Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.34309996544.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 8x^{6} + 28x^{5} + 31x^{4} - 36x^{3} - 22x^{2} + 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.139869\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 2.63640 | 1.52213 | 0.761065 | − | 0.648676i | \(-0.224677\pi\) | ||||
0.761065 | + | 0.648676i | \(0.224677\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.63403 | −1.17798 | −0.588988 | − | 0.808142i | \(-0.700473\pi\) | ||||
−0.588988 | + | 0.808142i | \(0.700473\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.88603 | 1.46878 | 0.734391 | − | 0.678727i | \(-0.237468\pi\) | ||||
0.734391 | + | 0.678727i | \(0.237468\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.95063 | 1.31688 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.95063 | 1.79418 | 0.897091 | − | 0.441845i | \(-0.145676\pi\) | ||||
0.897091 | + | 0.441845i | \(0.145676\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.14940 | −1.15084 | −0.575418 | − | 0.817859i | \(-0.695161\pi\) | ||||
−0.575418 | + | 0.817859i | \(0.695161\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.94438 | −1.79303 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.82843 | 0.443459 | 0.221729 | − | 0.975108i | \(-0.428830\pi\) | ||||
0.221729 | + | 0.975108i | \(0.428830\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.2452 | 2.23568 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.14940 | −0.865210 | −0.432605 | − | 0.901584i | \(-0.642406\pi\) | ||||
−0.432605 | + | 0.901584i | \(0.642406\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.93813 | 0.387627 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.50625 | 0.482328 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.19638 | 1.52203 | 0.761015 | − | 0.648735i | \(-0.224702\pi\) | ||||
0.761015 | + | 0.648735i | \(0.224702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.67631 | 0.301075 | 0.150537 | − | 0.988604i | \(-0.451900\pi\) | ||||
0.150537 | + | 0.988604i | \(0.451900\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.6883 | 2.73098 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.2359 | −1.73019 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.14452 | 1.33895 | 0.669476 | − | 0.742834i | \(-0.266519\pi\) | ||||
0.669476 | + | 0.742834i | \(0.266519\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.9395 | −1.75172 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.514201 | −0.0803047 | −0.0401524 | − | 0.999194i | \(-0.512784\pi\) | ||||
−0.0401524 | + | 0.999194i | \(0.512784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.9631 | 1.67186 | 0.835931 | − | 0.548835i | \(-0.184929\pi\) | ||||
0.835931 | + | 0.548835i | \(0.184929\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.4061 | −1.55125 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.3035 | −1.94051 | −0.970257 | − | 0.242075i | \(-0.922172\pi\) | ||||
−0.970257 | + | 0.242075i | \(0.922172\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.10124 | 1.15732 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.82047 | 0.675001 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.62446 | −0.223137 | −0.111568 | − | 0.993757i | \(-0.535587\pi\) | ||||
−0.111568 | + | 0.993757i | \(0.535587\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.6742 | −2.11350 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.63640 | −0.349200 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.2234 | 1.59136 | 0.795678 | − | 0.605720i | \(-0.207115\pi\) | ||||
0.795678 | + | 0.605720i | \(0.207115\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.98666 | 0.766513 | 0.383257 | − | 0.923642i | \(-0.374803\pi\) | ||||
0.383257 | + | 0.923642i | \(0.374803\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.3523 | 1.93420 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.9297 | 1.35566 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.09328 | −0.500074 | −0.250037 | − | 0.968236i | \(-0.580443\pi\) | ||||
−0.250037 | + | 0.968236i | \(0.580443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.9395 | −1.31696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.8696 | 1.40866 | 0.704332 | − | 0.709871i | \(-0.251247\pi\) | ||||
0.704332 | + | 0.709871i | \(0.251247\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.28531 | −1.08676 | −0.543381 | − | 0.839486i | \(-0.682856\pi\) | ||||
−0.543381 | + | 0.839486i | \(0.682856\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.10971 | 0.590018 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.1243 | 2.63526 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.42124 | −0.272410 | −0.136205 | − | 0.990681i | \(-0.543491\pi\) | ||||
−0.136205 | + | 0.990681i | \(0.543491\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.24441 | −0.582712 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.987504 | 0.108393 | 0.0541963 | − | 0.998530i | \(-0.482740\pi\) | ||||
0.0541963 | + | 0.998530i | \(0.482740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.81614 | −0.522384 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.6090 | 2.31672 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.25389 | −0.238912 | −0.119456 | − | 0.992840i | \(-0.538115\pi\) | ||||
−0.119456 | + | 0.992840i | \(0.538115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.1247 | −1.69033 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.41944 | 0.458274 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.63403 | 0.270246 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.27281 | 0.941511 | 0.470756 | − | 0.882264i | \(-0.343981\pi\) | ||||
0.470756 | + | 0.882264i | \(0.343981\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23.5087 | 2.36272 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3620 | 1.32957 | 0.664785 | − | 0.747034i | \(-0.268523\pi\) | ||||
0.664785 | + | 0.747034i | \(0.268523\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0094 | −0.986255 | −0.493127 | − | 0.869957i | \(-0.664146\pi\) | ||||
−0.493127 | + | 0.869957i | \(0.664146\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −26.9861 | −2.63357 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.85189 | −0.469050 | −0.234525 | − | 0.972110i | \(-0.575354\pi\) | ||||
−0.234525 | + | 0.972110i | \(0.575354\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1198 | −1.44822 | −0.724108 | − | 0.689687i | \(-0.757748\pi\) | ||||
−0.724108 | + | 0.689687i | \(0.757748\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.4723 | 2.03806 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.10175 | −0.291789 | −0.145894 | − | 0.989300i | \(-0.546606\pi\) | ||||
−0.145894 | + | 0.989300i | \(0.546606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.9297 | 1.01920 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.3928 | −1.51551 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.10532 | 0.651344 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.4100 | 2.21909 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.35564 | −0.122234 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.06506 | 0.721361 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.59176 | 0.318717 | 0.159358 | − | 0.987221i | \(-0.449057\pi\) | ||||
0.159358 | + | 0.987221i | \(0.449057\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28.9032 | 2.54479 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.76906 | −0.853527 | −0.426763 | − | 0.904363i | \(-0.640346\pi\) | ||||
−0.426763 | + | 0.904363i | \(0.640346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.88603 | −0.336962 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.60154 | −0.568170 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.25690 | 0.363692 | 0.181846 | − | 0.983327i | \(-0.441793\pi\) | ||||
0.181846 | + | 0.983327i | \(0.441793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.50875 | −0.806521 | −0.403261 | − | 0.915085i | \(-0.632123\pi\) | ||||
−0.403261 | + | 0.915085i | \(0.632123\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −35.0734 | −2.95371 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.6916 | −2.06481 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.5895 | −1.79291 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.3581 | 1.76159 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.13803 | −0.420924 | −0.210462 | − | 0.977602i | \(-0.567497\pi\) | ||||
−0.210462 | + | 0.977602i | \(0.567497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.26807 | 0.428709 | 0.214355 | − | 0.976756i | \(-0.431235\pi\) | ||||
0.214355 | + | 0.976756i | \(0.431235\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.22344 | 0.583981 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.41546 | −0.354659 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.12828 | −0.568899 | −0.284449 | − | 0.958691i | \(-0.591811\pi\) | ||||
−0.284449 | + | 0.958691i | \(0.591811\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.28273 | −0.339643 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16.1247 | −1.27080 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4060 | −0.971712 | −0.485856 | − | 0.874039i | \(-0.661492\pi\) | ||||
−0.485856 | + | 0.874039i | \(0.661492\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −41.3234 | −3.21703 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.80460 | −0.681320 | −0.340660 | − | 0.940187i | \(-0.610651\pi\) | ||||
−0.340660 | + | 0.940187i | \(0.610651\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.21753 | 0.324426 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.95063 | −0.302112 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.52203 | −0.115718 | −0.0578590 | − | 0.998325i | \(-0.518427\pi\) | ||||
−0.0578590 | + | 0.998325i | \(0.518427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.53165 | 0.569339 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32.2259 | 2.42225 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.6599 | 1.39470 | 0.697352 | − | 0.716729i | \(-0.254361\pi\) | ||||
0.697352 | + | 0.716729i | \(0.254361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.3132 | −0.840907 | −0.420453 | − | 0.907314i | \(-0.638129\pi\) | ||||
−0.420453 | + | 0.907314i | \(0.638129\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.7833 | 1.16673 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.4530 | −1.57725 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8803 | 0.795646 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.73936 | 0.708434 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5963 | 0.839078 | 0.419539 | − | 0.907737i | \(-0.362192\pi\) | ||||
0.419539 | + | 0.907737i | \(0.362192\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.78701 | −0.272595 | −0.136298 | − | 0.990668i | \(-0.543520\pi\) | ||||
−0.136298 | + | 0.990668i | \(0.543520\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 28.8150 | 2.06349 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.0803 | 1.85814 | 0.929071 | − | 0.369902i | \(-0.120609\pi\) | ||||
0.929071 | + | 0.369902i | \(0.120609\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.53452 | −0.250555 | −0.125278 | − | 0.992122i | \(-0.539982\pi\) | ||||
−0.125278 | + | 0.992122i | \(0.539982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.7916 | −0.761178 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 31.8514 | 2.23553 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.35442 | 0.0945970 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.3928 | −1.13938 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.95063 | −0.411614 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.84939 | 0.196160 | 0.0980802 | − | 0.995179i | \(-0.468730\pi\) | ||||
0.0980802 | + | 0.995179i | \(0.468730\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 31.2931 | 2.14417 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.8772 | −1.96941 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.51420 | 0.442213 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.4798 | −1.65419 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.58688 | −0.510349 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.4383 | −1.56954 | −0.784772 | − | 0.619785i | \(-0.787220\pi\) | ||||
−0.784772 | + | 0.619785i | \(0.787220\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.65685 | 0.510457 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.43341 | 0.493373 | 0.246686 | − | 0.969095i | \(-0.420658\pi\) | ||||
0.246686 | + | 0.969095i | \(0.420658\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.2316 | 1.27086 | 0.635431 | − | 0.772157i | \(-0.280822\pi\) | ||||
0.635431 | + | 0.772157i | \(0.280822\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 60.9651 | 4.01121 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.9306 | −1.96082 | −0.980411 | − | 0.196965i | \(-0.936892\pi\) | ||||
−0.980411 | + | 0.196965i | \(0.936892\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 35.0419 | 2.28588 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.38336 | −0.414644 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.0479 | 1.03805 | 0.519026 | − | 0.854758i | \(-0.326295\pi\) | ||||
0.519026 | + | 0.854758i | \(0.326295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9168 | 1.54061 | 0.770307 | − | 0.637673i | \(-0.220103\pi\) | ||||
0.770307 | + | 0.637673i | \(0.220103\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.3451 | −1.36929 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −21.3389 | −1.36329 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.14940 | 0.264020 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.60346 | 0.164988 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.1950 | 0.643505 | 0.321753 | − | 0.946824i | \(-0.395728\pi\) | ||||
0.321753 | + | 0.946824i | \(0.395728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.6916 | −1.55234 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.6973 | −0.795135 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.1866 | 1.25920 | 0.629602 | − | 0.776918i | \(-0.283218\pi\) | ||||
0.629602 | + | 0.776918i | \(0.283218\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.6499 | 1.96663 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 32.3809 | 2.00432 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.32659 | 0.328451 | 0.164226 | − | 0.986423i | \(-0.447487\pi\) | ||||
0.164226 | + | 0.986423i | \(0.447487\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.27888 | 0.262850 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.94216 | −0.363654 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.0564 | 0.857032 | 0.428516 | − | 0.903534i | \(-0.359037\pi\) | ||||
0.428516 | + | 0.903534i | \(0.359037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.56884 | 0.520520 | 0.260260 | − | 0.965539i | \(-0.416192\pi\) | ||||
0.260260 | + | 0.965539i | \(0.416192\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −42.5112 | −2.57290 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.5331 | 0.695474 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.7013 | 1.36399 | 0.681995 | − | 0.731357i | \(-0.261113\pi\) | ||||
0.681995 | + | 0.731357i | \(0.261113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.62249 | 0.396478 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.26940 | 0.493311 | 0.246656 | − | 0.969103i | \(-0.420668\pi\) | ||||
0.246656 | + | 0.969103i | \(0.420668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.7941 | 1.29552 | 0.647761 | − | 0.761844i | \(-0.275706\pi\) | ||||
0.647761 | + | 0.761844i | \(0.275706\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.94438 | 0.411350 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.99820 | −0.117950 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6569 | −0.803344 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.4469 | 1.43310 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.64036 | −0.504775 | −0.252388 | − | 0.967626i | \(-0.581216\pi\) | ||||
−0.252388 | + | 0.967626i | \(0.581216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −32.1970 | −1.87458 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.9138 | 0.865384 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.2175 | 0.995716 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.6031 | 2.45560 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 35.2277 | 2.02378 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.7691 | −0.902934 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.3871 | −0.649894 | −0.324947 | − | 0.945732i | \(-0.605346\pi\) | ||||
−0.324947 | + | 0.945732i | \(0.605346\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −26.3888 | −1.50121 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3199 | −0.641893 | −0.320947 | − | 0.947097i | \(-0.604001\pi\) | ||||
−0.320947 | + | 0.947097i | \(0.604001\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.3052 | 1.03467 | 0.517337 | − | 0.855782i | \(-0.326924\pi\) | ||||
0.517337 | + | 0.855782i | \(0.326924\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −40.4384 | −2.27845 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.0999 | −1.46592 | −0.732959 | − | 0.680273i | \(-0.761861\pi\) | ||||
−0.732959 | + | 0.680273i | \(0.761861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.7736 | 2.73080 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.7916 | −0.713955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.82843 | −0.101736 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.04210 | −0.446095 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −39.8619 | −2.20437 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −51.6978 | −2.85019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.2799 | −0.674962 | −0.337481 | − | 0.941332i | \(-0.609575\pi\) | ||||
−0.337481 | + | 0.941332i | \(0.609575\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32.1760 | 1.76323 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.7818 | 0.589075 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5263 | 0.845772 | 0.422886 | − | 0.906183i | \(-0.361017\pi\) | ||||
0.422886 | + | 0.906183i | \(0.361017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.17748 | −0.444140 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.97512 | 0.540183 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.27944 | 0.231068 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 28.8150 | 1.55135 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5212 | −0.672176 | −0.336088 | − | 0.941831i | \(-0.609104\pi\) | ||||
−0.336088 | + | 0.941831i | \(0.609104\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.36237 | −0.0729259 | −0.0364630 | − | 0.999335i | \(-0.511609\pi\) | ||||
−0.0364630 | + | 0.999335i | \(0.511609\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.3994 | −0.555081 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.3247 | −1.18822 | −0.594111 | − | 0.804383i | \(-0.702496\pi\) | ||||
−0.594111 | + | 0.804383i | \(0.702496\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.2650 | −1.65937 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.7325 | 0.991430 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.2824 | 0.859351 | 0.429676 | − | 0.902983i | \(-0.358628\pi\) | ||||
0.429676 | + | 0.902983i | \(0.358628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 64.3547 | 3.37774 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.4578 | 1.28018 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.6214 | −1.54623 | −0.773113 | − | 0.634268i | \(-0.781302\pi\) | ||||
−0.773113 | + | 0.634268i | \(0.781302\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.03142 | −0.105751 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.31270 | −0.327739 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.18659 | −0.268551 | −0.134276 | − | 0.990944i | \(-0.542871\pi\) | ||||
−0.134276 | + | 0.990944i | \(0.542871\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.2628 | 1.09800 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34.0101 | −1.75161 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6485 | 0.598344 | 0.299172 | − | 0.954199i | \(-0.403290\pi\) | ||||
0.299172 | + | 0.954199i | \(0.403290\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.46932 | 0.485128 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.3465 | 1.70393 | 0.851964 | − | 0.523600i | \(-0.175411\pi\) | ||||
0.851964 | + | 0.523600i | \(0.175411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −60.9103 | −3.10428 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 43.3113 | 2.20164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.51874 | 0.0770033 | 0.0385016 | − | 0.999259i | \(-0.487742\pi\) | ||||
0.0385016 | + | 0.999259i | \(0.487742\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.58688 | −0.383685 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −25.7552 | −1.29918 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.37762 | 0.320893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.4592 | −1.47852 | −0.739258 | − | 0.673422i | \(-0.764824\pi\) | ||||
−0.739258 | + | 0.673422i | \(0.764824\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.2452 | −0.512899 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.0523 | −1.60062 | −0.800308 | − | 0.599589i | \(-0.795331\pi\) | ||||
−0.800308 | + | 0.599589i | \(0.795331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.95569 | −0.346488 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.8139 | 0.686421 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.4651 | 2.40232 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.7427 | −0.531192 | −0.265596 | − | 0.964084i | \(-0.585569\pi\) | ||||
−0.265596 | + | 0.964084i | \(0.585569\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.2229 | 0.553586 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 47.5007 | 2.33736 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.60112 | −0.127684 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.0689 | −1.22763 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.9990 | 0.977013 | 0.488507 | − | 0.872560i | \(-0.337542\pi\) | ||||
0.488507 | + | 0.872560i | \(0.337542\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5670 | 0.515006 | 0.257503 | − | 0.966277i | \(-0.417100\pi\) | ||||
0.257503 | + | 0.966277i | \(0.417100\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −52.5572 | −2.55542 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.54374 | 0.171897 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.2643 | 1.12584 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −65.0969 | −3.14291 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.24892 | −0.156495 | −0.0782474 | − | 0.996934i | \(-0.524932\pi\) | ||||
−0.0782474 | + | 0.996934i | \(0.524932\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.4848 | −1.22472 | −0.612360 | − | 0.790579i | \(-0.709780\pi\) | ||||
−0.612360 | + | 0.790579i | \(0.709780\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −56.9188 | −2.72905 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.14940 | 0.198493 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.9520 | −0.856804 | −0.428402 | − | 0.903588i | \(-0.640923\pi\) | ||||
−0.428402 | + | 0.903588i | \(0.640923\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 32.0050 | 1.52405 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.68123 | −0.0798777 | −0.0399388 | − | 0.999202i | \(-0.512716\pi\) | ||||
−0.0399388 | + | 0.999202i | \(0.512716\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.93682 | 0.281432 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.5459 | −0.640700 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.8275 | −1.03010 | −0.515052 | − | 0.857159i | \(-0.672227\pi\) | ||||
−0.515052 | + | 0.857159i | \(0.672227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.05982 | −0.144081 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8888 | 0.652551 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 42.4730 | 1.99117 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.04431 | 0.376297 | 0.188148 | − | 0.982141i | \(-0.439751\pi\) | ||||
0.188148 | + | 0.982141i | \(0.439751\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.58249 | 0.213892 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.79339 | 0.316400 | 0.158200 | − | 0.987407i | \(-0.449431\pi\) | ||||
0.158200 | + | 0.987407i | \(0.449431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.2479 | −1.45221 | −0.726107 | − | 0.687582i | \(-0.758672\pi\) | ||||
−0.726107 | + | 0.687582i | \(0.758672\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.6409 | −0.539836 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.9113 | −1.70805 | −0.854026 | − | 0.520230i | \(-0.825846\pi\) | ||||
−0.854026 | + | 0.520230i | \(0.825846\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.9066 | −0.734500 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.7930 | −0.865938 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 65.2375 | 2.99962 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.93813 | −0.0889277 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.41764 | −0.293844 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.26161 | 0.331792 | 0.165896 | − | 0.986143i | \(-0.446948\pi\) | ||||
0.165896 | + | 0.986143i | \(0.446948\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.7949 | −1.54091 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −42.5112 | −1.93433 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.4249 | −1.10908 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00500 | −0.0455411 | −0.0227705 | − | 0.999741i | \(-0.507249\pi\) | ||||
−0.0227705 | + | 0.999741i | \(0.507249\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.7072 | −1.47907 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.12714 | 0.411902 | 0.205951 | − | 0.978562i | \(-0.433971\pi\) | ||||
0.205951 | + | 0.978562i | \(0.433971\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.9865 | 0.674957 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −61.9228 | −2.78322 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 46.1257 | 2.06902 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.8928 | −0.890524 | −0.445262 | − | 0.895400i | \(-0.646889\pi\) | ||||
−0.445262 | + | 0.895400i | \(0.646889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.2125 | −1.03706 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.9716 | −0.845904 | −0.422952 | − | 0.906152i | \(-0.639006\pi\) | ||||
−0.422952 | + | 0.906152i | \(0.639006\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.1960 | −1.56620 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.1191 | 0.493818 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.2981 | −1.07700 | −0.538498 | − | 0.842627i | \(-0.681008\pi\) | ||||
−0.538498 | + | 0.842627i | \(0.681008\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.0830 | −1.59622 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.50625 | −0.110654 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.3651 | 1.16178 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −79.1642 | −3.48164 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.01270 | −0.176138 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.1930 | −0.446563 | −0.223282 | − | 0.974754i | \(-0.571677\pi\) | ||||
−0.223282 | + | 0.974754i | \(0.571677\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.42683 | −0.0623907 | −0.0311954 | − | 0.999513i | \(-0.509931\pi\) | ||||
−0.0311954 | + | 0.999513i | \(0.509931\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.8565 | 0.866608 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.06501 | 0.133514 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.78247 | −0.251412 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 48.2903 | 2.09562 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.13363 | 0.0924176 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.7801 | 0.552530 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 49.1950 | 2.12292 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 48.2075 | 2.07644 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.1257 | 1.20922 | 0.604610 | − | 0.796522i | \(-0.293329\pi\) | ||||
0.604610 | + | 0.796522i | \(0.293329\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29.8263 | −1.27997 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.8261 | 1.70596 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.2937 | −1.93662 | −0.968310 | − | 0.249753i | \(-0.919651\pi\) | ||||
−0.968310 | + | 0.249753i | \(0.919651\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.6511 | 1.00940 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.19638 | −0.349177 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.40900 | −0.400111 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −56.5587 | −2.40078 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.9151 | 0.589601 | 0.294801 | − | 0.955559i | \(-0.404747\pi\) | ||||
0.294801 | + | 0.955559i | \(0.404747\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −45.4904 | −1.92404 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.6849 | 1.21108 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.3367 | −0.435641 | −0.217820 | − | 0.975989i | \(-0.569895\pi\) | ||||
−0.217820 | + | 0.975989i | \(0.569895\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.17013 | 0.343720 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.3799 | −0.855877 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.2369 | 1.64490 | 0.822448 | − | 0.568840i | \(-0.192608\pi\) | ||||
0.822448 | + | 0.568840i | \(0.192608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.4374 | −1.39931 | −0.699657 | − | 0.714479i | \(-0.746664\pi\) | ||||
−0.699657 | + | 0.714479i | \(0.746664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.5725 | 1.27718 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.04210 | −0.335379 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.3203 | −0.929206 | −0.464603 | − | 0.885519i | \(-0.653803\pi\) | ||||
−0.464603 | + | 0.885519i | \(0.653803\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.98409 | −0.414925 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.83747 | 0.159205 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.66656 | −0.400348 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 43.1791 | 1.78523 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −43.6753 | −1.80267 | −0.901337 | − | 0.433119i | \(-0.857413\pi\) | ||||
−0.901337 | + | 0.433119i | \(0.857413\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.67631 | −0.0690712 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 68.7581 | 2.82833 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.6978 | −0.808890 | −0.404445 | − | 0.914562i | \(-0.632535\pi\) | ||||
−0.404445 | + | 0.914562i | \(0.632535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.7157 | −0.767267 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.31842 | −0.381377 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.2570 | −1.39970 | −0.699851 | − | 0.714289i | \(-0.746750\pi\) | ||||
−0.699851 | + | 0.714289i | \(0.746750\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.1801 | −0.782373 | −0.391186 | − | 0.920311i | \(-0.627935\pi\) | ||||
−0.391186 | + | 0.920311i | \(0.627935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.1711 | −0.658536 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −64.2968 | −2.61404 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.1796 | −0.697297 | −0.348649 | − | 0.937253i | \(-0.613359\pi\) | ||||
−0.348649 | + | 0.937253i | \(0.613359\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 83.9731 | 3.40276 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 55.2016 | 2.23322 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.4502 | −0.543247 | −0.271623 | − | 0.962404i | \(-0.587561\pi\) | ||||
−0.271623 | + | 0.962404i | \(0.587561\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.57081 | 0.143989 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.2065 | −0.612191 | −0.306095 | − | 0.952001i | \(-0.599023\pi\) | ||||
−0.306095 | + | 0.952001i | \(0.599023\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.1696 | −1.61455 | −0.807277 | − | 0.590173i | \(-0.799060\pi\) | ||||
−0.807277 | + | 0.590173i | \(0.799060\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.3994 | −0.417315 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.75868 | −0.350909 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9343 | −1.23737 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.6883 | −0.626529 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.8917 | 0.593770 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0318 | 0.478980 | 0.239490 | − | 0.970899i | \(-0.423020\pi\) | ||||
0.239490 | + | 0.970899i | \(0.423020\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.51216 | 0.298581 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.46081 | −0.375441 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.6153 | −1.33189 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 46.8925 | 1.85504 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.1707 | 1.11267 | 0.556337 | − | 0.830957i | \(-0.312206\pi\) | ||||
0.556337 | + | 0.830957i | \(0.312206\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.2190 | −1.50721 | −0.753605 | − | 0.657327i | \(-0.771687\pi\) | ||||
−0.753605 | + | 0.657327i | \(0.771687\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −76.1321 | −2.99770 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.26170 | 0.285487 | 0.142743 | − | 0.989760i | \(-0.454408\pi\) | ||||
0.142743 | + | 0.989760i | \(0.454408\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 72.7372 | 2.85518 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.1741 | 0.673105 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.0972 | −0.629932 | −0.314966 | − | 0.949103i | \(-0.601993\pi\) | ||||
−0.314966 | + | 0.949103i | \(0.601993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.7320 | 1.00543 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.6828 | −1.43113 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.8679 | 0.696035 | 0.348018 | − | 0.937488i | \(-0.386855\pi\) | ||||
0.348018 | + | 0.937488i | \(0.386855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.6386 | 0.841644 | 0.420822 | − | 0.907143i | \(-0.361742\pi\) | ||||
0.420822 | + | 0.907143i | \(0.361742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.0021 | −0.776817 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.2359 | 0.396933 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.0101 | −1.31687 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −61.7928 | −2.38905 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.6244 | 1.37526 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.9881 | −1.69561 | −0.847807 | − | 0.530304i | \(-0.822078\pi\) | ||||
−0.847807 | + | 0.530304i | \(0.822078\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.85745 | 0.186963 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.6983 | 1.14140 | 0.570699 | − | 0.821160i | \(-0.306672\pi\) | ||||
0.570699 | + | 0.821160i | \(0.306672\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.0344 | 1.38287 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.5975 | 0.750977 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.20351 | 0.237371 | 0.118685 | − | 0.992932i | \(-0.462132\pi\) | ||||
0.118685 | + | 0.992932i | \(0.462132\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2128 | −0.428420 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.7024 | 1.93442 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.74053 | 0.256794 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.1172 | 1.06963 | 0.534814 | − | 0.844970i | \(-0.320382\pi\) | ||||
0.534814 | + | 0.844970i | \(0.320382\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 91.3557 | 3.47032 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.0464 | 0.950063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.940179 | −0.0356118 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −78.9093 | −2.98462 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.35403 | 0.315527 | 0.157764 | − | 0.987477i | \(-0.449572\pi\) | ||||
0.157764 | + | 0.987477i | \(0.449572\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.14452 | −0.307177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 92.3846 | 3.47940 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 51.9252 | 1.95285 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.7187 | −1.19122 | −0.595610 | − | 0.803274i | \(-0.703090\pi\) | ||||
−0.595610 | + | 0.803274i | \(0.703090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.56541 | −0.358731 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.95569 | −0.260493 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 65.0384 | 2.43230 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 42.3088 | 1.58005 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.7972 | 1.26042 | 0.630211 | − | 0.776424i | \(-0.282968\pi\) | ||||
0.630211 | + | 0.776424i | \(0.282968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.8968 | −1.44859 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 63.0543 | 2.34501 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.8857 | 0.589979 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32.8637 | 1.21885 | 0.609423 | − | 0.792845i | \(-0.291401\pi\) | ||||
0.609423 | + | 0.792845i | \(0.291401\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −40.5412 | −1.50153 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.0453 | 0.741401 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.3118 | −0.528618 | −0.264309 | − | 0.964438i | \(-0.585144\pi\) | ||||
−0.264309 | + | 0.964438i | \(0.585144\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −56.2581 | −2.07511 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.3576 | −0.897225 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.6101 | 0.831726 | 0.415863 | − | 0.909427i | \(-0.363480\pi\) | ||||
0.415863 | + | 0.909427i | \(0.363480\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.9395 | 0.401873 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.6222 | 0.463062 | 0.231531 | − | 0.972828i | \(-0.425627\pi\) | ||||
0.231531 | + | 0.972828i | \(0.425627\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5337 | 0.495838 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.90126 | 0.142740 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.8546 | −0.688932 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.69943 | −0.171485 | −0.0857423 | − | 0.996317i | \(-0.527326\pi\) | ||||
−0.0857423 | + | 0.996317i | \(0.527326\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.8783 | 0.979498 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.8763 | −0.505009 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.8920 | 0.795679 | 0.397839 | − | 0.917455i | \(-0.369760\pi\) | ||||
0.397839 | + | 0.917455i | \(0.369760\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −65.0969 | −2.36287 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.164985 | −0.00598068 | −0.00299034 | − | 0.999996i | \(-0.500952\pi\) | ||||
−0.00299034 | + | 0.999996i | \(0.500952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −58.7560 | −2.12711 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.0268 | −0.687915 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −50.7200 | −1.83139 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.55812 | −0.308614 | −0.154307 | − | 0.988023i | \(-0.549314\pi\) | ||||
−0.154307 | + | 0.988023i | \(0.549314\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 53.2200 | 1.91667 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.49557 | 0.341532 | 0.170766 | − | 0.985312i | \(-0.445376\pi\) | ||||
0.170766 | + | 0.985312i | \(0.445376\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.24892 | 0.116705 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 83.4419 | 2.99346 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.514201 | 0.0184232 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 70.6317 | 2.52740 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.5422 | 0.734117 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.7761 | 0.670149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.59840 | −0.306500 | −0.153250 | − | 0.988187i | \(-0.548974\pi\) | ||||
−0.153250 | + | 0.988187i | \(0.548974\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.0430 | 0.499945 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0535 | −0.428574 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.8410 | −0.882131 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.2809 | 0.400091 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.3568 | 0.827340 | 0.413670 | − | 0.910427i | \(-0.364247\pi\) | ||||
0.413670 | + | 0.910427i | \(0.364247\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.3245 | −0.860538 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.90428 | −0.314617 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −55.2534 | −1.94985 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 42.4730 | 1.49698 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.0583 | 1.30451 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.0634 | −0.388968 | −0.194484 | − | 0.980906i | \(-0.562303\pi\) | ||||
−0.194484 | + | 0.980906i | \(0.562303\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.9630 | 0.455193 | 0.227596 | − | 0.973756i | \(-0.426913\pi\) | ||||
0.227596 | + | 0.973756i | \(0.426913\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.5909 | 0.792299 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.6778 | 1.14465 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.9631 | −0.383551 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −63.7028 | −2.22595 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.8255 | −0.517415 | −0.258707 | − | 0.965956i | \(-0.583297\pi\) | ||||
−0.258707 | + | 0.965956i | \(0.583297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.04240 | 0.140909 | 0.0704547 | − | 0.997515i | \(-0.477555\pi\) | ||||
0.0704547 | + | 0.997515i | \(0.477555\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.4060 | 1.05860 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.6070 | −1.16863 | −0.584314 | − | 0.811527i | \(-0.698636\pi\) | ||||
−0.584314 | + | 0.811527i | \(0.698636\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.3399 | −1.33160 | −0.665800 | − | 0.746130i | \(-0.731910\pi\) | ||||
−0.665800 | + | 0.746130i | \(0.731910\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 59.8498 | 2.07617 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.8125 | 0.513223 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.1916 | 0.802579 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.20125 | 0.145217 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.6832 | −1.30097 | −0.650484 | − | 0.759520i | \(-0.725434\pi\) | ||||
−0.650484 | + | 0.759520i | \(0.725434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 38.1806 | 1.31657 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.8015 | 0.750883 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.1091 | −0.382165 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 94.8581 | 3.25936 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 57.4580 | 1.97195 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.7949 | −1.15847 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.06647 | −0.241951 | −0.120976 | − | 0.992655i | \(-0.538602\pi\) | ||||
−0.120976 | + | 0.992655i | \(0.538602\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.4061 | 0.355881 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.95910 | 0.271878 | 0.135939 | − | 0.990717i | \(-0.456595\pi\) | ||||
0.135939 | + | 0.990717i | \(0.456595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.1466 | 0.448558 | 0.224279 | − | 0.974525i | \(-0.427997\pi\) | ||||
0.224279 | + | 0.974525i | \(0.427997\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.26807 | −0.179535 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.9886 | 1.19102 | 0.595512 | − | 0.803346i | \(-0.296949\pi\) | ||||
0.595512 | + | 0.803346i | \(0.296949\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.00909 | 0.136313 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −36.0050 | −1.22279 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.4079 | −0.488754 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9847 | 0.575504 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.6335 | 1.23985 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.3411 | 1.05952 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.1816 | −1.66075 | −0.830373 | − | 0.557208i | \(-0.811873\pi\) | ||||
−0.830373 | + | 0.557208i | \(0.811873\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.7795 | −0.768333 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.58658 | −0.255598 | −0.127799 | − | 0.991800i | \(-0.540791\pi\) | ||||
−0.127799 | + | 0.991800i | \(0.540791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.1875 | 0.511101 | 0.255551 | − | 0.966796i | \(-0.417743\pi\) | ||||
0.255551 | + | 0.966796i | \(0.417743\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −84.8842 | −2.85335 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.9000 | 1.10467 | 0.552337 | − | 0.833621i | \(-0.313736\pi\) | ||||
0.552337 | + | 0.833621i | \(0.313736\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.9577 | 0.468125 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.2075 | −1.04549 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.3035 | 0.445185 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −49.1507 | −1.64293 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 45.3924 | 1.51561 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.7397 | 0.458244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.97021 | −0.0989519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 112.319 | 3.73774 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29.7995 | 0.990568 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.9392 | −1.85743 | −0.928715 | − | 0.370793i | \(-0.879086\pi\) | ||||
−0.928715 | + | 0.370793i | \(0.879086\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 52.7884 | 1.75088 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.6551 | −1.47949 | −0.739745 | − | 0.672887i | \(-0.765054\pi\) | ||||
−0.739745 | + | 0.672887i | \(0.765054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.87627 | 0.194476 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −41.5736 | −1.37438 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37.9629 | −1.25364 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.52507 | 0.248229 | 0.124115 | − | 0.992268i | \(-0.460391\pi\) | ||||
0.124115 | + | 0.992268i | \(0.460391\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.0209 | −0.989222 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49.2518 | −1.62114 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.7852 | 0.519014 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −39.5434 | −1.29878 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.4360 | −0.342395 | −0.171198 | − | 0.985237i | \(-0.554764\pi\) | ||||
−0.171198 | + | 0.985237i | \(0.554764\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.10124 | −0.265507 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.8439 | −0.977044 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −28.6591 | −0.937252 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.1073 | −0.624207 | −0.312104 | − | 0.950048i | \(-0.601034\pi\) | ||||
−0.312104 | + | 0.950048i | \(0.601034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 48.2600 | 1.57491 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.2146 | −1.40875 | −0.704377 | − | 0.709826i | \(-0.748774\pi\) | ||||
−0.704377 | + | 0.709826i | \(0.748774\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.13363 | 0.0694804 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25.6538 | −0.834518 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.25385 | 0.0407446 | 0.0203723 | − | 0.999792i | \(-0.493515\pi\) | ||||
0.0203723 | + | 0.999792i | \(0.493515\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.5285 | 1.25069 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −68.8100 | −2.23132 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.0739 | −1.13616 | −0.568078 | − | 0.822975i | \(-0.692313\pi\) | ||||
−0.568078 | + | 0.822975i | \(0.692313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.5450 | −0.988413 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 128.587 | 4.15663 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.5425 | 0.534184 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.1900 | −0.909354 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.1680 | −0.617681 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.97512 | 0.321110 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.66764 | 0.0536275 | 0.0268138 | − | 0.999640i | \(-0.491464\pi\) | ||||
0.0268138 | + | 0.999640i | \(0.491464\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.82047 | −0.154856 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.1136 | 0.517110 | 0.258555 | − | 0.965996i | \(-0.416754\pi\) | ||||
0.258555 | + | 0.965996i | \(0.416754\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −36.9513 | −1.18460 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21.2022 | −0.679015 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.8857 | 1.08410 | 0.542051 | − | 0.840346i | \(-0.317648\pi\) | ||||
0.542051 | + | 0.840346i | \(0.317648\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.4121 | −0.428651 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −59.7328 | −1.90712 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.89492 | 0.315599 | 0.157799 | − | 0.987471i | \(-0.449560\pi\) | ||||
0.157799 | + | 0.987471i | \(0.449560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −68.6963 | −2.18885 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −136.296 | −4.33836 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45.4904 | −1.44651 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.3693 | −0.996478 | −0.498239 | − | 0.867040i | \(-0.666020\pi\) | ||||
−0.498239 | + | 0.867040i | \(0.666020\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −32.3747 | −1.02738 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.31004 | 0.295148 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.55606 | −0.144292 | −0.0721459 | − | 0.997394i | \(-0.522985\pi\) | ||||
−0.0721459 | + | 0.997394i | \(0.522985\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.4122 | 0.645813 |
(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 | 4864.2.a.br.1.7 | 8 | ||
4.3 | odd | 2 | 4864.2.a.bm.1.1 | 8 | |||
8.3 | odd | 2 | inner | 4864.2.a.br.1.8 | 8 | ||
8.5 | even | 2 | 4864.2.a.bm.1.2 | 8 | |||
16.3 | odd | 4 | 2432.2.c.i.1217.2 | yes | 16 | ||
16.5 | even | 4 | 2432.2.c.i.1217.1 | ✓ | 16 | ||
16.11 | odd | 4 | 2432.2.c.i.1217.15 | yes | 16 | ||
16.13 | even | 4 | 2432.2.c.i.1217.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.i.1217.1 | ✓ | 16 | 16.5 | even | 4 | ||
2432.2.c.i.1217.2 | yes | 16 | 16.3 | odd | 4 | ||
2432.2.c.i.1217.15 | yes | 16 | 16.11 | odd | 4 | ||
2432.2.c.i.1217.16 | yes | 16 | 16.13 | even | 4 | ||
4864.2.a.bm.1.1 | 8 | 4.3 | odd | 2 | |||
4864.2.a.bm.1.2 | 8 | 8.5 | even | 2 | |||
4864.2.a.br.1.7 | 8 | 1.1 | even | 1 | trivial | ||
4864.2.a.br.1.8 | 8 | 8.3 | odd | 2 | inner |