Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.14656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.385537\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38554 | −0.979723 | −0.489861 | − | 0.871800i | \(-0.662953\pi\) | ||||
−0.489861 | + | 0.871800i | \(0.662953\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.0802864 | −0.0401432 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.38554 | −0.565643 | ||||||||
\(7\) | −4.18757 | −1.58275 | −0.791375 | − | 0.611330i | \(-0.790635\pi\) | ||||
−0.791375 | + | 0.611330i | \(0.790635\pi\) | |||||||
\(8\) | 2.88231 | 1.01905 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.919714 | 0.277304 | 0.138652 | − | 0.990341i | \(-0.455723\pi\) | ||||
0.138652 | + | 0.990341i | \(0.455723\pi\) | |||||||
\(12\) | −0.0802864 | −0.0231767 | ||||||||
\(13\) | 0.614463 | 0.170421 | 0.0852106 | − | 0.996363i | \(-0.472844\pi\) | ||||
0.0852106 | + | 0.996363i | \(0.472844\pi\) | |||||||
\(14\) | 5.80203 | 1.55066 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.83298 | −0.958245 | ||||||||
\(17\) | −6.98959 | −1.69523 | −0.847613 | − | 0.530615i | \(-0.821961\pi\) | ||||
−0.847613 | + | 0.530615i | \(0.821961\pi\) | |||||||
\(18\) | −1.38554 | −0.326574 | ||||||||
\(19\) | 1.12962 | 0.259152 | 0.129576 | − | 0.991569i | \(-0.458638\pi\) | ||||
0.129576 | + | 0.991569i | \(0.458638\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.18757 | −0.913802 | ||||||||
\(22\) | −1.27430 | −0.271681 | ||||||||
\(23\) | −8.34814 | −1.74071 | −0.870354 | − | 0.492427i | \(-0.836110\pi\) | ||||
−0.870354 | + | 0.492427i | \(0.836110\pi\) | |||||||
\(24\) | 2.88231 | 0.588350 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.851361 | −0.166966 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.336204 | 0.0635366 | ||||||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.59544 | −0.645761 | −0.322880 | − | 0.946440i | \(-0.604651\pi\) | ||||
−0.322880 | + | 0.946440i | \(0.604651\pi\) | |||||||
\(32\) | −0.453890 | −0.0802372 | ||||||||
\(33\) | 0.919714 | 0.160102 | ||||||||
\(34\) | 9.68434 | 1.66085 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0802864 | −0.0133811 | ||||||||
\(37\) | 3.75270 | 0.616939 | 0.308470 | − | 0.951234i | \(-0.400183\pi\) | ||||
0.308470 | + | 0.951234i | \(0.400183\pi\) | |||||||
\(38\) | −1.56513 | −0.253898 | ||||||||
\(39\) | 0.614463 | 0.0983928 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.08029 | 0.949581 | 0.474791 | − | 0.880099i | \(-0.342524\pi\) | ||||
0.474791 | + | 0.880099i | \(0.342524\pi\) | |||||||
\(42\) | 5.80203 | 0.895272 | ||||||||
\(43\) | 8.21456 | 1.25271 | 0.626354 | − | 0.779539i | \(-0.284546\pi\) | ||||
0.626354 | + | 0.779539i | \(0.284546\pi\) | |||||||
\(44\) | −0.0738405 | −0.0111319 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11.5667 | 1.70541 | ||||||||
\(47\) | −1.00000 | −0.145865 | ||||||||
\(48\) | −3.83298 | −0.553243 | ||||||||
\(49\) | 10.5357 | 1.50510 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.98959 | −0.978739 | ||||||||
\(52\) | −0.0493330 | −0.00684125 | ||||||||
\(53\) | 1.49282 | 0.205054 | 0.102527 | − | 0.994730i | \(-0.467307\pi\) | ||||
0.102527 | + | 0.994730i | \(0.467307\pi\) | |||||||
\(54\) | −1.38554 | −0.188548 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.0699 | −1.61291 | ||||||||
\(57\) | 1.12962 | 0.149622 | ||||||||
\(58\) | −6.92769 | −0.909650 | ||||||||
\(59\) | −2.57310 | −0.334989 | −0.167495 | − | 0.985873i | \(-0.553568\pi\) | ||||
−0.167495 | + | 0.985873i | \(0.553568\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.86974 | −0.751543 | −0.375772 | − | 0.926712i | \(-0.622622\pi\) | ||||
−0.375772 | + | 0.926712i | \(0.622622\pi\) | |||||||
\(62\) | 4.98162 | 0.632666 | ||||||||
\(63\) | −4.18757 | −0.527584 | ||||||||
\(64\) | 8.29484 | 1.03686 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.27430 | −0.156855 | ||||||||
\(67\) | 0.824368 | 0.100713 | 0.0503563 | − | 0.998731i | \(-0.483964\pi\) | ||||
0.0503563 | + | 0.998731i | \(0.483964\pi\) | |||||||
\(68\) | 0.561169 | 0.0680517 | ||||||||
\(69\) | −8.34814 | −1.00500 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1232 | 1.43876 | 0.719378 | − | 0.694619i | \(-0.244427\pi\) | ||||
0.719378 | + | 0.694619i | \(0.244427\pi\) | |||||||
\(72\) | 2.88231 | 0.339684 | ||||||||
\(73\) | −11.7732 | −1.37795 | −0.688977 | − | 0.724783i | \(-0.741940\pi\) | ||||
−0.688977 | + | 0.724783i | \(0.741940\pi\) | |||||||
\(74\) | −5.19950 | −0.604429 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0906930 | −0.0104032 | ||||||||
\(77\) | −3.85136 | −0.438903 | ||||||||
\(78\) | −0.851361 | −0.0963976 | ||||||||
\(79\) | −4.06592 | −0.457452 | −0.228726 | − | 0.973491i | \(-0.573456\pi\) | ||||
−0.228726 | + | 0.973491i | \(0.573456\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.42446 | −0.930326 | ||||||||
\(83\) | 14.4738 | 1.58871 | 0.794353 | − | 0.607457i | \(-0.207810\pi\) | ||||
0.794353 | + | 0.607457i | \(0.207810\pi\) | |||||||
\(84\) | 0.336204 | 0.0366829 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.3816 | −1.22731 | ||||||||
\(87\) | 5.00000 | 0.536056 | ||||||||
\(88\) | 2.65090 | 0.282587 | ||||||||
\(89\) | −16.7049 | −1.77071 | −0.885357 | − | 0.464911i | \(-0.846086\pi\) | ||||
−0.885357 | + | 0.464911i | \(0.846086\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.57310 | −0.269734 | ||||||||
\(92\) | 0.670242 | 0.0698775 | ||||||||
\(93\) | −3.59544 | −0.372830 | ||||||||
\(94\) | 1.38554 | 0.142907 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.453890 | −0.0463250 | ||||||||
\(97\) | 1.93809 | 0.196784 | 0.0983918 | − | 0.995148i | \(-0.468630\pi\) | ||||
0.0983918 | + | 0.995148i | \(0.468630\pi\) | |||||||
\(98\) | −14.5976 | −1.47458 | ||||||||
\(99\) | 0.919714 | 0.0924347 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.94026 | −0.491574 | −0.245787 | − | 0.969324i | \(-0.579046\pi\) | ||||
−0.245787 | + | 0.969324i | \(0.579046\pi\) | |||||||
\(102\) | 9.68434 | 0.958893 | ||||||||
\(103\) | 8.87191 | 0.874175 | 0.437088 | − | 0.899419i | \(-0.356010\pi\) | ||||
0.437088 | + | 0.899419i | \(0.356010\pi\) | |||||||
\(104\) | 1.77107 | 0.173668 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.06835 | −0.200896 | ||||||||
\(107\) | −8.21456 | −0.794131 | −0.397066 | − | 0.917790i | \(-0.629971\pi\) | ||||
−0.397066 | + | 0.917790i | \(0.629971\pi\) | |||||||
\(108\) | −0.0802864 | −0.00772556 | ||||||||
\(109\) | −10.1692 | −0.974031 | −0.487016 | − | 0.873393i | \(-0.661915\pi\) | ||||
−0.487016 | + | 0.873393i | \(0.661915\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.75270 | 0.356190 | ||||||||
\(112\) | 16.0509 | 1.51666 | ||||||||
\(113\) | 6.01193 | 0.565555 | 0.282778 | − | 0.959186i | \(-0.408744\pi\) | ||||
0.282778 | + | 0.959186i | \(0.408744\pi\) | |||||||
\(114\) | −1.56513 | −0.146588 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.401432 | −0.0372720 | ||||||||
\(117\) | 0.614463 | 0.0568071 | ||||||||
\(118\) | 3.56513 | 0.328197 | ||||||||
\(119\) | 29.2694 | 2.68312 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1541 | −0.923102 | ||||||||
\(122\) | 8.13274 | 0.736304 | ||||||||
\(123\) | 6.08029 | 0.548241 | ||||||||
\(124\) | 0.288665 | 0.0259229 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.80203 | 0.516886 | ||||||||
\(127\) | 8.69628 | 0.771670 | 0.385835 | − | 0.922568i | \(-0.373913\pi\) | ||||
0.385835 | + | 0.922568i | \(0.373913\pi\) | |||||||
\(128\) | −10.5850 | −0.935594 | ||||||||
\(129\) | 8.21456 | 0.723251 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1073 | 1.05782 | 0.528909 | − | 0.848679i | \(-0.322601\pi\) | ||||
0.528909 | + | 0.848679i | \(0.322601\pi\) | |||||||
\(132\) | −0.0738405 | −0.00642699 | ||||||||
\(133\) | −4.73035 | −0.410174 | ||||||||
\(134\) | −1.14219 | −0.0986705 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −20.1462 | −1.72752 | ||||||||
\(137\) | 17.9792 | 1.53607 | 0.768033 | − | 0.640411i | \(-0.221236\pi\) | ||||
0.768033 | + | 0.640411i | \(0.221236\pi\) | |||||||
\(138\) | 11.5667 | 0.984619 | ||||||||
\(139\) | 9.65671 | 0.819071 | 0.409536 | − | 0.912294i | \(-0.365691\pi\) | ||||
0.409536 | + | 0.912294i | \(0.365691\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.00000 | −0.0842152 | ||||||||
\(142\) | −16.7971 | −1.40958 | ||||||||
\(143\) | 0.565130 | 0.0472585 | ||||||||
\(144\) | −3.83298 | −0.319415 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.3123 | 1.35001 | ||||||||
\(147\) | 10.5357 | 0.868970 | ||||||||
\(148\) | −0.301290 | −0.0247659 | ||||||||
\(149\) | 20.5529 | 1.68376 | 0.841881 | − | 0.539664i | \(-0.181449\pi\) | ||||
0.841881 | + | 0.539664i | \(0.181449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.64146 | 0.784611 | 0.392305 | − | 0.919835i | \(-0.371678\pi\) | ||||
0.392305 | + | 0.919835i | \(0.371678\pi\) | |||||||
\(152\) | 3.25592 | 0.264090 | ||||||||
\(153\) | −6.98959 | −0.565075 | ||||||||
\(154\) | 5.33620 | 0.430004 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.0493330 | −0.00394980 | ||||||||
\(157\) | 12.6724 | 1.01137 | 0.505684 | − | 0.862719i | \(-0.331240\pi\) | ||||
0.505684 | + | 0.862719i | \(0.331240\pi\) | |||||||
\(158\) | 5.63348 | 0.448176 | ||||||||
\(159\) | 1.49282 | 0.118388 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 34.9584 | 2.75511 | ||||||||
\(162\) | −1.38554 | −0.108858 | ||||||||
\(163\) | −6.16057 | −0.482533 | −0.241267 | − | 0.970459i | \(-0.577563\pi\) | ||||
−0.241267 | + | 0.970459i | \(0.577563\pi\) | |||||||
\(164\) | −0.488164 | −0.0381192 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.0540 | −1.55649 | ||||||||
\(167\) | 3.84159 | 0.297272 | 0.148636 | − | 0.988892i | \(-0.452512\pi\) | ||||
0.148636 | + | 0.988892i | \(0.452512\pi\) | |||||||
\(168\) | −12.0699 | −0.931211 | ||||||||
\(169\) | −12.6224 | −0.970957 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.12962 | 0.0863841 | ||||||||
\(172\) | −0.659517 | −0.0502877 | ||||||||
\(173\) | 14.2964 | 1.08693 | 0.543466 | − | 0.839431i | \(-0.317111\pi\) | ||||
0.543466 | + | 0.839431i | \(0.317111\pi\) | |||||||
\(174\) | −6.92769 | −0.525187 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.52525 | −0.265725 | ||||||||
\(177\) | −2.57310 | −0.193406 | ||||||||
\(178\) | 23.1452 | 1.73481 | ||||||||
\(179\) | 15.8633 | 1.18568 | 0.592839 | − | 0.805321i | \(-0.298007\pi\) | ||||
0.592839 | + | 0.805321i | \(0.298007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.639928 | −0.0475655 | −0.0237827 | − | 0.999717i | \(-0.507571\pi\) | ||||
−0.0237827 | + | 0.999717i | \(0.507571\pi\) | |||||||
\(182\) | 3.56513 | 0.264265 | ||||||||
\(183\) | −5.86974 | −0.433904 | ||||||||
\(184\) | −24.0620 | −1.77387 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.98162 | 0.365270 | ||||||||
\(187\) | −6.42842 | −0.470093 | ||||||||
\(188\) | 0.0802864 | 0.00585548 | ||||||||
\(189\) | −4.18757 | −0.304601 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.31539 | −0.529323 | −0.264662 | − | 0.964341i | \(-0.585260\pi\) | ||||
−0.264662 | + | 0.964341i | \(0.585260\pi\) | |||||||
\(192\) | 8.29484 | 0.598629 | ||||||||
\(193\) | −9.10083 | −0.655092 | −0.327546 | − | 0.944835i | \(-0.606222\pi\) | ||||
−0.327546 | + | 0.944835i | \(0.606222\pi\) | |||||||
\(194\) | −2.68530 | −0.192793 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.845873 | −0.0604195 | ||||||||
\(197\) | −18.3950 | −1.31059 | −0.655296 | − | 0.755372i | \(-0.727456\pi\) | ||||
−0.655296 | + | 0.755372i | \(0.727456\pi\) | |||||||
\(198\) | −1.27430 | −0.0905604 | ||||||||
\(199\) | 17.9798 | 1.27456 | 0.637278 | − | 0.770634i | \(-0.280060\pi\) | ||||
0.637278 | + | 0.770634i | \(0.280060\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.824368 | 0.0581465 | ||||||||
\(202\) | 6.84492 | 0.481607 | ||||||||
\(203\) | −20.9378 | −1.46955 | ||||||||
\(204\) | 0.561169 | 0.0392897 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.2924 | −0.856449 | ||||||||
\(207\) | −8.34814 | −0.580236 | ||||||||
\(208\) | −2.35522 | −0.163305 | ||||||||
\(209\) | 1.03893 | 0.0718640 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2375 | 0.911310 | 0.455655 | − | 0.890157i | \(-0.349405\pi\) | ||||
0.455655 | + | 0.890157i | \(0.349405\pi\) | |||||||
\(212\) | −0.119853 | −0.00823152 | ||||||||
\(213\) | 12.1232 | 0.830666 | ||||||||
\(214\) | 11.3816 | 0.778029 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.88231 | 0.196117 | ||||||||
\(217\) | 15.0562 | 1.02208 | ||||||||
\(218\) | 14.0898 | 0.954281 | ||||||||
\(219\) | −11.7732 | −0.795562 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.29484 | −0.288902 | ||||||||
\(222\) | −5.19950 | −0.348968 | ||||||||
\(223\) | −7.05974 | −0.472755 | −0.236378 | − | 0.971661i | \(-0.575960\pi\) | ||||
−0.236378 | + | 0.971661i | \(0.575960\pi\) | |||||||
\(224\) | 1.90069 | 0.126995 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.32976 | −0.554087 | ||||||||
\(227\) | 24.3720 | 1.61763 | 0.808813 | − | 0.588065i | \(-0.200110\pi\) | ||||
0.808813 | + | 0.588065i | \(0.200110\pi\) | |||||||
\(228\) | −0.0906930 | −0.00600629 | ||||||||
\(229\) | 19.8640 | 1.31265 | 0.656325 | − | 0.754479i | \(-0.272110\pi\) | ||||
0.656325 | + | 0.754479i | \(0.272110\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.85136 | −0.253401 | ||||||||
\(232\) | 14.4116 | 0.946166 | ||||||||
\(233\) | 0.923726 | 0.0605153 | 0.0302576 | − | 0.999542i | \(-0.490367\pi\) | ||||
0.0302576 | + | 0.999542i | \(0.490367\pi\) | |||||||
\(234\) | −0.851361 | −0.0556552 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.206585 | 0.0134475 | ||||||||
\(237\) | −4.06592 | −0.264110 | ||||||||
\(238\) | −40.5538 | −2.62871 | ||||||||
\(239\) | 12.1073 | 0.783155 | 0.391577 | − | 0.920145i | \(-0.371930\pi\) | ||||
0.391577 | + | 0.920145i | \(0.371930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.8870 | −0.765707 | −0.382853 | − | 0.923809i | \(-0.625059\pi\) | ||||
−0.382853 | + | 0.923809i | \(0.625059\pi\) | |||||||
\(242\) | 14.0689 | 0.904385 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.471260 | 0.0301693 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.42446 | −0.537124 | ||||||||
\(247\) | 0.694109 | 0.0441651 | ||||||||
\(248\) | −10.3632 | −0.658064 | ||||||||
\(249\) | 14.4738 | 0.917240 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.0858 | 1.39404 | 0.697022 | − | 0.717049i | \(-0.254508\pi\) | ||||
0.697022 | + | 0.717049i | \(0.254508\pi\) | |||||||
\(252\) | 0.336204 | 0.0211789 | ||||||||
\(253\) | −7.67790 | −0.482705 | ||||||||
\(254\) | −12.0490 | −0.756022 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.92373 | −0.120233 | ||||||||
\(257\) | 5.60004 | 0.349321 | 0.174661 | − | 0.984629i | \(-0.444117\pi\) | ||||
0.174661 | + | 0.984629i | \(0.444117\pi\) | |||||||
\(258\) | −11.3816 | −0.708586 | ||||||||
\(259\) | −15.7147 | −0.976461 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | 0.309492 | ||||||||
\(262\) | −16.7751 | −1.03637 | ||||||||
\(263\) | 13.7892 | 0.850278 | 0.425139 | − | 0.905128i | \(-0.360225\pi\) | ||||
0.425139 | + | 0.905128i | \(0.360225\pi\) | |||||||
\(264\) | 2.65090 | 0.163152 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.55408 | 0.401857 | ||||||||
\(267\) | −16.7049 | −1.02232 | ||||||||
\(268\) | −0.0661855 | −0.00404292 | ||||||||
\(269\) | −4.57374 | −0.278866 | −0.139433 | − | 0.990232i | \(-0.544528\pi\) | ||||
−0.139433 | + | 0.990232i | \(0.544528\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.8057 | −1.81057 | −0.905284 | − | 0.424806i | \(-0.860342\pi\) | ||||
−0.905284 | + | 0.424806i | \(0.860342\pi\) | |||||||
\(272\) | 26.7910 | 1.62444 | ||||||||
\(273\) | −2.57310 | −0.155731 | ||||||||
\(274\) | −24.9108 | −1.50492 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.670242 | 0.0403438 | ||||||||
\(277\) | −19.4187 | −1.16675 | −0.583377 | − | 0.812201i | \(-0.698269\pi\) | ||||
−0.583377 | + | 0.812201i | \(0.698269\pi\) | |||||||
\(278\) | −13.3797 | −0.802463 | ||||||||
\(279\) | −3.59544 | −0.215254 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0239 | 1.01556 | 0.507779 | − | 0.861487i | \(-0.330467\pi\) | ||||
0.507779 | + | 0.861487i | \(0.330467\pi\) | |||||||
\(282\) | 1.38554 | 0.0825075 | ||||||||
\(283\) | 11.0303 | 0.655684 | 0.327842 | − | 0.944733i | \(-0.393679\pi\) | ||||
0.327842 | + | 0.944733i | \(0.393679\pi\) | |||||||
\(284\) | −0.973325 | −0.0577562 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.783008 | −0.0463003 | ||||||||
\(287\) | −25.4616 | −1.50295 | ||||||||
\(288\) | −0.453890 | −0.0267457 | ||||||||
\(289\) | 31.8544 | 1.87379 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.93809 | 0.113613 | ||||||||
\(292\) | 0.945231 | 0.0553154 | ||||||||
\(293\) | 33.5084 | 1.95758 | 0.978792 | − | 0.204856i | \(-0.0656726\pi\) | ||||
0.978792 | + | 0.204856i | \(0.0656726\pi\) | |||||||
\(294\) | −14.5976 | −0.851350 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 10.8164 | 0.628693 | ||||||||
\(297\) | 0.919714 | 0.0533672 | ||||||||
\(298\) | −28.4769 | −1.64962 | ||||||||
\(299\) | −5.12962 | −0.296654 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.3990 | −1.98273 | ||||||||
\(302\) | −13.3586 | −0.768701 | ||||||||
\(303\) | −4.94026 | −0.283811 | ||||||||
\(304\) | −4.32981 | −0.248332 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.68434 | 0.553617 | ||||||||
\(307\) | −9.98494 | −0.569871 | −0.284935 | − | 0.958547i | \(-0.591972\pi\) | ||||
−0.284935 | + | 0.958547i | \(0.591972\pi\) | |||||||
\(308\) | 0.309212 | 0.0176190 | ||||||||
\(309\) | 8.87191 | 0.504705 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.9816 | 0.736120 | 0.368060 | − | 0.929802i | \(-0.380022\pi\) | ||||
0.368060 | + | 0.929802i | \(0.380022\pi\) | |||||||
\(312\) | 1.77107 | 0.100267 | ||||||||
\(313\) | 21.9378 | 1.24000 | 0.619998 | − | 0.784603i | \(-0.287133\pi\) | ||||
0.619998 | + | 0.784603i | \(0.287133\pi\) | |||||||
\(314\) | −17.5581 | −0.990861 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.326438 | 0.0183636 | ||||||||
\(317\) | −11.0856 | −0.622628 | −0.311314 | − | 0.950307i | \(-0.600769\pi\) | ||||
−0.311314 | + | 0.950307i | \(0.600769\pi\) | |||||||
\(318\) | −2.06835 | −0.115987 | ||||||||
\(319\) | 4.59857 | 0.257470 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.21456 | −0.458492 | ||||||||
\(322\) | −48.4361 | −2.69924 | ||||||||
\(323\) | −7.89558 | −0.439322 | ||||||||
\(324\) | −0.0802864 | −0.00446035 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.53570 | 0.472749 | ||||||||
\(327\) | −10.1692 | −0.562357 | ||||||||
\(328\) | 17.5253 | 0.967673 | ||||||||
\(329\) | 4.18757 | 0.230868 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.88716 | 0.433518 | 0.216759 | − | 0.976225i | \(-0.430451\pi\) | ||||
0.216759 | + | 0.976225i | \(0.430451\pi\) | |||||||
\(332\) | −1.16205 | −0.0637757 | ||||||||
\(333\) | 3.75270 | 0.205646 | ||||||||
\(334\) | −5.32267 | −0.291244 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 16.0509 | 0.875646 | ||||||||
\(337\) | 22.0819 | 1.20288 | 0.601438 | − | 0.798920i | \(-0.294595\pi\) | ||||
0.601438 | + | 0.798920i | \(0.294595\pi\) | |||||||
\(338\) | 17.4889 | 0.951268 | ||||||||
\(339\) | 6.01193 | 0.326523 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.30678 | −0.179072 | ||||||||
\(342\) | −1.56513 | −0.0846325 | ||||||||
\(343\) | −14.8060 | −0.799448 | ||||||||
\(344\) | 23.6769 | 1.27657 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.8082 | −1.06489 | ||||||||
\(347\) | 24.5149 | 1.31603 | 0.658014 | − | 0.753006i | \(-0.271397\pi\) | ||||
0.658014 | + | 0.753006i | \(0.271397\pi\) | |||||||
\(348\) | −0.401432 | −0.0215190 | ||||||||
\(349\) | −28.2103 | −1.51006 | −0.755031 | − | 0.655689i | \(-0.772378\pi\) | ||||
−0.755031 | + | 0.655689i | \(0.772378\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.614463 | 0.0327976 | ||||||||
\(352\) | −0.417449 | −0.0222501 | ||||||||
\(353\) | 32.9115 | 1.75170 | 0.875852 | − | 0.482580i | \(-0.160300\pi\) | ||||
0.875852 | + | 0.482580i | \(0.160300\pi\) | |||||||
\(354\) | 3.56513 | 0.189485 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.34117 | 0.0710821 | ||||||||
\(357\) | 29.2694 | 1.54910 | ||||||||
\(358\) | −21.9792 | −1.16164 | ||||||||
\(359\) | −17.7819 | −0.938490 | −0.469245 | − | 0.883068i | \(-0.655474\pi\) | ||||
−0.469245 | + | 0.883068i | \(0.655474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7240 | −0.932840 | ||||||||
\(362\) | 0.886645 | 0.0466010 | ||||||||
\(363\) | −10.1541 | −0.532953 | ||||||||
\(364\) | 0.206585 | 0.0108280 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.13274 | 0.425105 | ||||||||
\(367\) | −14.0079 | −0.731208 | −0.365604 | − | 0.930771i | \(-0.619137\pi\) | ||||
−0.365604 | + | 0.930771i | \(0.619137\pi\) | |||||||
\(368\) | 31.9983 | 1.66802 | ||||||||
\(369\) | 6.08029 | 0.316527 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.25127 | −0.324550 | ||||||||
\(372\) | 0.288665 | 0.0149666 | ||||||||
\(373\) | −21.9577 | −1.13693 | −0.568463 | − | 0.822709i | \(-0.692462\pi\) | ||||
−0.568463 | + | 0.822709i | \(0.692462\pi\) | |||||||
\(374\) | 8.90682 | 0.460561 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.88231 | −0.148644 | ||||||||
\(377\) | 3.07231 | 0.158232 | ||||||||
\(378\) | 5.80203 | 0.298424 | ||||||||
\(379\) | −5.10415 | −0.262183 | −0.131091 | − | 0.991370i | \(-0.541848\pi\) | ||||
−0.131091 | + | 0.991370i | \(0.541848\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.69628 | 0.445524 | ||||||||
\(382\) | 10.1357 | 0.518590 | ||||||||
\(383\) | −6.43635 | −0.328882 | −0.164441 | − | 0.986387i | \(-0.552582\pi\) | ||||
−0.164441 | + | 0.986387i | \(0.552582\pi\) | |||||||
\(384\) | −10.5850 | −0.540165 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.6095 | 0.641809 | ||||||||
\(387\) | 8.21456 | 0.417569 | ||||||||
\(388\) | −0.155602 | −0.00789952 | ||||||||
\(389\) | −36.7518 | −1.86339 | −0.931696 | − | 0.363239i | \(-0.881671\pi\) | ||||
−0.931696 | + | 0.363239i | \(0.881671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 58.3501 | 2.95089 | ||||||||
\(392\) | 30.3672 | 1.53378 | ||||||||
\(393\) | 12.1073 | 0.610731 | ||||||||
\(394\) | 25.4870 | 1.28402 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.0738405 | −0.00371062 | ||||||||
\(397\) | 20.7423 | 1.04103 | 0.520514 | − | 0.853853i | \(-0.325740\pi\) | ||||
0.520514 | + | 0.853853i | \(0.325740\pi\) | |||||||
\(398\) | −24.9117 | −1.24871 | ||||||||
\(399\) | −4.73035 | −0.236814 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.7899 | 1.88714 | 0.943568 | − | 0.331178i | \(-0.107446\pi\) | ||||
0.943568 | + | 0.331178i | \(0.107446\pi\) | |||||||
\(402\) | −1.14219 | −0.0569674 | ||||||||
\(403\) | −2.20927 | −0.110051 | ||||||||
\(404\) | 0.396635 | 0.0197334 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 29.0101 | 1.43975 | ||||||||
\(407\) | 3.45140 | 0.171080 | ||||||||
\(408\) | −20.1462 | −0.997386 | ||||||||
\(409\) | −1.49678 | −0.0740109 | −0.0370054 | − | 0.999315i | \(-0.511782\pi\) | ||||
−0.0370054 | + | 0.999315i | \(0.511782\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.9792 | 0.886848 | ||||||||
\(412\) | −0.712293 | −0.0350922 | ||||||||
\(413\) | 10.7750 | 0.530205 | ||||||||
\(414\) | 11.5667 | 0.568470 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.278898 | −0.0136741 | ||||||||
\(417\) | 9.65671 | 0.472891 | ||||||||
\(418\) | −1.43947 | −0.0704068 | ||||||||
\(419\) | −2.85379 | −0.139417 | −0.0697085 | − | 0.997567i | \(-0.522207\pi\) | ||||
−0.0697085 | + | 0.997567i | \(0.522207\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0334 | −1.31753 | −0.658763 | − | 0.752351i | \(-0.728920\pi\) | ||||
−0.658763 | + | 0.752351i | \(0.728920\pi\) | |||||||
\(422\) | −18.3411 | −0.892831 | ||||||||
\(423\) | −1.00000 | −0.0486217 | ||||||||
\(424\) | 4.30277 | 0.208961 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16.7971 | −0.813823 | ||||||||
\(427\) | 24.5799 | 1.18951 | ||||||||
\(428\) | 0.659517 | 0.0318790 | ||||||||
\(429\) | 0.565130 | 0.0272847 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.47444 | −0.311863 | −0.155931 | − | 0.987768i | \(-0.549838\pi\) | ||||
−0.155931 | + | 0.987768i | \(0.549838\pi\) | |||||||
\(432\) | −3.83298 | −0.184414 | ||||||||
\(433\) | 37.4885 | 1.80158 | 0.900792 | − | 0.434251i | \(-0.142987\pi\) | ||||
0.900792 | + | 0.434251i | \(0.142987\pi\) | |||||||
\(434\) | −20.8609 | −1.00135 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.816447 | 0.0391007 | ||||||||
\(437\) | −9.43022 | −0.451109 | ||||||||
\(438\) | 16.3123 | 0.779430 | ||||||||
\(439\) | 31.0135 | 1.48019 | 0.740097 | − | 0.672500i | \(-0.234780\pi\) | ||||
0.740097 | + | 0.672500i | \(0.234780\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.5357 | 0.501700 | ||||||||
\(442\) | 5.95067 | 0.283044 | ||||||||
\(443\) | −7.04971 | −0.334942 | −0.167471 | − | 0.985877i | \(-0.553560\pi\) | ||||
−0.167471 | + | 0.985877i | \(0.553560\pi\) | |||||||
\(444\) | −0.301290 | −0.0142986 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.78153 | 0.463169 | ||||||||
\(447\) | 20.5529 | 0.972120 | ||||||||
\(448\) | −34.7352 | −1.64108 | ||||||||
\(449\) | −5.58166 | −0.263415 | −0.131708 | − | 0.991289i | \(-0.542046\pi\) | ||||
−0.131708 | + | 0.991289i | \(0.542046\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.59212 | 0.263323 | ||||||||
\(452\) | −0.482676 | −0.0227032 | ||||||||
\(453\) | 9.64146 | 0.452995 | ||||||||
\(454\) | −33.7683 | −1.58483 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.25592 | 0.152472 | ||||||||
\(457\) | 1.07141 | 0.0501183 | 0.0250591 | − | 0.999686i | \(-0.492023\pi\) | ||||
0.0250591 | + | 0.999686i | \(0.492023\pi\) | |||||||
\(458\) | −27.5223 | −1.28603 | ||||||||
\(459\) | −6.98959 | −0.326246 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.04754 | 0.235087 | 0.117544 | − | 0.993068i | \(-0.462498\pi\) | ||||
0.117544 | + | 0.993068i | \(0.462498\pi\) | |||||||
\(462\) | 5.33620 | 0.248263 | ||||||||
\(463\) | −6.75454 | −0.313910 | −0.156955 | − | 0.987606i | \(-0.550168\pi\) | ||||
−0.156955 | + | 0.987606i | \(0.550168\pi\) | |||||||
\(464\) | −19.1649 | −0.889708 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.27986 | −0.0592882 | ||||||||
\(467\) | −19.5324 | −0.903851 | −0.451925 | − | 0.892056i | \(-0.649263\pi\) | ||||
−0.451925 | + | 0.892056i | \(0.649263\pi\) | |||||||
\(468\) | −0.0493330 | −0.00228042 | ||||||||
\(469\) | −3.45210 | −0.159403 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6724 | 0.583914 | ||||||||
\(472\) | −7.41649 | −0.341372 | ||||||||
\(473\) | 7.55504 | 0.347381 | ||||||||
\(474\) | 5.63348 | 0.258754 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.34993 | −0.107709 | ||||||||
\(477\) | 1.49282 | 0.0683514 | ||||||||
\(478\) | −16.7751 | −0.767275 | ||||||||
\(479\) | −10.9843 | −0.501886 | −0.250943 | − | 0.968002i | \(-0.580741\pi\) | ||||
−0.250943 | + | 0.968002i | \(0.580741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.30589 | 0.105140 | ||||||||
\(482\) | 16.4698 | 0.750180 | ||||||||
\(483\) | 34.9584 | 1.59066 | ||||||||
\(484\) | 0.815238 | 0.0370563 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.38554 | −0.0628492 | ||||||||
\(487\) | 25.9801 | 1.17727 | 0.588635 | − | 0.808399i | \(-0.299666\pi\) | ||||
0.588635 | + | 0.808399i | \(0.299666\pi\) | |||||||
\(488\) | −16.9184 | −0.765862 | ||||||||
\(489\) | −6.16057 | −0.278591 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.1879 | 1.31723 | 0.658617 | − | 0.752479i | \(-0.271142\pi\) | ||||
0.658617 | + | 0.752479i | \(0.271142\pi\) | |||||||
\(492\) | −0.488164 | −0.0220081 | ||||||||
\(493\) | −34.9480 | −1.57398 | ||||||||
\(494\) | −0.961714 | −0.0432696 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.7813 | 0.618797 | ||||||||
\(497\) | −50.7666 | −2.27719 | ||||||||
\(498\) | −20.0540 | −0.898641 | ||||||||
\(499\) | −2.73795 | −0.122568 | −0.0612838 | − | 0.998120i | \(-0.519519\pi\) | ||||
−0.0612838 | + | 0.998120i | \(0.519519\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.84159 | 0.171630 | ||||||||
\(502\) | −30.6007 | −1.36578 | ||||||||
\(503\) | −6.50871 | −0.290209 | −0.145105 | − | 0.989416i | \(-0.546352\pi\) | ||||
−0.145105 | + | 0.989416i | \(0.546352\pi\) | |||||||
\(504\) | −12.0699 | −0.537635 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.6380 | 0.472917 | ||||||||
\(507\) | −12.6224 | −0.560582 | ||||||||
\(508\) | −0.698192 | −0.0309773 | ||||||||
\(509\) | −10.4054 | −0.461213 | −0.230607 | − | 0.973047i | \(-0.574071\pi\) | ||||
−0.230607 | + | 0.973047i | \(0.574071\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 49.3012 | 2.18096 | ||||||||
\(512\) | 23.8355 | 1.05339 | ||||||||
\(513\) | 1.12962 | 0.0498739 | ||||||||
\(514\) | −7.75907 | −0.342238 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.659517 | −0.0290336 | ||||||||
\(517\) | −0.919714 | −0.0404490 | ||||||||
\(518\) | 21.7732 | 0.956661 | ||||||||
\(519\) | 14.2964 | 0.627541 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2017 | −0.446943 | −0.223472 | − | 0.974710i | \(-0.571739\pi\) | ||||
−0.223472 | + | 0.974710i | \(0.571739\pi\) | |||||||
\(522\) | −6.92769 | −0.303217 | ||||||||
\(523\) | −10.8838 | −0.475917 | −0.237959 | − | 0.971275i | \(-0.576478\pi\) | ||||
−0.237959 | + | 0.971275i | \(0.576478\pi\) | |||||||
\(524\) | −0.972049 | −0.0424642 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.1054 | −0.833037 | ||||||||
\(527\) | 25.1307 | 1.09471 | ||||||||
\(528\) | −3.52525 | −0.153417 | ||||||||
\(529\) | 46.6914 | 2.03006 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.57310 | −0.111663 | ||||||||
\(532\) | 0.379783 | 0.0164657 | ||||||||
\(533\) | 3.73611 | 0.161829 | ||||||||
\(534\) | 23.1452 | 1.00159 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.37609 | 0.102631 | ||||||||
\(537\) | 15.8633 | 0.684552 | ||||||||
\(538\) | 6.33709 | 0.273211 | ||||||||
\(539\) | 9.68983 | 0.417371 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.50138 | −0.193529 | −0.0967647 | − | 0.995307i | \(-0.530849\pi\) | ||||
−0.0967647 | + | 0.995307i | \(0.530849\pi\) | |||||||
\(542\) | 41.2969 | 1.77386 | ||||||||
\(543\) | −0.639928 | −0.0274620 | ||||||||
\(544\) | 3.17251 | 0.136020 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.56513 | 0.152573 | ||||||||
\(547\) | −42.9758 | −1.83751 | −0.918756 | − | 0.394825i | \(-0.870805\pi\) | ||||
−0.918756 | + | 0.394825i | \(0.870805\pi\) | |||||||
\(548\) | −1.44348 | −0.0616626 | ||||||||
\(549\) | −5.86974 | −0.250514 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.64810 | 0.240617 | ||||||||
\(552\) | −24.0620 | −1.02414 | ||||||||
\(553\) | 17.0263 | 0.724032 | ||||||||
\(554\) | 26.9053 | 1.14310 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.775302 | −0.0328801 | ||||||||
\(557\) | −27.3479 | −1.15877 | −0.579383 | − | 0.815055i | \(-0.696707\pi\) | ||||
−0.579383 | + | 0.815055i | \(0.696707\pi\) | |||||||
\(558\) | 4.98162 | 0.210889 | ||||||||
\(559\) | 5.04754 | 0.213488 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.42842 | −0.271408 | ||||||||
\(562\) | −23.5872 | −0.994966 | ||||||||
\(563\) | 21.5293 | 0.907350 | 0.453675 | − | 0.891167i | \(-0.350113\pi\) | ||||
0.453675 | + | 0.891167i | \(0.350113\pi\) | |||||||
\(564\) | 0.0802864 | 0.00338067 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15.2829 | −0.642389 | ||||||||
\(567\) | −4.18757 | −0.175861 | ||||||||
\(568\) | 34.9428 | 1.46617 | ||||||||
\(569\) | 9.20811 | 0.386024 | 0.193012 | − | 0.981196i | \(-0.438174\pi\) | ||||
0.193012 | + | 0.981196i | \(0.438174\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.9531 | 1.25350 | 0.626749 | − | 0.779221i | \(-0.284385\pi\) | ||||
0.626749 | + | 0.779221i | \(0.284385\pi\) | |||||||
\(572\) | −0.0453722 | −0.00189711 | ||||||||
\(573\) | −7.31539 | −0.305605 | ||||||||
\(574\) | 35.2780 | 1.47247 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.29484 | 0.345619 | ||||||||
\(577\) | −41.6419 | −1.73357 | −0.866787 | − | 0.498678i | \(-0.833819\pi\) | ||||
−0.866787 | + | 0.498678i | \(0.833819\pi\) | |||||||
\(578\) | −44.1355 | −1.83579 | ||||||||
\(579\) | −9.10083 | −0.378218 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −60.6100 | −2.51453 | ||||||||
\(582\) | −2.68530 | −0.111309 | ||||||||
\(583\) | 1.37296 | 0.0568623 | ||||||||
\(584\) | −33.9342 | −1.40421 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −46.4272 | −1.91789 | ||||||||
\(587\) | 36.9519 | 1.52517 | 0.762585 | − | 0.646888i | \(-0.223930\pi\) | ||||
0.762585 | + | 0.646888i | \(0.223930\pi\) | |||||||
\(588\) | −0.845873 | −0.0348832 | ||||||||
\(589\) | −4.06148 | −0.167350 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.3950 | −0.756671 | ||||||||
\(592\) | −14.3840 | −0.591179 | ||||||||
\(593\) | 27.6951 | 1.13730 | 0.568651 | − | 0.822579i | \(-0.307465\pi\) | ||||
0.568651 | + | 0.822579i | \(0.307465\pi\) | |||||||
\(594\) | −1.27430 | −0.0522851 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.65012 | −0.0675915 | ||||||||
\(597\) | 17.9798 | 0.735865 | ||||||||
\(598\) | 7.10728 | 0.290638 | ||||||||
\(599\) | −6.30033 | −0.257425 | −0.128712 | − | 0.991682i | \(-0.541084\pi\) | ||||
−0.128712 | + | 0.991682i | \(0.541084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.1106 | −0.861119 | −0.430560 | − | 0.902562i | \(-0.641684\pi\) | ||||
−0.430560 | + | 0.902562i | \(0.641684\pi\) | |||||||
\(602\) | 47.6611 | 1.94252 | ||||||||
\(603\) | 0.824368 | 0.0335709 | ||||||||
\(604\) | −0.774077 | −0.0314968 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.84492 | 0.278056 | ||||||||
\(607\) | 40.9648 | 1.66271 | 0.831355 | − | 0.555741i | \(-0.187565\pi\) | ||||
0.831355 | + | 0.555741i | \(0.187565\pi\) | |||||||
\(608\) | −0.512723 | −0.0207937 | ||||||||
\(609\) | −20.9378 | −0.848444 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.614463 | −0.0248585 | ||||||||
\(612\) | 0.561169 | 0.0226839 | ||||||||
\(613\) | 48.1149 | 1.94334 | 0.971672 | − | 0.236334i | \(-0.0759459\pi\) | ||||
0.971672 | + | 0.236334i | \(0.0759459\pi\) | |||||||
\(614\) | 13.8345 | 0.558315 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.1008 | −0.447265 | ||||||||
\(617\) | 3.74809 | 0.150893 | 0.0754463 | − | 0.997150i | \(-0.475962\pi\) | ||||
0.0754463 | + | 0.997150i | \(0.475962\pi\) | |||||||
\(618\) | −12.2924 | −0.494471 | ||||||||
\(619\) | −15.6789 | −0.630186 | −0.315093 | − | 0.949061i | \(-0.602036\pi\) | ||||
−0.315093 | + | 0.949061i | \(0.602036\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.34814 | −0.334999 | ||||||||
\(622\) | −17.9865 | −0.721194 | ||||||||
\(623\) | 69.9528 | 2.80260 | ||||||||
\(624\) | −2.35522 | −0.0942844 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −30.3956 | −1.21485 | ||||||||
\(627\) | 1.03893 | 0.0414907 | ||||||||
\(628\) | −1.01742 | −0.0405995 | ||||||||
\(629\) | −26.2298 | −1.04585 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.2501 | −1.20424 | −0.602119 | − | 0.798407i | \(-0.705677\pi\) | ||||
−0.602119 | + | 0.798407i | \(0.705677\pi\) | |||||||
\(632\) | −11.7193 | −0.466167 | ||||||||
\(633\) | 13.2375 | 0.526145 | ||||||||
\(634\) | 15.3595 | 0.610003 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.119853 | −0.00475247 | ||||||||
\(637\) | 6.47380 | 0.256501 | ||||||||
\(638\) | −6.37149 | −0.252250 | ||||||||
\(639\) | 12.1232 | 0.479585 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.5134 | −0.928724 | −0.464362 | − | 0.885645i | \(-0.653716\pi\) | ||||
−0.464362 | + | 0.885645i | \(0.653716\pi\) | |||||||
\(642\) | 11.3816 | 0.449195 | ||||||||
\(643\) | 24.5259 | 0.967209 | 0.483604 | − | 0.875287i | \(-0.339327\pi\) | ||||
0.483604 | + | 0.875287i | \(0.339327\pi\) | |||||||
\(644\) | −2.80668 | −0.110599 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.9396 | 0.430414 | ||||||||
\(647\) | −10.2318 | −0.402253 | −0.201126 | − | 0.979565i | \(-0.564460\pi\) | ||||
−0.201126 | + | 0.979565i | \(0.564460\pi\) | |||||||
\(648\) | 2.88231 | 0.113228 | ||||||||
\(649\) | −2.36652 | −0.0928939 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.0562 | 0.590097 | ||||||||
\(652\) | 0.494610 | 0.0193704 | ||||||||
\(653\) | −15.4266 | −0.603691 | −0.301845 | − | 0.953357i | \(-0.597603\pi\) | ||||
−0.301845 | + | 0.953357i | \(0.597603\pi\) | |||||||
\(654\) | 14.0898 | 0.550954 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −23.3056 | −0.909932 | ||||||||
\(657\) | −11.7732 | −0.459318 | ||||||||
\(658\) | −5.80203 | −0.226187 | ||||||||
\(659\) | −40.8238 | −1.59027 | −0.795135 | − | 0.606432i | \(-0.792600\pi\) | ||||
−0.795135 | + | 0.606432i | \(0.792600\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.2581 | −1.09911 | −0.549556 | − | 0.835457i | \(-0.685203\pi\) | ||||
−0.549556 | + | 0.835457i | \(0.685203\pi\) | |||||||
\(662\) | −10.9280 | −0.424727 | ||||||||
\(663\) | −4.29484 | −0.166798 | ||||||||
\(664\) | 41.7180 | 1.61897 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.19950 | −0.201476 | ||||||||
\(667\) | −41.7407 | −1.61621 | ||||||||
\(668\) | −0.308428 | −0.0119334 | ||||||||
\(669\) | −7.05974 | −0.272945 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.39848 | −0.208406 | ||||||||
\(672\) | 1.90069 | 0.0733209 | ||||||||
\(673\) | 13.6620 | 0.526631 | 0.263316 | − | 0.964710i | \(-0.415184\pi\) | ||||
0.263316 | + | 0.964710i | \(0.415184\pi\) | |||||||
\(674\) | −30.5952 | −1.17848 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.01341 | 0.0389773 | ||||||||
\(677\) | −50.5626 | −1.94328 | −0.971640 | − | 0.236466i | \(-0.924011\pi\) | ||||
−0.971640 | + | 0.236466i | \(0.924011\pi\) | |||||||
\(678\) | −8.32976 | −0.319902 | ||||||||
\(679\) | −8.11589 | −0.311459 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.3720 | 0.933937 | ||||||||
\(682\) | 4.58166 | 0.175441 | ||||||||
\(683\) | −20.6092 | −0.788590 | −0.394295 | − | 0.918984i | \(-0.629011\pi\) | ||||
−0.394295 | + | 0.918984i | \(0.629011\pi\) | |||||||
\(684\) | −0.0906930 | −0.00346773 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.5142 | 0.783238 | ||||||||
\(687\) | 19.8640 | 0.757858 | ||||||||
\(688\) | −31.4862 | −1.20040 | ||||||||
\(689\) | 0.917280 | 0.0349456 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.9719 | 0.988018 | 0.494009 | − | 0.869457i | \(-0.335531\pi\) | ||||
0.494009 | + | 0.869457i | \(0.335531\pi\) | |||||||
\(692\) | −1.14780 | −0.0436329 | ||||||||
\(693\) | −3.85136 | −0.146301 | ||||||||
\(694\) | −33.9663 | −1.28934 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 14.4116 | 0.546269 | ||||||||
\(697\) | −42.4987 | −1.60975 | ||||||||
\(698\) | 39.0864 | 1.47944 | ||||||||
\(699\) | 0.923726 | 0.0349385 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.7609 | −1.42621 | −0.713105 | − | 0.701057i | \(-0.752712\pi\) | ||||
−0.713105 | + | 0.701057i | \(0.752712\pi\) | |||||||
\(702\) | −0.851361 | −0.0321325 | ||||||||
\(703\) | 4.23912 | 0.159881 | ||||||||
\(704\) | 7.62888 | 0.287524 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.6001 | −1.71618 | ||||||||
\(707\) | 20.6877 | 0.778040 | ||||||||
\(708\) | 0.206585 | 0.00776394 | ||||||||
\(709\) | 27.1125 | 1.01823 | 0.509116 | − | 0.860698i | \(-0.329973\pi\) | ||||
0.509116 | + | 0.860698i | \(0.329973\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.06592 | −0.152484 | ||||||||
\(712\) | −48.1487 | −1.80445 | ||||||||
\(713\) | 30.0153 | 1.12408 | ||||||||
\(714\) | −40.5538 | −1.51769 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.27361 | −0.0475969 | ||||||||
\(717\) | 12.1073 | 0.452155 | ||||||||
\(718\) | 24.6374 | 0.919460 | ||||||||
\(719\) | 5.44412 | 0.203032 | 0.101516 | − | 0.994834i | \(-0.467631\pi\) | ||||
0.101516 | + | 0.994834i | \(0.467631\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.1517 | −1.38360 | ||||||||
\(722\) | 24.5572 | 0.913925 | ||||||||
\(723\) | −11.8870 | −0.442081 | ||||||||
\(724\) | 0.0513775 | 0.00190943 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14.0689 | 0.522147 | ||||||||
\(727\) | −32.3623 | −1.20025 | −0.600126 | − | 0.799905i | \(-0.704883\pi\) | ||||
−0.600126 | + | 0.799905i | \(0.704883\pi\) | |||||||
\(728\) | −7.41649 | −0.274873 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −57.4164 | −2.12362 | ||||||||
\(732\) | 0.471260 | 0.0174183 | ||||||||
\(733\) | 22.6016 | 0.834810 | 0.417405 | − | 0.908721i | \(-0.362940\pi\) | ||||
0.417405 | + | 0.908721i | \(0.362940\pi\) | |||||||
\(734\) | 19.4085 | 0.716381 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.78914 | 0.139669 | ||||||||
\(737\) | 0.758183 | 0.0279280 | ||||||||
\(738\) | −8.42446 | −0.310109 | ||||||||
\(739\) | −10.6215 | −0.390717 | −0.195359 | − | 0.980732i | \(-0.562587\pi\) | ||||
−0.195359 | + | 0.980732i | \(0.562587\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.694109 | 0.0254987 | ||||||||
\(742\) | 8.66136 | 0.317969 | ||||||||
\(743\) | −10.2836 | −0.377269 | −0.188634 | − | 0.982047i | \(-0.560406\pi\) | ||||
−0.188634 | + | 0.982047i | \(0.560406\pi\) | |||||||
\(744\) | −10.3632 | −0.379933 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 30.4232 | 1.11387 | ||||||||
\(747\) | 14.4738 | 0.529569 | ||||||||
\(748\) | 0.516115 | 0.0188710 | ||||||||
\(749\) | 34.3990 | 1.25691 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.6206 | 0.570005 | 0.285003 | − | 0.958527i | \(-0.408006\pi\) | ||||
0.285003 | + | 0.958527i | \(0.408006\pi\) | |||||||
\(752\) | 3.83298 | 0.139774 | ||||||||
\(753\) | 22.0858 | 0.804852 | ||||||||
\(754\) | −4.25680 | −0.155024 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.336204 | 0.0122276 | ||||||||
\(757\) | −30.0073 | −1.09064 | −0.545318 | − | 0.838230i | \(-0.683591\pi\) | ||||
−0.545318 | + | 0.838230i | \(0.683591\pi\) | |||||||
\(758\) | 7.07200 | 0.256866 | ||||||||
\(759\) | −7.67790 | −0.278690 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.88716 | −0.213409 | −0.106705 | − | 0.994291i | \(-0.534030\pi\) | ||||
−0.106705 | + | 0.994291i | \(0.534030\pi\) | |||||||
\(762\) | −12.0490 | −0.436490 | ||||||||
\(763\) | 42.5841 | 1.54165 | ||||||||
\(764\) | 0.587326 | 0.0212487 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.91780 | 0.322213 | ||||||||
\(767\) | −1.58108 | −0.0570893 | ||||||||
\(768\) | −1.92373 | −0.0694165 | ||||||||
\(769\) | −28.8029 | −1.03866 | −0.519329 | − | 0.854574i | \(-0.673818\pi\) | ||||
−0.519329 | + | 0.854574i | \(0.673818\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.60004 | 0.201681 | ||||||||
\(772\) | 0.730673 | 0.0262975 | ||||||||
\(773\) | 24.5651 | 0.883546 | 0.441773 | − | 0.897127i | \(-0.354350\pi\) | ||||
0.441773 | + | 0.897127i | \(0.354350\pi\) | |||||||
\(774\) | −11.3816 | −0.409102 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.58619 | 0.200533 | ||||||||
\(777\) | −15.7147 | −0.563760 | ||||||||
\(778\) | 50.9210 | 1.82561 | ||||||||
\(779\) | 6.86841 | 0.246086 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.1498 | 0.398973 | ||||||||
\(782\) | −80.8462 | −2.89106 | ||||||||
\(783\) | 5.00000 | 0.178685 | ||||||||
\(784\) | −40.3832 | −1.44226 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.7751 | −0.598348 | ||||||||
\(787\) | 51.2953 | 1.82848 | 0.914239 | − | 0.405174i | \(-0.132789\pi\) | ||||
0.914239 | + | 0.405174i | \(0.132789\pi\) | |||||||
\(788\) | 1.47687 | 0.0526113 | ||||||||
\(789\) | 13.7892 | 0.490908 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.1754 | −0.895133 | ||||||||
\(792\) | 2.65090 | 0.0941958 | ||||||||
\(793\) | −3.60674 | −0.128079 | ||||||||
\(794\) | −28.7393 | −1.01992 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.44353 | −0.0511647 | ||||||||
\(797\) | −32.4937 | −1.15098 | −0.575492 | − | 0.817807i | \(-0.695189\pi\) | ||||
−0.575492 | + | 0.817807i | \(0.695189\pi\) | |||||||
\(798\) | 6.55408 | 0.232012 | ||||||||
\(799\) | 6.98959 | 0.247274 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.7049 | −0.590238 | ||||||||
\(802\) | −52.3593 | −1.84887 | ||||||||
\(803\) | −10.8280 | −0.382112 | ||||||||
\(804\) | −0.0661855 | −0.00233418 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.06102 | 0.107820 | ||||||||
\(807\) | −4.57374 | −0.161003 | ||||||||
\(808\) | −14.2394 | −0.500940 | ||||||||
\(809\) | 49.2124 | 1.73022 | 0.865109 | − | 0.501584i | \(-0.167249\pi\) | ||||
0.865109 | + | 0.501584i | \(0.167249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.70917 | 0.235591 | 0.117795 | − | 0.993038i | \(-0.462417\pi\) | ||||
0.117795 | + | 0.993038i | \(0.462417\pi\) | |||||||
\(812\) | 1.68102 | 0.0589923 | ||||||||
\(813\) | −29.8057 | −1.04533 | ||||||||
\(814\) | −4.78205 | −0.167611 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 26.7910 | 0.937872 | ||||||||
\(817\) | 9.27932 | 0.324642 | ||||||||
\(818\) | 2.07384 | 0.0725101 | ||||||||
\(819\) | −2.57310 | −0.0899115 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.5348 | 1.58918 | 0.794589 | − | 0.607148i | \(-0.207687\pi\) | ||||
0.794589 | + | 0.607148i | \(0.207687\pi\) | |||||||
\(822\) | −24.9108 | −0.868865 | ||||||||
\(823\) | 8.76979 | 0.305696 | 0.152848 | − | 0.988250i | \(-0.451156\pi\) | ||||
0.152848 | + | 0.988250i | \(0.451156\pi\) | |||||||
\(824\) | 25.5716 | 0.890830 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −14.9292 | −0.519454 | ||||||||
\(827\) | −49.4171 | −1.71840 | −0.859201 | − | 0.511639i | \(-0.829039\pi\) | ||||
−0.859201 | + | 0.511639i | \(0.829039\pi\) | |||||||
\(828\) | 0.670242 | 0.0232925 | ||||||||
\(829\) | −56.2875 | −1.95495 | −0.977474 | − | 0.211058i | \(-0.932309\pi\) | ||||
−0.977474 | + | 0.211058i | \(0.932309\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.4187 | −0.673626 | ||||||||
\(832\) | 5.09687 | 0.176702 | ||||||||
\(833\) | −73.6403 | −2.55148 | ||||||||
\(834\) | −13.3797 | −0.463302 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.0834116 | −0.00288485 | ||||||||
\(837\) | −3.59544 | −0.124277 | ||||||||
\(838\) | 3.95404 | 0.136590 | ||||||||
\(839\) | 22.8330 | 0.788282 | 0.394141 | − | 0.919050i | \(-0.371042\pi\) | ||||
0.394141 | + | 0.919050i | \(0.371042\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 37.4557 | 1.29081 | ||||||||
\(843\) | 17.0239 | 0.586333 | ||||||||
\(844\) | −1.06279 | −0.0365829 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.38554 | 0.0476358 | ||||||||
\(847\) | 42.5211 | 1.46104 | ||||||||
\(848\) | −5.72194 | −0.196492 | ||||||||
\(849\) | 11.0303 | 0.378559 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.3280 | −1.07391 | ||||||||
\(852\) | −0.973325 | −0.0333456 | ||||||||
\(853\) | 12.4069 | 0.424805 | 0.212402 | − | 0.977182i | \(-0.431871\pi\) | ||||
0.212402 | + | 0.977182i | \(0.431871\pi\) | |||||||
\(854\) | −34.0564 | −1.16539 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.6769 | −0.809261 | ||||||||
\(857\) | 28.5268 | 0.974458 | 0.487229 | − | 0.873274i | \(-0.338008\pi\) | ||||
0.487229 | + | 0.873274i | \(0.338008\pi\) | |||||||
\(858\) | −0.783008 | −0.0267315 | ||||||||
\(859\) | −27.2313 | −0.929121 | −0.464561 | − | 0.885541i | \(-0.653788\pi\) | ||||
−0.464561 | + | 0.885541i | \(0.653788\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −25.4616 | −0.867729 | ||||||||
\(862\) | 8.97057 | 0.305539 | ||||||||
\(863\) | −8.61981 | −0.293422 | −0.146711 | − | 0.989179i | \(-0.546869\pi\) | ||||
−0.146711 | + | 0.989179i | \(0.546869\pi\) | |||||||
\(864\) | −0.453890 | −0.0154417 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −51.9418 | −1.76505 | ||||||||
\(867\) | 31.8544 | 1.08183 | ||||||||
\(868\) | −1.20880 | −0.0410295 | ||||||||
\(869\) | −3.73948 | −0.126853 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.506544 | 0.0171636 | ||||||||
\(872\) | −29.3108 | −0.992589 | ||||||||
\(873\) | 1.93809 | 0.0655945 | ||||||||
\(874\) | 13.0659 | 0.441961 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.945231 | 0.0319364 | ||||||||
\(877\) | −28.3424 | −0.957056 | −0.478528 | − | 0.878072i | \(-0.658829\pi\) | ||||
−0.478528 | + | 0.878072i | \(0.658829\pi\) | |||||||
\(878\) | −42.9704 | −1.45018 | ||||||||
\(879\) | 33.5084 | 1.13021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.8920 | 0.434344 | 0.217172 | − | 0.976133i | \(-0.430317\pi\) | ||||
0.217172 | + | 0.976133i | \(0.430317\pi\) | |||||||
\(882\) | −14.5976 | −0.491527 | ||||||||
\(883\) | −48.1627 | −1.62081 | −0.810403 | − | 0.585873i | \(-0.800752\pi\) | ||||
−0.810403 | + | 0.585873i | \(0.800752\pi\) | |||||||
\(884\) | 0.344817 | 0.0115975 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.76763 | 0.328150 | ||||||||
\(887\) | 17.0254 | 0.571659 | 0.285829 | − | 0.958281i | \(-0.407731\pi\) | ||||
0.285829 | + | 0.958281i | \(0.407731\pi\) | |||||||
\(888\) | 10.8164 | 0.362976 | ||||||||
\(889\) | −36.4162 | −1.22136 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.919714 | 0.0308116 | ||||||||
\(892\) | 0.566801 | 0.0189779 | ||||||||
\(893\) | −1.12962 | −0.0378013 | ||||||||
\(894\) | −28.4769 | −0.952408 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 44.3255 | 1.48081 | ||||||||
\(897\) | −5.12962 | −0.171273 | ||||||||
\(898\) | 7.73360 | 0.258074 | ||||||||
\(899\) | −17.9772 | −0.599574 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.4342 | −0.347613 | ||||||||
\(902\) | −7.74809 | −0.257983 | ||||||||
\(903\) | −34.3990 | −1.14473 | ||||||||
\(904\) | 17.3283 | 0.576330 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.3586 | −0.443810 | ||||||||
\(907\) | 19.3378 | 0.642101 | 0.321050 | − | 0.947062i | \(-0.395964\pi\) | ||||
0.321050 | + | 0.947062i | \(0.395964\pi\) | |||||||
\(908\) | −1.95674 | −0.0649367 | ||||||||
\(909\) | −4.94026 | −0.163858 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8527 | −1.55230 | −0.776149 | − | 0.630549i | \(-0.782830\pi\) | ||||
−0.776149 | + | 0.630549i | \(0.782830\pi\) | |||||||
\(912\) | −4.32981 | −0.143374 | ||||||||
\(913\) | 13.3117 | 0.440555 | ||||||||
\(914\) | −1.48447 | −0.0491020 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.59481 | −0.0526939 | ||||||||
\(917\) | −50.7000 | −1.67426 | ||||||||
\(918\) | 9.68434 | 0.319631 | ||||||||
\(919\) | 26.0103 | 0.858002 | 0.429001 | − | 0.903304i | \(-0.358866\pi\) | ||||
0.429001 | + | 0.903304i | \(0.358866\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.98494 | −0.329015 | ||||||||
\(922\) | −6.99355 | −0.230320 | ||||||||
\(923\) | 7.44924 | 0.245195 | ||||||||
\(924\) | 0.309212 | 0.0101723 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.35867 | 0.307545 | ||||||||
\(927\) | 8.87191 | 0.291392 | ||||||||
\(928\) | −2.26945 | −0.0744983 | ||||||||
\(929\) | 57.6243 | 1.89059 | 0.945297 | − | 0.326212i | \(-0.105772\pi\) | ||||
0.945297 | + | 0.326212i | \(0.105772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.9013 | 0.390050 | ||||||||
\(932\) | −0.0741626 | −0.00242928 | ||||||||
\(933\) | 12.9816 | 0.424999 | ||||||||
\(934\) | 27.0628 | 0.885523 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.77107 | 0.0578894 | ||||||||
\(937\) | −61.0181 | −1.99337 | −0.996687 | − | 0.0813275i | \(-0.974084\pi\) | ||||
−0.996687 | + | 0.0813275i | \(0.974084\pi\) | |||||||
\(938\) | 4.78301 | 0.156171 | ||||||||
\(939\) | 21.9378 | 0.715912 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 43.9597 | 1.43304 | 0.716522 | − | 0.697565i | \(-0.245733\pi\) | ||||
0.716522 | + | 0.697565i | \(0.245733\pi\) | |||||||
\(942\) | −17.5581 | −0.572074 | ||||||||
\(943\) | −50.7591 | −1.65294 | ||||||||
\(944\) | 9.86265 | 0.321002 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.4678 | −0.340337 | ||||||||
\(947\) | −44.4156 | −1.44331 | −0.721657 | − | 0.692251i | \(-0.756619\pi\) | ||||
−0.721657 | + | 0.692251i | \(0.756619\pi\) | |||||||
\(948\) | 0.326438 | 0.0106022 | ||||||||
\(949\) | −7.23422 | −0.234833 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.0856 | −0.359475 | ||||||||
\(952\) | 84.3636 | 2.73424 | ||||||||
\(953\) | 56.6835 | 1.83616 | 0.918079 | − | 0.396397i | \(-0.129740\pi\) | ||||
0.918079 | + | 0.396397i | \(0.129740\pi\) | |||||||
\(954\) | −2.06835 | −0.0669654 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.972049 | −0.0314383 | ||||||||
\(957\) | 4.59857 | 0.148651 | ||||||||
\(958\) | 15.2192 | 0.491709 | ||||||||
\(959\) | −75.2890 | −2.43121 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.0728 | −0.582993 | ||||||||
\(962\) | −3.19490 | −0.103008 | ||||||||
\(963\) | −8.21456 | −0.264710 | ||||||||
\(964\) | 0.954361 | 0.0307379 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −48.4361 | −1.55841 | ||||||||
\(967\) | −9.38822 | −0.301905 | −0.150952 | − | 0.988541i | \(-0.548234\pi\) | ||||
−0.150952 | + | 0.988541i | \(0.548234\pi\) | |||||||
\(968\) | −29.2674 | −0.940689 | ||||||||
\(969\) | −7.89558 | −0.253643 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.85360 | −0.0594848 | −0.0297424 | − | 0.999558i | \(-0.509469\pi\) | ||||
−0.0297424 | + | 0.999558i | \(0.509469\pi\) | |||||||
\(972\) | −0.0802864 | −0.00257519 | ||||||||
\(973\) | −40.4381 | −1.29639 | ||||||||
\(974\) | −35.9964 | −1.15340 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.4986 | 0.720163 | ||||||||
\(977\) | −39.6717 | −1.26921 | −0.634605 | − | 0.772837i | \(-0.718837\pi\) | ||||
−0.634605 | + | 0.772837i | \(0.718837\pi\) | |||||||
\(978\) | 8.53570 | 0.272942 | ||||||||
\(979\) | −15.3637 | −0.491026 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.1692 | −0.324677 | ||||||||
\(982\) | −40.4410 | −1.29052 | ||||||||
\(983\) | −3.32976 | −0.106203 | −0.0531014 | − | 0.998589i | \(-0.516911\pi\) | ||||
−0.0531014 | + | 0.998589i | \(0.516911\pi\) | |||||||
\(984\) | 17.5253 | 0.558686 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 48.4217 | 1.54206 | ||||||||
\(987\) | 4.18757 | 0.133292 | ||||||||
\(988\) | −0.0557275 | −0.00177293 | ||||||||
\(989\) | −68.5763 | −2.18060 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.6961 | 0.752731 | 0.376365 | − | 0.926471i | \(-0.377174\pi\) | ||||
0.376365 | + | 0.926471i | \(0.377174\pi\) | |||||||
\(992\) | 1.63194 | 0.0518140 | ||||||||
\(993\) | 7.88716 | 0.250292 | ||||||||
\(994\) | 70.3390 | 2.23102 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.16205 | −0.0368209 | ||||||||
\(997\) | 12.5238 | 0.396633 | 0.198317 | − | 0.980138i | \(-0.436453\pi\) | ||||
0.198317 | + | 0.980138i | \(0.436453\pi\) | |||||||
\(998\) | 3.79354 | 0.120082 | ||||||||
\(999\) | 3.75270 | 0.118730 |
(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 | 3525.2.a.u.1.2 | 4 | ||
5.4 | even | 2 | 705.2.a.j.1.3 | ✓ | 4 | ||
15.14 | odd | 2 | 2115.2.a.p.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.a.j.1.3 | ✓ | 4 | 5.4 | even | 2 | ||
2115.2.a.p.1.2 | 4 | 15.14 | odd | 2 | |||
3525.2.a.u.1.2 | 4 | 1.1 | even | 1 | trivial |