Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,4,Mod(1,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, 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("675.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.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: | \(39.8262892539\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.467024.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 26x^{2} + 101 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 135) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-4.60936\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.56155 | 1.25920 | 0.629600 | − | 0.776920i | \(-0.283219\pi\) | ||||
0.629600 | + | 0.776920i | \(0.283219\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.68466 | 0.585582 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.06288 | −0.327365 | −0.163682 | − | 0.986513i | \(-0.552337\pi\) | ||||
−0.163682 | + | 0.986513i | \(0.552337\pi\) | |||||||
\(8\) | −11.8078 | −0.521834 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 61.3752 | 1.68230 | 0.841151 | − | 0.540800i | \(-0.181878\pi\) | ||||
0.841151 | + | 0.540800i | \(0.181878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −70.8427 | −1.51140 | −0.755702 | − | 0.654916i | \(-0.772704\pi\) | ||||
−0.755702 | + | 0.654916i | \(0.772704\pi\) | |||||||
\(14\) | −21.5933 | −0.412218 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −79.5312 | −1.24268 | ||||||||
\(17\) | −51.5464 | −0.735402 | −0.367701 | − | 0.929944i | \(-0.619855\pi\) | ||||
−0.367701 | + | 0.929944i | \(0.619855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 15.7926 | 0.190688 | 0.0953440 | − | 0.995444i | \(-0.469605\pi\) | ||||
0.0953440 | + | 0.995444i | \(0.469605\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 218.591 | 2.11835 | ||||||||
\(23\) | −114.885 | −1.04153 | −0.520767 | − | 0.853699i | \(-0.674354\pi\) | ||||
−0.520767 | + | 0.853699i | \(0.674354\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −252.310 | −1.90316 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −28.4025 | −0.191699 | ||||||||
\(29\) | 39.7819 | 0.254735 | 0.127368 | − | 0.991856i | \(-0.459347\pi\) | ||||
0.127368 | + | 0.991856i | \(0.459347\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −240.170 | −1.39148 | −0.695740 | − | 0.718294i | \(-0.744923\pi\) | ||||
−0.695740 | + | 0.718294i | \(0.744923\pi\) | |||||||
\(32\) | −188.793 | −1.04294 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −183.585 | −0.926018 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −129.560 | −0.575662 | −0.287831 | − | 0.957681i | \(-0.592934\pi\) | ||||
−0.287831 | + | 0.957681i | \(0.592934\pi\) | |||||||
\(38\) | 56.2462 | 0.240114 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 262.524 | 0.999985 | 0.499992 | − | 0.866030i | \(-0.333336\pi\) | ||||
0.499992 | + | 0.866030i | \(0.333336\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 127.648 | 0.452700 | 0.226350 | − | 0.974046i | \(-0.427321\pi\) | ||||
0.226350 | + | 0.974046i | \(0.427321\pi\) | |||||||
\(44\) | 287.522 | 0.985126 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −409.170 | −1.31150 | ||||||||
\(47\) | −85.2140 | −0.264463 | −0.132231 | − | 0.991219i | \(-0.542214\pi\) | ||||
−0.132231 | + | 0.991219i | \(0.542214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −306.241 | −0.892832 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −331.874 | −0.885051 | ||||||||
\(53\) | −328.184 | −0.850557 | −0.425278 | − | 0.905063i | \(-0.639824\pi\) | ||||
−0.425278 | + | 0.905063i | \(0.639824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 71.5891 | 0.170830 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 141.685 | 0.320762 | ||||||||
\(59\) | −687.580 | −1.51721 | −0.758605 | − | 0.651551i | \(-0.774119\pi\) | ||||
−0.758605 | + | 0.651551i | \(0.774119\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −455.685 | −0.956466 | −0.478233 | − | 0.878233i | \(-0.658723\pi\) | ||||
−0.478233 | + | 0.878233i | \(0.658723\pi\) | |||||||
\(62\) | −855.380 | −1.75215 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −36.1449 | −0.0705955 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −955.421 | −1.74214 | −0.871069 | − | 0.491161i | \(-0.836573\pi\) | ||||
−0.871069 | + | 0.491161i | \(0.836573\pi\) | |||||||
\(68\) | −241.477 | −0.430639 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −160.201 | −0.267780 | −0.133890 | − | 0.990996i | \(-0.542747\pi\) | ||||
−0.133890 | + | 0.990996i | \(0.542747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 702.364 | 1.12610 | 0.563052 | − | 0.826422i | \(-0.309627\pi\) | ||||
0.563052 | + | 0.826422i | \(0.309627\pi\) | |||||||
\(74\) | −461.434 | −0.724873 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 73.9830 | 0.111664 | ||||||||
\(77\) | −372.111 | −0.550727 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 65.3608 | 0.0930844 | 0.0465422 | − | 0.998916i | \(-0.485180\pi\) | ||||
0.0465422 | + | 0.998916i | \(0.485180\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 934.993 | 1.25918 | ||||||||
\(83\) | 996.623 | 1.31800 | 0.658998 | − | 0.752145i | \(-0.270981\pi\) | ||||
0.658998 | + | 0.752145i | \(0.270981\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 454.624 | 0.570040 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −724.704 | −0.877883 | ||||||||
\(89\) | 1337.71 | 1.59322 | 0.796612 | − | 0.604491i | \(-0.206623\pi\) | ||||
0.796612 | + | 0.604491i | \(0.206623\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 429.511 | 0.494780 | ||||||||
\(92\) | −538.199 | −0.609903 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −303.494 | −0.333011 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1404.40 | 1.47006 | 0.735028 | − | 0.678037i | \(-0.237169\pi\) | ||||
0.735028 | + | 0.678037i | \(0.237169\pi\) | |||||||
\(98\) | −1090.70 | −1.12425 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1110.40 | −1.09395 | −0.546974 | − | 0.837150i | \(-0.684220\pi\) | ||||
−0.546974 | + | 0.837150i | \(0.684220\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 509.937 | 0.487821 | 0.243911 | − | 0.969798i | \(-0.421570\pi\) | ||||
0.243911 | + | 0.969798i | \(0.421570\pi\) | |||||||
\(104\) | 836.494 | 0.788702 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1168.84 | −1.07102 | ||||||||
\(107\) | −1748.35 | −1.57962 | −0.789809 | − | 0.613353i | \(-0.789820\pi\) | ||||
−0.789809 | + | 0.613353i | \(0.789820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1357.35 | 1.19276 | 0.596381 | − | 0.802702i | \(-0.296605\pi\) | ||||
0.596381 | + | 0.802702i | \(0.296605\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 482.189 | 0.406809 | ||||||||
\(113\) | −1153.33 | −0.960139 | −0.480070 | − | 0.877230i | \(-0.659389\pi\) | ||||
−0.480070 | + | 0.877230i | \(0.659389\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 186.365 | 0.149168 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2448.85 | −1.91047 | ||||||||
\(119\) | 312.520 | 0.240745 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2435.92 | 1.83014 | ||||||||
\(122\) | −1622.94 | −1.20438 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1125.12 | −0.814826 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1978.79 | −1.38259 | −0.691297 | − | 0.722571i | \(-0.742960\pi\) | ||||
−0.691297 | + | 0.722571i | \(0.742960\pi\) | |||||||
\(128\) | 1381.61 | 0.954048 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −160.293 | −0.106908 | −0.0534538 | − | 0.998570i | \(-0.517023\pi\) | ||||
−0.0534538 | + | 0.998570i | \(0.517023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −95.7488 | −0.0624246 | ||||||||
\(134\) | −3402.78 | −2.19370 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 608.648 | 0.383758 | ||||||||
\(137\) | −661.330 | −0.412418 | −0.206209 | − | 0.978508i | \(-0.566113\pi\) | ||||
−0.206209 | + | 0.978508i | \(0.566113\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2126.16 | 1.29740 | 0.648699 | − | 0.761045i | \(-0.275313\pi\) | ||||
0.648699 | + | 0.761045i | \(0.275313\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −570.566 | −0.337189 | ||||||||
\(143\) | −4347.99 | −2.54264 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2501.51 | 1.41799 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −606.943 | −0.337097 | ||||||||
\(149\) | −670.649 | −0.368736 | −0.184368 | − | 0.982857i | \(-0.559024\pi\) | ||||
−0.184368 | + | 0.982857i | \(0.559024\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1440.42 | 0.776291 | 0.388146 | − | 0.921598i | \(-0.373116\pi\) | ||||
0.388146 | + | 0.921598i | \(0.373116\pi\) | |||||||
\(152\) | −186.475 | −0.0995076 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1325.29 | −0.693475 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3037.28 | 1.54396 | 0.771979 | − | 0.635648i | \(-0.219267\pi\) | ||||
0.771979 | + | 0.635648i | \(0.219267\pi\) | |||||||
\(158\) | 232.786 | 0.117212 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 696.537 | 0.340961 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1243.27 | 0.597426 | 0.298713 | − | 0.954343i | \(-0.403443\pi\) | ||||
0.298713 | + | 0.954343i | \(0.403443\pi\) | |||||||
\(164\) | 1229.84 | 0.585573 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3549.53 | 1.65962 | ||||||||
\(167\) | 165.425 | 0.0766526 | 0.0383263 | − | 0.999265i | \(-0.487797\pi\) | ||||
0.0383263 | + | 0.999265i | \(0.487797\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2821.69 | 1.28434 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 597.986 | 0.265093 | ||||||||
\(173\) | 1931.11 | 0.848666 | 0.424333 | − | 0.905506i | \(-0.360509\pi\) | ||||
0.424333 | + | 0.905506i | \(0.360509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4881.25 | −2.09056 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4764.32 | 2.00619 | ||||||||
\(179\) | −623.874 | −0.260506 | −0.130253 | − | 0.991481i | \(-0.541579\pi\) | ||||
−0.130253 | + | 0.991481i | \(0.541579\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1139.12 | 0.467792 | 0.233896 | − | 0.972262i | \(-0.424853\pi\) | ||||
0.233896 | + | 0.972262i | \(0.424853\pi\) | |||||||
\(182\) | 1529.73 | 0.623027 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1356.54 | 0.543508 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3163.67 | −1.23717 | ||||||||
\(188\) | −399.199 | −0.154865 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −468.059 | −0.177317 | −0.0886586 | − | 0.996062i | \(-0.528258\pi\) | ||||
−0.0886586 | + | 0.996062i | \(0.528258\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2479.17 | −0.924634 | −0.462317 | − | 0.886715i | \(-0.652982\pi\) | ||||
−0.462317 | + | 0.886715i | \(0.652982\pi\) | |||||||
\(194\) | 5001.85 | 1.85109 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1434.64 | −0.522827 | ||||||||
\(197\) | −2401.87 | −0.868660 | −0.434330 | − | 0.900754i | \(-0.643015\pi\) | ||||
−0.434330 | + | 0.900754i | \(0.643015\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1039.02 | −0.370121 | −0.185061 | − | 0.982727i | \(-0.559248\pi\) | ||||
−0.185061 | + | 0.982727i | \(0.559248\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3954.74 | −1.37750 | ||||||||
\(203\) | −241.193 | −0.0833914 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1816.17 | 0.614264 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5634.21 | 1.87818 | ||||||||
\(209\) | 969.275 | 0.320795 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3311.99 | 1.08060 | 0.540301 | − | 0.841472i | \(-0.318310\pi\) | ||||
0.540301 | + | 0.841472i | \(0.318310\pi\) | |||||||
\(212\) | −1537.43 | −0.498071 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6226.83 | −1.98905 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1456.13 | 0.455522 | ||||||||
\(218\) | 4834.29 | 1.50192 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3651.69 | 1.11149 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3985.66 | −1.19686 | −0.598429 | − | 0.801176i | \(-0.704208\pi\) | ||||
−0.598429 | + | 0.801176i | \(0.704208\pi\) | |||||||
\(224\) | 1144.63 | 0.341423 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4107.63 | −1.20901 | ||||||||
\(227\) | 4430.88 | 1.29554 | 0.647770 | − | 0.761836i | \(-0.275702\pi\) | ||||
0.647770 | + | 0.761836i | \(0.275702\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4653.72 | 1.34291 | 0.671456 | − | 0.741045i | \(-0.265669\pi\) | ||||
0.671456 | + | 0.741045i | \(0.265669\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −469.736 | −0.132930 | ||||||||
\(233\) | −2296.46 | −0.645692 | −0.322846 | − | 0.946452i | \(-0.604640\pi\) | ||||
−0.322846 | + | 0.946452i | \(0.604640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3221.08 | −0.888451 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1113.06 | 0.303146 | ||||||||
\(239\) | −3418.55 | −0.925220 | −0.462610 | − | 0.886562i | \(-0.653087\pi\) | ||||
−0.462610 | + | 0.886562i | \(0.653087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5904.16 | −1.57809 | −0.789047 | − | 0.614333i | \(-0.789425\pi\) | ||||
−0.789047 | + | 0.614333i | \(0.789425\pi\) | |||||||
\(242\) | 8675.65 | 2.30451 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2134.73 | −0.560090 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1118.79 | −0.288206 | ||||||||
\(248\) | 2835.88 | 0.726122 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2391.39 | 0.601368 | 0.300684 | − | 0.953724i | \(-0.402785\pi\) | ||||
0.300684 | + | 0.953724i | \(0.402785\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7051.12 | −1.75217 | ||||||||
\(254\) | −7047.57 | −1.74096 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5209.83 | 1.27193 | ||||||||
\(257\) | 3580.72 | 0.869102 | 0.434551 | − | 0.900647i | \(-0.356907\pi\) | ||||
0.434551 | + | 0.900647i | \(0.356907\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 785.505 | 0.188451 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −570.893 | −0.134618 | ||||||||
\(263\) | 1703.58 | 0.399419 | 0.199709 | − | 0.979855i | \(-0.436000\pi\) | ||||
0.199709 | + | 0.979855i | \(0.436000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −341.014 | −0.0786050 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4475.82 | −1.02017 | ||||||||
\(269\) | −4087.14 | −0.926385 | −0.463192 | − | 0.886258i | \(-0.653296\pi\) | ||||
−0.463192 | + | 0.886258i | \(0.653296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4572.37 | −1.02492 | −0.512458 | − | 0.858713i | \(-0.671265\pi\) | ||||
−0.512458 | + | 0.858713i | \(0.671265\pi\) | |||||||
\(272\) | 4099.55 | 0.913866 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2355.36 | −0.519316 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8334.59 | 1.80786 | 0.903929 | − | 0.427682i | \(-0.140670\pi\) | ||||
0.903929 | + | 0.427682i | \(0.140670\pi\) | |||||||
\(278\) | 7572.43 | 1.63368 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2490.50 | −0.528721 | −0.264360 | − | 0.964424i | \(-0.585161\pi\) | ||||
−0.264360 | + | 0.964424i | \(0.585161\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7132.72 | 1.49822 | 0.749110 | − | 0.662445i | \(-0.230481\pi\) | ||||
0.749110 | + | 0.662445i | \(0.230481\pi\) | |||||||
\(284\) | −750.489 | −0.156807 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15485.6 | −3.20169 | ||||||||
\(287\) | −1591.65 | −0.327360 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2255.97 | −0.459184 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3290.34 | 0.659426 | ||||||||
\(293\) | −4915.24 | −0.980039 | −0.490020 | − | 0.871711i | \(-0.663010\pi\) | ||||
−0.490020 | + | 0.871711i | \(0.663010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1529.81 | 0.300400 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2388.55 | −0.464313 | ||||||||
\(299\) | 8138.80 | 1.57418 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −773.914 | −0.148198 | ||||||||
\(302\) | 5130.14 | 0.977505 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1256.01 | −0.236963 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5798.84 | 1.07804 | 0.539018 | − | 0.842294i | \(-0.318795\pi\) | ||||
0.539018 | + | 0.842294i | \(0.318795\pi\) | |||||||
\(308\) | −1743.21 | −0.322496 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −60.3935 | −0.0110116 | −0.00550579 | − | 0.999985i | \(-0.501753\pi\) | ||||
−0.00550579 | + | 0.999985i | \(0.501753\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 605.307 | 0.109310 | 0.0546549 | − | 0.998505i | \(-0.482594\pi\) | ||||
0.0546549 | + | 0.998505i | \(0.482594\pi\) | |||||||
\(314\) | 10817.4 | 1.94415 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 306.193 | 0.0545086 | ||||||||
\(317\) | −3144.61 | −0.557157 | −0.278578 | − | 0.960414i | \(-0.589863\pi\) | ||||
−0.278578 | + | 0.960414i | \(0.589863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2441.63 | 0.428542 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2480.75 | 0.429338 | ||||||||
\(323\) | −814.052 | −0.140232 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4427.97 | 0.752278 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3099.82 | −0.521826 | ||||||||
\(329\) | 516.643 | 0.0865758 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2122.94 | −0.352529 | −0.176265 | − | 0.984343i | \(-0.556401\pi\) | ||||
−0.176265 | + | 0.984343i | \(0.556401\pi\) | |||||||
\(332\) | 4668.84 | 0.771795 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 589.170 | 0.0965209 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1486.39 | −0.240263 | −0.120132 | − | 0.992758i | \(-0.538332\pi\) | ||||
−0.120132 | + | 0.992758i | \(0.538332\pi\) | |||||||
\(338\) | 10049.6 | 1.61724 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14740.5 | −2.34089 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3936.28 | 0.619647 | ||||||||
\(344\) | −1507.24 | −0.236235 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6877.74 | 1.06864 | ||||||||
\(347\) | 7649.36 | 1.18340 | 0.591699 | − | 0.806159i | \(-0.298457\pi\) | ||||
0.591699 | + | 0.806159i | \(0.298457\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1123.61 | −0.172337 | −0.0861683 | − | 0.996281i | \(-0.527462\pi\) | ||||
−0.0861683 | + | 0.996281i | \(0.527462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11587.2 | −1.75454 | ||||||||
\(353\) | −12564.5 | −1.89446 | −0.947228 | − | 0.320560i | \(-0.896129\pi\) | ||||
−0.947228 | + | 0.320560i | \(0.896129\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6266.71 | 0.932964 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2221.96 | −0.328029 | ||||||||
\(359\) | 2491.02 | 0.366214 | 0.183107 | − | 0.983093i | \(-0.441384\pi\) | ||||
0.183107 | + | 0.983093i | \(0.441384\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6609.59 | −0.963638 | ||||||||
\(362\) | 4057.04 | 0.589043 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2012.11 | 0.289735 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12962.0 | −1.84363 | −0.921816 | − | 0.387629i | \(-0.873294\pi\) | ||||
−0.921816 | + | 0.387629i | \(0.873294\pi\) | |||||||
\(368\) | 9136.98 | 1.29429 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1989.74 | 0.278442 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5045.73 | −0.700424 | −0.350212 | − | 0.936670i | \(-0.613890\pi\) | ||||
−0.350212 | + | 0.936670i | \(0.613890\pi\) | |||||||
\(374\) | −11267.6 | −1.55784 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1006.19 | 0.138006 | ||||||||
\(377\) | −2818.26 | −0.385008 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 357.793 | 0.0484923 | 0.0242461 | − | 0.999706i | \(-0.492281\pi\) | ||||
0.0242461 | + | 0.999706i | \(0.492281\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1667.02 | −0.223278 | ||||||||
\(383\) | −886.550 | −0.118278 | −0.0591391 | − | 0.998250i | \(-0.518836\pi\) | ||||
−0.0591391 | + | 0.998250i | \(0.518836\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8829.69 | −1.16430 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6579.14 | 0.860838 | ||||||||
\(389\) | −8284.92 | −1.07985 | −0.539926 | − | 0.841713i | \(-0.681548\pi\) | ||||
−0.539926 | + | 0.841713i | \(0.681548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5921.93 | 0.765946 | ||||||||
\(392\) | 3616.03 | 0.465911 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8554.38 | −1.09382 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4474.56 | −0.565672 | −0.282836 | − | 0.959168i | \(-0.591275\pi\) | ||||
−0.282836 | + | 0.959168i | \(0.591275\pi\) | |||||||
\(398\) | −3700.52 | −0.466056 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10558.3 | 1.31486 | 0.657428 | − | 0.753517i | \(-0.271644\pi\) | ||||
0.657428 | + | 0.753517i | \(0.271644\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17014.3 | 2.10309 | ||||||||
\(404\) | −5201.83 | −0.640596 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −859.023 | −0.105006 | ||||||||
\(407\) | −7951.75 | −0.968437 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5232.44 | −0.632586 | −0.316293 | − | 0.948662i | \(-0.602438\pi\) | ||||
−0.316293 | + | 0.948662i | \(0.602438\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2388.88 | 0.285659 | ||||||||
\(413\) | 4168.72 | 0.496681 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 13374.6 | 1.57631 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3452.12 | 0.403945 | ||||||||
\(419\) | 3903.81 | 0.455164 | 0.227582 | − | 0.973759i | \(-0.426918\pi\) | ||||
0.227582 | + | 0.973759i | \(0.426918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6274.83 | 0.726405 | 0.363203 | − | 0.931710i | \(-0.381683\pi\) | ||||
0.363203 | + | 0.931710i | \(0.381683\pi\) | |||||||
\(422\) | 11795.8 | 1.36069 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3875.12 | 0.443850 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2762.76 | 0.313114 | ||||||||
\(428\) | −8190.41 | −0.924996 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8040.40 | 0.898590 | 0.449295 | − | 0.893383i | \(-0.351675\pi\) | ||||
0.449295 | + | 0.893383i | \(0.351675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3121.18 | −0.346407 | −0.173204 | − | 0.984886i | \(-0.555412\pi\) | ||||
−0.173204 | + | 0.984886i | \(0.555412\pi\) | |||||||
\(434\) | 5186.07 | 0.573593 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6358.74 | 0.698460 | ||||||||
\(437\) | −1814.34 | −0.198608 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2373.05 | −0.257994 | −0.128997 | − | 0.991645i | \(-0.541176\pi\) | ||||
−0.128997 | + | 0.991645i | \(0.541176\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13005.7 | 1.39959 | ||||||||
\(443\) | −13152.7 | −1.41062 | −0.705311 | − | 0.708898i | \(-0.749193\pi\) | ||||
−0.705311 | + | 0.708898i | \(0.749193\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14195.1 | −1.50708 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 219.142 | 0.0231105 | ||||||||
\(449\) | 9265.76 | 0.973893 | 0.486947 | − | 0.873432i | \(-0.338111\pi\) | ||||
0.486947 | + | 0.873432i | \(0.338111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16112.5 | 1.68228 | ||||||||
\(452\) | −5402.94 | −0.562241 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15780.8 | 1.63134 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6314.89 | −0.646385 | −0.323193 | − | 0.946333i | \(-0.604756\pi\) | ||||
−0.323193 | + | 0.946333i | \(0.604756\pi\) | |||||||
\(458\) | 16574.5 | 1.69099 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4870.70 | −0.492084 | −0.246042 | − | 0.969259i | \(-0.579130\pi\) | ||||
−0.246042 | + | 0.969259i | \(0.579130\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4892.25 | −0.491063 | −0.245531 | − | 0.969389i | \(-0.578962\pi\) | ||||
−0.245531 | + | 0.969389i | \(0.578962\pi\) | |||||||
\(464\) | −3163.91 | −0.316553 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8178.97 | −0.813055 | ||||||||
\(467\) | −6854.09 | −0.679164 | −0.339582 | − | 0.940577i | \(-0.610286\pi\) | ||||
−0.339582 | + | 0.940577i | \(0.610286\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5792.61 | 0.570315 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8118.79 | 0.791732 | ||||||||
\(473\) | 7834.41 | 0.761579 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1464.05 | 0.140976 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12175.3 | −1.16504 | ||||||||
\(479\) | 8572.26 | 0.817696 | 0.408848 | − | 0.912602i | \(-0.365931\pi\) | ||||
0.408848 | + | 0.912602i | \(0.365931\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9178.36 | 0.870057 | ||||||||
\(482\) | −21028.0 | −1.98713 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11411.4 | 1.07170 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5413.38 | 0.503704 | 0.251852 | − | 0.967766i | \(-0.418960\pi\) | ||||
0.251852 | + | 0.967766i | \(0.418960\pi\) | |||||||
\(488\) | 5380.62 | 0.499117 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10314.3 | −0.948025 | −0.474012 | − | 0.880518i | \(-0.657195\pi\) | ||||
−0.474012 | + | 0.880518i | \(0.657195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2050.62 | −0.187333 | ||||||||
\(494\) | −3984.64 | −0.362909 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19101.1 | 1.72916 | ||||||||
\(497\) | 971.282 | 0.0876619 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13527.2 | −1.21355 | −0.606774 | − | 0.794874i | \(-0.707537\pi\) | ||||
−0.606774 | + | 0.794874i | \(0.707537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8517.08 | 0.757243 | ||||||||
\(503\) | 245.421 | 0.0217550 | 0.0108775 | − | 0.999941i | \(-0.496538\pi\) | ||||
0.0108775 | + | 0.999941i | \(0.496538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −25112.9 | −2.20634 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9269.96 | −0.809622 | ||||||||
\(509\) | 4680.90 | 0.407617 | 0.203809 | − | 0.979011i | \(-0.434668\pi\) | ||||
0.203809 | + | 0.979011i | \(0.434668\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4258.35 | −0.368647 | ||||||||
\(512\) | 7502.22 | 0.647567 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12752.9 | 1.09437 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5230.03 | −0.444906 | ||||||||
\(518\) | 2797.62 | 0.237298 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10212.1 | 0.858735 | 0.429368 | − | 0.903130i | \(-0.358736\pi\) | ||||
0.429368 | + | 0.903130i | \(0.358736\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8159.59 | 0.682207 | 0.341103 | − | 0.940026i | \(-0.389199\pi\) | ||||
0.341103 | + | 0.940026i | \(0.389199\pi\) | |||||||
\(524\) | −750.919 | −0.0626032 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6067.38 | 0.502947 | ||||||||
\(527\) | 12379.9 | 1.02330 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1031.66 | 0.0847913 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −448.550 | −0.0365547 | ||||||||
\(533\) | −18597.9 | −1.51138 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11281.4 | 0.909108 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14556.6 | −1.16650 | ||||||||
\(539\) | −18795.6 | −1.50201 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7889.11 | −0.626949 | −0.313474 | − | 0.949597i | \(-0.601493\pi\) | ||||
−0.313474 | + | 0.949597i | \(0.601493\pi\) | |||||||
\(542\) | −16284.8 | −1.29057 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9731.58 | 0.766982 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1394.62 | 0.109012 | 0.0545060 | − | 0.998513i | \(-0.482642\pi\) | ||||
0.0545060 | + | 0.998513i | \(0.482642\pi\) | |||||||
\(548\) | −3098.11 | −0.241505 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 628.261 | 0.0485750 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −396.275 | −0.0304726 | ||||||||
\(554\) | 29684.1 | 2.27645 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9960.33 | 0.759734 | ||||||||
\(557\) | −19617.8 | −1.49234 | −0.746169 | − | 0.665756i | \(-0.768109\pi\) | ||||
−0.746169 | + | 0.665756i | \(0.768109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9042.92 | −0.684212 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8870.03 | −0.665765 | ||||||||
\(563\) | 1339.24 | 0.100253 | 0.0501263 | − | 0.998743i | \(-0.484038\pi\) | ||||
0.0501263 | + | 0.998743i | \(0.484038\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25403.6 | 1.88656 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1891.62 | 0.139737 | ||||||||
\(569\) | −26030.2 | −1.91783 | −0.958914 | − | 0.283696i | \(-0.908439\pi\) | ||||
−0.958914 | + | 0.283696i | \(0.908439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10020.8 | −0.734426 | −0.367213 | − | 0.930137i | \(-0.619688\pi\) | ||||
−0.367213 | + | 0.930137i | \(0.619688\pi\) | |||||||
\(572\) | −20368.8 | −1.48892 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5668.76 | −0.412211 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11192.7 | −0.807550 | −0.403775 | − | 0.914858i | \(-0.632302\pi\) | ||||
−0.403775 | + | 0.914858i | \(0.632302\pi\) | |||||||
\(578\) | −8034.75 | −0.578204 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6042.41 | −0.431465 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20142.3 | −1.43089 | ||||||||
\(584\) | −8293.35 | −0.587639 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17505.9 | −1.23406 | ||||||||
\(587\) | −11087.1 | −0.779578 | −0.389789 | − | 0.920904i | \(-0.627452\pi\) | ||||
−0.389789 | + | 0.920904i | \(0.627452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3792.92 | −0.265339 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10304.0 | 0.715361 | ||||||||
\(593\) | −14525.9 | −1.00592 | −0.502958 | − | 0.864311i | \(-0.667755\pi\) | ||||
−0.502958 | + | 0.864311i | \(0.667755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3141.76 | −0.215925 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28986.8 | 1.98220 | ||||||||
\(599\) | −16502.5 | −1.12567 | −0.562833 | − | 0.826570i | \(-0.690289\pi\) | ||||
−0.562833 | + | 0.826570i | \(0.690289\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15945.4 | 1.08224 | 0.541119 | − | 0.840946i | \(-0.318001\pi\) | ||||
0.541119 | + | 0.840946i | \(0.318001\pi\) | |||||||
\(602\) | −2756.34 | −0.186611 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6747.89 | 0.454582 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −935.699 | −0.0625681 | −0.0312841 | − | 0.999511i | \(-0.509960\pi\) | ||||
−0.0312841 | + | 0.999511i | \(0.509960\pi\) | |||||||
\(608\) | −2981.53 | −0.198877 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6036.80 | 0.399710 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 375.796 | 0.0247606 | 0.0123803 | − | 0.999923i | \(-0.496059\pi\) | ||||
0.0123803 | + | 0.999923i | \(0.496059\pi\) | |||||||
\(614\) | 20652.9 | 1.35746 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4393.80 | 0.287388 | ||||||||
\(617\) | −14932.2 | −0.974306 | −0.487153 | − | 0.873317i | \(-0.661965\pi\) | ||||
−0.487153 | + | 0.873317i | \(0.661965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11320.8 | 0.735090 | 0.367545 | − | 0.930006i | \(-0.380198\pi\) | ||||
0.367545 | + | 0.930006i | \(0.380198\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −215.095 | −0.0138658 | ||||||||
\(623\) | −8110.38 | −0.521566 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2155.83 | 0.137643 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14228.6 | 0.904115 | ||||||||
\(629\) | 6678.34 | 0.423343 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15521.7 | −0.979253 | −0.489627 | − | 0.871932i | \(-0.662867\pi\) | ||||
−0.489627 | + | 0.871932i | \(0.662867\pi\) | |||||||
\(632\) | −771.765 | −0.0485746 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11199.7 | −0.701571 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21695.0 | 1.34943 | ||||||||
\(638\) | 8695.98 | 0.539619 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20110.1 | 1.23916 | 0.619579 | − | 0.784934i | \(-0.287303\pi\) | ||||
0.619579 | + | 0.784934i | \(0.287303\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16073.4 | 0.985808 | 0.492904 | − | 0.870084i | \(-0.335935\pi\) | ||||
0.492904 | + | 0.870084i | \(0.335935\pi\) | |||||||
\(644\) | 3263.04 | 0.199661 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2899.29 | −0.176581 | ||||||||
\(647\) | 3841.57 | 0.233427 | 0.116714 | − | 0.993166i | \(-0.462764\pi\) | ||||
0.116714 | + | 0.993166i | \(0.462764\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −42200.4 | −2.55240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5824.30 | 0.349842 | ||||||||
\(653\) | −14694.4 | −0.880609 | −0.440304 | − | 0.897849i | \(-0.645129\pi\) | ||||
−0.440304 | + | 0.897849i | \(0.645129\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −20878.9 | −1.24266 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1840.05 | 0.109016 | ||||||||
\(659\) | 8601.76 | 0.508463 | 0.254231 | − | 0.967143i | \(-0.418177\pi\) | ||||
0.254231 | + | 0.967143i | \(0.418177\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21709.0 | −1.27743 | −0.638717 | − | 0.769442i | \(-0.720534\pi\) | ||||
−0.638717 | + | 0.769442i | \(0.720534\pi\) | |||||||
\(662\) | −7560.96 | −0.443905 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11767.9 | −0.687775 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4570.36 | −0.265315 | ||||||||
\(668\) | 774.960 | 0.0448864 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27967.7 | −1.60907 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13192.3 | 0.755611 | 0.377806 | − | 0.925885i | \(-0.376679\pi\) | ||||
0.377806 | + | 0.925885i | \(0.376679\pi\) | |||||||
\(674\) | −5293.85 | −0.302539 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13218.7 | 0.752086 | ||||||||
\(677\) | −4885.74 | −0.277362 | −0.138681 | − | 0.990337i | \(-0.544286\pi\) | ||||
−0.138681 | + | 0.990337i | \(0.544286\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8514.72 | −0.481245 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −52499.1 | −2.94765 | ||||||||
\(683\) | −17180.4 | −0.962502 | −0.481251 | − | 0.876583i | \(-0.659818\pi\) | ||||
−0.481251 | + | 0.876583i | \(0.659818\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14019.3 | 0.780259 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10152.0 | −0.562560 | ||||||||
\(689\) | 23249.4 | 1.28553 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21428.3 | −1.17970 | −0.589850 | − | 0.807513i | \(-0.700813\pi\) | ||||
−0.589850 | + | 0.807513i | \(0.700813\pi\) | |||||||
\(692\) | 9046.57 | 0.496964 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27243.6 | 1.49013 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13532.2 | −0.735391 | ||||||||
\(698\) | −4001.80 | −0.217006 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9809.73 | −0.528543 | −0.264271 | − | 0.964448i | \(-0.585131\pi\) | ||||
−0.264271 | + | 0.964448i | \(0.585131\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2046.09 | −0.109772 | ||||||||
\(704\) | −2218.40 | −0.118763 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −44749.3 | −2.38550 | ||||||||
\(707\) | 6732.21 | 0.358120 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13541.9 | 0.717315 | 0.358658 | − | 0.933469i | \(-0.383235\pi\) | ||||
0.358658 | + | 0.933469i | \(0.383235\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15795.4 | −0.831399 | ||||||||
\(713\) | 27592.1 | 1.44927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2922.64 | −0.152548 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8871.89 | 0.461137 | ||||||||
\(719\) | 344.757 | 0.0178822 | 0.00894109 | − | 0.999960i | \(-0.497154\pi\) | ||||
0.00894109 | + | 0.999960i | \(0.497154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3091.69 | −0.159696 | ||||||||
\(722\) | −23540.4 | −1.21341 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5336.40 | 0.273930 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10425.2 | 0.531841 | 0.265921 | − | 0.963995i | \(-0.414324\pi\) | ||||
0.265921 | + | 0.963995i | \(0.414324\pi\) | |||||||
\(728\) | −5071.57 | −0.258193 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6579.79 | −0.332917 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12660.4 | −0.637956 | −0.318978 | − | 0.947762i | \(-0.603340\pi\) | ||||
−0.318978 | + | 0.947762i | \(0.603340\pi\) | |||||||
\(734\) | −46165.0 | −2.32150 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21689.5 | 1.08626 | ||||||||
\(737\) | −58639.2 | −2.93080 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35663.9 | −1.77526 | −0.887630 | − | 0.460557i | \(-0.847650\pi\) | ||||
−0.887630 | + | 0.460557i | \(0.847650\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7086.56 | 0.350614 | ||||||||
\(743\) | 9880.98 | 0.487884 | 0.243942 | − | 0.969790i | \(-0.421559\pi\) | ||||
0.243942 | + | 0.969790i | \(0.421559\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17970.6 | −0.881973 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14820.7 | −0.724464 | ||||||||
\(749\) | 10600.0 | 0.517112 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7951.18 | −0.386342 | −0.193171 | − | 0.981165i | \(-0.561877\pi\) | ||||
−0.193171 | + | 0.981165i | \(0.561877\pi\) | |||||||
\(752\) | 6777.18 | 0.328641 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10037.4 | −0.484801 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26539.3 | 1.27422 | 0.637112 | − | 0.770771i | \(-0.280129\pi\) | ||||
0.637112 | + | 0.770771i | \(0.280129\pi\) | |||||||
\(758\) | 1274.30 | 0.0610614 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6411.70 | 0.305419 | 0.152710 | − | 0.988271i | \(-0.451200\pi\) | ||||
0.152710 | + | 0.988271i | \(0.451200\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8229.49 | −0.390468 | ||||||||
\(764\) | −2192.70 | −0.103834 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3157.49 | −0.148936 | ||||||||
\(767\) | 48710.1 | 2.29311 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21232.0 | 0.995636 | 0.497818 | − | 0.867282i | \(-0.334135\pi\) | ||||
0.497818 | + | 0.867282i | \(0.334135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11614.1 | −0.541450 | ||||||||
\(773\) | −12948.2 | −0.602478 | −0.301239 | − | 0.953549i | \(-0.597400\pi\) | ||||
−0.301239 | + | 0.953549i | \(0.597400\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16582.8 | −0.767126 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29507.2 | −1.35975 | ||||||||
\(779\) | 4145.94 | 0.190685 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9832.39 | −0.450487 | ||||||||
\(782\) | 21091.3 | 0.964478 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 24355.8 | 1.10950 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16388.9 | 0.742315 | 0.371158 | − | 0.928570i | \(-0.378961\pi\) | ||||
0.371158 | + | 0.928570i | \(0.378961\pi\) | |||||||
\(788\) | −11251.9 | −0.508672 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6992.48 | 0.314316 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32281.9 | 1.44561 | ||||||||
\(794\) | −15936.4 | −0.712294 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4867.45 | −0.216737 | ||||||||
\(797\) | 22291.8 | 0.990734 | 0.495367 | − | 0.868684i | \(-0.335034\pi\) | ||||
0.495367 | + | 0.868684i | \(0.335034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4392.48 | 0.194486 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 37604.0 | 1.65567 | ||||||||
\(803\) | 43107.8 | 1.89445 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 60597.4 | 2.64821 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13111.3 | 0.570859 | ||||||||
\(809\) | 36536.8 | 1.58784 | 0.793921 | − | 0.608020i | \(-0.208036\pi\) | ||||
0.793921 | + | 0.608020i | \(0.208036\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22132.8 | −0.958309 | −0.479155 | − | 0.877730i | \(-0.659057\pi\) | ||||
−0.479155 | + | 0.877730i | \(0.659057\pi\) | |||||||
\(812\) | −1129.91 | −0.0488325 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −28320.6 | −1.21945 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2015.89 | 0.0863245 | ||||||||
\(818\) | −18635.6 | −0.796552 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28628.6 | 1.21698 | 0.608492 | − | 0.793560i | \(-0.291775\pi\) | ||||
0.608492 | + | 0.793560i | \(0.291775\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42695.0 | −1.80833 | −0.904164 | − | 0.427185i | \(-0.859505\pi\) | ||||
−0.904164 | + | 0.427185i | \(0.859505\pi\) | |||||||
\(824\) | −6021.21 | −0.254562 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14847.1 | 0.625421 | ||||||||
\(827\) | 25905.2 | 1.08925 | 0.544627 | − | 0.838678i | \(-0.316671\pi\) | ||||
0.544627 | + | 0.838678i | \(0.316671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9952.93 | −0.416984 | −0.208492 | − | 0.978024i | \(-0.566856\pi\) | ||||
−0.208492 | + | 0.978024i | \(0.566856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2560.60 | 0.106698 | ||||||||
\(833\) | 15785.6 | 0.656591 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4540.72 | 0.187852 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13903.6 | 0.573142 | ||||||||
\(839\) | −16474.0 | −0.677886 | −0.338943 | − | 0.940807i | \(-0.610069\pi\) | ||||
−0.338943 | + | 0.940807i | \(0.610069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22806.4 | −0.935110 | ||||||||
\(842\) | 22348.1 | 0.914689 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15515.5 | 0.632781 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14768.7 | −0.599124 | ||||||||
\(848\) | 26100.9 | 1.05697 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14884.5 | 0.599571 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22391.0 | −0.898772 | −0.449386 | − | 0.893338i | \(-0.648357\pi\) | ||||
−0.449386 | + | 0.893338i | \(0.648357\pi\) | |||||||
\(854\) | 9839.73 | 0.394272 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20644.1 | 0.824299 | ||||||||
\(857\) | 15349.4 | 0.611814 | 0.305907 | − | 0.952061i | \(-0.401040\pi\) | ||||
0.305907 | + | 0.952061i | \(0.401040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5218.87 | −0.207294 | −0.103647 | − | 0.994614i | \(-0.533051\pi\) | ||||
−0.103647 | + | 0.994614i | \(0.533051\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28636.3 | 1.13150 | ||||||||
\(863\) | 12101.4 | 0.477330 | 0.238665 | − | 0.971102i | \(-0.423290\pi\) | ||||
0.238665 | + | 0.971102i | \(0.423290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11116.2 | −0.436196 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6821.45 | 0.266746 | ||||||||
\(869\) | 4011.53 | 0.156596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 67684.6 | 2.63307 | ||||||||
\(872\) | −16027.3 | −0.622424 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6461.87 | −0.250087 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24268.8 | 0.934435 | 0.467218 | − | 0.884142i | \(-0.345256\pi\) | ||||
0.467218 | + | 0.884142i | \(0.345256\pi\) | |||||||
\(878\) | −8451.75 | −0.324866 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24286.6 | −0.928758 | −0.464379 | − | 0.885637i | \(-0.653722\pi\) | ||||
−0.464379 | + | 0.885637i | \(0.653722\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48922.2 | −1.86451 | −0.932255 | − | 0.361801i | \(-0.882162\pi\) | ||||
−0.932255 | + | 0.361801i | \(0.882162\pi\) | |||||||
\(884\) | 17106.9 | 0.650868 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −46844.2 | −1.77626 | ||||||||
\(887\) | −1678.06 | −0.0635215 | −0.0317608 | − | 0.999495i | \(-0.510111\pi\) | ||||
−0.0317608 | + | 0.999495i | \(0.510111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11997.2 | 0.452613 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18671.4 | −0.700859 | ||||||||
\(893\) | −1345.75 | −0.0504299 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8376.54 | −0.312322 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33000.5 | 1.22633 | ||||||||
\(899\) | −9554.45 | −0.354459 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16916.7 | 0.625501 | ||||||||
\(902\) | 57385.4 | 2.11832 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13618.2 | 0.501034 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14710.6 | 0.538541 | 0.269271 | − | 0.963065i | \(-0.413217\pi\) | ||||
0.269271 | + | 0.963065i | \(0.413217\pi\) | |||||||
\(908\) | 20757.2 | 0.758646 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30257.7 | −1.10042 | −0.550209 | − | 0.835027i | \(-0.685452\pi\) | ||||
−0.550209 | + | 0.835027i | \(0.685452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 61168.0 | 2.21727 | ||||||||
\(914\) | −22490.8 | −0.813928 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21801.1 | 0.786385 | ||||||||
\(917\) | 971.839 | 0.0349978 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51369.1 | 1.84386 | 0.921931 | − | 0.387355i | \(-0.126611\pi\) | ||||
0.921931 | + | 0.387355i | \(0.126611\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17347.2 | −0.619632 | ||||||||
\(923\) | 11349.1 | 0.404724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −17424.0 | −0.618346 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7510.54 | −0.265674 | ||||||||
\(929\) | −40968.5 | −1.44686 | −0.723430 | − | 0.690398i | \(-0.757436\pi\) | ||||
−0.723430 | + | 0.690398i | \(0.757436\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4836.35 | −0.170252 | ||||||||
\(932\) | −10758.1 | −0.378106 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24411.2 | −0.855202 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26835.8 | −0.935632 | −0.467816 | − | 0.883826i | \(-0.654959\pi\) | ||||
−0.467816 | + | 0.883826i | \(0.654959\pi\) | |||||||
\(938\) | 20630.7 | 0.718140 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41221.5 | −1.42803 | −0.714017 | − | 0.700128i | \(-0.753126\pi\) | ||||
−0.714017 | + | 0.700128i | \(0.753126\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30160.2 | −1.04152 | ||||||||
\(944\) | 54684.1 | 1.88540 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27902.7 | 0.958979 | ||||||||
\(947\) | −14488.5 | −0.497164 | −0.248582 | − | 0.968611i | \(-0.579965\pi\) | ||||
−0.248582 | + | 0.968611i | \(0.579965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49757.4 | −1.70200 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3690.16 | −0.125629 | ||||||||
\(953\) | −32207.2 | −1.09475 | −0.547373 | − | 0.836889i | \(-0.684372\pi\) | ||||
−0.547373 | + | 0.836889i | \(0.684372\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −16014.7 | −0.541792 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30530.5 | 1.02964 | ||||||||
\(959\) | 4009.57 | 0.135011 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27890.8 | 0.936217 | ||||||||
\(962\) | 32689.2 | 1.09557 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −27659.0 | −0.924104 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20552.1 | −0.683464 | −0.341732 | − | 0.939797i | \(-0.611014\pi\) | ||||
−0.341732 | + | 0.939797i | \(0.611014\pi\) | |||||||
\(968\) | −28762.7 | −0.955030 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23686.9 | 0.782852 | 0.391426 | − | 0.920210i | \(-0.371982\pi\) | ||||
0.391426 | + | 0.920210i | \(0.371982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12890.7 | −0.424723 | ||||||||
\(974\) | 19280.0 | 0.634263 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36241.2 | 1.18858 | ||||||||
\(977\) | 12597.1 | 0.412506 | 0.206253 | − | 0.978499i | \(-0.433873\pi\) | ||||
0.206253 | + | 0.978499i | \(0.433873\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 82102.2 | 2.68028 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −36735.1 | −1.19375 | ||||||||
\(983\) | 51076.9 | 1.65728 | 0.828638 | − | 0.559785i | \(-0.189116\pi\) | ||||
0.828638 | + | 0.559785i | \(0.189116\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7303.38 | −0.235889 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5241.16 | −0.168769 | ||||||||
\(989\) | −14664.9 | −0.471502 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27888.6 | 0.893957 | 0.446979 | − | 0.894545i | \(-0.352500\pi\) | ||||
0.446979 | + | 0.894545i | \(0.352500\pi\) | |||||||
\(992\) | 45342.4 | 1.45123 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3459.27 | 0.110384 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54930.0 | −1.74488 | −0.872442 | − | 0.488717i | \(-0.837465\pi\) | ||||
−0.872442 | + | 0.488717i | \(0.837465\pi\) | |||||||
\(998\) | −48177.8 | −1.52810 | ||||||||
\(999\) | 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 | 675.4.a.ba.1.3 | 4 | ||
3.2 | odd | 2 | 675.4.a.t.1.1 | 4 | |||
5.2 | odd | 4 | 135.4.b.b.109.8 | yes | 8 | ||
5.3 | odd | 4 | 135.4.b.b.109.2 | yes | 8 | ||
5.4 | even | 2 | 675.4.a.t.1.2 | 4 | |||
15.2 | even | 4 | 135.4.b.b.109.1 | ✓ | 8 | ||
15.8 | even | 4 | 135.4.b.b.109.7 | yes | 8 | ||
15.14 | odd | 2 | inner | 675.4.a.ba.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.b.b.109.1 | ✓ | 8 | 15.2 | even | 4 | ||
135.4.b.b.109.2 | yes | 8 | 5.3 | odd | 4 | ||
135.4.b.b.109.7 | yes | 8 | 15.8 | even | 4 | ||
135.4.b.b.109.8 | yes | 8 | 5.2 | odd | 4 | ||
675.4.a.t.1.1 | 4 | 3.2 | odd | 2 | |||
675.4.a.t.1.2 | 4 | 5.4 | even | 2 | |||
675.4.a.ba.1.3 | 4 | 1.1 | even | 1 | trivial | ||
675.4.a.ba.1.4 | 4 | 15.14 | odd | 2 | inner |