Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, 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("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.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: | \(45.7782354788\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.746052.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 7x^{3} + 8x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.00852\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00852 | 1.42024 | 0.710121 | − | 0.704080i | \(-0.248640\pi\) | ||||
0.710121 | + | 0.704080i | \(0.248640\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.03417 | 1.01709 | ||||||||
\(5\) | −0.905722 | −0.405051 | −0.202526 | − | 0.979277i | \(-0.564915\pi\) | ||||
−0.202526 | + | 0.979277i | \(0.564915\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.0686323 | 0.0242652 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.81916 | −0.575270 | ||||||||
\(11\) | −0.716361 | −0.215991 | −0.107996 | − | 0.994151i | \(-0.534443\pi\) | ||||
−0.107996 | + | 0.994151i | \(0.534443\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.93049 | −0.982623 | ||||||||
\(17\) | −2.35227 | −0.570510 | −0.285255 | − | 0.958452i | \(-0.592078\pi\) | ||||
−0.285255 | + | 0.958452i | \(0.592078\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.63591 | 1.52238 | 0.761191 | − | 0.648528i | \(-0.224615\pi\) | ||||
0.761191 | + | 0.648528i | \(0.224615\pi\) | |||||||
\(20\) | −1.84239 | −0.411971 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.43883 | −0.306759 | ||||||||
\(23\) | −3.75906 | −0.783817 | −0.391909 | − | 0.920004i | \(-0.628185\pi\) | ||||
−0.391909 | + | 0.920004i | \(0.628185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.17967 | −0.835934 | ||||||||
\(26\) | 2.00852 | 0.393904 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.25799 | −0.604994 | −0.302497 | − | 0.953150i | \(-0.597820\pi\) | ||||
−0.302497 | + | 0.953150i | \(0.597820\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.57050 | 0.282070 | 0.141035 | − | 0.990005i | \(-0.454957\pi\) | ||||
0.141035 | + | 0.990005i | \(0.454957\pi\) | |||||||
\(32\) | −8.03175 | −1.41983 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.72459 | −0.810261 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.20883 | 0.856326 | 0.428163 | − | 0.903702i | \(-0.359161\pi\) | ||||
0.428163 | + | 0.903702i | \(0.359161\pi\) | |||||||
\(38\) | 13.3284 | 2.16215 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0621618 | −0.00982864 | ||||||||
\(41\) | −4.92168 | −0.768637 | −0.384318 | − | 0.923201i | \(-0.625563\pi\) | ||||
−0.384318 | + | 0.923201i | \(0.625563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.43766 | −1.43923 | −0.719615 | − | 0.694373i | \(-0.755682\pi\) | ||||
−0.719615 | + | 0.694373i | \(0.755682\pi\) | |||||||
\(44\) | −1.45720 | −0.219681 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.55016 | −1.11321 | ||||||||
\(47\) | 8.31986 | 1.21358 | 0.606788 | − | 0.794863i | \(-0.292458\pi\) | ||||
0.606788 | + | 0.794863i | \(0.292458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −8.39497 | −1.18723 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.03417 | 0.282089 | ||||||||
\(53\) | −14.0833 | −1.93449 | −0.967243 | − | 0.253854i | \(-0.918302\pi\) | ||||
−0.967243 | + | 0.253854i | \(0.918302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.648824 | 0.0874874 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.54376 | −0.859238 | ||||||||
\(59\) | −0.716361 | −0.0932623 | −0.0466311 | − | 0.998912i | \(-0.514849\pi\) | ||||
−0.0466311 | + | 0.998912i | \(0.514849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.6527 | −1.49197 | −0.745986 | − | 0.665962i | \(-0.768021\pi\) | ||||
−0.745986 | + | 0.665962i | \(0.768021\pi\) | |||||||
\(62\) | 3.15439 | 0.400607 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.27099 | −1.03387 | ||||||||
\(65\) | −0.905722 | −0.112341 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.39174 | 1.14738 | 0.573692 | − | 0.819071i | \(-0.305511\pi\) | ||||
0.573692 | + | 0.819071i | \(0.305511\pi\) | |||||||
\(68\) | −4.78492 | −0.580257 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.9914 | −1.30444 | −0.652220 | − | 0.758030i | \(-0.726162\pi\) | ||||
−0.652220 | + | 0.758030i | \(0.726162\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.47300 | −0.406484 | −0.203242 | − | 0.979129i | \(-0.565148\pi\) | ||||
−0.203242 | + | 0.979129i | \(0.565148\pi\) | |||||||
\(74\) | 10.4621 | 1.21619 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.4986 | 1.54839 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.0082 | 1.46353 | 0.731766 | − | 0.681556i | \(-0.238696\pi\) | ||||
0.731766 | + | 0.681556i | \(0.238696\pi\) | |||||||
\(80\) | 3.55993 | 0.398012 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.88531 | −1.09165 | ||||||||
\(83\) | −3.54083 | −0.388656 | −0.194328 | − | 0.980937i | \(-0.562253\pi\) | ||||
−0.194328 | + | 0.980937i | \(0.562253\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.13050 | 0.231085 | ||||||||
\(86\) | −18.9558 | −2.04405 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0491655 | −0.00524106 | ||||||||
\(89\) | −12.0501 | −1.27730 | −0.638651 | − | 0.769496i | \(-0.720507\pi\) | ||||
−0.638651 | + | 0.769496i | \(0.720507\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.64656 | −0.797209 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 16.7106 | 1.72357 | ||||||||
\(95\) | −6.01029 | −0.616642 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.43766 | 0.755180 | 0.377590 | − | 0.925973i | \(-0.376753\pi\) | ||||
0.377590 | + | 0.925973i | \(0.376753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.50216 | −0.850216 | ||||||||
\(101\) | 1.19905 | 0.119310 | 0.0596551 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596551 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4123 | −1.42009 | −0.710043 | − | 0.704158i | \(-0.751325\pi\) | ||||
−0.710043 | + | 0.704158i | \(0.751325\pi\) | |||||||
\(104\) | 0.0686323 | 0.00672995 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28.2866 | −2.74744 | ||||||||
\(107\) | −13.5932 | −1.31411 | −0.657053 | − | 0.753845i | \(-0.728197\pi\) | ||||
−0.657053 | + | 0.753845i | \(0.728197\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.7248 | −1.31460 | −0.657299 | − | 0.753630i | \(-0.728301\pi\) | ||||
−0.657299 | + | 0.753630i | \(0.728301\pi\) | |||||||
\(110\) | 1.30318 | 0.124253 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.25799 | 0.306486 | 0.153243 | − | 0.988189i | \(-0.451028\pi\) | ||||
0.153243 | + | 0.988189i | \(0.451028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.40466 | 0.317486 | ||||||||
\(116\) | −6.62731 | −0.615331 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.43883 | −0.132455 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4868 | −0.953348 | ||||||||
\(122\) | −23.4047 | −2.11896 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.19466 | 0.286889 | ||||||||
\(125\) | 8.31422 | 0.743647 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.950834 | −0.0843729 | −0.0421865 | − | 0.999110i | \(-0.513432\pi\) | ||||
−0.0421865 | + | 0.999110i | \(0.513432\pi\) | |||||||
\(128\) | −0.548979 | −0.0485233 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.81916 | −0.159551 | ||||||||
\(131\) | 18.8196 | 1.64428 | 0.822138 | − | 0.569288i | \(-0.192781\pi\) | ||||
0.822138 | + | 0.569288i | \(0.192781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 18.8635 | 1.62956 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.161442 | −0.0138435 | ||||||||
\(137\) | −6.18179 | −0.528146 | −0.264073 | − | 0.964503i | \(-0.585066\pi\) | ||||
−0.264073 | + | 0.964503i | \(0.585066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −22.0765 | −1.85262 | ||||||||
\(143\) | −0.716361 | −0.0599051 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.95083 | 0.245053 | ||||||||
\(146\) | −6.97560 | −0.577305 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.5956 | 0.870956 | ||||||||
\(149\) | 21.0771 | 1.72670 | 0.863351 | − | 0.504604i | \(-0.168361\pi\) | ||||
0.863351 | + | 0.504604i | \(0.168361\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.7234 | −1.27955 | −0.639777 | − | 0.768560i | \(-0.720973\pi\) | ||||
−0.639777 | + | 0.768560i | \(0.720973\pi\) | |||||||
\(152\) | 0.455438 | 0.0369409 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.42244 | −0.114253 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.78499 | −0.621310 | −0.310655 | − | 0.950523i | \(-0.600548\pi\) | ||||
−0.310655 | + | 0.950523i | \(0.600548\pi\) | |||||||
\(158\) | 26.1272 | 2.07857 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.27453 | 0.575102 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.68991 | 0.132364 | 0.0661820 | − | 0.997808i | \(-0.478918\pi\) | ||||
0.0661820 | + | 0.997808i | \(0.478918\pi\) | |||||||
\(164\) | −10.0115 | −0.781769 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.11184 | −0.551986 | ||||||||
\(167\) | 21.8667 | 1.69210 | 0.846049 | − | 0.533105i | \(-0.178975\pi\) | ||||
0.846049 | + | 0.533105i | \(0.178975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.27917 | 0.328197 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −19.1978 | −1.46382 | ||||||||
\(173\) | −5.84122 | −0.444100 | −0.222050 | − | 0.975035i | \(-0.571275\pi\) | ||||
−0.222050 | + | 0.975035i | \(0.571275\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.81565 | 0.212238 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −24.2028 | −1.81408 | ||||||||
\(179\) | −2.53427 | −0.189421 | −0.0947103 | − | 0.995505i | \(-0.530192\pi\) | ||||
−0.0947103 | + | 0.995505i | \(0.530192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.7248 | −0.797169 | −0.398585 | − | 0.917132i | \(-0.630498\pi\) | ||||
−0.398585 | + | 0.917132i | \(0.630498\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.257993 | −0.0190195 | ||||||||
\(185\) | −4.71775 | −0.346856 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.68508 | 0.123225 | ||||||||
\(188\) | 16.9240 | 1.23431 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0718 | −0.875781 | ||||||||
\(191\) | 1.67861 | 0.121460 | 0.0607298 | − | 0.998154i | \(-0.480657\pi\) | ||||
0.0607298 | + | 0.998154i | \(0.480657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.44816 | −0.464148 | −0.232074 | − | 0.972698i | \(-0.574551\pi\) | ||||
−0.232074 | + | 0.972698i | \(0.574551\pi\) | |||||||
\(194\) | 14.9387 | 1.07254 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.87251 | −0.133411 | −0.0667054 | − | 0.997773i | \(-0.521249\pi\) | ||||
−0.0667054 | + | 0.997773i | \(0.521249\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3967 | −0.807888 | −0.403944 | − | 0.914784i | \(-0.632361\pi\) | ||||
−0.403944 | + | 0.914784i | \(0.632361\pi\) | |||||||
\(200\) | −0.286860 | −0.0202841 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.40833 | 0.169449 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.45767 | 0.311337 | ||||||||
\(206\) | −28.9475 | −2.01687 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.93049 | −0.272531 | ||||||||
\(209\) | −4.75371 | −0.328821 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.53599 | 0.518799 | 0.259400 | − | 0.965770i | \(-0.416475\pi\) | ||||
0.259400 | + | 0.965770i | \(0.416475\pi\) | |||||||
\(212\) | −28.6478 | −1.96754 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −27.3023 | −1.86635 | ||||||||
\(215\) | 8.54789 | 0.582962 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −27.5666 | −1.86705 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.31982 | 0.0889821 | ||||||||
\(221\) | −2.35227 | −0.158231 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6349 | 1.18092 | 0.590459 | − | 0.807067i | \(-0.298947\pi\) | ||||
0.590459 | + | 0.807067i | \(0.298947\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.54376 | 0.435284 | ||||||||
\(227\) | 5.32904 | 0.353701 | 0.176851 | − | 0.984238i | \(-0.443409\pi\) | ||||
0.176851 | + | 0.984238i | \(0.443409\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.51900 | −0.562951 | −0.281476 | − | 0.959568i | \(-0.590824\pi\) | ||||
−0.281476 | + | 0.959568i | \(0.590824\pi\) | |||||||
\(230\) | 6.83834 | 0.450907 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.223604 | −0.0146803 | ||||||||
\(233\) | −4.75371 | −0.311426 | −0.155713 | − | 0.987802i | \(-0.549767\pi\) | ||||
−0.155713 | + | 0.987802i | \(0.549767\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.53548 | −0.491561 | ||||||||
\(236\) | −1.45720 | −0.0948557 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.8314 | −0.959365 | −0.479682 | − | 0.877442i | \(-0.659248\pi\) | ||||
−0.479682 | + | 0.877442i | \(0.659248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.12131 | −0.394308 | −0.197154 | − | 0.980373i | \(-0.563170\pi\) | ||||
−0.197154 | + | 0.980373i | \(0.563170\pi\) | |||||||
\(242\) | −21.0630 | −1.35398 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −23.7035 | −1.51746 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.63591 | 0.422233 | ||||||||
\(248\) | 0.107787 | 0.00684448 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.6993 | 1.05616 | ||||||||
\(251\) | 13.9708 | 0.881832 | 0.440916 | − | 0.897548i | \(-0.354654\pi\) | ||||
0.440916 | + | 0.897548i | \(0.354654\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.69284 | 0.169298 | ||||||||
\(254\) | −1.90977 | −0.119830 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.4393 | 0.964959 | ||||||||
\(257\) | −17.2651 | −1.07696 | −0.538482 | − | 0.842637i | \(-0.681002\pi\) | ||||
−0.538482 | + | 0.842637i | \(0.681002\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.84239 | −0.114260 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 37.7996 | 2.33527 | ||||||||
\(263\) | 2.60672 | 0.160737 | 0.0803687 | − | 0.996765i | \(-0.474390\pi\) | ||||
0.0803687 | + | 0.996765i | \(0.474390\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.7555 | 0.783565 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.1044 | 1.16699 | ||||||||
\(269\) | 14.4895 | 0.883443 | 0.441721 | − | 0.897152i | \(-0.354368\pi\) | ||||
0.441721 | + | 0.897152i | \(0.354368\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.63591 | −0.524594 | −0.262297 | − | 0.964987i | \(-0.584480\pi\) | ||||
−0.262297 | + | 0.964987i | \(0.584480\pi\) | |||||||
\(272\) | 9.24558 | 0.560596 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.4163 | −0.750095 | ||||||||
\(275\) | 2.99415 | 0.180554 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.2270 | 0.734647 | 0.367324 | − | 0.930093i | \(-0.380274\pi\) | ||||
0.367324 | + | 0.930093i | \(0.380274\pi\) | |||||||
\(278\) | −8.03410 | −0.481853 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1822 | 1.44259 | 0.721293 | − | 0.692630i | \(-0.243548\pi\) | ||||
0.721293 | + | 0.692630i | \(0.243548\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.7683 | −1.82899 | −0.914493 | − | 0.404601i | \(-0.867410\pi\) | ||||
−0.914493 | + | 0.404601i | \(0.867410\pi\) | |||||||
\(284\) | −22.3584 | −1.32673 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.43883 | −0.0850797 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4668 | −0.674519 | ||||||||
\(290\) | 5.92682 | 0.348035 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.06467 | −0.413429 | ||||||||
\(293\) | 31.8295 | 1.85950 | 0.929749 | − | 0.368193i | \(-0.120024\pi\) | ||||
0.929749 | + | 0.368193i | \(0.120024\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.648824 | 0.0377760 | ||||||||
\(296\) | 0.357494 | 0.0207789 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 42.3338 | 2.45233 | ||||||||
\(299\) | −3.75906 | −0.217392 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −31.5809 | −1.81728 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −26.0824 | −1.49593 | ||||||||
\(305\) | 10.5541 | 0.604324 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.7884 | 1.64304 | 0.821520 | − | 0.570179i | \(-0.193126\pi\) | ||||
0.821520 | + | 0.570179i | \(0.193126\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.85700 | −0.162266 | ||||||||
\(311\) | −5.51862 | −0.312932 | −0.156466 | − | 0.987683i | \(-0.550010\pi\) | ||||
−0.156466 | + | 0.987683i | \(0.550010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.84799 | −0.274024 | −0.137012 | − | 0.990569i | \(-0.543750\pi\) | ||||
−0.137012 | + | 0.990569i | \(0.543750\pi\) | |||||||
\(314\) | −15.6363 | −0.882410 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.4608 | 1.48854 | ||||||||
\(317\) | 7.65511 | 0.429954 | 0.214977 | − | 0.976619i | \(-0.431032\pi\) | ||||
0.214977 | + | 0.976619i | \(0.431032\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.33390 | 0.130673 | ||||||||
\(320\) | 7.49121 | 0.418772 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.6095 | −0.868534 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.17967 | −0.231846 | ||||||||
\(326\) | 3.39423 | 0.187989 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.337786 | −0.0186511 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3432 | 0.623477 | 0.311739 | − | 0.950168i | \(-0.399089\pi\) | ||||
0.311739 | + | 0.950168i | \(0.399089\pi\) | |||||||
\(332\) | −7.20265 | −0.395297 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 43.9199 | 2.40319 | ||||||||
\(335\) | −8.50631 | −0.464749 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.74149 | 0.0948649 | 0.0474324 | − | 0.998874i | \(-0.484896\pi\) | ||||
0.0474324 | + | 0.998874i | \(0.484896\pi\) | |||||||
\(338\) | 2.00852 | 0.109249 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.33381 | 0.235034 | ||||||||
\(341\) | −1.12504 | −0.0609246 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.647729 | −0.0349232 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.7322 | −0.630729 | ||||||||
\(347\) | −21.0503 | −1.13004 | −0.565019 | − | 0.825078i | \(-0.691131\pi\) | ||||
−0.565019 | + | 0.825078i | \(0.691131\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.35601 | −0.447287 | −0.223643 | − | 0.974671i | \(-0.571795\pi\) | ||||
−0.223643 | + | 0.974671i | \(0.571795\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.75364 | 0.306670 | ||||||||
\(353\) | 8.53355 | 0.454195 | 0.227097 | − | 0.973872i | \(-0.427076\pi\) | ||||
0.227097 | + | 0.973872i | \(0.427076\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.95515 | 0.528365 | ||||||||
\(356\) | −24.5119 | −1.29913 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.09015 | −0.269023 | ||||||||
\(359\) | 16.1713 | 0.853488 | 0.426744 | − | 0.904372i | \(-0.359661\pi\) | ||||
0.426744 | + | 0.904372i | \(0.359661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.0353 | 1.31765 | ||||||||
\(362\) | −21.5410 | −1.13217 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.14557 | 0.164647 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.1540 | 1.46963 | 0.734813 | − | 0.678269i | \(-0.237270\pi\) | ||||
0.734813 | + | 0.678269i | \(0.237270\pi\) | |||||||
\(368\) | 14.7749 | 0.770197 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.47571 | −0.492619 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.5037 | −1.47586 | −0.737932 | − | 0.674875i | \(-0.764197\pi\) | ||||
−0.737932 | + | 0.674875i | \(0.764197\pi\) | |||||||
\(374\) | 3.38452 | 0.175009 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.571012 | 0.0294477 | ||||||||
\(377\) | −3.25799 | −0.167795 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.26263 | −0.373056 | −0.186528 | − | 0.982450i | \(-0.559724\pi\) | ||||
−0.186528 | + | 0.982450i | \(0.559724\pi\) | |||||||
\(380\) | −12.2259 | −0.627178 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.37152 | 0.172502 | ||||||||
\(383\) | −12.9325 | −0.660822 | −0.330411 | − | 0.943837i | \(-0.607187\pi\) | ||||
−0.330411 | + | 0.943837i | \(0.607187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.9513 | −0.659203 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.1295 | 0.768083 | ||||||||
\(389\) | 21.1357 | 1.07162 | 0.535811 | − | 0.844338i | \(-0.320006\pi\) | ||||
0.535811 | + | 0.844338i | \(0.320006\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.84232 | 0.447175 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.76098 | −0.189476 | ||||||||
\(395\) | −11.7818 | −0.592805 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.2073 | 0.963988 | 0.481994 | − | 0.876175i | \(-0.339913\pi\) | ||||
0.481994 | + | 0.876175i | \(0.339913\pi\) | |||||||
\(398\) | −22.8905 | −1.14740 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.4282 | 0.821408 | ||||||||
\(401\) | −16.6692 | −0.832420 | −0.416210 | − | 0.909268i | \(-0.636642\pi\) | ||||
−0.416210 | + | 0.909268i | \(0.636642\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.57050 | 0.0782321 | ||||||||
\(404\) | 2.43908 | 0.121349 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.73140 | −0.184959 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.3483 | 0.610585 | 0.305293 | − | 0.952259i | \(-0.401246\pi\) | ||||
0.305293 | + | 0.952259i | \(0.401246\pi\) | |||||||
\(410\) | 8.95333 | 0.442174 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.3171 | −1.44435 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.20700 | 0.157426 | ||||||||
\(416\) | −8.03175 | −0.393789 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.54794 | −0.467005 | ||||||||
\(419\) | −4.35934 | −0.212968 | −0.106484 | − | 0.994314i | \(-0.533959\pi\) | ||||
−0.106484 | + | 0.994314i | \(0.533959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | 15.1362 | 0.736820 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.966567 | −0.0469407 | ||||||||
\(425\) | 9.83171 | 0.476908 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −27.6509 | −1.33656 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.1687 | 0.827946 | ||||||||
\(431\) | 23.3626 | 1.12533 | 0.562667 | − | 0.826683i | \(-0.309775\pi\) | ||||
0.562667 | + | 0.826683i | \(0.309775\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.71285 | −0.130371 | −0.0651856 | − | 0.997873i | \(-0.520764\pi\) | ||||
−0.0651856 | + | 0.997873i | \(0.520764\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −27.9186 | −1.33706 | ||||||||
\(437\) | −24.9448 | −1.19327 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.83519 | −0.421681 | −0.210840 | − | 0.977521i | \(-0.567620\pi\) | ||||
−0.210840 | + | 0.977521i | \(0.567620\pi\) | |||||||
\(440\) | 0.0445303 | 0.00212290 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.72459 | −0.224726 | ||||||||
\(443\) | 2.90558 | 0.138048 | 0.0690240 | − | 0.997615i | \(-0.478011\pi\) | ||||
0.0690240 | + | 0.997615i | \(0.478011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.9140 | 0.517373 | ||||||||
\(446\) | 35.4201 | 1.67719 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.2777 | 0.720998 | 0.360499 | − | 0.932760i | \(-0.382606\pi\) | ||||
0.360499 | + | 0.932760i | \(0.382606\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.52570 | 0.166019 | ||||||||
\(452\) | 6.62731 | 0.311723 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10.7035 | 0.502341 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.6600 | 1.10677 | 0.553384 | − | 0.832926i | \(-0.313336\pi\) | ||||
0.553384 | + | 0.832926i | \(0.313336\pi\) | |||||||
\(458\) | −17.1106 | −0.799527 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.92566 | 0.322910 | ||||||||
\(461\) | 26.6170 | 1.23968 | 0.619839 | − | 0.784729i | \(-0.287198\pi\) | ||||
0.619839 | + | 0.784729i | \(0.287198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.44250 | −0.0670385 | −0.0335193 | − | 0.999438i | \(-0.510672\pi\) | ||||
−0.0335193 | + | 0.999438i | \(0.510672\pi\) | |||||||
\(464\) | 12.8055 | 0.594481 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.54794 | −0.442300 | ||||||||
\(467\) | 8.38959 | 0.388224 | 0.194112 | − | 0.980979i | \(-0.437817\pi\) | ||||
0.194112 | + | 0.980979i | \(0.437817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −15.1352 | −0.698135 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.0491655 | −0.00226303 | ||||||||
\(473\) | 6.76077 | 0.310861 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.7359 | −1.27261 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −29.7893 | −1.36253 | ||||||||
\(479\) | −12.6122 | −0.576265 | −0.288132 | − | 0.957591i | \(-0.593034\pi\) | ||||
−0.288132 | + | 0.957591i | \(0.593034\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.20883 | 0.237502 | ||||||||
\(482\) | −12.2948 | −0.560013 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.3320 | −0.969636 | ||||||||
\(485\) | −6.73645 | −0.305886 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.5680 | 0.977341 | 0.488671 | − | 0.872468i | \(-0.337482\pi\) | ||||
0.488671 | + | 0.872468i | \(0.337482\pi\) | |||||||
\(488\) | −0.799750 | −0.0362030 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.2347 | −1.77064 | −0.885318 | − | 0.464987i | \(-0.846059\pi\) | ||||
−0.885318 | + | 0.464987i | \(0.846059\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.66368 | 0.345155 | ||||||||
\(494\) | 13.3284 | 0.599673 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.17283 | −0.277168 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.16814 | 0.410422 | 0.205211 | − | 0.978718i | \(-0.434212\pi\) | ||||
0.205211 | + | 0.978718i | \(0.434212\pi\) | |||||||
\(500\) | 16.9125 | 0.756352 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 28.0608 | 1.25241 | ||||||||
\(503\) | −24.9370 | −1.11188 | −0.555942 | − | 0.831221i | \(-0.687642\pi\) | ||||
−0.555942 | + | 0.831221i | \(0.687642\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.08601 | −0.0483267 | ||||||||
\(506\) | 5.40864 | 0.240443 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.93416 | −0.0858144 | ||||||||
\(509\) | −5.89807 | −0.261428 | −0.130714 | − | 0.991420i | \(-0.541727\pi\) | ||||
−0.130714 | + | 0.991420i | \(0.541727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 32.1083 | 1.41900 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −34.6773 | −1.52955 | ||||||||
\(515\) | 13.0535 | 0.575208 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.96003 | −0.262122 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0621618 | −0.00272597 | ||||||||
\(521\) | 37.1895 | 1.62930 | 0.814652 | − | 0.579950i | \(-0.196928\pi\) | ||||
0.814652 | + | 0.579950i | \(0.196928\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.09080 | −0.222605 | −0.111303 | − | 0.993787i | \(-0.535502\pi\) | ||||
−0.111303 | + | 0.993787i | \(0.535502\pi\) | |||||||
\(524\) | 38.2823 | 1.67237 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.23567 | 0.228286 | ||||||||
\(527\) | −3.69424 | −0.160924 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.86950 | −0.385630 | ||||||||
\(530\) | 25.6198 | 1.11285 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.92168 | −0.213181 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.3117 | 0.532280 | ||||||||
\(536\) | 0.644577 | 0.0278415 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.1026 | 1.25470 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.766850 | −0.0329694 | −0.0164847 | − | 0.999864i | \(-0.505247\pi\) | ||||
−0.0164847 | + | 0.999864i | \(0.505247\pi\) | |||||||
\(542\) | −17.3454 | −0.745050 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.8929 | 0.810025 | ||||||||
\(545\) | 12.4309 | 0.532480 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.1428 | 0.604702 | 0.302351 | − | 0.953197i | \(-0.402229\pi\) | ||||
0.302351 | + | 0.953197i | \(0.402229\pi\) | |||||||
\(548\) | −12.5748 | −0.537170 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.01383 | 0.256430 | ||||||||
\(551\) | −21.6197 | −0.921032 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.5582 | 1.04338 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.13668 | −0.345072 | ||||||||
\(557\) | 24.8627 | 1.05347 | 0.526733 | − | 0.850031i | \(-0.323417\pi\) | ||||
0.526733 | + | 0.850031i | \(0.323417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.43766 | −0.399171 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 48.5705 | 2.04882 | ||||||||
\(563\) | −44.0094 | −1.85478 | −0.927388 | − | 0.374101i | \(-0.877951\pi\) | ||||
−0.927388 | + | 0.374101i | \(0.877951\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.95083 | −0.124143 | ||||||||
\(566\) | −61.7989 | −2.59760 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.754366 | −0.0316525 | ||||||||
\(569\) | 33.2616 | 1.39440 | 0.697199 | − | 0.716877i | \(-0.254429\pi\) | ||||
0.697199 | + | 0.716877i | \(0.254429\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.3540 | −0.516998 | −0.258499 | − | 0.966011i | \(-0.583228\pi\) | ||||
−0.258499 | + | 0.966011i | \(0.583228\pi\) | |||||||
\(572\) | −1.45720 | −0.0609286 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.7116 | 0.655219 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.9659 | −1.08097 | −0.540486 | − | 0.841353i | \(-0.681760\pi\) | ||||
−0.540486 | + | 0.841353i | \(0.681760\pi\) | |||||||
\(578\) | −23.0314 | −0.957979 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.00250 | 0.249240 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0887 | 0.417831 | ||||||||
\(584\) | −0.238360 | −0.00986341 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 63.9303 | 2.64094 | ||||||||
\(587\) | 23.9747 | 0.989543 | 0.494771 | − | 0.869023i | \(-0.335252\pi\) | ||||
0.494771 | + | 0.869023i | \(0.335252\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.4217 | 0.429418 | ||||||||
\(590\) | 1.30318 | 0.0536510 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.4733 | −0.841445 | ||||||||
\(593\) | −47.0480 | −1.93203 | −0.966015 | − | 0.258484i | \(-0.916777\pi\) | ||||
−0.966015 | + | 0.258484i | \(0.916777\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 42.8744 | 1.75620 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.55016 | −0.308749 | ||||||||
\(599\) | −20.1736 | −0.824271 | −0.412135 | − | 0.911123i | \(-0.635217\pi\) | ||||
−0.412135 | + | 0.911123i | \(0.635217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.5773 | 1.20648 | 0.603242 | − | 0.797558i | \(-0.293875\pi\) | ||||
0.603242 | + | 0.797558i | \(0.293875\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −31.9841 | −1.30142 | ||||||||
\(605\) | 9.49815 | 0.386155 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.4420 | −0.626771 | −0.313385 | − | 0.949626i | \(-0.601463\pi\) | ||||
−0.313385 | + | 0.949626i | \(0.601463\pi\) | |||||||
\(608\) | −53.2980 | −2.16152 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21.1981 | 0.858287 | ||||||||
\(611\) | 8.31986 | 0.336586 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.99485 | 0.0805711 | 0.0402855 | − | 0.999188i | \(-0.487173\pi\) | ||||
0.0402855 | + | 0.999188i | \(0.487173\pi\) | |||||||
\(614\) | 57.8222 | 2.33351 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.85584 | 0.114972 | 0.0574858 | − | 0.998346i | \(-0.481692\pi\) | ||||
0.0574858 | + | 0.998346i | \(0.481692\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.9823 | 1.28548 | 0.642738 | − | 0.766086i | \(-0.277798\pi\) | ||||
0.642738 | + | 0.766086i | \(0.277798\pi\) | |||||||
\(620\) | −2.89348 | −0.116205 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.0843 | −0.444440 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.3680 | 0.534719 | ||||||||
\(626\) | −9.73730 | −0.389181 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.8360 | −0.631925 | ||||||||
\(629\) | −12.2526 | −0.488542 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.1115 | 1.27834 | 0.639169 | − | 0.769066i | \(-0.279278\pi\) | ||||
0.639169 | + | 0.769066i | \(0.279278\pi\) | |||||||
\(632\) | 0.892781 | 0.0355129 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.3755 | 0.610638 | ||||||||
\(635\) | 0.861191 | 0.0341753 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.68769 | 0.185588 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.497222 | 0.0196544 | ||||||||
\(641\) | −33.0248 | −1.30440 | −0.652200 | − | 0.758047i | \(-0.726154\pi\) | ||||
−0.652200 | + | 0.758047i | \(0.726154\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.7942 | 0.622863 | 0.311432 | − | 0.950269i | \(-0.399192\pi\) | ||||
0.311432 | + | 0.950269i | \(0.399192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.3520 | −1.23353 | ||||||||
\(647\) | 4.64072 | 0.182445 | 0.0912227 | − | 0.995831i | \(-0.470922\pi\) | ||||
0.0912227 | + | 0.995831i | \(0.470922\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.513173 | 0.0201438 | ||||||||
\(650\) | −8.39497 | −0.329278 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.43757 | 0.134626 | ||||||||
\(653\) | −26.8285 | −1.04988 | −0.524941 | − | 0.851139i | \(-0.675913\pi\) | ||||
−0.524941 | + | 0.851139i | \(0.675913\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.0453 | −0.666016 | ||||||||
\(656\) | 19.3446 | 0.755280 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.9889 | 1.67461 | 0.837306 | − | 0.546735i | \(-0.184129\pi\) | ||||
0.837306 | + | 0.546735i | \(0.184129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.4698 | −1.14624 | −0.573122 | − | 0.819470i | \(-0.694268\pi\) | ||||
−0.573122 | + | 0.819470i | \(0.694268\pi\) | |||||||
\(662\) | 22.7830 | 0.885488 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.243015 | −0.00943082 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.2470 | 0.474205 | ||||||||
\(668\) | 44.4806 | 1.72101 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17.0851 | −0.660056 | ||||||||
\(671\) | 8.34752 | 0.322252 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20.1702 | −0.777504 | −0.388752 | − | 0.921342i | \(-0.627094\pi\) | ||||
−0.388752 | + | 0.921342i | \(0.627094\pi\) | |||||||
\(674\) | 3.49782 | 0.134731 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.03417 | 0.0782373 | ||||||||
\(677\) | 6.20481 | 0.238470 | 0.119235 | − | 0.992866i | \(-0.461956\pi\) | ||||
0.119235 | + | 0.992866i | \(0.461956\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.146221 | 0.00560733 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.25968 | −0.0865276 | ||||||||
\(683\) | 1.76952 | 0.0677087 | 0.0338543 | − | 0.999427i | \(-0.489222\pi\) | ||||
0.0338543 | + | 0.999427i | \(0.489222\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.59899 | 0.213926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 37.0946 | 1.41422 | ||||||||
\(689\) | −14.0833 | −0.536530 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.9317 | 1.70928 | 0.854641 | − | 0.519219i | \(-0.173777\pi\) | ||||
0.854641 | + | 0.519219i | \(0.173777\pi\) | |||||||
\(692\) | −11.8820 | −0.451688 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −42.2800 | −1.60493 | ||||||||
\(695\) | 3.62289 | 0.137424 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.5771 | 0.438515 | ||||||||
\(698\) | −16.7832 | −0.635255 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.5707 | −1.45679 | −0.728397 | − | 0.685156i | \(-0.759734\pi\) | ||||
−0.728397 | + | 0.685156i | \(0.759734\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.5653 | 1.30366 | ||||||||
\(704\) | 5.92501 | 0.223307 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.1398 | 0.645066 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.77731 | 0.329639 | 0.164819 | − | 0.986324i | \(-0.447296\pi\) | ||||
0.164819 | + | 0.986324i | \(0.447296\pi\) | |||||||
\(710\) | 19.9952 | 0.750405 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.827023 | −0.0309940 | ||||||||
\(713\) | −5.90360 | −0.221091 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.648824 | 0.0242646 | ||||||||
\(716\) | −5.15515 | −0.192657 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32.4804 | 1.21216 | ||||||||
\(719\) | −4.20437 | −0.156796 | −0.0783982 | − | 0.996922i | \(-0.524981\pi\) | ||||
−0.0783982 | + | 0.996922i | \(0.524981\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 50.2840 | 1.87138 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.8161 | −0.810789 | ||||||||
\(725\) | 13.6173 | 0.505735 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.9856 | −1.07502 | −0.537509 | − | 0.843258i | \(-0.680634\pi\) | ||||
−0.537509 | + | 0.843258i | \(0.680634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.31796 | 0.233838 | ||||||||
\(731\) | 22.1999 | 0.821094 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.0345 | −0.887733 | −0.443867 | − | 0.896093i | \(-0.646394\pi\) | ||||
−0.443867 | + | 0.896093i | \(0.646394\pi\) | |||||||
\(734\) | 56.5480 | 2.08722 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.1918 | 1.11288 | ||||||||
\(737\) | −6.72788 | −0.247825 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.8055 | 0.434273 | 0.217136 | − | 0.976141i | \(-0.430328\pi\) | ||||
0.217136 | + | 0.976141i | \(0.430328\pi\) | |||||||
\(740\) | −9.59670 | −0.352782 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.2786 | −1.73448 | −0.867241 | − | 0.497888i | \(-0.834109\pi\) | ||||
−0.867241 | + | 0.497888i | \(0.834109\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.0900 | −0.699402 | ||||||||
\(746\) | −57.2503 | −2.09608 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.42773 | 0.125330 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.47700 | 0.199859 | 0.0999294 | − | 0.994995i | \(-0.468138\pi\) | ||||
0.0999294 | + | 0.994995i | \(0.468138\pi\) | |||||||
\(752\) | −32.7012 | −1.19249 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.54376 | −0.238310 | ||||||||
\(755\) | 14.2410 | 0.518285 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.7453 | 0.390546 | 0.195273 | − | 0.980749i | \(-0.437441\pi\) | ||||
0.195273 | + | 0.980749i | \(0.437441\pi\) | |||||||
\(758\) | −14.5872 | −0.529830 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.412500 | −0.0149630 | ||||||||
\(761\) | 33.0399 | 1.19770 | 0.598848 | − | 0.800863i | \(-0.295625\pi\) | ||||
0.598848 | + | 0.800863i | \(0.295625\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.41457 | 0.123535 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.9753 | −0.938527 | ||||||||
\(767\) | −0.716361 | −0.0258663 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.98332 | 0.107581 | 0.0537907 | − | 0.998552i | \(-0.482870\pi\) | ||||
0.0537907 | + | 0.998552i | \(0.482870\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.1167 | −0.472079 | ||||||||
\(773\) | 21.9085 | 0.787995 | 0.393998 | − | 0.919111i | \(-0.371092\pi\) | ||||
0.393998 | + | 0.919111i | \(0.371092\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.56417 | −0.235792 | ||||||||
\(776\) | 0.510464 | 0.0183246 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 42.4516 | 1.52196 | ||||||||
\(779\) | −32.6598 | −1.17016 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.87381 | 0.281747 | ||||||||
\(782\) | 17.7600 | 0.635097 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.05104 | 0.251662 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.3632 | −0.476347 | −0.238174 | − | 0.971223i | \(-0.576549\pi\) | ||||
−0.238174 | + | 0.971223i | \(0.576549\pi\) | |||||||
\(788\) | −3.80900 | −0.135690 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −23.6640 | −0.841927 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.6527 | −0.413798 | ||||||||
\(794\) | 38.5784 | 1.36910 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −23.1827 | −0.821691 | ||||||||
\(797\) | −32.5388 | −1.15258 | −0.576292 | − | 0.817244i | \(-0.695501\pi\) | ||||
−0.576292 | + | 0.817244i | \(0.695501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.5706 | −0.692357 | ||||||||
\(800\) | 33.5701 | 1.18688 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −33.4805 | −1.18224 | ||||||||
\(803\) | 2.48792 | 0.0877969 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.15439 | 0.111109 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.0822938 | 0.00289509 | ||||||||
\(809\) | −7.68827 | −0.270305 | −0.135153 | − | 0.990825i | \(-0.543152\pi\) | ||||
−0.135153 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.3178 | −1.69667 | −0.848334 | − | 0.529461i | \(-0.822394\pi\) | ||||
−0.848334 | + | 0.529461i | \(0.822394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.49461 | −0.262686 | ||||||||
\(815\) | −1.53059 | −0.0536142 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −62.6275 | −2.19106 | ||||||||
\(818\) | 24.8019 | 0.867178 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.06766 | 0.316656 | ||||||||
\(821\) | 3.73442 | 0.130332 | 0.0651661 | − | 0.997874i | \(-0.479242\pi\) | ||||
0.0651661 | + | 0.997874i | \(0.479242\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.2318 | 0.496089 | 0.248045 | − | 0.968749i | \(-0.420212\pi\) | ||||
0.248045 | + | 0.968749i | \(0.420212\pi\) | |||||||
\(824\) | −0.989150 | −0.0344587 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.3016 | −1.67961 | −0.839805 | − | 0.542888i | \(-0.817331\pi\) | ||||
−0.839805 | + | 0.542888i | \(0.817331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.5101 | 0.399763 | 0.199882 | − | 0.979820i | \(-0.435944\pi\) | ||||
0.199882 | + | 0.979820i | \(0.435944\pi\) | |||||||
\(830\) | 6.44135 | 0.223582 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.27099 | −0.286745 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.8052 | −0.685386 | ||||||||
\(836\) | −9.66985 | −0.334439 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.75583 | −0.302465 | ||||||||
\(839\) | −13.1103 | −0.452616 | −0.226308 | − | 0.974056i | \(-0.572666\pi\) | ||||
−0.226308 | + | 0.974056i | \(0.572666\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.3855 | −0.633982 | ||||||||
\(842\) | −20.0852 | −0.692183 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.3295 | 0.527663 | ||||||||
\(845\) | −0.905722 | −0.0311578 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 55.3541 | 1.90087 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19.7472 | 0.677325 | ||||||||
\(851\) | −19.5803 | −0.671203 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.80346 | 0.301425 | 0.150712 | − | 0.988578i | \(-0.451843\pi\) | ||||
0.150712 | + | 0.988578i | \(0.451843\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.932934 | −0.0318870 | ||||||||
\(857\) | −16.9651 | −0.579516 | −0.289758 | − | 0.957100i | \(-0.593575\pi\) | ||||
−0.289758 | + | 0.957100i | \(0.593575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.5410 | 0.496132 | 0.248066 | − | 0.968743i | \(-0.420205\pi\) | ||||
0.248066 | + | 0.968743i | \(0.420205\pi\) | |||||||
\(860\) | 17.3879 | 0.592922 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 46.9243 | 1.59825 | ||||||||
\(863\) | −39.0444 | −1.32909 | −0.664544 | − | 0.747249i | \(-0.731374\pi\) | ||||
−0.664544 | + | 0.747249i | \(0.731374\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.29052 | 0.179883 | ||||||||
\(866\) | −5.44882 | −0.185159 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.31854 | −0.316110 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.39174 | 0.318227 | ||||||||
\(872\) | −0.941966 | −0.0318990 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −50.1022 | −1.69473 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.5941 | 1.10062 | 0.550312 | − | 0.834959i | \(-0.314509\pi\) | ||||
0.550312 | + | 0.834959i | \(0.314509\pi\) | |||||||
\(878\) | −17.7457 | −0.598888 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.55020 | −0.0859671 | ||||||||
\(881\) | 43.4141 | 1.46266 | 0.731330 | − | 0.682024i | \(-0.238900\pi\) | ||||
0.731330 | + | 0.682024i | \(0.238900\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.2902 | 0.952040 | 0.476020 | − | 0.879434i | \(-0.342079\pi\) | ||||
0.476020 | + | 0.879434i | \(0.342079\pi\) | |||||||
\(884\) | −4.78492 | −0.160934 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.83592 | 0.196062 | ||||||||
\(887\) | 50.2650 | 1.68773 | 0.843866 | − | 0.536554i | \(-0.180274\pi\) | ||||
0.843866 | + | 0.536554i | \(0.180274\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 21.9210 | 0.734794 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 35.8724 | 1.20110 | ||||||||
\(893\) | 55.2099 | 1.84753 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.29535 | 0.0767250 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.6856 | 1.02399 | ||||||||
\(899\) | −5.11668 | −0.170651 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.1277 | 1.10364 | ||||||||
\(902\) | 7.08145 | 0.235786 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.223604 | 0.00743695 | ||||||||
\(905\) | 9.71369 | 0.322894 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.8277 | 0.890798 | 0.445399 | − | 0.895332i | \(-0.353062\pi\) | ||||
0.445399 | + | 0.895332i | \(0.353062\pi\) | |||||||
\(908\) | 10.8402 | 0.359744 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.3560 | 0.740687 | 0.370344 | − | 0.928895i | \(-0.379240\pi\) | ||||
0.370344 | + | 0.928895i | \(0.379240\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.53651 | 0.0839463 | ||||||||
\(914\) | 47.5217 | 1.57188 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.3291 | −0.572569 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.62244 | −0.284428 | −0.142214 | − | 0.989836i | \(-0.545422\pi\) | ||||
−0.142214 | + | 0.989836i | \(0.545422\pi\) | |||||||
\(920\) | 0.233670 | 0.00770386 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 53.4609 | 1.76064 | ||||||||
\(923\) | −10.9914 | −0.361786 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.7712 | −0.715832 | ||||||||
\(926\) | −2.89729 | −0.0952109 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26.1674 | 0.858987 | ||||||||
\(929\) | −41.3861 | −1.35783 | −0.678916 | − | 0.734216i | \(-0.737550\pi\) | ||||
−0.678916 | + | 0.734216i | \(0.737550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.66985 | −0.316747 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.8507 | 0.551372 | ||||||||
\(935\) | −1.52621 | −0.0499124 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.3818 | 0.698514 | 0.349257 | − | 0.937027i | \(-0.386434\pi\) | ||||
0.349257 | + | 0.937027i | \(0.386434\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.3285 | −0.499959 | ||||||||
\(941\) | 53.1480 | 1.73258 | 0.866288 | − | 0.499545i | \(-0.166499\pi\) | ||||
0.866288 | + | 0.499545i | \(0.166499\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.5009 | 0.602471 | ||||||||
\(944\) | 2.81565 | 0.0916416 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.5792 | 0.441497 | ||||||||
\(947\) | 8.86936 | 0.288216 | 0.144108 | − | 0.989562i | \(-0.453969\pi\) | ||||
0.144108 | + | 0.989562i | \(0.453969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.47300 | −0.112738 | ||||||||
\(950\) | −55.7082 | −1.80741 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.8167 | 1.28979 | 0.644894 | − | 0.764272i | \(-0.276901\pi\) | ||||
0.644894 | + | 0.764272i | \(0.276901\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.52035 | −0.0491973 | ||||||||
\(956\) | −30.1696 | −0.975756 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25.3319 | −0.818435 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5335 | −0.920437 | ||||||||
\(962\) | 10.4621 | 0.337310 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.4518 | −0.401045 | ||||||||
\(965\) | 5.84024 | 0.188004 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.1611 | −0.712652 | −0.356326 | − | 0.934362i | \(-0.615971\pi\) | ||||
−0.356326 | + | 0.934362i | \(0.615971\pi\) | |||||||
\(968\) | −0.719735 | −0.0231332 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.5303 | −0.434433 | ||||||||
\(971\) | −36.0423 | −1.15665 | −0.578327 | − | 0.815805i | \(-0.696294\pi\) | ||||
−0.578327 | + | 0.815805i | \(0.696294\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 43.3199 | 1.38806 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 45.8007 | 1.46604 | ||||||||
\(977\) | −32.9416 | −1.05389 | −0.526947 | − | 0.849898i | \(-0.676664\pi\) | ||||
−0.526947 | + | 0.849898i | \(0.676664\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.63219 | 0.275886 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −78.8038 | −2.51473 | ||||||||
\(983\) | 4.19945 | 0.133942 | 0.0669709 | − | 0.997755i | \(-0.478667\pi\) | ||||
0.0669709 | + | 0.997755i | \(0.478667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.69597 | 0.0540382 | ||||||||
\(986\) | 15.3927 | 0.490203 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.4986 | 0.429447 | ||||||||
\(989\) | 35.4767 | 1.12809 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.4139 | −0.426105 | −0.213053 | − | 0.977041i | \(-0.568341\pi\) | ||||
−0.213053 | + | 0.977041i | \(0.568341\pi\) | |||||||
\(992\) | −12.6139 | −0.400491 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.3222 | 0.327236 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.8868 | −1.51659 | −0.758295 | − | 0.651911i | \(-0.773967\pi\) | ||||
−0.758295 | + | 0.651911i | \(0.773967\pi\) | |||||||
\(998\) | 18.4144 | 0.582899 | ||||||||
\(999\) | 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 | 5733.2.a.bl.1.5 | 5 | ||
3.2 | odd | 2 | 637.2.a.l.1.1 | 5 | |||
7.2 | even | 3 | 819.2.j.h.235.1 | 10 | |||
7.4 | even | 3 | 819.2.j.h.352.1 | 10 | |||
7.6 | odd | 2 | 5733.2.a.bm.1.5 | 5 | |||
21.2 | odd | 6 | 91.2.e.c.53.5 | ✓ | 10 | ||
21.5 | even | 6 | 637.2.e.m.508.5 | 10 | |||
21.11 | odd | 6 | 91.2.e.c.79.5 | yes | 10 | ||
21.17 | even | 6 | 637.2.e.m.79.5 | 10 | |||
21.20 | even | 2 | 637.2.a.k.1.1 | 5 | |||
39.38 | odd | 2 | 8281.2.a.bw.1.5 | 5 | |||
84.11 | even | 6 | 1456.2.r.p.625.4 | 10 | |||
84.23 | even | 6 | 1456.2.r.p.417.4 | 10 | |||
273.116 | odd | 6 | 1183.2.e.f.170.1 | 10 | |||
273.233 | odd | 6 | 1183.2.e.f.508.1 | 10 | |||
273.272 | even | 2 | 8281.2.a.bx.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.5 | ✓ | 10 | 21.2 | odd | 6 | ||
91.2.e.c.79.5 | yes | 10 | 21.11 | odd | 6 | ||
637.2.a.k.1.1 | 5 | 21.20 | even | 2 | |||
637.2.a.l.1.1 | 5 | 3.2 | odd | 2 | |||
637.2.e.m.79.5 | 10 | 21.17 | even | 6 | |||
637.2.e.m.508.5 | 10 | 21.5 | even | 6 | |||
819.2.j.h.235.1 | 10 | 7.2 | even | 3 | |||
819.2.j.h.352.1 | 10 | 7.4 | even | 3 | |||
1183.2.e.f.170.1 | 10 | 273.116 | odd | 6 | |||
1183.2.e.f.508.1 | 10 | 273.233 | odd | 6 | |||
1456.2.r.p.417.4 | 10 | 84.23 | even | 6 | |||
1456.2.r.p.625.4 | 10 | 84.11 | even | 6 | |||
5733.2.a.bl.1.5 | 5 | 1.1 | even | 1 | trivial | ||
5733.2.a.bm.1.5 | 5 | 7.6 | odd | 2 | |||
8281.2.a.bw.1.5 | 5 | 39.38 | odd | 2 | |||
8281.2.a.bx.1.5 | 5 | 273.272 | even | 2 |