Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2275,2,Mod(1,2275)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2275, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2275.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2275 = 5^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2275.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: | \(18.1659664598\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.34292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2275.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34292 | −1.65670 | −0.828348 | − | 0.560213i | \(-0.810719\pi\) | ||||
−0.828348 | + | 0.560213i | \(0.810719\pi\) | |||||||
\(3\) | 1.14637 | 0.661854 | 0.330927 | − | 0.943656i | \(-0.392639\pi\) | ||||
0.330927 | + | 0.943656i | \(0.392639\pi\) | |||||||
\(4\) | 3.48929 | 1.74464 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.68585 | −1.09649 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −3.48929 | −1.23365 | ||||||||
\(9\) | −1.68585 | −0.561949 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.14637 | 0.345642 | 0.172821 | − | 0.984953i | \(-0.444712\pi\) | ||||
0.172821 | + | 0.984953i | \(0.444712\pi\) | |||||||
\(12\) | 4.00000 | 1.15470 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.34292 | −0.626173 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.19656 | 0.299139 | ||||||||
\(17\) | −5.83221 | −1.41452 | −0.707260 | − | 0.706954i | \(-0.750069\pi\) | ||||
−0.707260 | + | 0.706954i | \(0.750069\pi\) | |||||||
\(18\) | 3.94981 | 0.930979 | ||||||||
\(19\) | −3.34292 | −0.766919 | −0.383460 | − | 0.923558i | \(-0.625267\pi\) | ||||
−0.383460 | + | 0.923558i | \(0.625267\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.14637 | 0.250157 | ||||||||
\(22\) | −2.68585 | −0.572624 | ||||||||
\(23\) | 3.17513 | 0.662061 | 0.331031 | − | 0.943620i | \(-0.392604\pi\) | ||||
0.331031 | + | 0.943620i | \(0.392604\pi\) | |||||||
\(24\) | −4.00000 | −0.816497 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.34292 | 0.459485 | ||||||||
\(27\) | −5.37169 | −1.03378 | ||||||||
\(28\) | 3.48929 | 0.659414 | ||||||||
\(29\) | 10.4893 | 1.94781 | 0.973906 | − | 0.226952i | \(-0.0728760\pi\) | ||||
0.973906 | + | 0.226952i | \(0.0728760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.63565 | 0.293772 | 0.146886 | − | 0.989153i | \(-0.453075\pi\) | ||||
0.146886 | + | 0.989153i | \(0.453075\pi\) | |||||||
\(32\) | 4.17513 | 0.738067 | ||||||||
\(33\) | 1.31415 | 0.228765 | ||||||||
\(34\) | 13.6644 | 2.34343 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.88240 | −0.980401 | ||||||||
\(37\) | −8.51806 | −1.40036 | −0.700180 | − | 0.713966i | \(-0.746897\pi\) | ||||
−0.700180 | + | 0.713966i | \(0.746897\pi\) | |||||||
\(38\) | 7.83221 | 1.27055 | ||||||||
\(39\) | −1.14637 | −0.183565 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.292731 | −0.0457169 | −0.0228584 | − | 0.999739i | \(-0.507277\pi\) | ||||
−0.0228584 | + | 0.999739i | \(0.507277\pi\) | |||||||
\(42\) | −2.68585 | −0.414435 | ||||||||
\(43\) | 8.15371 | 1.24343 | 0.621715 | − | 0.783244i | \(-0.286436\pi\) | ||||
0.621715 | + | 0.783244i | \(0.286436\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.43910 | −1.09683 | ||||||||
\(47\) | 10.6142 | 1.54824 | 0.774122 | − | 0.633036i | \(-0.218191\pi\) | ||||
0.774122 | + | 0.633036i | \(0.218191\pi\) | |||||||
\(48\) | 1.37169 | 0.197987 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.68585 | −0.936206 | ||||||||
\(52\) | −3.48929 | −0.483877 | ||||||||
\(53\) | 0.782020 | 0.107419 | 0.0537093 | − | 0.998557i | \(-0.482896\pi\) | ||||
0.0537093 | + | 0.998557i | \(0.482896\pi\) | |||||||
\(54\) | 12.5855 | 1.71266 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.48929 | −0.466276 | ||||||||
\(57\) | −3.83221 | −0.507589 | ||||||||
\(58\) | −24.5756 | −3.22693 | ||||||||
\(59\) | 12.6430 | 1.64598 | 0.822989 | − | 0.568057i | \(-0.192305\pi\) | ||||
0.822989 | + | 0.568057i | \(0.192305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | −3.83221 | −0.486691 | ||||||||
\(63\) | −1.68585 | −0.212397 | ||||||||
\(64\) | −12.1751 | −1.52189 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.07896 | −0.378994 | ||||||||
\(67\) | 6.10038 | 0.745281 | 0.372640 | − | 0.927976i | \(-0.378453\pi\) | ||||
0.372640 | + | 0.927976i | \(0.378453\pi\) | |||||||
\(68\) | −20.3503 | −2.46783 | ||||||||
\(69\) | 3.63986 | 0.438188 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.53948 | 0.182703 | 0.0913514 | − | 0.995819i | \(-0.470881\pi\) | ||||
0.0913514 | + | 0.995819i | \(0.470881\pi\) | |||||||
\(72\) | 5.88240 | 0.693248 | ||||||||
\(73\) | 15.3001 | 1.79074 | 0.895369 | − | 0.445324i | \(-0.146912\pi\) | ||||
0.895369 | + | 0.445324i | \(0.146912\pi\) | |||||||
\(74\) | 19.9572 | 2.31997 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.6644 | −1.33800 | ||||||||
\(77\) | 1.14637 | 0.130640 | ||||||||
\(78\) | 2.68585 | 0.304112 | ||||||||
\(79\) | 0.882404 | 0.0992782 | 0.0496391 | − | 0.998767i | \(-0.484193\pi\) | ||||
0.0496391 | + | 0.998767i | \(0.484193\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.10038 | −0.122265 | ||||||||
\(82\) | 0.685846 | 0.0757390 | ||||||||
\(83\) | 12.1292 | 1.33135 | 0.665674 | − | 0.746243i | \(-0.268144\pi\) | ||||
0.665674 | + | 0.746243i | \(0.268144\pi\) | |||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.1035 | −2.05999 | ||||||||
\(87\) | 12.0246 | 1.28917 | ||||||||
\(88\) | −4.00000 | −0.426401 | ||||||||
\(89\) | 5.73604 | 0.608019 | 0.304009 | − | 0.952669i | \(-0.401675\pi\) | ||||
0.304009 | + | 0.952669i | \(0.401675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 11.0790 | 1.15506 | ||||||||
\(93\) | 1.87506 | 0.194434 | ||||||||
\(94\) | −24.8683 | −2.56497 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.78623 | 0.488493 | ||||||||
\(97\) | 5.34292 | 0.542492 | 0.271246 | − | 0.962510i | \(-0.412564\pi\) | ||||
0.271246 | + | 0.962510i | \(0.412564\pi\) | |||||||
\(98\) | −2.34292 | −0.236671 | ||||||||
\(99\) | −1.93260 | −0.194233 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1464 | 1.10910 | 0.554552 | − | 0.832149i | \(-0.312889\pi\) | ||||
0.554552 | + | 0.832149i | \(0.312889\pi\) | |||||||
\(102\) | 15.6644 | 1.55101 | ||||||||
\(103\) | 3.41454 | 0.336444 | 0.168222 | − | 0.985749i | \(-0.446197\pi\) | ||||
0.168222 | + | 0.985749i | \(0.446197\pi\) | |||||||
\(104\) | 3.48929 | 0.342153 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.83221 | −0.177960 | ||||||||
\(107\) | −4.97858 | −0.481297 | −0.240649 | − | 0.970612i | \(-0.577360\pi\) | ||||
−0.240649 | + | 0.970612i | \(0.577360\pi\) | |||||||
\(108\) | −18.7434 | −1.80358 | ||||||||
\(109\) | −13.4966 | −1.29274 | −0.646372 | − | 0.763023i | \(-0.723714\pi\) | ||||
−0.646372 | + | 0.763023i | \(0.723714\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.76481 | −0.926835 | ||||||||
\(112\) | 1.19656 | 0.113064 | ||||||||
\(113\) | −16.4464 | −1.54715 | −0.773576 | − | 0.633704i | \(-0.781534\pi\) | ||||
−0.773576 | + | 0.633704i | \(0.781534\pi\) | |||||||
\(114\) | 8.97858 | 0.840921 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 36.6002 | 3.39824 | ||||||||
\(117\) | 1.68585 | 0.155857 | ||||||||
\(118\) | −29.6216 | −2.72689 | ||||||||
\(119\) | −5.83221 | −0.534638 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.68585 | −0.880531 | ||||||||
\(122\) | 4.68585 | 0.424237 | ||||||||
\(123\) | −0.335577 | −0.0302579 | ||||||||
\(124\) | 5.70727 | 0.512528 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.94981 | 0.351877 | ||||||||
\(127\) | −12.0575 | −1.06993 | −0.534967 | − | 0.844873i | \(-0.679676\pi\) | ||||
−0.534967 | + | 0.844873i | \(0.679676\pi\) | |||||||
\(128\) | 20.1751 | 1.78325 | ||||||||
\(129\) | 9.34713 | 0.822969 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.66442 | −0.320162 | −0.160081 | − | 0.987104i | \(-0.551176\pi\) | ||||
−0.160081 | + | 0.987104i | \(0.551176\pi\) | |||||||
\(132\) | 4.58546 | 0.399113 | ||||||||
\(133\) | −3.34292 | −0.289868 | ||||||||
\(134\) | −14.2927 | −1.23470 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.3503 | 1.74502 | ||||||||
\(137\) | 13.1035 | 1.11951 | 0.559755 | − | 0.828658i | \(-0.310895\pi\) | ||||
0.559755 | + | 0.828658i | \(0.310895\pi\) | |||||||
\(138\) | −8.52792 | −0.725945 | ||||||||
\(139\) | 7.49663 | 0.635856 | 0.317928 | − | 0.948115i | \(-0.397013\pi\) | ||||
0.317928 | + | 0.948115i | \(0.397013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1678 | 1.02471 | ||||||||
\(142\) | −3.60688 | −0.302683 | ||||||||
\(143\) | −1.14637 | −0.0958639 | ||||||||
\(144\) | −2.01721 | −0.168101 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −35.8469 | −2.96671 | ||||||||
\(147\) | 1.14637 | 0.0945506 | ||||||||
\(148\) | −29.7220 | −2.44313 | ||||||||
\(149\) | 2.16779 | 0.177592 | 0.0887961 | − | 0.996050i | \(-0.471698\pi\) | ||||
0.0887961 | + | 0.996050i | \(0.471698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.9112 | 1.21345 | 0.606727 | − | 0.794910i | \(-0.292482\pi\) | ||||
0.606727 | + | 0.794910i | \(0.292482\pi\) | |||||||
\(152\) | 11.6644 | 0.946110 | ||||||||
\(153\) | 9.83221 | 0.794887 | ||||||||
\(154\) | −2.68585 | −0.216432 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | −22.8683 | −1.82509 | −0.912546 | − | 0.408975i | \(-0.865886\pi\) | ||||
−0.912546 | + | 0.408975i | \(0.865886\pi\) | |||||||
\(158\) | −2.06740 | −0.164474 | ||||||||
\(159\) | 0.896480 | 0.0710955 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.17513 | 0.250236 | ||||||||
\(162\) | 2.57812 | 0.202556 | ||||||||
\(163\) | −7.07896 | −0.554467 | −0.277234 | − | 0.960803i | \(-0.589418\pi\) | ||||
−0.277234 | + | 0.960803i | \(0.589418\pi\) | |||||||
\(164\) | −1.02142 | −0.0797597 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −28.4177 | −2.20564 | ||||||||
\(167\) | −2.61423 | −0.202295 | −0.101148 | − | 0.994871i | \(-0.532251\pi\) | ||||
−0.101148 | + | 0.994871i | \(0.532251\pi\) | |||||||
\(168\) | −4.00000 | −0.308607 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.63565 | 0.430969 | ||||||||
\(172\) | 28.4507 | 2.16934 | ||||||||
\(173\) | −11.0031 | −0.836553 | −0.418276 | − | 0.908320i | \(-0.637366\pi\) | ||||
−0.418276 | + | 0.908320i | \(0.637366\pi\) | |||||||
\(174\) | −28.1726 | −2.13576 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.37169 | 0.103395 | ||||||||
\(177\) | 14.4935 | 1.08940 | ||||||||
\(178\) | −13.4391 | −1.00730 | ||||||||
\(179\) | 23.9614 | 1.79096 | 0.895478 | − | 0.445105i | \(-0.146834\pi\) | ||||
0.895478 | + | 0.445105i | \(0.146834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.56090 | 0.487668 | 0.243834 | − | 0.969817i | \(-0.421595\pi\) | ||||
0.243834 | + | 0.969817i | \(0.421595\pi\) | |||||||
\(182\) | 2.34292 | 0.173669 | ||||||||
\(183\) | −2.29273 | −0.169484 | ||||||||
\(184\) | −11.0790 | −0.816752 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.39312 | −0.322119 | ||||||||
\(187\) | −6.68585 | −0.488917 | ||||||||
\(188\) | 37.0361 | 2.70114 | ||||||||
\(189\) | −5.37169 | −0.390733 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.39312 | −0.317875 | −0.158937 | − | 0.987289i | \(-0.550807\pi\) | ||||
−0.158937 | + | 0.987289i | \(0.550807\pi\) | |||||||
\(192\) | −13.9572 | −1.00727 | ||||||||
\(193\) | 8.29273 | 0.596924 | 0.298462 | − | 0.954422i | \(-0.403526\pi\) | ||||
0.298462 | + | 0.954422i | \(0.403526\pi\) | |||||||
\(194\) | −12.5181 | −0.898744 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.48929 | 0.249235 | ||||||||
\(197\) | 3.17092 | 0.225919 | 0.112959 | − | 0.993600i | \(-0.463967\pi\) | ||||
0.112959 | + | 0.993600i | \(0.463967\pi\) | |||||||
\(198\) | 4.52792 | 0.321786 | ||||||||
\(199\) | −13.5970 | −0.963867 | −0.481934 | − | 0.876208i | \(-0.660065\pi\) | ||||
−0.481934 | + | 0.876208i | \(0.660065\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.99327 | 0.493267 | ||||||||
\(202\) | −26.1151 | −1.83745 | ||||||||
\(203\) | 10.4893 | 0.736204 | ||||||||
\(204\) | −23.3288 | −1.63335 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | −5.35279 | −0.372045 | ||||||||
\(208\) | −1.19656 | −0.0829663 | ||||||||
\(209\) | −3.83221 | −0.265080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.27552 | 0.638553 | 0.319277 | − | 0.947662i | \(-0.396560\pi\) | ||||
0.319277 | + | 0.947662i | \(0.396560\pi\) | |||||||
\(212\) | 2.72869 | 0.187407 | ||||||||
\(213\) | 1.76481 | 0.120923 | ||||||||
\(214\) | 11.6644 | 0.797364 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 18.7434 | 1.27533 | ||||||||
\(217\) | 1.63565 | 0.111035 | ||||||||
\(218\) | 31.6216 | 2.14168 | ||||||||
\(219\) | 17.5395 | 1.18521 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.83221 | 0.392317 | ||||||||
\(222\) | 22.8782 | 1.53548 | ||||||||
\(223\) | 19.5928 | 1.31203 | 0.656016 | − | 0.754747i | \(-0.272240\pi\) | ||||
0.656016 | + | 0.754747i | \(0.272240\pi\) | |||||||
\(224\) | 4.17513 | 0.278963 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 38.5328 | 2.56316 | ||||||||
\(227\) | 19.6644 | 1.30517 | 0.652587 | − | 0.757714i | \(-0.273684\pi\) | ||||
0.652587 | + | 0.757714i | \(0.273684\pi\) | |||||||
\(228\) | −13.3717 | −0.885562 | ||||||||
\(229\) | 7.76481 | 0.513113 | 0.256556 | − | 0.966529i | \(-0.417412\pi\) | ||||
0.256556 | + | 0.966529i | \(0.417412\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.31415 | 0.0864650 | ||||||||
\(232\) | −36.6002 | −2.40292 | ||||||||
\(233\) | −12.1966 | −0.799023 | −0.399512 | − | 0.916728i | \(-0.630820\pi\) | ||||
−0.399512 | + | 0.916728i | \(0.630820\pi\) | |||||||
\(234\) | −3.94981 | −0.258207 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 44.1151 | 2.87165 | ||||||||
\(237\) | 1.01156 | 0.0657077 | ||||||||
\(238\) | 13.6644 | 0.885733 | ||||||||
\(239\) | −10.2927 | −0.665781 | −0.332891 | − | 0.942965i | \(-0.608024\pi\) | ||||
−0.332891 | + | 0.942965i | \(0.608024\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.02877 | −0.259516 | −0.129758 | − | 0.991546i | \(-0.541420\pi\) | ||||
−0.129758 | + | 0.991546i | \(0.541420\pi\) | |||||||
\(242\) | 22.6932 | 1.45877 | ||||||||
\(243\) | 14.8536 | 0.952861 | ||||||||
\(244\) | −6.97858 | −0.446758 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.786230 | 0.0501282 | ||||||||
\(247\) | 3.34292 | 0.212705 | ||||||||
\(248\) | −5.70727 | −0.362412 | ||||||||
\(249\) | 13.9044 | 0.881158 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.91117 | 0.183752 | 0.0918758 | − | 0.995770i | \(-0.470714\pi\) | ||||
0.0918758 | + | 0.995770i | \(0.470714\pi\) | |||||||
\(252\) | −5.88240 | −0.370557 | ||||||||
\(253\) | 3.63986 | 0.228836 | ||||||||
\(254\) | 28.2499 | 1.77256 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −22.9185 | −1.43241 | ||||||||
\(257\) | 19.5970 | 1.22243 | 0.611214 | − | 0.791465i | \(-0.290681\pi\) | ||||
0.611214 | + | 0.791465i | \(0.290681\pi\) | |||||||
\(258\) | −21.8996 | −1.36341 | ||||||||
\(259\) | −8.51806 | −0.529286 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.6833 | −1.09457 | ||||||||
\(262\) | 8.58546 | 0.530412 | ||||||||
\(263\) | −7.56825 | −0.466678 | −0.233339 | − | 0.972395i | \(-0.574965\pi\) | ||||
−0.233339 | + | 0.972395i | \(0.574965\pi\) | |||||||
\(264\) | −4.58546 | −0.282216 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.83221 | 0.480224 | ||||||||
\(267\) | 6.57560 | 0.402420 | ||||||||
\(268\) | 21.2860 | 1.30025 | ||||||||
\(269\) | −9.47208 | −0.577523 | −0.288761 | − | 0.957401i | \(-0.593243\pi\) | ||||
−0.288761 | + | 0.957401i | \(0.593243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.3717 | 1.78420 | 0.892102 | − | 0.451835i | \(-0.149230\pi\) | ||||
0.892102 | + | 0.451835i | \(0.149230\pi\) | |||||||
\(272\) | −6.97858 | −0.423138 | ||||||||
\(273\) | −1.14637 | −0.0693812 | ||||||||
\(274\) | −30.7005 | −1.85469 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.7005 | 0.764483 | ||||||||
\(277\) | 1.90383 | 0.114390 | 0.0571949 | − | 0.998363i | \(-0.481784\pi\) | ||||
0.0571949 | + | 0.998363i | \(0.481784\pi\) | |||||||
\(278\) | −17.5640 | −1.05342 | ||||||||
\(279\) | −2.75746 | −0.165085 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.5756 | −1.22744 | −0.613719 | − | 0.789525i | \(-0.710327\pi\) | ||||
−0.613719 | + | 0.789525i | \(0.710327\pi\) | |||||||
\(282\) | −28.5082 | −1.69764 | ||||||||
\(283\) | 26.9933 | 1.60458 | 0.802292 | − | 0.596932i | \(-0.203614\pi\) | ||||
0.802292 | + | 0.596932i | \(0.203614\pi\) | |||||||
\(284\) | 5.37169 | 0.318751 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.68585 | 0.158817 | ||||||||
\(287\) | −0.292731 | −0.0172794 | ||||||||
\(288\) | −7.03863 | −0.414756 | ||||||||
\(289\) | 17.0147 | 1.00086 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.12494 | 0.359050 | ||||||||
\(292\) | 53.3864 | 3.12420 | ||||||||
\(293\) | 14.9070 | 0.870874 | 0.435437 | − | 0.900219i | \(-0.356594\pi\) | ||||
0.435437 | + | 0.900219i | \(0.356594\pi\) | |||||||
\(294\) | −2.68585 | −0.156642 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 29.7220 | 1.72755 | ||||||||
\(297\) | −6.15792 | −0.357319 | ||||||||
\(298\) | −5.07896 | −0.294216 | ||||||||
\(299\) | −3.17513 | −0.183623 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.15371 | 0.469972 | ||||||||
\(302\) | −34.9357 | −2.01033 | ||||||||
\(303\) | 12.7778 | 0.734066 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −23.0361 | −1.31689 | ||||||||
\(307\) | −26.0288 | −1.48554 | −0.742770 | − | 0.669546i | \(-0.766488\pi\) | ||||
−0.742770 | + | 0.669546i | \(0.766488\pi\) | |||||||
\(308\) | 4.00000 | 0.227921 | ||||||||
\(309\) | 3.91431 | 0.222677 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.4966 | 1.10555 | 0.552776 | − | 0.833330i | \(-0.313568\pi\) | ||||
0.552776 | + | 0.833330i | \(0.313568\pi\) | |||||||
\(312\) | 4.00000 | 0.226455 | ||||||||
\(313\) | 3.48194 | 0.196811 | 0.0984055 | − | 0.995146i | \(-0.468626\pi\) | ||||
0.0984055 | + | 0.995146i | \(0.468626\pi\) | |||||||
\(314\) | 53.5787 | 3.02362 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.07896 | 0.173205 | ||||||||
\(317\) | −5.02142 | −0.282031 | −0.141016 | − | 0.990007i | \(-0.545037\pi\) | ||||
−0.141016 | + | 0.990007i | \(0.545037\pi\) | |||||||
\(318\) | −2.10038 | −0.117784 | ||||||||
\(319\) | 12.0246 | 0.673246 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.70727 | −0.318549 | ||||||||
\(322\) | −7.43910 | −0.414565 | ||||||||
\(323\) | 19.4966 | 1.08482 | ||||||||
\(324\) | −3.83956 | −0.213309 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.5855 | 0.918584 | ||||||||
\(327\) | −15.4721 | −0.855608 | ||||||||
\(328\) | 1.02142 | 0.0563986 | ||||||||
\(329\) | 10.6142 | 0.585182 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.14950 | −0.338007 | −0.169004 | − | 0.985615i | \(-0.554055\pi\) | ||||
−0.169004 | + | 0.985615i | \(0.554055\pi\) | |||||||
\(332\) | 42.3221 | 2.32273 | ||||||||
\(333\) | 14.3601 | 0.786931 | ||||||||
\(334\) | 6.12494 | 0.335142 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.37169 | 0.0748320 | ||||||||
\(337\) | 25.6258 | 1.39593 | 0.697963 | − | 0.716134i | \(-0.254090\pi\) | ||||
0.697963 | + | 0.716134i | \(0.254090\pi\) | |||||||
\(338\) | −2.34292 | −0.127438 | ||||||||
\(339\) | −18.8536 | −1.02399 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.87506 | 0.101540 | ||||||||
\(342\) | −13.2039 | −0.713985 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −28.4507 | −1.53396 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.7795 | 1.38591 | ||||||||
\(347\) | 16.7005 | 0.896532 | 0.448266 | − | 0.893900i | \(-0.352042\pi\) | ||||
0.448266 | + | 0.893900i | \(0.352042\pi\) | |||||||
\(348\) | 41.9572 | 2.24914 | ||||||||
\(349\) | −23.5500 | −1.26060 | −0.630300 | − | 0.776351i | \(-0.717068\pi\) | ||||
−0.630300 | + | 0.776351i | \(0.717068\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.37169 | 0.286720 | ||||||||
\(352\) | 4.78623 | 0.255107 | ||||||||
\(353\) | 7.64973 | 0.407154 | 0.203577 | − | 0.979059i | \(-0.434743\pi\) | ||||
0.203577 | + | 0.979059i | \(0.434743\pi\) | |||||||
\(354\) | −33.9572 | −1.80480 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.0147 | 1.06078 | ||||||||
\(357\) | −6.68585 | −0.353853 | ||||||||
\(358\) | −56.1396 | −2.96707 | ||||||||
\(359\) | 18.3748 | 0.969786 | 0.484893 | − | 0.874573i | \(-0.338858\pi\) | ||||
0.484893 | + | 0.874573i | \(0.338858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.82487 | −0.411835 | ||||||||
\(362\) | −15.3717 | −0.807918 | ||||||||
\(363\) | −11.1035 | −0.582784 | ||||||||
\(364\) | −3.48929 | −0.182888 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.37169 | 0.280783 | ||||||||
\(367\) | −5.33871 | −0.278679 | −0.139339 | − | 0.990245i | \(-0.544498\pi\) | ||||
−0.139339 | + | 0.990245i | \(0.544498\pi\) | |||||||
\(368\) | 3.79923 | 0.198049 | ||||||||
\(369\) | 0.493499 | 0.0256906 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.782020 | 0.0406004 | ||||||||
\(372\) | 6.54262 | 0.339219 | ||||||||
\(373\) | −21.5212 | −1.11433 | −0.557163 | − | 0.830403i | \(-0.688110\pi\) | ||||
−0.557163 | + | 0.830403i | \(0.688110\pi\) | |||||||
\(374\) | 15.6644 | 0.809988 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −37.0361 | −1.90999 | ||||||||
\(377\) | −10.4893 | −0.540226 | ||||||||
\(378\) | 12.5855 | 0.647326 | ||||||||
\(379\) | 4.61002 | 0.236801 | 0.118400 | − | 0.992966i | \(-0.462223\pi\) | ||||
0.118400 | + | 0.992966i | \(0.462223\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.8223 | −0.708140 | ||||||||
\(382\) | 10.2927 | 0.526622 | ||||||||
\(383\) | 8.33558 | 0.425928 | 0.212964 | − | 0.977060i | \(-0.431688\pi\) | ||||
0.212964 | + | 0.977060i | \(0.431688\pi\) | |||||||
\(384\) | 23.1281 | 1.18025 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19.4292 | −0.988922 | ||||||||
\(387\) | −13.7459 | −0.698744 | ||||||||
\(388\) | 18.6430 | 0.946455 | ||||||||
\(389\) | −6.44223 | −0.326634 | −0.163317 | − | 0.986574i | \(-0.552219\pi\) | ||||
−0.163317 | + | 0.986574i | \(0.552219\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.5181 | −0.936498 | ||||||||
\(392\) | −3.48929 | −0.176236 | ||||||||
\(393\) | −4.20077 | −0.211901 | ||||||||
\(394\) | −7.42923 | −0.374279 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.74338 | −0.338868 | ||||||||
\(397\) | −1.40046 | −0.0702872 | −0.0351436 | − | 0.999382i | \(-0.511189\pi\) | ||||
−0.0351436 | + | 0.999382i | \(0.511189\pi\) | |||||||
\(398\) | 31.8568 | 1.59684 | ||||||||
\(399\) | −3.83221 | −0.191851 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.97858 | −0.348494 | −0.174247 | − | 0.984702i | \(-0.555749\pi\) | ||||
−0.174247 | + | 0.984702i | \(0.555749\pi\) | |||||||
\(402\) | −16.3847 | −0.817194 | ||||||||
\(403\) | −1.63565 | −0.0814777 | ||||||||
\(404\) | 38.8929 | 1.93499 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.5756 | −1.21967 | ||||||||
\(407\) | −9.76481 | −0.484024 | ||||||||
\(408\) | 23.3288 | 1.15495 | ||||||||
\(409\) | −18.3790 | −0.908785 | −0.454392 | − | 0.890802i | \(-0.650144\pi\) | ||||
−0.454392 | + | 0.890802i | \(0.650144\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.0214 | 0.740952 | ||||||||
\(412\) | 11.9143 | 0.586976 | ||||||||
\(413\) | 12.6430 | 0.622121 | ||||||||
\(414\) | 12.5412 | 0.616365 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.17513 | −0.204703 | ||||||||
\(417\) | 8.59388 | 0.420844 | ||||||||
\(418\) | 8.97858 | 0.439157 | ||||||||
\(419\) | −30.0393 | −1.46751 | −0.733757 | − | 0.679412i | \(-0.762235\pi\) | ||||
−0.733757 | + | 0.679412i | \(0.762235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.31729 | −0.405360 | −0.202680 | − | 0.979245i | \(-0.564965\pi\) | ||||
−0.202680 | + | 0.979245i | \(0.564965\pi\) | |||||||
\(422\) | −21.7318 | −1.05789 | ||||||||
\(423\) | −17.8940 | −0.870034 | ||||||||
\(424\) | −2.72869 | −0.132517 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.13481 | −0.200332 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | −17.3717 | −0.839692 | ||||||||
\(429\) | −1.31415 | −0.0634479 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.64973 | 0.464811 | 0.232406 | − | 0.972619i | \(-0.425340\pi\) | ||||
0.232406 | + | 0.972619i | \(0.425340\pi\) | |||||||
\(432\) | −6.42754 | −0.309245 | ||||||||
\(433\) | −26.3074 | −1.26425 | −0.632127 | − | 0.774865i | \(-0.717818\pi\) | ||||
−0.632127 | + | 0.774865i | \(0.717818\pi\) | |||||||
\(434\) | −3.83221 | −0.183952 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −47.0937 | −2.25538 | ||||||||
\(437\) | −10.6142 | −0.507748 | ||||||||
\(438\) | −41.0937 | −1.96353 | ||||||||
\(439\) | 33.8139 | 1.61385 | 0.806925 | − | 0.590654i | \(-0.201130\pi\) | ||||
0.806925 | + | 0.590654i | \(0.201130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.68585 | −0.0802784 | ||||||||
\(442\) | −13.6644 | −0.649950 | ||||||||
\(443\) | −26.4464 | −1.25651 | −0.628254 | − | 0.778008i | \(-0.716230\pi\) | ||||
−0.628254 | + | 0.778008i | \(0.716230\pi\) | |||||||
\(444\) | −34.0722 | −1.61700 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −45.9044 | −2.17364 | ||||||||
\(447\) | 2.48508 | 0.117540 | ||||||||
\(448\) | −12.1751 | −0.575221 | ||||||||
\(449\) | 2.64300 | 0.124731 | 0.0623655 | − | 0.998053i | \(-0.480136\pi\) | ||||
0.0623655 | + | 0.998053i | \(0.480136\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.335577 | −0.0158017 | ||||||||
\(452\) | −57.3864 | −2.69923 | ||||||||
\(453\) | 17.0937 | 0.803130 | ||||||||
\(454\) | −46.0722 | −2.16228 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.3717 | 0.626187 | ||||||||
\(457\) | 33.6890 | 1.57590 | 0.787952 | − | 0.615737i | \(-0.211141\pi\) | ||||
0.787952 | + | 0.615737i | \(0.211141\pi\) | |||||||
\(458\) | −18.1923 | −0.850073 | ||||||||
\(459\) | 31.3288 | 1.46231 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.0790 | 1.54064 | 0.770320 | − | 0.637657i | \(-0.220096\pi\) | ||||
0.770320 | + | 0.637657i | \(0.220096\pi\) | |||||||
\(462\) | −3.07896 | −0.143246 | ||||||||
\(463\) | 2.51806 | 0.117024 | 0.0585120 | − | 0.998287i | \(-0.481364\pi\) | ||||
0.0585120 | + | 0.998287i | \(0.481364\pi\) | |||||||
\(464\) | 12.5510 | 0.582667 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.5756 | 1.32374 | ||||||||
\(467\) | −2.57560 | −0.119184 | −0.0595922 | − | 0.998223i | \(-0.518980\pi\) | ||||
−0.0595922 | + | 0.998223i | \(0.518980\pi\) | |||||||
\(468\) | 5.88240 | 0.271914 | ||||||||
\(469\) | 6.10038 | 0.281690 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.2155 | −1.20794 | ||||||||
\(472\) | −44.1151 | −2.03056 | ||||||||
\(473\) | 9.34713 | 0.429782 | ||||||||
\(474\) | −2.37000 | −0.108858 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −20.3503 | −0.932753 | ||||||||
\(477\) | −1.31836 | −0.0603638 | ||||||||
\(478\) | 24.1151 | 1.10300 | ||||||||
\(479\) | 0.513847 | 0.0234783 | 0.0117391 | − | 0.999931i | \(-0.496263\pi\) | ||||
0.0117391 | + | 0.999931i | \(0.496263\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.51806 | 0.388390 | ||||||||
\(482\) | 9.43910 | 0.429939 | ||||||||
\(483\) | 3.63986 | 0.165620 | ||||||||
\(484\) | −33.7967 | −1.53621 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −34.8009 | −1.57860 | ||||||||
\(487\) | −36.0575 | −1.63392 | −0.816962 | − | 0.576692i | \(-0.804343\pi\) | ||||
−0.816962 | + | 0.576692i | \(0.804343\pi\) | |||||||
\(488\) | 6.97858 | 0.315905 | ||||||||
\(489\) | −8.11508 | −0.366976 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.22846 | −0.416475 | −0.208237 | − | 0.978078i | \(-0.566773\pi\) | ||||
−0.208237 | + | 0.978078i | \(0.566773\pi\) | |||||||
\(492\) | −1.17092 | −0.0527893 | ||||||||
\(493\) | −61.1758 | −2.75522 | ||||||||
\(494\) | −7.83221 | −0.352388 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.95715 | 0.0878788 | ||||||||
\(497\) | 1.53948 | 0.0690551 | ||||||||
\(498\) | −32.5770 | −1.45981 | ||||||||
\(499\) | 1.00314 | 0.0449065 | 0.0224533 | − | 0.999748i | \(-0.492852\pi\) | ||||
0.0224533 | + | 0.999748i | \(0.492852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.99686 | −0.133890 | ||||||||
\(502\) | −6.82065 | −0.304421 | ||||||||
\(503\) | 30.3503 | 1.35325 | 0.676626 | − | 0.736327i | \(-0.263441\pi\) | ||||
0.676626 | + | 0.736327i | \(0.263441\pi\) | |||||||
\(504\) | 5.88240 | 0.262023 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.52792 | −0.379112 | ||||||||
\(507\) | 1.14637 | 0.0509119 | ||||||||
\(508\) | −42.0722 | −1.86665 | ||||||||
\(509\) | 10.5995 | 0.469816 | 0.234908 | − | 0.972018i | \(-0.424521\pi\) | ||||
0.234908 | + | 0.972018i | \(0.424521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.3001 | 0.676836 | ||||||||
\(512\) | 13.3461 | 0.589818 | ||||||||
\(513\) | 17.9572 | 0.792828 | ||||||||
\(514\) | −45.9143 | −2.02519 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 32.6148 | 1.43579 | ||||||||
\(517\) | 12.1678 | 0.535139 | ||||||||
\(518\) | 19.9572 | 0.876867 | ||||||||
\(519\) | −12.6136 | −0.553676 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.2646 | −0.712564 | −0.356282 | − | 0.934378i | \(-0.615956\pi\) | ||||
−0.356282 | + | 0.934378i | \(0.615956\pi\) | |||||||
\(522\) | 41.4307 | 1.81337 | ||||||||
\(523\) | −7.22219 | −0.315804 | −0.157902 | − | 0.987455i | \(-0.550473\pi\) | ||||
−0.157902 | + | 0.987455i | \(0.550473\pi\) | |||||||
\(524\) | −12.7862 | −0.558569 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.7318 | 0.773144 | ||||||||
\(527\) | −9.53948 | −0.415546 | ||||||||
\(528\) | 1.57246 | 0.0684326 | ||||||||
\(529\) | −12.9185 | −0.561675 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21.3142 | −0.924955 | ||||||||
\(532\) | −11.6644 | −0.505717 | ||||||||
\(533\) | 0.292731 | 0.0126796 | ||||||||
\(534\) | −15.4061 | −0.666688 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −21.2860 | −0.919415 | ||||||||
\(537\) | 27.4685 | 1.18535 | ||||||||
\(538\) | 22.1923 | 0.956780 | ||||||||
\(539\) | 1.14637 | 0.0493775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.3534 | 0.746081 | 0.373041 | − | 0.927815i | \(-0.378315\pi\) | ||||
0.373041 | + | 0.927815i | \(0.378315\pi\) | |||||||
\(542\) | −68.8156 | −2.95588 | ||||||||
\(543\) | 7.52119 | 0.322765 | ||||||||
\(544\) | −24.3503 | −1.04401 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.68585 | 0.114944 | ||||||||
\(547\) | 34.1109 | 1.45848 | 0.729238 | − | 0.684261i | \(-0.239875\pi\) | ||||
0.729238 | + | 0.684261i | \(0.239875\pi\) | |||||||
\(548\) | 45.7220 | 1.95315 | ||||||||
\(549\) | 3.37169 | 0.143900 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.0649 | −1.49381 | ||||||||
\(552\) | −12.7005 | −0.540571 | ||||||||
\(553\) | 0.882404 | 0.0375236 | ||||||||
\(554\) | −4.46052 | −0.189509 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26.1579 | 1.10934 | ||||||||
\(557\) | 13.2222 | 0.560242 | 0.280121 | − | 0.959965i | \(-0.409625\pi\) | ||||
0.280121 | + | 0.959965i | \(0.409625\pi\) | |||||||
\(558\) | 6.46052 | 0.273496 | ||||||||
\(559\) | −8.15371 | −0.344865 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.66442 | −0.323592 | ||||||||
\(562\) | 48.2070 | 2.03349 | ||||||||
\(563\) | 41.3717 | 1.74361 | 0.871804 | − | 0.489854i | \(-0.162950\pi\) | ||||
0.871804 | + | 0.489854i | \(0.162950\pi\) | |||||||
\(564\) | 42.4569 | 1.78776 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −63.2432 | −2.65831 | ||||||||
\(567\) | −1.10038 | −0.0462118 | ||||||||
\(568\) | −5.37169 | −0.225391 | ||||||||
\(569\) | −2.68164 | −0.112420 | −0.0562100 | − | 0.998419i | \(-0.517902\pi\) | ||||
−0.0562100 | + | 0.998419i | \(0.517902\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.9315 | −1.21075 | −0.605373 | − | 0.795942i | \(-0.706976\pi\) | ||||
−0.605373 | + | 0.795942i | \(0.706976\pi\) | |||||||
\(572\) | −4.00000 | −0.167248 | ||||||||
\(573\) | −5.03612 | −0.210387 | ||||||||
\(574\) | 0.685846 | 0.0286267 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.5254 | 0.855225 | ||||||||
\(577\) | −37.5296 | −1.56238 | −0.781189 | − | 0.624294i | \(-0.785387\pi\) | ||||
−0.781189 | + | 0.624294i | \(0.785387\pi\) | |||||||
\(578\) | −39.8641 | −1.65813 | ||||||||
\(579\) | 9.50650 | 0.395077 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.1292 | 0.503202 | ||||||||
\(582\) | −14.3503 | −0.594838 | ||||||||
\(583\) | 0.896480 | 0.0371284 | ||||||||
\(584\) | −53.3864 | −2.20914 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34.9259 | −1.44277 | ||||||||
\(587\) | −23.0649 | −0.951990 | −0.475995 | − | 0.879448i | \(-0.657912\pi\) | ||||
−0.475995 | + | 0.879448i | \(0.657912\pi\) | |||||||
\(588\) | 4.00000 | 0.164957 | ||||||||
\(589\) | −5.46787 | −0.225299 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.63504 | 0.149525 | ||||||||
\(592\) | −10.1923 | −0.418903 | ||||||||
\(593\) | 11.0502 | 0.453777 | 0.226889 | − | 0.973921i | \(-0.427145\pi\) | ||||
0.226889 | + | 0.973921i | \(0.427145\pi\) | |||||||
\(594\) | 14.4275 | 0.591969 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.56404 | 0.309835 | ||||||||
\(597\) | −15.5872 | −0.637940 | ||||||||
\(598\) | 7.43910 | 0.304207 | ||||||||
\(599\) | −44.6044 | −1.82248 | −0.911242 | − | 0.411870i | \(-0.864876\pi\) | ||||
−0.911242 | + | 0.411870i | \(0.864876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 47.8715 | 1.95272 | 0.976359 | − | 0.216156i | \(-0.0693520\pi\) | ||||
0.976359 | + | 0.216156i | \(0.0693520\pi\) | |||||||
\(602\) | −19.1035 | −0.778601 | ||||||||
\(603\) | −10.2843 | −0.418809 | ||||||||
\(604\) | 52.0294 | 2.11705 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −29.9374 | −1.21612 | ||||||||
\(607\) | −45.0691 | −1.82930 | −0.914649 | − | 0.404249i | \(-0.867533\pi\) | ||||
−0.914649 | + | 0.404249i | \(0.867533\pi\) | |||||||
\(608\) | −13.9572 | −0.566037 | ||||||||
\(609\) | 12.0246 | 0.487260 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.6142 | −0.429406 | ||||||||
\(612\) | 34.3074 | 1.38680 | ||||||||
\(613\) | 25.5212 | 1.03079 | 0.515396 | − | 0.856952i | \(-0.327645\pi\) | ||||
0.515396 | + | 0.856952i | \(0.327645\pi\) | |||||||
\(614\) | 60.9834 | 2.46109 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | −0.161165 | ||||||||
\(617\) | −29.2432 | −1.17729 | −0.588643 | − | 0.808393i | \(-0.700337\pi\) | ||||
−0.588643 | + | 0.808393i | \(0.700337\pi\) | |||||||
\(618\) | −9.17092 | −0.368909 | ||||||||
\(619\) | 4.78623 | 0.192375 | 0.0961874 | − | 0.995363i | \(-0.469335\pi\) | ||||
0.0961874 | + | 0.995363i | \(0.469335\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.0558 | −0.684428 | ||||||||
\(622\) | −45.6791 | −1.83157 | ||||||||
\(623\) | 5.73604 | 0.229810 | ||||||||
\(624\) | −1.37169 | −0.0549116 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.15792 | −0.326056 | ||||||||
\(627\) | −4.39312 | −0.175444 | ||||||||
\(628\) | −79.7942 | −3.18413 | ||||||||
\(629\) | 49.6791 | 1.98084 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.3931 | −1.13031 | −0.565156 | − | 0.824984i | \(-0.691184\pi\) | ||||
−0.565156 | + | 0.824984i | \(0.691184\pi\) | |||||||
\(632\) | −3.07896 | −0.122475 | ||||||||
\(633\) | 10.6331 | 0.422629 | ||||||||
\(634\) | 11.7648 | 0.467240 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.12808 | 0.124036 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | −28.1726 | −1.11536 | ||||||||
\(639\) | −2.59533 | −0.102670 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.96137 | 0.235460 | 0.117730 | − | 0.993046i | \(-0.462438\pi\) | ||||
0.117730 | + | 0.993046i | \(0.462438\pi\) | |||||||
\(642\) | 13.3717 | 0.527739 | ||||||||
\(643\) | −31.1940 | −1.23017 | −0.615086 | − | 0.788460i | \(-0.710879\pi\) | ||||
−0.615086 | + | 0.788460i | \(0.710879\pi\) | |||||||
\(644\) | 11.0790 | 0.436572 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −45.6791 | −1.79722 | ||||||||
\(647\) | −14.9112 | −0.586219 | −0.293109 | − | 0.956079i | \(-0.594690\pi\) | ||||
−0.293109 | + | 0.956079i | \(0.594690\pi\) | |||||||
\(648\) | 3.83956 | 0.150832 | ||||||||
\(649\) | 14.4935 | 0.568920 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.87506 | 0.0734893 | ||||||||
\(652\) | −24.7005 | −0.967348 | ||||||||
\(653\) | 3.57246 | 0.139801 | 0.0699006 | − | 0.997554i | \(-0.477732\pi\) | ||||
0.0699006 | + | 0.997554i | \(0.477732\pi\) | |||||||
\(654\) | 36.2499 | 1.41748 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.350269 | −0.0136757 | ||||||||
\(657\) | −25.7936 | −1.00630 | ||||||||
\(658\) | −24.8683 | −0.969468 | ||||||||
\(659\) | −3.90383 | −0.152071 | −0.0760357 | − | 0.997105i | \(-0.524226\pi\) | ||||
−0.0760357 | + | 0.997105i | \(0.524226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7936 | 0.536508 | 0.268254 | − | 0.963348i | \(-0.413553\pi\) | ||||
0.268254 | + | 0.963348i | \(0.413553\pi\) | |||||||
\(662\) | 14.4078 | 0.559975 | ||||||||
\(663\) | 6.68585 | 0.259657 | ||||||||
\(664\) | −42.3221 | −1.64242 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −33.6447 | −1.30371 | ||||||||
\(667\) | 33.3049 | 1.28957 | ||||||||
\(668\) | −9.12181 | −0.352933 | ||||||||
\(669\) | 22.4605 | 0.868374 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.29273 | −0.0885099 | ||||||||
\(672\) | 4.78623 | 0.184633 | ||||||||
\(673\) | −5.70306 | −0.219837 | −0.109918 | − | 0.993941i | \(-0.535059\pi\) | ||||
−0.109918 | + | 0.993941i | \(0.535059\pi\) | |||||||
\(674\) | −60.0393 | −2.31263 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.48929 | 0.134203 | ||||||||
\(677\) | −35.2614 | −1.35521 | −0.677604 | − | 0.735427i | \(-0.736981\pi\) | ||||
−0.677604 | + | 0.735427i | \(0.736981\pi\) | |||||||
\(678\) | 44.1726 | 1.69644 | ||||||||
\(679\) | 5.34292 | 0.205043 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.5426 | 0.863835 | ||||||||
\(682\) | −4.39312 | −0.168221 | ||||||||
\(683\) | −1.03612 | −0.0396459 | −0.0198229 | − | 0.999804i | \(-0.506310\pi\) | ||||
−0.0198229 | + | 0.999804i | \(0.506310\pi\) | |||||||
\(684\) | 19.6644 | 0.751888 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.34292 | −0.0894532 | ||||||||
\(687\) | 8.90131 | 0.339606 | ||||||||
\(688\) | 9.75639 | 0.371959 | ||||||||
\(689\) | −0.782020 | −0.0297926 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.67850 | 0.139937 | 0.0699684 | − | 0.997549i | \(-0.477710\pi\) | ||||
0.0699684 | + | 0.997549i | \(0.477710\pi\) | |||||||
\(692\) | −38.3931 | −1.45949 | ||||||||
\(693\) | −1.93260 | −0.0734132 | ||||||||
\(694\) | −39.1281 | −1.48528 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −41.9572 | −1.59038 | ||||||||
\(697\) | 1.70727 | 0.0646674 | ||||||||
\(698\) | 55.1758 | 2.08843 | ||||||||
\(699\) | −13.9817 | −0.528837 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.0617493 | −0.00233224 | −0.00116612 | − | 0.999999i | \(-0.500371\pi\) | ||||
−0.00116612 | + | 0.999999i | \(0.500371\pi\) | |||||||
\(702\) | −12.5855 | −0.475008 | ||||||||
\(703\) | 28.4752 | 1.07396 | ||||||||
\(704\) | −13.9572 | −0.526030 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.9227 | −0.674531 | ||||||||
\(707\) | 11.1464 | 0.419202 | ||||||||
\(708\) | 50.5720 | 1.90061 | ||||||||
\(709\) | −42.9834 | −1.61428 | −0.807138 | − | 0.590363i | \(-0.798985\pi\) | ||||
−0.807138 | + | 0.590363i | \(0.798985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.48760 | −0.0557892 | ||||||||
\(712\) | −20.0147 | −0.750082 | ||||||||
\(713\) | 5.19342 | 0.194495 | ||||||||
\(714\) | 15.6644 | 0.586226 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 83.6081 | 3.12458 | ||||||||
\(717\) | −11.7992 | −0.440650 | ||||||||
\(718\) | −43.0508 | −1.60664 | ||||||||
\(719\) | 17.6546 | 0.658404 | 0.329202 | − | 0.944260i | \(-0.393220\pi\) | ||||
0.329202 | + | 0.944260i | \(0.393220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.41454 | 0.127164 | ||||||||
\(722\) | 18.3331 | 0.682286 | ||||||||
\(723\) | −4.61844 | −0.171762 | ||||||||
\(724\) | 22.8929 | 0.850807 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 26.0147 | 0.965496 | ||||||||
\(727\) | 23.8077 | 0.882977 | 0.441488 | − | 0.897267i | \(-0.354451\pi\) | ||||
0.441488 | + | 0.897267i | \(0.354451\pi\) | |||||||
\(728\) | 3.48929 | 0.129322 | ||||||||
\(729\) | 20.3288 | 0.752920 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.5542 | −1.75885 | ||||||||
\(732\) | −8.00000 | −0.295689 | ||||||||
\(733\) | −31.3492 | −1.15791 | −0.578954 | − | 0.815360i | \(-0.696539\pi\) | ||||
−0.578954 | + | 0.815360i | \(0.696539\pi\) | |||||||
\(734\) | 12.5082 | 0.461686 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.2566 | 0.488645 | ||||||||
\(737\) | 6.99327 | 0.257600 | ||||||||
\(738\) | −1.15623 | −0.0425615 | ||||||||
\(739\) | −24.8108 | −0.912680 | −0.456340 | − | 0.889806i | \(-0.650840\pi\) | ||||
−0.456340 | + | 0.889806i | \(0.650840\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.83221 | 0.140780 | ||||||||
\(742\) | −1.83221 | −0.0672626 | ||||||||
\(743\) | −21.3717 | −0.784051 | −0.392026 | − | 0.919954i | \(-0.628226\pi\) | ||||
−0.392026 | + | 0.919954i | \(0.628226\pi\) | |||||||
\(744\) | −6.54262 | −0.239864 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 50.4225 | 1.84610 | ||||||||
\(747\) | −20.4479 | −0.748149 | ||||||||
\(748\) | −23.3288 | −0.852987 | ||||||||
\(749\) | −4.97858 | −0.181913 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.2243 | 0.701503 | 0.350751 | − | 0.936469i | \(-0.385926\pi\) | ||||
0.350751 | + | 0.936469i | \(0.385926\pi\) | |||||||
\(752\) | 12.7005 | 0.463141 | ||||||||
\(753\) | 3.33727 | 0.121617 | ||||||||
\(754\) | 24.5756 | 0.894990 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −18.7434 | −0.681690 | ||||||||
\(757\) | 19.8610 | 0.721860 | 0.360930 | − | 0.932593i | \(-0.382459\pi\) | ||||
0.360930 | + | 0.932593i | \(0.382459\pi\) | |||||||
\(758\) | −10.8009 | −0.392307 | ||||||||
\(759\) | 4.17262 | 0.151456 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.12073 | 0.221876 | 0.110938 | − | 0.993827i | \(-0.464614\pi\) | ||||
0.110938 | + | 0.993827i | \(0.464614\pi\) | |||||||
\(762\) | 32.3847 | 1.17317 | ||||||||
\(763\) | −13.4966 | −0.488611 | ||||||||
\(764\) | −15.3288 | −0.554578 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.5296 | −0.705634 | ||||||||
\(767\) | −12.6430 | −0.456512 | ||||||||
\(768\) | −26.2730 | −0.948045 | ||||||||
\(769\) | 3.82800 | 0.138041 | 0.0690206 | − | 0.997615i | \(-0.478013\pi\) | ||||
0.0690206 | + | 0.997615i | \(0.478013\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.4653 | 0.809070 | ||||||||
\(772\) | 28.9357 | 1.04142 | ||||||||
\(773\) | 6.53635 | 0.235096 | 0.117548 | − | 0.993067i | \(-0.462497\pi\) | ||||
0.117548 | + | 0.993067i | \(0.462497\pi\) | |||||||
\(774\) | 32.2056 | 1.15761 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −18.6430 | −0.669245 | ||||||||
\(777\) | −9.76481 | −0.350311 | ||||||||
\(778\) | 15.0937 | 0.541134 | ||||||||
\(779\) | 0.978577 | 0.0350612 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.76481 | 0.0631498 | ||||||||
\(782\) | 43.3864 | 1.55149 | ||||||||
\(783\) | −56.3452 | −2.01361 | ||||||||
\(784\) | 1.19656 | 0.0427342 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.84208 | 0.351055 | ||||||||
\(787\) | −30.8066 | −1.09814 | −0.549068 | − | 0.835778i | \(-0.685017\pi\) | ||||
−0.549068 | + | 0.835778i | \(0.685017\pi\) | |||||||
\(788\) | 11.0643 | 0.394148 | ||||||||
\(789\) | −8.67598 | −0.308873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.4464 | −0.584768 | ||||||||
\(792\) | 6.74338 | 0.239616 | ||||||||
\(793\) | 2.00000 | 0.0710221 | ||||||||
\(794\) | 3.28117 | 0.116444 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −47.4439 | −1.68161 | ||||||||
\(797\) | 38.8156 | 1.37492 | 0.687460 | − | 0.726222i | \(-0.258726\pi\) | ||||
0.687460 | + | 0.726222i | \(0.258726\pi\) | |||||||
\(798\) | 8.97858 | 0.317838 | ||||||||
\(799\) | −61.9044 | −2.19002 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.67008 | −0.341675 | ||||||||
\(802\) | 16.3503 | 0.577348 | ||||||||
\(803\) | 17.5395 | 0.618955 | ||||||||
\(804\) | 24.4015 | 0.860576 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.83221 | 0.134984 | ||||||||
\(807\) | −10.8585 | −0.382236 | ||||||||
\(808\) | −38.8929 | −1.36825 | ||||||||
\(809\) | 1.04033 | 0.0365759 | 0.0182880 | − | 0.999833i | \(-0.494178\pi\) | ||||
0.0182880 | + | 0.999833i | \(0.494178\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.6712 | 0.444944 | 0.222472 | − | 0.974939i | \(-0.428587\pi\) | ||||
0.222472 | + | 0.974939i | \(0.428587\pi\) | |||||||
\(812\) | 36.6002 | 1.28441 | ||||||||
\(813\) | 33.6707 | 1.18088 | ||||||||
\(814\) | 22.8782 | 0.801880 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.00000 | −0.280056 | ||||||||
\(817\) | −27.2572 | −0.953610 | ||||||||
\(818\) | 43.0607 | 1.50558 | ||||||||
\(819\) | 1.68585 | 0.0589082 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.0361 | 0.943567 | 0.471783 | − | 0.881714i | \(-0.343610\pi\) | ||||
0.471783 | + | 0.881714i | \(0.343610\pi\) | |||||||
\(822\) | −35.1940 | −1.22753 | ||||||||
\(823\) | 31.6363 | 1.10277 | 0.551386 | − | 0.834251i | \(-0.314099\pi\) | ||||
0.551386 | + | 0.834251i | \(0.314099\pi\) | |||||||
\(824\) | −11.9143 | −0.415055 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.6216 | −1.03067 | ||||||||
\(827\) | −56.4800 | −1.96400 | −0.982002 | − | 0.188872i | \(-0.939517\pi\) | ||||
−0.982002 | + | 0.188872i | \(0.939517\pi\) | |||||||
\(828\) | −18.6774 | −0.649085 | ||||||||
\(829\) | −42.6760 | −1.48220 | −0.741099 | − | 0.671396i | \(-0.765695\pi\) | ||||
−0.741099 | + | 0.671396i | \(0.765695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.18248 | 0.0757094 | ||||||||
\(832\) | 12.1751 | 0.422097 | ||||||||
\(833\) | −5.83221 | −0.202074 | ||||||||
\(834\) | −20.1348 | −0.697211 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −13.3717 | −0.462470 | ||||||||
\(837\) | −8.78623 | −0.303697 | ||||||||
\(838\) | 70.3797 | 2.43122 | ||||||||
\(839\) | −40.1642 | −1.38662 | −0.693311 | − | 0.720639i | \(-0.743849\pi\) | ||||
−0.693311 | + | 0.720639i | \(0.743849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 81.0252 | 2.79397 | ||||||||
\(842\) | 19.4868 | 0.671558 | ||||||||
\(843\) | −23.5872 | −0.812385 | ||||||||
\(844\) | 32.3650 | 1.11405 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 41.9242 | 1.44138 | ||||||||
\(847\) | −9.68585 | −0.332810 | ||||||||
\(848\) | 0.935731 | 0.0321331 | ||||||||
\(849\) | 30.9442 | 1.06200 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.0460 | −0.927124 | ||||||||
\(852\) | 6.15792 | 0.210967 | ||||||||
\(853\) | −19.6932 | −0.674282 | −0.337141 | − | 0.941454i | \(-0.609460\pi\) | ||||
−0.337141 | + | 0.941454i | \(0.609460\pi\) | |||||||
\(854\) | 4.68585 | 0.160346 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.3717 | 0.593752 | ||||||||
\(857\) | −1.66442 | −0.0568556 | −0.0284278 | − | 0.999596i | \(-0.509050\pi\) | ||||
−0.0284278 | + | 0.999596i | \(0.509050\pi\) | |||||||
\(858\) | 3.07896 | 0.105114 | ||||||||
\(859\) | −41.2944 | −1.40895 | −0.704474 | − | 0.709730i | \(-0.748817\pi\) | ||||
−0.704474 | + | 0.709730i | \(0.748817\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.335577 | −0.0114364 | ||||||||
\(862\) | −22.6086 | −0.770051 | ||||||||
\(863\) | 31.3288 | 1.06645 | 0.533223 | − | 0.845975i | \(-0.320981\pi\) | ||||
0.533223 | + | 0.845975i | \(0.320981\pi\) | |||||||
\(864\) | −22.4275 | −0.763000 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 61.6363 | 2.09449 | ||||||||
\(867\) | 19.5051 | 0.662426 | ||||||||
\(868\) | 5.70727 | 0.193717 | ||||||||
\(869\) | 1.01156 | 0.0343147 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.10038 | −0.206704 | ||||||||
\(872\) | 47.0937 | 1.59479 | ||||||||
\(873\) | −9.00735 | −0.304852 | ||||||||
\(874\) | 24.8683 | 0.841184 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 61.2003 | 2.06777 | ||||||||
\(877\) | 53.8041 | 1.81683 | 0.908417 | − | 0.418065i | \(-0.137292\pi\) | ||||
0.908417 | + | 0.418065i | \(0.137292\pi\) | |||||||
\(878\) | −79.2234 | −2.67366 | ||||||||
\(879\) | 17.0888 | 0.576392 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.09196 | 0.272625 | 0.136313 | − | 0.990666i | \(-0.456475\pi\) | ||||
0.136313 | + | 0.990666i | \(0.456475\pi\) | |||||||
\(882\) | 3.94981 | 0.132997 | ||||||||
\(883\) | 27.0705 | 0.910996 | 0.455498 | − | 0.890237i | \(-0.349461\pi\) | ||||
0.455498 | + | 0.890237i | \(0.349461\pi\) | |||||||
\(884\) | 20.3503 | 0.684454 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 61.9620 | 2.08165 | ||||||||
\(887\) | 38.4935 | 1.29249 | 0.646243 | − | 0.763132i | \(-0.276339\pi\) | ||||
0.646243 | + | 0.763132i | \(0.276339\pi\) | |||||||
\(888\) | 34.0722 | 1.14339 | ||||||||
\(889\) | −12.0575 | −0.404397 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.26144 | −0.0422599 | ||||||||
\(892\) | 68.3650 | 2.28903 | ||||||||
\(893\) | −35.4826 | −1.18738 | ||||||||
\(894\) | −5.82235 | −0.194728 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 20.1751 | 0.674004 | ||||||||
\(897\) | −3.63986 | −0.121532 | ||||||||
\(898\) | −6.19235 | −0.206641 | ||||||||
\(899\) | 17.1568 | 0.572213 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.56090 | −0.151946 | ||||||||
\(902\) | 0.786230 | 0.0261786 | ||||||||
\(903\) | 9.34713 | 0.311053 | ||||||||
\(904\) | 57.3864 | 1.90864 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −40.0491 | −1.33054 | ||||||||
\(907\) | −15.7031 | −0.521411 | −0.260706 | − | 0.965418i | \(-0.583955\pi\) | ||||
−0.260706 | + | 0.965418i | \(0.583955\pi\) | |||||||
\(908\) | 68.6148 | 2.27706 | ||||||||
\(909\) | −18.7911 | −0.623260 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.9399 | 1.48893 | 0.744463 | − | 0.667663i | \(-0.232705\pi\) | ||||
0.744463 | + | 0.667663i | \(0.232705\pi\) | |||||||
\(912\) | −4.58546 | −0.151840 | ||||||||
\(913\) | 13.9044 | 0.460170 | ||||||||
\(914\) | −78.9307 | −2.61080 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.0937 | 0.895200 | ||||||||
\(917\) | −3.66442 | −0.121010 | ||||||||
\(918\) | −73.4011 | −2.42260 | ||||||||
\(919\) | −27.2432 | −0.898669 | −0.449334 | − | 0.893364i | \(-0.648339\pi\) | ||||
−0.449334 | + | 0.893364i | \(0.648339\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.8385 | −0.983211 | ||||||||
\(922\) | −77.5015 | −2.55237 | ||||||||
\(923\) | −1.53948 | −0.0506726 | ||||||||
\(924\) | 4.58546 | 0.150851 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.89962 | −0.193873 | ||||||||
\(927\) | −5.75639 | −0.189065 | ||||||||
\(928\) | 43.7942 | 1.43761 | ||||||||
\(929\) | −17.1422 | −0.562416 | −0.281208 | − | 0.959647i | \(-0.590735\pi\) | ||||
−0.281208 | + | 0.959647i | \(0.590735\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.34292 | −0.109560 | ||||||||
\(932\) | −42.5573 | −1.39401 | ||||||||
\(933\) | 22.3503 | 0.731715 | ||||||||
\(934\) | 6.03442 | 0.197452 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.88240 | −0.192272 | ||||||||
\(937\) | 51.5197 | 1.68308 | 0.841538 | − | 0.540197i | \(-0.181650\pi\) | ||||
0.841538 | + | 0.540197i | \(0.181650\pi\) | |||||||
\(938\) | −14.2927 | −0.466674 | ||||||||
\(939\) | 3.99158 | 0.130260 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.7575 | 1.06786 | 0.533931 | − | 0.845528i | \(-0.320714\pi\) | ||||
0.533931 | + | 0.845528i | \(0.320714\pi\) | |||||||
\(942\) | 61.4208 | 2.00120 | ||||||||
\(943\) | −0.929460 | −0.0302674 | ||||||||
\(944\) | 15.1281 | 0.492377 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21.8996 | −0.712018 | ||||||||
\(947\) | −20.9295 | −0.680116 | −0.340058 | − | 0.940404i | \(-0.610447\pi\) | ||||
−0.340058 | + | 0.940404i | \(0.610447\pi\) | |||||||
\(948\) | 3.52962 | 0.114637 | ||||||||
\(949\) | −15.3001 | −0.496662 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.75639 | −0.186664 | ||||||||
\(952\) | 20.3503 | 0.659556 | ||||||||
\(953\) | −46.4120 | −1.50343 | −0.751716 | − | 0.659487i | \(-0.770774\pi\) | ||||
−0.751716 | + | 0.659487i | \(0.770774\pi\) | |||||||
\(954\) | 3.08883 | 0.100004 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −35.9143 | −1.16155 | ||||||||
\(957\) | 13.7845 | 0.445591 | ||||||||
\(958\) | −1.20390 | −0.0388964 | ||||||||
\(959\) | 13.1035 | 0.423135 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3246 | −0.913698 | ||||||||
\(962\) | −19.9572 | −0.643444 | ||||||||
\(963\) | 8.39312 | 0.270464 | ||||||||
\(964\) | −14.0575 | −0.452763 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.52792 | −0.274381 | ||||||||
\(967\) | 23.2186 | 0.746660 | 0.373330 | − | 0.927699i | \(-0.378216\pi\) | ||||
0.373330 | + | 0.927699i | \(0.378216\pi\) | |||||||
\(968\) | 33.7967 | 1.08627 | ||||||||
\(969\) | 22.3503 | 0.717994 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.1004 | −0.452503 | −0.226251 | − | 0.974069i | \(-0.572647\pi\) | ||||
−0.226251 | + | 0.974069i | \(0.572647\pi\) | |||||||
\(972\) | 51.8286 | 1.66240 | ||||||||
\(973\) | 7.49663 | 0.240331 | ||||||||
\(974\) | 84.4800 | 2.70692 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.39312 | −0.0766018 | ||||||||
\(977\) | 2.95402 | 0.0945074 | 0.0472537 | − | 0.998883i | \(-0.484953\pi\) | ||||
0.0472537 | + | 0.998883i | \(0.484953\pi\) | |||||||
\(978\) | 19.0130 | 0.607969 | ||||||||
\(979\) | 6.57560 | 0.210157 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.7533 | 0.726455 | ||||||||
\(982\) | 21.6216 | 0.689972 | ||||||||
\(983\) | 35.0367 | 1.11750 | 0.558749 | − | 0.829337i | \(-0.311281\pi\) | ||||
0.558749 | + | 0.829337i | \(0.311281\pi\) | |||||||
\(984\) | 1.17092 | 0.0373277 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 143.330 | 4.56456 | ||||||||
\(987\) | 12.1678 | 0.387305 | ||||||||
\(988\) | 11.6644 | 0.371095 | ||||||||
\(989\) | 25.8891 | 0.823227 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.9718 | 1.52388 | 0.761938 | − | 0.647650i | \(-0.224248\pi\) | ||||
0.761938 | + | 0.647650i | \(0.224248\pi\) | |||||||
\(992\) | 6.82908 | 0.216823 | ||||||||
\(993\) | −7.04958 | −0.223712 | ||||||||
\(994\) | −3.60688 | −0.114403 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 48.5166 | 1.53731 | ||||||||
\(997\) | 38.4422 | 1.21748 | 0.608739 | − | 0.793371i | \(-0.291676\pi\) | ||||
0.608739 | + | 0.793371i | \(0.291676\pi\) | |||||||
\(998\) | −2.35027 | −0.0743965 | ||||||||
\(999\) | 45.7564 | 1.44767 |
(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 | 2275.2.a.m.1.1 | 3 | ||
5.4 | even | 2 | 91.2.a.d.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 819.2.a.i.1.1 | 3 | |||
20.19 | odd | 2 | 1456.2.a.t.1.2 | 3 | |||
35.4 | even | 6 | 637.2.e.j.79.1 | 6 | |||
35.9 | even | 6 | 637.2.e.j.508.1 | 6 | |||
35.19 | odd | 6 | 637.2.e.i.508.1 | 6 | |||
35.24 | odd | 6 | 637.2.e.i.79.1 | 6 | |||
35.34 | odd | 2 | 637.2.a.j.1.3 | 3 | |||
40.19 | odd | 2 | 5824.2.a.bs.1.2 | 3 | |||
40.29 | even | 2 | 5824.2.a.by.1.2 | 3 | |||
65.34 | odd | 4 | 1183.2.c.f.337.6 | 6 | |||
65.44 | odd | 4 | 1183.2.c.f.337.1 | 6 | |||
65.64 | even | 2 | 1183.2.a.i.1.1 | 3 | |||
105.104 | even | 2 | 5733.2.a.x.1.1 | 3 | |||
455.454 | odd | 2 | 8281.2.a.bg.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.a.d.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
637.2.a.j.1.3 | 3 | 35.34 | odd | 2 | |||
637.2.e.i.79.1 | 6 | 35.24 | odd | 6 | |||
637.2.e.i.508.1 | 6 | 35.19 | odd | 6 | |||
637.2.e.j.79.1 | 6 | 35.4 | even | 6 | |||
637.2.e.j.508.1 | 6 | 35.9 | even | 6 | |||
819.2.a.i.1.1 | 3 | 15.14 | odd | 2 | |||
1183.2.a.i.1.1 | 3 | 65.64 | even | 2 | |||
1183.2.c.f.337.1 | 6 | 65.44 | odd | 4 | |||
1183.2.c.f.337.6 | 6 | 65.34 | odd | 4 | |||
1456.2.a.t.1.2 | 3 | 20.19 | odd | 2 | |||
2275.2.a.m.1.1 | 3 | 1.1 | even | 1 | trivial | ||
5733.2.a.x.1.1 | 3 | 105.104 | even | 2 | |||
5824.2.a.bs.1.2 | 3 | 40.19 | odd | 2 | |||
5824.2.a.by.1.2 | 3 | 40.29 | even | 2 | |||
8281.2.a.bg.1.1 | 3 | 455.454 | odd | 2 |