Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.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: | \(69.3862461668\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.0000 | −1.07331 | −0.536656 | − | 0.843801i | \(-0.680313\pi\) | ||||
−0.536656 | + | 0.843801i | \(0.680313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −60.0000 | −1.64461 | −0.822304 | − | 0.569049i | \(-0.807311\pi\) | ||||
−0.822304 | + | 0.569049i | \(0.807311\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −44.0000 | −0.938723 | −0.469362 | − | 0.883006i | \(-0.655516\pi\) | ||||
−0.469362 | + | 0.883006i | \(0.655516\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 36.0000 | 0.619677 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 128.000 | 1.82615 | 0.913075 | − | 0.407791i | \(-0.133701\pi\) | ||||
0.913075 | + | 0.407791i | \(0.133701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −52.0000 | −0.627875 | −0.313937 | − | 0.949444i | \(-0.601648\pi\) | ||||
−0.313937 | + | 0.949444i | \(0.601648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −160.000 | −1.45054 | −0.725268 | − | 0.688467i | \(-0.758284\pi\) | ||||
−0.725268 | + | 0.688467i | \(0.758284\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −230.000 | −1.47276 | −0.736378 | − | 0.676570i | \(-0.763465\pi\) | ||||
−0.736378 | + | 0.676570i | \(0.763465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −136.000 | −0.787946 | −0.393973 | − | 0.919122i | \(-0.628900\pi\) | ||||
−0.393973 | + | 0.919122i | \(0.628900\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 180.000 | 0.949514 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −318.000 | −1.41294 | −0.706471 | − | 0.707742i | \(-0.749714\pi\) | ||||
−0.706471 | + | 0.707742i | \(0.749714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 132.000 | 0.541972 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 192.000 | 0.731350 | 0.365675 | − | 0.930743i | \(-0.380838\pi\) | ||||
0.365675 | + | 0.930743i | \(0.380838\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 220.000 | 0.780225 | 0.390113 | − | 0.920767i | \(-0.372436\pi\) | ||||
0.390113 | + | 0.920767i | \(0.372436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −108.000 | −0.357771 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −184.000 | −0.571046 | −0.285523 | − | 0.958372i | \(-0.592167\pi\) | ||||
−0.285523 | + | 0.958372i | \(0.592167\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −384.000 | −1.05433 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −498.000 | −1.29067 | −0.645335 | − | 0.763899i | \(-0.723282\pi\) | ||||
−0.645335 | + | 0.763899i | \(0.723282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 720.000 | 1.76518 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 156.000 | 0.362504 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 492.000 | 1.08564 | 0.542822 | − | 0.839848i | \(-0.317356\pi\) | ||||
0.542822 | + | 0.839848i | \(0.317356\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −20.0000 | −0.0419793 | −0.0209897 | − | 0.999780i | \(-0.506682\pi\) | ||||
−0.0209897 | + | 0.999780i | \(0.506682\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 528.000 | 1.00754 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 380.000 | 0.692901 | 0.346451 | − | 0.938068i | \(-0.387387\pi\) | ||||
0.346451 | + | 0.938068i | \(0.387387\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 480.000 | 0.837467 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −264.000 | −0.441282 | −0.220641 | − | 0.975355i | \(-0.570815\pi\) | ||||
−0.220641 | + | 0.975355i | \(0.570815\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 560.000 | 0.897850 | 0.448925 | − | 0.893569i | \(-0.351807\pi\) | ||||
0.448925 | + | 0.893569i | \(0.351807\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −57.0000 | −0.0877572 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 104.000 | 0.148113 | 0.0740564 | − | 0.997254i | \(-0.476406\pi\) | ||||
0.0740564 | + | 0.997254i | \(0.476406\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1508.00 | −1.99427 | −0.997136 | − | 0.0756351i | \(-0.975902\pi\) | ||||
−0.997136 | + | 0.0756351i | \(0.975902\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1536.00 | −1.96003 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 690.000 | 0.850296 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1144.00 | −1.36251 | −0.681257 | − | 0.732044i | \(-0.738566\pi\) | ||||
−0.681257 | + | 0.732044i | \(0.738566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 408.000 | 0.454921 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 624.000 | 0.673906 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 904.000 | 0.946261 | 0.473130 | − | 0.880992i | \(-0.343124\pi\) | ||||
0.473130 | + | 0.880992i | \(0.343124\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −540.000 | −0.548202 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 500.000 | 0.492593 | 0.246296 | − | 0.969195i | \(-0.420786\pi\) | ||||
0.246296 | + | 0.969195i | \(0.420786\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −248.000 | −0.237244 | −0.118622 | − | 0.992939i | \(-0.537848\pi\) | ||||
−0.118622 | + | 0.992939i | \(0.537848\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1028.00 | −0.928790 | −0.464395 | − | 0.885628i | \(-0.653728\pi\) | ||||
−0.464395 | + | 0.885628i | \(0.653728\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1066.00 | 0.936737 | 0.468368 | − | 0.883533i | \(-0.344842\pi\) | ||||
0.468368 | + | 0.883533i | \(0.344842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 954.000 | 0.815763 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 466.000 | 0.387943 | 0.193972 | − | 0.981007i | \(-0.437863\pi\) | ||||
0.193972 | + | 0.981007i | \(0.437863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1920.00 | 1.55688 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −396.000 | −0.312908 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2269.00 | 1.70473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −576.000 | −0.422245 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1272.00 | 0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1616.00 | 1.12911 | 0.564554 | − | 0.825396i | \(-0.309048\pi\) | ||||
0.564554 | + | 0.825396i | \(0.309048\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −660.000 | −0.450463 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1700.00 | −1.13381 | −0.566907 | − | 0.823782i | \(-0.691860\pi\) | ||||
−0.566907 | + | 0.823782i | \(0.691860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 324.000 | 0.206559 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1958.00 | 1.22105 | 0.610523 | − | 0.791999i | \(-0.290959\pi\) | ||||
0.610523 | + | 0.791999i | \(0.290959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1284.00 | 0.783507 | 0.391753 | − | 0.920070i | \(-0.371869\pi\) | ||||
0.391753 | + | 0.920070i | \(0.371869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 552.000 | 0.329694 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2640.00 | 1.54383 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2760.00 | 1.58073 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −306.000 | −0.168245 | −0.0841225 | − | 0.996455i | \(-0.526809\pi\) | ||||
−0.0841225 | + | 0.996455i | \(0.526809\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2264.00 | −1.22014 | −0.610072 | − | 0.792346i | \(-0.708859\pi\) | ||||
−0.610072 | + | 0.792346i | \(0.708859\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1152.00 | 0.608717 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1632.00 | 0.845712 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2068.00 | 1.05124 | 0.525619 | − | 0.850720i | \(-0.323834\pi\) | ||||
0.525619 | + | 0.850720i | \(0.323834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1494.00 | 0.745169 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1908.00 | 0.916847 | 0.458424 | − | 0.888734i | \(-0.348414\pi\) | ||||
0.458424 | + | 0.888734i | \(0.348414\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2160.00 | −1.01913 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3128.00 | 1.44941 | 0.724706 | − | 0.689058i | \(-0.241975\pi\) | ||||
0.724706 | + | 0.689058i | \(0.241975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −261.000 | −0.118798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −468.000 | −0.209292 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −532.000 | −0.233799 | −0.116899 | − | 0.993144i | \(-0.537296\pi\) | ||||
−0.116899 | + | 0.993144i | \(0.537296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1476.00 | −0.626796 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1068.00 | −0.445956 | −0.222978 | − | 0.974824i | \(-0.571578\pi\) | ||||
−0.222978 | + | 0.974824i | \(0.571578\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4164.00 | 1.70999 | 0.854994 | − | 0.518639i | \(-0.173561\pi\) | ||||
0.854994 | + | 0.518639i | \(0.173561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 60.0000 | 0.0242368 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3816.00 | 1.51653 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7680.00 | −3.00330 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −288.000 | −0.109104 | −0.0545522 | − | 0.998511i | \(-0.517373\pi\) | ||||
−0.0545522 | + | 0.998511i | \(0.517373\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1282.00 | 0.478137 | 0.239068 | − | 0.971003i | \(-0.423158\pi\) | ||||
0.239068 | + | 0.971003i | \(0.423158\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1584.00 | −0.581706 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2622.00 | 0.948273 | 0.474136 | − | 0.880451i | \(-0.342760\pi\) | ||||
0.474136 | + | 0.880451i | \(0.342760\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −776.000 | −0.276428 | −0.138214 | − | 0.990402i | \(-0.544136\pi\) | ||||
−0.138214 | + | 0.990402i | \(0.544136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1140.00 | −0.400047 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2304.00 | −0.784968 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1440.00 | −0.483512 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3120.00 | 1.03261 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5476.00 | −1.78665 | −0.893326 | − | 0.449410i | \(-0.851634\pi\) | ||||
−0.893326 | + | 0.449410i | \(0.851634\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 792.000 | 0.254774 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2640.00 | −0.837426 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1680.00 | −0.518374 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5632.00 | −1.71425 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5680.00 | −1.70565 | −0.852827 | − | 0.522193i | \(-0.825114\pi\) | ||||
−0.852827 | + | 0.522193i | \(0.825114\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 171.000 | 0.0506667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5180.00 | 1.51458 | 0.757288 | − | 0.653081i | \(-0.226524\pi\) | ||||
0.757288 | + | 0.653081i | \(0.226524\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2996.00 | 0.864547 | 0.432273 | − | 0.901743i | \(-0.357712\pi\) | ||||
0.432273 | + | 0.901743i | \(0.357712\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1818.00 | −0.511164 | −0.255582 | − | 0.966787i | \(-0.582267\pi\) | ||||
−0.255582 | + | 0.966787i | \(0.582267\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2208.00 | 0.612911 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −312.000 | −0.0855130 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2264.00 | 0.612745 | 0.306372 | − | 0.951912i | \(-0.400885\pi\) | ||||
0.306372 | + | 0.951912i | \(0.400885\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2952.00 | 0.789025 | 0.394513 | − | 0.918891i | \(-0.370913\pi\) | ||||
0.394513 | + | 0.918891i | \(0.370913\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2288.00 | 0.589401 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4524.00 | 1.15139 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2460.00 | −0.618621 | −0.309310 | − | 0.950961i | \(-0.600098\pi\) | ||||
−0.309310 | + | 0.950961i | \(0.600098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9600.00 | 2.38556 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4608.00 | 1.13162 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2952.00 | 0.716501 | 0.358250 | − | 0.933626i | \(-0.383373\pi\) | ||||
0.358250 | + | 0.933626i | \(0.383373\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2070.00 | −0.490919 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5448.00 | −1.27733 | −0.638666 | − | 0.769484i | \(-0.720513\pi\) | ||||
−0.638666 | + | 0.769484i | \(0.720513\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5976.00 | 1.38529 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3432.00 | 0.786648 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8052.00 | −1.82505 | −0.912526 | − | 0.409018i | \(-0.865871\pi\) | ||||
−0.912526 | + | 0.409018i | \(0.865871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3872.00 | −0.867923 | −0.433962 | − | 0.900931i | \(-0.642885\pi\) | ||||
−0.433962 | + | 0.900931i | \(0.642885\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1140.00 | −0.249980 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6062.00 | 1.31491 | 0.657455 | − | 0.753493i | \(-0.271633\pi\) | ||||
0.657455 | + | 0.753493i | \(0.271633\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1224.00 | −0.262649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7018.00 | −1.48989 | −0.744944 | − | 0.667127i | \(-0.767524\pi\) | ||||
−0.744944 | + | 0.667127i | \(0.767524\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3596.00 | 0.755336 | 0.377668 | − | 0.925941i | \(-0.376726\pi\) | ||||
0.377668 | + | 0.925941i | \(0.376726\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1872.00 | −0.389080 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11471.0 | 2.33483 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2712.00 | −0.546324 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8100.00 | 1.61504 | 0.807521 | − | 0.589839i | \(-0.200809\pi\) | ||||
0.807521 | + | 0.589839i | \(0.200809\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5904.00 | −1.16523 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1620.00 | 0.316505 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7040.00 | 1.36165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1500.00 | −0.284399 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 240.000 | 0.0450569 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7164.00 | 1.33183 | 0.665914 | − | 0.746029i | \(-0.268042\pi\) | ||||
0.665914 | + | 0.746029i | \(0.268042\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 744.000 | 0.136973 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 544.000 | 0.0991878 | 0.0495939 | − | 0.998769i | \(-0.484207\pi\) | ||||
0.0495939 | + | 0.998769i | \(0.484207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2792.00 | −0.504195 | −0.252098 | − | 0.967702i | \(-0.581120\pi\) | ||||
−0.252098 | + | 0.967702i | \(0.581120\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3642.00 | −0.645284 | −0.322642 | − | 0.946521i | \(-0.604571\pi\) | ||||
−0.322642 | + | 0.946521i | \(0.604571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13800.0 | 2.42211 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3084.00 | 0.536237 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6656.00 | −1.14659 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −836.000 | −0.142686 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3198.00 | −0.540825 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2380.00 | 0.395216 | 0.197608 | − | 0.980281i | \(-0.436683\pi\) | ||||
0.197608 | + | 0.980281i | \(0.436683\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2862.00 | −0.470981 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4560.00 | −0.743700 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12306.0 | −1.98917 | −0.994585 | − | 0.103923i | \(-0.966861\pi\) | ||||
−0.994585 | + | 0.103923i | \(0.966861\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1398.00 | −0.223979 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8160.00 | 1.29586 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5760.00 | −0.898864 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8244.00 | 1.27539 | 0.637696 | − | 0.770288i | \(-0.279888\pi\) | ||||
0.637696 | + | 0.770288i | \(0.279888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9276.00 | −1.42273 | −0.711365 | − | 0.702823i | \(-0.751923\pi\) | ||||
−0.711365 | + | 0.702823i | \(0.751923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1188.00 | 0.180657 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10648.0 | −1.60548 | −0.802742 | − | 0.596326i | \(-0.796626\pi\) | ||||
−0.802742 | + | 0.596326i | \(0.796626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3168.00 | 0.473634 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2000.00 | 0.294028 | 0.147014 | − | 0.989134i | \(-0.453034\pi\) | ||||
0.147014 | + | 0.989134i | \(0.453034\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4155.00 | −0.605773 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6807.00 | −0.984228 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6720.00 | −0.963674 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 848.000 | 0.120614 | 0.0603069 | − | 0.998180i | \(-0.480792\pi\) | ||||
0.0603069 | + | 0.998180i | \(0.480792\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1728.00 | 0.243783 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1810.00 | −0.251255 | −0.125628 | − | 0.992077i | \(-0.540094\pi\) | ||||
−0.125628 | + | 0.992077i | \(0.540094\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3816.00 | −0.525486 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10120.0 | 1.38251 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1668.00 | −0.226067 | −0.113034 | − | 0.993591i | \(-0.536057\pi\) | ||||
−0.113034 | + | 0.993591i | \(0.536057\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4848.00 | −0.651891 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11736.0 | −1.56575 | −0.782874 | − | 0.622180i | \(-0.786247\pi\) | ||||
−0.782874 | + | 0.622180i | \(0.786247\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1980.00 | 0.260075 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10046.0 | −1.30939 | −0.654695 | − | 0.755893i | \(-0.727203\pi\) | ||||
−0.654695 | + | 0.755893i | \(0.727203\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20480.0 | −2.64890 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5100.00 | 0.654608 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1248.00 | −0.158971 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7636.00 | 0.965340 | 0.482670 | − | 0.875802i | \(-0.339667\pi\) | ||||
0.482670 | + | 0.875802i | \(0.339667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1842.00 | −0.229389 | −0.114695 | − | 0.993401i | \(-0.536589\pi\) | ||||
−0.114695 | + | 0.993401i | \(0.536589\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5984.00 | 0.739663 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −972.000 | −0.119257 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19080.0 | 2.32374 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −664.000 | −0.0802755 | −0.0401378 | − | 0.999194i | \(-0.512780\pi\) | ||||
−0.0401378 | + | 0.999194i | \(0.512780\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5874.00 | −0.704971 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18096.0 | 2.14048 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3852.00 | −0.452358 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6572.00 | −0.766261 | −0.383130 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383130 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2370.00 | −0.274363 | −0.137181 | − | 0.990546i | \(-0.543804\pi\) | ||||
−0.137181 | + | 0.990546i | \(0.543804\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1656.00 | −0.190349 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2432.00 | 0.277575 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7920.00 | −0.891331 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9048.00 | 1.01120 | 0.505600 | − | 0.862768i | \(-0.331271\pi\) | ||||
0.505600 | + | 0.862768i | \(0.331271\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3208.00 | −0.356043 | −0.178022 | − | 0.984027i | \(-0.556970\pi\) | ||||
−0.178022 | + | 0.984027i | \(0.556970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8280.00 | −0.912634 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8320.00 | 0.910754 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8832.00 | −0.960201 | −0.480101 | − | 0.877213i | \(-0.659400\pi\) | ||||
−0.480101 | + | 0.877213i | \(0.659400\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16756.0 | −1.79707 | −0.898535 | − | 0.438903i | \(-0.855367\pi\) | ||||
−0.898535 | + | 0.438903i | \(0.855367\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13728.0 | 1.46240 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 918.000 | 0.0971363 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16994.0 | 1.78618 | 0.893092 | − | 0.449874i | \(-0.148531\pi\) | ||||
0.893092 | + | 0.449874i | \(0.148531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11520.0 | −1.20278 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6792.00 | 0.704450 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11194.0 | 1.14581 | 0.572903 | − | 0.819623i | \(-0.305817\pi\) | ||||
0.572903 | + | 0.819623i | \(0.305817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3456.00 | −0.351443 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4292.00 | −0.433619 | −0.216810 | − | 0.976214i | \(-0.569565\pi\) | ||||
−0.216810 | + | 0.976214i | \(0.569565\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4328.00 | −0.434426 | −0.217213 | − | 0.976124i | \(-0.569697\pi\) | ||||
−0.217213 | + | 0.976124i | \(0.569697\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4896.00 | −0.488272 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3844.00 | −0.380897 | −0.190449 | − | 0.981697i | \(-0.560994\pi\) | ||||
−0.190449 | + | 0.981697i | \(0.560994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6204.00 | −0.606933 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13200.0 | −1.28316 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −988.000 | −0.0954369 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4482.00 | −0.430224 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12712.0 | −1.21258 | −0.606290 | − | 0.795243i | \(-0.707343\pi\) | ||||
−0.606290 | + | 0.795243i | \(0.707343\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13992.0 | 1.32636 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10848.0 | −1.01563 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13912.0 | −1.29448 | −0.647241 | − | 0.762285i | \(-0.724077\pi\) | ||||
−0.647241 | + | 0.762285i | \(0.724077\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5724.00 | −0.529342 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11340.0 | 1.04230 | 0.521148 | − | 0.853467i | \(-0.325504\pi\) | ||||
0.521148 | + | 0.853467i | \(0.325504\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29440.0 | −2.68947 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6480.00 | 0.588393 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3444.00 | −0.308967 | −0.154484 | − | 0.987995i | \(-0.549371\pi\) | ||||
−0.154484 | + | 0.987995i | \(0.549371\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9384.00 | −0.836819 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7856.00 | −0.696385 | −0.348193 | − | 0.937423i | \(-0.613204\pi\) | ||||
−0.348193 | + | 0.937423i | \(0.613204\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6000.00 | −0.528706 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 783.000 | 0.0685883 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12460.0 | 1.08503 | 0.542515 | − | 0.840046i | \(-0.317472\pi\) | ||||
0.542515 | + | 0.840046i | \(0.317472\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1404.00 | 0.120835 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2976.00 | 0.254637 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11040.0 | 0.939146 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1596.00 | 0.134984 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3552.00 | 0.298687 | 0.149344 | − | 0.988785i | \(-0.452284\pi\) | ||||
0.149344 | + | 0.988785i | \(0.452284\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14380.0 | 1.20228 | 0.601141 | − | 0.799143i | \(-0.294713\pi\) | ||||
0.601141 | + | 0.799143i | \(0.294713\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17408.0 | −1.43891 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13433.0 | 1.10405 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4428.00 | 0.361881 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8448.00 | −0.686536 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12336.0 | 0.996882 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3204.00 | 0.257473 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14118.0 | 1.12196 | 0.560980 | − | 0.827829i | \(-0.310424\pi\) | ||||
0.560980 | + | 0.827829i | \(0.310424\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12492.0 | −0.987262 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12792.0 | −1.00541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3052.00 | −0.238563 | −0.119282 | − | 0.992860i | \(-0.538059\pi\) | ||||
−0.119282 | + | 0.992860i | \(0.538059\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −180.000 | −0.0139931 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11960.0 | 0.924706 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11448.0 | −0.875569 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17162.0 | −1.30552 | −0.652762 | − | 0.757563i | \(-0.726390\pi\) | ||||
−0.652762 | + | 0.757563i | \(0.726390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9680.00 | −0.732416 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23040.0 | 1.73396 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15948.0 | −1.19383 | −0.596917 | − | 0.802303i | \(-0.703608\pi\) | ||||
−0.596917 | + | 0.802303i | \(0.703608\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5592.00 | −0.416384 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15958.0 | 1.17574 | 0.587868 | − | 0.808957i | \(-0.299967\pi\) | ||||
0.587868 | + | 0.808957i | \(0.299967\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4548.00 | −0.333324 | −0.166662 | − | 0.986014i | \(-0.553299\pi\) | ||||
−0.166662 | + | 0.986014i | \(0.553299\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 864.000 | 0.0629915 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3040.00 | −0.220481 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12304.0 | −0.887733 | −0.443867 | − | 0.896093i | \(-0.646394\pi\) | ||||
−0.443867 | + | 0.896093i | \(0.646394\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3846.00 | −0.276052 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29880.0 | 2.12265 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4752.00 | 0.335848 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28236.0 | −1.98539 | −0.992695 | − | 0.120647i | \(-0.961503\pi\) | ||||
−0.992695 | + | 0.120647i | \(0.961503\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7072.00 | 0.494731 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7866.00 | −0.547486 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4888.00 | −0.338493 | −0.169246 | − | 0.985574i | \(-0.554133\pi\) | ||||
−0.169246 | + | 0.985574i | \(0.554133\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2328.00 | 0.159596 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5208.00 | −0.355247 | −0.177624 | − | 0.984098i | \(-0.556841\pi\) | ||||
−0.177624 | + | 0.984098i | \(0.556841\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27040.0 | 1.83525 | 0.917624 | − | 0.397449i | \(-0.130104\pi\) | ||||
0.917624 | + | 0.397449i | \(0.130104\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3420.00 | 0.230967 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27228.0 | −1.82971 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4032.00 | 0.269611 | 0.134805 | − | 0.990872i | \(-0.456959\pi\) | ||||
0.134805 | + | 0.990872i | \(0.456959\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8096.00 | 0.536054 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21602.0 | 1.42332 | 0.711661 | − | 0.702523i | \(-0.247943\pi\) | ||||
0.711661 | + | 0.702523i | \(0.247943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6912.00 | 0.453201 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2554.00 | −0.166645 | −0.0833227 | − | 0.996523i | \(-0.526553\pi\) | ||||
−0.0833227 | + | 0.996523i | \(0.526553\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12580.0 | −0.816854 | −0.408427 | − | 0.912791i | \(-0.633923\pi\) | ||||
−0.408427 | + | 0.912791i | \(0.633923\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4320.00 | 0.279156 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9360.00 | −0.596176 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40704.0 | −2.58025 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14784.0 | 0.932713 | 0.466356 | − | 0.884597i | \(-0.345566\pi\) | ||||
0.466356 | + | 0.884597i | \(0.345566\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16428.0 | 1.03152 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19392.0 | −1.21189 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2376.00 | −0.147094 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1278.00 | 0.0787488 | 0.0393744 | − | 0.999225i | \(-0.487464\pi\) | ||||
0.0393744 | + | 0.999225i | \(0.487464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24428.0 | −1.49821 | −0.749103 | − | 0.662454i | \(-0.769515\pi\) | ||||
−0.749103 | + | 0.662454i | \(0.769515\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7920.00 | 0.483488 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −424.000 | −0.0257638 | −0.0128819 | − | 0.999917i | \(-0.504101\pi\) | ||||
−0.0128819 | + | 0.999917i | \(0.504101\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29520.0 | −1.78546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15754.0 | 0.944107 | 0.472053 | − | 0.881570i | \(-0.343513\pi\) | ||||
0.472053 | + | 0.881570i | \(0.343513\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20400.0 | 1.21694 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5040.00 | 0.299283 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5860.00 | −0.346393 | −0.173197 | − | 0.984887i | \(-0.555410\pi\) | ||||
−0.173197 | + | 0.984887i | \(0.555410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10580.0 | −0.622563 | −0.311282 | − | 0.950318i | \(-0.600758\pi\) | ||||
−0.311282 | + | 0.950318i | \(0.600758\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16896.0 | 0.989723 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36800.0 | 2.13628 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17040.0 | 0.984760 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1200.00 | 0.0690395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8290.00 | −0.474823 | −0.237412 | − | 0.971409i | \(-0.576299\pi\) | ||||
−0.237412 | + | 0.971409i | \(0.576299\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −513.000 | −0.0292524 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14500.0 | −0.823161 | −0.411581 | − | 0.911373i | \(-0.635023\pi\) | ||||
−0.411581 | + | 0.911373i | \(0.635023\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15540.0 | −0.874441 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7572.00 | −0.424209 | −0.212104 | − | 0.977247i | \(-0.568032\pi\) | ||||
−0.212104 | + | 0.977247i | \(0.568032\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23496.0 | −1.31056 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8988.00 | −0.499146 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21912.0 | 1.21158 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17020.0 | 0.937006 | 0.468503 | − | 0.883462i | \(-0.344793\pi\) | ||||
0.468503 | + | 0.883462i | \(0.344793\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15408.0 | −0.840948 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24576.0 | 1.33556 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5454.00 | 0.295120 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12422.0 | −0.669290 | −0.334645 | − | 0.942344i | \(-0.608616\pi\) | ||||
−0.334645 | + | 0.942344i | \(0.608616\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16536.0 | 0.887151 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6624.00 | −0.353864 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22370.0 | 1.18494 | 0.592470 | − | 0.805592i | \(-0.298153\pi\) | ||||
0.592470 | + | 0.805592i | \(0.298153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 936.000 | 0.0493709 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21760.0 | 1.14294 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −31680.0 | −1.65701 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6792.00 | −0.353768 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14936.0 | 0.774713 | 0.387357 | − | 0.921930i | \(-0.373388\pi\) | ||||
0.387357 | + | 0.921930i | \(0.373388\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8856.00 | −0.455544 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4370.00 | −0.223859 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24456.0 | 1.24762 | 0.623812 | − | 0.781574i | \(-0.285583\pi\) | ||||
0.623812 | + | 0.781574i | \(0.285583\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28160.0 | 1.42481 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34796.0 | 1.75337 | 0.876685 | − | 0.481066i | \(-0.159750\pi\) | ||||
0.876685 | + | 0.481066i | \(0.159750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22800.0 | −1.13955 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14228.0 | 0.708235 | 0.354117 | − | 0.935201i | \(-0.384781\pi\) | ||||
0.354117 | + | 0.935201i | \(0.384781\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6864.00 | −0.340291 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14368.0 | 0.709436 | 0.354718 | − | 0.934973i | \(-0.384577\pi\) | ||||
0.354718 | + | 0.934973i | \(0.384577\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3672.00 | 0.180579 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13572.0 | −0.664757 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7360.00 | −0.357617 | −0.178808 | − | 0.983884i | \(-0.557224\pi\) | ||||
−0.178808 | + | 0.983884i | \(0.557224\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7380.00 | 0.357161 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27168.0 | 1.30960 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4558.00 | −0.218842 | −0.109421 | − | 0.993996i | \(-0.534900\pi\) | ||||
−0.109421 | + | 0.993996i | \(0.534900\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28800.0 | −1.37730 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13008.0 | 0.619632 | 0.309816 | − | 0.950797i | \(-0.399733\pi\) | ||||
0.309816 | + | 0.950797i | \(0.399733\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13824.0 | −0.653343 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21648.0 | −1.01912 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14168.0 | −0.664384 | −0.332192 | − | 0.943212i | \(-0.607788\pi\) | ||||
−0.332192 | + | 0.943212i | \(0.607788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8856.00 | −0.413672 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14700.0 | −0.683987 | −0.341994 | − | 0.939702i | \(-0.611102\pi\) | ||||
−0.341994 | + | 0.939702i | \(0.611102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2584.00 | −0.119768 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9984.00 | −0.459196 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15840.0 | 0.725736 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6210.00 | 0.283432 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24816.0 | −1.12831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8068.00 | −0.365430 | −0.182715 | − | 0.983166i | \(-0.558489\pi\) | ||||
−0.182715 | + | 0.983166i | \(0.558489\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 16344.0 | 0.737467 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 880.000 | 0.0394070 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17928.0 | −0.799800 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4228.00 | −0.187909 | −0.0939545 | − | 0.995576i | \(-0.529951\pi\) | ||||
−0.0939545 | + | 0.995576i | \(0.529951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23552.0 | −1.04282 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10296.0 | −0.454171 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33600.0 | −1.47661 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24156.0 | 1.05369 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36934.0 | −1.60511 | −0.802553 | − | 0.596581i | \(-0.796525\pi\) | ||||
−0.802553 | + | 0.596581i | \(0.796525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16540.0 | 0.716150 | 0.358075 | − | 0.933693i | \(-0.383433\pi\) | ||||
0.358075 | + | 0.933693i | \(0.383433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11616.0 | 0.501096 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22896.0 | −0.984064 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11440.0 | −0.489884 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40718.0 | 1.73090 | 0.865449 | − | 0.500996i | \(-0.167033\pi\) | ||||
0.865449 | + | 0.500996i | \(0.167033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34832.0 | −1.47529 | −0.737647 | − | 0.675186i | \(-0.764063\pi\) | ||||
−0.737647 | + | 0.675186i | \(0.764063\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3420.00 | 0.144326 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38300.0 | 1.61043 | 0.805213 | − | 0.592986i | \(-0.202051\pi\) | ||||
0.805213 | + | 0.592986i | \(0.202051\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20476.0 | 0.857854 | 0.428927 | − | 0.903339i | \(-0.358892\pi\) | ||||
0.428927 | + | 0.903339i | \(0.358892\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18186.0 | −0.759164 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37536.0 | −1.55567 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3672.00 | 0.151640 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42024.0 | 1.72924 | 0.864618 | − | 0.502429i | \(-0.167560\pi\) | ||||
0.864618 | + | 0.502429i | \(0.167560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28511.0 | 1.16901 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21054.0 | 0.860188 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3132.00 | 0.127508 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10788.0 | −0.436093 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50880.0 | 2.04952 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −412.000 | −0.0165376 | −0.00826882 | − | 0.999966i | \(-0.502632\pi\) | ||||
−0.00826882 | + | 0.999966i | \(0.502632\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5616.00 | 0.224635 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42816.0 | 1.70661 | 0.853306 | − | 0.521410i | \(-0.174594\pi\) | ||||
0.853306 | + | 0.521410i | \(0.174594\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43572.0 | 1.73068 | 0.865342 | − | 0.501182i | \(-0.167101\pi\) | ||||
0.865342 | + | 0.501182i | \(0.167101\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16208.0 | −0.639313 | −0.319656 | − | 0.947534i | \(-0.603567\pi\) | ||||
−0.319656 | + | 0.947534i | \(0.603567\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6384.00 | 0.250939 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34413.0 | −1.34801 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6240.00 | −0.243587 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16720.0 | −0.650443 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8136.00 | 0.315420 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34378.0 | 1.32367 | 0.661837 | − | 0.749648i | \(-0.269777\pi\) | ||||
0.661837 | + | 0.749648i | \(0.269777\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24300.0 | −0.932444 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7416.00 | 0.283600 | 0.141800 | − | 0.989895i | \(-0.454711\pi\) | ||||
0.141800 | + | 0.989895i | \(0.454711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16772.0 | −0.639210 | −0.319605 | − | 0.947551i | \(-0.603550\pi\) | ||||
−0.319605 | + | 0.947551i | \(0.603550\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17712.0 | 0.672748 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23336.0 | 0.883367 | 0.441683 | − | 0.897171i | \(-0.354381\pi\) | ||||
0.441683 | + | 0.897171i | \(0.354381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4860.00 | −0.182734 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9568.00 | 0.358545 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12816.0 | 0.478650 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21120.0 | −0.786150 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31280.0 | 1.16045 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −63744.0 | −2.35696 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49968.0 | −1.83535 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22732.0 | −0.832198 | −0.416099 | − | 0.909319i | \(-0.636603\pi\) | ||||
−0.416099 | + | 0.909319i | \(0.636603\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4500.00 | 0.164198 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16584.0 | 0.603131 | 0.301566 | − | 0.953445i | \(-0.402491\pi\) | ||||
0.301566 | + | 0.953445i | \(0.402491\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 90480.0 | 3.27979 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −720.000 | −0.0260136 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41616.0 | −1.49378 | −0.746891 | − | 0.664947i | \(-0.768454\pi\) | ||||
−0.746891 | + | 0.664947i | \(0.768454\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21492.0 | −0.768931 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11616.0 | 0.414242 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6042.00 | −0.214767 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2232.00 | −0.0790814 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41680.0 | −1.47199 | −0.735994 | − | 0.676988i | \(-0.763285\pi\) | ||||
−0.735994 | + | 0.676988i | \(0.763285\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1632.00 | −0.0572661 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 92160.0 | 3.22348 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13248.0 | −0.461893 | −0.230946 | − | 0.972967i | \(-0.574182\pi\) | ||||
−0.230946 | + | 0.972967i | \(0.574182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8376.00 | 0.291097 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6204.00 | −0.214925 | −0.107463 | − | 0.994209i | \(-0.534273\pi\) | ||||
−0.107463 | + | 0.994209i | \(0.534273\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30720.0 | −1.06085 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44996.0 | −1.54401 | −0.772003 | − | 0.635619i | \(-0.780745\pi\) | ||||
−0.772003 | + | 0.635619i | \(0.780745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24640.0 | −0.842833 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10926.0 | 0.372555 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24918.0 | −0.846981 | −0.423491 | − | 0.905900i | \(-0.639195\pi\) | ||||
−0.423491 | + | 0.905900i | \(0.639195\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3456.00 | 0.117103 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −41400.0 | −1.39840 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11295.0 | −0.379141 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9252.00 | −0.309597 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15384.0 | −0.513190 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8984.00 | −0.298765 | −0.149383 | − | 0.988779i | \(-0.547729\pi\) | ||||
−0.149383 | + | 0.988779i | \(0.547729\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19968.0 | 0.661986 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15020.0 | 0.496411 | 0.248205 | − | 0.968707i | \(-0.420159\pi\) | ||||
0.248205 | + | 0.968707i | \(0.420159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2508.00 | 0.0823798 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −53138.0 | −1.74006 | −0.870028 | − | 0.493002i | \(-0.835900\pi\) | ||||
−0.870028 | + | 0.493002i | \(0.835900\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68640.0 | 2.24080 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9594.00 | 0.312246 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2120.00 | 0.0687869 | 0.0343934 | − | 0.999408i | \(-0.489050\pi\) | ||||
0.0343934 | + | 0.999408i | \(0.489050\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31464.0 | −1.01779 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35200.0 | −1.13174 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18520.0 | 0.593650 | 0.296825 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296825 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7140.00 | −0.228178 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9312.00 | 0.296694 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46996.0 | −1.49286 | −0.746428 | − | 0.665466i | \(-0.768233\pi\) | ||||
−0.746428 | + | 0.665466i | \(0.768233\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8586.00 | 0.271921 |
(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 | 1176.4.a.b.1.1 | ✓ | 1 | |
4.3 | odd | 2 | 2352.4.a.x.1.1 | 1 | |||
7.6 | odd | 2 | 1176.4.a.o.1.1 | yes | 1 | ||
28.27 | even | 2 | 2352.4.a.p.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
1176.4.a.o.1.1 | yes | 1 | 7.6 | odd | 2 | ||
2352.4.a.p.1.1 | 1 | 28.27 | even | 2 | |||
2352.4.a.x.1.1 | 1 | 4.3 | odd | 2 |