Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,4,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1088.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1940780862\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 67x^{5} - 35x^{4} + 893x^{3} + 595x^{2} - 3064x - 2804 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 544) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.90461\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.01688 | −0.773048 | −0.386524 | − | 0.922279i | \(-0.626324\pi\) | ||||
−0.386524 | + | 0.922279i | \(0.626324\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.1958 | 1.26971 | 0.634857 | − | 0.772630i | \(-0.281059\pi\) | ||||
0.634857 | + | 0.772630i | \(0.281059\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9.87960 | 0.533448 | 0.266724 | − | 0.963773i | \(-0.414059\pi\) | ||||
0.266724 | + | 0.963773i | \(0.414059\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −10.8647 | −0.402396 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −60.2213 | −1.65067 | −0.825337 | − | 0.564640i | \(-0.809015\pi\) | ||||
−0.825337 | + | 0.564640i | \(0.809015\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 51.2168 | 1.09269 | 0.546346 | − | 0.837560i | \(-0.316019\pi\) | ||||
0.546346 | + | 0.837560i | \(0.316019\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −57.0229 | −0.981550 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.0000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −34.2361 | −0.413384 | −0.206692 | − | 0.978406i | \(-0.566270\pi\) | ||||
−0.206692 | + | 0.978406i | \(0.566270\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −39.6851 | −0.412381 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −39.8677 | −0.361435 | −0.180717 | − | 0.983535i | \(-0.557842\pi\) | ||||
−0.180717 | + | 0.983535i | \(0.557842\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 76.5216 | 0.612173 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 152.098 | 1.08412 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 196.276 | 1.25681 | 0.628407 | − | 0.777885i | \(-0.283707\pi\) | ||||
0.628407 | + | 0.777885i | \(0.283707\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 182.486 | 1.05727 | 0.528636 | − | 0.848849i | \(-0.322704\pi\) | ||||
0.528636 | + | 0.848849i | \(0.322704\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 241.902 | 1.27605 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 140.249 | 0.677326 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 255.616 | 1.13576 | 0.567878 | − | 0.823113i | \(-0.307765\pi\) | ||||
0.567878 | + | 0.823113i | \(0.307765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −205.732 | −0.844703 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −194.494 | −0.740848 | −0.370424 | − | 0.928863i | \(-0.620788\pi\) | ||||
−0.370424 | + | 0.928863i | \(0.620788\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 150.979 | 0.535443 | 0.267721 | − | 0.963496i | \(-0.413729\pi\) | ||||
0.267721 | + | 0.963496i | \(0.413729\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −154.233 | −0.510928 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −350.840 | −1.08884 | −0.544418 | − | 0.838814i | \(-0.683250\pi\) | ||||
−0.544418 | + | 0.838814i | \(0.683250\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −245.394 | −0.715433 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 68.2869 | 0.187492 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −71.9534 | −0.186482 | −0.0932412 | − | 0.995644i | \(-0.529723\pi\) | ||||
−0.0932412 | + | 0.995644i | \(0.529723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −854.892 | −2.09588 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 137.522 | 0.319566 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 142.346 | 0.314099 | 0.157049 | − | 0.987591i | \(-0.449802\pi\) | ||||
0.157049 | + | 0.987591i | \(0.449802\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 610.499 | 1.28142 | 0.640708 | − | 0.767785i | \(-0.278641\pi\) | ||||
0.640708 | + | 0.767785i | \(0.278641\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −107.339 | −0.214658 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 727.065 | 1.38741 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 368.545 | 0.672013 | 0.336007 | − | 0.941860i | \(-0.390924\pi\) | ||||
0.336007 | + | 0.941860i | \(0.390924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 160.144 | 0.279406 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −710.184 | −1.18709 | −0.593544 | − | 0.804801i | \(-0.702272\pi\) | ||||
−0.593544 | + | 0.804801i | \(0.702272\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1015.72 | 1.62851 | 0.814254 | − | 0.580509i | \(-0.197146\pi\) | ||||
0.814254 | + | 0.580509i | \(0.197146\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −307.378 | −0.473239 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −594.962 | −0.880549 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 374.294 | 0.533055 | 0.266528 | − | 0.963827i | \(-0.414124\pi\) | ||||
0.266528 | + | 0.963827i | \(0.414124\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −317.611 | −0.435681 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −773.711 | −1.02320 | −0.511601 | − | 0.859223i | \(-0.670948\pi\) | ||||
−0.511601 | + | 0.859223i | \(0.670948\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −241.329 | −0.307951 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −788.418 | −0.971578 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1052.83 | 1.25393 | 0.626966 | − | 0.779046i | \(-0.284296\pi\) | ||||
0.626966 | + | 0.779046i | \(0.284296\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 506.001 | 0.582894 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −733.023 | −0.817322 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −486.010 | −0.524880 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1596.33 | −1.67096 | −0.835479 | − | 0.549523i | \(-0.814810\pi\) | ||||
−0.835479 | + | 0.549523i | \(0.814810\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 654.287 | 0.664225 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1355.25 | 1.33517 | 0.667587 | − | 0.744532i | \(-0.267327\pi\) | ||||
0.667587 | + | 0.744532i | \(0.267327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1035.23 | 0.990330 | 0.495165 | − | 0.868799i | \(-0.335108\pi\) | ||||
0.495165 | + | 0.868799i | \(0.335108\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −563.363 | −0.523606 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −154.641 | −0.139717 | −0.0698585 | − | 0.997557i | \(-0.522255\pi\) | ||||
−0.0698585 | + | 0.997557i | \(0.522255\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 427.905 | 0.376017 | 0.188009 | − | 0.982167i | \(-0.439797\pi\) | ||||
0.188009 | + | 0.982167i | \(0.439797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1026.78 | −0.877994 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −772.563 | −0.643156 | −0.321578 | − | 0.946883i | \(-0.604213\pi\) | ||||
−0.321578 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −565.956 | −0.458918 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −556.455 | −0.439695 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −167.953 | −0.129380 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2295.61 | 1.72473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 781.257 | 0.572712 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −688.191 | −0.492429 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1179.19 | 0.823907 | 0.411954 | − | 0.911205i | \(-0.364847\pi\) | ||||
0.411954 | + | 0.911205i | \(0.364847\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −606.463 | −0.413923 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2519.21 | 1.68019 | 0.840093 | − | 0.542442i | \(-0.182500\pi\) | ||||
0.840093 | + | 0.542442i | \(0.182500\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −338.239 | −0.220519 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2159.16 | 1.37652 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 519.136 | 0.323743 | 0.161872 | − | 0.986812i | \(-0.448247\pi\) | ||||
0.161872 | + | 0.986812i | \(0.448247\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1381.62 | 0.843075 | 0.421537 | − | 0.906811i | \(-0.361491\pi\) | ||||
0.421537 | + | 0.906811i | \(0.361491\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1409.28 | 0.841723 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3084.34 | −1.80368 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2786.31 | 1.59579 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 985.716 | 0.553064 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1914.19 | 1.05246 | 0.526230 | − | 0.850343i | \(-0.323605\pi\) | ||||
0.526230 | + | 0.850343i | \(0.323605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1591.12 | 0.857506 | 0.428753 | − | 0.903422i | \(-0.358953\pi\) | ||||
0.428753 | + | 0.903422i | \(0.358953\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 184.700 | 0.0975954 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2590.54 | 1.34243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1017.70 | 0.517331 | 0.258665 | − | 0.965967i | \(-0.416717\pi\) | ||||
0.258665 | + | 0.965967i | \(0.416717\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 289.028 | 0.144160 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −393.877 | −0.192807 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3366.72 | −1.61780 | −0.808900 | − | 0.587946i | \(-0.799937\pi\) | ||||
−0.808900 | + | 0.587946i | \(0.799937\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3434.00 | 1.62022 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2328.20 | 1.07881 | 0.539405 | − | 0.842046i | \(-0.318649\pi\) | ||||
0.539405 | + | 0.842046i | \(0.318649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 426.162 | 0.193974 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 371.965 | 0.166344 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2292.81 | 1.00762 | 0.503812 | − | 0.863813i | \(-0.331930\pi\) | ||||
0.503812 | + | 0.863813i | \(0.331930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 756.003 | 0.326562 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −571.785 | −0.242814 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1836.72 | −0.766943 | −0.383472 | − | 0.923553i | \(-0.625272\pi\) | ||||
−0.383472 | + | 0.923553i | \(0.625272\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2746.26 | 1.12778 | 0.563889 | − | 0.825850i | \(-0.309304\pi\) | ||||
0.563889 | + | 0.825850i | \(0.309304\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2452.30 | −0.990596 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3628.68 | 1.44208 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1023.76 | 0.400347 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1502.67 | 0.578322 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3701.09 | −1.40210 | −0.701051 | − | 0.713111i | \(-0.747286\pi\) | ||||
−0.701051 | + | 0.713111i | \(0.747286\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1389.59 | 0.518262 | 0.259131 | − | 0.965842i | \(-0.416564\pi\) | ||||
0.259131 | + | 0.965842i | \(0.416564\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2920.53 | −1.07253 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3404.70 | 1.23134 | 0.615672 | − | 0.788003i | \(-0.288885\pi\) | ||||
0.615672 | + | 0.788003i | \(0.288885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4282.21 | 1.52542 | 0.762708 | − | 0.646744i | \(-0.223870\pi\) | ||||
0.762708 | + | 0.646744i | \(0.223870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1480.40 | −0.519499 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1939.13 | 0.670445 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2761.00 | −0.940665 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 433.151 | 0.145440 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2061.74 | 0.682363 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.1576 | −0.00592428 | −0.00296214 | − | 0.999996i | \(-0.500943\pi\) | ||||
−0.00296214 | + | 0.999996i | \(0.500943\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2852.72 | 0.917677 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2143.27 | 0.679859 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1802.89 | 0.563999 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4080.02 | −1.25891 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −870.686 | −0.265017 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4945.40 | 1.48506 | 0.742531 | − | 0.669812i | \(-0.233625\pi\) | ||||
0.742531 | + | 0.669812i | \(0.233625\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −831.384 | −0.246336 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6179.32 | −1.80677 | −0.903383 | − | 0.428835i | \(-0.858924\pi\) | ||||
−0.903383 | + | 0.428835i | \(0.858924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6838.27 | −1.97330 | −0.986650 | − | 0.162856i | \(-0.947929\pi\) | ||||
−0.986650 | + | 0.162856i | \(0.947929\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2389.89 | 0.680707 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6168.82 | 1.73447 | 0.867237 | − | 0.497895i | \(-0.165893\pi\) | ||||
0.867237 | + | 0.497895i | \(0.165893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4980.47 | −1.38251 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1503.49 | −0.412077 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −632.850 | −0.171279 | −0.0856394 | − | 0.996326i | \(-0.527293\pi\) | ||||
−0.0856394 | + | 0.996326i | \(0.527293\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 410.736 | 0.109783 | 0.0548917 | − | 0.998492i | \(-0.482519\pi\) | ||||
0.0548917 | + | 0.998492i | \(0.482519\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2830.84 | −0.747318 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3483.57 | −0.908395 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1753.46 | −0.451701 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3107.90 | 0.790985 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3392.00 | 0.852993 | 0.426497 | − | 0.904489i | \(-0.359748\pi\) | ||||
0.426497 | + | 0.904489i | \(0.359748\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2400.89 | 0.596611 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 969.389 | 0.238061 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4213.03 | −1.02257 | −0.511287 | − | 0.859410i | \(-0.670831\pi\) | ||||
−0.511287 | + | 0.859410i | \(0.670831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2525.38 | 0.605866 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2132.48 | −0.505738 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1282.19 | 0.300620 | 0.150310 | − | 0.988639i | \(-0.451973\pi\) | ||||
0.150310 | + | 0.988639i | \(0.451973\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1021.44 | −0.236779 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4229.10 | −0.969351 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5951.38 | 1.34893 | 0.674465 | − | 0.738307i | \(-0.264374\pi\) | ||||
0.674465 | + | 0.738307i | \(0.264374\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6709.65 | 1.50399 | 0.751997 | − | 0.659167i | \(-0.229091\pi\) | ||||
0.751997 | + | 0.659167i | \(0.229091\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2032.55 | −0.450605 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4608.23 | −1.01050 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3369.11 | −0.730794 | −0.365397 | − | 0.930852i | \(-0.619067\pi\) | ||||
−0.365397 | + | 0.930852i | \(0.619067\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1982.65 | −0.425442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1964.14 | −0.416978 | −0.208489 | − | 0.978025i | \(-0.566855\pi\) | ||||
−0.208489 | + | 0.978025i | \(0.566855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −116.659 | −0.0245042 | −0.0122521 | − | 0.999925i | \(-0.503900\pi\) | ||||
−0.0122521 | + | 0.999925i | \(0.503900\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1952.24 | 0.405757 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1921.52 | −0.395204 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6412.27 | 1.29173 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3801.24 | −0.757922 | −0.378961 | − | 0.925413i | \(-0.623718\pi\) | ||||
−0.378961 | + | 0.925413i | \(0.623718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2020.72 | 0.398816 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9159.53 | −1.78953 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2041.90 | −0.394936 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1491.61 | 0.285631 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5443.88 | −1.03215 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8666.54 | 1.62703 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4487.26 | 0.834207 | 0.417103 | − | 0.908859i | \(-0.363045\pi\) | ||||
0.417103 | + | 0.908859i | \(0.363045\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4158.38 | −0.765573 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4722.00 | 0.860965 | 0.430482 | − | 0.902599i | \(-0.358343\pi\) | ||||
0.430482 | + | 0.902599i | \(0.358343\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −980.994 | −0.177154 | −0.0885768 | − | 0.996069i | \(-0.528232\pi\) | ||||
−0.0885768 | + | 0.996069i | \(0.528232\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1523.76 | −0.272554 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3171.02 | 0.561837 | 0.280919 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280919 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11820.0 | −2.07459 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 621.174 | 0.108008 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 582.014 | 0.100260 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3919.19 | 0.668916 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1718.84 | −0.290680 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3466.16 | −0.580838 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1643.10 | 0.272850 | 0.136425 | − | 0.990650i | \(-0.456439\pi\) | ||||
0.136425 | + | 0.990650i | \(0.456439\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2777.19 | −0.457024 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5231.80 | 0.853264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9936.95 | −1.60623 | −0.803116 | − | 0.595822i | \(-0.796826\pi\) | ||||
−0.803116 | + | 0.595822i | \(0.796826\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3103.29 | 0.497191 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10989.5 | −1.74521 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5813.09 | −0.915094 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2273.37 | 0.354766 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11337.7 | 1.75401 | 0.877004 | − | 0.480484i | \(-0.159539\pi\) | ||||
0.877004 | + | 0.480484i | \(0.159539\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 627.001 | 0.0961678 | 0.0480839 | − | 0.998843i | \(-0.484689\pi\) | ||||
0.0480839 | + | 0.998843i | \(0.484689\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7789.97 | 1.18461 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5362.12 | 0.808490 | 0.404245 | − | 0.914651i | \(-0.367534\pi\) | ||||
0.404245 | + | 0.914651i | \(0.367534\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10081.6 | −1.50726 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 674.647 | 0.100017 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5063.48 | −0.744402 | −0.372201 | − | 0.928152i | \(-0.621397\pi\) | ||||
−0.372201 | + | 0.928152i | \(0.621397\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5686.89 | −0.829113 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9221.18 | −1.33330 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14419.0 | 2.06774 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 77.7642 | 0.0110607 | 0.00553033 | − | 0.999985i | \(-0.498240\pi\) | ||||
0.00553033 | + | 0.999985i | \(0.498240\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2113.11 | 0.298115 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −710.871 | −0.0994786 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2917.41 | −0.404981 | −0.202491 | − | 0.979284i | \(-0.564904\pi\) | ||||
−0.202491 | + | 0.979284i | \(0.564904\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2764.38 | 0.380672 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10052.7 | 1.37331 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13918.1 | −1.88634 | −0.943169 | − | 0.332313i | \(-0.892171\pi\) | ||||
−0.943169 | + | 0.332313i | \(0.892171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4736.66 | −0.636920 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2374.14 | 0.316744 | 0.158372 | − | 0.987380i | \(-0.449376\pi\) | ||||
0.158372 | + | 0.987380i | \(0.449376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8445.99 | −1.11804 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1640.34 | −0.215460 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3839.71 | −0.500465 | −0.250232 | − | 0.968186i | \(-0.580507\pi\) | ||||
−0.250232 | + | 0.968186i | \(0.580507\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 677.751 | 0.0876608 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10119.4 | −1.29887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5313.41 | 0.676827 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9335.29 | −1.18016 | −0.590082 | − | 0.807344i | \(-0.700904\pi\) | ||||
−0.590082 | + | 0.807344i | \(0.700904\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1358.66 | 0.170472 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3648.62 | −0.454373 | −0.227187 | − | 0.973851i | \(-0.572953\pi\) | ||||
−0.227187 | + | 0.973851i | \(0.572953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9346.34 | 1.15527 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4508.76 | −0.553190 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15393.5 | −1.87476 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3796.95 | 0.459040 | 0.229520 | − | 0.973304i | \(-0.426284\pi\) | ||||
0.229520 | + | 0.973304i | \(0.426284\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2085.31 | −0.250269 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1406.32 | 0.167555 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10983.5 | −1.29917 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5549.79 | −0.651737 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7116.97 | 0.829801 | 0.414901 | − | 0.909867i | \(-0.363816\pi\) | ||||
0.414901 | + | 0.909867i | \(0.363816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4495.19 | −0.520385 | −0.260192 | − | 0.965557i | \(-0.583786\pi\) | ||||
−0.260192 | + | 0.965557i | \(0.583786\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3811.77 | 0.438144 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1300.87 | −0.148474 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6031.48 | 0.683569 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12389.4 | 1.39433 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2891.80 | −0.323186 | −0.161593 | − | 0.986857i | \(-0.551663\pi\) | ||||
−0.161593 | + | 0.986857i | \(0.551663\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14298.6 | −1.58694 | −0.793471 | − | 0.608608i | \(-0.791728\pi\) | ||||
−0.793471 | + | 0.608608i | \(0.791728\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11192.3 | −1.23363 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1364.92 | 0.149411 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4699.43 | 0.510914 | 0.255457 | − | 0.966820i | \(-0.417774\pi\) | ||||
0.255457 | + | 0.966820i | \(0.417774\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2666.13 | 0.287888 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2195.37 | 0.235451 | 0.117726 | − | 0.993046i | \(-0.462440\pi\) | ||||
0.117726 | + | 0.993046i | \(0.462440\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14945.8 | 1.59214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7689.06 | −0.813602 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1843.65 | 0.193780 | 0.0968902 | − | 0.995295i | \(-0.469110\pi\) | ||||
0.0968902 | + | 0.995295i | \(0.469110\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11712.7 | 1.22290 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6391.33 | −0.662894 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7183.11 | 0.740109 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5769.52 | 0.590562 | 0.295281 | − | 0.955410i | \(-0.404587\pi\) | ||||
0.295281 | + | 0.955410i | \(0.404587\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2585.66 | −0.262938 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7335.80 | −0.741133 | −0.370567 | − | 0.928806i | \(-0.620836\pi\) | ||||
−0.370567 | + | 0.928806i | \(0.620836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2659.54 | −0.266953 | −0.133477 | − | 0.991052i | \(-0.542614\pi\) | ||||
−0.133477 | + | 0.991052i | \(0.542614\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10405.9 | −1.03776 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5657.03 | 0.560549 | 0.280274 | − | 0.959920i | \(-0.409575\pi\) | ||||
0.280274 | + | 0.959920i | \(0.409575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3641.07 | 0.358484 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4087.96 | −0.399922 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9092.14 | −0.883842 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2619.80 | −0.253063 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 781.753 | 0.0750398 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1924.95 | 0.183618 | 0.0918090 | − | 0.995777i | \(-0.470735\pi\) | ||||
0.0918090 | + | 0.995777i | \(0.470735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13091.8 | 1.24103 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1582.16 | 0.149049 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22661.2 | −2.12164 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9457.20 | −0.879973 | −0.439986 | − | 0.898004i | \(-0.645017\pi\) | ||||
−0.439986 | + | 0.898004i | \(0.645017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13523.7 | 1.25064 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17148.2 | 1.57615 | 0.788074 | − | 0.615580i | \(-0.211078\pi\) | ||||
0.788074 | + | 0.615580i | \(0.211078\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3336.70 | −0.304822 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9288.14 | 0.843376 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7016.33 | −0.633250 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19203.5 | 1.72278 | 0.861389 | − | 0.507946i | \(-0.169595\pi\) | ||||
0.861389 | + | 0.507946i | \(0.169595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9352.08 | −0.833973 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7853.63 | 0.696175 | 0.348087 | − | 0.937462i | \(-0.386831\pi\) | ||||
0.348087 | + | 0.937462i | \(0.386831\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19238.9 | 1.69529 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1711.84 | −0.149952 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6822.18 | 0.594082 | 0.297041 | − | 0.954865i | \(-0.404000\pi\) | ||||
0.297041 | + | 0.954865i | \(0.404000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10034.9 | 0.868724 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5207.24 | −0.448158 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14695.9 | 1.25744 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21128.1 | 1.79731 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9209.93 | −0.778942 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6072.25 | −0.510614 | −0.255307 | − | 0.966860i | \(-0.582177\pi\) | ||||
−0.255307 | + | 0.966860i | \(0.582177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13825.4 | 1.15591 | 0.577955 | − | 0.816069i | \(-0.303851\pi\) | ||||
0.577955 | + | 0.816069i | \(0.303851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3036.77 | −0.252449 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3102.26 | −0.256426 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10577.6 | −0.869365 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1546.54 | −0.126392 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9961.34 | −0.809519 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2195.26 | −0.177401 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7377.87 | 0.592884 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 14777.9 | 1.18095 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17020.5 | −1.35262 | −0.676312 | − | 0.736615i | \(-0.736423\pi\) | ||||
−0.676312 | + | 0.736615i | \(0.736423\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11031.4 | −0.871827 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6074.47 | 0.477435 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21180.6 | −1.65560 | −0.827802 | − | 0.561020i | \(-0.810409\pi\) | ||||
−0.827802 | + | 0.561020i | \(0.810409\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6632.89 | −0.515637 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6719.74 | −0.519547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3697.87 | 0.284357 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14575.9 | −1.11480 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12123.8 | −0.922263 | −0.461131 | − | 0.887332i | \(-0.652556\pi\) | ||||
−0.461131 | + | 0.887332i | \(0.652556\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7732.65 | 0.585074 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4112.33 | −0.309488 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3995.69 | 0.299108 | 0.149554 | − | 0.988754i | \(-0.452216\pi\) | ||||
0.149554 | + | 0.988754i | \(0.452216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10967.2 | −0.816624 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3137.87 | −0.232413 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19168.8 | −1.41230 | −0.706148 | − | 0.708064i | \(-0.749569\pi\) | ||||
−0.706148 | + | 0.708064i | \(0.749569\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19127.7 | 1.40187 | 0.700937 | − | 0.713223i | \(-0.252765\pi\) | ||||
0.700937 | + | 0.713223i | \(0.252765\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14866.8 | 1.08389 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3050.74 | −0.221260 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11272.7 | 0.813328 | 0.406664 | − | 0.913578i | \(-0.366692\pi\) | ||||
0.406664 | + | 0.913578i | \(0.366692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5581.80 | −0.400642 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7643.95 | −0.545825 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4333.13 | 0.307822 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7899.34 | −0.558287 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22029.2 | 1.54896 | 0.774482 | − | 0.632596i | \(-0.218011\pi\) | ||||
0.774482 | + | 0.632596i | \(0.218011\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6247.60 | −0.437059 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13676.3 | −0.951888 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20575.4 | −1.42484 | −0.712421 | − | 0.701753i | \(-0.752401\pi\) | ||||
−0.712421 | + | 0.701753i | \(0.752401\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2384.23 | −0.164276 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17201.1 | −1.17922 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21007.3 | −1.43295 | −0.716473 | − | 0.697615i | \(-0.754245\pi\) | ||||
−0.716473 | + | 0.697615i | \(0.754245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20499.1 | 1.39131 | 0.695653 | − | 0.718378i | \(-0.255115\pi\) | ||||
0.695653 | + | 0.718378i | \(0.255115\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4004.13 | −0.270416 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32588.1 | 2.18991 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2031.26 | 0.135826 | 0.0679131 | − | 0.997691i | \(-0.478366\pi\) | ||||
0.0679131 | + | 0.997691i | \(0.478366\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7789.25 | −0.518287 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17968.9 | −1.18976 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7817.91 | −0.515110 | −0.257555 | − | 0.966264i | \(-0.582917\pi\) | ||||
−0.257555 | + | 0.966264i | \(0.582917\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11090.6 | 0.727180 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18880.6 | −1.23194 | −0.615968 | − | 0.787771i | \(-0.711235\pi\) | ||||
−0.615968 | + | 0.787771i | \(0.711235\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16860.2 | −1.09478 | −0.547389 | − | 0.836879i | \(-0.684378\pi\) | ||||
−0.547389 | + | 0.836879i | \(0.684378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6063.80 | −0.391839 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10401.6 | 0.668908 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19334.6 | −1.23742 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8281.77 | −0.527499 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4345.47 | −0.275461 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5789.26 | 0.365241 | 0.182620 | − | 0.983184i | \(-0.441542\pi\) | ||||
0.182620 | + | 0.983184i | \(0.441542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 72.9370 | 0.00457976 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16739.6 | 1.04613 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12568.3 | −0.781748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7715.93 | 0.477680 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4747.96 | −0.292563 | −0.146282 | − | 0.989243i | \(-0.546731\pi\) | ||||
−0.146282 | + | 0.989243i | \(0.546731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24608.1 | −1.50925 | −0.754625 | − | 0.656157i | \(-0.772181\pi\) | ||||
−0.754625 | + | 0.656157i | \(0.772181\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8609.25 | −0.525564 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15126.4 | 0.919134 | 0.459567 | − | 0.888143i | \(-0.348005\pi\) | ||||
0.459567 | + | 0.888143i | \(0.348005\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8572.25 | −0.518475 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7241.97 | −0.435999 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17608.3 | 1.05523 | 0.527615 | − | 0.849484i | \(-0.323086\pi\) | ||||
0.527615 | + | 0.849484i | \(0.323086\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35762.3 | 2.13336 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11035.5 | −0.655305 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4983.53 | 0.294584 | 0.147292 | − | 0.989093i | \(-0.452944\pi\) | ||||
0.147292 | + | 0.989093i | \(0.452944\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12178.7 | 0.716636 | 0.358318 | − | 0.933600i | \(-0.383350\pi\) | ||||
0.358318 | + | 0.933600i | \(0.383350\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3497.44 | 0.204871 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4801.58 | −0.279996 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7825.10 | −0.454256 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19865.1 | −1.14802 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36765.1 | −2.11520 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13407.2 | −0.767917 | −0.383959 | − | 0.923350i | \(-0.625439\pi\) | ||||
−0.383959 | + | 0.923350i | \(0.625439\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11638.8 | 0.663669 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2154.14 | −0.122290 | −0.0611450 | − | 0.998129i | \(-0.519475\pi\) | ||||
−0.0611450 | + | 0.998129i | \(0.519475\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15771.1 | −0.891369 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24821.6 | 1.39672 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27829.8 | −1.55912 | −0.779558 | − | 0.626330i | \(-0.784556\pi\) | ||||
−0.779558 | + | 0.626330i | \(0.784556\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7369.57 | 0.411061 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27468.5 | 1.52546 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3685.23 | −0.203768 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2940.02 | −0.161857 | −0.0809287 | − | 0.996720i | \(-0.525789\pi\) | ||||
−0.0809287 | + | 0.996720i | \(0.525789\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6464.09 | 0.354330 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19613.2 | 1.07046 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3306.39 | 0.179682 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24779.4 | −1.34083 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31363.2 | −1.68983 | −0.844915 | − | 0.534900i | \(-0.820349\pi\) | ||||
−0.844915 | + | 0.534900i | \(0.820349\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8751.28 | −0.469503 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20005.9 | 1.06875 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13389.3 | 0.712246 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29484.9 | 1.56182 | 0.780910 | − | 0.624644i | \(-0.214756\pi\) | ||||
0.780910 | + | 0.624644i | \(0.214756\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4066.59 | −0.214499 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7275.29 | −0.382134 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43784.8 | −2.29015 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2542.08 | 0.132407 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2019.45 | −0.104746 | −0.0523732 | − | 0.998628i | \(-0.516679\pi\) | ||||
−0.0523732 | + | 0.998628i | \(0.516679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10227.6 | 0.528290 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1649.87 | −0.0848679 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15019.4 | 0.769388 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15239.9 | 0.777465 | 0.388733 | − | 0.921351i | \(-0.372913\pi\) | ||||
0.388733 | + | 0.921351i | \(0.372913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19946.6 | 1.01339 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2566.64 | −0.129864 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21343.6 | 1.07550 | 0.537752 | − | 0.843103i | \(-0.319274\pi\) | ||||
0.537752 | + | 0.843103i | \(0.319274\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13993.1 | 0.702233 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22194.2 | −1.10927 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10706.6 | 0.532949 | 0.266475 | − | 0.963842i | \(-0.414141\pi\) | ||||
0.266475 | + | 0.963842i | \(0.414141\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7043.45 | 0.349187 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29819.2 | −1.47235 | −0.736177 | − | 0.676789i | \(-0.763371\pi\) | ||||
−0.736177 | + | 0.676789i | \(0.763371\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27173.5 | 1.33632 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8406.14 | 0.411733 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1527.79 | −0.0745318 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17903.8 | 0.869934 | 0.434967 | − | 0.900447i | \(-0.356760\pi\) | ||||
0.434967 | + | 0.900447i | \(0.356760\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13625.3 | −0.659405 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22587.3 | 1.08879 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3664.20 | 0.175928 | 0.0879641 | − | 0.996124i | \(-0.471964\pi\) | ||||
0.0879641 | + | 0.996124i | \(0.471964\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9644.07 | −0.461209 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −603.032 | −0.0287252 | −0.0143626 | − | 0.999897i | \(-0.504572\pi\) | ||||
−0.0143626 | + | 0.999897i | \(0.504572\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4227.53 | 0.200586 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2621.97 | 0.123918 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7290.49 | 0.343213 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12780.9 | −0.599338 | −0.299669 | − | 0.954043i | \(-0.596876\pi\) | ||||
−0.299669 | + | 0.954043i | \(0.596876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16923.2 | 0.790499 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15919.8 | −0.740743 | −0.370372 | − | 0.928884i | \(-0.620770\pi\) | ||||
−0.370372 | + | 0.928884i | \(0.620770\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13964.1 | 0.647233 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10144.1 | −0.468364 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6658.70 | 0.306255 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42768.2 | 1.95950 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29853.2 | 1.36254 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14447.0 | 0.656862 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14004.2 | 0.634300 | 0.317150 | − | 0.948375i | \(-0.397274\pi\) | ||||
0.317150 | + | 0.948375i | \(0.397274\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5150.38 | −0.232393 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7632.61 | −0.343090 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31267.8 | 1.40019 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4102.99 | 0.183042 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35890.2 | 1.59510 | 0.797551 | − | 0.603252i | \(-0.206129\pi\) | ||||
0.797551 | + | 0.603252i | \(0.206129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5964.28 | 0.264082 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11438.7 | −0.504578 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −61168.0 | −2.68814 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5591.41 | −0.244809 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23906.0 | −1.04279 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3780.80 | 0.164309 | 0.0821544 | − | 0.996620i | \(-0.473820\pi\) | ||||
0.0821544 | + | 0.996620i | \(0.473820\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31627.6 | −1.36941 | −0.684707 | − | 0.728818i | \(-0.740070\pi\) | ||||
−0.684707 | + | 0.728818i | \(0.740070\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26951.8 | −1.16266 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −47793.3 | −2.05414 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5168.92 | −0.221344 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5497.55 | −0.234554 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36041.9 | −1.53212 | −0.766060 | − | 0.642769i | \(-0.777786\pi\) | ||||
−0.766060 | + | 0.642769i | \(0.777786\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5132.22 | 0.217373 | 0.108686 | − | 0.994076i | \(-0.465336\pi\) | ||||
0.108686 | + | 0.994076i | \(0.465336\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18510.7 | 0.781164 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43411.1 | −1.82533 | −0.912667 | − | 0.408703i | \(-0.865981\pi\) | ||||
−0.912667 | + | 0.408703i | \(0.865981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19608.0 | 0.821488 | 0.410744 | − | 0.911751i | \(-0.365269\pi\) | ||||
0.410744 | + | 0.911751i | \(0.365269\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13533.3 | 0.564939 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4171.69 | 0.173518 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33050.7 | 1.36978 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27755.7 | 1.14621 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39957.8 | −1.64422 | −0.822109 | − | 0.569331i | \(-0.807202\pi\) | ||||
−0.822109 | + | 0.569331i | \(0.807202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14135.4 | 0.579583 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7889.72 | 0.322344 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6049.72 | 0.246292 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22679.7 | 0.920051 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 468.607 | 0.0189429 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10190.8 | −0.410501 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15291.9 | 0.613814 | 0.306907 | − | 0.951739i | \(-0.400706\pi\) | ||||
0.306907 | + | 0.951739i | \(0.400706\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5280.35 | 0.211210 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46263.3 | 1.84402 | 0.922010 | − | 0.387166i | \(-0.126546\pi\) | ||||
0.922010 | + | 0.387166i | \(0.126546\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38492.2 | −1.52891 | −0.764457 | − | 0.644675i | \(-0.776993\pi\) | ||||
−0.764457 | + | 0.644675i | \(0.776993\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7718.50 | 0.305512 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33188.8 | −1.30911 | −0.654553 | − | 0.756016i | \(-0.727143\pi\) | ||||
−0.654553 | + | 0.756016i | \(0.727143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32548.3 | 1.27939 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1160.88 | −0.0454734 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22540.5 | −0.879900 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18875.7 | 0.734303 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17343.7 | 0.672387 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6799.05 | −0.262686 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8448.30 | −0.325289 | −0.162645 | − | 0.986685i | \(-0.552002\pi\) | ||||
−0.162645 | + | 0.986685i | \(0.552002\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15269.1 | 0.585910 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11721.8 | −0.448262 | −0.224131 | − | 0.974559i | \(-0.571954\pi\) | ||||
−0.224131 | + | 0.974559i | \(0.571954\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20348.6 | −0.775519 | −0.387760 | − | 0.921761i | \(-0.626751\pi\) | ||||
−0.387760 | + | 0.921761i | \(0.626751\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8116.96 | −0.308304 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41522.0 | 1.57178 | 0.785892 | − | 0.618363i | \(-0.212204\pi\) | ||||
0.785892 | + | 0.618363i | \(0.212204\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11649.9 | 0.439512 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19127.0 | 0.719167 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12011.4 | 0.450108 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26073.8 | −0.973798 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8202.05 | 0.305305 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35817.7 | 1.32879 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1223.21 | 0.0452286 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5991.61 | −0.220806 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38985.5 | 1.43196 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41036.0 | 1.50229 | 0.751145 | − | 0.660138i | \(-0.229502\pi\) | ||||
0.751145 | + | 0.660138i | \(0.229502\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14724.4 | −0.537269 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6771.68 | 0.246274 | 0.123137 | − | 0.992390i | \(-0.460705\pi\) | ||||
0.123137 | + | 0.992390i | \(0.460705\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 46593.9 | 1.68897 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −34812.4 | −1.25777 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24888.8 | 0.896292 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3589.93 | 0.128858 | 0.0644292 | − | 0.997922i | \(-0.479477\pi\) | ||||
0.0644292 | + | 0.997922i | \(0.479477\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18024.8 | −0.644882 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36373.3 | −1.29712 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19560.1 | 0.695279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11247.4 | −0.398505 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38282.3 | −1.35199 | −0.675996 | − | 0.736906i | \(-0.736286\pi\) | ||||
−0.675996 | + | 0.736906i | \(0.736286\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8401.32 | 0.295749 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18967.7 | −0.665568 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14533.2 | 0.508326 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26099.5 | −0.909961 | −0.454980 | − | 0.890501i | \(-0.650354\pi\) | ||||
−0.454980 | + | 0.890501i | \(0.650354\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3940.53 | 0.136948 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33481.9 | −1.15991 | −0.579956 | − | 0.814648i | \(-0.696930\pi\) | ||||
−0.579956 | + | 0.814648i | \(0.696930\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7754.02 | 0.267768 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 21331.6 | 0.734303 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25045.8 | 0.859430 | 0.429715 | − | 0.902964i | \(-0.358614\pi\) | ||||
0.429715 | + | 0.902964i | \(0.358614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 52021.9 | 1.77946 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12737.6 | −0.434327 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3465.20 | −0.117785 | −0.0588924 | − | 0.998264i | \(-0.518757\pi\) | ||||
−0.0588924 | + | 0.998264i | \(0.518757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −52540.1 | −1.78027 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 47479.6 | 1.60376 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5128.86 | 0.172700 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3510.05 | 0.117822 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1680.13 | 0.0562216 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19726.3 | 0.658045 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45361.5 | 1.50851 | 0.754254 | − | 0.656583i | \(-0.227999\pi\) | ||||
0.754254 | + | 0.656583i | \(0.227999\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2337.88 | −0.0775061 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50036.4 | 1.65370 | 0.826851 | − | 0.562421i | \(-0.190130\pi\) | ||||
0.826851 | + | 0.562421i | \(0.190130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13649.8 | 0.449737 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15742.9 | −0.517104 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6689.64 | −0.219059 | −0.109530 | − | 0.993984i | \(-0.534934\pi\) | ||||
−0.109530 | + | 0.993984i | \(0.534934\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −63403.0 | −2.06983 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4649.06 | −0.151308 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31585.2 | 1.02483 | 0.512416 | − | 0.858737i | \(-0.328751\pi\) | ||||
0.512416 | + | 0.858737i | \(0.328751\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48332.5 | 1.56345 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13923.1 | 0.449016 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6019.18 | −0.193528 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30182.2 | −0.967476 | −0.483738 | − | 0.875213i | \(-0.660721\pi\) | ||||
−0.483738 | + | 0.875213i | \(0.660721\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6600.15 | −0.210926 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 60789.5 | 1.93684 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24670.2 | 0.783663 | 0.391832 | − | 0.920037i | \(-0.371842\pi\) | ||||
0.391832 | + | 0.920037i | \(0.371842\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 38878.6 | 1.23130 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1088.4.a.bh.1.2 | 7 | ||
4.3 | odd | 2 | 1088.4.a.bg.1.6 | 7 | |||
8.3 | odd | 2 | 544.4.a.k.1.2 | ✓ | 7 | ||
8.5 | even | 2 | 544.4.a.l.1.6 | yes | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
544.4.a.k.1.2 | ✓ | 7 | 8.3 | odd | 2 | ||
544.4.a.l.1.6 | yes | 7 | 8.5 | even | 2 | ||
1088.4.a.bg.1.6 | 7 | 4.3 | odd | 2 | |||
1088.4.a.bh.1.2 | 7 | 1.1 | even | 1 | trivial |