Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,4,Mod(1,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2496.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.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: | \(147.268767374\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 16x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.20905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2496.1 |
$q$-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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.4322 | 1.02253 | 0.511264 | − | 0.859424i | \(-0.329178\pi\) | ||||
0.511264 | + | 0.859424i | \(0.329178\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.2543 | 0.607675 | 0.303838 | − | 0.952724i | \(-0.401732\pi\) | ||||
0.303838 | + | 0.952724i | \(0.401732\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25.8785 | 0.709333 | 0.354666 | − | 0.934993i | \(-0.384594\pi\) | ||||
0.354666 | + | 0.934993i | \(0.384594\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 34.2966 | 0.590356 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −20.3276 | −0.290010 | −0.145005 | − | 0.989431i | \(-0.546320\pi\) | ||||
−0.145005 | + | 0.989431i | \(0.546320\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 154.712 | 1.86807 | 0.934035 | − | 0.357181i | \(-0.116262\pi\) | ||||
0.934035 | + | 0.357181i | \(0.116262\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 33.7629 | 0.350841 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 180.418 | 1.63565 | 0.817823 | − | 0.575471i | \(-0.195181\pi\) | ||||
0.817823 | + | 0.575471i | \(0.195181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.69520 | 0.0455616 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.4522 | 0.130961 | 0.0654806 | − | 0.997854i | \(-0.479142\pi\) | ||||
0.0654806 | + | 0.997854i | \(0.479142\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −266.424 | −1.54359 | −0.771794 | − | 0.635873i | \(-0.780640\pi\) | ||||
−0.771794 | + | 0.635873i | \(0.780640\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 77.6355 | 0.409534 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 128.661 | 0.621364 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −115.984 | −0.515340 | −0.257670 | − | 0.966233i | \(-0.582955\pi\) | ||||
−0.257670 | + | 0.966233i | \(0.582955\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 391.184 | 1.49006 | 0.745032 | − | 0.667029i | \(-0.232434\pi\) | ||||
0.745032 | + | 0.667029i | \(0.232434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 151.407 | 0.536963 | 0.268482 | − | 0.963285i | \(-0.413478\pi\) | ||||
0.268482 | + | 0.963285i | \(0.413478\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 102.890 | 0.340842 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 467.365 | 1.45047 | 0.725236 | − | 0.688500i | \(-0.241731\pi\) | ||||
0.725236 | + | 0.688500i | \(0.241731\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −216.341 | −0.630731 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −60.9828 | −0.167437 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −79.9842 | −0.207296 | −0.103648 | − | 0.994614i | \(-0.533051\pi\) | ||||
−0.103648 | + | 0.994614i | \(0.533051\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 295.848 | 0.725312 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 464.136 | 1.07853 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −873.710 | −1.92792 | −0.963960 | − | 0.266045i | \(-0.914283\pi\) | ||||
−0.963960 | + | 0.266045i | \(0.914283\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 187.068 | 0.392649 | 0.196325 | − | 0.980539i | \(-0.437099\pi\) | ||||
0.196325 | + | 0.980539i | \(0.437099\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 101.289 | 0.202558 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −148.619 | −0.283598 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −609.204 | −1.11084 | −0.555418 | − | 0.831571i | \(-0.687442\pi\) | ||||
−0.555418 | + | 0.831571i | \(0.687442\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 541.255 | 0.944340 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −248.038 | −0.414601 | −0.207301 | − | 0.978277i | \(-0.566468\pi\) | ||||
−0.207301 | + | 0.978277i | \(0.566468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 852.765 | 1.36724 | 0.683621 | − | 0.729838i | \(-0.260404\pi\) | ||||
0.683621 | + | 0.729838i | \(0.260404\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.0856 | 0.0263050 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 291.244 | 0.431044 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 331.221 | 0.471712 | 0.235856 | − | 0.971788i | \(-0.424211\pi\) | ||||
0.235856 | + | 0.971788i | \(0.424211\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −435.432 | −0.575842 | −0.287921 | − | 0.957654i | \(-0.592964\pi\) | ||||
−0.287921 | + | 0.957654i | \(0.592964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −232.389 | −0.296543 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 61.3566 | 0.0756105 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 259.233 | 0.308749 | 0.154375 | − | 0.988012i | \(-0.450664\pi\) | ||||
0.154375 | + | 0.988012i | \(0.450664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −146.306 | −0.168539 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −799.273 | −0.891191 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1768.70 | 1.91015 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1225.17 | 1.28245 | 0.641223 | − | 0.767355i | \(-0.278428\pi\) | ||||
0.641223 | + | 0.767355i | \(0.278428\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 232.907 | 0.236444 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −645.416 | −0.635855 | −0.317927 | − | 0.948115i | \(-0.602987\pi\) | ||||
−0.317927 | + | 0.948115i | \(0.602987\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 511.137 | 0.488969 | 0.244484 | − | 0.969653i | \(-0.421381\pi\) | ||||
0.244484 | + | 0.969653i | \(0.421381\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 385.984 | 0.358745 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 608.195 | 0.549499 | 0.274750 | − | 0.961516i | \(-0.411405\pi\) | ||||
0.274750 | + | 0.961516i | \(0.411405\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1300.04 | 1.14239 | 0.571197 | − | 0.820813i | \(-0.306479\pi\) | ||||
0.571197 | + | 0.820813i | \(0.306479\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −347.951 | −0.297532 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 42.1953 | 0.0351274 | 0.0175637 | − | 0.999846i | \(-0.494409\pi\) | ||||
0.0175637 | + | 0.999846i | \(0.494409\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2062.58 | 1.67249 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −228.773 | −0.176232 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −661.303 | −0.496847 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1173.55 | 0.860289 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1363.92 | −0.975939 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 311.018 | 0.217310 | 0.108655 | − | 0.994080i | \(-0.465346\pi\) | ||||
0.108655 | + | 0.994080i | \(0.465346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 454.222 | 0.310016 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2000.98 | 1.33456 | 0.667278 | − | 0.744809i | \(-0.267459\pi\) | ||||
0.667278 | + | 0.744809i | \(0.267459\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1741.17 | 1.13518 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 308.669 | 0.196785 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1038.53 | 0.647644 | 0.323822 | − | 0.946118i | \(-0.395032\pi\) | ||||
0.323822 | + | 0.946118i | \(0.395032\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2858.46 | −1.74426 | −0.872128 | − | 0.489277i | \(-0.837261\pi\) | ||||
−0.872128 | + | 0.489277i | \(0.837261\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1402.09 | 0.837430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −336.421 | −0.196734 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 233.814 | 0.133911 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −649.022 | −0.364153 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −743.479 | −0.408780 | −0.204390 | − | 0.978890i | \(-0.565521\pi\) | ||||
−0.204390 | + | 0.978890i | \(0.565521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2277.24 | −1.22728 | −0.613640 | − | 0.789586i | \(-0.710295\pi\) | ||||
−0.613640 | + | 0.789586i | \(0.710295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −182.948 | −0.0966700 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3045.82 | −1.57836 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3173.51 | −1.61321 | −0.806605 | − | 0.591091i | \(-0.798697\pi\) | ||||
−0.806605 | + | 0.591091i | \(0.798697\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −239.953 | −0.119682 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2030.48 | 0.993941 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2314.65 | −1.11225 | −0.556126 | − | 0.831098i | \(-0.687713\pi\) | ||||
−0.556126 | + | 0.831098i | \(0.687713\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 887.545 | 0.418759 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2665.65 | 1.23517 | 0.617587 | − | 0.786502i | \(-0.288110\pi\) | ||||
0.617587 | + | 0.786502i | \(0.288110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1392.41 | 0.622690 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 165.243 | 0.0726198 | 0.0363099 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363099 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 64.0954 | 0.0276866 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2621.13 | −1.11309 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 712.339 | 0.297446 | 0.148723 | − | 0.988879i | \(-0.452484\pi\) | ||||
0.148723 | + | 0.988879i | \(0.452484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2206.53 | −0.906133 | −0.453066 | − | 0.891477i | \(-0.649670\pi\) | ||||
−0.453066 | + | 0.891477i | \(0.649670\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 561.204 | 0.226696 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1325.95 | −0.526949 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −526.048 | −0.205714 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 303.866 | 0.116947 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1470.64 | −0.557129 | −0.278565 | − | 0.960417i | \(-0.589859\pi\) | ||||
−0.278565 | + | 0.960417i | \(0.589859\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 369.560 | 0.137832 | 0.0689158 | − | 0.997622i | \(-0.478046\pi\) | ||||
0.0689158 | + | 0.997622i | \(0.478046\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −445.856 | −0.163735 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4273.41 | 1.54552 | 0.772761 | − | 0.634697i | \(-0.218875\pi\) | ||||
0.772761 | + | 0.634697i | \(0.218875\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4154.31 | −1.47985 | −0.739927 | − | 0.672687i | \(-0.765140\pi\) | ||||
−0.739927 | + | 0.672687i | \(0.765140\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1827.61 | −0.641342 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 230.175 | 0.0795819 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4472.09 | 1.52363 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1623.77 | 0.545215 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4003.71 | 1.32508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1231.59 | 0.401830 | 0.200915 | − | 0.979609i | \(-0.435608\pi\) | ||||
0.200915 | + | 0.979609i | \(0.435608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −744.114 | −0.239370 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1730.92 | 0.549059 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2998.42 | −0.938000 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2558.30 | 0.789377 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 264.259 | 0.0804343 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2187.24 | 0.656809 | 0.328404 | − | 0.944537i | \(-0.393489\pi\) | ||||
0.328404 | + | 0.944537i | \(0.393489\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.2568 | 0.0151872 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4138.67 | 1.21010 | 0.605051 | − | 0.796187i | \(-0.293153\pi\) | ||||
0.605051 | + | 0.796187i | \(0.293153\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 835.354 | 0.241056 | 0.120528 | − | 0.992710i | \(-0.461541\pi\) | ||||
0.120528 | + | 0.992710i | \(0.461541\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 873.733 | 0.248863 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3685.51 | 1.03625 | 0.518124 | − | 0.855305i | \(-0.326630\pi\) | ||||
0.518124 | + | 0.855305i | \(0.326630\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5343.01 | 1.48315 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 993.662 | 0.272343 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3026.21 | −0.819034 | −0.409517 | − | 0.912303i | \(-0.634303\pi\) | ||||
−0.409517 | + | 0.912303i | \(0.634303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3265.58 | 0.872839 | 0.436420 | − | 0.899743i | \(-0.356246\pi\) | ||||
0.436420 | + | 0.899743i | \(0.356246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2473.25 | −0.644940 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2011.25 | −0.518110 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1306.30 | −0.332463 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6363.16 | −1.60016 | −0.800078 | − | 0.599897i | \(-0.795208\pi\) | ||||
−0.800078 | + | 0.599897i | \(0.795208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4668.96 | 1.16022 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −697.168 | −0.171209 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6085.36 | −1.47702 | −0.738511 | − | 0.674242i | \(-0.764471\pi\) | ||||
−0.738511 | + | 0.674242i | \(0.764471\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1305.31 | −0.313159 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 184.070 | 0.0436538 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −123.227 | −0.0288916 | −0.0144458 | − | 0.999896i | \(-0.504598\pi\) | ||||
−0.0144458 | + | 0.999896i | \(0.504598\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −914.395 | −0.211965 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 777.700 | 0.178256 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1935.79 | 0.438763 | 0.219381 | − | 0.975639i | \(-0.429596\pi\) | ||||
0.219381 | + | 0.975639i | \(0.429596\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4612.69 | 1.03395 | 0.516976 | − | 0.856000i | \(-0.327058\pi\) | ||||
0.516976 | + | 0.856000i | \(0.327058\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −438.918 | −0.0973059 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 147.383 | 0.0323183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5834.30 | 1.26552 | 0.632761 | − | 0.774347i | \(-0.281922\pi\) | ||||
0.632761 | + | 0.774347i | \(0.281922\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2397.82 | −0.514529 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4691.91 | 0.996071 | 0.498036 | − | 0.867157i | \(-0.334055\pi\) | ||||
0.498036 | + | 0.867157i | \(0.334055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3465.60 | 0.727945 | 0.363973 | − | 0.931410i | \(-0.381420\pi\) | ||||
0.363973 | + | 0.931410i | \(0.381420\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5306.09 | 1.10283 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4402.50 | 0.905475 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4499.79 | −0.915894 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3675.51 | 0.740420 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2677.31 | −0.533822 | −0.266911 | − | 0.963721i | \(-0.586003\pi\) | ||||
−0.266911 | + | 0.963721i | \(0.586003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9988.43 | −1.97135 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 698.720 | 0.136511 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2345.44 | −0.453646 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1703.98 | 0.326299 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1936.25 | −0.367111 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2138.60 | 0.401494 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 471.915 | 0.0877316 | 0.0438658 | − | 0.999037i | \(-0.486033\pi\) | ||||
0.0438658 | + | 0.999037i | \(0.486033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1533.41 | 0.282306 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1518.52 | 0.276872 | 0.138436 | − | 0.990371i | \(-0.455793\pi\) | ||||
0.138436 | + | 0.990371i | \(0.455793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4049.86 | 0.731348 | 0.365674 | − | 0.930743i | \(-0.380839\pi\) | ||||
0.365674 | + | 0.930743i | \(0.380839\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1157.95 | 0.207121 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3253.96 | −0.576532 | −0.288266 | − | 0.957550i | \(-0.593079\pi\) | ||||
−0.288266 | + | 0.957550i | \(0.593079\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 529.272 | 0.0928951 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1824.59 | 0.317254 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3144.92 | −0.541759 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −74.0375 | −0.0126365 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3900.11 | 0.659561 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5259.86 | 0.881415 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3422.45 | −0.568322 | −0.284161 | − | 0.958777i | \(-0.591715\pi\) | ||||
−0.284161 | + | 0.958777i | \(0.591715\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1043.85 | −0.171780 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6964.54 | −1.13586 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9301.67 | −1.50354 | −0.751772 | − | 0.659423i | \(-0.770801\pi\) | ||||
−0.751772 | + | 0.659423i | \(0.770801\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 126.586 | 0.0202808 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6894.66 | −1.09492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6294.99 | −0.990955 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6187.74 | 0.965613 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 216.898 | 0.0335554 | 0.0167777 | − | 0.999859i | \(-0.494659\pi\) | ||||
0.0167777 | + | 0.999859i | \(0.494659\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4809.84 | 0.737721 | 0.368861 | − | 0.929485i | \(-0.379748\pi\) | ||||
0.368861 | + | 0.929485i | \(0.379748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2859.64 | −0.431170 | −0.215585 | − | 0.976485i | \(-0.569166\pi\) | ||||
−0.215585 | + | 0.976485i | \(0.569166\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2835.62 | −0.423941 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −686.319 | −0.101747 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3686.04 | −0.541899 | −0.270949 | − | 0.962594i | \(-0.587338\pi\) | ||||
−0.270949 | + | 0.962594i | \(0.587338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17076.8 | 2.48969 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1983.91 | −0.286855 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9748.98 | 1.39804 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3470.59 | 0.493633 | 0.246816 | − | 0.969062i | \(-0.420616\pi\) | ||||
0.246816 | + | 0.969062i | \(0.420616\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3520.65 | 0.496688 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −900.166 | −0.125968 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11963.4 | 1.66070 | 0.830352 | − | 0.557240i | \(-0.188140\pi\) | ||||
0.830352 | + | 0.557240i | \(0.188140\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4091.75 | −0.563459 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −265.879 | −0.0363221 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 345.604 | 0.0468403 | 0.0234202 | − | 0.999726i | \(-0.492544\pi\) | ||||
0.0234202 | + | 0.999726i | \(0.492544\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 933.055 | 0.125464 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3386.40 | 0.451793 | 0.225897 | − | 0.974151i | \(-0.427469\pi\) | ||||
0.225897 | + | 0.974151i | \(0.427469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3329.56 | 0.440754 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1362.67 | 0.178988 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1629.88 | 0.212438 | 0.106219 | − | 0.994343i | \(-0.466126\pi\) | ||||
0.106219 | + | 0.994343i | \(0.466126\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3667.47 | −0.474353 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6002.95 | 0.770506 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3786.58 | 0.482338 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7938.94 | −1.00364 | −0.501819 | − | 0.864973i | \(-0.667336\pi\) | ||||
−0.501819 | + | 0.864973i | \(0.667336\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5223.52 | 0.655396 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 214.402 | 0.0267001 | 0.0133500 | − | 0.999911i | \(-0.495750\pi\) | ||||
0.0133500 | + | 0.999911i | \(0.495750\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3463.52 | 0.428114 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 926.008 | 0.113614 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3001.48 | −0.365548 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4783.73 | −0.578338 | −0.289169 | − | 0.957278i | \(-0.593379\pi\) | ||||
−0.289169 | + | 0.957278i | \(0.593379\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3115.58 | 0.373917 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9832.99 | −1.17155 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4977.95 | −0.588815 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8575.39 | −1.00705 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9903.67 | −1.15472 | −0.577358 | − | 0.816491i | \(-0.695916\pi\) | ||||
−0.577358 | + | 0.816491i | \(0.695916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12120.6 | 1.40314 | 0.701572 | − | 0.712598i | \(-0.252482\pi\) | ||||
0.701572 | + | 0.712598i | \(0.252482\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4206.28 | 0.483491 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −115.770 | −0.0132133 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2105.32 | 0.238603 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1009.26 | −0.113584 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13672.6 | 1.52805 | 0.764023 | − | 0.645189i | \(-0.223221\pi\) | ||||
0.764023 | + | 0.645189i | \(0.223221\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7113.10 | 0.789455 | 0.394727 | − | 0.918798i | \(-0.370839\pi\) | ||||
0.394727 | + | 0.918798i | \(0.370839\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 701.441 | 0.0773138 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27912.9 | 3.05550 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6022.04 | 0.654707 | 0.327353 | − | 0.944902i | \(-0.393843\pi\) | ||||
0.327353 | + | 0.944902i | \(0.393843\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1947.07 | −0.210244 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12994.4 | −1.39364 | −0.696821 | − | 0.717245i | \(-0.745403\pi\) | ||||
−0.696821 | + | 0.717245i | \(0.745403\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2963.61 | 0.315704 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2230.44 | −0.236009 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10984.3 | 1.15452 | 0.577260 | − | 0.816560i | \(-0.304122\pi\) | ||||
0.577260 | + | 0.816560i | \(0.304122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10123.2 | 1.05695 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6831.72 | −0.708570 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1672.60 | −0.172335 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9834.10 | 1.00661 | 0.503304 | − | 0.864109i | \(-0.332118\pi\) | ||||
0.503304 | + | 0.864109i | \(0.332118\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −548.845 | −0.0558124 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3401.42 | −0.343644 | −0.171822 | − | 0.985128i | \(-0.554965\pi\) | ||||
−0.171822 | + | 0.985128i | \(0.554965\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1739.42 | −0.174596 | −0.0872979 | − | 0.996182i | \(-0.527823\pi\) | ||||
−0.0872979 | + | 0.996182i | \(0.527823\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9137.45 | −0.911267 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7958.82 | −0.788630 | −0.394315 | − | 0.918975i | \(-0.629018\pi\) | ||||
−0.394315 | + | 0.918975i | \(0.629018\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6856.16 | −0.675028 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9520.54 | −0.931387 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3918.20 | 0.380886 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 881.114 | 0.0851122 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −719.858 | −0.0690986 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8431.98 | −0.804315 | −0.402158 | − | 0.915570i | \(-0.631740\pi\) | ||||
−0.402158 | + | 0.915570i | \(0.631740\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1507.79 | 0.142930 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6091.45 | 0.573852 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14006.4 | 1.31133 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11684.7 | 1.08723 | 0.543617 | − | 0.839334i | \(-0.317055\pi\) | ||||
0.543617 | + | 0.839334i | \(0.317055\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6943.94 | −0.642159 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3954.70 | −0.363489 | −0.181745 | − | 0.983346i | \(-0.558174\pi\) | ||||
−0.181745 | + | 0.983346i | \(0.558174\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −415.744 | −0.0379801 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2662.63 | 0.241771 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2791.49 | −0.251943 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5690.37 | −0.510493 | −0.255246 | − | 0.966876i | \(-0.582157\pi\) | ||||
−0.255246 | + | 0.966876i | \(0.582157\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7996.95 | 0.713128 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10859.1 | −0.962595 | −0.481298 | − | 0.876557i | \(-0.659834\pi\) | ||||
−0.481298 | + | 0.876557i | \(0.659834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7378.53 | −0.650178 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18558.6 | 1.61610 | 0.808049 | − | 0.589115i | \(-0.200524\pi\) | ||||
0.808049 | + | 0.589115i | \(0.200524\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9597.27 | 0.830838 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4177.22 | 0.359510 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5843.42 | 0.499984 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12094.7 | 1.02887 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 495.730 | 0.0419271 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17297.5 | 1.45454 | 0.727271 | − | 0.686350i | \(-0.240788\pi\) | ||||
0.727271 | + | 0.686350i | \(0.240788\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5016.11 | −0.419386 | −0.209693 | − | 0.977767i | \(-0.567247\pi\) | ||||
−0.209693 | + | 0.977767i | \(0.567247\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 192.286 | 0.0159849 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5415.77 | 0.447656 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20383.8 | 1.67533 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7863.39 | −0.642640 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5085.39 | −0.413269 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6953.01 | 0.561878 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2137.02 | 0.171730 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5598.57 | −0.447398 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17642.3 | −1.40204 | −0.701018 | − | 0.713144i | \(-0.747271\pi\) | ||||
−0.701018 | + | 0.713144i | \(0.747271\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6619.59 | −0.523156 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14862.3 | 1.16813 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18414.9 | −1.43943 | −0.719713 | − | 0.694271i | \(-0.755727\pi\) | ||||
−0.719713 | + | 0.694271i | \(0.755727\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1683.61 | 0.130883 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3164.20 | 0.244645 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3727.66 | 0.286648 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3977.84 | −0.304234 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8179.15 | −0.622193 | −0.311096 | − | 0.950378i | \(-0.600696\pi\) | ||||
−0.311096 | + | 0.950378i | \(0.600696\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1968.30 | −0.148927 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1578.14 | −0.118769 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1880.07 | −0.140738 | −0.0703690 | − | 0.997521i | \(-0.522418\pi\) | ||||
−0.0703690 | + | 0.997521i | \(0.522418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 482.385 | 0.0359187 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 911.598 | 0.0675194 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10118.3 | 0.745485 | 0.372743 | − | 0.927935i | \(-0.378417\pi\) | ||||
0.372743 | + | 0.927935i | \(0.378417\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23428.9 | 1.71711 | 0.858555 | − | 0.512721i | \(-0.171362\pi\) | ||||
0.858555 | + | 0.512721i | \(0.171362\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4411.92 | −0.321659 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1027.52 | 0.0745225 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20508.1 | 1.47966 | 0.739831 | − | 0.672793i | \(-0.234906\pi\) | ||||
0.739831 | + | 0.672793i | \(0.234906\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1108.68 | 0.0795771 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4900.49 | −0.349925 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2069.87 | −0.147042 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1337.57 | −0.0945327 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5968.43 | −0.419665 | −0.209833 | − | 0.977737i | \(-0.567292\pi\) | ||||
−0.209833 | + | 0.977737i | \(0.567292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41219.0 | −2.88353 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12820.2 | 0.892308 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14659.5 | −1.01517 | −0.507584 | − | 0.861602i | \(-0.669461\pi\) | ||||
−0.507584 | + | 0.861602i | \(0.669461\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2615.38 | −0.180202 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12462.9 | −0.854394 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23635.9 | −1.61225 | −0.806125 | − | 0.591746i | \(-0.798439\pi\) | ||||
−0.806125 | + | 0.591746i | \(0.798439\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11527.0 | −0.782356 | −0.391178 | − | 0.920315i | \(-0.627932\pi\) | ||||
−0.391178 | + | 0.920315i | \(0.627932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5482.83 | −0.370279 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7560.15 | −0.508039 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5098.56 | 0.340930 | 0.170465 | − | 0.985364i | \(-0.445473\pi\) | ||||
0.170465 | + | 0.985364i | \(0.445473\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 690.525 | 0.0459466 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6075.74 | −0.402288 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1516.39 | −0.0999128 | −0.0499564 | − | 0.998751i | \(-0.515908\pi\) | ||||
−0.0499564 | + | 0.998751i | \(0.515908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13416.3 | 0.879668 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18539.3 | 1.20966 | 0.604832 | − | 0.796353i | \(-0.293240\pi\) | ||||
0.604832 | + | 0.796353i | \(0.293240\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25684.9 | 1.66779 | 0.833897 | − | 0.551920i | \(-0.186105\pi\) | ||||
0.833897 | + | 0.551920i | \(0.186105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4871.30 | 0.314780 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2917.49 | 0.187619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16304.5 | −1.04349 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12011.1 | 0.765038 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2357.67 | 0.149454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22410.9 | 1.41389 | 0.706945 | − | 0.707269i | \(-0.250073\pi\) | ||||
0.706945 | + | 0.707269i | \(0.250073\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3694.77 | 0.231997 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3555.62 | 0.222206 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2812.43 | 0.174933 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2232.34 | −0.138200 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6827.81 | 0.420721 | 0.210361 | − | 0.977624i | \(-0.432536\pi\) | ||||
0.210361 | + | 0.977624i | \(0.432536\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23264.3 | −1.42684 | −0.713418 | − | 0.700738i | \(-0.752854\pi\) | ||||
−0.713418 | + | 0.700738i | \(0.752854\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5192.76 | 0.316999 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14745.9 | −0.896014 | −0.448007 | − | 0.894030i | \(-0.647866\pi\) | ||||
−0.448007 | + | 0.894030i | \(0.647866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22610.3 | −1.36754 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8995.26 | −0.541554 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10909.0 | −0.653755 | −0.326878 | − | 0.945067i | \(-0.605997\pi\) | ||||
−0.326878 | + | 0.945067i | \(0.605997\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22875.7 | 1.36462 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7674.89 | 0.455747 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4182.99 | −0.247263 | −0.123631 | − | 0.992328i | \(-0.539454\pi\) | ||||
−0.123631 | + | 0.992328i | \(0.539454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2224.23 | −0.130881 | −0.0654406 | − | 0.997856i | \(-0.520845\pi\) | ||||
−0.0654406 | + | 0.997856i | \(0.520845\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 792.776 | 0.0464387 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19905.4 | 1.16075 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3689.95 | 0.214206 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6561.72 | 0.379209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4841.04 | 0.278519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24152.5 | −1.38337 | −0.691687 | − | 0.722197i | \(-0.743132\pi\) | ||||
−0.691687 | + | 0.722197i | \(0.743132\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 153.770 | 0.00876833 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15310.7 | 0.869187 | 0.434593 | − | 0.900627i | \(-0.356892\pi\) | ||||
0.434593 | + | 0.900627i | \(0.356892\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13788.4 | 0.779310 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12416.0 | 0.698652 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11399.6 | 0.638646 | 0.319323 | − | 0.947646i | \(-0.396545\pi\) | ||||
0.319323 | + | 0.947646i | \(0.396545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11872.6 | 0.662233 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2506.06 | 0.139174 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1039.79 | 0.0574935 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3323.23 | −0.182955 | −0.0914773 | − | 0.995807i | \(-0.529159\pi\) | ||||
−0.0914773 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2621.20 | 0.143681 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32678.5 | −1.78355 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7951.82 | −0.432133 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11056.5 | 0.598279 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12670.4 | 0.682673 | 0.341336 | − | 0.939941i | \(-0.389120\pi\) | ||||
0.341336 | + | 0.939941i | \(0.389120\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17944.0 | −0.962692 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16029.0 | 0.856295 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7263.71 | −0.386393 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13075.2 | −0.692594 | −0.346297 | − | 0.938125i | \(-0.612561\pi\) | ||||
−0.346297 | + | 0.938125i | \(0.612561\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2980.99 | 0.157237 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48067.8 | −2.52476 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3846.03 | −0.201165 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9078.62 | −0.472869 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2988.41 | 0.155005 | 0.0775026 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775026 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5752.48 | 0.297134 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9796.73 | 0.503934 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 116.479 | 0.00596680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5507.46 | 0.280963 | 0.140482 | − | 0.990083i | \(-0.455135\pi\) | ||||
0.140482 | + | 0.990083i | \(0.455135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3077.75 | −0.155725 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36585.2 | 1.84353 | 0.921764 | − | 0.387751i | \(-0.126748\pi\) | ||||
0.921764 | + | 0.387751i | \(0.126748\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7419.75 | −0.372356 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15765.3 | −0.787953 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6425.89 | 0.319865 | 0.159933 | − | 0.987128i | \(-0.448872\pi\) | ||||
0.159933 | + | 0.987128i | \(0.448872\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6033.76 | −0.299131 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20411.0 | −1.00782 | −0.503908 | − | 0.863757i | \(-0.668105\pi\) | ||||
−0.503908 | + | 0.863757i | \(0.668105\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8499.60 | −0.417988 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3918.89 | −0.191947 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6844.81 | 0.333917 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24259.5 | 1.17875 | 0.589375 | − | 0.807860i | \(-0.299374\pi\) | ||||
0.589375 | + | 0.807860i | \(0.299374\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19089.5 | −0.923850 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26033.9 | −1.25493 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9295.39 | −0.446297 | −0.223148 | − | 0.974785i | \(-0.571633\pi\) | ||||
−0.223148 | + | 0.974785i | \(0.571633\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14006.9 | 0.669851 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21974.7 | −1.04676 | −0.523378 | − | 0.852101i | \(-0.675328\pi\) | ||||
−0.523378 | + | 0.852101i | \(0.675328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14631.0 | 0.694204 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2091.50 | −0.0988476 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11358.2 | 0.534709 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22987.4 | 1.07795 | 0.538977 | − | 0.842320i | \(-0.318811\pi\) | ||||
0.538977 | + | 0.842320i | \(0.318811\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18256.1 | −0.852759 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31970.9 | −1.48760 | −0.743799 | − | 0.668404i | \(-0.766978\pi\) | ||||
−0.743799 | + | 0.668404i | \(0.766978\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1517.34 | −0.0703283 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3915.94 | −0.180803 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 60520.8 | 2.78354 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6418.85 | −0.294090 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 552.209 | 0.0252035 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36280.2 | −1.64955 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6087.26 | 0.275715 | 0.137857 | − | 0.990452i | \(-0.455978\pi\) | ||||
0.137857 | + | 0.990452i | \(0.455978\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −369.680 | −0.0166805 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 474.878 | 0.0213460 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2431.88 | −0.108901 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2743.19 | −0.122378 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23080.0 | −1.02577 | −0.512883 | − | 0.858458i | \(-0.671423\pi\) | ||||
−0.512883 | + | 0.858458i | \(0.671423\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9500.41 | −0.420651 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2333.10 | 0.102916 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22068.3 | 0.969829 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23212.9 | 1.01633 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5807.37 | 0.253320 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32377.8 | −1.40710 | −0.703550 | − | 0.710646i | \(-0.748403\pi\) | ||||
−0.703550 | + | 0.710646i | \(0.748403\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26352.8 | 1.14103 | 0.570513 | − | 0.821288i | \(-0.306744\pi\) | ||||
0.570513 | + | 0.821288i | \(0.306744\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13838.1 | 0.596952 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26461.5 | −1.13731 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23424.5 | 1.00308 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1316.75 | −0.0561796 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35355.3 | −1.50294 | −0.751468 | − | 0.659770i | \(-0.770654\pi\) | ||||
−0.751468 | + | 0.659770i | \(0.770654\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12663.3 | 0.536347 | 0.268173 | − | 0.963371i | \(-0.413580\pi\) | ||||
0.268173 | + | 0.963371i | \(0.413580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 442.149 | 0.0186590 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16295.2 | −0.685176 | −0.342588 | − | 0.939486i | \(-0.611303\pi\) | ||||
−0.342588 | + | 0.939486i | \(0.611303\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13638.9 | −0.571411 | −0.285705 | − | 0.958318i | \(-0.592228\pi\) | ||||
−0.285705 | + | 0.958318i | \(0.592228\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17502.9 | 0.730649 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4397.69 | 0.182918 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30474.2 | 1.26300 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7193.46 | −0.297064 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1890.31 | 0.0777838 | 0.0388919 | − | 0.999243i | \(-0.487617\pi\) | ||||
0.0388919 | + | 0.999243i | \(0.487617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23970.7 | −0.982849 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14075.7 | 0.575082 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1932.04 | 0.0786559 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7442.50 | −0.301921 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10396.8 | 0.420279 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20925.6 | −0.842914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1620.21 | −0.0650351 | −0.0325175 | − | 0.999471i | \(-0.510352\pi\) | ||||
−0.0325175 | + | 0.999471i | \(0.510352\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15918.3 | 0.636718 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14508.4 | −0.578292 | −0.289146 | − | 0.957285i | \(-0.593371\pi\) | ||||
−0.289146 | + | 0.957285i | \(0.593371\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29639.8 | 1.17730 | 0.588648 | − | 0.808389i | \(-0.299660\pi\) | ||||
0.588648 | + | 0.808389i | \(0.299660\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13207.5 | 0.522776 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21528.8 | −0.849186 | −0.424593 | − | 0.905384i | \(-0.639583\pi\) | ||||
−0.424593 | + | 0.905384i | \(0.639583\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1889.10 | 0.0742557 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13499.4 | −0.528792 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8571.50 | 0.334601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7919.65 | 0.308091 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11026.5 | 0.427482 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15349.9 | −0.593054 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14865.3 | −0.572366 | −0.286183 | − | 0.958175i | \(-0.592387\pi\) | ||||
−0.286183 | + | 0.958175i | \(0.592387\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8031.92 | −0.308202 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21336.0 | −0.815921 | −0.407961 | − | 0.913000i | \(-0.633760\pi\) | ||||
−0.407961 | + | 0.913000i | \(0.633760\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37538.2 | 1.43065 | 0.715323 | − | 0.698794i | \(-0.246280\pi\) | ||||
0.715323 | + | 0.698794i | \(0.246280\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −29965.3 | −1.13816 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34575.0 | −1.30881 | −0.654406 | − | 0.756144i | \(-0.727081\pi\) | ||||
−0.654406 | + | 0.756144i | \(0.727081\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3500.29 | 0.132054 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2096.16 | 0.0788148 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 72306.9 | 2.70958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8143.61 | 0.304146 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7036.32 | −0.261913 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5448.96 | −0.202150 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1625.89 | 0.0601178 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5111.95 | 0.188389 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25225.5 | −0.926545 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10424.8 | −0.381641 | −0.190820 | − | 0.981625i | \(-0.561115\pi\) | ||||
−0.190820 | + | 0.981625i | \(0.561115\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5808.75 | −0.211952 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10961.8 | −0.398661 | −0.199331 | − | 0.979932i | \(-0.563877\pi\) | ||||
−0.199331 | + | 0.979932i | \(0.563877\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11268.3 | −0.408464 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6415.80 | 0.231803 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22519.7 | 0.810976 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10779.2 | 0.386914 | 0.193457 | − | 0.981109i | \(-0.438030\pi\) | ||||
0.193457 | + | 0.981109i | \(0.438030\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1415.74 | 0.0506519 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3224.49 | 0.114990 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −660.549 | −0.0234797 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4600.23 | 0.162990 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5429.07 | 0.191735 | 0.0958675 | − | 0.995394i | \(-0.469437\pi\) | ||||
0.0958675 | + | 0.995394i | \(0.469437\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33470.5 | −1.17825 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4555.55 | 0.159852 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6013.88 | −0.210348 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21300.1 | −0.742631 | −0.371315 | − | 0.928507i | \(-0.621093\pi\) | ||||
−0.371315 | + | 0.928507i | \(0.621093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12149.6 | 0.422244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26851.2 | −0.930207 | −0.465103 | − | 0.885256i | \(-0.653983\pi\) | ||||
−0.465103 | + | 0.885256i | \(0.653983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70576.7 | 2.43722 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3473.86 | 0.119582 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8021.68 | −0.275258 | −0.137629 | − | 0.990484i | \(-0.543948\pi\) | ||||
−0.137629 | + | 0.990484i | \(0.543948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11085.9 | −0.379204 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9761.88 | −0.332861 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35715.0 | 1.21398 | 0.606990 | − | 0.794709i | \(-0.292377\pi\) | ||||
0.606990 | + | 0.794709i | \(0.292377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16812.6 | −0.569680 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1587.82 | 0.0536330 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11687.9 | 0.393557 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41190.9 | 1.38266 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5473.76 | 0.183166 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4224.88 | 0.140936 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53338.8 | −1.77380 | −0.886898 | − | 0.461965i | \(-0.847145\pi\) | ||||
−0.886898 | + | 0.461965i | \(0.847145\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9434.77 | −0.312785 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23112.9 | 0.763882 | 0.381941 | − | 0.924187i | \(-0.375256\pi\) | ||||
0.381941 | + | 0.924187i | \(0.375256\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32170.0 | −1.05994 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −222.113 | −0.00729569 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52874.6 | −1.73143 | −0.865715 | − | 0.500538i | \(-0.833136\pi\) | ||||
−0.865715 | + | 0.500538i | \(0.833136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6708.57 | 0.219006 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11700.3 | 0.380798 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45173.1 | −1.46572 | −0.732858 | − | 0.680381i | \(-0.761814\pi\) | ||||
−0.732858 | + | 0.680381i | \(0.761814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48854.5 | 1.58034 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15779.6 | 0.508885 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27316.7 | 0.878281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −60485.6 | −1.93884 | −0.969418 | − | 0.245414i | \(-0.921076\pi\) | ||||
−0.969418 | + | 0.245414i | \(0.921076\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10267.3 | −0.328121 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −47492.8 | −1.51319 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18108.1 | 0.575214 | 0.287607 | − | 0.957749i | \(-0.407140\pi\) | ||||
0.287607 | + | 0.957749i | \(0.407140\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3131.56 | −0.0991773 |
(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 | 2496.4.a.bp.1.3 | 3 | ||
4.3 | odd | 2 | 2496.4.a.bl.1.3 | 3 | |||
8.3 | odd | 2 | 39.4.a.c.1.3 | ✓ | 3 | ||
8.5 | even | 2 | 624.4.a.t.1.1 | 3 | |||
24.5 | odd | 2 | 1872.4.a.bk.1.3 | 3 | |||
24.11 | even | 2 | 117.4.a.f.1.1 | 3 | |||
40.19 | odd | 2 | 975.4.a.l.1.1 | 3 | |||
56.27 | even | 2 | 1911.4.a.k.1.3 | 3 | |||
104.51 | odd | 2 | 507.4.a.h.1.1 | 3 | |||
104.83 | even | 4 | 507.4.b.g.337.1 | 6 | |||
104.99 | even | 4 | 507.4.b.g.337.6 | 6 | |||
312.155 | even | 2 | 1521.4.a.u.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.c.1.3 | ✓ | 3 | 8.3 | odd | 2 | ||
117.4.a.f.1.1 | 3 | 24.11 | even | 2 | |||
507.4.a.h.1.1 | 3 | 104.51 | odd | 2 | |||
507.4.b.g.337.1 | 6 | 104.83 | even | 4 | |||
507.4.b.g.337.6 | 6 | 104.99 | even | 4 | |||
624.4.a.t.1.1 | 3 | 8.5 | even | 2 | |||
975.4.a.l.1.1 | 3 | 40.19 | odd | 2 | |||
1521.4.a.u.1.3 | 3 | 312.155 | even | 2 | |||
1872.4.a.bk.1.3 | 3 | 24.5 | odd | 2 | |||
1911.4.a.k.1.3 | 3 | 56.27 | even | 2 | |||
2496.4.a.bl.1.3 | 3 | 4.3 | odd | 2 | |||
2496.4.a.bp.1.3 | 3 | 1.1 | even | 1 | trivial |