Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.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: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 37 x^{13} + 39 x^{12} + 537 x^{11} - 616 x^{10} - 3853 x^{9} + 4929 x^{8} + 13971 x^{7} - 20311 x^{6} - 22309 x^{5} + 38415 x^{4} + 8429 x^{3} - 22584 x^{2} + \cdots + 3381 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1148) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-0.449590\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.449590 | 0.259571 | 0.129785 | − | 0.991542i | \(-0.458571\pi\) | ||||
0.129785 | + | 0.991542i | \(0.458571\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.787803 | −0.352316 | −0.176158 | − | 0.984362i | \(-0.556367\pi\) | ||||
−0.176158 | + | 0.984362i | \(0.556367\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.79787 | −0.932623 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.10400 | 0.935891 | 0.467946 | − | 0.883757i | \(-0.344994\pi\) | ||||
0.467946 | + | 0.883757i | \(0.344994\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.59137 | 1.55077 | 0.775383 | − | 0.631491i | \(-0.217557\pi\) | ||||
0.775383 | + | 0.631491i | \(0.217557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.354188 | −0.0914510 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.38244 | 1.30543 | 0.652717 | − | 0.757602i | \(-0.273629\pi\) | ||||
0.652717 | + | 0.757602i | \(0.273629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.82385 | 1.10667 | 0.553334 | − | 0.832960i | \(-0.313355\pi\) | ||||
0.553334 | + | 0.832960i | \(0.313355\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.02456 | 1.46472 | 0.732361 | − | 0.680917i | \(-0.238419\pi\) | ||||
0.732361 | + | 0.680917i | \(0.238419\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.37937 | −0.875873 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.60666 | −0.501652 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.52560 | −1.39747 | −0.698734 | − | 0.715382i | \(-0.746253\pi\) | ||||
−0.698734 | + | 0.715382i | \(0.746253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.90724 | 0.881366 | 0.440683 | − | 0.897663i | \(-0.354736\pi\) | ||||
0.440683 | + | 0.897663i | \(0.354736\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.39553 | 0.242930 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.21207 | −1.51446 | −0.757228 | − | 0.653151i | \(-0.773447\pi\) | ||||
−0.757228 | + | 0.653151i | \(0.773447\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.51382 | 0.402534 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7730 | 1.79536 | 0.897680 | − | 0.440648i | \(-0.145251\pi\) | ||||
0.897680 | + | 0.440648i | \(0.145251\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.20417 | 0.328578 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.56287 | −0.811428 | −0.405714 | − | 0.914000i | \(-0.632977\pi\) | ||||
−0.405714 | + | 0.914000i | \(0.632977\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.41989 | 0.338853 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.94752 | 0.816955 | 0.408477 | − | 0.912768i | \(-0.366060\pi\) | ||||
0.408477 | + | 0.912768i | \(0.366060\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.44534 | −0.329730 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.16875 | 0.287259 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.2017 | −1.32814 | −0.664071 | − | 0.747670i | \(-0.731173\pi\) | ||||
−0.664071 | + | 0.747670i | \(0.731173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.89403 | 0.626616 | 0.313308 | − | 0.949652i | \(-0.398563\pi\) | ||||
0.313308 | + | 0.949652i | \(0.398563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.40490 | −0.546360 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.7436 | 1.43472 | 0.717358 | − | 0.696705i | \(-0.245351\pi\) | ||||
0.717358 | + | 0.696705i | \(0.245351\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.15817 | 0.380199 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.39569 | −0.165638 | −0.0828188 | − | 0.996565i | \(-0.526392\pi\) | ||||
−0.0828188 | + | 0.996565i | \(0.526392\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.28028 | −0.500968 | −0.250484 | − | 0.968121i | \(-0.580590\pi\) | ||||
−0.250484 | + | 0.968121i | \(0.580590\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.96892 | −0.227351 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.10074 | 0.911404 | 0.455702 | − | 0.890132i | \(-0.349388\pi\) | ||||
0.455702 | + | 0.890132i | \(0.349388\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.22168 | 0.802409 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.10452 | 0.231001 | 0.115500 | − | 0.993307i | \(-0.463153\pi\) | ||||
0.115500 | + | 0.993307i | \(0.463153\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.24031 | −0.459926 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.38343 | −0.362742 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.1614 | −1.71311 | −0.856553 | − | 0.516059i | \(-0.827398\pi\) | ||||
−0.856553 | + | 0.516059i | \(0.827398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.20625 | 0.228777 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.80024 | −0.389897 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.23832 | 0.227267 | 0.113634 | − | 0.993523i | \(-0.463751\pi\) | ||||
0.113634 | + | 0.993523i | \(0.463751\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.68459 | −0.872834 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.14466 | −0.611416 | −0.305708 | − | 0.952125i | \(-0.598893\pi\) | ||||
−0.305708 | + | 0.952125i | \(0.598893\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.47349 | 0.145188 | 0.0725938 | − | 0.997362i | \(-0.476872\pi\) | ||||
0.0725938 | + | 0.997362i | \(0.476872\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.43556 | 0.815497 | 0.407748 | − | 0.913094i | \(-0.366314\pi\) | ||||
0.407748 | + | 0.913094i | \(0.366314\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.1612 | −0.973266 | −0.486633 | − | 0.873607i | \(-0.661775\pi\) | ||||
−0.486633 | + | 0.873607i | \(0.661775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.14165 | −0.393108 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.34801 | 0.785315 | 0.392657 | − | 0.919685i | \(-0.371556\pi\) | ||||
0.392657 | + | 0.919685i | \(0.371556\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.53397 | −0.516045 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.6439 | −1.44628 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.36518 | −0.124107 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.449590 | −0.0405381 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.38909 | 0.660901 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.6031 | −1.38455 | −0.692274 | − | 0.721635i | \(-0.743391\pi\) | ||||
−0.692274 | + | 0.721635i | \(0.743391\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.29300 | 0.466023 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.7626 | −1.02771 | −0.513853 | − | 0.857878i | \(-0.671782\pi\) | ||||
−0.513853 | + | 0.857878i | \(0.671782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.05354 | 0.176740 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.49604 | 0.384123 | 0.192061 | − | 0.981383i | \(-0.438483\pi\) | ||||
0.192061 | + | 0.981383i | \(0.438483\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41035 | 0.119624 | 0.0598121 | − | 0.998210i | \(-0.480950\pi\) | ||||
0.0598121 | + | 0.998210i | \(0.480950\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.50101 | −0.210623 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.3556 | 1.45135 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.92869 | 0.492351 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.50284 | 0.696580 | 0.348290 | − | 0.937387i | \(-0.386762\pi\) | ||||
0.348290 | + | 0.937387i | \(0.386762\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.68539 | −0.218534 | −0.109267 | − | 0.994012i | \(-0.534850\pi\) | ||||
−0.109267 | + | 0.994012i | \(0.534850\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.0594 | −1.21748 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.86594 | −0.310520 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.26751 | −0.340584 | −0.170292 | − | 0.985394i | \(-0.554471\pi\) | ||||
−0.170292 | + | 0.985394i | \(0.554471\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.67394 | 0.212058 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.7332 | 1.46730 | 0.733649 | − | 0.679529i | \(-0.237816\pi\) | ||||
0.733649 | + | 0.679529i | \(0.237816\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.09940 | −0.0855882 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3399 | 0.877510 | 0.438755 | − | 0.898607i | \(-0.355420\pi\) | ||||
0.438755 | + | 0.898607i | \(0.355420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.2634 | 1.40488 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.4965 | −1.03210 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.5023 | −0.950531 | −0.475266 | − | 0.879842i | \(-0.657648\pi\) | ||||
−0.475266 | + | 0.879842i | \(0.657648\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.58656 | −0.344747 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.96188 | −0.520355 | −0.260178 | − | 0.965561i | \(-0.583781\pi\) | ||||
−0.260178 | + | 0.965561i | \(0.583781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.3297 | 1.36244 | 0.681219 | − | 0.732080i | \(-0.261450\pi\) | ||||
0.681219 | + | 0.732080i | \(0.261450\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.20031 | 0.162651 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.25730 | 0.533567 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.7071 | 1.22174 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.2841 | 1.39535 | 0.697675 | − | 0.716414i | \(-0.254218\pi\) | ||||
0.697675 | + | 0.716414i | \(0.254218\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.39703 | 0.100561 | 0.0502803 | − | 0.998735i | \(-0.483989\pi\) | ||||
0.0502803 | + | 0.998735i | \(0.483989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.98040 | −0.141819 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.8161 | 0.913108 | 0.456554 | − | 0.889696i | \(-0.349084\pi\) | ||||
0.456554 | + | 0.889696i | \(0.349084\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.67339 | −0.118624 | −0.0593119 | − | 0.998239i | \(-0.518891\pi\) | ||||
−0.0593119 | + | 0.998239i | \(0.518891\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.27982 | 0.372410 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.787803 | 0.0550225 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −19.6538 | −1.36603 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.9732 | 1.03572 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.1602 | −0.905984 | −0.452992 | − | 0.891515i | \(-0.649643\pi\) | ||||
−0.452992 | + | 0.891515i | \(0.649643\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.627487 | −0.0429947 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.27478 | −0.632535 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.92437 | −0.130037 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.0952 | 2.02442 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1114 | 0.744072 | 0.372036 | − | 0.928218i | \(-0.378660\pi\) | ||||
0.372036 | + | 0.928218i | \(0.378660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2529 | 0.816860 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.0652 | −1.06628 | −0.533142 | − | 0.846026i | \(-0.678989\pi\) | ||||
−0.533142 | + | 0.846026i | \(0.678989\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.4126 | −1.67931 | −0.839655 | − | 0.543120i | \(-0.817243\pi\) | ||||
−0.839655 | + | 0.543120i | \(0.817243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.0557 | 1.31390 | 0.656948 | − | 0.753936i | \(-0.271847\pi\) | ||||
0.656948 | + | 0.753936i | \(0.271847\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.38245 | 0.285879 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.64201 | 0.236574 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.32352 | 0.409034 | 0.204517 | − | 0.978863i | \(-0.434438\pi\) | ||||
0.204517 | + | 0.978863i | \(0.434438\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.2122 | 1.62406 | 0.812030 | − | 0.583616i | \(-0.198363\pi\) | ||||
0.812030 | + | 0.583616i | \(0.198363\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0668 | 0.709934 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.9719 | 1.71618 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.946169 | 0.0599610 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.3360 | 0.967998 | 0.483999 | − | 0.875069i | \(-0.339184\pi\) | ||||
0.483999 | + | 0.875069i | \(0.339184\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.8042 | 1.37082 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.90640 | −0.119383 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.2711 | 0.952587 | 0.476293 | − | 0.879286i | \(-0.341980\pi\) | ||||
0.476293 | + | 0.879286i | \(0.341980\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.0556 | 1.30331 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.2720 | 1.55834 | 0.779169 | − | 0.626814i | \(-0.215642\pi\) | ||||
0.779169 | + | 0.626814i | \(0.215642\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.68547 | −0.287826 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.26600 | −0.444672 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.10754 | −0.433355 | −0.216677 | − | 0.976243i | \(-0.569522\pi\) | ||||
−0.216677 | + | 0.976243i | \(0.569522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.01526 | 0.0616727 | 0.0308363 | − | 0.999524i | \(-0.490183\pi\) | ||||
0.0308363 | + | 0.999524i | \(0.490183\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.5936 | −0.819722 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.0775 | −1.38659 | −0.693296 | − | 0.720653i | \(-0.743842\pi\) | ||||
−0.693296 | + | 0.720653i | \(0.743842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.7298 | −0.821983 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.3572 | −1.15475 | −0.577377 | − | 0.816478i | \(-0.695924\pi\) | ||||
−0.577377 | + | 0.816478i | \(0.695924\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.177467 | 0.0105493 | 0.00527466 | − | 0.999986i | \(-0.498321\pi\) | ||||
0.00527466 | + | 0.999986i | \(0.498321\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.70855 | −0.101206 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.9707 | 0.704159 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.00633 | 0.0589919 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.8143 | 1.62493 | 0.812465 | − | 0.583010i | \(-0.198125\pi\) | ||||
0.812465 | + | 0.583010i | \(0.198125\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.03689 | 0.467926 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.09108 | −0.469492 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 39.2769 | 2.27144 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.76257 | −0.158706 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.85553 | −0.220767 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.7021 | 1.46690 | 0.733448 | − | 0.679745i | \(-0.237910\pi\) | ||||
0.733448 | + | 0.679745i | \(0.237910\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.662468 | 0.0376865 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.5756 | −0.883213 | −0.441606 | − | 0.897209i | \(-0.645591\pi\) | ||||
−0.441606 | + | 0.897209i | \(0.645591\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.6373 | 1.22301 | 0.611505 | − | 0.791241i | \(-0.290564\pi\) | ||||
0.611505 | + | 0.791241i | \(0.290564\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.9737 | 1.34650 | 0.673248 | − | 0.739417i | \(-0.264899\pi\) | ||||
0.673248 | + | 0.739417i | \(0.264899\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.3595 | −1.30788 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.79254 | 0.211679 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.9641 | 1.44468 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.4867 | −1.35828 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.56837 | −0.252631 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.64917 | −0.530366 | −0.265183 | − | 0.964198i | \(-0.585432\pi\) | ||||
−0.265183 | + | 0.964198i | \(0.585432\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.7742 | 1.41242 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.25168 | −0.505473 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.606481 | −0.0330371 | −0.0165186 | − | 0.999864i | \(-0.505258\pi\) | ||||
−0.0165186 | + | 0.999864i | \(0.505258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.75318 | 0.203845 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.2321 | 0.824863 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.48801 | −0.133950 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.7135 | 1.00459 | 0.502296 | − | 0.864696i | \(-0.332489\pi\) | ||||
0.502296 | + | 0.864696i | \(0.332489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.5477 | 1.09989 | 0.549945 | − | 0.835201i | \(-0.314649\pi\) | ||||
0.549945 | + | 0.835201i | \(0.314649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.5748 | −0.777946 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.94997 | −0.210235 | −0.105118 | − | 0.994460i | \(-0.533522\pi\) | ||||
−0.105118 | + | 0.994460i | \(0.533522\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.09953 | 0.0583568 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.04134 | 0.107738 | 0.0538690 | − | 0.998548i | \(-0.482845\pi\) | ||||
0.0538690 | + | 0.998548i | \(0.482845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.26954 | 0.224713 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.613771 | −0.0322146 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.37201 | 0.176499 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.6087 | −0.866969 | −0.433485 | − | 0.901161i | \(-0.642716\pi\) | ||||
−0.433485 | + | 0.901161i | \(0.642716\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.79787 | 0.145651 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.8375 | −0.716479 | −0.358239 | − | 0.933630i | \(-0.616623\pi\) | ||||
−0.358239 | + | 0.933630i | \(0.616623\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.32206 | 0.171550 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −42.0784 | −2.16715 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.23579 | −0.268944 | −0.134472 | − | 0.990917i | \(-0.542934\pi\) | ||||
−0.134472 | + | 0.990917i | \(0.542934\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.01498 | −0.359388 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.45623 | 0.432093 | 0.216047 | − | 0.976383i | \(-0.430684\pi\) | ||||
0.216047 | + | 0.976383i | \(0.430684\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.9392 | −1.67439 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.0414 | −1.32035 | −0.660175 | − | 0.751112i | \(-0.729518\pi\) | ||||
−0.660175 | + | 0.751112i | \(0.729518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.8093 | 1.91210 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.28836 | −0.266762 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.38179 | −0.321103 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.42795 | −0.172044 | −0.0860220 | − | 0.996293i | \(-0.527416\pi\) | ||||
−0.0860220 | + | 0.996293i | \(0.527416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.26799 | 0.113258 | 0.0566289 | − | 0.998395i | \(-0.481965\pi\) | ||||
0.0566289 | + | 0.998395i | \(0.481965\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.4382 | 1.36679 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.68926 | −0.282702 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.5943 | −1.41737 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0462 | −0.546198 | −0.273099 | − | 0.961986i | \(-0.588049\pi\) | ||||
−0.273099 | + | 0.961986i | \(0.588049\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.02138 | 0.0997071 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.65794 | −0.0813853 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.634078 | 0.0310509 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.0178 | −1.41761 | −0.708805 | − | 0.705404i | \(-0.750765\pi\) | ||||
−0.708805 | + | 0.705404i | \(0.750765\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.2610 | 0.548827 | 0.274414 | − | 0.961612i | \(-0.411516\pi\) | ||||
0.274414 | + | 0.961612i | \(0.411516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.5642 | 0.756756 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.5717 | −1.14340 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.80291 | 0.376728 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5476 | 0.797071 | 0.398535 | − | 0.917153i | \(-0.369519\pi\) | ||||
0.398535 | + | 0.917153i | \(0.369519\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.65533 | −0.223721 | −0.111860 | − | 0.993724i | \(-0.535681\pi\) | ||||
−0.111860 | + | 0.993724i | \(0.535681\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.66548 | 0.127800 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.8854 | 1.62096 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.7846 | −1.08745 | −0.543725 | − | 0.839263i | \(-0.682987\pi\) | ||||
−0.543725 | + | 0.839263i | \(0.682987\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.6057 | −1.40661 | −0.703305 | − | 0.710888i | \(-0.748293\pi\) | ||||
−0.703305 | + | 0.710888i | \(0.748293\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.7320 | 0.603555 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.82279 | 0.180812 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.83513 | −0.133798 | −0.0668990 | − | 0.997760i | \(-0.521311\pi\) | ||||
−0.0668990 | + | 0.997760i | \(0.521311\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.10400 | −0.146162 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.20732 | −0.0567250 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.6601 | 1.29389 | 0.646943 | − | 0.762538i | \(-0.276047\pi\) | ||||
0.646943 | + | 0.762538i | \(0.276047\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.0302 | −0.654874 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.80680 | 0.223875 | 0.111937 | − | 0.993715i | \(-0.464294\pi\) | ||||
0.111937 | + | 0.993715i | \(0.464294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.2899 | 1.45416 | 0.727082 | − | 0.686551i | \(-0.240876\pi\) | ||||
0.727082 | + | 0.686551i | \(0.240876\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.73809 | −0.0806018 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.8937 | 0.504100 | 0.252050 | − | 0.967714i | \(-0.418895\pi\) | ||||
0.252050 | + | 0.967714i | \(0.418895\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.91863 | −0.0884057 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.5433 | 1.68026 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.1254 | −0.969300 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.6404 | −0.761911 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.1384 | 0.646000 | 0.323000 | − | 0.946399i | \(-0.395309\pi\) | ||||
0.323000 | + | 0.946399i | \(0.395309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −51.5081 | −2.34857 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.76336 | −0.0800699 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.7768 | −1.57589 | −0.787945 | − | 0.615746i | \(-0.788855\pi\) | ||||
−0.787945 | + | 0.615746i | \(0.788855\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.42226 | 0.380868 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.6187 | 1.42693 | 0.713466 | − | 0.700690i | \(-0.247124\pi\) | ||||
0.713466 | + | 0.700690i | \(0.247124\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.5061 | −1.82430 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.84174 | 0.307514 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.8653 | 1.38172 | 0.690860 | − | 0.722989i | \(-0.257232\pi\) | ||||
0.690860 | + | 0.722989i | \(0.257232\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.09832 | 0.227776 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.3660 | −0.818900 | −0.409450 | − | 0.912333i | \(-0.634279\pi\) | ||||
−0.409450 | + | 0.912333i | \(0.634279\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.84078 | 0.215412 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.21104 | 0.364665 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.0290 | −1.64128 | −0.820641 | − | 0.571444i | \(-0.806384\pi\) | ||||
−0.820641 | + | 0.571444i | \(0.806384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.5742 | −0.555162 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.16082 | −0.0511520 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.2672 | −0.759408 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.62090 | −0.246730 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.2351 | −1.14938 | −0.574690 | − | 0.818371i | \(-0.694878\pi\) | ||||
−0.574690 | + | 0.818371i | \(0.694878\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.74603 | 0.0763485 | 0.0381742 | − | 0.999271i | \(-0.487846\pi\) | ||||
0.0381742 | + | 0.999271i | \(0.487846\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.4129 | 1.15057 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 26.3444 | 1.14541 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.5429 | 1.23866 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.59137 | −0.242189 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.64556 | −0.287313 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.12999 | −0.135069 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.3096 | 0.615219 | 0.307609 | − | 0.951513i | \(-0.400471\pi\) | ||||
0.307609 | + | 0.951513i | \(0.400471\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.24086 | 0.353649 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.00502 | 0.342897 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.40140 | 0.0599194 | 0.0299597 | − | 0.999551i | \(-0.490462\pi\) | ||||
0.0299597 | + | 0.999551i | \(0.490462\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.6929 | −0.584397 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −36.3024 | −1.54653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.26281 | 0.138498 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.4128 | −0.568318 | −0.284159 | − | 0.958777i | \(-0.591714\pi\) | ||||
−0.284159 | + | 0.958777i | \(0.591714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 65.8270 | 2.78419 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.51135 | 0.317129 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.3679 | −0.858404 | −0.429202 | − | 0.903208i | \(-0.641205\pi\) | ||||
−0.429202 | + | 0.903208i | \(0.641205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.57659 | −0.276679 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.9245 | −0.583746 | −0.291873 | − | 0.956457i | \(-0.594278\pi\) | ||||
−0.291873 | + | 0.956457i | \(0.594278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0547 | 1.67624 | 0.838118 | − | 0.545489i | \(-0.183656\pi\) | ||||
0.838118 | + | 0.545489i | \(0.183656\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.66995 | 0.362192 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.7631 | −1.28291 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 41.8713 | 1.74312 | 0.871562 | − | 0.490285i | \(-0.163107\pi\) | ||||
0.871562 | + | 0.490285i | \(0.163107\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.628092 | 0.0261026 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.4611 | 0.764581 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.3243 | 0.509548 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.4478 | 0.513775 | 0.256888 | − | 0.966441i | \(-0.417303\pi\) | ||||
0.256888 | + | 0.966441i | \(0.417303\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.6718 | 0.975379 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.76198 | 0.237016 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.6955 | −0.521342 | −0.260671 | − | 0.965428i | \(-0.583944\pi\) | ||||
−0.260671 | + | 0.965428i | \(0.583944\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.752341 | −0.0307913 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.9084 | 1.54890 | 0.774448 | − | 0.632637i | \(-0.218028\pi\) | ||||
0.774448 | + | 0.632637i | \(0.218028\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3859 | 0.913139 | 0.456569 | − | 0.889688i | \(-0.349078\pi\) | ||||
0.456569 | + | 0.889688i | \(0.349078\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −32.8572 | −1.33805 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.07549 | 0.0437250 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.7440 | 1.89728 | 0.948640 | − | 0.316357i | \(-0.102460\pi\) | ||||
0.948640 | + | 0.316357i | \(0.102460\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.1041 | −1.25834 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.295420 | −0.0119319 | −0.00596596 | − | 0.999982i | \(-0.501899\pi\) | ||||
−0.00596596 | + | 0.999982i | \(0.501899\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.354188 | 0.0142822 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.2704 | −1.70174 | −0.850871 | − | 0.525375i | \(-0.823925\pi\) | ||||
−0.850871 | + | 0.525375i | \(0.823925\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.9134 | 1.28271 | 0.641354 | − | 0.767245i | \(-0.278373\pi\) | ||||
0.641354 | + | 0.767245i | \(0.278373\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.3106 | −0.734781 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.0757 | 0.643027 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.73181 | 0.268843 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −49.5835 | −1.97702 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.19942 | −0.206986 | −0.103493 | − | 0.994630i | \(-0.533002\pi\) | ||||
−0.103493 | + | 0.994630i | \(0.533002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.91668 | −0.235167 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.2921 | 0.487799 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.90495 | 0.154478 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.90534 | −0.351740 | −0.175870 | − | 0.984413i | \(-0.556274\pi\) | ||||
−0.175870 | + | 0.984413i | \(0.556274\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.4281 | −0.963350 | −0.481675 | − | 0.876350i | \(-0.659971\pi\) | ||||
−0.481675 | + | 0.876350i | \(0.659971\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.16984 | −0.164187 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.8284 | −0.976104 | −0.488052 | − | 0.872814i | \(-0.662292\pi\) | ||||
−0.488052 | + | 0.872814i | \(0.662292\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.6659 | −1.24300 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.0715 | −0.941990 | −0.470995 | − | 0.882136i | \(-0.656105\pi\) | ||||
−0.470995 | + | 0.882136i | \(0.656105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.26663 | 0.362077 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.9756 | 0.467215 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.61093 | −0.140662 | −0.0703310 | − | 0.997524i | \(-0.522406\pi\) | ||||
−0.0703310 | + | 0.997524i | \(0.522406\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.0885 | −1.09252 | −0.546258 | − | 0.837617i | \(-0.683948\pi\) | ||||
−0.546258 | + | 0.837617i | \(0.683948\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.5305 | 0.525481 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −52.8640 | −2.04690 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.99556 | 0.193139 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.1911 | 0.586445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0798 | 1.31368 | 0.656840 | − | 0.754030i | \(-0.271893\pi\) | ||||
0.656840 | + | 0.754030i | \(0.271893\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.4155 | 0.439384 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.32910 | 0.358546 | 0.179273 | − | 0.983799i | \(-0.442625\pi\) | ||||
0.179273 | + | 0.983799i | \(0.442625\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.22274 | −0.276776 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.7903 | −0.565933 | −0.282967 | − | 0.959130i | \(-0.591319\pi\) | ||||
−0.282967 | + | 0.959130i | \(0.591319\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.54200 | −0.135333 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.4252 | −0.435900 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 33.2548 | 1.26691 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.7101 | −1.05414 | −0.527072 | − | 0.849821i | \(-0.676710\pi\) | ||||
−0.527072 | + | 0.849821i | \(0.676710\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.11108 | −0.0421455 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.38244 | −0.203875 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.01686 | 0.341049 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.12039 | −0.117856 | −0.0589278 | − | 0.998262i | \(-0.518768\pi\) | ||||
−0.0589278 | + | 0.998262i | \(0.518768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.4377 | −1.67600 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.97030 | 0.0742059 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.9063 | 1.31093 | 0.655467 | − | 0.755224i | \(-0.272472\pi\) | ||||
0.655467 | + | 0.755224i | \(0.272472\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.6648 | −0.849997 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34.4712 | 1.29096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.6728 | −0.511334 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.84299 | 0.106173 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.8654 | −1.33755 | −0.668777 | − | 0.743463i | \(-0.733182\pi\) | ||||
−0.668777 | + | 0.743463i | \(0.733182\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.3351 | 0.421558 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.9573 | 1.22400 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.15799 | −0.302563 | −0.151282 | − | 0.988491i | \(-0.548340\pi\) | ||||
−0.151282 | + | 0.988491i | \(0.548340\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.6895 | −0.618131 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 63.3673 | 2.34373 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.3000 | 1.37771 | 0.688854 | − | 0.724900i | \(-0.258114\pi\) | ||||
0.688854 | + | 0.724900i | \(0.258114\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.4523 | 1.34274 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.801245 | 0.0294743 | 0.0147371 | − | 0.999891i | \(-0.495309\pi\) | ||||
0.0147371 | + | 0.999891i | \(0.495309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.1263 | 0.445471 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.3460 | 0.599678 | 0.299839 | − | 0.953990i | \(-0.403067\pi\) | ||||
0.299839 | + | 0.953990i | \(0.403067\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.69856 | −0.245416 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.88816 | −0.215437 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.8775 | −1.45515 | −0.727575 | − | 0.686028i | \(-0.759353\pi\) | ||||
−0.727575 | + | 0.686028i | \(0.759353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.89489 | 0.251264 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.11556 | 0.0769930 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.7946 | 0.901177 | 0.450588 | − | 0.892732i | \(-0.351214\pi\) | ||||
0.450588 | + | 0.892732i | \(0.351214\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.80296 | 0.355825 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.8427 | 0.465549 | 0.232774 | − | 0.972531i | \(-0.425220\pi\) | ||||
0.232774 | + | 0.972531i | \(0.425220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.8638 | 0.428937 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −57.0412 | −2.05964 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.3315 | −1.56258 | −0.781288 | − | 0.624171i | \(-0.785437\pi\) | ||||
−0.781288 | + | 0.624171i | \(0.785437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.86574 | 0.247264 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.3550 | 1.59534 | 0.797669 | − | 0.603096i | \(-0.206066\pi\) | ||||
0.797669 | + | 0.603096i | \(0.206066\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.4906 | −0.771965 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.82385 | −0.172832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.33222 | −0.155019 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.6167 | 0.701043 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.36195 | 0.119993 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.8939 | −1.38642 | −0.693208 | − | 0.720737i | \(-0.743803\pi\) | ||||
−0.693208 | + | 0.720737i | \(0.743803\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.3620 | 0.404499 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.3643 | 0.971736 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.10654 | −0.0747113 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.0342 | −0.638803 | −0.319401 | − | 0.947619i | \(-0.603482\pi\) | ||||
−0.319401 | + | 0.947619i | \(0.603482\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.9418 | −1.05927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 45.2175 | 1.59768 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.2860 | −0.468852 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.19548 | −0.112486 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.9425 | −1.75589 | −0.877943 | − | 0.478765i | \(-0.841085\pi\) | ||||
−0.877943 | + | 0.478765i | \(0.841085\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.43604 | 0.0855409 | 0.0427705 | − | 0.999085i | \(-0.486382\pi\) | ||||
0.0427705 | + | 0.999085i | \(0.486382\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.456451 | 0.0160084 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.7581 | −0.516953 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.7910 | 1.98687 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.6180 | −0.370572 | −0.185286 | − | 0.982685i | \(-0.559321\pi\) | ||||
−0.185286 | + | 0.982685i | \(0.559321\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.4401 | 1.75823 | 0.879116 | − | 0.476608i | \(-0.158134\pi\) | ||||
0.879116 | + | 0.476608i | \(0.158134\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.11152 | −0.212776 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.6086 | 0.577538 | 0.288769 | − | 0.957399i | \(-0.406754\pi\) | ||||
0.288769 | + | 0.957399i | \(0.406754\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.8505 | −0.550512 | −0.275256 | − | 0.961371i | \(-0.588763\pi\) | ||||
−0.275256 | + | 0.961371i | \(0.588763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.3754 | −0.359919 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.93363 | −0.309161 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.7915 | −0.442140 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.4364 | −0.705544 | −0.352772 | − | 0.935709i | \(-0.614761\pi\) | ||||
−0.352772 | + | 0.935709i | \(0.614761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.6346 | 0.952917 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.70280 | −0.299740 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.3880 | −0.494961 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.0797873 | 0.00273829 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −64.7107 | −2.21825 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.5432 | −1.31969 | −0.659847 | − | 0.751400i | \(-0.729379\pi\) | ||||
−0.659847 | + | 0.751400i | \(0.729379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.6326 | 0.363627 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.1391 | 1.43945 | 0.719723 | − | 0.694261i | \(-0.244269\pi\) | ||||
0.719723 | + | 0.694261i | \(0.244269\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.2451 | −0.486037 | −0.243018 | − | 0.970022i | \(-0.578138\pi\) | ||||
−0.243018 | + | 0.970022i | \(0.578138\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.4037 | 0.354146 | 0.177073 | − | 0.984198i | \(-0.443337\pi\) | ||||
0.177073 | + | 0.984198i | \(0.443337\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.84934 | 0.334888 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.38191 | 0.182779 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.1447 | 0.852975 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65.6631 | 2.22491 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.26253 | −0.211955 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.38200 | −0.0804344 | −0.0402172 | − | 0.999191i | \(-0.512805\pi\) | ||||
−0.0402172 | + | 0.999191i | \(0.512805\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.5050 | 0.421784 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.7986 | −1.30716 | −0.653579 | − | 0.756858i | \(-0.726733\pi\) | ||||
−0.653579 | + | 0.756858i | \(0.726733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.8165 | −1.20532 | −0.602660 | − | 0.797998i | \(-0.705892\pi\) | ||||
−0.602660 | + | 0.797998i | \(0.705892\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.61330 | 0.121460 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.4998 | 1.15839 | 0.579196 | − | 0.815189i | \(-0.303367\pi\) | ||||
0.579196 | + | 0.815189i | \(0.303367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.4161 | 0.750967 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.8345 | −0.897981 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.48459 | 0.183330 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.6585 | 0.589600 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.9299 | −1.23168 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.0122 | 1.06648 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.4402 | −0.480009 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.75723 | 0.0915523 | 0.0457761 | − | 0.998952i | \(-0.485424\pi\) | ||||
0.0457761 | + | 0.998952i | \(0.485424\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.1919 | 0.570221 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.19693 | 0.139051 | 0.0695253 | − | 0.997580i | \(-0.477852\pi\) | ||||
0.0695253 | + | 0.997580i | \(0.477852\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.53242 | 0.216192 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.73341 | −0.0573047 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.8130 | 0.356689 | 0.178344 | − | 0.983968i | \(-0.442926\pi\) | ||||
0.178344 | + | 0.983968i | \(0.442926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.5554 | 0.380763 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.80381 | −0.256865 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.3430 | 1.32647 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.12264 | −0.135405 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.3572 | −0.930370 | −0.465185 | − | 0.885214i | \(-0.654012\pi\) | ||||
−0.465185 | + | 0.885214i | \(0.654012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.00264 | −0.229256 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −13.1619 | −0.430441 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.1289 | −0.363565 | −0.181783 | − | 0.983339i | \(-0.558187\pi\) | ||||
−0.181783 | + | 0.983339i | \(0.558187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.72789 | 0.317458 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.0876 | −1.40462 | −0.702308 | − | 0.711873i | \(-0.747847\pi\) | ||||
−0.702308 | + | 0.711873i | \(0.747847\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.02456 | −0.228751 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.7408 | 0.608996 | 0.304498 | − | 0.952513i | \(-0.401511\pi\) | ||||
0.304498 | + | 0.952513i | \(0.401511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.9326 | −0.776885 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.7783 | 0.349511 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.7933 | −0.446807 | −0.223404 | − | 0.974726i | \(-0.571717\pi\) | ||||
−0.223404 | + | 0.974726i | \(0.571717\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.1921 | −0.491605 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.5022 | −0.339487 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.91899 | −0.223193 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.6016 | −0.760551 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.10059 | −0.0354291 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.71189 | −0.312313 | −0.156157 | − | 0.987732i | \(-0.549910\pi\) | ||||
−0.156157 | + | 0.987732i | \(0.549910\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.6732 | 0.374997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −58.4091 | −1.87444 | −0.937218 | − | 0.348743i | \(-0.886609\pi\) | ||||
−0.937218 | + | 0.348743i | \(0.886609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.0089 | −0.352569 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 51.0637 | 1.63367 | 0.816837 | − | 0.576869i | \(-0.195726\pi\) | ||||
0.816837 | + | 0.576869i | \(0.195726\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −50.1650 | −1.60328 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.4297 | 0.907690 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −61.7375 | −1.96912 | −0.984560 | − | 0.175046i | \(-0.943993\pi\) | ||||
−0.984560 | + | 0.175046i | \(0.943993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0965 | −0.321703 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 82.6998 | 2.62970 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.0099 | −1.14389 | −0.571946 | − | 0.820292i | \(-0.693811\pi\) | ||||
−0.571946 | + | 0.820292i | \(0.693811\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.33817 | −0.137668 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.31831 | 0.0417931 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.7614 | −0.499169 | −0.249585 | − | 0.968353i | \(-0.580294\pi\) | ||||
−0.249585 | + | 0.968353i | \(0.580294\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.0128 | 0.759730 |
(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 | 8036.2.a.q.1.9 | 15 | ||
7.2 | even | 3 | 1148.2.i.e.165.7 | ✓ | 30 | ||
7.4 | even | 3 | 1148.2.i.e.821.7 | yes | 30 | ||
7.6 | odd | 2 | 8036.2.a.r.1.7 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.i.e.165.7 | ✓ | 30 | 7.2 | even | 3 | ||
1148.2.i.e.821.7 | yes | 30 | 7.4 | even | 3 | ||
8036.2.a.q.1.9 | 15 | 1.1 | even | 1 | trivial | ||
8036.2.a.r.1.7 | 15 | 7.6 | odd | 2 |