Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [272,4,Mod(1,272)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(272, 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("272.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 272 = 2^{4} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 272.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: | \(16.0485195216\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 272.1 |
$q$-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 | \(-0.456710\pi\) | ||||
0.135582 | + | 0.990766i | \(0.456710\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.94049 | 0.428746 | 0.214373 | − | 0.976752i | \(-0.431229\pi\) | ||||
0.214373 | + | 0.976752i | \(0.431229\pi\) | |||||||
\(8\) | 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 | \(-0.287175\pi\) | ||||
0.619896 | + | 0.784684i | \(0.287175\pi\) | |||||||
\(14\) | 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 | \(-0.324997\pi\) | ||||
0.522507 | + | 0.852635i | \(0.324997\pi\) | |||||||
\(24\) | 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 | \(-0.635028\pi\) | ||||
−0.411596 | + | 0.911367i | \(0.635028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −273.460 | −1.58435 | −0.792174 | − | 0.610295i | \(-0.791051\pi\) | ||||
−0.792174 | + | 0.610295i | \(0.791051\pi\) | |||||||
\(32\) | 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 | \(-0.594997\pi\) | ||||
−0.294031 | + | 0.955796i | \(0.594997\pi\) | |||||||
\(38\) | 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 | \(-0.576097\pi\) | ||||
−0.236795 | + | 0.971560i | \(0.576097\pi\) | |||||||
\(48\) | 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 | \(-0.260365\pi\) | ||||
0.683711 | + | 0.729753i | \(0.260365\pi\) | |||||||
\(54\) | 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 | \(-0.518014\pi\) | ||||
−0.0565632 | + | 0.998399i | \(0.518014\pi\) | |||||||
\(62\) | 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 | \(-0.728984\pi\) | ||||
−0.658915 | + | 0.752218i | \(0.728984\pi\) | |||||||
\(72\) | 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 | \(-0.328560\pi\) | ||||
0.512930 | + | 0.858430i | \(0.328560\pi\) | |||||||
\(80\) | 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 | \(-0.458249\pi\) | ||||
0.130790 | + | 0.991410i | \(0.458249\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −523.107 | −0.500420 | −0.250210 | − | 0.968192i | \(-0.580500\pi\) | ||||
−0.250210 | + | 0.968192i | \(0.580500\pi\) | |||||||
\(104\) | 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 | \(-0.206320\pi\) | ||||
0.797188 | + | 0.603732i | \(0.206320\pi\) | |||||||
\(110\) | 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 | \(-0.876062\pi\) | ||||
−0.925151 | + | 0.379600i | \(0.876062\pi\) | |||||||
\(128\) | 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 | \(-0.525055\pi\) | ||||
−0.0786316 | + | 0.996904i | \(0.525055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 669.626 | 0.360883 | 0.180442 | − | 0.983586i | \(-0.442247\pi\) | ||||
0.180442 | + | 0.983586i | \(0.442247\pi\) | |||||||
\(152\) | 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 | \(-0.441352\pi\) | ||||
0.183206 | + | 0.983074i | \(0.441352\pi\) | |||||||
\(158\) | 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 | \(-0.271834\pi\) | ||||
0.656979 | + | 0.753909i | \(0.271834\pi\) | |||||||
\(168\) | 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 | \(-0.512405\pi\) | ||||
−0.0389621 | + | 0.999241i | \(0.512405\pi\) | |||||||
\(174\) | 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 | \(-0.750597\pi\) | ||||
−0.708432 | + | 0.705779i | \(0.750597\pi\) | |||||||
\(182\) | 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 | \(-0.470360\pi\) | ||||
0.0929839 | + | 0.995668i | \(0.470360\pi\) | |||||||
\(192\) | 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 | \(-0.420720\pi\) | ||||
0.246498 | + | 0.969143i | \(0.420720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3737.46 | −1.33137 | −0.665683 | − | 0.746235i | \(-0.731860\pi\) | ||||
−0.665683 | + | 0.746235i | \(0.731860\pi\) | |||||||
\(200\) | 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 | \(-0.533735\pi\) | ||||
−0.105785 | + | 0.994389i | \(0.533735\pi\) | |||||||
\(224\) | 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 | \(-0.691181\pi\) | ||||
−0.565149 | + | 0.824989i | \(0.691181\pi\) | |||||||
\(230\) | 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 | \(-0.514405\pi\) | ||||
−0.0452393 | + | 0.998976i | \(0.514405\pi\) | |||||||
\(240\) | 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 | \(-0.652580\pi\) | ||||
−0.461198 | + | 0.887297i | \(0.652580\pi\) | |||||||
\(264\) | 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 | \(-0.373151\pi\) | ||||
0.388044 | + | 0.921641i | \(0.373151\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −549.034 | −0.123068 | −0.0615340 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615340 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(272\) | 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 | \(-0.309122\pi\) | ||||
0.564363 | + | 0.825527i | \(0.309122\pi\) | |||||||
\(278\) | 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 | \(-0.754950\pi\) | ||||
−0.718017 | + | 0.696025i | \(0.754950\pi\) | |||||||
\(294\) | 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 | \(-0.164011\pi\) | ||||
0.870167 | + | 0.492757i | \(0.164011\pi\) | |||||||
\(312\) | 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 | \(-0.262846\pi\) | ||||
0.678001 | + | 0.735061i | \(0.262846\pi\) | |||||||
\(318\) | 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 | \(-0.463410\pi\) | ||||
0.114697 | + | 0.993401i | \(0.463410\pi\) | |||||||
\(350\) | 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 | \(-0.381624\pi\) | ||||
0.363376 | + | 0.931643i | \(0.381624\pi\) | |||||||
\(360\) | 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 | \(-0.499663\pi\) | ||||
0.00105872 | + | 0.999999i | \(0.499663\pi\) | |||||||
\(368\) | 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 | \(-0.457384\pi\) | ||||
0.133483 | + | 0.991051i | \(0.457384\pi\) | |||||||
\(374\) | 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 | \(-0.292793\pi\) | ||||
0.605951 | + | 0.795502i | \(0.292793\pi\) | |||||||
\(384\) | 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 | \(-0.523749\pi\) | ||||
−0.0745396 | + | 0.997218i | \(0.523749\pi\) | |||||||
\(390\) | 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 | \(-0.266162\pi\) | ||||
0.670307 | + | 0.742084i | \(0.266162\pi\) | |||||||
\(398\) | 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 | \(-0.753775\pi\) | ||||
−0.715444 | + | 0.698671i | \(0.753775\pi\) | |||||||
\(422\) | 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 | \(-0.553084\pi\) | ||||
−0.165995 | + | 0.986127i | \(0.553084\pi\) | |||||||
\(432\) | 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 | \(-0.455824\pi\) | ||||
0.138339 | + | 0.990385i | \(0.455824\pi\) | |||||||
\(440\) | 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 | \(-0.619578\pi\) | ||||
−0.366892 | + | 0.930264i | \(0.619578\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −352.898 | −0.0354224 | −0.0177112 | − | 0.999843i | \(-0.505638\pi\) | ||||
−0.0177112 | + | 0.999843i | \(0.505638\pi\) | |||||||
\(464\) | 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 | \(-0.341916\pi\) | ||||
0.476471 | + | 0.879190i | \(0.341916\pi\) | |||||||
\(480\) | 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 | \(-0.483260\pi\) | ||||
0.0525663 | + | 0.998617i | \(0.483260\pi\) | |||||||
\(488\) | 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 | \(-0.125288\pi\) | ||||
0.923533 | + | 0.383518i | \(0.125288\pi\) | |||||||
\(504\) | 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 | \(-0.327680\pi\) | ||||
0.515301 | + | 0.857009i | \(0.327680\pi\) | |||||||
\(510\) | 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 | \(-0.506912\pi\) | ||||
−0.0217145 | + | 0.999764i | \(0.506912\pi\) | |||||||
\(542\) | 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 | \(-0.559447\pi\) | ||||
−0.185675 | + | 0.982611i | \(0.559447\pi\) | |||||||
\(558\) | 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 | \(-0.655084\pi\) | ||||
−0.468164 | + | 0.883642i | \(0.655084\pi\) | |||||||
\(600\) | 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 | \(-0.501969\pi\) | ||||
−0.00618540 | + | 0.999981i | \(0.501969\pi\) | |||||||
\(608\) | 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 | \(-0.698254\pi\) | ||||
−0.583339 | + | 0.812228i | \(0.698254\pi\) | |||||||
\(614\) | 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 | \(-0.774191\pi\) | ||||
−0.758752 | + | 0.651379i | \(0.774191\pi\) | |||||||
\(632\) | 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 | \(-0.457529\pi\) | ||||
0.133030 | + | 0.991112i | \(0.457529\pi\) | |||||||
\(648\) | 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 | \(-0.573768\pi\) | ||||
−0.229679 | + | 0.973266i | \(0.573768\pi\) | |||||||
\(654\) | 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 | \(-0.871743\pi\) | ||||
−0.919916 | + | 0.392116i | \(0.871743\pi\) | |||||||
\(662\) | 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 | \(-0.502616\pi\) | ||||
−0.00821829 | + | 0.999966i | \(0.502616\pi\) | |||||||
\(678\) | 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 | \(-0.276423\pi\) | ||||
0.646043 | + | 0.763301i | \(0.276423\pi\) | |||||||
\(702\) | 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 | \(-0.565453\pi\) | ||||
−0.204181 | + | 0.978933i | \(0.565453\pi\) | |||||||
\(710\) | 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 | \(-0.399468\pi\) | ||||
0.310605 | + | 0.950539i | \(0.399468\pi\) | |||||||
\(720\) | 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 | \(-0.342675\pi\) | ||||
0.474372 | + | 0.880324i | \(0.342675\pi\) | |||||||
\(728\) | 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 | \(-0.702386\pi\) | ||||
−0.593833 | + | 0.804588i | \(0.702386\pi\) | |||||||
\(734\) | 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 | \(-0.740325\pi\) | ||||
−0.685291 | + | 0.728269i | \(0.740325\pi\) | |||||||
\(744\) | 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 | \(-0.493695\pi\) | ||||
0.0198056 | + | 0.999804i | \(0.493695\pi\) | |||||||
\(752\) | 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 | \(-0.602954\pi\) | ||||
−0.317829 | + | 0.948148i | \(0.602954\pi\) | |||||||
\(758\) | 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 | \(-0.142823\pi\) | ||||
0.901016 | + | 0.433786i | \(0.142823\pi\) | |||||||
\(774\) | 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 | \(-0.614734\pi\) | ||||
−0.352693 | + | 0.935739i | \(0.614734\pi\) | |||||||
\(798\) | 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 | \(-0.591079\pi\) | ||||
−0.282244 | + | 0.959343i | \(0.591079\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28934.0 | −1.22549 | −0.612745 | − | 0.790281i | \(-0.709935\pi\) | ||||
−0.612745 | + | 0.790281i | \(0.709935\pi\) | |||||||
\(824\) | 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 | \(-0.387559\pi\) | ||||
0.345943 | + | 0.938256i | \(0.387559\pi\) | |||||||
\(830\) | 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 | \(-0.499424\pi\) | ||||
0.00181022 | + | 0.999998i | \(0.499424\pi\) | |||||||
\(840\) | 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 | \(-0.447615\pi\) | ||||
0.163830 | + | 0.986489i | \(0.447615\pi\) | |||||||
\(854\) | 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 | \(-0.694670\pi\) | ||||
−0.574157 | + | 0.818746i | \(0.694670\pi\) | |||||||
\(864\) | 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 | \(-0.228143\pi\) | ||||
0.753957 | + | 0.656924i | \(0.228143\pi\) | |||||||
\(878\) | 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 | \(-0.580975\pi\) | ||||
−0.251654 | + | 0.967817i | \(0.580975\pi\) | |||||||
\(888\) | 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 | \(-0.609537\pi\) | ||||
−0.337369 | + | 0.941372i | \(0.609537\pi\) | |||||||
\(912\) | 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 | \(-0.708601\pi\) | ||||
−0.609429 | + | 0.792841i | \(0.708601\pi\) | |||||||
\(920\) | 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 | \(-0.361188\pi\) | ||||
0.422400 | + | 0.906410i | \(0.361188\pi\) | |||||||
\(942\) | 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 | \(-0.635104\pi\) | ||||
−0.411813 | + | 0.911269i | \(0.635104\pi\) | |||||||
\(968\) | 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 | \(-0.441252\pi\) | ||||
0.183516 | + | 0.983017i | \(0.441252\pi\) | |||||||
\(984\) | 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 | \(-0.343788\pi\) | ||||
0.471290 | + | 0.881978i | \(0.343788\pi\) | |||||||
\(992\) | 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 | \(-0.837216\pi\) | ||||
−0.872060 | + | 0.489398i | \(0.837216\pi\) | |||||||
\(998\) | 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 | 272.4.a.h.1.2 | 3 | ||
3.2 | odd | 2 | 2448.4.a.bi.1.1 | 3 | |||
4.3 | odd | 2 | 17.4.a.b.1.2 | ✓ | 3 | ||
8.3 | odd | 2 | 1088.4.a.v.1.2 | 3 | |||
8.5 | even | 2 | 1088.4.a.x.1.2 | 3 | |||
12.11 | even | 2 | 153.4.a.g.1.2 | 3 | |||
20.3 | even | 4 | 425.4.b.f.324.3 | 6 | |||
20.7 | even | 4 | 425.4.b.f.324.4 | 6 | |||
20.19 | odd | 2 | 425.4.a.g.1.2 | 3 | |||
28.27 | even | 2 | 833.4.a.d.1.2 | 3 | |||
44.43 | even | 2 | 2057.4.a.e.1.2 | 3 | |||
68.47 | odd | 4 | 289.4.b.b.288.4 | 6 | |||
68.55 | odd | 4 | 289.4.b.b.288.3 | 6 | |||
68.67 | odd | 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 | 4.3 | odd | 2 | ||
153.4.a.g.1.2 | 3 | 12.11 | even | 2 | |||
272.4.a.h.1.2 | 3 | 1.1 | even | 1 | trivial | ||
289.4.a.b.1.2 | 3 | 68.67 | odd | 2 | |||
289.4.b.b.288.3 | 6 | 68.55 | odd | 4 | |||
289.4.b.b.288.4 | 6 | 68.47 | odd | 4 | |||
425.4.a.g.1.2 | 3 | 20.19 | odd | 2 | |||
425.4.b.f.324.3 | 6 | 20.3 | even | 4 | |||
425.4.b.f.324.4 | 6 | 20.7 | even | 4 | |||
833.4.a.d.1.2 | 3 | 28.27 | even | 2 | |||
1088.4.a.v.1.2 | 3 | 8.3 | odd | 2 | |||
1088.4.a.x.1.2 | 3 | 8.5 | even | 2 | |||
2057.4.a.e.1.2 | 3 | 44.43 | even | 2 | |||
2448.4.a.bi.1.1 | 3 | 3.2 | odd | 2 |