Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.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: | \(54.8093159474\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.70164.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 10x^{2} + 10x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3432) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.279954\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.279954 | 0.125199 | 0.0625997 | − | 0.998039i | \(-0.480061\pi\) | ||||
0.0625997 | + | 0.998039i | \(0.480061\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.36642 | 1.65035 | 0.825176 | − | 0.564875i | \(-0.191076\pi\) | ||||
0.825176 | + | 0.564875i | \(0.191076\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.279954 | 0.0722839 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.64638 | 0.641841 | 0.320920 | − | 0.947106i | \(-0.396008\pi\) | ||||
0.320920 | + | 0.947106i | \(0.396008\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.58412 | −1.05167 | −0.525834 | − | 0.850587i | \(-0.676247\pi\) | ||||
−0.525834 | + | 0.850587i | \(0.676247\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.36642 | 0.952832 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.80651 | −0.376684 | −0.188342 | − | 0.982103i | \(-0.560311\pi\) | ||||
−0.188342 | + | 0.982103i | \(0.560311\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.92163 | −0.984325 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.30887 | 0.614441 | 0.307221 | − | 0.951638i | \(-0.400601\pi\) | ||||
0.307221 | + | 0.951638i | \(0.400601\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.50235 | 0.269831 | 0.134915 | − | 0.990857i | \(-0.456924\pi\) | ||||
0.134915 | + | 0.990857i | \(0.456924\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.22240 | 0.206623 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.559909 | −0.0920484 | −0.0460242 | − | 0.998940i | \(-0.514655\pi\) | ||||
−0.0460242 | + | 0.998940i | \(0.514655\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.36642 | 0.994268 | 0.497134 | − | 0.867674i | \(-0.334386\pi\) | ||||
0.497134 | + | 0.867674i | \(0.334386\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.97918 | 1.06432 | 0.532158 | − | 0.846645i | \(-0.321381\pi\) | ||||
0.532158 | + | 0.846645i | \(0.321381\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.279954 | 0.0417331 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.73285 | −0.398627 | −0.199313 | − | 0.979936i | \(-0.563871\pi\) | ||||
−0.199313 | + | 0.979936i | \(0.563871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.0656 | 1.72366 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.64638 | 0.370567 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.99529 | 0.411435 | 0.205718 | − | 0.978611i | \(-0.434047\pi\) | ||||
0.205718 | + | 0.978611i | \(0.434047\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.279954 | −0.0377490 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.58412 | −0.607181 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.39063 | 1.09237 | 0.546184 | − | 0.837666i | \(-0.316080\pi\) | ||||
0.546184 | + | 0.837666i | \(0.316080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.10729 | −0.141774 | −0.0708868 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708868 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.36642 | 0.550118 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.279954 | −0.0347241 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.39507 | 0.536943 | 0.268471 | − | 0.963288i | \(-0.413482\pi\) | ||||
0.268471 | + | 0.963288i | \(0.413482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.80651 | −0.217479 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.99529 | 0.355476 | 0.177738 | − | 0.984078i | \(-0.443122\pi\) | ||||
0.177738 | + | 0.984078i | \(0.443122\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6498 | 1.59758 | 0.798792 | − | 0.601607i | \(-0.205473\pi\) | ||||
0.798792 | + | 0.601607i | \(0.205473\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.92163 | −0.568300 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.36642 | −0.497600 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.9344 | 1.68025 | 0.840127 | − | 0.542390i | \(-0.182480\pi\) | ||||
0.840127 | + | 0.542390i | \(0.182480\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7281 | 1.50686 | 0.753430 | − | 0.657529i | \(-0.228398\pi\) | ||||
0.753430 | + | 0.657529i | \(0.228398\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.740865 | 0.0803580 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.30887 | 0.354748 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.49765 | 0.264750 | 0.132375 | − | 0.991200i | \(-0.457740\pi\) | ||||
0.132375 | + | 0.991200i | \(0.457740\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.36642 | −0.457726 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.50235 | 0.155787 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.28334 | −0.131668 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.0162 | −1.62620 | −0.813099 | − | 0.582126i | \(-0.802221\pi\) | ||||
−0.813099 | + | 0.582126i | \(0.802221\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.4896 | −1.04376 | −0.521879 | − | 0.853020i | \(-0.674769\pi\) | ||||
−0.521879 | + | 0.853020i | \(0.674769\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.10729 | 0.503236 | 0.251618 | − | 0.967827i | \(-0.419037\pi\) | ||||
0.251618 | + | 0.967827i | \(0.419037\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.22240 | 0.119294 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.8354 | 1.04750 | 0.523750 | − | 0.851872i | \(-0.324533\pi\) | ||||
0.523750 | + | 0.851872i | \(0.324533\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.58882 | −0.918443 | −0.459221 | − | 0.888322i | \(-0.651871\pi\) | ||||
−0.459221 | + | 0.888322i | \(0.651871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.559909 | −0.0531442 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.77760 | −0.261295 | −0.130647 | − | 0.991429i | \(-0.541706\pi\) | ||||
−0.130647 | + | 0.991429i | \(0.541706\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.505741 | −0.0471606 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.5552 | 1.05926 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.36642 | 0.574041 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.77760 | −0.248436 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.08176 | 0.628405 | 0.314202 | − | 0.949356i | \(-0.398263\pi\) | ||||
0.314202 | + | 0.949356i | \(0.398263\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.97918 | 0.614483 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.22710 | 0.194583 | 0.0972915 | − | 0.995256i | \(-0.468982\pi\) | ||||
0.0972915 | + | 0.995256i | \(0.468982\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.0162 | −1.73562 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.279954 | 0.0240946 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.6384 | 1.59238 | 0.796191 | − | 0.605045i | \(-0.206845\pi\) | ||||
0.796191 | + | 0.605045i | \(0.206845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.5313 | −1.06289 | −0.531444 | − | 0.847093i | \(-0.678350\pi\) | ||||
−0.531444 | + | 0.847093i | \(0.678350\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.73285 | −0.230147 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.926332 | 0.0769276 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.0656 | 0.995158 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.70393 | 0.631131 | 0.315565 | − | 0.948904i | \(-0.397806\pi\) | ||||
0.315565 | + | 0.948904i | \(0.397806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.14873 | −0.337619 | −0.168809 | − | 0.985649i | \(-0.553992\pi\) | ||||
−0.168809 | + | 0.985649i | \(0.553992\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.64638 | 0.213947 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.420590 | 0.0337826 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.59353 | −0.206986 | −0.103493 | − | 0.994630i | \(-0.533002\pi\) | ||||
−0.103493 | + | 0.994630i | \(0.533002\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.99529 | 0.237542 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.88801 | −0.621662 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00809 | −0.470590 | −0.235295 | − | 0.971924i | \(-0.575606\pi\) | ||||
−0.235295 | + | 0.971924i | \(0.575606\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.279954 | −0.0217944 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.2177 | 1.25496 | 0.627481 | − | 0.778632i | \(-0.284086\pi\) | ||||
0.627481 | + | 0.778632i | \(0.284086\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.58412 | −0.350556 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.42398 | 0.260320 | 0.130160 | − | 0.991493i | \(-0.458451\pi\) | ||||
0.130160 | + | 0.991493i | \(0.458451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.4899 | −1.62448 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.39063 | 0.630678 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0498 | −1.19962 | −0.599809 | − | 0.800143i | \(-0.704757\pi\) | ||||
−0.599809 | + | 0.800143i | \(0.704757\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.70393 | 0.126652 | 0.0633262 | − | 0.997993i | \(-0.479829\pi\) | ||||
0.0633262 | + | 0.997993i | \(0.479829\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.10729 | −0.0818531 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.156749 | −0.0115244 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.64638 | −0.193522 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.36642 | 0.317611 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.5683 | 1.41591 | 0.707955 | − | 0.706257i | \(-0.249618\pi\) | ||||
0.707955 | + | 0.706257i | \(0.249618\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.8305 | −1.93130 | −0.965652 | − | 0.259840i | \(-0.916330\pi\) | ||||
−0.965652 | + | 0.259840i | \(0.916330\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.279954 | −0.0200479 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.6466 | −1.39977 | −0.699883 | − | 0.714258i | \(-0.746764\pi\) | ||||
−0.699883 | + | 0.714258i | \(0.746764\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.55208 | 0.535353 | 0.267677 | − | 0.963509i | \(-0.413744\pi\) | ||||
0.267677 | + | 0.963509i | \(0.413744\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.39507 | 0.310004 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.4479 | 1.01404 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.78231 | 0.124482 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.80651 | −0.125561 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.58412 | 0.317090 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.4849 | −1.20371 | −0.601856 | − | 0.798605i | \(-0.705572\pi\) | ||||
−0.601856 | + | 0.798605i | \(0.705572\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.99529 | 0.205234 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.95385 | 0.133252 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.55991 | 0.445316 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.6498 | 0.922366 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.64638 | −0.178015 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.38724 | 0.494686 | 0.247343 | − | 0.968928i | \(-0.420443\pi\) | ||||
0.247343 | + | 0.968928i | \(0.420443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.92163 | −0.328108 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.02891 | −0.466525 | −0.233263 | − | 0.972414i | \(-0.574940\pi\) | ||||
−0.233263 | + | 0.972414i | \(0.574940\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.6834 | −0.904224 | −0.452112 | − | 0.891961i | \(-0.649329\pi\) | ||||
−0.452112 | + | 0.891961i | \(0.649329\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.36642 | −0.287290 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.6464 | −1.09054 | −0.545270 | − | 0.838260i | \(-0.683573\pi\) | ||||
−0.545270 | + | 0.838260i | \(0.683573\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.765072 | −0.0499078 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.9344 | 0.970095 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.9795 | 0.774886 | 0.387443 | − | 0.921894i | \(-0.373358\pi\) | ||||
0.387443 | + | 0.921894i | \(0.373358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.5808 | 1.13248 | 0.566240 | − | 0.824241i | \(-0.308398\pi\) | ||||
0.566240 | + | 0.824241i | \(0.308398\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.37783 | 0.215802 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.58412 | 0.291680 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.7281 | 0.869986 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.8480 | 1.18967 | 0.594836 | − | 0.803847i | \(-0.297217\pi\) | ||||
0.594836 | + | 0.803847i | \(0.297217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.80651 | 0.113575 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.740865 | 0.0463947 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.3953 | −1.08509 | −0.542546 | − | 0.840026i | \(-0.682539\pi\) | ||||
−0.542546 | + | 0.840026i | \(0.682539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.44480 | −0.151912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.30887 | 0.204814 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.1151 | 0.623724 | 0.311862 | − | 0.950127i | \(-0.399047\pi\) | ||||
0.311862 | + | 0.950127i | \(0.399047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.838545 | 0.0515114 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.49765 | 0.152854 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.8385 | −0.660838 | −0.330419 | − | 0.943834i | \(-0.607190\pi\) | ||||
−0.330419 | + | 0.943834i | \(0.607190\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.03362 | −0.123534 | −0.0617668 | − | 0.998091i | \(-0.519674\pi\) | ||||
−0.0617668 | + | 0.998091i | \(0.519674\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.36642 | −0.264268 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.92163 | 0.296785 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.55208 | −0.0932557 | −0.0466279 | − | 0.998912i | \(-0.514847\pi\) | ||||
−0.0466279 | + | 0.998912i | \(0.514847\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.50235 | 0.0899435 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9747 | 0.654698 | 0.327349 | − | 0.944903i | \(-0.393845\pi\) | ||||
0.327349 | + | 0.944903i | \(0.393845\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.1615 | −1.37681 | −0.688405 | − | 0.725326i | \(-0.741689\pi\) | ||||
−0.688405 | + | 0.725326i | \(0.741689\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.28334 | −0.0760187 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.7985 | 1.64089 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.99669 | −0.588040 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.0162 | −0.938886 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.6097 | 1.20403 | 0.602016 | − | 0.798484i | \(-0.294364\pi\) | ||||
0.602016 | + | 0.798484i | \(0.294364\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.34899 | 0.136764 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.80651 | 0.104473 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.4741 | 1.75650 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.4896 | −0.602613 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.309990 | −0.0177500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.1118 | −0.976622 | −0.488311 | − | 0.872670i | \(-0.662387\pi\) | ||||
−0.488311 | + | 0.872670i | \(0.662387\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.10729 | 0.290543 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9873 | 1.07667 | 0.538335 | − | 0.842731i | \(-0.319054\pi\) | ||||
0.538335 | + | 0.842731i | \(0.319054\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.2050 | −1.19858 | −0.599288 | − | 0.800534i | \(-0.704549\pi\) | ||||
−0.599288 | + | 0.800534i | \(0.704549\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.22240 | 0.0688744 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.4738 | −1.43075 | −0.715375 | − | 0.698741i | \(-0.753744\pi\) | ||||
−0.715375 | + | 0.698741i | \(0.753744\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.30887 | −0.185261 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.8354 | 0.604775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.1313 | −0.675004 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.92163 | 0.273003 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.58882 | −0.530263 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.9328 | −0.657874 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.03561 | −0.166852 | −0.0834262 | − | 0.996514i | \(-0.526586\pi\) | ||||
−0.0834262 | + | 0.996514i | \(0.526586\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.559909 | −0.0306828 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.23042 | 0.0672249 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.58080 | −0.304006 | −0.152003 | − | 0.988380i | \(-0.548572\pi\) | ||||
−0.152003 | + | 0.988380i | \(0.548572\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.77760 | −0.150859 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.50235 | −0.0813570 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 22.1188 | 1.19430 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.505741 | −0.0272282 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.78597 | 0.525338 | 0.262669 | − | 0.964886i | \(-0.415397\pi\) | ||||
0.262669 | + | 0.964886i | \(0.415397\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.55050 | 0.457698 | 0.228849 | − | 0.973462i | \(-0.426504\pi\) | ||||
0.228849 | + | 0.973462i | \(0.426504\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.2608 | −1.61062 | −0.805310 | − | 0.592854i | \(-0.798001\pi\) | ||||
−0.805310 | + | 0.592854i | \(0.798001\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.838545 | 0.0445054 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.5552 | 0.611566 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.5555 | −1.29599 | −0.647996 | − | 0.761644i | \(-0.724393\pi\) | ||||
−0.647996 | + | 0.761644i | \(0.724393\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.01412 | 0.106006 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.82131 | 0.200017 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.7006 | 1.49816 | 0.749080 | − | 0.662479i | \(-0.230496\pi\) | ||||
0.749080 | + | 0.662479i | \(0.230496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.36642 | 0.331423 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0787 | 0.679013 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.63026 | 0.239746 | 0.119873 | − | 0.992789i | \(-0.461751\pi\) | ||||
0.119873 | + | 0.992789i | \(0.461751\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.77760 | −0.143435 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.30887 | −0.170415 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.5091 | −1.31032 | −0.655158 | − | 0.755492i | \(-0.727398\pi\) | ||||
−0.655158 | + | 0.755492i | \(0.727398\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.08176 | 0.362810 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.95836 | −0.508849 | −0.254424 | − | 0.967093i | \(-0.581886\pi\) | ||||
−0.254424 | + | 0.967093i | \(0.581886\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.22240 | −0.0622992 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.97918 | 0.354772 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.34117 | −0.372212 | −0.186106 | − | 0.982530i | \(-0.559587\pi\) | ||||
−0.186106 | + | 0.982530i | \(0.559587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.78072 | −0.241771 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.22710 | 0.112343 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.18096 | 0.210367 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8354 | 0.744569 | 0.372284 | − | 0.928119i | \(-0.378575\pi\) | ||||
0.372284 | + | 0.928119i | \(0.378575\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.0162 | −1.00206 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.3940 | 1.16824 | 0.584121 | − | 0.811667i | \(-0.301439\pi\) | ||||
0.584121 | + | 0.811667i | \(0.301439\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.50235 | −0.0748375 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.279954 | 0.0139110 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.559909 | 0.0277536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.8549 | 1.27844 | 0.639222 | − | 0.769022i | \(-0.279257\pi\) | ||||
0.639222 | + | 0.769022i | \(0.279257\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.6384 | 0.919362 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.6370 | 1.80279 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.84325 | 0.188658 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.5313 | −0.613659 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.1024 | 1.03092 | 0.515460 | − | 0.856914i | \(-0.327621\pi\) | ||||
0.515460 | + | 0.856914i | \(0.327621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.3678 | −0.602770 | −0.301385 | − | 0.953502i | \(-0.597449\pi\) | ||||
−0.301385 | + | 0.953502i | \(0.597449\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.73285 | −0.132876 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.0245 | −0.631780 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.83489 | −0.233977 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.2880 | 1.65160 | 0.825799 | − | 0.563965i | \(-0.190725\pi\) | ||||
0.825799 | + | 0.563965i | \(0.190725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.08184 | 0.436445 | 0.218223 | − | 0.975899i | \(-0.429974\pi\) | ||||
0.218223 | + | 0.975899i | \(0.429974\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.926332 | 0.0444142 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.28127 | 0.396147 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.1330 | −1.58135 | −0.790675 | − | 0.612236i | \(-0.790270\pi\) | ||||
−0.790675 | + | 0.612236i | \(0.790270\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.0656 | 0.574555 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.11982 | 0.243250 | 0.121625 | − | 0.992576i | \(-0.461189\pi\) | ||||
0.121625 | + | 0.992576i | \(0.461189\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.699227 | 0.0331465 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.70393 | 0.364384 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.8320 | 0.747160 | 0.373580 | − | 0.927598i | \(-0.378130\pi\) | ||||
0.373580 | + | 0.927598i | \(0.378130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.36642 | −0.299783 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.14873 | −0.194924 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.22240 | −0.0573069 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.01253 | 0.281254 | 0.140627 | − | 0.990063i | \(-0.455088\pi\) | ||||
0.140627 | + | 0.990063i | \(0.455088\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.64638 | 0.123522 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.3998 | −0.996690 | −0.498345 | − | 0.866979i | \(-0.666059\pi\) | ||||
−0.498345 | + | 0.866979i | \(0.666059\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.2420 | 1.77726 | 0.888628 | − | 0.458629i | \(-0.151659\pi\) | ||||
0.888628 | + | 0.458629i | \(0.151659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.420590 | 0.0195044 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.8190 | 0.639469 | 0.319735 | − | 0.947507i | \(-0.396406\pi\) | ||||
0.319735 | + | 0.947507i | \(0.396406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.1907 | 0.886145 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.59353 | −0.119503 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.97918 | −0.320903 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.5613 | 1.03518 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.99529 | 0.137145 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.4546 | −1.61996 | −0.809980 | − | 0.586457i | \(-0.800522\pi\) | ||||
−0.809980 | + | 0.586457i | \(0.800522\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.559909 | 0.0255296 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.88801 | −0.358917 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.48380 | −0.203599 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.6175 | −1.34210 | −0.671048 | − | 0.741414i | \(-0.734155\pi\) | ||||
−0.671048 | + | 0.741414i | \(0.734155\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.00809 | −0.271695 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.5892 | 0.929176 | 0.464588 | − | 0.885527i | \(-0.346202\pi\) | ||||
0.464588 | + | 0.885527i | \(0.346202\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.75651 | 0.394373 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.279954 | −0.0125830 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.0787 | 0.586661 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.45760 | −0.0652510 | −0.0326255 | − | 0.999468i | \(-0.510387\pi\) | ||||
−0.0326255 | + | 0.999468i | \(0.510387\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.2177 | 0.724553 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.10570 | −0.361415 | −0.180708 | − | 0.983537i | \(-0.557839\pi\) | ||||
−0.180708 | + | 0.983537i | \(0.557839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.93662 | −0.130678 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.2145 | −1.38356 | −0.691778 | − | 0.722110i | \(-0.743172\pi\) | ||||
−0.691778 | + | 0.722110i | \(0.743172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 59.6007 | 2.63658 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.58412 | −0.202394 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.42981 | 0.0630048 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.73285 | 0.120190 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.42398 | 0.150296 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.9620 | −1.57552 | −0.787762 | − | 0.615979i | \(-0.788761\pi\) | ||||
−0.787762 | + | 0.615979i | \(0.788761\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.6579 | 0.772124 | 0.386062 | − | 0.922473i | \(-0.373835\pi\) | ||||
0.386062 | + | 0.922473i | \(0.373835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.4899 | −0.937896 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.97579 | 0.173188 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.7365 | −0.858109 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.39063 | 0.364122 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.36642 | −0.275760 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.03342 | 0.131146 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.0498 | −0.692600 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.0656 | −0.519704 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6771 | −1.01796 | −0.508979 | − | 0.860779i | \(-0.669977\pi\) | ||||
−0.508979 | + | 0.860779i | \(0.669977\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.70393 | 0.0731228 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.68443 | −0.114988 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.24217 | 0.138625 | 0.0693126 | − | 0.997595i | \(-0.477919\pi\) | ||||
0.0693126 | + | 0.997595i | \(0.477919\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.10729 | −0.0472579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.1682 | −0.646188 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 65.2100 | 2.77301 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.156749 | −0.00665361 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 38.9550 | 1.65058 | 0.825289 | − | 0.564710i | \(-0.191012\pi\) | ||||
0.825289 | + | 0.564710i | \(0.191012\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.97918 | −0.295188 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.64638 | −0.111730 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.246259 | 0.0103786 | 0.00518930 | − | 0.999987i | \(-0.498348\pi\) | ||||
0.00518930 | + | 0.999987i | \(0.498348\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.777601 | −0.0327139 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.36642 | 0.183373 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.13905 | 0.131596 | 0.0657979 | − | 0.997833i | \(-0.479041\pi\) | ||||
0.0657979 | + | 0.997833i | \(0.479041\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.8318 | −1.87615 | −0.938077 | − | 0.346426i | \(-0.887395\pi\) | ||||
−0.938077 | + | 0.346426i | \(0.887395\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.5683 | 0.817476 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.89099 | 0.370780 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.1933 | −0.965549 | −0.482775 | − | 0.875745i | \(-0.660371\pi\) | ||||
−0.482775 | + | 0.875745i | \(0.660371\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.8305 | −1.11504 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 59.9429 | 2.48685 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.99529 | −0.124052 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.279954 | −0.0115747 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.27081 | −0.135001 | −0.0675005 | − | 0.997719i | \(-0.521502\pi\) | ||||
−0.0675005 | + | 0.997719i | \(0.521502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.88696 | −0.283772 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.6466 | −0.808155 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.85598 | −0.199411 | −0.0997055 | − | 0.995017i | \(-0.531790\pi\) | ||||
−0.0997055 | + | 0.995017i | \(0.531790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.23493 | 0.132619 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.55208 | 0.309086 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.9089 | −0.445726 | −0.222863 | − | 0.974850i | \(-0.571540\pi\) | ||||
−0.222863 | + | 0.974850i | \(0.571540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9011 | 0.974945 | 0.487473 | − | 0.873138i | \(-0.337919\pi\) | ||||
0.487473 | + | 0.873138i | \(0.337919\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.39507 | 0.178981 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.279954 | 0.0113818 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.13905 | −0.289765 | −0.144883 | − | 0.989449i | \(-0.546280\pi\) | ||||
−0.144883 | + | 0.989449i | \(0.546280\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.4479 | 0.585459 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.73285 | 0.110559 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.6306 | 1.43911 | 0.719553 | − | 0.694437i | \(-0.244347\pi\) | ||||
0.719553 | + | 0.694437i | \(0.244347\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.78231 | 0.0718696 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.6133 | 0.990894 | 0.495447 | − | 0.868638i | \(-0.335004\pi\) | ||||
0.495447 | + | 0.868638i | \(0.335004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6300 | −0.708609 | −0.354305 | − | 0.935130i | \(-0.615282\pi\) | ||||
−0.354305 | + | 0.935130i | \(0.615282\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.80651 | −0.0724929 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.9058 | 0.436931 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.8305 | 0.953221 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.58412 | 0.183072 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.48173 | −0.0590804 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.8919 | 0.831695 | 0.415847 | − | 0.909434i | \(-0.363485\pi\) | ||||
0.415847 | + | 0.909434i | \(0.363485\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.4849 | −0.694963 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.98257 | 0.0786759 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0656 | −0.478058 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.99529 | 0.118492 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.4594 | 0.452619 | 0.226310 | − | 0.974055i | \(-0.427334\pi\) | ||||
0.226310 | + | 0.974055i | \(0.427334\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.8275 | 0.742484 | 0.371242 | − | 0.928536i | \(-0.378932\pi\) | ||||
0.371242 | + | 0.928536i | \(0.378932\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.95385 | 0.0769328 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.2739 | 0.679108 | 0.339554 | − | 0.940587i | \(-0.389724\pi\) | ||||
0.339554 | + | 0.940587i | \(0.389724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.39063 | −0.329361 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.55991 | 0.257103 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.0512 | 0.549866 | 0.274933 | − | 0.961463i | \(-0.411344\pi\) | ||||
0.274933 | + | 0.961463i | \(0.411344\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.623487 | 0.0243617 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.6498 | 0.532528 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.5120 | −0.799035 | −0.399518 | − | 0.916725i | \(-0.630822\pi\) | ||||
−0.399518 | + | 0.916725i | \(0.630822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.5230 | 0.759356 | 0.379678 | − | 0.925119i | \(-0.376035\pi\) | ||||
0.379678 | + | 0.925119i | \(0.376035\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.64638 | −0.102777 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.60362 | −0.217299 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.97752 | −0.231450 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.38724 | 0.285607 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.10729 | 0.0427464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.65467 | −0.0637827 | −0.0318914 | − | 0.999491i | \(-0.510153\pi\) | ||||
−0.0318914 | + | 0.999491i | \(0.510153\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.92163 | −0.189433 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.6209 | −1.02313 | −0.511563 | − | 0.859246i | \(-0.670933\pi\) | ||||
−0.511563 | + | 0.859246i | \(0.670933\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −69.9335 | −2.68380 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.02891 | −0.269349 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.8563 | −0.912837 | −0.456418 | − | 0.889765i | \(-0.650868\pi\) | ||||
−0.456418 | + | 0.889765i | \(0.650868\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.21789 | 0.199365 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.6834 | −0.522054 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.99529 | −0.114112 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.5811 | −0.630774 | −0.315387 | − | 0.948963i | \(-0.602134\pi\) | ||||
−0.315387 | + | 0.948963i | \(0.602134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.36642 | −0.165867 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.50818 | −0.133073 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8480 | 0.638162 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.6464 | −0.629624 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.8622 | 1.65665 | 0.828325 | − | 0.560247i | \(-0.189294\pi\) | ||||
0.828325 | + | 0.560247i | \(0.189294\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.56669 | 0.0968044 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.765072 | −0.0288143 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −45.8022 | −1.72257 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.1557 | −0.644296 | −0.322148 | − | 0.946689i | \(-0.604405\pi\) | ||||
−0.322148 | + | 0.946689i | \(0.604405\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.9344 | 0.560085 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.71402 | −0.101641 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.279954 | 0.0104697 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.9795 | 0.447381 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.4256 | −0.612573 | −0.306287 | − | 0.951939i | \(-0.599087\pi\) | ||||
−0.306287 | + | 0.951939i | \(0.599087\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.3006 | 0.830517 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.5808 | 0.653837 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.2850 | −0.604810 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.65221 | 0.320893 | 0.160446 | − | 0.987045i | \(-0.448707\pi\) | ||||
0.160446 | + | 0.987045i | \(0.448707\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.4695 | 0.683121 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.9758 | −0.811694 | −0.405847 | − | 0.913941i | \(-0.633023\pi\) | ||||
−0.405847 | + | 0.913941i | \(0.633023\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.37783 | 0.124593 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.39507 | −0.161894 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.9857 | −0.735188 | −0.367594 | − | 0.929986i | \(-0.619818\pi\) | ||||
−0.367594 | + | 0.929986i | \(0.619818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.58412 | 0.168402 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.4021 | −0.931913 | −0.465957 | − | 0.884808i | \(-0.654290\pi\) | ||||
−0.465957 | + | 0.884808i | \(0.654290\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.15675 | 0.0790172 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.7281 | 0.502286 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 47.3121 | 1.72875 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.2158 | −0.628212 | −0.314106 | − | 0.949388i | \(-0.601705\pi\) | ||||
−0.314106 | + | 0.949388i | \(0.601705\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.8480 | 0.686858 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.16145 | −0.0422697 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.1076 | 1.16697 | 0.583486 | − | 0.812123i | \(-0.301688\pi\) | ||||
0.583486 | + | 0.812123i | \(0.301688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.80651 | 0.0655723 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2353 | −0.443528 | −0.221764 | − | 0.975100i | \(-0.571182\pi\) | ||||
−0.221764 | + | 0.975100i | \(0.571182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.8689 | −1.51575 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.740865 | 0.0267860 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.39063 | −0.302968 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.1027 | −1.01341 | −0.506705 | − | 0.862119i | \(-0.669137\pi\) | ||||
−0.506705 | + | 0.862119i | \(0.669137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.3953 | −0.626478 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.8686 | 1.68575 | 0.842873 | − | 0.538113i | \(-0.180863\pi\) | ||||
0.842873 | + | 0.538113i | \(0.180863\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.39402 | −0.265601 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.44480 | −0.0877066 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.1844 | −1.04564 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.99529 | −0.107180 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.30887 | 0.118249 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.726069 | −0.0259145 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.9415 | 1.49505 | 0.747526 | − | 0.664233i | \(-0.231242\pi\) | ||||
0.747526 | + | 0.664233i | \(0.231242\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.1151 | 0.360107 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.1282 | −0.431229 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.10729 | 0.0393209 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.838545 | 0.0297401 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.31836 | 0.330073 | 0.165037 | − | 0.986287i | \(-0.447226\pi\) | ||||
0.165037 | + | 0.986287i | \(0.447226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.23214 | −0.255855 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.49765 | 0.0882500 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.6498 | −0.481690 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.20828 | −0.0778317 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.8385 | −0.381535 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.8839 | −0.945188 | −0.472594 | − | 0.881280i | \(-0.656682\pi\) | ||||
−0.472594 | + | 0.881280i | \(0.656682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.9763 | −0.771693 | −0.385847 | − | 0.922563i | \(-0.626091\pi\) | ||||
−0.385847 | + | 0.922563i | \(0.626091\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.03362 | −0.0713221 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.68199 | −0.0589176 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.9934 | −1.11931 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.36642 | −0.152575 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7362 | −0.549196 | −0.274598 | − | 0.961559i | \(-0.588545\pi\) | ||||
−0.274598 | + | 0.961559i | \(0.588545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.0932 | −0.839835 | −0.419918 | − | 0.907562i | \(-0.637941\pi\) | ||||
−0.419918 | + | 0.907562i | \(0.637941\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.92163 | 0.171349 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.491819 | 0.0171022 | 0.00855111 | − | 0.999963i | \(-0.497278\pi\) | ||||
0.00855111 | + | 0.999963i | \(0.497278\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.35945 | −0.186141 | −0.0930707 | − | 0.995660i | \(-0.529668\pi\) | ||||
−0.0930707 | + | 0.995660i | \(0.529668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.55208 | −0.0538412 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.9303 | 1.10632 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.54021 | 0.157121 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.50235 | 0.0519289 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.9442 | 0.723076 | 0.361538 | − | 0.932357i | \(-0.382252\pi\) | ||||
0.361538 | + | 0.932357i | \(0.382252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.0514 | −0.622462 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.9747 | 0.377990 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.279954 | 0.00963072 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.36642 | 0.150032 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.1615 | −0.794902 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.01148 | 0.0346732 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.4288 | −1.79513 | −0.897563 | − | 0.440886i | \(-0.854664\pi\) | ||||
−0.897563 | + | 0.440886i | \(0.854664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.28334 | −0.0438894 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.5616 | −0.941485 | −0.470743 | − | 0.882271i | \(-0.656014\pi\) | ||||
−0.470743 | + | 0.882271i | \(0.656014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.6428 | −0.499606 | −0.249803 | − | 0.968297i | \(-0.580366\pi\) | ||||
−0.249803 | + | 0.968297i | \(0.580366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.7985 | 0.947370 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.7396 | 1.86336 | 0.931679 | − | 0.363282i | \(-0.118344\pi\) | ||||
0.931679 | + | 0.363282i | \(0.118344\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.958557 | 0.0325919 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.99669 | −0.339505 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.9344 | −0.506616 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.39507 | −0.148921 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.0162 | −0.542066 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1282 | −0.410007 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.14542 | −0.308819 | −0.154409 | − | 0.988007i | \(-0.549347\pi\) | ||||
−0.154409 | + | 0.988007i | \(0.549347\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.6097 | 0.695148 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.8631 | −1.54517 | −0.772584 | − | 0.634913i | \(-0.781036\pi\) | ||||
−0.772584 | + | 0.634913i | \(0.781036\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.3131 | −0.885507 | −0.442753 | − | 0.896643i | \(-0.645998\pi\) | ||||
−0.442753 | + | 0.896643i | \(0.645998\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.34899 | 0.0789605 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.09230 | 0.0702525 | 0.0351262 | − | 0.999383i | \(-0.488817\pi\) | ||||
0.0351262 | + | 0.999383i | \(0.488817\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.9220 | 1.03709 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.5277 | 0.419223 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.49321 | −0.150192 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.80651 | 0.0603178 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.97109 | 0.165795 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.92668 | 0.264076 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 30.4741 | 1.01411 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.477023 | 0.0158568 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.6641 | 0.387299 | 0.193650 | − | 0.981071i | \(-0.437967\pi\) | ||||
0.193650 | + | 0.981071i | \(0.437967\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.4896 | −0.347919 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.1635 | 0.336733 | 0.168366 | − | 0.985724i | \(-0.446151\pi\) | ||||
0.168366 | + | 0.985724i | \(0.446151\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7281 | −0.454335 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.309990 | −0.0102479 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.72448 | 0.321131 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.6215 | −1.66985 | −0.834924 | − | 0.550365i | \(-0.814489\pi\) | ||||
−0.834924 | + | 0.550365i | \(0.814489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.1118 | −0.563853 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.99529 | −0.0985913 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.75566 | 0.0906055 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.10729 | 0.167745 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3524 | 0.766167 | 0.383083 | − | 0.923714i | \(-0.374862\pi\) | ||||
0.383083 | + | 0.923714i | \(0.374862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −55.3103 | −1.81272 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.9873 | 0.621615 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.740865 | −0.0242289 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.8553 | 1.00800 | 0.503999 | − | 0.863704i | \(-0.331862\pi\) | ||||
0.503999 | + | 0.863704i | \(0.331862\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −21.2050 | −0.691998 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.8237 | −0.548439 | −0.274219 | − | 0.961667i | \(-0.588419\pi\) | ||||
−0.274219 | + | 0.961667i | \(0.588419\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.5010 | −0.374525 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.22240 | 0.0397646 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.3991 | −1.47527 | −0.737637 | − | 0.675197i | \(-0.764058\pi\) | ||||
−0.737637 | + | 0.675197i | \(0.764058\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.6498 | −0.443090 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.4738 | −0.826044 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −49.2871 | −1.59657 | −0.798283 | − | 0.602283i | \(-0.794258\pi\) | ||||
−0.798283 | + | 0.602283i | \(0.794258\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.47822 | 0.177271 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.30887 | −0.106960 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 81.3830 | 2.62799 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7429 | −0.927191 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.8354 | 0.349167 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.51132 | −0.241798 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.9587 | 1.18851 | 0.594256 | − | 0.804276i | \(-0.297447\pi\) | ||||
0.594256 | + | 0.804276i | \(0.297447\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.1313 | −0.389713 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.2638 | −1.29213 | −0.646064 | − | 0.763283i | \(-0.723586\pi\) | ||||
−0.646064 | + | 0.763283i | \(0.723586\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54.7168 | −1.75414 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.92163 | 0.157618 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.7237 | −0.695003 | −0.347501 | − | 0.937679i | \(-0.612970\pi\) | ||||
−0.347501 | + | 0.937679i | \(0.612970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.49765 | −0.0798251 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.58882 | −0.306148 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.72868 | −0.246507 | −0.123253 | − | 0.992375i | \(-0.539333\pi\) | ||||
−0.123253 | + | 0.992375i | \(0.539333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.50016 | −0.175250 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.9328 | −0.379824 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.6080 | −0.400911 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.8563 | 0.948417 | 0.474209 | − | 0.880412i | \(-0.342734\pi\) | ||||
0.474209 | + | 0.880412i | \(0.342734\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.03561 | −0.0963323 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.11424 | 0.0670259 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.9856 | −0.854641 | −0.427320 | − | 0.904100i | \(-0.640542\pi\) | ||||
−0.427320 | + | 0.904100i | \(0.640542\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.559909 | −0.0177147 |
(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 | 6864.2.a.ca.1.2 | 4 | ||
4.3 | odd | 2 | 3432.2.a.r.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3432.2.a.r.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
6864.2.a.ca.1.2 | 4 | 1.1 | even | 1 | trivial |