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 | \(-0.435085\pi\) | ||||
0.202526 | + | 0.979277i | \(0.435085\pi\) | |||||||
\(6\) | 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 | \(-0.407922\pi\) | ||||
0.285255 | + | 0.958452i | \(0.407922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.63591 | −1.52238 | −0.761191 | − | 0.648528i | \(-0.775385\pi\) | ||||
−0.761191 | + | 0.648528i | \(0.775385\pi\) | |||||||
\(20\) | 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 | \(-0.545043\pi\) | ||||
−0.141035 | + | 0.990005i | \(0.545043\pi\) | |||||||
\(32\) | −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 | \(-0.374437\pi\) | ||||
0.384318 | + | 0.923201i | \(0.374437\pi\) | |||||||
\(42\) | 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 | \(-0.707542\pi\) | ||||
−0.606788 | + | 0.794863i | \(0.707542\pi\) | |||||||
\(48\) | 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 | \(-0.485151\pi\) | ||||
0.0466311 | + | 0.998912i | \(0.485151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6527 | 1.49197 | 0.745986 | − | 0.665962i | \(-0.231979\pi\) | ||||
0.745986 | + | 0.665962i | \(0.231979\pi\) | |||||||
\(62\) | −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 | \(-0.434852\pi\) | ||||
0.203242 | + | 0.979129i | \(0.434852\pi\) | |||||||
\(74\) | 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 | \(-0.437747\pi\) | ||||
0.194328 | + | 0.980937i | \(0.437747\pi\) | |||||||
\(84\) | 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 | \(-0.279493\pi\) | ||||
0.638651 | + | 0.769496i | \(0.279493\pi\) | |||||||
\(90\) | 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 | \(-0.623247\pi\) | ||||
−0.377590 | + | 0.925973i | \(0.623247\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.50216 | −0.850216 | ||||||||
\(101\) | −1.19905 | −0.119310 | −0.0596551 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596551 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4123 | 1.42009 | 0.710043 | − | 0.704158i | \(-0.248675\pi\) | ||||
0.710043 | + | 0.704158i | \(0.248675\pi\) | |||||||
\(104\) | −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 | \(-0.807219\pi\) | ||||
−0.822138 | + | 0.569288i | \(0.807219\pi\) | |||||||
\(132\) | 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 | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 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 | \(-0.399452\pi\) | ||||
0.310655 | + | 0.950523i | \(0.399452\pi\) | |||||||
\(158\) | 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 | \(-0.821025\pi\) | ||||
−0.846049 | + | 0.533105i | \(0.821025\pi\) | |||||||
\(168\) | 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 | \(-0.428725\pi\) | ||||
0.222050 | + | 0.975035i | \(0.428725\pi\) | |||||||
\(174\) | 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 | \(-0.369502\pi\) | ||||
0.398585 | + | 0.917132i | \(0.369502\pi\) | |||||||
\(182\) | 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 | \(-0.367639\pi\) | ||||
0.403944 | + | 0.914784i | \(0.367639\pi\) | |||||||
\(200\) | −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 | \(-0.701053\pi\) | ||||
−0.590459 | + | 0.807067i | \(0.701053\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.54376 | 0.435284 | ||||||||
\(227\) | −5.32904 | −0.353701 | −0.176851 | − | 0.984238i | \(-0.556591\pi\) | ||||
−0.176851 | + | 0.984238i | \(0.556591\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.51900 | 0.562951 | 0.281476 | − | 0.959568i | \(-0.409176\pi\) | ||||
0.281476 | + | 0.959568i | \(0.409176\pi\) | |||||||
\(230\) | −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 | \(-0.436830\pi\) | ||||
0.197154 | + | 0.980373i | \(0.436830\pi\) | |||||||
\(242\) | −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 | \(-0.645346\pi\) | ||||
−0.440916 | + | 0.897548i | \(0.645346\pi\) | |||||||
\(252\) | 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 | \(-0.318998\pi\) | ||||
0.538482 | + | 0.842637i | \(0.318998\pi\) | |||||||
\(258\) | 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 | \(-0.645632\pi\) | ||||
−0.441721 | + | 0.897152i | \(0.645632\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.63591 | 0.524594 | 0.262297 | − | 0.964987i | \(-0.415520\pi\) | ||||
0.262297 | + | 0.964987i | \(0.415520\pi\) | |||||||
\(272\) | −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 | \(-0.132590\pi\) | ||||
0.914493 | + | 0.404601i | \(0.132590\pi\) | |||||||
\(284\) | −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 | \(-0.879976\pi\) | ||||
−0.929749 | + | 0.368193i | \(0.879976\pi\) | |||||||
\(294\) | 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 | \(-0.806874\pi\) | ||||
−0.821520 | + | 0.570179i | \(0.806874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.85700 | −0.162266 | ||||||||
\(311\) | 5.51862 | 0.312932 | 0.156466 | − | 0.987683i | \(-0.449990\pi\) | ||||
0.156466 | + | 0.987683i | \(0.449990\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.84799 | 0.274024 | 0.137012 | − | 0.990569i | \(-0.456250\pi\) | ||||
0.137012 | + | 0.990569i | \(0.456250\pi\) | |||||||
\(314\) | 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 | \(-0.428205\pi\) | ||||
0.223643 | + | 0.974671i | \(0.428205\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.75364 | 0.306670 | ||||||||
\(353\) | −8.53355 | −0.454195 | −0.227097 | − | 0.973872i | \(-0.572924\pi\) | ||||
−0.227097 | + | 0.973872i | \(0.572924\pi\) | |||||||
\(354\) | 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 | \(-0.762730\pi\) | ||||
−0.734813 | + | 0.678269i | \(0.762730\pi\) | |||||||
\(368\) | 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 | \(-0.392813\pi\) | ||||
0.330411 | + | 0.943837i | \(0.392813\pi\) | |||||||
\(384\) | 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 | \(-0.660087\pi\) | ||||
−0.481994 | + | 0.876175i | \(0.660087\pi\) | |||||||
\(398\) | 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 | \(-0.598754\pi\) | ||||
−0.305293 | + | 0.952259i | \(0.598754\pi\) | |||||||
\(410\) | 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 | \(-0.466041\pi\) | ||||
0.106484 | + | 0.994314i | \(0.466041\pi\) | |||||||
\(420\) | 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 | \(-0.479236\pi\) | ||||
0.0651856 | + | 0.997873i | \(0.479236\pi\) | |||||||
\(434\) | 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 | \(-0.432380\pi\) | ||||
0.210840 | + | 0.977521i | \(0.432380\pi\) | |||||||
\(440\) | −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 | \(-0.712802\pi\) | ||||
−0.619839 | + | 0.784729i | \(0.712802\pi\) | |||||||
\(462\) | 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 | \(-0.562183\pi\) | ||||
−0.194112 | + | 0.980979i | \(0.562183\pi\) | |||||||
\(468\) | 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 | \(-0.406966\pi\) | ||||
0.288132 | + | 0.957591i | \(0.406966\pi\) | |||||||
\(480\) | 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 | \(-0.312358\pi\) | ||||
0.555942 | + | 0.831221i | \(0.312358\pi\) | |||||||
\(504\) | 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 | \(-0.458273\pi\) | ||||
0.130714 | + | 0.991420i | \(0.458273\pi\) | |||||||
\(510\) | 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 | \(-0.803072\pi\) | ||||
−0.814652 | + | 0.579950i | \(0.803072\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.09080 | 0.222605 | 0.111303 | − | 0.993787i | \(-0.464498\pi\) | ||||
0.111303 | + | 0.993787i | \(0.464498\pi\) | |||||||
\(524\) | −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 | \(-0.122049\pi\) | ||||
0.927388 | + | 0.374101i | \(0.122049\pi\) | |||||||
\(564\) | 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 | \(-0.318240\pi\) | ||||
0.540486 | + | 0.841353i | \(0.318240\pi\) | |||||||
\(578\) | −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 | \(-0.664748\pi\) | ||||
−0.494771 | + | 0.869023i | \(0.664748\pi\) | |||||||
\(588\) | 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 | \(-0.0832230\pi\) | ||||
0.966015 | + | 0.258484i | \(0.0832230\pi\) | |||||||
\(594\) | 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 | \(-0.706125\pi\) | ||||
−0.603242 | + | 0.797558i | \(0.706125\pi\) | |||||||
\(602\) | 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 | \(-0.398537\pi\) | ||||
0.313385 | + | 0.949626i | \(0.398537\pi\) | |||||||
\(608\) | 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 | \(-0.722202\pi\) | ||||
−0.642738 | + | 0.766086i | \(0.722202\pi\) | |||||||
\(620\) | −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 | \(-0.600808\pi\) | ||||
−0.311432 | + | 0.950269i | \(0.600808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.3520 | −1.23353 | ||||||||
\(647\) | −4.64072 | −0.182445 | −0.0912227 | − | 0.995831i | \(-0.529078\pi\) | ||||
−0.0912227 | + | 0.995831i | \(0.529078\pi\) | |||||||
\(648\) | 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 | \(-0.305732\pi\) | ||||
0.573122 | + | 0.819470i | \(0.305732\pi\) | |||||||
\(662\) | 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 | \(-0.538044\pi\) | ||||
−0.119235 | + | 0.992866i | \(0.538044\pi\) | |||||||
\(678\) | 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 | \(-0.826223\pi\) | ||||
−0.854641 | + | 0.519219i | \(0.826223\pi\) | |||||||
\(692\) | 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 | \(-0.475019\pi\) | ||||
0.0783982 | + | 0.996922i | \(0.475019\pi\) | |||||||
\(720\) | 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 | \(-0.319366\pi\) | ||||
0.537509 | + | 0.843258i | \(0.319366\pi\) | |||||||
\(728\) | 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 | \(-0.353606\pi\) | ||||
0.443867 | + | 0.896093i | \(0.353606\pi\) | |||||||
\(734\) | −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 | \(-0.704375\pi\) | ||||
−0.598848 | + | 0.800863i | \(0.704375\pi\) | |||||||
\(762\) | 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 | \(-0.517130\pi\) | ||||
−0.0537907 | + | 0.998552i | \(0.517130\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.1167 | −0.472079 | ||||||||
\(773\) | −21.9085 | −0.787995 | −0.393998 | − | 0.919111i | \(-0.628908\pi\) | ||||
−0.393998 | + | 0.919111i | \(0.628908\pi\) | |||||||
\(774\) | 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 | \(-0.423451\pi\) | ||||
0.238174 | + | 0.971223i | \(0.423451\pi\) | |||||||
\(788\) | −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 | \(-0.304499\pi\) | ||||
0.576292 | + | 0.817244i | \(0.304499\pi\) | |||||||
\(798\) | 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 | \(-0.177606\pi\) | ||||
0.848334 | + | 0.529461i | \(0.177606\pi\) | |||||||
\(812\) | 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 | \(-0.564056\pi\) | ||||
−0.199882 | + | 0.979820i | \(0.564056\pi\) | |||||||
\(830\) | 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 | \(-0.427334\pi\) | ||||
0.226308 | + | 0.974056i | \(0.427334\pi\) | |||||||
\(840\) | 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 | \(-0.548157\pi\) | ||||
−0.150712 | + | 0.988578i | \(0.548157\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.932934 | −0.0318870 | ||||||||
\(857\) | 16.9651 | 0.579516 | 0.289758 | − | 0.957100i | \(-0.406425\pi\) | ||||
0.289758 | + | 0.957100i | \(0.406425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.5410 | −0.496132 | −0.248066 | − | 0.968743i | \(-0.579795\pi\) | ||||
−0.248066 | + | 0.968743i | \(0.579795\pi\) | |||||||
\(860\) | −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 | \(-0.761100\pi\) | ||||
−0.731330 | + | 0.682024i | \(0.761100\pi\) | |||||||
\(882\) | 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 | \(-0.819726\pi\) | ||||
−0.843866 | + | 0.536554i | \(0.819726\pi\) | |||||||
\(888\) | 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 | \(-0.262450\pi\) | ||||
0.678916 | + | 0.734216i | \(0.262450\pi\) | |||||||
\(930\) | 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 | \(-0.613566\pi\) | ||||
−0.349257 | + | 0.937027i | \(0.613566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.3285 | −0.499959 | ||||||||
\(941\) | −53.1480 | −1.73258 | −0.866288 | − | 0.499545i | \(-0.833501\pi\) | ||||
−0.866288 | + | 0.499545i | \(0.833501\pi\) | |||||||
\(942\) | 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 | \(-0.303706\pi\) | ||||
0.578327 | + | 0.815805i | \(0.303706\pi\) | |||||||
\(972\) | 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 | \(-0.521333\pi\) | ||||
−0.0669709 | + | 0.997755i | \(0.521333\pi\) | |||||||
\(984\) | 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 | \(-0.226033\pi\) | ||||
0.758295 | + | 0.651911i | \(0.226033\pi\) | |||||||
\(998\) | 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.bm.1.5 | 5 | ||
3.2 | odd | 2 | 637.2.a.k.1.1 | 5 | |||
7.3 | odd | 6 | 819.2.j.h.352.1 | 10 | |||
7.5 | odd | 6 | 819.2.j.h.235.1 | 10 | |||
7.6 | odd | 2 | 5733.2.a.bl.1.5 | 5 | |||
21.2 | odd | 6 | 637.2.e.m.508.5 | 10 | |||
21.5 | even | 6 | 91.2.e.c.53.5 | ✓ | 10 | ||
21.11 | odd | 6 | 637.2.e.m.79.5 | 10 | |||
21.17 | even | 6 | 91.2.e.c.79.5 | yes | 10 | ||
21.20 | even | 2 | 637.2.a.l.1.1 | 5 | |||
39.38 | odd | 2 | 8281.2.a.bx.1.5 | 5 | |||
84.47 | odd | 6 | 1456.2.r.p.417.4 | 10 | |||
84.59 | odd | 6 | 1456.2.r.p.625.4 | 10 | |||
273.38 | even | 6 | 1183.2.e.f.170.1 | 10 | |||
273.194 | even | 6 | 1183.2.e.f.508.1 | 10 | |||
273.272 | even | 2 | 8281.2.a.bw.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.5 | ✓ | 10 | 21.5 | even | 6 | ||
91.2.e.c.79.5 | yes | 10 | 21.17 | even | 6 | ||
637.2.a.k.1.1 | 5 | 3.2 | odd | 2 | |||
637.2.a.l.1.1 | 5 | 21.20 | even | 2 | |||
637.2.e.m.79.5 | 10 | 21.11 | odd | 6 | |||
637.2.e.m.508.5 | 10 | 21.2 | odd | 6 | |||
819.2.j.h.235.1 | 10 | 7.5 | odd | 6 | |||
819.2.j.h.352.1 | 10 | 7.3 | odd | 6 | |||
1183.2.e.f.170.1 | 10 | 273.38 | even | 6 | |||
1183.2.e.f.508.1 | 10 | 273.194 | even | 6 | |||
1456.2.r.p.417.4 | 10 | 84.47 | odd | 6 | |||
1456.2.r.p.625.4 | 10 | 84.59 | odd | 6 | |||
5733.2.a.bl.1.5 | 5 | 7.6 | odd | 2 | |||
5733.2.a.bm.1.5 | 5 | 1.1 | even | 1 | trivial | ||
8281.2.a.bw.1.5 | 5 | 273.272 | even | 2 | |||
8281.2.a.bx.1.5 | 5 | 39.38 | odd | 2 |