Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(1\) |
Dimension: | \(81\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-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 | ||||||||
\(3\) | −2.34885 | −1.35611 | −0.678054 | − | 0.735012i | \(-0.737176\pi\) | ||||
−0.678054 | + | 0.735012i | \(0.737176\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.93410 | 1.75938 | 0.879692 | − | 0.475545i | \(-0.157749\pi\) | ||||
0.879692 | + | 0.475545i | \(0.157749\pi\) | |||||||
\(6\) | 2.34885 | 0.958913 | ||||||||
\(7\) | −0.279699 | −0.105716 | −0.0528581 | − | 0.998602i | \(-0.516833\pi\) | ||||
−0.0528581 | + | 0.998602i | \(0.516833\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.51708 | 0.839028 | ||||||||
\(10\) | −3.93410 | −1.24407 | ||||||||
\(11\) | 0.973217 | 0.293436 | 0.146718 | − | 0.989178i | \(-0.453129\pi\) | ||||
0.146718 | + | 0.989178i | \(0.453129\pi\) | |||||||
\(12\) | −2.34885 | −0.678054 | ||||||||
\(13\) | −0.411920 | −0.114246 | −0.0571230 | − | 0.998367i | \(-0.518193\pi\) | ||||
−0.0571230 | + | 0.998367i | \(0.518193\pi\) | |||||||
\(14\) | 0.279699 | 0.0747527 | ||||||||
\(15\) | −9.24060 | −2.38591 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.47119 | −0.356816 | −0.178408 | − | 0.983957i | \(-0.557095\pi\) | ||||
−0.178408 | + | 0.983957i | \(0.557095\pi\) | |||||||
\(18\) | −2.51708 | −0.593282 | ||||||||
\(19\) | −7.83609 | −1.79772 | −0.898862 | − | 0.438233i | \(-0.855605\pi\) | ||||
−0.898862 | + | 0.438233i | \(0.855605\pi\) | |||||||
\(20\) | 3.93410 | 0.879692 | ||||||||
\(21\) | 0.656970 | 0.143363 | ||||||||
\(22\) | −0.973217 | −0.207491 | ||||||||
\(23\) | −2.84547 | −0.593322 | −0.296661 | − | 0.954983i | \(-0.595873\pi\) | ||||
−0.296661 | + | 0.954983i | \(0.595873\pi\) | |||||||
\(24\) | 2.34885 | 0.479456 | ||||||||
\(25\) | 10.4771 | 2.09543 | ||||||||
\(26\) | 0.411920 | 0.0807841 | ||||||||
\(27\) | 1.13430 | 0.218296 | ||||||||
\(28\) | −0.279699 | −0.0528581 | ||||||||
\(29\) | 4.82149 | 0.895328 | 0.447664 | − | 0.894202i | \(-0.352256\pi\) | ||||
0.447664 | + | 0.894202i | \(0.352256\pi\) | |||||||
\(30\) | 9.24060 | 1.68709 | ||||||||
\(31\) | −5.14273 | −0.923661 | −0.461830 | − | 0.886968i | \(-0.652807\pi\) | ||||
−0.461830 | + | 0.886968i | \(0.652807\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.28594 | −0.397931 | ||||||||
\(34\) | 1.47119 | 0.252307 | ||||||||
\(35\) | −1.10036 | −0.185995 | ||||||||
\(36\) | 2.51708 | 0.419514 | ||||||||
\(37\) | 4.41180 | 0.725295 | 0.362647 | − | 0.931926i | \(-0.381873\pi\) | ||||
0.362647 | + | 0.931926i | \(0.381873\pi\) | |||||||
\(38\) | 7.83609 | 1.27118 | ||||||||
\(39\) | 0.967537 | 0.154930 | ||||||||
\(40\) | −3.93410 | −0.622036 | ||||||||
\(41\) | −3.33780 | −0.521277 | −0.260639 | − | 0.965436i | \(-0.583933\pi\) | ||||
−0.260639 | + | 0.965436i | \(0.583933\pi\) | |||||||
\(42\) | −0.656970 | −0.101373 | ||||||||
\(43\) | 5.27289 | 0.804108 | 0.402054 | − | 0.915616i | \(-0.368296\pi\) | ||||
0.402054 | + | 0.915616i | \(0.368296\pi\) | |||||||
\(44\) | 0.973217 | 0.146718 | ||||||||
\(45\) | 9.90246 | 1.47617 | ||||||||
\(46\) | 2.84547 | 0.419542 | ||||||||
\(47\) | −1.59196 | −0.232211 | −0.116105 | − | 0.993237i | \(-0.537041\pi\) | ||||
−0.116105 | + | 0.993237i | \(0.537041\pi\) | |||||||
\(48\) | −2.34885 | −0.339027 | ||||||||
\(49\) | −6.92177 | −0.988824 | ||||||||
\(50\) | −10.4771 | −1.48169 | ||||||||
\(51\) | 3.45560 | 0.483881 | ||||||||
\(52\) | −0.411920 | −0.0571230 | ||||||||
\(53\) | 10.2898 | 1.41342 | 0.706709 | − | 0.707504i | \(-0.250179\pi\) | ||||
0.706709 | + | 0.707504i | \(0.250179\pi\) | |||||||
\(54\) | −1.13430 | −0.154358 | ||||||||
\(55\) | 3.82873 | 0.516266 | ||||||||
\(56\) | 0.279699 | 0.0373763 | ||||||||
\(57\) | 18.4058 | 2.43791 | ||||||||
\(58\) | −4.82149 | −0.633092 | ||||||||
\(59\) | 3.83766 | 0.499621 | 0.249811 | − | 0.968295i | \(-0.419632\pi\) | ||||
0.249811 | + | 0.968295i | \(0.419632\pi\) | |||||||
\(60\) | −9.24060 | −1.19296 | ||||||||
\(61\) | 11.1929 | 1.43310 | 0.716551 | − | 0.697535i | \(-0.245720\pi\) | ||||
0.716551 | + | 0.697535i | \(0.245720\pi\) | |||||||
\(62\) | 5.14273 | 0.653127 | ||||||||
\(63\) | −0.704025 | −0.0886989 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.62053 | −0.201003 | ||||||||
\(66\) | 2.28594 | 0.281380 | ||||||||
\(67\) | −7.74705 | −0.946452 | −0.473226 | − | 0.880941i | \(-0.656911\pi\) | ||||
−0.473226 | + | 0.880941i | \(0.656911\pi\) | |||||||
\(68\) | −1.47119 | −0.178408 | ||||||||
\(69\) | 6.68358 | 0.804609 | ||||||||
\(70\) | 1.10036 | 0.131519 | ||||||||
\(71\) | −0.378148 | −0.0448780 | −0.0224390 | − | 0.999748i | \(-0.507143\pi\) | ||||
−0.0224390 | + | 0.999748i | \(0.507143\pi\) | |||||||
\(72\) | −2.51708 | −0.296641 | ||||||||
\(73\) | −11.8009 | −1.38119 | −0.690595 | − | 0.723242i | \(-0.742651\pi\) | ||||
−0.690595 | + | 0.723242i | \(0.742651\pi\) | |||||||
\(74\) | −4.41180 | −0.512861 | ||||||||
\(75\) | −24.6092 | −2.84163 | ||||||||
\(76\) | −7.83609 | −0.898862 | ||||||||
\(77\) | −0.272208 | −0.0310210 | ||||||||
\(78\) | −0.967537 | −0.109552 | ||||||||
\(79\) | 0.341349 | 0.0384048 | 0.0192024 | − | 0.999816i | \(-0.493887\pi\) | ||||
0.0192024 | + | 0.999816i | \(0.493887\pi\) | |||||||
\(80\) | 3.93410 | 0.439846 | ||||||||
\(81\) | −10.2155 | −1.13506 | ||||||||
\(82\) | 3.33780 | 0.368599 | ||||||||
\(83\) | −10.7671 | −1.18184 | −0.590921 | − | 0.806730i | \(-0.701235\pi\) | ||||
−0.590921 | + | 0.806730i | \(0.701235\pi\) | |||||||
\(84\) | 0.656970 | 0.0716813 | ||||||||
\(85\) | −5.78781 | −0.627776 | ||||||||
\(86\) | −5.27289 | −0.568590 | ||||||||
\(87\) | −11.3249 | −1.21416 | ||||||||
\(88\) | −0.973217 | −0.103745 | ||||||||
\(89\) | −3.35948 | −0.356105 | −0.178052 | − | 0.984021i | \(-0.556980\pi\) | ||||
−0.178052 | + | 0.984021i | \(0.556980\pi\) | |||||||
\(90\) | −9.90246 | −1.04381 | ||||||||
\(91\) | 0.115214 | 0.0120777 | ||||||||
\(92\) | −2.84547 | −0.296661 | ||||||||
\(93\) | 12.0795 | 1.25258 | ||||||||
\(94\) | 1.59196 | 0.164198 | ||||||||
\(95\) | −30.8280 | −3.16288 | ||||||||
\(96\) | 2.34885 | 0.239728 | ||||||||
\(97\) | −0.405935 | −0.0412165 | −0.0206082 | − | 0.999788i | \(-0.506560\pi\) | ||||
−0.0206082 | + | 0.999788i | \(0.506560\pi\) | |||||||
\(98\) | 6.92177 | 0.699204 | ||||||||
\(99\) | 2.44967 | 0.246201 | ||||||||
\(100\) | 10.4771 | 1.04771 | ||||||||
\(101\) | 7.88785 | 0.784870 | 0.392435 | − | 0.919780i | \(-0.371633\pi\) | ||||
0.392435 | + | 0.919780i | \(0.371633\pi\) | |||||||
\(102\) | −3.45560 | −0.342156 | ||||||||
\(103\) | −3.63531 | −0.358197 | −0.179099 | − | 0.983831i | \(-0.557318\pi\) | ||||
−0.179099 | + | 0.983831i | \(0.557318\pi\) | |||||||
\(104\) | 0.411920 | 0.0403921 | ||||||||
\(105\) | 2.58459 | 0.252230 | ||||||||
\(106\) | −10.2898 | −0.999437 | ||||||||
\(107\) | 9.95348 | 0.962239 | 0.481120 | − | 0.876655i | \(-0.340230\pi\) | ||||
0.481120 | + | 0.876655i | \(0.340230\pi\) | |||||||
\(108\) | 1.13430 | 0.109148 | ||||||||
\(109\) | −5.47783 | −0.524681 | −0.262340 | − | 0.964975i | \(-0.584494\pi\) | ||||
−0.262340 | + | 0.964975i | \(0.584494\pi\) | |||||||
\(110\) | −3.82873 | −0.365055 | ||||||||
\(111\) | −10.3626 | −0.983578 | ||||||||
\(112\) | −0.279699 | −0.0264291 | ||||||||
\(113\) | −7.48323 | −0.703963 | −0.351981 | − | 0.936007i | \(-0.614492\pi\) | ||||
−0.351981 | + | 0.936007i | \(0.614492\pi\) | |||||||
\(114\) | −18.4058 | −1.72386 | ||||||||
\(115\) | −11.1944 | −1.04388 | ||||||||
\(116\) | 4.82149 | 0.447664 | ||||||||
\(117\) | −1.03684 | −0.0958556 | ||||||||
\(118\) | −3.83766 | −0.353286 | ||||||||
\(119\) | 0.411490 | 0.0377213 | ||||||||
\(120\) | 9.24060 | 0.843547 | ||||||||
\(121\) | −10.0528 | −0.913895 | ||||||||
\(122\) | −11.1929 | −1.01336 | ||||||||
\(123\) | 7.83999 | 0.706908 | ||||||||
\(124\) | −5.14273 | −0.461830 | ||||||||
\(125\) | 21.5476 | 1.92728 | ||||||||
\(126\) | 0.704025 | 0.0627196 | ||||||||
\(127\) | −0.276800 | −0.0245621 | −0.0122810 | − | 0.999925i | \(-0.503909\pi\) | ||||
−0.0122810 | + | 0.999925i | \(0.503909\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −12.3852 | −1.09046 | ||||||||
\(130\) | 1.62053 | 0.142130 | ||||||||
\(131\) | 4.09617 | 0.357884 | 0.178942 | − | 0.983860i | \(-0.442733\pi\) | ||||
0.178942 | + | 0.983860i | \(0.442733\pi\) | |||||||
\(132\) | −2.28594 | −0.198965 | ||||||||
\(133\) | 2.19175 | 0.190049 | ||||||||
\(134\) | 7.74705 | 0.669243 | ||||||||
\(135\) | 4.46244 | 0.384066 | ||||||||
\(136\) | 1.47119 | 0.126154 | ||||||||
\(137\) | 6.29922 | 0.538179 | 0.269089 | − | 0.963115i | \(-0.413277\pi\) | ||||
0.269089 | + | 0.963115i | \(0.413277\pi\) | |||||||
\(138\) | −6.68358 | −0.568944 | ||||||||
\(139\) | −0.391750 | −0.0332278 | −0.0166139 | − | 0.999862i | \(-0.505289\pi\) | ||||
−0.0166139 | + | 0.999862i | \(0.505289\pi\) | |||||||
\(140\) | −1.10036 | −0.0929977 | ||||||||
\(141\) | 3.73926 | 0.314903 | ||||||||
\(142\) | 0.378148 | 0.0317335 | ||||||||
\(143\) | −0.400888 | −0.0335239 | ||||||||
\(144\) | 2.51708 | 0.209757 | ||||||||
\(145\) | 18.9682 | 1.57522 | ||||||||
\(146\) | 11.8009 | 0.976649 | ||||||||
\(147\) | 16.2582 | 1.34095 | ||||||||
\(148\) | 4.41180 | 0.362647 | ||||||||
\(149\) | −11.2133 | −0.918626 | −0.459313 | − | 0.888274i | \(-0.651904\pi\) | ||||
−0.459313 | + | 0.888274i | \(0.651904\pi\) | |||||||
\(150\) | 24.6092 | 2.00933 | ||||||||
\(151\) | −7.54365 | −0.613894 | −0.306947 | − | 0.951727i | \(-0.599307\pi\) | ||||
−0.306947 | + | 0.951727i | \(0.599307\pi\) | |||||||
\(152\) | 7.83609 | 0.635591 | ||||||||
\(153\) | −3.70311 | −0.299379 | ||||||||
\(154\) | 0.272208 | 0.0219351 | ||||||||
\(155\) | −20.2320 | −1.62507 | ||||||||
\(156\) | 0.967537 | 0.0774649 | ||||||||
\(157\) | −12.5208 | −0.999272 | −0.499636 | − | 0.866235i | \(-0.666533\pi\) | ||||
−0.499636 | + | 0.866235i | \(0.666533\pi\) | |||||||
\(158\) | −0.341349 | −0.0271563 | ||||||||
\(159\) | −24.1693 | −1.91675 | ||||||||
\(160\) | −3.93410 | −0.311018 | ||||||||
\(161\) | 0.795876 | 0.0627238 | ||||||||
\(162\) | 10.2155 | 0.802609 | ||||||||
\(163\) | 3.30396 | 0.258786 | 0.129393 | − | 0.991593i | \(-0.458697\pi\) | ||||
0.129393 | + | 0.991593i | \(0.458697\pi\) | |||||||
\(164\) | −3.33780 | −0.260639 | ||||||||
\(165\) | −8.99311 | −0.700113 | ||||||||
\(166\) | 10.7671 | 0.835688 | ||||||||
\(167\) | −21.6536 | −1.67561 | −0.837804 | − | 0.545971i | \(-0.816161\pi\) | ||||
−0.837804 | + | 0.545971i | \(0.816161\pi\) | |||||||
\(168\) | −0.656970 | −0.0506863 | ||||||||
\(169\) | −12.8303 | −0.986948 | ||||||||
\(170\) | 5.78781 | 0.443905 | ||||||||
\(171\) | −19.7241 | −1.50834 | ||||||||
\(172\) | 5.27289 | 0.402054 | ||||||||
\(173\) | 2.39732 | 0.182265 | 0.0911323 | − | 0.995839i | \(-0.470951\pi\) | ||||
0.0911323 | + | 0.995839i | \(0.470951\pi\) | |||||||
\(174\) | 11.3249 | 0.858541 | ||||||||
\(175\) | −2.93045 | −0.221521 | ||||||||
\(176\) | 0.973217 | 0.0733590 | ||||||||
\(177\) | −9.01409 | −0.677540 | ||||||||
\(178\) | 3.35948 | 0.251804 | ||||||||
\(179\) | 21.8559 | 1.63358 | 0.816792 | − | 0.576933i | \(-0.195751\pi\) | ||||
0.816792 | + | 0.576933i | \(0.195751\pi\) | |||||||
\(180\) | 9.90246 | 0.738086 | ||||||||
\(181\) | −5.04230 | −0.374791 | −0.187395 | − | 0.982285i | \(-0.560005\pi\) | ||||
−0.187395 | + | 0.982285i | \(0.560005\pi\) | |||||||
\(182\) | −0.115214 | −0.00854019 | ||||||||
\(183\) | −26.2904 | −1.94344 | ||||||||
\(184\) | 2.84547 | 0.209771 | ||||||||
\(185\) | 17.3564 | 1.27607 | ||||||||
\(186\) | −12.0795 | −0.885710 | ||||||||
\(187\) | −1.43179 | −0.104703 | ||||||||
\(188\) | −1.59196 | −0.116105 | ||||||||
\(189\) | −0.317262 | −0.0230774 | ||||||||
\(190\) | 30.8280 | 2.23650 | ||||||||
\(191\) | −18.2990 | −1.32407 | −0.662035 | − | 0.749473i | \(-0.730307\pi\) | ||||
−0.662035 | + | 0.749473i | \(0.730307\pi\) | |||||||
\(192\) | −2.34885 | −0.169513 | ||||||||
\(193\) | 8.37506 | 0.602850 | 0.301425 | − | 0.953490i | \(-0.402538\pi\) | ||||
0.301425 | + | 0.953490i | \(0.402538\pi\) | |||||||
\(194\) | 0.405935 | 0.0291444 | ||||||||
\(195\) | 3.80639 | 0.272581 | ||||||||
\(196\) | −6.92177 | −0.494412 | ||||||||
\(197\) | 10.9612 | 0.780952 | 0.390476 | − | 0.920613i | \(-0.372311\pi\) | ||||
0.390476 | + | 0.920613i | \(0.372311\pi\) | |||||||
\(198\) | −2.44967 | −0.174090 | ||||||||
\(199\) | −20.8954 | −1.48124 | −0.740619 | − | 0.671925i | \(-0.765468\pi\) | ||||
−0.740619 | + | 0.671925i | \(0.765468\pi\) | |||||||
\(200\) | −10.4771 | −0.740846 | ||||||||
\(201\) | 18.1966 | 1.28349 | ||||||||
\(202\) | −7.88785 | −0.554987 | ||||||||
\(203\) | −1.34856 | −0.0946507 | ||||||||
\(204\) | 3.45560 | 0.241941 | ||||||||
\(205\) | −13.1313 | −0.917127 | ||||||||
\(206\) | 3.63531 | 0.253284 | ||||||||
\(207\) | −7.16229 | −0.497814 | ||||||||
\(208\) | −0.411920 | −0.0285615 | ||||||||
\(209\) | −7.62622 | −0.527517 | ||||||||
\(210\) | −2.58459 | −0.178353 | ||||||||
\(211\) | 20.1820 | 1.38939 | 0.694693 | − | 0.719306i | \(-0.255540\pi\) | ||||
0.694693 | + | 0.719306i | \(0.255540\pi\) | |||||||
\(212\) | 10.2898 | 0.706709 | ||||||||
\(213\) | 0.888213 | 0.0608593 | ||||||||
\(214\) | −9.95348 | −0.680406 | ||||||||
\(215\) | 20.7441 | 1.41473 | ||||||||
\(216\) | −1.13430 | −0.0771792 | ||||||||
\(217\) | 1.43841 | 0.0976460 | ||||||||
\(218\) | 5.47783 | 0.371005 | ||||||||
\(219\) | 27.7185 | 1.87304 | ||||||||
\(220\) | 3.82873 | 0.258133 | ||||||||
\(221\) | 0.606013 | 0.0407648 | ||||||||
\(222\) | 10.3626 | 0.695494 | ||||||||
\(223\) | 0.688835 | 0.0461278 | 0.0230639 | − | 0.999734i | \(-0.492658\pi\) | ||||
0.0230639 | + | 0.999734i | \(0.492658\pi\) | |||||||
\(224\) | 0.279699 | 0.0186882 | ||||||||
\(225\) | 26.3718 | 1.75812 | ||||||||
\(226\) | 7.48323 | 0.497777 | ||||||||
\(227\) | −28.0232 | −1.85996 | −0.929982 | − | 0.367606i | \(-0.880178\pi\) | ||||
−0.929982 | + | 0.367606i | \(0.880178\pi\) | |||||||
\(228\) | 18.4058 | 1.21895 | ||||||||
\(229\) | −4.68908 | −0.309863 | −0.154932 | − | 0.987925i | \(-0.549516\pi\) | ||||
−0.154932 | + | 0.987925i | \(0.549516\pi\) | |||||||
\(230\) | 11.1944 | 0.738135 | ||||||||
\(231\) | 0.639374 | 0.0420677 | ||||||||
\(232\) | −4.82149 | −0.316546 | ||||||||
\(233\) | 7.02459 | 0.460196 | 0.230098 | − | 0.973167i | \(-0.426095\pi\) | ||||
0.230098 | + | 0.973167i | \(0.426095\pi\) | |||||||
\(234\) | 1.03684 | 0.0677801 | ||||||||
\(235\) | −6.26292 | −0.408548 | ||||||||
\(236\) | 3.83766 | 0.249811 | ||||||||
\(237\) | −0.801777 | −0.0520810 | ||||||||
\(238\) | −0.411490 | −0.0266730 | ||||||||
\(239\) | −9.43944 | −0.610587 | −0.305293 | − | 0.952258i | \(-0.598755\pi\) | ||||
−0.305293 | + | 0.952258i | \(0.598755\pi\) | |||||||
\(240\) | −9.24060 | −0.596478 | ||||||||
\(241\) | −21.0367 | −1.35510 | −0.677548 | − | 0.735479i | \(-0.736957\pi\) | ||||
−0.677548 | + | 0.735479i | \(0.736957\pi\) | |||||||
\(242\) | 10.0528 | 0.646222 | ||||||||
\(243\) | 20.5919 | 1.32097 | ||||||||
\(244\) | 11.1929 | 0.716551 | ||||||||
\(245\) | −27.2309 | −1.73972 | ||||||||
\(246\) | −7.83999 | −0.499860 | ||||||||
\(247\) | 3.22784 | 0.205383 | ||||||||
\(248\) | 5.14273 | 0.326563 | ||||||||
\(249\) | 25.2902 | 1.60270 | ||||||||
\(250\) | −21.5476 | −1.36279 | ||||||||
\(251\) | 8.33760 | 0.526265 | 0.263132 | − | 0.964760i | \(-0.415244\pi\) | ||||
0.263132 | + | 0.964760i | \(0.415244\pi\) | |||||||
\(252\) | −0.704025 | −0.0443494 | ||||||||
\(253\) | −2.76926 | −0.174102 | ||||||||
\(254\) | 0.276800 | 0.0173680 | ||||||||
\(255\) | 13.5947 | 0.851332 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.43675 | −0.0896218 | −0.0448109 | − | 0.998995i | \(-0.514269\pi\) | ||||
−0.0448109 | + | 0.998995i | \(0.514269\pi\) | |||||||
\(258\) | 12.3852 | 0.771069 | ||||||||
\(259\) | −1.23397 | −0.0766754 | ||||||||
\(260\) | −1.62053 | −0.100501 | ||||||||
\(261\) | 12.1361 | 0.751205 | ||||||||
\(262\) | −4.09617 | −0.253062 | ||||||||
\(263\) | 23.1216 | 1.42574 | 0.712869 | − | 0.701297i | \(-0.247395\pi\) | ||||
0.712869 | + | 0.701297i | \(0.247395\pi\) | |||||||
\(264\) | 2.28594 | 0.140690 | ||||||||
\(265\) | 40.4812 | 2.48674 | ||||||||
\(266\) | −2.19175 | −0.134385 | ||||||||
\(267\) | 7.89091 | 0.482916 | ||||||||
\(268\) | −7.74705 | −0.473226 | ||||||||
\(269\) | −6.83237 | −0.416577 | −0.208289 | − | 0.978067i | \(-0.566789\pi\) | ||||
−0.208289 | + | 0.978067i | \(0.566789\pi\) | |||||||
\(270\) | −4.46244 | −0.271576 | ||||||||
\(271\) | 13.4951 | 0.819771 | 0.409885 | − | 0.912137i | \(-0.365569\pi\) | ||||
0.409885 | + | 0.912137i | \(0.365569\pi\) | |||||||
\(272\) | −1.47119 | −0.0892040 | ||||||||
\(273\) | −0.270619 | −0.0163786 | ||||||||
\(274\) | −6.29922 | −0.380550 | ||||||||
\(275\) | 10.1965 | 0.614874 | ||||||||
\(276\) | 6.68358 | 0.402304 | ||||||||
\(277\) | 9.70591 | 0.583171 | 0.291586 | − | 0.956545i | \(-0.405817\pi\) | ||||
0.291586 | + | 0.956545i | \(0.405817\pi\) | |||||||
\(278\) | 0.391750 | 0.0234956 | ||||||||
\(279\) | −12.9447 | −0.774977 | ||||||||
\(280\) | 1.10036 | 0.0657593 | ||||||||
\(281\) | 10.9873 | 0.655447 | 0.327723 | − | 0.944774i | \(-0.393719\pi\) | ||||
0.327723 | + | 0.944774i | \(0.393719\pi\) | |||||||
\(282\) | −3.73926 | −0.222670 | ||||||||
\(283\) | −22.9974 | −1.36706 | −0.683528 | − | 0.729924i | \(-0.739555\pi\) | ||||
−0.683528 | + | 0.729924i | \(0.739555\pi\) | |||||||
\(284\) | −0.378148 | −0.0224390 | ||||||||
\(285\) | 72.4102 | 4.28921 | ||||||||
\(286\) | 0.400888 | 0.0237050 | ||||||||
\(287\) | 0.933580 | 0.0551075 | ||||||||
\(288\) | −2.51708 | −0.148321 | ||||||||
\(289\) | −14.8356 | −0.872682 | ||||||||
\(290\) | −18.9682 | −1.11385 | ||||||||
\(291\) | 0.953479 | 0.0558940 | ||||||||
\(292\) | −11.8009 | −0.690595 | ||||||||
\(293\) | 18.7803 | 1.09715 | 0.548577 | − | 0.836100i | \(-0.315170\pi\) | ||||
0.548577 | + | 0.836100i | \(0.315170\pi\) | |||||||
\(294\) | −16.2582 | −0.948196 | ||||||||
\(295\) | 15.0978 | 0.879025 | ||||||||
\(296\) | −4.41180 | −0.256430 | ||||||||
\(297\) | 1.10392 | 0.0640558 | ||||||||
\(298\) | 11.2133 | 0.649567 | ||||||||
\(299\) | 1.17211 | 0.0677847 | ||||||||
\(300\) | −24.6092 | −1.42081 | ||||||||
\(301\) | −1.47482 | −0.0850072 | ||||||||
\(302\) | 7.54365 | 0.434089 | ||||||||
\(303\) | −18.5274 | −1.06437 | ||||||||
\(304\) | −7.83609 | −0.449431 | ||||||||
\(305\) | 44.0339 | 2.52137 | ||||||||
\(306\) | 3.70311 | 0.211693 | ||||||||
\(307\) | −2.16399 | −0.123506 | −0.0617529 | − | 0.998091i | \(-0.519669\pi\) | ||||
−0.0617529 | + | 0.998091i | \(0.519669\pi\) | |||||||
\(308\) | −0.272208 | −0.0155105 | ||||||||
\(309\) | 8.53878 | 0.485754 | ||||||||
\(310\) | 20.2320 | 1.14910 | ||||||||
\(311\) | 0.454201 | 0.0257554 | 0.0128777 | − | 0.999917i | \(-0.495901\pi\) | ||||
0.0128777 | + | 0.999917i | \(0.495901\pi\) | |||||||
\(312\) | −0.967537 | −0.0547760 | ||||||||
\(313\) | 13.9830 | 0.790365 | 0.395183 | − | 0.918603i | \(-0.370681\pi\) | ||||
0.395183 | + | 0.918603i | \(0.370681\pi\) | |||||||
\(314\) | 12.5208 | 0.706592 | ||||||||
\(315\) | −2.76971 | −0.156055 | ||||||||
\(316\) | 0.341349 | 0.0192024 | ||||||||
\(317\) | 20.2358 | 1.13655 | 0.568277 | − | 0.822837i | \(-0.307610\pi\) | ||||
0.568277 | + | 0.822837i | \(0.307610\pi\) | |||||||
\(318\) | 24.1693 | 1.35534 | ||||||||
\(319\) | 4.69235 | 0.262721 | ||||||||
\(320\) | 3.93410 | 0.219923 | ||||||||
\(321\) | −23.3792 | −1.30490 | ||||||||
\(322\) | −0.795876 | −0.0443524 | ||||||||
\(323\) | 11.5284 | 0.641457 | ||||||||
\(324\) | −10.2155 | −0.567530 | ||||||||
\(325\) | −4.31574 | −0.239394 | ||||||||
\(326\) | −3.30396 | −0.182989 | ||||||||
\(327\) | 12.8666 | 0.711524 | ||||||||
\(328\) | 3.33780 | 0.184299 | ||||||||
\(329\) | 0.445269 | 0.0245484 | ||||||||
\(330\) | 8.99311 | 0.495054 | ||||||||
\(331\) | −16.1563 | −0.888030 | −0.444015 | − | 0.896019i | \(-0.646446\pi\) | ||||
−0.444015 | + | 0.896019i | \(0.646446\pi\) | |||||||
\(332\) | −10.7671 | −0.590921 | ||||||||
\(333\) | 11.1049 | 0.608542 | ||||||||
\(334\) | 21.6536 | 1.18483 | ||||||||
\(335\) | −30.4777 | −1.66517 | ||||||||
\(336\) | 0.656970 | 0.0358406 | ||||||||
\(337\) | 6.64099 | 0.361758 | 0.180879 | − | 0.983505i | \(-0.442106\pi\) | ||||
0.180879 | + | 0.983505i | \(0.442106\pi\) | |||||||
\(338\) | 12.8303 | 0.697878 | ||||||||
\(339\) | 17.5770 | 0.954649 | ||||||||
\(340\) | −5.78781 | −0.313888 | ||||||||
\(341\) | −5.00499 | −0.271035 | ||||||||
\(342\) | 19.7241 | 1.06656 | ||||||||
\(343\) | 3.89390 | 0.210251 | ||||||||
\(344\) | −5.27289 | −0.284295 | ||||||||
\(345\) | 26.2939 | 1.41561 | ||||||||
\(346\) | −2.39732 | −0.128881 | ||||||||
\(347\) | 22.8869 | 1.22863 | 0.614317 | − | 0.789060i | \(-0.289432\pi\) | ||||
0.614317 | + | 0.789060i | \(0.289432\pi\) | |||||||
\(348\) | −11.3249 | −0.607080 | ||||||||
\(349\) | 8.68372 | 0.464829 | 0.232414 | − | 0.972617i | \(-0.425337\pi\) | ||||
0.232414 | + | 0.972617i | \(0.425337\pi\) | |||||||
\(350\) | 2.93045 | 0.156639 | ||||||||
\(351\) | −0.467240 | −0.0249394 | ||||||||
\(352\) | −0.973217 | −0.0518726 | ||||||||
\(353\) | −29.6885 | −1.58016 | −0.790080 | − | 0.613004i | \(-0.789961\pi\) | ||||
−0.790080 | + | 0.613004i | \(0.789961\pi\) | |||||||
\(354\) | 9.01409 | 0.479093 | ||||||||
\(355\) | −1.48767 | −0.0789575 | ||||||||
\(356\) | −3.35948 | −0.178052 | ||||||||
\(357\) | −0.966528 | −0.0511541 | ||||||||
\(358\) | −21.8559 | −1.15512 | ||||||||
\(359\) | −20.9634 | −1.10641 | −0.553203 | − | 0.833047i | \(-0.686595\pi\) | ||||
−0.553203 | + | 0.833047i | \(0.686595\pi\) | |||||||
\(360\) | −9.90246 | −0.521905 | ||||||||
\(361\) | 42.4044 | 2.23181 | ||||||||
\(362\) | 5.04230 | 0.265017 | ||||||||
\(363\) | 23.6126 | 1.23934 | ||||||||
\(364\) | 0.115214 | 0.00603883 | ||||||||
\(365\) | −46.4259 | −2.43004 | ||||||||
\(366\) | 26.2904 | 1.37422 | ||||||||
\(367\) | 12.5856 | 0.656964 | 0.328482 | − | 0.944510i | \(-0.393463\pi\) | ||||
0.328482 | + | 0.944510i | \(0.393463\pi\) | |||||||
\(368\) | −2.84547 | −0.148331 | ||||||||
\(369\) | −8.40153 | −0.437366 | ||||||||
\(370\) | −17.3564 | −0.902319 | ||||||||
\(371\) | −2.87806 | −0.149421 | ||||||||
\(372\) | 12.0795 | 0.626292 | ||||||||
\(373\) | −20.6444 | −1.06892 | −0.534462 | − | 0.845192i | \(-0.679486\pi\) | ||||
−0.534462 | + | 0.845192i | \(0.679486\pi\) | |||||||
\(374\) | 1.43179 | 0.0740360 | ||||||||
\(375\) | −50.6121 | −2.61360 | ||||||||
\(376\) | 1.59196 | 0.0820989 | ||||||||
\(377\) | −1.98607 | −0.102288 | ||||||||
\(378\) | 0.317262 | 0.0163182 | ||||||||
\(379\) | −36.4215 | −1.87085 | −0.935424 | − | 0.353528i | \(-0.884982\pi\) | ||||
−0.935424 | + | 0.353528i | \(0.884982\pi\) | |||||||
\(380\) | −30.8280 | −1.58144 | ||||||||
\(381\) | 0.650162 | 0.0333088 | ||||||||
\(382\) | 18.2990 | 0.936258 | ||||||||
\(383\) | −28.6532 | −1.46411 | −0.732056 | − | 0.681244i | \(-0.761439\pi\) | ||||
−0.732056 | + | 0.681244i | \(0.761439\pi\) | |||||||
\(384\) | 2.34885 | 0.119864 | ||||||||
\(385\) | −1.07089 | −0.0545777 | ||||||||
\(386\) | −8.37506 | −0.426279 | ||||||||
\(387\) | 13.2723 | 0.674669 | ||||||||
\(388\) | −0.405935 | −0.0206082 | ||||||||
\(389\) | 23.4401 | 1.18846 | 0.594231 | − | 0.804294i | \(-0.297457\pi\) | ||||
0.594231 | + | 0.804294i | \(0.297457\pi\) | |||||||
\(390\) | −3.80639 | −0.192744 | ||||||||
\(391\) | 4.18623 | 0.211707 | ||||||||
\(392\) | 6.92177 | 0.349602 | ||||||||
\(393\) | −9.62127 | −0.485329 | ||||||||
\(394\) | −10.9612 | −0.552216 | ||||||||
\(395\) | 1.34290 | 0.0675687 | ||||||||
\(396\) | 2.44967 | 0.123100 | ||||||||
\(397\) | −8.53221 | −0.428219 | −0.214110 | − | 0.976810i | \(-0.568685\pi\) | ||||
−0.214110 | + | 0.976810i | \(0.568685\pi\) | |||||||
\(398\) | 20.8954 | 1.04739 | ||||||||
\(399\) | −5.14808 | −0.257726 | ||||||||
\(400\) | 10.4771 | 0.523857 | ||||||||
\(401\) | −6.88659 | −0.343900 | −0.171950 | − | 0.985106i | \(-0.555007\pi\) | ||||
−0.171950 | + | 0.985106i | \(0.555007\pi\) | |||||||
\(402\) | −18.1966 | −0.907565 | ||||||||
\(403\) | 2.11839 | 0.105525 | ||||||||
\(404\) | 7.88785 | 0.392435 | ||||||||
\(405\) | −40.1890 | −1.99701 | ||||||||
\(406\) | 1.34856 | 0.0669281 | ||||||||
\(407\) | 4.29364 | 0.212828 | ||||||||
\(408\) | −3.45560 | −0.171078 | ||||||||
\(409\) | 6.40048 | 0.316483 | 0.158242 | − | 0.987400i | \(-0.449417\pi\) | ||||
0.158242 | + | 0.987400i | \(0.449417\pi\) | |||||||
\(410\) | 13.1313 | 0.648506 | ||||||||
\(411\) | −14.7959 | −0.729828 | ||||||||
\(412\) | −3.63531 | −0.179099 | ||||||||
\(413\) | −1.07339 | −0.0528181 | ||||||||
\(414\) | 7.16229 | 0.352007 | ||||||||
\(415\) | −42.3588 | −2.07931 | ||||||||
\(416\) | 0.411920 | 0.0201960 | ||||||||
\(417\) | 0.920160 | 0.0450604 | ||||||||
\(418\) | 7.62622 | 0.373011 | ||||||||
\(419\) | −28.9035 | −1.41203 | −0.706013 | − | 0.708199i | \(-0.749508\pi\) | ||||
−0.706013 | + | 0.708199i | \(0.749508\pi\) | |||||||
\(420\) | 2.58459 | 0.126115 | ||||||||
\(421\) | −37.0768 | −1.80701 | −0.903507 | − | 0.428574i | \(-0.859016\pi\) | ||||
−0.903507 | + | 0.428574i | \(0.859016\pi\) | |||||||
\(422\) | −20.1820 | −0.982444 | ||||||||
\(423\) | −4.00709 | −0.194831 | ||||||||
\(424\) | −10.2898 | −0.499719 | ||||||||
\(425\) | −15.4139 | −0.747683 | ||||||||
\(426\) | −0.888213 | −0.0430340 | ||||||||
\(427\) | −3.13064 | −0.151502 | ||||||||
\(428\) | 9.95348 | 0.481120 | ||||||||
\(429\) | 0.941623 | 0.0454620 | ||||||||
\(430\) | −20.7441 | −1.00037 | ||||||||
\(431\) | 21.4172 | 1.03163 | 0.515816 | − | 0.856699i | \(-0.327489\pi\) | ||||
0.515816 | + | 0.856699i | \(0.327489\pi\) | |||||||
\(432\) | 1.13430 | 0.0545739 | ||||||||
\(433\) | −11.0724 | −0.532106 | −0.266053 | − | 0.963958i | \(-0.585720\pi\) | ||||
−0.266053 | + | 0.963958i | \(0.585720\pi\) | |||||||
\(434\) | −1.43841 | −0.0690461 | ||||||||
\(435\) | −44.5534 | −2.13617 | ||||||||
\(436\) | −5.47783 | −0.262340 | ||||||||
\(437\) | 22.2974 | 1.06663 | ||||||||
\(438\) | −27.7185 | −1.32444 | ||||||||
\(439\) | −14.9576 | −0.713890 | −0.356945 | − | 0.934125i | \(-0.616182\pi\) | ||||
−0.356945 | + | 0.934125i | \(0.616182\pi\) | |||||||
\(440\) | −3.82873 | −0.182528 | ||||||||
\(441\) | −17.4227 | −0.829651 | ||||||||
\(442\) | −0.606013 | −0.0288251 | ||||||||
\(443\) | 11.7114 | 0.556427 | 0.278214 | − | 0.960519i | \(-0.410258\pi\) | ||||
0.278214 | + | 0.960519i | \(0.410258\pi\) | |||||||
\(444\) | −10.3626 | −0.491789 | ||||||||
\(445\) | −13.2165 | −0.626524 | ||||||||
\(446\) | −0.688835 | −0.0326173 | ||||||||
\(447\) | 26.3382 | 1.24576 | ||||||||
\(448\) | −0.279699 | −0.0132145 | ||||||||
\(449\) | −4.90126 | −0.231305 | −0.115652 | − | 0.993290i | \(-0.536896\pi\) | ||||
−0.115652 | + | 0.993290i | \(0.536896\pi\) | |||||||
\(450\) | −26.3718 | −1.24318 | ||||||||
\(451\) | −3.24841 | −0.152962 | ||||||||
\(452\) | −7.48323 | −0.351981 | ||||||||
\(453\) | 17.7189 | 0.832506 | ||||||||
\(454\) | 28.0232 | 1.31519 | ||||||||
\(455\) | 0.453262 | 0.0212492 | ||||||||
\(456\) | −18.4058 | −0.861930 | ||||||||
\(457\) | −3.76798 | −0.176259 | −0.0881293 | − | 0.996109i | \(-0.528089\pi\) | ||||
−0.0881293 | + | 0.996109i | \(0.528089\pi\) | |||||||
\(458\) | 4.68908 | 0.219106 | ||||||||
\(459\) | −1.66877 | −0.0778914 | ||||||||
\(460\) | −11.1944 | −0.521940 | ||||||||
\(461\) | −20.9688 | −0.976615 | −0.488307 | − | 0.872672i | \(-0.662385\pi\) | ||||
−0.488307 | + | 0.872672i | \(0.662385\pi\) | |||||||
\(462\) | −0.639374 | −0.0297464 | ||||||||
\(463\) | 25.8109 | 1.19953 | 0.599767 | − | 0.800175i | \(-0.295260\pi\) | ||||
0.599767 | + | 0.800175i | \(0.295260\pi\) | |||||||
\(464\) | 4.82149 | 0.223832 | ||||||||
\(465\) | 47.5219 | 2.20377 | ||||||||
\(466\) | −7.02459 | −0.325408 | ||||||||
\(467\) | −11.4599 | −0.530302 | −0.265151 | − | 0.964207i | \(-0.585422\pi\) | ||||
−0.265151 | + | 0.964207i | \(0.585422\pi\) | |||||||
\(468\) | −1.03684 | −0.0479278 | ||||||||
\(469\) | 2.16684 | 0.100055 | ||||||||
\(470\) | 6.26292 | 0.288887 | ||||||||
\(471\) | 29.4096 | 1.35512 | ||||||||
\(472\) | −3.83766 | −0.176643 | ||||||||
\(473\) | 5.13166 | 0.235954 | ||||||||
\(474\) | 0.801777 | 0.0368268 | ||||||||
\(475\) | −82.0999 | −3.76700 | ||||||||
\(476\) | 0.411490 | 0.0188606 | ||||||||
\(477\) | 25.9004 | 1.18590 | ||||||||
\(478\) | 9.43944 | 0.431750 | ||||||||
\(479\) | −0.722672 | −0.0330197 | −0.0165099 | − | 0.999864i | \(-0.505255\pi\) | ||||
−0.0165099 | + | 0.999864i | \(0.505255\pi\) | |||||||
\(480\) | 9.24060 | 0.421774 | ||||||||
\(481\) | −1.81731 | −0.0828620 | ||||||||
\(482\) | 21.0367 | 0.958197 | ||||||||
\(483\) | −1.86939 | −0.0850602 | ||||||||
\(484\) | −10.0528 | −0.456948 | ||||||||
\(485\) | −1.59699 | −0.0725155 | ||||||||
\(486\) | −20.5919 | −0.934065 | ||||||||
\(487\) | 24.3721 | 1.10441 | 0.552203 | − | 0.833710i | \(-0.313787\pi\) | ||||
0.552203 | + | 0.833710i | \(0.313787\pi\) | |||||||
\(488\) | −11.1929 | −0.506678 | ||||||||
\(489\) | −7.76050 | −0.350942 | ||||||||
\(490\) | 27.2309 | 1.23017 | ||||||||
\(491\) | −21.6203 | −0.975713 | −0.487856 | − | 0.872924i | \(-0.662221\pi\) | ||||
−0.487856 | + | 0.872924i | \(0.662221\pi\) | |||||||
\(492\) | 7.83999 | 0.353454 | ||||||||
\(493\) | −7.09333 | −0.319467 | ||||||||
\(494\) | −3.22784 | −0.145228 | ||||||||
\(495\) | 9.63724 | 0.433162 | ||||||||
\(496\) | −5.14273 | −0.230915 | ||||||||
\(497\) | 0.105768 | 0.00474433 | ||||||||
\(498\) | −25.2902 | −1.13328 | ||||||||
\(499\) | −9.82237 | −0.439710 | −0.219855 | − | 0.975533i | \(-0.570558\pi\) | ||||
−0.219855 | + | 0.975533i | \(0.570558\pi\) | |||||||
\(500\) | 21.5476 | 0.963639 | ||||||||
\(501\) | 50.8611 | 2.27231 | ||||||||
\(502\) | −8.33760 | −0.372125 | ||||||||
\(503\) | 3.54808 | 0.158201 | 0.0791006 | − | 0.996867i | \(-0.474795\pi\) | ||||
0.0791006 | + | 0.996867i | \(0.474795\pi\) | |||||||
\(504\) | 0.704025 | 0.0313598 | ||||||||
\(505\) | 31.0316 | 1.38089 | ||||||||
\(506\) | 2.76926 | 0.123109 | ||||||||
\(507\) | 30.1365 | 1.33841 | ||||||||
\(508\) | −0.276800 | −0.0122810 | ||||||||
\(509\) | 23.3137 | 1.03336 | 0.516681 | − | 0.856178i | \(-0.327167\pi\) | ||||
0.516681 | + | 0.856178i | \(0.327167\pi\) | |||||||
\(510\) | −13.5947 | −0.601983 | ||||||||
\(511\) | 3.30070 | 0.146014 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −8.88847 | −0.392435 | ||||||||
\(514\) | 1.43675 | 0.0633722 | ||||||||
\(515\) | −14.3017 | −0.630206 | ||||||||
\(516\) | −12.3852 | −0.545228 | ||||||||
\(517\) | −1.54932 | −0.0681390 | ||||||||
\(518\) | 1.23397 | 0.0542177 | ||||||||
\(519\) | −5.63093 | −0.247170 | ||||||||
\(520\) | 1.62053 | 0.0710651 | ||||||||
\(521\) | −17.0410 | −0.746579 | −0.373290 | − | 0.927715i | \(-0.621770\pi\) | ||||
−0.373290 | + | 0.927715i | \(0.621770\pi\) | |||||||
\(522\) | −12.1361 | −0.531182 | ||||||||
\(523\) | 40.1166 | 1.75418 | 0.877088 | − | 0.480329i | \(-0.159483\pi\) | ||||
0.877088 | + | 0.480329i | \(0.159483\pi\) | |||||||
\(524\) | 4.09617 | 0.178942 | ||||||||
\(525\) | 6.88317 | 0.300406 | ||||||||
\(526\) | −23.1216 | −1.00815 | ||||||||
\(527\) | 7.56593 | 0.329577 | ||||||||
\(528\) | −2.28594 | −0.0994827 | ||||||||
\(529\) | −14.9033 | −0.647969 | ||||||||
\(530\) | −40.4812 | −1.75839 | ||||||||
\(531\) | 9.65972 | 0.419196 | ||||||||
\(532\) | 2.19175 | 0.0950243 | ||||||||
\(533\) | 1.37491 | 0.0595539 | ||||||||
\(534\) | −7.89091 | −0.341473 | ||||||||
\(535\) | 39.1580 | 1.69295 | ||||||||
\(536\) | 7.74705 | 0.334621 | ||||||||
\(537\) | −51.3361 | −2.21531 | ||||||||
\(538\) | 6.83237 | 0.294565 | ||||||||
\(539\) | −6.73638 | −0.290157 | ||||||||
\(540\) | 4.46244 | 0.192033 | ||||||||
\(541\) | −6.69422 | −0.287807 | −0.143904 | − | 0.989592i | \(-0.545965\pi\) | ||||
−0.143904 | + | 0.989592i | \(0.545965\pi\) | |||||||
\(542\) | −13.4951 | −0.579665 | ||||||||
\(543\) | 11.8436 | 0.508257 | ||||||||
\(544\) | 1.47119 | 0.0630768 | ||||||||
\(545\) | −21.5503 | −0.923115 | ||||||||
\(546\) | 0.270619 | 0.0115814 | ||||||||
\(547\) | −6.03681 | −0.258116 | −0.129058 | − | 0.991637i | \(-0.541195\pi\) | ||||
−0.129058 | + | 0.991637i | \(0.541195\pi\) | |||||||
\(548\) | 6.29922 | 0.269089 | ||||||||
\(549\) | 28.1734 | 1.20241 | ||||||||
\(550\) | −10.1965 | −0.434782 | ||||||||
\(551\) | −37.7816 | −1.60955 | ||||||||
\(552\) | −6.68358 | −0.284472 | ||||||||
\(553\) | −0.0954750 | −0.00406001 | ||||||||
\(554\) | −9.70591 | −0.412364 | ||||||||
\(555\) | −40.7676 | −1.73049 | ||||||||
\(556\) | −0.391750 | −0.0166139 | ||||||||
\(557\) | 4.83205 | 0.204740 | 0.102370 | − | 0.994746i | \(-0.467357\pi\) | ||||
0.102370 | + | 0.994746i | \(0.467357\pi\) | |||||||
\(558\) | 12.9447 | 0.547992 | ||||||||
\(559\) | −2.17201 | −0.0918661 | ||||||||
\(560\) | −1.10036 | −0.0464988 | ||||||||
\(561\) | 3.36305 | 0.141988 | ||||||||
\(562\) | −10.9873 | −0.463471 | ||||||||
\(563\) | 0.793724 | 0.0334515 | 0.0167257 | − | 0.999860i | \(-0.494676\pi\) | ||||
0.0167257 | + | 0.999860i | \(0.494676\pi\) | |||||||
\(564\) | 3.73926 | 0.157451 | ||||||||
\(565\) | −29.4398 | −1.23854 | ||||||||
\(566\) | 22.9974 | 0.966655 | ||||||||
\(567\) | 2.85728 | 0.119994 | ||||||||
\(568\) | 0.378148 | 0.0158668 | ||||||||
\(569\) | 0.829034 | 0.0347549 | 0.0173774 | − | 0.999849i | \(-0.494468\pi\) | ||||
0.0173774 | + | 0.999849i | \(0.494468\pi\) | |||||||
\(570\) | −72.4102 | −3.03293 | ||||||||
\(571\) | −9.07103 | −0.379611 | −0.189805 | − | 0.981822i | \(-0.560786\pi\) | ||||
−0.189805 | + | 0.981822i | \(0.560786\pi\) | |||||||
\(572\) | −0.400888 | −0.0167619 | ||||||||
\(573\) | 42.9816 | 1.79558 | ||||||||
\(574\) | −0.933580 | −0.0389669 | ||||||||
\(575\) | −29.8124 | −1.24326 | ||||||||
\(576\) | 2.51708 | 0.104878 | ||||||||
\(577\) | 22.3568 | 0.930725 | 0.465362 | − | 0.885120i | \(-0.345924\pi\) | ||||
0.465362 | + | 0.885120i | \(0.345924\pi\) | |||||||
\(578\) | 14.8356 | 0.617080 | ||||||||
\(579\) | −19.6717 | −0.817529 | ||||||||
\(580\) | 18.9682 | 0.787612 | ||||||||
\(581\) | 3.01154 | 0.124940 | ||||||||
\(582\) | −0.953479 | −0.0395230 | ||||||||
\(583\) | 10.0142 | 0.414748 | ||||||||
\(584\) | 11.8009 | 0.488325 | ||||||||
\(585\) | −4.07902 | −0.168647 | ||||||||
\(586\) | −18.7803 | −0.775806 | ||||||||
\(587\) | −34.6229 | −1.42904 | −0.714520 | − | 0.699615i | \(-0.753355\pi\) | ||||
−0.714520 | + | 0.699615i | \(0.753355\pi\) | |||||||
\(588\) | 16.2582 | 0.670476 | ||||||||
\(589\) | 40.2989 | 1.66049 | ||||||||
\(590\) | −15.0978 | −0.621565 | ||||||||
\(591\) | −25.7461 | −1.05905 | ||||||||
\(592\) | 4.41180 | 0.181324 | ||||||||
\(593\) | −13.1463 | −0.539855 | −0.269928 | − | 0.962881i | \(-0.587000\pi\) | ||||
−0.269928 | + | 0.962881i | \(0.587000\pi\) | |||||||
\(594\) | −1.10392 | −0.0452943 | ||||||||
\(595\) | 1.61884 | 0.0663661 | ||||||||
\(596\) | −11.2133 | −0.459313 | ||||||||
\(597\) | 49.0802 | 2.00872 | ||||||||
\(598\) | −1.17211 | −0.0479310 | ||||||||
\(599\) | −20.8726 | −0.852833 | −0.426416 | − | 0.904527i | \(-0.640224\pi\) | ||||
−0.426416 | + | 0.904527i | \(0.640224\pi\) | |||||||
\(600\) | 24.6092 | 1.00467 | ||||||||
\(601\) | −1.94377 | −0.0792878 | −0.0396439 | − | 0.999214i | \(-0.512622\pi\) | ||||
−0.0396439 | + | 0.999214i | \(0.512622\pi\) | |||||||
\(602\) | 1.47482 | 0.0601092 | ||||||||
\(603\) | −19.5000 | −0.794100 | ||||||||
\(604\) | −7.54365 | −0.306947 | ||||||||
\(605\) | −39.5489 | −1.60789 | ||||||||
\(606\) | 18.5274 | 0.752622 | ||||||||
\(607\) | −38.2873 | −1.55403 | −0.777016 | − | 0.629480i | \(-0.783268\pi\) | ||||
−0.777016 | + | 0.629480i | \(0.783268\pi\) | |||||||
\(608\) | 7.83609 | 0.317796 | ||||||||
\(609\) | 3.16757 | 0.128356 | ||||||||
\(610\) | −44.0339 | −1.78288 | ||||||||
\(611\) | 0.655759 | 0.0265292 | ||||||||
\(612\) | −3.70311 | −0.149689 | ||||||||
\(613\) | −43.7352 | −1.76645 | −0.883224 | − | 0.468950i | \(-0.844632\pi\) | ||||
−0.883224 | + | 0.468950i | \(0.844632\pi\) | |||||||
\(614\) | 2.16399 | 0.0873317 | ||||||||
\(615\) | 30.8433 | 1.24372 | ||||||||
\(616\) | 0.272208 | 0.0109676 | ||||||||
\(617\) | −13.7553 | −0.553770 | −0.276885 | − | 0.960903i | \(-0.589302\pi\) | ||||
−0.276885 | + | 0.960903i | \(0.589302\pi\) | |||||||
\(618\) | −8.53878 | −0.343480 | ||||||||
\(619\) | −2.96219 | −0.119061 | −0.0595303 | − | 0.998226i | \(-0.518960\pi\) | ||||
−0.0595303 | + | 0.998226i | \(0.518960\pi\) | |||||||
\(620\) | −20.2320 | −0.812537 | ||||||||
\(621\) | −3.22761 | −0.129520 | ||||||||
\(622\) | −0.454201 | −0.0182118 | ||||||||
\(623\) | 0.939644 | 0.0376460 | ||||||||
\(624\) | 0.967537 | 0.0387325 | ||||||||
\(625\) | 32.3848 | 1.29539 | ||||||||
\(626\) | −13.9830 | −0.558873 | ||||||||
\(627\) | 17.9128 | 0.715369 | ||||||||
\(628\) | −12.5208 | −0.499636 | ||||||||
\(629\) | −6.49059 | −0.258797 | ||||||||
\(630\) | 2.76971 | 0.110348 | ||||||||
\(631\) | −18.8091 | −0.748778 | −0.374389 | − | 0.927272i | \(-0.622148\pi\) | ||||
−0.374389 | + | 0.927272i | \(0.622148\pi\) | |||||||
\(632\) | −0.341349 | −0.0135781 | ||||||||
\(633\) | −47.4044 | −1.88416 | ||||||||
\(634\) | −20.2358 | −0.803666 | ||||||||
\(635\) | −1.08896 | −0.0432141 | ||||||||
\(636\) | −24.1693 | −0.958373 | ||||||||
\(637\) | 2.85121 | 0.112969 | ||||||||
\(638\) | −4.69235 | −0.185772 | ||||||||
\(639\) | −0.951831 | −0.0376538 | ||||||||
\(640\) | −3.93410 | −0.155509 | ||||||||
\(641\) | −29.1444 | −1.15113 | −0.575567 | − | 0.817755i | \(-0.695219\pi\) | ||||
−0.575567 | + | 0.817755i | \(0.695219\pi\) | |||||||
\(642\) | 23.3792 | 0.922704 | ||||||||
\(643\) | 4.57593 | 0.180457 | 0.0902286 | − | 0.995921i | \(-0.471240\pi\) | ||||
0.0902286 | + | 0.995921i | \(0.471240\pi\) | |||||||
\(644\) | 0.795876 | 0.0313619 | ||||||||
\(645\) | −48.7246 | −1.91853 | ||||||||
\(646\) | −11.5284 | −0.453578 | ||||||||
\(647\) | 19.3417 | 0.760403 | 0.380201 | − | 0.924904i | \(-0.375855\pi\) | ||||
0.380201 | + | 0.924904i | \(0.375855\pi\) | |||||||
\(648\) | 10.2155 | 0.401304 | ||||||||
\(649\) | 3.73488 | 0.146607 | ||||||||
\(650\) | 4.31574 | 0.169277 | ||||||||
\(651\) | −3.37862 | −0.132418 | ||||||||
\(652\) | 3.30396 | 0.129393 | ||||||||
\(653\) | −36.2160 | −1.41724 | −0.708620 | − | 0.705590i | \(-0.750682\pi\) | ||||
−0.708620 | + | 0.705590i | \(0.750682\pi\) | |||||||
\(654\) | −12.8666 | −0.503123 | ||||||||
\(655\) | 16.1147 | 0.629655 | ||||||||
\(656\) | −3.33780 | −0.130319 | ||||||||
\(657\) | −29.7038 | −1.15886 | ||||||||
\(658\) | −0.445269 | −0.0173584 | ||||||||
\(659\) | 11.5159 | 0.448596 | 0.224298 | − | 0.974521i | \(-0.427991\pi\) | ||||
0.224298 | + | 0.974521i | \(0.427991\pi\) | |||||||
\(660\) | −8.99311 | −0.350056 | ||||||||
\(661\) | −2.88262 | −0.112121 | −0.0560605 | − | 0.998427i | \(-0.517854\pi\) | ||||
−0.0560605 | + | 0.998427i | \(0.517854\pi\) | |||||||
\(662\) | 16.1563 | 0.627932 | ||||||||
\(663\) | −1.42343 | −0.0552815 | ||||||||
\(664\) | 10.7671 | 0.417844 | ||||||||
\(665\) | 8.62255 | 0.334368 | ||||||||
\(666\) | −11.1049 | −0.430304 | ||||||||
\(667\) | −13.7194 | −0.531218 | ||||||||
\(668\) | −21.6536 | −0.837804 | ||||||||
\(669\) | −1.61797 | −0.0625543 | ||||||||
\(670\) | 30.4777 | 1.17745 | ||||||||
\(671\) | 10.8931 | 0.420523 | ||||||||
\(672\) | −0.656970 | −0.0253432 | ||||||||
\(673\) | 34.4693 | 1.32869 | 0.664347 | − | 0.747424i | \(-0.268710\pi\) | ||||
0.664347 | + | 0.747424i | \(0.268710\pi\) | |||||||
\(674\) | −6.64099 | −0.255801 | ||||||||
\(675\) | 11.8842 | 0.457423 | ||||||||
\(676\) | −12.8303 | −0.493474 | ||||||||
\(677\) | −1.17801 | −0.0452744 | −0.0226372 | − | 0.999744i | \(-0.507206\pi\) | ||||
−0.0226372 | + | 0.999744i | \(0.507206\pi\) | |||||||
\(678\) | −17.5770 | −0.675039 | ||||||||
\(679\) | 0.113540 | 0.00435725 | ||||||||
\(680\) | 5.78781 | 0.221952 | ||||||||
\(681\) | 65.8222 | 2.52231 | ||||||||
\(682\) | 5.00499 | 0.191651 | ||||||||
\(683\) | 3.20480 | 0.122628 | 0.0613141 | − | 0.998119i | \(-0.480471\pi\) | ||||
0.0613141 | + | 0.998119i | \(0.480471\pi\) | |||||||
\(684\) | −19.7241 | −0.754170 | ||||||||
\(685\) | 24.7818 | 0.946863 | ||||||||
\(686\) | −3.89390 | −0.148670 | ||||||||
\(687\) | 11.0139 | 0.420208 | ||||||||
\(688\) | 5.27289 | 0.201027 | ||||||||
\(689\) | −4.23859 | −0.161477 | ||||||||
\(690\) | −26.2939 | −1.00099 | ||||||||
\(691\) | −13.5900 | −0.516988 | −0.258494 | − | 0.966013i | \(-0.583226\pi\) | ||||
−0.258494 | + | 0.966013i | \(0.583226\pi\) | |||||||
\(692\) | 2.39732 | 0.0911323 | ||||||||
\(693\) | −0.685170 | −0.0260274 | ||||||||
\(694\) | −22.8869 | −0.868775 | ||||||||
\(695\) | −1.54118 | −0.0584604 | ||||||||
\(696\) | 11.3249 | 0.429271 | ||||||||
\(697\) | 4.91055 | 0.186000 | ||||||||
\(698\) | −8.68372 | −0.328684 | ||||||||
\(699\) | −16.4997 | −0.624076 | ||||||||
\(700\) | −2.93045 | −0.110760 | ||||||||
\(701\) | 11.3833 | 0.429942 | 0.214971 | − | 0.976620i | \(-0.431034\pi\) | ||||
0.214971 | + | 0.976620i | \(0.431034\pi\) | |||||||
\(702\) | 0.467240 | 0.0176348 | ||||||||
\(703\) | −34.5712 | −1.30388 | ||||||||
\(704\) | 0.973217 | 0.0366795 | ||||||||
\(705\) | 14.7106 | 0.554035 | ||||||||
\(706\) | 29.6885 | 1.11734 | ||||||||
\(707\) | −2.20622 | −0.0829736 | ||||||||
\(708\) | −9.01409 | −0.338770 | ||||||||
\(709\) | −37.5605 | −1.41061 | −0.705307 | − | 0.708902i | \(-0.749191\pi\) | ||||
−0.705307 | + | 0.708902i | \(0.749191\pi\) | |||||||
\(710\) | 1.48767 | 0.0558314 | ||||||||
\(711\) | 0.859204 | 0.0322227 | ||||||||
\(712\) | 3.35948 | 0.125902 | ||||||||
\(713\) | 14.6335 | 0.548028 | ||||||||
\(714\) | 0.966528 | 0.0361714 | ||||||||
\(715\) | −1.57713 | −0.0589814 | ||||||||
\(716\) | 21.8559 | 0.816792 | ||||||||
\(717\) | 22.1718 | 0.828021 | ||||||||
\(718\) | 20.9634 | 0.782347 | ||||||||
\(719\) | −10.9029 | −0.406611 | −0.203305 | − | 0.979115i | \(-0.565168\pi\) | ||||
−0.203305 | + | 0.979115i | \(0.565168\pi\) | |||||||
\(720\) | 9.90246 | 0.369043 | ||||||||
\(721\) | 1.01679 | 0.0378673 | ||||||||
\(722\) | −42.4044 | −1.57813 | ||||||||
\(723\) | 49.4121 | 1.83766 | ||||||||
\(724\) | −5.04230 | −0.187395 | ||||||||
\(725\) | 50.5154 | 1.87610 | ||||||||
\(726\) | −23.6126 | −0.876346 | ||||||||
\(727\) | 6.85830 | 0.254360 | 0.127180 | − | 0.991880i | \(-0.459407\pi\) | ||||
0.127180 | + | 0.991880i | \(0.459407\pi\) | |||||||
\(728\) | −0.115214 | −0.00427010 | ||||||||
\(729\) | −17.7205 | −0.656314 | ||||||||
\(730\) | 46.4259 | 1.71830 | ||||||||
\(731\) | −7.75742 | −0.286919 | ||||||||
\(732\) | −26.2904 | −0.971720 | ||||||||
\(733\) | −15.4801 | −0.571770 | −0.285885 | − | 0.958264i | \(-0.592287\pi\) | ||||
−0.285885 | + | 0.958264i | \(0.592287\pi\) | |||||||
\(734\) | −12.5856 | −0.464543 | ||||||||
\(735\) | 63.9613 | 2.35925 | ||||||||
\(736\) | 2.84547 | 0.104886 | ||||||||
\(737\) | −7.53956 | −0.277723 | ||||||||
\(738\) | 8.40153 | 0.309265 | ||||||||
\(739\) | −16.4301 | −0.604392 | −0.302196 | − | 0.953246i | \(-0.597720\pi\) | ||||
−0.302196 | + | 0.953246i | \(0.597720\pi\) | |||||||
\(740\) | 17.3564 | 0.638036 | ||||||||
\(741\) | −7.58171 | −0.278521 | ||||||||
\(742\) | 2.87806 | 0.105657 | ||||||||
\(743\) | 24.8397 | 0.911280 | 0.455640 | − | 0.890164i | \(-0.349410\pi\) | ||||
0.455640 | + | 0.890164i | \(0.349410\pi\) | |||||||
\(744\) | −12.0795 | −0.442855 | ||||||||
\(745\) | −44.1141 | −1.61622 | ||||||||
\(746\) | 20.6444 | 0.755844 | ||||||||
\(747\) | −27.1016 | −0.991597 | ||||||||
\(748\) | −1.43179 | −0.0523514 | ||||||||
\(749\) | −2.78398 | −0.101724 | ||||||||
\(750\) | 50.6121 | 1.84809 | ||||||||
\(751\) | 9.02626 | 0.329373 | 0.164686 | − | 0.986346i | \(-0.447339\pi\) | ||||
0.164686 | + | 0.986346i | \(0.447339\pi\) | |||||||
\(752\) | −1.59196 | −0.0580527 | ||||||||
\(753\) | −19.5838 | −0.713672 | ||||||||
\(754\) | 1.98607 | 0.0723283 | ||||||||
\(755\) | −29.6775 | −1.08007 | ||||||||
\(756\) | −0.317262 | −0.0115387 | ||||||||
\(757\) | 38.8981 | 1.41377 | 0.706887 | − | 0.707327i | \(-0.250099\pi\) | ||||
0.706887 | + | 0.707327i | \(0.250099\pi\) | |||||||
\(758\) | 36.4215 | 1.32289 | ||||||||
\(759\) | 6.50458 | 0.236101 | ||||||||
\(760\) | 30.8280 | 1.11825 | ||||||||
\(761\) | 1.55368 | 0.0563209 | 0.0281604 | − | 0.999603i | \(-0.491035\pi\) | ||||
0.0281604 | + | 0.999603i | \(0.491035\pi\) | |||||||
\(762\) | −0.650162 | −0.0235529 | ||||||||
\(763\) | 1.53214 | 0.0554673 | ||||||||
\(764\) | −18.2990 | −0.662035 | ||||||||
\(765\) | −14.5684 | −0.526722 | ||||||||
\(766\) | 28.6532 | 1.03528 | ||||||||
\(767\) | −1.58081 | −0.0570797 | ||||||||
\(768\) | −2.34885 | −0.0847567 | ||||||||
\(769\) | −26.9405 | −0.971499 | −0.485750 | − | 0.874098i | \(-0.661453\pi\) | ||||
−0.485750 | + | 0.874098i | \(0.661453\pi\) | |||||||
\(770\) | 1.07089 | 0.0385923 | ||||||||
\(771\) | 3.37470 | 0.121537 | ||||||||
\(772\) | 8.37506 | 0.301425 | ||||||||
\(773\) | −51.8772 | −1.86589 | −0.932947 | − | 0.360013i | \(-0.882772\pi\) | ||||
−0.932947 | + | 0.360013i | \(0.882772\pi\) | |||||||
\(774\) | −13.2723 | −0.477063 | ||||||||
\(775\) | −53.8811 | −1.93547 | ||||||||
\(776\) | 0.405935 | 0.0145722 | ||||||||
\(777\) | 2.89842 | 0.103980 | ||||||||
\(778\) | −23.4401 | −0.840369 | ||||||||
\(779\) | 26.1553 | 0.937112 | ||||||||
\(780\) | 3.80639 | 0.136291 | ||||||||
\(781\) | −0.368020 | −0.0131688 | ||||||||
\(782\) | −4.18623 | −0.149699 | ||||||||
\(783\) | 5.46900 | 0.195446 | ||||||||
\(784\) | −6.92177 | −0.247206 | ||||||||
\(785\) | −49.2583 | −1.75810 | ||||||||
\(786\) | 9.62127 | 0.343179 | ||||||||
\(787\) | 46.1091 | 1.64361 | 0.821806 | − | 0.569767i | \(-0.192966\pi\) | ||||
0.821806 | + | 0.569767i | \(0.192966\pi\) | |||||||
\(788\) | 10.9612 | 0.390476 | ||||||||
\(789\) | −54.3091 | −1.93345 | ||||||||
\(790\) | −1.34290 | −0.0477783 | ||||||||
\(791\) | 2.09305 | 0.0744203 | ||||||||
\(792\) | −2.44967 | −0.0870452 | ||||||||
\(793\) | −4.61057 | −0.163726 | ||||||||
\(794\) | 8.53221 | 0.302797 | ||||||||
\(795\) | −95.0843 | −3.37229 | ||||||||
\(796\) | −20.8954 | −0.740619 | ||||||||
\(797\) | −6.85170 | −0.242700 | −0.121350 | − | 0.992610i | \(-0.538722\pi\) | ||||
−0.121350 | + | 0.992610i | \(0.538722\pi\) | |||||||
\(798\) | 5.14808 | 0.182240 | ||||||||
\(799\) | 2.34207 | 0.0828566 | ||||||||
\(800\) | −10.4771 | −0.370423 | ||||||||
\(801\) | −8.45610 | −0.298782 | ||||||||
\(802\) | 6.88659 | 0.243174 | ||||||||
\(803\) | −11.4848 | −0.405291 | ||||||||
\(804\) | 18.1966 | 0.641746 | ||||||||
\(805\) | 3.13105 | 0.110355 | ||||||||
\(806\) | −2.11839 | −0.0746172 | ||||||||
\(807\) | 16.0482 | 0.564923 | ||||||||
\(808\) | −7.88785 | −0.277494 | ||||||||
\(809\) | −30.3448 | −1.06687 | −0.533433 | − | 0.845842i | \(-0.679098\pi\) | ||||
−0.533433 | + | 0.845842i | \(0.679098\pi\) | |||||||
\(810\) | 40.1890 | 1.41210 | ||||||||
\(811\) | 5.96595 | 0.209493 | 0.104746 | − | 0.994499i | \(-0.466597\pi\) | ||||
0.104746 | + | 0.994499i | \(0.466597\pi\) | |||||||
\(812\) | −1.34856 | −0.0473253 | ||||||||
\(813\) | −31.6980 | −1.11170 | ||||||||
\(814\) | −4.29364 | −0.150492 | ||||||||
\(815\) | 12.9981 | 0.455304 | ||||||||
\(816\) | 3.45560 | 0.120970 | ||||||||
\(817\) | −41.3188 | −1.44556 | ||||||||
\(818\) | −6.40048 | −0.223788 | ||||||||
\(819\) | 0.290002 | 0.0101335 | ||||||||
\(820\) | −13.1313 | −0.458563 | ||||||||
\(821\) | 36.8966 | 1.28770 | 0.643851 | − | 0.765151i | \(-0.277336\pi\) | ||||
0.643851 | + | 0.765151i | \(0.277336\pi\) | |||||||
\(822\) | 14.7959 | 0.516067 | ||||||||
\(823\) | −47.2113 | −1.64568 | −0.822841 | − | 0.568271i | \(-0.807613\pi\) | ||||
−0.822841 | + | 0.568271i | \(0.807613\pi\) | |||||||
\(824\) | 3.63531 | 0.126642 | ||||||||
\(825\) | −23.9501 | −0.833836 | ||||||||
\(826\) | 1.07339 | 0.0373480 | ||||||||
\(827\) | 30.9725 | 1.07702 | 0.538510 | − | 0.842619i | \(-0.318987\pi\) | ||||
0.538510 | + | 0.842619i | \(0.318987\pi\) | |||||||
\(828\) | −7.16229 | −0.248907 | ||||||||
\(829\) | −19.9418 | −0.692607 | −0.346303 | − | 0.938123i | \(-0.612563\pi\) | ||||
−0.346303 | + | 0.938123i | \(0.612563\pi\) | |||||||
\(830\) | 42.3588 | 1.47029 | ||||||||
\(831\) | −22.7977 | −0.790843 | ||||||||
\(832\) | −0.411920 | −0.0142808 | ||||||||
\(833\) | 10.1832 | 0.352828 | ||||||||
\(834\) | −0.920160 | −0.0318625 | ||||||||
\(835\) | −85.1876 | −2.94804 | ||||||||
\(836\) | −7.62622 | −0.263758 | ||||||||
\(837\) | −5.83338 | −0.201631 | ||||||||
\(838\) | 28.9035 | 0.998453 | ||||||||
\(839\) | 11.2315 | 0.387753 | 0.193877 | − | 0.981026i | \(-0.437894\pi\) | ||||
0.193877 | + | 0.981026i | \(0.437894\pi\) | |||||||
\(840\) | −2.58459 | −0.0891767 | ||||||||
\(841\) | −5.75327 | −0.198389 | ||||||||
\(842\) | 37.0768 | 1.27775 | ||||||||
\(843\) | −25.8075 | −0.888857 | ||||||||
\(844\) | 20.1820 | 0.694693 | ||||||||
\(845\) | −50.4758 | −1.73642 | ||||||||
\(846\) | 4.00709 | 0.137767 | ||||||||
\(847\) | 2.81177 | 0.0966136 | ||||||||
\(848\) | 10.2898 | 0.353354 | ||||||||
\(849\) | 54.0175 | 1.85388 | ||||||||
\(850\) | 15.4139 | 0.528692 | ||||||||
\(851\) | −12.5536 | −0.430333 | ||||||||
\(852\) | 0.888213 | 0.0304297 | ||||||||
\(853\) | 33.8446 | 1.15882 | 0.579409 | − | 0.815037i | \(-0.303283\pi\) | ||||
0.579409 | + | 0.815037i | \(0.303283\pi\) | |||||||
\(854\) | 3.13064 | 0.107128 | ||||||||
\(855\) | −77.5966 | −2.65375 | ||||||||
\(856\) | −9.95348 | −0.340203 | ||||||||
\(857\) | −53.5592 | −1.82955 | −0.914774 | − | 0.403966i | \(-0.867631\pi\) | ||||
−0.914774 | + | 0.403966i | \(0.867631\pi\) | |||||||
\(858\) | −0.941623 | −0.0321465 | ||||||||
\(859\) | −2.49569 | −0.0851517 | −0.0425758 | − | 0.999093i | \(-0.513556\pi\) | ||||
−0.0425758 | + | 0.999093i | \(0.513556\pi\) | |||||||
\(860\) | 20.7441 | 0.707367 | ||||||||
\(861\) | −2.19284 | −0.0747317 | ||||||||
\(862\) | −21.4172 | −0.729474 | ||||||||
\(863\) | 22.6794 | 0.772015 | 0.386008 | − | 0.922496i | \(-0.373854\pi\) | ||||
0.386008 | + | 0.922496i | \(0.373854\pi\) | |||||||
\(864\) | −1.13430 | −0.0385896 | ||||||||
\(865\) | 9.43128 | 0.320673 | ||||||||
\(866\) | 11.0724 | 0.376256 | ||||||||
\(867\) | 34.8466 | 1.18345 | ||||||||
\(868\) | 1.43841 | 0.0488230 | ||||||||
\(869\) | 0.332207 | 0.0112693 | ||||||||
\(870\) | 44.5534 | 1.51050 | ||||||||
\(871\) | 3.19116 | 0.108128 | ||||||||
\(872\) | 5.47783 | 0.185503 | ||||||||
\(873\) | −1.02177 | −0.0345818 | ||||||||
\(874\) | −22.2974 | −0.754221 | ||||||||
\(875\) | −6.02685 | −0.203745 | ||||||||
\(876\) | 27.7185 | 0.936521 | ||||||||
\(877\) | −17.1912 | −0.580505 | −0.290252 | − | 0.956950i | \(-0.593739\pi\) | ||||
−0.290252 | + | 0.956950i | \(0.593739\pi\) | |||||||
\(878\) | 14.9576 | 0.504796 | ||||||||
\(879\) | −44.1120 | −1.48786 | ||||||||
\(880\) | 3.82873 | 0.129067 | ||||||||
\(881\) | −26.6406 | −0.897543 | −0.448772 | − | 0.893647i | \(-0.648138\pi\) | ||||
−0.448772 | + | 0.893647i | \(0.648138\pi\) | |||||||
\(882\) | 17.4227 | 0.586652 | ||||||||
\(883\) | 38.0916 | 1.28188 | 0.640942 | − | 0.767589i | \(-0.278544\pi\) | ||||
0.640942 | + | 0.767589i | \(0.278544\pi\) | |||||||
\(884\) | 0.606013 | 0.0203824 | ||||||||
\(885\) | −35.4623 | −1.19205 | ||||||||
\(886\) | −11.7114 | −0.393454 | ||||||||
\(887\) | 24.0173 | 0.806422 | 0.403211 | − | 0.915107i | \(-0.367894\pi\) | ||||
0.403211 | + | 0.915107i | \(0.367894\pi\) | |||||||
\(888\) | 10.3626 | 0.347747 | ||||||||
\(889\) | 0.0774208 | 0.00259661 | ||||||||
\(890\) | 13.2165 | 0.443020 | ||||||||
\(891\) | −9.94194 | −0.333068 | ||||||||
\(892\) | 0.688835 | 0.0230639 | ||||||||
\(893\) | 12.4747 | 0.417451 | ||||||||
\(894\) | −26.3382 | −0.880883 | ||||||||
\(895\) | 85.9831 | 2.87410 | ||||||||
\(896\) | 0.279699 | 0.00934408 | ||||||||
\(897\) | −2.75310 | −0.0919233 | ||||||||
\(898\) | 4.90126 | 0.163557 | ||||||||
\(899\) | −24.7956 | −0.826979 | ||||||||
\(900\) | 26.3718 | 0.879061 | ||||||||
\(901\) | −15.1383 | −0.504330 | ||||||||
\(902\) | 3.24841 | 0.108160 | ||||||||
\(903\) | 3.46413 | 0.115279 | ||||||||
\(904\) | 7.48323 | 0.248888 | ||||||||
\(905\) | −19.8369 | −0.659401 | ||||||||
\(906\) | −17.7189 | −0.588671 | ||||||||
\(907\) | 14.3891 | 0.477782 | 0.238891 | − | 0.971046i | \(-0.423216\pi\) | ||||
0.238891 | + | 0.971046i | \(0.423216\pi\) | |||||||
\(908\) | −28.0232 | −0.929982 | ||||||||
\(909\) | 19.8544 | 0.658528 | ||||||||
\(910\) | −0.453262 | −0.0150255 | ||||||||
\(911\) | 9.39761 | 0.311357 | 0.155678 | − | 0.987808i | \(-0.450244\pi\) | ||||
0.155678 | + | 0.987808i | \(0.450244\pi\) | |||||||
\(912\) | 18.4058 | 0.609477 | ||||||||
\(913\) | −10.4787 | −0.346795 | ||||||||
\(914\) | 3.76798 | 0.124634 | ||||||||
\(915\) | −103.429 | −3.41925 | ||||||||
\(916\) | −4.68908 | −0.154932 | ||||||||
\(917\) | −1.14569 | −0.0378341 | ||||||||
\(918\) | 1.66877 | 0.0550776 | ||||||||
\(919\) | −17.8134 | −0.587610 | −0.293805 | − | 0.955865i | \(-0.594922\pi\) | ||||
−0.293805 | + | 0.955865i | \(0.594922\pi\) | |||||||
\(920\) | 11.1944 | 0.369068 | ||||||||
\(921\) | 5.08289 | 0.167487 | ||||||||
\(922\) | 20.9688 | 0.690571 | ||||||||
\(923\) | 0.155767 | 0.00512713 | ||||||||
\(924\) | 0.639374 | 0.0210339 | ||||||||
\(925\) | 46.2230 | 1.51980 | ||||||||
\(926\) | −25.8109 | −0.848198 | ||||||||
\(927\) | −9.15037 | −0.300538 | ||||||||
\(928\) | −4.82149 | −0.158273 | ||||||||
\(929\) | −43.8538 | −1.43880 | −0.719398 | − | 0.694598i | \(-0.755582\pi\) | ||||
−0.719398 | + | 0.694598i | \(0.755582\pi\) | |||||||
\(930\) | −47.5219 | −1.55830 | ||||||||
\(931\) | 54.2396 | 1.77763 | ||||||||
\(932\) | 7.02459 | 0.230098 | ||||||||
\(933\) | −1.06685 | −0.0349270 | ||||||||
\(934\) | 11.4599 | 0.374980 | ||||||||
\(935\) | −5.63280 | −0.184212 | ||||||||
\(936\) | 1.03684 | 0.0338901 | ||||||||
\(937\) | −14.2223 | −0.464622 | −0.232311 | − | 0.972642i | \(-0.574629\pi\) | ||||
−0.232311 | + | 0.972642i | \(0.574629\pi\) | |||||||
\(938\) | −2.16684 | −0.0707498 | ||||||||
\(939\) | −32.8439 | −1.07182 | ||||||||
\(940\) | −6.26292 | −0.204274 | ||||||||
\(941\) | −38.8780 | −1.26739 | −0.633694 | − | 0.773584i | \(-0.718462\pi\) | ||||
−0.633694 | + | 0.773584i | \(0.718462\pi\) | |||||||
\(942\) | −29.4096 | −0.958215 | ||||||||
\(943\) | 9.49763 | 0.309285 | ||||||||
\(944\) | 3.83766 | 0.124905 | ||||||||
\(945\) | −1.24814 | −0.0406020 | ||||||||
\(946\) | −5.13166 | −0.166845 | ||||||||
\(947\) | −16.4489 | −0.534516 | −0.267258 | − | 0.963625i | \(-0.586118\pi\) | ||||
−0.267258 | + | 0.963625i | \(0.586118\pi\) | |||||||
\(948\) | −0.801777 | −0.0260405 | ||||||||
\(949\) | 4.86102 | 0.157795 | ||||||||
\(950\) | 82.0999 | 2.66367 | ||||||||
\(951\) | −47.5308 | −1.54129 | ||||||||
\(952\) | −0.411490 | −0.0133365 | ||||||||
\(953\) | 30.9997 | 1.00418 | 0.502090 | − | 0.864815i | \(-0.332565\pi\) | ||||
0.502090 | + | 0.864815i | \(0.332565\pi\) | |||||||
\(954\) | −25.9004 | −0.838556 | ||||||||
\(955\) | −71.9901 | −2.32955 | ||||||||
\(956\) | −9.43944 | −0.305293 | ||||||||
\(957\) | −11.0216 | −0.356278 | ||||||||
\(958\) | 0.722672 | 0.0233485 | ||||||||
\(959\) | −1.76188 | −0.0568942 | ||||||||
\(960\) | −9.24060 | −0.298239 | ||||||||
\(961\) | −4.55236 | −0.146850 | ||||||||
\(962\) | 1.81731 | 0.0585923 | ||||||||
\(963\) | 25.0537 | 0.807346 | ||||||||
\(964\) | −21.0367 | −0.677548 | ||||||||
\(965\) | 32.9483 | 1.06064 | ||||||||
\(966\) | 1.86939 | 0.0601466 | ||||||||
\(967\) | −10.4119 | −0.334824 | −0.167412 | − | 0.985887i | \(-0.553541\pi\) | ||||
−0.167412 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(968\) | 10.0528 | 0.323111 | ||||||||
\(969\) | −27.0784 | −0.869884 | ||||||||
\(970\) | 1.59699 | 0.0512762 | ||||||||
\(971\) | 32.5080 | 1.04323 | 0.521616 | − | 0.853180i | \(-0.325329\pi\) | ||||
0.521616 | + | 0.853180i | \(0.325329\pi\) | |||||||
\(972\) | 20.5919 | 0.660484 | ||||||||
\(973\) | 0.109572 | 0.00351271 | ||||||||
\(974\) | −24.3721 | −0.780933 | ||||||||
\(975\) | 10.1370 | 0.324645 | ||||||||
\(976\) | 11.1929 | 0.358275 | ||||||||
\(977\) | 14.1647 | 0.453169 | 0.226584 | − | 0.973992i | \(-0.427244\pi\) | ||||
0.226584 | + | 0.973992i | \(0.427244\pi\) | |||||||
\(978\) | 7.76050 | 0.248153 | ||||||||
\(979\) | −3.26951 | −0.104494 | ||||||||
\(980\) | −27.2309 | −0.869860 | ||||||||
\(981\) | −13.7882 | −0.440222 | ||||||||
\(982\) | 21.6203 | 0.689933 | ||||||||
\(983\) | −37.2717 | −1.18878 | −0.594392 | − | 0.804176i | \(-0.702607\pi\) | ||||
−0.594392 | + | 0.804176i | \(0.702607\pi\) | |||||||
\(984\) | −7.83999 | −0.249930 | ||||||||
\(985\) | 43.1224 | 1.37399 | ||||||||
\(986\) | 7.09333 | 0.225898 | ||||||||
\(987\) | −1.04587 | −0.0332903 | ||||||||
\(988\) | 3.22784 | 0.102691 | ||||||||
\(989\) | −15.0039 | −0.477095 | ||||||||
\(990\) | −9.63724 | −0.306292 | ||||||||
\(991\) | −16.1211 | −0.512105 | −0.256052 | − | 0.966663i | \(-0.582422\pi\) | ||||
−0.256052 | + | 0.966663i | \(0.582422\pi\) | |||||||
\(992\) | 5.14273 | 0.163282 | ||||||||
\(993\) | 37.9486 | 1.20426 | ||||||||
\(994\) | −0.105768 | −0.00335475 | ||||||||
\(995\) | −82.2048 | −2.60607 | ||||||||
\(996\) | 25.2902 | 0.801352 | ||||||||
\(997\) | 39.0214 | 1.23582 | 0.617910 | − | 0.786249i | \(-0.287980\pi\) | ||||
0.617910 | + | 0.786249i | \(0.287980\pi\) | |||||||
\(998\) | 9.82237 | 0.310922 | ||||||||
\(999\) | 5.00429 | 0.158329 |
(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 | 8026.2.a.b.1.16 | ✓ | 81 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.b.1.16 | ✓ | 81 | 1.1 | even | 1 | trivial |