Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(1,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.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: | \(19.1166188419\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1509.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 36) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.47735\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.8439 | −1.23823 | −0.619117 | − | 0.785299i | \(-0.712509\pi\) | ||||
−0.619117 | + | 0.785299i | \(0.712509\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.7080 | 1.65808 | 0.829038 | − | 0.559192i | \(-0.188889\pi\) | ||||
0.829038 | + | 0.559192i | \(0.188889\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −43.9046 | −1.20343 | −0.601715 | − | 0.798711i | \(-0.705516\pi\) | ||||
−0.601715 | + | 0.798711i | \(0.705516\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.2371 | −0.261073 | −0.130536 | − | 0.991444i | \(-0.541670\pi\) | ||||
−0.130536 | + | 0.991444i | \(0.541670\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 76.0286 | 1.08468 | 0.542342 | − | 0.840158i | \(-0.317538\pi\) | ||||
0.542342 | + | 0.840158i | \(0.317538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −44.1789 | −0.533439 | −0.266720 | − | 0.963774i | \(-0.585940\pi\) | ||||
−0.266720 | + | 0.963774i | \(0.585940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −78.6271 | −0.712821 | −0.356410 | − | 0.934330i | \(-0.615999\pi\) | ||||
−0.356410 | + | 0.934330i | \(0.615999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 66.6530 | 0.533224 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −92.7806 | −0.594101 | −0.297050 | − | 0.954862i | \(-0.596003\pi\) | ||||
−0.297050 | + | 0.954862i | \(0.596003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −143.066 | −0.828884 | −0.414442 | − | 0.910076i | \(-0.636023\pi\) | ||||
−0.414442 | + | 0.910076i | \(0.636023\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −425.118 | −2.05309 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −32.4741 | −0.144289 | −0.0721447 | − | 0.997394i | \(-0.522984\pi\) | ||||
−0.0721447 | + | 0.997394i | \(0.522984\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −335.555 | −1.27817 | −0.639084 | − | 0.769137i | \(-0.720686\pi\) | ||||
−0.639084 | + | 0.769137i | \(0.720686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −498.331 | −1.76732 | −0.883660 | − | 0.468129i | \(-0.844928\pi\) | ||||
−0.883660 | + | 0.468129i | \(0.844928\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −281.765 | −0.874461 | −0.437230 | − | 0.899350i | \(-0.644041\pi\) | ||||
−0.437230 | + | 0.899350i | \(0.644041\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 599.981 | 1.74922 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −628.565 | −1.62906 | −0.814529 | − | 0.580123i | \(-0.803005\pi\) | ||||
−0.814529 | + | 0.580123i | \(0.803005\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 607.810 | 1.49013 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 504.654 | 1.11356 | 0.556782 | − | 0.830658i | \(-0.312036\pi\) | ||||
0.556782 | + | 0.830658i | \(0.312036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 371.901 | 0.780607 | 0.390304 | − | 0.920686i | \(-0.372370\pi\) | ||||
0.390304 | + | 0.920686i | \(0.372370\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 169.408 | 0.323269 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −162.661 | −0.296600 | −0.148300 | − | 0.988942i | \(-0.547380\pi\) | ||||
−0.148300 | + | 0.988942i | \(0.547380\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 433.512 | 0.724626 | 0.362313 | − | 0.932056i | \(-0.381987\pi\) | ||||
0.362313 | + | 0.932056i | \(0.381987\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −629.645 | −1.00951 | −0.504756 | − | 0.863262i | \(-0.668418\pi\) | ||||
−0.504756 | + | 0.863262i | \(0.668418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1348.22 | −1.99538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 172.730 | 0.245995 | 0.122998 | − | 0.992407i | \(-0.460749\pi\) | ||||
0.122998 | + | 0.992407i | \(0.460749\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −174.858 | −0.231242 | −0.115621 | − | 0.993293i | \(-0.536886\pi\) | ||||
−0.115621 | + | 0.993293i | \(0.536886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1052.53 | −1.34309 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 336.716 | 0.401032 | 0.200516 | − | 0.979690i | \(-0.435738\pi\) | ||||
0.200516 | + | 0.979690i | \(0.435738\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −375.775 | −0.432879 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 611.608 | 0.660523 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 84.3187 | 0.0882605 | 0.0441303 | − | 0.999026i | \(-0.485948\pi\) | ||||
0.0441303 | + | 0.999026i | \(0.485948\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1749.80 | −1.72388 | −0.861941 | − | 0.507008i | \(-0.830751\pi\) | ||||
−0.861941 | + | 0.507008i | \(0.830751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 111.396 | 0.106564 | 0.0532822 | − | 0.998579i | \(-0.483032\pi\) | ||||
0.0532822 | + | 0.998579i | \(0.483032\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 895.520 | 0.809095 | 0.404548 | − | 0.914517i | \(-0.367429\pi\) | ||||
0.404548 | + | 0.914517i | \(0.367429\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −716.957 | −0.630019 | −0.315009 | − | 0.949089i | \(-0.602008\pi\) | ||||
−0.315009 | + | 0.949089i | \(0.602008\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 231.051 | 0.192349 | 0.0961746 | − | 0.995364i | \(-0.469339\pi\) | ||||
0.0961746 | + | 0.995364i | \(0.469339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1088.50 | 0.882639 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2334.68 | 1.79849 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 596.612 | 0.448244 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 807.748 | 0.577978 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1715.22 | 1.19843 | 0.599217 | − | 0.800586i | \(-0.295478\pi\) | ||||
0.599217 | + | 0.800586i | \(0.295478\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1332.87 | 0.888957 | 0.444479 | − | 0.895789i | \(-0.353389\pi\) | ||||
0.444479 | + | 0.895789i | \(0.353389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1356.65 | −0.884483 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2518.98 | 1.57089 | 0.785443 | − | 0.618935i | \(-0.212435\pi\) | ||||
0.785443 | + | 0.618935i | \(0.212435\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 622.883 | 0.380088 | 0.190044 | − | 0.981776i | \(-0.439137\pi\) | ||||
0.190044 | + | 0.981776i | \(0.439137\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 537.263 | 0.314183 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1284.44 | 0.735636 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2408.95 | 1.32449 | 0.662243 | − | 0.749289i | \(-0.269604\pi\) | ||||
0.662243 | + | 0.749289i | \(0.269604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 67.6436 | 0.0364553 | 0.0182277 | − | 0.999834i | \(-0.494198\pi\) | ||||
0.0182277 | + | 0.999834i | \(0.494198\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1980.59 | 1.02635 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.39352 | −0.00223338 | −0.00111669 | − | 0.999999i | \(-0.500355\pi\) | ||||
−0.00111669 | + | 0.999999i | \(0.500355\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2414.48 | −1.18191 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2863.88 | −1.37617 | −0.688087 | − | 0.725628i | \(-0.741549\pi\) | ||||
−0.688087 | + | 0.725628i | \(0.741549\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 429.514 | 0.199023 | 0.0995114 | − | 0.995036i | \(-0.468272\pi\) | ||||
0.0995114 | + | 0.995036i | \(0.468272\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2047.25 | −0.931841 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2574.29 | −1.13133 | −0.565663 | − | 0.824637i | \(-0.691380\pi\) | ||||
−0.565663 | + | 0.824637i | \(0.691380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2046.78 | 0.884126 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 807.448 | 0.337159 | 0.168580 | − | 0.985688i | \(-0.446082\pi\) | ||||
0.168580 | + | 0.985688i | \(0.446082\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4296.57 | 1.76443 | 0.882215 | − | 0.470847i | \(-0.156052\pi\) | ||||
0.882215 | + | 0.470847i | \(0.156052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 449.568 | 0.178664 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3338.00 | −1.30534 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −306.295 | −0.116035 | −0.0580176 | − | 0.998316i | \(-0.518478\pi\) | ||||
−0.0580176 | + | 0.998316i | \(0.518478\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1712.35 | −0.638642 | −0.319321 | − | 0.947647i | \(-0.603455\pi\) | ||||
−0.319321 | + | 0.947647i | \(0.603455\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −263.636 | −0.0953466 | −0.0476733 | − | 0.998863i | \(-0.515181\pi\) | ||||
−0.0476733 | + | 0.998863i | \(0.515181\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3835.87 | −1.36642 | −0.683211 | − | 0.730221i | \(-0.739417\pi\) | ||||
−0.683211 | + | 0.730221i | \(0.739417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2849.11 | −0.985064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4645.38 | 1.58267 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1939.66 | 0.641957 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4069.32 | −1.32770 | −0.663848 | − | 0.747867i | \(-0.731078\pi\) | ||||
−0.663848 | + | 0.747867i | \(0.731078\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6898.84 | 2.18836 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4393.27 | −1.37435 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −930.365 | −0.283182 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6156.14 | 1.84864 | 0.924318 | − | 0.381622i | \(-0.124635\pi\) | ||||
0.924318 | + | 0.381622i | \(0.124635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.2614 | 0.00709378 | 0.00354689 | − | 0.999994i | \(-0.498871\pi\) | ||||
0.00354689 | + | 0.999994i | \(0.498871\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −632.419 | −0.182495 | −0.0912476 | − | 0.995828i | \(-0.529085\pi\) | ||||
−0.0912476 | + | 0.995828i | \(0.529085\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3163.59 | −0.889502 | −0.444751 | − | 0.895654i | \(-0.646708\pi\) | ||||
−0.444751 | + | 0.895654i | \(0.646708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3900.72 | 1.08279 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2221.15 | 0.601147 | 0.300573 | − | 0.953759i | \(-0.402822\pi\) | ||||
0.300573 | + | 0.953759i | \(0.402822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −601.459 | −0.160761 | −0.0803805 | − | 0.996764i | \(-0.525614\pi\) | ||||
−0.0803805 | + | 0.996764i | \(0.525614\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8306.07 | −2.16594 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 540.620 | 0.139266 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1350.71 | 0.339665 | 0.169833 | − | 0.985473i | \(-0.445677\pi\) | ||||
0.169833 | + | 0.985473i | \(0.445677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3452.09 | 0.857830 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7043.91 | −1.70968 | −0.854838 | − | 0.518894i | \(-0.826344\pi\) | ||||
−0.854838 | + | 0.518894i | \(0.826344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −997.215 | −0.239243 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2324.26 | 0.544944 | 0.272472 | − | 0.962164i | \(-0.412159\pi\) | ||||
0.272472 | + | 0.962164i | \(0.412159\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8701.78 | 2.01716 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3675.87 | −0.833167 | −0.416584 | − | 0.909097i | \(-0.636773\pi\) | ||||
−0.416584 | + | 0.909097i | \(0.636773\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1881.48 | −0.421741 | −0.210871 | − | 0.977514i | \(-0.567630\pi\) | ||||
−0.210871 | + | 0.977514i | \(0.567630\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2926.37 | −0.641698 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1464.02 | 0.317560 | 0.158780 | − | 0.987314i | \(-0.449244\pi\) | ||||
0.158780 | + | 0.987314i | \(0.449244\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8232.56 | −1.74773 | −0.873867 | − | 0.486165i | \(-0.838395\pi\) | ||||
−0.873867 | + | 0.486165i | \(0.838395\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1688.73 | 0.354715 | 0.177358 | − | 0.984146i | \(-0.443245\pi\) | ||||
0.177358 | + | 0.984146i | \(0.443245\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10304.2 | −2.11930 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 867.343 | 0.176540 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 511.732 | 0.102033 | 0.0510166 | − | 0.998698i | \(-0.483754\pi\) | ||||
0.0510166 | + | 0.998698i | \(0.483754\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6986.37 | −1.37885 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 962.163 | 0.186098 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15302.7 | −2.93035 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5148.55 | −0.966575 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3171.98 | −0.589690 | −0.294845 | − | 0.955545i | \(-0.595268\pi\) | ||||
−0.294845 | + | 0.955545i | \(0.595268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5060.78 | 0.922735 | 0.461367 | − | 0.887209i | \(-0.347359\pi\) | ||||
0.461367 | + | 0.887209i | \(0.347359\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9465.84 | −1.70940 | −0.854698 | − | 0.519125i | \(-0.826258\pi\) | ||||
−0.854698 | + | 0.519125i | \(0.826258\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6417.13 | 1.13698 | 0.568489 | − | 0.822691i | \(-0.307528\pi\) | ||||
0.568489 | + | 0.822691i | \(0.307528\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4073.49 | 0.714959 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3358.86 | −0.578613 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −815.637 | −0.139210 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8652.44 | −1.44992 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6664.74 | 1.10673 | 0.553364 | − | 0.832940i | \(-0.313344\pi\) | ||||
0.553364 | + | 0.832940i | \(0.313344\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2251.86 | 0.367260 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10488.1 | 1.69532 | 0.847660 | − | 0.530540i | \(-0.178011\pi\) | ||||
0.847660 | + | 0.530540i | \(0.178011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6281.25 | 0.997503 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7891.37 | 1.24226 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2148.96 | 0.332455 | 0.166228 | − | 0.986087i | \(-0.446841\pi\) | ||||
0.166228 | + | 0.986087i | \(0.446841\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2777.06 | −0.425939 | −0.212969 | − | 0.977059i | \(-0.568313\pi\) | ||||
−0.212969 | + | 0.977059i | \(0.568313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7797.44 | 1.17568 | 0.587841 | − | 0.808976i | \(-0.299978\pi\) | ||||
0.587841 | + | 0.808976i | \(0.299978\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6001.49 | −0.897257 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2309.31 | 0.339500 | 0.169750 | − | 0.985487i | \(-0.445704\pi\) | ||||
0.169750 | + | 0.985487i | \(0.445704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4907.22 | −0.715443 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8716.73 | 1.25001 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6211.32 | −0.883455 | −0.441728 | − | 0.897149i | \(-0.645634\pi\) | ||||
−0.441728 | + | 0.897149i | \(0.645634\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19302.0 | −2.70110 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8699.22 | 1.20758 | 0.603792 | − | 0.797142i | \(-0.293656\pi\) | ||||
0.603792 | + | 0.797142i | \(0.293656\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1135.36 | 0.155104 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5954.77 | 0.807061 | 0.403531 | − | 0.914966i | \(-0.367783\pi\) | ||||
0.403531 | + | 0.914966i | \(0.367783\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4256.70 | 0.567904 | 0.283952 | − | 0.958839i | \(-0.408354\pi\) | ||||
0.283952 | + | 0.958839i | \(0.408354\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18664.6 | 2.47075 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1602.04 | 0.208809 | 0.104404 | − | 0.994535i | \(-0.466706\pi\) | ||||
0.104404 | + | 0.994535i | \(0.466706\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5977.90 | −0.773186 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2391.25 | −0.304600 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7987.87 | −1.00982 | −0.504912 | − | 0.863171i | \(-0.668475\pi\) | ||||
−0.504912 | + | 0.863171i | \(0.668475\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7069.49 | −0.880383 | −0.440191 | − | 0.897904i | \(-0.645089\pi\) | ||||
−0.440191 | + | 0.897904i | \(0.645089\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1750.70 | 0.216399 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1425.76 | 0.173642 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11864.8 | −1.43441 | −0.717207 | − | 0.696861i | \(-0.754580\pi\) | ||||
−0.717207 | + | 0.696861i | \(0.754580\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15496.9 | 1.84637 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2420.71 | 0.286332 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12342.6 | −1.43908 | −0.719541 | − | 0.694450i | \(-0.755648\pi\) | ||||
−0.719541 | + | 0.694450i | \(0.755648\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5465.86 | 0.632755 | 0.316377 | − | 0.948633i | \(-0.397533\pi\) | ||||
0.316377 | + | 0.948633i | \(0.397533\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5067.54 | 0.578380 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11420.3 | 1.29431 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8997.67 | 1.00557 | 0.502787 | − | 0.864410i | \(-0.332308\pi\) | ||||
0.502787 | + | 0.864410i | \(0.332308\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10967.4 | −1.21723 | −0.608615 | − | 0.793466i | \(-0.708275\pi\) | ||||
−0.608615 | + | 0.793466i | \(0.708275\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3473.66 | 0.380246 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7127.02 | 0.774838 | 0.387419 | − | 0.921904i | \(-0.373367\pi\) | ||||
0.387419 | + | 0.921904i | \(0.373367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8868.55 | 0.951146 | 0.475573 | − | 0.879676i | \(-0.342241\pi\) | ||||
0.475573 | + | 0.879676i | \(0.342241\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4661.46 | −0.496571 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9835.05 | 1.03373 | 0.516865 | − | 0.856067i | \(-0.327099\pi\) | ||||
0.516865 | + | 0.856067i | \(0.327099\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14732.4 | 1.53819 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5202.19 | 0.536005 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8886.49 | −0.909612 | −0.454806 | − | 0.890591i | \(-0.650291\pi\) | ||||
−0.454806 | + | 0.890591i | \(0.650291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1865.79 | 0.188500 | 0.0942499 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942499 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13623.4 | −1.36746 | −0.683729 | − | 0.729736i | \(-0.739643\pi\) | ||||
−0.683729 | + | 0.729736i | \(0.739643\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9328.97 | −0.924397 | −0.462199 | − | 0.886776i | \(-0.652939\pi\) | ||||
−0.462199 | + | 0.886776i | \(0.652939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4994.99 | −0.491785 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21879.0 | 2.12685 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2944.66 | −0.284443 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2660.30 | 0.253762 | 0.126881 | − | 0.991918i | \(-0.459503\pi\) | ||||
0.126881 | + | 0.991918i | \(0.459503\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 397.387 | 0.0376701 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1167.30 | −0.109287 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20450.7 | −1.90289 | −0.951447 | − | 0.307813i | \(-0.900403\pi\) | ||||
−0.951447 | + | 0.307813i | \(0.900403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20654.9 | 1.89846 | 0.949228 | − | 0.314588i | \(-0.101866\pi\) | ||||
0.949228 | + | 0.314588i | \(0.101866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7053.98 | −0.644412 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13312.3 | 1.20149 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17466.6 | 1.56696 | 0.783480 | − | 0.621417i | \(-0.213443\pi\) | ||||
0.783480 | + | 0.621417i | \(0.213443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19951.2 | 1.76855 | 0.884275 | − | 0.466966i | \(-0.154653\pi\) | ||||
0.884275 | + | 0.466966i | \(0.154653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24224.1 | 2.13457 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7277.77 | −0.633755 | −0.316878 | − | 0.948466i | \(-0.602634\pi\) | ||||
−0.316878 | + | 0.948466i | \(0.602634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19335.1 | −1.67385 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1542.15 | −0.131952 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12370.8 | 1.05235 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11664.5 | −0.980866 | −0.490433 | − | 0.871479i | \(-0.663161\pi\) | ||||
−0.490433 | + | 0.871479i | \(0.663161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8925.51 | −0.746243 | −0.373122 | − | 0.927782i | \(-0.621713\pi\) | ||||
−0.373122 | + | 0.927782i | \(0.621713\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10877.1 | −0.899077 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5984.78 | −0.491887 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4106.20 | 0.333695 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12397.5 | −1.00185 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26341.9 | −2.10506 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12334.1 | 0.980193 | 0.490097 | − | 0.871668i | \(-0.336962\pi\) | ||||
0.490097 | + | 0.871668i | \(0.336962\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9925.47 | 0.780111 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4569.63 | 0.357190 | 0.178595 | − | 0.983923i | \(-0.442845\pi\) | ||||
0.178595 | + | 0.983923i | \(0.442845\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4098.95 | 0.316917 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5304.19 | 0.407879 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8154.40 | −0.620310 | −0.310155 | − | 0.950686i | \(-0.600381\pi\) | ||||
−0.310155 | + | 0.950686i | \(0.600381\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6098.10 | 0.461399 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16173.6 | −1.21072 | −0.605362 | − | 0.795950i | \(-0.706972\pi\) | ||||
−0.605362 | + | 0.795950i | \(0.706972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3198.65 | −0.238174 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9097.53 | −0.670278 | −0.335139 | − | 0.942169i | \(-0.608783\pi\) | ||||
−0.335139 | + | 0.942169i | \(0.608783\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3295.09 | −0.241498 | −0.120749 | − | 0.992683i | \(-0.538530\pi\) | ||||
−0.120749 | + | 0.992683i | \(0.538530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5240.73 | −0.380093 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15544.7 | 1.12155 | 0.560775 | − | 0.827968i | \(-0.310503\pi\) | ||||
0.560775 | + | 0.827968i | \(0.310503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5369.52 | −0.383417 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27596.9 | 1.96046 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4688.66 | −0.329680 | −0.164840 | − | 0.986320i | \(-0.552711\pi\) | ||||
−0.164840 | + | 0.986320i | \(0.552711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6320.50 | 0.442159 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16637.6 | 1.15215 | 0.576075 | − | 0.817397i | \(-0.304584\pi\) | ||||
0.576075 | + | 0.817397i | \(0.304584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32321.1 | −2.22695 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5867.46 | −0.400230 | −0.200115 | − | 0.979772i | \(-0.564132\pi\) | ||||
−0.200115 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20675.8 | 1.40330 | 0.701649 | − | 0.712522i | \(-0.252447\pi\) | ||||
0.701649 | + | 0.712522i | \(0.252447\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8259.43 | −0.555031 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12607.7 | 0.843051 | 0.421525 | − | 0.906817i | \(-0.361495\pi\) | ||||
0.421525 | + | 0.906817i | \(0.361495\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3447.97 | 0.228298 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12469.7 | 0.821608 | 0.410804 | − | 0.911724i | \(-0.365248\pi\) | ||||
0.410804 | + | 0.911724i | \(0.365248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18587.0 | 1.21278 | 0.606388 | − | 0.795169i | \(-0.292618\pi\) | ||||
0.606388 | + | 0.795169i | \(0.292618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11945.9 | −0.775682 | −0.387841 | − | 0.921726i | \(-0.626779\pi\) | ||||
−0.387841 | + | 0.921726i | \(0.626779\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10339.9 | 0.664941 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19514.0 | −1.24890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2468.96 | −0.156509 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4285.35 | 0.270360 | 0.135180 | − | 0.990821i | \(-0.456839\pi\) | ||||
0.135180 | + | 0.990821i | \(0.456839\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −23745.3 | −1.48394 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7342.00 | −0.456673 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21758.2 | −1.34071 | −0.670357 | − | 0.742039i | \(-0.733859\pi\) | ||||
−0.670357 | + | 0.742039i | \(0.733859\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7343.09 | −0.450363 | −0.225181 | − | 0.974317i | \(-0.572297\pi\) | ||||
−0.225181 | + | 0.974317i | \(0.572297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9483.24 | 0.576236 | 0.288118 | − | 0.957595i | \(-0.406970\pi\) | ||||
0.288118 | + | 0.957595i | \(0.406970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22156.6 | −1.34010 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4784.18 | 0.286707 | 0.143353 | − | 0.989672i | \(-0.454211\pi\) | ||||
0.143353 | + | 0.989672i | \(0.454211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18452.1 | −1.10074 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32067.9 | −1.89558 | −0.947791 | − | 0.318892i | \(-0.896689\pi\) | ||||
−0.947791 | + | 0.318892i | \(0.896689\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7525.28 | −0.442813 | −0.221407 | − | 0.975182i | \(-0.571065\pi\) | ||||
−0.221407 | + | 0.975182i | \(0.571065\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18781.3 | 1.09520 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7295.07 | 0.423487 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16328.2 | −0.939406 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7341.95 | −0.420522 | −0.210261 | − | 0.977645i | \(-0.567431\pi\) | ||||
−0.210261 | + | 0.977645i | \(0.567431\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9521.03 | 0.540507 | 0.270253 | − | 0.962789i | \(-0.412893\pi\) | ||||
0.270253 | + | 0.962789i | \(0.412893\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2589.26 | 0.146343 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1475.06 | −0.0826377 | −0.0413188 | − | 0.999146i | \(-0.513156\pi\) | ||||
−0.0413188 | + | 0.999146i | \(0.513156\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34872.5 | −1.94512 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7691.79 | 0.425303 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34160.7 | 1.88066 | 0.940329 | − | 0.340267i | \(-0.110518\pi\) | ||||
0.940329 | + | 0.340267i | \(0.110518\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8623.12 | −0.470638 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25511.8 | −1.38641 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29427.2 | −1.58552 | −0.792759 | − | 0.609535i | \(-0.791356\pi\) | ||||
−0.792759 | + | 0.609535i | \(0.791356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1434.67 | 0.0769696 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −53733.0 | −2.85833 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19692.9 | 1.04313 | 0.521566 | − | 0.853211i | \(-0.325348\pi\) | ||||
0.521566 | + | 0.853211i | \(0.325348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11248.8 | 0.590845 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7437.80 | −0.389032 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33746.9 | −1.75041 | −0.875206 | − | 0.483751i | \(-0.839274\pi\) | ||||
−0.875206 | + | 0.483751i | \(0.839274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3420.74 | 0.176692 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6184.11 | −0.316789 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20760.8 | 1.05912 | 0.529558 | − | 0.848274i | \(-0.322358\pi\) | ||||
0.529558 | + | 0.848274i | \(0.322358\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37887.4 | −1.91698 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14244.0 | 0.717757 | 0.358878 | − | 0.933384i | \(-0.383159\pi\) | ||||
0.358878 | + | 0.933384i | \(0.383159\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7141.55 | 0.356937 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27490.2 | 1.36839 | 0.684196 | − | 0.729298i | \(-0.260153\pi\) | ||||
0.684196 | + | 0.729298i | \(0.260153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36468.1 | 1.80065 | 0.900326 | − | 0.435217i | \(-0.143328\pi\) | ||||
0.900326 | + | 0.435217i | \(0.143328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33349.2 | −1.64003 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27499.6 | 1.34154 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38683.1 | 1.87958 | 0.939791 | − | 0.341751i | \(-0.111020\pi\) | ||||
0.939791 | + | 0.341751i | \(0.111020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −936.449 | −0.0451402 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37768.4 | 1.81337 | 0.906683 | − | 0.421813i | \(-0.138606\pi\) | ||||
0.906683 | + | 0.421813i | \(0.138606\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20813.2 | −0.991429 | −0.495714 | − | 0.868486i | \(-0.665094\pi\) | ||||
−0.495714 | + | 0.868486i | \(0.665094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22016.3 | −1.04462 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6175.47 | −0.290722 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6121.70 | 0.287067 | 0.143533 | − | 0.989645i | \(-0.454154\pi\) | ||||
0.143533 | + | 0.989645i | \(0.454154\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34251.2 | −1.59370 | −0.796850 | − | 0.604177i | \(-0.793502\pi\) | ||||
−0.796850 | + | 0.604177i | \(0.793502\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9535.78 | −0.441981 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14824.5 | 0.681825 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19033.2 | −0.872037 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60.8234 | 0.00276545 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9122.68 | −0.413200 | −0.206600 | − | 0.978425i | \(-0.566240\pi\) | ||||
−0.206600 | + | 0.978425i | \(0.566240\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7095.12 | 0.318930 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4550.97 | −0.203795 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10012.2 | −0.444983 | −0.222492 | − | 0.974935i | \(-0.571419\pi\) | ||||
−0.222492 | + | 0.974935i | \(0.571419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21422.2 | −0.948514 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27644.3 | 1.21488 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33425.8 | 1.46348 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22375.5 | 0.972413 | 0.486207 | − | 0.873844i | \(-0.338380\pi\) | ||||
0.486207 | + | 0.873844i | \(0.338380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 970.867 | 0.0420367 | 0.0210183 | − | 0.999779i | \(-0.493309\pi\) | ||||
0.0210183 | + | 0.999779i | \(0.493309\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39647.2 | 1.70403 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22015.7 | 0.942758 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3334.40 | 0.141743 | 0.0708717 | − | 0.997485i | \(-0.477422\pi\) | ||||
0.0708717 | + | 0.997485i | \(0.477422\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3714.29 | 0.157317 | 0.0786585 | − | 0.996902i | \(-0.474936\pi\) | ||||
0.0786585 | + | 0.996902i | \(0.474936\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30744.8 | −1.29275 | −0.646374 | − | 0.763020i | \(-0.723716\pi\) | ||||
−0.646374 | + | 0.763020i | \(0.723716\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29789.6 | −1.24805 | −0.624026 | − | 0.781404i | \(-0.714504\pi\) | ||||
−0.624026 | + | 0.781404i | \(0.714504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 45615.7 | 1.89735 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5946.14 | −0.246437 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32304.0 | 1.32927 | 0.664635 | − | 0.747168i | \(-0.268587\pi\) | ||||
0.664635 | + | 0.747168i | \(0.268587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15780.8 | −0.647044 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28341.9 | 1.15384 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18320.8 | 0.743222 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2553.34 | 0.102853 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17420.6 | −0.699260 | −0.349630 | − | 0.936888i | \(-0.613693\pi\) | ||||
−0.349630 | + | 0.936888i | \(0.613693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34483.8 | −1.37450 | −0.687248 | − | 0.726423i | \(-0.741182\pi\) | ||||
−0.687248 | + | 0.726423i | \(0.741182\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15174.4 | −0.602730 | −0.301365 | − | 0.953509i | \(-0.597442\pi\) | ||||
−0.301365 | + | 0.953509i | \(0.597442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 19314.7 | 0.761852 | 0.380926 | − | 0.924605i | \(-0.375605\pi\) | ||||
0.380926 | + | 0.924605i | \(0.375605\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35638.1 | 1.40085 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7583.63 | −0.296038 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1990.49 | 0.0774341 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24804.3 | 0.958331 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13744.8 | −0.529222 | −0.264611 | − | 0.964355i | \(-0.585244\pi\) | ||||
−0.264611 | + | 0.964355i | \(0.585244\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13269.0 | −0.507429 | −0.253714 | − | 0.967279i | \(-0.581652\pi\) | ||||
−0.253714 | + | 0.967279i | \(0.581652\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5785.26 | −0.220487 | −0.110243 | − | 0.993905i | \(-0.535163\pi\) | ||||
−0.110243 | + | 0.993905i | \(0.535163\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1338.82 | 0.0506802 | 0.0253401 | − | 0.999679i | \(-0.491933\pi\) | ||||
0.0253401 | + | 0.999679i | \(0.491933\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 52671.0 | 1.98710 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12448.1 | 0.466471 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11178.2 | −0.417482 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13273.7 | 0.492440 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47788.9 | −1.76701 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −59481.3 | −2.18478 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13647.5 | −0.499622 | −0.249811 | − | 0.968295i | \(-0.580368\pi\) | ||||
−0.249811 | + | 0.968295i | \(0.580368\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39201.3 | 1.42568 | 0.712842 | − | 0.701325i | \(-0.247408\pi\) | ||||
0.712842 | + | 0.701325i | \(0.247408\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7677.05 | 0.278284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40929.8 | 1.47396 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4733.10 | −0.169892 | −0.0849459 | − | 0.996386i | \(-0.527072\pi\) | ||||
−0.0849459 | + | 0.996386i | \(0.527072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5304.91 | −0.189180 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2164.50 | −0.0769386 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29332.8 | −1.03593 | −0.517964 | − | 0.855402i | \(-0.673310\pi\) | ||||
−0.517964 | + | 0.855402i | \(0.673310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26506.5 | −0.933100 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46210.9 | 1.61632 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39028.8 | −1.36074 | −0.680371 | − | 0.732867i | \(-0.738182\pi\) | ||||
−0.680371 | + | 0.732867i | \(0.738182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26632.5 | −0.922629 | −0.461314 | − | 0.887237i | \(-0.652622\pi\) | ||||
−0.461314 | + | 0.887237i | \(0.652622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26383.7 | 0.911105 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −51212.3 | −1.75731 | −0.878657 | − | 0.477454i | \(-0.841560\pi\) | ||||
−0.878657 | + | 0.477454i | \(0.841560\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7705.00 | 0.263556 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6350.46 | −0.215857 | −0.107928 | − | 0.994159i | \(-0.534422\pi\) | ||||
−0.107928 | + | 0.994159i | \(0.534422\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4240.31 | 0.143679 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 77352.9 | 2.60465 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9323.16 | −0.312952 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23705.6 | 0.790788 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39546.1 | −1.31512 | −0.657558 | − | 0.753404i | \(-0.728411\pi\) | ||||
−0.657558 | + | 0.753404i | \(0.728411\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21043.4 | −0.695483 | −0.347742 | − | 0.937590i | \(-0.613051\pi\) | ||||
−0.347742 | + | 0.937590i | \(0.613051\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19127.5 | 0.630215 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28818.1 | 0.943677 | 0.471838 | − | 0.881685i | \(-0.343591\pi\) | ||||
0.471838 | + | 0.881685i | \(0.343591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14783.4 | −0.482614 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29223.7 | −0.948210 | −0.474105 | − | 0.880468i | \(-0.657228\pi\) | ||||
−0.474105 | + | 0.880468i | \(0.657228\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3649.75 | 0.118061 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39182.3 | 1.25978 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1667.46 | 0.0534496 | 0.0267248 | − | 0.999643i | \(-0.491492\pi\) | ||||
0.0267248 | + | 0.999643i | \(0.491492\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 53103.4 | 1.69195 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33972.0 | 1.07914 | 0.539571 | − | 0.841940i | \(-0.318587\pi\) | ||||
0.539571 | + | 0.841940i | \(0.318587\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 324.4.a.c.1.1 | 3 | ||
3.2 | odd | 2 | 324.4.a.d.1.3 | 3 | |||
4.3 | odd | 2 | 1296.4.a.v.1.1 | 3 | |||
9.2 | odd | 6 | 108.4.e.a.37.1 | 6 | |||
9.4 | even | 3 | 36.4.e.a.25.1 | yes | 6 | ||
9.5 | odd | 6 | 108.4.e.a.73.1 | 6 | |||
9.7 | even | 3 | 36.4.e.a.13.1 | ✓ | 6 | ||
12.11 | even | 2 | 1296.4.a.w.1.3 | 3 | |||
36.7 | odd | 6 | 144.4.i.d.49.3 | 6 | |||
36.11 | even | 6 | 432.4.i.d.145.1 | 6 | |||
36.23 | even | 6 | 432.4.i.d.289.1 | 6 | |||
36.31 | odd | 6 | 144.4.i.d.97.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.4.e.a.13.1 | ✓ | 6 | 9.7 | even | 3 | ||
36.4.e.a.25.1 | yes | 6 | 9.4 | even | 3 | ||
108.4.e.a.37.1 | 6 | 9.2 | odd | 6 | |||
108.4.e.a.73.1 | 6 | 9.5 | odd | 6 | |||
144.4.i.d.49.3 | 6 | 36.7 | odd | 6 | |||
144.4.i.d.97.3 | 6 | 36.31 | odd | 6 | |||
324.4.a.c.1.1 | 3 | 1.1 | even | 1 | trivial | ||
324.4.a.d.1.3 | 3 | 3.2 | odd | 2 | |||
432.4.i.d.145.1 | 6 | 36.11 | even | 6 | |||
432.4.i.d.289.1 | 6 | 36.23 | even | 6 | |||
1296.4.a.v.1.1 | 3 | 4.3 | odd | 2 | |||
1296.4.a.w.1.3 | 3 | 12.11 | even | 2 |