Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.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: | \(48.2216577807\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.44801 | −1.73101 | −0.865504 | − | 0.500902i | \(-0.833002\pi\) | ||||
−0.865504 | + | 0.500902i | \(0.833002\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.99278 | 1.99639 | ||||||||
\(5\) | 1.89686 | 0.848301 | 0.424151 | − | 0.905592i | \(-0.360573\pi\) | ||||
0.424151 | + | 0.905592i | \(0.360573\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.969789 | −0.366546 | −0.183273 | − | 0.983062i | \(-0.558669\pi\) | ||||
−0.183273 | + | 0.983062i | \(0.558669\pi\) | |||||||
\(8\) | −4.87834 | −1.72476 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.64354 | −1.46842 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.38040 | −0.382853 | −0.191427 | − | 0.981507i | \(-0.561311\pi\) | ||||
−0.191427 | + | 0.981507i | \(0.561311\pi\) | |||||||
\(14\) | 2.37406 | 0.634493 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.95671 | 0.989177 | ||||||||
\(17\) | 0.855355 | 0.207454 | 0.103727 | − | 0.994606i | \(-0.466923\pi\) | ||||
0.103727 | + | 0.994606i | \(0.466923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.83285 | 1.33815 | 0.669073 | − | 0.743196i | \(-0.266691\pi\) | ||||
0.669073 | + | 0.743196i | \(0.266691\pi\) | |||||||
\(20\) | 7.57373 | 1.69354 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.44801 | −0.521918 | ||||||||
\(23\) | 3.24050 | 0.675691 | 0.337846 | − | 0.941202i | \(-0.390302\pi\) | ||||
0.337846 | + | 0.941202i | \(0.390302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.40193 | −0.280385 | ||||||||
\(26\) | 3.37923 | 0.662722 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.87215 | −0.731767 | ||||||||
\(29\) | 7.17008 | 1.33145 | 0.665725 | − | 0.746197i | \(-0.268122\pi\) | ||||
0.665725 | + | 0.746197i | \(0.268122\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.46194 | −0.621782 | −0.310891 | − | 0.950446i | \(-0.600627\pi\) | ||||
−0.310891 | + | 0.950446i | \(0.600627\pi\) | |||||||
\(32\) | 0.0706103 | 0.0124823 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.09392 | −0.359105 | ||||||||
\(35\) | −1.83955 | −0.310941 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.28798 | 0.869339 | 0.434670 | − | 0.900590i | \(-0.356865\pi\) | ||||
0.434670 | + | 0.900590i | \(0.356865\pi\) | |||||||
\(38\) | −14.2789 | −2.31634 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.25353 | −1.46311 | ||||||||
\(41\) | 6.09420 | 0.951754 | 0.475877 | − | 0.879512i | \(-0.342131\pi\) | ||||
0.475877 | + | 0.879512i | \(0.342131\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.07616 | 0.164113 | 0.0820567 | − | 0.996628i | \(-0.473851\pi\) | ||||
0.0820567 | + | 0.996628i | \(0.473851\pi\) | |||||||
\(44\) | 3.99278 | 0.601934 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.93279 | −1.16963 | ||||||||
\(47\) | 6.02763 | 0.879221 | 0.439610 | − | 0.898189i | \(-0.355117\pi\) | ||||
0.439610 | + | 0.898189i | \(0.355117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.05951 | −0.865644 | ||||||||
\(50\) | 3.43194 | 0.485349 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.51162 | −0.764324 | ||||||||
\(53\) | −2.06446 | −0.283576 | −0.141788 | − | 0.989897i | \(-0.545285\pi\) | ||||
−0.141788 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.89686 | 0.255772 | ||||||||
\(56\) | 4.73096 | 0.632202 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −17.5525 | −2.30475 | ||||||||
\(59\) | 5.72346 | 0.745131 | 0.372566 | − | 0.928006i | \(-0.378478\pi\) | ||||
0.372566 | + | 0.928006i | \(0.378478\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 8.47487 | 1.07631 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.08627 | −1.01078 | ||||||||
\(65\) | −2.61842 | −0.324775 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.3644 | −1.38839 | −0.694193 | − | 0.719789i | \(-0.744239\pi\) | ||||
−0.694193 | + | 0.719789i | \(0.744239\pi\) | |||||||
\(68\) | 3.41524 | 0.414159 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.50325 | 0.538241 | ||||||||
\(71\) | −7.88328 | −0.935574 | −0.467787 | − | 0.883841i | \(-0.654949\pi\) | ||||
−0.467787 | + | 0.883841i | \(0.654949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.611985 | 0.0716274 | 0.0358137 | − | 0.999358i | \(-0.488598\pi\) | ||||
0.0358137 | + | 0.999358i | \(0.488598\pi\) | |||||||
\(74\) | −12.9451 | −1.50483 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 23.2893 | 2.67146 | ||||||||
\(77\) | −0.969789 | −0.110518 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1792 | 1.14525 | 0.572627 | − | 0.819816i | \(-0.305924\pi\) | ||||
0.572627 | + | 0.819816i | \(0.305924\pi\) | |||||||
\(80\) | 7.50532 | 0.839120 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.9187 | −1.64749 | ||||||||
\(83\) | −4.28509 | −0.470350 | −0.235175 | − | 0.971953i | \(-0.575566\pi\) | ||||
−0.235175 | + | 0.971953i | \(0.575566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.62249 | 0.175983 | ||||||||
\(86\) | −2.63446 | −0.284082 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.87834 | −0.520033 | ||||||||
\(89\) | −14.0115 | −1.48521 | −0.742606 | − | 0.669728i | \(-0.766411\pi\) | ||||
−0.742606 | + | 0.669728i | \(0.766411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.33869 | 0.140333 | ||||||||
\(92\) | 12.9386 | 1.34894 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.7557 | −1.52194 | ||||||||
\(95\) | 11.0641 | 1.13515 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.51129 | −0.254983 | −0.127492 | − | 0.991840i | \(-0.540693\pi\) | ||||
−0.127492 | + | 0.991840i | \(0.540693\pi\) | |||||||
\(98\) | 14.8338 | 1.49844 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.59758 | −0.559758 | ||||||||
\(101\) | 14.2789 | 1.42080 | 0.710401 | − | 0.703798i | \(-0.248514\pi\) | ||||
0.710401 | + | 0.703798i | \(0.248514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.93576 | −0.781934 | −0.390967 | − | 0.920405i | \(-0.627859\pi\) | ||||
−0.390967 | + | 0.920405i | \(0.627859\pi\) | |||||||
\(104\) | 6.73405 | 0.660328 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.05384 | 0.490872 | ||||||||
\(107\) | 12.2576 | 1.18499 | 0.592494 | − | 0.805575i | \(-0.298143\pi\) | ||||
0.592494 | + | 0.805575i | \(0.298143\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.54910 | 0.723073 | 0.361536 | − | 0.932358i | \(-0.382252\pi\) | ||||
0.361536 | + | 0.932358i | \(0.382252\pi\) | |||||||
\(110\) | −4.64354 | −0.442744 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.83717 | −0.362579 | ||||||||
\(113\) | 6.19099 | 0.582400 | 0.291200 | − | 0.956662i | \(-0.405946\pi\) | ||||
0.291200 | + | 0.956662i | \(0.405946\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.14677 | 0.573189 | ||||||||
\(116\) | 28.6285 | 2.65809 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.0111 | −1.28983 | ||||||||
\(119\) | −0.829513 | −0.0760414 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.44801 | 0.221633 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.8227 | −1.24132 | ||||||||
\(125\) | −12.1436 | −1.08615 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.7585 | −1.57581 | −0.787907 | − | 0.615794i | \(-0.788835\pi\) | ||||
−0.787907 | + | 0.615794i | \(0.788835\pi\) | |||||||
\(128\) | 19.6541 | 1.73719 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.40993 | 0.562188 | ||||||||
\(131\) | 8.09154 | 0.706961 | 0.353480 | − | 0.935442i | \(-0.384998\pi\) | ||||
0.353480 | + | 0.935442i | \(0.384998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.65663 | −0.490492 | ||||||||
\(134\) | 27.8203 | 2.40331 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.17272 | −0.357807 | ||||||||
\(137\) | −2.99237 | −0.255656 | −0.127828 | − | 0.991796i | \(-0.540800\pi\) | ||||
−0.127828 | + | 0.991796i | \(0.540800\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.5771 | −0.981953 | −0.490976 | − | 0.871173i | \(-0.663360\pi\) | ||||
−0.490976 | + | 0.871173i | \(0.663360\pi\) | |||||||
\(140\) | −7.34492 | −0.620759 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.2984 | 1.61949 | ||||||||
\(143\) | −1.38040 | −0.115435 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.6006 | 1.12947 | ||||||||
\(146\) | −1.49815 | −0.123988 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 21.1137 | 1.73554 | ||||||||
\(149\) | 13.7136 | 1.12346 | 0.561731 | − | 0.827320i | \(-0.310135\pi\) | ||||
0.561731 | + | 0.827320i | \(0.310135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.8159 | 1.44984 | 0.724921 | − | 0.688833i | \(-0.241876\pi\) | ||||
0.724921 | + | 0.688833i | \(0.241876\pi\) | |||||||
\(152\) | −28.4546 | −2.30798 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.37406 | 0.191307 | ||||||||
\(155\) | −6.56681 | −0.527459 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.5321 | 1.07998 | 0.539989 | − | 0.841672i | \(-0.318428\pi\) | ||||
0.539989 | + | 0.841672i | \(0.318428\pi\) | |||||||
\(158\) | −24.9189 | −1.98244 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.133938 | 0.0105887 | ||||||||
\(161\) | −3.14260 | −0.247672 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8613 | 1.16402 | 0.582012 | − | 0.813180i | \(-0.302266\pi\) | ||||
0.582012 | + | 0.813180i | \(0.302266\pi\) | |||||||
\(164\) | 24.3328 | 1.90007 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.4900 | 0.814179 | ||||||||
\(167\) | −13.7794 | −1.06628 | −0.533141 | − | 0.846026i | \(-0.678989\pi\) | ||||
−0.533141 | + | 0.846026i | \(0.678989\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0945 | −0.853423 | ||||||||
\(170\) | −3.97187 | −0.304629 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.29688 | 0.327634 | ||||||||
\(173\) | 12.4898 | 0.949582 | 0.474791 | − | 0.880098i | \(-0.342524\pi\) | ||||
0.474791 | + | 0.880098i | \(0.342524\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.35957 | 0.102774 | ||||||||
\(176\) | 3.95671 | 0.298248 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 34.3003 | 2.57091 | ||||||||
\(179\) | 19.0115 | 1.42098 | 0.710492 | − | 0.703705i | \(-0.248472\pi\) | ||||
0.710492 | + | 0.703705i | \(0.248472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.660327 | 0.0490818 | 0.0245409 | − | 0.999699i | \(-0.492188\pi\) | ||||
0.0245409 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(182\) | −3.27714 | −0.242918 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.8083 | −1.16540 | ||||||||
\(185\) | 10.0306 | 0.737461 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.855355 | 0.0625497 | ||||||||
\(188\) | 24.0670 | 1.75527 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −27.0850 | −1.96496 | ||||||||
\(191\) | 23.1136 | 1.67244 | 0.836222 | − | 0.548391i | \(-0.184760\pi\) | ||||
0.836222 | + | 0.548391i | \(0.184760\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.20067 | 0.0864258 | 0.0432129 | − | 0.999066i | \(-0.486241\pi\) | ||||
0.0432129 | + | 0.999066i | \(0.486241\pi\) | |||||||
\(194\) | 6.14769 | 0.441378 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.1943 | −1.72816 | ||||||||
\(197\) | −5.69586 | −0.405813 | −0.202907 | − | 0.979198i | \(-0.565039\pi\) | ||||
−0.202907 | + | 0.979198i | \(0.565039\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.20131 | −0.368711 | −0.184356 | − | 0.982860i | \(-0.559020\pi\) | ||||
−0.184356 | + | 0.982860i | \(0.559020\pi\) | |||||||
\(200\) | 6.83908 | 0.483596 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −34.9549 | −2.45942 | ||||||||
\(203\) | −6.95346 | −0.488038 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.5598 | 0.807374 | ||||||||
\(206\) | 19.4269 | 1.35353 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.46183 | −0.378710 | ||||||||
\(209\) | 5.83285 | 0.403466 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.38195 | −0.508195 | −0.254097 | − | 0.967179i | \(-0.581778\pi\) | ||||
−0.254097 | + | 0.967179i | \(0.581778\pi\) | |||||||
\(212\) | −8.24294 | −0.566128 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −30.0068 | −2.05122 | ||||||||
\(215\) | 2.04133 | 0.139218 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.35735 | 0.227912 | ||||||||
\(218\) | −18.4803 | −1.25164 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.57373 | 0.510621 | ||||||||
\(221\) | −1.18073 | −0.0794245 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.03118 | 0.470843 | 0.235421 | − | 0.971893i | \(-0.424353\pi\) | ||||
0.235421 | + | 0.971893i | \(0.424353\pi\) | |||||||
\(224\) | −0.0684771 | −0.00457532 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.1556 | −1.00814 | ||||||||
\(227\) | −19.4013 | −1.28771 | −0.643855 | − | 0.765148i | \(-0.722666\pi\) | ||||
−0.643855 | + | 0.765148i | \(0.722666\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.22075 | 0.609324 | 0.304662 | − | 0.952461i | \(-0.401456\pi\) | ||||
0.304662 | + | 0.952461i | \(0.401456\pi\) | |||||||
\(230\) | −15.0474 | −0.992195 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −34.9781 | −2.29643 | ||||||||
\(233\) | −20.1940 | −1.32295 | −0.661476 | − | 0.749966i | \(-0.730070\pi\) | ||||
−0.661476 | + | 0.749966i | \(0.730070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.4336 | 0.745844 | ||||||||
\(236\) | 22.8525 | 1.48757 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.03066 | 0.131628 | ||||||||
\(239\) | −5.63737 | −0.364651 | −0.182325 | − | 0.983238i | \(-0.558362\pi\) | ||||
−0.182325 | + | 0.983238i | \(0.558362\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.1402 | 1.10410 | 0.552050 | − | 0.833811i | \(-0.313846\pi\) | ||||
0.552050 | + | 0.833811i | \(0.313846\pi\) | |||||||
\(242\) | −2.44801 | −0.157364 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.99278 | −0.255611 | ||||||||
\(245\) | −11.4940 | −0.734327 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.05165 | −0.512314 | ||||||||
\(248\) | 16.8885 | 1.07242 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 29.7276 | 1.88014 | ||||||||
\(251\) | −1.16912 | −0.0737943 | −0.0368971 | − | 0.999319i | \(-0.511747\pi\) | ||||
−0.0368971 | + | 0.999319i | \(0.511747\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.24050 | 0.203729 | ||||||||
\(254\) | 43.4731 | 2.72775 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −31.9410 | −1.99631 | ||||||||
\(257\) | −14.1284 | −0.881307 | −0.440654 | − | 0.897677i | \(-0.645253\pi\) | ||||
−0.440654 | + | 0.897677i | \(0.645253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.12823 | −0.318653 | ||||||||
\(260\) | −10.4548 | −0.648377 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −19.8082 | −1.22375 | ||||||||
\(263\) | 5.39904 | 0.332919 | 0.166460 | − | 0.986048i | \(-0.446766\pi\) | ||||
0.166460 | + | 0.986048i | \(0.446766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.91600 | −0.240558 | ||||||||
\(266\) | 13.8475 | 0.849045 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −45.3756 | −2.77176 | ||||||||
\(269\) | −23.2326 | −1.41652 | −0.708258 | − | 0.705954i | \(-0.750519\pi\) | ||||
−0.708258 | + | 0.705954i | \(0.750519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.968446 | 0.0588289 | 0.0294144 | − | 0.999567i | \(-0.490636\pi\) | ||||
0.0294144 | + | 0.999567i | \(0.490636\pi\) | |||||||
\(272\) | 3.38439 | 0.205209 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.32537 | 0.442542 | ||||||||
\(275\) | −1.40193 | −0.0845394 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.925052 | −0.0555810 | −0.0277905 | − | 0.999614i | \(-0.508847\pi\) | ||||
−0.0277905 | + | 0.999614i | \(0.508847\pi\) | |||||||
\(278\) | 28.3408 | 1.69977 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.97397 | 0.536297 | ||||||||
\(281\) | 22.4103 | 1.33688 | 0.668442 | − | 0.743764i | \(-0.266961\pi\) | ||||
0.668442 | + | 0.743764i | \(0.266961\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.1312 | −1.55334 | −0.776669 | − | 0.629909i | \(-0.783092\pi\) | ||||
−0.776669 | + | 0.629909i | \(0.783092\pi\) | |||||||
\(284\) | −31.4762 | −1.86777 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.37923 | 0.199818 | ||||||||
\(287\) | −5.91009 | −0.348861 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2684 | −0.956963 | ||||||||
\(290\) | −33.2946 | −1.95512 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.44352 | 0.142996 | ||||||||
\(293\) | −11.5708 | −0.675974 | −0.337987 | − | 0.941151i | \(-0.609746\pi\) | ||||
−0.337987 | + | 0.941151i | \(0.609746\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8566 | 0.632096 | ||||||||
\(296\) | −25.7966 | −1.49940 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −33.5711 | −1.94472 | ||||||||
\(299\) | −4.47318 | −0.258691 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.04365 | −0.0601551 | ||||||||
\(302\) | −43.6137 | −2.50969 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 23.0789 | 1.32366 | ||||||||
\(305\) | −1.89686 | −0.108614 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.6298 | −1.00619 | −0.503093 | − | 0.864232i | \(-0.667805\pi\) | ||||
−0.503093 | + | 0.864232i | \(0.667805\pi\) | |||||||
\(308\) | −3.87215 | −0.220636 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 16.0756 | 0.913035 | ||||||||
\(311\) | −4.59243 | −0.260413 | −0.130206 | − | 0.991487i | \(-0.541564\pi\) | ||||
−0.130206 | + | 0.991487i | \(0.541564\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0068 | 0.791709 | 0.395854 | − | 0.918313i | \(-0.370448\pi\) | ||||
0.395854 | + | 0.918313i | \(0.370448\pi\) | |||||||
\(314\) | −33.1268 | −1.86945 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 40.6434 | 2.28637 | ||||||||
\(317\) | 27.7798 | 1.56027 | 0.780136 | − | 0.625610i | \(-0.215150\pi\) | ||||
0.780136 | + | 0.625610i | \(0.215150\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.17008 | 0.401448 | ||||||||
\(320\) | −15.3385 | −0.857449 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.69313 | 0.428722 | ||||||||
\(323\) | 4.98915 | 0.277604 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.93522 | 0.107346 | ||||||||
\(326\) | −36.3806 | −2.01494 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −29.7296 | −1.64154 | ||||||||
\(329\) | −5.84553 | −0.322275 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34.0813 | 1.87328 | 0.936640 | − | 0.350294i | \(-0.113918\pi\) | ||||
0.936640 | + | 0.350294i | \(0.113918\pi\) | |||||||
\(332\) | −17.1094 | −0.939001 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 33.7322 | 1.84574 | ||||||||
\(335\) | −21.5567 | −1.17777 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.84351 | 0.100422 | 0.0502112 | − | 0.998739i | \(-0.484011\pi\) | ||||
0.0502112 | + | 0.998739i | \(0.484011\pi\) | |||||||
\(338\) | 27.1595 | 1.47728 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.47823 | 0.351331 | ||||||||
\(341\) | −3.46194 | −0.187474 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6650 | 0.683844 | ||||||||
\(344\) | −5.24990 | −0.283056 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.5752 | −1.64373 | ||||||||
\(347\) | 3.94391 | 0.211720 | 0.105860 | − | 0.994381i | \(-0.466240\pi\) | ||||
0.105860 | + | 0.994381i | \(0.466240\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1806 | 0.544956 | 0.272478 | − | 0.962162i | \(-0.412157\pi\) | ||||
0.272478 | + | 0.962162i | \(0.412157\pi\) | |||||||
\(350\) | −3.32825 | −0.177903 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0706103 | 0.00376354 | ||||||||
\(353\) | 13.6707 | 0.727616 | 0.363808 | − | 0.931474i | \(-0.381477\pi\) | ||||
0.363808 | + | 0.931474i | \(0.381477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.9535 | −0.793648 | ||||||||
\(356\) | −55.9446 | −2.96506 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −46.5404 | −2.45974 | ||||||||
\(359\) | 3.82844 | 0.202057 | 0.101029 | − | 0.994884i | \(-0.467787\pi\) | ||||
0.101029 | + | 0.994884i | \(0.467787\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0221 | 0.790637 | ||||||||
\(362\) | −1.61649 | −0.0849609 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.34510 | 0.280160 | ||||||||
\(365\) | 1.16085 | 0.0607616 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.5024 | 1.27901 | 0.639506 | − | 0.768786i | \(-0.279139\pi\) | ||||
0.639506 | + | 0.768786i | \(0.279139\pi\) | |||||||
\(368\) | 12.8217 | 0.668378 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24.5550 | −1.27655 | ||||||||
\(371\) | 2.00209 | 0.103944 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.3103 | 1.15518 | 0.577591 | − | 0.816326i | \(-0.303993\pi\) | ||||
0.577591 | + | 0.816326i | \(0.303993\pi\) | |||||||
\(374\) | −2.09392 | −0.108274 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −29.4049 | −1.51644 | ||||||||
\(377\) | −9.89756 | −0.509750 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0926 | 0.621156 | 0.310578 | − | 0.950548i | \(-0.399477\pi\) | ||||
0.310578 | + | 0.950548i | \(0.399477\pi\) | |||||||
\(380\) | 44.1764 | 2.26620 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −56.5825 | −2.89501 | ||||||||
\(383\) | −36.3134 | −1.85553 | −0.927764 | − | 0.373168i | \(-0.878271\pi\) | ||||
−0.927764 | + | 0.373168i | \(0.878271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.83955 | −0.0937523 | ||||||||
\(386\) | −2.93925 | −0.149604 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.0270 | −0.509046 | ||||||||
\(389\) | −1.16648 | −0.0591427 | −0.0295713 | − | 0.999563i | \(-0.509414\pi\) | ||||
−0.0295713 | + | 0.999563i | \(0.509414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.77178 | 0.140175 | ||||||||
\(392\) | 29.5604 | 1.49302 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.9436 | 0.702466 | ||||||||
\(395\) | 19.3086 | 0.971520 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.54740 | 0.428982 | 0.214491 | − | 0.976726i | \(-0.431191\pi\) | ||||
0.214491 | + | 0.976726i | \(0.431191\pi\) | |||||||
\(398\) | 12.7329 | 0.638242 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.54701 | −0.277351 | ||||||||
\(401\) | −34.2861 | −1.71217 | −0.856084 | − | 0.516837i | \(-0.827109\pi\) | ||||
−0.856084 | + | 0.516837i | \(0.827109\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.77885 | 0.238051 | ||||||||
\(404\) | 57.0124 | 2.83647 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.0222 | 0.844797 | ||||||||
\(407\) | 5.28798 | 0.262116 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.5074 | 0.915134 | 0.457567 | − | 0.889175i | \(-0.348721\pi\) | ||||
0.457567 | + | 0.889175i | \(0.348721\pi\) | |||||||
\(410\) | −28.2987 | −1.39757 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −31.6857 | −1.56104 | ||||||||
\(413\) | −5.55055 | −0.273125 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.12821 | −0.398998 | ||||||||
\(416\) | −0.0974703 | −0.00477887 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.2789 | −0.698404 | ||||||||
\(419\) | 20.0178 | 0.977932 | 0.488966 | − | 0.872303i | \(-0.337374\pi\) | ||||
0.488966 | + | 0.872303i | \(0.337374\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.2596 | 1.62097 | 0.810486 | − | 0.585758i | \(-0.199203\pi\) | ||||
0.810486 | + | 0.585758i | \(0.199203\pi\) | |||||||
\(422\) | 18.0711 | 0.879689 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.0712 | 0.489099 | ||||||||
\(425\) | −1.19914 | −0.0581671 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.969789 | 0.0469314 | ||||||||
\(428\) | 48.9419 | 2.36570 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.99721 | −0.240987 | ||||||||
\(431\) | −29.9785 | −1.44401 | −0.722007 | − | 0.691886i | \(-0.756780\pi\) | ||||
−0.722007 | + | 0.691886i | \(0.756780\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.4446 | −0.549991 | −0.274995 | − | 0.961446i | \(-0.588676\pi\) | ||||
−0.274995 | + | 0.961446i | \(0.588676\pi\) | |||||||
\(434\) | −8.21883 | −0.394517 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.1419 | 1.44353 | ||||||||
\(437\) | 18.9013 | 0.904174 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.54994 | 0.360339 | 0.180170 | − | 0.983636i | \(-0.442335\pi\) | ||||
0.180170 | + | 0.983636i | \(0.442335\pi\) | |||||||
\(440\) | −9.25353 | −0.441145 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.89044 | 0.137484 | ||||||||
\(443\) | −6.08354 | −0.289038 | −0.144519 | − | 0.989502i | \(-0.546163\pi\) | ||||
−0.144519 | + | 0.989502i | \(0.546163\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.5778 | −1.25991 | ||||||||
\(446\) | −17.2124 | −0.815033 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.84197 | 0.370498 | ||||||||
\(449\) | 1.43753 | 0.0678413 | 0.0339207 | − | 0.999425i | \(-0.489201\pi\) | ||||
0.0339207 | + | 0.999425i | \(0.489201\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.09420 | 0.286965 | ||||||||
\(452\) | 24.7192 | 1.16270 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 47.4947 | 2.22904 | ||||||||
\(455\) | 2.53931 | 0.119045 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.9601 | −1.44825 | −0.724127 | − | 0.689667i | \(-0.757757\pi\) | ||||
−0.724127 | + | 0.689667i | \(0.757757\pi\) | |||||||
\(458\) | −22.5725 | −1.05474 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 24.5427 | 1.14431 | ||||||||
\(461\) | 24.2494 | 1.12941 | 0.564704 | − | 0.825294i | \(-0.308991\pi\) | ||||
0.564704 | + | 0.825294i | \(0.308991\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.0262 | −1.30249 | −0.651245 | − | 0.758868i | \(-0.725753\pi\) | ||||
−0.651245 | + | 0.758868i | \(0.725753\pi\) | |||||||
\(464\) | 28.3699 | 1.31704 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 49.4352 | 2.29004 | ||||||||
\(467\) | 5.16196 | 0.238867 | 0.119434 | − | 0.992842i | \(-0.461892\pi\) | ||||
0.119434 | + | 0.992842i | \(0.461892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0211 | 0.508907 | ||||||||
\(470\) | −27.9895 | −1.29106 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −27.9210 | −1.28517 | ||||||||
\(473\) | 1.07616 | 0.0494821 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.17722 | −0.375197 | ||||||||
\(476\) | −3.31206 | −0.151808 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.8004 | 0.631214 | ||||||||
\(479\) | 0.552200 | 0.0252307 | 0.0126153 | − | 0.999920i | \(-0.495984\pi\) | ||||
0.0126153 | + | 0.999920i | \(0.495984\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.29952 | −0.332829 | ||||||||
\(482\) | −41.9596 | −1.91121 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.99278 | 0.181490 | ||||||||
\(485\) | −4.76357 | −0.216303 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.7046 | −1.30073 | −0.650366 | − | 0.759621i | \(-0.725384\pi\) | ||||
−0.650366 | + | 0.759621i | \(0.725384\pi\) | |||||||
\(488\) | 4.87834 | 0.220832 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 28.1376 | 1.27113 | ||||||||
\(491\) | 19.7847 | 0.892870 | 0.446435 | − | 0.894816i | \(-0.352693\pi\) | ||||
0.446435 | + | 0.894816i | \(0.352693\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.13296 | 0.276215 | ||||||||
\(494\) | 19.7105 | 0.886820 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13.6979 | −0.615053 | ||||||||
\(497\) | 7.64512 | 0.342930 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.8129 | 0.842182 | 0.421091 | − | 0.907018i | \(-0.361647\pi\) | ||||
0.421091 | + | 0.907018i | \(0.361647\pi\) | |||||||
\(500\) | −48.4865 | −2.16838 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.86203 | 0.127738 | ||||||||
\(503\) | −8.44822 | −0.376687 | −0.188344 | − | 0.982103i | \(-0.560312\pi\) | ||||
−0.188344 | + | 0.982103i | \(0.560312\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.0850 | 1.20527 | ||||||||
\(506\) | −7.93279 | −0.352656 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −70.9058 | −3.14594 | ||||||||
\(509\) | −3.24496 | −0.143830 | −0.0719152 | − | 0.997411i | \(-0.522911\pi\) | ||||
−0.0719152 | + | 0.997411i | \(0.522911\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.593496 | −0.0262547 | ||||||||
\(512\) | 38.8838 | 1.71844 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 34.5866 | 1.52555 | ||||||||
\(515\) | −15.0530 | −0.663315 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.02763 | 0.265095 | ||||||||
\(518\) | 12.5540 | 0.551590 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.7736 | 0.560157 | ||||||||
\(521\) | 11.3259 | 0.496196 | 0.248098 | − | 0.968735i | \(-0.420195\pi\) | ||||
0.248098 | + | 0.968735i | \(0.420195\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.8169 | 1.52244 | 0.761218 | − | 0.648496i | \(-0.224602\pi\) | ||||
0.761218 | + | 0.648496i | \(0.224602\pi\) | |||||||
\(524\) | 32.3077 | 1.41137 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.2169 | −0.576286 | ||||||||
\(527\) | −2.96118 | −0.128991 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.4992 | −0.543442 | ||||||||
\(530\) | 9.58642 | 0.416407 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −22.5857 | −0.979212 | ||||||||
\(533\) | −8.41242 | −0.364382 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.2510 | 1.00523 | ||||||||
\(536\) | 55.4396 | 2.39463 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 56.8737 | 2.45200 | ||||||||
\(539\) | −6.05951 | −0.261002 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.2014 | −1.77139 | −0.885693 | − | 0.464271i | \(-0.846316\pi\) | ||||
−0.885693 | + | 0.464271i | \(0.846316\pi\) | |||||||
\(542\) | −2.37077 | −0.101833 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.0603969 | 0.00258949 | ||||||||
\(545\) | 14.3196 | 0.613383 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.19226 | 0.393033 | 0.196516 | − | 0.980501i | \(-0.437037\pi\) | ||||
0.196516 | + | 0.980501i | \(0.437037\pi\) | |||||||
\(548\) | −11.9479 | −0.510388 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.43194 | 0.146338 | ||||||||
\(551\) | 41.8220 | 1.78168 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.87171 | −0.419788 | ||||||||
\(554\) | 2.26454 | 0.0962111 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −46.2246 | −1.96036 | ||||||||
\(557\) | 5.68316 | 0.240803 | 0.120402 | − | 0.992725i | \(-0.461582\pi\) | ||||
0.120402 | + | 0.992725i | \(0.461582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.48553 | −0.0628314 | ||||||||
\(560\) | −7.27857 | −0.307576 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −54.8607 | −2.31416 | ||||||||
\(563\) | 2.01368 | 0.0848663 | 0.0424332 | − | 0.999099i | \(-0.486489\pi\) | ||||
0.0424332 | + | 0.999099i | \(0.486489\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.7434 | 0.494050 | ||||||||
\(566\) | 63.9695 | 2.68884 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 38.4574 | 1.61364 | ||||||||
\(569\) | −14.5668 | −0.610670 | −0.305335 | − | 0.952245i | \(-0.598768\pi\) | ||||
−0.305335 | + | 0.952245i | \(0.598768\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.23602 | −0.0935744 | −0.0467872 | − | 0.998905i | \(-0.514898\pi\) | ||||
−0.0467872 | + | 0.998905i | \(0.514898\pi\) | |||||||
\(572\) | −5.51162 | −0.230452 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.4680 | 0.603882 | ||||||||
\(575\) | −4.54294 | −0.189454 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.6123 | 0.816472 | 0.408236 | − | 0.912876i | \(-0.366144\pi\) | ||||
0.408236 | + | 0.912876i | \(0.366144\pi\) | |||||||
\(578\) | 39.8252 | 1.65651 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 54.3043 | 2.25486 | ||||||||
\(581\) | 4.15563 | 0.172405 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.06446 | −0.0855014 | ||||||||
\(584\) | −2.98547 | −0.123540 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.3255 | 1.17012 | ||||||||
\(587\) | −10.0921 | −0.416546 | −0.208273 | − | 0.978071i | \(-0.566784\pi\) | ||||
−0.208273 | + | 0.978071i | \(0.566784\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1929 | −0.832036 | ||||||||
\(590\) | −26.5771 | −1.09416 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 20.9230 | 0.859930 | ||||||||
\(593\) | 47.5052 | 1.95081 | 0.975403 | − | 0.220431i | \(-0.0707464\pi\) | ||||
0.975403 | + | 0.220431i | \(0.0707464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.57347 | −0.0645060 | ||||||||
\(596\) | 54.7554 | 2.24287 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.9504 | 0.447795 | ||||||||
\(599\) | 39.8977 | 1.63017 | 0.815087 | − | 0.579339i | \(-0.196689\pi\) | ||||
0.815087 | + | 0.579339i | \(0.196689\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.2220 | 1.02883 | 0.514413 | − | 0.857543i | \(-0.328010\pi\) | ||||
0.514413 | + | 0.857543i | \(0.328010\pi\) | |||||||
\(602\) | 2.55487 | 0.104129 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 71.1351 | 2.89445 | ||||||||
\(605\) | 1.89686 | 0.0771183 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.3949 | 1.55840 | 0.779201 | − | 0.626774i | \(-0.215625\pi\) | ||||
0.779201 | + | 0.626774i | \(0.215625\pi\) | |||||||
\(608\) | 0.411859 | 0.0167031 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.64354 | 0.188011 | ||||||||
\(611\) | −8.32053 | −0.336613 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.87322 | 0.0756586 | 0.0378293 | − | 0.999284i | \(-0.487956\pi\) | ||||
0.0378293 | + | 0.999284i | \(0.487956\pi\) | |||||||
\(614\) | 43.1580 | 1.74172 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.73096 | 0.190616 | ||||||||
\(617\) | 20.1184 | 0.809935 | 0.404967 | − | 0.914331i | \(-0.367283\pi\) | ||||
0.404967 | + | 0.914331i | \(0.367283\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.2869 | −0.534046 | −0.267023 | − | 0.963690i | \(-0.586040\pi\) | ||||
−0.267023 | + | 0.963690i | \(0.586040\pi\) | |||||||
\(620\) | −26.2198 | −1.05301 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.2423 | 0.450776 | ||||||||
\(623\) | 13.5882 | 0.544398 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.0250 | −0.640999 | ||||||||
\(626\) | −34.2887 | −1.37045 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 54.0306 | 2.15606 | ||||||||
\(629\) | 4.52310 | 0.180348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.52495 | 0.339373 | 0.169686 | − | 0.985498i | \(-0.445725\pi\) | ||||
0.169686 | + | 0.985498i | \(0.445725\pi\) | |||||||
\(632\) | −49.6578 | −1.97528 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −68.0055 | −2.70084 | ||||||||
\(635\) | −33.6854 | −1.33676 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.36453 | 0.331415 | ||||||||
\(638\) | −17.5525 | −0.694909 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 37.2810 | 1.47366 | ||||||||
\(641\) | −1.32404 | −0.0522966 | −0.0261483 | − | 0.999658i | \(-0.508324\pi\) | ||||
−0.0261483 | + | 0.999658i | \(0.508324\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.703946 | −0.0277609 | −0.0138805 | − | 0.999904i | \(-0.504418\pi\) | ||||
−0.0138805 | + | 0.999904i | \(0.504418\pi\) | |||||||
\(644\) | −12.5477 | −0.494449 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.2135 | −0.480535 | ||||||||
\(647\) | 6.76756 | 0.266060 | 0.133030 | − | 0.991112i | \(-0.457529\pi\) | ||||
0.133030 | + | 0.991112i | \(0.457529\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.72346 | 0.224665 | ||||||||
\(650\) | −4.73744 | −0.185818 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 59.3377 | 2.32384 | ||||||||
\(653\) | 24.1785 | 0.946176 | 0.473088 | − | 0.881015i | \(-0.343139\pi\) | ||||
0.473088 | + | 0.881015i | \(0.343139\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.3485 | 0.599716 | ||||||||
\(656\) | 24.1130 | 0.941453 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.3099 | 0.557860 | ||||||||
\(659\) | 31.2395 | 1.21692 | 0.608458 | − | 0.793586i | \(-0.291788\pi\) | ||||
0.608458 | + | 0.793586i | \(0.291788\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.3254 | 0.946150 | 0.473075 | − | 0.881022i | \(-0.343144\pi\) | ||||
0.473075 | + | 0.881022i | \(0.343144\pi\) | |||||||
\(662\) | −83.4316 | −3.24266 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.9041 | 0.811238 | ||||||||
\(665\) | −10.7298 | −0.416085 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.2347 | 0.899650 | ||||||||
\(668\) | −55.0181 | −2.12871 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 52.7711 | 2.03873 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.12355 | −0.236045 | −0.118023 | − | 0.993011i | \(-0.537656\pi\) | ||||
−0.118023 | + | 0.993011i | \(0.537656\pi\) | |||||||
\(674\) | −4.51294 | −0.173832 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −44.2979 | −1.70376 | ||||||||
\(677\) | 12.4601 | 0.478879 | 0.239440 | − | 0.970911i | \(-0.423036\pi\) | ||||
0.239440 | + | 0.970911i | \(0.423036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.43543 | 0.0934630 | ||||||||
\(680\) | −7.91505 | −0.303528 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.47487 | 0.324520 | ||||||||
\(683\) | 0.225362 | 0.00862325 | 0.00431162 | − | 0.999991i | \(-0.498628\pi\) | ||||
0.00431162 | + | 0.999991i | \(0.498628\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.67611 | −0.216873 | ||||||||
\(686\) | −31.0040 | −1.18374 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.25807 | 0.162337 | ||||||||
\(689\) | 2.84978 | 0.108568 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.8903 | −0.680578 | −0.340289 | − | 0.940321i | \(-0.610525\pi\) | ||||
−0.340289 | + | 0.940321i | \(0.610525\pi\) | |||||||
\(692\) | 49.8690 | 1.89573 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.65475 | −0.366489 | ||||||||
\(695\) | −21.9600 | −0.832992 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.21270 | 0.197445 | ||||||||
\(698\) | −24.9223 | −0.943323 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.42847 | 0.205177 | ||||||||
\(701\) | 33.9483 | 1.28221 | 0.641104 | − | 0.767454i | \(-0.278477\pi\) | ||||
0.641104 | + | 0.767454i | \(0.278477\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.8440 | 1.16330 | ||||||||
\(704\) | −8.08627 | −0.304763 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33.4660 | −1.25951 | ||||||||
\(707\) | −13.8475 | −0.520789 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8681 | 1.42217 | 0.711083 | − | 0.703108i | \(-0.248205\pi\) | ||||
0.711083 | + | 0.703108i | \(0.248205\pi\) | |||||||
\(710\) | 36.6063 | 1.37381 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 68.3528 | 2.56163 | ||||||||
\(713\) | −11.2184 | −0.420133 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.61842 | −0.0979233 | ||||||||
\(716\) | 75.9086 | 2.83684 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.37208 | −0.349763 | ||||||||
\(719\) | −12.9954 | −0.484647 | −0.242324 | − | 0.970195i | \(-0.577910\pi\) | ||||
−0.242324 | + | 0.970195i | \(0.577910\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.69601 | 0.286614 | ||||||||
\(722\) | −36.7743 | −1.36860 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.63654 | 0.0979862 | ||||||||
\(725\) | −10.0519 | −0.373319 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −41.5701 | −1.54175 | −0.770875 | − | 0.636987i | \(-0.780181\pi\) | ||||
−0.770875 | + | 0.636987i | \(0.780181\pi\) | |||||||
\(728\) | −6.53061 | −0.242040 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.84177 | −0.105179 | ||||||||
\(731\) | 0.920502 | 0.0340460 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.3844 | −1.19614 | −0.598072 | − | 0.801442i | \(-0.704066\pi\) | ||||
−0.598072 | + | 0.801442i | \(0.704066\pi\) | |||||||
\(734\) | −59.9821 | −2.21398 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.228813 | 0.00843415 | ||||||||
\(737\) | −11.3644 | −0.418614 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.9538 | 1.13865 | 0.569326 | − | 0.822112i | \(-0.307204\pi\) | ||||
0.569326 | + | 0.822112i | \(0.307204\pi\) | |||||||
\(740\) | 40.0498 | 1.47226 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.90115 | −0.179927 | ||||||||
\(743\) | 4.25715 | 0.156180 | 0.0780899 | − | 0.996946i | \(-0.475118\pi\) | ||||
0.0780899 | + | 0.996946i | \(0.475118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.0128 | 0.953035 | ||||||||
\(746\) | −54.6158 | −1.99963 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.41524 | 0.124874 | ||||||||
\(749\) | −11.8873 | −0.434352 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.95075 | 0.326618 | 0.163309 | − | 0.986575i | \(-0.447783\pi\) | ||||
0.163309 | + | 0.986575i | \(0.447783\pi\) | |||||||
\(752\) | 23.8496 | 0.869705 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.2294 | 0.882382 | ||||||||
\(755\) | 33.7943 | 1.22990 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.4763 | 0.671533 | 0.335767 | − | 0.941945i | \(-0.391005\pi\) | ||||
0.335767 | + | 0.941945i | \(0.391005\pi\) | |||||||
\(758\) | −29.6029 | −1.07523 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −53.9744 | −1.95786 | ||||||||
\(761\) | 19.7949 | 0.717566 | 0.358783 | − | 0.933421i | \(-0.383192\pi\) | ||||
0.358783 | + | 0.933421i | \(0.383192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.32103 | −0.265039 | ||||||||
\(764\) | 92.2876 | 3.33885 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 88.8957 | 3.21193 | ||||||||
\(767\) | −7.90065 | −0.285276 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.56813 | −0.0565482 | −0.0282741 | − | 0.999600i | \(-0.509001\pi\) | ||||
−0.0282741 | + | 0.999600i | \(0.509001\pi\) | |||||||
\(770\) | 4.50325 | 0.162286 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.79399 | 0.172539 | ||||||||
\(773\) | 20.2661 | 0.728921 | 0.364460 | − | 0.931219i | \(-0.381254\pi\) | ||||
0.364460 | + | 0.931219i | \(0.381254\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.85338 | 0.174339 | ||||||||
\(776\) | 12.2510 | 0.439784 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.85555 | 0.102376 | ||||||||
\(779\) | 35.5465 | 1.27359 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.88328 | −0.282086 | ||||||||
\(782\) | −6.78535 | −0.242644 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −23.9757 | −0.856275 | ||||||||
\(785\) | 25.6685 | 0.916147 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.6985 | 0.987346 | 0.493673 | − | 0.869648i | \(-0.335654\pi\) | ||||
0.493673 | + | 0.869648i | \(0.335654\pi\) | |||||||
\(788\) | −22.7423 | −0.810161 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −47.2677 | −1.68171 | ||||||||
\(791\) | −6.00395 | −0.213476 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.38040 | 0.0490193 | ||||||||
\(794\) | −20.9242 | −0.742571 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.7677 | −0.736091 | ||||||||
\(797\) | 11.7709 | 0.416945 | 0.208473 | − | 0.978028i | \(-0.433151\pi\) | ||||
0.208473 | + | 0.978028i | \(0.433151\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.15577 | 0.182398 | ||||||||
\(800\) | −0.0989905 | −0.00349984 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 83.9329 | 2.96378 | ||||||||
\(803\) | 0.611985 | 0.0215965 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.96107 | −0.210100 | ||||||||
\(806\) | −11.6987 | −0.412069 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −69.6573 | −2.45053 | ||||||||
\(809\) | −0.583252 | −0.0205061 | −0.0102530 | − | 0.999947i | \(-0.503264\pi\) | ||||
−0.0102530 | + | 0.999947i | \(0.503264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.2823 | 0.361062 | 0.180531 | − | 0.983569i | \(-0.442218\pi\) | ||||
0.180531 | + | 0.983569i | \(0.442218\pi\) | |||||||
\(812\) | −27.7636 | −0.974312 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.9451 | −0.453724 | ||||||||
\(815\) | 28.1897 | 0.987443 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.27710 | 0.219608 | ||||||||
\(818\) | −45.3065 | −1.58410 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 46.1558 | 1.61183 | ||||||||
\(821\) | −22.6306 | −0.789812 | −0.394906 | − | 0.918722i | \(-0.629223\pi\) | ||||
−0.394906 | + | 0.918722i | \(0.629223\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.1404 | 0.492905 | 0.246453 | − | 0.969155i | \(-0.420735\pi\) | ||||
0.246453 | + | 0.969155i | \(0.420735\pi\) | |||||||
\(824\) | 38.7134 | 1.34864 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.5878 | 0.472781 | ||||||||
\(827\) | 14.3417 | 0.498710 | 0.249355 | − | 0.968412i | \(-0.419781\pi\) | ||||
0.249355 | + | 0.968412i | \(0.419781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.1526 | 1.29036 | 0.645181 | − | 0.764030i | \(-0.276782\pi\) | ||||
0.645181 | + | 0.764030i | \(0.276782\pi\) | |||||||
\(830\) | 19.8980 | 0.690669 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 11.1623 | 0.386982 | ||||||||
\(833\) | −5.18303 | −0.179581 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.1376 | −0.904529 | ||||||||
\(836\) | 23.2893 | 0.805476 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −49.0038 | −1.69281 | ||||||||
\(839\) | 19.6392 | 0.678021 | 0.339011 | − | 0.940783i | \(-0.389908\pi\) | ||||
0.339011 | + | 0.940783i | \(0.389908\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.4101 | 0.772762 | ||||||||
\(842\) | −81.4199 | −2.80592 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −29.4745 | −1.01455 | ||||||||
\(845\) | −21.0447 | −0.723960 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.969789 | −0.0333223 | ||||||||
\(848\) | −8.16848 | −0.280507 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.93552 | 0.100688 | ||||||||
\(851\) | 17.1357 | 0.587405 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.3177 | −0.832622 | −0.416311 | − | 0.909222i | \(-0.636677\pi\) | ||||
−0.416311 | + | 0.909222i | \(0.636677\pi\) | |||||||
\(854\) | −2.37406 | −0.0812386 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −59.7969 | −2.04382 | ||||||||
\(857\) | 39.1805 | 1.33838 | 0.669190 | − | 0.743092i | \(-0.266641\pi\) | ||||
0.669190 | + | 0.743092i | \(0.266641\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.7150 | −1.45742 | −0.728709 | − | 0.684824i | \(-0.759879\pi\) | ||||
−0.728709 | + | 0.684824i | \(0.759879\pi\) | |||||||
\(860\) | 8.15058 | 0.277932 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 73.3878 | 2.49960 | ||||||||
\(863\) | −3.67478 | −0.125091 | −0.0625454 | − | 0.998042i | \(-0.519922\pi\) | ||||
−0.0625454 | + | 0.998042i | \(0.519922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.6914 | 0.805532 | ||||||||
\(866\) | 28.0165 | 0.952039 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.4051 | 0.455000 | ||||||||
\(869\) | 10.1792 | 0.345307 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.6874 | 0.531548 | ||||||||
\(872\) | −36.8271 | −1.24712 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −46.2708 | −1.56513 | ||||||||
\(875\) | 11.7767 | 0.398124 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.17385 | −0.208476 | −0.104238 | − | 0.994552i | \(-0.533240\pi\) | ||||
−0.104238 | + | 0.994552i | \(0.533240\pi\) | |||||||
\(878\) | −18.4824 | −0.623750 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.50532 | 0.253004 | ||||||||
\(881\) | 23.7564 | 0.800372 | 0.400186 | − | 0.916434i | \(-0.368945\pi\) | ||||
0.400186 | + | 0.916434i | \(0.368945\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.0631 | −1.61745 | −0.808727 | − | 0.588185i | \(-0.799843\pi\) | ||||
−0.808727 | + | 0.588185i | \(0.799843\pi\) | |||||||
\(884\) | −4.71439 | −0.158562 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.8926 | 0.500326 | ||||||||
\(887\) | −57.4994 | −1.93064 | −0.965320 | − | 0.261070i | \(-0.915925\pi\) | ||||
−0.965320 | + | 0.261070i | \(0.915925\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.2220 | 0.577608 | ||||||||
\(890\) | 65.0628 | 2.18091 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.0739 | 0.939985 | ||||||||
\(893\) | 35.1583 | 1.17653 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0621 | 1.20542 | ||||||||
\(896\) | −19.0603 | −0.636760 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.51910 | −0.117434 | ||||||||
\(899\) | −24.8224 | −0.827873 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.76585 | −0.0588290 | ||||||||
\(902\) | −14.9187 | −0.496738 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.2018 | −1.00450 | ||||||||
\(905\) | 1.25255 | 0.0416361 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.7430 | −1.08721 | −0.543607 | − | 0.839340i | \(-0.682942\pi\) | ||||
−0.543607 | + | 0.839340i | \(0.682942\pi\) | |||||||
\(908\) | −77.4651 | −2.57077 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.21628 | −0.206068 | ||||||||
\(911\) | 10.1712 | 0.336988 | 0.168494 | − | 0.985703i | \(-0.446110\pi\) | ||||
0.168494 | + | 0.985703i | \(0.446110\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.28509 | −0.141816 | ||||||||
\(914\) | 75.7908 | 2.50694 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.8164 | 1.21645 | ||||||||
\(917\) | −7.84708 | −0.259133 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.9136 | −0.887799 | −0.443900 | − | 0.896077i | \(-0.646405\pi\) | ||||
−0.443900 | + | 0.896077i | \(0.646405\pi\) | |||||||
\(920\) | −29.9861 | −0.988612 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −59.3629 | −1.95501 | ||||||||
\(923\) | 10.8821 | 0.358187 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.41337 | −0.243750 | ||||||||
\(926\) | 68.6086 | 2.25462 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.506282 | 0.0166195 | ||||||||
\(929\) | −29.6568 | −0.973007 | −0.486504 | − | 0.873679i | \(-0.661728\pi\) | ||||
−0.486504 | + | 0.873679i | \(0.661728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.3442 | −1.15836 | ||||||||
\(932\) | −80.6301 | −2.64113 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.6366 | −0.413481 | ||||||||
\(935\) | 1.62249 | 0.0530610 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.53343 | −0.148101 | −0.0740503 | − | 0.997255i | \(-0.523593\pi\) | ||||
−0.0740503 | + | 0.997255i | \(0.523593\pi\) | |||||||
\(938\) | −26.9798 | −0.880921 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 45.6517 | 1.48899 | ||||||||
\(941\) | −12.7808 | −0.416641 | −0.208320 | − | 0.978061i | \(-0.566800\pi\) | ||||
−0.208320 | + | 0.978061i | \(0.566800\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.7483 | 0.643092 | ||||||||
\(944\) | 22.6461 | 0.737067 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.63446 | −0.0856538 | ||||||||
\(947\) | 16.7702 | 0.544959 | 0.272480 | − | 0.962162i | \(-0.412156\pi\) | ||||
0.272480 | + | 0.962162i | \(0.412156\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.844782 | −0.0274228 | ||||||||
\(950\) | 20.0180 | 0.649468 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.04665 | 0.131153 | ||||||||
\(953\) | 46.2301 | 1.49754 | 0.748769 | − | 0.662831i | \(-0.230645\pi\) | ||||
0.748769 | + | 0.662831i | \(0.230645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 43.8433 | 1.41874 | ||||||||
\(956\) | −22.5087 | −0.727985 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.35179 | −0.0436745 | ||||||||
\(959\) | 2.90197 | 0.0937095 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0150 | −0.613387 | ||||||||
\(962\) | 17.8693 | 0.576130 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 68.4371 | 2.20421 | ||||||||
\(965\) | 2.27749 | 0.0733151 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.8990 | 1.18659 | 0.593296 | − | 0.804985i | \(-0.297827\pi\) | ||||
0.593296 | + | 0.804985i | \(0.297827\pi\) | |||||||
\(968\) | −4.87834 | −0.156796 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.6613 | 0.374422 | ||||||||
\(971\) | 4.65238 | 0.149302 | 0.0746510 | − | 0.997210i | \(-0.476216\pi\) | ||||
0.0746510 | + | 0.997210i | \(0.476216\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.2273 | 0.359931 | ||||||||
\(974\) | 70.2694 | 2.25158 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.95671 | −0.126651 | ||||||||
\(977\) | −25.0717 | −0.802113 | −0.401057 | − | 0.916053i | \(-0.631357\pi\) | ||||
−0.401057 | + | 0.916053i | \(0.631357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.0115 | −0.447808 | ||||||||
\(980\) | −45.8931 | −1.46600 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −48.4332 | −1.54556 | ||||||||
\(983\) | −30.2899 | −0.966098 | −0.483049 | − | 0.875593i | \(-0.660471\pi\) | ||||
−0.483049 | + | 0.875593i | \(0.660471\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.8042 | −0.344252 | ||||||||
\(986\) | −15.0136 | −0.478130 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −32.1484 | −1.02278 | ||||||||
\(989\) | 3.48731 | 0.110890 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.9628 | −0.951800 | −0.475900 | − | 0.879499i | \(-0.657878\pi\) | ||||
−0.475900 | + | 0.879499i | \(0.657878\pi\) | |||||||
\(992\) | −0.244448 | −0.00776125 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.7154 | −0.593615 | ||||||||
\(995\) | −9.86615 | −0.312778 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.0514 | 0.951739 | 0.475869 | − | 0.879516i | \(-0.342133\pi\) | ||||
0.475869 | + | 0.879516i | \(0.342133\pi\) | |||||||
\(998\) | −46.0543 | −1.45782 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.o.1.2 | yes | 25 | |
3.2 | odd | 2 | 6039.2.a.n.1.24 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.n.1.24 | ✓ | 25 | 3.2 | odd | 2 | ||
6039.2.a.o.1.2 | yes | 25 | 1.1 | even | 1 | trivial |