Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2960,2,Mod(1,2960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2960 = 2^{4} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2960.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: | \(23.6357189983\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.6397264.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 10x^{3} - 2x^{2} + 14x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1480) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.925120\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2960.1 |
$q$-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 | ||||||||
\(3\) | 0.925120 | 0.534118 | 0.267059 | − | 0.963680i | \(-0.413948\pi\) | ||||
0.267059 | + | 0.963680i | \(0.413948\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.763238 | −0.288477 | −0.144239 | − | 0.989543i | \(-0.546073\pi\) | ||||
−0.144239 | + | 0.989543i | \(0.546073\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.14415 | −0.714718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.44732 | 1.94394 | 0.971970 | − | 0.235106i | \(-0.0755438\pi\) | ||||
0.971970 | + | 0.235106i | \(0.0755438\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.67063 | −0.740699 | −0.370350 | − | 0.928892i | \(-0.620762\pi\) | ||||
−0.370350 | + | 0.928892i | \(0.620762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.925120 | −0.238865 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.30316 | 1.28621 | 0.643103 | − | 0.765780i | \(-0.277647\pi\) | ||||
0.643103 | + | 0.765780i | \(0.277647\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.88966 | −1.12177 | −0.560883 | − | 0.827895i | \(-0.689538\pi\) | ||||
−0.560883 | + | 0.827895i | \(0.689538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.706087 | −0.154081 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.149760 | −0.0312271 | −0.0156136 | − | 0.999878i | \(-0.504970\pi\) | ||||
−0.0156136 | + | 0.999878i | \(0.504970\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.75896 | −0.915862 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.21771 | 0.968904 | 0.484452 | − | 0.874818i | \(-0.339019\pi\) | ||||
0.484452 | + | 0.874818i | \(0.339019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.912998 | −0.163979 | −0.0819897 | − | 0.996633i | \(-0.526127\pi\) | ||||
−0.0819897 | + | 0.996633i | \(0.526127\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.96454 | 1.03829 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.763238 | 0.129011 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.47065 | −0.395621 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7711 | 1.68216 | 0.841080 | − | 0.540911i | \(-0.181920\pi\) | ||||
0.841080 | + | 0.540911i | \(0.181920\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.12355 | 1.23883 | 0.619415 | − | 0.785064i | \(-0.287370\pi\) | ||||
0.619415 | + | 0.785064i | \(0.287370\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.14415 | 0.319631 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.51008 | −0.511997 | −0.255999 | − | 0.966677i | \(-0.582404\pi\) | ||||
−0.255999 | + | 0.966677i | \(0.582404\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.41747 | −0.916781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.90606 | 0.686986 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.5971 | 1.45562 | 0.727810 | − | 0.685779i | \(-0.240538\pi\) | ||||
0.727810 | + | 0.685779i | \(0.240538\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.44732 | −0.869356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.52352 | −0.599156 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.45447 | −0.579922 | −0.289961 | − | 0.957038i | \(-0.593642\pi\) | ||||
−0.289961 | + | 0.957038i | \(0.593642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.26210 | −1.05785 | −0.528927 | − | 0.848667i | \(-0.677405\pi\) | ||||
−0.528927 | + | 0.848667i | \(0.677405\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.63650 | 0.206180 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.67063 | 0.331251 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.88966 | 0.841706 | 0.420853 | − | 0.907129i | \(-0.361731\pi\) | ||||
0.420853 | + | 0.907129i | \(0.361731\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.138546 | −0.0166790 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.03546 | −0.241564 | −0.120782 | − | 0.992679i | \(-0.538540\pi\) | ||||
−0.120782 | + | 0.992679i | \(0.538540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.81478 | 1.14873 | 0.574367 | − | 0.818598i | \(-0.305248\pi\) | ||||
0.574367 | + | 0.818598i | \(0.305248\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.925120 | 0.106824 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.92084 | −0.560782 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.83384 | 0.206323 | 0.103161 | − | 0.994665i | \(-0.467104\pi\) | ||||
0.103161 | + | 0.994665i | \(0.467104\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.02985 | 0.225539 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.03942 | −0.114091 | −0.0570457 | − | 0.998372i | \(-0.518168\pi\) | ||||
−0.0570457 | + | 0.998372i | \(0.518168\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.30316 | −0.575209 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.82700 | 0.517509 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.9301 | 1.79459 | 0.897293 | − | 0.441435i | \(-0.145531\pi\) | ||||
0.897293 | + | 0.441435i | \(0.145531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.03833 | 0.213675 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.844633 | −0.0875844 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.88966 | 0.501669 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.18225 | −0.526178 | −0.263089 | − | 0.964772i | \(-0.584741\pi\) | ||||
−0.263089 | + | 0.964772i | \(0.584741\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13.8240 | −1.38937 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.84463 | 0.880074 | 0.440037 | − | 0.897980i | \(-0.354965\pi\) | ||||
0.440037 | + | 0.897980i | \(0.354965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.30580 | −0.522796 | −0.261398 | − | 0.965231i | \(-0.584184\pi\) | ||||
−0.261398 | + | 0.965231i | \(0.584184\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.706087 | 0.0689071 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3249 | 1.09482 | 0.547408 | − | 0.836866i | \(-0.315615\pi\) | ||||
0.547408 | + | 0.836866i | \(0.315615\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.24460 | 0.693907 | 0.346954 | − | 0.937882i | \(-0.387216\pi\) | ||||
0.346954 | + | 0.937882i | \(0.387216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.925120 | 0.0878085 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.3207 | 1.34717 | 0.673587 | − | 0.739108i | \(-0.264753\pi\) | ||||
0.673587 | + | 0.739108i | \(0.264753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.149760 | 0.0139652 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.72624 | 0.529391 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.04758 | −0.371041 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.5679 | 2.77890 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.96454 | 0.898473 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8310 | 1.04983 | 0.524914 | − | 0.851155i | \(-0.324097\pi\) | ||||
0.524914 | + | 0.851155i | \(0.324097\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.51526 | 0.661682 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.127834 | −0.0111689 | −0.00558444 | − | 0.999984i | \(-0.501778\pi\) | ||||
−0.00558444 | + | 0.999984i | \(0.501778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.73198 | 0.323604 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.75896 | 0.409586 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.81478 | 0.496790 | 0.248395 | − | 0.968659i | \(-0.420097\pi\) | ||||
0.248395 | + | 0.968659i | \(0.420097\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.1922 | −1.79750 | −0.898749 | − | 0.438463i | \(-0.855523\pi\) | ||||
−0.898749 | + | 0.438463i | \(0.855523\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.24724 | −0.273467 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.2184 | −1.43987 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.21771 | −0.433307 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.93693 | −0.489670 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.08546 | −0.170847 | −0.0854237 | − | 0.996345i | \(-0.527224\pi\) | ||||
−0.0854237 | + | 0.996345i | \(0.527224\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.13855 | −0.336790 | −0.168395 | − | 0.985720i | \(-0.553858\pi\) | ||||
−0.168395 | + | 0.985720i | \(0.553858\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.3708 | −0.919274 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.912998 | 0.0733338 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.42307 | −0.353000 | −0.176500 | − | 0.984301i | \(-0.556478\pi\) | ||||
−0.176500 | + | 0.984301i | \(0.556478\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.80357 | 0.777474 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.114303 | 0.00900830 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.9795 | 1.09496 | 0.547481 | − | 0.836818i | \(-0.315587\pi\) | ||||
0.547481 | + | 0.836818i | \(0.315587\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.96454 | −0.464339 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.01750 | 0.543030 | 0.271515 | − | 0.962434i | \(-0.412475\pi\) | ||||
0.271515 | + | 0.962434i | \(0.412475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.86774 | −0.451364 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.4842 | 0.801746 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.823027 | −0.0625736 | −0.0312868 | − | 0.999510i | \(-0.509961\pi\) | ||||
−0.0312868 | + | 0.999510i | \(0.509961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.763238 | −0.0576954 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.12092 | −0.309747 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.54575 | −0.115535 | −0.0577673 | − | 0.998330i | \(-0.518398\pi\) | ||||
−0.0577673 | + | 0.998330i | \(0.518398\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.20285 | 0.609713 | 0.304856 | − | 0.952398i | \(-0.401392\pi\) | ||||
0.304856 | + | 0.952398i | \(0.401392\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.64343 | −0.565019 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.00000 | −0.0735215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 34.1912 | 2.50031 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.63222 | 0.264205 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2642 | 1.61098 | 0.805491 | − | 0.592609i | \(-0.201902\pi\) | ||||
0.805491 | + | 0.592609i | \(0.201902\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.7893 | −1.71239 | −0.856195 | − | 0.516654i | \(-0.827178\pi\) | ||||
−0.856195 | + | 0.516654i | \(0.827178\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.47065 | 0.176927 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.20845 | −0.228593 | −0.114296 | − | 0.993447i | \(-0.536461\pi\) | ||||
−0.114296 | + | 0.993447i | \(0.536461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.2403 | −1.08036 | −0.540179 | − | 0.841550i | \(-0.681643\pi\) | ||||
−0.540179 | + | 0.841550i | \(0.681643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.37377 | 0.449571 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.98235 | −0.279506 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.7711 | −0.752285 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.321108 | 0.0223186 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31.5252 | −2.18064 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.93834 | −0.408812 | −0.204406 | − | 0.978886i | \(-0.565526\pi\) | ||||
−0.204406 | + | 0.978886i | \(0.565526\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.88304 | −0.129024 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.12355 | −0.554022 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.696835 | 0.0473043 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.07985 | 0.613560 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.1628 | −0.952692 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.6010 | 1.31258 | 0.656291 | − | 0.754507i | \(-0.272124\pi\) | ||||
0.656291 | + | 0.754507i | \(0.272124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.14415 | −0.142944 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.09666 | −0.139160 | −0.0695800 | − | 0.997576i | \(-0.522166\pi\) | ||||
−0.0695800 | + | 0.997576i | \(0.522166\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.9036 | 1.71176 | 0.855878 | − | 0.517178i | \(-0.173017\pi\) | ||||
0.855878 | + | 0.517178i | \(0.173017\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.55237 | −0.299524 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00266 | 0.262223 | 0.131111 | − | 0.991368i | \(-0.458145\pi\) | ||||
0.131111 | + | 0.991368i | \(0.458145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.51008 | 0.228972 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.69652 | 0.110201 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.2402 | −1.56797 | −0.783983 | − | 0.620782i | \(-0.786815\pi\) | ||||
−0.783983 | + | 0.620782i | \(0.786815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.7439 | −1.40065 | −0.700323 | − | 0.713826i | \(-0.746961\pi\) | ||||
−0.700323 | + | 0.713826i | \(0.746961\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1547 | 1.03633 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.41747 | 0.409997 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.0585 | 0.830891 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.961591 | −0.0609383 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.95957 | 0.123687 | 0.0618435 | − | 0.998086i | \(-0.480302\pi\) | ||||
0.0618435 | + | 0.998086i | \(0.480302\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.965550 | −0.0607036 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.90606 | −0.307230 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.23522 | −0.513699 | −0.256849 | − | 0.966451i | \(-0.582684\pi\) | ||||
−0.256849 | + | 0.966451i | \(0.582684\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.763238 | −0.0474253 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.1876 | −0.692492 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.5352 | −1.69789 | −0.848947 | − | 0.528477i | \(-0.822763\pi\) | ||||
−0.848947 | + | 0.528477i | \(0.822763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5971 | −0.650973 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.6624 | 0.958521 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.7093 | 1.32364 | 0.661819 | − | 0.749663i | \(-0.269785\pi\) | ||||
0.661819 | + | 0.749663i | \(0.269785\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.2359 | −1.59372 | −0.796859 | − | 0.604166i | \(-0.793506\pi\) | ||||
−0.796859 | + | 0.604166i | \(0.793506\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.88570 | 0.114128 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.44732 | 0.388788 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.7007 | 1.54421 | 0.772103 | − | 0.635497i | \(-0.219205\pi\) | ||||
0.772103 | + | 0.635497i | \(0.219205\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.95761 | 0.117199 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.867736 | −0.0517648 | −0.0258824 | − | 0.999665i | \(-0.508240\pi\) | ||||
−0.0258824 | + | 0.999665i | \(0.508240\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.6481 | −1.04907 | −0.524534 | − | 0.851389i | \(-0.675761\pi\) | ||||
−0.524534 | + | 0.851389i | \(0.675761\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.52352 | 0.267950 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.22090 | −0.485265 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.1236 | 0.654327 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.79420 | −0.281041 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.5092 | −0.964478 | −0.482239 | − | 0.876040i | \(-0.660176\pi\) | ||||
−0.482239 | + | 0.876040i | \(0.660176\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.45447 | 0.259349 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −30.6825 | −1.78038 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.399953 | 0.0231299 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.20021 | −0.357374 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.18235 | 0.470064 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.26210 | 0.473086 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.4962 | 1.34100 | 0.670500 | − | 0.741910i | \(-0.266080\pi\) | ||||
0.670500 | + | 0.741910i | \(0.266080\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.90850 | −0.279235 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.41970 | 0.477438 | 0.238719 | − | 0.971089i | \(-0.423273\pi\) | ||||
0.238719 | + | 0.971089i | \(0.423273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.1041 | −0.740687 | −0.370344 | − | 0.928895i | \(-0.620760\pi\) | ||||
−0.370344 | + | 0.928895i | \(0.620760\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.63650 | −0.0922063 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.7653 | −0.941635 | −0.470818 | − | 0.882231i | \(-0.656041\pi\) | ||||
−0.470818 | + | 0.882231i | \(0.656041\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.6402 | 1.88349 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4769 | 0.584761 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −25.9307 | −1.44282 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.67063 | −0.148140 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.70213 | 0.370629 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.67902 | 0.147699 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.2690 | 0.784297 | 0.392149 | − | 0.919902i | \(-0.371732\pi\) | ||||
0.392149 | + | 0.919902i | \(0.371732\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.14415 | −0.117499 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.88966 | −0.376422 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.1570 | 0.553290 | 0.276645 | − | 0.960972i | \(-0.410777\pi\) | ||||
0.276645 | + | 0.960972i | \(0.410777\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.2483 | 0.719551 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.88639 | −0.318766 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.2407 | 0.552947 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.138546 | 0.00745906 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.98570 | 0.321329 | 0.160665 | − | 0.987009i | \(-0.448636\pi\) | ||||
0.160665 | + | 0.987009i | \(0.448636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.43246 | −0.397850 | −0.198925 | − | 0.980015i | \(-0.563745\pi\) | ||||
−0.198925 | + | 0.980015i | \(0.563745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.7094 | 0.678379 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.9383 | 0.848312 | 0.424156 | − | 0.905589i | \(-0.360571\pi\) | ||||
0.424156 | + | 0.905589i | \(0.360571\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.03546 | 0.108031 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.74450 | −0.198180 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.73759 | −0.461152 | −0.230576 | − | 0.973054i | \(-0.574061\pi\) | ||||
−0.230576 | + | 0.973054i | \(0.574061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.90880 | 0.258358 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.2790 | 1.48426 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.81478 | −0.513729 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.6585 | −1.91356 | −0.956778 | − | 0.290819i | \(-0.906072\pi\) | ||||
−0.956778 | + | 0.290819i | \(0.906072\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.0948 | −1.20227 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.08810 | −0.419913 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.1385 | 0.732066 | 0.366033 | − | 0.930602i | \(-0.380716\pi\) | ||||
0.366033 | + | 0.930602i | \(0.380716\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.925120 | −0.0477730 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.9346 | −0.717666 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.84450 | 0.0947456 | 0.0473728 | − | 0.998877i | \(-0.484915\pi\) | ||||
0.0473728 | + | 0.998877i | \(0.484915\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.9451 | 0.560733 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.1041 | −0.771783 | −0.385892 | − | 0.922544i | \(-0.626106\pi\) | ||||
−0.385892 | + | 0.922544i | \(0.626106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.92084 | 0.250789 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.4181 | −0.885414 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.5262 | −1.14212 | −0.571061 | − | 0.820908i | \(-0.693468\pi\) | ||||
−0.571061 | + | 0.820908i | \(0.693468\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.794201 | −0.0401645 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.118262 | −0.00596551 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.83384 | −0.0922704 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.93009 | 0.247434 | 0.123717 | − | 0.992318i | \(-0.460518\pi\) | ||||
0.123717 | + | 0.992318i | \(0.460518\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.45253 | 0.172843 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.2106 | −0.659708 | −0.329854 | − | 0.944032i | \(-0.607000\pi\) | ||||
−0.329854 | + | 0.944032i | \(0.607000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.43828 | 0.121459 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.02985 | −0.100864 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.44732 | 0.319582 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.31575 | 0.460634 | 0.230317 | − | 0.973116i | \(-0.426024\pi\) | ||||
0.230317 | + | 0.973116i | \(0.426024\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.37937 | 0.265345 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.39982 | 0.167294 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.03942 | 0.0510232 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.6053 | −0.960077 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.9278 | 1.85290 | 0.926448 | − | 0.376424i | \(-0.122846\pi\) | ||||
0.926448 | + | 0.376424i | \(0.122846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.8534 | 1.60118 | 0.800589 | − | 0.599213i | \(-0.204520\pi\) | ||||
0.800589 | + | 0.599213i | \(0.204520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.52614 | 0.365933 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.30316 | 0.257241 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.30595 | 0.305166 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.9291 | −0.769063 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.2266 | −0.685269 | −0.342635 | − | 0.939469i | \(-0.611319\pi\) | ||||
−0.342635 | + | 0.939469i | \(0.611319\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.07885 | 0.196017 | 0.0980084 | − | 0.995186i | \(-0.468753\pi\) | ||||
0.0980084 | + | 0.995186i | \(0.468753\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.82700 | −0.231437 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.732275 | 0.0350295 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.1333 | −1.10409 | −0.552045 | − | 0.833814i | \(-0.686152\pi\) | ||||
−0.552045 | + | 0.833814i | \(0.686152\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.7600 | 0.655240 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.2393 | 1.05662 | 0.528310 | − | 0.849052i | \(-0.322826\pi\) | ||||
0.528310 | + | 0.849052i | \(0.322826\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.9301 | −0.802563 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.92930 | −0.0912528 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.07885 | 0.381264 | 0.190632 | − | 0.981662i | \(-0.438946\pi\) | ||||
0.190632 | + | 0.981662i | \(0.438946\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 69.4446 | 3.27002 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.82865 | −0.179886 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.03833 | −0.0955583 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.48177 | −0.0693142 | −0.0346571 | − | 0.999399i | \(-0.511034\pi\) | ||||
−0.0346571 | + | 0.999399i | \(0.511034\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.2375 | −1.17799 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.4069 | −1.83536 | −0.917682 | − | 0.397316i | \(-0.869942\pi\) | ||||
−0.917682 | + | 0.397316i | \(0.869942\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.7687 | −1.70878 | −0.854392 | − | 0.519629i | \(-0.826070\pi\) | ||||
−0.854392 | + | 0.519629i | \(0.826070\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.844633 | 0.0391689 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.80288 | 0.453623 | 0.226811 | − | 0.973939i | \(-0.427170\pi\) | ||||
0.226811 | + | 0.973939i | \(0.427170\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.25846 | −0.242813 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.09187 | −0.188544 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.3751 | 2.40821 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.88966 | −0.224353 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −22.7218 | −1.04036 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.3721 | −1.84465 | −0.922325 | − | 0.386416i | \(-0.873713\pi\) | ||||
−0.922325 | + | 0.386416i | \(0.873713\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.67063 | −0.121770 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.105744 | 0.00481150 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.18225 | 0.235314 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.4425 | 1.28885 | 0.644427 | − | 0.764666i | \(-0.277096\pi\) | ||||
0.644427 | + | 0.764666i | \(0.277096\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.9327 | 0.584839 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.2761 | −0.960176 | −0.480088 | − | 0.877220i | \(-0.659395\pi\) | ||||
−0.480088 | + | 0.877220i | \(0.659395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.6703 | 1.24621 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.8240 | 0.621344 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.55354 | 0.0696858 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.8222 | 0.708297 | 0.354149 | − | 0.935189i | \(-0.384771\pi\) | ||||
0.354149 | + | 0.935189i | \(0.384771\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.49203 | 0.290042 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.47252 | −0.422359 | −0.211179 | − | 0.977447i | \(-0.567730\pi\) | ||||
−0.211179 | + | 0.977447i | \(0.567730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.84463 | −0.393581 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.42836 | −0.241082 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.8991 | −0.616067 | −0.308033 | − | 0.951376i | \(-0.599671\pi\) | ||||
−0.308033 | + | 0.951376i | \(0.599671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.49102 | −0.331383 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23.2697 | 1.02738 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.30580 | 0.233802 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.6306 | −0.995291 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.761399 | −0.0334217 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0655 | −0.922898 | −0.461449 | − | 0.887167i | \(-0.652670\pi\) | ||||
−0.461449 | + | 0.887167i | \(0.652670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.2202 | 1.05908 | 0.529538 | − | 0.848286i | \(-0.322365\pi\) | ||||
0.529538 | + | 0.848286i | \(0.322365\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.706087 | −0.0308162 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.84178 | −0.210911 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9776 | −0.999025 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.55106 | 0.414481 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.7656 | −1.24598 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.3249 | −0.489616 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.43000 | −0.0617092 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −41.3754 | −1.78217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.9977 | 1.59066 | 0.795328 | − | 0.606179i | \(-0.207299\pi\) | ||||
0.795328 | + | 0.606179i | \(0.207299\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.58862 | 0.325659 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.24460 | −0.310325 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.3652 | −0.785239 | −0.392619 | − | 0.919701i | \(-0.628431\pi\) | ||||
−0.392619 | + | 0.919701i | \(0.628431\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 17.7152 | 0.756067 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.5128 | −1.08688 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.39966 | −0.0595194 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.925120 | −0.0392692 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.4948 | −0.487051 | −0.243525 | − | 0.969895i | \(-0.578304\pi\) | ||||
−0.243525 | + | 0.969895i | \(0.578304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.6950 | −0.917601 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 31.6310 | 1.33546 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.78904 | −0.412559 | −0.206279 | − | 0.978493i | \(-0.566136\pi\) | ||||
−0.206279 | + | 0.978493i | \(0.566136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.3207 | −0.602475 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.54926 | −0.0650628 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.5575 | −0.442592 | −0.221296 | − | 0.975207i | \(-0.571029\pi\) | ||||
−0.221296 | + | 0.975207i | \(0.571029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.64556 | −0.361806 | −0.180903 | − | 0.983501i | \(-0.557902\pi\) | ||||
−0.180903 | + | 0.983501i | \(0.557902\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.5971 | 0.860455 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.149760 | −0.00624542 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.16430 | −0.173362 | −0.0866811 | − | 0.996236i | \(-0.527626\pi\) | ||||
−0.0866811 | + | 0.996236i | \(0.527626\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.0079 | −0.914618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.793327 | 0.0329128 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 68.3227 | 2.82964 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.72624 | −0.236751 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.3122 | −1.29239 | −0.646197 | − | 0.763171i | \(-0.723642\pi\) | ||||
−0.646197 | + | 0.763171i | \(0.723642\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.46425 | 0.183946 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.96820 | −0.122096 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 27.6422 | 1.13513 | 0.567564 | − | 0.823329i | \(-0.307886\pi\) | ||||
0.567564 | + | 0.823329i | \(0.307886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.04758 | 0.165935 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.0991 | −0.577039 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.1328 | −0.822604 | −0.411302 | − | 0.911499i | \(-0.634926\pi\) | ||||
−0.411302 | + | 0.911499i | \(0.634926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.88733 | 0.280940 | 0.140470 | − | 0.990085i | \(-0.455139\pi\) | ||||
0.140470 | + | 0.990085i | \(0.455139\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.7725 | −0.601582 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.5679 | −1.24276 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.0574 | 1.42294 | 0.711468 | − | 0.702718i | \(-0.248030\pi\) | ||||
0.711468 | + | 0.702718i | \(0.248030\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.68415 | −0.149289 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.37411 | 0.379236 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.4218 | 0.905608 | 0.452804 | − | 0.891610i | \(-0.350424\pi\) | ||||
0.452804 | + | 0.891610i | \(0.350424\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.96454 | −0.401809 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.94076 | 0.158649 | 0.0793246 | − | 0.996849i | \(-0.474724\pi\) | ||||
0.0793246 | + | 0.996849i | \(0.474724\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.426159 | 0.0171288 | 0.00856439 | − | 0.999963i | \(-0.497274\pi\) | ||||
0.00856439 | + | 0.999963i | \(0.497274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.712701 | 0.0285997 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.9217 | −0.517697 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −29.1646 | −1.16472 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.30316 | 0.211451 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.7364 | −0.507028 | −0.253514 | − | 0.967332i | \(-0.581586\pi\) | ||||
−0.253514 | + | 0.967332i | \(0.581586\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.49367 | −0.218354 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.8310 | −0.469498 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.1387 | 0.679059 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.36433 | 0.172650 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.0295361 | 0.00116660 | 0.000583302 | − | 1.00000i | \(-0.499814\pi\) | ||||
0.000583302 | 1.00000i | \(0.499814\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.6321 | −1.12914 | −0.564569 | − | 0.825386i | \(-0.690958\pi\) | ||||
−0.564569 | + | 0.825386i | \(0.690958\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.51526 | −0.295913 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.3744 | 0.486489 | 0.243245 | − | 0.969965i | \(-0.421788\pi\) | ||||
0.243245 | + | 0.969965i | \(0.421788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.7194 | −1.12733 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.644656 | 0.0252661 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4413 | 0.760795 | 0.380398 | − | 0.924823i | \(-0.375787\pi\) | ||||
0.380398 | + | 0.924823i | \(0.375787\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.127834 | 0.00499488 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.0444 | −0.821020 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −47.4358 | −1.84784 | −0.923918 | − | 0.382591i | \(-0.875032\pi\) | ||||
−0.923918 | + | 0.382591i | \(0.875032\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.0577 | −1.44138 | −0.720688 | − | 0.693260i | \(-0.756174\pi\) | ||||
−0.720688 | + | 0.693260i | \(0.756174\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.1023 | −0.508850 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.73198 | −0.144720 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.781403 | −0.0302560 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.1333 | 0.701075 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −53.2684 | −2.05640 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.0843 | −1.58368 | −0.791842 | − | 0.610726i | \(-0.790878\pi\) | ||||
−0.791842 | + | 0.610726i | \(0.790878\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.75896 | −0.183172 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.26815 | −0.0487391 | −0.0243696 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243696 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.95529 | 0.151790 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.93966 | −0.0743279 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.43429 | −0.0931454 | −0.0465727 | − | 0.998915i | \(-0.514830\pi\) | ||||
−0.0465727 | + | 0.998915i | \(0.514830\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.81478 | −0.222171 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.9639 | 0.914280 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.3009 | −1.07818 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.8823 | 0.490066 | 0.245033 | − | 0.969515i | \(-0.421201\pi\) | ||||
0.245033 | + | 0.969515i | \(0.421201\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.5510 | 0.400801 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.1922 | 0.803866 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 57.1208 | 2.16361 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.70294 | 0.140058 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.9659 | 0.905181 | 0.452590 | − | 0.891719i | \(-0.350500\pi\) | ||||
0.452590 | + | 0.891719i | \(0.350500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.88966 | −0.184417 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.24724 | 0.122298 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.75056 | −0.253881 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −50.1842 | −1.88471 | −0.942353 | − | 0.334620i | \(-0.891392\pi\) | ||||
−0.942353 | + | 0.334620i | \(0.891392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.93203 | −0.147463 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.136731 | 0.00512060 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.2184 | 0.643932 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.4251 | −0.837480 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.2628 | 0.755675 | 0.377837 | − | 0.925872i | \(-0.376668\pi\) | ||||
0.377837 | + | 0.925872i | \(0.376668\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.04959 | 0.150815 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.1157 | −0.748110 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.21771 | 0.193781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.8924 | −1.55370 | −0.776851 | − | 0.629685i | \(-0.783184\pi\) | ||||
−0.776851 | + | 0.629685i | \(0.783184\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.85552 | 0.327982 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.0805 | 1.59339 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.9524 | 1.06938 | 0.534690 | − | 0.845048i | \(-0.320428\pi\) | ||||
0.534690 | + | 0.845048i | \(0.320428\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.93693 | 0.218987 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 44.4198 | 1.63623 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.191814 | 0.00705599 | 0.00352800 | − | 0.999994i | \(-0.498877\pi\) | ||||
0.00352800 | + | 0.999994i | \(0.498877\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0807 | 0.443794 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.5661 | 1.59828 | 0.799142 | − | 0.601142i | \(-0.205287\pi\) | ||||
0.799142 | + | 0.601142i | \(0.205287\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.08546 | 0.0764053 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.22868 | 0.0815432 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.64357 | −0.315829 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.1963 | −1.28433 | −0.642166 | − | 0.766565i | \(-0.721964\pi\) | ||||
−0.642166 | + | 0.766565i | \(0.721964\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.81284 | 0.0660635 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.13855 | 0.150617 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.9437 | −0.942939 | −0.471469 | − | 0.881882i | \(-0.656276\pi\) | ||||
−0.471469 | + | 0.881882i | \(0.656276\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.893249 | −0.0324229 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.3048 | −1.31605 | −0.658025 | − | 0.752996i | \(-0.728608\pi\) | ||||
−0.658025 | + | 0.752996i | \(0.728608\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.52936 | −0.200176 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.3708 | 0.411112 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.8962 | 0.429548 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.8359 | 0.859546 | 0.429773 | − | 0.902937i | \(-0.358594\pi\) | ||||
0.429773 | + | 0.902937i | \(0.358594\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.61857 | −0.274376 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 53.4424 | 1.92219 | 0.961095 | − | 0.276220i | \(-0.0890818\pi\) | ||||
0.961095 | + | 0.276220i | \(0.0890818\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.912998 | −0.0327959 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.706087 | −0.0253307 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −52.6670 | −1.88699 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.1232 | −0.469586 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.8308 | −0.887382 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.42307 | 0.157866 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.0591 | 1.24972 | 0.624860 | − | 0.780737i | \(-0.285156\pi\) | ||||
0.624860 | + | 0.780737i | \(0.285156\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.4734 | −0.906877 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.9301 | −0.388629 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.0650 | 0.783552 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.80357 | −0.347697 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.3477 | 0.827018 | 0.413509 | − | 0.910500i | \(-0.364303\pi\) | ||||
0.413509 | + | 0.910500i | \(0.364303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.6145 | −0.658534 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36.3007 | −1.28262 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 63.2790 | 2.23307 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.114303 | −0.00402863 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.0837 | 0.706980 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.9233 | 1.05205 | 0.526024 | − | 0.850469i | \(-0.323682\pi\) | ||||
0.526024 | + | 0.850469i | \(0.323682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.99426 | −0.140257 | −0.0701287 | − | 0.997538i | \(-0.522341\pi\) | ||||
−0.0701287 | + | 0.997538i | \(0.522341\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.2714 | −0.851233 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.9795 | −0.489682 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −39.7214 | −1.38968 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.37049 | −0.152717 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.8542 | 1.46072 | 0.730362 | − | 0.683061i | \(-0.239352\pi\) | ||||
0.730362 | + | 0.683061i | \(0.239352\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 48.8580 | 1.70308 | 0.851541 | − | 0.524287i | \(-0.175668\pi\) | ||||
0.851541 | + | 0.524287i | \(0.175668\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.96454 | 0.207659 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.9524 | −1.28496 | −0.642480 | − | 0.766302i | \(-0.722094\pi\) | ||||
−0.642480 | + | 0.766302i | \(0.722094\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.04955 | 0.0711840 | 0.0355920 | − | 0.999366i | \(-0.488668\pi\) | ||||
0.0355920 | + | 0.999366i | \(0.488668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23.7763 | 0.824789 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −34.0329 | −1.17917 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.01750 | −0.242850 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.34492 | 0.150182 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −51.2252 | −1.76849 | −0.884246 | − | 0.467022i | \(-0.845327\pi\) | ||||
−0.884246 | + | 0.467022i | \(0.845327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.77555 | −0.0612259 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.802760 | −0.0276485 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.86774 | 0.201856 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.3306 | −0.801649 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.3266 | −0.560327 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.149760 | −0.00513370 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −56.0152 | −1.91792 | −0.958962 | − | 0.283534i | \(-0.908493\pi\) | ||||
−0.958962 | + | 0.283534i | \(0.908493\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.4842 | −0.358552 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 53.9011 | 1.84123 | 0.920614 | − | 0.390474i | \(-0.127689\pi\) | ||||
0.920614 | + | 0.390474i | \(0.127689\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.9051 | −1.32742 | −0.663712 | − | 0.747988i | \(-0.731020\pi\) | ||||
−0.663712 | + | 0.747988i | \(0.731020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.60532 | −0.259189 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.0560 | −1.12524 | −0.562619 | − | 0.826716i | \(-0.690206\pi\) | ||||
−0.562619 | + | 0.826716i | \(0.690206\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.823027 | 0.0279838 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.2906 | 0.349488 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.8233 | 0.401079 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.3997 | −0.623451 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.1115 | 0.376068 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.763238 | 0.0258022 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.6062 | 0.459448 | 0.229724 | − | 0.973256i | \(-0.426218\pi\) | ||||
0.229724 | + | 0.973256i | \(0.426218\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.2730 | −0.515145 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.8714 | −1.07377 | −0.536887 | − | 0.843654i | \(-0.680400\pi\) | ||||
−0.536887 | + | 0.843654i | \(0.680400\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.5744 | 0.826994 | 0.413497 | − | 0.910506i | \(-0.364307\pi\) | ||||
0.413497 | + | 0.910506i | \(0.364307\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.12092 | 0.138523 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.2709 | 1.18428 | 0.592141 | − | 0.805834i | \(-0.298283\pi\) | ||||
0.592141 | + | 0.805834i | \(0.298283\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.02985 | −0.302851 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.0871 | 0.438434 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.1631 | 0.574341 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.54575 | 0.0516687 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.370005 | 0.0123541 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.76376 | −0.158880 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.1980 | 1.87223 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.73594 | −0.190880 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.20285 | −0.272672 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.1346 | 0.369719 | 0.184859 | − | 0.982765i | \(-0.440817\pi\) | ||||
0.184859 | + | 0.982765i | \(0.440817\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.9642 | −0.629004 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.81469 | −0.0601235 | −0.0300618 | − | 0.999548i | \(-0.509570\pi\) | ||||
−0.0300618 | + | 0.999548i | \(0.509570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.70149 | −0.221787 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.64343 | 0.252684 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0975676 | 0.00322197 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.9790 | 0.758009 | 0.379004 | − | 0.925395i | \(-0.376267\pi\) | ||||
0.379004 | + | 0.925395i | \(0.376267\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.7368 | 0.716252 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.43595 | 0.178927 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.3765 | 0.373652 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.1891 | −1.54822 | −0.774112 | − | 0.633049i | \(-0.781803\pi\) | ||||
−0.774112 | + | 0.633049i | \(0.781803\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.3792 | 1.02841 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.78924 | 0.255008 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −34.1912 | −1.11817 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.4516 | 0.766132 | 0.383066 | − | 0.923721i | \(-0.374868\pi\) | ||||
0.383066 | + | 0.923721i | \(0.374868\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.1229 | −0.395615 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.9562 | 1.30253 | 0.651267 | − | 0.758848i | \(-0.274238\pi\) | ||||
0.651267 | + | 0.758848i | \(0.274238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.61308 | −0.0525290 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.63222 | −0.118156 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.9868 | 0.649485 | 0.324742 | − | 0.945803i | \(-0.394722\pi\) | ||||
0.324742 | + | 0.945803i | \(0.394722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.2117 | −0.850866 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.5100 | −0.502945 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.0082 | −1.81428 | −0.907142 | − | 0.420825i | \(-0.861741\pi\) | ||||
−0.907142 | + | 0.420825i | \(0.861741\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.2642 | −0.720453 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 31.1212 | 1.00601 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.43807 | −0.143313 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1664 | −0.973111 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.2822 | −0.782484 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.7893 | 0.765804 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −59.2145 | −1.90421 | −0.952105 | − | 0.305773i | \(-0.901085\pi\) | ||||
−0.952105 | + | 0.305773i | \(0.901085\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.9890 | −0.770638 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.5034 | 0.497526 | 0.248763 | − | 0.968564i | \(-0.419976\pi\) | ||||
0.248763 | + | 0.968564i | \(0.419976\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.1747 | 0.518537 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.47065 | −0.0791242 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.51823 | −0.0805654 | −0.0402827 | − | 0.999188i | \(-0.512826\pi\) | ||||
−0.0402827 | + | 0.999188i | \(0.512826\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 109.154 | 3.48857 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.5335 | −0.495948 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.5856 | 1.16690 | 0.583449 | − | 0.812150i | \(-0.301703\pi\) | ||||
0.583449 | + | 0.812150i | \(0.301703\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.20845 | 0.102230 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.47842 | 0.0788890 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.21658 | −0.0386851 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.6644 | −1.03762 | −0.518810 | − | 0.854890i | \(-0.673625\pi\) | ||||
−0.518810 | + | 0.854890i | \(0.673625\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.2006 | 0.418907 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.2403 | 0.483151 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.24180 | 0.0709985 | 0.0354992 | − | 0.999370i | \(-0.488698\pi\) | ||||
0.0354992 | + | 0.999370i | \(0.488698\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.75896 | −0.150567 |
(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 | 2960.2.a.y.1.4 | 5 | ||
4.3 | odd | 2 | 1480.2.a.i.1.2 | ✓ | 5 | ||
20.19 | odd | 2 | 7400.2.a.p.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1480.2.a.i.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
2960.2.a.y.1.4 | 5 | 1.1 | even | 1 | trivial | ||
7400.2.a.p.1.4 | 5 | 20.19 | odd | 2 |