Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [238,2,Mod(1,238)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(238, 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("238.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 238 = 2 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 238.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: | \(1.90043956811\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 238.1 |
$q$-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 | ||||||||
\(3\) | 3.23607 | 1.86834 | 0.934172 | − | 0.356822i | \(-0.116140\pi\) | ||||
0.934172 | + | 0.356822i | \(0.116140\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.23607 | −0.552786 | −0.276393 | − | 0.961045i | \(-0.589139\pi\) | ||||
−0.276393 | + | 0.961045i | \(0.589139\pi\) | |||||||
\(6\) | −3.23607 | −1.32112 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 1.23607 | 0.390879 | ||||||||
\(11\) | 5.23607 | 1.57873 | 0.789367 | − | 0.613922i | \(-0.210409\pi\) | ||||
0.789367 | + | 0.613922i | \(0.210409\pi\) | |||||||
\(12\) | 3.23607 | 0.934172 | ||||||||
\(13\) | −2.47214 | −0.685647 | −0.342824 | − | 0.939400i | \(-0.611383\pi\) | ||||
−0.342824 | + | 0.939400i | \(0.611383\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −4.00000 | −1.03280 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −7.47214 | −1.76120 | ||||||||
\(19\) | −8.47214 | −1.94364 | −0.971821 | − | 0.235722i | \(-0.924255\pi\) | ||||
−0.971821 | + | 0.235722i | \(0.924255\pi\) | |||||||
\(20\) | −1.23607 | −0.276393 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | −5.23607 | −1.11633 | ||||||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | −3.23607 | −0.660560 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 2.47214 | 0.484826 | ||||||||
\(27\) | 14.4721 | 2.78516 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −5.70820 | −1.05999 | −0.529993 | − | 0.848002i | \(-0.677806\pi\) | ||||
−0.529993 | + | 0.848002i | \(0.677806\pi\) | |||||||
\(30\) | 4.00000 | 0.730297 | ||||||||
\(31\) | −1.52786 | −0.274412 | −0.137206 | − | 0.990543i | \(-0.543812\pi\) | ||||
−0.137206 | + | 0.990543i | \(0.543812\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 16.9443 | 2.94962 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 1.23607 | 0.208934 | ||||||||
\(36\) | 7.47214 | 1.24536 | ||||||||
\(37\) | −3.23607 | −0.532006 | −0.266003 | − | 0.963972i | \(-0.585703\pi\) | ||||
−0.266003 | + | 0.963972i | \(0.585703\pi\) | |||||||
\(38\) | 8.47214 | 1.37436 | ||||||||
\(39\) | −8.00000 | −1.28103 | ||||||||
\(40\) | 1.23607 | 0.195440 | ||||||||
\(41\) | −3.52786 | −0.550960 | −0.275480 | − | 0.961307i | \(-0.588837\pi\) | ||||
−0.275480 | + | 0.961307i | \(0.588837\pi\) | |||||||
\(42\) | 3.23607 | 0.499336 | ||||||||
\(43\) | 2.47214 | 0.376997 | 0.188499 | − | 0.982073i | \(-0.439638\pi\) | ||||
0.188499 | + | 0.982073i | \(0.439638\pi\) | |||||||
\(44\) | 5.23607 | 0.789367 | ||||||||
\(45\) | −9.23607 | −1.37683 | ||||||||
\(46\) | −8.00000 | −1.17954 | ||||||||
\(47\) | −2.47214 | −0.360598 | −0.180299 | − | 0.983612i | \(-0.557707\pi\) | ||||
−0.180299 | + | 0.983612i | \(0.557707\pi\) | |||||||
\(48\) | 3.23607 | 0.467086 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.47214 | 0.491034 | ||||||||
\(51\) | 3.23607 | 0.453140 | ||||||||
\(52\) | −2.47214 | −0.342824 | ||||||||
\(53\) | −4.47214 | −0.614295 | −0.307148 | − | 0.951662i | \(-0.599375\pi\) | ||||
−0.307148 | + | 0.951662i | \(0.599375\pi\) | |||||||
\(54\) | −14.4721 | −1.96941 | ||||||||
\(55\) | −6.47214 | −0.872703 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −27.4164 | −3.63139 | ||||||||
\(58\) | 5.70820 | 0.749524 | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | −4.00000 | −0.516398 | ||||||||
\(61\) | 1.23607 | 0.158262 | 0.0791311 | − | 0.996864i | \(-0.474785\pi\) | ||||
0.0791311 | + | 0.996864i | \(0.474785\pi\) | |||||||
\(62\) | 1.52786 | 0.194039 | ||||||||
\(63\) | −7.47214 | −0.941401 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.05573 | 0.379016 | ||||||||
\(66\) | −16.9443 | −2.08570 | ||||||||
\(67\) | −1.52786 | −0.186658 | −0.0933292 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933292 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 25.8885 | 3.11661 | ||||||||
\(70\) | −1.23607 | −0.147738 | ||||||||
\(71\) | −2.47214 | −0.293389 | −0.146694 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146694 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(72\) | −7.47214 | −0.880600 | ||||||||
\(73\) | 13.4164 | 1.57027 | 0.785136 | − | 0.619324i | \(-0.212593\pi\) | ||||
0.785136 | + | 0.619324i | \(0.212593\pi\) | |||||||
\(74\) | 3.23607 | 0.376185 | ||||||||
\(75\) | −11.2361 | −1.29743 | ||||||||
\(76\) | −8.47214 | −0.971821 | ||||||||
\(77\) | −5.23607 | −0.596705 | ||||||||
\(78\) | 8.00000 | 0.905822 | ||||||||
\(79\) | −10.4721 | −1.17821 | −0.589104 | − | 0.808057i | \(-0.700519\pi\) | ||||
−0.589104 | + | 0.808057i | \(0.700519\pi\) | |||||||
\(80\) | −1.23607 | −0.138197 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 3.52786 | 0.389587 | ||||||||
\(83\) | 2.00000 | 0.219529 | 0.109764 | − | 0.993958i | \(-0.464990\pi\) | ||||
0.109764 | + | 0.993958i | \(0.464990\pi\) | |||||||
\(84\) | −3.23607 | −0.353084 | ||||||||
\(85\) | −1.23607 | −0.134070 | ||||||||
\(86\) | −2.47214 | −0.266577 | ||||||||
\(87\) | −18.4721 | −1.98042 | ||||||||
\(88\) | −5.23607 | −0.558167 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 9.23607 | 0.973567 | ||||||||
\(91\) | 2.47214 | 0.259150 | ||||||||
\(92\) | 8.00000 | 0.834058 | ||||||||
\(93\) | −4.94427 | −0.512697 | ||||||||
\(94\) | 2.47214 | 0.254981 | ||||||||
\(95\) | 10.4721 | 1.07442 | ||||||||
\(96\) | −3.23607 | −0.330280 | ||||||||
\(97\) | −8.47214 | −0.860215 | −0.430108 | − | 0.902778i | \(-0.641524\pi\) | ||||
−0.430108 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 39.1246 | 3.93217 | ||||||||
\(100\) | −3.47214 | −0.347214 | ||||||||
\(101\) | −6.47214 | −0.644002 | −0.322001 | − | 0.946739i | \(-0.604355\pi\) | ||||
−0.322001 | + | 0.946739i | \(0.604355\pi\) | |||||||
\(102\) | −3.23607 | −0.320418 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 2.47214 | 0.242413 | ||||||||
\(105\) | 4.00000 | 0.390360 | ||||||||
\(106\) | 4.47214 | 0.434372 | ||||||||
\(107\) | −1.23607 | −0.119495 | −0.0597476 | − | 0.998214i | \(-0.519030\pi\) | ||||
−0.0597476 | + | 0.998214i | \(0.519030\pi\) | |||||||
\(108\) | 14.4721 | 1.39258 | ||||||||
\(109\) | 12.1803 | 1.16666 | 0.583332 | − | 0.812233i | \(-0.301748\pi\) | ||||
0.583332 | + | 0.812233i | \(0.301748\pi\) | |||||||
\(110\) | 6.47214 | 0.617094 | ||||||||
\(111\) | −10.4721 | −0.993971 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 13.4164 | 1.26211 | 0.631055 | − | 0.775738i | \(-0.282622\pi\) | ||||
0.631055 | + | 0.775738i | \(0.282622\pi\) | |||||||
\(114\) | 27.4164 | 2.56778 | ||||||||
\(115\) | −9.88854 | −0.922111 | ||||||||
\(116\) | −5.70820 | −0.529993 | ||||||||
\(117\) | −18.4721 | −1.70775 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 4.00000 | 0.365148 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | −1.23607 | −0.111908 | ||||||||
\(123\) | −11.4164 | −1.02938 | ||||||||
\(124\) | −1.52786 | −0.137206 | ||||||||
\(125\) | 10.4721 | 0.936656 | ||||||||
\(126\) | 7.47214 | 0.665671 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | −3.05573 | −0.268005 | ||||||||
\(131\) | 1.70820 | 0.149246 | 0.0746232 | − | 0.997212i | \(-0.476225\pi\) | ||||
0.0746232 | + | 0.997212i | \(0.476225\pi\) | |||||||
\(132\) | 16.9443 | 1.47481 | ||||||||
\(133\) | 8.47214 | 0.734627 | ||||||||
\(134\) | 1.52786 | 0.131987 | ||||||||
\(135\) | −17.8885 | −1.53960 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | 3.52786 | 0.301406 | 0.150703 | − | 0.988579i | \(-0.451846\pi\) | ||||
0.150703 | + | 0.988579i | \(0.451846\pi\) | |||||||
\(138\) | −25.8885 | −2.20378 | ||||||||
\(139\) | −12.1803 | −1.03312 | −0.516561 | − | 0.856250i | \(-0.672788\pi\) | ||||
−0.516561 | + | 0.856250i | \(0.672788\pi\) | |||||||
\(140\) | 1.23607 | 0.104467 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 2.47214 | 0.207457 | ||||||||
\(143\) | −12.9443 | −1.08245 | ||||||||
\(144\) | 7.47214 | 0.622678 | ||||||||
\(145\) | 7.05573 | 0.585946 | ||||||||
\(146\) | −13.4164 | −1.11035 | ||||||||
\(147\) | 3.23607 | 0.266906 | ||||||||
\(148\) | −3.23607 | −0.266003 | ||||||||
\(149\) | 18.9443 | 1.55198 | 0.775988 | − | 0.630748i | \(-0.217252\pi\) | ||||
0.775988 | + | 0.630748i | \(0.217252\pi\) | |||||||
\(150\) | 11.2361 | 0.917421 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 8.47214 | 0.687181 | ||||||||
\(153\) | 7.47214 | 0.604086 | ||||||||
\(154\) | 5.23607 | 0.421934 | ||||||||
\(155\) | 1.88854 | 0.151691 | ||||||||
\(156\) | −8.00000 | −0.640513 | ||||||||
\(157\) | 20.9443 | 1.67153 | 0.835767 | − | 0.549084i | \(-0.185023\pi\) | ||||
0.835767 | + | 0.549084i | \(0.185023\pi\) | |||||||
\(158\) | 10.4721 | 0.833118 | ||||||||
\(159\) | −14.4721 | −1.14772 | ||||||||
\(160\) | 1.23607 | 0.0977198 | ||||||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | −24.4164 | −1.91833 | ||||||||
\(163\) | −0.291796 | −0.0228552 | −0.0114276 | − | 0.999935i | \(-0.503638\pi\) | ||||
−0.0114276 | + | 0.999935i | \(0.503638\pi\) | |||||||
\(164\) | −3.52786 | −0.275480 | ||||||||
\(165\) | −20.9443 | −1.63051 | ||||||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | −14.4721 | −1.11989 | −0.559944 | − | 0.828531i | \(-0.689177\pi\) | ||||
−0.559944 | + | 0.828531i | \(0.689177\pi\) | |||||||
\(168\) | 3.23607 | 0.249668 | ||||||||
\(169\) | −6.88854 | −0.529888 | ||||||||
\(170\) | 1.23607 | 0.0948021 | ||||||||
\(171\) | −63.3050 | −4.84105 | ||||||||
\(172\) | 2.47214 | 0.188499 | ||||||||
\(173\) | 20.6525 | 1.57018 | 0.785089 | − | 0.619383i | \(-0.212617\pi\) | ||||
0.785089 | + | 0.619383i | \(0.212617\pi\) | |||||||
\(174\) | 18.4721 | 1.40037 | ||||||||
\(175\) | 3.47214 | 0.262469 | ||||||||
\(176\) | 5.23607 | 0.394683 | ||||||||
\(177\) | −19.4164 | −1.45943 | ||||||||
\(178\) | −2.00000 | −0.149906 | ||||||||
\(179\) | −8.94427 | −0.668526 | −0.334263 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334263 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(180\) | −9.23607 | −0.688416 | ||||||||
\(181\) | −2.76393 | −0.205441 | −0.102721 | − | 0.994710i | \(-0.532755\pi\) | ||||
−0.102721 | + | 0.994710i | \(0.532755\pi\) | |||||||
\(182\) | −2.47214 | −0.183247 | ||||||||
\(183\) | 4.00000 | 0.295689 | ||||||||
\(184\) | −8.00000 | −0.589768 | ||||||||
\(185\) | 4.00000 | 0.294086 | ||||||||
\(186\) | 4.94427 | 0.362532 | ||||||||
\(187\) | 5.23607 | 0.382899 | ||||||||
\(188\) | −2.47214 | −0.180299 | ||||||||
\(189\) | −14.4721 | −1.05269 | ||||||||
\(190\) | −10.4721 | −0.759729 | ||||||||
\(191\) | 12.9443 | 0.936615 | 0.468307 | − | 0.883566i | \(-0.344864\pi\) | ||||
0.468307 | + | 0.883566i | \(0.344864\pi\) | |||||||
\(192\) | 3.23607 | 0.233543 | ||||||||
\(193\) | −11.8885 | −0.855756 | −0.427878 | − | 0.903836i | \(-0.640739\pi\) | ||||
−0.427878 | + | 0.903836i | \(0.640739\pi\) | |||||||
\(194\) | 8.47214 | 0.608264 | ||||||||
\(195\) | 9.88854 | 0.708133 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 21.7082 | 1.54665 | 0.773323 | − | 0.634013i | \(-0.218593\pi\) | ||||
0.773323 | + | 0.634013i | \(0.218593\pi\) | |||||||
\(198\) | −39.1246 | −2.78047 | ||||||||
\(199\) | 14.4721 | 1.02590 | 0.512951 | − | 0.858418i | \(-0.328552\pi\) | ||||
0.512951 | + | 0.858418i | \(0.328552\pi\) | |||||||
\(200\) | 3.47214 | 0.245517 | ||||||||
\(201\) | −4.94427 | −0.348742 | ||||||||
\(202\) | 6.47214 | 0.455378 | ||||||||
\(203\) | 5.70820 | 0.400637 | ||||||||
\(204\) | 3.23607 | 0.226570 | ||||||||
\(205\) | 4.36068 | 0.304563 | ||||||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | 59.7771 | 4.15479 | ||||||||
\(208\) | −2.47214 | −0.171412 | ||||||||
\(209\) | −44.3607 | −3.06849 | ||||||||
\(210\) | −4.00000 | −0.276026 | ||||||||
\(211\) | −27.7082 | −1.90751 | −0.953756 | − | 0.300583i | \(-0.902819\pi\) | ||||
−0.953756 | + | 0.300583i | \(0.902819\pi\) | |||||||
\(212\) | −4.47214 | −0.307148 | ||||||||
\(213\) | −8.00000 | −0.548151 | ||||||||
\(214\) | 1.23607 | 0.0844959 | ||||||||
\(215\) | −3.05573 | −0.208399 | ||||||||
\(216\) | −14.4721 | −0.984704 | ||||||||
\(217\) | 1.52786 | 0.103718 | ||||||||
\(218\) | −12.1803 | −0.824957 | ||||||||
\(219\) | 43.4164 | 2.93381 | ||||||||
\(220\) | −6.47214 | −0.436351 | ||||||||
\(221\) | −2.47214 | −0.166294 | ||||||||
\(222\) | 10.4721 | 0.702844 | ||||||||
\(223\) | 1.52786 | 0.102313 | 0.0511567 | − | 0.998691i | \(-0.483709\pi\) | ||||
0.0511567 | + | 0.998691i | \(0.483709\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −25.9443 | −1.72962 | ||||||||
\(226\) | −13.4164 | −0.892446 | ||||||||
\(227\) | 27.5967 | 1.83166 | 0.915830 | − | 0.401566i | \(-0.131534\pi\) | ||||
0.915830 | + | 0.401566i | \(0.131534\pi\) | |||||||
\(228\) | −27.4164 | −1.81570 | ||||||||
\(229\) | −4.94427 | −0.326727 | −0.163363 | − | 0.986566i | \(-0.552234\pi\) | ||||
−0.163363 | + | 0.986566i | \(0.552234\pi\) | |||||||
\(230\) | 9.88854 | 0.652031 | ||||||||
\(231\) | −16.9443 | −1.11485 | ||||||||
\(232\) | 5.70820 | 0.374762 | ||||||||
\(233\) | 19.8885 | 1.30294 | 0.651471 | − | 0.758674i | \(-0.274152\pi\) | ||||
0.651471 | + | 0.758674i | \(0.274152\pi\) | |||||||
\(234\) | 18.4721 | 1.20756 | ||||||||
\(235\) | 3.05573 | 0.199334 | ||||||||
\(236\) | −6.00000 | −0.390567 | ||||||||
\(237\) | −33.8885 | −2.20130 | ||||||||
\(238\) | 1.00000 | 0.0648204 | ||||||||
\(239\) | −4.94427 | −0.319818 | −0.159909 | − | 0.987132i | \(-0.551120\pi\) | ||||
−0.159909 | + | 0.987132i | \(0.551120\pi\) | |||||||
\(240\) | −4.00000 | −0.258199 | ||||||||
\(241\) | 11.8885 | 0.765808 | 0.382904 | − | 0.923788i | \(-0.374924\pi\) | ||||
0.382904 | + | 0.923788i | \(0.374924\pi\) | |||||||
\(242\) | −16.4164 | −1.05529 | ||||||||
\(243\) | 35.5967 | 2.28353 | ||||||||
\(244\) | 1.23607 | 0.0791311 | ||||||||
\(245\) | −1.23607 | −0.0789695 | ||||||||
\(246\) | 11.4164 | 0.727884 | ||||||||
\(247\) | 20.9443 | 1.33265 | ||||||||
\(248\) | 1.52786 | 0.0970195 | ||||||||
\(249\) | 6.47214 | 0.410155 | ||||||||
\(250\) | −10.4721 | −0.662316 | ||||||||
\(251\) | 14.0000 | 0.883672 | 0.441836 | − | 0.897096i | \(-0.354327\pi\) | ||||
0.441836 | + | 0.897096i | \(0.354327\pi\) | |||||||
\(252\) | −7.47214 | −0.470700 | ||||||||
\(253\) | 41.8885 | 2.63351 | ||||||||
\(254\) | −12.0000 | −0.752947 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.00000 | −0.124757 | −0.0623783 | − | 0.998053i | \(-0.519869\pi\) | ||||
−0.0623783 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(258\) | −8.00000 | −0.498058 | ||||||||
\(259\) | 3.23607 | 0.201079 | ||||||||
\(260\) | 3.05573 | 0.189508 | ||||||||
\(261\) | −42.6525 | −2.64012 | ||||||||
\(262\) | −1.70820 | −0.105533 | ||||||||
\(263\) | 7.05573 | 0.435075 | 0.217537 | − | 0.976052i | \(-0.430198\pi\) | ||||
0.217537 | + | 0.976052i | \(0.430198\pi\) | |||||||
\(264\) | −16.9443 | −1.04285 | ||||||||
\(265\) | 5.52786 | 0.339574 | ||||||||
\(266\) | −8.47214 | −0.519460 | ||||||||
\(267\) | 6.47214 | 0.396088 | ||||||||
\(268\) | −1.52786 | −0.0933292 | ||||||||
\(269\) | −0.291796 | −0.0177911 | −0.00889556 | − | 0.999960i | \(-0.502832\pi\) | ||||
−0.00889556 | + | 0.999960i | \(0.502832\pi\) | |||||||
\(270\) | 17.8885 | 1.08866 | ||||||||
\(271\) | 19.4164 | 1.17946 | 0.589731 | − | 0.807599i | \(-0.299234\pi\) | ||||
0.589731 | + | 0.807599i | \(0.299234\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 8.00000 | 0.484182 | ||||||||
\(274\) | −3.52786 | −0.213126 | ||||||||
\(275\) | −18.1803 | −1.09632 | ||||||||
\(276\) | 25.8885 | 1.55831 | ||||||||
\(277\) | −22.6525 | −1.36106 | −0.680528 | − | 0.732722i | \(-0.738249\pi\) | ||||
−0.680528 | + | 0.732722i | \(0.738249\pi\) | |||||||
\(278\) | 12.1803 | 0.730528 | ||||||||
\(279\) | −11.4164 | −0.683482 | ||||||||
\(280\) | −1.23607 | −0.0738692 | ||||||||
\(281\) | 3.52786 | 0.210455 | 0.105227 | − | 0.994448i | \(-0.466443\pi\) | ||||
0.105227 | + | 0.994448i | \(0.466443\pi\) | |||||||
\(282\) | 8.00000 | 0.476393 | ||||||||
\(283\) | 10.2918 | 0.611784 | 0.305892 | − | 0.952066i | \(-0.401045\pi\) | ||||
0.305892 | + | 0.952066i | \(0.401045\pi\) | |||||||
\(284\) | −2.47214 | −0.146694 | ||||||||
\(285\) | 33.8885 | 2.00738 | ||||||||
\(286\) | 12.9443 | 0.765411 | ||||||||
\(287\) | 3.52786 | 0.208243 | ||||||||
\(288\) | −7.47214 | −0.440300 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −7.05573 | −0.414327 | ||||||||
\(291\) | −27.4164 | −1.60718 | ||||||||
\(292\) | 13.4164 | 0.785136 | ||||||||
\(293\) | −28.0000 | −1.63578 | −0.817889 | − | 0.575376i | \(-0.804856\pi\) | ||||
−0.817889 | + | 0.575376i | \(0.804856\pi\) | |||||||
\(294\) | −3.23607 | −0.188731 | ||||||||
\(295\) | 7.41641 | 0.431800 | ||||||||
\(296\) | 3.23607 | 0.188093 | ||||||||
\(297\) | 75.7771 | 4.39703 | ||||||||
\(298\) | −18.9443 | −1.09741 | ||||||||
\(299\) | −19.7771 | −1.14374 | ||||||||
\(300\) | −11.2361 | −0.648715 | ||||||||
\(301\) | −2.47214 | −0.142492 | ||||||||
\(302\) | −4.00000 | −0.230174 | ||||||||
\(303\) | −20.9443 | −1.20322 | ||||||||
\(304\) | −8.47214 | −0.485910 | ||||||||
\(305\) | −1.52786 | −0.0874852 | ||||||||
\(306\) | −7.47214 | −0.427154 | ||||||||
\(307\) | −3.52786 | −0.201346 | −0.100673 | − | 0.994920i | \(-0.532100\pi\) | ||||
−0.100673 | + | 0.994920i | \(0.532100\pi\) | |||||||
\(308\) | −5.23607 | −0.298353 | ||||||||
\(309\) | −12.9443 | −0.736374 | ||||||||
\(310\) | −1.88854 | −0.107262 | ||||||||
\(311\) | −20.9443 | −1.18764 | −0.593820 | − | 0.804598i | \(-0.702381\pi\) | ||||
−0.593820 | + | 0.804598i | \(0.702381\pi\) | |||||||
\(312\) | 8.00000 | 0.452911 | ||||||||
\(313\) | −5.41641 | −0.306153 | −0.153077 | − | 0.988214i | \(-0.548918\pi\) | ||||
−0.153077 | + | 0.988214i | \(0.548918\pi\) | |||||||
\(314\) | −20.9443 | −1.18195 | ||||||||
\(315\) | 9.23607 | 0.520393 | ||||||||
\(316\) | −10.4721 | −0.589104 | ||||||||
\(317\) | −28.1803 | −1.58277 | −0.791383 | − | 0.611321i | \(-0.790638\pi\) | ||||
−0.791383 | + | 0.611321i | \(0.790638\pi\) | |||||||
\(318\) | 14.4721 | 0.811557 | ||||||||
\(319\) | −29.8885 | −1.67344 | ||||||||
\(320\) | −1.23607 | −0.0690983 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 8.00000 | 0.445823 | ||||||||
\(323\) | −8.47214 | −0.471402 | ||||||||
\(324\) | 24.4164 | 1.35647 | ||||||||
\(325\) | 8.58359 | 0.476132 | ||||||||
\(326\) | 0.291796 | 0.0161611 | ||||||||
\(327\) | 39.4164 | 2.17973 | ||||||||
\(328\) | 3.52786 | 0.194794 | ||||||||
\(329\) | 2.47214 | 0.136293 | ||||||||
\(330\) | 20.9443 | 1.15294 | ||||||||
\(331\) | −20.3607 | −1.11912 | −0.559562 | − | 0.828788i | \(-0.689031\pi\) | ||||
−0.559562 | + | 0.828788i | \(0.689031\pi\) | |||||||
\(332\) | 2.00000 | 0.109764 | ||||||||
\(333\) | −24.1803 | −1.32507 | ||||||||
\(334\) | 14.4721 | 0.791880 | ||||||||
\(335\) | 1.88854 | 0.103182 | ||||||||
\(336\) | −3.23607 | −0.176542 | ||||||||
\(337\) | −20.4721 | −1.11519 | −0.557594 | − | 0.830114i | \(-0.688275\pi\) | ||||
−0.557594 | + | 0.830114i | \(0.688275\pi\) | |||||||
\(338\) | 6.88854 | 0.374687 | ||||||||
\(339\) | 43.4164 | 2.35806 | ||||||||
\(340\) | −1.23607 | −0.0670352 | ||||||||
\(341\) | −8.00000 | −0.433224 | ||||||||
\(342\) | 63.3050 | 3.42314 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −2.47214 | −0.133289 | ||||||||
\(345\) | −32.0000 | −1.72282 | ||||||||
\(346\) | −20.6525 | −1.11028 | ||||||||
\(347\) | 4.65248 | 0.249758 | 0.124879 | − | 0.992172i | \(-0.460146\pi\) | ||||
0.124879 | + | 0.992172i | \(0.460146\pi\) | |||||||
\(348\) | −18.4721 | −0.990210 | ||||||||
\(349\) | −21.5279 | −1.15236 | −0.576180 | − | 0.817323i | \(-0.695457\pi\) | ||||
−0.576180 | + | 0.817323i | \(0.695457\pi\) | |||||||
\(350\) | −3.47214 | −0.185593 | ||||||||
\(351\) | −35.7771 | −1.90964 | ||||||||
\(352\) | −5.23607 | −0.279083 | ||||||||
\(353\) | −11.8885 | −0.632763 | −0.316382 | − | 0.948632i | \(-0.602468\pi\) | ||||
−0.316382 | + | 0.948632i | \(0.602468\pi\) | |||||||
\(354\) | 19.4164 | 1.03197 | ||||||||
\(355\) | 3.05573 | 0.162181 | ||||||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | −3.23607 | −0.171271 | ||||||||
\(358\) | 8.94427 | 0.472719 | ||||||||
\(359\) | 22.8328 | 1.20507 | 0.602535 | − | 0.798092i | \(-0.294157\pi\) | ||||
0.602535 | + | 0.798092i | \(0.294157\pi\) | |||||||
\(360\) | 9.23607 | 0.486784 | ||||||||
\(361\) | 52.7771 | 2.77774 | ||||||||
\(362\) | 2.76393 | 0.145269 | ||||||||
\(363\) | 53.1246 | 2.78832 | ||||||||
\(364\) | 2.47214 | 0.129575 | ||||||||
\(365\) | −16.5836 | −0.868025 | ||||||||
\(366\) | −4.00000 | −0.209083 | ||||||||
\(367\) | −28.9443 | −1.51088 | −0.755439 | − | 0.655219i | \(-0.772577\pi\) | ||||
−0.755439 | + | 0.655219i | \(0.772577\pi\) | |||||||
\(368\) | 8.00000 | 0.417029 | ||||||||
\(369\) | −26.3607 | −1.37228 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 4.47214 | 0.232182 | ||||||||
\(372\) | −4.94427 | −0.256349 | ||||||||
\(373\) | 13.4164 | 0.694675 | 0.347338 | − | 0.937740i | \(-0.387086\pi\) | ||||
0.347338 | + | 0.937740i | \(0.387086\pi\) | |||||||
\(374\) | −5.23607 | −0.270751 | ||||||||
\(375\) | 33.8885 | 1.75000 | ||||||||
\(376\) | 2.47214 | 0.127491 | ||||||||
\(377\) | 14.1115 | 0.726777 | ||||||||
\(378\) | 14.4721 | 0.744366 | ||||||||
\(379\) | −17.5967 | −0.903884 | −0.451942 | − | 0.892047i | \(-0.649269\pi\) | ||||
−0.451942 | + | 0.892047i | \(0.649269\pi\) | |||||||
\(380\) | 10.4721 | 0.537209 | ||||||||
\(381\) | 38.8328 | 1.98947 | ||||||||
\(382\) | −12.9443 | −0.662287 | ||||||||
\(383\) | −8.94427 | −0.457031 | −0.228515 | − | 0.973540i | \(-0.573387\pi\) | ||||
−0.228515 | + | 0.973540i | \(0.573387\pi\) | |||||||
\(384\) | −3.23607 | −0.165140 | ||||||||
\(385\) | 6.47214 | 0.329851 | ||||||||
\(386\) | 11.8885 | 0.605111 | ||||||||
\(387\) | 18.4721 | 0.938991 | ||||||||
\(388\) | −8.47214 | −0.430108 | ||||||||
\(389\) | 26.0000 | 1.31825 | 0.659126 | − | 0.752032i | \(-0.270926\pi\) | ||||
0.659126 | + | 0.752032i | \(0.270926\pi\) | |||||||
\(390\) | −9.88854 | −0.500726 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 5.52786 | 0.278844 | ||||||||
\(394\) | −21.7082 | −1.09364 | ||||||||
\(395\) | 12.9443 | 0.651297 | ||||||||
\(396\) | 39.1246 | 1.96609 | ||||||||
\(397\) | 18.1803 | 0.912445 | 0.456223 | − | 0.889866i | \(-0.349202\pi\) | ||||
0.456223 | + | 0.889866i | \(0.349202\pi\) | |||||||
\(398\) | −14.4721 | −0.725423 | ||||||||
\(399\) | 27.4164 | 1.37254 | ||||||||
\(400\) | −3.47214 | −0.173607 | ||||||||
\(401\) | 2.94427 | 0.147030 | 0.0735150 | − | 0.997294i | \(-0.476578\pi\) | ||||
0.0735150 | + | 0.997294i | \(0.476578\pi\) | |||||||
\(402\) | 4.94427 | 0.246598 | ||||||||
\(403\) | 3.77709 | 0.188150 | ||||||||
\(404\) | −6.47214 | −0.322001 | ||||||||
\(405\) | −30.1803 | −1.49967 | ||||||||
\(406\) | −5.70820 | −0.283293 | ||||||||
\(407\) | −16.9443 | −0.839896 | ||||||||
\(408\) | −3.23607 | −0.160209 | ||||||||
\(409\) | 14.9443 | 0.738947 | 0.369473 | − | 0.929241i | \(-0.379538\pi\) | ||||
0.369473 | + | 0.929241i | \(0.379538\pi\) | |||||||
\(410\) | −4.36068 | −0.215359 | ||||||||
\(411\) | 11.4164 | 0.563130 | ||||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 6.00000 | 0.295241 | ||||||||
\(414\) | −59.7771 | −2.93788 | ||||||||
\(415\) | −2.47214 | −0.121352 | ||||||||
\(416\) | 2.47214 | 0.121206 | ||||||||
\(417\) | −39.4164 | −1.93023 | ||||||||
\(418\) | 44.3607 | 2.16975 | ||||||||
\(419\) | −30.0689 | −1.46896 | −0.734481 | − | 0.678630i | \(-0.762574\pi\) | ||||
−0.734481 | + | 0.678630i | \(0.762574\pi\) | |||||||
\(420\) | 4.00000 | 0.195180 | ||||||||
\(421\) | −15.5279 | −0.756782 | −0.378391 | − | 0.925646i | \(-0.623522\pi\) | ||||
−0.378391 | + | 0.925646i | \(0.623522\pi\) | |||||||
\(422\) | 27.7082 | 1.34881 | ||||||||
\(423\) | −18.4721 | −0.898146 | ||||||||
\(424\) | 4.47214 | 0.217186 | ||||||||
\(425\) | −3.47214 | −0.168423 | ||||||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | −1.23607 | −0.0598175 | ||||||||
\(428\) | −1.23607 | −0.0597476 | ||||||||
\(429\) | −41.8885 | −2.02240 | ||||||||
\(430\) | 3.05573 | 0.147360 | ||||||||
\(431\) | −12.9443 | −0.623504 | −0.311752 | − | 0.950164i | \(-0.600916\pi\) | ||||
−0.311752 | + | 0.950164i | \(0.600916\pi\) | |||||||
\(432\) | 14.4721 | 0.696291 | ||||||||
\(433\) | 10.9443 | 0.525948 | 0.262974 | − | 0.964803i | \(-0.415297\pi\) | ||||
0.262974 | + | 0.964803i | \(0.415297\pi\) | |||||||
\(434\) | −1.52786 | −0.0733398 | ||||||||
\(435\) | 22.8328 | 1.09475 | ||||||||
\(436\) | 12.1803 | 0.583332 | ||||||||
\(437\) | −67.7771 | −3.24222 | ||||||||
\(438\) | −43.4164 | −2.07452 | ||||||||
\(439\) | −3.05573 | −0.145842 | −0.0729210 | − | 0.997338i | \(-0.523232\pi\) | ||||
−0.0729210 | + | 0.997338i | \(0.523232\pi\) | |||||||
\(440\) | 6.47214 | 0.308547 | ||||||||
\(441\) | 7.47214 | 0.355816 | ||||||||
\(442\) | 2.47214 | 0.117588 | ||||||||
\(443\) | −8.36068 | −0.397228 | −0.198614 | − | 0.980078i | \(-0.563644\pi\) | ||||
−0.198614 | + | 0.980078i | \(0.563644\pi\) | |||||||
\(444\) | −10.4721 | −0.496986 | ||||||||
\(445\) | −2.47214 | −0.117190 | ||||||||
\(446\) | −1.52786 | −0.0723465 | ||||||||
\(447\) | 61.3050 | 2.89962 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | 9.41641 | 0.444388 | 0.222194 | − | 0.975003i | \(-0.428678\pi\) | ||||
0.222194 | + | 0.975003i | \(0.428678\pi\) | |||||||
\(450\) | 25.9443 | 1.22302 | ||||||||
\(451\) | −18.4721 | −0.869819 | ||||||||
\(452\) | 13.4164 | 0.631055 | ||||||||
\(453\) | 12.9443 | 0.608175 | ||||||||
\(454\) | −27.5967 | −1.29518 | ||||||||
\(455\) | −3.05573 | −0.143255 | ||||||||
\(456\) | 27.4164 | 1.28389 | ||||||||
\(457\) | 15.8885 | 0.743235 | 0.371617 | − | 0.928386i | \(-0.378803\pi\) | ||||
0.371617 | + | 0.928386i | \(0.378803\pi\) | |||||||
\(458\) | 4.94427 | 0.231031 | ||||||||
\(459\) | 14.4721 | 0.675501 | ||||||||
\(460\) | −9.88854 | −0.461056 | ||||||||
\(461\) | −5.52786 | −0.257458 | −0.128729 | − | 0.991680i | \(-0.541090\pi\) | ||||
−0.128729 | + | 0.991680i | \(0.541090\pi\) | |||||||
\(462\) | 16.9443 | 0.788319 | ||||||||
\(463\) | 32.9443 | 1.53105 | 0.765525 | − | 0.643406i | \(-0.222479\pi\) | ||||
0.765525 | + | 0.643406i | \(0.222479\pi\) | |||||||
\(464\) | −5.70820 | −0.264997 | ||||||||
\(465\) | 6.11146 | 0.283412 | ||||||||
\(466\) | −19.8885 | −0.921319 | ||||||||
\(467\) | −10.3607 | −0.479435 | −0.239718 | − | 0.970843i | \(-0.577055\pi\) | ||||
−0.239718 | + | 0.970843i | \(0.577055\pi\) | |||||||
\(468\) | −18.4721 | −0.853875 | ||||||||
\(469\) | 1.52786 | 0.0705502 | ||||||||
\(470\) | −3.05573 | −0.140950 | ||||||||
\(471\) | 67.7771 | 3.12300 | ||||||||
\(472\) | 6.00000 | 0.276172 | ||||||||
\(473\) | 12.9443 | 0.595178 | ||||||||
\(474\) | 33.8885 | 1.55655 | ||||||||
\(475\) | 29.4164 | 1.34972 | ||||||||
\(476\) | −1.00000 | −0.0458349 | ||||||||
\(477\) | −33.4164 | −1.53003 | ||||||||
\(478\) | 4.94427 | 0.226146 | ||||||||
\(479\) | −19.4164 | −0.887158 | −0.443579 | − | 0.896235i | \(-0.646291\pi\) | ||||
−0.443579 | + | 0.896235i | \(0.646291\pi\) | |||||||
\(480\) | 4.00000 | 0.182574 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | −11.8885 | −0.541508 | ||||||||
\(483\) | −25.8885 | −1.17797 | ||||||||
\(484\) | 16.4164 | 0.746200 | ||||||||
\(485\) | 10.4721 | 0.475515 | ||||||||
\(486\) | −35.5967 | −1.61470 | ||||||||
\(487\) | 3.05573 | 0.138468 | 0.0692341 | − | 0.997600i | \(-0.477944\pi\) | ||||
0.0692341 | + | 0.997600i | \(0.477944\pi\) | |||||||
\(488\) | −1.23607 | −0.0559542 | ||||||||
\(489\) | −0.944272 | −0.0427015 | ||||||||
\(490\) | 1.23607 | 0.0558399 | ||||||||
\(491\) | −32.9443 | −1.48675 | −0.743377 | − | 0.668873i | \(-0.766777\pi\) | ||||
−0.743377 | + | 0.668873i | \(0.766777\pi\) | |||||||
\(492\) | −11.4164 | −0.514691 | ||||||||
\(493\) | −5.70820 | −0.257085 | ||||||||
\(494\) | −20.9443 | −0.942327 | ||||||||
\(495\) | −48.3607 | −2.17365 | ||||||||
\(496\) | −1.52786 | −0.0686031 | ||||||||
\(497\) | 2.47214 | 0.110890 | ||||||||
\(498\) | −6.47214 | −0.290023 | ||||||||
\(499\) | −40.6525 | −1.81985 | −0.909927 | − | 0.414768i | \(-0.863863\pi\) | ||||
−0.909927 | + | 0.414768i | \(0.863863\pi\) | |||||||
\(500\) | 10.4721 | 0.468328 | ||||||||
\(501\) | −46.8328 | −2.09234 | ||||||||
\(502\) | −14.0000 | −0.624851 | ||||||||
\(503\) | 12.9443 | 0.577157 | 0.288578 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288578 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(504\) | 7.47214 | 0.332835 | ||||||||
\(505\) | 8.00000 | 0.355995 | ||||||||
\(506\) | −41.8885 | −1.86217 | ||||||||
\(507\) | −22.2918 | −0.990013 | ||||||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | −3.05573 | −0.135443 | −0.0677214 | − | 0.997704i | \(-0.521573\pi\) | ||||
−0.0677214 | + | 0.997704i | \(0.521573\pi\) | |||||||
\(510\) | 4.00000 | 0.177123 | ||||||||
\(511\) | −13.4164 | −0.593507 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −122.610 | −5.41336 | ||||||||
\(514\) | 2.00000 | 0.0882162 | ||||||||
\(515\) | 4.94427 | 0.217871 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | −12.9443 | −0.569288 | ||||||||
\(518\) | −3.23607 | −0.142185 | ||||||||
\(519\) | 66.8328 | 2.93364 | ||||||||
\(520\) | −3.05573 | −0.134003 | ||||||||
\(521\) | −1.05573 | −0.0462523 | −0.0231261 | − | 0.999733i | \(-0.507362\pi\) | ||||
−0.0231261 | + | 0.999733i | \(0.507362\pi\) | |||||||
\(522\) | 42.6525 | 1.86685 | ||||||||
\(523\) | −42.9443 | −1.87782 | −0.938911 | − | 0.344160i | \(-0.888164\pi\) | ||||
−0.938911 | + | 0.344160i | \(0.888164\pi\) | |||||||
\(524\) | 1.70820 | 0.0746232 | ||||||||
\(525\) | 11.2361 | 0.490382 | ||||||||
\(526\) | −7.05573 | −0.307644 | ||||||||
\(527\) | −1.52786 | −0.0665548 | ||||||||
\(528\) | 16.9443 | 0.737405 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | −5.52786 | −0.240115 | ||||||||
\(531\) | −44.8328 | −1.94558 | ||||||||
\(532\) | 8.47214 | 0.367314 | ||||||||
\(533\) | 8.72136 | 0.377764 | ||||||||
\(534\) | −6.47214 | −0.280077 | ||||||||
\(535\) | 1.52786 | 0.0660553 | ||||||||
\(536\) | 1.52786 | 0.0659937 | ||||||||
\(537\) | −28.9443 | −1.24904 | ||||||||
\(538\) | 0.291796 | 0.0125802 | ||||||||
\(539\) | 5.23607 | 0.225533 | ||||||||
\(540\) | −17.8885 | −0.769800 | ||||||||
\(541\) | −23.2361 | −0.998997 | −0.499498 | − | 0.866315i | \(-0.666482\pi\) | ||||
−0.499498 | + | 0.866315i | \(0.666482\pi\) | |||||||
\(542\) | −19.4164 | −0.834006 | ||||||||
\(543\) | −8.94427 | −0.383835 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −15.0557 | −0.644917 | ||||||||
\(546\) | −8.00000 | −0.342368 | ||||||||
\(547\) | 41.5967 | 1.77855 | 0.889274 | − | 0.457374i | \(-0.151210\pi\) | ||||
0.889274 | + | 0.457374i | \(0.151210\pi\) | |||||||
\(548\) | 3.52786 | 0.150703 | ||||||||
\(549\) | 9.23607 | 0.394186 | ||||||||
\(550\) | 18.1803 | 0.775212 | ||||||||
\(551\) | 48.3607 | 2.06023 | ||||||||
\(552\) | −25.8885 | −1.10189 | ||||||||
\(553\) | 10.4721 | 0.445321 | ||||||||
\(554\) | 22.6525 | 0.962411 | ||||||||
\(555\) | 12.9443 | 0.549454 | ||||||||
\(556\) | −12.1803 | −0.516561 | ||||||||
\(557\) | 34.3607 | 1.45591 | 0.727954 | − | 0.685626i | \(-0.240471\pi\) | ||||
0.727954 | + | 0.685626i | \(0.240471\pi\) | |||||||
\(558\) | 11.4164 | 0.483295 | ||||||||
\(559\) | −6.11146 | −0.258487 | ||||||||
\(560\) | 1.23607 | 0.0522334 | ||||||||
\(561\) | 16.9443 | 0.715388 | ||||||||
\(562\) | −3.52786 | −0.148814 | ||||||||
\(563\) | −32.8328 | −1.38374 | −0.691869 | − | 0.722023i | \(-0.743212\pi\) | ||||
−0.691869 | + | 0.722023i | \(0.743212\pi\) | |||||||
\(564\) | −8.00000 | −0.336861 | ||||||||
\(565\) | −16.5836 | −0.697677 | ||||||||
\(566\) | −10.2918 | −0.432596 | ||||||||
\(567\) | −24.4164 | −1.02539 | ||||||||
\(568\) | 2.47214 | 0.103729 | ||||||||
\(569\) | 15.8885 | 0.666082 | 0.333041 | − | 0.942912i | \(-0.391925\pi\) | ||||
0.333041 | + | 0.942912i | \(0.391925\pi\) | |||||||
\(570\) | −33.8885 | −1.41943 | ||||||||
\(571\) | −13.2361 | −0.553912 | −0.276956 | − | 0.960883i | \(-0.589326\pi\) | ||||
−0.276956 | + | 0.960883i | \(0.589326\pi\) | |||||||
\(572\) | −12.9443 | −0.541227 | ||||||||
\(573\) | 41.8885 | 1.74992 | ||||||||
\(574\) | −3.52786 | −0.147250 | ||||||||
\(575\) | −27.7771 | −1.15838 | ||||||||
\(576\) | 7.47214 | 0.311339 | ||||||||
\(577\) | 30.0000 | 1.24892 | 0.624458 | − | 0.781058i | \(-0.285320\pi\) | ||||
0.624458 | + | 0.781058i | \(0.285320\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −38.4721 | −1.59885 | ||||||||
\(580\) | 7.05573 | 0.292973 | ||||||||
\(581\) | −2.00000 | −0.0829740 | ||||||||
\(582\) | 27.4164 | 1.13645 | ||||||||
\(583\) | −23.4164 | −0.969809 | ||||||||
\(584\) | −13.4164 | −0.555175 | ||||||||
\(585\) | 22.8328 | 0.944021 | ||||||||
\(586\) | 28.0000 | 1.15667 | ||||||||
\(587\) | 21.4164 | 0.883950 | 0.441975 | − | 0.897027i | \(-0.354278\pi\) | ||||
0.441975 | + | 0.897027i | \(0.354278\pi\) | |||||||
\(588\) | 3.23607 | 0.133453 | ||||||||
\(589\) | 12.9443 | 0.533359 | ||||||||
\(590\) | −7.41641 | −0.305329 | ||||||||
\(591\) | 70.2492 | 2.88967 | ||||||||
\(592\) | −3.23607 | −0.133002 | ||||||||
\(593\) | −2.94427 | −0.120907 | −0.0604534 | − | 0.998171i | \(-0.519255\pi\) | ||||
−0.0604534 | + | 0.998171i | \(0.519255\pi\) | |||||||
\(594\) | −75.7771 | −3.10917 | ||||||||
\(595\) | 1.23607 | 0.0506738 | ||||||||
\(596\) | 18.9443 | 0.775988 | ||||||||
\(597\) | 46.8328 | 1.91674 | ||||||||
\(598\) | 19.7771 | 0.808745 | ||||||||
\(599\) | 31.7771 | 1.29838 | 0.649188 | − | 0.760628i | \(-0.275109\pi\) | ||||
0.649188 | + | 0.760628i | \(0.275109\pi\) | |||||||
\(600\) | 11.2361 | 0.458711 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 2.47214 | 0.100757 | ||||||||
\(603\) | −11.4164 | −0.464912 | ||||||||
\(604\) | 4.00000 | 0.162758 | ||||||||
\(605\) | −20.2918 | −0.824979 | ||||||||
\(606\) | 20.9443 | 0.850803 | ||||||||
\(607\) | −8.00000 | −0.324710 | −0.162355 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(608\) | 8.47214 | 0.343590 | ||||||||
\(609\) | 18.4721 | 0.748529 | ||||||||
\(610\) | 1.52786 | 0.0618614 | ||||||||
\(611\) | 6.11146 | 0.247243 | ||||||||
\(612\) | 7.47214 | 0.302043 | ||||||||
\(613\) | −44.8328 | −1.81078 | −0.905390 | − | 0.424581i | \(-0.860422\pi\) | ||||
−0.905390 | + | 0.424581i | \(0.860422\pi\) | |||||||
\(614\) | 3.52786 | 0.142373 | ||||||||
\(615\) | 14.1115 | 0.569029 | ||||||||
\(616\) | 5.23607 | 0.210967 | ||||||||
\(617\) | 10.3607 | 0.417105 | 0.208553 | − | 0.978011i | \(-0.433125\pi\) | ||||
0.208553 | + | 0.978011i | \(0.433125\pi\) | |||||||
\(618\) | 12.9443 | 0.520695 | ||||||||
\(619\) | 25.7082 | 1.03330 | 0.516650 | − | 0.856197i | \(-0.327179\pi\) | ||||
0.516650 | + | 0.856197i | \(0.327179\pi\) | |||||||
\(620\) | 1.88854 | 0.0758457 | ||||||||
\(621\) | 115.777 | 4.64597 | ||||||||
\(622\) | 20.9443 | 0.839789 | ||||||||
\(623\) | −2.00000 | −0.0801283 | ||||||||
\(624\) | −8.00000 | −0.320256 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | 5.41641 | 0.216483 | ||||||||
\(627\) | −143.554 | −5.73300 | ||||||||
\(628\) | 20.9443 | 0.835767 | ||||||||
\(629\) | −3.23607 | −0.129030 | ||||||||
\(630\) | −9.23607 | −0.367974 | ||||||||
\(631\) | 3.05573 | 0.121647 | 0.0608233 | − | 0.998149i | \(-0.480627\pi\) | ||||
0.0608233 | + | 0.998149i | \(0.480627\pi\) | |||||||
\(632\) | 10.4721 | 0.416559 | ||||||||
\(633\) | −89.6656 | −3.56389 | ||||||||
\(634\) | 28.1803 | 1.11918 | ||||||||
\(635\) | −14.8328 | −0.588622 | ||||||||
\(636\) | −14.4721 | −0.573858 | ||||||||
\(637\) | −2.47214 | −0.0979496 | ||||||||
\(638\) | 29.8885 | 1.18330 | ||||||||
\(639\) | −18.4721 | −0.730746 | ||||||||
\(640\) | 1.23607 | 0.0488599 | ||||||||
\(641\) | 9.05573 | 0.357680 | 0.178840 | − | 0.983878i | \(-0.442766\pi\) | ||||
0.178840 | + | 0.983878i | \(0.442766\pi\) | |||||||
\(642\) | 4.00000 | 0.157867 | ||||||||
\(643\) | 13.1246 | 0.517584 | 0.258792 | − | 0.965933i | \(-0.416676\pi\) | ||||
0.258792 | + | 0.965933i | \(0.416676\pi\) | |||||||
\(644\) | −8.00000 | −0.315244 | ||||||||
\(645\) | −9.88854 | −0.389361 | ||||||||
\(646\) | 8.47214 | 0.333332 | ||||||||
\(647\) | 20.3607 | 0.800461 | 0.400230 | − | 0.916415i | \(-0.368930\pi\) | ||||
0.400230 | + | 0.916415i | \(0.368930\pi\) | |||||||
\(648\) | −24.4164 | −0.959167 | ||||||||
\(649\) | −31.4164 | −1.23320 | ||||||||
\(650\) | −8.58359 | −0.336676 | ||||||||
\(651\) | 4.94427 | 0.193781 | ||||||||
\(652\) | −0.291796 | −0.0114276 | ||||||||
\(653\) | −7.59675 | −0.297284 | −0.148642 | − | 0.988891i | \(-0.547490\pi\) | ||||
−0.148642 | + | 0.988891i | \(0.547490\pi\) | |||||||
\(654\) | −39.4164 | −1.54130 | ||||||||
\(655\) | −2.11146 | −0.0825014 | ||||||||
\(656\) | −3.52786 | −0.137740 | ||||||||
\(657\) | 100.249 | 3.91109 | ||||||||
\(658\) | −2.47214 | −0.0963739 | ||||||||
\(659\) | −20.9443 | −0.815873 | −0.407936 | − | 0.913010i | \(-0.633752\pi\) | ||||
−0.407936 | + | 0.913010i | \(0.633752\pi\) | |||||||
\(660\) | −20.9443 | −0.815255 | ||||||||
\(661\) | −3.41641 | −0.132883 | −0.0664414 | − | 0.997790i | \(-0.521165\pi\) | ||||
−0.0664414 | + | 0.997790i | \(0.521165\pi\) | |||||||
\(662\) | 20.3607 | 0.791340 | ||||||||
\(663\) | −8.00000 | −0.310694 | ||||||||
\(664\) | −2.00000 | −0.0776151 | ||||||||
\(665\) | −10.4721 | −0.406092 | ||||||||
\(666\) | 24.1803 | 0.936969 | ||||||||
\(667\) | −45.6656 | −1.76818 | ||||||||
\(668\) | −14.4721 | −0.559944 | ||||||||
\(669\) | 4.94427 | 0.191157 | ||||||||
\(670\) | −1.88854 | −0.0729608 | ||||||||
\(671\) | 6.47214 | 0.249854 | ||||||||
\(672\) | 3.23607 | 0.124834 | ||||||||
\(673\) | −23.3050 | −0.898340 | −0.449170 | − | 0.893446i | \(-0.648280\pi\) | ||||
−0.449170 | + | 0.893446i | \(0.648280\pi\) | |||||||
\(674\) | 20.4721 | 0.788557 | ||||||||
\(675\) | −50.2492 | −1.93409 | ||||||||
\(676\) | −6.88854 | −0.264944 | ||||||||
\(677\) | 34.1803 | 1.31366 | 0.656829 | − | 0.754040i | \(-0.271898\pi\) | ||||
0.656829 | + | 0.754040i | \(0.271898\pi\) | |||||||
\(678\) | −43.4164 | −1.66740 | ||||||||
\(679\) | 8.47214 | 0.325131 | ||||||||
\(680\) | 1.23607 | 0.0474010 | ||||||||
\(681\) | 89.3050 | 3.42217 | ||||||||
\(682\) | 8.00000 | 0.306336 | ||||||||
\(683\) | 46.1803 | 1.76704 | 0.883521 | − | 0.468392i | \(-0.155166\pi\) | ||||
0.883521 | + | 0.468392i | \(0.155166\pi\) | |||||||
\(684\) | −63.3050 | −2.42053 | ||||||||
\(685\) | −4.36068 | −0.166613 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −16.0000 | −0.610438 | ||||||||
\(688\) | 2.47214 | 0.0942493 | ||||||||
\(689\) | 11.0557 | 0.421190 | ||||||||
\(690\) | 32.0000 | 1.21822 | ||||||||
\(691\) | −34.6525 | −1.31824 | −0.659121 | − | 0.752037i | \(-0.729072\pi\) | ||||
−0.659121 | + | 0.752037i | \(0.729072\pi\) | |||||||
\(692\) | 20.6525 | 0.785089 | ||||||||
\(693\) | −39.1246 | −1.48622 | ||||||||
\(694\) | −4.65248 | −0.176606 | ||||||||
\(695\) | 15.0557 | 0.571096 | ||||||||
\(696\) | 18.4721 | 0.700185 | ||||||||
\(697\) | −3.52786 | −0.133627 | ||||||||
\(698\) | 21.5279 | 0.814842 | ||||||||
\(699\) | 64.3607 | 2.43434 | ||||||||
\(700\) | 3.47214 | 0.131234 | ||||||||
\(701\) | −36.2492 | −1.36911 | −0.684557 | − | 0.728959i | \(-0.740004\pi\) | ||||
−0.684557 | + | 0.728959i | \(0.740004\pi\) | |||||||
\(702\) | 35.7771 | 1.35032 | ||||||||
\(703\) | 27.4164 | 1.03403 | ||||||||
\(704\) | 5.23607 | 0.197342 | ||||||||
\(705\) | 9.88854 | 0.372424 | ||||||||
\(706\) | 11.8885 | 0.447431 | ||||||||
\(707\) | 6.47214 | 0.243410 | ||||||||
\(708\) | −19.4164 | −0.729713 | ||||||||
\(709\) | −23.5967 | −0.886194 | −0.443097 | − | 0.896474i | \(-0.646120\pi\) | ||||
−0.443097 | + | 0.896474i | \(0.646120\pi\) | |||||||
\(710\) | −3.05573 | −0.114679 | ||||||||
\(711\) | −78.2492 | −2.93458 | ||||||||
\(712\) | −2.00000 | −0.0749532 | ||||||||
\(713\) | −12.2229 | −0.457752 | ||||||||
\(714\) | 3.23607 | 0.121107 | ||||||||
\(715\) | 16.0000 | 0.598366 | ||||||||
\(716\) | −8.94427 | −0.334263 | ||||||||
\(717\) | −16.0000 | −0.597531 | ||||||||
\(718\) | −22.8328 | −0.852113 | ||||||||
\(719\) | −27.4164 | −1.02246 | −0.511230 | − | 0.859444i | \(-0.670810\pi\) | ||||
−0.511230 | + | 0.859444i | \(0.670810\pi\) | |||||||
\(720\) | −9.23607 | −0.344208 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | −52.7771 | −1.96416 | ||||||||
\(723\) | 38.4721 | 1.43079 | ||||||||
\(724\) | −2.76393 | −0.102721 | ||||||||
\(725\) | 19.8197 | 0.736084 | ||||||||
\(726\) | −53.1246 | −1.97164 | ||||||||
\(727\) | −37.5279 | −1.39183 | −0.695916 | − | 0.718123i | \(-0.745001\pi\) | ||||
−0.695916 | + | 0.718123i | \(0.745001\pi\) | |||||||
\(728\) | −2.47214 | −0.0916235 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 16.5836 | 0.613786 | ||||||||
\(731\) | 2.47214 | 0.0914353 | ||||||||
\(732\) | 4.00000 | 0.147844 | ||||||||
\(733\) | −4.58359 | −0.169299 | −0.0846494 | − | 0.996411i | \(-0.526977\pi\) | ||||
−0.0846494 | + | 0.996411i | \(0.526977\pi\) | |||||||
\(734\) | 28.9443 | 1.06835 | ||||||||
\(735\) | −4.00000 | −0.147542 | ||||||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | −8.00000 | −0.294684 | ||||||||
\(738\) | 26.3607 | 0.970350 | ||||||||
\(739\) | 46.8328 | 1.72277 | 0.861386 | − | 0.507950i | \(-0.169597\pi\) | ||||
0.861386 | + | 0.507950i | \(0.169597\pi\) | |||||||
\(740\) | 4.00000 | 0.147043 | ||||||||
\(741\) | 67.7771 | 2.48985 | ||||||||
\(742\) | −4.47214 | −0.164177 | ||||||||
\(743\) | 29.5279 | 1.08327 | 0.541636 | − | 0.840613i | \(-0.317805\pi\) | ||||
0.541636 | + | 0.840613i | \(0.317805\pi\) | |||||||
\(744\) | 4.94427 | 0.181266 | ||||||||
\(745\) | −23.4164 | −0.857911 | ||||||||
\(746\) | −13.4164 | −0.491210 | ||||||||
\(747\) | 14.9443 | 0.546782 | ||||||||
\(748\) | 5.23607 | 0.191450 | ||||||||
\(749\) | 1.23607 | 0.0451649 | ||||||||
\(750\) | −33.8885 | −1.23743 | ||||||||
\(751\) | 28.9443 | 1.05619 | 0.528096 | − | 0.849185i | \(-0.322906\pi\) | ||||
0.528096 | + | 0.849185i | \(0.322906\pi\) | |||||||
\(752\) | −2.47214 | −0.0901495 | ||||||||
\(753\) | 45.3050 | 1.65100 | ||||||||
\(754\) | −14.1115 | −0.513909 | ||||||||
\(755\) | −4.94427 | −0.179940 | ||||||||
\(756\) | −14.4721 | −0.526346 | ||||||||
\(757\) | 18.0000 | 0.654221 | 0.327111 | − | 0.944986i | \(-0.393925\pi\) | ||||
0.327111 | + | 0.944986i | \(0.393925\pi\) | |||||||
\(758\) | 17.5967 | 0.639143 | ||||||||
\(759\) | 135.554 | 4.92030 | ||||||||
\(760\) | −10.4721 | −0.379864 | ||||||||
\(761\) | 3.88854 | 0.140960 | 0.0704798 | − | 0.997513i | \(-0.477547\pi\) | ||||
0.0704798 | + | 0.997513i | \(0.477547\pi\) | |||||||
\(762\) | −38.8328 | −1.40676 | ||||||||
\(763\) | −12.1803 | −0.440958 | ||||||||
\(764\) | 12.9443 | 0.468307 | ||||||||
\(765\) | −9.23607 | −0.333931 | ||||||||
\(766\) | 8.94427 | 0.323170 | ||||||||
\(767\) | 14.8328 | 0.535582 | ||||||||
\(768\) | 3.23607 | 0.116772 | ||||||||
\(769\) | −4.83282 | −0.174276 | −0.0871379 | − | 0.996196i | \(-0.527772\pi\) | ||||
−0.0871379 | + | 0.996196i | \(0.527772\pi\) | |||||||
\(770\) | −6.47214 | −0.233240 | ||||||||
\(771\) | −6.47214 | −0.233088 | ||||||||
\(772\) | −11.8885 | −0.427878 | ||||||||
\(773\) | 4.00000 | 0.143870 | 0.0719350 | − | 0.997409i | \(-0.477083\pi\) | ||||
0.0719350 | + | 0.997409i | \(0.477083\pi\) | |||||||
\(774\) | −18.4721 | −0.663967 | ||||||||
\(775\) | 5.30495 | 0.190559 | ||||||||
\(776\) | 8.47214 | 0.304132 | ||||||||
\(777\) | 10.4721 | 0.375686 | ||||||||
\(778\) | −26.0000 | −0.932145 | ||||||||
\(779\) | 29.8885 | 1.07087 | ||||||||
\(780\) | 9.88854 | 0.354067 | ||||||||
\(781\) | −12.9443 | −0.463182 | ||||||||
\(782\) | −8.00000 | −0.286079 | ||||||||
\(783\) | −82.6099 | −2.95224 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −25.8885 | −0.924002 | ||||||||
\(786\) | −5.52786 | −0.197172 | ||||||||
\(787\) | 9.70820 | 0.346060 | 0.173030 | − | 0.984917i | \(-0.444644\pi\) | ||||
0.173030 | + | 0.984917i | \(0.444644\pi\) | |||||||
\(788\) | 21.7082 | 0.773323 | ||||||||
\(789\) | 22.8328 | 0.812870 | ||||||||
\(790\) | −12.9443 | −0.460537 | ||||||||
\(791\) | −13.4164 | −0.477033 | ||||||||
\(792\) | −39.1246 | −1.39023 | ||||||||
\(793\) | −3.05573 | −0.108512 | ||||||||
\(794\) | −18.1803 | −0.645196 | ||||||||
\(795\) | 17.8885 | 0.634441 | ||||||||
\(796\) | 14.4721 | 0.512951 | ||||||||
\(797\) | 39.4164 | 1.39620 | 0.698100 | − | 0.716000i | \(-0.254029\pi\) | ||||
0.698100 | + | 0.716000i | \(0.254029\pi\) | |||||||
\(798\) | −27.4164 | −0.970530 | ||||||||
\(799\) | −2.47214 | −0.0874579 | ||||||||
\(800\) | 3.47214 | 0.122759 | ||||||||
\(801\) | 14.9443 | 0.528030 | ||||||||
\(802\) | −2.94427 | −0.103966 | ||||||||
\(803\) | 70.2492 | 2.47904 | ||||||||
\(804\) | −4.94427 | −0.174371 | ||||||||
\(805\) | 9.88854 | 0.348525 | ||||||||
\(806\) | −3.77709 | −0.133042 | ||||||||
\(807\) | −0.944272 | −0.0332399 | ||||||||
\(808\) | 6.47214 | 0.227689 | ||||||||
\(809\) | 1.05573 | 0.0371174 | 0.0185587 | − | 0.999828i | \(-0.494092\pi\) | ||||
0.0185587 | + | 0.999828i | \(0.494092\pi\) | |||||||
\(810\) | 30.1803 | 1.06043 | ||||||||
\(811\) | −19.8197 | −0.695962 | −0.347981 | − | 0.937502i | \(-0.613133\pi\) | ||||
−0.347981 | + | 0.937502i | \(0.613133\pi\) | |||||||
\(812\) | 5.70820 | 0.200319 | ||||||||
\(813\) | 62.8328 | 2.20364 | ||||||||
\(814\) | 16.9443 | 0.593896 | ||||||||
\(815\) | 0.360680 | 0.0126341 | ||||||||
\(816\) | 3.23607 | 0.113285 | ||||||||
\(817\) | −20.9443 | −0.732747 | ||||||||
\(818\) | −14.9443 | −0.522514 | ||||||||
\(819\) | 18.4721 | 0.645469 | ||||||||
\(820\) | 4.36068 | 0.152282 | ||||||||
\(821\) | −43.0132 | −1.50117 | −0.750585 | − | 0.660774i | \(-0.770228\pi\) | ||||
−0.750585 | + | 0.660774i | \(0.770228\pi\) | |||||||
\(822\) | −11.4164 | −0.398193 | ||||||||
\(823\) | −2.47214 | −0.0861732 | −0.0430866 | − | 0.999071i | \(-0.513719\pi\) | ||||
−0.0430866 | + | 0.999071i | \(0.513719\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | −58.8328 | −2.04830 | ||||||||
\(826\) | −6.00000 | −0.208767 | ||||||||
\(827\) | −37.5967 | −1.30737 | −0.653684 | − | 0.756768i | \(-0.726777\pi\) | ||||
−0.653684 | + | 0.756768i | \(0.726777\pi\) | |||||||
\(828\) | 59.7771 | 2.07740 | ||||||||
\(829\) | 40.9443 | 1.42205 | 0.711027 | − | 0.703165i | \(-0.248231\pi\) | ||||
0.711027 | + | 0.703165i | \(0.248231\pi\) | |||||||
\(830\) | 2.47214 | 0.0858091 | ||||||||
\(831\) | −73.3050 | −2.54292 | ||||||||
\(832\) | −2.47214 | −0.0857059 | ||||||||
\(833\) | 1.00000 | 0.0346479 | ||||||||
\(834\) | 39.4164 | 1.36488 | ||||||||
\(835\) | 17.8885 | 0.619059 | ||||||||
\(836\) | −44.3607 | −1.53425 | ||||||||
\(837\) | −22.1115 | −0.764284 | ||||||||
\(838\) | 30.0689 | 1.03871 | ||||||||
\(839\) | 7.63932 | 0.263739 | 0.131869 | − | 0.991267i | \(-0.457902\pi\) | ||||
0.131869 | + | 0.991267i | \(0.457902\pi\) | |||||||
\(840\) | −4.00000 | −0.138013 | ||||||||
\(841\) | 3.58359 | 0.123572 | ||||||||
\(842\) | 15.5279 | 0.535126 | ||||||||
\(843\) | 11.4164 | 0.393202 | ||||||||
\(844\) | −27.7082 | −0.953756 | ||||||||
\(845\) | 8.51471 | 0.292915 | ||||||||
\(846\) | 18.4721 | 0.635085 | ||||||||
\(847\) | −16.4164 | −0.564074 | ||||||||
\(848\) | −4.47214 | −0.153574 | ||||||||
\(849\) | 33.3050 | 1.14302 | ||||||||
\(850\) | 3.47214 | 0.119093 | ||||||||
\(851\) | −25.8885 | −0.887448 | ||||||||
\(852\) | −8.00000 | −0.274075 | ||||||||
\(853\) | −21.2361 | −0.727109 | −0.363555 | − | 0.931573i | \(-0.618437\pi\) | ||||
−0.363555 | + | 0.931573i | \(0.618437\pi\) | |||||||
\(854\) | 1.23607 | 0.0422974 | ||||||||
\(855\) | 78.2492 | 2.67607 | ||||||||
\(856\) | 1.23607 | 0.0422479 | ||||||||
\(857\) | −3.52786 | −0.120510 | −0.0602548 | − | 0.998183i | \(-0.519191\pi\) | ||||
−0.0602548 | + | 0.998183i | \(0.519191\pi\) | |||||||
\(858\) | 41.8885 | 1.43005 | ||||||||
\(859\) | −35.8885 | −1.22450 | −0.612251 | − | 0.790664i | \(-0.709736\pi\) | ||||
−0.612251 | + | 0.790664i | \(0.709736\pi\) | |||||||
\(860\) | −3.05573 | −0.104199 | ||||||||
\(861\) | 11.4164 | 0.389070 | ||||||||
\(862\) | 12.9443 | 0.440884 | ||||||||
\(863\) | 16.9443 | 0.576790 | 0.288395 | − | 0.957512i | \(-0.406878\pi\) | ||||
0.288395 | + | 0.957512i | \(0.406878\pi\) | |||||||
\(864\) | −14.4721 | −0.492352 | ||||||||
\(865\) | −25.5279 | −0.867973 | ||||||||
\(866\) | −10.9443 | −0.371901 | ||||||||
\(867\) | 3.23607 | 0.109903 | ||||||||
\(868\) | 1.52786 | 0.0518591 | ||||||||
\(869\) | −54.8328 | −1.86008 | ||||||||
\(870\) | −22.8328 | −0.774105 | ||||||||
\(871\) | 3.77709 | 0.127982 | ||||||||
\(872\) | −12.1803 | −0.412478 | ||||||||
\(873\) | −63.3050 | −2.14255 | ||||||||
\(874\) | 67.7771 | 2.29259 | ||||||||
\(875\) | −10.4721 | −0.354023 | ||||||||
\(876\) | 43.4164 | 1.46690 | ||||||||
\(877\) | 9.12461 | 0.308116 | 0.154058 | − | 0.988062i | \(-0.450766\pi\) | ||||
0.154058 | + | 0.988062i | \(0.450766\pi\) | |||||||
\(878\) | 3.05573 | 0.103126 | ||||||||
\(879\) | −90.6099 | −3.05620 | ||||||||
\(880\) | −6.47214 | −0.218176 | ||||||||
\(881\) | −46.9443 | −1.58159 | −0.790796 | − | 0.612079i | \(-0.790333\pi\) | ||||
−0.790796 | + | 0.612079i | \(0.790333\pi\) | |||||||
\(882\) | −7.47214 | −0.251600 | ||||||||
\(883\) | 3.41641 | 0.114971 | 0.0574856 | − | 0.998346i | \(-0.481692\pi\) | ||||
0.0574856 | + | 0.998346i | \(0.481692\pi\) | |||||||
\(884\) | −2.47214 | −0.0831469 | ||||||||
\(885\) | 24.0000 | 0.806751 | ||||||||
\(886\) | 8.36068 | 0.280883 | ||||||||
\(887\) | −24.3607 | −0.817952 | −0.408976 | − | 0.912545i | \(-0.634114\pi\) | ||||
−0.408976 | + | 0.912545i | \(0.634114\pi\) | |||||||
\(888\) | 10.4721 | 0.351422 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 2.47214 | 0.0828662 | ||||||||
\(891\) | 127.846 | 4.28300 | ||||||||
\(892\) | 1.52786 | 0.0511567 | ||||||||
\(893\) | 20.9443 | 0.700873 | ||||||||
\(894\) | −61.3050 | −2.05034 | ||||||||
\(895\) | 11.0557 | 0.369552 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −64.0000 | −2.13690 | ||||||||
\(898\) | −9.41641 | −0.314230 | ||||||||
\(899\) | 8.72136 | 0.290874 | ||||||||
\(900\) | −25.9443 | −0.864809 | ||||||||
\(901\) | −4.47214 | −0.148988 | ||||||||
\(902\) | 18.4721 | 0.615055 | ||||||||
\(903\) | −8.00000 | −0.266223 | ||||||||
\(904\) | −13.4164 | −0.446223 | ||||||||
\(905\) | 3.41641 | 0.113565 | ||||||||
\(906\) | −12.9443 | −0.430045 | ||||||||
\(907\) | −6.76393 | −0.224593 | −0.112296 | − | 0.993675i | \(-0.535821\pi\) | ||||
−0.112296 | + | 0.993675i | \(0.535821\pi\) | |||||||
\(908\) | 27.5967 | 0.915830 | ||||||||
\(909\) | −48.3607 | −1.60402 | ||||||||
\(910\) | 3.05573 | 0.101296 | ||||||||
\(911\) | 12.3607 | 0.409528 | 0.204764 | − | 0.978811i | \(-0.434357\pi\) | ||||
0.204764 | + | 0.978811i | \(0.434357\pi\) | |||||||
\(912\) | −27.4164 | −0.907848 | ||||||||
\(913\) | 10.4721 | 0.346577 | ||||||||
\(914\) | −15.8885 | −0.525546 | ||||||||
\(915\) | −4.94427 | −0.163453 | ||||||||
\(916\) | −4.94427 | −0.163363 | ||||||||
\(917\) | −1.70820 | −0.0564099 | ||||||||
\(918\) | −14.4721 | −0.477652 | ||||||||
\(919\) | −27.0557 | −0.892486 | −0.446243 | − | 0.894912i | \(-0.647238\pi\) | ||||
−0.446243 | + | 0.894912i | \(0.647238\pi\) | |||||||
\(920\) | 9.88854 | 0.326016 | ||||||||
\(921\) | −11.4164 | −0.376183 | ||||||||
\(922\) | 5.52786 | 0.182051 | ||||||||
\(923\) | 6.11146 | 0.201161 | ||||||||
\(924\) | −16.9443 | −0.557426 | ||||||||
\(925\) | 11.2361 | 0.369440 | ||||||||
\(926\) | −32.9443 | −1.08262 | ||||||||
\(927\) | −29.8885 | −0.981669 | ||||||||
\(928\) | 5.70820 | 0.187381 | ||||||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | −6.11146 | −0.200403 | ||||||||
\(931\) | −8.47214 | −0.277663 | ||||||||
\(932\) | 19.8885 | 0.651471 | ||||||||
\(933\) | −67.7771 | −2.21892 | ||||||||
\(934\) | 10.3607 | 0.339012 | ||||||||
\(935\) | −6.47214 | −0.211661 | ||||||||
\(936\) | 18.4721 | 0.603781 | ||||||||
\(937\) | 20.1115 | 0.657013 | 0.328506 | − | 0.944502i | \(-0.393455\pi\) | ||||
0.328506 | + | 0.944502i | \(0.393455\pi\) | |||||||
\(938\) | −1.52786 | −0.0498865 | ||||||||
\(939\) | −17.5279 | −0.572000 | ||||||||
\(940\) | 3.05573 | 0.0996669 | ||||||||
\(941\) | 59.1246 | 1.92741 | 0.963704 | − | 0.266974i | \(-0.0860239\pi\) | ||||
0.963704 | + | 0.266974i | \(0.0860239\pi\) | |||||||
\(942\) | −67.7771 | −2.20830 | ||||||||
\(943\) | −28.2229 | −0.919064 | ||||||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 17.8885 | 0.581914 | ||||||||
\(946\) | −12.9443 | −0.420855 | ||||||||
\(947\) | −47.1246 | −1.53134 | −0.765672 | − | 0.643231i | \(-0.777593\pi\) | ||||
−0.765672 | + | 0.643231i | \(0.777593\pi\) | |||||||
\(948\) | −33.8885 | −1.10065 | ||||||||
\(949\) | −33.1672 | −1.07665 | ||||||||
\(950\) | −29.4164 | −0.954394 | ||||||||
\(951\) | −91.1935 | −2.95715 | ||||||||
\(952\) | 1.00000 | 0.0324102 | ||||||||
\(953\) | 5.05573 | 0.163771 | 0.0818855 | − | 0.996642i | \(-0.473906\pi\) | ||||
0.0818855 | + | 0.996642i | \(0.473906\pi\) | |||||||
\(954\) | 33.4164 | 1.08190 | ||||||||
\(955\) | −16.0000 | −0.517748 | ||||||||
\(956\) | −4.94427 | −0.159909 | ||||||||
\(957\) | −96.7214 | −3.12656 | ||||||||
\(958\) | 19.4164 | 0.627316 | ||||||||
\(959\) | −3.52786 | −0.113921 | ||||||||
\(960\) | −4.00000 | −0.129099 | ||||||||
\(961\) | −28.6656 | −0.924698 | ||||||||
\(962\) | −8.00000 | −0.257930 | ||||||||
\(963\) | −9.23607 | −0.297628 | ||||||||
\(964\) | 11.8885 | 0.382904 | ||||||||
\(965\) | 14.6950 | 0.473050 | ||||||||
\(966\) | 25.8885 | 0.832950 | ||||||||
\(967\) | 44.9443 | 1.44531 | 0.722655 | − | 0.691209i | \(-0.242921\pi\) | ||||
0.722655 | + | 0.691209i | \(0.242921\pi\) | |||||||
\(968\) | −16.4164 | −0.527643 | ||||||||
\(969\) | −27.4164 | −0.880742 | ||||||||
\(970\) | −10.4721 | −0.336240 | ||||||||
\(971\) | 24.8328 | 0.796923 | 0.398461 | − | 0.917185i | \(-0.369544\pi\) | ||||
0.398461 | + | 0.917185i | \(0.369544\pi\) | |||||||
\(972\) | 35.5967 | 1.14177 | ||||||||
\(973\) | 12.1803 | 0.390484 | ||||||||
\(974\) | −3.05573 | −0.0979118 | ||||||||
\(975\) | 27.7771 | 0.889579 | ||||||||
\(976\) | 1.23607 | 0.0395656 | ||||||||
\(977\) | −58.9443 | −1.88579 | −0.942897 | − | 0.333084i | \(-0.891911\pi\) | ||||
−0.942897 | + | 0.333084i | \(0.891911\pi\) | |||||||
\(978\) | 0.944272 | 0.0301945 | ||||||||
\(979\) | 10.4721 | 0.334691 | ||||||||
\(980\) | −1.23607 | −0.0394847 | ||||||||
\(981\) | 91.0132 | 2.90583 | ||||||||
\(982\) | 32.9443 | 1.05129 | ||||||||
\(983\) | 54.4721 | 1.73739 | 0.868696 | − | 0.495346i | \(-0.164959\pi\) | ||||
0.868696 | + | 0.495346i | \(0.164959\pi\) | |||||||
\(984\) | 11.4164 | 0.363942 | ||||||||
\(985\) | −26.8328 | −0.854965 | ||||||||
\(986\) | 5.70820 | 0.181786 | ||||||||
\(987\) | 8.00000 | 0.254643 | ||||||||
\(988\) | 20.9443 | 0.666326 | ||||||||
\(989\) | 19.7771 | 0.628875 | ||||||||
\(990\) | 48.3607 | 1.53700 | ||||||||
\(991\) | −22.2492 | −0.706770 | −0.353385 | − | 0.935478i | \(-0.614969\pi\) | ||||
−0.353385 | + | 0.935478i | \(0.614969\pi\) | |||||||
\(992\) | 1.52786 | 0.0485097 | ||||||||
\(993\) | −65.8885 | −2.09091 | ||||||||
\(994\) | −2.47214 | −0.0784114 | ||||||||
\(995\) | −17.8885 | −0.567105 | ||||||||
\(996\) | 6.47214 | 0.205077 | ||||||||
\(997\) | −47.4853 | −1.50387 | −0.751937 | − | 0.659235i | \(-0.770880\pi\) | ||||
−0.751937 | + | 0.659235i | \(0.770880\pi\) | |||||||
\(998\) | 40.6525 | 1.28683 | ||||||||
\(999\) | −46.8328 | −1.48172 |
(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 | 238.2.a.f.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 2142.2.a.x.1.2 | 2 | |||
4.3 | odd | 2 | 1904.2.a.f.1.1 | 2 | |||
5.4 | even | 2 | 5950.2.a.x.1.1 | 2 | |||
7.6 | odd | 2 | 1666.2.a.o.1.1 | 2 | |||
8.3 | odd | 2 | 7616.2.a.y.1.2 | 2 | |||
8.5 | even | 2 | 7616.2.a.n.1.1 | 2 | |||
17.16 | even | 2 | 4046.2.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
238.2.a.f.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1666.2.a.o.1.1 | 2 | 7.6 | odd | 2 | |||
1904.2.a.f.1.1 | 2 | 4.3 | odd | 2 | |||
2142.2.a.x.1.2 | 2 | 3.2 | odd | 2 | |||
4046.2.a.v.1.1 | 2 | 17.16 | even | 2 | |||
5950.2.a.x.1.1 | 2 | 5.4 | even | 2 | |||
7616.2.a.n.1.1 | 2 | 8.5 | even | 2 | |||
7616.2.a.y.1.2 | 2 | 8.3 | odd | 2 |