Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,4,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, 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("2166.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(127.798137072\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.373564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 106x - 348 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.80115\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −18.3722 | −1.64326 | −0.821629 | − | 0.570022i | \(-0.806935\pi\) | ||||
−0.821629 | + | 0.570022i | \(0.806935\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −27.9745 | −1.51048 | −0.755240 | − | 0.655448i | \(-0.772480\pi\) | ||||
−0.755240 | + | 0.655448i | \(0.772480\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 36.7444 | 1.16196 | ||||||||
\(11\) | 65.1791 | 1.78657 | 0.893283 | − | 0.449494i | \(-0.148396\pi\) | ||||
0.893283 | + | 0.449494i | \(0.148396\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 89.0910 | 1.90072 | 0.950362 | − | 0.311147i | \(-0.100713\pi\) | ||||
0.950362 | + | 0.311147i | \(0.100713\pi\) | |||||||
\(14\) | 55.9490 | 1.06807 | ||||||||
\(15\) | 55.1166 | 0.948736 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −27.5143 | −0.392541 | −0.196270 | − | 0.980550i | \(-0.562883\pi\) | ||||
−0.196270 | + | 0.980550i | \(0.562883\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −73.4887 | −0.821629 | ||||||||
\(21\) | 83.9235 | 0.872076 | ||||||||
\(22\) | −130.358 | −1.26329 | ||||||||
\(23\) | −79.9605 | −0.724909 | −0.362455 | − | 0.932001i | \(-0.618061\pi\) | ||||
−0.362455 | + | 0.932001i | \(0.618061\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | 212.537 | 1.70030 | ||||||||
\(26\) | −178.182 | −1.34401 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −111.898 | −0.755240 | ||||||||
\(29\) | 288.131 | 1.84499 | 0.922493 | − | 0.386014i | \(-0.126148\pi\) | ||||
0.922493 | + | 0.386014i | \(0.126148\pi\) | |||||||
\(30\) | −110.233 | −0.670857 | ||||||||
\(31\) | −7.47726 | −0.0433211 | −0.0216606 | − | 0.999765i | \(-0.506895\pi\) | ||||
−0.0216606 | + | 0.999765i | \(0.506895\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −195.537 | −1.03147 | ||||||||
\(34\) | 55.0285 | 0.277568 | ||||||||
\(35\) | 513.952 | 2.48211 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −18.9090 | −0.0840166 | −0.0420083 | − | 0.999117i | \(-0.513376\pi\) | ||||
−0.0420083 | + | 0.999117i | \(0.513376\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −267.273 | −1.09738 | ||||||||
\(40\) | 146.977 | 0.580980 | ||||||||
\(41\) | 129.177 | 0.492048 | 0.246024 | − | 0.969264i | \(-0.420876\pi\) | ||||
0.246024 | + | 0.969264i | \(0.420876\pi\) | |||||||
\(42\) | −167.847 | −0.616651 | ||||||||
\(43\) | 90.9800 | 0.322659 | 0.161329 | − | 0.986901i | \(-0.448422\pi\) | ||||
0.161329 | + | 0.986901i | \(0.448422\pi\) | |||||||
\(44\) | 260.716 | 0.893283 | ||||||||
\(45\) | −165.350 | −0.547753 | ||||||||
\(46\) | 159.921 | 0.512588 | ||||||||
\(47\) | 33.8549 | 0.105069 | 0.0525345 | − | 0.998619i | \(-0.483270\pi\) | ||||
0.0525345 | + | 0.998619i | \(0.483270\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 439.572 | 1.28155 | ||||||||
\(50\) | −425.074 | −1.20229 | ||||||||
\(51\) | 82.5428 | 0.226633 | ||||||||
\(52\) | 356.364 | 0.950362 | ||||||||
\(53\) | −227.188 | −0.588804 | −0.294402 | − | 0.955682i | \(-0.595120\pi\) | ||||
−0.294402 | + | 0.955682i | \(0.595120\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | −1197.48 | −2.93579 | ||||||||
\(56\) | 223.796 | 0.534035 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −576.262 | −1.30460 | ||||||||
\(59\) | −726.808 | −1.60377 | −0.801885 | − | 0.597479i | \(-0.796169\pi\) | ||||
−0.801885 | + | 0.597479i | \(0.796169\pi\) | |||||||
\(60\) | 220.466 | 0.474368 | ||||||||
\(61\) | 658.958 | 1.38313 | 0.691565 | − | 0.722314i | \(-0.256922\pi\) | ||||
0.691565 | + | 0.722314i | \(0.256922\pi\) | |||||||
\(62\) | 14.9545 | 0.0306327 | ||||||||
\(63\) | −251.770 | −0.503493 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −1636.80 | −3.12338 | ||||||||
\(66\) | 391.074 | 0.729363 | ||||||||
\(67\) | −545.672 | −0.994991 | −0.497496 | − | 0.867466i | \(-0.665747\pi\) | ||||
−0.497496 | + | 0.867466i | \(0.665747\pi\) | |||||||
\(68\) | −110.057 | −0.196270 | ||||||||
\(69\) | 239.881 | 0.418526 | ||||||||
\(70\) | −1027.90 | −1.75512 | ||||||||
\(71\) | −136.091 | −0.227479 | −0.113740 | − | 0.993511i | \(-0.536283\pi\) | ||||
−0.113740 | + | 0.993511i | \(0.536283\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | 174.940 | 0.280482 | 0.140241 | − | 0.990117i | \(-0.455212\pi\) | ||||
0.140241 | + | 0.990117i | \(0.455212\pi\) | |||||||
\(74\) | 37.8179 | 0.0594087 | ||||||||
\(75\) | −637.612 | −0.981667 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1823.35 | −2.69857 | ||||||||
\(78\) | 534.546 | 0.775967 | ||||||||
\(79\) | −260.421 | −0.370881 | −0.185441 | − | 0.982655i | \(-0.559371\pi\) | ||||
−0.185441 | + | 0.982655i | \(0.559371\pi\) | |||||||
\(80\) | −293.955 | −0.410815 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −258.353 | −0.347931 | ||||||||
\(83\) | −562.814 | −0.744300 | −0.372150 | − | 0.928173i | \(-0.621379\pi\) | ||||
−0.372150 | + | 0.928173i | \(0.621379\pi\) | |||||||
\(84\) | 335.694 | 0.436038 | ||||||||
\(85\) | 505.497 | 0.645045 | ||||||||
\(86\) | −181.960 | −0.228154 | ||||||||
\(87\) | −864.393 | −1.06520 | ||||||||
\(88\) | −521.433 | −0.631647 | ||||||||
\(89\) | 627.905 | 0.747840 | 0.373920 | − | 0.927461i | \(-0.378013\pi\) | ||||
0.373920 | + | 0.927461i | \(0.378013\pi\) | |||||||
\(90\) | 330.699 | 0.387320 | ||||||||
\(91\) | −2492.28 | −2.87101 | ||||||||
\(92\) | −319.842 | −0.362455 | ||||||||
\(93\) | 22.4318 | 0.0250115 | ||||||||
\(94\) | −67.7098 | −0.0742951 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 1089.92 | 1.14087 | 0.570436 | − | 0.821342i | \(-0.306774\pi\) | ||||
0.570436 | + | 0.821342i | \(0.306774\pi\) | |||||||
\(98\) | −879.144 | −0.906193 | ||||||||
\(99\) | 586.612 | 0.595522 | ||||||||
\(100\) | 850.149 | 0.850149 | ||||||||
\(101\) | −904.524 | −0.891123 | −0.445562 | − | 0.895251i | \(-0.646996\pi\) | ||||
−0.445562 | + | 0.895251i | \(0.646996\pi\) | |||||||
\(102\) | −165.086 | −0.160254 | ||||||||
\(103\) | 600.162 | 0.574133 | 0.287066 | − | 0.957911i | \(-0.407320\pi\) | ||||
0.287066 | + | 0.957911i | \(0.407320\pi\) | |||||||
\(104\) | −712.728 | −0.672007 | ||||||||
\(105\) | −1541.86 | −1.43305 | ||||||||
\(106\) | 454.375 | 0.416347 | ||||||||
\(107\) | 1023.13 | 0.924388 | 0.462194 | − | 0.886779i | \(-0.347062\pi\) | ||||
0.462194 | + | 0.886779i | \(0.347062\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −1580.94 | −1.38924 | −0.694620 | − | 0.719377i | \(-0.744427\pi\) | ||||
−0.694620 | + | 0.719377i | \(0.744427\pi\) | |||||||
\(110\) | 2394.96 | 2.07592 | ||||||||
\(111\) | 56.7269 | 0.0485070 | ||||||||
\(112\) | −447.592 | −0.377620 | ||||||||
\(113\) | −1552.87 | −1.29276 | −0.646380 | − | 0.763016i | \(-0.723718\pi\) | ||||
−0.646380 | + | 0.763016i | \(0.723718\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1469.05 | 1.19121 | ||||||||
\(116\) | 1152.52 | 0.922493 | ||||||||
\(117\) | 801.819 | 0.633575 | ||||||||
\(118\) | 1453.62 | 1.13404 | ||||||||
\(119\) | 769.697 | 0.592925 | ||||||||
\(120\) | −440.932 | −0.335429 | ||||||||
\(121\) | 2917.31 | 2.19182 | ||||||||
\(122\) | −1317.92 | −0.978021 | ||||||||
\(123\) | −387.530 | −0.284084 | ||||||||
\(124\) | −29.9090 | −0.0216606 | ||||||||
\(125\) | −1608.25 | −1.15077 | ||||||||
\(126\) | 503.541 | 0.356024 | ||||||||
\(127\) | −790.821 | −0.552551 | −0.276275 | − | 0.961078i | \(-0.589100\pi\) | ||||
−0.276275 | + | 0.961078i | \(0.589100\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −272.940 | −0.186287 | ||||||||
\(130\) | 3273.59 | 2.20856 | ||||||||
\(131\) | 1549.85 | 1.03367 | 0.516835 | − | 0.856085i | \(-0.327110\pi\) | ||||
0.516835 | + | 0.856085i | \(0.327110\pi\) | |||||||
\(132\) | −782.149 | −0.515737 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1091.34 | 0.703565 | ||||||||
\(135\) | 496.049 | 0.316245 | ||||||||
\(136\) | 220.114 | 0.138784 | ||||||||
\(137\) | −890.286 | −0.555199 | −0.277599 | − | 0.960697i | \(-0.589539\pi\) | ||||
−0.277599 | + | 0.960697i | \(0.589539\pi\) | |||||||
\(138\) | −479.763 | −0.295943 | ||||||||
\(139\) | −2272.69 | −1.38681 | −0.693407 | − | 0.720546i | \(-0.743891\pi\) | ||||
−0.693407 | + | 0.720546i | \(0.743891\pi\) | |||||||
\(140\) | 2055.81 | 1.24105 | ||||||||
\(141\) | −101.565 | −0.0606617 | ||||||||
\(142\) | 272.182 | 0.160852 | ||||||||
\(143\) | 5806.87 | 3.39577 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −5293.60 | −3.03179 | ||||||||
\(146\) | −349.880 | −0.198331 | ||||||||
\(147\) | −1318.72 | −0.739903 | ||||||||
\(148\) | −75.6358 | −0.0420083 | ||||||||
\(149\) | 1145.68 | 0.629918 | 0.314959 | − | 0.949105i | \(-0.398009\pi\) | ||||
0.314959 | + | 0.949105i | \(0.398009\pi\) | |||||||
\(150\) | 1275.22 | 0.694144 | ||||||||
\(151\) | 2001.84 | 1.07886 | 0.539430 | − | 0.842031i | \(-0.318640\pi\) | ||||
0.539430 | + | 0.842031i | \(0.318640\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −247.628 | −0.130847 | ||||||||
\(154\) | 3646.70 | 1.90818 | ||||||||
\(155\) | 137.374 | 0.0711878 | ||||||||
\(156\) | −1069.09 | −0.548692 | ||||||||
\(157\) | 1897.03 | 0.964330 | 0.482165 | − | 0.876080i | \(-0.339851\pi\) | ||||
0.482165 | + | 0.876080i | \(0.339851\pi\) | |||||||
\(158\) | 520.841 | 0.262253 | ||||||||
\(159\) | 681.563 | 0.339946 | ||||||||
\(160\) | 587.910 | 0.290490 | ||||||||
\(161\) | 2236.85 | 1.09496 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | 826.207 | 0.397015 | 0.198508 | − | 0.980099i | \(-0.436391\pi\) | ||||
0.198508 | + | 0.980099i | \(0.436391\pi\) | |||||||
\(164\) | 516.706 | 0.246024 | ||||||||
\(165\) | 3592.45 | 1.69498 | ||||||||
\(166\) | 1125.63 | 0.526300 | ||||||||
\(167\) | −716.397 | −0.331955 | −0.165977 | − | 0.986130i | \(-0.553078\pi\) | ||||
−0.165977 | + | 0.986130i | \(0.553078\pi\) | |||||||
\(168\) | −671.388 | −0.308325 | ||||||||
\(169\) | 5740.21 | 2.61275 | ||||||||
\(170\) | −1010.99 | −0.456116 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 363.920 | 0.161329 | ||||||||
\(173\) | −2149.19 | −0.944508 | −0.472254 | − | 0.881462i | \(-0.656560\pi\) | ||||
−0.472254 | + | 0.881462i | \(0.656560\pi\) | |||||||
\(174\) | 1728.79 | 0.753212 | ||||||||
\(175\) | −5945.62 | −2.56827 | ||||||||
\(176\) | 1042.87 | 0.446642 | ||||||||
\(177\) | 2180.43 | 0.925937 | ||||||||
\(178\) | −1255.81 | −0.528803 | ||||||||
\(179\) | −3096.34 | −1.29291 | −0.646457 | − | 0.762951i | \(-0.723750\pi\) | ||||
−0.646457 | + | 0.762951i | \(0.723750\pi\) | |||||||
\(180\) | −661.399 | −0.273876 | ||||||||
\(181\) | 635.770 | 0.261085 | 0.130542 | − | 0.991443i | \(-0.458328\pi\) | ||||
0.130542 | + | 0.991443i | \(0.458328\pi\) | |||||||
\(182\) | 4984.55 | 2.03011 | ||||||||
\(183\) | −1976.87 | −0.798550 | ||||||||
\(184\) | 639.684 | 0.256294 | ||||||||
\(185\) | 347.399 | 0.138061 | ||||||||
\(186\) | −44.8635 | −0.0176858 | ||||||||
\(187\) | −1793.35 | −0.701300 | ||||||||
\(188\) | 135.420 | 0.0525345 | ||||||||
\(189\) | 755.311 | 0.290692 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1005.89 | 0.381065 | 0.190533 | − | 0.981681i | \(-0.438979\pi\) | ||||
0.190533 | + | 0.981681i | \(0.438979\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | −3119.86 | −1.16359 | −0.581793 | − | 0.813337i | \(-0.697649\pi\) | ||||
−0.581793 | + | 0.813337i | \(0.697649\pi\) | |||||||
\(194\) | −2179.84 | −0.806718 | ||||||||
\(195\) | 4910.39 | 1.80328 | ||||||||
\(196\) | 1758.29 | 0.640775 | ||||||||
\(197\) | 4018.89 | 1.45347 | 0.726736 | − | 0.686917i | \(-0.241036\pi\) | ||||
0.726736 | + | 0.686917i | \(0.241036\pi\) | |||||||
\(198\) | −1173.22 | −0.421098 | ||||||||
\(199\) | 4225.98 | 1.50539 | 0.752693 | − | 0.658371i | \(-0.228754\pi\) | ||||
0.752693 | + | 0.658371i | \(0.228754\pi\) | |||||||
\(200\) | −1700.30 | −0.601146 | ||||||||
\(201\) | 1637.02 | 0.574459 | ||||||||
\(202\) | 1809.05 | 0.630119 | ||||||||
\(203\) | −8060.32 | −2.78681 | ||||||||
\(204\) | 330.171 | 0.113317 | ||||||||
\(205\) | −2373.26 | −0.808563 | ||||||||
\(206\) | −1200.32 | −0.405973 | ||||||||
\(207\) | −719.644 | −0.241636 | ||||||||
\(208\) | 1425.46 | 0.475181 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3083.71 | 1.01332 | ||||||||
\(211\) | −1322.32 | −0.431433 | −0.215717 | − | 0.976456i | \(-0.569209\pi\) | ||||
−0.215717 | + | 0.976456i | \(0.569209\pi\) | |||||||
\(212\) | −908.751 | −0.294402 | ||||||||
\(213\) | 408.273 | 0.131335 | ||||||||
\(214\) | −2046.26 | −0.653641 | ||||||||
\(215\) | −1671.50 | −0.530212 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 209.172 | 0.0654357 | ||||||||
\(218\) | 3161.89 | 0.982340 | ||||||||
\(219\) | −524.820 | −0.161936 | ||||||||
\(220\) | −4789.93 | −1.46790 | ||||||||
\(221\) | −2451.27 | −0.746111 | ||||||||
\(222\) | −113.454 | −0.0342996 | ||||||||
\(223\) | 1951.65 | 0.586065 | 0.293032 | − | 0.956103i | \(-0.405336\pi\) | ||||
0.293032 | + | 0.956103i | \(0.405336\pi\) | |||||||
\(224\) | 895.184 | 0.267018 | ||||||||
\(225\) | 1912.84 | 0.566766 | ||||||||
\(226\) | 3105.74 | 0.914119 | ||||||||
\(227\) | −2592.81 | −0.758110 | −0.379055 | − | 0.925374i | \(-0.623751\pi\) | ||||
−0.379055 | + | 0.925374i | \(0.623751\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2517.84 | 0.726566 | 0.363283 | − | 0.931679i | \(-0.381656\pi\) | ||||
0.363283 | + | 0.931679i | \(0.381656\pi\) | |||||||
\(230\) | −2938.10 | −0.842315 | ||||||||
\(231\) | 5470.05 | 1.55802 | ||||||||
\(232\) | −2305.05 | −0.652301 | ||||||||
\(233\) | −4616.68 | −1.29806 | −0.649032 | − | 0.760761i | \(-0.724826\pi\) | ||||
−0.649032 | + | 0.760761i | \(0.724826\pi\) | |||||||
\(234\) | −1603.64 | −0.448005 | ||||||||
\(235\) | −621.989 | −0.172656 | ||||||||
\(236\) | −2907.23 | −0.801885 | ||||||||
\(237\) | 781.262 | 0.214128 | ||||||||
\(238\) | −1539.39 | −0.419261 | ||||||||
\(239\) | 1825.28 | 0.494006 | 0.247003 | − | 0.969015i | \(-0.420554\pi\) | ||||
0.247003 | + | 0.969015i | \(0.420554\pi\) | |||||||
\(240\) | 881.865 | 0.237184 | ||||||||
\(241\) | 5738.83 | 1.53390 | 0.766951 | − | 0.641706i | \(-0.221773\pi\) | ||||
0.766951 | + | 0.641706i | \(0.221773\pi\) | |||||||
\(242\) | −5834.62 | −1.54985 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 2635.83 | 0.691565 | ||||||||
\(245\) | −8075.89 | −2.10592 | ||||||||
\(246\) | 775.059 | 0.200878 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 59.8181 | 0.0153163 | ||||||||
\(249\) | 1688.44 | 0.429722 | ||||||||
\(250\) | 3216.50 | 0.813718 | ||||||||
\(251\) | −4617.24 | −1.16110 | −0.580552 | − | 0.814223i | \(-0.697163\pi\) | ||||
−0.580552 | + | 0.814223i | \(0.697163\pi\) | |||||||
\(252\) | −1007.08 | −0.251747 | ||||||||
\(253\) | −5211.75 | −1.29510 | ||||||||
\(254\) | 1581.64 | 0.390713 | ||||||||
\(255\) | −1516.49 | −0.372417 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5790.72 | −1.40551 | −0.702753 | − | 0.711433i | \(-0.748046\pi\) | ||||
−0.702753 | + | 0.711433i | \(0.748046\pi\) | |||||||
\(258\) | 545.880 | 0.131725 | ||||||||
\(259\) | 528.968 | 0.126905 | ||||||||
\(260\) | −6547.19 | −1.56169 | ||||||||
\(261\) | 2593.18 | 0.614995 | ||||||||
\(262\) | −3099.69 | −0.730915 | ||||||||
\(263\) | 825.091 | 0.193450 | 0.0967249 | − | 0.995311i | \(-0.469163\pi\) | ||||
0.0967249 | + | 0.995311i | \(0.469163\pi\) | |||||||
\(264\) | 1564.30 | 0.364681 | ||||||||
\(265\) | 4173.93 | 0.967557 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1883.71 | −0.431766 | ||||||||
\(268\) | −2182.69 | −0.497496 | ||||||||
\(269\) | −2140.39 | −0.485137 | −0.242568 | − | 0.970134i | \(-0.577990\pi\) | ||||
−0.242568 | + | 0.970134i | \(0.577990\pi\) | |||||||
\(270\) | −992.098 | −0.223619 | ||||||||
\(271\) | 3265.58 | 0.731991 | 0.365996 | − | 0.930617i | \(-0.380729\pi\) | ||||
0.365996 | + | 0.930617i | \(0.380729\pi\) | |||||||
\(272\) | −440.228 | −0.0981351 | ||||||||
\(273\) | 7476.83 | 1.65758 | ||||||||
\(274\) | 1780.57 | 0.392585 | ||||||||
\(275\) | 13853.0 | 3.03770 | ||||||||
\(276\) | 959.525 | 0.209263 | ||||||||
\(277\) | 1560.60 | 0.338510 | 0.169255 | − | 0.985572i | \(-0.445864\pi\) | ||||
0.169255 | + | 0.985572i | \(0.445864\pi\) | |||||||
\(278\) | 4545.38 | 0.980626 | ||||||||
\(279\) | −67.2953 | −0.0144404 | ||||||||
\(280\) | −4111.62 | −0.877558 | ||||||||
\(281\) | 5449.39 | 1.15688 | 0.578440 | − | 0.815725i | \(-0.303662\pi\) | ||||
0.578440 | + | 0.815725i | \(0.303662\pi\) | |||||||
\(282\) | 203.129 | 0.0428943 | ||||||||
\(283\) | −3911.92 | −0.821694 | −0.410847 | − | 0.911704i | \(-0.634767\pi\) | ||||
−0.410847 | + | 0.911704i | \(0.634767\pi\) | |||||||
\(284\) | −544.364 | −0.113740 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11613.7 | −2.40117 | ||||||||
\(287\) | −3613.65 | −0.743229 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −4155.97 | −0.845912 | ||||||||
\(290\) | 10587.2 | 2.14380 | ||||||||
\(291\) | −3269.76 | −0.658683 | ||||||||
\(292\) | 699.760 | 0.140241 | ||||||||
\(293\) | 989.750 | 0.197344 | 0.0986720 | − | 0.995120i | \(-0.468541\pi\) | ||||
0.0986720 | + | 0.995120i | \(0.468541\pi\) | |||||||
\(294\) | 2637.43 | 0.523191 | ||||||||
\(295\) | 13353.1 | 2.63541 | ||||||||
\(296\) | 151.272 | 0.0297043 | ||||||||
\(297\) | −1759.84 | −0.343825 | ||||||||
\(298\) | −2291.36 | −0.445419 | ||||||||
\(299\) | −7123.76 | −1.37785 | ||||||||
\(300\) | −2550.45 | −0.490834 | ||||||||
\(301\) | −2545.12 | −0.487370 | ||||||||
\(302\) | −4003.69 | −0.762869 | ||||||||
\(303\) | 2713.57 | 0.514490 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12106.5 | −2.27284 | ||||||||
\(306\) | 495.257 | 0.0925227 | ||||||||
\(307\) | 6992.74 | 1.29999 | 0.649994 | − | 0.759939i | \(-0.274771\pi\) | ||||
0.649994 | + | 0.759939i | \(0.274771\pi\) | |||||||
\(308\) | −7293.40 | −1.34929 | ||||||||
\(309\) | −1800.48 | −0.331476 | ||||||||
\(310\) | −274.747 | −0.0503374 | ||||||||
\(311\) | −2876.02 | −0.524385 | −0.262193 | − | 0.965016i | \(-0.584446\pi\) | ||||
−0.262193 | + | 0.965016i | \(0.584446\pi\) | |||||||
\(312\) | 2138.19 | 0.387984 | ||||||||
\(313\) | 6200.47 | 1.11972 | 0.559858 | − | 0.828588i | \(-0.310856\pi\) | ||||
0.559858 | + | 0.828588i | \(0.310856\pi\) | |||||||
\(314\) | −3794.07 | −0.681884 | ||||||||
\(315\) | 4625.57 | 0.827370 | ||||||||
\(316\) | −1041.68 | −0.185441 | ||||||||
\(317\) | 674.175 | 0.119449 | 0.0597247 | − | 0.998215i | \(-0.480978\pi\) | ||||
0.0597247 | + | 0.998215i | \(0.480978\pi\) | |||||||
\(318\) | −1363.13 | −0.240378 | ||||||||
\(319\) | 18780.1 | 3.29619 | ||||||||
\(320\) | −1175.82 | −0.205407 | ||||||||
\(321\) | −3069.39 | −0.533696 | ||||||||
\(322\) | −4473.71 | −0.774254 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 18935.2 | 3.23180 | ||||||||
\(326\) | −1652.41 | −0.280732 | ||||||||
\(327\) | 4742.83 | 0.802078 | ||||||||
\(328\) | −1033.41 | −0.173965 | ||||||||
\(329\) | −947.074 | −0.158705 | ||||||||
\(330\) | −7184.89 | −1.19853 | ||||||||
\(331\) | 7356.68 | 1.22163 | 0.610815 | − | 0.791773i | \(-0.290842\pi\) | ||||
0.610815 | + | 0.791773i | \(0.290842\pi\) | |||||||
\(332\) | −2251.26 | −0.372150 | ||||||||
\(333\) | −170.181 | −0.0280055 | ||||||||
\(334\) | 1432.79 | 0.234728 | ||||||||
\(335\) | 10025.2 | 1.63503 | ||||||||
\(336\) | 1342.78 | 0.218019 | ||||||||
\(337\) | 1916.40 | 0.309771 | 0.154885 | − | 0.987932i | \(-0.450499\pi\) | ||||
0.154885 | + | 0.987932i | \(0.450499\pi\) | |||||||
\(338\) | −11480.4 | −1.84749 | ||||||||
\(339\) | 4658.61 | 0.746375 | ||||||||
\(340\) | 2021.99 | 0.322523 | ||||||||
\(341\) | −487.361 | −0.0773961 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2701.55 | −0.425276 | ||||||||
\(344\) | −727.840 | −0.114077 | ||||||||
\(345\) | −4407.15 | −0.687747 | ||||||||
\(346\) | 4298.38 | 0.667868 | ||||||||
\(347\) | −27.7822 | −0.00429807 | −0.00214903 | − | 0.999998i | \(-0.500684\pi\) | ||||
−0.00214903 | + | 0.999998i | \(0.500684\pi\) | |||||||
\(348\) | −3457.57 | −0.532602 | ||||||||
\(349\) | −1867.83 | −0.286484 | −0.143242 | − | 0.989688i | \(-0.545753\pi\) | ||||
−0.143242 | + | 0.989688i | \(0.545753\pi\) | |||||||
\(350\) | 11891.2 | 1.81604 | ||||||||
\(351\) | −2405.46 | −0.365794 | ||||||||
\(352\) | −2085.73 | −0.315823 | ||||||||
\(353\) | 5429.71 | 0.818680 | 0.409340 | − | 0.912382i | \(-0.365759\pi\) | ||||
0.409340 | + | 0.912382i | \(0.365759\pi\) | |||||||
\(354\) | −4360.85 | −0.654736 | ||||||||
\(355\) | 2500.29 | 0.373808 | ||||||||
\(356\) | 2511.62 | 0.373920 | ||||||||
\(357\) | −2309.09 | −0.342325 | ||||||||
\(358\) | 6192.68 | 0.914228 | ||||||||
\(359\) | 4944.58 | 0.726922 | 0.363461 | − | 0.931609i | \(-0.381595\pi\) | ||||
0.363461 | + | 0.931609i | \(0.381595\pi\) | |||||||
\(360\) | 1322.80 | 0.193660 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −1271.54 | −0.184615 | ||||||||
\(363\) | −8751.94 | −1.26545 | ||||||||
\(364\) | −9969.10 | −1.43550 | ||||||||
\(365\) | −3214.03 | −0.460904 | ||||||||
\(366\) | 3953.75 | 0.564660 | ||||||||
\(367\) | −9812.06 | −1.39560 | −0.697801 | − | 0.716292i | \(-0.745838\pi\) | ||||
−0.697801 | + | 0.716292i | \(0.745838\pi\) | |||||||
\(368\) | −1279.37 | −0.181227 | ||||||||
\(369\) | 1162.59 | 0.164016 | ||||||||
\(370\) | −694.798 | −0.0976238 | ||||||||
\(371\) | 6355.46 | 0.889377 | ||||||||
\(372\) | 89.7271 | 0.0125057 | ||||||||
\(373\) | −269.962 | −0.0374748 | −0.0187374 | − | 0.999824i | \(-0.505965\pi\) | ||||
−0.0187374 | + | 0.999824i | \(0.505965\pi\) | |||||||
\(374\) | 3586.71 | 0.495894 | ||||||||
\(375\) | 4824.75 | 0.664398 | ||||||||
\(376\) | −270.839 | −0.0371475 | ||||||||
\(377\) | 25669.9 | 3.50681 | ||||||||
\(378\) | −1510.62 | −0.205550 | ||||||||
\(379\) | −3021.23 | −0.409473 | −0.204736 | − | 0.978817i | \(-0.565634\pi\) | ||||
−0.204736 | + | 0.978817i | \(0.565634\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2372.46 | 0.319015 | ||||||||
\(382\) | −2011.77 | −0.269454 | ||||||||
\(383\) | 1804.33 | 0.240723 | 0.120361 | − | 0.992730i | \(-0.461595\pi\) | ||||
0.120361 | + | 0.992730i | \(0.461595\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 33498.9 | 4.43445 | ||||||||
\(386\) | 6239.71 | 0.822780 | ||||||||
\(387\) | 818.820 | 0.107553 | ||||||||
\(388\) | 4359.68 | 0.570436 | ||||||||
\(389\) | −4112.87 | −0.536069 | −0.268035 | − | 0.963409i | \(-0.586374\pi\) | ||||
−0.268035 | + | 0.963409i | \(0.586374\pi\) | |||||||
\(390\) | −9820.78 | −1.27511 | ||||||||
\(391\) | 2200.05 | 0.284556 | ||||||||
\(392\) | −3516.57 | −0.453096 | ||||||||
\(393\) | −4649.54 | −0.596790 | ||||||||
\(394\) | −8037.78 | −1.02776 | ||||||||
\(395\) | 4784.50 | 0.609454 | ||||||||
\(396\) | 2346.45 | 0.297761 | ||||||||
\(397\) | −2793.39 | −0.353139 | −0.176569 | − | 0.984288i | \(-0.556500\pi\) | ||||
−0.176569 | + | 0.984288i | \(0.556500\pi\) | |||||||
\(398\) | −8451.96 | −1.06447 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3400.60 | 0.425074 | ||||||||
\(401\) | 936.825 | 0.116665 | 0.0583327 | − | 0.998297i | \(-0.481422\pi\) | ||||
0.0583327 | + | 0.998297i | \(0.481422\pi\) | |||||||
\(402\) | −3274.03 | −0.406204 | ||||||||
\(403\) | −666.157 | −0.0823415 | ||||||||
\(404\) | −3618.09 | −0.445562 | ||||||||
\(405\) | −1488.15 | −0.182584 | ||||||||
\(406\) | 16120.6 | 1.97058 | ||||||||
\(407\) | −1232.47 | −0.150101 | ||||||||
\(408\) | −660.342 | −0.0801270 | ||||||||
\(409\) | −2318.72 | −0.280326 | −0.140163 | − | 0.990128i | \(-0.544763\pi\) | ||||
−0.140163 | + | 0.990128i | \(0.544763\pi\) | |||||||
\(410\) | 4746.51 | 0.571740 | ||||||||
\(411\) | 2670.86 | 0.320544 | ||||||||
\(412\) | 2400.65 | 0.287066 | ||||||||
\(413\) | 20332.1 | 2.42246 | ||||||||
\(414\) | 1439.29 | 0.170863 | ||||||||
\(415\) | 10340.1 | 1.22308 | ||||||||
\(416\) | −2850.91 | −0.336004 | ||||||||
\(417\) | 6818.08 | 0.800678 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5725.14 | −0.667521 | −0.333761 | − | 0.942658i | \(-0.608318\pi\) | ||||
−0.333761 | + | 0.942658i | \(0.608318\pi\) | |||||||
\(420\) | −6167.43 | −0.716523 | ||||||||
\(421\) | 8066.56 | 0.933824 | 0.466912 | − | 0.884304i | \(-0.345366\pi\) | ||||
0.466912 | + | 0.884304i | \(0.345366\pi\) | |||||||
\(422\) | 2644.65 | 0.305070 | ||||||||
\(423\) | 304.694 | 0.0350230 | ||||||||
\(424\) | 1817.50 | 0.208174 | ||||||||
\(425\) | −5847.81 | −0.667436 | ||||||||
\(426\) | −816.547 | −0.0928681 | ||||||||
\(427\) | −18434.0 | −2.08919 | ||||||||
\(428\) | 4092.51 | 0.462194 | ||||||||
\(429\) | −17420.6 | −1.96055 | ||||||||
\(430\) | 3343.00 | 0.374916 | ||||||||
\(431\) | 11173.1 | 1.24870 | 0.624349 | − | 0.781145i | \(-0.285364\pi\) | ||||
0.624349 | + | 0.781145i | \(0.285364\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | 2150.59 | 0.238686 | 0.119343 | − | 0.992853i | \(-0.461921\pi\) | ||||
0.119343 | + | 0.992853i | \(0.461921\pi\) | |||||||
\(434\) | −418.345 | −0.0462700 | ||||||||
\(435\) | 15880.8 | 1.75040 | ||||||||
\(436\) | −6323.78 | −0.694620 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1049.64 | 0.114506 | ||||||||
\(439\) | −16649.7 | −1.81013 | −0.905063 | − | 0.425277i | \(-0.860177\pi\) | ||||
−0.905063 | + | 0.425277i | \(0.860177\pi\) | |||||||
\(440\) | 9579.86 | 1.03796 | ||||||||
\(441\) | 3956.15 | 0.427183 | ||||||||
\(442\) | 4902.55 | 0.527580 | ||||||||
\(443\) | 2507.67 | 0.268946 | 0.134473 | − | 0.990917i | \(-0.457066\pi\) | ||||
0.134473 | + | 0.990917i | \(0.457066\pi\) | |||||||
\(444\) | 226.907 | 0.0242535 | ||||||||
\(445\) | −11536.0 | −1.22889 | ||||||||
\(446\) | −3903.31 | −0.414410 | ||||||||
\(447\) | −3437.04 | −0.363683 | ||||||||
\(448\) | −1790.37 | −0.188810 | ||||||||
\(449\) | −17958.0 | −1.88750 | −0.943752 | − | 0.330655i | \(-0.892730\pi\) | ||||
−0.943752 | + | 0.330655i | \(0.892730\pi\) | |||||||
\(450\) | −3825.67 | −0.400764 | ||||||||
\(451\) | 8419.61 | 0.879077 | ||||||||
\(452\) | −6211.48 | −0.646380 | ||||||||
\(453\) | −6005.53 | −0.622880 | ||||||||
\(454\) | 5185.63 | 0.536065 | ||||||||
\(455\) | 45788.6 | 4.71780 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9750.15 | −0.998015 | −0.499007 | − | 0.866598i | \(-0.666302\pi\) | ||||
−0.499007 | + | 0.866598i | \(0.666302\pi\) | |||||||
\(458\) | −5035.68 | −0.513760 | ||||||||
\(459\) | 742.885 | 0.0755445 | ||||||||
\(460\) | 5876.19 | 0.595606 | ||||||||
\(461\) | 2514.25 | 0.254014 | 0.127007 | − | 0.991902i | \(-0.459463\pi\) | ||||
0.127007 | + | 0.991902i | \(0.459463\pi\) | |||||||
\(462\) | −10940.1 | −1.10169 | ||||||||
\(463\) | 9017.89 | 0.905177 | 0.452589 | − | 0.891719i | \(-0.350501\pi\) | ||||
0.452589 | + | 0.891719i | \(0.350501\pi\) | |||||||
\(464\) | 4610.10 | 0.461247 | ||||||||
\(465\) | −412.121 | −0.0411003 | ||||||||
\(466\) | 9233.36 | 0.917869 | ||||||||
\(467\) | −16395.0 | −1.62457 | −0.812283 | − | 0.583263i | \(-0.801776\pi\) | ||||
−0.812283 | + | 0.583263i | \(0.801776\pi\) | |||||||
\(468\) | 3207.28 | 0.316787 | ||||||||
\(469\) | 15264.9 | 1.50291 | ||||||||
\(470\) | 1243.98 | 0.122086 | ||||||||
\(471\) | −5691.10 | −0.556756 | ||||||||
\(472\) | 5814.47 | 0.567018 | ||||||||
\(473\) | 5929.99 | 0.576451 | ||||||||
\(474\) | −1562.52 | −0.151412 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3078.79 | 0.296462 | ||||||||
\(477\) | −2044.69 | −0.196268 | ||||||||
\(478\) | −3650.56 | −0.349315 | ||||||||
\(479\) | −10658.5 | −1.01670 | −0.508350 | − | 0.861151i | \(-0.669744\pi\) | ||||
−0.508350 | + | 0.861151i | \(0.669744\pi\) | |||||||
\(480\) | −1763.73 | −0.167714 | ||||||||
\(481\) | −1684.62 | −0.159692 | ||||||||
\(482\) | −11477.7 | −1.08463 | ||||||||
\(483\) | −6710.56 | −0.632176 | ||||||||
\(484\) | 11669.2 | 1.09591 | ||||||||
\(485\) | −20024.2 | −1.87475 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 13987.7 | 1.30153 | 0.650763 | − | 0.759281i | \(-0.274449\pi\) | ||||
0.650763 | + | 0.759281i | \(0.274449\pi\) | |||||||
\(488\) | −5271.66 | −0.489010 | ||||||||
\(489\) | −2478.62 | −0.229217 | ||||||||
\(490\) | 16151.8 | 1.48911 | ||||||||
\(491\) | 11659.2 | 1.07163 | 0.535815 | − | 0.844335i | \(-0.320004\pi\) | ||||
0.535815 | + | 0.844335i | \(0.320004\pi\) | |||||||
\(492\) | −1550.12 | −0.142042 | ||||||||
\(493\) | −7927.71 | −0.724232 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10777.3 | −0.978597 | ||||||||
\(496\) | −119.636 | −0.0108303 | ||||||||
\(497\) | 3807.08 | 0.343603 | ||||||||
\(498\) | −3376.89 | −0.303859 | ||||||||
\(499\) | −2154.41 | −0.193276 | −0.0966379 | − | 0.995320i | \(-0.530809\pi\) | ||||
−0.0966379 | + | 0.995320i | \(0.530809\pi\) | |||||||
\(500\) | −6433.00 | −0.575385 | ||||||||
\(501\) | 2149.19 | 0.191654 | ||||||||
\(502\) | 9234.47 | 0.821025 | ||||||||
\(503\) | 22014.5 | 1.95144 | 0.975722 | − | 0.219013i | \(-0.0702837\pi\) | ||||
0.975722 | + | 0.219013i | \(0.0702837\pi\) | |||||||
\(504\) | 2014.16 | 0.178012 | ||||||||
\(505\) | 16618.1 | 1.46435 | ||||||||
\(506\) | 10423.5 | 0.915773 | ||||||||
\(507\) | −17220.6 | −1.50847 | ||||||||
\(508\) | −3163.28 | −0.276275 | ||||||||
\(509\) | −17247.4 | −1.50192 | −0.750958 | − | 0.660350i | \(-0.770408\pi\) | ||||
−0.750958 | + | 0.660350i | \(0.770408\pi\) | |||||||
\(510\) | 3032.98 | 0.263339 | ||||||||
\(511\) | −4893.86 | −0.423663 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11581.4 | 0.993843 | ||||||||
\(515\) | −11026.3 | −0.943448 | ||||||||
\(516\) | −1091.76 | −0.0931435 | ||||||||
\(517\) | 2206.63 | 0.187713 | ||||||||
\(518\) | −1057.94 | −0.0897356 | ||||||||
\(519\) | 6447.57 | 0.545312 | ||||||||
\(520\) | 13094.4 | 1.10428 | ||||||||
\(521\) | −20135.5 | −1.69319 | −0.846593 | − | 0.532240i | \(-0.821350\pi\) | ||||
−0.846593 | + | 0.532240i | \(0.821350\pi\) | |||||||
\(522\) | −5186.36 | −0.434867 | ||||||||
\(523\) | 9426.66 | 0.788143 | 0.394072 | − | 0.919080i | \(-0.371066\pi\) | ||||
0.394072 | + | 0.919080i | \(0.371066\pi\) | |||||||
\(524\) | 6199.39 | 0.516835 | ||||||||
\(525\) | 17836.9 | 1.48279 | ||||||||
\(526\) | −1650.18 | −0.136790 | ||||||||
\(527\) | 205.731 | 0.0170053 | ||||||||
\(528\) | −3128.60 | −0.257869 | ||||||||
\(529\) | −5773.33 | −0.474507 | ||||||||
\(530\) | −8347.87 | −0.684166 | ||||||||
\(531\) | −6541.28 | −0.534590 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11508.5 | 0.935248 | ||||||||
\(534\) | 3767.43 | 0.305304 | ||||||||
\(535\) | −18797.1 | −1.51901 | ||||||||
\(536\) | 4365.37 | 0.351783 | ||||||||
\(537\) | 9289.03 | 0.746464 | ||||||||
\(538\) | 4280.78 | 0.343043 | ||||||||
\(539\) | 28650.9 | 2.28958 | ||||||||
\(540\) | 1984.20 | 0.158123 | ||||||||
\(541\) | 13265.7 | 1.05422 | 0.527112 | − | 0.849796i | \(-0.323275\pi\) | ||||
0.527112 | + | 0.849796i | \(0.323275\pi\) | |||||||
\(542\) | −6531.15 | −0.517596 | ||||||||
\(543\) | −1907.31 | −0.150737 | ||||||||
\(544\) | 880.456 | 0.0693920 | ||||||||
\(545\) | 29045.4 | 2.28288 | ||||||||
\(546\) | −14953.7 | −1.17208 | ||||||||
\(547\) | 15466.4 | 1.20895 | 0.604473 | − | 0.796625i | \(-0.293384\pi\) | ||||
0.604473 | + | 0.796625i | \(0.293384\pi\) | |||||||
\(548\) | −3561.14 | −0.277599 | ||||||||
\(549\) | 5930.62 | 0.461043 | ||||||||
\(550\) | −27706.0 | −2.14798 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1919.05 | −0.147971 | ||||||||
\(553\) | 7285.13 | 0.560209 | ||||||||
\(554\) | −3121.20 | −0.239363 | ||||||||
\(555\) | −1042.20 | −0.0797095 | ||||||||
\(556\) | −9090.77 | −0.693407 | ||||||||
\(557\) | 9057.64 | 0.689021 | 0.344510 | − | 0.938783i | \(-0.388045\pi\) | ||||
0.344510 | + | 0.938783i | \(0.388045\pi\) | |||||||
\(558\) | 134.591 | 0.0102109 | ||||||||
\(559\) | 8105.51 | 0.613285 | ||||||||
\(560\) | 8223.24 | 0.620527 | ||||||||
\(561\) | 5380.06 | 0.404896 | ||||||||
\(562\) | −10898.8 | −0.818037 | ||||||||
\(563\) | −11473.8 | −0.858908 | −0.429454 | − | 0.903089i | \(-0.641294\pi\) | ||||
−0.429454 | + | 0.903089i | \(0.641294\pi\) | |||||||
\(564\) | −406.259 | −0.0303308 | ||||||||
\(565\) | 28529.6 | 2.12434 | ||||||||
\(566\) | 7823.83 | 0.581025 | ||||||||
\(567\) | −2265.93 | −0.167831 | ||||||||
\(568\) | 1088.73 | 0.0804261 | ||||||||
\(569\) | 6042.56 | 0.445197 | 0.222599 | − | 0.974910i | \(-0.428546\pi\) | ||||
0.222599 | + | 0.974910i | \(0.428546\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18696.1 | 1.37024 | 0.685121 | − | 0.728429i | \(-0.259749\pi\) | ||||
0.685121 | + | 0.728429i | \(0.259749\pi\) | |||||||
\(572\) | 23227.5 | 1.69788 | ||||||||
\(573\) | −3017.66 | −0.220008 | ||||||||
\(574\) | 7227.29 | 0.525543 | ||||||||
\(575\) | −16994.6 | −1.23256 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −10918.2 | −0.787746 | −0.393873 | − | 0.919165i | \(-0.628865\pi\) | ||||
−0.393873 | + | 0.919165i | \(0.628865\pi\) | |||||||
\(578\) | 8311.93 | 0.598150 | ||||||||
\(579\) | 9359.57 | 0.671797 | ||||||||
\(580\) | −21174.4 | −1.51589 | ||||||||
\(581\) | 15744.4 | 1.12425 | ||||||||
\(582\) | 6539.52 | 0.465759 | ||||||||
\(583\) | −14807.9 | −1.05194 | ||||||||
\(584\) | −1399.52 | −0.0991654 | ||||||||
\(585\) | −14731.2 | −1.04113 | ||||||||
\(586\) | −1979.50 | −0.139543 | ||||||||
\(587\) | −8385.30 | −0.589605 | −0.294803 | − | 0.955558i | \(-0.595254\pi\) | ||||
−0.294803 | + | 0.955558i | \(0.595254\pi\) | |||||||
\(588\) | −5274.86 | −0.369952 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −26706.1 | −1.86351 | ||||||||
\(591\) | −12056.7 | −0.839163 | ||||||||
\(592\) | −302.543 | −0.0210041 | ||||||||
\(593\) | −17150.0 | −1.18763 | −0.593817 | − | 0.804600i | \(-0.702380\pi\) | ||||
−0.593817 | + | 0.804600i | \(0.702380\pi\) | |||||||
\(594\) | 3519.67 | 0.243121 | ||||||||
\(595\) | −14141.0 | −0.974328 | ||||||||
\(596\) | 4582.72 | 0.314959 | ||||||||
\(597\) | −12677.9 | −0.869135 | ||||||||
\(598\) | 14247.5 | 0.974288 | ||||||||
\(599\) | −11258.5 | −0.767963 | −0.383981 | − | 0.923341i | \(-0.625447\pi\) | ||||
−0.383981 | + | 0.923341i | \(0.625447\pi\) | |||||||
\(600\) | 5100.89 | 0.347072 | ||||||||
\(601\) | 4693.83 | 0.318578 | 0.159289 | − | 0.987232i | \(-0.449080\pi\) | ||||
0.159289 | + | 0.987232i | \(0.449080\pi\) | |||||||
\(602\) | 5090.24 | 0.344622 | ||||||||
\(603\) | −4911.05 | −0.331664 | ||||||||
\(604\) | 8007.38 | 0.539430 | ||||||||
\(605\) | −53597.4 | −3.60173 | ||||||||
\(606\) | −5427.14 | −0.363800 | ||||||||
\(607\) | −6223.14 | −0.416127 | −0.208064 | − | 0.978115i | \(-0.566716\pi\) | ||||
−0.208064 | + | 0.978115i | \(0.566716\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24181.0 | 1.60897 | ||||||||
\(610\) | 24213.0 | 1.60714 | ||||||||
\(611\) | 3016.17 | 0.199707 | ||||||||
\(612\) | −990.513 | −0.0654234 | ||||||||
\(613\) | −20857.8 | −1.37429 | −0.687144 | − | 0.726521i | \(-0.741136\pi\) | ||||
−0.687144 | + | 0.726521i | \(0.741136\pi\) | |||||||
\(614\) | −13985.5 | −0.919231 | ||||||||
\(615\) | 7119.77 | 0.466824 | ||||||||
\(616\) | 14586.8 | 0.954090 | ||||||||
\(617\) | 5605.82 | 0.365772 | 0.182886 | − | 0.983134i | \(-0.441456\pi\) | ||||
0.182886 | + | 0.983134i | \(0.441456\pi\) | |||||||
\(618\) | 3600.97 | 0.234389 | ||||||||
\(619\) | −20849.5 | −1.35382 | −0.676908 | − | 0.736068i | \(-0.736681\pi\) | ||||
−0.676908 | + | 0.736068i | \(0.736681\pi\) | |||||||
\(620\) | 549.494 | 0.0355939 | ||||||||
\(621\) | 2158.93 | 0.139509 | ||||||||
\(622\) | 5752.03 | 0.370797 | ||||||||
\(623\) | −17565.3 | −1.12960 | ||||||||
\(624\) | −4276.37 | −0.274346 | ||||||||
\(625\) | 2979.92 | 0.190715 | ||||||||
\(626\) | −12400.9 | −0.791759 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7588.14 | 0.482165 | ||||||||
\(629\) | 520.266 | 0.0329799 | ||||||||
\(630\) | −9251.14 | −0.585039 | ||||||||
\(631\) | −608.986 | −0.0384205 | −0.0192103 | − | 0.999815i | \(-0.506115\pi\) | ||||
−0.0192103 | + | 0.999815i | \(0.506115\pi\) | |||||||
\(632\) | 2083.37 | 0.131126 | ||||||||
\(633\) | 3966.97 | 0.249088 | ||||||||
\(634\) | −1348.35 | −0.0844634 | ||||||||
\(635\) | 14529.1 | 0.907984 | ||||||||
\(636\) | 2726.25 | 0.169973 | ||||||||
\(637\) | 39161.9 | 2.43587 | ||||||||
\(638\) | −37560.2 | −2.33076 | ||||||||
\(639\) | −1224.82 | −0.0758265 | ||||||||
\(640\) | 2351.64 | 0.145245 | ||||||||
\(641\) | 22925.4 | 1.41263 | 0.706316 | − | 0.707896i | \(-0.250356\pi\) | ||||
0.706316 | + | 0.707896i | \(0.250356\pi\) | |||||||
\(642\) | 6138.77 | 0.377380 | ||||||||
\(643\) | 840.855 | 0.0515709 | 0.0257855 | − | 0.999667i | \(-0.491791\pi\) | ||||
0.0257855 | + | 0.999667i | \(0.491791\pi\) | |||||||
\(644\) | 8947.41 | 0.547480 | ||||||||
\(645\) | 5014.51 | 0.306118 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17094.5 | −1.03872 | −0.519361 | − | 0.854555i | \(-0.673830\pi\) | ||||
−0.519361 | + | 0.854555i | \(0.673830\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | −47372.7 | −2.86524 | ||||||||
\(650\) | −37870.3 | −2.28523 | ||||||||
\(651\) | −627.517 | −0.0377793 | ||||||||
\(652\) | 3304.83 | 0.198508 | ||||||||
\(653\) | 15727.5 | 0.942520 | 0.471260 | − | 0.881994i | \(-0.343799\pi\) | ||||
0.471260 | + | 0.881994i | \(0.343799\pi\) | |||||||
\(654\) | −9485.67 | −0.567154 | ||||||||
\(655\) | −28474.1 | −1.69859 | ||||||||
\(656\) | 2066.82 | 0.123012 | ||||||||
\(657\) | 1574.46 | 0.0934940 | ||||||||
\(658\) | 1894.15 | 0.112221 | ||||||||
\(659\) | 16360.3 | 0.967082 | 0.483541 | − | 0.875322i | \(-0.339350\pi\) | ||||
0.483541 | + | 0.875322i | \(0.339350\pi\) | |||||||
\(660\) | 14369.8 | 0.847490 | ||||||||
\(661\) | 14548.3 | 0.856074 | 0.428037 | − | 0.903761i | \(-0.359205\pi\) | ||||
0.428037 | + | 0.903761i | \(0.359205\pi\) | |||||||
\(662\) | −14713.4 | −0.863823 | ||||||||
\(663\) | 7353.82 | 0.430767 | ||||||||
\(664\) | 4502.52 | 0.263150 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 340.361 | 0.0198029 | ||||||||
\(667\) | −23039.1 | −1.33745 | ||||||||
\(668\) | −2865.59 | −0.165977 | ||||||||
\(669\) | −5854.96 | −0.338365 | ||||||||
\(670\) | −20050.4 | −1.15614 | ||||||||
\(671\) | 42950.3 | 2.47105 | ||||||||
\(672\) | −2685.55 | −0.154163 | ||||||||
\(673\) | 26460.4 | 1.51556 | 0.757781 | − | 0.652509i | \(-0.226283\pi\) | ||||
0.757781 | + | 0.652509i | \(0.226283\pi\) | |||||||
\(674\) | −3832.79 | −0.219041 | ||||||||
\(675\) | −5738.51 | −0.327222 | ||||||||
\(676\) | 22960.9 | 1.30638 | ||||||||
\(677\) | 16458.2 | 0.934327 | 0.467163 | − | 0.884171i | \(-0.345276\pi\) | ||||
0.467163 | + | 0.884171i | \(0.345276\pi\) | |||||||
\(678\) | −9317.22 | −0.527767 | ||||||||
\(679\) | −30489.9 | −1.72326 | ||||||||
\(680\) | −4043.98 | −0.228058 | ||||||||
\(681\) | 7778.44 | 0.437695 | ||||||||
\(682\) | 974.721 | 0.0547273 | ||||||||
\(683\) | −1114.16 | −0.0624189 | −0.0312095 | − | 0.999513i | \(-0.509936\pi\) | ||||
−0.0312095 | + | 0.999513i | \(0.509936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16356.5 | 0.912335 | ||||||||
\(686\) | 5403.09 | 0.300716 | ||||||||
\(687\) | −7553.53 | −0.419483 | ||||||||
\(688\) | 1455.68 | 0.0806647 | ||||||||
\(689\) | −20240.4 | −1.11915 | ||||||||
\(690\) | 8814.29 | 0.486311 | ||||||||
\(691\) | −18406.3 | −1.01333 | −0.506663 | − | 0.862144i | \(-0.669121\pi\) | ||||
−0.506663 | + | 0.862144i | \(0.669121\pi\) | |||||||
\(692\) | −8596.76 | −0.472254 | ||||||||
\(693\) | −16410.2 | −0.899524 | ||||||||
\(694\) | 55.5645 | 0.00303919 | ||||||||
\(695\) | 41754.3 | 2.27889 | ||||||||
\(696\) | 6915.15 | 0.376606 | ||||||||
\(697\) | −3554.20 | −0.193149 | ||||||||
\(698\) | 3735.67 | 0.202575 | ||||||||
\(699\) | 13850.0 | 0.749437 | ||||||||
\(700\) | −23782.5 | −1.28413 | ||||||||
\(701\) | −23488.3 | −1.26554 | −0.632768 | − | 0.774341i | \(-0.718081\pi\) | ||||
−0.632768 | + | 0.774341i | \(0.718081\pi\) | |||||||
\(702\) | 4810.92 | 0.258656 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4171.46 | 0.223321 | ||||||||
\(705\) | 1865.97 | 0.0996828 | ||||||||
\(706\) | −10859.4 | −0.578894 | ||||||||
\(707\) | 25303.6 | 1.34602 | ||||||||
\(708\) | 8721.70 | 0.462968 | ||||||||
\(709\) | 18132.1 | 0.960458 | 0.480229 | − | 0.877143i | \(-0.340554\pi\) | ||||
0.480229 | + | 0.877143i | \(0.340554\pi\) | |||||||
\(710\) | −5000.58 | −0.264322 | ||||||||
\(711\) | −2343.79 | −0.123627 | ||||||||
\(712\) | −5023.24 | −0.264401 | ||||||||
\(713\) | 597.885 | 0.0314039 | ||||||||
\(714\) | 4618.18 | 0.242060 | ||||||||
\(715\) | −106685. | −5.58013 | ||||||||
\(716\) | −12385.4 | −0.646457 | ||||||||
\(717\) | −5475.84 | −0.285215 | ||||||||
\(718\) | −9889.16 | −0.514011 | ||||||||
\(719\) | 13429.0 | 0.696547 | 0.348274 | − | 0.937393i | \(-0.386768\pi\) | ||||
0.348274 | + | 0.937393i | \(0.386768\pi\) | |||||||
\(720\) | −2645.59 | −0.136938 | ||||||||
\(721\) | −16789.2 | −0.867216 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17216.5 | −0.885599 | ||||||||
\(724\) | 2543.08 | 0.130542 | ||||||||
\(725\) | 61238.6 | 3.13703 | ||||||||
\(726\) | 17503.9 | 0.894807 | ||||||||
\(727\) | −34284.0 | −1.74900 | −0.874500 | − | 0.485025i | \(-0.838811\pi\) | ||||
−0.874500 | + | 0.485025i | \(0.838811\pi\) | |||||||
\(728\) | 19938.2 | 1.01505 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 6428.06 | 0.325909 | ||||||||
\(731\) | −2503.25 | −0.126657 | ||||||||
\(732\) | −7907.50 | −0.399275 | ||||||||
\(733\) | 21537.1 | 1.08525 | 0.542626 | − | 0.839975i | \(-0.317430\pi\) | ||||
0.542626 | + | 0.839975i | \(0.317430\pi\) | |||||||
\(734\) | 19624.1 | 0.986839 | ||||||||
\(735\) | 24227.7 | 1.21585 | ||||||||
\(736\) | 2558.73 | 0.128147 | ||||||||
\(737\) | −35566.4 | −1.77762 | ||||||||
\(738\) | −2325.18 | −0.115977 | ||||||||
\(739\) | 34455.2 | 1.71510 | 0.857548 | − | 0.514404i | \(-0.171987\pi\) | ||||
0.857548 | + | 0.514404i | \(0.171987\pi\) | |||||||
\(740\) | 1389.60 | 0.0690305 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12710.9 | −0.628885 | ||||||||
\(743\) | 18369.9 | 0.907034 | 0.453517 | − | 0.891248i | \(-0.350169\pi\) | ||||
0.453517 | + | 0.891248i | \(0.350169\pi\) | |||||||
\(744\) | −179.454 | −0.00884289 | ||||||||
\(745\) | −21048.6 | −1.03512 | ||||||||
\(746\) | 539.925 | 0.0264987 | ||||||||
\(747\) | −5065.33 | −0.248100 | ||||||||
\(748\) | −7173.42 | −0.350650 | ||||||||
\(749\) | −28621.5 | −1.39627 | ||||||||
\(750\) | −9649.50 | −0.469800 | ||||||||
\(751\) | 9712.59 | 0.471927 | 0.235964 | − | 0.971762i | \(-0.424175\pi\) | ||||
0.235964 | + | 0.971762i | \(0.424175\pi\) | |||||||
\(752\) | 541.679 | 0.0262673 | ||||||||
\(753\) | 13851.7 | 0.670364 | ||||||||
\(754\) | −51339.8 | −2.47969 | ||||||||
\(755\) | −36778.3 | −1.77284 | ||||||||
\(756\) | 3021.24 | 0.145346 | ||||||||
\(757\) | 39989.4 | 1.92000 | 0.960000 | − | 0.280002i | \(-0.0903350\pi\) | ||||
0.960000 | + | 0.280002i | \(0.0903350\pi\) | |||||||
\(758\) | 6042.46 | 0.289541 | ||||||||
\(759\) | 15635.2 | 0.747725 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19958.4 | 0.950714 | 0.475357 | − | 0.879793i | \(-0.342319\pi\) | ||||
0.475357 | + | 0.879793i | \(0.342319\pi\) | |||||||
\(762\) | −4744.92 | −0.225578 | ||||||||
\(763\) | 44226.1 | 2.09842 | ||||||||
\(764\) | 4023.55 | 0.190533 | ||||||||
\(765\) | 4549.47 | 0.215015 | ||||||||
\(766\) | −3608.65 | −0.170217 | ||||||||
\(767\) | −64752.1 | −3.04832 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 34776.3 | 1.63077 | 0.815387 | − | 0.578917i | \(-0.196524\pi\) | ||||
0.815387 | + | 0.578917i | \(0.196524\pi\) | |||||||
\(770\) | −66997.9 | −3.13563 | ||||||||
\(771\) | 17372.2 | 0.811470 | ||||||||
\(772\) | −12479.4 | −0.581793 | ||||||||
\(773\) | 6353.52 | 0.295628 | 0.147814 | − | 0.989015i | \(-0.452776\pi\) | ||||
0.147814 | + | 0.989015i | \(0.452776\pi\) | |||||||
\(774\) | −1637.64 | −0.0760514 | ||||||||
\(775\) | −1589.20 | −0.0736588 | ||||||||
\(776\) | −8719.36 | −0.403359 | ||||||||
\(777\) | −1586.90 | −0.0732688 | ||||||||
\(778\) | 8225.74 | 0.379058 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 19641.6 | 0.901642 | ||||||||
\(781\) | −8870.29 | −0.406407 | ||||||||
\(782\) | −4400.11 | −0.201212 | ||||||||
\(783\) | −7779.54 | −0.355068 | ||||||||
\(784\) | 7033.15 | 0.320388 | ||||||||
\(785\) | −34852.7 | −1.58464 | ||||||||
\(786\) | 9299.08 | 0.421994 | ||||||||
\(787\) | −24842.0 | −1.12519 | −0.562593 | − | 0.826734i | \(-0.690196\pi\) | ||||
−0.562593 | + | 0.826734i | \(0.690196\pi\) | |||||||
\(788\) | 16075.6 | 0.726736 | ||||||||
\(789\) | −2475.27 | −0.111688 | ||||||||
\(790\) | −9568.99 | −0.430949 | ||||||||
\(791\) | 43440.8 | 1.95269 | ||||||||
\(792\) | −4692.89 | −0.210549 | ||||||||
\(793\) | 58707.3 | 2.62895 | ||||||||
\(794\) | 5586.77 | 0.249707 | ||||||||
\(795\) | −12521.8 | −0.558620 | ||||||||
\(796\) | 16903.9 | 0.752693 | ||||||||
\(797\) | −33078.4 | −1.47013 | −0.735067 | − | 0.677995i | \(-0.762849\pi\) | ||||
−0.735067 | + | 0.677995i | \(0.762849\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −931.493 | −0.0412439 | ||||||||
\(800\) | −6801.19 | −0.300573 | ||||||||
\(801\) | 5651.14 | 0.249280 | ||||||||
\(802\) | −1873.65 | −0.0824948 | ||||||||
\(803\) | 11402.4 | 0.501100 | ||||||||
\(804\) | 6548.06 | 0.287229 | ||||||||
\(805\) | −41095.9 | −1.79930 | ||||||||
\(806\) | 1332.31 | 0.0582242 | ||||||||
\(807\) | 6421.16 | 0.280094 | ||||||||
\(808\) | 7236.19 | 0.315060 | ||||||||
\(809\) | 18929.2 | 0.822641 | 0.411320 | − | 0.911491i | \(-0.365068\pi\) | ||||
0.411320 | + | 0.911491i | \(0.365068\pi\) | |||||||
\(810\) | 2976.29 | 0.129107 | ||||||||
\(811\) | 29073.5 | 1.25883 | 0.629414 | − | 0.777070i | \(-0.283295\pi\) | ||||
0.629414 | + | 0.777070i | \(0.283295\pi\) | |||||||
\(812\) | −32241.3 | −1.39341 | ||||||||
\(813\) | −9796.73 | −0.422615 | ||||||||
\(814\) | 2464.94 | 0.106138 | ||||||||
\(815\) | −15179.2 | −0.652399 | ||||||||
\(816\) | 1320.68 | 0.0566583 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 4637.45 | 0.198221 | ||||||||
\(819\) | −22430.5 | −0.957002 | ||||||||
\(820\) | −9493.02 | −0.404281 | ||||||||
\(821\) | 30121.9 | 1.28047 | 0.640233 | − | 0.768181i | \(-0.278838\pi\) | ||||
0.640233 | + | 0.768181i | \(0.278838\pi\) | |||||||
\(822\) | −5341.71 | −0.226659 | ||||||||
\(823\) | −774.261 | −0.0327935 | −0.0163967 | − | 0.999866i | \(-0.505219\pi\) | ||||
−0.0163967 | + | 0.999866i | \(0.505219\pi\) | |||||||
\(824\) | −4801.29 | −0.202987 | ||||||||
\(825\) | −41558.9 | −1.75381 | ||||||||
\(826\) | −40664.2 | −1.71294 | ||||||||
\(827\) | 30520.1 | 1.28330 | 0.641650 | − | 0.766998i | \(-0.278250\pi\) | ||||
0.641650 | + | 0.766998i | \(0.278250\pi\) | |||||||
\(828\) | −2878.58 | −0.120818 | ||||||||
\(829\) | −29677.4 | −1.24335 | −0.621675 | − | 0.783275i | \(-0.713548\pi\) | ||||
−0.621675 | + | 0.783275i | \(0.713548\pi\) | |||||||
\(830\) | −20680.3 | −0.864846 | ||||||||
\(831\) | −4681.79 | −0.195439 | ||||||||
\(832\) | 5701.83 | 0.237590 | ||||||||
\(833\) | −12094.5 | −0.503060 | ||||||||
\(834\) | −13636.2 | −0.566165 | ||||||||
\(835\) | 13161.8 | 0.545488 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 201.886 | 0.00833716 | ||||||||
\(838\) | 11450.3 | 0.472009 | ||||||||
\(839\) | −28290.1 | −1.16410 | −0.582051 | − | 0.813152i | \(-0.697750\pi\) | ||||
−0.582051 | + | 0.813152i | \(0.697750\pi\) | |||||||
\(840\) | 12334.9 | 0.506658 | ||||||||
\(841\) | 58630.5 | 2.40397 | ||||||||
\(842\) | −16133.1 | −0.660313 | ||||||||
\(843\) | −16348.2 | −0.667925 | ||||||||
\(844\) | −5289.29 | −0.215717 | ||||||||
\(845\) | −105460. | −4.29343 | ||||||||
\(846\) | −609.388 | −0.0247650 | ||||||||
\(847\) | −81610.3 | −3.31070 | ||||||||
\(848\) | −3635.00 | −0.147201 | ||||||||
\(849\) | 11735.8 | 0.474405 | ||||||||
\(850\) | 11695.6 | 0.471948 | ||||||||
\(851\) | 1511.97 | 0.0609044 | ||||||||
\(852\) | 1633.09 | 0.0656677 | ||||||||
\(853\) | 8208.45 | 0.329486 | 0.164743 | − | 0.986336i | \(-0.447320\pi\) | ||||
0.164743 | + | 0.986336i | \(0.447320\pi\) | |||||||
\(854\) | 36868.0 | 1.47728 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8185.03 | −0.326821 | ||||||||
\(857\) | −18254.3 | −0.727602 | −0.363801 | − | 0.931477i | \(-0.618521\pi\) | ||||
−0.363801 | + | 0.931477i | \(0.618521\pi\) | |||||||
\(858\) | 34841.2 | 1.38632 | ||||||||
\(859\) | 26966.6 | 1.07111 | 0.535557 | − | 0.844499i | \(-0.320102\pi\) | ||||
0.535557 | + | 0.844499i | \(0.320102\pi\) | |||||||
\(860\) | −6686.01 | −0.265106 | ||||||||
\(861\) | 10840.9 | 0.429104 | ||||||||
\(862\) | −22346.2 | −0.882963 | ||||||||
\(863\) | 1058.61 | 0.0417562 | 0.0208781 | − | 0.999782i | \(-0.493354\pi\) | ||||
0.0208781 | + | 0.999782i | \(0.493354\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | 39485.3 | 1.55207 | ||||||||
\(866\) | −4301.18 | −0.168776 | ||||||||
\(867\) | 12467.9 | 0.488387 | ||||||||
\(868\) | 836.690 | 0.0327179 | ||||||||
\(869\) | −16974.0 | −0.662604 | ||||||||
\(870\) | −31761.6 | −1.23772 | ||||||||
\(871\) | −48614.5 | −1.89120 | ||||||||
\(872\) | 12647.6 | 0.491170 | ||||||||
\(873\) | 9809.28 | 0.380291 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 44990.0 | 1.73822 | ||||||||
\(876\) | −2099.28 | −0.0809682 | ||||||||
\(877\) | −12516.9 | −0.481946 | −0.240973 | − | 0.970532i | \(-0.577467\pi\) | ||||
−0.240973 | + | 0.970532i | \(0.577467\pi\) | |||||||
\(878\) | 33299.3 | 1.27995 | ||||||||
\(879\) | −2969.25 | −0.113937 | ||||||||
\(880\) | −19159.7 | −0.733948 | ||||||||
\(881\) | 46916.2 | 1.79415 | 0.897075 | − | 0.441879i | \(-0.145688\pi\) | ||||
0.897075 | + | 0.441879i | \(0.145688\pi\) | |||||||
\(882\) | −7912.29 | −0.302064 | ||||||||
\(883\) | −36806.4 | −1.40276 | −0.701379 | − | 0.712789i | \(-0.747432\pi\) | ||||
−0.701379 | + | 0.712789i | \(0.747432\pi\) | |||||||
\(884\) | −9805.10 | −0.373056 | ||||||||
\(885\) | −40059.2 | −1.52155 | ||||||||
\(886\) | −5015.35 | −0.190174 | ||||||||
\(887\) | 41126.7 | 1.55682 | 0.778410 | − | 0.627757i | \(-0.216027\pi\) | ||||
0.778410 | + | 0.627757i | \(0.216027\pi\) | |||||||
\(888\) | −453.815 | −0.0171498 | ||||||||
\(889\) | 22122.8 | 0.834617 | ||||||||
\(890\) | 23072.0 | 0.868960 | ||||||||
\(891\) | 5279.51 | 0.198507 | ||||||||
\(892\) | 7806.61 | 0.293032 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 6874.08 | 0.257163 | ||||||||
\(895\) | 56886.6 | 2.12459 | ||||||||
\(896\) | 3580.73 | 0.133509 | ||||||||
\(897\) | 21371.3 | 0.795503 | ||||||||
\(898\) | 35915.9 | 1.33467 | ||||||||
\(899\) | −2154.43 | −0.0799269 | ||||||||
\(900\) | 7651.34 | 0.283383 | ||||||||
\(901\) | 6250.90 | 0.231129 | ||||||||
\(902\) | −16839.2 | −0.621602 | ||||||||
\(903\) | 7635.36 | 0.281383 | ||||||||
\(904\) | 12423.0 | 0.457059 | ||||||||
\(905\) | −11680.5 | −0.429030 | ||||||||
\(906\) | 12011.1 | 0.440443 | ||||||||
\(907\) | 856.416 | 0.0313526 | 0.0156763 | − | 0.999877i | \(-0.495010\pi\) | ||||
0.0156763 | + | 0.999877i | \(0.495010\pi\) | |||||||
\(908\) | −10371.3 | −0.379055 | ||||||||
\(909\) | −8140.71 | −0.297041 | ||||||||
\(910\) | −91577.1 | −3.33599 | ||||||||
\(911\) | −1594.94 | −0.0580053 | −0.0290027 | − | 0.999579i | \(-0.509233\pi\) | ||||
−0.0290027 | + | 0.999579i | \(0.509233\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36683.7 | −1.32974 | ||||||||
\(914\) | 19500.3 | 0.705703 | ||||||||
\(915\) | 36319.5 | 1.31222 | ||||||||
\(916\) | 10071.4 | 0.363283 | ||||||||
\(917\) | −43356.2 | −1.56134 | ||||||||
\(918\) | −1485.77 | −0.0534180 | ||||||||
\(919\) | 15691.8 | 0.563246 | 0.281623 | − | 0.959525i | \(-0.409127\pi\) | ||||
0.281623 | + | 0.959525i | \(0.409127\pi\) | |||||||
\(920\) | −11752.4 | −0.421157 | ||||||||
\(921\) | −20978.2 | −0.750549 | ||||||||
\(922\) | −5028.51 | −0.179615 | ||||||||
\(923\) | −12124.5 | −0.432376 | ||||||||
\(924\) | 21880.2 | 0.779011 | ||||||||
\(925\) | −4018.86 | −0.142853 | ||||||||
\(926\) | −18035.8 | −0.640057 | ||||||||
\(927\) | 5401.45 | 0.191378 | ||||||||
\(928\) | −9220.19 | −0.326151 | ||||||||
\(929\) | −27745.1 | −0.979856 | −0.489928 | − | 0.871763i | \(-0.662977\pi\) | ||||
−0.489928 | + | 0.871763i | \(0.662977\pi\) | |||||||
\(930\) | 824.241 | 0.0290623 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18466.7 | −0.649032 | ||||||||
\(933\) | 8628.05 | 0.302754 | ||||||||
\(934\) | 32790.1 | 1.14874 | ||||||||
\(935\) | 32947.8 | 1.15242 | ||||||||
\(936\) | −6414.56 | −0.224002 | ||||||||
\(937\) | 5892.63 | 0.205447 | 0.102724 | − | 0.994710i | \(-0.467244\pi\) | ||||
0.102724 | + | 0.994710i | \(0.467244\pi\) | |||||||
\(938\) | −30529.8 | −1.06272 | ||||||||
\(939\) | −18601.4 | −0.646469 | ||||||||
\(940\) | −2487.96 | −0.0863278 | ||||||||
\(941\) | 17630.1 | 0.610759 | 0.305380 | − | 0.952231i | \(-0.401217\pi\) | ||||
0.305380 | + | 0.952231i | \(0.401217\pi\) | |||||||
\(942\) | 11382.2 | 0.393686 | ||||||||
\(943\) | −10329.0 | −0.356690 | ||||||||
\(944\) | −11628.9 | −0.400942 | ||||||||
\(945\) | −13876.7 | −0.477682 | ||||||||
\(946\) | −11860.0 | −0.407613 | ||||||||
\(947\) | 35788.8 | 1.22807 | 0.614034 | − | 0.789280i | \(-0.289546\pi\) | ||||
0.614034 | + | 0.789280i | \(0.289546\pi\) | |||||||
\(948\) | 3125.05 | 0.107064 | ||||||||
\(949\) | 15585.6 | 0.533119 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2022.52 | −0.0689641 | ||||||||
\(952\) | −6157.58 | −0.209631 | ||||||||
\(953\) | −24674.4 | −0.838700 | −0.419350 | − | 0.907825i | \(-0.637742\pi\) | ||||
−0.419350 | + | 0.907825i | \(0.637742\pi\) | |||||||
\(954\) | 4089.38 | 0.138782 | ||||||||
\(955\) | −18480.3 | −0.626188 | ||||||||
\(956\) | 7301.12 | 0.247003 | ||||||||
\(957\) | −56340.4 | −1.90306 | ||||||||
\(958\) | 21317.0 | 0.718915 | ||||||||
\(959\) | 24905.3 | 0.838617 | ||||||||
\(960\) | 3527.46 | 0.118592 | ||||||||
\(961\) | −29735.1 | −0.998123 | ||||||||
\(962\) | 3369.24 | 0.112920 | ||||||||
\(963\) | 9208.16 | 0.308129 | ||||||||
\(964\) | 22955.3 | 0.766951 | ||||||||
\(965\) | 57318.6 | 1.91207 | ||||||||
\(966\) | 13421.1 | 0.447016 | ||||||||
\(967\) | −2214.12 | −0.0736312 | −0.0368156 | − | 0.999322i | \(-0.511721\pi\) | ||||
−0.0368156 | + | 0.999322i | \(0.511721\pi\) | |||||||
\(968\) | −23338.5 | −0.774925 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 40048.4 | 1.32565 | ||||||||
\(971\) | −9586.90 | −0.316847 | −0.158423 | − | 0.987371i | \(-0.550641\pi\) | ||||
−0.158423 | + | 0.987371i | \(0.550641\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 63577.4 | 2.09476 | ||||||||
\(974\) | −27975.4 | −0.920318 | ||||||||
\(975\) | −56805.5 | −1.86588 | ||||||||
\(976\) | 10543.3 | 0.345782 | ||||||||
\(977\) | −8218.01 | −0.269107 | −0.134553 | − | 0.990906i | \(-0.542960\pi\) | ||||
−0.134553 | + | 0.990906i | \(0.542960\pi\) | |||||||
\(978\) | 4957.24 | 0.162081 | ||||||||
\(979\) | 40926.3 | 1.33607 | ||||||||
\(980\) | −32303.6 | −1.05296 | ||||||||
\(981\) | −14228.5 | −0.463080 | ||||||||
\(982\) | −23318.3 | −0.757757 | ||||||||
\(983\) | −23537.3 | −0.763705 | −0.381852 | − | 0.924223i | \(-0.624714\pi\) | ||||
−0.381852 | + | 0.924223i | \(0.624714\pi\) | |||||||
\(984\) | 3100.24 | 0.100439 | ||||||||
\(985\) | −73835.8 | −2.38843 | ||||||||
\(986\) | 15855.4 | 0.512109 | ||||||||
\(987\) | 2841.22 | 0.0916282 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7274.80 | −0.233898 | ||||||||
\(990\) | 21554.7 | 0.691972 | ||||||||
\(991\) | −37511.7 | −1.20242 | −0.601211 | − | 0.799091i | \(-0.705315\pi\) | ||||
−0.601211 | + | 0.799091i | \(0.705315\pi\) | |||||||
\(992\) | 239.272 | 0.00765817 | ||||||||
\(993\) | −22070.0 | −0.705309 | ||||||||
\(994\) | −7614.16 | −0.242964 | ||||||||
\(995\) | −77640.5 | −2.47374 | ||||||||
\(996\) | 6753.77 | 0.214861 | ||||||||
\(997\) | −35906.3 | −1.14058 | −0.570292 | − | 0.821442i | \(-0.693170\pi\) | ||||
−0.570292 | + | 0.821442i | \(0.693170\pi\) | |||||||
\(998\) | 4308.82 | 0.136667 | ||||||||
\(999\) | 510.542 | 0.0161690 |
(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 | 2166.4.a.r.1.1 | ✓ | 3 | |
19.18 | odd | 2 | 2166.4.a.v.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2166.4.a.r.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2166.4.a.v.1.1 | yes | 3 | 19.18 | odd | 2 |