Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8022,2,Mod(1,8022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8022.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: | \(64.0559925015\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 19x^{8} + 28x^{7} + 114x^{6} - 110x^{5} - 282x^{4} + 149x^{3} + 285x^{2} - 49x - 79 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-3.07769\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8022.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.07769 | 1.82360 | 0.911800 | − | 0.410635i | \(-0.134693\pi\) | ||||
0.911800 | + | 0.410635i | \(0.134693\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.07769 | 1.28948 | ||||||||
\(11\) | 2.56478 | 0.773311 | 0.386656 | − | 0.922224i | \(-0.373630\pi\) | ||||
0.386656 | + | 0.922224i | \(0.373630\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.57278 | 0.436211 | 0.218105 | − | 0.975925i | \(-0.430012\pi\) | ||||
0.218105 | + | 0.975925i | \(0.430012\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −4.07769 | −1.05286 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.73372 | −1.39063 | −0.695316 | − | 0.718704i | \(-0.744735\pi\) | ||||
−0.695316 | + | 0.718704i | \(0.744735\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 3.75278 | 0.860947 | 0.430474 | − | 0.902603i | \(-0.358347\pi\) | ||||
0.430474 | + | 0.902603i | \(0.358347\pi\) | |||||||
\(20\) | 4.07769 | 0.911800 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 2.56478 | 0.546814 | ||||||||
\(23\) | 3.96884 | 0.827560 | 0.413780 | − | 0.910377i | \(-0.364208\pi\) | ||||
0.413780 | + | 0.910377i | \(0.364208\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 11.6276 | 2.32552 | ||||||||
\(26\) | 1.57278 | 0.308448 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −3.01074 | −0.559081 | −0.279540 | − | 0.960134i | \(-0.590182\pi\) | ||||
−0.279540 | + | 0.960134i | \(0.590182\pi\) | |||||||
\(30\) | −4.07769 | −0.744482 | ||||||||
\(31\) | −3.45946 | −0.621336 | −0.310668 | − | 0.950518i | \(-0.600553\pi\) | ||||
−0.310668 | + | 0.950518i | \(0.600553\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.56478 | −0.446471 | ||||||||
\(34\) | −5.73372 | −0.983325 | ||||||||
\(35\) | 4.07769 | 0.689256 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.32402 | −0.382067 | −0.191034 | − | 0.981584i | \(-0.561184\pi\) | ||||
−0.191034 | + | 0.981584i | \(0.561184\pi\) | |||||||
\(38\) | 3.75278 | 0.608782 | ||||||||
\(39\) | −1.57278 | −0.251847 | ||||||||
\(40\) | 4.07769 | 0.644740 | ||||||||
\(41\) | 9.32677 | 1.45660 | 0.728298 | − | 0.685261i | \(-0.240312\pi\) | ||||
0.728298 | + | 0.685261i | \(0.240312\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −6.29321 | −0.959706 | −0.479853 | − | 0.877349i | \(-0.659310\pi\) | ||||
−0.479853 | + | 0.877349i | \(0.659310\pi\) | |||||||
\(44\) | 2.56478 | 0.386656 | ||||||||
\(45\) | 4.07769 | 0.607867 | ||||||||
\(46\) | 3.96884 | 0.585173 | ||||||||
\(47\) | 5.11837 | 0.746591 | 0.373295 | − | 0.927713i | \(-0.378228\pi\) | ||||
0.373295 | + | 0.927713i | \(0.378228\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 11.6276 | 1.64439 | ||||||||
\(51\) | 5.73372 | 0.802881 | ||||||||
\(52\) | 1.57278 | 0.218105 | ||||||||
\(53\) | −1.69413 | −0.232706 | −0.116353 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116353 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 10.4584 | 1.41021 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −3.75278 | −0.497068 | ||||||||
\(58\) | −3.01074 | −0.395330 | ||||||||
\(59\) | −2.33548 | −0.304054 | −0.152027 | − | 0.988376i | \(-0.548580\pi\) | ||||
−0.152027 | + | 0.988376i | \(0.548580\pi\) | |||||||
\(60\) | −4.07769 | −0.526428 | ||||||||
\(61\) | 0.135157 | 0.0173050 | 0.00865252 | − | 0.999963i | \(-0.497246\pi\) | ||||
0.00865252 | + | 0.999963i | \(0.497246\pi\) | |||||||
\(62\) | −3.45946 | −0.439351 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.41332 | 0.795474 | ||||||||
\(66\) | −2.56478 | −0.315703 | ||||||||
\(67\) | 0.892401 | 0.109024 | 0.0545121 | − | 0.998513i | \(-0.482640\pi\) | ||||
0.0545121 | + | 0.998513i | \(0.482640\pi\) | |||||||
\(68\) | −5.73372 | −0.695316 | ||||||||
\(69\) | −3.96884 | −0.477792 | ||||||||
\(70\) | 4.07769 | 0.487378 | ||||||||
\(71\) | 0.594616 | 0.0705679 | 0.0352839 | − | 0.999377i | \(-0.488766\pi\) | ||||
0.0352839 | + | 0.999377i | \(0.488766\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 7.96042 | 0.931697 | 0.465848 | − | 0.884865i | \(-0.345749\pi\) | ||||
0.465848 | + | 0.884865i | \(0.345749\pi\) | |||||||
\(74\) | −2.32402 | −0.270162 | ||||||||
\(75\) | −11.6276 | −1.34264 | ||||||||
\(76\) | 3.75278 | 0.430474 | ||||||||
\(77\) | 2.56478 | 0.292284 | ||||||||
\(78\) | −1.57278 | −0.178082 | ||||||||
\(79\) | 5.28701 | 0.594835 | 0.297417 | − | 0.954748i | \(-0.403875\pi\) | ||||
0.297417 | + | 0.954748i | \(0.403875\pi\) | |||||||
\(80\) | 4.07769 | 0.455900 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.32677 | 1.02997 | ||||||||
\(83\) | −4.59673 | −0.504557 | −0.252278 | − | 0.967655i | \(-0.581180\pi\) | ||||
−0.252278 | + | 0.967655i | \(0.581180\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −23.3804 | −2.53596 | ||||||||
\(86\) | −6.29321 | −0.678615 | ||||||||
\(87\) | 3.01074 | 0.322785 | ||||||||
\(88\) | 2.56478 | 0.273407 | ||||||||
\(89\) | 0.429519 | 0.0455290 | 0.0227645 | − | 0.999741i | \(-0.492753\pi\) | ||||
0.0227645 | + | 0.999741i | \(0.492753\pi\) | |||||||
\(90\) | 4.07769 | 0.429827 | ||||||||
\(91\) | 1.57278 | 0.164872 | ||||||||
\(92\) | 3.96884 | 0.413780 | ||||||||
\(93\) | 3.45946 | 0.358729 | ||||||||
\(94\) | 5.11837 | 0.527919 | ||||||||
\(95\) | 15.3027 | 1.57002 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 1.46339 | 0.148584 | 0.0742922 | − | 0.997237i | \(-0.476330\pi\) | ||||
0.0742922 | + | 0.997237i | \(0.476330\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 2.56478 | 0.257770 | ||||||||
\(100\) | 11.6276 | 1.16276 | ||||||||
\(101\) | −7.75739 | −0.771890 | −0.385945 | − | 0.922522i | \(-0.626124\pi\) | ||||
−0.385945 | + | 0.922522i | \(0.626124\pi\) | |||||||
\(102\) | 5.73372 | 0.567723 | ||||||||
\(103\) | 7.79971 | 0.768528 | 0.384264 | − | 0.923223i | \(-0.374455\pi\) | ||||
0.384264 | + | 0.923223i | \(0.374455\pi\) | |||||||
\(104\) | 1.57278 | 0.154224 | ||||||||
\(105\) | −4.07769 | −0.397942 | ||||||||
\(106\) | −1.69413 | −0.164548 | ||||||||
\(107\) | 3.74273 | 0.361823 | 0.180912 | − | 0.983499i | \(-0.442095\pi\) | ||||
0.180912 | + | 0.983499i | \(0.442095\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 2.11979 | 0.203039 | 0.101520 | − | 0.994834i | \(-0.467630\pi\) | ||||
0.101520 | + | 0.994834i | \(0.467630\pi\) | |||||||
\(110\) | 10.4584 | 0.997169 | ||||||||
\(111\) | 2.32402 | 0.220587 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 4.22957 | 0.397884 | 0.198942 | − | 0.980011i | \(-0.436249\pi\) | ||||
0.198942 | + | 0.980011i | \(0.436249\pi\) | |||||||
\(114\) | −3.75278 | −0.351480 | ||||||||
\(115\) | 16.1837 | 1.50914 | ||||||||
\(116\) | −3.01074 | −0.279540 | ||||||||
\(117\) | 1.57278 | 0.145404 | ||||||||
\(118\) | −2.33548 | −0.214999 | ||||||||
\(119\) | −5.73372 | −0.525609 | ||||||||
\(120\) | −4.07769 | −0.372241 | ||||||||
\(121\) | −4.42189 | −0.401990 | ||||||||
\(122\) | 0.135157 | 0.0122365 | ||||||||
\(123\) | −9.32677 | −0.840966 | ||||||||
\(124\) | −3.45946 | −0.310668 | ||||||||
\(125\) | 27.0252 | 2.41721 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −11.6091 | −1.03014 | −0.515069 | − | 0.857149i | \(-0.672234\pi\) | ||||
−0.515069 | + | 0.857149i | \(0.672234\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 6.29321 | 0.554086 | ||||||||
\(130\) | 6.41332 | 0.562485 | ||||||||
\(131\) | 11.3478 | 0.991460 | 0.495730 | − | 0.868477i | \(-0.334901\pi\) | ||||
0.495730 | + | 0.868477i | \(0.334901\pi\) | |||||||
\(132\) | −2.56478 | −0.223236 | ||||||||
\(133\) | 3.75278 | 0.325408 | ||||||||
\(134\) | 0.892401 | 0.0770917 | ||||||||
\(135\) | −4.07769 | −0.350952 | ||||||||
\(136\) | −5.73372 | −0.491662 | ||||||||
\(137\) | −7.15669 | −0.611437 | −0.305719 | − | 0.952122i | \(-0.598897\pi\) | ||||
−0.305719 | + | 0.952122i | \(0.598897\pi\) | |||||||
\(138\) | −3.96884 | −0.337850 | ||||||||
\(139\) | −7.99822 | −0.678400 | −0.339200 | − | 0.940714i | \(-0.610156\pi\) | ||||
−0.339200 | + | 0.940714i | \(0.610156\pi\) | |||||||
\(140\) | 4.07769 | 0.344628 | ||||||||
\(141\) | −5.11837 | −0.431044 | ||||||||
\(142\) | 0.594616 | 0.0498990 | ||||||||
\(143\) | 4.03384 | 0.337327 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −12.2769 | −1.01954 | ||||||||
\(146\) | 7.96042 | 0.658809 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −2.32402 | −0.191034 | ||||||||
\(149\) | −12.3489 | −1.01166 | −0.505830 | − | 0.862633i | \(-0.668814\pi\) | ||||
−0.505830 | + | 0.862633i | \(0.668814\pi\) | |||||||
\(150\) | −11.6276 | −0.949388 | ||||||||
\(151\) | −3.04757 | −0.248008 | −0.124004 | − | 0.992282i | \(-0.539574\pi\) | ||||
−0.124004 | + | 0.992282i | \(0.539574\pi\) | |||||||
\(152\) | 3.75278 | 0.304391 | ||||||||
\(153\) | −5.73372 | −0.463544 | ||||||||
\(154\) | 2.56478 | 0.206676 | ||||||||
\(155\) | −14.1066 | −1.13307 | ||||||||
\(156\) | −1.57278 | −0.125923 | ||||||||
\(157\) | −16.4234 | −1.31073 | −0.655363 | − | 0.755314i | \(-0.727484\pi\) | ||||
−0.655363 | + | 0.755314i | \(0.727484\pi\) | |||||||
\(158\) | 5.28701 | 0.420612 | ||||||||
\(159\) | 1.69413 | 0.134353 | ||||||||
\(160\) | 4.07769 | 0.322370 | ||||||||
\(161\) | 3.96884 | 0.312788 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 9.19645 | 0.720322 | 0.360161 | − | 0.932890i | \(-0.382722\pi\) | ||||
0.360161 | + | 0.932890i | \(0.382722\pi\) | |||||||
\(164\) | 9.32677 | 0.728298 | ||||||||
\(165\) | −10.4584 | −0.814185 | ||||||||
\(166\) | −4.59673 | −0.356776 | ||||||||
\(167\) | 23.3380 | 1.80595 | 0.902976 | − | 0.429692i | \(-0.141378\pi\) | ||||
0.902976 | + | 0.429692i | \(0.141378\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −10.5264 | −0.809720 | ||||||||
\(170\) | −23.3804 | −1.79319 | ||||||||
\(171\) | 3.75278 | 0.286982 | ||||||||
\(172\) | −6.29321 | −0.479853 | ||||||||
\(173\) | −2.19648 | −0.166995 | −0.0834976 | − | 0.996508i | \(-0.526609\pi\) | ||||
−0.0834976 | + | 0.996508i | \(0.526609\pi\) | |||||||
\(174\) | 3.01074 | 0.228244 | ||||||||
\(175\) | 11.6276 | 0.878963 | ||||||||
\(176\) | 2.56478 | 0.193328 | ||||||||
\(177\) | 2.33548 | 0.175546 | ||||||||
\(178\) | 0.429519 | 0.0321938 | ||||||||
\(179\) | 1.59185 | 0.118980 | 0.0594902 | − | 0.998229i | \(-0.481052\pi\) | ||||
0.0594902 | + | 0.998229i | \(0.481052\pi\) | |||||||
\(180\) | 4.07769 | 0.303933 | ||||||||
\(181\) | −10.1396 | −0.753668 | −0.376834 | − | 0.926281i | \(-0.622987\pi\) | ||||
−0.376834 | + | 0.926281i | \(0.622987\pi\) | |||||||
\(182\) | 1.57278 | 0.116582 | ||||||||
\(183\) | −0.135157 | −0.00999107 | ||||||||
\(184\) | 3.96884 | 0.292587 | ||||||||
\(185\) | −9.47665 | −0.696737 | ||||||||
\(186\) | 3.45946 | 0.253660 | ||||||||
\(187\) | −14.7057 | −1.07539 | ||||||||
\(188\) | 5.11837 | 0.373295 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 15.3027 | 1.11017 | ||||||||
\(191\) | 1.00000 | 0.0723575 | ||||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 17.6252 | 1.26869 | 0.634346 | − | 0.773049i | \(-0.281269\pi\) | ||||
0.634346 | + | 0.773049i | \(0.281269\pi\) | |||||||
\(194\) | 1.46339 | 0.105065 | ||||||||
\(195\) | −6.41332 | −0.459267 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −17.5489 | −1.25031 | −0.625155 | − | 0.780501i | \(-0.714964\pi\) | ||||
−0.625155 | + | 0.780501i | \(0.714964\pi\) | |||||||
\(198\) | 2.56478 | 0.182271 | ||||||||
\(199\) | −14.5178 | −1.02914 | −0.514569 | − | 0.857449i | \(-0.672048\pi\) | ||||
−0.514569 | + | 0.857449i | \(0.672048\pi\) | |||||||
\(200\) | 11.6276 | 0.822194 | ||||||||
\(201\) | −0.892401 | −0.0629451 | ||||||||
\(202\) | −7.75739 | −0.545808 | ||||||||
\(203\) | −3.01074 | −0.211313 | ||||||||
\(204\) | 5.73372 | 0.401441 | ||||||||
\(205\) | 38.0317 | 2.65625 | ||||||||
\(206\) | 7.79971 | 0.543431 | ||||||||
\(207\) | 3.96884 | 0.275853 | ||||||||
\(208\) | 1.57278 | 0.109053 | ||||||||
\(209\) | 9.62507 | 0.665780 | ||||||||
\(210\) | −4.07769 | −0.281388 | ||||||||
\(211\) | 13.8456 | 0.953171 | 0.476585 | − | 0.879128i | \(-0.341874\pi\) | ||||
0.476585 | + | 0.879128i | \(0.341874\pi\) | |||||||
\(212\) | −1.69413 | −0.116353 | ||||||||
\(213\) | −0.594616 | −0.0407424 | ||||||||
\(214\) | 3.74273 | 0.255848 | ||||||||
\(215\) | −25.6618 | −1.75012 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.45946 | −0.234843 | ||||||||
\(218\) | 2.11979 | 0.143570 | ||||||||
\(219\) | −7.96042 | −0.537915 | ||||||||
\(220\) | 10.4584 | 0.705105 | ||||||||
\(221\) | −9.01789 | −0.606609 | ||||||||
\(222\) | 2.32402 | 0.155978 | ||||||||
\(223\) | 5.47594 | 0.366696 | 0.183348 | − | 0.983048i | \(-0.441306\pi\) | ||||
0.183348 | + | 0.983048i | \(0.441306\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 11.6276 | 0.775172 | ||||||||
\(226\) | 4.22957 | 0.281347 | ||||||||
\(227\) | 13.7497 | 0.912601 | 0.456301 | − | 0.889826i | \(-0.349174\pi\) | ||||
0.456301 | + | 0.889826i | \(0.349174\pi\) | |||||||
\(228\) | −3.75278 | −0.248534 | ||||||||
\(229\) | −2.69390 | −0.178018 | −0.0890089 | − | 0.996031i | \(-0.528370\pi\) | ||||
−0.0890089 | + | 0.996031i | \(0.528370\pi\) | |||||||
\(230\) | 16.1837 | 1.06712 | ||||||||
\(231\) | −2.56478 | −0.168750 | ||||||||
\(232\) | −3.01074 | −0.197665 | ||||||||
\(233\) | 11.4638 | 0.751021 | 0.375511 | − | 0.926818i | \(-0.377467\pi\) | ||||
0.375511 | + | 0.926818i | \(0.377467\pi\) | |||||||
\(234\) | 1.57278 | 0.102816 | ||||||||
\(235\) | 20.8711 | 1.36148 | ||||||||
\(236\) | −2.33548 | −0.152027 | ||||||||
\(237\) | −5.28701 | −0.343428 | ||||||||
\(238\) | −5.73372 | −0.371662 | ||||||||
\(239\) | −20.2601 | −1.31052 | −0.655258 | − | 0.755406i | \(-0.727440\pi\) | ||||
−0.655258 | + | 0.755406i | \(0.727440\pi\) | |||||||
\(240\) | −4.07769 | −0.263214 | ||||||||
\(241\) | 10.0873 | 0.649779 | 0.324890 | − | 0.945752i | \(-0.394673\pi\) | ||||
0.324890 | + | 0.945752i | \(0.394673\pi\) | |||||||
\(242\) | −4.42189 | −0.284250 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.135157 | 0.00865252 | ||||||||
\(245\) | 4.07769 | 0.260514 | ||||||||
\(246\) | −9.32677 | −0.594653 | ||||||||
\(247\) | 5.90231 | 0.375555 | ||||||||
\(248\) | −3.45946 | −0.219676 | ||||||||
\(249\) | 4.59673 | 0.291306 | ||||||||
\(250\) | 27.0252 | 1.70923 | ||||||||
\(251\) | −17.4515 | −1.10153 | −0.550764 | − | 0.834661i | \(-0.685664\pi\) | ||||
−0.550764 | + | 0.834661i | \(0.685664\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 10.1792 | 0.639961 | ||||||||
\(254\) | −11.6091 | −0.728418 | ||||||||
\(255\) | 23.3804 | 1.46413 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.6271 | −1.16193 | −0.580965 | − | 0.813929i | \(-0.697325\pi\) | ||||
−0.580965 | + | 0.813929i | \(0.697325\pi\) | |||||||
\(258\) | 6.29321 | 0.391798 | ||||||||
\(259\) | −2.32402 | −0.144408 | ||||||||
\(260\) | 6.41332 | 0.397737 | ||||||||
\(261\) | −3.01074 | −0.186360 | ||||||||
\(262\) | 11.3478 | 0.701068 | ||||||||
\(263\) | 12.7520 | 0.786324 | 0.393162 | − | 0.919469i | \(-0.371381\pi\) | ||||
0.393162 | + | 0.919469i | \(0.371381\pi\) | |||||||
\(264\) | −2.56478 | −0.157851 | ||||||||
\(265\) | −6.90814 | −0.424363 | ||||||||
\(266\) | 3.75278 | 0.230098 | ||||||||
\(267\) | −0.429519 | −0.0262862 | ||||||||
\(268\) | 0.892401 | 0.0545121 | ||||||||
\(269\) | −19.8773 | −1.21194 | −0.605972 | − | 0.795486i | \(-0.707216\pi\) | ||||
−0.605972 | + | 0.795486i | \(0.707216\pi\) | |||||||
\(270\) | −4.07769 | −0.248161 | ||||||||
\(271\) | 0.00929113 | 0.000564396 0 | 0.000282198 | − | 1.00000i | \(-0.499910\pi\) | ||||
0.000282198 | 1.00000i | \(0.499910\pi\) | ||||||||
\(272\) | −5.73372 | −0.347658 | ||||||||
\(273\) | −1.57278 | −0.0951890 | ||||||||
\(274\) | −7.15669 | −0.432351 | ||||||||
\(275\) | 29.8222 | 1.79835 | ||||||||
\(276\) | −3.96884 | −0.238896 | ||||||||
\(277\) | 20.3778 | 1.22438 | 0.612192 | − | 0.790709i | \(-0.290288\pi\) | ||||
0.612192 | + | 0.790709i | \(0.290288\pi\) | |||||||
\(278\) | −7.99822 | −0.479701 | ||||||||
\(279\) | −3.45946 | −0.207112 | ||||||||
\(280\) | 4.07769 | 0.243689 | ||||||||
\(281\) | −32.5466 | −1.94157 | −0.970784 | − | 0.239954i | \(-0.922867\pi\) | ||||
−0.970784 | + | 0.239954i | \(0.922867\pi\) | |||||||
\(282\) | −5.11837 | −0.304794 | ||||||||
\(283\) | −12.0390 | −0.715642 | −0.357821 | − | 0.933790i | \(-0.616480\pi\) | ||||
−0.357821 | + | 0.933790i | \(0.616480\pi\) | |||||||
\(284\) | 0.594616 | 0.0352839 | ||||||||
\(285\) | −15.3027 | −0.906454 | ||||||||
\(286\) | 4.03384 | 0.238526 | ||||||||
\(287\) | 9.32677 | 0.550542 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 15.8755 | 0.933856 | ||||||||
\(290\) | −12.2769 | −0.720923 | ||||||||
\(291\) | −1.46339 | −0.0857852 | ||||||||
\(292\) | 7.96042 | 0.465848 | ||||||||
\(293\) | −7.57841 | −0.442735 | −0.221368 | − | 0.975190i | \(-0.571052\pi\) | ||||
−0.221368 | + | 0.975190i | \(0.571052\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | −9.52338 | −0.554473 | ||||||||
\(296\) | −2.32402 | −0.135081 | ||||||||
\(297\) | −2.56478 | −0.148824 | ||||||||
\(298\) | −12.3489 | −0.715352 | ||||||||
\(299\) | 6.24211 | 0.360991 | ||||||||
\(300\) | −11.6276 | −0.671319 | ||||||||
\(301\) | −6.29321 | −0.362735 | ||||||||
\(302\) | −3.04757 | −0.175368 | ||||||||
\(303\) | 7.75739 | 0.445651 | ||||||||
\(304\) | 3.75278 | 0.215237 | ||||||||
\(305\) | 0.551128 | 0.0315575 | ||||||||
\(306\) | −5.73372 | −0.327775 | ||||||||
\(307\) | −9.76130 | −0.557107 | −0.278554 | − | 0.960421i | \(-0.589855\pi\) | ||||
−0.278554 | + | 0.960421i | \(0.589855\pi\) | |||||||
\(308\) | 2.56478 | 0.146142 | ||||||||
\(309\) | −7.79971 | −0.443710 | ||||||||
\(310\) | −14.1066 | −0.801201 | ||||||||
\(311\) | 24.7211 | 1.40180 | 0.700901 | − | 0.713258i | \(-0.252781\pi\) | ||||
0.700901 | + | 0.713258i | \(0.252781\pi\) | |||||||
\(312\) | −1.57278 | −0.0890412 | ||||||||
\(313\) | 20.9113 | 1.18198 | 0.590989 | − | 0.806680i | \(-0.298738\pi\) | ||||
0.590989 | + | 0.806680i | \(0.298738\pi\) | |||||||
\(314\) | −16.4234 | −0.926823 | ||||||||
\(315\) | 4.07769 | 0.229752 | ||||||||
\(316\) | 5.28701 | 0.297417 | ||||||||
\(317\) | −16.1572 | −0.907478 | −0.453739 | − | 0.891135i | \(-0.649910\pi\) | ||||
−0.453739 | + | 0.891135i | \(0.649910\pi\) | |||||||
\(318\) | 1.69413 | 0.0950020 | ||||||||
\(319\) | −7.72190 | −0.432343 | ||||||||
\(320\) | 4.07769 | 0.227950 | ||||||||
\(321\) | −3.74273 | −0.208899 | ||||||||
\(322\) | 3.96884 | 0.221175 | ||||||||
\(323\) | −21.5174 | −1.19726 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 18.2876 | 1.01442 | ||||||||
\(326\) | 9.19645 | 0.509344 | ||||||||
\(327\) | −2.11979 | −0.117225 | ||||||||
\(328\) | 9.32677 | 0.514984 | ||||||||
\(329\) | 5.11837 | 0.282185 | ||||||||
\(330\) | −10.4584 | −0.575716 | ||||||||
\(331\) | 5.72173 | 0.314495 | 0.157247 | − | 0.987559i | \(-0.449738\pi\) | ||||
0.157247 | + | 0.987559i | \(0.449738\pi\) | |||||||
\(332\) | −4.59673 | −0.252278 | ||||||||
\(333\) | −2.32402 | −0.127356 | ||||||||
\(334\) | 23.3380 | 1.27700 | ||||||||
\(335\) | 3.63894 | 0.198816 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | −4.89728 | −0.266772 | −0.133386 | − | 0.991064i | \(-0.542585\pi\) | ||||
−0.133386 | + | 0.991064i | \(0.542585\pi\) | |||||||
\(338\) | −10.5264 | −0.572559 | ||||||||
\(339\) | −4.22957 | −0.229719 | ||||||||
\(340\) | −23.3804 | −1.26798 | ||||||||
\(341\) | −8.87275 | −0.480486 | ||||||||
\(342\) | 3.75278 | 0.202927 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −6.29321 | −0.339307 | ||||||||
\(345\) | −16.1837 | −0.871301 | ||||||||
\(346\) | −2.19648 | −0.118083 | ||||||||
\(347\) | −6.51461 | −0.349723 | −0.174861 | − | 0.984593i | \(-0.555948\pi\) | ||||
−0.174861 | + | 0.984593i | \(0.555948\pi\) | |||||||
\(348\) | 3.01074 | 0.161393 | ||||||||
\(349\) | −6.41046 | −0.343144 | −0.171572 | − | 0.985172i | \(-0.554885\pi\) | ||||
−0.171572 | + | 0.985172i | \(0.554885\pi\) | |||||||
\(350\) | 11.6276 | 0.621520 | ||||||||
\(351\) | −1.57278 | −0.0839488 | ||||||||
\(352\) | 2.56478 | 0.136703 | ||||||||
\(353\) | −13.6793 | −0.728075 | −0.364037 | − | 0.931384i | \(-0.618602\pi\) | ||||
−0.364037 | + | 0.931384i | \(0.618602\pi\) | |||||||
\(354\) | 2.33548 | 0.124129 | ||||||||
\(355\) | 2.42466 | 0.128688 | ||||||||
\(356\) | 0.429519 | 0.0227645 | ||||||||
\(357\) | 5.73372 | 0.303461 | ||||||||
\(358\) | 1.59185 | 0.0841319 | ||||||||
\(359\) | −23.8330 | −1.25786 | −0.628930 | − | 0.777462i | \(-0.716507\pi\) | ||||
−0.628930 | + | 0.777462i | \(0.716507\pi\) | |||||||
\(360\) | 4.07769 | 0.214913 | ||||||||
\(361\) | −4.91662 | −0.258769 | ||||||||
\(362\) | −10.1396 | −0.532923 | ||||||||
\(363\) | 4.42189 | 0.232089 | ||||||||
\(364\) | 1.57278 | 0.0824361 | ||||||||
\(365\) | 32.4602 | 1.69904 | ||||||||
\(366\) | −0.135157 | −0.00706476 | ||||||||
\(367\) | 14.5553 | 0.759781 | 0.379891 | − | 0.925031i | \(-0.375962\pi\) | ||||
0.379891 | + | 0.925031i | \(0.375962\pi\) | |||||||
\(368\) | 3.96884 | 0.206890 | ||||||||
\(369\) | 9.32677 | 0.485532 | ||||||||
\(370\) | −9.47665 | −0.492668 | ||||||||
\(371\) | −1.69413 | −0.0879548 | ||||||||
\(372\) | 3.45946 | 0.179364 | ||||||||
\(373\) | −28.7370 | −1.48795 | −0.743974 | − | 0.668209i | \(-0.767061\pi\) | ||||
−0.743974 | + | 0.668209i | \(0.767061\pi\) | |||||||
\(374\) | −14.7057 | −0.760416 | ||||||||
\(375\) | −27.0252 | −1.39558 | ||||||||
\(376\) | 5.11837 | 0.263960 | ||||||||
\(377\) | −4.73524 | −0.243877 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 2.21881 | 0.113972 | 0.0569862 | − | 0.998375i | \(-0.481851\pi\) | ||||
0.0569862 | + | 0.998375i | \(0.481851\pi\) | |||||||
\(380\) | 15.3027 | 0.785012 | ||||||||
\(381\) | 11.6091 | 0.594751 | ||||||||
\(382\) | 1.00000 | 0.0511645 | ||||||||
\(383\) | 2.18019 | 0.111402 | 0.0557012 | − | 0.998447i | \(-0.482261\pi\) | ||||
0.0557012 | + | 0.998447i | \(0.482261\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 10.4584 | 0.533009 | ||||||||
\(386\) | 17.6252 | 0.897101 | ||||||||
\(387\) | −6.29321 | −0.319902 | ||||||||
\(388\) | 1.46339 | 0.0742922 | ||||||||
\(389\) | −27.0514 | −1.37156 | −0.685779 | − | 0.727810i | \(-0.740538\pi\) | ||||
−0.685779 | + | 0.727810i | \(0.740538\pi\) | |||||||
\(390\) | −6.41332 | −0.324751 | ||||||||
\(391\) | −22.7562 | −1.15083 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −11.3478 | −0.572420 | ||||||||
\(394\) | −17.5489 | −0.884103 | ||||||||
\(395\) | 21.5588 | 1.08474 | ||||||||
\(396\) | 2.56478 | 0.128885 | ||||||||
\(397\) | 31.7466 | 1.59331 | 0.796657 | − | 0.604432i | \(-0.206600\pi\) | ||||
0.796657 | + | 0.604432i | \(0.206600\pi\) | |||||||
\(398\) | −14.5178 | −0.727710 | ||||||||
\(399\) | −3.75278 | −0.187874 | ||||||||
\(400\) | 11.6276 | 0.581379 | ||||||||
\(401\) | 22.3567 | 1.11644 | 0.558221 | − | 0.829692i | \(-0.311484\pi\) | ||||
0.558221 | + | 0.829692i | \(0.311484\pi\) | |||||||
\(402\) | −0.892401 | −0.0445089 | ||||||||
\(403\) | −5.44097 | −0.271034 | ||||||||
\(404\) | −7.75739 | −0.385945 | ||||||||
\(405\) | 4.07769 | 0.202622 | ||||||||
\(406\) | −3.01074 | −0.149421 | ||||||||
\(407\) | −5.96061 | −0.295457 | ||||||||
\(408\) | 5.73372 | 0.283861 | ||||||||
\(409\) | 24.7892 | 1.22575 | 0.612875 | − | 0.790180i | \(-0.290013\pi\) | ||||
0.612875 | + | 0.790180i | \(0.290013\pi\) | |||||||
\(410\) | 38.0317 | 1.87825 | ||||||||
\(411\) | 7.15669 | 0.353014 | ||||||||
\(412\) | 7.79971 | 0.384264 | ||||||||
\(413\) | −2.33548 | −0.114922 | ||||||||
\(414\) | 3.96884 | 0.195058 | ||||||||
\(415\) | −18.7441 | −0.920110 | ||||||||
\(416\) | 1.57278 | 0.0771119 | ||||||||
\(417\) | 7.99822 | 0.391674 | ||||||||
\(418\) | 9.62507 | 0.470778 | ||||||||
\(419\) | 7.62384 | 0.372449 | 0.186225 | − | 0.982507i | \(-0.440375\pi\) | ||||
0.186225 | + | 0.982507i | \(0.440375\pi\) | |||||||
\(420\) | −4.07769 | −0.198971 | ||||||||
\(421\) | −9.35074 | −0.455727 | −0.227863 | − | 0.973693i | \(-0.573174\pi\) | ||||
−0.227863 | + | 0.973693i | \(0.573174\pi\) | |||||||
\(422\) | 13.8456 | 0.673993 | ||||||||
\(423\) | 5.11837 | 0.248864 | ||||||||
\(424\) | −1.69413 | −0.0822742 | ||||||||
\(425\) | −66.6693 | −3.23394 | ||||||||
\(426\) | −0.594616 | −0.0288092 | ||||||||
\(427\) | 0.135157 | 0.00654069 | ||||||||
\(428\) | 3.74273 | 0.180912 | ||||||||
\(429\) | −4.03384 | −0.194756 | ||||||||
\(430\) | −25.6618 | −1.23752 | ||||||||
\(431\) | −4.62815 | −0.222930 | −0.111465 | − | 0.993768i | \(-0.535554\pi\) | ||||
−0.111465 | + | 0.993768i | \(0.535554\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −1.89413 | −0.0910261 | −0.0455131 | − | 0.998964i | \(-0.514492\pi\) | ||||
−0.0455131 | + | 0.998964i | \(0.514492\pi\) | |||||||
\(434\) | −3.45946 | −0.166059 | ||||||||
\(435\) | 12.2769 | 0.588631 | ||||||||
\(436\) | 2.11979 | 0.101520 | ||||||||
\(437\) | 14.8942 | 0.712486 | ||||||||
\(438\) | −7.96042 | −0.380364 | ||||||||
\(439\) | −13.9275 | −0.664723 | −0.332362 | − | 0.943152i | \(-0.607845\pi\) | ||||
−0.332362 | + | 0.943152i | \(0.607845\pi\) | |||||||
\(440\) | 10.4584 | 0.498585 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −9.01789 | −0.428937 | ||||||||
\(443\) | 8.69247 | 0.412992 | 0.206496 | − | 0.978447i | \(-0.433794\pi\) | ||||
0.206496 | + | 0.978447i | \(0.433794\pi\) | |||||||
\(444\) | 2.32402 | 0.110293 | ||||||||
\(445\) | 1.75145 | 0.0830266 | ||||||||
\(446\) | 5.47594 | 0.259293 | ||||||||
\(447\) | 12.3489 | 0.584082 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 29.6829 | 1.40082 | 0.700412 | − | 0.713739i | \(-0.253000\pi\) | ||||
0.700412 | + | 0.713739i | \(0.253000\pi\) | |||||||
\(450\) | 11.6276 | 0.548129 | ||||||||
\(451\) | 23.9211 | 1.12640 | ||||||||
\(452\) | 4.22957 | 0.198942 | ||||||||
\(453\) | 3.04757 | 0.143187 | ||||||||
\(454\) | 13.7497 | 0.645307 | ||||||||
\(455\) | 6.41332 | 0.300661 | ||||||||
\(456\) | −3.75278 | −0.175740 | ||||||||
\(457\) | 13.7098 | 0.641319 | 0.320659 | − | 0.947195i | \(-0.396096\pi\) | ||||
0.320659 | + | 0.947195i | \(0.396096\pi\) | |||||||
\(458\) | −2.69390 | −0.125878 | ||||||||
\(459\) | 5.73372 | 0.267627 | ||||||||
\(460\) | 16.1837 | 0.754569 | ||||||||
\(461\) | −22.5901 | −1.05213 | −0.526063 | − | 0.850446i | \(-0.676332\pi\) | ||||
−0.526063 | + | 0.850446i | \(0.676332\pi\) | |||||||
\(462\) | −2.56478 | −0.119324 | ||||||||
\(463\) | 20.8874 | 0.970721 | 0.485360 | − | 0.874314i | \(-0.338688\pi\) | ||||
0.485360 | + | 0.874314i | \(0.338688\pi\) | |||||||
\(464\) | −3.01074 | −0.139770 | ||||||||
\(465\) | 14.1066 | 0.654178 | ||||||||
\(466\) | 11.4638 | 0.531052 | ||||||||
\(467\) | 17.6380 | 0.816188 | 0.408094 | − | 0.912940i | \(-0.366194\pi\) | ||||
0.408094 | + | 0.912940i | \(0.366194\pi\) | |||||||
\(468\) | 1.57278 | 0.0727018 | ||||||||
\(469\) | 0.892401 | 0.0412072 | ||||||||
\(470\) | 20.8711 | 0.962714 | ||||||||
\(471\) | 16.4234 | 0.756748 | ||||||||
\(472\) | −2.33548 | −0.107499 | ||||||||
\(473\) | −16.1407 | −0.742151 | ||||||||
\(474\) | −5.28701 | −0.242840 | ||||||||
\(475\) | 43.6358 | 2.00215 | ||||||||
\(476\) | −5.73372 | −0.262805 | ||||||||
\(477\) | −1.69413 | −0.0775688 | ||||||||
\(478\) | −20.2601 | −0.926674 | ||||||||
\(479\) | 28.7142 | 1.31199 | 0.655993 | − | 0.754767i | \(-0.272250\pi\) | ||||
0.655993 | + | 0.754767i | \(0.272250\pi\) | |||||||
\(480\) | −4.07769 | −0.186120 | ||||||||
\(481\) | −3.65518 | −0.166662 | ||||||||
\(482\) | 10.0873 | 0.459463 | ||||||||
\(483\) | −3.96884 | −0.180588 | ||||||||
\(484\) | −4.42189 | −0.200995 | ||||||||
\(485\) | 5.96724 | 0.270958 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −9.60371 | −0.435186 | −0.217593 | − | 0.976040i | \(-0.569820\pi\) | ||||
−0.217593 | + | 0.976040i | \(0.569820\pi\) | |||||||
\(488\) | 0.135157 | 0.00611826 | ||||||||
\(489\) | −9.19645 | −0.415878 | ||||||||
\(490\) | 4.07769 | 0.184211 | ||||||||
\(491\) | 19.0198 | 0.858350 | 0.429175 | − | 0.903221i | \(-0.358804\pi\) | ||||
0.429175 | + | 0.903221i | \(0.358804\pi\) | |||||||
\(492\) | −9.32677 | −0.420483 | ||||||||
\(493\) | 17.2627 | 0.777475 | ||||||||
\(494\) | 5.90231 | 0.265557 | ||||||||
\(495\) | 10.4584 | 0.470070 | ||||||||
\(496\) | −3.45946 | −0.155334 | ||||||||
\(497\) | 0.594616 | 0.0266722 | ||||||||
\(498\) | 4.59673 | 0.205984 | ||||||||
\(499\) | −1.33794 | −0.0598943 | −0.0299472 | − | 0.999551i | \(-0.509534\pi\) | ||||
−0.0299472 | + | 0.999551i | \(0.509534\pi\) | |||||||
\(500\) | 27.0252 | 1.20861 | ||||||||
\(501\) | −23.3380 | −1.04267 | ||||||||
\(502\) | −17.4515 | −0.778898 | ||||||||
\(503\) | 4.43400 | 0.197702 | 0.0988511 | − | 0.995102i | \(-0.468483\pi\) | ||||
0.0988511 | + | 0.995102i | \(0.468483\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −31.6323 | −1.40762 | ||||||||
\(506\) | 10.1792 | 0.452521 | ||||||||
\(507\) | 10.5264 | 0.467492 | ||||||||
\(508\) | −11.6091 | −0.515069 | ||||||||
\(509\) | −6.59567 | −0.292348 | −0.146174 | − | 0.989259i | \(-0.546696\pi\) | ||||
−0.146174 | + | 0.989259i | \(0.546696\pi\) | |||||||
\(510\) | 23.3804 | 1.03530 | ||||||||
\(511\) | 7.96042 | 0.352148 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.75278 | −0.165689 | ||||||||
\(514\) | −18.6271 | −0.821608 | ||||||||
\(515\) | 31.8048 | 1.40149 | ||||||||
\(516\) | 6.29321 | 0.277043 | ||||||||
\(517\) | 13.1275 | 0.577347 | ||||||||
\(518\) | −2.32402 | −0.102112 | ||||||||
\(519\) | 2.19648 | 0.0964147 | ||||||||
\(520\) | 6.41332 | 0.281243 | ||||||||
\(521\) | 6.18280 | 0.270873 | 0.135437 | − | 0.990786i | \(-0.456756\pi\) | ||||
0.135437 | + | 0.990786i | \(0.456756\pi\) | |||||||
\(522\) | −3.01074 | −0.131777 | ||||||||
\(523\) | 15.8645 | 0.693708 | 0.346854 | − | 0.937919i | \(-0.387250\pi\) | ||||
0.346854 | + | 0.937919i | \(0.387250\pi\) | |||||||
\(524\) | 11.3478 | 0.495730 | ||||||||
\(525\) | −11.6276 | −0.507469 | ||||||||
\(526\) | 12.7520 | 0.556015 | ||||||||
\(527\) | 19.8355 | 0.864050 | ||||||||
\(528\) | −2.56478 | −0.111618 | ||||||||
\(529\) | −7.24832 | −0.315144 | ||||||||
\(530\) | −6.90814 | −0.300070 | ||||||||
\(531\) | −2.33548 | −0.101351 | ||||||||
\(532\) | 3.75278 | 0.162704 | ||||||||
\(533\) | 14.6690 | 0.635383 | ||||||||
\(534\) | −0.429519 | −0.0185871 | ||||||||
\(535\) | 15.2617 | 0.659821 | ||||||||
\(536\) | 0.892401 | 0.0385458 | ||||||||
\(537\) | −1.59185 | −0.0686934 | ||||||||
\(538\) | −19.8773 | −0.856973 | ||||||||
\(539\) | 2.56478 | 0.110473 | ||||||||
\(540\) | −4.07769 | −0.175476 | ||||||||
\(541\) | 4.59720 | 0.197649 | 0.0988246 | − | 0.995105i | \(-0.468492\pi\) | ||||
0.0988246 | + | 0.995105i | \(0.468492\pi\) | |||||||
\(542\) | 0.00929113 | 0.000399088 0 | ||||||||
\(543\) | 10.1396 | 0.435130 | ||||||||
\(544\) | −5.73372 | −0.245831 | ||||||||
\(545\) | 8.64386 | 0.370262 | ||||||||
\(546\) | −1.57278 | −0.0673088 | ||||||||
\(547\) | 6.93569 | 0.296549 | 0.148274 | − | 0.988946i | \(-0.452628\pi\) | ||||
0.148274 | + | 0.988946i | \(0.452628\pi\) | |||||||
\(548\) | −7.15669 | −0.305719 | ||||||||
\(549\) | 0.135157 | 0.00576835 | ||||||||
\(550\) | 29.8222 | 1.27162 | ||||||||
\(551\) | −11.2987 | −0.481339 | ||||||||
\(552\) | −3.96884 | −0.168925 | ||||||||
\(553\) | 5.28701 | 0.224826 | ||||||||
\(554\) | 20.3778 | 0.865771 | ||||||||
\(555\) | 9.47665 | 0.402262 | ||||||||
\(556\) | −7.99822 | −0.339200 | ||||||||
\(557\) | 43.7679 | 1.85450 | 0.927252 | − | 0.374437i | \(-0.122164\pi\) | ||||
0.927252 | + | 0.374437i | \(0.122164\pi\) | |||||||
\(558\) | −3.45946 | −0.146450 | ||||||||
\(559\) | −9.89785 | −0.418634 | ||||||||
\(560\) | 4.07769 | 0.172314 | ||||||||
\(561\) | 14.7057 | 0.620877 | ||||||||
\(562\) | −32.5466 | −1.37290 | ||||||||
\(563\) | 9.14786 | 0.385536 | 0.192768 | − | 0.981244i | \(-0.438253\pi\) | ||||
0.192768 | + | 0.981244i | \(0.438253\pi\) | |||||||
\(564\) | −5.11837 | −0.215522 | ||||||||
\(565\) | 17.2469 | 0.725582 | ||||||||
\(566\) | −12.0390 | −0.506035 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0.594616 | 0.0249495 | ||||||||
\(569\) | 17.4815 | 0.732863 | 0.366432 | − | 0.930445i | \(-0.380579\pi\) | ||||
0.366432 | + | 0.930445i | \(0.380579\pi\) | |||||||
\(570\) | −15.3027 | −0.640959 | ||||||||
\(571\) | 37.3185 | 1.56173 | 0.780865 | − | 0.624700i | \(-0.214779\pi\) | ||||
0.780865 | + | 0.624700i | \(0.214779\pi\) | |||||||
\(572\) | 4.03384 | 0.168663 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | 9.32677 | 0.389292 | ||||||||
\(575\) | 46.1480 | 1.92450 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 17.6927 | 0.736555 | 0.368277 | − | 0.929716i | \(-0.379948\pi\) | ||||
0.368277 | + | 0.929716i | \(0.379948\pi\) | |||||||
\(578\) | 15.8755 | 0.660336 | ||||||||
\(579\) | −17.6252 | −0.732480 | ||||||||
\(580\) | −12.2769 | −0.509770 | ||||||||
\(581\) | −4.59673 | −0.190705 | ||||||||
\(582\) | −1.46339 | −0.0606593 | ||||||||
\(583\) | −4.34507 | −0.179954 | ||||||||
\(584\) | 7.96042 | 0.329405 | ||||||||
\(585\) | 6.41332 | 0.265158 | ||||||||
\(586\) | −7.57841 | −0.313061 | ||||||||
\(587\) | −4.97625 | −0.205392 | −0.102696 | − | 0.994713i | \(-0.532747\pi\) | ||||
−0.102696 | + | 0.994713i | \(0.532747\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | −12.9826 | −0.534938 | ||||||||
\(590\) | −9.52338 | −0.392071 | ||||||||
\(591\) | 17.5489 | 0.721867 | ||||||||
\(592\) | −2.32402 | −0.0955168 | ||||||||
\(593\) | −6.09259 | −0.250193 | −0.125096 | − | 0.992145i | \(-0.539924\pi\) | ||||
−0.125096 | + | 0.992145i | \(0.539924\pi\) | |||||||
\(594\) | −2.56478 | −0.105234 | ||||||||
\(595\) | −23.3804 | −0.958501 | ||||||||
\(596\) | −12.3489 | −0.505830 | ||||||||
\(597\) | 14.5178 | 0.594173 | ||||||||
\(598\) | 6.24211 | 0.255259 | ||||||||
\(599\) | 5.24382 | 0.214257 | 0.107128 | − | 0.994245i | \(-0.465834\pi\) | ||||
0.107128 | + | 0.994245i | \(0.465834\pi\) | |||||||
\(600\) | −11.6276 | −0.474694 | ||||||||
\(601\) | −13.8564 | −0.565213 | −0.282607 | − | 0.959236i | \(-0.591199\pi\) | ||||
−0.282607 | + | 0.959236i | \(0.591199\pi\) | |||||||
\(602\) | −6.29321 | −0.256492 | ||||||||
\(603\) | 0.892401 | 0.0363414 | ||||||||
\(604\) | −3.04757 | −0.124004 | ||||||||
\(605\) | −18.0311 | −0.733069 | ||||||||
\(606\) | 7.75739 | 0.315123 | ||||||||
\(607\) | −13.5037 | −0.548096 | −0.274048 | − | 0.961716i | \(-0.588363\pi\) | ||||
−0.274048 | + | 0.961716i | \(0.588363\pi\) | |||||||
\(608\) | 3.75278 | 0.152195 | ||||||||
\(609\) | 3.01074 | 0.122001 | ||||||||
\(610\) | 0.551128 | 0.0223145 | ||||||||
\(611\) | 8.05007 | 0.325671 | ||||||||
\(612\) | −5.73372 | −0.231772 | ||||||||
\(613\) | −41.5318 | −1.67745 | −0.838727 | − | 0.544551i | \(-0.816700\pi\) | ||||
−0.838727 | + | 0.544551i | \(0.816700\pi\) | |||||||
\(614\) | −9.76130 | −0.393934 | ||||||||
\(615\) | −38.0317 | −1.53359 | ||||||||
\(616\) | 2.56478 | 0.103338 | ||||||||
\(617\) | 34.0369 | 1.37027 | 0.685137 | − | 0.728414i | \(-0.259742\pi\) | ||||
0.685137 | + | 0.728414i | \(0.259742\pi\) | |||||||
\(618\) | −7.79971 | −0.313750 | ||||||||
\(619\) | −28.1786 | −1.13259 | −0.566297 | − | 0.824202i | \(-0.691624\pi\) | ||||
−0.566297 | + | 0.824202i | \(0.691624\pi\) | |||||||
\(620\) | −14.1066 | −0.566535 | ||||||||
\(621\) | −3.96884 | −0.159264 | ||||||||
\(622\) | 24.7211 | 0.991224 | ||||||||
\(623\) | 0.429519 | 0.0172083 | ||||||||
\(624\) | −1.57278 | −0.0629616 | ||||||||
\(625\) | 52.0628 | 2.08251 | ||||||||
\(626\) | 20.9113 | 0.835784 | ||||||||
\(627\) | −9.62507 | −0.384388 | ||||||||
\(628\) | −16.4234 | −0.655363 | ||||||||
\(629\) | 13.3253 | 0.531314 | ||||||||
\(630\) | 4.07769 | 0.162459 | ||||||||
\(631\) | −33.2427 | −1.32337 | −0.661686 | − | 0.749781i | \(-0.730159\pi\) | ||||
−0.661686 | + | 0.749781i | \(0.730159\pi\) | |||||||
\(632\) | 5.28701 | 0.210306 | ||||||||
\(633\) | −13.8456 | −0.550313 | ||||||||
\(634\) | −16.1572 | −0.641684 | ||||||||
\(635\) | −47.3382 | −1.87856 | ||||||||
\(636\) | 1.69413 | 0.0671766 | ||||||||
\(637\) | 1.57278 | 0.0623159 | ||||||||
\(638\) | −7.72190 | −0.305713 | ||||||||
\(639\) | 0.594616 | 0.0235226 | ||||||||
\(640\) | 4.07769 | 0.161185 | ||||||||
\(641\) | −44.1877 | −1.74531 | −0.872655 | − | 0.488338i | \(-0.837603\pi\) | ||||
−0.872655 | + | 0.488338i | \(0.837603\pi\) | |||||||
\(642\) | −3.74273 | −0.147714 | ||||||||
\(643\) | 20.4912 | 0.808092 | 0.404046 | − | 0.914739i | \(-0.367604\pi\) | ||||
0.404046 | + | 0.914739i | \(0.367604\pi\) | |||||||
\(644\) | 3.96884 | 0.156394 | ||||||||
\(645\) | 25.6618 | 1.01043 | ||||||||
\(646\) | −21.5174 | −0.846591 | ||||||||
\(647\) | 27.5450 | 1.08290 | 0.541452 | − | 0.840732i | \(-0.317875\pi\) | ||||
0.541452 | + | 0.840732i | \(0.317875\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −5.99001 | −0.235128 | ||||||||
\(650\) | 18.2876 | 0.717300 | ||||||||
\(651\) | 3.45946 | 0.135587 | ||||||||
\(652\) | 9.19645 | 0.360161 | ||||||||
\(653\) | 20.9651 | 0.820429 | 0.410214 | − | 0.911989i | \(-0.365454\pi\) | ||||
0.410214 | + | 0.911989i | \(0.365454\pi\) | |||||||
\(654\) | −2.11979 | −0.0828904 | ||||||||
\(655\) | 46.2728 | 1.80803 | ||||||||
\(656\) | 9.32677 | 0.364149 | ||||||||
\(657\) | 7.96042 | 0.310566 | ||||||||
\(658\) | 5.11837 | 0.199535 | ||||||||
\(659\) | −6.45875 | −0.251597 | −0.125799 | − | 0.992056i | \(-0.540149\pi\) | ||||
−0.125799 | + | 0.992056i | \(0.540149\pi\) | |||||||
\(660\) | −10.4584 | −0.407093 | ||||||||
\(661\) | 9.51195 | 0.369972 | 0.184986 | − | 0.982741i | \(-0.440776\pi\) | ||||
0.184986 | + | 0.982741i | \(0.440776\pi\) | |||||||
\(662\) | 5.72173 | 0.222381 | ||||||||
\(663\) | 9.01789 | 0.350226 | ||||||||
\(664\) | −4.59673 | −0.178388 | ||||||||
\(665\) | 15.3027 | 0.593413 | ||||||||
\(666\) | −2.32402 | −0.0900541 | ||||||||
\(667\) | −11.9491 | −0.462673 | ||||||||
\(668\) | 23.3380 | 0.902976 | ||||||||
\(669\) | −5.47594 | −0.211712 | ||||||||
\(670\) | 3.63894 | 0.140584 | ||||||||
\(671\) | 0.346648 | 0.0133822 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −37.5547 | −1.44763 | −0.723813 | − | 0.689996i | \(-0.757612\pi\) | ||||
−0.723813 | + | 0.689996i | \(0.757612\pi\) | |||||||
\(674\) | −4.89728 | −0.188636 | ||||||||
\(675\) | −11.6276 | −0.447546 | ||||||||
\(676\) | −10.5264 | −0.404860 | ||||||||
\(677\) | 12.6435 | 0.485931 | 0.242965 | − | 0.970035i | \(-0.421880\pi\) | ||||
0.242965 | + | 0.970035i | \(0.421880\pi\) | |||||||
\(678\) | −4.22957 | −0.162436 | ||||||||
\(679\) | 1.46339 | 0.0561596 | ||||||||
\(680\) | −23.3804 | −0.896596 | ||||||||
\(681\) | −13.7497 | −0.526891 | ||||||||
\(682\) | −8.87275 | −0.339755 | ||||||||
\(683\) | −17.7185 | −0.677979 | −0.338989 | − | 0.940790i | \(-0.610085\pi\) | ||||
−0.338989 | + | 0.940790i | \(0.610085\pi\) | |||||||
\(684\) | 3.75278 | 0.143491 | ||||||||
\(685\) | −29.1828 | −1.11502 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 2.69390 | 0.102779 | ||||||||
\(688\) | −6.29321 | −0.239926 | ||||||||
\(689\) | −2.66449 | −0.101509 | ||||||||
\(690\) | −16.1837 | −0.616103 | ||||||||
\(691\) | 7.09699 | 0.269982 | 0.134991 | − | 0.990847i | \(-0.456899\pi\) | ||||
0.134991 | + | 0.990847i | \(0.456899\pi\) | |||||||
\(692\) | −2.19648 | −0.0834976 | ||||||||
\(693\) | 2.56478 | 0.0974280 | ||||||||
\(694\) | −6.51461 | −0.247291 | ||||||||
\(695\) | −32.6143 | −1.23713 | ||||||||
\(696\) | 3.01074 | 0.114122 | ||||||||
\(697\) | −53.4771 | −2.02559 | ||||||||
\(698\) | −6.41046 | −0.242640 | ||||||||
\(699\) | −11.4638 | −0.433602 | ||||||||
\(700\) | 11.6276 | 0.439481 | ||||||||
\(701\) | −5.18003 | −0.195647 | −0.0978234 | − | 0.995204i | \(-0.531188\pi\) | ||||
−0.0978234 | + | 0.995204i | \(0.531188\pi\) | |||||||
\(702\) | −1.57278 | −0.0593608 | ||||||||
\(703\) | −8.72156 | −0.328940 | ||||||||
\(704\) | 2.56478 | 0.0966639 | ||||||||
\(705\) | −20.8711 | −0.786053 | ||||||||
\(706\) | −13.6793 | −0.514827 | ||||||||
\(707\) | −7.75739 | −0.291747 | ||||||||
\(708\) | 2.33548 | 0.0877728 | ||||||||
\(709\) | −34.2080 | −1.28471 | −0.642355 | − | 0.766407i | \(-0.722043\pi\) | ||||
−0.642355 | + | 0.766407i | \(0.722043\pi\) | |||||||
\(710\) | 2.42466 | 0.0909959 | ||||||||
\(711\) | 5.28701 | 0.198278 | ||||||||
\(712\) | 0.429519 | 0.0160969 | ||||||||
\(713\) | −13.7300 | −0.514193 | ||||||||
\(714\) | 5.73372 | 0.214579 | ||||||||
\(715\) | 16.4488 | 0.615149 | ||||||||
\(716\) | 1.59185 | 0.0594902 | ||||||||
\(717\) | 20.2601 | 0.756626 | ||||||||
\(718\) | −23.8330 | −0.889441 | ||||||||
\(719\) | −3.65623 | −0.136354 | −0.0681771 | − | 0.997673i | \(-0.521718\pi\) | ||||
−0.0681771 | + | 0.997673i | \(0.521718\pi\) | |||||||
\(720\) | 4.07769 | 0.151967 | ||||||||
\(721\) | 7.79971 | 0.290476 | ||||||||
\(722\) | −4.91662 | −0.182978 | ||||||||
\(723\) | −10.0873 | −0.375150 | ||||||||
\(724\) | −10.1396 | −0.376834 | ||||||||
\(725\) | −35.0076 | −1.30015 | ||||||||
\(726\) | 4.42189 | 0.164112 | ||||||||
\(727\) | −36.8838 | −1.36794 | −0.683971 | − | 0.729509i | \(-0.739749\pi\) | ||||
−0.683971 | + | 0.729509i | \(0.739749\pi\) | |||||||
\(728\) | 1.57278 | 0.0582911 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 32.4602 | 1.20140 | ||||||||
\(731\) | 36.0835 | 1.33460 | ||||||||
\(732\) | −0.135157 | −0.00499554 | ||||||||
\(733\) | 18.0900 | 0.668170 | 0.334085 | − | 0.942543i | \(-0.391573\pi\) | ||||
0.334085 | + | 0.942543i | \(0.391573\pi\) | |||||||
\(734\) | 14.5553 | 0.537247 | ||||||||
\(735\) | −4.07769 | −0.150408 | ||||||||
\(736\) | 3.96884 | 0.146293 | ||||||||
\(737\) | 2.28881 | 0.0843096 | ||||||||
\(738\) | 9.32677 | 0.343323 | ||||||||
\(739\) | 15.0147 | 0.552323 | 0.276162 | − | 0.961111i | \(-0.410937\pi\) | ||||
0.276162 | + | 0.961111i | \(0.410937\pi\) | |||||||
\(740\) | −9.47665 | −0.348369 | ||||||||
\(741\) | −5.90231 | −0.216827 | ||||||||
\(742\) | −1.69413 | −0.0621934 | ||||||||
\(743\) | 35.6810 | 1.30901 | 0.654504 | − | 0.756059i | \(-0.272878\pi\) | ||||
0.654504 | + | 0.756059i | \(0.272878\pi\) | |||||||
\(744\) | 3.45946 | 0.126830 | ||||||||
\(745\) | −50.3550 | −1.84486 | ||||||||
\(746\) | −28.7370 | −1.05214 | ||||||||
\(747\) | −4.59673 | −0.168186 | ||||||||
\(748\) | −14.7057 | −0.537695 | ||||||||
\(749\) | 3.74273 | 0.136756 | ||||||||
\(750\) | −27.0252 | −0.986823 | ||||||||
\(751\) | −21.6705 | −0.790768 | −0.395384 | − | 0.918516i | \(-0.629389\pi\) | ||||
−0.395384 | + | 0.918516i | \(0.629389\pi\) | |||||||
\(752\) | 5.11837 | 0.186648 | ||||||||
\(753\) | 17.4515 | 0.635968 | ||||||||
\(754\) | −4.73524 | −0.172447 | ||||||||
\(755\) | −12.4271 | −0.452267 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | −34.3745 | −1.24936 | −0.624681 | − | 0.780880i | \(-0.714771\pi\) | ||||
−0.624681 | + | 0.780880i | \(0.714771\pi\) | |||||||
\(758\) | 2.21881 | 0.0805907 | ||||||||
\(759\) | −10.1792 | −0.369482 | ||||||||
\(760\) | 15.3027 | 0.555087 | ||||||||
\(761\) | −38.0492 | −1.37928 | −0.689641 | − | 0.724152i | \(-0.742232\pi\) | ||||
−0.689641 | + | 0.724152i | \(0.742232\pi\) | |||||||
\(762\) | 11.6091 | 0.420552 | ||||||||
\(763\) | 2.11979 | 0.0767416 | ||||||||
\(764\) | 1.00000 | 0.0361787 | ||||||||
\(765\) | −23.3804 | −0.845318 | ||||||||
\(766\) | 2.18019 | 0.0787734 | ||||||||
\(767\) | −3.67320 | −0.132632 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 38.3242 | 1.38201 | 0.691003 | − | 0.722852i | \(-0.257169\pi\) | ||||
0.691003 | + | 0.722852i | \(0.257169\pi\) | |||||||
\(770\) | 10.4584 | 0.376894 | ||||||||
\(771\) | 18.6271 | 0.670840 | ||||||||
\(772\) | 17.6252 | 0.634346 | ||||||||
\(773\) | −51.4478 | −1.85045 | −0.925225 | − | 0.379419i | \(-0.876124\pi\) | ||||
−0.925225 | + | 0.379419i | \(0.876124\pi\) | |||||||
\(774\) | −6.29321 | −0.226205 | ||||||||
\(775\) | −40.2251 | −1.44493 | ||||||||
\(776\) | 1.46339 | 0.0525325 | ||||||||
\(777\) | 2.32402 | 0.0833739 | ||||||||
\(778\) | −27.0514 | −0.969838 | ||||||||
\(779\) | 35.0013 | 1.25405 | ||||||||
\(780\) | −6.41332 | −0.229634 | ||||||||
\(781\) | 1.52506 | 0.0545709 | ||||||||
\(782\) | −22.7562 | −0.813760 | ||||||||
\(783\) | 3.01074 | 0.107595 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −66.9694 | −2.39024 | ||||||||
\(786\) | −11.3478 | −0.404762 | ||||||||
\(787\) | 29.6509 | 1.05694 | 0.528471 | − | 0.848952i | \(-0.322766\pi\) | ||||
0.528471 | + | 0.848952i | \(0.322766\pi\) | |||||||
\(788\) | −17.5489 | −0.625155 | ||||||||
\(789\) | −12.7520 | −0.453984 | ||||||||
\(790\) | 21.5588 | 0.767027 | ||||||||
\(791\) | 4.22957 | 0.150386 | ||||||||
\(792\) | 2.56478 | 0.0911356 | ||||||||
\(793\) | 0.212572 | 0.00754865 | ||||||||
\(794\) | 31.7466 | 1.12664 | ||||||||
\(795\) | 6.90814 | 0.245006 | ||||||||
\(796\) | −14.5178 | −0.514569 | ||||||||
\(797\) | 27.1118 | 0.960349 | 0.480174 | − | 0.877173i | \(-0.340573\pi\) | ||||
0.480174 | + | 0.877173i | \(0.340573\pi\) | |||||||
\(798\) | −3.75278 | −0.132847 | ||||||||
\(799\) | −29.3473 | −1.03823 | ||||||||
\(800\) | 11.6276 | 0.411097 | ||||||||
\(801\) | 0.429519 | 0.0151763 | ||||||||
\(802\) | 22.3567 | 0.789444 | ||||||||
\(803\) | 20.4168 | 0.720491 | ||||||||
\(804\) | −0.892401 | −0.0314726 | ||||||||
\(805\) | 16.1837 | 0.570401 | ||||||||
\(806\) | −5.44097 | −0.191650 | ||||||||
\(807\) | 19.8773 | 0.699716 | ||||||||
\(808\) | −7.75739 | −0.272904 | ||||||||
\(809\) | −19.3607 | −0.680685 | −0.340343 | − | 0.940301i | \(-0.610543\pi\) | ||||
−0.340343 | + | 0.940301i | \(0.610543\pi\) | |||||||
\(810\) | 4.07769 | 0.143276 | ||||||||
\(811\) | −4.24813 | −0.149172 | −0.0745861 | − | 0.997215i | \(-0.523764\pi\) | ||||
−0.0745861 | + | 0.997215i | \(0.523764\pi\) | |||||||
\(812\) | −3.01074 | −0.105656 | ||||||||
\(813\) | −0.00929113 | −0.000325854 0 | ||||||||
\(814\) | −5.96061 | −0.208919 | ||||||||
\(815\) | 37.5003 | 1.31358 | ||||||||
\(816\) | 5.73372 | 0.200720 | ||||||||
\(817\) | −23.6171 | −0.826256 | ||||||||
\(818\) | 24.7892 | 0.866735 | ||||||||
\(819\) | 1.57278 | 0.0549574 | ||||||||
\(820\) | 38.0317 | 1.32812 | ||||||||
\(821\) | 5.13428 | 0.179188 | 0.0895939 | − | 0.995978i | \(-0.471443\pi\) | ||||
0.0895939 | + | 0.995978i | \(0.471443\pi\) | |||||||
\(822\) | 7.15669 | 0.249618 | ||||||||
\(823\) | 6.50021 | 0.226583 | 0.113291 | − | 0.993562i | \(-0.463861\pi\) | ||||
0.113291 | + | 0.993562i | \(0.463861\pi\) | |||||||
\(824\) | 7.79971 | 0.271716 | ||||||||
\(825\) | −29.8222 | −1.03828 | ||||||||
\(826\) | −2.33548 | −0.0812618 | ||||||||
\(827\) | −3.45720 | −0.120219 | −0.0601093 | − | 0.998192i | \(-0.519145\pi\) | ||||
−0.0601093 | + | 0.998192i | \(0.519145\pi\) | |||||||
\(828\) | 3.96884 | 0.137927 | ||||||||
\(829\) | 2.37343 | 0.0824327 | 0.0412164 | − | 0.999150i | \(-0.486877\pi\) | ||||
0.0412164 | + | 0.999150i | \(0.486877\pi\) | |||||||
\(830\) | −18.7441 | −0.650616 | ||||||||
\(831\) | −20.3778 | −0.706899 | ||||||||
\(832\) | 1.57278 | 0.0545264 | ||||||||
\(833\) | −5.73372 | −0.198662 | ||||||||
\(834\) | 7.99822 | 0.276956 | ||||||||
\(835\) | 95.1653 | 3.29333 | ||||||||
\(836\) | 9.62507 | 0.332890 | ||||||||
\(837\) | 3.45946 | 0.119576 | ||||||||
\(838\) | 7.62384 | 0.263361 | ||||||||
\(839\) | 15.6160 | 0.539126 | 0.269563 | − | 0.962983i | \(-0.413121\pi\) | ||||
0.269563 | + | 0.962983i | \(0.413121\pi\) | |||||||
\(840\) | −4.07769 | −0.140694 | ||||||||
\(841\) | −19.9354 | −0.687429 | ||||||||
\(842\) | −9.35074 | −0.322248 | ||||||||
\(843\) | 32.5466 | 1.12096 | ||||||||
\(844\) | 13.8456 | 0.476585 | ||||||||
\(845\) | −42.9233 | −1.47661 | ||||||||
\(846\) | 5.11837 | 0.175973 | ||||||||
\(847\) | −4.42189 | −0.151938 | ||||||||
\(848\) | −1.69413 | −0.0581766 | ||||||||
\(849\) | 12.0390 | 0.413176 | ||||||||
\(850\) | −66.6693 | −2.28674 | ||||||||
\(851\) | −9.22367 | −0.316183 | ||||||||
\(852\) | −0.594616 | −0.0203712 | ||||||||
\(853\) | 32.7032 | 1.11974 | 0.559868 | − | 0.828582i | \(-0.310852\pi\) | ||||
0.559868 | + | 0.828582i | \(0.310852\pi\) | |||||||
\(854\) | 0.135157 | 0.00462497 | ||||||||
\(855\) | 15.3027 | 0.523341 | ||||||||
\(856\) | 3.74273 | 0.127924 | ||||||||
\(857\) | 50.0858 | 1.71090 | 0.855450 | − | 0.517886i | \(-0.173281\pi\) | ||||
0.855450 | + | 0.517886i | \(0.173281\pi\) | |||||||
\(858\) | −4.03384 | −0.137713 | ||||||||
\(859\) | 34.4917 | 1.17684 | 0.588421 | − | 0.808555i | \(-0.299750\pi\) | ||||
0.588421 | + | 0.808555i | \(0.299750\pi\) | |||||||
\(860\) | −25.6618 | −0.875060 | ||||||||
\(861\) | −9.32677 | −0.317855 | ||||||||
\(862\) | −4.62815 | −0.157635 | ||||||||
\(863\) | −54.6981 | −1.86194 | −0.930972 | − | 0.365090i | \(-0.881038\pi\) | ||||
−0.930972 | + | 0.365090i | \(0.881038\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −8.95657 | −0.304532 | ||||||||
\(866\) | −1.89413 | −0.0643652 | ||||||||
\(867\) | −15.8755 | −0.539162 | ||||||||
\(868\) | −3.45946 | −0.117422 | ||||||||
\(869\) | 13.5600 | 0.459992 | ||||||||
\(870\) | 12.2769 | 0.416225 | ||||||||
\(871\) | 1.40355 | 0.0475575 | ||||||||
\(872\) | 2.11979 | 0.0717852 | ||||||||
\(873\) | 1.46339 | 0.0495281 | ||||||||
\(874\) | 14.8942 | 0.503803 | ||||||||
\(875\) | 27.0252 | 0.913620 | ||||||||
\(876\) | −7.96042 | −0.268958 | ||||||||
\(877\) | −29.5356 | −0.997348 | −0.498674 | − | 0.866790i | \(-0.666179\pi\) | ||||
−0.498674 | + | 0.866790i | \(0.666179\pi\) | |||||||
\(878\) | −13.9275 | −0.470030 | ||||||||
\(879\) | 7.57841 | 0.255613 | ||||||||
\(880\) | 10.4584 | 0.352553 | ||||||||
\(881\) | −50.7049 | −1.70829 | −0.854145 | − | 0.520035i | \(-0.825919\pi\) | ||||
−0.854145 | + | 0.520035i | \(0.825919\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | 4.30851 | 0.144993 | 0.0724965 | − | 0.997369i | \(-0.476903\pi\) | ||||
0.0724965 | + | 0.997369i | \(0.476903\pi\) | |||||||
\(884\) | −9.01789 | −0.303304 | ||||||||
\(885\) | 9.52338 | 0.320125 | ||||||||
\(886\) | 8.69247 | 0.292029 | ||||||||
\(887\) | 15.3016 | 0.513778 | 0.256889 | − | 0.966441i | \(-0.417302\pi\) | ||||
0.256889 | + | 0.966441i | \(0.417302\pi\) | |||||||
\(888\) | 2.32402 | 0.0779891 | ||||||||
\(889\) | −11.6091 | −0.389356 | ||||||||
\(890\) | 1.75145 | 0.0587087 | ||||||||
\(891\) | 2.56478 | 0.0859235 | ||||||||
\(892\) | 5.47594 | 0.183348 | ||||||||
\(893\) | 19.2081 | 0.642776 | ||||||||
\(894\) | 12.3489 | 0.413009 | ||||||||
\(895\) | 6.49108 | 0.216973 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −6.24211 | −0.208418 | ||||||||
\(898\) | 29.6829 | 0.990532 | ||||||||
\(899\) | 10.4155 | 0.347377 | ||||||||
\(900\) | 11.6276 | 0.387586 | ||||||||
\(901\) | 9.71366 | 0.323609 | ||||||||
\(902\) | 23.9211 | 0.796486 | ||||||||
\(903\) | 6.29321 | 0.209425 | ||||||||
\(904\) | 4.22957 | 0.140673 | ||||||||
\(905\) | −41.3460 | −1.37439 | ||||||||
\(906\) | 3.04757 | 0.101249 | ||||||||
\(907\) | 4.70366 | 0.156182 | 0.0780912 | − | 0.996946i | \(-0.475117\pi\) | ||||
0.0780912 | + | 0.996946i | \(0.475117\pi\) | |||||||
\(908\) | 13.7497 | 0.456301 | ||||||||
\(909\) | −7.75739 | −0.257297 | ||||||||
\(910\) | 6.41332 | 0.212599 | ||||||||
\(911\) | −6.11806 | −0.202700 | −0.101350 | − | 0.994851i | \(-0.532316\pi\) | ||||
−0.101350 | + | 0.994851i | \(0.532316\pi\) | |||||||
\(912\) | −3.75278 | −0.124267 | ||||||||
\(913\) | −11.7896 | −0.390179 | ||||||||
\(914\) | 13.7098 | 0.453481 | ||||||||
\(915\) | −0.551128 | −0.0182197 | ||||||||
\(916\) | −2.69390 | −0.0890089 | ||||||||
\(917\) | 11.3478 | 0.374737 | ||||||||
\(918\) | 5.73372 | 0.189241 | ||||||||
\(919\) | −28.7886 | −0.949647 | −0.474823 | − | 0.880081i | \(-0.657488\pi\) | ||||
−0.474823 | + | 0.880081i | \(0.657488\pi\) | |||||||
\(920\) | 16.1837 | 0.533561 | ||||||||
\(921\) | 9.76130 | 0.321646 | ||||||||
\(922\) | −22.5901 | −0.743965 | ||||||||
\(923\) | 0.935200 | 0.0307825 | ||||||||
\(924\) | −2.56478 | −0.0843752 | ||||||||
\(925\) | −27.0228 | −0.888503 | ||||||||
\(926\) | 20.8874 | 0.686403 | ||||||||
\(927\) | 7.79971 | 0.256176 | ||||||||
\(928\) | −3.01074 | −0.0988324 | ||||||||
\(929\) | −8.07840 | −0.265044 | −0.132522 | − | 0.991180i | \(-0.542307\pi\) | ||||
−0.132522 | + | 0.991180i | \(0.542307\pi\) | |||||||
\(930\) | 14.1066 | 0.462574 | ||||||||
\(931\) | 3.75278 | 0.122992 | ||||||||
\(932\) | 11.4638 | 0.375511 | ||||||||
\(933\) | −24.7211 | −0.809331 | ||||||||
\(934\) | 17.6380 | 0.577132 | ||||||||
\(935\) | −59.9655 | −1.96108 | ||||||||
\(936\) | 1.57278 | 0.0514080 | ||||||||
\(937\) | −51.6971 | −1.68887 | −0.844436 | − | 0.535657i | \(-0.820064\pi\) | ||||
−0.844436 | + | 0.535657i | \(0.820064\pi\) | |||||||
\(938\) | 0.892401 | 0.0291379 | ||||||||
\(939\) | −20.9113 | −0.682415 | ||||||||
\(940\) | 20.8711 | 0.680742 | ||||||||
\(941\) | 9.47125 | 0.308754 | 0.154377 | − | 0.988012i | \(-0.450663\pi\) | ||||
0.154377 | + | 0.988012i | \(0.450663\pi\) | |||||||
\(942\) | 16.4234 | 0.535102 | ||||||||
\(943\) | 37.0164 | 1.20542 | ||||||||
\(944\) | −2.33548 | −0.0760135 | ||||||||
\(945\) | −4.07769 | −0.132647 | ||||||||
\(946\) | −16.1407 | −0.524780 | ||||||||
\(947\) | −8.38667 | −0.272530 | −0.136265 | − | 0.990672i | \(-0.543510\pi\) | ||||
−0.136265 | + | 0.990672i | \(0.543510\pi\) | |||||||
\(948\) | −5.28701 | −0.171714 | ||||||||
\(949\) | 12.5200 | 0.406416 | ||||||||
\(950\) | 43.6358 | 1.41573 | ||||||||
\(951\) | 16.1572 | 0.523932 | ||||||||
\(952\) | −5.73372 | −0.185831 | ||||||||
\(953\) | −5.93373 | −0.192212 | −0.0961061 | − | 0.995371i | \(-0.530639\pi\) | ||||
−0.0961061 | + | 0.995371i | \(0.530639\pi\) | |||||||
\(954\) | −1.69413 | −0.0548494 | ||||||||
\(955\) | 4.07769 | 0.131951 | ||||||||
\(956\) | −20.2601 | −0.655258 | ||||||||
\(957\) | 7.72190 | 0.249613 | ||||||||
\(958\) | 28.7142 | 0.927714 | ||||||||
\(959\) | −7.15669 | −0.231102 | ||||||||
\(960\) | −4.07769 | −0.131607 | ||||||||
\(961\) | −19.0322 | −0.613941 | ||||||||
\(962\) | −3.65518 | −0.117848 | ||||||||
\(963\) | 3.74273 | 0.120608 | ||||||||
\(964\) | 10.0873 | 0.324890 | ||||||||
\(965\) | 71.8703 | 2.31359 | ||||||||
\(966\) | −3.96884 | −0.127695 | ||||||||
\(967\) | −54.0140 | −1.73697 | −0.868487 | − | 0.495713i | \(-0.834907\pi\) | ||||
−0.868487 | + | 0.495713i | \(0.834907\pi\) | |||||||
\(968\) | −4.42189 | −0.142125 | ||||||||
\(969\) | 21.5174 | 0.691239 | ||||||||
\(970\) | 5.96724 | 0.191597 | ||||||||
\(971\) | 42.2203 | 1.35491 | 0.677457 | − | 0.735562i | \(-0.263082\pi\) | ||||
0.677457 | + | 0.735562i | \(0.263082\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −7.99822 | −0.256411 | ||||||||
\(974\) | −9.60371 | −0.307723 | ||||||||
\(975\) | −18.2876 | −0.585673 | ||||||||
\(976\) | 0.135157 | 0.00432626 | ||||||||
\(977\) | 11.4062 | 0.364915 | 0.182458 | − | 0.983214i | \(-0.441595\pi\) | ||||
0.182458 | + | 0.983214i | \(0.441595\pi\) | |||||||
\(978\) | −9.19645 | −0.294070 | ||||||||
\(979\) | 1.10162 | 0.0352081 | ||||||||
\(980\) | 4.07769 | 0.130257 | ||||||||
\(981\) | 2.11979 | 0.0676798 | ||||||||
\(982\) | 19.0198 | 0.606945 | ||||||||
\(983\) | −40.3992 | −1.28853 | −0.644267 | − | 0.764801i | \(-0.722837\pi\) | ||||
−0.644267 | + | 0.764801i | \(0.722837\pi\) | |||||||
\(984\) | −9.32677 | −0.297326 | ||||||||
\(985\) | −71.5592 | −2.28007 | ||||||||
\(986\) | 17.2627 | 0.549758 | ||||||||
\(987\) | −5.11837 | −0.162919 | ||||||||
\(988\) | 5.90231 | 0.187777 | ||||||||
\(989\) | −24.9767 | −0.794214 | ||||||||
\(990\) | 10.4584 | 0.332390 | ||||||||
\(991\) | −8.41459 | −0.267298 | −0.133649 | − | 0.991029i | \(-0.542670\pi\) | ||||
−0.133649 | + | 0.991029i | \(0.542670\pi\) | |||||||
\(992\) | −3.45946 | −0.109838 | ||||||||
\(993\) | −5.72173 | −0.181574 | ||||||||
\(994\) | 0.594616 | 0.0188601 | ||||||||
\(995\) | −59.1990 | −1.87674 | ||||||||
\(996\) | 4.59673 | 0.145653 | ||||||||
\(997\) | −46.9059 | −1.48552 | −0.742762 | − | 0.669556i | \(-0.766485\pi\) | ||||
−0.742762 | + | 0.669556i | \(0.766485\pi\) | |||||||
\(998\) | −1.33794 | −0.0423517 | ||||||||
\(999\) | 2.32402 | 0.0735288 |
(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 | 8022.2.a.r.1.10 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8022.2.a.r.1.10 | ✓ | 10 | 1.1 | even | 1 | trivial |