Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.19520000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 12x^{6} + 16x^{5} + 50x^{4} - 24x^{3} - 72x^{2} - 32x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.04552\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 3.13415 | 1.80950 | 0.904750 | − | 0.425942i | \(-0.140057\pi\) | ||||
0.904750 | + | 0.425942i | \(0.140057\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.529405 | −0.236757 | −0.118379 | − | 0.992969i | \(-0.537770\pi\) | ||||
−0.118379 | + | 0.992969i | \(0.537770\pi\) | |||||||
\(6\) | −3.13415 | −1.27951 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.82288 | 2.27429 | ||||||||
\(10\) | 0.529405 | 0.167413 | ||||||||
\(11\) | −3.29795 | −0.994369 | −0.497185 | − | 0.867645i | \(-0.665633\pi\) | ||||
−0.497185 | + | 0.867645i | \(0.665633\pi\) | |||||||
\(12\) | 3.13415 | 0.904750 | ||||||||
\(13\) | 0.516798 | 0.143334 | 0.0716670 | − | 0.997429i | \(-0.477168\pi\) | ||||
0.0716670 | + | 0.997429i | \(0.477168\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.65923 | −0.428412 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.14185 | 1.48962 | 0.744809 | − | 0.667278i | \(-0.232541\pi\) | ||||
0.744809 | + | 0.667278i | \(0.232541\pi\) | |||||||
\(18\) | −6.82288 | −1.60817 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.529405 | −0.118379 | ||||||||
\(21\) | 3.13415 | 0.683927 | ||||||||
\(22\) | 3.29795 | 0.703125 | ||||||||
\(23\) | −5.69094 | −1.18664 | −0.593321 | − | 0.804966i | \(-0.702184\pi\) | ||||
−0.593321 | + | 0.804966i | \(0.702184\pi\) | |||||||
\(24\) | −3.13415 | −0.639755 | ||||||||
\(25\) | −4.71973 | −0.943946 | ||||||||
\(26\) | −0.516798 | −0.101352 | ||||||||
\(27\) | 11.9815 | 2.30583 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 0.202602 | 0.0376223 | 0.0188112 | − | 0.999823i | \(-0.494012\pi\) | ||||
0.0188112 | + | 0.999823i | \(0.494012\pi\) | |||||||
\(30\) | 1.65923 | 0.302933 | ||||||||
\(31\) | 0.736319 | 0.132247 | 0.0661234 | − | 0.997811i | \(-0.478937\pi\) | ||||
0.0661234 | + | 0.997811i | \(0.478937\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −10.3363 | −1.79931 | ||||||||
\(34\) | −6.14185 | −1.05332 | ||||||||
\(35\) | −0.529405 | −0.0894858 | ||||||||
\(36\) | 6.82288 | 1.13715 | ||||||||
\(37\) | 10.8924 | 1.79070 | 0.895348 | − | 0.445368i | \(-0.146927\pi\) | ||||
0.895348 | + | 0.445368i | \(0.146927\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.61972 | 0.259363 | ||||||||
\(40\) | 0.529405 | 0.0837063 | ||||||||
\(41\) | −3.68913 | −0.576145 | −0.288073 | − | 0.957609i | \(-0.593014\pi\) | ||||
−0.288073 | + | 0.957609i | \(0.593014\pi\) | |||||||
\(42\) | −3.13415 | −0.483609 | ||||||||
\(43\) | 7.19952 | 1.09792 | 0.548958 | − | 0.835850i | \(-0.315025\pi\) | ||||
0.548958 | + | 0.835850i | \(0.315025\pi\) | |||||||
\(44\) | −3.29795 | −0.497185 | ||||||||
\(45\) | −3.61206 | −0.538455 | ||||||||
\(46\) | 5.69094 | 0.839083 | ||||||||
\(47\) | 12.1388 | 1.77062 | 0.885311 | − | 0.464999i | \(-0.153945\pi\) | ||||
0.885311 | + | 0.464999i | \(0.153945\pi\) | |||||||
\(48\) | 3.13415 | 0.452375 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.71973 | 0.667471 | ||||||||
\(51\) | 19.2495 | 2.69546 | ||||||||
\(52\) | 0.516798 | 0.0716670 | ||||||||
\(53\) | −3.18512 | −0.437509 | −0.218755 | − | 0.975780i | \(-0.570199\pi\) | ||||
−0.218755 | + | 0.975780i | \(0.570199\pi\) | |||||||
\(54\) | −11.9815 | −1.63047 | ||||||||
\(55\) | 1.74595 | 0.235424 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.202602 | −0.0266030 | ||||||||
\(59\) | 3.91656 | 0.509893 | 0.254947 | − | 0.966955i | \(-0.417942\pi\) | ||||
0.254947 | + | 0.966955i | \(0.417942\pi\) | |||||||
\(60\) | −1.65923 | −0.214206 | ||||||||
\(61\) | 3.73389 | 0.478075 | 0.239038 | − | 0.971010i | \(-0.423168\pi\) | ||||
0.239038 | + | 0.971010i | \(0.423168\pi\) | |||||||
\(62\) | −0.736319 | −0.0935126 | ||||||||
\(63\) | 6.82288 | 0.859602 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.273596 | −0.0339354 | ||||||||
\(66\) | 10.3363 | 1.27231 | ||||||||
\(67\) | 9.77683 | 1.19443 | 0.597215 | − | 0.802081i | \(-0.296274\pi\) | ||||
0.597215 | + | 0.802081i | \(0.296274\pi\) | |||||||
\(68\) | 6.14185 | 0.744809 | ||||||||
\(69\) | −17.8362 | −2.14723 | ||||||||
\(70\) | 0.529405 | 0.0632760 | ||||||||
\(71\) | −6.75039 | −0.801123 | −0.400562 | − | 0.916270i | \(-0.631185\pi\) | ||||
−0.400562 | + | 0.916270i | \(0.631185\pi\) | |||||||
\(72\) | −6.82288 | −0.804084 | ||||||||
\(73\) | 16.3744 | 1.91648 | 0.958238 | − | 0.285971i | \(-0.0923161\pi\) | ||||
0.958238 | + | 0.285971i | \(0.0923161\pi\) | |||||||
\(74\) | −10.8924 | −1.26621 | ||||||||
\(75\) | −14.7923 | −1.70807 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.29795 | −0.375836 | ||||||||
\(78\) | −1.61972 | −0.183397 | ||||||||
\(79\) | 8.69327 | 0.978069 | 0.489035 | − | 0.872264i | \(-0.337349\pi\) | ||||
0.489035 | + | 0.872264i | \(0.337349\pi\) | |||||||
\(80\) | −0.529405 | −0.0591893 | ||||||||
\(81\) | 17.0830 | 1.89811 | ||||||||
\(82\) | 3.68913 | 0.407396 | ||||||||
\(83\) | −18.0349 | −1.97959 | −0.989796 | − | 0.142489i | \(-0.954489\pi\) | ||||
−0.989796 | + | 0.142489i | \(0.954489\pi\) | |||||||
\(84\) | 3.13415 | 0.341963 | ||||||||
\(85\) | −3.25153 | −0.352678 | ||||||||
\(86\) | −7.19952 | −0.776344 | ||||||||
\(87\) | 0.634986 | 0.0680776 | ||||||||
\(88\) | 3.29795 | 0.351563 | ||||||||
\(89\) | 16.2090 | 1.71815 | 0.859074 | − | 0.511851i | \(-0.171040\pi\) | ||||
0.859074 | + | 0.511851i | \(0.171040\pi\) | |||||||
\(90\) | 3.61206 | 0.380745 | ||||||||
\(91\) | 0.516798 | 0.0541752 | ||||||||
\(92\) | −5.69094 | −0.593321 | ||||||||
\(93\) | 2.30773 | 0.239301 | ||||||||
\(94\) | −12.1388 | −1.25202 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.13415 | −0.319878 | ||||||||
\(97\) | −2.63263 | −0.267303 | −0.133652 | − | 0.991028i | \(-0.542670\pi\) | ||||
−0.133652 | + | 0.991028i | \(0.542670\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −22.5015 | −2.26149 | ||||||||
\(100\) | −4.71973 | −0.471973 | ||||||||
\(101\) | 9.83739 | 0.978856 | 0.489428 | − | 0.872044i | \(-0.337206\pi\) | ||||
0.489428 | + | 0.872044i | \(0.337206\pi\) | |||||||
\(102\) | −19.2495 | −1.90598 | ||||||||
\(103\) | −4.31612 | −0.425280 | −0.212640 | − | 0.977131i | \(-0.568206\pi\) | ||||
−0.212640 | + | 0.977131i | \(0.568206\pi\) | |||||||
\(104\) | −0.516798 | −0.0506762 | ||||||||
\(105\) | −1.65923 | −0.161925 | ||||||||
\(106\) | 3.18512 | 0.309366 | ||||||||
\(107\) | 18.9251 | 1.82956 | 0.914779 | − | 0.403954i | \(-0.132364\pi\) | ||||
0.914779 | + | 0.403954i | \(0.132364\pi\) | |||||||
\(108\) | 11.9815 | 1.15292 | ||||||||
\(109\) | −14.8991 | −1.42707 | −0.713536 | − | 0.700618i | \(-0.752908\pi\) | ||||
−0.713536 | + | 0.700618i | \(0.752908\pi\) | |||||||
\(110\) | −1.74595 | −0.166470 | ||||||||
\(111\) | 34.1383 | 3.24026 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 1.20410 | 0.113272 | 0.0566361 | − | 0.998395i | \(-0.481963\pi\) | ||||
0.0566361 | + | 0.998395i | \(0.481963\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.01281 | 0.280946 | ||||||||
\(116\) | 0.202602 | 0.0188112 | ||||||||
\(117\) | 3.52605 | 0.325983 | ||||||||
\(118\) | −3.91656 | −0.360549 | ||||||||
\(119\) | 6.14185 | 0.563023 | ||||||||
\(120\) | 1.65923 | 0.151467 | ||||||||
\(121\) | −0.123528 | −0.0112298 | ||||||||
\(122\) | −3.73389 | −0.338050 | ||||||||
\(123\) | −11.5623 | −1.04254 | ||||||||
\(124\) | 0.736319 | 0.0661234 | ||||||||
\(125\) | 5.14567 | 0.460243 | ||||||||
\(126\) | −6.82288 | −0.607830 | ||||||||
\(127\) | −0.707401 | −0.0627717 | −0.0313858 | − | 0.999507i | \(-0.509992\pi\) | ||||
−0.0313858 | + | 0.999507i | \(0.509992\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 22.5644 | 1.98668 | ||||||||
\(130\) | 0.273596 | 0.0239959 | ||||||||
\(131\) | −10.3358 | −0.903044 | −0.451522 | − | 0.892260i | \(-0.649119\pi\) | ||||
−0.451522 | + | 0.892260i | \(0.649119\pi\) | |||||||
\(132\) | −10.3363 | −0.899656 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.77683 | −0.844590 | ||||||||
\(135\) | −6.34304 | −0.545922 | ||||||||
\(136\) | −6.14185 | −0.526659 | ||||||||
\(137\) | 4.56839 | 0.390304 | 0.195152 | − | 0.980773i | \(-0.437480\pi\) | ||||
0.195152 | + | 0.980773i | \(0.437480\pi\) | |||||||
\(138\) | 17.8362 | 1.51832 | ||||||||
\(139\) | −6.04179 | −0.512458 | −0.256229 | − | 0.966616i | \(-0.582480\pi\) | ||||
−0.256229 | + | 0.966616i | \(0.582480\pi\) | |||||||
\(140\) | −0.529405 | −0.0447429 | ||||||||
\(141\) | 38.0447 | 3.20394 | ||||||||
\(142\) | 6.75039 | 0.566480 | ||||||||
\(143\) | −1.70437 | −0.142527 | ||||||||
\(144\) | 6.82288 | 0.568573 | ||||||||
\(145\) | −0.107259 | −0.00890735 | ||||||||
\(146\) | −16.3744 | −1.35515 | ||||||||
\(147\) | 3.13415 | 0.258500 | ||||||||
\(148\) | 10.8924 | 0.895348 | ||||||||
\(149\) | −18.2013 | −1.49111 | −0.745553 | − | 0.666447i | \(-0.767814\pi\) | ||||
−0.745553 | + | 0.666447i | \(0.767814\pi\) | |||||||
\(150\) | 14.7923 | 1.20779 | ||||||||
\(151\) | −20.7582 | −1.68928 | −0.844641 | − | 0.535334i | \(-0.820186\pi\) | ||||
−0.844641 | + | 0.535334i | \(0.820186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 41.9051 | 3.38783 | ||||||||
\(154\) | 3.29795 | 0.265756 | ||||||||
\(155\) | −0.389811 | −0.0313104 | ||||||||
\(156\) | 1.61972 | 0.129682 | ||||||||
\(157\) | 10.4064 | 0.830519 | 0.415259 | − | 0.909703i | \(-0.363691\pi\) | ||||
0.415259 | + | 0.909703i | \(0.363691\pi\) | |||||||
\(158\) | −8.69327 | −0.691599 | ||||||||
\(159\) | −9.98262 | −0.791673 | ||||||||
\(160\) | 0.529405 | 0.0418531 | ||||||||
\(161\) | −5.69094 | −0.448509 | ||||||||
\(162\) | −17.0830 | −1.34217 | ||||||||
\(163\) | −17.8149 | −1.39537 | −0.697687 | − | 0.716402i | \(-0.745787\pi\) | ||||
−0.697687 | + | 0.716402i | \(0.745787\pi\) | |||||||
\(164\) | −3.68913 | −0.288073 | ||||||||
\(165\) | 5.47207 | 0.426000 | ||||||||
\(166\) | 18.0349 | 1.39978 | ||||||||
\(167\) | 7.93765 | 0.614234 | 0.307117 | − | 0.951672i | \(-0.400636\pi\) | ||||
0.307117 | + | 0.951672i | \(0.400636\pi\) | |||||||
\(168\) | −3.13415 | −0.241805 | ||||||||
\(169\) | −12.7329 | −0.979455 | ||||||||
\(170\) | 3.25153 | 0.249381 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.19952 | 0.548958 | ||||||||
\(173\) | 9.69338 | 0.736974 | 0.368487 | − | 0.929633i | \(-0.379876\pi\) | ||||
0.368487 | + | 0.929633i | \(0.379876\pi\) | |||||||
\(174\) | −0.634986 | −0.0481382 | ||||||||
\(175\) | −4.71973 | −0.356778 | ||||||||
\(176\) | −3.29795 | −0.248592 | ||||||||
\(177\) | 12.2751 | 0.922652 | ||||||||
\(178\) | −16.2090 | −1.21491 | ||||||||
\(179\) | −13.9458 | −1.04236 | −0.521178 | − | 0.853448i | \(-0.674507\pi\) | ||||
−0.521178 | + | 0.853448i | \(0.674507\pi\) | |||||||
\(180\) | −3.61206 | −0.269227 | ||||||||
\(181\) | 19.1572 | 1.42395 | 0.711973 | − | 0.702207i | \(-0.247802\pi\) | ||||
0.711973 | + | 0.702207i | \(0.247802\pi\) | |||||||
\(182\) | −0.516798 | −0.0383076 | ||||||||
\(183\) | 11.7025 | 0.865077 | ||||||||
\(184\) | 5.69094 | 0.419542 | ||||||||
\(185\) | −5.76648 | −0.423960 | ||||||||
\(186\) | −2.30773 | −0.169211 | ||||||||
\(187\) | −20.2555 | −1.48123 | ||||||||
\(188\) | 12.1388 | 0.885311 | ||||||||
\(189\) | 11.9815 | 0.871523 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.7895 | −0.925418 | −0.462709 | − | 0.886510i | \(-0.653122\pi\) | ||||
−0.462709 | + | 0.886510i | \(0.653122\pi\) | |||||||
\(192\) | 3.13415 | 0.226188 | ||||||||
\(193\) | 10.4419 | 0.751622 | 0.375811 | − | 0.926696i | \(-0.377364\pi\) | ||||
0.375811 | + | 0.926696i | \(0.377364\pi\) | |||||||
\(194\) | 2.63263 | 0.189012 | ||||||||
\(195\) | −0.857489 | −0.0614060 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 0.817360 | 0.0582345 | 0.0291173 | − | 0.999576i | \(-0.490730\pi\) | ||||
0.0291173 | + | 0.999576i | \(0.490730\pi\) | |||||||
\(198\) | 22.5015 | 1.59911 | ||||||||
\(199\) | −7.81078 | −0.553691 | −0.276846 | − | 0.960914i | \(-0.589289\pi\) | ||||
−0.276846 | + | 0.960914i | \(0.589289\pi\) | |||||||
\(200\) | 4.71973 | 0.333735 | ||||||||
\(201\) | 30.6420 | 2.16132 | ||||||||
\(202\) | −9.83739 | −0.692156 | ||||||||
\(203\) | 0.202602 | 0.0142199 | ||||||||
\(204\) | 19.2495 | 1.34773 | ||||||||
\(205\) | 1.95304 | 0.136406 | ||||||||
\(206\) | 4.31612 | 0.300718 | ||||||||
\(207\) | −38.8286 | −2.69877 | ||||||||
\(208\) | 0.516798 | 0.0358335 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.65923 | 0.114498 | ||||||||
\(211\) | 24.5746 | 1.69179 | 0.845893 | − | 0.533353i | \(-0.179068\pi\) | ||||
0.845893 | + | 0.533353i | \(0.179068\pi\) | |||||||
\(212\) | −3.18512 | −0.218755 | ||||||||
\(213\) | −21.1567 | −1.44963 | ||||||||
\(214\) | −18.9251 | −1.29369 | ||||||||
\(215\) | −3.81146 | −0.259940 | ||||||||
\(216\) | −11.9815 | −0.815235 | ||||||||
\(217\) | 0.736319 | 0.0499846 | ||||||||
\(218\) | 14.8991 | 1.00909 | ||||||||
\(219\) | 51.3197 | 3.46787 | ||||||||
\(220\) | 1.74595 | 0.117712 | ||||||||
\(221\) | 3.17410 | 0.213513 | ||||||||
\(222\) | −34.1383 | −2.29121 | ||||||||
\(223\) | 18.4764 | 1.23727 | 0.618635 | − | 0.785679i | \(-0.287686\pi\) | ||||
0.618635 | + | 0.785679i | \(0.287686\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −32.2021 | −2.14681 | ||||||||
\(226\) | −1.20410 | −0.0800956 | ||||||||
\(227\) | 3.85747 | 0.256029 | 0.128015 | − | 0.991772i | \(-0.459140\pi\) | ||||
0.128015 | + | 0.991772i | \(0.459140\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.4759 | −0.758350 | −0.379175 | − | 0.925325i | \(-0.623792\pi\) | ||||
−0.379175 | + | 0.925325i | \(0.623792\pi\) | |||||||
\(230\) | −3.01281 | −0.198659 | ||||||||
\(231\) | −10.3363 | −0.680076 | ||||||||
\(232\) | −0.202602 | −0.0133015 | ||||||||
\(233\) | −10.2608 | −0.672206 | −0.336103 | − | 0.941825i | \(-0.609109\pi\) | ||||
−0.336103 | + | 0.941825i | \(0.609109\pi\) | |||||||
\(234\) | −3.52605 | −0.230505 | ||||||||
\(235\) | −6.42633 | −0.419208 | ||||||||
\(236\) | 3.91656 | 0.254947 | ||||||||
\(237\) | 27.2460 | 1.76982 | ||||||||
\(238\) | −6.14185 | −0.398117 | ||||||||
\(239\) | −18.9095 | −1.22315 | −0.611577 | − | 0.791185i | \(-0.709464\pi\) | ||||
−0.611577 | + | 0.791185i | \(0.709464\pi\) | |||||||
\(240\) | −1.65923 | −0.107103 | ||||||||
\(241\) | 11.5763 | 0.745698 | 0.372849 | − | 0.927892i | \(-0.378381\pi\) | ||||
0.372849 | + | 0.927892i | \(0.378381\pi\) | |||||||
\(242\) | 0.123528 | 0.00794066 | ||||||||
\(243\) | 17.5963 | 1.12880 | ||||||||
\(244\) | 3.73389 | 0.239038 | ||||||||
\(245\) | −0.529405 | −0.0338224 | ||||||||
\(246\) | 11.5623 | 0.737184 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.736319 | −0.0467563 | ||||||||
\(249\) | −56.5242 | −3.58207 | ||||||||
\(250\) | −5.14567 | −0.325441 | ||||||||
\(251\) | 26.8853 | 1.69698 | 0.848492 | − | 0.529208i | \(-0.177511\pi\) | ||||
0.848492 | + | 0.529208i | \(0.177511\pi\) | |||||||
\(252\) | 6.82288 | 0.429801 | ||||||||
\(253\) | 18.7684 | 1.17996 | ||||||||
\(254\) | 0.707401 | 0.0443863 | ||||||||
\(255\) | −10.1908 | −0.638170 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.2469 | 0.826318 | 0.413159 | − | 0.910659i | \(-0.364425\pi\) | ||||
0.413159 | + | 0.910659i | \(0.364425\pi\) | |||||||
\(258\) | −22.5644 | −1.40480 | ||||||||
\(259\) | 10.8924 | 0.676819 | ||||||||
\(260\) | −0.273596 | −0.0169677 | ||||||||
\(261\) | 1.38233 | 0.0855642 | ||||||||
\(262\) | 10.3358 | 0.638548 | ||||||||
\(263\) | −1.67507 | −0.103289 | −0.0516445 | − | 0.998666i | \(-0.516446\pi\) | ||||
−0.0516445 | + | 0.998666i | \(0.516446\pi\) | |||||||
\(264\) | 10.3363 | 0.636153 | ||||||||
\(265\) | 1.68622 | 0.103583 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 50.8013 | 3.10899 | ||||||||
\(268\) | 9.77683 | 0.597215 | ||||||||
\(269\) | −13.7127 | −0.836077 | −0.418038 | − | 0.908429i | \(-0.637282\pi\) | ||||
−0.418038 | + | 0.908429i | \(0.637282\pi\) | |||||||
\(270\) | 6.34304 | 0.386025 | ||||||||
\(271\) | −21.3184 | −1.29500 | −0.647501 | − | 0.762065i | \(-0.724186\pi\) | ||||
−0.647501 | + | 0.762065i | \(0.724186\pi\) | |||||||
\(272\) | 6.14185 | 0.372404 | ||||||||
\(273\) | 1.61972 | 0.0980300 | ||||||||
\(274\) | −4.56839 | −0.275986 | ||||||||
\(275\) | 15.5654 | 0.938631 | ||||||||
\(276\) | −17.8362 | −1.07362 | ||||||||
\(277\) | 12.9204 | 0.776312 | 0.388156 | − | 0.921594i | \(-0.373112\pi\) | ||||
0.388156 | + | 0.921594i | \(0.373112\pi\) | |||||||
\(278\) | 6.04179 | 0.362362 | ||||||||
\(279\) | 5.02381 | 0.300768 | ||||||||
\(280\) | 0.529405 | 0.0316380 | ||||||||
\(281\) | 2.53217 | 0.151057 | 0.0755283 | − | 0.997144i | \(-0.475936\pi\) | ||||
0.0755283 | + | 0.997144i | \(0.475936\pi\) | |||||||
\(282\) | −38.0447 | −2.26553 | ||||||||
\(283\) | 7.18663 | 0.427201 | 0.213601 | − | 0.976921i | \(-0.431481\pi\) | ||||
0.213601 | + | 0.976921i | \(0.431481\pi\) | |||||||
\(284\) | −6.75039 | −0.400562 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.70437 | 0.100782 | ||||||||
\(287\) | −3.68913 | −0.217762 | ||||||||
\(288\) | −6.82288 | −0.402042 | ||||||||
\(289\) | 20.7223 | 1.21896 | ||||||||
\(290\) | 0.107259 | 0.00629845 | ||||||||
\(291\) | −8.25105 | −0.483685 | ||||||||
\(292\) | 16.3744 | 0.958238 | ||||||||
\(293\) | 1.03791 | 0.0606352 | 0.0303176 | − | 0.999540i | \(-0.490348\pi\) | ||||
0.0303176 | + | 0.999540i | \(0.490348\pi\) | |||||||
\(294\) | −3.13415 | −0.182787 | ||||||||
\(295\) | −2.07345 | −0.120721 | ||||||||
\(296\) | −10.8924 | −0.633106 | ||||||||
\(297\) | −39.5142 | −2.29285 | ||||||||
\(298\) | 18.2013 | 1.05437 | ||||||||
\(299\) | −2.94107 | −0.170086 | ||||||||
\(300\) | −14.7923 | −0.854035 | ||||||||
\(301\) | 7.19952 | 0.414973 | ||||||||
\(302\) | 20.7582 | 1.19450 | ||||||||
\(303\) | 30.8318 | 1.77124 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.97674 | −0.113188 | ||||||||
\(306\) | −41.9051 | −2.39555 | ||||||||
\(307\) | −8.78461 | −0.501364 | −0.250682 | − | 0.968069i | \(-0.580655\pi\) | ||||
−0.250682 | + | 0.968069i | \(0.580655\pi\) | |||||||
\(308\) | −3.29795 | −0.187918 | ||||||||
\(309\) | −13.5273 | −0.769544 | ||||||||
\(310\) | 0.389811 | 0.0221398 | ||||||||
\(311\) | −0.240874 | −0.0136587 | −0.00682936 | − | 0.999977i | \(-0.502174\pi\) | ||||
−0.00682936 | + | 0.999977i | \(0.502174\pi\) | |||||||
\(312\) | −1.61972 | −0.0916987 | ||||||||
\(313\) | 1.87814 | 0.106159 | 0.0530795 | − | 0.998590i | \(-0.483096\pi\) | ||||
0.0530795 | + | 0.998590i | \(0.483096\pi\) | |||||||
\(314\) | −10.4064 | −0.587266 | ||||||||
\(315\) | −3.61206 | −0.203517 | ||||||||
\(316\) | 8.69327 | 0.489035 | ||||||||
\(317\) | −33.6024 | −1.88730 | −0.943648 | − | 0.330950i | \(-0.892631\pi\) | ||||
−0.943648 | + | 0.330950i | \(0.892631\pi\) | |||||||
\(318\) | 9.98262 | 0.559798 | ||||||||
\(319\) | −0.668173 | −0.0374105 | ||||||||
\(320\) | −0.529405 | −0.0295946 | ||||||||
\(321\) | 59.3140 | 3.31059 | ||||||||
\(322\) | 5.69094 | 0.317144 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 17.0830 | 0.949056 | ||||||||
\(325\) | −2.43915 | −0.135300 | ||||||||
\(326\) | 17.8149 | 0.986679 | ||||||||
\(327\) | −46.6959 | −2.58229 | ||||||||
\(328\) | 3.68913 | 0.203698 | ||||||||
\(329\) | 12.1388 | 0.669233 | ||||||||
\(330\) | −5.47207 | −0.301227 | ||||||||
\(331\) | −11.1959 | −0.615383 | −0.307691 | − | 0.951486i | \(-0.599556\pi\) | ||||
−0.307691 | + | 0.951486i | \(0.599556\pi\) | |||||||
\(332\) | −18.0349 | −0.989796 | ||||||||
\(333\) | 74.3173 | 4.07256 | ||||||||
\(334\) | −7.93765 | −0.434329 | ||||||||
\(335\) | −5.17590 | −0.282790 | ||||||||
\(336\) | 3.13415 | 0.170982 | ||||||||
\(337\) | 15.5993 | 0.849746 | 0.424873 | − | 0.905253i | \(-0.360319\pi\) | ||||
0.424873 | + | 0.905253i | \(0.360319\pi\) | |||||||
\(338\) | 12.7329 | 0.692580 | ||||||||
\(339\) | 3.77383 | 0.204966 | ||||||||
\(340\) | −3.25153 | −0.176339 | ||||||||
\(341\) | −2.42834 | −0.131502 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −7.19952 | −0.388172 | ||||||||
\(345\) | 9.44259 | 0.508372 | ||||||||
\(346\) | −9.69338 | −0.521119 | ||||||||
\(347\) | −17.2497 | −0.926011 | −0.463006 | − | 0.886355i | \(-0.653229\pi\) | ||||
−0.463006 | + | 0.886355i | \(0.653229\pi\) | |||||||
\(348\) | 0.634986 | 0.0340388 | ||||||||
\(349\) | 2.55529 | 0.136782 | 0.0683908 | − | 0.997659i | \(-0.478214\pi\) | ||||
0.0683908 | + | 0.997659i | \(0.478214\pi\) | |||||||
\(350\) | 4.71973 | 0.252280 | ||||||||
\(351\) | 6.19199 | 0.330504 | ||||||||
\(352\) | 3.29795 | 0.175781 | ||||||||
\(353\) | −27.4877 | −1.46302 | −0.731511 | − | 0.681829i | \(-0.761185\pi\) | ||||
−0.731511 | + | 0.681829i | \(0.761185\pi\) | |||||||
\(354\) | −12.2751 | −0.652414 | ||||||||
\(355\) | 3.57369 | 0.189672 | ||||||||
\(356\) | 16.2090 | 0.859074 | ||||||||
\(357\) | 19.2495 | 1.01879 | ||||||||
\(358\) | 13.9458 | 0.737058 | ||||||||
\(359\) | −15.4937 | −0.817727 | −0.408864 | − | 0.912595i | \(-0.634075\pi\) | ||||
−0.408864 | + | 0.912595i | \(0.634075\pi\) | |||||||
\(360\) | 3.61206 | 0.190373 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −19.1572 | −1.00688 | ||||||||
\(363\) | −0.387154 | −0.0203203 | ||||||||
\(364\) | 0.516798 | 0.0270876 | ||||||||
\(365\) | −8.66868 | −0.453739 | ||||||||
\(366\) | −11.7025 | −0.611702 | ||||||||
\(367\) | −26.5673 | −1.38680 | −0.693401 | − | 0.720552i | \(-0.743889\pi\) | ||||
−0.693401 | + | 0.720552i | \(0.743889\pi\) | |||||||
\(368\) | −5.69094 | −0.296661 | ||||||||
\(369\) | −25.1705 | −1.31032 | ||||||||
\(370\) | 5.76648 | 0.299785 | ||||||||
\(371\) | −3.18512 | −0.165363 | ||||||||
\(372\) | 2.30773 | 0.119650 | ||||||||
\(373\) | 14.5329 | 0.752487 | 0.376244 | − | 0.926521i | \(-0.377216\pi\) | ||||
0.376244 | + | 0.926521i | \(0.377216\pi\) | |||||||
\(374\) | 20.2555 | 1.04739 | ||||||||
\(375\) | 16.1273 | 0.832810 | ||||||||
\(376\) | −12.1388 | −0.626010 | ||||||||
\(377\) | 0.104705 | 0.00539256 | ||||||||
\(378\) | −11.9815 | −0.616260 | ||||||||
\(379\) | 23.1135 | 1.18726 | 0.593631 | − | 0.804738i | \(-0.297694\pi\) | ||||
0.593631 | + | 0.804738i | \(0.297694\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.21710 | −0.113585 | ||||||||
\(382\) | 12.7895 | 0.654369 | ||||||||
\(383\) | −25.5356 | −1.30481 | −0.652405 | − | 0.757871i | \(-0.726240\pi\) | ||||
−0.652405 | + | 0.757871i | \(0.726240\pi\) | |||||||
\(384\) | −3.13415 | −0.159939 | ||||||||
\(385\) | 1.74595 | 0.0889819 | ||||||||
\(386\) | −10.4419 | −0.531477 | ||||||||
\(387\) | 49.1214 | 2.49698 | ||||||||
\(388\) | −2.63263 | −0.133652 | ||||||||
\(389\) | −30.1536 | −1.52885 | −0.764424 | − | 0.644714i | \(-0.776976\pi\) | ||||
−0.764424 | + | 0.644714i | \(0.776976\pi\) | |||||||
\(390\) | 0.857489 | 0.0434206 | ||||||||
\(391\) | −34.9529 | −1.76764 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | −32.3939 | −1.63406 | ||||||||
\(394\) | −0.817360 | −0.0411780 | ||||||||
\(395\) | −4.60226 | −0.231565 | ||||||||
\(396\) | −22.5015 | −1.13074 | ||||||||
\(397\) | −13.9802 | −0.701647 | −0.350824 | − | 0.936442i | \(-0.614098\pi\) | ||||
−0.350824 | + | 0.936442i | \(0.614098\pi\) | |||||||
\(398\) | 7.81078 | 0.391519 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.71973 | −0.235987 | ||||||||
\(401\) | −17.6953 | −0.883661 | −0.441830 | − | 0.897099i | \(-0.645671\pi\) | ||||
−0.441830 | + | 0.897099i | \(0.645671\pi\) | |||||||
\(402\) | −30.6420 | −1.52829 | ||||||||
\(403\) | 0.380528 | 0.0189555 | ||||||||
\(404\) | 9.83739 | 0.489428 | ||||||||
\(405\) | −9.04383 | −0.449392 | ||||||||
\(406\) | −0.202602 | −0.0100550 | ||||||||
\(407\) | −35.9225 | −1.78061 | ||||||||
\(408\) | −19.2495 | −0.952990 | ||||||||
\(409\) | 12.5454 | 0.620329 | 0.310165 | − | 0.950683i | \(-0.399616\pi\) | ||||
0.310165 | + | 0.950683i | \(0.399616\pi\) | |||||||
\(410\) | −1.95304 | −0.0964540 | ||||||||
\(411\) | 14.3180 | 0.706255 | ||||||||
\(412\) | −4.31612 | −0.212640 | ||||||||
\(413\) | 3.91656 | 0.192722 | ||||||||
\(414\) | 38.8286 | 1.90832 | ||||||||
\(415\) | 9.54779 | 0.468683 | ||||||||
\(416\) | −0.516798 | −0.0253381 | ||||||||
\(417\) | −18.9358 | −0.927292 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.81346 | −0.381713 | −0.190856 | − | 0.981618i | \(-0.561126\pi\) | ||||
−0.190856 | + | 0.981618i | \(0.561126\pi\) | |||||||
\(420\) | −1.65923 | −0.0809623 | ||||||||
\(421\) | −29.1874 | −1.42251 | −0.711253 | − | 0.702936i | \(-0.751872\pi\) | ||||
−0.711253 | + | 0.702936i | \(0.751872\pi\) | |||||||
\(422\) | −24.5746 | −1.19627 | ||||||||
\(423\) | 82.8214 | 4.02691 | ||||||||
\(424\) | 3.18512 | 0.154683 | ||||||||
\(425\) | −28.9879 | −1.40612 | ||||||||
\(426\) | 21.1567 | 1.02505 | ||||||||
\(427\) | 3.73389 | 0.180695 | ||||||||
\(428\) | 18.9251 | 0.914779 | ||||||||
\(429\) | −5.34176 | −0.257903 | ||||||||
\(430\) | 3.81146 | 0.183805 | ||||||||
\(431\) | 1.27732 | 0.0615266 | 0.0307633 | − | 0.999527i | \(-0.490206\pi\) | ||||
0.0307633 | + | 0.999527i | \(0.490206\pi\) | |||||||
\(432\) | 11.9815 | 0.576458 | ||||||||
\(433\) | 15.5705 | 0.748272 | 0.374136 | − | 0.927374i | \(-0.377939\pi\) | ||||
0.374136 | + | 0.927374i | \(0.377939\pi\) | |||||||
\(434\) | −0.736319 | −0.0353444 | ||||||||
\(435\) | −0.336165 | −0.0161179 | ||||||||
\(436\) | −14.8991 | −0.713536 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −51.3197 | −2.45215 | ||||||||
\(439\) | 20.3046 | 0.969084 | 0.484542 | − | 0.874768i | \(-0.338986\pi\) | ||||
0.484542 | + | 0.874768i | \(0.338986\pi\) | |||||||
\(440\) | −1.74595 | −0.0832349 | ||||||||
\(441\) | 6.82288 | 0.324899 | ||||||||
\(442\) | −3.17410 | −0.150976 | ||||||||
\(443\) | −5.99965 | −0.285052 | −0.142526 | − | 0.989791i | \(-0.545522\pi\) | ||||
−0.142526 | + | 0.989791i | \(0.545522\pi\) | |||||||
\(444\) | 34.1383 | 1.62013 | ||||||||
\(445\) | −8.58112 | −0.406784 | ||||||||
\(446\) | −18.4764 | −0.874882 | ||||||||
\(447\) | −57.0454 | −2.69816 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −22.1087 | −1.04338 | −0.521688 | − | 0.853136i | \(-0.674698\pi\) | ||||
−0.521688 | + | 0.853136i | \(0.674698\pi\) | |||||||
\(450\) | 32.2021 | 1.51802 | ||||||||
\(451\) | 12.1666 | 0.572901 | ||||||||
\(452\) | 1.20410 | 0.0566361 | ||||||||
\(453\) | −65.0594 | −3.05676 | ||||||||
\(454\) | −3.85747 | −0.181040 | ||||||||
\(455\) | −0.273596 | −0.0128264 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.4648 | −0.629859 | −0.314929 | − | 0.949115i | \(-0.601981\pi\) | ||||
−0.314929 | + | 0.949115i | \(0.601981\pi\) | |||||||
\(458\) | 11.4759 | 0.536234 | ||||||||
\(459\) | 73.5883 | 3.43481 | ||||||||
\(460\) | 3.01281 | 0.140473 | ||||||||
\(461\) | 7.05129 | 0.328411 | 0.164206 | − | 0.986426i | \(-0.447494\pi\) | ||||
0.164206 | + | 0.986426i | \(0.447494\pi\) | |||||||
\(462\) | 10.3363 | 0.480886 | ||||||||
\(463\) | 8.47412 | 0.393826 | 0.196913 | − | 0.980421i | \(-0.436908\pi\) | ||||
0.196913 | + | 0.980421i | \(0.436908\pi\) | |||||||
\(464\) | 0.202602 | 0.00940558 | ||||||||
\(465\) | −1.22172 | −0.0566561 | ||||||||
\(466\) | 10.2608 | 0.475321 | ||||||||
\(467\) | 30.8727 | 1.42862 | 0.714308 | − | 0.699832i | \(-0.246742\pi\) | ||||
0.714308 | + | 0.699832i | \(0.246742\pi\) | |||||||
\(468\) | 3.52605 | 0.162992 | ||||||||
\(469\) | 9.77683 | 0.451452 | ||||||||
\(470\) | 6.42633 | 0.296424 | ||||||||
\(471\) | 32.6151 | 1.50282 | ||||||||
\(472\) | −3.91656 | −0.180275 | ||||||||
\(473\) | −23.7437 | −1.09173 | ||||||||
\(474\) | −27.2460 | −1.25145 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.14185 | 0.281511 | ||||||||
\(477\) | −21.7317 | −0.995024 | ||||||||
\(478\) | 18.9095 | 0.864900 | ||||||||
\(479\) | −28.5989 | −1.30671 | −0.653357 | − | 0.757050i | \(-0.726640\pi\) | ||||
−0.653357 | + | 0.757050i | \(0.726640\pi\) | |||||||
\(480\) | 1.65923 | 0.0757333 | ||||||||
\(481\) | 5.62916 | 0.256668 | ||||||||
\(482\) | −11.5763 | −0.527288 | ||||||||
\(483\) | −17.8362 | −0.811577 | ||||||||
\(484\) | −0.123528 | −0.00561489 | ||||||||
\(485\) | 1.39373 | 0.0632859 | ||||||||
\(486\) | −17.5963 | −0.798184 | ||||||||
\(487\) | 35.6285 | 1.61448 | 0.807240 | − | 0.590223i | \(-0.200960\pi\) | ||||
0.807240 | + | 0.590223i | \(0.200960\pi\) | |||||||
\(488\) | −3.73389 | −0.169025 | ||||||||
\(489\) | −55.8347 | −2.52493 | ||||||||
\(490\) | 0.529405 | 0.0239161 | ||||||||
\(491\) | 12.1881 | 0.550039 | 0.275020 | − | 0.961439i | \(-0.411316\pi\) | ||||
0.275020 | + | 0.961439i | \(0.411316\pi\) | |||||||
\(492\) | −11.5623 | −0.521268 | ||||||||
\(493\) | 1.24435 | 0.0560429 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.9124 | 0.535423 | ||||||||
\(496\) | 0.736319 | 0.0330617 | ||||||||
\(497\) | −6.75039 | −0.302796 | ||||||||
\(498\) | 56.5242 | 2.53291 | ||||||||
\(499\) | 1.69496 | 0.0758766 | 0.0379383 | − | 0.999280i | \(-0.487921\pi\) | ||||
0.0379383 | + | 0.999280i | \(0.487921\pi\) | |||||||
\(500\) | 5.14567 | 0.230122 | ||||||||
\(501\) | 24.8778 | 1.11146 | ||||||||
\(502\) | −26.8853 | −1.19995 | ||||||||
\(503\) | 6.70132 | 0.298797 | 0.149398 | − | 0.988777i | \(-0.452266\pi\) | ||||
0.149398 | + | 0.988777i | \(0.452266\pi\) | |||||||
\(504\) | −6.82288 | −0.303915 | ||||||||
\(505\) | −5.20796 | −0.231751 | ||||||||
\(506\) | −18.7684 | −0.834358 | ||||||||
\(507\) | −39.9068 | −1.77232 | ||||||||
\(508\) | −0.707401 | −0.0313858 | ||||||||
\(509\) | 16.9421 | 0.750946 | 0.375473 | − | 0.926833i | \(-0.377480\pi\) | ||||
0.375473 | + | 0.926833i | \(0.377480\pi\) | |||||||
\(510\) | 10.1908 | 0.451255 | ||||||||
\(511\) | 16.3744 | 0.724360 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.2469 | −0.584295 | ||||||||
\(515\) | 2.28497 | 0.100688 | ||||||||
\(516\) | 22.5644 | 0.993340 | ||||||||
\(517\) | −40.0331 | −1.76065 | ||||||||
\(518\) | −10.8924 | −0.478583 | ||||||||
\(519\) | 30.3805 | 1.33356 | ||||||||
\(520\) | 0.273596 | 0.0119980 | ||||||||
\(521\) | −11.8846 | −0.520675 | −0.260338 | − | 0.965518i | \(-0.583834\pi\) | ||||
−0.260338 | + | 0.965518i | \(0.583834\pi\) | |||||||
\(522\) | −1.38233 | −0.0605030 | ||||||||
\(523\) | −4.32787 | −0.189244 | −0.0946222 | − | 0.995513i | \(-0.530164\pi\) | ||||
−0.0946222 | + | 0.995513i | \(0.530164\pi\) | |||||||
\(524\) | −10.3358 | −0.451522 | ||||||||
\(525\) | −14.7923 | −0.645590 | ||||||||
\(526\) | 1.67507 | 0.0730364 | ||||||||
\(527\) | 4.52236 | 0.196997 | ||||||||
\(528\) | −10.3363 | −0.449828 | ||||||||
\(529\) | 9.38678 | 0.408121 | ||||||||
\(530\) | −1.68622 | −0.0732446 | ||||||||
\(531\) | 26.7222 | 1.15965 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.90654 | −0.0825812 | ||||||||
\(534\) | −50.8013 | −2.19839 | ||||||||
\(535\) | −10.0190 | −0.433161 | ||||||||
\(536\) | −9.77683 | −0.422295 | ||||||||
\(537\) | −43.7081 | −1.88615 | ||||||||
\(538\) | 13.7127 | 0.591196 | ||||||||
\(539\) | −3.29795 | −0.142053 | ||||||||
\(540\) | −6.34304 | −0.272961 | ||||||||
\(541\) | −24.5223 | −1.05430 | −0.527148 | − | 0.849773i | \(-0.676739\pi\) | ||||
−0.527148 | + | 0.849773i | \(0.676739\pi\) | |||||||
\(542\) | 21.3184 | 0.915704 | ||||||||
\(543\) | 60.0416 | 2.57663 | ||||||||
\(544\) | −6.14185 | −0.263330 | ||||||||
\(545\) | 7.88765 | 0.337870 | ||||||||
\(546\) | −1.61972 | −0.0693177 | ||||||||
\(547\) | −5.73732 | −0.245310 | −0.122655 | − | 0.992449i | \(-0.539141\pi\) | ||||
−0.122655 | + | 0.992449i | \(0.539141\pi\) | |||||||
\(548\) | 4.56839 | 0.195152 | ||||||||
\(549\) | 25.4758 | 1.08728 | ||||||||
\(550\) | −15.5654 | −0.663712 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 17.8362 | 0.759161 | ||||||||
\(553\) | 8.69327 | 0.369675 | ||||||||
\(554\) | −12.9204 | −0.548936 | ||||||||
\(555\) | −18.0730 | −0.767155 | ||||||||
\(556\) | −6.04179 | −0.256229 | ||||||||
\(557\) | 24.4382 | 1.03548 | 0.517741 | − | 0.855537i | \(-0.326773\pi\) | ||||
0.517741 | + | 0.855537i | \(0.326773\pi\) | |||||||
\(558\) | −5.02381 | −0.212675 | ||||||||
\(559\) | 3.72070 | 0.157369 | ||||||||
\(560\) | −0.529405 | −0.0223714 | ||||||||
\(561\) | −63.4838 | −2.68029 | ||||||||
\(562\) | −2.53217 | −0.106813 | ||||||||
\(563\) | −17.0563 | −0.718837 | −0.359419 | − | 0.933176i | \(-0.617025\pi\) | ||||
−0.359419 | + | 0.933176i | \(0.617025\pi\) | |||||||
\(564\) | 38.0447 | 1.60197 | ||||||||
\(565\) | −0.637457 | −0.0268180 | ||||||||
\(566\) | −7.18663 | −0.302077 | ||||||||
\(567\) | 17.0830 | 0.717419 | ||||||||
\(568\) | 6.75039 | 0.283240 | ||||||||
\(569\) | 12.1689 | 0.510148 | 0.255074 | − | 0.966922i | \(-0.417900\pi\) | ||||
0.255074 | + | 0.966922i | \(0.417900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.5696 | −1.19560 | −0.597801 | − | 0.801644i | \(-0.703959\pi\) | ||||
−0.597801 | + | 0.801644i | \(0.703959\pi\) | |||||||
\(572\) | −1.70437 | −0.0712635 | ||||||||
\(573\) | −40.0842 | −1.67454 | ||||||||
\(574\) | 3.68913 | 0.153981 | ||||||||
\(575\) | 26.8597 | 1.12013 | ||||||||
\(576\) | 6.82288 | 0.284287 | ||||||||
\(577\) | 11.2721 | 0.469263 | 0.234632 | − | 0.972084i | \(-0.424612\pi\) | ||||
0.234632 | + | 0.972084i | \(0.424612\pi\) | |||||||
\(578\) | −20.7223 | −0.861936 | ||||||||
\(579\) | 32.7263 | 1.36006 | ||||||||
\(580\) | −0.107259 | −0.00445368 | ||||||||
\(581\) | −18.0349 | −0.748216 | ||||||||
\(582\) | 8.25105 | 0.342017 | ||||||||
\(583\) | 10.5044 | 0.435046 | ||||||||
\(584\) | −16.3744 | −0.677577 | ||||||||
\(585\) | −1.86671 | −0.0771789 | ||||||||
\(586\) | −1.03791 | −0.0428755 | ||||||||
\(587\) | 19.7831 | 0.816537 | 0.408269 | − | 0.912862i | \(-0.366133\pi\) | ||||
0.408269 | + | 0.912862i | \(0.366133\pi\) | |||||||
\(588\) | 3.13415 | 0.129250 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 2.07345 | 0.0853625 | ||||||||
\(591\) | 2.56173 | 0.105375 | ||||||||
\(592\) | 10.8924 | 0.447674 | ||||||||
\(593\) | 23.3997 | 0.960911 | 0.480455 | − | 0.877019i | \(-0.340471\pi\) | ||||
0.480455 | + | 0.877019i | \(0.340471\pi\) | |||||||
\(594\) | 39.5142 | 1.62129 | ||||||||
\(595\) | −3.25153 | −0.133300 | ||||||||
\(596\) | −18.2013 | −0.745553 | ||||||||
\(597\) | −24.4801 | −1.00190 | ||||||||
\(598\) | 2.94107 | 0.120269 | ||||||||
\(599\) | 15.5005 | 0.633334 | 0.316667 | − | 0.948537i | \(-0.397436\pi\) | ||||
0.316667 | + | 0.948537i | \(0.397436\pi\) | |||||||
\(600\) | 14.7923 | 0.603894 | ||||||||
\(601\) | 41.8017 | 1.70513 | 0.852564 | − | 0.522623i | \(-0.175046\pi\) | ||||
0.852564 | + | 0.522623i | \(0.175046\pi\) | |||||||
\(602\) | −7.19952 | −0.293431 | ||||||||
\(603\) | 66.7061 | 2.71648 | ||||||||
\(604\) | −20.7582 | −0.844641 | ||||||||
\(605\) | 0.0653962 | 0.00265873 | ||||||||
\(606\) | −30.8318 | −1.25246 | ||||||||
\(607\) | −45.2892 | −1.83823 | −0.919117 | − | 0.393985i | \(-0.871096\pi\) | ||||
−0.919117 | + | 0.393985i | \(0.871096\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.634986 | 0.0257309 | ||||||||
\(610\) | 1.97674 | 0.0800358 | ||||||||
\(611\) | 6.27330 | 0.253791 | ||||||||
\(612\) | 41.9051 | 1.69391 | ||||||||
\(613\) | 26.3197 | 1.06304 | 0.531521 | − | 0.847045i | \(-0.321621\pi\) | ||||
0.531521 | + | 0.847045i | \(0.321621\pi\) | |||||||
\(614\) | 8.78461 | 0.354518 | ||||||||
\(615\) | 6.12113 | 0.246828 | ||||||||
\(616\) | 3.29795 | 0.132878 | ||||||||
\(617\) | 40.1140 | 1.61493 | 0.807464 | − | 0.589917i | \(-0.200840\pi\) | ||||
0.807464 | + | 0.589917i | \(0.200840\pi\) | |||||||
\(618\) | 13.5273 | 0.544150 | ||||||||
\(619\) | −28.6211 | −1.15038 | −0.575191 | − | 0.818019i | \(-0.695072\pi\) | ||||
−0.575191 | + | 0.818019i | \(0.695072\pi\) | |||||||
\(620\) | −0.389811 | −0.0156552 | ||||||||
\(621\) | −68.1857 | −2.73620 | ||||||||
\(622\) | 0.240874 | 0.00965818 | ||||||||
\(623\) | 16.2090 | 0.649399 | ||||||||
\(624\) | 1.61972 | 0.0648408 | ||||||||
\(625\) | 20.8745 | 0.834980 | ||||||||
\(626\) | −1.87814 | −0.0750658 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.4064 | 0.415259 | ||||||||
\(629\) | 66.8993 | 2.66745 | ||||||||
\(630\) | 3.61206 | 0.143908 | ||||||||
\(631\) | −13.9752 | −0.556345 | −0.278172 | − | 0.960531i | \(-0.589729\pi\) | ||||
−0.278172 | + | 0.960531i | \(0.589729\pi\) | |||||||
\(632\) | −8.69327 | −0.345800 | ||||||||
\(633\) | 77.0204 | 3.06129 | ||||||||
\(634\) | 33.6024 | 1.33452 | ||||||||
\(635\) | 0.374502 | 0.0148616 | ||||||||
\(636\) | −9.98262 | −0.395837 | ||||||||
\(637\) | 0.516798 | 0.0204763 | ||||||||
\(638\) | 0.668173 | 0.0264532 | ||||||||
\(639\) | −46.0571 | −1.82199 | ||||||||
\(640\) | 0.529405 | 0.0209266 | ||||||||
\(641\) | −40.3587 | −1.59407 | −0.797037 | − | 0.603931i | \(-0.793600\pi\) | ||||
−0.797037 | + | 0.603931i | \(0.793600\pi\) | |||||||
\(642\) | −59.3140 | −2.34094 | ||||||||
\(643\) | 0.0182292 | 0.000718890 0 | 0.000359445 | − | 1.00000i | \(-0.499886\pi\) | ||||
0.000359445 | 1.00000i | \(0.499886\pi\) | ||||||||
\(644\) | −5.69094 | −0.224254 | ||||||||
\(645\) | −11.9457 | −0.470361 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.8386 | 0.779937 | 0.389968 | − | 0.920828i | \(-0.372486\pi\) | ||||
0.389968 | + | 0.920828i | \(0.372486\pi\) | |||||||
\(648\) | −17.0830 | −0.671084 | ||||||||
\(649\) | −12.9166 | −0.507022 | ||||||||
\(650\) | 2.43915 | 0.0956713 | ||||||||
\(651\) | 2.30773 | 0.0904472 | ||||||||
\(652\) | −17.8149 | −0.697687 | ||||||||
\(653\) | −42.0361 | −1.64500 | −0.822500 | − | 0.568765i | \(-0.807421\pi\) | ||||
−0.822500 | + | 0.568765i | \(0.807421\pi\) | |||||||
\(654\) | 46.6959 | 1.82595 | ||||||||
\(655\) | 5.47183 | 0.213802 | ||||||||
\(656\) | −3.68913 | −0.144036 | ||||||||
\(657\) | 111.720 | 4.35863 | ||||||||
\(658\) | −12.1388 | −0.473219 | ||||||||
\(659\) | −16.5518 | −0.644765 | −0.322382 | − | 0.946610i | \(-0.604484\pi\) | ||||
−0.322382 | + | 0.946610i | \(0.604484\pi\) | |||||||
\(660\) | 5.47207 | 0.213000 | ||||||||
\(661\) | −29.7497 | −1.15713 | −0.578565 | − | 0.815636i | \(-0.696387\pi\) | ||||
−0.578565 | + | 0.815636i | \(0.696387\pi\) | |||||||
\(662\) | 11.1959 | 0.435141 | ||||||||
\(663\) | 9.94809 | 0.386352 | ||||||||
\(664\) | 18.0349 | 0.699892 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −74.3173 | −2.87974 | ||||||||
\(667\) | −1.15300 | −0.0446443 | ||||||||
\(668\) | 7.93765 | 0.307117 | ||||||||
\(669\) | 57.9077 | 2.23884 | ||||||||
\(670\) | 5.17590 | 0.199963 | ||||||||
\(671\) | −12.3142 | −0.475383 | ||||||||
\(672\) | −3.13415 | −0.120902 | ||||||||
\(673\) | −13.3441 | −0.514376 | −0.257188 | − | 0.966361i | \(-0.582796\pi\) | ||||
−0.257188 | + | 0.966361i | \(0.582796\pi\) | |||||||
\(674\) | −15.5993 | −0.600861 | ||||||||
\(675\) | −56.5492 | −2.17658 | ||||||||
\(676\) | −12.7329 | −0.489728 | ||||||||
\(677\) | 18.0194 | 0.692543 | 0.346271 | − | 0.938134i | \(-0.387448\pi\) | ||||
0.346271 | + | 0.938134i | \(0.387448\pi\) | |||||||
\(678\) | −3.77383 | −0.144933 | ||||||||
\(679\) | −2.63263 | −0.101031 | ||||||||
\(680\) | 3.25153 | 0.124690 | ||||||||
\(681\) | 12.0899 | 0.463285 | ||||||||
\(682\) | 2.42834 | 0.0929861 | ||||||||
\(683\) | −11.8762 | −0.454431 | −0.227216 | − | 0.973845i | \(-0.572962\pi\) | ||||
−0.227216 | + | 0.973845i | \(0.572962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.41853 | −0.0924072 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −35.9672 | −1.37223 | ||||||||
\(688\) | 7.19952 | 0.274479 | ||||||||
\(689\) | −1.64606 | −0.0627100 | ||||||||
\(690\) | −9.44259 | −0.359473 | ||||||||
\(691\) | 10.8249 | 0.411799 | 0.205899 | − | 0.978573i | \(-0.433988\pi\) | ||||
0.205899 | + | 0.978573i | \(0.433988\pi\) | |||||||
\(692\) | 9.69338 | 0.368487 | ||||||||
\(693\) | −22.5015 | −0.854761 | ||||||||
\(694\) | 17.2497 | 0.654789 | ||||||||
\(695\) | 3.19855 | 0.121328 | ||||||||
\(696\) | −0.634986 | −0.0240691 | ||||||||
\(697\) | −22.6581 | −0.858236 | ||||||||
\(698\) | −2.55529 | −0.0967193 | ||||||||
\(699\) | −32.1588 | −1.21636 | ||||||||
\(700\) | −4.71973 | −0.178389 | ||||||||
\(701\) | 13.6726 | 0.516408 | 0.258204 | − | 0.966090i | \(-0.416869\pi\) | ||||
0.258204 | + | 0.966090i | \(0.416869\pi\) | |||||||
\(702\) | −6.19199 | −0.233702 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −3.29795 | −0.124296 | ||||||||
\(705\) | −20.1411 | −0.758556 | ||||||||
\(706\) | 27.4877 | 1.03451 | ||||||||
\(707\) | 9.83739 | 0.369973 | ||||||||
\(708\) | 12.2751 | 0.461326 | ||||||||
\(709\) | −46.0283 | −1.72863 | −0.864314 | − | 0.502953i | \(-0.832247\pi\) | ||||
−0.864314 | + | 0.502953i | \(0.832247\pi\) | |||||||
\(710\) | −3.57369 | −0.134118 | ||||||||
\(711\) | 59.3131 | 2.22441 | ||||||||
\(712\) | −16.2090 | −0.607457 | ||||||||
\(713\) | −4.19035 | −0.156930 | ||||||||
\(714\) | −19.2495 | −0.720393 | ||||||||
\(715\) | 0.902304 | 0.0337443 | ||||||||
\(716\) | −13.9458 | −0.521178 | ||||||||
\(717\) | −59.2651 | −2.21330 | ||||||||
\(718\) | 15.4937 | 0.578221 | ||||||||
\(719\) | 19.4728 | 0.726214 | 0.363107 | − | 0.931748i | \(-0.381716\pi\) | ||||
0.363107 | + | 0.931748i | \(0.381716\pi\) | |||||||
\(720\) | −3.61206 | −0.134614 | ||||||||
\(721\) | −4.31612 | −0.160741 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.2820 | 1.34934 | ||||||||
\(724\) | 19.1572 | 0.711973 | ||||||||
\(725\) | −0.956229 | −0.0355135 | ||||||||
\(726\) | 0.387154 | 0.0143686 | ||||||||
\(727\) | 39.9706 | 1.48243 | 0.741214 | − | 0.671269i | \(-0.234250\pi\) | ||||
0.741214 | + | 0.671269i | \(0.234250\pi\) | |||||||
\(728\) | −0.516798 | −0.0191538 | ||||||||
\(729\) | 3.90035 | 0.144458 | ||||||||
\(730\) | 8.66868 | 0.320842 | ||||||||
\(731\) | 44.2184 | 1.63548 | ||||||||
\(732\) | 11.7025 | 0.432539 | ||||||||
\(733\) | −21.1476 | −0.781105 | −0.390553 | − | 0.920581i | \(-0.627716\pi\) | ||||
−0.390553 | + | 0.920581i | \(0.627716\pi\) | |||||||
\(734\) | 26.5673 | 0.980617 | ||||||||
\(735\) | −1.65923 | −0.0612017 | ||||||||
\(736\) | 5.69094 | 0.209771 | ||||||||
\(737\) | −32.2435 | −1.18770 | ||||||||
\(738\) | 25.1705 | 0.926538 | ||||||||
\(739\) | −42.1012 | −1.54872 | −0.774359 | − | 0.632746i | \(-0.781928\pi\) | ||||
−0.774359 | + | 0.632746i | \(0.781928\pi\) | |||||||
\(740\) | −5.76648 | −0.211980 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.18512 | 0.116929 | ||||||||
\(743\) | −18.1350 | −0.665308 | −0.332654 | − | 0.943049i | \(-0.607944\pi\) | ||||
−0.332654 | + | 0.943049i | \(0.607944\pi\) | |||||||
\(744\) | −2.30773 | −0.0846056 | ||||||||
\(745\) | 9.63584 | 0.353030 | ||||||||
\(746\) | −14.5329 | −0.532089 | ||||||||
\(747\) | −123.050 | −4.50217 | ||||||||
\(748\) | −20.2555 | −0.740615 | ||||||||
\(749\) | 18.9251 | 0.691508 | ||||||||
\(750\) | −16.1273 | −0.588886 | ||||||||
\(751\) | 10.4898 | 0.382780 | 0.191390 | − | 0.981514i | \(-0.438700\pi\) | ||||
0.191390 | + | 0.981514i | \(0.438700\pi\) | |||||||
\(752\) | 12.1388 | 0.442656 | ||||||||
\(753\) | 84.2625 | 3.07069 | ||||||||
\(754\) | −0.104705 | −0.00381312 | ||||||||
\(755\) | 10.9895 | 0.399949 | ||||||||
\(756\) | 11.9815 | 0.435761 | ||||||||
\(757\) | 12.0758 | 0.438904 | 0.219452 | − | 0.975623i | \(-0.429573\pi\) | ||||
0.219452 | + | 0.975623i | \(0.429573\pi\) | |||||||
\(758\) | −23.1135 | −0.839521 | ||||||||
\(759\) | 58.8230 | 2.13514 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.0992 | −1.01859 | −0.509297 | − | 0.860591i | \(-0.670094\pi\) | ||||
−0.509297 | + | 0.860591i | \(0.670094\pi\) | |||||||
\(762\) | 2.21710 | 0.0803170 | ||||||||
\(763\) | −14.8991 | −0.539383 | ||||||||
\(764\) | −12.7895 | −0.462709 | ||||||||
\(765\) | −22.1848 | −0.802092 | ||||||||
\(766\) | 25.5356 | 0.922639 | ||||||||
\(767\) | 2.02407 | 0.0730851 | ||||||||
\(768\) | 3.13415 | 0.113094 | ||||||||
\(769\) | 34.2232 | 1.23412 | 0.617060 | − | 0.786916i | \(-0.288324\pi\) | ||||
0.617060 | + | 0.786916i | \(0.288324\pi\) | |||||||
\(770\) | −1.74595 | −0.0629197 | ||||||||
\(771\) | 41.5177 | 1.49522 | ||||||||
\(772\) | 10.4419 | 0.375811 | ||||||||
\(773\) | −34.5711 | −1.24344 | −0.621719 | − | 0.783241i | \(-0.713565\pi\) | ||||
−0.621719 | + | 0.783241i | \(0.713565\pi\) | |||||||
\(774\) | −49.1214 | −1.76563 | ||||||||
\(775\) | −3.47523 | −0.124834 | ||||||||
\(776\) | 2.63263 | 0.0945059 | ||||||||
\(777\) | 34.1383 | 1.22470 | ||||||||
\(778\) | 30.1536 | 1.08106 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.857489 | −0.0307030 | ||||||||
\(781\) | 22.2624 | 0.796613 | ||||||||
\(782\) | 34.9529 | 1.24991 | ||||||||
\(783\) | 2.42747 | 0.0867508 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −5.50919 | −0.196631 | ||||||||
\(786\) | 32.3939 | 1.15545 | ||||||||
\(787\) | 38.3673 | 1.36765 | 0.683823 | − | 0.729648i | \(-0.260316\pi\) | ||||
0.683823 | + | 0.729648i | \(0.260316\pi\) | |||||||
\(788\) | 0.817360 | 0.0291173 | ||||||||
\(789\) | −5.24991 | −0.186902 | ||||||||
\(790\) | 4.60226 | 0.163741 | ||||||||
\(791\) | 1.20410 | 0.0428129 | ||||||||
\(792\) | 22.5015 | 0.799556 | ||||||||
\(793\) | 1.92967 | 0.0685244 | ||||||||
\(794\) | 13.9802 | 0.496139 | ||||||||
\(795\) | 5.28485 | 0.187434 | ||||||||
\(796\) | −7.81078 | −0.276846 | ||||||||
\(797\) | 35.5206 | 1.25820 | 0.629102 | − | 0.777323i | \(-0.283423\pi\) | ||||
0.629102 | + | 0.777323i | \(0.283423\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 74.5546 | 2.63755 | ||||||||
\(800\) | 4.71973 | 0.166868 | ||||||||
\(801\) | 110.592 | 3.90757 | ||||||||
\(802\) | 17.6953 | 0.624843 | ||||||||
\(803\) | −54.0019 | −1.90569 | ||||||||
\(804\) | 30.6420 | 1.08066 | ||||||||
\(805\) | 3.01281 | 0.106188 | ||||||||
\(806\) | −0.380528 | −0.0134035 | ||||||||
\(807\) | −42.9776 | −1.51288 | ||||||||
\(808\) | −9.83739 | −0.346078 | ||||||||
\(809\) | 12.0795 | 0.424693 | 0.212347 | − | 0.977194i | \(-0.431889\pi\) | ||||
0.212347 | + | 0.977194i | \(0.431889\pi\) | |||||||
\(810\) | 9.04383 | 0.317768 | ||||||||
\(811\) | 28.4964 | 1.00065 | 0.500323 | − | 0.865839i | \(-0.333215\pi\) | ||||
0.500323 | + | 0.865839i | \(0.333215\pi\) | |||||||
\(812\) | 0.202602 | 0.00710995 | ||||||||
\(813\) | −66.8150 | −2.34331 | ||||||||
\(814\) | 35.9225 | 1.25908 | ||||||||
\(815\) | 9.43132 | 0.330365 | ||||||||
\(816\) | 19.2495 | 0.673866 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −12.5454 | −0.438639 | ||||||||
\(819\) | 3.52605 | 0.123210 | ||||||||
\(820\) | 1.95304 | 0.0682032 | ||||||||
\(821\) | 37.6434 | 1.31376 | 0.656882 | − | 0.753993i | \(-0.271875\pi\) | ||||
0.656882 | + | 0.753993i | \(0.271875\pi\) | |||||||
\(822\) | −14.3180 | −0.499398 | ||||||||
\(823\) | −9.09651 | −0.317084 | −0.158542 | − | 0.987352i | \(-0.550679\pi\) | ||||
−0.158542 | + | 0.987352i | \(0.550679\pi\) | |||||||
\(824\) | 4.31612 | 0.150359 | ||||||||
\(825\) | 48.7844 | 1.69845 | ||||||||
\(826\) | −3.91656 | −0.136275 | ||||||||
\(827\) | 11.1658 | 0.388274 | 0.194137 | − | 0.980974i | \(-0.437809\pi\) | ||||
0.194137 | + | 0.980974i | \(0.437809\pi\) | |||||||
\(828\) | −38.8286 | −1.34939 | ||||||||
\(829\) | 29.0197 | 1.00790 | 0.503948 | − | 0.863734i | \(-0.331880\pi\) | ||||
0.503948 | + | 0.863734i | \(0.331880\pi\) | |||||||
\(830\) | −9.54779 | −0.331409 | ||||||||
\(831\) | 40.4945 | 1.40474 | ||||||||
\(832\) | 0.516798 | 0.0179168 | ||||||||
\(833\) | 6.14185 | 0.212803 | ||||||||
\(834\) | 18.9358 | 0.655695 | ||||||||
\(835\) | −4.20223 | −0.145424 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.82217 | 0.304939 | ||||||||
\(838\) | 7.81346 | 0.269912 | ||||||||
\(839\) | 16.3525 | 0.564552 | 0.282276 | − | 0.959333i | \(-0.408911\pi\) | ||||
0.282276 | + | 0.959333i | \(0.408911\pi\) | |||||||
\(840\) | 1.65923 | 0.0572490 | ||||||||
\(841\) | −28.9590 | −0.998585 | ||||||||
\(842\) | 29.1874 | 1.00586 | ||||||||
\(843\) | 7.93619 | 0.273337 | ||||||||
\(844\) | 24.5746 | 0.845893 | ||||||||
\(845\) | 6.74087 | 0.231893 | ||||||||
\(846\) | −82.8214 | −2.84746 | ||||||||
\(847\) | −0.123528 | −0.00424446 | ||||||||
\(848\) | −3.18512 | −0.109377 | ||||||||
\(849\) | 22.5240 | 0.773020 | ||||||||
\(850\) | 28.9879 | 0.994276 | ||||||||
\(851\) | −61.9878 | −2.12492 | ||||||||
\(852\) | −21.1567 | −0.724817 | ||||||||
\(853\) | 2.01194 | 0.0688873 | 0.0344437 | − | 0.999407i | \(-0.489034\pi\) | ||||
0.0344437 | + | 0.999407i | \(0.489034\pi\) | |||||||
\(854\) | −3.73389 | −0.127771 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.9251 | −0.646847 | ||||||||
\(857\) | 24.2234 | 0.827454 | 0.413727 | − | 0.910401i | \(-0.364227\pi\) | ||||
0.413727 | + | 0.910401i | \(0.364227\pi\) | |||||||
\(858\) | 5.34176 | 0.182365 | ||||||||
\(859\) | 3.77776 | 0.128895 | 0.0644477 | − | 0.997921i | \(-0.479471\pi\) | ||||
0.0644477 | + | 0.997921i | \(0.479471\pi\) | |||||||
\(860\) | −3.81146 | −0.129970 | ||||||||
\(861\) | −11.5623 | −0.394041 | ||||||||
\(862\) | −1.27732 | −0.0435059 | ||||||||
\(863\) | −14.3259 | −0.487658 | −0.243829 | − | 0.969818i | \(-0.578404\pi\) | ||||
−0.243829 | + | 0.969818i | \(0.578404\pi\) | |||||||
\(864\) | −11.9815 | −0.407617 | ||||||||
\(865\) | −5.13172 | −0.174484 | ||||||||
\(866\) | −15.5705 | −0.529108 | ||||||||
\(867\) | 64.9469 | 2.20571 | ||||||||
\(868\) | 0.736319 | 0.0249923 | ||||||||
\(869\) | −28.6700 | −0.972562 | ||||||||
\(870\) | 0.336165 | 0.0113971 | ||||||||
\(871\) | 5.05265 | 0.171203 | ||||||||
\(872\) | 14.8991 | 0.504546 | ||||||||
\(873\) | −17.9621 | −0.607925 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.14567 | 0.173956 | ||||||||
\(876\) | 51.3197 | 1.73393 | ||||||||
\(877\) | −16.9707 | −0.573060 | −0.286530 | − | 0.958071i | \(-0.592502\pi\) | ||||
−0.286530 | + | 0.958071i | \(0.592502\pi\) | |||||||
\(878\) | −20.3046 | −0.685246 | ||||||||
\(879\) | 3.25295 | 0.109719 | ||||||||
\(880\) | 1.74595 | 0.0588560 | ||||||||
\(881\) | −13.8679 | −0.467221 | −0.233611 | − | 0.972330i | \(-0.575054\pi\) | ||||
−0.233611 | + | 0.972330i | \(0.575054\pi\) | |||||||
\(882\) | −6.82288 | −0.229738 | ||||||||
\(883\) | −12.6029 | −0.424123 | −0.212061 | − | 0.977256i | \(-0.568018\pi\) | ||||
−0.212061 | + | 0.977256i | \(0.568018\pi\) | |||||||
\(884\) | 3.17410 | 0.106756 | ||||||||
\(885\) | −6.49849 | −0.218444 | ||||||||
\(886\) | 5.99965 | 0.201562 | ||||||||
\(887\) | −49.9001 | −1.67548 | −0.837740 | − | 0.546069i | \(-0.816124\pi\) | ||||
−0.837740 | + | 0.546069i | \(0.816124\pi\) | |||||||
\(888\) | −34.1383 | −1.14561 | ||||||||
\(889\) | −0.707401 | −0.0237255 | ||||||||
\(890\) | 8.58112 | 0.287640 | ||||||||
\(891\) | −56.3389 | −1.88742 | ||||||||
\(892\) | 18.4764 | 0.618635 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 57.0454 | 1.90788 | ||||||||
\(895\) | 7.38297 | 0.246785 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −9.21773 | −0.307771 | ||||||||
\(898\) | 22.1087 | 0.737778 | ||||||||
\(899\) | 0.149180 | 0.00497543 | ||||||||
\(900\) | −32.2021 | −1.07340 | ||||||||
\(901\) | −19.5625 | −0.651722 | ||||||||
\(902\) | −12.1666 | −0.405102 | ||||||||
\(903\) | 22.5644 | 0.750895 | ||||||||
\(904\) | −1.20410 | −0.0400478 | ||||||||
\(905\) | −10.1419 | −0.337129 | ||||||||
\(906\) | 65.0594 | 2.16145 | ||||||||
\(907\) | −3.19849 | −0.106204 | −0.0531020 | − | 0.998589i | \(-0.516911\pi\) | ||||
−0.0531020 | + | 0.998589i | \(0.516911\pi\) | |||||||
\(908\) | 3.85747 | 0.128015 | ||||||||
\(909\) | 67.1193 | 2.22621 | ||||||||
\(910\) | 0.273596 | 0.00906960 | ||||||||
\(911\) | −29.5246 | −0.978195 | −0.489097 | − | 0.872229i | \(-0.662674\pi\) | ||||
−0.489097 | + | 0.872229i | \(0.662674\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 59.4784 | 1.96845 | ||||||||
\(914\) | 13.4648 | 0.445378 | ||||||||
\(915\) | −6.19539 | −0.204813 | ||||||||
\(916\) | −11.4759 | −0.379175 | ||||||||
\(917\) | −10.3358 | −0.341318 | ||||||||
\(918\) | −73.5883 | −2.42878 | ||||||||
\(919\) | 4.15733 | 0.137138 | 0.0685689 | − | 0.997646i | \(-0.478157\pi\) | ||||
0.0685689 | + | 0.997646i | \(0.478157\pi\) | |||||||
\(920\) | −3.01281 | −0.0993294 | ||||||||
\(921\) | −27.5323 | −0.907219 | ||||||||
\(922\) | −7.05129 | −0.232222 | ||||||||
\(923\) | −3.48859 | −0.114828 | ||||||||
\(924\) | −10.3363 | −0.340038 | ||||||||
\(925\) | −51.4091 | −1.69032 | ||||||||
\(926\) | −8.47412 | −0.278477 | ||||||||
\(927\) | −29.4483 | −0.967210 | ||||||||
\(928\) | −0.202602 | −0.00665075 | ||||||||
\(929\) | 30.8217 | 1.01123 | 0.505614 | − | 0.862760i | \(-0.331266\pi\) | ||||
0.505614 | + | 0.862760i | \(0.331266\pi\) | |||||||
\(930\) | 1.22172 | 0.0400619 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.2608 | −0.336103 | ||||||||
\(933\) | −0.754935 | −0.0247155 | ||||||||
\(934\) | −30.8727 | −1.01018 | ||||||||
\(935\) | 10.7234 | 0.350692 | ||||||||
\(936\) | −3.52605 | −0.115253 | ||||||||
\(937\) | 42.3822 | 1.38457 | 0.692284 | − | 0.721626i | \(-0.256605\pi\) | ||||
0.692284 | + | 0.721626i | \(0.256605\pi\) | |||||||
\(938\) | −9.77683 | −0.319225 | ||||||||
\(939\) | 5.88638 | 0.192095 | ||||||||
\(940\) | −6.42633 | −0.209604 | ||||||||
\(941\) | −39.7048 | −1.29434 | −0.647170 | − | 0.762346i | \(-0.724048\pi\) | ||||
−0.647170 | + | 0.762346i | \(0.724048\pi\) | |||||||
\(942\) | −32.6151 | −1.06266 | ||||||||
\(943\) | 20.9946 | 0.683679 | ||||||||
\(944\) | 3.91656 | 0.127473 | ||||||||
\(945\) | −6.34304 | −0.206339 | ||||||||
\(946\) | 23.7437 | 0.771973 | ||||||||
\(947\) | 52.6101 | 1.70960 | 0.854799 | − | 0.518959i | \(-0.173680\pi\) | ||||
0.854799 | + | 0.518959i | \(0.173680\pi\) | |||||||
\(948\) | 27.2460 | 0.884908 | ||||||||
\(949\) | 8.46225 | 0.274696 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −105.315 | −3.41506 | ||||||||
\(952\) | −6.14185 | −0.199059 | ||||||||
\(953\) | 12.3258 | 0.399271 | 0.199636 | − | 0.979870i | \(-0.436024\pi\) | ||||
0.199636 | + | 0.979870i | \(0.436024\pi\) | |||||||
\(954\) | 21.7317 | 0.703588 | ||||||||
\(955\) | 6.77084 | 0.219099 | ||||||||
\(956\) | −18.9095 | −0.611577 | ||||||||
\(957\) | −2.09415 | −0.0676943 | ||||||||
\(958\) | 28.5989 | 0.923987 | ||||||||
\(959\) | 4.56839 | 0.147521 | ||||||||
\(960\) | −1.65923 | −0.0535515 | ||||||||
\(961\) | −30.4578 | −0.982511 | ||||||||
\(962\) | −5.62916 | −0.181491 | ||||||||
\(963\) | 129.124 | 4.16095 | ||||||||
\(964\) | 11.5763 | 0.372849 | ||||||||
\(965\) | −5.52798 | −0.177952 | ||||||||
\(966\) | 17.8362 | 0.573871 | ||||||||
\(967\) | −26.2329 | −0.843594 | −0.421797 | − | 0.906690i | \(-0.638601\pi\) | ||||
−0.421797 | + | 0.906690i | \(0.638601\pi\) | |||||||
\(968\) | 0.123528 | 0.00397033 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.39373 | −0.0447499 | ||||||||
\(971\) | −38.3207 | −1.22977 | −0.614884 | − | 0.788617i | \(-0.710797\pi\) | ||||
−0.614884 | + | 0.788617i | \(0.710797\pi\) | |||||||
\(972\) | 17.5963 | 0.564402 | ||||||||
\(973\) | −6.04179 | −0.193691 | ||||||||
\(974\) | −35.6285 | −1.14161 | ||||||||
\(975\) | −7.64465 | −0.244825 | ||||||||
\(976\) | 3.73389 | 0.119519 | ||||||||
\(977\) | −30.1695 | −0.965209 | −0.482604 | − | 0.875838i | \(-0.660309\pi\) | ||||
−0.482604 | + | 0.875838i | \(0.660309\pi\) | |||||||
\(978\) | 55.8347 | 1.78540 | ||||||||
\(979\) | −53.4564 | −1.70847 | ||||||||
\(980\) | −0.529405 | −0.0169112 | ||||||||
\(981\) | −101.655 | −3.24558 | ||||||||
\(982\) | −12.1881 | −0.388937 | ||||||||
\(983\) | 10.5645 | 0.336955 | 0.168478 | − | 0.985705i | \(-0.446115\pi\) | ||||
0.168478 | + | 0.985705i | \(0.446115\pi\) | |||||||
\(984\) | 11.5623 | 0.368592 | ||||||||
\(985\) | −0.432715 | −0.0137874 | ||||||||
\(986\) | −1.24435 | −0.0396283 | ||||||||
\(987\) | 38.0447 | 1.21098 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −40.9720 | −1.30283 | ||||||||
\(990\) | −11.9124 | −0.378601 | ||||||||
\(991\) | 11.1078 | 0.352850 | 0.176425 | − | 0.984314i | \(-0.443547\pi\) | ||||
0.176425 | + | 0.984314i | \(0.443547\pi\) | |||||||
\(992\) | −0.736319 | −0.0233782 | ||||||||
\(993\) | −35.0896 | −1.11354 | ||||||||
\(994\) | 6.75039 | 0.214109 | ||||||||
\(995\) | 4.13506 | 0.131090 | ||||||||
\(996\) | −56.5242 | −1.79104 | ||||||||
\(997\) | 34.4533 | 1.09115 | 0.545573 | − | 0.838063i | \(-0.316312\pi\) | ||||
0.545573 | + | 0.838063i | \(0.316312\pi\) | |||||||
\(998\) | −1.69496 | −0.0536529 | ||||||||
\(999\) | 130.506 | 4.12904 |
(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 | 5054.2.a.bg.1.8 | ✓ | 8 | |
19.18 | odd | 2 | 5054.2.a.bh.1.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.bg.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
5054.2.a.bh.1.1 | yes | 8 | 19.18 | odd | 2 |