Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,4,Mod(1,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("135.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.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: | \(7.96525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.5637.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 23x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-4.45938\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.45938 | 1.57663 | 0.788315 | − | 0.615272i | \(-0.210954\pi\) | ||||
0.788315 | + | 0.615272i | \(0.210954\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 11.8861 | 1.48576 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.08123 | 0.274361 | 0.137180 | − | 0.990546i | \(-0.456196\pi\) | ||||
0.137180 | + | 0.990546i | \(0.456196\pi\) | |||||||
\(8\) | 17.3296 | 0.765867 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 22.2969 | 0.705090 | ||||||||
\(11\) | 58.3007 | 1.59803 | 0.799014 | − | 0.601312i | \(-0.205355\pi\) | ||||
0.799014 | + | 0.601312i | \(0.205355\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.2119 | 0.452548 | 0.226274 | − | 0.974064i | \(-0.427345\pi\) | ||||
0.226274 | + | 0.974064i | \(0.427345\pi\) | |||||||
\(14\) | 22.6592 | 0.432566 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −17.8095 | −0.278274 | ||||||||
\(17\) | −68.8451 | −0.982199 | −0.491099 | − | 0.871104i | \(-0.663405\pi\) | ||||
−0.491099 | + | 0.871104i | \(0.663405\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −40.8133 | −0.492800 | −0.246400 | − | 0.969168i | \(-0.579248\pi\) | ||||
−0.246400 | + | 0.969168i | \(0.579248\pi\) | |||||||
\(20\) | 59.4305 | 0.664453 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 259.985 | 2.51950 | ||||||||
\(23\) | −144.318 | −1.30837 | −0.654184 | − | 0.756336i | \(-0.726988\pi\) | ||||
−0.654184 | + | 0.756336i | \(0.726988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 94.5921 | 0.713501 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 60.3960 | 0.407635 | ||||||||
\(29\) | −220.058 | −1.40909 | −0.704547 | − | 0.709657i | \(-0.748850\pi\) | ||||
−0.704547 | + | 0.709657i | \(0.748850\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 291.545 | 1.68913 | 0.844566 | − | 0.535452i | \(-0.179859\pi\) | ||||
0.844566 | + | 0.535452i | \(0.179859\pi\) | |||||||
\(32\) | −218.056 | −1.20460 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −307.006 | −1.54856 | ||||||||
\(35\) | 25.4062 | 0.122698 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 260.637 | 1.15807 | 0.579033 | − | 0.815304i | \(-0.303430\pi\) | ||||
0.579033 | + | 0.815304i | \(0.303430\pi\) | |||||||
\(38\) | −182.002 | −0.776964 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 86.6479 | 0.342506 | ||||||||
\(41\) | −169.766 | −0.646660 | −0.323330 | − | 0.946286i | \(-0.604802\pi\) | ||||
−0.323330 | + | 0.946286i | \(0.604802\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −438.596 | −1.55547 | −0.777735 | − | 0.628592i | \(-0.783631\pi\) | ||||
−0.777735 | + | 0.628592i | \(0.783631\pi\) | |||||||
\(44\) | 692.967 | 2.37429 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −643.571 | −2.06281 | ||||||||
\(47\) | −255.481 | −0.792887 | −0.396444 | − | 0.918059i | \(-0.629756\pi\) | ||||
−0.396444 | + | 0.918059i | \(0.629756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −317.181 | −0.924726 | ||||||||
\(50\) | 111.485 | 0.315326 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 252.127 | 0.672379 | ||||||||
\(53\) | 214.714 | 0.556477 | 0.278239 | − | 0.960512i | \(-0.410249\pi\) | ||||
0.278239 | + | 0.960512i | \(0.410249\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 291.503 | 0.714660 | ||||||||
\(56\) | 88.0557 | 0.210124 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −981.322 | −2.22162 | ||||||||
\(59\) | 331.524 | 0.731537 | 0.365769 | − | 0.930706i | \(-0.380806\pi\) | ||||
0.365769 | + | 0.930706i | \(0.380806\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 54.9647 | 0.115369 | 0.0576845 | − | 0.998335i | \(-0.481628\pi\) | ||||
0.0576845 | + | 0.998335i | \(0.481628\pi\) | |||||||
\(62\) | 1300.11 | 2.66314 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −829.920 | −1.62094 | ||||||||
\(65\) | 106.060 | 0.202386 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 758.179 | 1.38248 | 0.691241 | − | 0.722624i | \(-0.257064\pi\) | ||||
0.691241 | + | 0.722624i | \(0.257064\pi\) | |||||||
\(68\) | −818.299 | −1.45931 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 113.296 | 0.193449 | ||||||||
\(71\) | −904.348 | −1.51164 | −0.755819 | − | 0.654780i | \(-0.772761\pi\) | ||||
−0.755819 | + | 0.654780i | \(0.772761\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 866.622 | 1.38946 | 0.694729 | − | 0.719271i | \(-0.255524\pi\) | ||||
0.694729 | + | 0.719271i | \(0.255524\pi\) | |||||||
\(74\) | 1162.28 | 1.82584 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −485.110 | −0.732184 | ||||||||
\(77\) | 296.239 | 0.438437 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 206.961 | 0.294746 | 0.147373 | − | 0.989081i | \(-0.452918\pi\) | ||||
0.147373 | + | 0.989081i | \(0.452918\pi\) | |||||||
\(80\) | −89.0475 | −0.124448 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −757.054 | −1.01954 | ||||||||
\(83\) | −463.397 | −0.612825 | −0.306412 | − | 0.951899i | \(-0.599129\pi\) | ||||
−0.306412 | + | 0.951899i | \(0.599129\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −344.225 | −0.439253 | ||||||||
\(86\) | −1955.87 | −2.45240 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1010.33 | 1.22388 | ||||||||
\(89\) | 601.736 | 0.716673 | 0.358337 | − | 0.933592i | \(-0.383344\pi\) | ||||
0.358337 | + | 0.933592i | \(0.383344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 107.783 | 0.124162 | ||||||||
\(92\) | −1715.38 | −1.94392 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1139.29 | −1.25009 | ||||||||
\(95\) | −204.066 | −0.220387 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 229.363 | 0.240086 | 0.120043 | − | 0.992769i | \(-0.461697\pi\) | ||||
0.120043 | + | 0.992769i | \(0.461697\pi\) | |||||||
\(98\) | −1414.43 | −1.45795 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 297.152 | 0.297152 | ||||||||
\(101\) | 1345.66 | 1.32573 | 0.662863 | − | 0.748740i | \(-0.269341\pi\) | ||||
0.662863 | + | 0.748740i | \(0.269341\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1596.30 | −1.52707 | −0.763534 | − | 0.645768i | \(-0.776537\pi\) | ||||
−0.763534 | + | 0.645768i | \(0.776537\pi\) | |||||||
\(104\) | 367.594 | 0.346592 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 957.494 | 0.877358 | ||||||||
\(107\) | 958.786 | 0.866256 | 0.433128 | − | 0.901333i | \(-0.357410\pi\) | ||||
0.433128 | + | 0.901333i | \(0.357410\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1690.23 | 1.48527 | 0.742635 | − | 0.669696i | \(-0.233576\pi\) | ||||
0.742635 | + | 0.669696i | \(0.233576\pi\) | |||||||
\(110\) | 1299.93 | 1.12675 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −90.4943 | −0.0763474 | ||||||||
\(113\) | −11.6211 | −0.00967456 | −0.00483728 | − | 0.999988i | \(-0.501540\pi\) | ||||
−0.00483728 | + | 0.999988i | \(0.501540\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −721.592 | −0.585120 | ||||||||
\(116\) | −2615.63 | −2.09358 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1478.39 | 1.15336 | ||||||||
\(119\) | −349.818 | −0.269477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2067.97 | 1.55370 | ||||||||
\(122\) | 245.109 | 0.181894 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3465.34 | 2.50965 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 309.141 | 0.215999 | 0.107999 | − | 0.994151i | \(-0.465556\pi\) | ||||
0.107999 | + | 0.994151i | \(0.465556\pi\) | |||||||
\(128\) | −1956.48 | −1.35102 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 472.960 | 0.319087 | ||||||||
\(131\) | 2785.03 | 1.85747 | 0.928736 | − | 0.370742i | \(-0.120897\pi\) | ||||
0.928736 | + | 0.370742i | \(0.120897\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −207.382 | −0.135205 | ||||||||
\(134\) | 3381.01 | 2.17966 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1193.06 | −0.752233 | ||||||||
\(137\) | −2489.41 | −1.55244 | −0.776222 | − | 0.630460i | \(-0.782866\pi\) | ||||
−0.776222 | + | 0.630460i | \(0.782866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1786.05 | 1.08986 | 0.544931 | − | 0.838481i | \(-0.316556\pi\) | ||||
0.544931 | + | 0.838481i | \(0.316556\pi\) | |||||||
\(140\) | 301.980 | 0.182300 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4032.83 | −2.38329 | ||||||||
\(143\) | 1236.67 | 0.723185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1100.29 | −0.630166 | ||||||||
\(146\) | 3864.60 | 2.19066 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3097.95 | 1.72061 | ||||||||
\(149\) | 1568.83 | 0.862575 | 0.431288 | − | 0.902214i | \(-0.358059\pi\) | ||||
0.431288 | + | 0.902214i | \(0.358059\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −438.327 | −0.236229 | −0.118114 | − | 0.993000i | \(-0.537685\pi\) | ||||
−0.118114 | + | 0.993000i | \(0.537685\pi\) | |||||||
\(152\) | −707.277 | −0.377419 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1321.04 | 0.691252 | ||||||||
\(155\) | 1457.73 | 0.755403 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −44.7479 | −0.0227469 | −0.0113735 | − | 0.999935i | \(-0.503620\pi\) | ||||
−0.0113735 | + | 0.999935i | \(0.503620\pi\) | |||||||
\(158\) | 922.917 | 0.464705 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1090.28 | −0.538714 | ||||||||
\(161\) | −733.315 | −0.358965 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2611.84 | −1.25506 | −0.627531 | − | 0.778591i | \(-0.715935\pi\) | ||||
−0.627531 | + | 0.778591i | \(0.715935\pi\) | |||||||
\(164\) | −2017.86 | −0.960783 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2066.47 | −0.966198 | ||||||||
\(167\) | −188.947 | −0.0875516 | −0.0437758 | − | 0.999041i | \(-0.513939\pi\) | ||||
−0.0437758 | + | 0.999041i | \(0.513939\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1747.05 | −0.795200 | ||||||||
\(170\) | −1535.03 | −0.692539 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5213.19 | −2.31106 | ||||||||
\(173\) | −1505.02 | −0.661413 | −0.330707 | − | 0.943734i | \(-0.607287\pi\) | ||||
−0.330707 | + | 0.943734i | \(0.607287\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 127.031 | 0.0548722 | ||||||||
\(176\) | −1038.31 | −0.444689 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2683.37 | 1.12993 | ||||||||
\(179\) | −3136.62 | −1.30973 | −0.654865 | − | 0.755746i | \(-0.727275\pi\) | ||||
−0.654865 | + | 0.755746i | \(0.727275\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4512.67 | 1.85317 | 0.926586 | − | 0.376084i | \(-0.122730\pi\) | ||||
0.926586 | + | 0.376084i | \(0.122730\pi\) | |||||||
\(182\) | 480.644 | 0.195757 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2500.98 | −1.00204 | ||||||||
\(185\) | 1303.18 | 0.517902 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4013.71 | −1.56958 | ||||||||
\(188\) | −3036.67 | −1.17804 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −910.010 | −0.347469 | ||||||||
\(191\) | 1207.43 | 0.457418 | 0.228709 | − | 0.973495i | \(-0.426550\pi\) | ||||
0.228709 | + | 0.973495i | \(0.426550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 923.164 | 0.344305 | 0.172152 | − | 0.985070i | \(-0.444928\pi\) | ||||
0.172152 | + | 0.985070i | \(0.444928\pi\) | |||||||
\(194\) | 1022.82 | 0.378526 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3770.04 | −1.37392 | ||||||||
\(197\) | −1180.87 | −0.427075 | −0.213537 | − | 0.976935i | \(-0.568499\pi\) | ||||
−0.213537 | + | 0.976935i | \(0.568499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −839.805 | −0.299157 | −0.149578 | − | 0.988750i | \(-0.547792\pi\) | ||||
−0.149578 | + | 0.988750i | \(0.547792\pi\) | |||||||
\(200\) | 433.240 | 0.153173 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6000.82 | 2.09018 | ||||||||
\(203\) | −1118.17 | −0.386600 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −848.832 | −0.289195 | ||||||||
\(206\) | −7118.51 | −2.40762 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −377.774 | −0.125932 | ||||||||
\(209\) | −2379.44 | −0.787509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2589.65 | −0.844923 | −0.422461 | − | 0.906381i | \(-0.638834\pi\) | ||||
−0.422461 | + | 0.906381i | \(0.638834\pi\) | |||||||
\(212\) | 2552.12 | 0.826792 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4275.59 | 1.36576 | ||||||||
\(215\) | −2192.98 | −0.695627 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1481.41 | 0.463432 | ||||||||
\(218\) | 7537.38 | 2.34172 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3464.84 | 1.06181 | ||||||||
\(221\) | −1460.34 | −0.444492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4180.76 | −1.25544 | −0.627722 | − | 0.778437i | \(-0.716013\pi\) | ||||
−0.627722 | + | 0.778437i | \(0.716013\pi\) | |||||||
\(224\) | −1107.99 | −0.330495 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −51.8232 | −0.0152532 | ||||||||
\(227\) | −2602.67 | −0.760993 | −0.380497 | − | 0.924782i | \(-0.624247\pi\) | ||||
−0.380497 | + | 0.924782i | \(0.624247\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1845.35 | −0.532508 | −0.266254 | − | 0.963903i | \(-0.585786\pi\) | ||||
−0.266254 | + | 0.963903i | \(0.585786\pi\) | |||||||
\(230\) | −3217.85 | −0.922517 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3813.51 | −1.07918 | ||||||||
\(233\) | 240.637 | 0.0676594 | 0.0338297 | − | 0.999428i | \(-0.489230\pi\) | ||||
0.0338297 | + | 0.999428i | \(0.489230\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1277.40 | −0.354590 | ||||||||
\(236\) | 3940.52 | 1.08689 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1559.97 | −0.424865 | ||||||||
\(239\) | 2567.64 | 0.694924 | 0.347462 | − | 0.937694i | \(-0.387044\pi\) | ||||
0.347462 | + | 0.937694i | \(0.387044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3987.99 | 1.06593 | 0.532965 | − | 0.846137i | \(-0.321078\pi\) | ||||
0.532965 | + | 0.846137i | \(0.321078\pi\) | |||||||
\(242\) | 9221.86 | 2.44960 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 653.315 | 0.171411 | ||||||||
\(245\) | −1585.91 | −0.413550 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −865.728 | −0.223016 | ||||||||
\(248\) | 5052.36 | 1.29365 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 557.423 | 0.141018 | ||||||||
\(251\) | 967.393 | 0.243272 | 0.121636 | − | 0.992575i | \(-0.461186\pi\) | ||||
0.121636 | + | 0.992575i | \(0.461186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8413.86 | −2.09081 | ||||||||
\(254\) | 1378.58 | 0.340550 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2085.34 | −0.509116 | ||||||||
\(257\) | 3743.03 | 0.908498 | 0.454249 | − | 0.890875i | \(-0.349908\pi\) | ||||
0.454249 | + | 0.890875i | \(0.349908\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1324.36 | 0.317728 | ||||||||
\(260\) | 1260.63 | 0.300697 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12419.5 | 2.92855 | ||||||||
\(263\) | −2497.47 | −0.585554 | −0.292777 | − | 0.956181i | \(-0.594579\pi\) | ||||
−0.292777 | + | 0.956181i | \(0.594579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1073.57 | 0.248864 | ||||||||
\(266\) | −924.795 | −0.213168 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9011.79 | 2.05404 | ||||||||
\(269\) | −2142.91 | −0.485709 | −0.242855 | − | 0.970063i | \(-0.578084\pi\) | ||||
−0.242855 | + | 0.970063i | \(0.578084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1540.64 | 0.345341 | 0.172671 | − | 0.984980i | \(-0.444760\pi\) | ||||
0.172671 | + | 0.984980i | \(0.444760\pi\) | |||||||
\(272\) | 1226.10 | 0.273320 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11101.2 | −2.44763 | ||||||||
\(275\) | 1457.52 | 0.319606 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6777.80 | 1.47018 | 0.735088 | − | 0.677972i | \(-0.237141\pi\) | ||||
0.735088 | + | 0.677972i | \(0.237141\pi\) | |||||||
\(278\) | 7964.69 | 1.71831 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 440.278 | 0.0939702 | ||||||||
\(281\) | 827.653 | 0.175707 | 0.0878535 | − | 0.996133i | \(-0.471999\pi\) | ||||
0.0878535 | + | 0.996133i | \(0.471999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3171.98 | −0.666270 | −0.333135 | − | 0.942879i | \(-0.608106\pi\) | ||||
−0.333135 | + | 0.942879i | \(0.608106\pi\) | |||||||
\(284\) | −10749.2 | −2.24593 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5514.78 | 1.14020 | ||||||||
\(287\) | −862.623 | −0.177418 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −173.358 | −0.0352856 | ||||||||
\(290\) | −4906.61 | −0.993539 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10300.8 | 2.06440 | ||||||||
\(293\) | 1376.02 | 0.274362 | 0.137181 | − | 0.990546i | \(-0.456196\pi\) | ||||
0.137181 | + | 0.990546i | \(0.456196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1657.62 | 0.327153 | ||||||||
\(296\) | 4516.73 | 0.886923 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6996.02 | 1.35996 | ||||||||
\(299\) | −3061.27 | −0.592099 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2228.61 | −0.426760 | ||||||||
\(302\) | −1954.67 | −0.372445 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 726.864 | 0.137133 | ||||||||
\(305\) | 274.823 | 0.0515946 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −119.504 | −0.0222165 | −0.0111083 | − | 0.999938i | \(-0.503536\pi\) | ||||
−0.0111083 | + | 0.999938i | \(0.503536\pi\) | |||||||
\(308\) | 3521.13 | 0.651412 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6500.56 | 1.19099 | ||||||||
\(311\) | 2139.35 | 0.390069 | 0.195035 | − | 0.980796i | \(-0.437518\pi\) | ||||
0.195035 | + | 0.980796i | \(0.437518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5163.50 | 0.932455 | 0.466227 | − | 0.884665i | \(-0.345613\pi\) | ||||
0.466227 | + | 0.884665i | \(0.345613\pi\) | |||||||
\(314\) | −199.548 | −0.0358635 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2459.95 | 0.437922 | ||||||||
\(317\) | −8631.69 | −1.52935 | −0.764675 | − | 0.644416i | \(-0.777101\pi\) | ||||
−0.764675 | + | 0.644416i | \(0.777101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12829.5 | −2.25177 | ||||||||
\(320\) | −4149.60 | −0.724905 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3270.13 | −0.565955 | ||||||||
\(323\) | 2809.79 | 0.484028 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 530.298 | 0.0905097 | ||||||||
\(326\) | −11647.2 | −1.97877 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2941.98 | −0.495255 | ||||||||
\(329\) | −1298.16 | −0.217537 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2942.34 | −0.488597 | −0.244298 | − | 0.969700i | \(-0.578558\pi\) | ||||
−0.244298 | + | 0.969700i | \(0.578558\pi\) | |||||||
\(332\) | −5507.98 | −0.910512 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −842.585 | −0.138037 | ||||||||
\(335\) | 3790.90 | 0.618265 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9897.46 | 1.59985 | 0.799924 | − | 0.600101i | \(-0.204873\pi\) | ||||
0.799924 | + | 0.600101i | \(0.204873\pi\) | |||||||
\(338\) | −7790.79 | −1.25374 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4091.49 | −0.652625 | ||||||||
\(341\) | 16997.3 | 2.69928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3354.53 | −0.528070 | ||||||||
\(344\) | −7600.68 | −1.19128 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6711.46 | −1.04280 | ||||||||
\(347\) | −12015.7 | −1.85890 | −0.929451 | − | 0.368947i | \(-0.879718\pi\) | ||||
−0.929451 | + | 0.368947i | \(0.879718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7894.62 | 1.21086 | 0.605428 | − | 0.795900i | \(-0.293002\pi\) | ||||
0.605428 | + | 0.795900i | \(0.293002\pi\) | |||||||
\(350\) | 566.479 | 0.0865131 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12712.8 | −1.92499 | ||||||||
\(353\) | 741.154 | 0.111750 | 0.0558748 | − | 0.998438i | \(-0.482205\pi\) | ||||
0.0558748 | + | 0.998438i | \(0.482205\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4521.74 | −0.676025 | ||||||||
\(356\) | 7152.30 | 1.06481 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13987.4 | −2.06496 | ||||||||
\(359\) | −11564.4 | −1.70012 | −0.850060 | − | 0.526685i | \(-0.823435\pi\) | ||||
−0.850060 | + | 0.526685i | \(0.823435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5193.28 | −0.757148 | ||||||||
\(362\) | 20123.7 | 2.92177 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1281.12 | 0.184474 | ||||||||
\(365\) | 4333.11 | 0.621385 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1148.57 | −0.163365 | −0.0816823 | − | 0.996658i | \(-0.526029\pi\) | ||||
−0.0816823 | + | 0.996658i | \(0.526029\pi\) | |||||||
\(368\) | 2570.24 | 0.364084 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5811.39 | 0.816540 | ||||||||
\(371\) | 1091.01 | 0.152676 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4602.98 | −0.638963 | −0.319481 | − | 0.947593i | \(-0.603509\pi\) | ||||
−0.319481 | + | 0.947593i | \(0.603509\pi\) | |||||||
\(374\) | −17898.7 | −2.47465 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4427.38 | −0.607246 | ||||||||
\(377\) | −4667.85 | −0.637683 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3988.46 | −0.540563 | −0.270282 | − | 0.962781i | \(-0.587117\pi\) | ||||
−0.270282 | + | 0.962781i | \(0.587117\pi\) | |||||||
\(380\) | −2425.55 | −0.327443 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5384.41 | 0.721179 | ||||||||
\(383\) | 7788.20 | 1.03906 | 0.519528 | − | 0.854454i | \(-0.326108\pi\) | ||||
0.519528 | + | 0.854454i | \(0.326108\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1481.20 | 0.196075 | ||||||||
\(386\) | 4116.74 | 0.542841 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2726.23 | 0.356710 | ||||||||
\(389\) | 8524.87 | 1.11113 | 0.555563 | − | 0.831474i | \(-0.312503\pi\) | ||||
0.555563 | + | 0.831474i | \(0.312503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9935.60 | 1.28508 | ||||||||
\(392\) | −5496.62 | −0.708217 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5265.97 | −0.673339 | ||||||||
\(395\) | 1034.80 | 0.131814 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −155.729 | −0.0196872 | −0.00984361 | − | 0.999952i | \(-0.503133\pi\) | ||||
−0.00984361 | + | 0.999952i | \(0.503133\pi\) | |||||||
\(398\) | −3745.01 | −0.471659 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −445.238 | −0.0556547 | ||||||||
\(401\) | 5933.96 | 0.738972 | 0.369486 | − | 0.929236i | \(-0.379534\pi\) | ||||
0.369486 | + | 0.929236i | \(0.379534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6184.23 | 0.764414 | ||||||||
\(404\) | 15994.7 | 1.96971 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4986.33 | −0.609526 | ||||||||
\(407\) | 15195.3 | 1.85062 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14161.4 | 1.71207 | 0.856035 | − | 0.516917i | \(-0.172921\pi\) | ||||
0.856035 | + | 0.516917i | \(0.172921\pi\) | |||||||
\(410\) | −3785.27 | −0.455954 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18973.8 | −2.26886 | ||||||||
\(413\) | 1684.55 | 0.200705 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2316.99 | −0.274064 | ||||||||
\(416\) | −4625.39 | −0.545140 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10610.8 | −1.24161 | ||||||||
\(419\) | 9624.24 | 1.12214 | 0.561068 | − | 0.827770i | \(-0.310391\pi\) | ||||
0.561068 | + | 0.827770i | \(0.310391\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1536.26 | −0.177845 | −0.0889223 | − | 0.996039i | \(-0.528342\pi\) | ||||
−0.0889223 | + | 0.996039i | \(0.528342\pi\) | |||||||
\(422\) | −11548.2 | −1.33213 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3720.91 | 0.426187 | ||||||||
\(425\) | −1721.13 | −0.196440 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 279.288 | 0.0316527 | ||||||||
\(428\) | 11396.2 | 1.28705 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9779.33 | −1.09675 | ||||||||
\(431\) | 11582.2 | 1.29441 | 0.647207 | − | 0.762314i | \(-0.275937\pi\) | ||||
0.647207 | + | 0.762314i | \(0.275937\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14892.6 | 1.65287 | 0.826437 | − | 0.563029i | \(-0.190364\pi\) | ||||
0.826437 | + | 0.563029i | \(0.190364\pi\) | |||||||
\(434\) | 6606.17 | 0.730660 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20090.2 | 2.20676 | ||||||||
\(437\) | 5890.10 | 0.644764 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1642.51 | −0.178571 | −0.0892853 | − | 0.996006i | \(-0.528458\pi\) | ||||
−0.0892853 | + | 0.996006i | \(0.528458\pi\) | |||||||
\(440\) | 5051.63 | 0.547334 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6512.20 | −0.700800 | ||||||||
\(443\) | 3916.31 | 0.420021 | 0.210011 | − | 0.977699i | \(-0.432650\pi\) | ||||
0.210011 | + | 0.977699i | \(0.432650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3008.68 | 0.320506 | ||||||||
\(446\) | −18643.6 | −1.97937 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4217.02 | −0.444722 | ||||||||
\(449\) | −3985.25 | −0.418876 | −0.209438 | − | 0.977822i | \(-0.567163\pi\) | ||||
−0.209438 | + | 0.977822i | \(0.567163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9897.50 | −1.03338 | ||||||||
\(452\) | −138.130 | −0.0143741 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11606.3 | −1.19980 | ||||||||
\(455\) | 538.914 | 0.0555267 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14177.8 | −1.45122 | −0.725611 | − | 0.688105i | \(-0.758443\pi\) | ||||
−0.725611 | + | 0.688105i | \(0.758443\pi\) | |||||||
\(458\) | −8229.13 | −0.839567 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8576.91 | −0.869349 | ||||||||
\(461\) | −16394.3 | −1.65631 | −0.828154 | − | 0.560500i | \(-0.810609\pi\) | ||||
−0.828154 | + | 0.560500i | \(0.810609\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3319.60 | 0.333207 | 0.166603 | − | 0.986024i | \(-0.446720\pi\) | ||||
0.166603 | + | 0.986024i | \(0.446720\pi\) | |||||||
\(464\) | 3919.12 | 0.392114 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1073.09 | 0.106674 | ||||||||
\(467\) | −2529.79 | −0.250674 | −0.125337 | − | 0.992114i | \(-0.540001\pi\) | ||||
−0.125337 | + | 0.992114i | \(0.540001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3852.49 | 0.379299 | ||||||||
\(470\) | −5696.43 | −0.559057 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5745.17 | 0.560260 | ||||||||
\(473\) | −25570.4 | −2.48569 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1020.33 | −0.0985601 | ||||||||
\(476\) | −4157.97 | −0.400379 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11450.1 | 1.09564 | ||||||||
\(479\) | −8646.75 | −0.824802 | −0.412401 | − | 0.911002i | \(-0.635310\pi\) | ||||
−0.412401 | + | 0.911002i | \(0.635310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5528.60 | 0.524080 | ||||||||
\(482\) | 17784.0 | 1.68058 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 24580.1 | 2.30842 | ||||||||
\(485\) | 1146.82 | 0.107370 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15251.7 | −1.41914 | −0.709569 | − | 0.704636i | \(-0.751110\pi\) | ||||
−0.709569 | + | 0.704636i | \(0.751110\pi\) | |||||||
\(488\) | 952.515 | 0.0883572 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7072.16 | −0.652015 | ||||||||
\(491\) | −1766.87 | −0.162398 | −0.0811992 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0811992 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15149.9 | 1.38401 | ||||||||
\(494\) | −3860.61 | −0.351614 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5192.28 | −0.470041 | ||||||||
\(497\) | −4595.20 | −0.414734 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11733.8 | 1.05266 | 0.526332 | − | 0.850279i | \(-0.323567\pi\) | ||||
0.526332 | + | 0.850279i | \(0.323567\pi\) | |||||||
\(500\) | 1485.76 | 0.132891 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4313.98 | 0.383550 | ||||||||
\(503\) | −977.608 | −0.0866589 | −0.0433294 | − | 0.999061i | \(-0.513797\pi\) | ||||
−0.0433294 | + | 0.999061i | \(0.513797\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6728.31 | 0.592883 | ||||||||
\(506\) | −37520.6 | −3.29643 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3674.48 | 0.320923 | ||||||||
\(509\) | 9674.72 | 0.842484 | 0.421242 | − | 0.906948i | \(-0.361594\pi\) | ||||
0.421242 | + | 0.906948i | \(0.361594\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4403.51 | 0.381213 | ||||||||
\(512\) | 6352.52 | 0.548329 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16691.6 | 1.43237 | ||||||||
\(515\) | −7981.49 | −0.682926 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14894.7 | −1.26706 | ||||||||
\(518\) | 5905.81 | 0.500939 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1837.97 | 0.155000 | ||||||||
\(521\) | 5178.95 | 0.435497 | 0.217748 | − | 0.976005i | \(-0.430129\pi\) | ||||
0.217748 | + | 0.976005i | \(0.430129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14280.7 | 1.19398 | 0.596992 | − | 0.802248i | \(-0.296363\pi\) | ||||
0.596992 | + | 0.802248i | \(0.296363\pi\) | |||||||
\(524\) | 33103.1 | 2.75976 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11137.2 | −0.923203 | ||||||||
\(527\) | −20071.5 | −1.65906 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8660.78 | 0.711826 | ||||||||
\(530\) | 4787.47 | 0.392367 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2464.96 | −0.200883 | ||||||||
\(533\) | −3601.07 | −0.292645 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4793.93 | 0.387401 | ||||||||
\(536\) | 13138.9 | 1.05880 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9556.08 | −0.765784 | ||||||||
\(539\) | −18491.9 | −1.47774 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12923.8 | 1.02706 | 0.513529 | − | 0.858072i | \(-0.328338\pi\) | ||||
0.513529 | + | 0.858072i | \(0.328338\pi\) | |||||||
\(542\) | 6870.32 | 0.544475 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15012.1 | 1.18316 | ||||||||
\(545\) | 8451.14 | 0.664233 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13653.3 | 1.06723 | 0.533614 | − | 0.845728i | \(-0.320834\pi\) | ||||
0.533614 | + | 0.845728i | \(0.320834\pi\) | |||||||
\(548\) | −29589.4 | −2.30656 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6499.63 | 0.503900 | ||||||||
\(551\) | 8981.28 | 0.694402 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1051.62 | 0.0808666 | ||||||||
\(554\) | 30224.8 | 2.31792 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 21229.2 | 1.61928 | ||||||||
\(557\) | −9313.63 | −0.708494 | −0.354247 | − | 0.935152i | \(-0.615263\pi\) | ||||
−0.354247 | + | 0.935152i | \(0.615263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9303.46 | −0.703925 | ||||||||
\(560\) | −452.471 | −0.0341436 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3690.82 | 0.277025 | ||||||||
\(563\) | −10625.4 | −0.795394 | −0.397697 | − | 0.917517i | \(-0.630190\pi\) | ||||
−0.397697 | + | 0.917517i | \(0.630190\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −58.1057 | −0.00432660 | ||||||||
\(566\) | −14145.1 | −1.05046 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15672.0 | −1.15771 | ||||||||
\(569\) | 9060.50 | 0.667550 | 0.333775 | − | 0.942653i | \(-0.391677\pi\) | ||||
0.333775 | + | 0.942653i | \(0.391677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21379.1 | −1.56688 | −0.783440 | − | 0.621467i | \(-0.786537\pi\) | ||||
−0.783440 | + | 0.621467i | \(0.786537\pi\) | |||||||
\(572\) | 14699.2 | 1.07448 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3846.77 | −0.279723 | ||||||||
\(575\) | −3607.96 | −0.261674 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6347.76 | 0.457991 | 0.228996 | − | 0.973427i | \(-0.426456\pi\) | ||||
0.228996 | + | 0.973427i | \(0.426456\pi\) | |||||||
\(578\) | −773.071 | −0.0556324 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13078.1 | −0.936277 | ||||||||
\(581\) | −2354.63 | −0.168135 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12518.0 | 0.889266 | ||||||||
\(584\) | 15018.2 | 1.06414 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6136.22 | 0.432568 | ||||||||
\(587\) | 14773.7 | 1.03880 | 0.519401 | − | 0.854531i | \(-0.326155\pi\) | ||||
0.519401 | + | 0.854531i | \(0.326155\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11898.9 | −0.832405 | ||||||||
\(590\) | 7391.95 | 0.515800 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4641.81 | −0.322259 | ||||||||
\(593\) | 26868.1 | 1.86061 | 0.930304 | − | 0.366790i | \(-0.119543\pi\) | ||||
0.930304 | + | 0.366790i | \(0.119543\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1749.09 | −0.120514 | ||||||||
\(596\) | 18647.3 | 1.28158 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13651.4 | −0.933522 | ||||||||
\(599\) | −1749.83 | −0.119359 | −0.0596794 | − | 0.998218i | \(-0.519008\pi\) | ||||
−0.0596794 | + | 0.998218i | \(0.519008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17964.0 | −1.21924 | −0.609622 | − | 0.792692i | \(-0.708679\pi\) | ||||
−0.609622 | + | 0.792692i | \(0.708679\pi\) | |||||||
\(602\) | −9938.21 | −0.672843 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5209.99 | −0.350979 | ||||||||
\(605\) | 10339.8 | 0.694834 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4418.22 | −0.295437 | −0.147718 | − | 0.989029i | \(-0.547193\pi\) | ||||
−0.147718 | + | 0.989029i | \(0.547193\pi\) | |||||||
\(608\) | 8899.58 | 0.593628 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1225.54 | 0.0813455 | ||||||||
\(611\) | −5419.24 | −0.358820 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20179.7 | −1.32961 | −0.664804 | − | 0.747018i | \(-0.731485\pi\) | ||||
−0.664804 | + | 0.747018i | \(0.731485\pi\) | |||||||
\(614\) | −532.915 | −0.0350272 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5133.71 | 0.335784 | ||||||||
\(617\) | −4673.01 | −0.304908 | −0.152454 | − | 0.988311i | \(-0.548718\pi\) | ||||
−0.152454 | + | 0.988311i | \(0.548718\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19976.8 | −1.29715 | −0.648574 | − | 0.761151i | \(-0.724634\pi\) | ||||
−0.648574 | + | 0.761151i | \(0.724634\pi\) | |||||||
\(620\) | 17326.7 | 1.12235 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9540.19 | 0.614994 | ||||||||
\(623\) | 3057.56 | 0.196627 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 23026.0 | 1.47014 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −531.877 | −0.0337965 | ||||||||
\(629\) | −17943.5 | −1.13745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10457.5 | 0.659757 | 0.329879 | − | 0.944023i | \(-0.392992\pi\) | ||||
0.329879 | + | 0.944023i | \(0.392992\pi\) | |||||||
\(632\) | 3586.54 | 0.225736 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −38492.0 | −2.41122 | ||||||||
\(635\) | 1545.70 | 0.0965975 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6728.02 | −0.418483 | ||||||||
\(638\) | −57211.8 | −3.55021 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9782.40 | −0.604193 | ||||||||
\(641\) | 4395.86 | 0.270867 | 0.135434 | − | 0.990786i | \(-0.456757\pi\) | ||||
0.135434 | + | 0.990786i | \(0.456757\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5786.36 | 0.354886 | 0.177443 | − | 0.984131i | \(-0.443217\pi\) | ||||
0.177443 | + | 0.984131i | \(0.443217\pi\) | |||||||
\(644\) | −8716.26 | −0.533336 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12529.9 | 0.763133 | ||||||||
\(647\) | −25367.7 | −1.54143 | −0.770717 | − | 0.637178i | \(-0.780102\pi\) | ||||
−0.770717 | + | 0.637178i | \(0.780102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19328.1 | 1.16902 | ||||||||
\(650\) | 2364.80 | 0.142700 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −31044.6 | −1.86472 | ||||||||
\(653\) | −21633.2 | −1.29644 | −0.648218 | − | 0.761454i | \(-0.724486\pi\) | ||||
−0.648218 | + | 0.761454i | \(0.724486\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13925.1 | 0.830687 | ||||||||
\(656\) | 3023.46 | 0.179948 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5788.98 | −0.342976 | ||||||||
\(659\) | 18312.4 | 1.08248 | 0.541238 | − | 0.840870i | \(-0.317956\pi\) | ||||
0.541238 | + | 0.840870i | \(0.317956\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5526.08 | −0.325174 | −0.162587 | − | 0.986694i | \(-0.551984\pi\) | ||||
−0.162587 | + | 0.986694i | \(0.551984\pi\) | |||||||
\(662\) | −13121.0 | −0.770337 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8030.48 | −0.469342 | ||||||||
\(665\) | −1036.91 | −0.0604656 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31758.4 | 1.84361 | ||||||||
\(668\) | −2245.84 | −0.130081 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16905.1 | 0.974775 | ||||||||
\(671\) | 3204.48 | 0.184363 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1437.24 | 0.0823204 | 0.0411602 | − | 0.999153i | \(-0.486895\pi\) | ||||
0.0411602 | + | 0.999153i | \(0.486895\pi\) | |||||||
\(674\) | 44136.6 | 2.52237 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20765.7 | −1.18148 | ||||||||
\(677\) | −23405.9 | −1.32875 | −0.664373 | − | 0.747401i | \(-0.731301\pi\) | ||||
−0.664373 | + | 0.747401i | \(0.731301\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1165.45 | 0.0658701 | ||||||||
\(680\) | −5965.28 | −0.336409 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 75797.4 | 4.25577 | ||||||||
\(683\) | 19227.4 | 1.07719 | 0.538593 | − | 0.842566i | \(-0.318956\pi\) | ||||
0.538593 | + | 0.842566i | \(0.318956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12447.1 | −0.694274 | ||||||||
\(686\) | −14959.2 | −0.832570 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7811.17 | 0.432846 | ||||||||
\(689\) | 4554.50 | 0.251833 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35284.8 | −1.94254 | −0.971271 | − | 0.237975i | \(-0.923516\pi\) | ||||
−0.971271 | + | 0.237975i | \(0.923516\pi\) | |||||||
\(692\) | −17888.8 | −0.982703 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −53582.8 | −2.93080 | ||||||||
\(695\) | 8930.26 | 0.487401 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11687.6 | 0.635149 | ||||||||
\(698\) | 35205.1 | 1.90907 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1509.90 | 0.0815270 | ||||||||
\(701\) | 9173.00 | 0.494236 | 0.247118 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247118 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10637.4 | −0.570695 | ||||||||
\(704\) | −48384.9 | −2.59030 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3305.09 | 0.176188 | ||||||||
\(707\) | 6837.63 | 0.363728 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33951.6 | −1.79842 | −0.899210 | − | 0.437517i | \(-0.855858\pi\) | ||||
−0.899210 | + | 0.437517i | \(0.855858\pi\) | |||||||
\(710\) | −20164.2 | −1.06584 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10427.8 | 0.548876 | ||||||||
\(713\) | −42075.3 | −2.21001 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6183.35 | 0.323418 | ||||||||
\(716\) | −37282.1 | −1.94595 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −51569.9 | −2.68046 | ||||||||
\(719\) | −6727.90 | −0.348968 | −0.174484 | − | 0.984660i | \(-0.555826\pi\) | ||||
−0.174484 | + | 0.984660i | \(0.555826\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8111.17 | −0.418968 | ||||||||
\(722\) | −23158.8 | −1.19374 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 53638.0 | 2.75337 | ||||||||
\(725\) | −5501.45 | −0.281819 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36726.1 | −1.87359 | −0.936793 | − | 0.349885i | \(-0.886221\pi\) | ||||
−0.936793 | + | 0.349885i | \(0.886221\pi\) | |||||||
\(728\) | 1867.83 | 0.0950912 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 19323.0 | 0.979694 | ||||||||
\(731\) | 30195.1 | 1.52778 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26691.4 | 1.34498 | 0.672489 | − | 0.740108i | \(-0.265225\pi\) | ||||
0.672489 | + | 0.740108i | \(0.265225\pi\) | |||||||
\(734\) | −5121.91 | −0.257566 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31469.5 | 1.57606 | ||||||||
\(737\) | 44202.4 | 2.20925 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12207.0 | 0.607634 | 0.303817 | − | 0.952730i | \(-0.401739\pi\) | ||||
0.303817 | + | 0.952730i | \(0.401739\pi\) | |||||||
\(740\) | 15489.8 | 0.769480 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4865.25 | 0.240713 | ||||||||
\(743\) | −12473.3 | −0.615882 | −0.307941 | − | 0.951405i | \(-0.599640\pi\) | ||||
−0.307941 | + | 0.951405i | \(0.599640\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7844.16 | 0.385755 | ||||||||
\(746\) | −20526.4 | −1.00741 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −47707.4 | −2.33202 | ||||||||
\(749\) | 4871.82 | 0.237667 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15102.6 | −0.733825 | −0.366913 | − | 0.930255i | \(-0.619585\pi\) | ||||
−0.366913 | + | 0.930255i | \(0.619585\pi\) | |||||||
\(752\) | 4549.99 | 0.220640 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20815.7 | −1.00539 | ||||||||
\(755\) | −2191.63 | −0.105645 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3418.34 | −0.164124 | −0.0820618 | − | 0.996627i | \(-0.526150\pi\) | ||||
−0.0820618 | + | 0.996627i | \(0.526150\pi\) | |||||||
\(758\) | −17786.1 | −0.852268 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3536.39 | −0.168787 | ||||||||
\(761\) | −12684.5 | −0.604224 | −0.302112 | − | 0.953272i | \(-0.597692\pi\) | ||||
−0.302112 | + | 0.953272i | \(0.597692\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8588.45 | 0.407500 | ||||||||
\(764\) | 14351.7 | 0.679614 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34730.6 | 1.63821 | ||||||||
\(767\) | 7032.25 | 0.331056 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27580.2 | −1.29333 | −0.646663 | − | 0.762776i | \(-0.723836\pi\) | ||||
−0.646663 | + | 0.762776i | \(0.723836\pi\) | |||||||
\(770\) | 6605.22 | 0.309137 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10972.8 | 0.511555 | ||||||||
\(773\) | 17386.0 | 0.808966 | 0.404483 | − | 0.914546i | \(-0.367452\pi\) | ||||
0.404483 | + | 0.914546i | \(0.367452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7288.63 | 0.337826 | ||||||||
\(776\) | 3974.77 | 0.183874 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38015.7 | 1.75183 | ||||||||
\(779\) | 6928.72 | 0.318674 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52724.1 | −2.41564 | ||||||||
\(782\) | 44306.7 | 2.02609 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5648.84 | 0.257327 | ||||||||
\(785\) | −223.739 | −0.0101727 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4680.29 | 0.211988 | 0.105994 | − | 0.994367i | \(-0.466198\pi\) | ||||
0.105994 | + | 0.994367i | \(0.466198\pi\) | |||||||
\(788\) | −14036.0 | −0.634531 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4614.58 | 0.207822 | ||||||||
\(791\) | −59.0498 | −0.00265432 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1165.91 | 0.0522100 | ||||||||
\(794\) | −694.456 | −0.0310395 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9982.00 | −0.444476 | ||||||||
\(797\) | 7278.62 | 0.323490 | 0.161745 | − | 0.986833i | \(-0.448288\pi\) | ||||
0.161745 | + | 0.986833i | \(0.448288\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17588.6 | 0.778773 | ||||||||
\(800\) | −5451.40 | −0.240920 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26461.8 | 1.16508 | ||||||||
\(803\) | 50524.7 | 2.22039 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3666.58 | −0.160534 | ||||||||
\(806\) | 27577.9 | 1.20520 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 23319.8 | 1.01533 | ||||||||
\(809\) | 29212.5 | 1.26954 | 0.634770 | − | 0.772701i | \(-0.281095\pi\) | ||||
0.634770 | + | 0.772701i | \(0.281095\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41992.4 | 1.81819 | 0.909094 | − | 0.416590i | \(-0.136775\pi\) | ||||
0.909094 | + | 0.416590i | \(0.136775\pi\) | |||||||
\(812\) | −13290.6 | −0.574396 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 67761.6 | 2.91774 | ||||||||
\(815\) | −13059.2 | −0.561281 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17900.5 | 0.766536 | ||||||||
\(818\) | 63151.2 | 2.69930 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10089.3 | −0.429675 | ||||||||
\(821\) | −8722.99 | −0.370809 | −0.185405 | − | 0.982662i | \(-0.559360\pi\) | ||||
−0.185405 | + | 0.982662i | \(0.559360\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13584.8 | 0.575379 | 0.287690 | − | 0.957724i | \(-0.407113\pi\) | ||||
0.287690 | + | 0.957724i | \(0.407113\pi\) | |||||||
\(824\) | −27663.2 | −1.16953 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7512.05 | 0.316438 | ||||||||
\(827\) | 26573.6 | 1.11736 | 0.558679 | − | 0.829384i | \(-0.311308\pi\) | ||||
0.558679 | + | 0.829384i | \(0.311308\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43238.4 | −1.81150 | −0.905748 | − | 0.423816i | \(-0.860690\pi\) | ||||
−0.905748 | + | 0.423816i | \(0.860690\pi\) | |||||||
\(830\) | −10332.3 | −0.432097 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17604.2 | −0.733552 | ||||||||
\(833\) | 21836.3 | 0.908265 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −944.733 | −0.0391543 | ||||||||
\(836\) | −28282.3 | −1.17005 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 42918.2 | 1.76919 | ||||||||
\(839\) | −4093.21 | −0.168431 | −0.0842154 | − | 0.996448i | \(-0.526838\pi\) | ||||
−0.0842154 | + | 0.996448i | \(0.526838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24036.5 | 0.985546 | ||||||||
\(842\) | −6850.75 | −0.280395 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30780.8 | −1.25535 | ||||||||
\(845\) | −8735.27 | −0.355624 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10507.8 | 0.426273 | ||||||||
\(848\) | −3823.96 | −0.154853 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7675.16 | −0.309713 | ||||||||
\(851\) | −37614.7 | −1.51517 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20201.5 | −0.810886 | −0.405443 | − | 0.914120i | \(-0.632883\pi\) | ||||
−0.405443 | + | 0.914120i | \(0.632883\pi\) | |||||||
\(854\) | 1245.45 | 0.0499046 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16615.4 | 0.663436 | ||||||||
\(857\) | 4551.65 | 0.181425 | 0.0907126 | − | 0.995877i | \(-0.471086\pi\) | ||||
0.0907126 | + | 0.995877i | \(0.471086\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11962.6 | 0.475154 | 0.237577 | − | 0.971369i | \(-0.423647\pi\) | ||||
0.237577 | + | 0.971369i | \(0.423647\pi\) | |||||||
\(860\) | −26065.9 | −1.03354 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 51649.3 | 2.04081 | ||||||||
\(863\) | −7164.61 | −0.282603 | −0.141301 | − | 0.989967i | \(-0.545129\pi\) | ||||
−0.141301 | + | 0.989967i | \(0.545129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7525.10 | −0.295793 | ||||||||
\(866\) | 66412.0 | 2.60597 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17608.2 | 0.688549 | ||||||||
\(869\) | 12065.9 | 0.471012 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16082.4 | 0.625640 | ||||||||
\(872\) | 29291.0 | 1.13752 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26266.2 | 1.01655 | ||||||||
\(875\) | 635.154 | 0.0245396 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19218.7 | −0.739987 | −0.369994 | − | 0.929034i | \(-0.620640\pi\) | ||||
−0.369994 | + | 0.929034i | \(0.620640\pi\) | |||||||
\(878\) | −7324.56 | −0.281540 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5191.53 | −0.198871 | ||||||||
\(881\) | −45914.5 | −1.75585 | −0.877923 | − | 0.478802i | \(-0.841071\pi\) | ||||
−0.877923 | + | 0.478802i | \(0.841071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44656.7 | −1.70194 | −0.850972 | − | 0.525211i | \(-0.823986\pi\) | ||||
−0.850972 | + | 0.525211i | \(0.823986\pi\) | |||||||
\(884\) | −17357.7 | −0.660410 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17464.3 | 0.662218 | ||||||||
\(887\) | 14975.2 | 0.566873 | 0.283437 | − | 0.958991i | \(-0.408525\pi\) | ||||
0.283437 | + | 0.958991i | \(0.408525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1570.82 | 0.0592616 | ||||||||
\(890\) | 13416.9 | 0.505319 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −49692.9 | −1.86529 | ||||||||
\(893\) | 10427.0 | 0.390735 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15683.1 | −0.585729 | ||||||||
\(896\) | −9941.33 | −0.370666 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17771.7 | −0.660413 | ||||||||
\(899\) | −64156.8 | −2.38015 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14782.0 | −0.546571 | ||||||||
\(902\) | −44136.7 | −1.62926 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −201.390 | −0.00740943 | ||||||||
\(905\) | 22563.3 | 0.828763 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14818.1 | −0.542479 | −0.271240 | − | 0.962512i | \(-0.587434\pi\) | ||||
−0.271240 | + | 0.962512i | \(0.587434\pi\) | |||||||
\(908\) | −30935.6 | −1.13065 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2403.22 | 0.0875451 | ||||||||
\(911\) | 21846.5 | 0.794518 | 0.397259 | − | 0.917707i | \(-0.369961\pi\) | ||||
0.397259 | + | 0.917707i | \(0.369961\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27016.4 | −0.979312 | ||||||||
\(914\) | −63224.2 | −2.28804 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21934.0 | −0.791179 | ||||||||
\(917\) | 14151.4 | 0.509618 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28878.9 | 1.03659 | 0.518296 | − | 0.855201i | \(-0.326566\pi\) | ||||
0.518296 | + | 0.855201i | \(0.326566\pi\) | |||||||
\(920\) | −12504.9 | −0.448124 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −73108.4 | −2.61139 | ||||||||
\(923\) | −19182.9 | −0.684089 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6515.92 | 0.231613 | ||||||||
\(926\) | 14803.4 | 0.525344 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 47985.0 | 1.69740 | ||||||||
\(929\) | 4608.79 | 0.162766 | 0.0813829 | − | 0.996683i | \(-0.474066\pi\) | ||||
0.0813829 | + | 0.996683i | \(0.474066\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12945.2 | 0.455705 | ||||||||
\(932\) | 2860.23 | 0.100526 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11281.3 | −0.395220 | ||||||||
\(935\) | −20068.6 | −0.701938 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21063.8 | −0.734391 | −0.367195 | − | 0.930144i | \(-0.619682\pi\) | ||||
−0.367195 | + | 0.930144i | \(0.619682\pi\) | |||||||
\(938\) | 17179.7 | 0.598014 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15183.3 | −0.526836 | ||||||||
\(941\) | −20244.8 | −0.701339 | −0.350670 | − | 0.936499i | \(-0.614046\pi\) | ||||
−0.350670 | + | 0.936499i | \(0.614046\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24500.4 | 0.846069 | ||||||||
\(944\) | −5904.27 | −0.203567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −114028. | −3.91901 | ||||||||
\(947\) | −29978.3 | −1.02868 | −0.514342 | − | 0.857585i | \(-0.671964\pi\) | ||||
−0.514342 | + | 0.857585i | \(0.671964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18382.7 | 0.628797 | ||||||||
\(950\) | −4550.05 | −0.155393 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6062.20 | −0.206383 | ||||||||
\(953\) | 5782.65 | 0.196556 | 0.0982782 | − | 0.995159i | \(-0.468666\pi\) | ||||
0.0982782 | + | 0.995159i | \(0.468666\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6037.17 | 0.204564 | ||||||||
\(956\) | 30519.2 | 1.03249 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38559.2 | −1.30041 | ||||||||
\(959\) | −12649.3 | −0.425930 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55207.7 | 1.85317 | ||||||||
\(962\) | 24654.2 | 0.826281 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 47401.6 | 1.58372 | ||||||||
\(965\) | 4615.82 | 0.153978 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26119.2 | −0.868600 | −0.434300 | − | 0.900768i | \(-0.643004\pi\) | ||||
−0.434300 | + | 0.900768i | \(0.643004\pi\) | |||||||
\(968\) | 35837.0 | 1.18992 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5114.09 | 0.169282 | ||||||||
\(971\) | 5101.93 | 0.168619 | 0.0843093 | − | 0.996440i | \(-0.473132\pi\) | ||||
0.0843093 | + | 0.996440i | \(0.473132\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9075.34 | 0.299016 | ||||||||
\(974\) | −68013.1 | −2.23746 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −978.894 | −0.0321041 | ||||||||
\(977\) | −45902.4 | −1.50312 | −0.751559 | − | 0.659666i | \(-0.770698\pi\) | ||||
−0.751559 | + | 0.659666i | \(0.770698\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35081.6 | 1.14526 | ||||||||
\(980\) | −18850.2 | −0.614437 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7879.14 | −0.256042 | ||||||||
\(983\) | 13416.5 | 0.435321 | 0.217661 | − | 0.976025i | \(-0.430157\pi\) | ||||
0.217661 | + | 0.976025i | \(0.430157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5904.37 | −0.190994 | ||||||||
\(986\) | 67559.2 | 2.18207 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10290.1 | −0.331349 | ||||||||
\(989\) | 63297.4 | 2.03513 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3806.66 | 0.122021 | 0.0610104 | − | 0.998137i | \(-0.480568\pi\) | ||||
0.0610104 | + | 0.998137i | \(0.480568\pi\) | |||||||
\(992\) | −63573.2 | −2.03473 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −20491.8 | −0.653883 | ||||||||
\(995\) | −4199.02 | −0.133787 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22523.8 | −0.715483 | −0.357742 | − | 0.933821i | \(-0.616453\pi\) | ||||
−0.357742 | + | 0.933821i | \(0.616453\pi\) | |||||||
\(998\) | 52325.7 | 1.65966 | ||||||||
\(999\) | 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 | 135.4.a.f.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 135.4.a.g.1.1 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bm.1.3 | 3 | |||
5.2 | odd | 4 | 675.4.b.l.649.5 | 6 | |||
5.3 | odd | 4 | 675.4.b.l.649.2 | 6 | |||
5.4 | even | 2 | 675.4.a.r.1.1 | 3 | |||
9.2 | odd | 6 | 405.4.e.r.271.3 | 6 | |||
9.4 | even | 3 | 405.4.e.t.136.1 | 6 | |||
9.5 | odd | 6 | 405.4.e.r.136.3 | 6 | |||
9.7 | even | 3 | 405.4.e.t.271.1 | 6 | |||
12.11 | even | 2 | 2160.4.a.be.1.3 | 3 | |||
15.2 | even | 4 | 675.4.b.k.649.2 | 6 | |||
15.8 | even | 4 | 675.4.b.k.649.5 | 6 | |||
15.14 | odd | 2 | 675.4.a.q.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.f.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
135.4.a.g.1.1 | yes | 3 | 3.2 | odd | 2 | ||
405.4.e.r.136.3 | 6 | 9.5 | odd | 6 | |||
405.4.e.r.271.3 | 6 | 9.2 | odd | 6 | |||
405.4.e.t.136.1 | 6 | 9.4 | even | 3 | |||
405.4.e.t.271.1 | 6 | 9.7 | even | 3 | |||
675.4.a.q.1.3 | 3 | 15.14 | odd | 2 | |||
675.4.a.r.1.1 | 3 | 5.4 | even | 2 | |||
675.4.b.k.649.2 | 6 | 15.2 | even | 4 | |||
675.4.b.k.649.5 | 6 | 15.8 | even | 4 | |||
675.4.b.l.649.2 | 6 | 5.3 | odd | 4 | |||
675.4.b.l.649.5 | 6 | 5.2 | odd | 4 | |||
2160.4.a.be.1.3 | 3 | 12.11 | even | 2 | |||
2160.4.a.bm.1.3 | 3 | 4.3 | odd | 2 |