Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3969,2,Mod(1,3969)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3969, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3969.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3969 = 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3969.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: | \(31.6926245622\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 22 x^{10} + 92 x^{9} + 125 x^{8} - 620 x^{7} - 94 x^{6} + 1280 x^{5} - 234 x^{4} - 736 x^{3} + 96 x^{2} + 60 x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 441) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.48259\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3969.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0683740 | −0.0483477 | −0.0241739 | − | 0.999708i | \(-0.507696\pi\) | ||||
−0.0241739 | + | 0.999708i | \(0.507696\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99532 | −0.997662 | ||||||||
\(5\) | 2.66379 | 1.19128 | 0.595642 | − | 0.803250i | \(-0.296898\pi\) | ||||
0.595642 | + | 0.803250i | \(0.296898\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.273176 | 0.0965824 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.182134 | −0.0575958 | ||||||||
\(11\) | 1.59913 | 0.482155 | 0.241077 | − | 0.970506i | \(-0.422499\pi\) | ||||
0.241077 | + | 0.970506i | \(0.422499\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.25380 | 1.45714 | 0.728571 | − | 0.684970i | \(-0.240185\pi\) | ||||
0.728571 | + | 0.684970i | \(0.240185\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.97197 | 0.992993 | ||||||||
\(17\) | 6.54721 | 1.58793 | 0.793966 | − | 0.607963i | \(-0.208013\pi\) | ||||
0.793966 | + | 0.607963i | \(0.208013\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.90194 | 0.436334 | 0.218167 | − | 0.975911i | \(-0.429992\pi\) | ||||
0.218167 | + | 0.975911i | \(0.429992\pi\) | |||||||
\(20\) | −5.31513 | −1.18850 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.109339 | −0.0233111 | ||||||||
\(23\) | 3.06837 | 0.639800 | 0.319900 | − | 0.947451i | \(-0.396351\pi\) | ||||
0.319900 | + | 0.947451i | \(0.396351\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.09578 | 0.419157 | ||||||||
\(26\) | −0.359223 | −0.0704495 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.38903 | −1.18641 | −0.593207 | − | 0.805050i | \(-0.702138\pi\) | ||||
−0.593207 | + | 0.805050i | \(0.702138\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.71923 | 1.20681 | 0.603405 | − | 0.797435i | \(-0.293810\pi\) | ||||
0.603405 | + | 0.797435i | \(0.293810\pi\) | |||||||
\(32\) | −0.817932 | −0.144591 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.447659 | −0.0767728 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.22955 | 0.695333 | 0.347667 | − | 0.937618i | \(-0.386974\pi\) | ||||
0.347667 | + | 0.937618i | \(0.386974\pi\) | |||||||
\(38\) | −0.130043 | −0.0210958 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.727684 | 0.115057 | ||||||||
\(41\) | −7.39296 | −1.15459 | −0.577293 | − | 0.816537i | \(-0.695891\pi\) | ||||
−0.577293 | + | 0.816537i | \(0.695891\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.2635 | −1.71767 | −0.858836 | − | 0.512251i | \(-0.828812\pi\) | ||||
−0.858836 | + | 0.512251i | \(0.828812\pi\) | |||||||
\(44\) | −3.19078 | −0.481028 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.209797 | −0.0309329 | ||||||||
\(47\) | −3.79918 | −0.554167 | −0.277083 | − | 0.960846i | \(-0.589368\pi\) | ||||
−0.277083 | + | 0.960846i | \(0.589368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.143297 | −0.0202653 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.4830 | −1.45374 | ||||||||
\(53\) | −8.89862 | −1.22232 | −0.611160 | − | 0.791507i | \(-0.709297\pi\) | ||||
−0.611160 | + | 0.791507i | \(0.709297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.25974 | 0.574383 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.436843 | 0.0573604 | ||||||||
\(59\) | 10.8928 | 1.41812 | 0.709060 | − | 0.705148i | \(-0.249120\pi\) | ||||
0.709060 | + | 0.705148i | \(0.249120\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.71386 | 0.347475 | 0.173737 | − | 0.984792i | \(-0.444416\pi\) | ||||
0.173737 | + | 0.984792i | \(0.444416\pi\) | |||||||
\(62\) | −0.459420 | −0.0583465 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.88802 | −0.986002 | ||||||||
\(65\) | 13.9950 | 1.73587 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.32533 | −0.406254 | −0.203127 | − | 0.979152i | \(-0.565110\pi\) | ||||
−0.203127 | + | 0.979152i | \(0.565110\pi\) | |||||||
\(68\) | −13.0638 | −1.58422 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.3890 | 1.47031 | 0.735154 | − | 0.677900i | \(-0.237110\pi\) | ||||
0.735154 | + | 0.677900i | \(0.237110\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.19863 | 0.257331 | 0.128665 | − | 0.991688i | \(-0.458931\pi\) | ||||
0.128665 | + | 0.991688i | \(0.458931\pi\) | |||||||
\(74\) | −0.289191 | −0.0336178 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.79498 | −0.435314 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.813556 | 0.0915322 | 0.0457661 | − | 0.998952i | \(-0.485427\pi\) | ||||
0.0457661 | + | 0.998952i | \(0.485427\pi\) | |||||||
\(80\) | 10.5805 | 1.18294 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.505486 | 0.0558216 | ||||||||
\(83\) | −6.83684 | −0.750441 | −0.375220 | − | 0.926936i | \(-0.622433\pi\) | ||||
−0.375220 | + | 0.926936i | \(0.622433\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.4404 | 1.89168 | ||||||||
\(86\) | 0.770132 | 0.0830455 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.436843 | 0.0465677 | ||||||||
\(89\) | −0.470572 | −0.0498805 | −0.0249403 | − | 0.999689i | \(-0.507940\pi\) | ||||
−0.0249403 | + | 0.999689i | \(0.507940\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.12240 | −0.638305 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.259765 | 0.0267927 | ||||||||
\(95\) | 5.06636 | 0.519798 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.15246 | −0.523153 | −0.261576 | − | 0.965183i | \(-0.584242\pi\) | ||||
−0.261576 | + | 0.965183i | \(0.584242\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.18177 | −0.418177 | ||||||||
\(101\) | 1.84488 | 0.183572 | 0.0917862 | − | 0.995779i | \(-0.470742\pi\) | ||||
0.0917862 | + | 0.995779i | \(0.470742\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.17802 | 0.510206 | 0.255103 | − | 0.966914i | \(-0.417891\pi\) | ||||
0.255103 | + | 0.966914i | \(0.417891\pi\) | |||||||
\(104\) | 1.43521 | 0.140734 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.608434 | 0.0590964 | ||||||||
\(107\) | 16.9489 | 1.63851 | 0.819256 | − | 0.573428i | \(-0.194387\pi\) | ||||
0.819256 | + | 0.573428i | \(0.194387\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.49992 | −0.814145 | −0.407073 | − | 0.913396i | \(-0.633450\pi\) | ||||
−0.407073 | + | 0.913396i | \(0.633450\pi\) | |||||||
\(110\) | −0.291255 | −0.0277701 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.90392 | −0.367250 | −0.183625 | − | 0.982996i | \(-0.558783\pi\) | ||||
−0.183625 | + | 0.982996i | \(0.558783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.17351 | 0.762183 | ||||||||
\(116\) | 12.7482 | 1.18364 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.744783 | −0.0685628 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.44279 | −0.767527 | ||||||||
\(122\) | −0.185558 | −0.0167996 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.4070 | −1.20399 | ||||||||
\(125\) | −7.73623 | −0.691949 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9533 | 0.971946 | 0.485973 | − | 0.873974i | \(-0.338465\pi\) | ||||
0.485973 | + | 0.873974i | \(0.338465\pi\) | |||||||
\(128\) | 2.17520 | 0.192262 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.956896 | −0.0839253 | ||||||||
\(131\) | 4.45342 | 0.389097 | 0.194549 | − | 0.980893i | \(-0.437676\pi\) | ||||
0.194549 | + | 0.980893i | \(0.437676\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.227366 | 0.0196414 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.78854 | 0.153366 | ||||||||
\(137\) | 19.5360 | 1.66907 | 0.834537 | − | 0.550952i | \(-0.185735\pi\) | ||||
0.834537 | + | 0.550952i | \(0.185735\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.63079 | 0.223141 | 0.111570 | − | 0.993757i | \(-0.464412\pi\) | ||||
0.111570 | + | 0.993757i | \(0.464412\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.847087 | −0.0710860 | ||||||||
\(143\) | 8.40149 | 0.702568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.0190 | −1.41335 | ||||||||
\(146\) | −0.150329 | −0.0124413 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.43932 | −0.693708 | ||||||||
\(149\) | 8.81281 | 0.721973 | 0.360987 | − | 0.932571i | \(-0.382440\pi\) | ||||
0.360987 | + | 0.932571i | \(0.382440\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.66422 | 0.379569 | 0.189784 | − | 0.981826i | \(-0.439221\pi\) | ||||
0.189784 | + | 0.981826i | \(0.439221\pi\) | |||||||
\(152\) | 0.519564 | 0.0421422 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.8986 | 1.43765 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.07294 | −0.325056 | −0.162528 | − | 0.986704i | \(-0.551965\pi\) | ||||
−0.162528 | + | 0.986704i | \(0.551965\pi\) | |||||||
\(158\) | −0.0556261 | −0.00442537 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.17880 | −0.172249 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.1222 | −0.949487 | −0.474744 | − | 0.880124i | \(-0.657459\pi\) | ||||
−0.474744 | + | 0.880124i | \(0.657459\pi\) | |||||||
\(164\) | 14.7514 | 1.15189 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.467462 | 0.0362821 | ||||||||
\(167\) | 4.79902 | 0.371360 | 0.185680 | − | 0.982610i | \(-0.440551\pi\) | ||||
0.185680 | + | 0.982610i | \(0.440551\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.6024 | 1.12326 | ||||||||
\(170\) | −1.19247 | −0.0914582 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 22.4744 | 1.71366 | ||||||||
\(173\) | −5.03171 | −0.382554 | −0.191277 | − | 0.981536i | \(-0.561263\pi\) | ||||
−0.191277 | + | 0.981536i | \(0.561263\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.35169 | 0.478776 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.0321749 | 0.00241161 | ||||||||
\(179\) | 16.3979 | 1.22564 | 0.612819 | − | 0.790224i | \(-0.290036\pi\) | ||||
0.612819 | + | 0.790224i | \(0.290036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.4345 | −1.07291 | −0.536454 | − | 0.843930i | \(-0.680237\pi\) | ||||
−0.536454 | + | 0.843930i | \(0.680237\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.838207 | 0.0617934 | ||||||||
\(185\) | 11.2666 | 0.828339 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.4698 | 0.765629 | ||||||||
\(188\) | 7.58059 | 0.552871 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.346407 | −0.0251310 | ||||||||
\(191\) | −2.84131 | −0.205590 | −0.102795 | − | 0.994703i | \(-0.532779\pi\) | ||||
−0.102795 | + | 0.994703i | \(0.532779\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.82886 | 0.635515 | 0.317758 | − | 0.948172i | \(-0.397070\pi\) | ||||
0.317758 | + | 0.948172i | \(0.397070\pi\) | |||||||
\(194\) | 0.352294 | 0.0252932 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.72354 | −0.407785 | −0.203893 | − | 0.978993i | \(-0.565359\pi\) | ||||
−0.203893 | + | 0.978993i | \(0.565359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.4150 | −0.809191 | −0.404596 | − | 0.914496i | \(-0.632588\pi\) | ||||
−0.404596 | + | 0.914496i | \(0.632588\pi\) | |||||||
\(200\) | 0.572518 | 0.0404832 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.126142 | −0.00887530 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.6933 | −1.37544 | ||||||||
\(206\) | −0.354042 | −0.0246673 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.8679 | 1.44693 | ||||||||
\(209\) | 3.04144 | 0.210381 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.3837 | −1.47212 | −0.736059 | − | 0.676918i | \(-0.763315\pi\) | ||||
−0.736059 | + | 0.676918i | \(0.763315\pi\) | |||||||
\(212\) | 17.7556 | 1.21946 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.15886 | −0.0792183 | ||||||||
\(215\) | −30.0037 | −2.04623 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.581174 | 0.0393620 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.49956 | −0.573041 | ||||||||
\(221\) | 34.3977 | 2.31384 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.16774 | 0.479987 | 0.239994 | − | 0.970774i | \(-0.422855\pi\) | ||||
0.239994 | + | 0.970774i | \(0.422855\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.266926 | 0.0177557 | ||||||||
\(227\) | 13.7887 | 0.915187 | 0.457593 | − | 0.889162i | \(-0.348712\pi\) | ||||
0.457593 | + | 0.889162i | \(0.348712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.3943 | −1.74418 | −0.872092 | − | 0.489341i | \(-0.837237\pi\) | ||||
−0.872092 | + | 0.489341i | \(0.837237\pi\) | |||||||
\(230\) | −0.558855 | −0.0368498 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.74533 | −0.114587 | ||||||||
\(233\) | 12.6446 | 0.828375 | 0.414187 | − | 0.910192i | \(-0.364066\pi\) | ||||
0.414187 | + | 0.910192i | \(0.364066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.1202 | −0.660170 | ||||||||
\(236\) | −21.7346 | −1.41481 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.4328 | 0.998265 | 0.499133 | − | 0.866526i | \(-0.333652\pi\) | ||||
0.499133 | + | 0.866526i | \(0.333652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.17988 | 0.0760029 | 0.0380015 | − | 0.999278i | \(-0.487901\pi\) | ||||
0.0380015 | + | 0.999278i | \(0.487901\pi\) | |||||||
\(242\) | 0.577267 | 0.0371082 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.41504 | −0.346662 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.99240 | 0.635801 | ||||||||
\(248\) | 1.83553 | 0.116557 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.528957 | 0.0334542 | ||||||||
\(251\) | −5.54970 | −0.350294 | −0.175147 | − | 0.984542i | \(-0.556040\pi\) | ||||
−0.175147 | + | 0.984542i | \(0.556040\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.90672 | 0.308483 | ||||||||
\(254\) | −0.748919 | −0.0469913 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.6273 | 0.976707 | ||||||||
\(257\) | −9.83076 | −0.613226 | −0.306613 | − | 0.951834i | \(-0.599196\pi\) | ||||
−0.306613 | + | 0.951834i | \(0.599196\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −27.9246 | −1.73181 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.304498 | −0.0188120 | ||||||||
\(263\) | −11.9322 | −0.735774 | −0.367887 | − | 0.929870i | \(-0.619919\pi\) | ||||
−0.367887 | + | 0.929870i | \(0.619919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.7041 | −1.45613 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.63512 | 0.405304 | ||||||||
\(269\) | −29.9648 | −1.82699 | −0.913494 | − | 0.406853i | \(-0.866626\pi\) | ||||
−0.913494 | + | 0.406853i | \(0.866626\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.09650 | −0.431082 | −0.215541 | − | 0.976495i | \(-0.569151\pi\) | ||||
−0.215541 | + | 0.976495i | \(0.569151\pi\) | |||||||
\(272\) | 26.0053 | 1.57680 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.33575 | −0.0806959 | ||||||||
\(275\) | 3.35142 | 0.202098 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.82351 | −0.590237 | −0.295119 | − | 0.955461i | \(-0.595359\pi\) | ||||
−0.295119 | + | 0.955461i | \(0.595359\pi\) | |||||||
\(278\) | −0.179878 | −0.0107883 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.8777 | 1.42443 | 0.712213 | − | 0.701963i | \(-0.247693\pi\) | ||||
0.712213 | + | 0.701963i | \(0.247693\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.01595 | −0.179280 | −0.0896399 | − | 0.995974i | \(-0.528572\pi\) | ||||
−0.0896399 | + | 0.995974i | \(0.528572\pi\) | |||||||
\(284\) | −24.7201 | −1.46687 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.574443 | −0.0339675 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.8659 | 1.52153 | ||||||||
\(290\) | 1.16366 | 0.0683324 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.38699 | −0.256729 | ||||||||
\(293\) | −17.0583 | −0.996554 | −0.498277 | − | 0.867018i | \(-0.666034\pi\) | ||||
−0.498277 | + | 0.867018i | \(0.666034\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 29.0161 | 1.68938 | ||||||||
\(296\) | 1.15541 | 0.0671570 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.602567 | −0.0349058 | ||||||||
\(299\) | 16.1206 | 0.932280 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.318911 | −0.0183513 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.55444 | 0.433277 | ||||||||
\(305\) | 7.22917 | 0.413941 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.2178 | 1.32511 | 0.662554 | − | 0.749014i | \(-0.269473\pi\) | ||||
0.662554 | + | 0.749014i | \(0.269473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.22380 | −0.0695072 | ||||||||
\(311\) | −1.79093 | −0.101555 | −0.0507773 | − | 0.998710i | \(-0.516170\pi\) | ||||
−0.0507773 | + | 0.998710i | \(0.516170\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.60917 | 0.260526 | 0.130263 | − | 0.991480i | \(-0.458418\pi\) | ||||
0.130263 | + | 0.991480i | \(0.458418\pi\) | |||||||
\(314\) | 0.278483 | 0.0157157 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.62331 | −0.0913183 | ||||||||
\(317\) | 25.8841 | 1.45380 | 0.726898 | − | 0.686745i | \(-0.240961\pi\) | ||||
0.726898 | + | 0.686745i | \(0.240961\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.2169 | −0.572035 | ||||||||
\(320\) | −21.0120 | −1.17461 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.4524 | 0.692869 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.0108 | 0.610771 | ||||||||
\(326\) | 0.828846 | 0.0459055 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.01958 | −0.111513 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.161323 | 0.00886714 | 0.00443357 | − | 0.999990i | \(-0.498589\pi\) | ||||
0.00443357 | + | 0.999990i | \(0.498589\pi\) | |||||||
\(332\) | 13.6417 | 0.748687 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.328128 | −0.0179544 | ||||||||
\(335\) | −8.85799 | −0.483964 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.05351 | −0.493176 | −0.246588 | − | 0.969120i | \(-0.579309\pi\) | ||||
−0.246588 | + | 0.969120i | \(0.579309\pi\) | |||||||
\(338\) | −0.998425 | −0.0543072 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −34.7993 | −1.88725 | ||||||||
\(341\) | 10.7449 | 0.581869 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3.07693 | −0.165897 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.344038 | 0.0184956 | ||||||||
\(347\) | 5.81968 | 0.312417 | 0.156208 | − | 0.987724i | \(-0.450073\pi\) | ||||
0.156208 | + | 0.987724i | \(0.450073\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.2619 | 1.45930 | 0.729648 | − | 0.683823i | \(-0.239684\pi\) | ||||
0.729648 | + | 0.683823i | \(0.239684\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.30798 | −0.0697154 | ||||||||
\(353\) | 24.1896 | 1.28748 | 0.643741 | − | 0.765244i | \(-0.277382\pi\) | ||||
0.643741 | + | 0.765244i | \(0.277382\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.0018 | 1.75155 | ||||||||
\(356\) | 0.938944 | 0.0497639 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.12119 | −0.0592568 | ||||||||
\(359\) | 21.0376 | 1.11032 | 0.555161 | − | 0.831743i | \(-0.312657\pi\) | ||||
0.555161 | + | 0.831743i | \(0.312657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3826 | −0.809612 | ||||||||
\(362\) | 0.986944 | 0.0518726 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.85670 | 0.306554 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.0380 | 1.82897 | 0.914485 | − | 0.404620i | \(-0.132596\pi\) | ||||
0.914485 | + | 0.404620i | \(0.132596\pi\) | |||||||
\(368\) | 12.1875 | 0.635317 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.770345 | −0.0400483 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.12862 | 0.0584377 | 0.0292189 | − | 0.999573i | \(-0.490698\pi\) | ||||
0.0292189 | + | 0.999573i | \(0.490698\pi\) | |||||||
\(374\) | −0.715863 | −0.0370164 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.03784 | −0.0535227 | ||||||||
\(377\) | −33.5667 | −1.72877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.9619 | −1.12811 | −0.564054 | − | 0.825738i | \(-0.690759\pi\) | ||||
−0.564054 | + | 0.825738i | \(0.690759\pi\) | |||||||
\(380\) | −10.1090 | −0.518583 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.194272 | 0.00993981 | ||||||||
\(383\) | 23.0401 | 1.17729 | 0.588647 | − | 0.808390i | \(-0.299661\pi\) | ||||
0.588647 | + | 0.808390i | \(0.299661\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.603664 | −0.0307257 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.2808 | 0.521930 | ||||||||
\(389\) | −15.7751 | −0.799828 | −0.399914 | − | 0.916553i | \(-0.630960\pi\) | ||||
−0.399914 | + | 0.916553i | \(0.630960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0893 | 1.01596 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.391341 | 0.0197155 | ||||||||
\(395\) | 2.16714 | 0.109041 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.5055 | 0.828389 | 0.414195 | − | 0.910188i | \(-0.364063\pi\) | ||||
0.414195 | + | 0.910188i | \(0.364063\pi\) | |||||||
\(398\) | 0.780492 | 0.0391225 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.32439 | 0.416220 | ||||||||
\(401\) | −21.6600 | −1.08165 | −0.540823 | − | 0.841136i | \(-0.681887\pi\) | ||||
−0.540823 | + | 0.841136i | \(0.681887\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.3015 | 1.75849 | ||||||||
\(404\) | −3.68113 | −0.183143 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.76358 | 0.335258 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.5721 | −1.51169 | −0.755846 | − | 0.654750i | \(-0.772774\pi\) | ||||
−0.755846 | + | 0.654750i | \(0.772774\pi\) | |||||||
\(410\) | 1.34651 | 0.0664993 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.3318 | −0.509013 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.2119 | −0.893988 | ||||||||
\(416\) | −4.29725 | −0.210690 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.207955 | −0.0101714 | ||||||||
\(419\) | 21.6162 | 1.05602 | 0.528011 | − | 0.849237i | \(-0.322938\pi\) | ||||
0.528011 | + | 0.849237i | \(0.322938\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.2434 | −1.32776 | −0.663881 | − | 0.747838i | \(-0.731092\pi\) | ||||
−0.663881 | + | 0.747838i | \(0.731092\pi\) | |||||||
\(422\) | 1.46209 | 0.0711735 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.43089 | −0.118055 | ||||||||
\(425\) | 13.7215 | 0.665592 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −33.8186 | −1.63468 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.05147 | 0.0989307 | ||||||||
\(431\) | −8.19687 | −0.394829 | −0.197415 | − | 0.980320i | \(-0.563255\pi\) | ||||
−0.197415 | + | 0.980320i | \(0.563255\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.41468 | 0.164099 | 0.0820494 | − | 0.996628i | \(-0.473853\pi\) | ||||
0.0820494 | + | 0.996628i | \(0.473853\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.9601 | 0.812242 | ||||||||
\(437\) | 5.83585 | 0.279167 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.58831 | 0.314443 | 0.157221 | − | 0.987563i | \(-0.449746\pi\) | ||||
0.157221 | + | 0.987563i | \(0.449746\pi\) | |||||||
\(440\) | 1.16366 | 0.0554753 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.35191 | −0.111869 | ||||||||
\(443\) | −28.6912 | −1.36316 | −0.681581 | − | 0.731743i | \(-0.738707\pi\) | ||||
−0.681581 | + | 0.731743i | \(0.738707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.25350 | −0.0594218 | ||||||||
\(446\) | −0.490087 | −0.0232063 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.457724 | −0.0216013 | −0.0108007 | − | 0.999942i | \(-0.503438\pi\) | ||||
−0.0108007 | + | 0.999942i | \(0.503438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.8223 | −0.556689 | ||||||||
\(452\) | 7.78958 | 0.366391 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.942787 | −0.0442472 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.2210 | 0.945900 | 0.472950 | − | 0.881089i | \(-0.343189\pi\) | ||||
0.472950 | + | 0.881089i | \(0.343189\pi\) | |||||||
\(458\) | 1.80468 | 0.0843273 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.3088 | −0.760402 | ||||||||
\(461\) | −24.2071 | −1.12744 | −0.563719 | − | 0.825967i | \(-0.690630\pi\) | ||||
−0.563719 | + | 0.825967i | \(0.690630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.80483 | −0.223299 | −0.111650 | − | 0.993748i | \(-0.535613\pi\) | ||||
−0.111650 | + | 0.993748i | \(0.535613\pi\) | |||||||
\(464\) | −25.3770 | −1.17810 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.864561 | −0.0400500 | ||||||||
\(467\) | 27.2456 | 1.26078 | 0.630389 | − | 0.776279i | \(-0.282895\pi\) | ||||
0.630389 | + | 0.776279i | \(0.282895\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.691959 | 0.0319177 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.97565 | 0.136965 | ||||||||
\(473\) | −18.0118 | −0.828184 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.98605 | 0.182892 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.05520 | −0.0482638 | ||||||||
\(479\) | −20.5255 | −0.937834 | −0.468917 | − | 0.883242i | \(-0.655356\pi\) | ||||
−0.468917 | + | 0.883242i | \(0.655356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.2212 | 1.01320 | ||||||||
\(482\) | −0.0806733 | −0.00367457 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.8461 | 0.765733 | ||||||||
\(485\) | −13.7251 | −0.623224 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.8449 | 1.17114 | 0.585571 | − | 0.810621i | \(-0.300870\pi\) | ||||
0.585571 | + | 0.810621i | \(0.300870\pi\) | |||||||
\(488\) | 0.741363 | 0.0335599 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6155 | −0.704718 | −0.352359 | − | 0.935865i | \(-0.614620\pi\) | ||||
−0.352359 | + | 0.935865i | \(0.614620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.8303 | −1.88394 | ||||||||
\(494\) | −0.683220 | −0.0307395 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.6886 | 1.19835 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.2690 | 0.952133 | 0.476066 | − | 0.879409i | \(-0.342062\pi\) | ||||
0.476066 | + | 0.879409i | \(0.342062\pi\) | |||||||
\(500\) | 15.4363 | 0.690332 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.379455 | 0.0169359 | ||||||||
\(503\) | 16.3298 | 0.728110 | 0.364055 | − | 0.931377i | \(-0.381392\pi\) | ||||
0.364055 | + | 0.931377i | \(0.381392\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.91437 | 0.218687 | ||||||||
\(506\) | −0.335492 | −0.0149144 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.8553 | −0.969674 | ||||||||
\(509\) | 13.4618 | 0.596683 | 0.298342 | − | 0.954459i | \(-0.403567\pi\) | ||||
0.298342 | + | 0.954459i | \(0.403567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.41890 | −0.239484 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.672168 | 0.0296481 | ||||||||
\(515\) | 13.7932 | 0.607800 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.07536 | −0.267194 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.82311 | 0.167654 | ||||||||
\(521\) | 1.42619 | 0.0624826 | 0.0312413 | − | 0.999512i | \(-0.490054\pi\) | ||||
0.0312413 | + | 0.999512i | \(0.490054\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.71060 | −0.337161 | −0.168581 | − | 0.985688i | \(-0.553918\pi\) | ||||
−0.168581 | + | 0.985688i | \(0.553918\pi\) | |||||||
\(524\) | −8.88603 | −0.388188 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.815855 | 0.0355730 | ||||||||
\(527\) | 43.9922 | 1.91633 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.5851 | −0.590656 | ||||||||
\(530\) | 1.62074 | 0.0704005 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.8411 | −1.68240 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 45.1483 | 1.95193 | ||||||||
\(536\) | −0.908402 | −0.0392370 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.04881 | 0.0883306 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.0456 | 1.20577 | 0.602886 | − | 0.797827i | \(-0.294017\pi\) | ||||
0.602886 | + | 0.797827i | \(0.294017\pi\) | |||||||
\(542\) | 0.485216 | 0.0208418 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.35517 | −0.229601 | ||||||||
\(545\) | −22.6420 | −0.969878 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.4610 | −1.51620 | −0.758101 | − | 0.652137i | \(-0.773873\pi\) | ||||
−0.758101 | + | 0.652137i | \(0.773873\pi\) | |||||||
\(548\) | −38.9807 | −1.66517 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.229150 | −0.00977099 | ||||||||
\(551\) | −12.1515 | −0.517673 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.671672 | 0.0285366 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.24928 | −0.222619 | ||||||||
\(557\) | −35.0419 | −1.48477 | −0.742386 | − | 0.669972i | \(-0.766306\pi\) | ||||
−0.742386 | + | 0.669972i | \(0.766306\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −59.1763 | −2.50289 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.63262 | −0.0688677 | ||||||||
\(563\) | −16.0262 | −0.675425 | −0.337712 | − | 0.941249i | \(-0.609653\pi\) | ||||
−0.337712 | + | 0.941249i | \(0.609653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.3992 | −0.437499 | ||||||||
\(566\) | 0.206213 | 0.00866776 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.38439 | 0.142006 | ||||||||
\(569\) | −0.371302 | −0.0155658 | −0.00778290 | − | 0.999970i | \(-0.502477\pi\) | ||||
−0.00778290 | + | 0.999970i | \(0.502477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.2304 | 1.22325 | 0.611626 | − | 0.791147i | \(-0.290516\pi\) | ||||
0.611626 | + | 0.791147i | \(0.290516\pi\) | |||||||
\(572\) | −16.7637 | −0.700926 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.43065 | 0.268177 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.0570 | −0.626833 | −0.313417 | − | 0.949616i | \(-0.601474\pi\) | ||||
−0.313417 | + | 0.949616i | \(0.601474\pi\) | |||||||
\(578\) | −1.76856 | −0.0735623 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 33.9585 | 1.41005 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.2300 | −0.589347 | ||||||||
\(584\) | 0.600615 | 0.0248536 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.16634 | 0.0481811 | ||||||||
\(587\) | −1.67180 | −0.0690026 | −0.0345013 | − | 0.999405i | \(-0.510984\pi\) | ||||
−0.0345013 | + | 0.999405i | \(0.510984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.7795 | 0.526572 | ||||||||
\(590\) | −1.98395 | −0.0816778 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.7996 | 0.690461 | ||||||||
\(593\) | 10.8174 | 0.444218 | 0.222109 | − | 0.975022i | \(-0.428706\pi\) | ||||
0.222109 | + | 0.975022i | \(0.428706\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.5844 | −0.720286 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.10223 | −0.0450736 | ||||||||
\(599\) | −16.6401 | −0.679898 | −0.339949 | − | 0.940444i | \(-0.610410\pi\) | ||||
−0.339949 | + | 0.940444i | \(0.610410\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.8022 | −1.05249 | −0.526246 | − | 0.850332i | \(-0.676401\pi\) | ||||
−0.526246 | + | 0.850332i | \(0.676401\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.30663 | −0.378681 | ||||||||
\(605\) | −22.4898 | −0.914342 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.8049 | −1.53445 | −0.767227 | − | 0.641376i | \(-0.778364\pi\) | ||||
−0.767227 | + | 0.641376i | \(0.778364\pi\) | |||||||
\(608\) | −1.55566 | −0.0630901 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.494287 | −0.0200131 | ||||||||
\(611\) | −19.9601 | −0.807499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.9544 | −0.523222 | −0.261611 | − | 0.965173i | \(-0.584254\pi\) | ||||
−0.261611 | + | 0.965173i | \(0.584254\pi\) | |||||||
\(614\) | −1.58749 | −0.0640659 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.4403 | 1.30600 | 0.652999 | − | 0.757359i | \(-0.273511\pi\) | ||||
0.652999 | + | 0.757359i | \(0.273511\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.1974 | −1.33431 | −0.667157 | − | 0.744917i | \(-0.732489\pi\) | ||||
−0.667157 | + | 0.744917i | \(0.732489\pi\) | |||||||
\(620\) | −35.7136 | −1.43429 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.122453 | 0.00490993 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0866 | −1.24346 | ||||||||
\(626\) | −0.315147 | −0.0125958 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.12683 | 0.324296 | ||||||||
\(629\) | 27.6917 | 1.10414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.2773 | 1.28494 | 0.642470 | − | 0.766311i | \(-0.277910\pi\) | ||||
0.642470 | + | 0.766311i | \(0.277910\pi\) | |||||||
\(632\) | 0.222244 | 0.00884040 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.76980 | −0.0702877 | ||||||||
\(635\) | 29.1772 | 1.15786 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.698568 | 0.0276566 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.79428 | 0.229039 | ||||||||
\(641\) | −43.0814 | −1.70161 | −0.850806 | − | 0.525480i | \(-0.823886\pi\) | ||||
−0.850806 | + | 0.525480i | \(0.823886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.40176 | −0.252461 | −0.126230 | − | 0.992001i | \(-0.540288\pi\) | ||||
−0.126230 | + | 0.992001i | \(0.540288\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.851419 | −0.0334986 | ||||||||
\(647\) | 3.88807 | 0.152856 | 0.0764278 | − | 0.997075i | \(-0.475649\pi\) | ||||
0.0764278 | + | 0.997075i | \(0.475649\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.4189 | 0.683753 | ||||||||
\(650\) | −0.752854 | −0.0295294 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.1878 | 0.947268 | ||||||||
\(653\) | −15.1035 | −0.591044 | −0.295522 | − | 0.955336i | \(-0.595494\pi\) | ||||
−0.295522 | + | 0.955336i | \(0.595494\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.8630 | 0.463525 | ||||||||
\(656\) | −29.3646 | −1.14650 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.2600 | −0.555492 | −0.277746 | − | 0.960655i | \(-0.589587\pi\) | ||||
−0.277746 | + | 0.960655i | \(0.589587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.4193 | 0.755323 | 0.377662 | − | 0.925944i | \(-0.376728\pi\) | ||||
0.377662 | + | 0.925944i | \(0.376728\pi\) | |||||||
\(662\) | −0.0110303 | −0.000428706 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.86766 | −0.0724794 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.6039 | −0.759067 | ||||||||
\(668\) | −9.57561 | −0.370492 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.605656 | 0.0233985 | ||||||||
\(671\) | 4.33981 | 0.167537 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.93126 | 0.228633 | 0.114317 | − | 0.993444i | \(-0.463532\pi\) | ||||
0.114317 | + | 0.993444i | \(0.463532\pi\) | |||||||
\(674\) | 0.619024 | 0.0238439 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.1366 | −1.12064 | ||||||||
\(677\) | 36.9826 | 1.42136 | 0.710678 | − | 0.703518i | \(-0.248388\pi\) | ||||
0.710678 | + | 0.703518i | \(0.248388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.76430 | 0.182703 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.734671 | −0.0281320 | ||||||||
\(683\) | −13.1360 | −0.502635 | −0.251317 | − | 0.967905i | \(-0.580864\pi\) | ||||
−0.251317 | + | 0.967905i | \(0.580864\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 52.0398 | 1.98834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −44.7384 | −1.70564 | ||||||||
\(689\) | −46.7516 | −1.78109 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.7658 | −0.561719 | −0.280860 | − | 0.959749i | \(-0.590620\pi\) | ||||
−0.280860 | + | 0.959749i | \(0.590620\pi\) | |||||||
\(692\) | 10.0399 | 0.381659 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.397915 | −0.0151046 | ||||||||
\(695\) | 7.00788 | 0.265824 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −48.4032 | −1.83340 | ||||||||
\(698\) | −1.86401 | −0.0705536 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.4627 | 1.15056 | 0.575281 | − | 0.817956i | \(-0.304893\pi\) | ||||
0.575281 | + | 0.817956i | \(0.304893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.04433 | 0.303398 | ||||||||
\(704\) | −12.6139 | −0.475406 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.65394 | −0.0622468 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.1030 | 0.529650 | 0.264825 | − | 0.964296i | \(-0.414686\pi\) | ||||
0.264825 | + | 0.964296i | \(0.414686\pi\) | |||||||
\(710\) | −2.25646 | −0.0846836 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.128549 | −0.00481758 | ||||||||
\(713\) | 20.6171 | 0.772117 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.3798 | 0.836958 | ||||||||
\(716\) | −32.7192 | −1.22277 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.43842 | −0.0536815 | ||||||||
\(719\) | 14.9958 | 0.559249 | 0.279624 | − | 0.960109i | \(-0.409790\pi\) | ||||
0.279624 | + | 0.960109i | \(0.409790\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.05177 | 0.0391429 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 28.8015 | 1.07040 | ||||||||
\(725\) | −13.3900 | −0.497293 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.1055 | −0.968199 | −0.484099 | − | 0.875013i | \(-0.660853\pi\) | ||||
−0.484099 | + | 0.875013i | \(0.660853\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.400446 | −0.0148212 | ||||||||
\(731\) | −73.7447 | −2.72754 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.3821 | −1.04832 | −0.524159 | − | 0.851621i | \(-0.675620\pi\) | ||||
−0.524159 | + | 0.851621i | \(0.675620\pi\) | |||||||
\(734\) | −2.39569 | −0.0884265 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.50972 | −0.0925096 | ||||||||
\(737\) | −5.31763 | −0.195877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.5865 | 1.71371 | 0.856857 | − | 0.515555i | \(-0.172414\pi\) | ||||
0.856857 | + | 0.515555i | \(0.172414\pi\) | |||||||
\(740\) | −22.4806 | −0.826403 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.339027 | −0.0124377 | −0.00621884 | − | 0.999981i | \(-0.501980\pi\) | ||||
−0.00621884 | + | 0.999981i | \(0.501980\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.4755 | 0.860075 | ||||||||
\(746\) | −0.0771683 | −0.00282533 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.8907 | −0.763839 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.3662 | −1.32702 | −0.663510 | − | 0.748168i | \(-0.730934\pi\) | ||||
−0.663510 | + | 0.748168i | \(0.730934\pi\) | |||||||
\(752\) | −15.0902 | −0.550284 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.29509 | 0.0835822 | ||||||||
\(755\) | 12.4245 | 0.452174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4703 | −0.998424 | −0.499212 | − | 0.866480i | \(-0.666377\pi\) | ||||
−0.499212 | + | 0.866480i | \(0.666377\pi\) | |||||||
\(758\) | 1.50162 | 0.0545415 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.38401 | 0.0502033 | ||||||||
\(761\) | 33.0357 | 1.19754 | 0.598771 | − | 0.800920i | \(-0.295656\pi\) | ||||
0.598771 | + | 0.800920i | \(0.295656\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.66934 | 0.205110 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.57534 | −0.0569194 | ||||||||
\(767\) | 57.2285 | 2.06640 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.57751 | −0.0929475 | −0.0464738 | − | 0.998920i | \(-0.514798\pi\) | ||||
−0.0464738 | + | 0.998920i | \(0.514798\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.6164 | −0.634030 | ||||||||
\(773\) | 6.72973 | 0.242051 | 0.121026 | − | 0.992649i | \(-0.461382\pi\) | ||||
0.121026 | + | 0.992649i | \(0.461382\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.0820 | 0.505842 | ||||||||
\(776\) | −1.40753 | −0.0505274 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.07860 | 0.0386698 | ||||||||
\(779\) | −14.0609 | −0.503785 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.8116 | 0.708916 | ||||||||
\(782\) | −1.37358 | −0.0491193 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.8495 | −0.387234 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.6683 | −1.02191 | −0.510956 | − | 0.859607i | \(-0.670709\pi\) | ||||
−0.510956 | + | 0.859607i | \(0.670709\pi\) | |||||||
\(788\) | 11.4203 | 0.406832 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.148176 | −0.00527187 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.2581 | 0.506320 | ||||||||
\(794\) | −1.12855 | −0.0400507 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.7767 | 0.807300 | ||||||||
\(797\) | −22.9825 | −0.814084 | −0.407042 | − | 0.913410i | \(-0.633440\pi\) | ||||
−0.407042 | + | 0.913410i | \(0.633440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.8740 | −0.879979 | ||||||||
\(800\) | −1.71421 | −0.0606064 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.48098 | 0.0522951 | ||||||||
\(803\) | 3.51589 | 0.124073 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.41370 | −0.0850191 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.503977 | 0.0177299 | ||||||||
\(809\) | 16.4779 | 0.579332 | 0.289666 | − | 0.957128i | \(-0.406456\pi\) | ||||
0.289666 | + | 0.957128i | \(0.406456\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.4318 | −1.41975 | −0.709876 | − | 0.704326i | \(-0.751249\pi\) | ||||
−0.709876 | + | 0.704326i | \(0.751249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.462453 | −0.0162090 | ||||||||
\(815\) | −32.2911 | −1.13111 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.4225 | −0.749479 | ||||||||
\(818\) | 2.09033 | 0.0730868 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 39.2945 | 1.37222 | ||||||||
\(821\) | 28.1086 | 0.980998 | 0.490499 | − | 0.871442i | \(-0.336814\pi\) | ||||
0.490499 | + | 0.871442i | \(0.336814\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.9058 | 0.903019 | 0.451510 | − | 0.892266i | \(-0.350886\pi\) | ||||
0.451510 | + | 0.892266i | \(0.350886\pi\) | |||||||
\(824\) | 1.41451 | 0.0492769 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.7998 | 0.618961 | 0.309480 | − | 0.950906i | \(-0.399845\pi\) | ||||
0.309480 | + | 0.950906i | \(0.399845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.7069 | 0.545523 | 0.272761 | − | 0.962082i | \(-0.412063\pi\) | ||||
0.272761 | + | 0.962082i | \(0.412063\pi\) | |||||||
\(830\) | 1.24522 | 0.0432223 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −41.4421 | −1.43675 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.7836 | 0.442395 | ||||||||
\(836\) | −6.06866 | −0.209889 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.47799 | −0.0510563 | ||||||||
\(839\) | 7.39643 | 0.255353 | 0.127677 | − | 0.991816i | \(-0.459248\pi\) | ||||
0.127677 | + | 0.991816i | \(0.459248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.8197 | 0.407576 | ||||||||
\(842\) | 1.86274 | 0.0641942 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 42.6675 | 1.46868 | ||||||||
\(845\) | 38.8978 | 1.33812 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −35.3451 | −1.21376 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.938196 | −0.0321798 | ||||||||
\(851\) | 12.9778 | 0.444874 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.1262 | −1.81901 | −0.909503 | − | 0.415698i | \(-0.863537\pi\) | ||||
−0.909503 | + | 0.415698i | \(0.863537\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.63004 | 0.158251 | ||||||||
\(857\) | 3.81530 | 0.130328 | 0.0651640 | − | 0.997875i | \(-0.479243\pi\) | ||||
0.0651640 | + | 0.997875i | \(0.479243\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.9768 | 1.32987 | 0.664936 | − | 0.746901i | \(-0.268459\pi\) | ||||
0.664936 | + | 0.746901i | \(0.268459\pi\) | |||||||
\(860\) | 59.8671 | 2.04145 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.560452 | 0.0190891 | ||||||||
\(863\) | −26.6736 | −0.907978 | −0.453989 | − | 0.891007i | \(-0.650000\pi\) | ||||
−0.453989 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.4034 | −0.455730 | ||||||||
\(866\) | −0.233475 | −0.00793380 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.30098 | 0.0441327 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.4706 | −0.591970 | ||||||||
\(872\) | −2.32198 | −0.0786321 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.399020 | −0.0134971 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.0135 | 0.810879 | 0.405440 | − | 0.914122i | \(-0.367118\pi\) | ||||
0.405440 | + | 0.914122i | \(0.367118\pi\) | |||||||
\(878\) | −0.450469 | −0.0152026 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 16.9196 | 0.570358 | ||||||||
\(881\) | 4.67326 | 0.157446 | 0.0787231 | − | 0.996897i | \(-0.474916\pi\) | ||||
0.0787231 | + | 0.996897i | \(0.474916\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6948 | −1.20122 | −0.600612 | − | 0.799541i | \(-0.705076\pi\) | ||||
−0.600612 | + | 0.799541i | \(0.705076\pi\) | |||||||
\(884\) | −68.6346 | −2.30843 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.96173 | 0.0659058 | ||||||||
\(887\) | −29.1032 | −0.977191 | −0.488596 | − | 0.872510i | \(-0.662491\pi\) | ||||
−0.488596 | + | 0.872510i | \(0.662491\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.0857071 | 0.00287291 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −14.3020 | −0.478865 | ||||||||
\(893\) | −7.22579 | −0.241802 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43.6806 | 1.46008 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.0312964 | 0.00104437 | ||||||||
\(899\) | −42.9294 | −1.43177 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.2611 | −1.94096 | ||||||||
\(902\) | 0.808336 | 0.0269146 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.06646 | −0.0354699 | ||||||||
\(905\) | −38.4505 | −1.27814 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.2142 | −1.36849 | −0.684247 | − | 0.729250i | \(-0.739869\pi\) | ||||
−0.684247 | + | 0.729250i | \(0.739869\pi\) | |||||||
\(908\) | −27.5129 | −0.913047 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.7239 | 1.91248 | 0.956239 | − | 0.292588i | \(-0.0945163\pi\) | ||||
0.956239 | + | 0.292588i | \(0.0945163\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.9330 | −0.361829 | ||||||||
\(914\) | −1.38259 | −0.0457321 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 52.6652 | 1.74011 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.5598 | −1.70080 | −0.850400 | − | 0.526137i | \(-0.823640\pi\) | ||||
−0.850400 | + | 0.526137i | \(0.823640\pi\) | |||||||
\(920\) | 2.23281 | 0.0736135 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.65514 | 0.0545090 | ||||||||
\(923\) | 65.0895 | 2.14245 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.86422 | 0.291454 | ||||||||
\(926\) | 0.328525 | 0.0107960 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.22579 | 0.171545 | ||||||||
\(929\) | 50.2824 | 1.64971 | 0.824856 | − | 0.565343i | \(-0.191256\pi\) | ||||
0.824856 | + | 0.565343i | \(0.191256\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −25.2301 | −0.826439 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.86289 | −0.0609557 | ||||||||
\(935\) | 27.8894 | 0.912081 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.1400 | 0.592607 | 0.296303 | − | 0.955094i | \(-0.404246\pi\) | ||||
0.296303 | + | 0.955094i | \(0.404246\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 20.1931 | 0.658627 | ||||||||
\(941\) | 17.0332 | 0.555267 | 0.277633 | − | 0.960687i | \(-0.410450\pi\) | ||||
0.277633 | + | 0.960687i | \(0.410450\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.6844 | −0.738704 | ||||||||
\(944\) | 43.2658 | 1.40818 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.23154 | 0.0400408 | ||||||||
\(947\) | −31.5059 | −1.02381 | −0.511903 | − | 0.859044i | \(-0.671059\pi\) | ||||
−0.511903 | + | 0.859044i | \(0.671059\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.5512 | 0.374967 | ||||||||
\(950\) | −0.272542 | −0.00884243 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.0677 | −0.520485 | −0.260242 | − | 0.965543i | \(-0.583803\pi\) | ||||
−0.260242 | + | 0.965543i | \(0.583803\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.56866 | −0.244916 | ||||||||
\(956\) | −30.7935 | −0.995932 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.40341 | 0.0453421 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1480 | 0.456388 | ||||||||
\(962\) | −1.51935 | −0.0489859 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.35425 | −0.0758253 | ||||||||
\(965\) | 23.5182 | 0.757079 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.6098 | −0.855713 | −0.427857 | − | 0.903847i | \(-0.640731\pi\) | ||||
−0.427857 | + | 0.903847i | \(0.640731\pi\) | |||||||
\(968\) | −2.30637 | −0.0741296 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.938438 | 0.0301314 | ||||||||
\(971\) | 56.5678 | 1.81535 | 0.907674 | − | 0.419676i | \(-0.137856\pi\) | ||||
0.907674 | + | 0.419676i | \(0.137856\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.76712 | −0.0566221 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.7794 | 0.345040 | ||||||||
\(977\) | −53.7560 | −1.71981 | −0.859904 | − | 0.510456i | \(-0.829477\pi\) | ||||
−0.859904 | + | 0.510456i | \(0.829477\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.752504 | −0.0240501 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.06769 | 0.0340715 | ||||||||
\(983\) | −27.4102 | −0.874249 | −0.437125 | − | 0.899401i | \(-0.644003\pi\) | ||||
−0.437125 | + | 0.899401i | \(0.644003\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.2463 | −0.485788 | ||||||||
\(986\) | 2.86011 | 0.0910843 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.9381 | −0.634315 | ||||||||
\(989\) | −34.5607 | −1.09897 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.3374 | −0.550740 | −0.275370 | − | 0.961338i | \(-0.588800\pi\) | ||||
−0.275370 | + | 0.961338i | \(0.588800\pi\) | |||||||
\(992\) | −5.49587 | −0.174494 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.4073 | −0.963976 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.6638 | −1.12948 | −0.564742 | − | 0.825268i | \(-0.691024\pi\) | ||||
−0.564742 | + | 0.825268i | \(0.691024\pi\) | |||||||
\(998\) | −1.45425 | −0.0460334 | ||||||||
\(999\) | 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 | 3969.2.a.bi.1.6 | 12 | ||
3.2 | odd | 2 | 3969.2.a.bh.1.7 | 12 | |||
7.6 | odd | 2 | inner | 3969.2.a.bi.1.5 | 12 | ||
9.2 | odd | 6 | 441.2.f.h.148.6 | yes | 24 | ||
9.4 | even | 3 | 1323.2.f.h.883.7 | 24 | |||
9.5 | odd | 6 | 441.2.f.h.295.6 | yes | 24 | ||
9.7 | even | 3 | 1323.2.f.h.442.7 | 24 | |||
21.20 | even | 2 | 3969.2.a.bh.1.8 | 12 | |||
63.2 | odd | 6 | 441.2.g.h.67.5 | 24 | |||
63.4 | even | 3 | 1323.2.g.h.667.8 | 24 | |||
63.5 | even | 6 | 441.2.h.h.214.8 | 24 | |||
63.11 | odd | 6 | 441.2.h.h.373.7 | 24 | |||
63.13 | odd | 6 | 1323.2.f.h.883.8 | 24 | |||
63.16 | even | 3 | 1323.2.g.h.361.8 | 24 | |||
63.20 | even | 6 | 441.2.f.h.148.5 | ✓ | 24 | ||
63.23 | odd | 6 | 441.2.h.h.214.7 | 24 | |||
63.25 | even | 3 | 1323.2.h.h.226.6 | 24 | |||
63.31 | odd | 6 | 1323.2.g.h.667.7 | 24 | |||
63.32 | odd | 6 | 441.2.g.h.79.5 | 24 | |||
63.34 | odd | 6 | 1323.2.f.h.442.8 | 24 | |||
63.38 | even | 6 | 441.2.h.h.373.8 | 24 | |||
63.40 | odd | 6 | 1323.2.h.h.802.5 | 24 | |||
63.41 | even | 6 | 441.2.f.h.295.5 | yes | 24 | ||
63.47 | even | 6 | 441.2.g.h.67.6 | 24 | |||
63.52 | odd | 6 | 1323.2.h.h.226.5 | 24 | |||
63.58 | even | 3 | 1323.2.h.h.802.6 | 24 | |||
63.59 | even | 6 | 441.2.g.h.79.6 | 24 | |||
63.61 | odd | 6 | 1323.2.g.h.361.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.5 | ✓ | 24 | 63.20 | even | 6 | ||
441.2.f.h.148.6 | yes | 24 | 9.2 | odd | 6 | ||
441.2.f.h.295.5 | yes | 24 | 63.41 | even | 6 | ||
441.2.f.h.295.6 | yes | 24 | 9.5 | odd | 6 | ||
441.2.g.h.67.5 | 24 | 63.2 | odd | 6 | |||
441.2.g.h.67.6 | 24 | 63.47 | even | 6 | |||
441.2.g.h.79.5 | 24 | 63.32 | odd | 6 | |||
441.2.g.h.79.6 | 24 | 63.59 | even | 6 | |||
441.2.h.h.214.7 | 24 | 63.23 | odd | 6 | |||
441.2.h.h.214.8 | 24 | 63.5 | even | 6 | |||
441.2.h.h.373.7 | 24 | 63.11 | odd | 6 | |||
441.2.h.h.373.8 | 24 | 63.38 | even | 6 | |||
1323.2.f.h.442.7 | 24 | 9.7 | even | 3 | |||
1323.2.f.h.442.8 | 24 | 63.34 | odd | 6 | |||
1323.2.f.h.883.7 | 24 | 9.4 | even | 3 | |||
1323.2.f.h.883.8 | 24 | 63.13 | odd | 6 | |||
1323.2.g.h.361.7 | 24 | 63.61 | odd | 6 | |||
1323.2.g.h.361.8 | 24 | 63.16 | even | 3 | |||
1323.2.g.h.667.7 | 24 | 63.31 | odd | 6 | |||
1323.2.g.h.667.8 | 24 | 63.4 | even | 3 | |||
1323.2.h.h.226.5 | 24 | 63.52 | odd | 6 | |||
1323.2.h.h.226.6 | 24 | 63.25 | even | 3 | |||
1323.2.h.h.802.5 | 24 | 63.40 | odd | 6 | |||
1323.2.h.h.802.6 | 24 | 63.58 | even | 3 | |||
3969.2.a.bh.1.7 | 12 | 3.2 | odd | 2 | |||
3969.2.a.bh.1.8 | 12 | 21.20 | even | 2 | |||
3969.2.a.bi.1.5 | 12 | 7.6 | odd | 2 | inner | ||
3969.2.a.bi.1.6 | 12 | 1.1 | even | 1 | trivial |