Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, 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("882.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.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: | \(52.0396846251\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{193}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.44622\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 3.44622 | 0.308239 | 0.154120 | − | 0.988052i | \(-0.450746\pi\) | ||||
0.154120 | + | 0.988052i | \(0.450746\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.89244 | 0.217958 | ||||||||
\(11\) | −36.1236 | −0.990151 | −0.495076 | − | 0.868850i | \(-0.664860\pi\) | ||||
−0.495076 | + | 0.868850i | \(0.664860\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.2311 | 0.218277 | 0.109138 | − | 0.994027i | \(-0.465191\pi\) | ||||
0.109138 | + | 0.994027i | \(0.465191\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −118.462 | −1.69008 | −0.845038 | − | 0.534705i | \(-0.820423\pi\) | ||||
−0.845038 | + | 0.534705i | \(0.820423\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −38.6613 | −0.466817 | −0.233408 | − | 0.972379i | \(-0.574988\pi\) | ||||
−0.233408 | + | 0.972379i | \(0.574988\pi\) | |||||||
\(20\) | 13.7849 | 0.154120 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −72.2471 | −0.700143 | ||||||||
\(23\) | 36.2471 | 0.328611 | 0.164305 | − | 0.986410i | \(-0.447462\pi\) | ||||
0.164305 | + | 0.986410i | \(0.447462\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −113.124 | −0.904988 | ||||||||
\(26\) | 20.4622 | 0.154345 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 12.1236 | 0.0776306 | 0.0388153 | − | 0.999246i | \(-0.487642\pi\) | ||||
0.0388153 | + | 0.999246i | \(0.487642\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −145.494 | −0.842953 | −0.421476 | − | 0.906839i | \(-0.638488\pi\) | ||||
−0.421476 | + | 0.906839i | \(0.638488\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −236.924 | −1.19506 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.37066 | −0.00609015 | −0.00304507 | − | 0.999995i | \(-0.500969\pi\) | ||||
−0.00304507 | + | 0.999995i | \(0.500969\pi\) | |||||||
\(38\) | −77.3227 | −0.330089 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 27.5698 | 0.108979 | ||||||||
\(41\) | −168.000 | −0.639932 | −0.319966 | − | 0.947429i | \(-0.603671\pi\) | ||||
−0.319966 | + | 0.947429i | \(0.603671\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 299.371 | 1.06171 | 0.530856 | − | 0.847462i | \(-0.321871\pi\) | ||||
0.530856 | + | 0.847462i | \(0.321871\pi\) | |||||||
\(44\) | −144.494 | −0.495076 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 72.4942 | 0.232363 | ||||||||
\(47\) | −502.709 | −1.56016 | −0.780082 | − | 0.625678i | \(-0.784823\pi\) | ||||
−0.780082 | + | 0.625678i | \(0.784823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −226.247 | −0.639923 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 40.9244 | 0.109138 | ||||||||
\(53\) | 625.112 | 1.62011 | 0.810054 | − | 0.586355i | \(-0.199438\pi\) | ||||
0.810054 | + | 0.586355i | \(0.199438\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −124.490 | −0.305204 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24.2471 | 0.0548931 | ||||||||
\(59\) | 42.2195 | 0.0931613 | 0.0465806 | − | 0.998915i | \(-0.485168\pi\) | ||||
0.0465806 | + | 0.998915i | \(0.485168\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −439.172 | −0.921806 | −0.460903 | − | 0.887451i | \(-0.652474\pi\) | ||||
−0.460903 | + | 0.887451i | \(0.652474\pi\) | |||||||
\(62\) | −290.988 | −0.596058 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 35.2587 | 0.0672815 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −763.618 | −1.39240 | −0.696200 | − | 0.717848i | \(-0.745127\pi\) | ||||
−0.696200 | + | 0.717848i | \(0.745127\pi\) | |||||||
\(68\) | −473.849 | −0.845038 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1020.49 | −1.70578 | −0.852890 | − | 0.522091i | \(-0.825152\pi\) | ||||
−0.852890 | + | 0.522091i | \(0.825152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 579.284 | 0.928767 | 0.464384 | − | 0.885634i | \(-0.346276\pi\) | ||||
0.464384 | + | 0.885634i | \(0.346276\pi\) | |||||||
\(74\) | −2.74132 | −0.00430638 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −154.645 | −0.233408 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 942.730 | 1.34260 | 0.671300 | − | 0.741186i | \(-0.265736\pi\) | ||||
0.671300 | + | 0.741186i | \(0.265736\pi\) | |||||||
\(80\) | 55.1396 | 0.0770599 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −336.000 | −0.452500 | ||||||||
\(83\) | 474.714 | 0.627790 | 0.313895 | − | 0.949458i | \(-0.398366\pi\) | ||||
0.313895 | + | 0.949458i | \(0.398366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −408.247 | −0.520948 | ||||||||
\(86\) | 598.741 | 0.750743 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −288.988 | −0.350071 | ||||||||
\(89\) | −821.904 | −0.978895 | −0.489447 | − | 0.872033i | \(-0.662802\pi\) | ||||
−0.489447 | + | 0.872033i | \(0.662802\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 144.988 | 0.164305 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1005.42 | −1.10320 | ||||||||
\(95\) | −133.236 | −0.143891 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1108.16 | −1.15997 | −0.579985 | − | 0.814627i | \(-0.696942\pi\) | ||||
−0.579985 | + | 0.814627i | \(0.696942\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −452.494 | −0.452494 | ||||||||
\(101\) | −1885.92 | −1.85798 | −0.928991 | − | 0.370102i | \(-0.879323\pi\) | ||||
−0.928991 | + | 0.370102i | \(0.879323\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 482.144 | 0.461234 | 0.230617 | − | 0.973045i | \(-0.425926\pi\) | ||||
0.230617 | + | 0.973045i | \(0.425926\pi\) | |||||||
\(104\) | 81.8489 | 0.0771725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1250.22 | 1.14559 | ||||||||
\(107\) | 1730.59 | 1.56358 | 0.781789 | − | 0.623543i | \(-0.214307\pi\) | ||||
0.781789 | + | 0.623543i | \(0.214307\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1148.83 | 1.00952 | 0.504761 | − | 0.863259i | \(-0.331580\pi\) | ||||
0.504761 | + | 0.863259i | \(0.331580\pi\) | |||||||
\(110\) | −248.980 | −0.215812 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1331.51 | −1.10847 | −0.554237 | − | 0.832359i | \(-0.686990\pi\) | ||||
−0.554237 | + | 0.832359i | \(0.686990\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 124.916 | 0.101291 | ||||||||
\(116\) | 48.4942 | 0.0388153 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 84.4391 | 0.0658750 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −26.0888 | −0.0196009 | ||||||||
\(122\) | −878.343 | −0.651815 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −581.977 | −0.421476 | ||||||||
\(125\) | −820.627 | −0.587193 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −830.236 | −0.580090 | −0.290045 | − | 0.957013i | \(-0.593670\pi\) | ||||
−0.290045 | + | 0.957013i | \(0.593670\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 70.5174 | 0.0475752 | ||||||||
\(131\) | −1972.49 | −1.31555 | −0.657776 | − | 0.753214i | \(-0.728503\pi\) | ||||
−0.657776 | + | 0.753214i | \(0.728503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1527.24 | −0.984575 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −947.698 | −0.597532 | ||||||||
\(137\) | 68.7876 | 0.0428972 | 0.0214486 | − | 0.999770i | \(-0.493172\pi\) | ||||
0.0214486 | + | 0.999770i | \(0.493172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1864.48 | 1.13772 | 0.568860 | − | 0.822435i | \(-0.307385\pi\) | ||||
0.568860 | + | 0.822435i | \(0.307385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2040.99 | −1.20617 | ||||||||
\(143\) | −369.584 | −0.216127 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 41.7805 | 0.0239288 | ||||||||
\(146\) | 1158.57 | 0.656738 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.48265 | −0.00304507 | ||||||||
\(149\) | 20.2934 | 0.0111577 | 0.00557885 | − | 0.999984i | \(-0.498224\pi\) | ||||
0.00557885 | + | 0.999984i | \(0.498224\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1580.32 | −0.851689 | −0.425844 | − | 0.904796i | \(-0.640023\pi\) | ||||
−0.425844 | + | 0.904796i | \(0.640023\pi\) | |||||||
\(152\) | −309.291 | −0.165045 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −501.405 | −0.259831 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3384.35 | 1.72039 | 0.860193 | − | 0.509968i | \(-0.170343\pi\) | ||||
0.860193 | + | 0.509968i | \(0.170343\pi\) | |||||||
\(158\) | 1885.46 | 0.949361 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 110.279 | 0.0544896 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1571.71 | 0.755249 | 0.377624 | − | 0.925959i | \(-0.376741\pi\) | ||||
0.377624 | + | 0.925959i | \(0.376741\pi\) | |||||||
\(164\) | −672.000 | −0.319966 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 949.428 | 0.443915 | ||||||||
\(167\) | −2473.92 | −1.14633 | −0.573167 | − | 0.819439i | \(-0.694285\pi\) | ||||
−0.573167 | + | 0.819439i | \(0.694285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2092.32 | −0.952355 | ||||||||
\(170\) | −816.494 | −0.368366 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1197.48 | 0.530856 | ||||||||
\(173\) | −4151.34 | −1.82440 | −0.912198 | − | 0.409749i | \(-0.865616\pi\) | ||||
−0.912198 | + | 0.409749i | \(0.865616\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −577.977 | −0.247538 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1643.81 | −0.692183 | ||||||||
\(179\) | 4217.93 | 1.76125 | 0.880623 | − | 0.473818i | \(-0.157125\pi\) | ||||
0.880623 | + | 0.473818i | \(0.157125\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3504.65 | 1.43922 | 0.719609 | − | 0.694380i | \(-0.244321\pi\) | ||||
0.719609 | + | 0.694380i | \(0.244321\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 289.977 | 0.116181 | ||||||||
\(185\) | −4.72361 | −0.00187722 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4279.28 | 1.67343 | ||||||||
\(188\) | −2010.84 | −0.780082 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −266.471 | −0.101747 | ||||||||
\(191\) | −1982.97 | −0.751216 | −0.375608 | − | 0.926779i | \(-0.622566\pi\) | ||||
−0.375608 | + | 0.926779i | \(0.622566\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2111.74 | 0.787598 | 0.393799 | − | 0.919197i | \(-0.371161\pi\) | ||||
0.393799 | + | 0.919197i | \(0.371161\pi\) | |||||||
\(194\) | −2216.33 | −0.820222 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3932.65 | −1.42228 | −0.711141 | − | 0.703049i | \(-0.751821\pi\) | ||||
−0.711141 | + | 0.703049i | \(0.751821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −552.704 | −0.196885 | −0.0984426 | − | 0.995143i | \(-0.531386\pi\) | ||||
−0.0984426 | + | 0.995143i | \(0.531386\pi\) | |||||||
\(200\) | −904.988 | −0.319962 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3771.84 | −1.31379 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −578.965 | −0.197252 | ||||||||
\(206\) | 964.288 | 0.326141 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 163.698 | 0.0545692 | ||||||||
\(209\) | 1396.58 | 0.462219 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1720.90 | 0.561476 | 0.280738 | − | 0.959784i | \(-0.409421\pi\) | ||||
0.280738 | + | 0.959784i | \(0.409421\pi\) | |||||||
\(212\) | 2500.45 | 0.810054 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3461.19 | 1.10562 | ||||||||
\(215\) | 1031.70 | 0.327261 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2297.66 | 0.713840 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −497.959 | −0.152602 | ||||||||
\(221\) | −1212.00 | −0.368905 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4788.43 | 1.43793 | 0.718963 | − | 0.695049i | \(-0.244617\pi\) | ||||
0.718963 | + | 0.695049i | \(0.244617\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2663.01 | −0.783809 | ||||||||
\(227\) | −4087.59 | −1.19517 | −0.597584 | − | 0.801807i | \(-0.703872\pi\) | ||||
−0.597584 | + | 0.801807i | \(0.703872\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4066.61 | −1.17349 | −0.586745 | − | 0.809772i | \(-0.699591\pi\) | ||||
−0.586745 | + | 0.809772i | \(0.699591\pi\) | |||||||
\(230\) | 249.831 | 0.0716234 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 96.9884 | 0.0274466 | ||||||||
\(233\) | −178.270 | −0.0501239 | −0.0250620 | − | 0.999686i | \(-0.507978\pi\) | ||||
−0.0250620 | + | 0.999686i | \(0.507978\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1732.45 | −0.480904 | ||||||||
\(236\) | 168.878 | 0.0465806 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2118.67 | 0.573412 | 0.286706 | − | 0.958019i | \(-0.407440\pi\) | ||||
0.286706 | + | 0.958019i | \(0.407440\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2398.31 | 0.641031 | 0.320516 | − | 0.947243i | \(-0.396144\pi\) | ||||
0.320516 | + | 0.947243i | \(0.396144\pi\) | |||||||
\(242\) | −52.1777 | −0.0138600 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1756.69 | −0.460903 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −395.548 | −0.101895 | ||||||||
\(248\) | −1163.95 | −0.298029 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1641.25 | −0.415208 | ||||||||
\(251\) | 1550.76 | 0.389973 | 0.194986 | − | 0.980806i | \(-0.437534\pi\) | ||||
0.194986 | + | 0.980806i | \(0.437534\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1309.37 | −0.325374 | ||||||||
\(254\) | −1660.47 | −0.410186 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5395.44 | 1.30957 | 0.654783 | − | 0.755817i | \(-0.272760\pi\) | ||||
0.654783 | + | 0.755817i | \(0.272760\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 141.035 | 0.0336408 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3944.98 | −0.930235 | ||||||||
\(263\) | −3581.93 | −0.839815 | −0.419907 | − | 0.907567i | \(-0.637937\pi\) | ||||
−0.419907 | + | 0.907567i | \(0.637937\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2154.27 | 0.499381 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3054.47 | −0.696200 | ||||||||
\(269\) | 1175.55 | 0.266448 | 0.133224 | − | 0.991086i | \(-0.457467\pi\) | ||||
0.133224 | + | 0.991086i | \(0.457467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 259.327 | 0.0581291 | 0.0290646 | − | 0.999578i | \(-0.490747\pi\) | ||||
0.0290646 | + | 0.999578i | \(0.490747\pi\) | |||||||
\(272\) | −1895.40 | −0.422519 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 137.575 | 0.0303329 | ||||||||
\(275\) | 4086.42 | 0.896075 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1298.92 | −0.281750 | −0.140875 | − | 0.990027i | \(-0.544992\pi\) | ||||
−0.140875 | + | 0.990027i | \(0.544992\pi\) | |||||||
\(278\) | 3728.96 | 0.804489 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4524.25 | 0.960477 | 0.480238 | − | 0.877138i | \(-0.340550\pi\) | ||||
0.480238 | + | 0.877138i | \(0.340550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6478.05 | 1.36071 | 0.680354 | − | 0.732884i | \(-0.261826\pi\) | ||||
0.680354 | + | 0.732884i | \(0.261826\pi\) | |||||||
\(284\) | −4081.98 | −0.852890 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −739.168 | −0.152825 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9120.30 | 1.85636 | ||||||||
\(290\) | 83.5609 | 0.0169202 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2317.13 | 0.464384 | ||||||||
\(293\) | 2890.91 | 0.576413 | 0.288207 | − | 0.957568i | \(-0.406941\pi\) | ||||
0.288207 | + | 0.957568i | \(0.406941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 145.498 | 0.0287160 | ||||||||
\(296\) | −10.9653 | −0.00215319 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 40.5868 | 0.00788969 | ||||||||
\(299\) | 370.848 | 0.0717281 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3160.65 | −0.602235 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −618.581 | −0.116704 | ||||||||
\(305\) | −1513.48 | −0.284137 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3137.42 | −0.583264 | −0.291632 | − | 0.956531i | \(-0.594198\pi\) | ||||
−0.291632 | + | 0.956531i | \(0.594198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1002.81 | −0.183728 | ||||||||
\(311\) | 7914.95 | 1.44314 | 0.721568 | − | 0.692343i | \(-0.243422\pi\) | ||||
0.721568 | + | 0.692343i | \(0.243422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7616.61 | 1.37545 | 0.687726 | − | 0.725971i | \(-0.258609\pi\) | ||||
0.687726 | + | 0.725971i | \(0.258609\pi\) | |||||||
\(314\) | 6768.70 | 1.21650 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3770.92 | 0.671300 | ||||||||
\(317\) | 1991.49 | 0.352849 | 0.176425 | − | 0.984314i | \(-0.443547\pi\) | ||||
0.176425 | + | 0.984314i | \(0.443547\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −437.946 | −0.0768660 | ||||||||
\(320\) | 220.558 | 0.0385299 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4579.91 | 0.788956 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1157.38 | −0.197538 | ||||||||
\(326\) | 3143.41 | 0.534042 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1344.00 | −0.226250 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2848.63 | 0.473036 | 0.236518 | − | 0.971627i | \(-0.423994\pi\) | ||||
0.236518 | + | 0.971627i | \(0.423994\pi\) | |||||||
\(332\) | 1898.86 | 0.313895 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4947.84 | −0.810581 | ||||||||
\(335\) | −2631.60 | −0.429192 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5813.87 | −0.939768 | −0.469884 | − | 0.882728i | \(-0.655704\pi\) | ||||
−0.469884 | + | 0.882728i | \(0.655704\pi\) | |||||||
\(338\) | −4184.65 | −0.673417 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1632.99 | −0.260474 | ||||||||
\(341\) | 5255.77 | 0.834650 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2394.97 | 0.375372 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8302.68 | −1.29004 | ||||||||
\(347\) | −3435.10 | −0.531430 | −0.265715 | − | 0.964052i | \(-0.585608\pi\) | ||||
−0.265715 | + | 0.964052i | \(0.585608\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3034.99 | −0.465499 | −0.232750 | − | 0.972537i | \(-0.574772\pi\) | ||||
−0.232750 | + | 0.972537i | \(0.574772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1155.95 | −0.175036 | ||||||||
\(353\) | 8220.44 | 1.23946 | 0.619730 | − | 0.784815i | \(-0.287242\pi\) | ||||
0.619730 | + | 0.784815i | \(0.287242\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3516.85 | −0.525789 | ||||||||
\(356\) | −3287.62 | −0.489447 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8435.86 | 1.24539 | ||||||||
\(359\) | −9901.59 | −1.45567 | −0.727836 | − | 0.685752i | \(-0.759474\pi\) | ||||
−0.727836 | + | 0.685752i | \(0.759474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5364.30 | −0.782082 | ||||||||
\(362\) | 7009.29 | 1.01768 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1996.34 | 0.286283 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11028.0 | 1.56855 | 0.784276 | − | 0.620412i | \(-0.213035\pi\) | ||||
0.784276 | + | 0.620412i | \(0.213035\pi\) | |||||||
\(368\) | 579.954 | 0.0821527 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.44721 | −0.00132740 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2746.37 | −0.381238 | −0.190619 | − | 0.981664i | \(-0.561050\pi\) | ||||
−0.190619 | + | 0.981664i | \(0.561050\pi\) | |||||||
\(374\) | 8558.55 | 1.18329 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4021.67 | −0.551601 | ||||||||
\(377\) | 124.037 | 0.0169450 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4184.22 | −0.567095 | −0.283547 | − | 0.958958i | \(-0.591511\pi\) | ||||
−0.283547 | + | 0.958958i | \(0.591511\pi\) | |||||||
\(380\) | −532.942 | −0.0719457 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3965.93 | −0.531190 | ||||||||
\(383\) | 3060.58 | 0.408324 | 0.204162 | − | 0.978937i | \(-0.434553\pi\) | ||||
0.204162 | + | 0.978937i | \(0.434553\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4223.48 | 0.556916 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4432.66 | −0.579985 | ||||||||
\(389\) | 4919.61 | 0.641219 | 0.320610 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320610 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4293.91 | −0.555377 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7865.30 | −1.00571 | ||||||||
\(395\) | 3248.86 | 0.413842 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13173.3 | −1.66536 | −0.832678 | − | 0.553757i | \(-0.813194\pi\) | ||||
−0.832678 | + | 0.553757i | \(0.813194\pi\) | |||||||
\(398\) | −1105.41 | −0.139219 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1809.98 | −0.226247 | ||||||||
\(401\) | −2662.38 | −0.331553 | −0.165777 | − | 0.986163i | \(-0.553013\pi\) | ||||
−0.165777 | + | 0.986163i | \(0.553013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1488.57 | −0.183997 | ||||||||
\(404\) | −7543.69 | −0.928991 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 49.5132 | 0.00603016 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12992.2 | −1.57071 | −0.785357 | − | 0.619043i | \(-0.787521\pi\) | ||||
−0.785357 | + | 0.619043i | \(0.787521\pi\) | |||||||
\(410\) | −1157.93 | −0.139478 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1928.58 | 0.230617 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1635.97 | 0.193510 | ||||||||
\(416\) | 327.396 | 0.0385863 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2793.17 | 0.326838 | ||||||||
\(419\) | 7236.96 | 0.843791 | 0.421896 | − | 0.906644i | \(-0.361365\pi\) | ||||
0.421896 | + | 0.906644i | \(0.361365\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3706.07 | 0.429032 | 0.214516 | − | 0.976720i | \(-0.431183\pi\) | ||||
0.214516 | + | 0.976720i | \(0.431183\pi\) | |||||||
\(422\) | 3441.79 | 0.397023 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5000.90 | 0.572795 | ||||||||
\(425\) | 13400.9 | 1.52950 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6922.38 | 0.781789 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2063.40 | 0.231409 | ||||||||
\(431\) | −6382.38 | −0.713291 | −0.356645 | − | 0.934240i | \(-0.616080\pi\) | ||||
−0.356645 | + | 0.934240i | \(0.616080\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7275.62 | −0.807492 | −0.403746 | − | 0.914871i | \(-0.632292\pi\) | ||||
−0.403746 | + | 0.914871i | \(0.632292\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4595.32 | 0.504761 | ||||||||
\(437\) | −1401.36 | −0.153401 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9760.36 | 1.06113 | 0.530566 | − | 0.847644i | \(-0.321980\pi\) | ||||
0.530566 | + | 0.847644i | \(0.321980\pi\) | |||||||
\(440\) | −995.918 | −0.107906 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2424.00 | −0.260855 | ||||||||
\(443\) | −5733.16 | −0.614877 | −0.307439 | − | 0.951568i | \(-0.599472\pi\) | ||||
−0.307439 | + | 0.951568i | \(0.599472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2832.46 | −0.301734 | ||||||||
\(446\) | 9576.87 | 1.01677 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16628.4 | 1.74775 | 0.873877 | − | 0.486147i | \(-0.161598\pi\) | ||||
0.873877 | + | 0.486147i | \(0.161598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6068.76 | 0.633629 | ||||||||
\(452\) | −5326.02 | −0.554237 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8175.18 | −0.845111 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17119.3 | 1.75231 | 0.876157 | − | 0.482027i | \(-0.160099\pi\) | ||||
0.876157 | + | 0.482027i | \(0.160099\pi\) | |||||||
\(458\) | −8133.22 | −0.829782 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 499.662 | 0.0506454 | ||||||||
\(461\) | −6956.95 | −0.702858 | −0.351429 | − | 0.936215i | \(-0.614304\pi\) | ||||
−0.351429 | + | 0.936215i | \(0.614304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6594.47 | 0.661924 | 0.330962 | − | 0.943644i | \(-0.392627\pi\) | ||||
0.330962 | + | 0.943644i | \(0.392627\pi\) | |||||||
\(464\) | 193.977 | 0.0194077 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −356.540 | −0.0354430 | ||||||||
\(467\) | 14465.8 | 1.43340 | 0.716700 | − | 0.697381i | \(-0.245652\pi\) | ||||
0.716700 | + | 0.697381i | \(0.245652\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3464.90 | −0.340050 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 337.756 | 0.0329375 | ||||||||
\(473\) | −10814.3 | −1.05125 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4373.51 | 0.422464 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4237.34 | 0.405464 | ||||||||
\(479\) | −4075.47 | −0.388754 | −0.194377 | − | 0.980927i | \(-0.562268\pi\) | ||||
−0.194377 | + | 0.980927i | \(0.562268\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.0234 | −0.00132934 | ||||||||
\(482\) | 4796.61 | 0.453277 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −104.355 | −0.00980047 | ||||||||
\(485\) | −3818.98 | −0.357548 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4378.79 | 0.407437 | 0.203719 | − | 0.979029i | \(-0.434697\pi\) | ||||
0.203719 | + | 0.979029i | \(0.434697\pi\) | |||||||
\(488\) | −3513.37 | −0.325908 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6612.37 | 0.607764 | 0.303882 | − | 0.952710i | \(-0.401717\pi\) | ||||
0.303882 | + | 0.952710i | \(0.401717\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1436.18 | −0.131202 | ||||||||
\(494\) | −791.097 | −0.0720509 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2327.91 | −0.210738 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11456.4 | −1.02778 | −0.513888 | − | 0.857857i | \(-0.671795\pi\) | ||||
−0.513888 | + | 0.857857i | \(0.671795\pi\) | |||||||
\(500\) | −3282.51 | −0.293596 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3101.52 | 0.275752 | ||||||||
\(503\) | 7697.10 | 0.682300 | 0.341150 | − | 0.940009i | \(-0.389184\pi\) | ||||
0.341150 | + | 0.940009i | \(0.389184\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6499.30 | −0.572704 | ||||||||
\(506\) | −2618.75 | −0.230074 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3320.94 | −0.290045 | ||||||||
\(509\) | −4623.97 | −0.402659 | −0.201330 | − | 0.979524i | \(-0.564526\pi\) | ||||
−0.201330 | + | 0.979524i | \(0.564526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10790.9 | 0.926003 | ||||||||
\(515\) | 1661.58 | 0.142170 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18159.6 | 1.54480 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 282.069 | 0.0237876 | ||||||||
\(521\) | −3486.70 | −0.293196 | −0.146598 | − | 0.989196i | \(-0.546832\pi\) | ||||
−0.146598 | + | 0.989196i | \(0.546832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4415.13 | −0.369140 | −0.184570 | − | 0.982819i | \(-0.559089\pi\) | ||||
−0.184570 | + | 0.982819i | \(0.559089\pi\) | |||||||
\(524\) | −7889.96 | −0.657776 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7163.86 | −0.593839 | ||||||||
\(527\) | 17235.6 | 1.42465 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10853.1 | −0.892015 | ||||||||
\(530\) | 4308.55 | 0.353116 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1718.83 | −0.139682 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5964.01 | 0.481957 | ||||||||
\(536\) | −6108.94 | −0.492288 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2351.10 | 0.188407 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10804.5 | −0.858634 | −0.429317 | − | 0.903154i | \(-0.641246\pi\) | ||||
−0.429317 | + | 0.903154i | \(0.641246\pi\) | |||||||
\(542\) | 518.654 | 0.0411035 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3790.79 | −0.298766 | ||||||||
\(545\) | 3959.12 | 0.311175 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18783.4 | 1.46823 | 0.734113 | − | 0.679027i | \(-0.237598\pi\) | ||||
0.734113 | + | 0.679027i | \(0.237598\pi\) | |||||||
\(548\) | 275.150 | 0.0214486 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8172.85 | 0.633621 | ||||||||
\(551\) | −468.713 | −0.0362393 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2597.85 | −0.199227 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7457.91 | 0.568860 | ||||||||
\(557\) | −1451.14 | −0.110389 | −0.0551944 | − | 0.998476i | \(-0.517578\pi\) | ||||
−0.0551944 | + | 0.998476i | \(0.517578\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3062.89 | 0.231747 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9048.49 | 0.679160 | ||||||||
\(563\) | 16781.1 | 1.25620 | 0.628098 | − | 0.778134i | \(-0.283834\pi\) | ||||
0.628098 | + | 0.778134i | \(0.283834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4588.66 | −0.341675 | ||||||||
\(566\) | 12956.1 | 0.962165 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8163.95 | −0.603084 | ||||||||
\(569\) | −14722.8 | −1.08473 | −0.542367 | − | 0.840142i | \(-0.682472\pi\) | ||||
−0.542367 | + | 0.840142i | \(0.682472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9717.12 | 0.712169 | 0.356085 | − | 0.934454i | \(-0.384111\pi\) | ||||
0.356085 | + | 0.934454i | \(0.384111\pi\) | |||||||
\(572\) | −1478.34 | −0.108064 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4100.40 | −0.297389 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20188.9 | −1.45663 | −0.728313 | − | 0.685244i | \(-0.759695\pi\) | ||||
−0.728313 | + | 0.685244i | \(0.759695\pi\) | |||||||
\(578\) | 18240.6 | 1.31264 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 167.122 | 0.0119644 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22581.3 | −1.60415 | ||||||||
\(584\) | 4634.27 | 0.328369 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5781.83 | 0.407586 | ||||||||
\(587\) | −21720.8 | −1.52728 | −0.763641 | − | 0.645641i | \(-0.776590\pi\) | ||||
−0.763641 | + | 0.645641i | \(0.776590\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5625.00 | 0.393504 | ||||||||
\(590\) | 290.996 | 0.0203053 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −21.9306 | −0.00152254 | ||||||||
\(593\) | −19524.3 | −1.35205 | −0.676025 | − | 0.736879i | \(-0.736299\pi\) | ||||
−0.676025 | + | 0.736879i | \(0.736299\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 81.1735 | 0.00557885 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 741.696 | 0.0507194 | ||||||||
\(599\) | 11598.7 | 0.791167 | 0.395583 | − | 0.918430i | \(-0.370542\pi\) | ||||
0.395583 | + | 0.918430i | \(0.370542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9335.68 | −0.633628 | −0.316814 | − | 0.948488i | \(-0.602613\pi\) | ||||
−0.316814 | + | 0.948488i | \(0.602613\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6321.30 | −0.425844 | ||||||||
\(605\) | −89.9080 | −0.00604178 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15150.9 | 1.01311 | 0.506553 | − | 0.862209i | \(-0.330919\pi\) | ||||
0.506553 | + | 0.862209i | \(0.330919\pi\) | |||||||
\(608\) | −1237.16 | −0.0825223 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3026.97 | −0.200915 | ||||||||
\(611\) | −5143.27 | −0.340548 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24793.4 | 1.63360 | 0.816798 | − | 0.576923i | \(-0.195747\pi\) | ||||
0.816798 | + | 0.576923i | \(0.195747\pi\) | |||||||
\(614\) | −6274.84 | −0.412430 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25194.6 | −1.64391 | −0.821957 | − | 0.569550i | \(-0.807118\pi\) | ||||
−0.821957 | + | 0.569550i | \(0.807118\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6046.47 | −0.392614 | −0.196307 | − | 0.980542i | \(-0.562895\pi\) | ||||
−0.196307 | + | 0.980542i | \(0.562895\pi\) | |||||||
\(620\) | −2005.62 | −0.129916 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15829.9 | 1.02045 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11312.4 | 0.723992 | ||||||||
\(626\) | 15233.2 | 0.972591 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13537.4 | 0.860193 | ||||||||
\(629\) | 162.372 | 0.0102928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6537.14 | −0.412424 | −0.206212 | − | 0.978507i | \(-0.566114\pi\) | ||||
−0.206212 | + | 0.978507i | \(0.566114\pi\) | |||||||
\(632\) | 7541.84 | 0.474681 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3982.98 | 0.249502 | ||||||||
\(635\) | −2861.18 | −0.178807 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −875.892 | −0.0543525 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 441.116 | 0.0272448 | ||||||||
\(641\) | 9246.78 | 0.569775 | 0.284888 | − | 0.958561i | \(-0.408044\pi\) | ||||
0.284888 | + | 0.958561i | \(0.408044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −157.563 | −0.00966355 | −0.00483178 | − | 0.999988i | \(-0.501538\pi\) | ||||
−0.00483178 | + | 0.999988i | \(0.501538\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9159.81 | 0.557876 | ||||||||
\(647\) | −12706.0 | −0.772062 | −0.386031 | − | 0.922486i | \(-0.626154\pi\) | ||||
−0.386031 | + | 0.922486i | \(0.626154\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1525.12 | −0.0922437 | ||||||||
\(650\) | −2314.76 | −0.139680 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6286.83 | 0.377624 | ||||||||
\(653\) | 17104.8 | 1.02506 | 0.512529 | − | 0.858670i | \(-0.328709\pi\) | ||||
0.512529 | + | 0.858670i | \(0.328709\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6797.64 | −0.405505 | ||||||||
\(656\) | −2688.00 | −0.159983 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12518.0 | −0.739956 | −0.369978 | − | 0.929040i | \(-0.620635\pi\) | ||||
−0.369978 | + | 0.929040i | \(0.620635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4780.48 | −0.281300 | −0.140650 | − | 0.990059i | \(-0.544919\pi\) | ||||
−0.140650 | + | 0.990059i | \(0.544919\pi\) | |||||||
\(662\) | 5697.26 | 0.334487 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3797.71 | 0.221957 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 439.444 | 0.0255102 | ||||||||
\(668\) | −9895.69 | −0.573167 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5263.19 | −0.303485 | ||||||||
\(671\) | 15864.4 | 0.912727 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28447.0 | −1.62935 | −0.814673 | − | 0.579920i | \(-0.803084\pi\) | ||||
−0.814673 | + | 0.579920i | \(0.803084\pi\) | |||||||
\(674\) | −11627.7 | −0.664516 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8369.30 | −0.476178 | ||||||||
\(677\) | −15878.5 | −0.901421 | −0.450710 | − | 0.892670i | \(-0.648829\pi\) | ||||
−0.450710 | + | 0.892670i | \(0.648829\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3265.98 | −0.184183 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10511.5 | 0.590187 | ||||||||
\(683\) | 2438.46 | 0.136610 | 0.0683052 | − | 0.997664i | \(-0.478241\pi\) | ||||
0.0683052 | + | 0.997664i | \(0.478241\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 237.057 | 0.0132226 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4789.93 | 0.265428 | ||||||||
\(689\) | 6395.59 | 0.353632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22486.9 | 1.23798 | 0.618990 | − | 0.785399i | \(-0.287542\pi\) | ||||
0.618990 | + | 0.785399i | \(0.287542\pi\) | |||||||
\(692\) | −16605.4 | −0.912198 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6870.21 | −0.375777 | ||||||||
\(695\) | 6425.41 | 0.350690 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19901.7 | 1.08153 | ||||||||
\(698\) | −6069.98 | −0.329158 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3916.29 | 0.211008 | 0.105504 | − | 0.994419i | \(-0.466354\pi\) | ||||
0.105504 | + | 0.994419i | \(0.466354\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.9916 | 0.00284298 | ||||||||
\(704\) | −2311.91 | −0.123769 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16440.9 | 0.876431 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22910.3 | −1.21356 | −0.606780 | − | 0.794869i | \(-0.707539\pi\) | ||||
−0.606780 | + | 0.794869i | \(0.707539\pi\) | |||||||
\(710\) | −7033.70 | −0.371789 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6575.23 | −0.346092 | ||||||||
\(713\) | −5273.74 | −0.277003 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1273.67 | −0.0666189 | ||||||||
\(716\) | 16871.7 | 0.880623 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19803.2 | −1.02932 | ||||||||
\(719\) | −20472.7 | −1.06190 | −0.530949 | − | 0.847404i | \(-0.678164\pi\) | ||||
−0.530949 | + | 0.847404i | \(0.678164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10728.6 | −0.553016 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14018.6 | 0.719609 | ||||||||
\(725\) | −1371.46 | −0.0702548 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11208.5 | 0.571802 | 0.285901 | − | 0.958259i | \(-0.407707\pi\) | ||||
0.285901 | + | 0.958259i | \(0.407707\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3992.68 | 0.202432 | ||||||||
\(731\) | −35464.1 | −1.79437 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35438.0 | −1.78572 | −0.892860 | − | 0.450334i | \(-0.851305\pi\) | ||||
−0.892860 | + | 0.450334i | \(0.851305\pi\) | |||||||
\(734\) | 22056.1 | 1.10913 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1159.91 | 0.0580907 | ||||||||
\(737\) | 27584.6 | 1.37869 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17935.4 | −0.892779 | −0.446389 | − | 0.894839i | \(-0.647290\pi\) | ||||
−0.446389 | + | 0.894839i | \(0.647290\pi\) | |||||||
\(740\) | −18.8944 | −0.000938612 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19031.0 | −0.939676 | −0.469838 | − | 0.882753i | \(-0.655688\pi\) | ||||
−0.469838 | + | 0.882753i | \(0.655688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 69.9355 | 0.00343925 | ||||||||
\(746\) | −5492.75 | −0.269576 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17117.1 | 0.836716 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2728.13 | −0.132558 | −0.0662790 | − | 0.997801i | \(-0.521113\pi\) | ||||
−0.0662790 | + | 0.997801i | \(0.521113\pi\) | |||||||
\(752\) | −8043.35 | −0.390041 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 248.075 | 0.0119819 | ||||||||
\(755\) | −5446.15 | −0.262524 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6617.58 | −0.317728 | −0.158864 | − | 0.987300i | \(-0.550783\pi\) | ||||
−0.158864 | + | 0.987300i | \(0.550783\pi\) | |||||||
\(758\) | −8368.44 | −0.400997 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1065.88 | −0.0508733 | ||||||||
\(761\) | 600.108 | 0.0285860 | 0.0142930 | − | 0.999898i | \(-0.495450\pi\) | ||||
0.0142930 | + | 0.999898i | \(0.495450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7931.86 | −0.375608 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6121.16 | 0.288729 | ||||||||
\(767\) | 431.953 | 0.0203350 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28329.2 | −1.32845 | −0.664223 | − | 0.747534i | \(-0.731238\pi\) | ||||
−0.664223 | + | 0.747534i | \(0.731238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8446.97 | 0.393799 | ||||||||
\(773\) | −23837.0 | −1.10913 | −0.554565 | − | 0.832140i | \(-0.687116\pi\) | ||||
−0.554565 | + | 0.832140i | \(0.687116\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16458.8 | 0.762862 | ||||||||
\(776\) | −8865.32 | −0.410111 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9839.23 | 0.453411 | ||||||||
\(779\) | 6495.10 | 0.298731 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36863.9 | 1.68898 | ||||||||
\(782\) | −8587.83 | −0.392711 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11663.2 | 0.530291 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −536.910 | −0.0243186 | −0.0121593 | − | 0.999926i | \(-0.503871\pi\) | ||||
−0.0121593 | + | 0.999926i | \(0.503871\pi\) | |||||||
\(788\) | −15730.6 | −0.711141 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6497.71 | 0.292631 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4493.21 | −0.201209 | ||||||||
\(794\) | −26346.5 | −1.17758 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2210.82 | −0.0984426 | ||||||||
\(797\) | 8857.47 | 0.393661 | 0.196830 | − | 0.980438i | \(-0.436935\pi\) | ||||
0.196830 | + | 0.980438i | \(0.436935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59552.1 | 2.63680 | ||||||||
\(800\) | −3619.95 | −0.159981 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5324.76 | −0.234444 | ||||||||
\(803\) | −20925.8 | −0.919620 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2977.13 | −0.130106 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15087.4 | −0.656896 | ||||||||
\(809\) | 21832.9 | 0.948832 | 0.474416 | − | 0.880301i | \(-0.342659\pi\) | ||||
0.474416 | + | 0.880301i | \(0.342659\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37942.3 | −1.64283 | −0.821415 | − | 0.570330i | \(-0.806815\pi\) | ||||
−0.821415 | + | 0.570330i | \(0.806815\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 99.0264 | 0.00426397 | ||||||||
\(815\) | 5416.45 | 0.232798 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11574.1 | −0.495625 | ||||||||
\(818\) | −25984.4 | −1.11066 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2315.86 | −0.0986261 | ||||||||
\(821\) | −18077.3 | −0.768456 | −0.384228 | − | 0.923238i | \(-0.625532\pi\) | ||||
−0.384228 | + | 0.923238i | \(0.625532\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4902.75 | −0.207654 | −0.103827 | − | 0.994595i | \(-0.533109\pi\) | ||||
−0.103827 | + | 0.994595i | \(0.533109\pi\) | |||||||
\(824\) | 3857.15 | 0.163071 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19578.9 | −0.823247 | −0.411623 | − | 0.911354i | \(-0.635038\pi\) | ||||
−0.411623 | + | 0.911354i | \(0.635038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37930.2 | −1.58911 | −0.794554 | − | 0.607194i | \(-0.792295\pi\) | ||||
−0.794554 | + | 0.607194i | \(0.792295\pi\) | |||||||
\(830\) | 3271.94 | 0.136832 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 654.791 | 0.0272846 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8525.68 | −0.353345 | ||||||||
\(836\) | 5586.34 | 0.231110 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14473.9 | 0.596651 | ||||||||
\(839\) | 5954.22 | 0.245009 | 0.122504 | − | 0.992468i | \(-0.460907\pi\) | ||||
0.122504 | + | 0.992468i | \(0.460907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24242.0 | −0.993973 | ||||||||
\(842\) | 7412.13 | 0.303372 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6883.58 | 0.280738 | ||||||||
\(845\) | −7210.61 | −0.293553 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10001.8 | 0.405027 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26801.7 | 1.08152 | ||||||||
\(851\) | −49.6825 | −0.00200129 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26196.2 | −1.05151 | −0.525757 | − | 0.850635i | \(-0.676218\pi\) | ||||
−0.525757 | + | 0.850635i | \(0.676218\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13844.8 | 0.552808 | ||||||||
\(857\) | −36877.2 | −1.46990 | −0.734949 | − | 0.678122i | \(-0.762794\pi\) | ||||
−0.734949 | + | 0.678122i | \(0.762794\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34478.2 | 1.36948 | 0.684740 | − | 0.728788i | \(-0.259916\pi\) | ||||
0.684740 | + | 0.728788i | \(0.259916\pi\) | |||||||
\(860\) | 4126.79 | 0.163631 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12764.8 | −0.504373 | ||||||||
\(863\) | −1679.69 | −0.0662542 | −0.0331271 | − | 0.999451i | \(-0.510547\pi\) | ||||
−0.0331271 | + | 0.999451i | \(0.510547\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14306.4 | −0.562351 | ||||||||
\(866\) | −14551.2 | −0.570983 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −34054.7 | −1.32938 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7812.66 | −0.303929 | ||||||||
\(872\) | 9190.64 | 0.356920 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2802.72 | −0.108471 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2503.82 | 0.0964060 | 0.0482030 | − | 0.998838i | \(-0.484651\pi\) | ||||
0.0482030 | + | 0.998838i | \(0.484651\pi\) | |||||||
\(878\) | 19520.7 | 0.750333 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1991.84 | −0.0763009 | ||||||||
\(881\) | −34886.0 | −1.33410 | −0.667048 | − | 0.745014i | \(-0.732443\pi\) | ||||
−0.667048 | + | 0.745014i | \(0.732443\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35334.0 | 1.34664 | 0.673320 | − | 0.739351i | \(-0.264868\pi\) | ||||
0.673320 | + | 0.739351i | \(0.264868\pi\) | |||||||
\(884\) | −4848.00 | −0.184452 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11466.3 | −0.434784 | ||||||||
\(887\) | −26652.8 | −1.00892 | −0.504460 | − | 0.863435i | \(-0.668308\pi\) | ||||
−0.504460 | + | 0.863435i | \(0.668308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −5664.93 | −0.213358 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19153.7 | 0.718963 | ||||||||
\(893\) | 19435.4 | 0.728311 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14535.9 | 0.542885 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33256.7 | 1.23585 | ||||||||
\(899\) | −1763.91 | −0.0654389 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −74052.2 | −2.73811 | ||||||||
\(902\) | 12137.5 | 0.448043 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10652.0 | −0.391905 | ||||||||
\(905\) | 12077.8 | 0.443624 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46055.0 | −1.68603 | −0.843016 | − | 0.537888i | \(-0.819222\pi\) | ||||
−0.843016 | + | 0.537888i | \(0.819222\pi\) | |||||||
\(908\) | −16350.4 | −0.597584 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14227.1 | 0.517416 | 0.258708 | − | 0.965956i | \(-0.416703\pi\) | ||||
0.258708 | + | 0.965956i | \(0.416703\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17148.3 | −0.621607 | ||||||||
\(914\) | 34238.6 | 1.23907 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16266.4 | −0.586745 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6686.95 | 0.240024 | 0.120012 | − | 0.992772i | \(-0.461707\pi\) | ||||
0.120012 | + | 0.992772i | \(0.461707\pi\) | |||||||
\(920\) | 999.325 | 0.0358117 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13913.9 | −0.496996 | ||||||||
\(923\) | −10440.8 | −0.372332 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 155.054 | 0.00551151 | ||||||||
\(926\) | 13188.9 | 0.468051 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 387.954 | 0.0137233 | ||||||||
\(929\) | −13539.6 | −0.478172 | −0.239086 | − | 0.970998i | \(-0.576848\pi\) | ||||
−0.239086 | + | 0.970998i | \(0.576848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −713.081 | −0.0250620 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28931.6 | 1.01357 | ||||||||
\(935\) | 14747.3 | 0.515818 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12017.0 | −0.418974 | −0.209487 | − | 0.977811i | \(-0.567179\pi\) | ||||
−0.209487 | + | 0.977811i | \(0.567179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6929.79 | −0.240452 | ||||||||
\(941\) | 55239.5 | 1.91366 | 0.956831 | − | 0.290646i | \(-0.0938703\pi\) | ||||
0.956831 | + | 0.290646i | \(0.0938703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6089.51 | −0.210288 | ||||||||
\(944\) | 675.513 | 0.0232903 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21628.7 | −0.743349 | ||||||||
\(947\) | −47989.8 | −1.64674 | −0.823368 | − | 0.567508i | \(-0.807907\pi\) | ||||
−0.823368 | + | 0.567508i | \(0.807907\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5926.71 | 0.202728 | ||||||||
\(950\) | 8747.02 | 0.298727 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19900.0 | −0.676415 | −0.338207 | − | 0.941072i | \(-0.609821\pi\) | ||||
−0.338207 | + | 0.941072i | \(0.609821\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6833.74 | −0.231555 | ||||||||
\(956\) | 8474.69 | 0.286706 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8150.94 | −0.274890 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8622.43 | −0.289431 | ||||||||
\(962\) | −28.0468 | −0.000939984 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9593.23 | 0.320516 | ||||||||
\(965\) | 7277.53 | 0.242769 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −423.293 | −0.0140767 | −0.00703836 | − | 0.999975i | \(-0.502240\pi\) | ||||
−0.00703836 | + | 0.999975i | \(0.502240\pi\) | |||||||
\(968\) | −208.711 | −0.00692998 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7637.96 | −0.252825 | ||||||||
\(971\) | 1744.60 | 0.0576590 | 0.0288295 | − | 0.999584i | \(-0.490822\pi\) | ||||
0.0288295 | + | 0.999584i | \(0.490822\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8757.58 | 0.288102 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7026.74 | −0.230451 | ||||||||
\(977\) | −3661.34 | −0.119894 | −0.0599472 | − | 0.998202i | \(-0.519093\pi\) | ||||
−0.0599472 | + | 0.998202i | \(0.519093\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29690.1 | 0.969254 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13224.7 | 0.429754 | ||||||||
\(983\) | −27194.1 | −0.882358 | −0.441179 | − | 0.897419i | \(-0.645440\pi\) | ||||
−0.441179 | + | 0.897419i | \(0.645440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13552.8 | −0.438404 | ||||||||
\(986\) | −2872.37 | −0.0927736 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1582.19 | −0.0509477 | ||||||||
\(989\) | 10851.3 | 0.348890 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13539.7 | −0.434008 | −0.217004 | − | 0.976171i | \(-0.569629\pi\) | ||||
−0.217004 | + | 0.976171i | \(0.569629\pi\) | |||||||
\(992\) | −4655.81 | −0.149014 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1904.74 | −0.0606878 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22863.8 | 0.726283 | 0.363142 | − | 0.931734i | \(-0.381704\pi\) | ||||
0.363142 | + | 0.931734i | \(0.381704\pi\) | |||||||
\(998\) | −22912.9 | −0.726747 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.4.a.bd.1.2 | 2 | ||
3.2 | odd | 2 | 882.4.a.ba.1.1 | 2 | |||
7.2 | even | 3 | 126.4.g.e.109.1 | yes | 4 | ||
7.3 | odd | 6 | 882.4.g.z.667.2 | 4 | |||
7.4 | even | 3 | 126.4.g.e.37.1 | ✓ | 4 | ||
7.5 | odd | 6 | 882.4.g.z.361.2 | 4 | |||
7.6 | odd | 2 | 882.4.a.bh.1.1 | 2 | |||
21.2 | odd | 6 | 126.4.g.f.109.2 | yes | 4 | ||
21.5 | even | 6 | 882.4.g.bj.361.1 | 4 | |||
21.11 | odd | 6 | 126.4.g.f.37.2 | yes | 4 | ||
21.17 | even | 6 | 882.4.g.bj.667.1 | 4 | |||
21.20 | even | 2 | 882.4.a.u.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.g.e.37.1 | ✓ | 4 | 7.4 | even | 3 | ||
126.4.g.e.109.1 | yes | 4 | 7.2 | even | 3 | ||
126.4.g.f.37.2 | yes | 4 | 21.11 | odd | 6 | ||
126.4.g.f.109.2 | yes | 4 | 21.2 | odd | 6 | ||
882.4.a.u.1.2 | 2 | 21.20 | even | 2 | |||
882.4.a.ba.1.1 | 2 | 3.2 | odd | 2 | |||
882.4.a.bd.1.2 | 2 | 1.1 | even | 1 | trivial | ||
882.4.a.bh.1.1 | 2 | 7.6 | odd | 2 | |||
882.4.g.z.361.2 | 4 | 7.5 | odd | 6 | |||
882.4.g.z.667.2 | 4 | 7.3 | odd | 6 | |||
882.4.g.bj.361.1 | 4 | 21.5 | even | 6 | |||
882.4.g.bj.667.1 | 4 | 21.17 | even | 6 |