Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(1,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.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: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1140) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.51414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32088 | 0.499247 | 0.249624 | − | 0.968343i | \(-0.419693\pi\) | ||||
0.249624 | + | 0.968343i | \(0.419693\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.70739 | −1.11782 | −0.558910 | − | 0.829228i | \(-0.688780\pi\) | ||||
−0.558910 | + | 0.829228i | \(0.688780\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.32088 | 0.921048 | 0.460524 | − | 0.887647i | \(-0.347662\pi\) | ||||
0.460524 | + | 0.887647i | \(0.347662\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.61350 | 0.391330 | 0.195665 | − | 0.980671i | \(-0.437313\pi\) | ||||
0.195665 | + | 0.980671i | \(0.437313\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.32088 | −0.288241 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.67004 | 1.59931 | 0.799657 | − | 0.600457i | \(-0.205015\pi\) | ||||
0.799657 | + | 0.600457i | \(0.205015\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.70739 | −0.317054 | −0.158527 | − | 0.987355i | \(-0.550675\pi\) | ||||
−0.158527 | + | 0.987355i | \(0.550675\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.67004 | −1.73679 | −0.868395 | − | 0.495872i | \(-0.834848\pi\) | ||||
−0.868395 | + | 0.495872i | \(0.834848\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.70739 | 0.645374 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.32088 | 0.223270 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.96265 | 0.980254 | 0.490127 | − | 0.871651i | \(-0.336950\pi\) | ||||
0.490127 | + | 0.871651i | \(0.336950\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.32088 | −0.531767 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.29261 | 0.358046 | 0.179023 | − | 0.983845i | \(-0.442706\pi\) | ||||
0.179023 | + | 0.983845i | \(0.442706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.73566 | 1.33218 | 0.666088 | − | 0.745873i | \(-0.267967\pi\) | ||||
0.666088 | + | 0.745873i | \(0.267967\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.6700 | −1.70225 | −0.851125 | − | 0.524963i | \(-0.824079\pi\) | ||||
−0.851125 | + | 0.524963i | \(0.824079\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.25526 | −0.750752 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.61350 | −0.225935 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4431 | 1.43446 | 0.717232 | − | 0.696835i | \(-0.245409\pi\) | ||||
0.717232 | + | 0.696835i | \(0.245409\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.70739 | −0.499904 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.6983 | −1.65318 | −0.826590 | − | 0.562805i | \(-0.809722\pi\) | ||||
−0.826590 | + | 0.562805i | \(0.809722\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.02827 | 1.15595 | 0.577976 | − | 0.816054i | \(-0.303843\pi\) | ||||
0.577976 | + | 0.816054i | \(0.303843\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.32088 | 0.166416 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.32088 | 0.411905 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.2835 | 1.62284 | 0.811421 | − | 0.584462i | \(-0.198694\pi\) | ||||
0.811421 | + | 0.584462i | \(0.198694\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.67004 | −0.923365 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.69832 | 1.03230 | 0.516150 | − | 0.856498i | \(-0.327365\pi\) | ||||
0.516150 | + | 0.856498i | \(0.327365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0565 | −1.41111 | −0.705556 | − | 0.708654i | \(-0.749303\pi\) | ||||
−0.705556 | + | 0.708654i | \(0.749303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.89703 | −0.558069 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0565 | 1.58149 | 0.790743 | − | 0.612149i | \(-0.209695\pi\) | ||||
0.790743 | + | 0.612149i | \(0.209695\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.02827 | −0.551925 | −0.275962 | − | 0.961168i | \(-0.588997\pi\) | ||||
−0.275962 | + | 0.961168i | \(0.588997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.61350 | 0.175008 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.70739 | 0.183051 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.70739 | −0.180983 | −0.0904915 | − | 0.995897i | \(-0.528844\pi\) | ||||
−0.0904915 | + | 0.995897i | \(0.528844\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.38650 | 0.459831 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.67004 | 1.00274 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.679116 | −0.0689537 | −0.0344769 | − | 0.999405i | \(-0.510977\pi\) | ||||
−0.0344769 | + | 0.999405i | \(0.510977\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.70739 | −0.372607 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.6418 | 1.25790 | 0.628952 | − | 0.777445i | \(-0.283484\pi\) | ||||
0.628952 | + | 0.777445i | \(0.283484\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.05655 | −0.596769 | −0.298385 | − | 0.954446i | \(-0.596448\pi\) | ||||
−0.298385 | + | 0.954446i | \(0.596448\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.32088 | −0.128905 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6983 | 1.02471 | 0.512356 | − | 0.858773i | \(-0.328773\pi\) | ||||
0.512356 | + | 0.858773i | \(0.328773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.96265 | −0.565950 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.3118 | −1.53449 | −0.767243 | − | 0.641356i | \(-0.778372\pi\) | ||||
−0.767243 | + | 0.641356i | \(0.778372\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.67004 | 0.715235 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.32088 | 0.307016 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.13124 | 0.195371 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.74474 | 0.249521 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.29261 | −0.206718 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.73566 | −0.769132 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.29261 | −0.375047 | −0.187524 | − | 0.982260i | \(-0.560046\pi\) | ||||
−0.187524 | + | 0.982260i | \(0.560046\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.32088 | 0.114535 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000 | 0.170872 | 0.0854358 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.58522 | 0.728189 | 0.364094 | − | 0.931362i | \(-0.381379\pi\) | ||||
0.364094 | + | 0.931362i | \(0.381379\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.6700 | 0.982795 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.3118 | −1.02957 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.70739 | −0.141791 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.25526 | 0.433447 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.0565 | 0.987711 | 0.493855 | − | 0.869544i | \(-0.335587\pi\) | ||||
0.493855 | + | 0.869544i | \(0.335587\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.9536 | 1.86794 | 0.933968 | − | 0.357357i | \(-0.116322\pi\) | ||||
0.933968 | + | 0.357357i | \(0.116322\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.61350 | 0.130443 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.67004 | −0.776717 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.8688 | −0.947230 | −0.473615 | − | 0.880732i | \(-0.657051\pi\) | ||||
−0.473615 | + | 0.880732i | \(0.657051\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.4431 | −0.828188 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.1312 | 0.798454 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0373465 | 0.00292520 | 0.00146260 | − | 0.999999i | \(-0.499534\pi\) | ||||
0.00146260 | + | 0.999999i | \(0.499534\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.70739 | 0.288620 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0283 | 0.853393 | 0.426697 | − | 0.904395i | \(-0.359677\pi\) | ||||
0.426697 | + | 0.904395i | \(0.359677\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.97173 | −0.151671 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.8578 | −1.35771 | −0.678853 | − | 0.734274i | \(-0.737523\pi\) | ||||
−0.678853 | + | 0.734274i | \(0.737523\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.32088 | 0.0998495 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.6983 | 0.954464 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.9253 | 1.48929 | 0.744644 | − | 0.667462i | \(-0.232619\pi\) | ||||
0.744644 | + | 0.667462i | \(0.232619\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4713 | −1.14997 | −0.574987 | − | 0.818162i | \(-0.694993\pi\) | ||||
−0.574987 | + | 0.818162i | \(0.694993\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.02827 | −0.667389 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.96265 | 0.438383 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.98185 | −0.437437 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.32088 | −0.0960802 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.3492 | −1.32770 | −0.663849 | − | 0.747866i | \(-0.731078\pi\) | ||||
−0.663849 | + | 0.747866i | \(0.731078\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0192 | 0.865161 | 0.432581 | − | 0.901595i | \(-0.357603\pi\) | ||||
0.432581 | + | 0.901595i | \(0.357603\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.32088 | −0.237813 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.84049 | 0.344870 | 0.172435 | − | 0.985021i | \(-0.444836\pi\) | ||||
0.172435 | + | 0.985021i | \(0.444836\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.6983 | 1.46726 | 0.733632 | − | 0.679547i | \(-0.237823\pi\) | ||||
0.733632 | + | 0.679547i | \(0.237823\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.2835 | −0.936949 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.25526 | −0.158289 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.29261 | 0.160123 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.67004 | 0.533105 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.70739 | −0.256445 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.05655 | −0.141579 | −0.0707893 | − | 0.997491i | \(-0.522552\pi\) | ||||
−0.0707893 | + | 0.997491i | \(0.522552\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.69832 | −0.595999 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.73566 | 0.595767 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.7730 | −0.867088 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.0565 | 0.814706 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.35823 | 0.360434 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.05655 | −0.405576 | −0.202788 | − | 0.979223i | \(-0.565000\pi\) | ||||
−0.202788 | + | 0.979223i | \(0.565000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 28.3118 | 1.87912 | 0.939560 | − | 0.342383i | \(-0.111234\pi\) | ||||
0.939560 | + | 0.342383i | \(0.111234\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.80128 | −0.119032 | −0.0595161 | − | 0.998227i | \(-0.518956\pi\) | ||||
−0.0595161 | + | 0.998227i | \(0.518956\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.89703 | 0.322201 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.94345 | −0.258344 | −0.129172 | − | 0.991622i | \(-0.541232\pi\) | ||||
−0.129172 | + | 0.991622i | \(0.541232\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.6700 | −0.761270 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.0565 | −0.913071 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.8031 | 1.08690 | 0.543452 | − | 0.839440i | \(-0.317117\pi\) | ||||
0.543452 | + | 0.839440i | \(0.317117\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.25526 | −0.335747 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.32088 | 0.211303 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.02827 | 0.318654 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9909 | −1.57741 | −0.788707 | − | 0.614770i | \(-0.789249\pi\) | ||||
−0.788707 | + | 0.614770i | \(0.789249\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.4358 | −1.78775 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.61350 | −0.101041 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.91518 | −0.181844 | −0.0909219 | − | 0.995858i | \(-0.528981\pi\) | ||||
−0.0909219 | + | 0.995858i | \(0.528981\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.87598 | 0.489389 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.70739 | −0.105685 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.3118 | 1.37581 | 0.687903 | − | 0.725803i | \(-0.258532\pi\) | ||||
0.687903 | + | 0.725803i | \(0.258532\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4431 | 0.641512 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.70739 | 0.104491 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.0656 | 0.918567 | 0.459284 | − | 0.888290i | \(-0.348106\pi\) | ||||
0.459284 | + | 0.888290i | \(0.348106\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.47133 | −0.332359 | −0.166180 | − | 0.986095i | \(-0.553143\pi\) | ||||
−0.166180 | + | 0.986095i | \(0.553143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.38650 | −0.265483 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.70739 | −0.223564 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7730 | −0.647287 | −0.323644 | − | 0.946179i | \(-0.604908\pi\) | ||||
−0.323644 | + | 0.946179i | \(0.604908\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.67004 | −0.578930 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.8205 | 1.06308 | 0.531540 | − | 0.847033i | \(-0.321613\pi\) | ||||
0.531540 | + | 0.847033i | \(0.321613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.2070 | 1.79562 | 0.897810 | − | 0.440384i | \(-0.145158\pi\) | ||||
0.897810 | + | 0.440384i | \(0.145158\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | −0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.02827 | 0.178753 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3966 | −0.846861 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.679116 | 0.0398105 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.2553 | −1.06648 | −0.533242 | − | 0.845963i | \(-0.679026\pi\) | ||||
−0.533242 | + | 0.845963i | \(0.679026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.6983 | −0.739325 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.70739 | 0.215125 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.4713 | 1.47304 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5388 | 0.665085 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.6418 | −0.726251 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.02827 | 0.516957 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5852 | 0.946569 | 0.473284 | − | 0.880910i | \(-0.343068\pi\) | ||||
0.473284 | + | 0.880910i | \(0.343068\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.05655 | 0.344545 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.5196 | −0.653217 | −0.326608 | − | 0.945160i | \(-0.605906\pi\) | ||||
−0.326608 | + | 0.945160i | \(0.605906\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.7549 | 1.85141 | 0.925707 | − | 0.378241i | \(-0.123471\pi\) | ||||
0.925707 | + | 0.378241i | \(0.123471\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.32088 | 0.0744234 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.2161 | 0.854619 | 0.427310 | − | 0.904105i | \(-0.359461\pi\) | ||||
0.427310 | + | 0.904105i | \(0.359461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.32996 | 0.354410 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.61350 | 0.0897773 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.32088 | 0.184210 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.6983 | −0.591618 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.4148 | −0.849844 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.9536 | 1.48150 | 0.740751 | − | 0.671779i | \(-0.234470\pi\) | ||||
0.740751 | + | 0.671779i | \(0.234470\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.96265 | 0.326751 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.2835 | 0.725757 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.5652 | −0.956839 | −0.478419 | − | 0.878132i | \(-0.658790\pi\) | ||||
−0.478419 | + | 0.878132i | \(0.658790\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.3118 | 0.885936 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.8506 | 1.94142 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1878 | −0.874058 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.67004 | −0.412941 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.3118 | 1.84195 | 0.920977 | − | 0.389616i | \(-0.127392\pi\) | ||||
0.920977 | + | 0.389616i | \(0.127392\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.2835 | 1.88868 | 0.944342 | − | 0.328965i | \(-0.106700\pi\) | ||||
0.944342 | + | 0.328965i | \(0.106700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.32088 | −0.177256 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.71646 | −0.463930 | −0.231965 | − | 0.972724i | \(-0.574516\pi\) | ||||
−0.231965 | + | 0.972724i | \(0.574516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.69832 | 0.461659 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.13124 | −0.112797 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.4623 | −1.60774 | −0.803868 | − | 0.594808i | \(-0.797228\pi\) | ||||
−0.803868 | + | 0.594808i | \(0.797228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.74474 | −0.144061 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0565 | −0.631069 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.5652 | 1.43889 | 0.719446 | − | 0.694548i | \(-0.244396\pi\) | ||||
0.719446 | + | 0.694548i | \(0.244396\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.29261 | 0.119349 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.7941 | 0.716152 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0939 | 0.833310 | 0.416655 | − | 0.909065i | \(-0.363202\pi\) | ||||
0.416655 | + | 0.909065i | \(0.363202\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.67004 | −0.292022 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.01013 | −0.462819 | −0.231410 | − | 0.972856i | \(-0.574334\pi\) | ||||
−0.231410 | + | 0.972856i | \(0.574334\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.3401 | 1.19262 | 0.596311 | − | 0.802753i | \(-0.296632\pi\) | ||||
0.596311 | + | 0.802753i | \(0.296632\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.89703 | −0.249576 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.73566 | 0.444059 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.0565 | 1.01691 | 0.508454 | − | 0.861089i | \(-0.330217\pi\) | ||||
0.508454 | + | 0.861089i | \(0.330217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.3756 | 0.625860 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.29261 | 0.216534 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.0565 | 0.707262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.7375 | −1.09097 | −0.545487 | − | 0.838119i | \(-0.683655\pi\) | ||||
−0.545487 | + | 0.838119i | \(0.683655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.32088 | −0.0661269 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.17872 | −0.358488 | −0.179244 | − | 0.983805i | \(-0.557365\pi\) | ||||
−0.179244 | + | 0.983805i | \(0.557365\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.1131 | −1.59967 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.1059 | −1.09575 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.2443 | 0.803231 | 0.401615 | − | 0.915808i | \(-0.368449\pi\) | ||||
0.401615 | + | 0.915808i | \(0.368449\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.7730 | −0.825346 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.02827 | −0.246828 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.58522 | −0.420420 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.9909 | −0.830061 | −0.415031 | − | 0.909807i | \(-0.636229\pi\) | ||||
−0.415031 | + | 0.909807i | \(0.636229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.6700 | −0.567417 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.61350 | 0.0782660 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.9253 | 0.577106 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.3118 | 0.594420 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.6418 | −1.09062 | −0.545308 | − | 0.838236i | \(-0.683587\pi\) | ||||
−0.545308 | + | 0.838236i | \(0.683587\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.2070 | −0.586630 | −0.293315 | − | 0.956016i | \(-0.594759\pi\) | ||||
−0.293315 | + | 0.956016i | \(0.594759\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.70739 | 0.0818631 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.67004 | 0.366908 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.8506 | 1.52015 | 0.760073 | − | 0.649837i | \(-0.225163\pi\) | ||||
0.760073 | + | 0.649837i | \(0.225163\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.25526 | −0.250251 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.95358 | −0.425397 | −0.212699 | − | 0.977118i | \(-0.568225\pi\) | ||||
−0.212699 | + | 0.977118i | \(0.568225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.70739 | −0.0809380 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.0565 | −0.570255 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.51960 | 0.260486 | 0.130243 | − | 0.991482i | \(-0.458424\pi\) | ||||
0.130243 | + | 0.991482i | \(0.458424\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.49960 | −0.400231 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.9536 | −1.07845 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.38650 | 0.205643 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.131241 | 0.00613918 | 0.00306959 | − | 0.999995i | \(-0.499023\pi\) | ||||
0.00306959 | + | 0.999995i | \(0.499023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.61350 | −0.0753115 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.1131 | −0.657312 | −0.328656 | − | 0.944450i | \(-0.606596\pi\) | ||||
−0.328656 | + | 0.944450i | \(0.606596\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.98080 | −0.277951 | −0.138976 | − | 0.990296i | \(-0.544381\pi\) | ||||
−0.138976 | + | 0.990296i | \(0.544381\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.67004 | 0.448437 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.38650 | 0.295532 | 0.147766 | − | 0.989022i | \(-0.452792\pi\) | ||||
0.147766 | + | 0.989022i | \(0.452792\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.5460 | 0.810200 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.8688 | 0.546884 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.3865 | −1.48913 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.4431 | 0.478155 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.8597 | −0.861721 | −0.430861 | − | 0.902419i | \(-0.641790\pi\) | ||||
−0.430861 | + | 0.902419i | \(0.641790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.8013 | 0.902861 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −10.1312 | −0.460987 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.679116 | −0.0308370 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.1312 | −0.459090 | −0.229545 | − | 0.973298i | \(-0.573724\pi\) | ||||
−0.229545 | + | 0.973298i | \(0.573724\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0373465 | −0.00168887 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.06562 | −0.0480908 | −0.0240454 | − | 0.999711i | \(-0.507655\pi\) | ||||
−0.0240454 | + | 0.999711i | \(0.507655\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.75486 | −0.124073 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.70739 | −0.166635 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.4895 | 0.515373 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.2443 | 0.637664 | 0.318832 | − | 0.947811i | \(-0.396709\pi\) | ||||
0.318832 | + | 0.947811i | \(0.396709\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.0283 | −0.492707 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.9717 | −1.38096 | −0.690481 | − | 0.723351i | \(-0.742601\pi\) | ||||
−0.690481 | + | 0.723351i | \(0.742601\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.6418 | 0.562551 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.97173 | 0.0875674 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −30.4057 | −1.34771 | −0.673855 | − | 0.738864i | \(-0.735363\pi\) | ||||
−0.673855 | + | 0.738864i | \(0.735363\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.9253 | −0.704494 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.05655 | −0.266883 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.2654 | 1.90281 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.8578 | 0.783872 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.34916 | −0.190540 | −0.0952700 | − | 0.995451i | \(-0.530371\pi\) | ||||
−0.0952700 | + | 0.995451i | \(0.530371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.69832 | 0.380351 | 0.190175 | − | 0.981750i | \(-0.439094\pi\) | ||||
0.190175 | + | 0.981750i | \(0.439094\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.32088 | −0.0576481 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.6026 | −0.679659 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.8296 | 1.55781 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.6983 | −0.551060 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.61350 | 0.329777 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.9253 | −0.859840 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.4833 | 0.839206 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.45398 | 0.363465 | 0.181733 | − | 0.983348i | \(-0.441830\pi\) | ||||
0.181733 | + | 0.983348i | \(0.441830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.4713 | 0.663938 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.6983 | 0.458266 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.5279 | −0.492896 | −0.246448 | − | 0.969156i | \(-0.579264\pi\) | ||||
−0.246448 | + | 0.969156i | \(0.579264\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.02827 | 0.385317 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.70739 | −0.0727372 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.5671 | 0.789552 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.96265 | −0.253101 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.22699 | 0.0519892 | 0.0259946 | − | 0.999662i | \(-0.491725\pi\) | ||||
0.0259946 | + | 0.999662i | \(0.491725\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.0101 | 1.22700 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.98185 | 0.252554 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.9144 | −0.839291 | −0.419646 | − | 0.907688i | \(-0.637846\pi\) | ||||
−0.419646 | + | 0.907688i | \(0.637846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.3118 | −0.686243 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.32088 | 0.0554719 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.5015 | −1.15292 | −0.576460 | − | 0.817125i | \(-0.695567\pi\) | ||||
−0.576460 | + | 0.817125i | \(0.695567\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.47133 | 0.396363 | 0.198181 | − | 0.980165i | \(-0.436497\pi\) | ||||
0.198181 | + | 0.980165i | \(0.436497\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.3492 | 0.766547 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.67004 | 0.319863 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.6418 | 1.52542 | 0.762708 | − | 0.646743i | \(-0.223869\pi\) | ||||
0.762708 | + | 0.646743i | \(0.223869\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.0192 | −0.499501 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.64177 | −0.275547 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −38.7165 | −1.60347 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.32088 | 0.137302 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.67004 | 0.151479 | 0.0757394 | − | 0.997128i | \(-0.475868\pi\) | ||||
0.0757394 | + | 0.997128i | \(0.475868\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.67004 | −0.398447 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.84049 | −0.199111 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.2270 | −0.707428 | −0.353714 | − | 0.935354i | \(-0.615081\pi\) | ||||
−0.353714 | + | 0.935354i | \(0.615081\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.13124 | 0.0873724 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.6983 | −0.847126 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.11310 | 0.331492 | 0.165746 | − | 0.986168i | \(-0.446997\pi\) | ||||
0.165746 | + | 0.986168i | \(0.446997\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.35823 | 0.300149 | 0.150074 | − | 0.988675i | \(-0.452049\pi\) | ||||
0.150074 | + | 0.988675i | \(0.452049\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.2835 | 0.540947 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.74474 | 0.111589 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9253 | −0.808743 | −0.404372 | − | 0.914595i | \(-0.632510\pi\) | ||||
−0.404372 | + | 0.914595i | \(0.632510\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.25526 | 0.0913879 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.7549 | −1.56785 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3219 | 1.58820 | 0.794099 | − | 0.607788i | \(-0.207943\pi\) | ||||
0.794099 | + | 0.607788i | \(0.207943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.29261 | −0.0924470 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0674757 | 0.00271647 | 0.00135823 | − | 0.999999i | \(-0.499568\pi\) | ||||
0.00135823 | + | 0.999999i | \(0.499568\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.8680 | −1.56224 | −0.781118 | − | 0.624384i | \(-0.785350\pi\) | ||||
−0.781118 | + | 0.624384i | \(0.785350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.67004 | −0.307788 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.25526 | −0.0903552 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.70739 | 0.148059 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.62071 | 0.383603 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.2835 | −1.16576 | −0.582880 | − | 0.812559i | \(-0.698074\pi\) | ||||
−0.582880 | + | 0.812559i | \(0.698074\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.05655 | 0.0817404 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | 0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.4521 | −0.691478 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.69832 | 0.344100 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.4057 | 0.411001 | 0.205500 | − | 0.978657i | \(-0.434118\pi\) | ||||
0.205500 | + | 0.978657i | \(0.434118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.3774 | 0.448682 | 0.224341 | − | 0.974511i | \(-0.427977\pi\) | ||||
0.224341 | + | 0.974511i | \(0.427977\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.73566 | −0.343966 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.5388 | −1.79032 | −0.895158 | − | 0.445750i | \(-0.852937\pi\) | ||||
−0.895158 | + | 0.445750i | \(0.852937\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 47.0776 | 1.84796 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.7730 | 0.500614 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.27341 | −0.0889654 | −0.0444827 | − | 0.999010i | \(-0.514164\pi\) | ||||
−0.0444827 | + | 0.999010i | \(0.514164\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.29261 | −0.167726 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.0565 | −0.470371 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.77301 | 0.341748 | 0.170874 | − | 0.985293i | \(-0.445341\pi\) | ||||
0.170874 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.4924 | −1.73055 | −0.865277 | − | 0.501295i | \(-0.832857\pi\) | ||||
−0.865277 | + | 0.501295i | \(0.832857\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.35823 | −0.208096 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.32088 | 0.0512217 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.0957 | −0.507069 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.05655 | 0.234160 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.4713 | −1.29215 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.96265 | −0.229843 | −0.114922 | − | 0.993375i | \(-0.536662\pi\) | ||||
−0.114922 | + | 0.993375i | \(0.536662\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.32996 | 0.243280 | 0.121640 | − | 0.992574i | \(-0.461185\pi\) | ||||
0.121640 | + | 0.992574i | \(0.461185\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.897033 | −0.0344250 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.3118 | −1.08491 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.8506 | −1.52484 | −0.762421 | − | 0.647082i | \(-0.775989\pi\) | ||||
−0.762421 | + | 0.647082i | \(0.775989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.00000 | 0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.80128 | 0.0687233 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.6802 | 1.32121 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.07469 | −0.307176 | −0.153588 | − | 0.988135i | \(-0.549083\pi\) | ||||
−0.153588 | + | 0.988135i | \(0.549083\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.89703 | −0.186023 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.58522 | 0.325656 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.69912 | 0.140114 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.94345 | 0.149155 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.77301 | −0.104735 | −0.0523676 | − | 0.998628i | \(-0.516677\pi\) | ||||
−0.0523676 | + | 0.998628i | \(0.516677\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.96265 | 0.224886 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.6700 | 0.439519 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.6983 | 0.628005 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.1987 | 0.383021 | 0.191510 | − | 0.981491i | \(-0.438661\pi\) | ||||
0.191510 | + | 0.981491i | \(0.438661\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.0565 | 0.527162 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −74.1696 | −2.77767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.3118 | −0.460436 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.8031 | −0.627525 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.2745 | −1.27822 | −0.639111 | − | 0.769115i | \(-0.720698\pi\) | ||||
−0.639111 | + | 0.769115i | \(0.720698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.0000 | −0.520666 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.70739 | −0.0634108 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.0939 | −0.819417 | −0.409709 | − | 0.912216i | \(-0.634370\pi\) | ||||
−0.409709 | + | 0.912216i | \(0.634370\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.0950 | 0.521321 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.3401 | −0.492727 | −0.246364 | − | 0.969177i | \(-0.579236\pi\) | ||||
−0.246364 | + | 0.969177i | \(0.579236\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.25526 | 0.193843 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −49.2472 | −1.81405 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.0000 | 1.03000 | 0.514998 | − | 0.857191i | \(-0.327793\pi\) | ||||
0.514998 | + | 0.857191i | \(0.327793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.32088 | −0.121996 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.8861 | −1.20647 | −0.603237 | − | 0.797562i | \(-0.706123\pi\) | ||||
−0.603237 | + | 0.797562i | \(0.706123\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0565 | 0.441718 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.02827 | −0.183975 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.4996 | −0.602079 | −0.301039 | − | 0.953612i | \(-0.597334\pi\) | ||||
−0.301039 | + | 0.953612i | \(0.597334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.9909 | 0.910720 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.9536 | 0.835366 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.5489 | −1.54647 | −0.773234 | − | 0.634121i | \(-0.781362\pi\) | ||||
−0.773234 | + | 0.634121i | \(0.781362\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.4358 | 1.03216 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.34009 | 0.193578 | 0.0967890 | − | 0.995305i | \(-0.469143\pi\) | ||||
0.0967890 | + | 0.995305i | \(0.469143\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.1312 | 0.511585 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.61350 | 0.0583360 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −42.1696 | −1.52266 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.28354 | −0.262651 | −0.131326 | − | 0.991339i | \(-0.541923\pi\) | ||||
−0.131326 | + | 0.991339i | \(0.541923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.91518 | 0.104988 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.1806 | −0.653910 | −0.326955 | − | 0.945040i | \(-0.606023\pi\) | ||||
−0.326955 | + | 0.945040i | \(0.606023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.67004 | −0.347358 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.87598 | −0.282549 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.29261 | 0.0821413 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.2480 | −1.15393 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.70739 | 0.0610171 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.8688 | −0.423614 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.8114 | −0.741847 | −0.370923 | − | 0.928663i | \(-0.620959\pi\) | ||||
−0.370923 | + | 0.928663i | \(0.620959\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.3118 | −0.794322 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.5460 | −0.766088 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.9819 | 1.06469 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.4431 | −0.370377 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.9354 | 1.45001 | 0.725004 | − | 0.688745i | \(-0.241838\pi\) | ||||
0.725004 | + | 0.688745i | \(0.241838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.8296 | −0.666142 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.70739 | −0.0603276 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44.6983 | 1.57737 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.1312 | 0.357079 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.0656 | −0.530335 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.48947 | −0.0523670 | −0.0261835 | − | 0.999657i | \(-0.508335\pi\) | ||||
−0.0261835 | + | 0.999657i | \(0.508335\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.5460 | −0.756583 | −0.378292 | − | 0.925687i | \(-0.623488\pi\) | ||||
−0.378292 | + | 0.925687i | \(0.623488\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.47133 | 0.191888 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0373465 | 0.00130819 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.73566 | 0.305622 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.38650 | 0.153277 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.9819 | −1.25578 | −0.627888 | − | 0.778304i | \(-0.716080\pi\) | ||||
−0.627888 | + | 0.778304i | \(0.716080\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.8880 | −0.553819 | −0.276910 | − | 0.960896i | \(-0.589310\pi\) | ||||
−0.276910 | + | 0.960896i | \(0.589310\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.70739 | 0.129075 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.8789 | −0.934671 | −0.467335 | − | 0.884080i | \(-0.654786\pi\) | ||||
−0.467335 | + | 0.884080i | \(0.654786\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.9253 | 0.622572 | 0.311286 | − | 0.950316i | \(-0.399240\pi\) | ||||
0.311286 | + | 0.950316i | \(0.399240\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.7730 | 0.373712 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.47934 | −0.293792 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.0283 | 0.381649 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.67004 | 0.334246 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.30168 | −0.252082 | −0.126041 | − | 0.992025i | \(-0.540227\pi\) | ||||
−0.126041 | + | 0.992025i | \(0.540227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0848 | −0.899477 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.8205 | −0.613770 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.97173 | −0.0678294 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.62548 | 0.124573 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.2070 | −1.03670 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.7338 | 1.56773 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.4148 | −1.28106 | −0.640529 | − | 0.767934i | \(-0.721285\pi\) | ||||
−0.640529 | + | 0.767934i | \(0.721285\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.1806 | −0.347762 | −0.173881 | − | 0.984767i | \(-0.555631\pi\) | ||||
−0.173881 | + | 0.984767i | \(0.555631\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.7367 | 1.38992 | 0.694959 | − | 0.719049i | \(-0.255422\pi\) | ||||
0.694959 | + | 0.719049i | \(0.255422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.02827 | −0.103203 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.11310 | 0.276173 | 0.138086 | − | 0.990420i | \(-0.455905\pi\) | ||||
0.138086 | + | 0.990420i | \(0.455905\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.8578 | −0.607184 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.3966 | 0.488935 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.1131 | −1.76782 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.1131 | 1.49472 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.679116 | −0.0229846 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.32088 | 0.0446540 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.8880 | 1.00924 | 0.504622 | − | 0.863340i | \(-0.331632\pi\) | ||||
0.504622 | + | 0.863340i | \(0.331632\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.2553 | 0.615735 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.8114 | 1.17283 | 0.586413 | − | 0.810012i | \(-0.300540\pi\) | ||||
0.586413 | + | 0.810012i | \(0.300540\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.8496 | −0.937212 | −0.468606 | − | 0.883407i | \(-0.655244\pi\) | ||||
−0.468606 | + | 0.883407i | \(0.655244\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.6983 | 0.426849 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50.7933 | 1.70547 | 0.852735 | − | 0.522343i | \(-0.174942\pi\) | ||||
0.852735 | + | 0.522343i | \(0.174942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.28354 | 0.177204 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.70739 | −0.124202 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.6700 | −0.390523 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.9253 | 0.666030 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.4713 | −0.850463 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.5105 | 0.550657 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.8498 | 0.561349 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.5388 | −0.383987 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.4713 | −0.514284 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.3009 | 1.07253 | 0.536267 | − | 0.844049i | \(-0.319834\pi\) | ||||
0.536267 | + | 0.844049i | \(0.319834\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.6418 | 0.419301 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.7367 | 1.74725 | 0.873623 | − | 0.486604i | \(-0.161764\pi\) | ||||
0.873623 | + | 0.486604i | \(0.161764\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.6418 | 0.616953 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.02827 | −0.298466 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.67004 | −0.187241 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.5105 | −1.73216 | −0.866081 | − | 0.499903i | \(-0.833369\pi\) | ||||
−0.866081 | + | 0.499903i | \(0.833369\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.5852 | −0.546502 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 28.8861 | 0.950798 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.96265 | 0.196051 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.05655 | −0.198923 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.8688 | −1.17682 | −0.588408 | − | 0.808564i | \(-0.700245\pi\) | ||||
−0.588408 | + | 0.808564i | \(0.700245\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.25526 | −0.172234 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.5196 | 0.377135 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.98185 | −0.195628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.6983 | 0.349499 | 0.174749 | − | 0.984613i | \(-0.444088\pi\) | ||||
0.174749 | + | 0.984613i | \(0.444088\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.7549 | −1.06891 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.3673 | −0.729153 | −0.364577 | − | 0.931173i | \(-0.618786\pi\) | ||||
−0.364577 | + | 0.931173i | \(0.618786\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.5844 | 0.572628 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.32088 | −0.0429684 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.8223 | −1.13157 | −0.565787 | − | 0.824551i | \(-0.691428\pi\) | ||||
−0.565787 | + | 0.824551i | \(0.691428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.0384 | −1.29970 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.2161 | −0.493415 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.4823 | −0.955024 | −0.477512 | − | 0.878625i | \(-0.658461\pi\) | ||||
−0.477512 | + | 0.878625i | \(0.658461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.3492 | −0.593765 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.32996 | −0.204618 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.64177 | 0.0853072 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.5097 | 2.01644 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.0192 | 0.386912 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.8669 | −0.606719 | −0.303359 | − | 0.952876i | \(-0.598108\pi\) | ||||
−0.303359 | + | 0.952876i | \(0.598108\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.61350 | −0.0518329 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.2270 | −1.00212 | −0.501061 | − | 0.865412i | \(-0.667057\pi\) | ||||
−0.501061 | + | 0.865412i | \(0.667057\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.3401 | 0.363546 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.32088 | −0.106353 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.44305 | 0.206132 | 0.103066 | − | 0.994675i | \(-0.467135\pi\) | ||||
0.103066 | + | 0.994675i | \(0.467135\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.32996 | 0.202306 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.6983 | 0.341571 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.57429 | −0.145897 | −0.0729486 | − | 0.997336i | \(-0.523241\pi\) | ||||
−0.0729486 | + | 0.997336i | \(0.523241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.84049 | 0.154231 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.4148 | 0.490658 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 67.0029 | 2.13057 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.8296 | 1.23346 | 0.616731 | − | 0.787174i | \(-0.288457\pi\) | ||||
0.616731 | + | 0.787174i | \(0.288457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.9536 | −0.855346 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.6983 | 0.656181 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.9245 | 1.73948 | 0.869738 | − | 0.493513i | \(-0.164288\pi\) | ||||
0.869738 | + | 0.493513i | \(0.164288\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.96265 | −0.188650 |
(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 | 4560.2.a.br.1.3 | 3 | ||
4.3 | odd | 2 | 1140.2.a.g.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 3420.2.a.m.1.1 | 3 | |||
20.3 | even | 4 | 5700.2.f.q.3649.6 | 6 | |||
20.7 | even | 4 | 5700.2.f.q.3649.1 | 6 | |||
20.19 | odd | 2 | 5700.2.a.w.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.a.g.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
3420.2.a.m.1.1 | 3 | 12.11 | even | 2 | |||
4560.2.a.br.1.3 | 3 | 1.1 | even | 1 | trivial | ||
5700.2.a.w.1.3 | 3 | 20.19 | odd | 2 | |||
5700.2.f.q.3649.1 | 6 | 20.7 | even | 4 | |||
5700.2.f.q.3649.6 | 6 | 20.3 | even | 4 |