Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(1,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, 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("1150.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.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: | \(67.8521965066\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 1150.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −2.00000 | −0.384900 | −0.192450 | − | 0.981307i | \(-0.561643\pi\) | ||||
−0.192450 | + | 0.981307i | \(0.561643\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.00000 | 0.272166 | ||||||||
\(7\) | −21.0000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 47.0000 | 1.28828 | 0.644138 | − | 0.764909i | \(-0.277216\pi\) | ||||
0.644138 | + | 0.764909i | \(0.277216\pi\) | |||||||
\(12\) | −8.00000 | −0.192450 | ||||||||
\(13\) | −57.0000 | −1.21607 | −0.608037 | − | 0.793909i | \(-0.708043\pi\) | ||||
−0.608037 | + | 0.793909i | \(0.708043\pi\) | |||||||
\(14\) | 42.0000 | 0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 84.0000 | 1.19841 | 0.599206 | − | 0.800595i | \(-0.295483\pi\) | ||||
0.599206 | + | 0.800595i | \(0.295483\pi\) | |||||||
\(18\) | 46.0000 | 0.602350 | ||||||||
\(19\) | −5.00000 | −0.0603726 | −0.0301863 | − | 0.999544i | \(-0.509610\pi\) | ||||
−0.0301863 | + | 0.999544i | \(0.509610\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 42.0000 | 0.436436 | ||||||||
\(22\) | −94.0000 | −0.910949 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 16.0000 | 0.136083 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 114.000 | 0.859894 | ||||||||
\(27\) | 100.000 | 0.712778 | ||||||||
\(28\) | −84.0000 | −0.566947 | ||||||||
\(29\) | 285.000 | 1.82494 | 0.912468 | − | 0.409147i | \(-0.134174\pi\) | ||||
0.912468 | + | 0.409147i | \(0.134174\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 82.0000 | 0.475085 | 0.237542 | − | 0.971377i | \(-0.423658\pi\) | ||||
0.237542 | + | 0.971377i | \(0.423658\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −94.0000 | −0.495858 | ||||||||
\(34\) | −168.000 | −0.847405 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −92.0000 | −0.425926 | ||||||||
\(37\) | 54.0000 | 0.239934 | 0.119967 | − | 0.992778i | \(-0.461721\pi\) | ||||
0.119967 | + | 0.992778i | \(0.461721\pi\) | |||||||
\(38\) | 10.0000 | 0.0426898 | ||||||||
\(39\) | 114.000 | 0.468067 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −53.0000 | −0.201883 | −0.100942 | − | 0.994892i | \(-0.532186\pi\) | ||||
−0.100942 | + | 0.994892i | \(0.532186\pi\) | |||||||
\(42\) | −84.0000 | −0.308607 | ||||||||
\(43\) | −197.000 | −0.698656 | −0.349328 | − | 0.937000i | \(-0.613590\pi\) | ||||
−0.349328 | + | 0.937000i | \(0.613590\pi\) | |||||||
\(44\) | 188.000 | 0.644138 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 124.000 | 0.384835 | 0.192418 | − | 0.981313i | \(-0.438367\pi\) | ||||
0.192418 | + | 0.981313i | \(0.438367\pi\) | |||||||
\(48\) | −32.0000 | −0.0962250 | ||||||||
\(49\) | 98.0000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −168.000 | −0.461269 | ||||||||
\(52\) | −228.000 | −0.608037 | ||||||||
\(53\) | 148.000 | 0.383573 | 0.191786 | − | 0.981437i | \(-0.438572\pi\) | ||||
0.191786 | + | 0.981437i | \(0.438572\pi\) | |||||||
\(54\) | −200.000 | −0.504010 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 168.000 | 0.400892 | ||||||||
\(57\) | 10.0000 | 0.0232374 | ||||||||
\(58\) | −570.000 | −1.29043 | ||||||||
\(59\) | 30.0000 | 0.0661978 | 0.0330989 | − | 0.999452i | \(-0.489462\pi\) | ||||
0.0330989 | + | 0.999452i | \(0.489462\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −578.000 | −1.21320 | −0.606601 | − | 0.795006i | \(-0.707467\pi\) | ||||
−0.606601 | + | 0.795006i | \(0.707467\pi\) | |||||||
\(62\) | −164.000 | −0.335936 | ||||||||
\(63\) | 483.000 | 0.965909 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 188.000 | 0.350624 | ||||||||
\(67\) | −296.000 | −0.539734 | −0.269867 | − | 0.962898i | \(-0.586980\pi\) | ||||
−0.269867 | + | 0.962898i | \(0.586980\pi\) | |||||||
\(68\) | 336.000 | 0.599206 | ||||||||
\(69\) | 46.0000 | 0.0802572 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 422.000 | 0.705383 | 0.352691 | − | 0.935740i | \(-0.385267\pi\) | ||||
0.352691 | + | 0.935740i | \(0.385267\pi\) | |||||||
\(72\) | 184.000 | 0.301175 | ||||||||
\(73\) | −487.000 | −0.780809 | −0.390404 | − | 0.920643i | \(-0.627665\pi\) | ||||
−0.390404 | + | 0.920643i | \(0.627665\pi\) | |||||||
\(74\) | −108.000 | −0.169659 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.0000 | −0.0301863 | ||||||||
\(77\) | −987.000 | −1.46077 | ||||||||
\(78\) | −228.000 | −0.330973 | ||||||||
\(79\) | −405.000 | −0.576786 | −0.288393 | − | 0.957512i | \(-0.593121\pi\) | ||||
−0.288393 | + | 0.957512i | \(0.593121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | 106.000 | 0.142753 | ||||||||
\(83\) | −397.000 | −0.525017 | −0.262509 | − | 0.964930i | \(-0.584550\pi\) | ||||
−0.262509 | + | 0.964930i | \(0.584550\pi\) | |||||||
\(84\) | 168.000 | 0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 394.000 | 0.494025 | ||||||||
\(87\) | −570.000 | −0.702419 | ||||||||
\(88\) | −376.000 | −0.455474 | ||||||||
\(89\) | 730.000 | 0.869436 | 0.434718 | − | 0.900567i | \(-0.356848\pi\) | ||||
0.434718 | + | 0.900567i | \(0.356848\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1197.00 | 1.37890 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −164.000 | −0.182860 | ||||||||
\(94\) | −248.000 | −0.272120 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 64.0000 | 0.0680414 | ||||||||
\(97\) | 64.0000 | 0.0669919 | 0.0334960 | − | 0.999439i | \(-0.489336\pi\) | ||||
0.0334960 | + | 0.999439i | \(0.489336\pi\) | |||||||
\(98\) | −196.000 | −0.202031 | ||||||||
\(99\) | −1081.00 | −1.09742 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1002.00 | 0.987156 | 0.493578 | − | 0.869702i | \(-0.335689\pi\) | ||||
0.493578 | + | 0.869702i | \(0.335689\pi\) | |||||||
\(102\) | 336.000 | 0.326166 | ||||||||
\(103\) | −1807.00 | −1.72863 | −0.864316 | − | 0.502950i | \(-0.832248\pi\) | ||||
−0.864316 | + | 0.502950i | \(0.832248\pi\) | |||||||
\(104\) | 456.000 | 0.429947 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −296.000 | −0.271227 | ||||||||
\(107\) | 1664.00 | 1.50341 | 0.751705 | − | 0.659499i | \(-0.229232\pi\) | ||||
0.751705 | + | 0.659499i | \(0.229232\pi\) | |||||||
\(108\) | 400.000 | 0.356389 | ||||||||
\(109\) | 470.000 | 0.413008 | 0.206504 | − | 0.978446i | \(-0.433791\pi\) | ||||
0.206504 | + | 0.978446i | \(0.433791\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −108.000 | −0.0923505 | ||||||||
\(112\) | −336.000 | −0.283473 | ||||||||
\(113\) | −992.000 | −0.825836 | −0.412918 | − | 0.910768i | \(-0.635490\pi\) | ||||
−0.412918 | + | 0.910768i | \(0.635490\pi\) | |||||||
\(114\) | −20.0000 | −0.0164313 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1140.00 | 0.912468 | ||||||||
\(117\) | 1311.00 | 1.03591 | ||||||||
\(118\) | −60.0000 | −0.0468089 | ||||||||
\(119\) | −1764.00 | −1.35887 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 878.000 | 0.659654 | ||||||||
\(122\) | 1156.00 | 0.857863 | ||||||||
\(123\) | 106.000 | 0.0777049 | ||||||||
\(124\) | 328.000 | 0.237542 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −966.000 | −0.683001 | ||||||||
\(127\) | 2274.00 | 1.58886 | 0.794429 | − | 0.607358i | \(-0.207770\pi\) | ||||
0.794429 | + | 0.607358i | \(0.207770\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 394.000 | 0.268913 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1802.00 | 1.20184 | 0.600922 | − | 0.799308i | \(-0.294800\pi\) | ||||
0.600922 | + | 0.799308i | \(0.294800\pi\) | |||||||
\(132\) | −376.000 | −0.247929 | ||||||||
\(133\) | 105.000 | 0.0684561 | ||||||||
\(134\) | 592.000 | 0.381649 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −672.000 | −0.423702 | ||||||||
\(137\) | −106.000 | −0.0661036 | −0.0330518 | − | 0.999454i | \(-0.510523\pi\) | ||||
−0.0330518 | + | 0.999454i | \(0.510523\pi\) | |||||||
\(138\) | −92.0000 | −0.0567504 | ||||||||
\(139\) | −2700.00 | −1.64756 | −0.823781 | − | 0.566909i | \(-0.808139\pi\) | ||||
−0.823781 | + | 0.566909i | \(0.808139\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −248.000 | −0.148123 | ||||||||
\(142\) | −844.000 | −0.498781 | ||||||||
\(143\) | −2679.00 | −1.56664 | ||||||||
\(144\) | −368.000 | −0.212963 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 974.000 | 0.552115 | ||||||||
\(147\) | −196.000 | −0.109971 | ||||||||
\(148\) | 216.000 | 0.119967 | ||||||||
\(149\) | −890.000 | −0.489340 | −0.244670 | − | 0.969606i | \(-0.578680\pi\) | ||||
−0.244670 | + | 0.969606i | \(0.578680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3398.00 | −1.83129 | −0.915647 | − | 0.401984i | \(-0.868321\pi\) | ||||
−0.915647 | + | 0.401984i | \(0.868321\pi\) | |||||||
\(152\) | 40.0000 | 0.0213449 | ||||||||
\(153\) | −1932.00 | −1.02087 | ||||||||
\(154\) | 1974.00 | 1.03292 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 456.000 | 0.234033 | ||||||||
\(157\) | −2976.00 | −1.51281 | −0.756403 | − | 0.654105i | \(-0.773045\pi\) | ||||
−0.756403 | + | 0.654105i | \(0.773045\pi\) | |||||||
\(158\) | 810.000 | 0.407849 | ||||||||
\(159\) | −296.000 | −0.147637 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 483.000 | 0.236433 | ||||||||
\(162\) | −842.000 | −0.408357 | ||||||||
\(163\) | −512.000 | −0.246030 | −0.123015 | − | 0.992405i | \(-0.539256\pi\) | ||||
−0.123015 | + | 0.992405i | \(0.539256\pi\) | |||||||
\(164\) | −212.000 | −0.100942 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 794.000 | 0.371243 | ||||||||
\(167\) | −1426.00 | −0.660762 | −0.330381 | − | 0.943848i | \(-0.607177\pi\) | ||||
−0.330381 | + | 0.943848i | \(0.607177\pi\) | |||||||
\(168\) | −336.000 | −0.154303 | ||||||||
\(169\) | 1052.00 | 0.478835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 115.000 | 0.0514285 | ||||||||
\(172\) | −788.000 | −0.349328 | ||||||||
\(173\) | −1047.00 | −0.460127 | −0.230063 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230063 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(174\) | 1140.00 | 0.496685 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 752.000 | 0.322069 | ||||||||
\(177\) | −60.0000 | −0.0254795 | ||||||||
\(178\) | −1460.00 | −0.614784 | ||||||||
\(179\) | −1380.00 | −0.576235 | −0.288117 | − | 0.957595i | \(-0.593029\pi\) | ||||
−0.288117 | + | 0.957595i | \(0.593029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1332.00 | 0.546999 | 0.273499 | − | 0.961872i | \(-0.411819\pi\) | ||||
0.273499 | + | 0.961872i | \(0.411819\pi\) | |||||||
\(182\) | −2394.00 | −0.975028 | ||||||||
\(183\) | 1156.00 | 0.466962 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 328.000 | 0.129302 | ||||||||
\(187\) | 3948.00 | 1.54388 | ||||||||
\(188\) | 496.000 | 0.192418 | ||||||||
\(189\) | −2100.00 | −0.808214 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1297.00 | 0.491349 | 0.245674 | − | 0.969352i | \(-0.420991\pi\) | ||||
0.245674 | + | 0.969352i | \(0.420991\pi\) | |||||||
\(192\) | −128.000 | −0.0481125 | ||||||||
\(193\) | −3902.00 | −1.45530 | −0.727648 | − | 0.685951i | \(-0.759387\pi\) | ||||
−0.727648 | + | 0.685951i | \(0.759387\pi\) | |||||||
\(194\) | −128.000 | −0.0473704 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 392.000 | 0.142857 | ||||||||
\(197\) | 149.000 | 0.0538874 | 0.0269437 | − | 0.999637i | \(-0.491423\pi\) | ||||
0.0269437 | + | 0.999637i | \(0.491423\pi\) | |||||||
\(198\) | 2162.00 | 0.775993 | ||||||||
\(199\) | −525.000 | −0.187016 | −0.0935082 | − | 0.995619i | \(-0.529808\pi\) | ||||
−0.0935082 | + | 0.995619i | \(0.529808\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 592.000 | 0.207744 | ||||||||
\(202\) | −2004.00 | −0.698024 | ||||||||
\(203\) | −5985.00 | −2.06928 | ||||||||
\(204\) | −672.000 | −0.230634 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3614.00 | 1.22233 | ||||||||
\(207\) | 529.000 | 0.177623 | ||||||||
\(208\) | −912.000 | −0.304018 | ||||||||
\(209\) | −235.000 | −0.0777765 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3518.00 | −1.14782 | −0.573908 | − | 0.818920i | \(-0.694573\pi\) | ||||
−0.573908 | + | 0.818920i | \(0.694573\pi\) | |||||||
\(212\) | 592.000 | 0.191786 | ||||||||
\(213\) | −844.000 | −0.271502 | ||||||||
\(214\) | −3328.00 | −1.06307 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −800.000 | −0.252005 | ||||||||
\(217\) | −1722.00 | −0.538696 | ||||||||
\(218\) | −940.000 | −0.292041 | ||||||||
\(219\) | 974.000 | 0.300533 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4788.00 | −1.45736 | ||||||||
\(222\) | 216.000 | 0.0653017 | ||||||||
\(223\) | 2968.00 | 0.891264 | 0.445632 | − | 0.895216i | \(-0.352979\pi\) | ||||
0.445632 | + | 0.895216i | \(0.352979\pi\) | |||||||
\(224\) | 672.000 | 0.200446 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1984.00 | 0.583954 | ||||||||
\(227\) | −4036.00 | −1.18008 | −0.590041 | − | 0.807373i | \(-0.700889\pi\) | ||||
−0.590041 | + | 0.807373i | \(0.700889\pi\) | |||||||
\(228\) | 40.0000 | 0.0116187 | ||||||||
\(229\) | −4190.00 | −1.20910 | −0.604548 | − | 0.796569i | \(-0.706646\pi\) | ||||
−0.604548 | + | 0.796569i | \(0.706646\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1974.00 | 0.562250 | ||||||||
\(232\) | −2280.00 | −0.645213 | ||||||||
\(233\) | −977.000 | −0.274701 | −0.137351 | − | 0.990522i | \(-0.543859\pi\) | ||||
−0.137351 | + | 0.990522i | \(0.543859\pi\) | |||||||
\(234\) | −2622.00 | −0.732502 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 120.000 | 0.0330989 | ||||||||
\(237\) | 810.000 | 0.222005 | ||||||||
\(238\) | 3528.00 | 0.960867 | ||||||||
\(239\) | −3740.00 | −1.01222 | −0.506110 | − | 0.862469i | \(-0.668917\pi\) | ||||
−0.506110 | + | 0.862469i | \(0.668917\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3692.00 | 0.986816 | 0.493408 | − | 0.869798i | \(-0.335751\pi\) | ||||
0.493408 | + | 0.869798i | \(0.335751\pi\) | |||||||
\(242\) | −1756.00 | −0.466446 | ||||||||
\(243\) | −3542.00 | −0.935059 | ||||||||
\(244\) | −2312.00 | −0.606601 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −212.000 | −0.0549456 | ||||||||
\(247\) | 285.000 | 0.0734175 | ||||||||
\(248\) | −656.000 | −0.167968 | ||||||||
\(249\) | 794.000 | 0.202079 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6468.00 | −1.62652 | −0.813260 | − | 0.581900i | \(-0.802309\pi\) | ||||
−0.813260 | + | 0.581900i | \(0.802309\pi\) | |||||||
\(252\) | 1932.00 | 0.482955 | ||||||||
\(253\) | −1081.00 | −0.268624 | ||||||||
\(254\) | −4548.00 | −1.12349 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5586.00 | −1.35582 | −0.677909 | − | 0.735146i | \(-0.737114\pi\) | ||||
−0.677909 | + | 0.735146i | \(0.737114\pi\) | |||||||
\(258\) | −788.000 | −0.190150 | ||||||||
\(259\) | −1134.00 | −0.272059 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6555.00 | −1.55458 | ||||||||
\(262\) | −3604.00 | −0.849832 | ||||||||
\(263\) | 6208.00 | 1.45552 | 0.727760 | − | 0.685832i | \(-0.240562\pi\) | ||||
0.727760 | + | 0.685832i | \(0.240562\pi\) | |||||||
\(264\) | 752.000 | 0.175312 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −210.000 | −0.0484057 | ||||||||
\(267\) | −1460.00 | −0.334646 | ||||||||
\(268\) | −1184.00 | −0.269867 | ||||||||
\(269\) | −7895.00 | −1.78947 | −0.894734 | − | 0.446600i | \(-0.852635\pi\) | ||||
−0.894734 | + | 0.446600i | \(0.852635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −68.0000 | −0.0152425 | −0.00762123 | − | 0.999971i | \(-0.502426\pi\) | ||||
−0.00762123 | + | 0.999971i | \(0.502426\pi\) | |||||||
\(272\) | 1344.00 | 0.299603 | ||||||||
\(273\) | −2394.00 | −0.530738 | ||||||||
\(274\) | 212.000 | 0.0467423 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 184.000 | 0.0401286 | ||||||||
\(277\) | 5289.00 | 1.14724 | 0.573620 | − | 0.819122i | \(-0.305539\pi\) | ||||
0.573620 | + | 0.819122i | \(0.305539\pi\) | |||||||
\(278\) | 5400.00 | 1.16500 | ||||||||
\(279\) | −1886.00 | −0.404702 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3408.00 | −0.723503 | −0.361751 | − | 0.932275i | \(-0.617821\pi\) | ||||
−0.361751 | + | 0.932275i | \(0.617821\pi\) | |||||||
\(282\) | 496.000 | 0.104739 | ||||||||
\(283\) | 1828.00 | 0.383969 | 0.191985 | − | 0.981398i | \(-0.438508\pi\) | ||||
0.191985 | + | 0.981398i | \(0.438508\pi\) | |||||||
\(284\) | 1688.00 | 0.352691 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5358.00 | 1.10778 | ||||||||
\(287\) | 1113.00 | 0.228914 | ||||||||
\(288\) | 736.000 | 0.150588 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −128.000 | −0.0257852 | ||||||||
\(292\) | −1948.00 | −0.390404 | ||||||||
\(293\) | 6388.00 | 1.27369 | 0.636845 | − | 0.770992i | \(-0.280239\pi\) | ||||
0.636845 | + | 0.770992i | \(0.280239\pi\) | |||||||
\(294\) | 392.000 | 0.0777616 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −432.000 | −0.0848294 | ||||||||
\(297\) | 4700.00 | 0.918255 | ||||||||
\(298\) | 1780.00 | 0.346016 | ||||||||
\(299\) | 1311.00 | 0.253569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4137.00 | 0.792202 | ||||||||
\(302\) | 6796.00 | 1.29492 | ||||||||
\(303\) | −2004.00 | −0.379956 | ||||||||
\(304\) | −80.0000 | −0.0150931 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3864.00 | 0.721863 | ||||||||
\(307\) | −5016.00 | −0.932502 | −0.466251 | − | 0.884652i | \(-0.654396\pi\) | ||||
−0.466251 | + | 0.884652i | \(0.654396\pi\) | |||||||
\(308\) | −3948.00 | −0.730384 | ||||||||
\(309\) | 3614.00 | 0.665350 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5542.00 | 1.01048 | 0.505238 | − | 0.862980i | \(-0.331405\pi\) | ||||
0.505238 | + | 0.862980i | \(0.331405\pi\) | |||||||
\(312\) | −912.000 | −0.165487 | ||||||||
\(313\) | 3838.00 | 0.693088 | 0.346544 | − | 0.938034i | \(-0.387355\pi\) | ||||
0.346544 | + | 0.938034i | \(0.387355\pi\) | |||||||
\(314\) | 5952.00 | 1.06972 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1620.00 | −0.288393 | ||||||||
\(317\) | −9771.00 | −1.73121 | −0.865606 | − | 0.500726i | \(-0.833066\pi\) | ||||
−0.865606 | + | 0.500726i | \(0.833066\pi\) | |||||||
\(318\) | 592.000 | 0.104395 | ||||||||
\(319\) | 13395.0 | 2.35102 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3328.00 | −0.578663 | ||||||||
\(322\) | −966.000 | −0.167183 | ||||||||
\(323\) | −420.000 | −0.0723512 | ||||||||
\(324\) | 1684.00 | 0.288752 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1024.00 | 0.173970 | ||||||||
\(327\) | −940.000 | −0.158967 | ||||||||
\(328\) | 424.000 | 0.0713765 | ||||||||
\(329\) | −2604.00 | −0.436362 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3982.00 | 0.661240 | 0.330620 | − | 0.943764i | \(-0.392742\pi\) | ||||
0.330620 | + | 0.943764i | \(0.392742\pi\) | |||||||
\(332\) | −1588.00 | −0.262509 | ||||||||
\(333\) | −1242.00 | −0.204388 | ||||||||
\(334\) | 2852.00 | 0.467229 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 672.000 | 0.109109 | ||||||||
\(337\) | −536.000 | −0.0866403 | −0.0433201 | − | 0.999061i | \(-0.513794\pi\) | ||||
−0.0433201 | + | 0.999061i | \(0.513794\pi\) | |||||||
\(338\) | −2104.00 | −0.338587 | ||||||||
\(339\) | 1984.00 | 0.317865 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3854.00 | 0.612040 | ||||||||
\(342\) | −230.000 | −0.0363654 | ||||||||
\(343\) | 5145.00 | 0.809924 | ||||||||
\(344\) | 1576.00 | 0.247012 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2094.00 | 0.325359 | ||||||||
\(347\) | 8024.00 | 1.24136 | 0.620679 | − | 0.784065i | \(-0.286857\pi\) | ||||
0.620679 | + | 0.784065i | \(0.286857\pi\) | |||||||
\(348\) | −2280.00 | −0.351209 | ||||||||
\(349\) | −4675.00 | −0.717040 | −0.358520 | − | 0.933522i | \(-0.616719\pi\) | ||||
−0.358520 | + | 0.933522i | \(0.616719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5700.00 | −0.866791 | ||||||||
\(352\) | −1504.00 | −0.227737 | ||||||||
\(353\) | −10347.0 | −1.56010 | −0.780050 | − | 0.625717i | \(-0.784806\pi\) | ||||
−0.780050 | + | 0.625717i | \(0.784806\pi\) | |||||||
\(354\) | 120.000 | 0.0180167 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2920.00 | 0.434718 | ||||||||
\(357\) | 3528.00 | 0.523030 | ||||||||
\(358\) | 2760.00 | 0.407460 | ||||||||
\(359\) | 12715.0 | 1.86928 | 0.934641 | − | 0.355593i | \(-0.115721\pi\) | ||||
0.934641 | + | 0.355593i | \(0.115721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6834.00 | −0.996355 | ||||||||
\(362\) | −2664.00 | −0.386787 | ||||||||
\(363\) | −1756.00 | −0.253901 | ||||||||
\(364\) | 4788.00 | 0.689449 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2312.00 | −0.330192 | ||||||||
\(367\) | 7999.00 | 1.13772 | 0.568862 | − | 0.822433i | \(-0.307384\pi\) | ||||
0.568862 | + | 0.822433i | \(0.307384\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 1219.00 | 0.171975 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3108.00 | −0.434931 | ||||||||
\(372\) | −656.000 | −0.0914301 | ||||||||
\(373\) | 3588.00 | 0.498069 | 0.249034 | − | 0.968495i | \(-0.419887\pi\) | ||||
0.249034 | + | 0.968495i | \(0.419887\pi\) | |||||||
\(374\) | −7896.00 | −1.09169 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −992.000 | −0.136060 | ||||||||
\(377\) | −16245.0 | −2.21926 | ||||||||
\(378\) | 4200.00 | 0.571494 | ||||||||
\(379\) | −2060.00 | −0.279195 | −0.139598 | − | 0.990208i | \(-0.544581\pi\) | ||||
−0.139598 | + | 0.990208i | \(0.544581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4548.00 | −0.611551 | ||||||||
\(382\) | −2594.00 | −0.347436 | ||||||||
\(383\) | 9943.00 | 1.32654 | 0.663268 | − | 0.748382i | \(-0.269169\pi\) | ||||
0.663268 | + | 0.748382i | \(0.269169\pi\) | |||||||
\(384\) | 256.000 | 0.0340207 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7804.00 | 1.02905 | ||||||||
\(387\) | 4531.00 | 0.595152 | ||||||||
\(388\) | 256.000 | 0.0334960 | ||||||||
\(389\) | −14580.0 | −1.90035 | −0.950174 | − | 0.311720i | \(-0.899095\pi\) | ||||
−0.950174 | + | 0.311720i | \(0.899095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1932.00 | −0.249886 | ||||||||
\(392\) | −784.000 | −0.101015 | ||||||||
\(393\) | −3604.00 | −0.462590 | ||||||||
\(394\) | −298.000 | −0.0381041 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4324.00 | −0.548710 | ||||||||
\(397\) | 14594.0 | 1.84497 | 0.922483 | − | 0.386037i | \(-0.126156\pi\) | ||||
0.922483 | + | 0.386037i | \(0.126156\pi\) | |||||||
\(398\) | 1050.00 | 0.132241 | ||||||||
\(399\) | −210.000 | −0.0263487 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9702.00 | 1.20822 | 0.604108 | − | 0.796902i | \(-0.293529\pi\) | ||||
0.604108 | + | 0.796902i | \(0.293529\pi\) | |||||||
\(402\) | −1184.00 | −0.146897 | ||||||||
\(403\) | −4674.00 | −0.577738 | ||||||||
\(404\) | 4008.00 | 0.493578 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11970.0 | 1.46320 | ||||||||
\(407\) | 2538.00 | 0.309101 | ||||||||
\(408\) | 1344.00 | 0.163083 | ||||||||
\(409\) | −14315.0 | −1.73064 | −0.865319 | − | 0.501221i | \(-0.832884\pi\) | ||||
−0.865319 | + | 0.501221i | \(0.832884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 212.000 | 0.0254433 | ||||||||
\(412\) | −7228.00 | −0.864316 | ||||||||
\(413\) | −630.000 | −0.0750612 | ||||||||
\(414\) | −1058.00 | −0.125599 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1824.00 | 0.214973 | ||||||||
\(417\) | 5400.00 | 0.634147 | ||||||||
\(418\) | 470.000 | 0.0549963 | ||||||||
\(419\) | −975.000 | −0.113680 | −0.0568399 | − | 0.998383i | \(-0.518102\pi\) | ||||
−0.0568399 | + | 0.998383i | \(0.518102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11138.0 | −1.28939 | −0.644695 | − | 0.764440i | \(-0.723015\pi\) | ||||
−0.644695 | + | 0.764440i | \(0.723015\pi\) | |||||||
\(422\) | 7036.00 | 0.811628 | ||||||||
\(423\) | −2852.00 | −0.327823 | ||||||||
\(424\) | −1184.00 | −0.135613 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1688.00 | 0.191981 | ||||||||
\(427\) | 12138.0 | 1.37564 | ||||||||
\(428\) | 6656.00 | 0.751705 | ||||||||
\(429\) | 5358.00 | 0.602999 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9568.00 | −1.06931 | −0.534657 | − | 0.845069i | \(-0.679559\pi\) | ||||
−0.534657 | + | 0.845069i | \(0.679559\pi\) | |||||||
\(432\) | 1600.00 | 0.178195 | ||||||||
\(433\) | −1762.00 | −0.195557 | −0.0977787 | − | 0.995208i | \(-0.531174\pi\) | ||||
−0.0977787 | + | 0.995208i | \(0.531174\pi\) | |||||||
\(434\) | 3444.00 | 0.380915 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1880.00 | 0.206504 | ||||||||
\(437\) | 115.000 | 0.0125885 | ||||||||
\(438\) | −1948.00 | −0.212509 | ||||||||
\(439\) | 4080.00 | 0.443571 | 0.221786 | − | 0.975095i | \(-0.428811\pi\) | ||||
0.221786 | + | 0.975095i | \(0.428811\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2254.00 | −0.243386 | ||||||||
\(442\) | 9576.00 | 1.03051 | ||||||||
\(443\) | −9582.00 | −1.02766 | −0.513831 | − | 0.857891i | \(-0.671774\pi\) | ||||
−0.513831 | + | 0.857891i | \(0.671774\pi\) | |||||||
\(444\) | −432.000 | −0.0461753 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5936.00 | −0.630219 | ||||||||
\(447\) | 1780.00 | 0.188347 | ||||||||
\(448\) | −1344.00 | −0.141737 | ||||||||
\(449\) | −3290.00 | −0.345801 | −0.172901 | − | 0.984939i | \(-0.555314\pi\) | ||||
−0.172901 | + | 0.984939i | \(0.555314\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2491.00 | −0.260081 | ||||||||
\(452\) | −3968.00 | −0.412918 | ||||||||
\(453\) | 6796.00 | 0.704865 | ||||||||
\(454\) | 8072.00 | 0.834444 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −80.0000 | −0.00821567 | ||||||||
\(457\) | 484.000 | 0.0495417 | 0.0247709 | − | 0.999693i | \(-0.492114\pi\) | ||||
0.0247709 | + | 0.999693i | \(0.492114\pi\) | |||||||
\(458\) | 8380.00 | 0.854960 | ||||||||
\(459\) | 8400.00 | 0.854201 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10243.0 | −1.03485 | −0.517423 | − | 0.855730i | \(-0.673109\pi\) | ||||
−0.517423 | + | 0.855730i | \(0.673109\pi\) | |||||||
\(462\) | −3948.00 | −0.397571 | ||||||||
\(463\) | 6208.00 | 0.623132 | 0.311566 | − | 0.950224i | \(-0.399146\pi\) | ||||
0.311566 | + | 0.950224i | \(0.399146\pi\) | |||||||
\(464\) | 4560.00 | 0.456234 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1954.00 | 0.194243 | ||||||||
\(467\) | 6089.00 | 0.603352 | 0.301676 | − | 0.953411i | \(-0.402454\pi\) | ||||
0.301676 | + | 0.953411i | \(0.402454\pi\) | |||||||
\(468\) | 5244.00 | 0.517957 | ||||||||
\(469\) | 6216.00 | 0.612000 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5952.00 | 0.582280 | ||||||||
\(472\) | −240.000 | −0.0234044 | ||||||||
\(473\) | −9259.00 | −0.900062 | ||||||||
\(474\) | −1620.00 | −0.156981 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7056.00 | −0.679435 | ||||||||
\(477\) | −3404.00 | −0.326747 | ||||||||
\(478\) | 7480.00 | 0.715747 | ||||||||
\(479\) | 8145.00 | 0.776941 | 0.388470 | − | 0.921461i | \(-0.373004\pi\) | ||||
0.388470 | + | 0.921461i | \(0.373004\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3078.00 | −0.291777 | ||||||||
\(482\) | −7384.00 | −0.697784 | ||||||||
\(483\) | −966.000 | −0.0910032 | ||||||||
\(484\) | 3512.00 | 0.329827 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7084.00 | 0.661187 | ||||||||
\(487\) | −1096.00 | −0.101980 | −0.0509902 | − | 0.998699i | \(-0.516238\pi\) | ||||
−0.0509902 | + | 0.998699i | \(0.516238\pi\) | |||||||
\(488\) | 4624.00 | 0.428932 | ||||||||
\(489\) | 1024.00 | 0.0946971 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15318.0 | −1.40793 | −0.703963 | − | 0.710237i | \(-0.748588\pi\) | ||||
−0.703963 | + | 0.710237i | \(0.748588\pi\) | |||||||
\(492\) | 424.000 | 0.0388524 | ||||||||
\(493\) | 23940.0 | 2.18703 | ||||||||
\(494\) | −570.000 | −0.0519140 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1312.00 | 0.118771 | ||||||||
\(497\) | −8862.00 | −0.799829 | ||||||||
\(498\) | −1588.00 | −0.142892 | ||||||||
\(499\) | −7440.00 | −0.667455 | −0.333728 | − | 0.942670i | \(-0.608307\pi\) | ||||
−0.333728 | + | 0.942670i | \(0.608307\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2852.00 | 0.254327 | ||||||||
\(502\) | 12936.0 | 1.15012 | ||||||||
\(503\) | −6147.00 | −0.544893 | −0.272447 | − | 0.962171i | \(-0.587833\pi\) | ||||
−0.272447 | + | 0.962171i | \(0.587833\pi\) | |||||||
\(504\) | −3864.00 | −0.341500 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2162.00 | 0.189946 | ||||||||
\(507\) | −2104.00 | −0.184304 | ||||||||
\(508\) | 9096.00 | 0.794429 | ||||||||
\(509\) | 1590.00 | 0.138459 | 0.0692294 | − | 0.997601i | \(-0.477946\pi\) | ||||
0.0692294 | + | 0.997601i | \(0.477946\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10227.0 | 0.885354 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −500.000 | −0.0430322 | ||||||||
\(514\) | 11172.0 | 0.958708 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1576.00 | 0.134456 | ||||||||
\(517\) | 5828.00 | 0.495774 | ||||||||
\(518\) | 2268.00 | 0.192375 | ||||||||
\(519\) | 2094.00 | 0.177103 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16638.0 | −1.39909 | −0.699543 | − | 0.714590i | \(-0.746613\pi\) | ||||
−0.699543 | + | 0.714590i | \(0.746613\pi\) | |||||||
\(522\) | 13110.0 | 1.09925 | ||||||||
\(523\) | 4453.00 | 0.372306 | 0.186153 | − | 0.982521i | \(-0.440398\pi\) | ||||
0.186153 | + | 0.982521i | \(0.440398\pi\) | |||||||
\(524\) | 7208.00 | 0.600922 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12416.0 | −1.02921 | ||||||||
\(527\) | 6888.00 | 0.569347 | ||||||||
\(528\) | −1504.00 | −0.123964 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −690.000 | −0.0563907 | ||||||||
\(532\) | 420.000 | 0.0342280 | ||||||||
\(533\) | 3021.00 | 0.245505 | ||||||||
\(534\) | 2920.00 | 0.236631 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2368.00 | 0.190825 | ||||||||
\(537\) | 2760.00 | 0.221793 | ||||||||
\(538\) | 15790.0 | 1.26534 | ||||||||
\(539\) | 4606.00 | 0.368079 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18077.0 | 1.43658 | 0.718291 | − | 0.695743i | \(-0.244925\pi\) | ||||
0.718291 | + | 0.695743i | \(0.244925\pi\) | |||||||
\(542\) | 136.000 | 0.0107780 | ||||||||
\(543\) | −2664.00 | −0.210540 | ||||||||
\(544\) | −2688.00 | −0.211851 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4788.00 | 0.375288 | ||||||||
\(547\) | 6644.00 | 0.519336 | 0.259668 | − | 0.965698i | \(-0.416387\pi\) | ||||
0.259668 | + | 0.965698i | \(0.416387\pi\) | |||||||
\(548\) | −424.000 | −0.0330518 | ||||||||
\(549\) | 13294.0 | 1.03347 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1425.00 | −0.110176 | ||||||||
\(552\) | −368.000 | −0.0283752 | ||||||||
\(553\) | 8505.00 | 0.654013 | ||||||||
\(554\) | −10578.0 | −0.811220 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10800.0 | −0.823781 | ||||||||
\(557\) | 6954.00 | 0.528995 | 0.264498 | − | 0.964386i | \(-0.414794\pi\) | ||||
0.264498 | + | 0.964386i | \(0.414794\pi\) | |||||||
\(558\) | 3772.00 | 0.286168 | ||||||||
\(559\) | 11229.0 | 0.849617 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7896.00 | −0.594241 | ||||||||
\(562\) | 6816.00 | 0.511594 | ||||||||
\(563\) | −77.0000 | −0.00576406 | −0.00288203 | − | 0.999996i | \(-0.500917\pi\) | ||||
−0.00288203 | + | 0.999996i | \(0.500917\pi\) | |||||||
\(564\) | −992.000 | −0.0740616 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3656.00 | −0.271507 | ||||||||
\(567\) | −8841.00 | −0.654827 | ||||||||
\(568\) | −3376.00 | −0.249391 | ||||||||
\(569\) | 14820.0 | 1.09189 | 0.545946 | − | 0.837820i | \(-0.316170\pi\) | ||||
0.545946 | + | 0.837820i | \(0.316170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2492.00 | 0.182639 | 0.0913196 | − | 0.995822i | \(-0.470892\pi\) | ||||
0.0913196 | + | 0.995822i | \(0.470892\pi\) | |||||||
\(572\) | −10716.0 | −0.783319 | ||||||||
\(573\) | −2594.00 | −0.189120 | ||||||||
\(574\) | −2226.00 | −0.161867 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1472.00 | −0.106481 | ||||||||
\(577\) | 5929.00 | 0.427777 | 0.213889 | − | 0.976858i | \(-0.431387\pi\) | ||||
0.213889 | + | 0.976858i | \(0.431387\pi\) | |||||||
\(578\) | −4286.00 | −0.308433 | ||||||||
\(579\) | 7804.00 | 0.560144 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8337.00 | 0.595313 | ||||||||
\(582\) | 256.000 | 0.0182329 | ||||||||
\(583\) | 6956.00 | 0.494148 | ||||||||
\(584\) | 3896.00 | 0.276058 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12776.0 | −0.900634 | ||||||||
\(587\) | 7274.00 | 0.511465 | 0.255733 | − | 0.966748i | \(-0.417683\pi\) | ||||
0.255733 | + | 0.966748i | \(0.417683\pi\) | |||||||
\(588\) | −784.000 | −0.0549857 | ||||||||
\(589\) | −410.000 | −0.0286821 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −298.000 | −0.0207413 | ||||||||
\(592\) | 864.000 | 0.0599834 | ||||||||
\(593\) | 5823.00 | 0.403241 | 0.201621 | − | 0.979464i | \(-0.435379\pi\) | ||||
0.201621 | + | 0.979464i | \(0.435379\pi\) | |||||||
\(594\) | −9400.00 | −0.649304 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3560.00 | −0.244670 | ||||||||
\(597\) | 1050.00 | 0.0719826 | ||||||||
\(598\) | −2622.00 | −0.179300 | ||||||||
\(599\) | 10430.0 | 0.711449 | 0.355725 | − | 0.934591i | \(-0.384234\pi\) | ||||
0.355725 | + | 0.934591i | \(0.384234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18998.0 | −1.28943 | −0.644713 | − | 0.764425i | \(-0.723023\pi\) | ||||
−0.644713 | + | 0.764425i | \(0.723023\pi\) | |||||||
\(602\) | −8274.00 | −0.560171 | ||||||||
\(603\) | 6808.00 | 0.459773 | ||||||||
\(604\) | −13592.0 | −0.915647 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4008.00 | 0.268670 | ||||||||
\(607\) | −26416.0 | −1.76638 | −0.883190 | − | 0.469016i | \(-0.844609\pi\) | ||||
−0.883190 | + | 0.469016i | \(0.844609\pi\) | |||||||
\(608\) | 160.000 | 0.0106725 | ||||||||
\(609\) | 11970.0 | 0.796468 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7068.00 | −0.467988 | ||||||||
\(612\) | −7728.00 | −0.510434 | ||||||||
\(613\) | −27262.0 | −1.79625 | −0.898125 | − | 0.439739i | \(-0.855071\pi\) | ||||
−0.898125 | + | 0.439739i | \(0.855071\pi\) | |||||||
\(614\) | 10032.0 | 0.659379 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7896.00 | 0.516459 | ||||||||
\(617\) | 25584.0 | 1.66932 | 0.834662 | − | 0.550762i | \(-0.185663\pi\) | ||||
0.834662 | + | 0.550762i | \(0.185663\pi\) | |||||||
\(618\) | −7228.00 | −0.470474 | ||||||||
\(619\) | −3640.00 | −0.236355 | −0.118178 | − | 0.992992i | \(-0.537705\pi\) | ||||
−0.118178 | + | 0.992992i | \(0.537705\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2300.00 | −0.148625 | ||||||||
\(622\) | −11084.0 | −0.714514 | ||||||||
\(623\) | −15330.0 | −0.985848 | ||||||||
\(624\) | 1824.00 | 0.117017 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7676.00 | −0.490087 | ||||||||
\(627\) | 470.000 | 0.0299362 | ||||||||
\(628\) | −11904.0 | −0.756403 | ||||||||
\(629\) | 4536.00 | 0.287539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19937.0 | 1.25781 | 0.628906 | − | 0.777481i | \(-0.283503\pi\) | ||||
0.628906 | + | 0.777481i | \(0.283503\pi\) | |||||||
\(632\) | 3240.00 | 0.203924 | ||||||||
\(633\) | 7036.00 | 0.441794 | ||||||||
\(634\) | 19542.0 | 1.22415 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1184.00 | −0.0738186 | ||||||||
\(637\) | −5586.00 | −0.347450 | ||||||||
\(638\) | −26790.0 | −1.66242 | ||||||||
\(639\) | −9706.00 | −0.600882 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14048.0 | −0.865620 | −0.432810 | − | 0.901485i | \(-0.642478\pi\) | ||||
−0.432810 | + | 0.901485i | \(0.642478\pi\) | |||||||
\(642\) | 6656.00 | 0.409177 | ||||||||
\(643\) | 13423.0 | 0.823253 | 0.411626 | − | 0.911353i | \(-0.364961\pi\) | ||||
0.411626 | + | 0.911353i | \(0.364961\pi\) | |||||||
\(644\) | 1932.00 | 0.118217 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 840.000 | 0.0511600 | ||||||||
\(647\) | 9024.00 | 0.548331 | 0.274165 | − | 0.961683i | \(-0.411598\pi\) | ||||
0.274165 | + | 0.961683i | \(0.411598\pi\) | |||||||
\(648\) | −3368.00 | −0.204178 | ||||||||
\(649\) | 1410.00 | 0.0852810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3444.00 | 0.207344 | ||||||||
\(652\) | −2048.00 | −0.123015 | ||||||||
\(653\) | 11263.0 | 0.674970 | 0.337485 | − | 0.941331i | \(-0.390424\pi\) | ||||
0.337485 | + | 0.941331i | \(0.390424\pi\) | |||||||
\(654\) | 1880.00 | 0.112406 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −848.000 | −0.0504708 | ||||||||
\(657\) | 11201.0 | 0.665133 | ||||||||
\(658\) | 5208.00 | 0.308555 | ||||||||
\(659\) | 7425.00 | 0.438903 | 0.219451 | − | 0.975623i | \(-0.429573\pi\) | ||||
0.219451 | + | 0.975623i | \(0.429573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2032.00 | 0.119570 | 0.0597849 | − | 0.998211i | \(-0.480959\pi\) | ||||
0.0597849 | + | 0.998211i | \(0.480959\pi\) | |||||||
\(662\) | −7964.00 | −0.467567 | ||||||||
\(663\) | 9576.00 | 0.560937 | ||||||||
\(664\) | 3176.00 | 0.185622 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2484.00 | 0.144524 | ||||||||
\(667\) | −6555.00 | −0.380526 | ||||||||
\(668\) | −5704.00 | −0.330381 | ||||||||
\(669\) | −5936.00 | −0.343048 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27166.0 | −1.56294 | ||||||||
\(672\) | −1344.00 | −0.0771517 | ||||||||
\(673\) | 11903.0 | 0.681764 | 0.340882 | − | 0.940106i | \(-0.389274\pi\) | ||||
0.340882 | + | 0.940106i | \(0.389274\pi\) | |||||||
\(674\) | 1072.00 | 0.0612639 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4208.00 | 0.239417 | ||||||||
\(677\) | 18654.0 | 1.05898 | 0.529491 | − | 0.848315i | \(-0.322383\pi\) | ||||
0.529491 | + | 0.848315i | \(0.322383\pi\) | |||||||
\(678\) | −3968.00 | −0.224764 | ||||||||
\(679\) | −1344.00 | −0.0759617 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8072.00 | 0.454214 | ||||||||
\(682\) | −7708.00 | −0.432778 | ||||||||
\(683\) | −23302.0 | −1.30546 | −0.652728 | − | 0.757592i | \(-0.726375\pi\) | ||||
−0.652728 | + | 0.757592i | \(0.726375\pi\) | |||||||
\(684\) | 460.000 | 0.0257142 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10290.0 | −0.572703 | ||||||||
\(687\) | 8380.00 | 0.465381 | ||||||||
\(688\) | −3152.00 | −0.174664 | ||||||||
\(689\) | −8436.00 | −0.466453 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16472.0 | 0.906837 | 0.453419 | − | 0.891298i | \(-0.350204\pi\) | ||||
0.453419 | + | 0.891298i | \(0.350204\pi\) | |||||||
\(692\) | −4188.00 | −0.230063 | ||||||||
\(693\) | 22701.0 | 1.24436 | ||||||||
\(694\) | −16048.0 | −0.877772 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4560.00 | 0.248342 | ||||||||
\(697\) | −4452.00 | −0.241939 | ||||||||
\(698\) | 9350.00 | 0.507024 | ||||||||
\(699\) | 1954.00 | 0.105733 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19008.0 | −1.02414 | −0.512070 | − | 0.858944i | \(-0.671121\pi\) | ||||
−0.512070 | + | 0.858944i | \(0.671121\pi\) | |||||||
\(702\) | 11400.0 | 0.612913 | ||||||||
\(703\) | −270.000 | −0.0144854 | ||||||||
\(704\) | 3008.00 | 0.161034 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20694.0 | 1.10316 | ||||||||
\(707\) | −21042.0 | −1.11933 | ||||||||
\(708\) | −240.000 | −0.0127398 | ||||||||
\(709\) | −35870.0 | −1.90004 | −0.950018 | − | 0.312194i | \(-0.898936\pi\) | ||||
−0.950018 | + | 0.312194i | \(0.898936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9315.00 | 0.491336 | ||||||||
\(712\) | −5840.00 | −0.307392 | ||||||||
\(713\) | −1886.00 | −0.0990621 | ||||||||
\(714\) | −7056.00 | −0.369838 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5520.00 | −0.288117 | ||||||||
\(717\) | 7480.00 | 0.389604 | ||||||||
\(718\) | −25430.0 | −1.32178 | ||||||||
\(719\) | 37610.0 | 1.95079 | 0.975394 | − | 0.220470i | \(-0.0707590\pi\) | ||||
0.975394 | + | 0.220470i | \(0.0707590\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37947.0 | 1.96008 | ||||||||
\(722\) | 13668.0 | 0.704529 | ||||||||
\(723\) | −7384.00 | −0.379826 | ||||||||
\(724\) | 5328.00 | 0.273499 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3512.00 | 0.179535 | ||||||||
\(727\) | −26176.0 | −1.33537 | −0.667685 | − | 0.744444i | \(-0.732715\pi\) | ||||
−0.667685 | + | 0.744444i | \(0.732715\pi\) | |||||||
\(728\) | −9576.00 | −0.487514 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16548.0 | −0.837278 | ||||||||
\(732\) | 4624.00 | 0.233481 | ||||||||
\(733\) | 17238.0 | 0.868622 | 0.434311 | − | 0.900763i | \(-0.356992\pi\) | ||||
0.434311 | + | 0.900763i | \(0.356992\pi\) | |||||||
\(734\) | −15998.0 | −0.804492 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −13912.0 | −0.695326 | ||||||||
\(738\) | −2438.00 | −0.121604 | ||||||||
\(739\) | −5910.00 | −0.294185 | −0.147093 | − | 0.989123i | \(-0.546992\pi\) | ||||
−0.147093 | + | 0.989123i | \(0.546992\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −570.000 | −0.0282584 | ||||||||
\(742\) | 6216.00 | 0.307543 | ||||||||
\(743\) | 31203.0 | 1.54068 | 0.770341 | − | 0.637632i | \(-0.220086\pi\) | ||||
0.770341 | + | 0.637632i | \(0.220086\pi\) | |||||||
\(744\) | 1312.00 | 0.0646509 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7176.00 | −0.352188 | ||||||||
\(747\) | 9131.00 | 0.447237 | ||||||||
\(748\) | 15792.0 | 0.771942 | ||||||||
\(749\) | −34944.0 | −1.70471 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36643.0 | −1.78046 | −0.890228 | − | 0.455516i | \(-0.849455\pi\) | ||||
−0.890228 | + | 0.455516i | \(0.849455\pi\) | |||||||
\(752\) | 1984.00 | 0.0962088 | ||||||||
\(753\) | 12936.0 | 0.626048 | ||||||||
\(754\) | 32490.0 | 1.56925 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8400.00 | −0.404107 | ||||||||
\(757\) | −846.000 | −0.0406187 | −0.0203094 | − | 0.999794i | \(-0.506465\pi\) | ||||
−0.0203094 | + | 0.999794i | \(0.506465\pi\) | |||||||
\(758\) | 4120.00 | 0.197421 | ||||||||
\(759\) | 2162.00 | 0.103393 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11303.0 | −0.538414 | −0.269207 | − | 0.963082i | \(-0.586762\pi\) | ||||
−0.269207 | + | 0.963082i | \(0.586762\pi\) | |||||||
\(762\) | 9096.00 | 0.432432 | ||||||||
\(763\) | −9870.00 | −0.468307 | ||||||||
\(764\) | 5188.00 | 0.245674 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19886.0 | −0.938003 | ||||||||
\(767\) | −1710.00 | −0.0805013 | ||||||||
\(768\) | −512.000 | −0.0240563 | ||||||||
\(769\) | −31830.0 | −1.49261 | −0.746306 | − | 0.665603i | \(-0.768175\pi\) | ||||
−0.746306 | + | 0.665603i | \(0.768175\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11172.0 | 0.521854 | ||||||||
\(772\) | −15608.0 | −0.727648 | ||||||||
\(773\) | −15562.0 | −0.724096 | −0.362048 | − | 0.932159i | \(-0.617922\pi\) | ||||
−0.362048 | + | 0.932159i | \(0.617922\pi\) | |||||||
\(774\) | −9062.00 | −0.420836 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −512.000 | −0.0236852 | ||||||||
\(777\) | 2268.00 | 0.104716 | ||||||||
\(778\) | 29160.0 | 1.34375 | ||||||||
\(779\) | 265.000 | 0.0121882 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19834.0 | 0.908728 | ||||||||
\(782\) | 3864.00 | 0.176696 | ||||||||
\(783\) | 28500.0 | 1.30078 | ||||||||
\(784\) | 1568.00 | 0.0714286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7208.00 | 0.327100 | ||||||||
\(787\) | −24771.0 | −1.12197 | −0.560985 | − | 0.827826i | \(-0.689578\pi\) | ||||
−0.560985 | + | 0.827826i | \(0.689578\pi\) | |||||||
\(788\) | 596.000 | 0.0269437 | ||||||||
\(789\) | −12416.0 | −0.560230 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20832.0 | 0.936410 | ||||||||
\(792\) | 8648.00 | 0.387997 | ||||||||
\(793\) | 32946.0 | 1.47534 | ||||||||
\(794\) | −29188.0 | −1.30459 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2100.00 | −0.0935082 | ||||||||
\(797\) | −24486.0 | −1.08825 | −0.544127 | − | 0.839003i | \(-0.683139\pi\) | ||||
−0.544127 | + | 0.839003i | \(0.683139\pi\) | |||||||
\(798\) | 420.000 | 0.0186314 | ||||||||
\(799\) | 10416.0 | 0.461191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16790.0 | −0.740631 | ||||||||
\(802\) | −19404.0 | −0.854338 | ||||||||
\(803\) | −22889.0 | −1.00590 | ||||||||
\(804\) | 2368.00 | 0.103872 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9348.00 | 0.408523 | ||||||||
\(807\) | 15790.0 | 0.688766 | ||||||||
\(808\) | −8016.00 | −0.349012 | ||||||||
\(809\) | 24705.0 | 1.07365 | 0.536824 | − | 0.843694i | \(-0.319624\pi\) | ||||
0.536824 | + | 0.843694i | \(0.319624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6392.00 | 0.276761 | 0.138381 | − | 0.990379i | \(-0.455810\pi\) | ||||
0.138381 | + | 0.990379i | \(0.455810\pi\) | |||||||
\(812\) | −23940.0 | −1.03464 | ||||||||
\(813\) | 136.000 | 0.00586682 | ||||||||
\(814\) | −5076.00 | −0.218567 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2688.00 | −0.115317 | ||||||||
\(817\) | 985.000 | 0.0421797 | ||||||||
\(818\) | 28630.0 | 1.22375 | ||||||||
\(819\) | −27531.0 | −1.17462 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39047.0 | 1.65987 | 0.829933 | − | 0.557863i | \(-0.188379\pi\) | ||||
0.829933 | + | 0.557863i | \(0.188379\pi\) | |||||||
\(822\) | −424.000 | −0.0179911 | ||||||||
\(823\) | 14348.0 | 0.607703 | 0.303852 | − | 0.952719i | \(-0.401727\pi\) | ||||
0.303852 | + | 0.952719i | \(0.401727\pi\) | |||||||
\(824\) | 14456.0 | 0.611163 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1260.00 | 0.0530763 | ||||||||
\(827\) | 23749.0 | 0.998590 | 0.499295 | − | 0.866432i | \(-0.333592\pi\) | ||||
0.499295 | + | 0.866432i | \(0.333592\pi\) | |||||||
\(828\) | 2116.00 | 0.0888117 | ||||||||
\(829\) | 25125.0 | 1.05263 | 0.526313 | − | 0.850291i | \(-0.323574\pi\) | ||||
0.526313 | + | 0.850291i | \(0.323574\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10578.0 | −0.441573 | ||||||||
\(832\) | −3648.00 | −0.152009 | ||||||||
\(833\) | 8232.00 | 0.342403 | ||||||||
\(834\) | −10800.0 | −0.448409 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −940.000 | −0.0388883 | ||||||||
\(837\) | 8200.00 | 0.338630 | ||||||||
\(838\) | 1950.00 | 0.0803838 | ||||||||
\(839\) | −32295.0 | −1.32890 | −0.664450 | − | 0.747333i | \(-0.731334\pi\) | ||||
−0.664450 | + | 0.747333i | \(0.731334\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56836.0 | 2.33039 | ||||||||
\(842\) | 22276.0 | 0.911736 | ||||||||
\(843\) | 6816.00 | 0.278476 | ||||||||
\(844\) | −14072.0 | −0.573908 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5704.00 | 0.231806 | ||||||||
\(847\) | −18438.0 | −0.747978 | ||||||||
\(848\) | 2368.00 | 0.0958932 | ||||||||
\(849\) | −3656.00 | −0.147790 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1242.00 | −0.0500296 | ||||||||
\(852\) | −3376.00 | −0.135751 | ||||||||
\(853\) | −29257.0 | −1.17437 | −0.587187 | − | 0.809451i | \(-0.699765\pi\) | ||||
−0.587187 | + | 0.809451i | \(0.699765\pi\) | |||||||
\(854\) | −24276.0 | −0.972726 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13312.0 | −0.531536 | ||||||||
\(857\) | −11766.0 | −0.468984 | −0.234492 | − | 0.972118i | \(-0.575343\pi\) | ||||
−0.234492 | + | 0.972118i | \(0.575343\pi\) | |||||||
\(858\) | −10716.0 | −0.426385 | ||||||||
\(859\) | −32390.0 | −1.28653 | −0.643267 | − | 0.765642i | \(-0.722421\pi\) | ||||
−0.643267 | + | 0.765642i | \(0.722421\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2226.00 | −0.0881090 | ||||||||
\(862\) | 19136.0 | 0.756119 | ||||||||
\(863\) | −16332.0 | −0.644204 | −0.322102 | − | 0.946705i | \(-0.604389\pi\) | ||||
−0.322102 | + | 0.946705i | \(0.604389\pi\) | |||||||
\(864\) | −3200.00 | −0.126003 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3524.00 | 0.138280 | ||||||||
\(867\) | −4286.00 | −0.167889 | ||||||||
\(868\) | −6888.00 | −0.269348 | ||||||||
\(869\) | −19035.0 | −0.743059 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16872.0 | 0.656356 | ||||||||
\(872\) | −3760.00 | −0.146020 | ||||||||
\(873\) | −1472.00 | −0.0570672 | ||||||||
\(874\) | −230.000 | −0.00890145 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3896.00 | 0.150267 | ||||||||
\(877\) | −42226.0 | −1.62585 | −0.812925 | − | 0.582368i | \(-0.802126\pi\) | ||||
−0.812925 | + | 0.582368i | \(0.802126\pi\) | |||||||
\(878\) | −8160.00 | −0.313652 | ||||||||
\(879\) | −12776.0 | −0.490243 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7158.00 | −0.273733 | −0.136867 | − | 0.990589i | \(-0.543703\pi\) | ||||
−0.136867 | + | 0.990589i | \(0.543703\pi\) | |||||||
\(882\) | 4508.00 | 0.172100 | ||||||||
\(883\) | −28672.0 | −1.09274 | −0.546370 | − | 0.837544i | \(-0.683991\pi\) | ||||
−0.546370 | + | 0.837544i | \(0.683991\pi\) | |||||||
\(884\) | −19152.0 | −0.728678 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19164.0 | 0.726667 | ||||||||
\(887\) | −5536.00 | −0.209561 | −0.104781 | − | 0.994495i | \(-0.533414\pi\) | ||||
−0.104781 | + | 0.994495i | \(0.533414\pi\) | |||||||
\(888\) | 864.000 | 0.0326508 | ||||||||
\(889\) | −47754.0 | −1.80159 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19787.0 | 0.743984 | ||||||||
\(892\) | 11872.0 | 0.445632 | ||||||||
\(893\) | −620.000 | −0.0232335 | ||||||||
\(894\) | −3560.00 | −0.133181 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2688.00 | 0.100223 | ||||||||
\(897\) | −2622.00 | −0.0975987 | ||||||||
\(898\) | 6580.00 | 0.244518 | ||||||||
\(899\) | 23370.0 | 0.867000 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12432.0 | 0.459678 | ||||||||
\(902\) | 4982.00 | 0.183905 | ||||||||
\(903\) | −8274.00 | −0.304919 | ||||||||
\(904\) | 7936.00 | 0.291977 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13592.0 | −0.498415 | ||||||||
\(907\) | −451.000 | −0.0165107 | −0.00825535 | − | 0.999966i | \(-0.502628\pi\) | ||||
−0.00825535 | + | 0.999966i | \(0.502628\pi\) | |||||||
\(908\) | −16144.0 | −0.590041 | ||||||||
\(909\) | −23046.0 | −0.840910 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21013.0 | −0.764206 | −0.382103 | − | 0.924120i | \(-0.624800\pi\) | ||||
−0.382103 | + | 0.924120i | \(0.624800\pi\) | |||||||
\(912\) | 160.000 | 0.00580935 | ||||||||
\(913\) | −18659.0 | −0.676367 | ||||||||
\(914\) | −968.000 | −0.0350313 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16760.0 | −0.604548 | ||||||||
\(917\) | −37842.0 | −1.36276 | ||||||||
\(918\) | −16800.0 | −0.604012 | ||||||||
\(919\) | 28800.0 | 1.03376 | 0.516879 | − | 0.856058i | \(-0.327094\pi\) | ||||
0.516879 | + | 0.856058i | \(0.327094\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10032.0 | 0.358920 | ||||||||
\(922\) | 20486.0 | 0.731747 | ||||||||
\(923\) | −24054.0 | −0.857797 | ||||||||
\(924\) | 7896.00 | 0.281125 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12416.0 | −0.440621 | ||||||||
\(927\) | 41561.0 | 1.47254 | ||||||||
\(928\) | −9120.00 | −0.322606 | ||||||||
\(929\) | 39555.0 | 1.39694 | 0.698470 | − | 0.715639i | \(-0.253865\pi\) | ||||
0.698470 | + | 0.715639i | \(0.253865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −490.000 | −0.0172493 | ||||||||
\(932\) | −3908.00 | −0.137351 | ||||||||
\(933\) | −11084.0 | −0.388932 | ||||||||
\(934\) | −12178.0 | −0.426634 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10488.0 | −0.366251 | ||||||||
\(937\) | −38756.0 | −1.35123 | −0.675615 | − | 0.737254i | \(-0.736122\pi\) | ||||
−0.675615 | + | 0.737254i | \(0.736122\pi\) | |||||||
\(938\) | −12432.0 | −0.432750 | ||||||||
\(939\) | −7676.00 | −0.266770 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3968.00 | −0.137463 | −0.0687317 | − | 0.997635i | \(-0.521895\pi\) | ||||
−0.0687317 | + | 0.997635i | \(0.521895\pi\) | |||||||
\(942\) | −11904.0 | −0.411734 | ||||||||
\(943\) | 1219.00 | 0.0420955 | ||||||||
\(944\) | 480.000 | 0.0165494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18518.0 | 0.636440 | ||||||||
\(947\) | 32374.0 | 1.11089 | 0.555445 | − | 0.831553i | \(-0.312548\pi\) | ||||
0.555445 | + | 0.831553i | \(0.312548\pi\) | |||||||
\(948\) | 3240.00 | 0.111002 | ||||||||
\(949\) | 27759.0 | 0.949521 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19542.0 | 0.666344 | ||||||||
\(952\) | 14112.0 | 0.480433 | ||||||||
\(953\) | −23122.0 | −0.785934 | −0.392967 | − | 0.919553i | \(-0.628551\pi\) | ||||
−0.392967 | + | 0.919553i | \(0.628551\pi\) | |||||||
\(954\) | 6808.00 | 0.231045 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14960.0 | −0.506110 | ||||||||
\(957\) | −26790.0 | −0.904909 | ||||||||
\(958\) | −16290.0 | −0.549380 | ||||||||
\(959\) | 2226.00 | 0.0749544 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23067.0 | −0.774294 | ||||||||
\(962\) | 6156.00 | 0.206317 | ||||||||
\(963\) | −38272.0 | −1.28068 | ||||||||
\(964\) | 14768.0 | 0.493408 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1932.00 | 0.0643489 | ||||||||
\(967\) | −16916.0 | −0.562546 | −0.281273 | − | 0.959628i | \(-0.590757\pi\) | ||||
−0.281273 | + | 0.959628i | \(0.590757\pi\) | |||||||
\(968\) | −7024.00 | −0.233223 | ||||||||
\(969\) | 840.000 | 0.0278480 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32277.0 | 1.06675 | 0.533377 | − | 0.845878i | \(-0.320923\pi\) | ||||
0.533377 | + | 0.845878i | \(0.320923\pi\) | |||||||
\(972\) | −14168.0 | −0.467530 | ||||||||
\(973\) | 56700.0 | 1.86816 | ||||||||
\(974\) | 2192.00 | 0.0721111 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9248.00 | −0.303300 | ||||||||
\(977\) | −48076.0 | −1.57430 | −0.787148 | − | 0.616764i | \(-0.788443\pi\) | ||||
−0.787148 | + | 0.616764i | \(0.788443\pi\) | |||||||
\(978\) | −2048.00 | −0.0669610 | ||||||||
\(979\) | 34310.0 | 1.12007 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10810.0 | −0.351821 | ||||||||
\(982\) | 30636.0 | 0.995554 | ||||||||
\(983\) | −37287.0 | −1.20984 | −0.604919 | − | 0.796287i | \(-0.706794\pi\) | ||||
−0.604919 | + | 0.796287i | \(0.706794\pi\) | |||||||
\(984\) | −848.000 | −0.0274728 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −47880.0 | −1.54646 | ||||||||
\(987\) | 5208.00 | 0.167956 | ||||||||
\(988\) | 1140.00 | 0.0367087 | ||||||||
\(989\) | 4531.00 | 0.145680 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4872.00 | 0.156170 | 0.0780849 | − | 0.996947i | \(-0.475119\pi\) | ||||
0.0780849 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(992\) | −2624.00 | −0.0839840 | ||||||||
\(993\) | −7964.00 | −0.254511 | ||||||||
\(994\) | 17724.0 | 0.565565 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3176.00 | 0.101040 | ||||||||
\(997\) | −24751.0 | −0.786231 | −0.393115 | − | 0.919489i | \(-0.628603\pi\) | ||||
−0.393115 | + | 0.919489i | \(0.628603\pi\) | |||||||
\(998\) | 14880.0 | 0.471962 | ||||||||
\(999\) | 5400.00 | 0.171019 |
(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 | 1150.4.a.a.1.1 | ✓ | 1 | |
5.2 | odd | 4 | 1150.4.b.g.599.1 | 2 | |||
5.3 | odd | 4 | 1150.4.b.g.599.2 | 2 | |||
5.4 | even | 2 | 1150.4.a.h.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1150.4.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
1150.4.a.h.1.1 | yes | 1 | 5.4 | even | 2 | ||
1150.4.b.g.599.1 | 2 | 5.2 | odd | 4 | |||
1150.4.b.g.599.2 | 2 | 5.3 | odd | 4 |