Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,4,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.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: | \(64.1940780862\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2636.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 14x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.87707\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.15463 | −0.607109 | −0.303555 | − | 0.952814i | \(-0.598173\pi\) | ||||
−0.303555 | + | 0.952814i | \(0.598173\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.03171 | −0.271164 | −0.135582 | − | 0.990766i | \(-0.543290\pi\) | ||||
−0.135582 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.94049 | −0.428746 | −0.214373 | − | 0.976752i | \(-0.568771\pi\) | ||||
−0.214373 | + | 0.976752i | \(0.568771\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −17.0483 | −0.631419 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −27.6161 | −0.756961 | −0.378481 | − | 0.925609i | \(-0.623553\pi\) | ||||
−0.378481 | + | 0.925609i | \(0.623553\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −58.1117 | −1.23979 | −0.619896 | − | 0.784684i | \(-0.712825\pi\) | ||||
−0.619896 | + | 0.784684i | \(0.712825\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.56391 | 0.164626 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.0000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −89.1688 | −1.07667 | −0.538335 | − | 0.842731i | \(-0.680946\pi\) | ||||
−0.538335 | + | 0.842731i | \(0.680946\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 25.0493 | 0.260296 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −115.269 | −1.04501 | −0.522507 | − | 0.852635i | \(-0.675003\pi\) | ||||
−0.522507 | + | 0.852635i | \(0.675003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −115.809 | −0.926470 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 138.956 | 0.990449 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 128.558 | 0.823191 | 0.411596 | − | 0.911367i | \(-0.364972\pi\) | ||||
0.411596 | + | 0.911367i | \(0.364972\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 273.460 | 1.58435 | 0.792174 | − | 0.610295i | \(-0.208949\pi\) | ||||
0.792174 | + | 0.610295i | \(0.208949\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 87.1187 | 0.459558 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 24.0732 | 0.116260 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 132.351 | 0.588063 | 0.294031 | − | 0.955796i | \(-0.405003\pi\) | ||||
0.294031 | + | 0.955796i | \(0.405003\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 183.321 | 0.752689 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −470.559 | −1.79241 | −0.896207 | − | 0.443636i | \(-0.853688\pi\) | ||||
−0.896207 | + | 0.443636i | \(0.853688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −352.642 | −1.25064 | −0.625318 | − | 0.780370i | \(-0.715031\pi\) | ||||
−0.625318 | + | 0.780370i | \(0.715031\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 51.6854 | 0.171218 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 152.598 | 0.473589 | 0.236795 | − | 0.971560i | \(-0.423903\pi\) | ||||
0.236795 | + | 0.971560i | \(0.423903\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.949 | −0.816177 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 53.6287 | 0.147246 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −527.614 | −1.36742 | −0.683711 | − | 0.729753i | \(-0.739635\pi\) | ||||
−0.683711 | + | 0.729753i | \(0.739635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 83.7239 | 0.205261 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 281.295 | 0.653656 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 292.020 | 0.644368 | 0.322184 | − | 0.946677i | \(-0.395583\pi\) | ||||
0.322184 | + | 0.946677i | \(0.395583\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 53.8962 | 0.113126 | 0.0565632 | − | 0.998399i | \(-0.481986\pi\) | ||||
0.0565632 | + | 0.998399i | \(0.481986\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 135.372 | 0.270718 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 176.178 | 0.336187 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −52.9572 | −0.0965635 | −0.0482817 | − | 0.998834i | \(-0.515375\pi\) | ||||
−0.0482817 | + | 0.998834i | \(0.515375\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 363.632 | 0.634437 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 788.400 | 1.31783 | 0.658915 | − | 0.752218i | \(-0.271016\pi\) | ||||
0.658915 | + | 0.752218i | \(0.271016\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 295.780 | 0.474224 | 0.237112 | − | 0.971482i | \(-0.423799\pi\) | ||||
0.237112 | + | 0.971482i | \(0.423799\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 365.334 | 0.562468 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 219.285 | 0.324544 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −720.325 | −1.02586 | −0.512930 | − | 0.858430i | \(-0.671440\pi\) | ||||
−0.512930 | + | 0.858430i | \(0.671440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 21.9487 | 0.0301079 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 116.051 | 0.153473 | 0.0767363 | − | 0.997051i | \(-0.475550\pi\) | ||||
0.0767363 | + | 0.997051i | \(0.475550\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 51.5390 | 0.0657669 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −405.552 | −0.499767 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −813.329 | −0.968682 | −0.484341 | − | 0.874879i | \(-0.660941\pi\) | ||||
−0.484341 | + | 0.874879i | \(0.660941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 461.435 | 0.531556 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −862.664 | −0.961872 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 270.334 | 0.291954 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 794.693 | 0.831844 | 0.415922 | − | 0.909400i | \(-0.363459\pi\) | ||||
0.415922 | + | 0.909400i | \(0.363459\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 470.808 | 0.477959 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −265.513 | −0.261579 | −0.130790 | − | 0.991410i | \(-0.541751\pi\) | ||||
−0.130790 | + | 0.991410i | \(0.541751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 523.107 | 0.500420 | 0.250210 | − | 0.968192i | \(-0.419500\pi\) | ||||
0.250210 | + | 0.968192i | \(0.419500\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −75.9421 | −0.0705828 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 986.039 | 0.890878 | 0.445439 | − | 0.895312i | \(-0.353048\pi\) | ||||
0.445439 | + | 0.895312i | \(0.353048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1814.39 | −1.59438 | −0.797188 | − | 0.603732i | \(-0.793680\pi\) | ||||
−0.797188 | + | 0.603732i | \(0.793680\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −417.518 | −0.357018 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −707.339 | −0.588857 | −0.294429 | − | 0.955673i | \(-0.595129\pi\) | ||||
−0.294429 | + | 0.955673i | \(0.595129\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 349.463 | 0.283370 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 990.706 | 0.782827 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 134.988 | 0.103986 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −568.350 | −0.427010 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1484.44 | 1.08819 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 730.061 | 0.522389 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2648.18 | 1.85030 | 0.925151 | − | 0.379600i | \(-0.123938\pi\) | ||||
0.925151 | + | 0.379600i | \(0.123938\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1112.46 | 0.759273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1979.08 | 1.31995 | 0.659974 | − | 0.751289i | \(-0.270567\pi\) | ||||
0.659974 | + | 0.751289i | \(0.270567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 708.044 | 0.461618 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −421.274 | −0.268574 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3141.92 | 1.95936 | 0.979679 | − | 0.200570i | \(-0.0642794\pi\) | ||||
0.979679 | + | 0.200570i | \(0.0642794\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1468.07 | −0.895830 | −0.447915 | − | 0.894076i | \(-0.647833\pi\) | ||||
−0.447915 | + | 0.894076i | \(0.647833\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −481.390 | −0.287520 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1604.82 | 0.938474 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −389.749 | −0.223220 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 883.135 | 0.495508 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 286.027 | 0.157263 | 0.0786316 | − | 0.996904i | \(-0.474945\pi\) | ||||
0.0786316 | + | 0.996904i | \(0.474945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −669.626 | −0.360883 | −0.180442 | − | 0.983586i | \(-0.557753\pi\) | ||||
−0.180442 | + | 0.983586i | \(0.557753\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 289.821 | 0.153141 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −829.049 | −0.429618 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −720.809 | −0.366413 | −0.183206 | − | 0.983074i | \(-0.558648\pi\) | ||||
−0.183206 | + | 0.983074i | \(0.558648\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1664.43 | 0.830174 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 915.294 | 0.448045 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 676.599 | 0.325125 | 0.162562 | − | 0.986698i | \(-0.448024\pi\) | ||||
0.162562 | + | 0.986698i | \(0.448024\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −264.118 | −0.124616 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2835.67 | −1.31396 | −0.656979 | − | 0.753909i | \(-0.728166\pi\) | ||||
−0.656979 | + | 0.753909i | \(0.728166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1179.97 | 0.537083 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1520.18 | 0.679829 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 177.314 | 0.0779243 | 0.0389621 | − | 0.999241i | \(-0.487595\pi\) | ||||
0.0389621 | + | 0.999241i | \(0.487595\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 919.578 | 0.397220 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −921.214 | −0.391202 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1023.76 | 0.427483 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3450.21 | 1.41686 | 0.708432 | − | 0.705779i | \(-0.249403\pi\) | ||||
0.708432 | + | 0.705779i | \(0.249403\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −170.023 | −0.0686800 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −401.248 | −0.159461 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 469.474 | 0.183590 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1103.38 | −0.424651 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −490.894 | −0.185968 | −0.0929839 | − | 0.995668i | \(-0.529640\pi\) | ||||
−0.0929839 | + | 0.995668i | \(0.529640\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3548.80 | −1.32357 | −0.661783 | − | 0.749696i | \(-0.730200\pi\) | ||||
−0.661783 | + | 0.749696i | \(0.730200\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −555.775 | −0.204102 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1363.15 | −0.492996 | −0.246498 | − | 0.969143i | \(-0.579280\pi\) | ||||
−0.246498 | + | 0.969143i | \(0.579280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3737.46 | 1.33137 | 0.665683 | − | 0.746235i | \(-0.268140\pi\) | ||||
0.665683 | + | 0.746235i | \(0.268140\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 167.060 | 0.0586246 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1020.81 | −0.352940 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1426.60 | 0.486038 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1965.15 | 0.659841 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2462.50 | 0.814997 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5266.12 | 1.71817 | 0.859087 | − | 0.511829i | \(-0.171032\pi\) | ||||
0.859087 | + | 0.511829i | \(0.171032\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2487.11 | −0.800066 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1069.11 | 0.339128 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2171.40 | −0.679283 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −933.075 | −0.287906 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 987.899 | 0.300694 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 704.546 | 0.211569 | 0.105785 | − | 0.994389i | \(-0.466265\pi\) | ||||
0.105785 | + | 0.994389i | \(0.466265\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1974.34 | 0.584990 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2151.26 | 0.629006 | 0.314503 | − | 0.949256i | \(-0.398162\pi\) | ||||
0.314503 | + | 0.949256i | \(0.398162\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3916.94 | 1.13030 | 0.565149 | − | 0.824989i | \(-0.308819\pi\) | ||||
0.565149 | + | 0.824989i | \(0.308819\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −691.764 | −0.197034 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5192.74 | −1.46003 | −0.730017 | − | 0.683429i | \(-0.760488\pi\) | ||||
−0.730017 | + | 0.683429i | \(0.760488\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −462.632 | −0.128420 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2272.36 | 0.622809 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 334.305 | 0.0904786 | 0.0452393 | − | 0.998976i | \(-0.485595\pi\) | ||||
0.0452393 | + | 0.998976i | \(0.485595\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1918.45 | −0.512773 | −0.256386 | − | 0.966574i | \(-0.582532\pi\) | ||||
−0.256386 | + | 0.966574i | \(0.582532\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3821.06 | −1.00873 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 848.722 | 0.221318 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5181.75 | 1.33485 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −366.097 | −0.0931746 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7695.71 | −1.93525 | −0.967627 | − | 0.252385i | \(-0.918785\pi\) | ||||
−0.967627 | + | 0.252385i | \(0.918785\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3183.29 | 0.791035 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −162.587 | −0.0399277 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5335.10 | 1.29492 | 0.647460 | − | 0.762099i | \(-0.275831\pi\) | ||||
0.647460 | + | 0.762099i | \(0.275831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1050.93 | −0.252130 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2191.69 | −0.519778 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3934.15 | 0.922396 | 0.461198 | − | 0.887297i | \(-0.347420\pi\) | ||||
0.461198 | + | 0.887297i | \(0.347420\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1599.57 | 0.370795 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2565.75 | 0.588095 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3424.04 | −0.776088 | −0.388044 | − | 0.921641i | \(-0.626849\pi\) | ||||
−0.388044 | + | 0.921641i | \(0.626849\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 549.034 | 0.123068 | 0.0615340 | − | 0.998105i | \(-0.480401\pi\) | ||||
0.0615340 | + | 0.998105i | \(0.480401\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1455.66 | −0.322712 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3198.19 | 0.701302 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5203.65 | −1.12873 | −0.564363 | − | 0.825527i | \(-0.690878\pi\) | ||||
−0.564363 | + | 0.825527i | \(0.690878\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4662.02 | −1.00039 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1986.73 | −0.421774 | −0.210887 | − | 0.977510i | \(-0.567635\pi\) | ||||
−0.210887 | + | 0.977510i | \(0.567635\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −753.696 | −0.158313 | −0.0791565 | − | 0.996862i | \(-0.525223\pi\) | ||||
−0.0791565 | + | 0.996862i | \(0.525223\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −852.803 | −0.177248 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3736.47 | 0.768490 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2506.96 | −0.505020 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7202.22 | 1.43603 | 0.718017 | − | 0.696025i | \(-0.245050\pi\) | ||||
0.718017 | + | 0.696025i | \(0.245050\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −885.318 | −0.174729 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3837.43 | −0.749731 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6698.50 | 1.29560 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2800.15 | 0.536205 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 837.595 | 0.158807 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −163.398 | −0.0306758 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2425.71 | −0.450953 | −0.225477 | − | 0.974249i | \(-0.572394\pi\) | ||||
−0.225477 | + | 0.974249i | \(0.572394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1650.21 | −0.303809 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9544.94 | −1.74033 | −0.870167 | − | 0.492757i | \(-0.835989\pi\) | ||||
−0.870167 | + | 0.492757i | \(0.835989\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 588.379 | 0.106253 | 0.0531264 | − | 0.998588i | \(-0.483081\pi\) | ||||
0.0531264 | + | 0.998588i | \(0.483081\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −410.407 | −0.0734090 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7653.31 | −1.35600 | −0.678001 | − | 0.735061i | \(-0.737154\pi\) | ||||
−0.678001 | + | 0.735061i | \(0.737154\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3550.26 | −0.623124 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3110.59 | −0.540860 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1515.87 | 0.261131 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6729.85 | 1.14863 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5723.73 | 0.967960 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1211.70 | −0.203050 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −752.266 | −0.124919 | −0.0624597 | − | 0.998047i | \(-0.519894\pi\) | ||||
−0.0624597 | + | 0.998047i | \(0.519894\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2256.36 | −0.371314 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 160.551 | 0.0261845 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1968.57 | −0.318204 | −0.159102 | − | 0.987262i | \(-0.550860\pi\) | ||||
−0.159102 | + | 0.987262i | \(0.550860\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2231.39 | 0.357501 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7551.89 | −1.19929 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4946.52 | 0.778678 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1102.43 | −0.172037 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3983.10 | −0.616207 | −0.308104 | − | 0.951353i | \(-0.599694\pi\) | ||||
−0.308104 | + | 0.951353i | \(0.599694\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1495.61 | −0.229393 | −0.114697 | − | 0.993401i | \(-0.536590\pi\) | ||||
−0.114697 | + | 0.993401i | \(0.536590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8074.98 | −1.22795 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6482.49 | 0.977417 | 0.488708 | − | 0.872447i | \(-0.337468\pi\) | ||||
0.488708 | + | 0.872447i | \(0.337468\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2390.20 | −0.357348 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −425.838 | −0.0631309 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4943.42 | −0.726751 | −0.363376 | − | 0.931643i | \(-0.618376\pi\) | ||||
−0.363376 | + | 0.931643i | \(0.618376\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1092.08 | 0.159218 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1792.94 | 0.259242 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −896.717 | −0.128593 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.8871 | −0.00211743 | −0.00105872 | − | 0.999999i | \(-0.500337\pi\) | ||||
−0.00105872 | + | 0.999999i | \(0.500337\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8022.23 | 1.13176 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4189.51 | 0.586276 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1923.18 | −0.266966 | −0.133483 | − | 0.991051i | \(-0.542616\pi\) | ||||
−0.133483 | + | 0.991051i | \(0.542616\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2303.07 | −0.317147 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7470.70 | −1.02059 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9592.87 | 1.30014 | 0.650069 | − | 0.759875i | \(-0.274740\pi\) | ||||
0.650069 | + | 0.759875i | \(0.274740\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8354.04 | −1.12333 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9083.77 | −1.21190 | −0.605951 | − | 0.795502i | \(-0.707207\pi\) | ||||
−0.605951 | + | 0.795502i | \(0.707207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −664.809 | −0.0880046 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6011.95 | 0.789675 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1143.78 | 0.149079 | 0.0745396 | − | 0.997218i | \(-0.476251\pi\) | ||||
0.0745396 | + | 0.997218i | \(0.476251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1959.58 | 0.253453 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6243.27 | −0.801352 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2183.81 | 0.278176 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10604.5 | −1.34061 | −0.670307 | − | 0.742084i | \(-0.733838\pi\) | ||||
−0.670307 | + | 0.742084i | \(0.733838\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2233.62 | −0.280252 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13785.4 | 1.71674 | 0.858368 | − | 0.513035i | \(-0.171479\pi\) | ||||
0.858368 | + | 0.513035i | \(0.171479\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15891.2 | −1.96426 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −66.5420 | −0.00816419 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3655.01 | −0.445141 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9505.94 | −1.14924 | −0.574619 | − | 0.818421i | \(-0.694850\pi\) | ||||
−0.574619 | + | 0.818421i | \(0.694850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9911.59 | −1.18954 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2318.78 | −0.276270 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −351.832 | −0.0416162 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4631.23 | 0.543866 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9680.86 | −1.12874 | −0.564369 | − | 0.825523i | \(-0.690880\pi\) | ||||
−0.564369 | + | 0.825523i | \(0.690880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12360.3 | 1.43089 | 0.715444 | − | 0.698671i | \(-0.246225\pi\) | ||||
0.715444 | + | 0.698671i | \(0.246225\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2601.54 | −0.299033 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1968.75 | 0.224702 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −427.962 | −0.0485025 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5062.61 | −0.569756 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2970.58 | 0.331990 | 0.165995 | − | 0.986127i | \(-0.446916\pi\) | ||||
0.165995 | + | 0.986127i | \(0.446916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6131.50 | 0.680510 | 0.340255 | − | 0.940333i | \(-0.389487\pi\) | ||||
0.340255 | + | 0.940333i | \(0.389487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1229.51 | 0.135519 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10278.4 | 1.12513 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2544.91 | −0.276679 | −0.138339 | − | 0.990385i | \(-0.544176\pi\) | ||||
−0.138339 | + | 0.990385i | \(0.544176\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4772.65 | 0.515349 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8529.82 | −0.914817 | −0.457408 | − | 0.889257i | \(-0.651222\pi\) | ||||
−0.457408 | + | 0.889257i | \(0.651222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2465.77 | 0.262672 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −902.308 | −0.0954759 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8855.74 | 0.930798 | 0.465399 | − | 0.885101i | \(-0.345911\pi\) | ||||
0.465399 | + | 0.885101i | \(0.345911\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12995.0 | 1.35679 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2112.42 | 0.219095 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1398.94 | −0.144139 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7154.78 | −0.732356 | −0.366178 | − | 0.930545i | \(-0.619334\pi\) | ||||
−0.366178 | + | 0.930545i | \(0.619334\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2362.25 | −0.240219 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7263.06 | 0.733784 | 0.366892 | − | 0.930264i | \(-0.380422\pi\) | ||||
0.366892 | + | 0.930264i | \(0.380422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 352.898 | 0.0354224 | 0.0177112 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177112 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2615.34 | 0.260825 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1483.02 | −0.146951 | −0.0734753 | − | 0.997297i | \(-0.523409\pi\) | ||||
−0.0734753 | + | 0.997297i | \(0.523409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 420.506 | 0.0414012 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2273.89 | 0.222452 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9738.60 | 0.946683 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10326.5 | 0.997502 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8994.92 | 0.863415 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9990.10 | −0.952942 | −0.476471 | − | 0.879190i | \(-0.658084\pi\) | ||||
−0.476471 | + | 0.879190i | \(0.658084\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7691.13 | −0.729075 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2887.42 | −0.272012 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2409.27 | −0.225566 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1129.88 | −0.105133 | −0.0525663 | − | 0.998617i | \(-0.516740\pi\) | ||||
−0.0525663 | + | 0.998617i | \(0.516740\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2134.42 | −0.197386 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18774.9 | −1.72566 | −0.862832 | − | 0.505491i | \(-0.831311\pi\) | ||||
−0.862832 | + | 0.505491i | \(0.831311\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2185.48 | −0.199653 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1427.35 | −0.129605 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6260.28 | −0.565014 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17329.1 | −1.55462 | −0.777310 | − | 0.629118i | \(-0.783416\pi\) | ||||
−0.777310 | + | 0.629118i | \(0.783416\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8945.50 | 0.797716 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20837.0 | −1.84707 | −0.923533 | − | 0.383518i | \(-0.874712\pi\) | ||||
−0.923533 | + | 0.383518i | \(0.874712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 804.957 | 0.0709309 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3722.37 | −0.326068 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11835.0 | −1.03060 | −0.515301 | − | 0.857009i | \(-0.672320\pi\) | ||||
−0.515301 | + | 0.857009i | \(0.672320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2348.63 | −0.203322 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12390.6 | −1.06639 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1585.91 | −0.135696 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4214.16 | −0.358489 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −559.359 | −0.0473086 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7686.37 | 0.646346 | 0.323173 | − | 0.946340i | \(-0.395250\pi\) | ||||
0.323173 | + | 0.946340i | \(0.395250\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11476.4 | −0.959518 | −0.479759 | − | 0.877400i | \(-0.659276\pi\) | ||||
−0.479759 | + | 0.877400i | \(0.659276\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2900.93 | −0.241156 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4648.81 | −0.384261 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1120.01 | 0.0920535 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4978.44 | −0.406866 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27345.0 | 2.22222 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2989.38 | −0.241574 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3229.59 | −0.259529 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7731.09 | 0.617814 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 546.481 | 0.0434289 | 0.0217145 | − | 0.999764i | \(-0.493088\pi\) | ||||
0.0217145 | + | 0.999764i | \(0.493088\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10884.1 | −0.860191 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5500.69 | 0.432337 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8397.33 | −0.656388 | −0.328194 | − | 0.944610i | \(-0.606440\pi\) | ||||
−0.328194 | + | 0.944610i | \(0.606440\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −918.839 | −0.0714301 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11463.3 | −0.886305 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5719.73 | 0.439833 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1265.79 | 0.0968105 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4881.65 | 0.371350 | 0.185675 | − | 0.982611i | \(-0.440553\pi\) | ||||
0.185675 | + | 0.982611i | \(0.440553\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20492.6 | 1.55053 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1481.02 | −0.111459 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7198.57 | −0.538870 | −0.269435 | − | 0.963019i | \(-0.586837\pi\) | ||||
−0.269435 | + | 0.963019i | \(0.586837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2144.44 | 0.159677 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −174.283 | −0.0129087 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23946.9 | −1.76433 | −0.882167 | − | 0.470937i | \(-0.843916\pi\) | ||||
−0.882167 | + | 0.470937i | \(0.843916\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1593.15 | −0.116763 | −0.0583813 | − | 0.998294i | \(-0.518594\pi\) | ||||
−0.0583813 | + | 0.998294i | \(0.518594\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1548.59 | 0.112903 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13349.2 | 0.968174 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12937.4 | 0.933435 | 0.466717 | − | 0.884406i | \(-0.345436\pi\) | ||||
0.466717 | + | 0.884406i | \(0.345436\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11195.2 | 0.803549 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −921.499 | −0.0658007 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14570.6 | 1.03508 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3003.53 | −0.212275 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12899.2 | 0.906998 | 0.453499 | − | 0.891257i | \(-0.350176\pi\) | ||||
0.453499 | + | 0.891257i | \(0.350176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24384.1 | −1.70582 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4300.23 | 0.299302 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4357.13 | 0.301730 | 0.150865 | − | 0.988554i | \(-0.451794\pi\) | ||||
0.150865 | + | 0.988554i | \(0.451794\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −409.245 | −0.0281973 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11790.3 | −0.808284 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13726.8 | 0.936328 | 0.468164 | − | 0.883642i | \(-0.344916\pi\) | ||||
0.468164 | + | 0.883642i | \(0.344916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2531.41 | 0.171811 | 0.0859056 | − | 0.996303i | \(-0.472622\pi\) | ||||
0.0859056 | + | 0.996303i | \(0.472622\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 902.830 | 0.0609720 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1723.07 | 0.115790 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 185.004 | 0.0123708 | 0.00618540 | − | 0.999981i | \(-0.498031\pi\) | ||||
0.00618540 | + | 0.999981i | \(0.498031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3220.28 | 0.214273 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8867.73 | −0.587152 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17706.9 | 1.16668 | 0.583339 | − | 0.812228i | \(-0.301746\pi\) | ||||
0.583339 | + | 0.812228i | \(0.301746\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4500.39 | −0.295078 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6183.89 | −0.403491 | −0.201746 | − | 0.979438i | \(-0.564661\pi\) | ||||
−0.201746 | + | 0.979438i | \(0.564661\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1247.51 | 0.0810046 | 0.0405023 | − | 0.999179i | \(-0.487104\pi\) | ||||
0.0405023 | + | 0.999179i | \(0.487104\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16017.4 | −1.03503 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6458.23 | 0.415318 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12262.8 | 0.784817 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7768.27 | −0.494792 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2249.96 | −0.142626 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24053.3 | 1.51750 | 0.758752 | − | 0.651379i | \(-0.225809\pi\) | ||||
0.758752 | + | 0.651379i | \(0.225809\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16612.7 | −1.04312 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8028.51 | −0.501735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16268.3 | 1.01189 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13440.9 | −0.832102 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21286.8 | −1.31167 | −0.655834 | − | 0.754905i | \(-0.727683\pi\) | ||||
−0.655834 | + | 0.754905i | \(0.727683\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1789.41 | 0.109747 | 0.0548736 | − | 0.998493i | \(-0.482524\pi\) | ||||
0.0548736 | + | 0.998493i | \(0.482524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3372.64 | −0.205888 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4378.61 | −0.266060 | −0.133030 | − | 0.991112i | \(-0.542471\pi\) | ||||
−0.133030 | + | 0.991112i | \(0.542471\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8064.45 | −0.487762 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6849.97 | 0.412399 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7665.15 | 0.459358 | 0.229679 | − | 0.973266i | \(-0.426232\pi\) | ||||
0.229679 | + | 0.973266i | \(0.426232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5999.99 | −0.357922 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5042.54 | −0.299434 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4710.22 | 0.278428 | 0.139214 | − | 0.990262i | \(-0.455542\pi\) | ||||
0.139214 | + | 0.990262i | \(0.455542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31266.6 | 1.83983 | 0.919916 | − | 0.392116i | \(-0.128257\pi\) | ||||
0.919916 | + | 0.392116i | \(0.128257\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3116.46 | −0.182554 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2146.58 | −0.125174 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14818.7 | −0.860246 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2222.58 | −0.128446 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1488.40 | −0.0856322 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11723.0 | 0.671454 | 0.335727 | − | 0.941959i | \(-0.391018\pi\) | ||||
0.335727 | + | 0.941959i | \(0.391018\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16092.3 | −0.917621 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 289.531 | 0.0164366 | 0.00821829 | − | 0.999966i | \(-0.497384\pi\) | ||||
0.00821829 | + | 0.999966i | \(0.497384\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6310.25 | −0.356650 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6786.45 | −0.381875 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1720.10 | −0.0963660 | −0.0481830 | − | 0.998839i | \(-0.515343\pi\) | ||||
−0.0481830 | + | 0.998839i | \(0.515343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9525.37 | −0.531308 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12356.5 | −0.686215 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30660.5 | 1.69532 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16777.7 | 0.923665 | 0.461832 | − | 0.886967i | \(-0.347192\pi\) | ||||
0.461832 | + | 0.886967i | \(0.347192\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3738.44 | −0.204923 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4450.77 | 0.242917 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7999.50 | 0.434724 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16381.2 | 0.886400 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23981.1 | −1.29209 | −0.646043 | − | 0.763301i | \(-0.723577\pi\) | ||||
−0.646043 | + | 0.763301i | \(0.723577\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11801.6 | −0.633150 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1459.43 | 0.0779652 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2108.30 | 0.112151 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7709.28 | 0.408361 | 0.204181 | − | 0.978933i | \(-0.434547\pi\) | ||||
0.204181 | + | 0.978933i | \(0.434547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12280.3 | 0.647747 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31521.5 | −1.65567 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4865.34 | −0.254480 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1054.61 | −0.0549304 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11976.5 | −0.621209 | −0.310605 | − | 0.950539i | \(-0.600532\pi\) | ||||
−0.310605 | + | 0.950539i | \(0.600532\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4153.72 | −0.214553 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6052.00 | 0.311309 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14888.1 | −0.762662 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18597.3 | −0.948745 | −0.474372 | − | 0.880324i | \(-0.657325\pi\) | ||||
−0.474372 | + | 0.880324i | \(0.657325\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11461.4 | 0.582300 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5994.91 | 0.303324 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23569.5 | 1.18767 | 0.593833 | − | 0.804588i | \(-0.297614\pi\) | ||||
0.593833 | + | 0.804588i | \(0.297614\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2677.41 | −0.134364 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1462.47 | 0.0730948 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10149.1 | −0.505199 | −0.252599 | − | 0.967571i | \(-0.581285\pi\) | ||||
−0.252599 | + | 0.967571i | \(0.581285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16346.5 | −0.810397 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27758.0 | 1.37058 | 0.685291 | − | 0.728269i | \(-0.259675\pi\) | ||||
0.685291 | + | 0.728269i | \(0.259675\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −867.148 | −0.0426441 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1978.47 | −0.0969054 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7829.63 | −0.381960 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −815.225 | −0.0396112 | −0.0198056 | − | 0.999804i | \(-0.506305\pi\) | ||||
−0.0198056 | + | 0.999804i | \(0.506305\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24277.1 | 1.17491 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2030.11 | 0.0978585 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13239.4 | 0.635659 | 0.317829 | − | 0.948148i | \(-0.397046\pi\) | ||||
0.317829 | + | 0.948148i | \(0.397046\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10042.1 | −0.480244 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11028.2 | −0.525324 | −0.262662 | − | 0.964888i | \(-0.584600\pi\) | ||||
−0.262662 | + | 0.964888i | \(0.584600\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14407.1 | 0.683582 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −878.652 | −0.0415265 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16969.8 | −0.798882 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18921.2 | −0.887277 | −0.443639 | − | 0.896206i | \(-0.646313\pi\) | ||||
−0.443639 | + | 0.896206i | \(0.646313\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16830.3 | −0.786158 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38728.6 | −1.80203 | −0.901016 | − | 0.433786i | \(-0.857177\pi\) | ||||
−0.901016 | + | 0.433786i | \(0.857177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31669.0 | −1.46785 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3315.29 | 0.153070 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 41959.2 | 1.92984 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21772.5 | −0.997545 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17863.9 | 0.815329 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2185.28 | 0.0993579 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20587.3 | 0.932477 | 0.466239 | − | 0.884659i | \(-0.345609\pi\) | ||||
0.466239 | + | 0.884659i | \(0.345609\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12410.8 | −0.559995 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5616.62 | 0.252470 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3132.00 | −0.140253 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5046.05 | −0.225113 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15871.4 | 0.705385 | 0.352693 | − | 0.935739i | \(-0.385266\pi\) | ||||
0.352693 | + | 0.935739i | \(0.385266\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2594.17 | −0.114862 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13865.9 | 0.611644 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8168.28 | −0.358969 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2774.90 | −0.121494 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10801.6 | 0.471170 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 39667.1 | 1.72388 | 0.861942 | − | 0.507007i | \(-0.169248\pi\) | ||||
0.861942 | + | 0.507007i | \(0.169248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8003.87 | −0.346552 | −0.173276 | − | 0.984873i | \(-0.555435\pi\) | ||||
−0.173276 | + | 0.984873i | \(0.555435\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1732.00 | −0.0747157 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2051.25 | −0.0881621 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31444.7 | 1.34652 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7866.69 | −0.335634 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13279.1 | 0.564489 | 0.282244 | − | 0.959343i | \(-0.408921\pi\) | ||||
0.282244 | + | 0.959343i | \(0.408921\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28934.0 | 1.22549 | 0.612745 | − | 0.790281i | \(-0.290065\pi\) | ||||
0.612745 | + | 0.790281i | \(0.290065\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10089.1 | −0.425767 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13679.6 | 0.575193 | 0.287597 | − | 0.957752i | \(-0.407144\pi\) | ||||
0.287597 | + | 0.957752i | \(0.407144\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16514.5 | −0.691886 | −0.345943 | − | 0.938256i | \(-0.612441\pi\) | ||||
−0.345943 | + | 0.938256i | \(0.612441\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16415.6 | 0.685260 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4759.13 | 0.197952 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8596.93 | 0.356298 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37998.9 | 1.56922 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −87.9839 | −0.00362043 | −0.00181022 | − | 0.999998i | \(-0.500576\pi\) | ||||
−0.00181022 | + | 0.999998i | \(0.500576\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7861.94 | −0.322356 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6267.41 | 0.256063 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3577.33 | −0.145638 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4512.98 | 0.183079 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2377.63 | 0.0961133 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15256.0 | −0.614534 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8162.96 | −0.327660 | −0.163830 | − | 0.986489i | \(-0.552385\pi\) | ||||
−0.163830 | + | 0.986489i | \(0.552385\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4608.73 | −0.184345 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18724.9 | 0.746361 | 0.373181 | − | 0.927759i | \(-0.378267\pi\) | ||||
0.373181 | + | 0.927759i | \(0.378267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46422.5 | 1.84391 | 0.921953 | − | 0.387301i | \(-0.126593\pi\) | ||||
0.921953 | + | 0.387301i | \(0.126593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11787.2 | −0.466557 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29112.3 | 1.14831 | 0.574157 | − | 0.818746i | \(-0.305330\pi\) | ||||
0.574157 | + | 0.818746i | \(0.305330\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −537.563 | −0.0211303 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −911.688 | −0.0357123 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19892.6 | 0.776536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3077.43 | 0.119719 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13548.2 | −0.525241 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5797.04 | −0.223972 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39163.0 | −1.50791 | −0.753957 | − | 0.656924i | \(-0.771857\pi\) | ||||
−0.753957 | + | 0.656924i | \(0.771857\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22720.3 | −0.871830 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35073.2 | −1.34125 | −0.670627 | − | 0.741795i | \(-0.733975\pi\) | ||||
−0.670627 | + | 0.741795i | \(0.733975\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48775.7 | 1.85893 | 0.929463 | − | 0.368915i | \(-0.120271\pi\) | ||||
0.929463 | + | 0.368915i | \(0.120271\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2792.85 | 0.106080 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13296.0 | 0.503309 | 0.251654 | − | 0.967817i | \(-0.419025\pi\) | ||||
0.251654 | + | 0.967817i | \(0.419025\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21027.9 | −0.793309 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −606.137 | −0.0227905 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13607.0 | −0.509899 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3103.74 | −0.115918 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21131.3 | −0.786570 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35155.3 | 1.30422 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8969.43 | 0.331648 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8833.44 | −0.325535 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10460.0 | −0.384202 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11675.0 | 0.427410 | 0.213705 | − | 0.976898i | \(-0.431447\pi\) | ||||
0.213705 | + | 0.976898i | \(0.431447\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4526.54 | 0.165166 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18552.9 | 0.674738 | 0.337369 | − | 0.941372i | \(-0.390463\pi\) | ||||
0.337369 | + | 0.941372i | \(0.390463\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3204.87 | −0.116173 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 515.459 | 0.0186235 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15714.9 | −0.565922 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33956.8 | 1.21886 | 0.609429 | − | 0.792841i | \(-0.291399\pi\) | ||||
0.609429 | + | 0.792841i | \(0.291399\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7652.23 | 0.273778 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45815.3 | −1.63383 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15327.4 | −0.544823 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8918.08 | −0.315974 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23695.3 | −0.836832 | −0.418416 | − | 0.908256i | \(-0.637415\pi\) | ||||
−0.418416 | + | 0.908256i | \(0.637415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24962.7 | 0.878753 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30110.8 | 1.05657 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1423.31 | −0.0497830 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7990.62 | 0.278593 | 0.139297 | − | 0.990251i | \(-0.455516\pi\) | ||||
0.139297 | + | 0.990251i | \(0.455516\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1856.12 | −0.0645071 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24385.9 | −0.844799 | −0.422400 | − | 0.906410i | \(-0.638812\pi\) | ||||
−0.422400 | + | 0.906410i | \(0.638812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54241.0 | 1.87310 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3345.12 | 0.115150 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1174.62 | 0.0403064 | 0.0201532 | − | 0.999797i | \(-0.493585\pi\) | ||||
0.0201532 | + | 0.999797i | \(0.493585\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17188.3 | −0.587939 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24143.4 | 0.823241 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33546.9 | −1.14029 | −0.570143 | − | 0.821546i | \(-0.693112\pi\) | ||||
−0.570143 | + | 0.821546i | \(0.693112\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1488.25 | 0.0504277 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11199.8 | 0.378304 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24948.4 | −0.840067 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44989.1 | 1.51016 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16810.3 | −0.562517 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10758.9 | 0.358903 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24766.8 | 0.823625 | 0.411813 | − | 0.911269i | \(-0.364896\pi\) | ||||
0.411813 | + | 0.911269i | \(0.364896\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4782.01 | −0.158535 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42324.3 | −1.39882 | −0.699409 | − | 0.714721i | \(-0.746553\pi\) | ||||
−0.699409 | + | 0.714721i | \(0.746553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11657.2 | 0.384083 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −21230.2 | −0.697344 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11320.4 | −0.370698 | −0.185349 | − | 0.982673i | \(-0.559342\pi\) | ||||
−0.185349 | + | 0.982673i | \(0.559342\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22461.0 | 0.733254 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 30932.2 | 1.00672 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11311.9 | −0.367032 | −0.183516 | − | 0.983017i | \(-0.558748\pi\) | ||||
−0.183516 | + | 0.983017i | \(0.558748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4132.66 | 0.133683 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3822.47 | 0.123273 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40648.8 | 1.30693 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29405.5 | −0.942580 | −0.471290 | − | 0.881978i | \(-0.656212\pi\) | ||||
−0.471290 | + | 0.881978i | \(0.656212\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2373.12 | 0.0758397 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11330.9 | −0.361018 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54905.9 | 1.74412 | 0.872060 | − | 0.489398i | \(-0.162784\pi\) | ||||
0.872060 | + | 0.489398i | \(0.162784\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18390.9 | 0.582446 |
(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 | 1088.4.a.v.1.2 | 3 | ||
4.3 | odd | 2 | 1088.4.a.x.1.2 | 3 | |||
8.3 | odd | 2 | 272.4.a.h.1.2 | 3 | |||
8.5 | even | 2 | 17.4.a.b.1.2 | ✓ | 3 | ||
24.5 | odd | 2 | 153.4.a.g.1.2 | 3 | |||
24.11 | even | 2 | 2448.4.a.bi.1.1 | 3 | |||
40.13 | odd | 4 | 425.4.b.f.324.3 | 6 | |||
40.29 | even | 2 | 425.4.a.g.1.2 | 3 | |||
40.37 | odd | 4 | 425.4.b.f.324.4 | 6 | |||
56.13 | odd | 2 | 833.4.a.d.1.2 | 3 | |||
88.21 | odd | 2 | 2057.4.a.e.1.2 | 3 | |||
136.13 | even | 4 | 289.4.b.b.288.4 | 6 | |||
136.21 | even | 4 | 289.4.b.b.288.3 | 6 | |||
136.101 | even | 2 | 289.4.a.b.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.a.b.1.2 | ✓ | 3 | 8.5 | even | 2 | ||
153.4.a.g.1.2 | 3 | 24.5 | odd | 2 | |||
272.4.a.h.1.2 | 3 | 8.3 | odd | 2 | |||
289.4.a.b.1.2 | 3 | 136.101 | even | 2 | |||
289.4.b.b.288.3 | 6 | 136.21 | even | 4 | |||
289.4.b.b.288.4 | 6 | 136.13 | even | 4 | |||
425.4.a.g.1.2 | 3 | 40.29 | even | 2 | |||
425.4.b.f.324.3 | 6 | 40.13 | odd | 4 | |||
425.4.b.f.324.4 | 6 | 40.37 | odd | 4 | |||
833.4.a.d.1.2 | 3 | 56.13 | odd | 2 | |||
1088.4.a.v.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1088.4.a.x.1.2 | 3 | 4.3 | odd | 2 | |||
2057.4.a.e.1.2 | 3 | 88.21 | odd | 2 | |||
2448.4.a.bi.1.1 | 3 | 24.11 | even | 2 |