Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,4,Mod(1,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(92.9280082590\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 525) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.561553 | −0.198539 | −0.0992695 | − | 0.995061i | \(-0.531651\pi\) | ||||
−0.0992695 | + | 0.995061i | \(0.531651\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.68466 | −0.960582 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.80776 | 0.389252 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25.8078 | 0.707394 | 0.353697 | − | 0.935360i | \(-0.384924\pi\) | ||||
0.353697 | + | 0.935360i | \(0.384924\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.5464 | 0.331677 | 0.165838 | − | 0.986153i | \(-0.446967\pi\) | ||||
0.165838 | + | 0.986153i | \(0.446967\pi\) | |||||||
\(14\) | −3.93087 | −0.0750407 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 56.5312 | 0.883301 | ||||||||
\(17\) | −95.1619 | −1.35766 | −0.678828 | − | 0.734297i | \(-0.737512\pi\) | ||||
−0.678828 | + | 0.734297i | \(0.737512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −143.447 | −1.73205 | −0.866026 | − | 0.499999i | \(-0.833334\pi\) | ||||
−0.866026 | + | 0.499999i | \(0.833334\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.4924 | −0.140445 | ||||||||
\(23\) | 77.5227 | 0.702809 | 0.351405 | − | 0.936224i | \(-0.385704\pi\) | ||||
0.351405 | + | 0.936224i | \(0.385704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −8.73012 | −0.0658507 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −53.7926 | −0.363066 | ||||||||
\(29\) | 204.170 | 1.30736 | 0.653681 | − | 0.756770i | \(-0.273224\pi\) | ||||
0.653681 | + | 0.756770i | \(0.273224\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −40.6998 | −0.235803 | −0.117902 | − | 0.993025i | \(-0.537617\pi\) | ||||
−0.117902 | + | 0.993025i | \(0.537617\pi\) | |||||||
\(32\) | −102.207 | −0.564621 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 53.4384 | 0.269548 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −95.6695 | −0.425080 | −0.212540 | − | 0.977152i | \(-0.568174\pi\) | ||||
−0.212540 | + | 0.977152i | \(0.568174\pi\) | |||||||
\(38\) | 80.5530 | 0.343880 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −24.7301 | −0.0941999 | −0.0471000 | − | 0.998890i | \(-0.514998\pi\) | ||||
−0.0471000 | + | 0.998890i | \(0.514998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −282.430 | −1.00163 | −0.500816 | − | 0.865554i | \(-0.666967\pi\) | ||||
−0.500816 | + | 0.865554i | \(0.666967\pi\) | |||||||
\(44\) | −198.324 | −0.679510 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −43.5331 | −0.139535 | ||||||||
\(47\) | 257.417 | 0.798895 | 0.399448 | − | 0.916756i | \(-0.369202\pi\) | ||||
0.399448 | + | 0.916756i | \(0.369202\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −119.469 | −0.318603 | ||||||||
\(53\) | 257.978 | 0.668604 | 0.334302 | − | 0.942466i | \(-0.391499\pi\) | ||||
0.334302 | + | 0.942466i | \(0.391499\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 61.6543 | 0.147123 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −114.652 | −0.259562 | ||||||||
\(59\) | 651.365 | 1.43730 | 0.718648 | − | 0.695374i | \(-0.244761\pi\) | ||||
0.718648 | + | 0.695374i | \(0.244761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 451.304 | 0.947271 | 0.473636 | − | 0.880721i | \(-0.342941\pi\) | ||||
0.473636 | + | 0.880721i | \(0.342941\pi\) | |||||||
\(62\) | 22.8551 | 0.0468161 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −394.855 | −0.771201 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −832.071 | −1.51722 | −0.758609 | − | 0.651546i | \(-0.774121\pi\) | ||||
−0.758609 | + | 0.651546i | \(0.774121\pi\) | |||||||
\(68\) | 731.287 | 1.30414 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 174.965 | 0.292458 | 0.146229 | − | 0.989251i | \(-0.453286\pi\) | ||||
0.146229 | + | 0.989251i | \(0.453286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 47.4166 | 0.0760233 | 0.0380116 | − | 0.999277i | \(-0.487898\pi\) | ||||
0.0380116 | + | 0.999277i | \(0.487898\pi\) | |||||||
\(74\) | 53.7235 | 0.0843950 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1102.34 | 1.66378 | ||||||||
\(77\) | 180.654 | 0.267370 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.16006 | −0.00165211 | −0.000826057 | − | 1.00000i | \(-0.500263\pi\) | ||||
−0.000826057 | 1.00000i | \(0.500263\pi\) | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 13.8873 | 0.0187023 | ||||||||
\(83\) | 1494.03 | 1.97580 | 0.987898 | − | 0.155107i | \(-0.0495722\pi\) | ||||
0.987898 | + | 0.155107i | \(0.0495722\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 158.599 | 0.198863 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 227.309 | 0.275354 | ||||||||
\(89\) | −1309.13 | −1.55919 | −0.779593 | − | 0.626286i | \(-0.784574\pi\) | ||||
−0.779593 | + | 0.626286i | \(0.784574\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 108.825 | 0.125362 | ||||||||
\(92\) | −595.736 | −0.675106 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −144.553 | −0.158612 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1365.33 | 1.42916 | 0.714580 | − | 0.699553i | \(-0.246618\pi\) | ||||
0.714580 | + | 0.699553i | \(0.246618\pi\) | |||||||
\(98\) | −27.5161 | −0.0283627 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1155.99 | −1.13887 | −0.569434 | − | 0.822037i | \(-0.692838\pi\) | ||||
−0.569434 | + | 0.822037i | \(0.692838\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 78.2074 | 0.0748156 | 0.0374078 | − | 0.999300i | \(-0.488090\pi\) | ||||
0.0374078 | + | 0.999300i | \(0.488090\pi\) | |||||||
\(104\) | 136.929 | 0.129106 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −144.868 | −0.132744 | ||||||||
\(107\) | −94.0814 | −0.0850018 | −0.0425009 | − | 0.999096i | \(-0.513533\pi\) | ||||
−0.0425009 | + | 0.999096i | \(0.513533\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2128.25 | −1.87018 | −0.935088 | − | 0.354417i | \(-0.884679\pi\) | ||||
−0.935088 | + | 0.354417i | \(0.884679\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 395.719 | 0.333856 | ||||||||
\(113\) | −596.493 | −0.496578 | −0.248289 | − | 0.968686i | \(-0.579868\pi\) | ||||
−0.248289 | + | 0.968686i | \(0.579868\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1568.98 | −1.25583 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −365.776 | −0.285359 | ||||||||
\(119\) | −666.133 | −0.513146 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −664.959 | −0.499594 | ||||||||
\(122\) | −253.431 | −0.188070 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 312.764 | 0.226508 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2088.21 | −1.45904 | −0.729522 | − | 0.683957i | \(-0.760257\pi\) | ||||
−0.729522 | + | 0.683957i | \(0.760257\pi\) | |||||||
\(128\) | 1039.39 | 0.717735 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −416.142 | −0.277546 | −0.138773 | − | 0.990324i | \(-0.544316\pi\) | ||||
−0.138773 | + | 0.990324i | \(0.544316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1004.13 | −0.654654 | ||||||||
\(134\) | 467.252 | 0.301227 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −838.164 | −0.528470 | ||||||||
\(137\) | 619.252 | 0.386177 | 0.193089 | − | 0.981181i | \(-0.438150\pi\) | ||||
0.193089 | + | 0.981181i | \(0.438150\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −266.994 | −0.162922 | −0.0814610 | − | 0.996677i | \(-0.525959\pi\) | ||||
−0.0814610 | + | 0.996677i | \(0.525959\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −98.2520 | −0.0580643 | ||||||||
\(143\) | 401.218 | 0.234626 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −26.6270 | −0.0150936 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 735.187 | 0.408325 | ||||||||
\(149\) | −2551.80 | −1.40303 | −0.701515 | − | 0.712655i | \(-0.747493\pi\) | ||||
−0.701515 | + | 0.712655i | \(0.747493\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1117.38 | 0.602195 | 0.301097 | − | 0.953593i | \(-0.402647\pi\) | ||||
0.301097 | + | 0.953593i | \(0.402647\pi\) | |||||||
\(152\) | −1263.45 | −0.674204 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −101.447 | −0.0530833 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 456.104 | 0.231854 | 0.115927 | − | 0.993258i | \(-0.463016\pi\) | ||||
0.115927 | + | 0.993258i | \(0.463016\pi\) | |||||||
\(158\) | 0.651435 | 0.000328009 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 542.659 | 0.265637 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 105.490 | 0.0506907 | 0.0253453 | − | 0.999679i | \(-0.491931\pi\) | ||||
0.0253453 | + | 0.999679i | \(0.491931\pi\) | |||||||
\(164\) | 190.043 | 0.0904868 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −838.976 | −0.392272 | ||||||||
\(167\) | −2482.54 | −1.15033 | −0.575164 | − | 0.818038i | \(-0.695062\pi\) | ||||
−0.575164 | + | 0.818038i | \(0.695062\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1955.31 | −0.889991 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2170.38 | 0.962150 | ||||||||
\(173\) | 516.708 | 0.227079 | 0.113539 | − | 0.993534i | \(-0.463781\pi\) | ||||
0.113539 | + | 0.993534i | \(0.463781\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1458.94 | 0.624842 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 735.146 | 0.309559 | ||||||||
\(179\) | −3847.77 | −1.60668 | −0.803341 | − | 0.595519i | \(-0.796946\pi\) | ||||
−0.803341 | + | 0.595519i | \(0.796946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3026.41 | −1.24282 | −0.621411 | − | 0.783484i | \(-0.713440\pi\) | ||||
−0.621411 | + | 0.783484i | \(0.713440\pi\) | |||||||
\(182\) | −61.1109 | −0.0248892 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 682.802 | 0.273570 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2455.92 | −0.960398 | ||||||||
\(188\) | −1978.16 | −0.767405 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1271.09 | −0.481532 | −0.240766 | − | 0.970583i | \(-0.577399\pi\) | ||||
−0.240766 | + | 0.970583i | \(0.577399\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1896.09 | 0.707170 | 0.353585 | − | 0.935402i | \(-0.384963\pi\) | ||||
0.353585 | + | 0.935402i | \(0.384963\pi\) | |||||||
\(194\) | −766.707 | −0.283744 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −376.548 | −0.137226 | ||||||||
\(197\) | 4067.89 | 1.47119 | 0.735597 | − | 0.677419i | \(-0.236902\pi\) | ||||
0.735597 | + | 0.677419i | \(0.236902\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 78.1366 | 0.0278340 | 0.0139170 | − | 0.999903i | \(-0.495570\pi\) | ||||
0.0139170 | + | 0.999903i | \(0.495570\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 649.152 | 0.226110 | ||||||||
\(203\) | 1429.19 | 0.494136 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −43.9176 | −0.0148538 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 878.857 | 0.292970 | ||||||||
\(209\) | −3702.05 | −1.22524 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1293.02 | −0.421872 | −0.210936 | − | 0.977500i | \(-0.567651\pi\) | ||||
−0.210936 | + | 0.977500i | \(0.567651\pi\) | |||||||
\(212\) | −1982.47 | −0.642250 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 52.8317 | 0.0168762 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −284.899 | −0.0891253 | ||||||||
\(218\) | 1195.12 | 0.371303 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1479.43 | −0.450303 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1786.65 | 0.536515 | 0.268257 | − | 0.963347i | \(-0.413552\pi\) | ||||
0.268257 | + | 0.963347i | \(0.413552\pi\) | |||||||
\(224\) | −715.452 | −0.213407 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 334.962 | 0.0985901 | ||||||||
\(227\) | −4242.02 | −1.24032 | −0.620161 | − | 0.784475i | \(-0.712933\pi\) | ||||
−0.620161 | + | 0.784475i | \(0.712933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3403.36 | 0.982096 | 0.491048 | − | 0.871132i | \(-0.336614\pi\) | ||||
0.491048 | + | 0.871132i | \(0.336614\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1798.29 | 0.508893 | ||||||||
\(233\) | −3904.09 | −1.09771 | −0.548853 | − | 0.835919i | \(-0.684935\pi\) | ||||
−0.548853 | + | 0.835919i | \(0.684935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5005.51 | −1.38064 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 374.069 | 0.101879 | ||||||||
\(239\) | −6667.83 | −1.80463 | −0.902314 | − | 0.431079i | \(-0.858133\pi\) | ||||
−0.902314 | + | 0.431079i | \(0.858133\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6003.99 | −1.60478 | −0.802388 | − | 0.596803i | \(-0.796437\pi\) | ||||
−0.802388 | + | 0.596803i | \(0.796437\pi\) | |||||||
\(242\) | 373.410 | 0.0991888 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3468.12 | −0.909932 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2230.08 | −0.574481 | ||||||||
\(248\) | −358.474 | −0.0917869 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −728.467 | −0.183189 | −0.0915945 | − | 0.995796i | \(-0.529196\pi\) | ||||
−0.0915945 | + | 0.995796i | \(0.529196\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2000.69 | 0.497163 | ||||||||
\(254\) | 1172.64 | 0.289677 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2575.17 | 0.628703 | ||||||||
\(257\) | −1479.86 | −0.359187 | −0.179593 | − | 0.983741i | \(-0.557478\pi\) | ||||
−0.179593 | + | 0.983741i | \(0.557478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −669.687 | −0.160665 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 233.686 | 0.0551036 | ||||||||
\(263\) | −6367.31 | −1.49287 | −0.746435 | − | 0.665458i | \(-0.768236\pi\) | ||||
−0.746435 | + | 0.665458i | \(0.768236\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 563.871 | 0.129974 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6394.18 | 1.45741 | ||||||||
\(269\) | −1787.18 | −0.405079 | −0.202539 | − | 0.979274i | \(-0.564919\pi\) | ||||
−0.202539 | + | 0.979274i | \(0.564919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3907.65 | 0.875915 | 0.437957 | − | 0.898996i | \(-0.355702\pi\) | ||||
0.437957 | + | 0.898996i | \(0.355702\pi\) | |||||||
\(272\) | −5379.62 | −1.19922 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −347.743 | −0.0766712 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3978.33 | −0.862942 | −0.431471 | − | 0.902127i | \(-0.642005\pi\) | ||||
−0.431471 | + | 0.902127i | \(0.642005\pi\) | |||||||
\(278\) | 149.931 | 0.0323464 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6488.04 | 1.37738 | 0.688690 | − | 0.725055i | \(-0.258186\pi\) | ||||
0.688690 | + | 0.725055i | \(0.258186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 164.336 | 0.0345185 | 0.0172592 | − | 0.999851i | \(-0.494506\pi\) | ||||
0.0172592 | + | 0.999851i | \(0.494506\pi\) | |||||||
\(284\) | −1344.55 | −0.280930 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −225.305 | −0.0465824 | ||||||||
\(287\) | −173.111 | −0.0356042 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4142.79 | 0.843231 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −364.381 | −0.0730266 | ||||||||
\(293\) | 5004.57 | 0.997851 | 0.498925 | − | 0.866645i | \(-0.333728\pi\) | ||||
0.498925 | + | 0.866645i | \(0.333728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −842.634 | −0.165463 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1432.97 | 0.278556 | ||||||||
\(299\) | 1205.20 | 0.233105 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1977.01 | −0.378581 | ||||||||
\(302\) | −627.470 | −0.119559 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8109.23 | −1.52992 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 190.167 | 0.0353531 | 0.0176765 | − | 0.999844i | \(-0.494373\pi\) | ||||
0.0176765 | + | 0.999844i | \(0.494373\pi\) | |||||||
\(308\) | −1388.27 | −0.256831 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1182.57 | 0.215619 | 0.107810 | − | 0.994172i | \(-0.465616\pi\) | ||||
0.107810 | + | 0.994172i | \(0.465616\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4659.05 | 0.841358 | 0.420679 | − | 0.907209i | \(-0.361792\pi\) | ||||
0.420679 | + | 0.907209i | \(0.361792\pi\) | |||||||
\(314\) | −256.127 | −0.0460320 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.91467 | 0.00158699 | ||||||||
\(317\) | −3694.55 | −0.654595 | −0.327297 | − | 0.944921i | \(-0.606138\pi\) | ||||
−0.327297 | + | 0.944921i | \(0.606138\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5269.18 | 0.924820 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −304.732 | −0.0527392 | ||||||||
\(323\) | 13650.7 | 2.35153 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −59.2379 | −0.0100641 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −217.817 | −0.0366675 | ||||||||
\(329\) | 1801.92 | 0.301954 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8632.79 | −1.43354 | −0.716769 | − | 0.697310i | \(-0.754380\pi\) | ||||
−0.716769 | + | 0.697310i | \(0.754380\pi\) | |||||||
\(332\) | −11481.1 | −1.89791 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1394.08 | 0.228385 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8136.61 | 1.31522 | 0.657610 | − | 0.753358i | \(-0.271567\pi\) | ||||
0.657610 | + | 0.753358i | \(0.271567\pi\) | |||||||
\(338\) | 1098.01 | 0.176698 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1050.37 | −0.166806 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −2487.58 | −0.389887 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −290.159 | −0.0450839 | ||||||||
\(347\) | 8646.33 | 1.33763 | 0.668817 | − | 0.743427i | \(-0.266801\pi\) | ||||
0.668817 | + | 0.743427i | \(0.266801\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7455.43 | −1.14350 | −0.571748 | − | 0.820429i | \(-0.693734\pi\) | ||||
−0.571748 | + | 0.820429i | \(0.693734\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2637.74 | −0.399410 | ||||||||
\(353\) | 5450.21 | 0.821771 | 0.410886 | − | 0.911687i | \(-0.365220\pi\) | ||||
0.410886 | + | 0.911687i | \(0.365220\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10060.2 | 1.49773 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2160.73 | 0.318989 | ||||||||
\(359\) | −4775.79 | −0.702107 | −0.351053 | − | 0.936355i | \(-0.614176\pi\) | ||||
−0.351053 | + | 0.936355i | \(0.614176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13718.0 | 2.00000 | ||||||||
\(362\) | 1699.49 | 0.246749 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −836.281 | −0.120420 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9636.30 | −1.37060 | −0.685301 | − | 0.728260i | \(-0.740329\pi\) | ||||
−0.685301 | + | 0.728260i | \(0.740329\pi\) | |||||||
\(368\) | 4382.46 | 0.620792 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1805.85 | 0.252709 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12180.4 | −1.69082 | −0.845412 | − | 0.534115i | \(-0.820645\pi\) | ||||
−0.845412 | + | 0.534115i | \(0.820645\pi\) | |||||||
\(374\) | 1379.13 | 0.190676 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2267.27 | 0.310971 | ||||||||
\(377\) | 3174.11 | 0.433621 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1689.39 | 0.228966 | 0.114483 | − | 0.993425i | \(-0.463479\pi\) | ||||
0.114483 | + | 0.993425i | \(0.463479\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 713.783 | 0.0956029 | ||||||||
\(383\) | 1513.13 | 0.201872 | 0.100936 | − | 0.994893i | \(-0.467816\pi\) | ||||
0.100936 | + | 0.994893i | \(0.467816\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1064.76 | −0.140401 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10492.1 | −1.37283 | ||||||||
\(389\) | −12165.5 | −1.58564 | −0.792822 | − | 0.609453i | \(-0.791389\pi\) | ||||
−0.792822 | + | 0.609453i | \(0.791389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7377.21 | −0.954173 | ||||||||
\(392\) | 431.580 | 0.0556074 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2284.34 | −0.292089 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7353.40 | −0.929613 | −0.464807 | − | 0.885412i | \(-0.653876\pi\) | ||||
−0.464807 | + | 0.885412i | \(0.653876\pi\) | |||||||
\(398\) | −43.8778 | −0.00552612 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7481.62 | −0.931707 | −0.465853 | − | 0.884862i | \(-0.654253\pi\) | ||||
−0.465853 | + | 0.884862i | \(0.654253\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −632.735 | −0.0782104 | ||||||||
\(404\) | 8883.42 | 1.09398 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −802.567 | −0.0981053 | ||||||||
\(407\) | −2469.02 | −0.300699 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9248.94 | 1.11817 | 0.559084 | − | 0.829111i | \(-0.311153\pi\) | ||||
0.559084 | + | 0.829111i | \(0.311153\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −600.997 | −0.0718665 | ||||||||
\(413\) | 4559.55 | 0.543247 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1588.96 | −0.187272 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2078.89 | 0.243258 | ||||||||
\(419\) | 3363.39 | 0.392154 | 0.196077 | − | 0.980589i | \(-0.437180\pi\) | ||||
0.196077 | + | 0.980589i | \(0.437180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3638.86 | −0.421252 | −0.210626 | − | 0.977567i | \(-0.567550\pi\) | ||||
−0.210626 | + | 0.977567i | \(0.567550\pi\) | |||||||
\(422\) | 726.097 | 0.0837579 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2272.21 | 0.260255 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3159.13 | 0.358035 | ||||||||
\(428\) | 722.983 | 0.0816512 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11243.2 | −1.25653 | −0.628264 | − | 0.778000i | \(-0.716234\pi\) | ||||
−0.628264 | + | 0.778000i | \(0.716234\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −187.332 | −0.0207912 | −0.0103956 | − | 0.999946i | \(-0.503309\pi\) | ||||
−0.0103956 | + | 0.999946i | \(0.503309\pi\) | |||||||
\(434\) | 159.986 | 0.0176948 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16354.9 | 1.79646 | ||||||||
\(437\) | −11120.4 | −1.21730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11479.4 | −1.24802 | −0.624011 | − | 0.781415i | \(-0.714498\pi\) | ||||
−0.624011 | + | 0.781415i | \(0.714498\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 830.775 | 0.0894026 | ||||||||
\(443\) | −9490.56 | −1.01786 | −0.508928 | − | 0.860809i | \(-0.669958\pi\) | ||||
−0.508928 | + | 0.860809i | \(0.669958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1003.30 | −0.106519 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2763.99 | −0.291487 | ||||||||
\(449\) | 5546.58 | 0.582982 | 0.291491 | − | 0.956574i | \(-0.405849\pi\) | ||||
0.291491 | + | 0.956574i | \(0.405849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −638.229 | −0.0666364 | ||||||||
\(452\) | 4583.85 | 0.477004 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2382.12 | 0.246252 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1776.94 | −0.181885 | −0.0909426 | − | 0.995856i | \(-0.528988\pi\) | ||||
−0.0909426 | + | 0.995856i | \(0.528988\pi\) | |||||||
\(458\) | −1911.16 | −0.194984 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9059.81 | 0.915309 | 0.457655 | − | 0.889130i | \(-0.348690\pi\) | ||||
0.457655 | + | 0.889130i | \(0.348690\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14878.5 | −1.49344 | −0.746719 | − | 0.665139i | \(-0.768372\pi\) | ||||
−0.746719 | + | 0.665139i | \(0.768372\pi\) | |||||||
\(464\) | 11542.0 | 1.15479 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2192.35 | 0.217937 | ||||||||
\(467\) | 14275.8 | 1.41458 | 0.707288 | − | 0.706926i | \(-0.249918\pi\) | ||||
0.707288 | + | 0.706926i | \(0.249918\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5824.50 | −0.573455 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5737.07 | 0.559470 | ||||||||
\(473\) | −7288.89 | −0.708548 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5119.01 | 0.492919 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3744.34 | 0.358289 | ||||||||
\(479\) | 15377.8 | 1.46687 | 0.733433 | − | 0.679761i | \(-0.237917\pi\) | ||||
0.733433 | + | 0.679761i | \(0.237917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1487.32 | −0.140989 | ||||||||
\(482\) | 3371.56 | 0.318610 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5109.99 | 0.479901 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19683.3 | −1.83149 | −0.915747 | − | 0.401756i | \(-0.868400\pi\) | ||||
−0.915747 | + | 0.401756i | \(0.868400\pi\) | |||||||
\(488\) | 3974.98 | 0.368727 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19585.1 | −1.80013 | −0.900065 | − | 0.435755i | \(-0.856481\pi\) | ||||
−0.900065 | + | 0.435755i | \(0.856481\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19429.3 | −1.77495 | ||||||||
\(494\) | 1252.31 | 0.114057 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2300.81 | −0.208285 | ||||||||
\(497\) | 1224.75 | 0.110539 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6888.47 | −0.617977 | −0.308988 | − | 0.951066i | \(-0.599990\pi\) | ||||
−0.308988 | + | 0.951066i | \(0.599990\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 409.073 | 0.0363701 | ||||||||
\(503\) | 14878.0 | 1.31885 | 0.659423 | − | 0.751772i | \(-0.270801\pi\) | ||||
0.659423 | + | 0.751772i | \(0.270801\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1123.49 | −0.0987062 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16047.2 | 1.40153 | ||||||||
\(509\) | −1935.28 | −0.168526 | −0.0842629 | − | 0.996444i | \(-0.526854\pi\) | ||||
−0.0842629 | + | 0.996444i | \(0.526854\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 331.917 | 0.0287341 | ||||||||
\(512\) | −9761.22 | −0.842557 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 831.019 | 0.0713126 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6643.35 | 0.565134 | ||||||||
\(518\) | 376.064 | 0.0318983 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6892.28 | 0.579570 | 0.289785 | − | 0.957092i | \(-0.406416\pi\) | ||||
0.289785 | + | 0.957092i | \(0.406416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1074.60 | 0.0898447 | 0.0449223 | − | 0.998990i | \(-0.485696\pi\) | ||||
0.0449223 | + | 0.998990i | \(0.485696\pi\) | |||||||
\(524\) | 3197.91 | 0.266606 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3575.58 | 0.296393 | ||||||||
\(527\) | 3873.07 | 0.320140 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6157.23 | −0.506060 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7716.39 | 0.628849 | ||||||||
\(533\) | −384.464 | −0.0312439 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7328.69 | −0.590580 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1003.60 | 0.0804239 | ||||||||
\(539\) | 1264.58 | 0.101056 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8660.23 | 0.688230 | 0.344115 | − | 0.938928i | \(-0.388179\pi\) | ||||
0.344115 | + | 0.938928i | \(0.388179\pi\) | |||||||
\(542\) | −2194.35 | −0.173903 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9726.25 | 0.766562 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15346.1 | 1.19954 | 0.599771 | − | 0.800171i | \(-0.295258\pi\) | ||||
0.599771 | + | 0.800171i | \(0.295258\pi\) | |||||||
\(548\) | −4758.74 | −0.370955 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29287.6 | −2.26442 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.12042 | −0.000624440 0 | ||||||||
\(554\) | 2234.04 | 0.171328 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2051.76 | 0.156500 | ||||||||
\(557\) | 15544.9 | 1.18251 | 0.591257 | − | 0.806483i | \(-0.298632\pi\) | ||||
0.591257 | + | 0.806483i | \(0.298632\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4390.77 | −0.332218 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3643.38 | −0.273464 | ||||||||
\(563\) | −18511.9 | −1.38576 | −0.692881 | − | 0.721052i | \(-0.743659\pi\) | ||||
−0.692881 | + | 0.721052i | \(0.743659\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −92.2831 | −0.00685326 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1541.05 | 0.113840 | ||||||||
\(569\) | −2157.36 | −0.158948 | −0.0794738 | − | 0.996837i | \(-0.525324\pi\) | ||||
−0.0794738 | + | 0.996837i | \(0.525324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16010.3 | 1.17340 | 0.586700 | − | 0.809805i | \(-0.300427\pi\) | ||||
0.586700 | + | 0.809805i | \(0.300427\pi\) | |||||||
\(572\) | −3083.22 | −0.225378 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 97.2109 | 0.00706882 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2164.01 | 0.156134 | 0.0780668 | − | 0.996948i | \(-0.475125\pi\) | ||||
0.0780668 | + | 0.996948i | \(0.475125\pi\) | |||||||
\(578\) | −2326.40 | −0.167414 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10458.2 | 0.746780 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6657.84 | 0.472967 | ||||||||
\(584\) | 417.635 | 0.0295922 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2810.33 | −0.198112 | ||||||||
\(587\) | 27616.6 | 1.94184 | 0.970918 | − | 0.239412i | \(-0.0769546\pi\) | ||||
0.970918 | + | 0.239412i | \(0.0769546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5838.26 | 0.408424 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5408.32 | −0.375474 | ||||||||
\(593\) | −10205.4 | −0.706718 | −0.353359 | − | 0.935488i | \(-0.614961\pi\) | ||||
−0.353359 | + | 0.935488i | \(0.614961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19609.7 | 1.34773 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −676.783 | −0.0462805 | ||||||||
\(599\) | −11090.5 | −0.756501 | −0.378251 | − | 0.925703i | \(-0.623474\pi\) | ||||
−0.378251 | + | 0.925703i | \(0.623474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26537.0 | −1.80111 | −0.900555 | − | 0.434742i | \(-0.856839\pi\) | ||||
−0.900555 | + | 0.434742i | \(0.856839\pi\) | |||||||
\(602\) | 1110.20 | 0.0751631 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8586.71 | −0.578457 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11234.5 | 0.751226 | 0.375613 | − | 0.926777i | \(-0.377432\pi\) | ||||
0.375613 | + | 0.926777i | \(0.377432\pi\) | |||||||
\(608\) | 14661.3 | 0.977954 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4001.90 | 0.264975 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10622.5 | 0.699900 | 0.349950 | − | 0.936768i | \(-0.386199\pi\) | ||||
0.349950 | + | 0.936768i | \(0.386199\pi\) | |||||||
\(614\) | −106.789 | −0.00701896 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1591.16 | 0.104074 | ||||||||
\(617\) | 20433.3 | 1.33325 | 0.666623 | − | 0.745395i | \(-0.267739\pi\) | ||||
0.666623 | + | 0.745395i | \(0.267739\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7963.57 | −0.517097 | −0.258549 | − | 0.965998i | \(-0.583244\pi\) | ||||
−0.258549 | + | 0.965998i | \(0.583244\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −664.077 | −0.0428088 | ||||||||
\(623\) | −9163.91 | −0.589317 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2616.30 | −0.167042 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3505.01 | −0.222715 | ||||||||
\(629\) | 9104.09 | 0.577113 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14703.1 | −0.927608 | −0.463804 | − | 0.885938i | \(-0.653516\pi\) | ||||
−0.463804 | + | 0.885938i | \(0.653516\pi\) | |||||||
\(632\) | −10.2175 | −0.000643088 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2074.68 | 0.129963 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 761.773 | 0.0473824 | ||||||||
\(638\) | −2958.92 | −0.183613 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3353.41 | −0.206633 | −0.103317 | − | 0.994649i | \(-0.532945\pi\) | ||||
−0.103317 | + | 0.994649i | \(0.532945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31862.0 | −1.95415 | −0.977073 | − | 0.212906i | \(-0.931707\pi\) | ||||
−0.977073 | + | 0.212906i | \(0.931707\pi\) | |||||||
\(644\) | −4170.15 | −0.255166 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7665.58 | −0.466870 | ||||||||
\(647\) | −8518.46 | −0.517612 | −0.258806 | − | 0.965929i | \(-0.583329\pi\) | ||||
−0.258806 | + | 0.965929i | \(0.583329\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16810.3 | 1.01673 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −810.651 | −0.0486925 | ||||||||
\(653\) | −28509.3 | −1.70851 | −0.854254 | − | 0.519856i | \(-0.825986\pi\) | ||||
−0.854254 | + | 0.519856i | \(0.825986\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1398.02 | −0.0832068 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1011.87 | −0.0599496 | ||||||||
\(659\) | 27632.4 | 1.63339 | 0.816697 | − | 0.577066i | \(-0.195803\pi\) | ||||
0.816697 | + | 0.577066i | \(0.195803\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27052.8 | −1.59188 | −0.795941 | − | 0.605374i | \(-0.793023\pi\) | ||||
−0.795941 | + | 0.605374i | \(0.793023\pi\) | |||||||
\(662\) | 4847.77 | 0.284613 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13159.1 | 0.769082 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15827.9 | 0.918826 | ||||||||
\(668\) | 19077.5 | 1.10498 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11647.1 | 0.670094 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1569.99 | 0.0899235 | 0.0449618 | − | 0.998989i | \(-0.485683\pi\) | ||||
0.0449618 | + | 0.998989i | \(0.485683\pi\) | |||||||
\(674\) | −4569.13 | −0.261122 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15025.9 | 0.854909 | ||||||||
\(677\) | 13853.9 | 0.786482 | 0.393241 | − | 0.919435i | \(-0.371354\pi\) | ||||
0.393241 | + | 0.919435i | \(0.371354\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9557.33 | 0.540172 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 589.839 | 0.0331174 | ||||||||
\(683\) | −28337.1 | −1.58754 | −0.793769 | − | 0.608219i | \(-0.791884\pi\) | ||||
−0.793769 | + | 0.608219i | \(0.791884\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −192.613 | −0.0107201 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15966.1 | −0.884742 | ||||||||
\(689\) | 4010.63 | 0.221760 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16936.5 | 0.932410 | 0.466205 | − | 0.884677i | \(-0.345621\pi\) | ||||
0.466205 | + | 0.884677i | \(0.345621\pi\) | |||||||
\(692\) | −3970.73 | −0.218128 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4855.37 | −0.265572 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2353.37 | 0.127891 | ||||||||
\(698\) | 4186.62 | 0.227028 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29744.0 | 1.60259 | 0.801294 | − | 0.598271i | \(-0.204145\pi\) | ||||
0.801294 | + | 0.598271i | \(0.204145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13723.5 | 0.736261 | ||||||||
\(704\) | −10190.3 | −0.545543 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3060.58 | −0.163154 | ||||||||
\(707\) | −8091.96 | −0.430452 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34264.7 | 1.81500 | 0.907502 | − | 0.420047i | \(-0.137986\pi\) | ||||
0.907502 | + | 0.420047i | \(0.137986\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11530.5 | −0.606916 | ||||||||
\(713\) | −3155.16 | −0.165725 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29568.8 | 1.54335 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2681.86 | 0.139396 | ||||||||
\(719\) | 25469.2 | 1.32106 | 0.660529 | − | 0.750801i | \(-0.270332\pi\) | ||||
0.660529 | + | 0.750801i | \(0.270332\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 547.452 | 0.0282776 | ||||||||
\(722\) | −7703.40 | −0.397079 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23256.9 | 1.19383 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24294.6 | 1.23939 | 0.619695 | − | 0.784843i | \(-0.287256\pi\) | ||||
0.619695 | + | 0.784843i | \(0.287256\pi\) | |||||||
\(728\) | 958.503 | 0.0487974 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26876.6 | 1.35987 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34870.8 | 1.75714 | 0.878569 | − | 0.477615i | \(-0.158499\pi\) | ||||
0.878569 | + | 0.477615i | \(0.158499\pi\) | |||||||
\(734\) | 5411.29 | 0.272118 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7923.40 | −0.396821 | ||||||||
\(737\) | −21473.9 | −1.07327 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7028.81 | 0.349877 | 0.174938 | − | 0.984579i | \(-0.444027\pi\) | ||||
0.174938 | + | 0.984579i | \(0.444027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1014.08 | −0.0501725 | ||||||||
\(743\) | −1368.74 | −0.0675831 | −0.0337915 | − | 0.999429i | \(-0.510758\pi\) | ||||
−0.0337915 | + | 0.999429i | \(0.510758\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6839.94 | 0.335694 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18872.9 | 0.922541 | ||||||||
\(749\) | −658.570 | −0.0321276 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37144.0 | 1.80480 | 0.902400 | − | 0.430900i | \(-0.141804\pi\) | ||||
0.902400 | + | 0.430900i | \(0.141804\pi\) | |||||||
\(752\) | 14552.1 | 0.705665 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1782.43 | −0.0860907 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12042.4 | 0.578189 | 0.289095 | − | 0.957301i | \(-0.406646\pi\) | ||||
0.289095 | + | 0.957301i | \(0.406646\pi\) | |||||||
\(758\) | −948.683 | −0.0454588 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6112.92 | −0.291187 | −0.145593 | − | 0.989345i | \(-0.546509\pi\) | ||||
−0.145593 | + | 0.989345i | \(0.546509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14897.7 | −0.706860 | ||||||||
\(764\) | 9767.88 | 0.462552 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −849.700 | −0.0400795 | ||||||||
\(767\) | 10126.4 | 0.476717 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −957.146 | −0.0448837 | −0.0224418 | − | 0.999748i | \(-0.507144\pi\) | ||||
−0.0224418 | + | 0.999748i | \(0.507144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14570.8 | −0.679295 | ||||||||
\(773\) | −32867.9 | −1.52934 | −0.764668 | − | 0.644424i | \(-0.777097\pi\) | ||||
−0.764668 | + | 0.644424i | \(0.777097\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12025.5 | 0.556303 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6831.58 | 0.314812 | ||||||||
\(779\) | 3547.46 | 0.163159 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4515.45 | 0.206883 | ||||||||
\(782\) | 4142.69 | 0.189440 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2770.03 | 0.126186 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15320.0 | 0.693900 | 0.346950 | − | 0.937884i | \(-0.387217\pi\) | ||||
0.346950 | + | 0.937884i | \(0.387217\pi\) | |||||||
\(788\) | −31260.4 | −1.41320 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4175.45 | −0.187689 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7016.15 | 0.314188 | ||||||||
\(794\) | 4129.32 | 0.184564 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −600.453 | −0.0267368 | ||||||||
\(797\) | −43629.0 | −1.93904 | −0.969522 | − | 0.245004i | \(-0.921211\pi\) | ||||
−0.969522 | + | 0.245004i | \(0.921211\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24496.3 | −1.08463 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4201.33 | 0.184980 | ||||||||
\(803\) | 1223.72 | 0.0537784 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 355.314 | 0.0155278 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10181.7 | −0.443307 | ||||||||
\(809\) | −127.735 | −0.00555119 | −0.00277560 | − | 0.999996i | \(-0.500884\pi\) | ||||
−0.00277560 | + | 0.999996i | \(0.500884\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16227.5 | 0.702618 | 0.351309 | − | 0.936260i | \(-0.385737\pi\) | ||||
0.351309 | + | 0.936260i | \(0.385737\pi\) | |||||||
\(812\) | −10982.9 | −0.474659 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1386.48 | 0.0597005 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40513.7 | 1.73488 | ||||||||
\(818\) | −5193.77 | −0.222000 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34249.2 | −1.45591 | −0.727957 | − | 0.685623i | \(-0.759530\pi\) | ||||
−0.727957 | + | 0.685623i | \(0.759530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6624.51 | −0.280578 | −0.140289 | − | 0.990111i | \(-0.544803\pi\) | ||||
−0.140289 | + | 0.990111i | \(0.544803\pi\) | |||||||
\(824\) | 688.832 | 0.0291221 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2560.43 | −0.107856 | ||||||||
\(827\) | 33786.8 | 1.42065 | 0.710327 | − | 0.703872i | \(-0.248547\pi\) | ||||
0.710327 | + | 0.703872i | \(0.248547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30283.8 | −1.26876 | −0.634378 | − | 0.773023i | \(-0.718744\pi\) | ||||
−0.634378 | + | 0.773023i | \(0.718744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6138.57 | −0.255789 | ||||||||
\(833\) | −4662.93 | −0.193951 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 28449.0 | 1.17695 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1888.72 | −0.0778578 | ||||||||
\(839\) | −16810.9 | −0.691750 | −0.345875 | − | 0.938281i | \(-0.612418\pi\) | ||||
−0.345875 | + | 0.938281i | \(0.612418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17296.6 | 0.709195 | ||||||||
\(842\) | 2043.41 | 0.0836350 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9936.39 | 0.405242 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4654.72 | −0.188829 | ||||||||
\(848\) | 14583.8 | 0.590579 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7416.56 | −0.298750 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14875.8 | 0.597112 | 0.298556 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298556 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(854\) | −1774.02 | −0.0710839 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −828.647 | −0.0330871 | ||||||||
\(857\) | 3987.55 | 0.158941 | 0.0794703 | − | 0.996837i | \(-0.474677\pi\) | ||||
0.0794703 | + | 0.996837i | \(0.474677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39344.7 | 1.56278 | 0.781388 | − | 0.624046i | \(-0.214512\pi\) | ||||
0.781388 | + | 0.624046i | \(0.214512\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6313.63 | 0.249470 | ||||||||
\(863\) | 15627.0 | 0.616397 | 0.308198 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308198 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 105.197 | 0.00412787 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2189.35 | 0.0856122 | ||||||||
\(869\) | −29.9386 | −0.00116870 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12935.7 | −0.503226 | ||||||||
\(872\) | −18745.1 | −0.727969 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6244.69 | 0.241682 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14519.0 | −0.559034 | −0.279517 | − | 0.960141i | \(-0.590174\pi\) | ||||
−0.279517 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(878\) | 6446.29 | 0.247781 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24177.7 | −0.924592 | −0.462296 | − | 0.886726i | \(-0.652974\pi\) | ||||
−0.462296 | + | 0.886726i | \(0.652974\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10340.3 | 0.394089 | 0.197044 | − | 0.980395i | \(-0.436866\pi\) | ||||
0.197044 | + | 0.980395i | \(0.436866\pi\) | |||||||
\(884\) | 11368.9 | 0.432553 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5329.45 | 0.202084 | ||||||||
\(887\) | 3222.62 | 0.121990 | 0.0609949 | − | 0.998138i | \(-0.480573\pi\) | ||||
0.0609949 | + | 0.998138i | \(0.480573\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14617.5 | −0.551467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13729.8 | −0.515367 | ||||||||
\(893\) | −36925.6 | −1.38373 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7275.74 | 0.271278 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3114.70 | −0.115745 | ||||||||
\(899\) | −8309.70 | −0.308280 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24549.7 | −0.907735 | ||||||||
\(902\) | 358.399 | 0.0132299 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5253.77 | −0.193294 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31692.8 | −1.16025 | −0.580123 | − | 0.814529i | \(-0.696995\pi\) | ||||
−0.580123 | + | 0.814529i | \(0.696995\pi\) | |||||||
\(908\) | 32598.5 | 1.19143 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2403.15 | −0.0873985 | −0.0436993 | − | 0.999045i | \(-0.513914\pi\) | ||||
−0.0436993 | + | 0.999045i | \(0.513914\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38557.6 | 1.39767 | ||||||||
\(914\) | 997.843 | 0.0361113 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −26153.6 | −0.943385 | ||||||||
\(917\) | −2912.99 | −0.104902 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19622.5 | 0.704339 | 0.352170 | − | 0.935936i | \(-0.385444\pi\) | ||||
0.352170 | + | 0.935936i | \(0.385444\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5087.56 | −0.181724 | ||||||||
\(923\) | 2720.07 | 0.0970014 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8355.06 | 0.296506 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20867.7 | −0.738165 | ||||||||
\(929\) | 12930.5 | 0.456660 | 0.228330 | − | 0.973584i | \(-0.426673\pi\) | ||||
0.228330 | + | 0.973584i | \(0.426673\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7028.90 | −0.247436 | ||||||||
\(932\) | 30001.6 | 1.05444 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8016.64 | −0.280848 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18717.1 | −0.652573 | −0.326287 | − | 0.945271i | \(-0.605797\pi\) | ||||
−0.326287 | + | 0.945271i | \(0.605797\pi\) | |||||||
\(938\) | 3270.76 | 0.113853 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10152.9 | 0.351727 | 0.175863 | − | 0.984415i | \(-0.443728\pi\) | ||||
0.175863 | + | 0.984415i | \(0.443728\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1917.15 | −0.0662045 | ||||||||
\(944\) | 36822.4 | 1.26956 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4093.09 | 0.140674 | ||||||||
\(947\) | 15836.2 | 0.543408 | 0.271704 | − | 0.962381i | \(-0.412413\pi\) | ||||
0.271704 | + | 0.962381i | \(0.412413\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 737.158 | 0.0252151 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5867.15 | −0.199743 | ||||||||
\(953\) | 4847.86 | 0.164782 | 0.0823911 | − | 0.996600i | \(-0.473744\pi\) | ||||
0.0823911 | + | 0.996600i | \(0.473744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 51240.0 | 1.73349 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8635.44 | −0.291230 | ||||||||
\(959\) | 4334.76 | 0.145961 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28134.5 | −0.944397 | ||||||||
\(962\) | 835.207 | 0.0279918 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46138.6 | 1.54152 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17153.8 | −0.570454 | −0.285227 | − | 0.958460i | \(-0.592069\pi\) | ||||
−0.285227 | + | 0.958460i | \(0.592069\pi\) | |||||||
\(968\) | −5856.80 | −0.194468 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50352.2 | −1.66414 | −0.832070 | − | 0.554670i | \(-0.812844\pi\) | ||||
−0.832070 | + | 0.554670i | \(0.812844\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1868.96 | −0.0615788 | ||||||||
\(974\) | 11053.2 | 0.363623 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 25512.8 | 0.836725 | ||||||||
\(977\) | 1510.03 | 0.0494474 | 0.0247237 | − | 0.999694i | \(-0.492129\pi\) | ||||
0.0247237 | + | 0.999694i | \(0.492129\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33785.7 | −1.10296 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10998.1 | 0.357396 | ||||||||
\(983\) | −5310.89 | −0.172321 | −0.0861603 | − | 0.996281i | \(-0.527460\pi\) | ||||
−0.0861603 | + | 0.996281i | \(0.527460\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10910.6 | 0.352396 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17137.4 | 0.551836 | ||||||||
\(989\) | −21894.7 | −0.703956 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35845.4 | 1.14901 | 0.574505 | − | 0.818501i | \(-0.305195\pi\) | ||||
0.574505 | + | 0.818501i | \(0.305195\pi\) | |||||||
\(992\) | 4159.82 | 0.133140 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −687.764 | −0.0219462 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17857.5 | 0.567253 | 0.283627 | − | 0.958935i | \(-0.408462\pi\) | ||||
0.283627 | + | 0.958935i | \(0.408462\pi\) | |||||||
\(998\) | 3868.24 | 0.122692 | ||||||||
\(999\) | 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 | 1575.4.a.x.1.1 | 2 | ||
3.2 | odd | 2 | 525.4.a.j.1.2 | ✓ | 2 | ||
5.4 | even | 2 | 1575.4.a.o.1.2 | 2 | |||
15.2 | even | 4 | 525.4.d.m.274.3 | 4 | |||
15.8 | even | 4 | 525.4.d.m.274.2 | 4 | |||
15.14 | odd | 2 | 525.4.a.m.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.4.a.j.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
525.4.a.m.1.1 | yes | 2 | 15.14 | odd | 2 | ||
525.4.d.m.274.2 | 4 | 15.8 | even | 4 | |||
525.4.d.m.274.3 | 4 | 15.2 | even | 4 | |||
1575.4.a.o.1.2 | 2 | 5.4 | even | 2 | |||
1575.4.a.x.1.1 | 2 | 1.1 | even | 1 | trivial |