0.900003i | \(0.643564\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.93119 | 0.0693704 | ||||||||
\(776\) | 4.70312 | 0.168832 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.9842 | −1.03913 | ||||||||
\(779\) | −49.4332 | −1.77113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.1559 | −2.54616 | ||||||||
\(782\) | −18.9330 | −0.677041 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.8687 | 0.388167 | ||||||||
\(785\) | 47.5820 | 1.69827 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.5238 | 1.12370 | 0.561851 | − | 0.827239i | \(-0.310090\pi\) | ||||
0.561851 | + | 0.827239i | \(0.310090\pi\) | |||||||
\(788\) | 9.02457 | 0.321487 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −30.1945 | −1.07427 | ||||||||
\(791\) | 58.5364 | 2.08132 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.671374 | −0.0238412 | ||||||||
\(794\) | 37.7072 | 1.33818 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.68635 | 0.201547 | ||||||||
\(797\) | 8.97485 | 0.317905 | 0.158953 | − | 0.987286i | \(-0.449188\pi\) | ||||
0.158953 | + | 0.987286i | \(0.449188\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.9615 | 0.706186 | ||||||||
\(800\) | 1.13324 | 0.0400661 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0873 | 0.426816 | ||||||||
\(803\) | 60.9730 | 2.15169 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −58.8205 | −2.07315 | ||||||||
\(806\) | −0.677330 | −0.0238579 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.51418 | −0.264348 | ||||||||
\(809\) | −24.5036 | −0.861502 | −0.430751 | − | 0.902471i | \(-0.641751\pi\) | ||||
−0.430751 | + | 0.902471i | \(0.641751\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.1995 | 1.30625 | 0.653125 | − | 0.757250i | \(-0.273457\pi\) | ||||
0.653125 | + | 0.757250i | \(0.273457\pi\) | |||||||
\(812\) | −28.2812 | −0.992474 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 52.9397 | 1.85553 | ||||||||
\(815\) | 5.02902 | 0.176159 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −60.9768 | −2.13331 | ||||||||
\(818\) | −31.4033 | −1.09799 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19.4871 | 0.680518 | ||||||||
\(821\) | 30.1711 | 1.05298 | 0.526489 | − | 0.850182i | \(-0.323508\pi\) | ||||
0.526489 | + | 0.850182i | \(0.323508\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.8780 | 0.379184 | 0.189592 | − | 0.981863i | \(-0.439284\pi\) | ||||
0.189592 | + | 0.981863i | \(0.439284\pi\) | |||||||
\(824\) | −3.47096 | −0.120917 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.81933 | −0.167686 | ||||||||
\(827\) | −21.3568 | −0.742649 | −0.371325 | − | 0.928503i | \(-0.621096\pi\) | ||||
−0.371325 | + | 0.928503i | \(0.621096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.22558 | 0.181492 | 0.0907460 | − | 0.995874i | \(-0.471075\pi\) | ||||
0.0907460 | + | 0.995874i | \(0.471075\pi\) | |||||||
\(830\) | −28.6532 | −0.994568 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.397464 | −0.0137796 | ||||||||
\(833\) | −36.6233 | −1.26892 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.5682 | 0.573366 | ||||||||
\(836\) | 33.0695 | 1.14373 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.07737 | 0.0717617 | ||||||||
\(839\) | −16.1254 | −0.556712 | −0.278356 | − | 0.960478i | \(-0.589790\pi\) | ||||
−0.278356 | + | 0.960478i | \(0.589790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.7612 | 0.543490 | ||||||||
\(842\) | −4.49258 | −0.154824 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.0768 | 0.484543 | ||||||||
\(845\) | 31.8038 | 1.09408 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 70.6310 | 2.42691 | ||||||||
\(848\) | 9.23536 | 0.317143 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.81859 | −0.130976 | ||||||||
\(851\) | 56.5078 | 1.93706 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.7847 | 1.46492 | 0.732460 | − | 0.680810i | \(-0.238372\pi\) | ||||
0.732460 | + | 0.680810i | \(0.238372\pi\) | |||||||
\(854\) | 7.14025 | 0.244334 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.40486 | 0.116376 | ||||||||
\(857\) | 5.07221 | 0.173263 | 0.0866317 | − | 0.996240i | \(-0.472390\pi\) | ||||
0.0866317 | + | 0.996240i | \(0.472390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.98017 | −0.272280 | −0.136140 | − | 0.990690i | \(-0.543470\pi\) | ||||
−0.136140 | + | 0.990690i | \(0.543470\pi\) | |||||||
\(860\) | 24.0377 | 0.819678 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.9570 | −0.713800 | ||||||||
\(863\) | −45.1182 | −1.53584 | −0.767921 | − | 0.640545i | \(-0.778709\pi\) | ||||
−0.767921 | + | 0.640545i | \(0.778709\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.1622 | 0.787537 | ||||||||
\(866\) | −34.8960 | −1.18582 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.20360 | 0.244506 | ||||||||
\(869\) | 64.1790 | 2.17712 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.26252 | 0.110546 | ||||||||
\(872\) | 3.16765 | 0.107270 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 35.2984 | 1.19399 | ||||||||
\(875\) | 40.4798 | 1.36847 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 50.7208 | 1.71272 | 0.856360 | − | 0.516379i | \(-0.172720\pi\) | ||||
0.856360 | + | 0.516379i | \(0.172720\pi\) | |||||||
\(878\) | −30.0750 | −1.01498 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.0363 | −0.439454 | ||||||||
\(881\) | 36.5785 | 1.23236 | 0.616180 | − | 0.787605i | \(-0.288679\pi\) | ||||
0.616180 | + | 0.787605i | \(0.288679\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.9380 | −1.14211 | −0.571053 | − | 0.820913i | \(-0.693465\pi\) | ||||
−0.571053 | + | 0.820913i | \(0.693465\pi\) | |||||||
\(884\) | 1.33930 | 0.0450455 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.1760 | 0.442657 | ||||||||
\(887\) | −42.7657 | −1.43593 | −0.717966 | − | 0.696078i | \(-0.754927\pi\) | ||||
−0.717966 | + | 0.696078i | \(0.754927\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 60.7976 | 2.03909 | ||||||||
\(890\) | −5.50621 | −0.184569 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.00000 | 0.0334825 | ||||||||
\(893\) | −37.2160 | −1.24538 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.6033 | −1.19009 | ||||||||
\(896\) | 4.22714 | 0.141219 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.67959 | 0.289642 | ||||||||
\(899\) | −11.4013 | −0.380254 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.1196 | −1.03674 | ||||||||
\(902\) | −41.4202 | −1.37914 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.8478 | 0.460570 | ||||||||
\(905\) | 20.5869 | 0.684330 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.7298 | −0.356276 | −0.178138 | − | 0.984006i | \(-0.557007\pi\) | ||||
−0.178138 | + | 0.984006i | \(0.557007\pi\) | |||||||
\(908\) | −18.5581 | −0.615874 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.16091 | 0.137933 | ||||||||
\(911\) | −0.975965 | −0.0323352 | −0.0161676 | − | 0.999869i | \(-0.505147\pi\) | ||||
−0.0161676 | + | 0.999869i | \(0.505147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 60.9030 | 2.01559 | ||||||||
\(914\) | −6.35788 | −0.210300 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.97505 | −0.230462 | ||||||||
\(917\) | 48.3057 | 1.59519 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.3707 | −1.36470 | −0.682348 | − | 0.731028i | \(-0.739041\pi\) | ||||
−0.682348 | + | 0.731028i | \(0.739041\pi\) | |||||||
\(920\) | −13.9150 | −0.458763 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.87973 | 0.160705 | ||||||||
\(923\) | 5.37277 | 0.176847 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.3971 | 0.374733 | ||||||||
\(926\) | −23.0302 | −0.756820 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.69038 | −0.219623 | ||||||||
\(929\) | 8.17093 | 0.268080 | 0.134040 | − | 0.990976i | \(-0.457205\pi\) | ||||
0.134040 | + | 0.990976i | \(0.457205\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 68.2801 | 2.23779 | ||||||||
\(932\) | 20.7728 | 0.680437 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −38.8138 | −1.27003 | ||||||||
\(935\) | 43.9274 | 1.43658 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.3751 | 1.25366 | 0.626830 | − | 0.779156i | \(-0.284352\pi\) | ||||
0.626830 | + | 0.779156i | \(0.284352\pi\) | |||||||
\(938\) | −34.6978 | −1.13292 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 14.6709 | 0.478512 | ||||||||
\(941\) | 11.6893 | 0.381059 | 0.190529 | − | 0.981681i | \(-0.438980\pi\) | ||||
0.190529 | + | 0.981681i | \(0.438980\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.2119 | −1.43974 | ||||||||
\(944\) | −1.14009 | −0.0371069 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −51.0925 | −1.66116 | ||||||||
\(947\) | 7.00317 | 0.227572 | 0.113786 | − | 0.993505i | \(-0.463702\pi\) | ||||
0.113786 | + | 0.993505i | \(0.463702\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.60389 | −0.149448 | ||||||||
\(950\) | 7.11933 | 0.230982 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.2438 | −0.461645 | ||||||||
\(953\) | −45.5838 | −1.47660 | −0.738302 | − | 0.674470i | \(-0.764372\pi\) | ||||
−0.738302 | + | 0.674470i | \(0.764372\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.6180 | −0.343590 | ||||||||
\(956\) | 6.29587 | 0.203623 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −23.9684 | −0.774383 | ||||||||
\(959\) | 52.7008 | 1.70180 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.0959 | −0.906320 | ||||||||
\(962\) | −3.99731 | −0.128879 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.597940 | 0.0192583 | ||||||||
\(965\) | 29.9150 | 0.962999 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.1510 | −1.09822 | −0.549110 | − | 0.835750i | \(-0.685033\pi\) | ||||
−0.549110 | + | 0.835750i | \(0.685033\pi\) | |||||||
\(968\) | 16.7090 | 0.537046 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.6475 | −0.373978 | ||||||||
\(971\) | −20.0028 | −0.641919 | −0.320960 | − | 0.947093i | \(-0.604005\pi\) | ||||
−0.320960 | + | 0.947093i | \(0.604005\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −67.4326 | −2.16179 | ||||||||
\(974\) | 24.0747 | 0.771403 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.68915 | 0.0540682 | ||||||||
\(977\) | −5.58881 | −0.178802 | −0.0894010 | − | 0.995996i | \(-0.528495\pi\) | ||||
−0.0894010 | + | 0.995996i | \(0.528495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.7036 | 0.374048 | ||||||||
\(980\) | −26.9167 | −0.859822 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.3355 | −0.585109 | ||||||||
\(983\) | 39.2388 | 1.25152 | 0.625762 | − | 0.780014i | \(-0.284788\pi\) | ||||
0.625762 | + | 0.780014i | \(0.284788\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.3497 | −0.712120 | ||||||||
\(986\) | 22.5440 | 0.717948 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.49698 | −0.0794394 | ||||||||
\(989\) | −54.5362 | −1.73415 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.4150 | −0.934400 | −0.467200 | − | 0.884152i | \(-0.654737\pi\) | ||||
−0.467200 | + | 0.884152i | \(0.654737\pi\) | |||||||
\(992\) | 1.70413 | 0.0541062 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −57.1409 | −1.81240 | ||||||||
\(995\) | −14.0825 | −0.446444 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.7737 | −1.60802 | −0.804010 | − | 0.594616i | \(-0.797304\pi\) | ||||
−0.804010 | + | 0.594616i | \(0.797304\pi\) | |||||||
\(998\) | 18.3146 | 0.579738 | ||||||||
\(999\) | 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.z.1.3 | 8 | ||
3.2 | odd | 2 | 446.2.a.f.1.2 | ✓ | 8 | ||
12.11 | even | 2 | 3568.2.a.n.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
446.2.a.f.1.2 | ✓ | 8 | 3.2 | odd | 2 | ||
3568.2.a.n.1.7 | 8 | 12.11 | even | 2 | |||
4014.2.a.z.1.3 | 8 | 1.1 | even | 1 | trivial |