Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2450,4,Mod(1,2450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2450, 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("2450.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2450.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: | \(144.554679514\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 33x^{2} - 37x + 70 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 350) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4.67931\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2450.1 |
$q$-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 | ||||||||
\(3\) | −3.07686 | −0.592141 | −0.296071 | − | 0.955166i | \(-0.595676\pi\) | ||||
−0.296071 | + | 0.955166i | \(0.595676\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.15371 | 0.418707 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −17.5330 | −0.649369 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 61.2624 | 1.67921 | 0.839605 | − | 0.543197i | \(-0.182786\pi\) | ||||
0.839605 | + | 0.543197i | \(0.182786\pi\) | |||||||
\(12\) | −12.3074 | −0.296071 | ||||||||
\(13\) | −23.4940 | −0.501236 | −0.250618 | − | 0.968086i | \(-0.580634\pi\) | ||||
−0.250618 | + | 0.968086i | \(0.580634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 135.796 | 1.93737 | 0.968684 | − | 0.248297i | \(-0.0798709\pi\) | ||||
0.968684 | + | 0.248297i | \(0.0798709\pi\) | |||||||
\(18\) | 35.0659 | 0.459173 | ||||||||
\(19\) | −62.0807 | −0.749594 | −0.374797 | − | 0.927107i | \(-0.622288\pi\) | ||||
−0.374797 | + | 0.927107i | \(0.622288\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −122.525 | −1.18738 | ||||||||
\(23\) | −73.7964 | −0.669027 | −0.334513 | − | 0.942391i | \(-0.608572\pi\) | ||||
−0.334513 | + | 0.942391i | \(0.608572\pi\) | |||||||
\(24\) | 24.6149 | 0.209354 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 46.9880 | 0.354427 | ||||||||
\(27\) | 137.022 | 0.976659 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −303.131 | −1.94103 | −0.970517 | − | 0.241035i | \(-0.922513\pi\) | ||||
−0.970517 | + | 0.241035i | \(0.922513\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −172.308 | −0.998306 | −0.499153 | − | 0.866514i | \(-0.666356\pi\) | ||||
−0.499153 | + | 0.866514i | \(0.666356\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −188.496 | −0.994330 | ||||||||
\(34\) | −271.591 | −1.36993 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −70.1318 | −0.324684 | ||||||||
\(37\) | 381.789 | 1.69637 | 0.848186 | − | 0.529699i | \(-0.177695\pi\) | ||||
0.848186 | + | 0.529699i | \(0.177695\pi\) | |||||||
\(38\) | 124.161 | 0.530043 | ||||||||
\(39\) | 72.2877 | 0.296802 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −163.265 | −0.621896 | −0.310948 | − | 0.950427i | \(-0.600646\pi\) | ||||
−0.310948 | + | 0.950427i | \(0.600646\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 174.819 | 0.619991 | 0.309996 | − | 0.950738i | \(-0.399672\pi\) | ||||
0.309996 | + | 0.950738i | \(0.399672\pi\) | |||||||
\(44\) | 245.050 | 0.839605 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 147.593 | 0.473073 | ||||||||
\(47\) | −225.177 | −0.698838 | −0.349419 | − | 0.936966i | \(-0.613621\pi\) | ||||
−0.349419 | + | 0.936966i | \(0.613621\pi\) | |||||||
\(48\) | −49.2297 | −0.148035 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −417.823 | −1.14720 | ||||||||
\(52\) | −93.9760 | −0.250618 | ||||||||
\(53\) | −194.699 | −0.504604 | −0.252302 | − | 0.967649i | \(-0.581188\pi\) | ||||
−0.252302 | + | 0.967649i | \(0.581188\pi\) | |||||||
\(54\) | −274.043 | −0.690602 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 191.013 | 0.443866 | ||||||||
\(58\) | 606.261 | 1.37252 | ||||||||
\(59\) | −72.0183 | −0.158915 | −0.0794575 | − | 0.996838i | \(-0.525319\pi\) | ||||
−0.0794575 | + | 0.996838i | \(0.525319\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 163.464 | 0.343106 | 0.171553 | − | 0.985175i | \(-0.445122\pi\) | ||||
0.171553 | + | 0.985175i | \(0.445122\pi\) | |||||||
\(62\) | 344.617 | 0.705909 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 376.991 | 0.703097 | ||||||||
\(67\) | 114.450 | 0.208691 | 0.104346 | − | 0.994541i | \(-0.466725\pi\) | ||||
0.104346 | + | 0.994541i | \(0.466725\pi\) | |||||||
\(68\) | 543.182 | 0.968684 | ||||||||
\(69\) | 227.061 | 0.396158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 442.836 | 0.740210 | 0.370105 | − | 0.928990i | \(-0.379322\pi\) | ||||
0.370105 | + | 0.928990i | \(0.379322\pi\) | |||||||
\(72\) | 140.264 | 0.229586 | ||||||||
\(73\) | −805.426 | −1.29134 | −0.645671 | − | 0.763616i | \(-0.723422\pi\) | ||||
−0.645671 | + | 0.763616i | \(0.723422\pi\) | |||||||
\(74\) | −763.578 | −1.19952 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −248.323 | −0.374797 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −144.575 | −0.209871 | ||||||||
\(79\) | 259.359 | 0.369369 | 0.184684 | − | 0.982798i | \(-0.440874\pi\) | ||||
0.184684 | + | 0.982798i | \(0.440874\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 51.7942 | 0.0710482 | ||||||||
\(82\) | 326.530 | 0.439747 | ||||||||
\(83\) | 1069.71 | 1.41465 | 0.707325 | − | 0.706889i | \(-0.249902\pi\) | ||||
0.707325 | + | 0.706889i | \(0.249902\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −349.638 | −0.438400 | ||||||||
\(87\) | 932.690 | 1.14937 | ||||||||
\(88\) | −490.099 | −0.593691 | ||||||||
\(89\) | 1037.39 | 1.23554 | 0.617769 | − | 0.786360i | \(-0.288037\pi\) | ||||
0.617769 | + | 0.786360i | \(0.288037\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −295.186 | −0.334513 | ||||||||
\(93\) | 530.168 | 0.591138 | ||||||||
\(94\) | 450.354 | 0.494153 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 98.4594 | 0.104677 | ||||||||
\(97\) | −749.409 | −0.784443 | −0.392221 | − | 0.919871i | \(-0.628293\pi\) | ||||
−0.392221 | + | 0.919871i | \(0.628293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1074.11 | −1.09043 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1935.20 | −1.90653 | −0.953265 | − | 0.302135i | \(-0.902301\pi\) | ||||
−0.953265 | + | 0.302135i | \(0.902301\pi\) | |||||||
\(102\) | 835.647 | 0.811190 | ||||||||
\(103\) | 1143.34 | 1.09376 | 0.546878 | − | 0.837212i | \(-0.315816\pi\) | ||||
0.546878 | + | 0.837212i | \(0.315816\pi\) | |||||||
\(104\) | 187.952 | 0.177214 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 389.399 | 0.356809 | ||||||||
\(107\) | −1066.76 | −0.963806 | −0.481903 | − | 0.876225i | \(-0.660054\pi\) | ||||
−0.481903 | + | 0.876225i | \(0.660054\pi\) | |||||||
\(108\) | 548.086 | 0.488330 | ||||||||
\(109\) | 472.984 | 0.415630 | 0.207815 | − | 0.978168i | \(-0.433365\pi\) | ||||
0.207815 | + | 0.978168i | \(0.433365\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1174.71 | −1.00449 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −231.260 | −0.192523 | −0.0962615 | − | 0.995356i | \(-0.530689\pi\) | ||||
−0.0962615 | + | 0.995356i | \(0.530689\pi\) | |||||||
\(114\) | −382.027 | −0.313861 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1212.52 | −0.970517 | ||||||||
\(117\) | 411.919 | 0.325487 | ||||||||
\(118\) | 144.037 | 0.112370 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2422.08 | 1.81975 | ||||||||
\(122\) | −326.928 | −0.242612 | ||||||||
\(123\) | 502.343 | 0.368250 | ||||||||
\(124\) | −689.233 | −0.499153 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −663.818 | −0.463814 | −0.231907 | − | 0.972738i | \(-0.574496\pi\) | ||||
−0.231907 | + | 0.972738i | \(0.574496\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −537.892 | −0.367122 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2455.73 | −1.63785 | −0.818923 | − | 0.573903i | \(-0.805428\pi\) | ||||
−0.818923 | + | 0.573903i | \(0.805428\pi\) | |||||||
\(132\) | −753.983 | −0.497165 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −228.900 | −0.147567 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1086.36 | −0.684963 | ||||||||
\(137\) | 1245.41 | 0.776658 | 0.388329 | − | 0.921521i | \(-0.373052\pi\) | ||||
0.388329 | + | 0.921521i | \(0.373052\pi\) | |||||||
\(138\) | −454.122 | −0.280126 | ||||||||
\(139\) | −1132.68 | −0.691172 | −0.345586 | − | 0.938387i | \(-0.612320\pi\) | ||||
−0.345586 | + | 0.938387i | \(0.612320\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 692.837 | 0.413811 | ||||||||
\(142\) | −885.671 | −0.523408 | ||||||||
\(143\) | −1439.30 | −0.841680 | ||||||||
\(144\) | −280.527 | −0.162342 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1610.85 | 0.913116 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1527.16 | 0.848186 | ||||||||
\(149\) | 521.136 | 0.286531 | 0.143266 | − | 0.989684i | \(-0.454240\pi\) | ||||
0.143266 | + | 0.989684i | \(0.454240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1512.53 | 0.815154 | 0.407577 | − | 0.913171i | \(-0.366374\pi\) | ||||
0.407577 | + | 0.913171i | \(0.366374\pi\) | |||||||
\(152\) | 496.646 | 0.265022 | ||||||||
\(153\) | −2380.90 | −1.25807 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 289.151 | 0.148401 | ||||||||
\(157\) | 624.232 | 0.317319 | 0.158660 | − | 0.987333i | \(-0.449283\pi\) | ||||
0.158660 | + | 0.987333i | \(0.449283\pi\) | |||||||
\(158\) | −518.717 | −0.261183 | ||||||||
\(159\) | 599.062 | 0.298797 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −103.588 | −0.0502387 | ||||||||
\(163\) | 1954.65 | 0.939262 | 0.469631 | − | 0.882863i | \(-0.344387\pi\) | ||||
0.469631 | + | 0.882863i | \(0.344387\pi\) | |||||||
\(164\) | −653.060 | −0.310948 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2139.42 | −1.00031 | ||||||||
\(167\) | 1937.11 | 0.897595 | 0.448797 | − | 0.893634i | \(-0.351853\pi\) | ||||
0.448797 | + | 0.893634i | \(0.351853\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1645.03 | −0.748763 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1088.46 | 0.486763 | ||||||||
\(172\) | 699.275 | 0.309996 | ||||||||
\(173\) | 1462.15 | 0.642575 | 0.321287 | − | 0.946982i | \(-0.395884\pi\) | ||||
0.321287 | + | 0.946982i | \(0.395884\pi\) | |||||||
\(174\) | −1865.38 | −0.812724 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 980.199 | 0.419803 | ||||||||
\(177\) | 221.590 | 0.0941002 | ||||||||
\(178\) | −2074.78 | −0.873657 | ||||||||
\(179\) | 1712.22 | 0.714958 | 0.357479 | − | 0.933921i | \(-0.383636\pi\) | ||||
0.357479 | + | 0.933921i | \(0.383636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 871.858 | 0.358037 | 0.179018 | − | 0.983846i | \(-0.442708\pi\) | ||||
0.179018 | + | 0.983846i | \(0.442708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −502.956 | −0.203167 | ||||||||
\(184\) | 590.371 | 0.236537 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1060.34 | −0.417998 | ||||||||
\(187\) | 8319.16 | 3.25325 | ||||||||
\(188\) | −900.707 | −0.349419 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1600.35 | −0.606270 | −0.303135 | − | 0.952948i | \(-0.598033\pi\) | ||||
−0.303135 | + | 0.952948i | \(0.598033\pi\) | |||||||
\(192\) | −196.919 | −0.0740177 | ||||||||
\(193\) | 3282.35 | 1.22419 | 0.612095 | − | 0.790784i | \(-0.290327\pi\) | ||||
0.612095 | + | 0.790784i | \(0.290327\pi\) | |||||||
\(194\) | 1498.82 | 0.554685 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1203.84 | 0.435381 | 0.217690 | − | 0.976018i | \(-0.430148\pi\) | ||||
0.217690 | + | 0.976018i | \(0.430148\pi\) | |||||||
\(198\) | 2148.22 | 0.771048 | ||||||||
\(199\) | −2871.43 | −1.02287 | −0.511433 | − | 0.859323i | \(-0.670885\pi\) | ||||
−0.511433 | + | 0.859323i | \(0.670885\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −352.147 | −0.123575 | ||||||||
\(202\) | 3870.40 | 1.34812 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1671.29 | −0.573598 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2286.69 | −0.773402 | ||||||||
\(207\) | 1293.87 | 0.434445 | ||||||||
\(208\) | −375.904 | −0.125309 | ||||||||
\(209\) | −3803.21 | −1.25873 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3370.71 | −1.09976 | −0.549879 | − | 0.835244i | \(-0.685326\pi\) | ||||
−0.549879 | + | 0.835244i | \(0.685326\pi\) | |||||||
\(212\) | −778.797 | −0.252302 | ||||||||
\(213\) | −1362.54 | −0.438309 | ||||||||
\(214\) | 2133.51 | 0.681514 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1096.17 | −0.345301 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −945.969 | −0.293895 | ||||||||
\(219\) | 2478.18 | 0.764657 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3190.38 | −0.971078 | ||||||||
\(222\) | 2349.42 | 0.710283 | ||||||||
\(223\) | 30.9182 | 0.00928445 | 0.00464223 | − | 0.999989i | \(-0.498522\pi\) | ||||
0.00464223 | + | 0.999989i | \(0.498522\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 462.520 | 0.136134 | ||||||||
\(227\) | 4554.25 | 1.33161 | 0.665807 | − | 0.746124i | \(-0.268088\pi\) | ||||
0.665807 | + | 0.746124i | \(0.268088\pi\) | |||||||
\(228\) | 764.054 | 0.221933 | ||||||||
\(229\) | −2804.55 | −0.809302 | −0.404651 | − | 0.914471i | \(-0.632607\pi\) | ||||
−0.404651 | + | 0.914471i | \(0.632607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2425.05 | 0.686259 | ||||||||
\(233\) | −2705.06 | −0.760575 | −0.380288 | − | 0.924868i | \(-0.624175\pi\) | ||||
−0.380288 | + | 0.924868i | \(0.624175\pi\) | |||||||
\(234\) | −823.839 | −0.230154 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −288.073 | −0.0794575 | ||||||||
\(237\) | −798.009 | −0.218718 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −63.8334 | −0.0172763 | −0.00863815 | − | 0.999963i | \(-0.502750\pi\) | ||||
−0.00863815 | + | 0.999963i | \(0.502750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −89.8729 | −0.0240217 | −0.0120108 | − | 0.999928i | \(-0.503823\pi\) | ||||
−0.0120108 | + | 0.999928i | \(0.503823\pi\) | |||||||
\(242\) | −4844.17 | −1.28676 | ||||||||
\(243\) | −3858.94 | −1.01873 | ||||||||
\(244\) | 653.857 | 0.171553 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1004.69 | −0.260392 | ||||||||
\(247\) | 1458.53 | 0.375724 | ||||||||
\(248\) | 1378.47 | 0.352955 | ||||||||
\(249\) | −3291.34 | −0.837673 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6502.83 | −1.63528 | −0.817639 | − | 0.575731i | \(-0.804717\pi\) | ||||
−0.817639 | + | 0.575731i | \(0.804717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4520.95 | −1.12344 | ||||||||
\(254\) | 1327.64 | 0.327966 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −4772.32 | −1.15832 | −0.579161 | − | 0.815213i | \(-0.696620\pi\) | ||||
−0.579161 | + | 0.815213i | \(0.696620\pi\) | |||||||
\(258\) | 1075.78 | 0.259595 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5314.78 | 1.26045 | ||||||||
\(262\) | 4911.45 | 1.15813 | ||||||||
\(263\) | −4345.48 | −1.01884 | −0.509418 | − | 0.860519i | \(-0.670139\pi\) | ||||
−0.509418 | + | 0.860519i | \(0.670139\pi\) | |||||||
\(264\) | 1507.97 | 0.351549 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3191.89 | −0.731613 | ||||||||
\(268\) | 457.801 | 0.104346 | ||||||||
\(269\) | −4476.62 | −1.01466 | −0.507332 | − | 0.861751i | \(-0.669368\pi\) | ||||
−0.507332 | + | 0.861751i | \(0.669368\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7295.74 | 1.63537 | 0.817683 | − | 0.575668i | \(-0.195258\pi\) | ||||
0.817683 | + | 0.575668i | \(0.195258\pi\) | |||||||
\(272\) | 2172.73 | 0.484342 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2490.81 | −0.549180 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 908.244 | 0.198079 | ||||||||
\(277\) | 6038.54 | 1.30982 | 0.654911 | − | 0.755706i | \(-0.272706\pi\) | ||||
0.654911 | + | 0.755706i | \(0.272706\pi\) | |||||||
\(278\) | 2265.37 | 0.488732 | ||||||||
\(279\) | 3021.07 | 0.648269 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7320.70 | 1.55415 | 0.777076 | − | 0.629407i | \(-0.216702\pi\) | ||||
0.777076 | + | 0.629407i | \(0.216702\pi\) | |||||||
\(282\) | −1385.67 | −0.292609 | ||||||||
\(283\) | −2104.81 | −0.442113 | −0.221056 | − | 0.975261i | \(-0.570950\pi\) | ||||
−0.221056 | + | 0.975261i | \(0.570950\pi\) | |||||||
\(284\) | 1771.34 | 0.370105 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2878.60 | 0.595158 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 561.054 | 0.114793 | ||||||||
\(289\) | 13527.4 | 2.75339 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2305.82 | 0.464501 | ||||||||
\(292\) | −3221.70 | −0.645671 | ||||||||
\(293\) | −5907.76 | −1.17793 | −0.588967 | − | 0.808157i | \(-0.700465\pi\) | ||||
−0.588967 | + | 0.808157i | \(0.700465\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3054.31 | −0.599758 | ||||||||
\(297\) | 8394.27 | 1.64002 | ||||||||
\(298\) | −1042.27 | −0.202608 | ||||||||
\(299\) | 1733.77 | 0.335340 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3025.07 | −0.576401 | ||||||||
\(303\) | 5954.33 | 1.12894 | ||||||||
\(304\) | −993.291 | −0.187399 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4761.79 | 0.889587 | ||||||||
\(307\) | 3189.84 | 0.593008 | 0.296504 | − | 0.955032i | \(-0.404179\pi\) | ||||
0.296504 | + | 0.955032i | \(0.404179\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3517.90 | −0.647658 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5219.07 | −0.951597 | −0.475798 | − | 0.879554i | \(-0.657841\pi\) | ||||
−0.475798 | + | 0.879554i | \(0.657841\pi\) | |||||||
\(312\) | −578.302 | −0.104936 | ||||||||
\(313\) | −6111.76 | −1.10370 | −0.551848 | − | 0.833945i | \(-0.686077\pi\) | ||||
−0.551848 | + | 0.833945i | \(0.686077\pi\) | |||||||
\(314\) | −1248.46 | −0.224379 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1037.43 | 0.184684 | ||||||||
\(317\) | −2564.29 | −0.454337 | −0.227168 | − | 0.973856i | \(-0.572947\pi\) | ||||
−0.227168 | + | 0.973856i | \(0.572947\pi\) | |||||||
\(318\) | −1198.12 | −0.211281 | ||||||||
\(319\) | −18570.5 | −3.25940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3282.26 | 0.570709 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8430.28 | −1.45224 | ||||||||
\(324\) | 207.177 | 0.0355241 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3909.29 | −0.664158 | ||||||||
\(327\) | −1455.31 | −0.246112 | ||||||||
\(328\) | 1306.12 | 0.219873 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4112.90 | −0.682978 | −0.341489 | − | 0.939886i | \(-0.610931\pi\) | ||||
−0.341489 | + | 0.939886i | \(0.610931\pi\) | |||||||
\(332\) | 4278.84 | 0.707325 | ||||||||
\(333\) | −6693.89 | −1.10157 | ||||||||
\(334\) | −3874.23 | −0.634695 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7901.44 | −1.27721 | −0.638604 | − | 0.769536i | \(-0.720488\pi\) | ||||
−0.638604 | + | 0.769536i | \(0.720488\pi\) | |||||||
\(338\) | 3290.06 | 0.529455 | ||||||||
\(339\) | 711.553 | 0.114001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10556.0 | −1.67637 | ||||||||
\(342\) | −2176.92 | −0.344193 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1398.55 | −0.219200 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2924.31 | −0.454369 | ||||||||
\(347\) | −3558.19 | −0.550472 | −0.275236 | − | 0.961377i | \(-0.588756\pi\) | ||||
−0.275236 | + | 0.961377i | \(0.588756\pi\) | |||||||
\(348\) | 3730.76 | 0.574683 | ||||||||
\(349\) | −3116.92 | −0.478066 | −0.239033 | − | 0.971011i | \(-0.576830\pi\) | ||||
−0.239033 | + | 0.971011i | \(0.576830\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3219.19 | −0.489537 | ||||||||
\(352\) | −1960.40 | −0.296845 | ||||||||
\(353\) | −722.396 | −0.108921 | −0.0544607 | − | 0.998516i | \(-0.517344\pi\) | ||||
−0.0544607 | + | 0.998516i | \(0.517344\pi\) | |||||||
\(354\) | −443.180 | −0.0665389 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4149.55 | 0.617769 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3424.45 | −0.505552 | ||||||||
\(359\) | 9421.21 | 1.38505 | 0.692524 | − | 0.721395i | \(-0.256499\pi\) | ||||
0.692524 | + | 0.721395i | \(0.256499\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3004.99 | −0.438108 | ||||||||
\(362\) | −1743.72 | −0.253170 | ||||||||
\(363\) | −7452.40 | −1.07755 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1005.91 | 0.143661 | ||||||||
\(367\) | −7672.31 | −1.09126 | −0.545628 | − | 0.838027i | \(-0.683709\pi\) | ||||
−0.545628 | + | 0.838027i | \(0.683709\pi\) | |||||||
\(368\) | −1180.74 | −0.167257 | ||||||||
\(369\) | 2862.52 | 0.403840 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2120.67 | 0.295569 | ||||||||
\(373\) | −4773.43 | −0.662624 | −0.331312 | − | 0.943521i | \(-0.607491\pi\) | ||||
−0.331312 | + | 0.943521i | \(0.607491\pi\) | |||||||
\(374\) | −16638.3 | −2.30039 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1801.41 | 0.247077 | ||||||||
\(377\) | 7121.76 | 0.972915 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3204.14 | 0.434263 | 0.217131 | − | 0.976142i | \(-0.430330\pi\) | ||||
0.217131 | + | 0.976142i | \(0.430330\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2042.47 | 0.274643 | ||||||||
\(382\) | 3200.71 | 0.428697 | ||||||||
\(383\) | −5050.35 | −0.673788 | −0.336894 | − | 0.941542i | \(-0.609376\pi\) | ||||
−0.336894 | + | 0.941542i | \(0.609376\pi\) | |||||||
\(384\) | 393.838 | 0.0523384 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6564.70 | −0.865633 | ||||||||
\(387\) | −3065.09 | −0.402603 | ||||||||
\(388\) | −2997.64 | −0.392221 | ||||||||
\(389\) | −555.527 | −0.0724070 | −0.0362035 | − | 0.999344i | \(-0.511526\pi\) | ||||
−0.0362035 | + | 0.999344i | \(0.511526\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10021.2 | −1.29615 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7555.92 | 0.969836 | ||||||||
\(394\) | −2407.68 | −0.307861 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4296.44 | −0.545213 | ||||||||
\(397\) | −6644.56 | −0.840002 | −0.420001 | − | 0.907524i | \(-0.637970\pi\) | ||||
−0.420001 | + | 0.907524i | \(0.637970\pi\) | |||||||
\(398\) | 5742.86 | 0.723275 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6641.71 | 0.827111 | 0.413555 | − | 0.910479i | \(-0.364287\pi\) | ||||
0.413555 | + | 0.910479i | \(0.364287\pi\) | |||||||
\(402\) | 704.293 | 0.0873805 | ||||||||
\(403\) | 4048.21 | 0.500387 | ||||||||
\(404\) | −7740.80 | −0.953265 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23389.3 | 2.84856 | ||||||||
\(408\) | 3342.59 | 0.405595 | ||||||||
\(409\) | −8776.36 | −1.06103 | −0.530517 | − | 0.847674i | \(-0.678002\pi\) | ||||
−0.530517 | + | 0.847674i | \(0.678002\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3831.93 | −0.459891 | ||||||||
\(412\) | 4573.37 | 0.546878 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2587.74 | −0.307199 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 751.808 | 0.0886068 | ||||||||
\(417\) | 3485.10 | 0.409272 | ||||||||
\(418\) | 7606.43 | 0.890054 | ||||||||
\(419\) | −9298.31 | −1.08413 | −0.542067 | − | 0.840335i | \(-0.682358\pi\) | ||||
−0.542067 | + | 0.840335i | \(0.682358\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17174.4 | −1.98819 | −0.994094 | − | 0.108520i | \(-0.965389\pi\) | ||||
−0.994094 | + | 0.108520i | \(0.965389\pi\) | |||||||
\(422\) | 6741.41 | 0.777646 | ||||||||
\(423\) | 3948.01 | 0.453804 | ||||||||
\(424\) | 1557.59 | 0.178404 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2725.08 | 0.309931 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4267.03 | −0.481903 | ||||||||
\(429\) | 4428.52 | 0.498394 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5772.97 | 0.645184 | 0.322592 | − | 0.946538i | \(-0.395446\pi\) | ||||
0.322592 | + | 0.946538i | \(0.395446\pi\) | |||||||
\(432\) | 2192.34 | 0.244165 | ||||||||
\(433\) | −12106.8 | −1.34368 | −0.671841 | − | 0.740696i | \(-0.734496\pi\) | ||||
−0.671841 | + | 0.740696i | \(0.734496\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1891.94 | 0.207815 | ||||||||
\(437\) | 4581.33 | 0.501499 | ||||||||
\(438\) | −4956.36 | −0.540694 | ||||||||
\(439\) | 2039.96 | 0.221781 | 0.110890 | − | 0.993833i | \(-0.464630\pi\) | ||||
0.110890 | + | 0.993833i | \(0.464630\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6380.76 | 0.686656 | ||||||||
\(443\) | 6362.47 | 0.682370 | 0.341185 | − | 0.939996i | \(-0.389172\pi\) | ||||
0.341185 | + | 0.939996i | \(0.389172\pi\) | |||||||
\(444\) | −4698.84 | −0.502246 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −61.8363 | −0.00656510 | ||||||||
\(447\) | −1603.46 | −0.169667 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 343.694 | 0.0361245 | 0.0180623 | − | 0.999837i | \(-0.494250\pi\) | ||||
0.0180623 | + | 0.999837i | \(0.494250\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10002.0 | −1.04429 | ||||||||
\(452\) | −925.039 | −0.0962615 | ||||||||
\(453\) | −4653.85 | −0.482687 | ||||||||
\(454\) | −9108.50 | −0.941593 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1528.11 | −0.156930 | ||||||||
\(457\) | −18326.5 | −1.87589 | −0.937943 | − | 0.346790i | \(-0.887272\pi\) | ||||
−0.937943 | + | 0.346790i | \(0.887272\pi\) | |||||||
\(458\) | 5609.11 | 0.572263 | ||||||||
\(459\) | 18606.9 | 1.89215 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14825.2 | −1.49779 | −0.748893 | − | 0.662691i | \(-0.769414\pi\) | ||||
−0.748893 | + | 0.662691i | \(0.769414\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12332.9 | −1.23793 | −0.618964 | − | 0.785419i | \(-0.712447\pi\) | ||||
−0.618964 | + | 0.785419i | \(0.712447\pi\) | |||||||
\(464\) | −4850.09 | −0.485258 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5410.11 | 0.537808 | ||||||||
\(467\) | 6199.53 | 0.614304 | 0.307152 | − | 0.951660i | \(-0.400624\pi\) | ||||
0.307152 | + | 0.951660i | \(0.400624\pi\) | |||||||
\(468\) | 1647.68 | 0.162743 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1920.67 | −0.187898 | ||||||||
\(472\) | 576.147 | 0.0561850 | ||||||||
\(473\) | 10709.8 | 1.04110 | ||||||||
\(474\) | 1596.02 | 0.154657 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3413.65 | 0.327674 | ||||||||
\(478\) | 127.667 | 0.0122162 | ||||||||
\(479\) | −17624.2 | −1.68115 | −0.840575 | − | 0.541696i | \(-0.817783\pi\) | ||||
−0.840575 | + | 0.541696i | \(0.817783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8969.76 | −0.850282 | ||||||||
\(482\) | 179.746 | 0.0169859 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9688.33 | 0.909874 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7717.89 | 0.720351 | ||||||||
\(487\) | 7963.06 | 0.740946 | 0.370473 | − | 0.928843i | \(-0.379196\pi\) | ||||
0.370473 | + | 0.928843i | \(0.379196\pi\) | |||||||
\(488\) | −1307.71 | −0.121306 | ||||||||
\(489\) | −6014.17 | −0.556176 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11418.2 | 1.04948 | 0.524741 | − | 0.851262i | \(-0.324162\pi\) | ||||
0.524741 | + | 0.851262i | \(0.324162\pi\) | |||||||
\(492\) | 2009.37 | 0.184125 | ||||||||
\(493\) | −41163.8 | −3.76050 | ||||||||
\(494\) | −2917.05 | −0.265677 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2756.93 | −0.249577 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6582.69 | 0.592324 | ||||||||
\(499\) | −4665.89 | −0.418585 | −0.209293 | − | 0.977853i | \(-0.567116\pi\) | ||||
−0.209293 | + | 0.977853i | \(0.567116\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5960.22 | −0.531503 | ||||||||
\(502\) | 13005.7 | 1.15632 | ||||||||
\(503\) | −14883.1 | −1.31929 | −0.659647 | − | 0.751575i | \(-0.729294\pi\) | ||||
−0.659647 | + | 0.751575i | \(0.729294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9041.89 | 0.794389 | ||||||||
\(507\) | 5061.53 | 0.443373 | ||||||||
\(508\) | −2655.27 | −0.231907 | ||||||||
\(509\) | −4223.58 | −0.367793 | −0.183897 | − | 0.982946i | \(-0.558871\pi\) | ||||
−0.183897 | + | 0.982946i | \(0.558871\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −8506.39 | −0.732098 | ||||||||
\(514\) | 9544.63 | 0.819058 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2151.57 | −0.183561 | ||||||||
\(517\) | −13794.9 | −1.17350 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4498.83 | −0.380495 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12866.9 | 1.08197 | 0.540987 | − | 0.841031i | \(-0.318051\pi\) | ||||
0.540987 | + | 0.841031i | \(0.318051\pi\) | |||||||
\(522\) | −10629.6 | −0.891270 | ||||||||
\(523\) | −11867.9 | −0.992248 | −0.496124 | − | 0.868252i | \(-0.665244\pi\) | ||||
−0.496124 | + | 0.868252i | \(0.665244\pi\) | |||||||
\(524\) | −9822.91 | −0.818923 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8690.96 | 0.720426 | ||||||||
\(527\) | −23398.7 | −1.93409 | ||||||||
\(528\) | −3015.93 | −0.248582 | ||||||||
\(529\) | −6721.09 | −0.552403 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1262.69 | 0.103194 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3835.75 | 0.311716 | ||||||||
\(534\) | 6383.79 | 0.517329 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −915.601 | −0.0737835 | ||||||||
\(537\) | −5268.26 | −0.423356 | ||||||||
\(538\) | 8953.25 | 0.717476 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1277.17 | 0.101497 | 0.0507483 | − | 0.998711i | \(-0.483839\pi\) | ||||
0.0507483 | + | 0.998711i | \(0.483839\pi\) | |||||||
\(542\) | −14591.5 | −1.15638 | ||||||||
\(543\) | −2682.58 | −0.212008 | ||||||||
\(544\) | −4345.46 | −0.342481 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4959.59 | −0.387672 | −0.193836 | − | 0.981034i | \(-0.562093\pi\) | ||||
−0.193836 | + | 0.981034i | \(0.562093\pi\) | |||||||
\(548\) | 4981.62 | 0.388329 | ||||||||
\(549\) | −2866.01 | −0.222802 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18818.6 | 1.45499 | ||||||||
\(552\) | −1816.49 | −0.140063 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12077.1 | −0.926184 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4530.73 | −0.345586 | ||||||||
\(557\) | −7600.52 | −0.578177 | −0.289088 | − | 0.957302i | \(-0.593352\pi\) | ||||
−0.289088 | + | 0.957302i | \(0.593352\pi\) | |||||||
\(558\) | −6042.15 | −0.458395 | ||||||||
\(559\) | −4107.20 | −0.310762 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25596.9 | −1.92638 | ||||||||
\(562\) | −14641.4 | −1.09895 | ||||||||
\(563\) | 16028.4 | 1.19985 | 0.599925 | − | 0.800056i | \(-0.295197\pi\) | ||||
0.599925 | + | 0.800056i | \(0.295197\pi\) | |||||||
\(564\) | 2771.35 | 0.206906 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4209.62 | 0.312621 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3542.68 | −0.261704 | ||||||||
\(569\) | −6178.27 | −0.455196 | −0.227598 | − | 0.973755i | \(-0.573087\pi\) | ||||
−0.227598 | + | 0.973755i | \(0.573087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21842.6 | 1.60085 | 0.800423 | − | 0.599436i | \(-0.204608\pi\) | ||||
0.800423 | + | 0.599436i | \(0.204608\pi\) | |||||||
\(572\) | −5757.20 | −0.420840 | ||||||||
\(573\) | 4924.06 | 0.358997 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1122.11 | −0.0811711 | ||||||||
\(577\) | 2007.48 | 0.144839 | 0.0724197 | − | 0.997374i | \(-0.476928\pi\) | ||||
0.0724197 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(578\) | −27054.9 | −1.94694 | ||||||||
\(579\) | −10099.3 | −0.724893 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4611.65 | −0.328452 | ||||||||
\(583\) | −11927.8 | −0.847336 | ||||||||
\(584\) | 6443.40 | 0.456558 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11815.5 | 0.832925 | ||||||||
\(587\) | −14036.0 | −0.986928 | −0.493464 | − | 0.869766i | \(-0.664270\pi\) | ||||
−0.493464 | + | 0.869766i | \(0.664270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10697.0 | 0.748325 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3704.04 | −0.257807 | ||||||||
\(592\) | 6108.63 | 0.424093 | ||||||||
\(593\) | 10361.9 | 0.717562 | 0.358781 | − | 0.933422i | \(-0.383193\pi\) | ||||
0.358781 | + | 0.933422i | \(0.383193\pi\) | |||||||
\(594\) | −16788.5 | −1.15967 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2084.54 | 0.143266 | ||||||||
\(597\) | 8834.98 | 0.605681 | ||||||||
\(598\) | −3467.55 | −0.237121 | ||||||||
\(599\) | −23395.4 | −1.59584 | −0.797922 | − | 0.602761i | \(-0.794067\pi\) | ||||
−0.797922 | + | 0.602761i | \(0.794067\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3167.68 | 0.214996 | 0.107498 | − | 0.994205i | \(-0.465716\pi\) | ||||
0.107498 | + | 0.994205i | \(0.465716\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2006.65 | −0.135518 | ||||||||
\(604\) | 6050.14 | 0.407577 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11908.7 | −0.798278 | ||||||||
\(607\) | −13767.6 | −0.920612 | −0.460306 | − | 0.887760i | \(-0.652260\pi\) | ||||
−0.460306 | + | 0.887760i | \(0.652260\pi\) | |||||||
\(608\) | 1986.58 | 0.132511 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5290.31 | 0.350283 | ||||||||
\(612\) | −9523.59 | −0.629033 | ||||||||
\(613\) | 10803.7 | 0.711841 | 0.355920 | − | 0.934516i | \(-0.384167\pi\) | ||||
0.355920 | + | 0.934516i | \(0.384167\pi\) | |||||||
\(614\) | −6379.67 | −0.419320 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 979.937 | 0.0639397 | 0.0319698 | − | 0.999489i | \(-0.489822\pi\) | ||||
0.0319698 | + | 0.999489i | \(0.489822\pi\) | |||||||
\(618\) | 7035.80 | 0.457964 | ||||||||
\(619\) | −15163.8 | −0.984626 | −0.492313 | − | 0.870418i | \(-0.663848\pi\) | ||||
−0.492313 | + | 0.870418i | \(0.663848\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10111.7 | −0.653411 | ||||||||
\(622\) | 10438.1 | 0.672881 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1156.60 | 0.0742006 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12223.5 | 0.780431 | ||||||||
\(627\) | 11701.9 | 0.745344 | ||||||||
\(628\) | 2496.93 | 0.158660 | ||||||||
\(629\) | 51845.3 | 3.28650 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4762.00 | −0.300431 | −0.150216 | − | 0.988653i | \(-0.547997\pi\) | ||||
−0.150216 | + | 0.988653i | \(0.547997\pi\) | |||||||
\(632\) | −2074.87 | −0.130592 | ||||||||
\(633\) | 10371.2 | 0.651212 | ||||||||
\(634\) | 5128.57 | 0.321264 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2396.25 | 0.149398 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 37141.0 | 2.30475 | ||||||||
\(639\) | −7764.21 | −0.480669 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8916.25 | 0.549408 | 0.274704 | − | 0.961529i | \(-0.411420\pi\) | ||||
0.274704 | + | 0.961529i | \(0.411420\pi\) | |||||||
\(642\) | −6564.51 | −0.403552 | ||||||||
\(643\) | 9106.58 | 0.558520 | 0.279260 | − | 0.960216i | \(-0.409911\pi\) | ||||
0.279260 | + | 0.960216i | \(0.409911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16860.6 | 1.02689 | ||||||||
\(647\) | −5973.31 | −0.362960 | −0.181480 | − | 0.983395i | \(-0.558089\pi\) | ||||
−0.181480 | + | 0.983395i | \(0.558089\pi\) | |||||||
\(648\) | −414.353 | −0.0251193 | ||||||||
\(649\) | −4412.02 | −0.266852 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7818.58 | 0.469631 | ||||||||
\(653\) | 25352.2 | 1.51931 | 0.759655 | − | 0.650327i | \(-0.225368\pi\) | ||||
0.759655 | + | 0.650327i | \(0.225368\pi\) | |||||||
\(654\) | 2910.61 | 0.174027 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2612.24 | −0.155474 | ||||||||
\(657\) | 14121.5 | 0.838557 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5808.17 | −0.343330 | −0.171665 | − | 0.985155i | \(-0.554915\pi\) | ||||
−0.171665 | + | 0.985155i | \(0.554915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25774.4 | −1.51665 | −0.758327 | − | 0.651875i | \(-0.773983\pi\) | ||||
−0.758327 | + | 0.651875i | \(0.773983\pi\) | |||||||
\(662\) | 8225.81 | 0.482938 | ||||||||
\(663\) | 9816.35 | 0.575016 | ||||||||
\(664\) | −8557.68 | −0.500154 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13387.8 | 0.778928 | ||||||||
\(667\) | 22370.0 | 1.29860 | ||||||||
\(668\) | 7748.45 | 0.448797 | ||||||||
\(669\) | −95.1307 | −0.00549771 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10014.2 | 0.576146 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14454.0 | 0.827877 | 0.413938 | − | 0.910305i | \(-0.364153\pi\) | ||||
0.413938 | + | 0.910305i | \(0.364153\pi\) | |||||||
\(674\) | 15802.9 | 0.903122 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6580.13 | −0.374381 | ||||||||
\(677\) | −6457.39 | −0.366584 | −0.183292 | − | 0.983058i | \(-0.558675\pi\) | ||||
−0.183292 | + | 0.983058i | \(0.558675\pi\) | |||||||
\(678\) | −1423.11 | −0.0806107 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14012.8 | −0.788503 | ||||||||
\(682\) | 21112.1 | 1.18537 | ||||||||
\(683\) | 15065.5 | 0.844019 | 0.422010 | − | 0.906591i | \(-0.361325\pi\) | ||||
0.422010 | + | 0.906591i | \(0.361325\pi\) | |||||||
\(684\) | 4353.83 | 0.243382 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8629.21 | 0.479221 | ||||||||
\(688\) | 2797.10 | 0.154998 | ||||||||
\(689\) | 4574.27 | 0.252926 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2946.42 | 0.162210 | 0.0811050 | − | 0.996706i | \(-0.474155\pi\) | ||||
0.0811050 | + | 0.996706i | \(0.474155\pi\) | |||||||
\(692\) | 5848.61 | 0.321287 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7116.38 | 0.389242 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7461.52 | −0.406362 | ||||||||
\(697\) | −22170.7 | −1.20484 | ||||||||
\(698\) | 6233.84 | 0.338044 | ||||||||
\(699\) | 8323.07 | 0.450368 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7121.87 | −0.383722 | −0.191861 | − | 0.981422i | \(-0.561452\pi\) | ||||
−0.191861 | + | 0.981422i | \(0.561452\pi\) | |||||||
\(702\) | 6438.37 | 0.346155 | ||||||||
\(703\) | −23701.7 | −1.27159 | ||||||||
\(704\) | 3920.79 | 0.209901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1444.79 | 0.0770190 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 886.360 | 0.0470501 | ||||||||
\(709\) | 8487.07 | 0.449561 | 0.224780 | − | 0.974409i | \(-0.427834\pi\) | ||||
0.224780 | + | 0.974409i | \(0.427834\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4547.32 | −0.239856 | ||||||||
\(712\) | −8299.10 | −0.436829 | ||||||||
\(713\) | 12715.7 | 0.667894 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6848.89 | 0.357479 | ||||||||
\(717\) | 196.406 | 0.0102300 | ||||||||
\(718\) | −18842.4 | −0.979377 | ||||||||
\(719\) | 10839.5 | 0.562232 | 0.281116 | − | 0.959674i | \(-0.409295\pi\) | ||||
0.281116 | + | 0.959674i | \(0.409295\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6009.97 | 0.309789 | ||||||||
\(723\) | 276.526 | 0.0142242 | ||||||||
\(724\) | 3487.43 | 0.179018 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 14904.8 | 0.761941 | ||||||||
\(727\) | 2690.67 | 0.137265 | 0.0686323 | − | 0.997642i | \(-0.478136\pi\) | ||||
0.0686323 | + | 0.997642i | \(0.478136\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10475.0 | 0.532184 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23739.6 | 1.20115 | ||||||||
\(732\) | −2011.82 | −0.101583 | ||||||||
\(733\) | −650.576 | −0.0327825 | −0.0163913 | − | 0.999866i | \(-0.505218\pi\) | ||||
−0.0163913 | + | 0.999866i | \(0.505218\pi\) | |||||||
\(734\) | 15344.6 | 0.771635 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2361.48 | 0.118268 | ||||||||
\(737\) | 7011.49 | 0.350436 | ||||||||
\(738\) | −5725.04 | −0.285558 | ||||||||
\(739\) | −5111.18 | −0.254422 | −0.127211 | − | 0.991876i | \(-0.540603\pi\) | ||||
−0.127211 | + | 0.991876i | \(0.540603\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4487.67 | −0.222481 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9963.89 | −0.491978 | −0.245989 | − | 0.969273i | \(-0.579113\pi\) | ||||
−0.245989 | + | 0.969273i | \(0.579113\pi\) | |||||||
\(744\) | −4241.35 | −0.208999 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9546.86 | 0.468546 | ||||||||
\(747\) | −18755.2 | −0.918629 | ||||||||
\(748\) | 33276.6 | 1.62662 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32255.0 | −1.56724 | −0.783622 | − | 0.621238i | \(-0.786630\pi\) | ||||
−0.783622 | + | 0.621238i | \(0.786630\pi\) | |||||||
\(752\) | −3602.83 | −0.174710 | ||||||||
\(753\) | 20008.3 | 0.968316 | ||||||||
\(754\) | −14243.5 | −0.687955 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 494.472 | 0.0237409 | 0.0118705 | − | 0.999930i | \(-0.496221\pi\) | ||||
0.0118705 | + | 0.999930i | \(0.496221\pi\) | |||||||
\(758\) | −6408.28 | −0.307070 | ||||||||
\(759\) | 13910.3 | 0.665233 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22486.7 | 1.07115 | 0.535573 | − | 0.844489i | \(-0.320096\pi\) | ||||
0.535573 | + | 0.844489i | \(0.320096\pi\) | |||||||
\(762\) | −4084.95 | −0.194202 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6401.41 | −0.303135 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10100.7 | 0.476440 | ||||||||
\(767\) | 1692.00 | 0.0796539 | ||||||||
\(768\) | −787.675 | −0.0370088 | ||||||||
\(769\) | −18773.7 | −0.880362 | −0.440181 | − | 0.897909i | \(-0.645086\pi\) | ||||
−0.440181 | + | 0.897909i | \(0.645086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14683.7 | 0.685891 | ||||||||
\(772\) | 13129.4 | 0.612095 | ||||||||
\(773\) | 10106.1 | 0.470233 | 0.235117 | − | 0.971967i | \(-0.424453\pi\) | ||||
0.235117 | + | 0.971967i | \(0.424453\pi\) | |||||||
\(774\) | 6130.18 | 0.284683 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5995.27 | 0.277342 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1111.05 | 0.0511995 | ||||||||
\(779\) | 10135.6 | 0.466169 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27129.2 | 1.24297 | ||||||||
\(782\) | 20042.4 | 0.916517 | ||||||||
\(783\) | −41535.4 | −1.89573 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15111.8 | −0.685778 | ||||||||
\(787\) | −43336.0 | −1.96285 | −0.981425 | − | 0.191848i | \(-0.938552\pi\) | ||||
−0.981425 | + | 0.191848i | \(0.938552\pi\) | |||||||
\(788\) | 4815.36 | 0.217690 | ||||||||
\(789\) | 13370.4 | 0.603295 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8592.89 | 0.385524 | ||||||||
\(793\) | −3840.43 | −0.171977 | ||||||||
\(794\) | 13289.1 | 0.593971 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11485.7 | −0.511433 | ||||||||
\(797\) | 6500.55 | 0.288910 | 0.144455 | − | 0.989511i | \(-0.453857\pi\) | ||||
0.144455 | + | 0.989511i | \(0.453857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30578.0 | −1.35391 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18188.5 | −0.802320 | ||||||||
\(802\) | −13283.4 | −0.584855 | ||||||||
\(803\) | −49342.3 | −2.16843 | ||||||||
\(804\) | −1408.59 | −0.0617873 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8096.43 | −0.353827 | ||||||||
\(807\) | 13773.9 | 0.600824 | ||||||||
\(808\) | 15481.6 | 0.674060 | ||||||||
\(809\) | −15002.6 | −0.651993 | −0.325997 | − | 0.945371i | \(-0.605700\pi\) | ||||
−0.325997 | + | 0.945371i | \(0.605700\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6871.29 | 0.297514 | 0.148757 | − | 0.988874i | \(-0.452473\pi\) | ||||
0.148757 | + | 0.988874i | \(0.452473\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22447.9 | −0.968368 | ||||||||
\(814\) | −46778.6 | −2.01424 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6685.17 | −0.286799 | ||||||||
\(817\) | −10852.9 | −0.464742 | ||||||||
\(818\) | 17552.7 | 0.750265 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5647.23 | 0.240061 | 0.120030 | − | 0.992770i | \(-0.461701\pi\) | ||||
0.120030 | + | 0.992770i | \(0.461701\pi\) | |||||||
\(822\) | 7663.87 | 0.325192 | ||||||||
\(823\) | 3345.59 | 0.141701 | 0.0708505 | − | 0.997487i | \(-0.477429\pi\) | ||||
0.0708505 | + | 0.997487i | \(0.477429\pi\) | |||||||
\(824\) | −9146.74 | −0.386701 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19034.4 | −0.800351 | −0.400176 | − | 0.916439i | \(-0.631051\pi\) | ||||
−0.400176 | + | 0.916439i | \(0.631051\pi\) | |||||||
\(828\) | 5175.47 | 0.217222 | ||||||||
\(829\) | 20374.7 | 0.853610 | 0.426805 | − | 0.904344i | \(-0.359639\pi\) | ||||
0.426805 | + | 0.904344i | \(0.359639\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18579.7 | −0.775600 | ||||||||
\(832\) | −1503.62 | −0.0626545 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6970.21 | −0.289399 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −15212.9 | −0.629363 | ||||||||
\(837\) | −23610.0 | −0.975005 | ||||||||
\(838\) | 18596.6 | 0.766598 | ||||||||
\(839\) | −27187.7 | −1.11874 | −0.559370 | − | 0.828918i | \(-0.688957\pi\) | ||||
−0.559370 | + | 0.828918i | \(0.688957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 67499.2 | 2.76761 | ||||||||
\(842\) | 34348.7 | 1.40586 | ||||||||
\(843\) | −22524.8 | −0.920277 | ||||||||
\(844\) | −13482.8 | −0.549879 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7896.03 | −0.320888 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3115.19 | −0.126151 | ||||||||
\(849\) | 6476.20 | 0.261793 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28174.7 | −1.13492 | ||||||||
\(852\) | −5450.17 | −0.219154 | ||||||||
\(853\) | −45014.0 | −1.80686 | −0.903429 | − | 0.428737i | \(-0.858959\pi\) | ||||
−0.903429 | + | 0.428737i | \(0.858959\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8534.05 | 0.340757 | ||||||||
\(857\) | 29713.4 | 1.18435 | 0.592176 | − | 0.805809i | \(-0.298269\pi\) | ||||
0.592176 | + | 0.805809i | \(0.298269\pi\) | |||||||
\(858\) | −8857.04 | −0.352418 | ||||||||
\(859\) | −29637.3 | −1.17720 | −0.588598 | − | 0.808426i | \(-0.700320\pi\) | ||||
−0.588598 | + | 0.808426i | \(0.700320\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11545.9 | −0.456214 | ||||||||
\(863\) | −32883.9 | −1.29708 | −0.648540 | − | 0.761181i | \(-0.724620\pi\) | ||||
−0.648540 | + | 0.761181i | \(0.724620\pi\) | |||||||
\(864\) | −4384.69 | −0.172651 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 24213.5 | 0.950126 | ||||||||
\(867\) | −41622.0 | −1.63040 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15888.9 | 0.620248 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2688.89 | −0.104604 | ||||||||
\(872\) | −3783.88 | −0.146947 | ||||||||
\(873\) | 13139.4 | 0.509393 | ||||||||
\(874\) | −9162.67 | −0.354613 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9912.72 | 0.382328 | ||||||||
\(877\) | −12292.6 | −0.473309 | −0.236655 | − | 0.971594i | \(-0.576051\pi\) | ||||
−0.236655 | + | 0.971594i | \(0.576051\pi\) | |||||||
\(878\) | −4079.91 | −0.156823 | ||||||||
\(879\) | 18177.3 | 0.697504 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23257.3 | −0.889395 | −0.444697 | − | 0.895681i | \(-0.646689\pi\) | ||||
−0.444697 | + | 0.895681i | \(0.646689\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10929.8 | 0.416555 | 0.208278 | − | 0.978070i | \(-0.433214\pi\) | ||||
0.208278 | + | 0.978070i | \(0.433214\pi\) | |||||||
\(884\) | −12761.5 | −0.485539 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12724.9 | −0.482508 | ||||||||
\(887\) | 6285.76 | 0.237943 | 0.118971 | − | 0.992898i | \(-0.462040\pi\) | ||||
0.118971 | + | 0.992898i | \(0.462040\pi\) | |||||||
\(888\) | 9397.68 | 0.355141 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3173.04 | 0.119305 | ||||||||
\(892\) | 123.673 | 0.00464223 | ||||||||
\(893\) | 13979.1 | 0.523845 | ||||||||
\(894\) | 3206.92 | 0.119973 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5334.57 | −0.198569 | ||||||||
\(898\) | −687.387 | −0.0255439 | ||||||||
\(899\) | 52232.0 | 1.93775 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26439.3 | −0.977603 | ||||||||
\(902\) | 20004.0 | 0.738427 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1850.08 | 0.0680671 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9307.70 | 0.341311 | ||||||||
\(907\) | 12943.4 | 0.473847 | 0.236924 | − | 0.971528i | \(-0.423861\pi\) | ||||
0.236924 | + | 0.971528i | \(0.423861\pi\) | |||||||
\(908\) | 18217.0 | 0.665807 | ||||||||
\(909\) | 33929.8 | 1.23804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18006.8 | −0.654875 | −0.327437 | − | 0.944873i | \(-0.606185\pi\) | ||||
−0.327437 | + | 0.944873i | \(0.606185\pi\) | |||||||
\(912\) | 3056.22 | 0.110966 | ||||||||
\(913\) | 65533.0 | 2.37549 | ||||||||
\(914\) | 36653.1 | 1.32645 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11218.2 | −0.404651 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −37213.8 | −1.33795 | ||||||||
\(919\) | −48868.4 | −1.75410 | −0.877051 | − | 0.480397i | \(-0.840493\pi\) | ||||
−0.877051 | + | 0.480397i | \(0.840493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9814.67 | −0.351145 | ||||||||
\(922\) | 29650.4 | 1.05909 | ||||||||
\(923\) | −10404.0 | −0.371020 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24665.9 | 0.875347 | ||||||||
\(927\) | −20046.2 | −0.710251 | ||||||||
\(928\) | 9700.18 | 0.343129 | ||||||||
\(929\) | 44492.8 | 1.57133 | 0.785664 | − | 0.618654i | \(-0.212322\pi\) | ||||
0.785664 | + | 0.618654i | \(0.212322\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10820.2 | −0.380288 | ||||||||
\(933\) | 16058.3 | 0.563480 | ||||||||
\(934\) | −12399.1 | −0.434379 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3295.36 | −0.115077 | ||||||||
\(937\) | 25114.8 | 0.875631 | 0.437815 | − | 0.899065i | \(-0.355752\pi\) | ||||
0.437815 | + | 0.899065i | \(0.355752\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18805.0 | 0.653544 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4877.52 | 0.168972 | 0.0844859 | − | 0.996425i | \(-0.473075\pi\) | ||||
0.0844859 | + | 0.996425i | \(0.473075\pi\) | |||||||
\(942\) | 3841.34 | 0.132864 | ||||||||
\(943\) | 12048.4 | 0.416065 | ||||||||
\(944\) | −1152.29 | −0.0397288 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21419.6 | −0.736166 | ||||||||
\(947\) | −22786.4 | −0.781897 | −0.390949 | − | 0.920412i | \(-0.627853\pi\) | ||||
−0.390949 | + | 0.920412i | \(0.627853\pi\) | |||||||
\(948\) | −3192.04 | −0.109359 | ||||||||
\(949\) | 18922.7 | 0.647267 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7889.94 | 0.269031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19829.0 | 0.674001 | 0.337001 | − | 0.941504i | \(-0.390588\pi\) | ||||
0.337001 | + | 0.941504i | \(0.390588\pi\) | |||||||
\(954\) | −6827.31 | −0.231700 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −255.334 | −0.00863815 | ||||||||
\(957\) | 57138.8 | 1.93003 | ||||||||
\(958\) | 35248.4 | 1.18875 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −100.826 | −0.00338445 | ||||||||
\(962\) | 17939.5 | 0.601240 | ||||||||
\(963\) | 18703.4 | 0.625865 | ||||||||
\(964\) | −359.492 | −0.0120108 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34545.8 | −1.14883 | −0.574415 | − | 0.818565i | \(-0.694770\pi\) | ||||
−0.574415 | + | 0.818565i | \(0.694770\pi\) | |||||||
\(968\) | −19376.7 | −0.643378 | ||||||||
\(969\) | 25938.8 | 0.859931 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7539.06 | −0.249166 | −0.124583 | − | 0.992209i | \(-0.539759\pi\) | ||||
−0.124583 | + | 0.992209i | \(0.539759\pi\) | |||||||
\(972\) | −15435.8 | −0.509365 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −15926.1 | −0.523928 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2615.43 | 0.0857764 | ||||||||
\(977\) | 33471.7 | 1.09606 | 0.548032 | − | 0.836457i | \(-0.315377\pi\) | ||||
0.548032 | + | 0.836457i | \(0.315377\pi\) | |||||||
\(978\) | 12028.3 | 0.393276 | ||||||||
\(979\) | 63552.9 | 2.07473 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8292.81 | −0.269897 | ||||||||
\(982\) | −22836.4 | −0.742096 | ||||||||
\(983\) | −10059.6 | −0.326399 | −0.163199 | − | 0.986593i | \(-0.552181\pi\) | ||||
−0.163199 | + | 0.986593i | \(0.552181\pi\) | |||||||
\(984\) | −4018.75 | −0.130196 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 82327.6 | 2.65907 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5834.10 | 0.187862 | ||||||||
\(989\) | −12901.0 | −0.414791 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30773.7 | −0.986436 | −0.493218 | − | 0.869906i | \(-0.664180\pi\) | ||||
−0.493218 | + | 0.869906i | \(0.664180\pi\) | |||||||
\(992\) | 5513.87 | 0.176477 | ||||||||
\(993\) | 12654.8 | 0.404419 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13165.4 | −0.418836 | ||||||||
\(997\) | −20870.8 | −0.662974 | −0.331487 | − | 0.943460i | \(-0.607550\pi\) | ||||
−0.331487 | + | 0.943460i | \(0.607550\pi\) | |||||||
\(998\) | 9331.79 | 0.295984 | ||||||||
\(999\) | 52313.3 | 1.65678 |
(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 | 2450.4.a.ck.1.2 | 4 | ||
5.4 | even | 2 | 2450.4.a.cu.1.3 | 4 | |||
7.3 | odd | 6 | 350.4.e.m.51.2 | yes | 8 | ||
7.5 | odd | 6 | 350.4.e.m.151.2 | yes | 8 | ||
7.6 | odd | 2 | 2450.4.a.co.1.3 | 4 | |||
35.3 | even | 12 | 350.4.j.j.149.3 | 16 | |||
35.12 | even | 12 | 350.4.j.j.249.3 | 16 | |||
35.17 | even | 12 | 350.4.j.j.149.6 | 16 | |||
35.19 | odd | 6 | 350.4.e.l.151.3 | yes | 8 | ||
35.24 | odd | 6 | 350.4.e.l.51.3 | ✓ | 8 | ||
35.33 | even | 12 | 350.4.j.j.249.6 | 16 | |||
35.34 | odd | 2 | 2450.4.a.cq.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.4.e.l.51.3 | ✓ | 8 | 35.24 | odd | 6 | ||
350.4.e.l.151.3 | yes | 8 | 35.19 | odd | 6 | ||
350.4.e.m.51.2 | yes | 8 | 7.3 | odd | 6 | ||
350.4.e.m.151.2 | yes | 8 | 7.5 | odd | 6 | ||
350.4.j.j.149.3 | 16 | 35.3 | even | 12 | |||
350.4.j.j.149.6 | 16 | 35.17 | even | 12 | |||
350.4.j.j.249.3 | 16 | 35.12 | even | 12 | |||
350.4.j.j.249.6 | 16 | 35.33 | even | 12 | |||
2450.4.a.ck.1.2 | 4 | 1.1 | even | 1 | trivial | ||
2450.4.a.co.1.3 | 4 | 7.6 | odd | 2 | |||
2450.4.a.cq.1.2 | 4 | 35.34 | odd | 2 | |||
2450.4.a.cu.1.3 | 4 | 5.4 | even | 2 |