Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.488861\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.158731 | 0.0916432 | 0.0458216 | − | 0.998950i | \(-0.485409\pi\) | ||||
0.0458216 | + | 0.998950i | \(0.485409\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.07692 | 1.37604 | 0.688019 | − | 0.725692i | \(-0.258480\pi\) | ||||
0.688019 | + | 0.725692i | \(0.258480\pi\) | |||||||
\(6\) | −0.158731 | −0.0648015 | ||||||||
\(7\) | −1.35199 | −0.511003 | −0.255502 | − | 0.966809i | \(-0.582241\pi\) | ||||
−0.255502 | + | 0.966809i | \(0.582241\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.97480 | −0.991602 | ||||||||
\(10\) | −3.07692 | −0.973007 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.158731 | 0.0458216 | ||||||||
\(13\) | 0.526746 | 0.146093 | 0.0730466 | − | 0.997329i | \(-0.476728\pi\) | ||||
0.0730466 | + | 0.997329i | \(0.476728\pi\) | |||||||
\(14\) | 1.35199 | 0.361334 | ||||||||
\(15\) | 0.488401 | 0.126105 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.23593 | −1.75497 | −0.877485 | − | 0.479604i | \(-0.840780\pi\) | ||||
−0.877485 | + | 0.479604i | \(0.840780\pi\) | |||||||
\(18\) | 2.97480 | 0.701168 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 3.07692 | 0.688019 | ||||||||
\(21\) | −0.214602 | −0.0468300 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.09183 | 0.436176 | 0.218088 | − | 0.975929i | \(-0.430018\pi\) | ||||
0.218088 | + | 0.975929i | \(0.430018\pi\) | |||||||
\(24\) | −0.158731 | −0.0324008 | ||||||||
\(25\) | 4.46742 | 0.893483 | ||||||||
\(26\) | −0.526746 | −0.103303 | ||||||||
\(27\) | −0.948385 | −0.182517 | ||||||||
\(28\) | −1.35199 | −0.255502 | ||||||||
\(29\) | 0.277873 | 0.0515998 | 0.0257999 | − | 0.999667i | \(-0.491787\pi\) | ||||
0.0257999 | + | 0.999667i | \(0.491787\pi\) | |||||||
\(30\) | −0.488401 | −0.0891694 | ||||||||
\(31\) | −1.72447 | −0.309724 | −0.154862 | − | 0.987936i | \(-0.549493\pi\) | ||||
−0.154862 | + | 0.987936i | \(0.549493\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.23593 | 1.24095 | ||||||||
\(35\) | −4.15995 | −0.703161 | ||||||||
\(36\) | −2.97480 | −0.495801 | ||||||||
\(37\) | 8.91226 | 1.46517 | 0.732584 | − | 0.680677i | \(-0.238314\pi\) | ||||
0.732584 | + | 0.680677i | \(0.238314\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 0.0836108 | 0.0133884 | ||||||||
\(40\) | −3.07692 | −0.486503 | ||||||||
\(41\) | 8.37354 | 1.30773 | 0.653864 | − | 0.756612i | \(-0.273147\pi\) | ||||
0.653864 | + | 0.756612i | \(0.273147\pi\) | |||||||
\(42\) | 0.214602 | 0.0331138 | ||||||||
\(43\) | −6.30119 | −0.960923 | −0.480461 | − | 0.877016i | \(-0.659531\pi\) | ||||
−0.480461 | + | 0.877016i | \(0.659531\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.15323 | −1.36448 | ||||||||
\(46\) | −2.09183 | −0.308423 | ||||||||
\(47\) | 1.96711 | 0.286933 | 0.143466 | − | 0.989655i | \(-0.454175\pi\) | ||||
0.143466 | + | 0.989655i | \(0.454175\pi\) | |||||||
\(48\) | 0.158731 | 0.0229108 | ||||||||
\(49\) | −5.17213 | −0.738875 | ||||||||
\(50\) | −4.46742 | −0.631788 | ||||||||
\(51\) | −1.14856 | −0.160831 | ||||||||
\(52\) | 0.526746 | 0.0730466 | ||||||||
\(53\) | −2.20703 | −0.303158 | −0.151579 | − | 0.988445i | \(-0.548436\pi\) | ||||
−0.151579 | + | 0.988445i | \(0.548436\pi\) | |||||||
\(54\) | 0.948385 | 0.129059 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.35199 | 0.180667 | ||||||||
\(57\) | 0.158731 | 0.0210244 | ||||||||
\(58\) | −0.277873 | −0.0364866 | ||||||||
\(59\) | 8.72295 | 1.13563 | 0.567816 | − | 0.823156i | \(-0.307789\pi\) | ||||
0.567816 | + | 0.823156i | \(0.307789\pi\) | |||||||
\(60\) | 0.488401 | 0.0630523 | ||||||||
\(61\) | −6.38710 | −0.817785 | −0.408892 | − | 0.912583i | \(-0.634085\pi\) | ||||
−0.408892 | + | 0.912583i | \(0.634085\pi\) | |||||||
\(62\) | 1.72447 | 0.219008 | ||||||||
\(63\) | 4.02190 | 0.506712 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.62075 | 0.201030 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.02001 | −0.124614 | −0.0623071 | − | 0.998057i | \(-0.519846\pi\) | ||||
−0.0623071 | + | 0.998057i | \(0.519846\pi\) | |||||||
\(68\) | −7.23593 | −0.877485 | ||||||||
\(69\) | 0.332037 | 0.0399726 | ||||||||
\(70\) | 4.15995 | 0.497210 | ||||||||
\(71\) | −3.71385 | −0.440753 | −0.220376 | − | 0.975415i | \(-0.570729\pi\) | ||||
−0.220376 | + | 0.975415i | \(0.570729\pi\) | |||||||
\(72\) | 2.97480 | 0.350584 | ||||||||
\(73\) | −1.72161 | −0.201499 | −0.100750 | − | 0.994912i | \(-0.532124\pi\) | ||||
−0.100750 | + | 0.994912i | \(0.532124\pi\) | |||||||
\(74\) | −8.91226 | −1.03603 | ||||||||
\(75\) | 0.709116 | 0.0818817 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.0836108 | −0.00946706 | ||||||||
\(79\) | −7.53423 | −0.847667 | −0.423833 | − | 0.905740i | \(-0.639316\pi\) | ||||
−0.423833 | + | 0.905740i | \(0.639316\pi\) | |||||||
\(80\) | 3.07692 | 0.344010 | ||||||||
\(81\) | 8.77388 | 0.974875 | ||||||||
\(82\) | −8.37354 | −0.924703 | ||||||||
\(83\) | −6.49693 | −0.713131 | −0.356565 | − | 0.934270i | \(-0.616052\pi\) | ||||
−0.356565 | + | 0.934270i | \(0.616052\pi\) | |||||||
\(84\) | −0.214602 | −0.0234150 | ||||||||
\(85\) | −22.2643 | −2.41491 | ||||||||
\(86\) | 6.30119 | 0.679475 | ||||||||
\(87\) | 0.0441070 | 0.00472877 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.3518 | −1.09728 | −0.548642 | − | 0.836057i | \(-0.684855\pi\) | ||||
−0.548642 | + | 0.836057i | \(0.684855\pi\) | |||||||
\(90\) | 9.15323 | 0.964835 | ||||||||
\(91\) | −0.712155 | −0.0746541 | ||||||||
\(92\) | 2.09183 | 0.218088 | ||||||||
\(93\) | −0.273726 | −0.0283841 | ||||||||
\(94\) | −1.96711 | −0.202892 | ||||||||
\(95\) | 3.07692 | 0.315685 | ||||||||
\(96\) | −0.158731 | −0.0162004 | ||||||||
\(97\) | −10.4421 | −1.06023 | −0.530116 | − | 0.847925i | \(-0.677852\pi\) | ||||
−0.530116 | + | 0.847925i | \(0.677852\pi\) | |||||||
\(98\) | 5.17213 | 0.522464 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.46742 | 0.446742 | ||||||||
\(101\) | −16.6075 | −1.65251 | −0.826254 | − | 0.563298i | \(-0.809532\pi\) | ||||
−0.826254 | + | 0.563298i | \(0.809532\pi\) | |||||||
\(102\) | 1.14856 | 0.113725 | ||||||||
\(103\) | −6.30847 | −0.621592 | −0.310796 | − | 0.950477i | \(-0.600596\pi\) | ||||
−0.310796 | + | 0.950477i | \(0.600596\pi\) | |||||||
\(104\) | −0.526746 | −0.0516517 | ||||||||
\(105\) | −0.660313 | −0.0644399 | ||||||||
\(106\) | 2.20703 | 0.214365 | ||||||||
\(107\) | −13.1999 | −1.27608 | −0.638041 | − | 0.770002i | \(-0.720255\pi\) | ||||
−0.638041 | + | 0.770002i | \(0.720255\pi\) | |||||||
\(108\) | −0.948385 | −0.0912584 | ||||||||
\(109\) | −4.47355 | −0.428488 | −0.214244 | − | 0.976780i | \(-0.568729\pi\) | ||||
−0.214244 | + | 0.976780i | \(0.568729\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.41465 | 0.134273 | ||||||||
\(112\) | −1.35199 | −0.127751 | ||||||||
\(113\) | −12.5601 | −1.18156 | −0.590778 | − | 0.806834i | \(-0.701179\pi\) | ||||
−0.590778 | + | 0.806834i | \(0.701179\pi\) | |||||||
\(114\) | −0.158731 | −0.0148665 | ||||||||
\(115\) | 6.43637 | 0.600195 | ||||||||
\(116\) | 0.277873 | 0.0257999 | ||||||||
\(117\) | −1.56697 | −0.144866 | ||||||||
\(118\) | −8.72295 | −0.803012 | ||||||||
\(119\) | 9.78288 | 0.896796 | ||||||||
\(120\) | −0.488401 | −0.0445847 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.38710 | 0.578261 | ||||||||
\(123\) | 1.32914 | 0.119844 | ||||||||
\(124\) | −1.72447 | −0.154862 | ||||||||
\(125\) | −1.63872 | −0.146571 | ||||||||
\(126\) | −4.02190 | −0.358299 | ||||||||
\(127\) | 16.4582 | 1.46042 | 0.730212 | − | 0.683220i | \(-0.239421\pi\) | ||||
0.730212 | + | 0.683220i | \(0.239421\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.00019 | −0.0880621 | ||||||||
\(130\) | −1.62075 | −0.142150 | ||||||||
\(131\) | −15.1571 | −1.32428 | −0.662140 | − | 0.749380i | \(-0.730352\pi\) | ||||
−0.662140 | + | 0.749380i | \(0.730352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.35199 | −0.117232 | ||||||||
\(134\) | 1.02001 | 0.0881156 | ||||||||
\(135\) | −2.91810 | −0.251150 | ||||||||
\(136\) | 7.23593 | 0.620475 | ||||||||
\(137\) | −5.46038 | −0.466512 | −0.233256 | − | 0.972415i | \(-0.574938\pi\) | ||||
−0.233256 | + | 0.972415i | \(0.574938\pi\) | |||||||
\(138\) | −0.332037 | −0.0282649 | ||||||||
\(139\) | 9.22943 | 0.782830 | 0.391415 | − | 0.920214i | \(-0.371986\pi\) | ||||
0.391415 | + | 0.920214i | \(0.371986\pi\) | |||||||
\(140\) | −4.15995 | −0.351580 | ||||||||
\(141\) | 0.312241 | 0.0262954 | ||||||||
\(142\) | 3.71385 | 0.311659 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.97480 | −0.247900 | ||||||||
\(145\) | 0.854993 | 0.0710033 | ||||||||
\(146\) | 1.72161 | 0.142481 | ||||||||
\(147\) | −0.820976 | −0.0677129 | ||||||||
\(148\) | 8.91226 | 0.732584 | ||||||||
\(149\) | 12.3302 | 1.01013 | 0.505065 | − | 0.863081i | \(-0.331469\pi\) | ||||
0.505065 | + | 0.863081i | \(0.331469\pi\) | |||||||
\(150\) | −0.709116 | −0.0578991 | ||||||||
\(151\) | −3.63459 | −0.295779 | −0.147889 | − | 0.989004i | \(-0.547248\pi\) | ||||
−0.147889 | + | 0.989004i | \(0.547248\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 21.5255 | 1.74023 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.30605 | −0.426192 | ||||||||
\(156\) | 0.0836108 | 0.00669422 | ||||||||
\(157\) | −0.871549 | −0.0695572 | −0.0347786 | − | 0.999395i | \(-0.511073\pi\) | ||||
−0.0347786 | + | 0.999395i | \(0.511073\pi\) | |||||||
\(158\) | 7.53423 | 0.599391 | ||||||||
\(159\) | −0.350323 | −0.0277824 | ||||||||
\(160\) | −3.07692 | −0.243252 | ||||||||
\(161\) | −2.82812 | −0.222887 | ||||||||
\(162\) | −8.77388 | −0.689341 | ||||||||
\(163\) | −7.73571 | −0.605908 | −0.302954 | − | 0.953005i | \(-0.597973\pi\) | ||||
−0.302954 | + | 0.953005i | \(0.597973\pi\) | |||||||
\(164\) | 8.37354 | 0.653864 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.49693 | 0.504259 | ||||||||
\(167\) | −21.8284 | −1.68913 | −0.844566 | − | 0.535451i | \(-0.820142\pi\) | ||||
−0.844566 | + | 0.535451i | \(0.820142\pi\) | |||||||
\(168\) | 0.214602 | 0.0165569 | ||||||||
\(169\) | −12.7225 | −0.978657 | ||||||||
\(170\) | 22.2643 | 1.70760 | ||||||||
\(171\) | −2.97480 | −0.227489 | ||||||||
\(172\) | −6.30119 | −0.480461 | ||||||||
\(173\) | 11.0102 | 0.837086 | 0.418543 | − | 0.908197i | \(-0.362541\pi\) | ||||
0.418543 | + | 0.908197i | \(0.362541\pi\) | |||||||
\(174\) | −0.0441070 | −0.00334375 | ||||||||
\(175\) | −6.03989 | −0.456573 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.38460 | 0.104073 | ||||||||
\(178\) | 10.3518 | 0.775897 | ||||||||
\(179\) | −12.5527 | −0.938233 | −0.469116 | − | 0.883136i | \(-0.655428\pi\) | ||||
−0.469116 | + | 0.883136i | \(0.655428\pi\) | |||||||
\(180\) | −9.15323 | −0.682241 | ||||||||
\(181\) | −3.45298 | −0.256658 | −0.128329 | − | 0.991732i | \(-0.540961\pi\) | ||||
−0.128329 | + | 0.991732i | \(0.540961\pi\) | |||||||
\(182\) | 0.712155 | 0.0527884 | ||||||||
\(183\) | −1.01383 | −0.0749444 | ||||||||
\(184\) | −2.09183 | −0.154211 | ||||||||
\(185\) | 27.4223 | 2.01613 | ||||||||
\(186\) | 0.273726 | 0.0200706 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.96711 | 0.143466 | ||||||||
\(189\) | 1.28221 | 0.0932667 | ||||||||
\(190\) | −3.07692 | −0.223223 | ||||||||
\(191\) | 21.3218 | 1.54279 | 0.771397 | − | 0.636354i | \(-0.219558\pi\) | ||||
0.771397 | + | 0.636354i | \(0.219558\pi\) | |||||||
\(192\) | 0.158731 | 0.0114554 | ||||||||
\(193\) | −23.4522 | −1.68813 | −0.844063 | − | 0.536243i | \(-0.819843\pi\) | ||||
−0.844063 | + | 0.536243i | \(0.819843\pi\) | |||||||
\(194\) | 10.4421 | 0.749697 | ||||||||
\(195\) | 0.257263 | 0.0184230 | ||||||||
\(196\) | −5.17213 | −0.369438 | ||||||||
\(197\) | 7.79605 | 0.555445 | 0.277723 | − | 0.960661i | \(-0.410420\pi\) | ||||
0.277723 | + | 0.960661i | \(0.410420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.48281 | −0.672219 | −0.336109 | − | 0.941823i | \(-0.609111\pi\) | ||||
−0.336109 | + | 0.941823i | \(0.609111\pi\) | |||||||
\(200\) | −4.46742 | −0.315894 | ||||||||
\(201\) | −0.161907 | −0.0114200 | ||||||||
\(202\) | 16.6075 | 1.16850 | ||||||||
\(203\) | −0.375681 | −0.0263677 | ||||||||
\(204\) | −1.14856 | −0.0804155 | ||||||||
\(205\) | 25.7647 | 1.79948 | ||||||||
\(206\) | 6.30847 | 0.439532 | ||||||||
\(207\) | −6.22277 | −0.432513 | ||||||||
\(208\) | 0.526746 | 0.0365233 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.660313 | 0.0455659 | ||||||||
\(211\) | −15.5951 | −1.07361 | −0.536805 | − | 0.843707i | \(-0.680369\pi\) | ||||
−0.536805 | + | 0.843707i | \(0.680369\pi\) | |||||||
\(212\) | −2.20703 | −0.151579 | ||||||||
\(213\) | −0.589502 | −0.0403920 | ||||||||
\(214\) | 13.1999 | 0.902327 | ||||||||
\(215\) | −19.3882 | −1.32227 | ||||||||
\(216\) | 0.948385 | 0.0645294 | ||||||||
\(217\) | 2.33146 | 0.158270 | ||||||||
\(218\) | 4.47355 | 0.302987 | ||||||||
\(219\) | −0.273272 | −0.0184660 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.81150 | −0.256389 | ||||||||
\(222\) | −1.41465 | −0.0949451 | ||||||||
\(223\) | −24.4375 | −1.63646 | −0.818230 | − | 0.574892i | \(-0.805044\pi\) | ||||
−0.818230 | + | 0.574892i | \(0.805044\pi\) | |||||||
\(224\) | 1.35199 | 0.0903335 | ||||||||
\(225\) | −13.2897 | −0.885979 | ||||||||
\(226\) | 12.5601 | 0.835486 | ||||||||
\(227\) | 23.2524 | 1.54332 | 0.771659 | − | 0.636037i | \(-0.219427\pi\) | ||||
0.771659 | + | 0.636037i | \(0.219427\pi\) | |||||||
\(228\) | 0.158731 | 0.0105122 | ||||||||
\(229\) | −1.94364 | −0.128439 | −0.0642197 | − | 0.997936i | \(-0.520456\pi\) | ||||
−0.0642197 | + | 0.997936i | \(0.520456\pi\) | |||||||
\(230\) | −6.43637 | −0.424402 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.277873 | −0.0182433 | ||||||||
\(233\) | −5.46260 | −0.357867 | −0.178933 | − | 0.983861i | \(-0.557265\pi\) | ||||
−0.178933 | + | 0.983861i | \(0.557265\pi\) | |||||||
\(234\) | 1.56697 | 0.102436 | ||||||||
\(235\) | 6.05264 | 0.394831 | ||||||||
\(236\) | 8.72295 | 0.567816 | ||||||||
\(237\) | −1.19591 | −0.0776829 | ||||||||
\(238\) | −9.78288 | −0.634130 | ||||||||
\(239\) | 16.1582 | 1.04519 | 0.522595 | − | 0.852581i | \(-0.324964\pi\) | ||||
0.522595 | + | 0.852581i | \(0.324964\pi\) | |||||||
\(240\) | 0.488401 | 0.0315262 | ||||||||
\(241\) | 17.9215 | 1.15442 | 0.577212 | − | 0.816594i | \(-0.304141\pi\) | ||||
0.577212 | + | 0.816594i | \(0.304141\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.23784 | 0.271857 | ||||||||
\(244\) | −6.38710 | −0.408892 | ||||||||
\(245\) | −15.9142 | −1.01672 | ||||||||
\(246\) | −1.32914 | −0.0847428 | ||||||||
\(247\) | 0.526746 | 0.0335161 | ||||||||
\(248\) | 1.72447 | 0.109504 | ||||||||
\(249\) | −1.03126 | −0.0653536 | ||||||||
\(250\) | 1.63872 | 0.103641 | ||||||||
\(251\) | 26.9550 | 1.70139 | 0.850693 | − | 0.525663i | \(-0.176183\pi\) | ||||
0.850693 | + | 0.525663i | \(0.176183\pi\) | |||||||
\(252\) | 4.02190 | 0.253356 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −16.4582 | −1.03268 | ||||||||
\(255\) | −3.53403 | −0.221310 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.2307 | −1.38671 | −0.693357 | − | 0.720594i | \(-0.743869\pi\) | ||||
−0.693357 | + | 0.720594i | \(0.743869\pi\) | |||||||
\(258\) | 1.00019 | 0.0622693 | ||||||||
\(259\) | −12.0493 | −0.748706 | ||||||||
\(260\) | 1.62075 | 0.100515 | ||||||||
\(261\) | −0.826619 | −0.0511664 | ||||||||
\(262\) | 15.1571 | 0.936407 | ||||||||
\(263\) | 0.840832 | 0.0518479 | 0.0259240 | − | 0.999664i | \(-0.491747\pi\) | ||||
0.0259240 | + | 0.999664i | \(0.491747\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.79084 | −0.417158 | ||||||||
\(266\) | 1.35199 | 0.0828957 | ||||||||
\(267\) | −1.64314 | −0.100559 | ||||||||
\(268\) | −1.02001 | −0.0623071 | ||||||||
\(269\) | 26.6280 | 1.62354 | 0.811770 | − | 0.583978i | \(-0.198504\pi\) | ||||
0.811770 | + | 0.583978i | \(0.198504\pi\) | |||||||
\(270\) | 2.91810 | 0.177590 | ||||||||
\(271\) | 25.3809 | 1.54178 | 0.770889 | − | 0.636970i | \(-0.219812\pi\) | ||||
0.770889 | + | 0.636970i | \(0.219812\pi\) | |||||||
\(272\) | −7.23593 | −0.438742 | ||||||||
\(273\) | −0.113041 | −0.00684154 | ||||||||
\(274\) | 5.46038 | 0.329874 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.332037 | 0.0199863 | ||||||||
\(277\) | 30.1812 | 1.81341 | 0.906706 | − | 0.421763i | \(-0.138589\pi\) | ||||
0.906706 | + | 0.421763i | \(0.138589\pi\) | |||||||
\(278\) | −9.22943 | −0.553544 | ||||||||
\(279\) | 5.12996 | 0.307123 | ||||||||
\(280\) | 4.15995 | 0.248605 | ||||||||
\(281\) | −16.8269 | −1.00381 | −0.501904 | − | 0.864923i | \(-0.667367\pi\) | ||||
−0.501904 | + | 0.864923i | \(0.667367\pi\) | |||||||
\(282\) | −0.312241 | −0.0185937 | ||||||||
\(283\) | 10.4403 | 0.620611 | 0.310305 | − | 0.950637i | \(-0.399569\pi\) | ||||
0.310305 | + | 0.950637i | \(0.399569\pi\) | |||||||
\(284\) | −3.71385 | −0.220376 | ||||||||
\(285\) | 0.488401 | 0.0289304 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3209 | −0.668253 | ||||||||
\(288\) | 2.97480 | 0.175292 | ||||||||
\(289\) | 35.3586 | 2.07992 | ||||||||
\(290\) | −0.854993 | −0.0502069 | ||||||||
\(291\) | −1.65748 | −0.0971631 | ||||||||
\(292\) | −1.72161 | −0.100750 | ||||||||
\(293\) | −13.4022 | −0.782965 | −0.391482 | − | 0.920186i | \(-0.628038\pi\) | ||||
−0.391482 | + | 0.920186i | \(0.628038\pi\) | |||||||
\(294\) | 0.820976 | 0.0478803 | ||||||||
\(295\) | 26.8398 | 1.56267 | ||||||||
\(296\) | −8.91226 | −0.518015 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.3302 | −0.714270 | ||||||||
\(299\) | 1.10186 | 0.0637223 | ||||||||
\(300\) | 0.709116 | 0.0409408 | ||||||||
\(301\) | 8.51914 | 0.491035 | ||||||||
\(302\) | 3.63459 | 0.209147 | ||||||||
\(303\) | −2.63612 | −0.151441 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −19.6526 | −1.12530 | ||||||||
\(306\) | −21.5255 | −1.23053 | ||||||||
\(307\) | 18.9800 | 1.08325 | 0.541623 | − | 0.840622i | \(-0.317810\pi\) | ||||
0.541623 | + | 0.840622i | \(0.317810\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00135 | −0.0569646 | ||||||||
\(310\) | 5.30605 | 0.301363 | ||||||||
\(311\) | 12.4757 | 0.707430 | 0.353715 | − | 0.935353i | \(-0.384918\pi\) | ||||
0.353715 | + | 0.935353i | \(0.384918\pi\) | |||||||
\(312\) | −0.0836108 | −0.00473353 | ||||||||
\(313\) | −18.2742 | −1.03292 | −0.516459 | − | 0.856312i | \(-0.672750\pi\) | ||||
−0.516459 | + | 0.856312i | \(0.672750\pi\) | |||||||
\(314\) | 0.871549 | 0.0491844 | ||||||||
\(315\) | 12.3751 | 0.697255 | ||||||||
\(316\) | −7.53423 | −0.423833 | ||||||||
\(317\) | −13.1830 | −0.740432 | −0.370216 | − | 0.928946i | \(-0.620716\pi\) | ||||
−0.370216 | + | 0.928946i | \(0.620716\pi\) | |||||||
\(318\) | 0.350323 | 0.0196451 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.07692 | 0.172005 | ||||||||
\(321\) | −2.09523 | −0.116944 | ||||||||
\(322\) | 2.82812 | 0.157605 | ||||||||
\(323\) | −7.23593 | −0.402618 | ||||||||
\(324\) | 8.77388 | 0.487438 | ||||||||
\(325\) | 2.35319 | 0.130532 | ||||||||
\(326\) | 7.73571 | 0.428441 | ||||||||
\(327\) | −0.710090 | −0.0392681 | ||||||||
\(328\) | −8.37354 | −0.462352 | ||||||||
\(329\) | −2.65951 | −0.146624 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.69222 | 0.202943 | 0.101471 | − | 0.994838i | \(-0.467645\pi\) | ||||
0.101471 | + | 0.994838i | \(0.467645\pi\) | |||||||
\(332\) | −6.49693 | −0.356565 | ||||||||
\(333\) | −26.5122 | −1.45286 | ||||||||
\(334\) | 21.8284 | 1.19440 | ||||||||
\(335\) | −3.13849 | −0.171474 | ||||||||
\(336\) | −0.214602 | −0.0117075 | ||||||||
\(337\) | −26.2983 | −1.43256 | −0.716279 | − | 0.697814i | \(-0.754156\pi\) | ||||
−0.716279 | + | 0.697814i | \(0.754156\pi\) | |||||||
\(338\) | 12.7225 | 0.692015 | ||||||||
\(339\) | −1.99368 | −0.108282 | ||||||||
\(340\) | −22.2643 | −1.20745 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.97480 | 0.160859 | ||||||||
\(343\) | 16.4566 | 0.888571 | ||||||||
\(344\) | 6.30119 | 0.339738 | ||||||||
\(345\) | 1.02165 | 0.0550038 | ||||||||
\(346\) | −11.0102 | −0.591909 | ||||||||
\(347\) | 5.33343 | 0.286313 | 0.143157 | − | 0.989700i | \(-0.454275\pi\) | ||||
0.143157 | + | 0.989700i | \(0.454275\pi\) | |||||||
\(348\) | 0.0441070 | 0.00236439 | ||||||||
\(349\) | −19.4450 | −1.04087 | −0.520433 | − | 0.853903i | \(-0.674229\pi\) | ||||
−0.520433 | + | 0.853903i | \(0.674229\pi\) | |||||||
\(350\) | 6.03989 | 0.322846 | ||||||||
\(351\) | −0.499558 | −0.0266644 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.8728 | −1.48352 | −0.741761 | − | 0.670665i | \(-0.766009\pi\) | ||||
−0.741761 | + | 0.670665i | \(0.766009\pi\) | |||||||
\(354\) | −1.38460 | −0.0735906 | ||||||||
\(355\) | −11.4272 | −0.606493 | ||||||||
\(356\) | −10.3518 | −0.548642 | ||||||||
\(357\) | 1.55284 | 0.0821852 | ||||||||
\(358\) | 12.5527 | 0.663431 | ||||||||
\(359\) | −35.7338 | −1.88596 | −0.942978 | − | 0.332856i | \(-0.891988\pi\) | ||||
−0.942978 | + | 0.332856i | \(0.891988\pi\) | |||||||
\(360\) | 9.15323 | 0.482417 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 3.45298 | 0.181485 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.712155 | −0.0373270 | ||||||||
\(365\) | −5.29725 | −0.277271 | ||||||||
\(366\) | 1.01383 | 0.0529937 | ||||||||
\(367\) | 37.8147 | 1.97391 | 0.986956 | − | 0.160991i | \(-0.0514691\pi\) | ||||
0.986956 | + | 0.160991i | \(0.0514691\pi\) | |||||||
\(368\) | 2.09183 | 0.109044 | ||||||||
\(369\) | −24.9097 | −1.29675 | ||||||||
\(370\) | −27.4223 | −1.42562 | ||||||||
\(371\) | 2.98387 | 0.154915 | ||||||||
\(372\) | −0.273726 | −0.0141920 | ||||||||
\(373\) | 20.1806 | 1.04491 | 0.522456 | − | 0.852667i | \(-0.325016\pi\) | ||||
0.522456 | + | 0.852667i | \(0.325016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.260114 | −0.0134322 | ||||||||
\(376\) | −1.96711 | −0.101446 | ||||||||
\(377\) | 0.146369 | 0.00753837 | ||||||||
\(378\) | −1.28221 | −0.0659495 | ||||||||
\(379\) | −32.7152 | −1.68047 | −0.840233 | − | 0.542225i | \(-0.817582\pi\) | ||||
−0.840233 | + | 0.542225i | \(0.817582\pi\) | |||||||
\(380\) | 3.07692 | 0.157842 | ||||||||
\(381\) | 2.61241 | 0.133838 | ||||||||
\(382\) | −21.3218 | −1.09092 | ||||||||
\(383\) | −25.6817 | −1.31227 | −0.656136 | − | 0.754643i | \(-0.727810\pi\) | ||||
−0.656136 | + | 0.754643i | \(0.727810\pi\) | |||||||
\(384\) | −0.158731 | −0.00810019 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.4522 | 1.19369 | ||||||||
\(387\) | 18.7448 | 0.952853 | ||||||||
\(388\) | −10.4421 | −0.530116 | ||||||||
\(389\) | −4.46845 | −0.226559 | −0.113280 | − | 0.993563i | \(-0.536136\pi\) | ||||
−0.113280 | + | 0.993563i | \(0.536136\pi\) | |||||||
\(390\) | −0.257263 | −0.0130270 | ||||||||
\(391\) | −15.1363 | −0.765475 | ||||||||
\(392\) | 5.17213 | 0.261232 | ||||||||
\(393\) | −2.40589 | −0.121361 | ||||||||
\(394\) | −7.79605 | −0.392759 | ||||||||
\(395\) | −23.1822 | −1.16642 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.8810 | 1.44950 | 0.724748 | − | 0.689014i | \(-0.241956\pi\) | ||||
0.724748 | + | 0.689014i | \(0.241956\pi\) | |||||||
\(398\) | 9.48281 | 0.475330 | ||||||||
\(399\) | −0.214602 | −0.0107435 | ||||||||
\(400\) | 4.46742 | 0.223371 | ||||||||
\(401\) | 0.797439 | 0.0398222 | 0.0199111 | − | 0.999802i | \(-0.493662\pi\) | ||||
0.0199111 | + | 0.999802i | \(0.493662\pi\) | |||||||
\(402\) | 0.161907 | 0.00807519 | ||||||||
\(403\) | −0.908358 | −0.0452485 | ||||||||
\(404\) | −16.6075 | −0.826254 | ||||||||
\(405\) | 26.9965 | 1.34147 | ||||||||
\(406\) | 0.375681 | 0.0186448 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.14856 | 0.0568624 | ||||||||
\(409\) | −22.7240 | −1.12363 | −0.561814 | − | 0.827263i | \(-0.689897\pi\) | ||||
−0.561814 | + | 0.827263i | \(0.689897\pi\) | |||||||
\(410\) | −25.7647 | −1.27243 | ||||||||
\(411\) | −0.866730 | −0.0427527 | ||||||||
\(412\) | −6.30847 | −0.310796 | ||||||||
\(413\) | −11.7933 | −0.580311 | ||||||||
\(414\) | 6.22277 | 0.305833 | ||||||||
\(415\) | −19.9905 | −0.981296 | ||||||||
\(416\) | −0.526746 | −0.0258259 | ||||||||
\(417\) | 1.46499 | 0.0717410 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.427754 | −0.0208971 | −0.0104486 | − | 0.999945i | \(-0.503326\pi\) | ||||
−0.0104486 | + | 0.999945i | \(0.503326\pi\) | |||||||
\(420\) | −0.660313 | −0.0322200 | ||||||||
\(421\) | −9.69726 | −0.472615 | −0.236308 | − | 0.971678i | \(-0.575937\pi\) | ||||
−0.236308 | + | 0.971678i | \(0.575937\pi\) | |||||||
\(422\) | 15.5951 | 0.759156 | ||||||||
\(423\) | −5.85177 | −0.284523 | ||||||||
\(424\) | 2.20703 | 0.107183 | ||||||||
\(425\) | −32.3259 | −1.56804 | ||||||||
\(426\) | 0.589502 | 0.0285615 | ||||||||
\(427\) | 8.63529 | 0.417891 | ||||||||
\(428\) | −13.1999 | −0.638041 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 19.3882 | 0.934984 | ||||||||
\(431\) | 6.70352 | 0.322897 | 0.161449 | − | 0.986881i | \(-0.448383\pi\) | ||||
0.161449 | + | 0.986881i | \(0.448383\pi\) | |||||||
\(432\) | −0.948385 | −0.0456292 | ||||||||
\(433\) | −15.3773 | −0.738988 | −0.369494 | − | 0.929233i | \(-0.620469\pi\) | ||||
−0.369494 | + | 0.929233i | \(0.620469\pi\) | |||||||
\(434\) | −2.33146 | −0.111914 | ||||||||
\(435\) | 0.135714 | 0.00650697 | ||||||||
\(436\) | −4.47355 | −0.214244 | ||||||||
\(437\) | 2.09183 | 0.100066 | ||||||||
\(438\) | 0.273272 | 0.0130575 | ||||||||
\(439\) | 2.15073 | 0.102649 | 0.0513244 | − | 0.998682i | \(-0.483656\pi\) | ||||
0.0513244 | + | 0.998682i | \(0.483656\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.3861 | 0.732670 | ||||||||
\(442\) | 3.81150 | 0.181294 | ||||||||
\(443\) | 30.3841 | 1.44359 | 0.721797 | − | 0.692105i | \(-0.243317\pi\) | ||||
0.721797 | + | 0.692105i | \(0.243317\pi\) | |||||||
\(444\) | 1.41465 | 0.0671363 | ||||||||
\(445\) | −31.8515 | −1.50991 | ||||||||
\(446\) | 24.4375 | 1.15715 | ||||||||
\(447\) | 1.95718 | 0.0925715 | ||||||||
\(448\) | −1.35199 | −0.0638754 | ||||||||
\(449\) | 3.34155 | 0.157698 | 0.0788488 | − | 0.996887i | \(-0.474876\pi\) | ||||
0.0788488 | + | 0.996887i | \(0.474876\pi\) | |||||||
\(450\) | 13.2897 | 0.626482 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −12.5601 | −0.590778 | ||||||||
\(453\) | −0.576921 | −0.0271061 | ||||||||
\(454\) | −23.2524 | −1.09129 | ||||||||
\(455\) | −2.19124 | −0.102727 | ||||||||
\(456\) | −0.158731 | −0.00743325 | ||||||||
\(457\) | −29.3880 | −1.37471 | −0.687356 | − | 0.726321i | \(-0.741229\pi\) | ||||
−0.687356 | + | 0.726321i | \(0.741229\pi\) | |||||||
\(458\) | 1.94364 | 0.0908204 | ||||||||
\(459\) | 6.86244 | 0.320311 | ||||||||
\(460\) | 6.43637 | 0.300097 | ||||||||
\(461\) | 1.74308 | 0.0811833 | 0.0405917 | − | 0.999176i | \(-0.487076\pi\) | ||||
0.0405917 | + | 0.999176i | \(0.487076\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.2015 | −1.45006 | −0.725029 | − | 0.688718i | \(-0.758174\pi\) | ||||
−0.725029 | + | 0.688718i | \(0.758174\pi\) | |||||||
\(464\) | 0.277873 | 0.0128999 | ||||||||
\(465\) | −0.842233 | −0.0390576 | ||||||||
\(466\) | 5.46260 | 0.253050 | ||||||||
\(467\) | 26.0733 | 1.20653 | 0.603264 | − | 0.797542i | \(-0.293867\pi\) | ||||
0.603264 | + | 0.797542i | \(0.293867\pi\) | |||||||
\(468\) | −1.56697 | −0.0724331 | ||||||||
\(469\) | 1.37904 | 0.0636783 | ||||||||
\(470\) | −6.05264 | −0.279187 | ||||||||
\(471\) | −0.138342 | −0.00637444 | ||||||||
\(472\) | −8.72295 | −0.401506 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 1.19591 | 0.0549301 | ||||||||
\(475\) | 4.46742 | 0.204979 | ||||||||
\(476\) | 9.78288 | 0.448398 | ||||||||
\(477\) | 6.56547 | 0.300612 | ||||||||
\(478\) | −16.1582 | −0.739061 | ||||||||
\(479\) | 29.3946 | 1.34307 | 0.671536 | − | 0.740972i | \(-0.265635\pi\) | ||||
0.671536 | + | 0.740972i | \(0.265635\pi\) | |||||||
\(480\) | −0.488401 | −0.0222924 | ||||||||
\(481\) | 4.69450 | 0.214051 | ||||||||
\(482\) | −17.9215 | −0.816301 | ||||||||
\(483\) | −0.448910 | −0.0204261 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −32.1294 | −1.45892 | ||||||||
\(486\) | −4.23784 | −0.192232 | ||||||||
\(487\) | 43.0919 | 1.95268 | 0.976340 | − | 0.216242i | \(-0.0693801\pi\) | ||||
0.976340 | + | 0.216242i | \(0.0693801\pi\) | |||||||
\(488\) | 6.38710 | 0.289131 | ||||||||
\(489\) | −1.22790 | −0.0555273 | ||||||||
\(490\) | 15.9142 | 0.718931 | ||||||||
\(491\) | 29.5401 | 1.33313 | 0.666563 | − | 0.745449i | \(-0.267765\pi\) | ||||
0.666563 | + | 0.745449i | \(0.267765\pi\) | |||||||
\(492\) | 1.32914 | 0.0599222 | ||||||||
\(493\) | −2.01067 | −0.0905561 | ||||||||
\(494\) | −0.526746 | −0.0236994 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.72447 | −0.0774309 | ||||||||
\(497\) | 5.02108 | 0.225226 | ||||||||
\(498\) | 1.03126 | 0.0462120 | ||||||||
\(499\) | −27.8915 | −1.24859 | −0.624297 | − | 0.781187i | \(-0.714615\pi\) | ||||
−0.624297 | + | 0.781187i | \(0.714615\pi\) | |||||||
\(500\) | −1.63872 | −0.0732856 | ||||||||
\(501\) | −3.46484 | −0.154798 | ||||||||
\(502\) | −26.9550 | −1.20306 | ||||||||
\(503\) | −0.0484888 | −0.00216201 | −0.00108100 | − | 0.999999i | \(-0.500344\pi\) | ||||
−0.00108100 | + | 0.999999i | \(0.500344\pi\) | |||||||
\(504\) | −4.02190 | −0.179150 | ||||||||
\(505\) | −51.0999 | −2.27392 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.01946 | −0.0896873 | ||||||||
\(508\) | 16.4582 | 0.730212 | ||||||||
\(509\) | 9.75291 | 0.432290 | 0.216145 | − | 0.976361i | \(-0.430652\pi\) | ||||
0.216145 | + | 0.976361i | \(0.430652\pi\) | |||||||
\(510\) | 3.53403 | 0.156490 | ||||||||
\(511\) | 2.32759 | 0.102967 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.948385 | −0.0418722 | ||||||||
\(514\) | 22.2307 | 0.980555 | ||||||||
\(515\) | −19.4106 | −0.855334 | ||||||||
\(516\) | −1.00019 | −0.0440310 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 12.0493 | 0.529415 | ||||||||
\(519\) | 1.74765 | 0.0767133 | ||||||||
\(520\) | −1.62075 | −0.0710748 | ||||||||
\(521\) | −40.4077 | −1.77029 | −0.885147 | − | 0.465312i | \(-0.845942\pi\) | ||||
−0.885147 | + | 0.465312i | \(0.845942\pi\) | |||||||
\(522\) | 0.826619 | 0.0361801 | ||||||||
\(523\) | −22.7718 | −0.995742 | −0.497871 | − | 0.867251i | \(-0.665885\pi\) | ||||
−0.497871 | + | 0.867251i | \(0.665885\pi\) | |||||||
\(524\) | −15.1571 | −0.662140 | ||||||||
\(525\) | −0.958717 | −0.0418418 | ||||||||
\(526\) | −0.840832 | −0.0366620 | ||||||||
\(527\) | 12.4781 | 0.543556 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.6243 | −0.809751 | ||||||||
\(530\) | 6.79084 | 0.294975 | ||||||||
\(531\) | −25.9491 | −1.12609 | ||||||||
\(532\) | −1.35199 | −0.0586161 | ||||||||
\(533\) | 4.41073 | 0.191050 | ||||||||
\(534\) | 1.64314 | 0.0711057 | ||||||||
\(535\) | −40.6150 | −1.75594 | ||||||||
\(536\) | 1.02001 | 0.0440578 | ||||||||
\(537\) | −1.99250 | −0.0859827 | ||||||||
\(538\) | −26.6280 | −1.14802 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.91810 | −0.125575 | ||||||||
\(541\) | 7.41552 | 0.318818 | 0.159409 | − | 0.987213i | \(-0.449041\pi\) | ||||
0.159409 | + | 0.987213i | \(0.449041\pi\) | |||||||
\(542\) | −25.3809 | −1.09020 | ||||||||
\(543\) | −0.548094 | −0.0235210 | ||||||||
\(544\) | 7.23593 | 0.310238 | ||||||||
\(545\) | −13.7647 | −0.589617 | ||||||||
\(546\) | 0.113041 | 0.00483770 | ||||||||
\(547\) | −2.41910 | −0.103433 | −0.0517167 | − | 0.998662i | \(-0.516469\pi\) | ||||
−0.0517167 | + | 0.998662i | \(0.516469\pi\) | |||||||
\(548\) | −5.46038 | −0.233256 | ||||||||
\(549\) | 19.0004 | 0.810917 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.277873 | 0.0118378 | ||||||||
\(552\) | −0.332037 | −0.0141324 | ||||||||
\(553\) | 10.1862 | 0.433161 | ||||||||
\(554\) | −30.1812 | −1.28228 | ||||||||
\(555\) | 4.35276 | 0.184764 | ||||||||
\(556\) | 9.22943 | 0.391415 | ||||||||
\(557\) | −0.412176 | −0.0174645 | −0.00873224 | − | 0.999962i | \(-0.502780\pi\) | ||||
−0.00873224 | + | 0.999962i | \(0.502780\pi\) | |||||||
\(558\) | −5.12996 | −0.217168 | ||||||||
\(559\) | −3.31913 | −0.140384 | ||||||||
\(560\) | −4.15995 | −0.175790 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.8269 | 0.709800 | ||||||||
\(563\) | −4.49045 | −0.189250 | −0.0946249 | − | 0.995513i | \(-0.530165\pi\) | ||||
−0.0946249 | + | 0.995513i | \(0.530165\pi\) | |||||||
\(564\) | 0.312241 | 0.0131477 | ||||||||
\(565\) | −38.6464 | −1.62587 | ||||||||
\(566\) | −10.4403 | −0.438838 | ||||||||
\(567\) | −11.8622 | −0.498165 | ||||||||
\(568\) | 3.71385 | 0.155830 | ||||||||
\(569\) | 32.6319 | 1.36800 | 0.684000 | − | 0.729482i | \(-0.260239\pi\) | ||||
0.684000 | + | 0.729482i | \(0.260239\pi\) | |||||||
\(570\) | −0.488401 | −0.0204569 | ||||||||
\(571\) | −18.1484 | −0.759486 | −0.379743 | − | 0.925092i | \(-0.623988\pi\) | ||||
−0.379743 | + | 0.925092i | \(0.623988\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.38443 | 0.141387 | ||||||||
\(574\) | 11.3209 | 0.472527 | ||||||||
\(575\) | 9.34506 | 0.389716 | ||||||||
\(576\) | −2.97480 | −0.123950 | ||||||||
\(577\) | −21.9198 | −0.912532 | −0.456266 | − | 0.889843i | \(-0.650814\pi\) | ||||
−0.456266 | + | 0.889843i | \(0.650814\pi\) | |||||||
\(578\) | −35.3586 | −1.47072 | ||||||||
\(579\) | −3.72259 | −0.154705 | ||||||||
\(580\) | 0.854993 | 0.0355017 | ||||||||
\(581\) | 8.78377 | 0.364412 | ||||||||
\(582\) | 1.65748 | 0.0687047 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.72161 | 0.0712407 | ||||||||
\(585\) | −4.82143 | −0.199341 | ||||||||
\(586\) | 13.4022 | 0.553640 | ||||||||
\(587\) | 16.9253 | 0.698581 | 0.349291 | − | 0.937014i | \(-0.386423\pi\) | ||||
0.349291 | + | 0.937014i | \(0.386423\pi\) | |||||||
\(588\) | −0.820976 | −0.0338565 | ||||||||
\(589\) | −1.72447 | −0.0710555 | ||||||||
\(590\) | −26.8398 | −1.10498 | ||||||||
\(591\) | 1.23747 | 0.0509028 | ||||||||
\(592\) | 8.91226 | 0.366292 | ||||||||
\(593\) | −9.83301 | −0.403793 | −0.201897 | − | 0.979407i | \(-0.564710\pi\) | ||||
−0.201897 | + | 0.979407i | \(0.564710\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.1011 | 1.23403 | ||||||||
\(596\) | 12.3302 | 0.505065 | ||||||||
\(597\) | −1.50521 | −0.0616043 | ||||||||
\(598\) | −1.10186 | −0.0450585 | ||||||||
\(599\) | 43.2136 | 1.76566 | 0.882829 | − | 0.469694i | \(-0.155636\pi\) | ||||
0.882829 | + | 0.469694i | \(0.155636\pi\) | |||||||
\(600\) | −0.709116 | −0.0289495 | ||||||||
\(601\) | 6.60416 | 0.269389 | 0.134695 | − | 0.990887i | \(-0.456995\pi\) | ||||
0.134695 | + | 0.990887i | \(0.456995\pi\) | |||||||
\(602\) | −8.51914 | −0.347214 | ||||||||
\(603\) | 3.03433 | 0.123568 | ||||||||
\(604\) | −3.63459 | −0.147889 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.63612 | 0.107085 | ||||||||
\(607\) | −19.6695 | −0.798359 | −0.399180 | − | 0.916873i | \(-0.630705\pi\) | ||||
−0.399180 | + | 0.916873i | \(0.630705\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −0.0596322 | −0.00241642 | ||||||||
\(610\) | 19.6526 | 0.795710 | ||||||||
\(611\) | 1.03617 | 0.0419189 | ||||||||
\(612\) | 21.5255 | 0.870115 | ||||||||
\(613\) | 1.55586 | 0.0628407 | 0.0314203 | − | 0.999506i | \(-0.489997\pi\) | ||||
0.0314203 | + | 0.999506i | \(0.489997\pi\) | |||||||
\(614\) | −18.9800 | −0.765970 | ||||||||
\(615\) | 4.08965 | 0.164911 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.2521 | −1.74126 | −0.870632 | − | 0.491935i | \(-0.836290\pi\) | ||||
−0.870632 | + | 0.491935i | \(0.836290\pi\) | |||||||
\(618\) | 1.00135 | 0.0402801 | ||||||||
\(619\) | 3.26969 | 0.131420 | 0.0657100 | − | 0.997839i | \(-0.479069\pi\) | ||||
0.0657100 | + | 0.997839i | \(0.479069\pi\) | |||||||
\(620\) | −5.30605 | −0.213096 | ||||||||
\(621\) | −1.98386 | −0.0796094 | ||||||||
\(622\) | −12.4757 | −0.500228 | ||||||||
\(623\) | 13.9955 | 0.560716 | ||||||||
\(624\) | 0.0836108 | 0.00334711 | ||||||||
\(625\) | −27.3793 | −1.09517 | ||||||||
\(626\) | 18.2742 | 0.730383 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.871549 | −0.0347786 | ||||||||
\(629\) | −64.4885 | −2.57132 | ||||||||
\(630\) | −12.3751 | −0.493034 | ||||||||
\(631\) | 27.6628 | 1.10124 | 0.550620 | − | 0.834756i | \(-0.314391\pi\) | ||||
0.550620 | + | 0.834756i | \(0.314391\pi\) | |||||||
\(632\) | 7.53423 | 0.299695 | ||||||||
\(633\) | −2.47542 | −0.0983890 | ||||||||
\(634\) | 13.1830 | 0.523565 | ||||||||
\(635\) | 50.6404 | 2.00960 | ||||||||
\(636\) | −0.350323 | −0.0138912 | ||||||||
\(637\) | −2.72440 | −0.107945 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.0480 | 0.437051 | ||||||||
\(640\) | −3.07692 | −0.121626 | ||||||||
\(641\) | −40.1504 | −1.58585 | −0.792924 | − | 0.609321i | \(-0.791442\pi\) | ||||
−0.792924 | + | 0.609321i | \(0.791442\pi\) | |||||||
\(642\) | 2.09523 | 0.0826921 | ||||||||
\(643\) | −29.3892 | −1.15900 | −0.579499 | − | 0.814973i | \(-0.696752\pi\) | ||||
−0.579499 | + | 0.814973i | \(0.696752\pi\) | |||||||
\(644\) | −2.82812 | −0.111444 | ||||||||
\(645\) | −3.07751 | −0.121177 | ||||||||
\(646\) | 7.23593 | 0.284694 | ||||||||
\(647\) | 3.63135 | 0.142763 | 0.0713816 | − | 0.997449i | \(-0.477259\pi\) | ||||
0.0713816 | + | 0.997449i | \(0.477259\pi\) | |||||||
\(648\) | −8.77388 | −0.344670 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.35319 | −0.0922999 | ||||||||
\(651\) | 0.370075 | 0.0145044 | ||||||||
\(652\) | −7.73571 | −0.302954 | ||||||||
\(653\) | −25.9076 | −1.01384 | −0.506921 | − | 0.861992i | \(-0.669217\pi\) | ||||
−0.506921 | + | 0.861992i | \(0.669217\pi\) | |||||||
\(654\) | 0.710090 | 0.0277667 | ||||||||
\(655\) | −46.6371 | −1.82226 | ||||||||
\(656\) | 8.37354 | 0.326932 | ||||||||
\(657\) | 5.12145 | 0.199807 | ||||||||
\(658\) | 2.65951 | 0.103679 | ||||||||
\(659\) | 22.9664 | 0.894644 | 0.447322 | − | 0.894373i | \(-0.352378\pi\) | ||||
0.447322 | + | 0.894373i | \(0.352378\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.4685 | 1.69073 | 0.845365 | − | 0.534189i | \(-0.179383\pi\) | ||||
0.845365 | + | 0.534189i | \(0.179383\pi\) | |||||||
\(662\) | −3.69222 | −0.143502 | ||||||||
\(663\) | −0.605002 | −0.0234963 | ||||||||
\(664\) | 6.49693 | 0.252130 | ||||||||
\(665\) | −4.15995 | −0.161316 | ||||||||
\(666\) | 26.5122 | 1.02733 | ||||||||
\(667\) | 0.581263 | 0.0225066 | ||||||||
\(668\) | −21.8284 | −0.844566 | ||||||||
\(669\) | −3.87899 | −0.149970 | ||||||||
\(670\) | 3.13849 | 0.121250 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.214602 | 0.00827845 | ||||||||
\(673\) | 29.2936 | 1.12918 | 0.564592 | − | 0.825370i | \(-0.309033\pi\) | ||||
0.564592 | + | 0.825370i | \(0.309033\pi\) | |||||||
\(674\) | 26.2983 | 1.01297 | ||||||||
\(675\) | −4.23683 | −0.163076 | ||||||||
\(676\) | −12.7225 | −0.489328 | ||||||||
\(677\) | 38.9988 | 1.49884 | 0.749422 | − | 0.662093i | \(-0.230331\pi\) | ||||
0.749422 | + | 0.662093i | \(0.230331\pi\) | |||||||
\(678\) | 1.99368 | 0.0765667 | ||||||||
\(679\) | 14.1176 | 0.541782 | ||||||||
\(680\) | 22.2643 | 0.853798 | ||||||||
\(681\) | 3.69087 | 0.141435 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.6716 | −0.523130 | −0.261565 | − | 0.965186i | \(-0.584239\pi\) | ||||
−0.261565 | + | 0.965186i | \(0.584239\pi\) | |||||||
\(684\) | −2.97480 | −0.113744 | ||||||||
\(685\) | −16.8011 | −0.641939 | ||||||||
\(686\) | −16.4566 | −0.628315 | ||||||||
\(687\) | −0.308515 | −0.0117706 | ||||||||
\(688\) | −6.30119 | −0.240231 | ||||||||
\(689\) | −1.16254 | −0.0442894 | ||||||||
\(690\) | −1.02165 | −0.0388936 | ||||||||
\(691\) | 8.06092 | 0.306652 | 0.153326 | − | 0.988176i | \(-0.451002\pi\) | ||||
0.153326 | + | 0.988176i | \(0.451002\pi\) | |||||||
\(692\) | 11.0102 | 0.418543 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.33343 | −0.202454 | ||||||||
\(695\) | 28.3982 | 1.07720 | ||||||||
\(696\) | −0.0441070 | −0.00167187 | ||||||||
\(697\) | −60.5903 | −2.29502 | ||||||||
\(698\) | 19.4450 | 0.736003 | ||||||||
\(699\) | −0.867082 | −0.0327961 | ||||||||
\(700\) | −6.03989 | −0.228287 | ||||||||
\(701\) | 11.0066 | 0.415713 | 0.207857 | − | 0.978159i | \(-0.433351\pi\) | ||||
0.207857 | + | 0.978159i | \(0.433351\pi\) | |||||||
\(702\) | 0.499558 | 0.0188546 | ||||||||
\(703\) | 8.91226 | 0.336132 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.960740 | 0.0361836 | ||||||||
\(706\) | 27.8728 | 1.04901 | ||||||||
\(707\) | 22.4531 | 0.844437 | ||||||||
\(708\) | 1.38460 | 0.0520364 | ||||||||
\(709\) | 3.81971 | 0.143452 | 0.0717260 | − | 0.997424i | \(-0.477149\pi\) | ||||
0.0717260 | + | 0.997424i | \(0.477149\pi\) | |||||||
\(710\) | 11.4272 | 0.428855 | ||||||||
\(711\) | 22.4129 | 0.840548 | ||||||||
\(712\) | 10.3518 | 0.387948 | ||||||||
\(713\) | −3.60729 | −0.135094 | ||||||||
\(714\) | −1.55284 | −0.0581137 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.5527 | −0.469116 | ||||||||
\(717\) | 2.56481 | 0.0957846 | ||||||||
\(718\) | 35.7338 | 1.33357 | ||||||||
\(719\) | 12.4943 | 0.465958 | 0.232979 | − | 0.972482i | \(-0.425153\pi\) | ||||
0.232979 | + | 0.972482i | \(0.425153\pi\) | |||||||
\(720\) | −9.15323 | −0.341121 | ||||||||
\(721\) | 8.52897 | 0.317635 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 2.84469 | 0.105795 | ||||||||
\(724\) | −3.45298 | −0.128329 | ||||||||
\(725\) | 1.24138 | 0.0461036 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.9023 | 0.812311 | 0.406155 | − | 0.913804i | \(-0.366869\pi\) | ||||
0.406155 | + | 0.913804i | \(0.366869\pi\) | |||||||
\(728\) | 0.712155 | 0.0263942 | ||||||||
\(729\) | −25.6490 | −0.949961 | ||||||||
\(730\) | 5.29725 | 0.196060 | ||||||||
\(731\) | 45.5950 | 1.68639 | ||||||||
\(732\) | −1.01383 | −0.0374722 | ||||||||
\(733\) | −27.3319 | −1.00953 | −0.504764 | − | 0.863257i | \(-0.668421\pi\) | ||||
−0.504764 | + | 0.863257i | \(0.668421\pi\) | |||||||
\(734\) | −37.8147 | −1.39577 | ||||||||
\(735\) | −2.52607 | −0.0931756 | ||||||||
\(736\) | −2.09183 | −0.0771057 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 24.9097 | 0.916937 | ||||||||
\(739\) | 6.87044 | 0.252733 | 0.126367 | − | 0.991984i | \(-0.459668\pi\) | ||||
0.126367 | + | 0.991984i | \(0.459668\pi\) | |||||||
\(740\) | 27.4223 | 1.00806 | ||||||||
\(741\) | 0.0836108 | 0.00307152 | ||||||||
\(742\) | −2.98387 | −0.109541 | ||||||||
\(743\) | 38.5332 | 1.41365 | 0.706824 | − | 0.707390i | \(-0.250127\pi\) | ||||
0.706824 | + | 0.707390i | \(0.250127\pi\) | |||||||
\(744\) | 0.273726 | 0.0100353 | ||||||||
\(745\) | 37.9390 | 1.38998 | ||||||||
\(746\) | −20.1806 | −0.738864 | ||||||||
\(747\) | 19.3271 | 0.707141 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.8461 | 0.652083 | ||||||||
\(750\) | 0.260114 | 0.00949803 | ||||||||
\(751\) | 19.0301 | 0.694418 | 0.347209 | − | 0.937788i | \(-0.387130\pi\) | ||||
0.347209 | + | 0.937788i | \(0.387130\pi\) | |||||||
\(752\) | 1.96711 | 0.0717332 | ||||||||
\(753\) | 4.27859 | 0.155920 | ||||||||
\(754\) | −0.146369 | −0.00533044 | ||||||||
\(755\) | −11.1833 | −0.407003 | ||||||||
\(756\) | 1.28221 | 0.0466333 | ||||||||
\(757\) | −42.0004 | −1.52653 | −0.763266 | − | 0.646084i | \(-0.776405\pi\) | ||||
−0.763266 | + | 0.646084i | \(0.776405\pi\) | |||||||
\(758\) | 32.7152 | 1.18827 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.07692 | −0.111612 | ||||||||
\(761\) | 21.9298 | 0.794955 | 0.397477 | − | 0.917612i | \(-0.369886\pi\) | ||||
0.397477 | + | 0.917612i | \(0.369886\pi\) | |||||||
\(762\) | −2.61241 | −0.0946378 | ||||||||
\(763\) | 6.04819 | 0.218959 | ||||||||
\(764\) | 21.3218 | 0.771397 | ||||||||
\(765\) | 66.2321 | 2.39463 | ||||||||
\(766\) | 25.6817 | 0.927917 | ||||||||
\(767\) | 4.59478 | 0.165908 | ||||||||
\(768\) | 0.158731 | 0.00572770 | ||||||||
\(769\) | 20.9969 | 0.757167 | 0.378584 | − | 0.925567i | \(-0.376411\pi\) | ||||
0.378584 | + | 0.925567i | \(0.376411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.52870 | −0.127083 | ||||||||
\(772\) | −23.4522 | −0.844063 | ||||||||
\(773\) | 38.3380 | 1.37892 | 0.689460 | − | 0.724323i | \(-0.257848\pi\) | ||||
0.689460 | + | 0.724323i | \(0.257848\pi\) | |||||||
\(774\) | −18.7448 | −0.673769 | ||||||||
\(775\) | −7.70392 | −0.276733 | ||||||||
\(776\) | 10.4421 | 0.374849 | ||||||||
\(777\) | −1.91259 | −0.0686138 | ||||||||
\(778\) | 4.46845 | 0.160202 | ||||||||
\(779\) | 8.37354 | 0.300013 | ||||||||
\(780\) | 0.257263 | 0.00921151 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 15.1363 | 0.541273 | ||||||||
\(783\) | −0.263531 | −0.00941783 | ||||||||
\(784\) | −5.17213 | −0.184719 | ||||||||
\(785\) | −2.68168 | −0.0957134 | ||||||||
\(786\) | 2.40589 | 0.0858154 | ||||||||
\(787\) | −3.85555 | −0.137435 | −0.0687177 | − | 0.997636i | \(-0.521891\pi\) | ||||
−0.0687177 | + | 0.997636i | \(0.521891\pi\) | |||||||
\(788\) | 7.79605 | 0.277723 | ||||||||
\(789\) | 0.133466 | 0.00475151 | ||||||||
\(790\) | 23.1822 | 0.824785 | ||||||||
\(791\) | 16.9811 | 0.603779 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.36438 | −0.119473 | ||||||||
\(794\) | −28.8810 | −1.02495 | ||||||||
\(795\) | −1.07791 | −0.0382297 | ||||||||
\(796\) | −9.48281 | −0.336109 | ||||||||
\(797\) | 7.72685 | 0.273699 | 0.136850 | − | 0.990592i | \(-0.456302\pi\) | ||||
0.136850 | + | 0.990592i | \(0.456302\pi\) | |||||||
\(798\) | 0.214602 | 0.00759683 | ||||||||
\(799\) | −14.2339 | −0.503558 | ||||||||
\(800\) | −4.46742 | −0.157947 | ||||||||
\(801\) | 30.7945 | 1.08807 | ||||||||
\(802\) | −0.797439 | −0.0281586 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.161907 | −0.00571002 | ||||||||
\(805\) | −8.70190 | −0.306702 | ||||||||
\(806\) | 0.908358 | 0.0319955 | ||||||||
\(807\) | 4.22669 | 0.148786 | ||||||||
\(808\) | 16.6075 | 0.584250 | ||||||||
\(809\) | 45.8483 | 1.61194 | 0.805970 | − | 0.591957i | \(-0.201644\pi\) | ||||
0.805970 | + | 0.591957i | \(0.201644\pi\) | |||||||
\(810\) | −26.9965 | −0.948560 | ||||||||
\(811\) | 11.9071 | 0.418115 | 0.209058 | − | 0.977903i | \(-0.432960\pi\) | ||||
0.209058 | + | 0.977903i | \(0.432960\pi\) | |||||||
\(812\) | −0.375681 | −0.0131838 | ||||||||
\(813\) | 4.02872 | 0.141293 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.8021 | −0.833753 | ||||||||
\(816\) | −1.14856 | −0.0402078 | ||||||||
\(817\) | −6.30119 | −0.220451 | ||||||||
\(818\) | 22.7240 | 0.794526 | ||||||||
\(819\) | 2.11852 | 0.0740271 | ||||||||
\(820\) | 25.7647 | 0.899742 | ||||||||
\(821\) | 25.0389 | 0.873865 | 0.436932 | − | 0.899494i | \(-0.356065\pi\) | ||||
0.436932 | + | 0.899494i | \(0.356065\pi\) | |||||||
\(822\) | 0.866730 | 0.0302307 | ||||||||
\(823\) | −4.14621 | −0.144528 | −0.0722639 | − | 0.997386i | \(-0.523022\pi\) | ||||
−0.0722639 | + | 0.997386i | \(0.523022\pi\) | |||||||
\(824\) | 6.30847 | 0.219766 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.7933 | 0.410342 | ||||||||
\(827\) | 47.6070 | 1.65546 | 0.827729 | − | 0.561127i | \(-0.189632\pi\) | ||||
0.827729 | + | 0.561127i | \(0.189632\pi\) | |||||||
\(828\) | −6.22277 | −0.216256 | ||||||||
\(829\) | 5.19254 | 0.180344 | 0.0901722 | − | 0.995926i | \(-0.471258\pi\) | ||||
0.0901722 | + | 0.995926i | \(0.471258\pi\) | |||||||
\(830\) | 19.9905 | 0.693881 | ||||||||
\(831\) | 4.79068 | 0.166187 | ||||||||
\(832\) | 0.526746 | 0.0182616 | ||||||||
\(833\) | 37.4251 | 1.29670 | ||||||||
\(834\) | −1.46499 | −0.0507286 | ||||||||
\(835\) | −67.1642 | −2.32431 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.63546 | 0.0565298 | ||||||||
\(838\) | 0.427754 | 0.0147765 | ||||||||
\(839\) | −43.4560 | −1.50027 | −0.750133 | − | 0.661287i | \(-0.770011\pi\) | ||||
−0.750133 | + | 0.661287i | \(0.770011\pi\) | |||||||
\(840\) | 0.660313 | 0.0227829 | ||||||||
\(841\) | −28.9228 | −0.997337 | ||||||||
\(842\) | 9.69726 | 0.334190 | ||||||||
\(843\) | −2.67094 | −0.0919922 | ||||||||
\(844\) | −15.5951 | −0.536805 | ||||||||
\(845\) | −39.1462 | −1.34667 | ||||||||
\(846\) | 5.85177 | 0.201188 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.20703 | −0.0757896 | ||||||||
\(849\) | 1.65719 | 0.0568748 | ||||||||
\(850\) | 32.3259 | 1.10877 | ||||||||
\(851\) | 18.6429 | 0.639071 | ||||||||
\(852\) | −0.589502 | −0.0201960 | ||||||||
\(853\) | 29.3178 | 1.00382 | 0.501911 | − | 0.864919i | \(-0.332631\pi\) | ||||
0.501911 | + | 0.864919i | \(0.332631\pi\) | |||||||
\(854\) | −8.63529 | −0.295493 | ||||||||
\(855\) | −9.15323 | −0.313034 | ||||||||
\(856\) | 13.1999 | 0.451163 | ||||||||
\(857\) | −3.67262 | −0.125454 | −0.0627272 | − | 0.998031i | \(-0.519980\pi\) | ||||
−0.0627272 | + | 0.998031i | \(0.519980\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.7758 | −0.674742 | −0.337371 | − | 0.941372i | \(-0.609538\pi\) | ||||
−0.337371 | + | 0.941372i | \(0.609538\pi\) | |||||||
\(860\) | −19.3882 | −0.661134 | ||||||||
\(861\) | −1.79698 | −0.0612409 | ||||||||
\(862\) | −6.70352 | −0.228323 | ||||||||
\(863\) | −33.2555 | −1.13203 | −0.566015 | − | 0.824395i | \(-0.691516\pi\) | ||||
−0.566015 | + | 0.824395i | \(0.691516\pi\) | |||||||
\(864\) | 0.948385 | 0.0322647 | ||||||||
\(865\) | 33.8773 | 1.15186 | ||||||||
\(866\) | 15.3773 | 0.522544 | ||||||||
\(867\) | 5.61250 | 0.190610 | ||||||||
\(868\) | 2.33146 | 0.0791350 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.135714 | −0.00460112 | ||||||||
\(871\) | −0.537287 | −0.0182053 | ||||||||
\(872\) | 4.47355 | 0.151494 | ||||||||
\(873\) | 31.0631 | 1.05133 | ||||||||
\(874\) | −2.09183 | −0.0707571 | ||||||||
\(875\) | 2.21552 | 0.0748984 | ||||||||
\(876\) | −0.273272 | −0.00923301 | ||||||||
\(877\) | 14.7200 | 0.497060 | 0.248530 | − | 0.968624i | \(-0.420052\pi\) | ||||
0.248530 | + | 0.968624i | \(0.420052\pi\) | |||||||
\(878\) | −2.15073 | −0.0725837 | ||||||||
\(879\) | −2.12734 | −0.0717534 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.16151 | −0.0728230 | −0.0364115 | − | 0.999337i | \(-0.511593\pi\) | ||||
−0.0364115 | + | 0.999337i | \(0.511593\pi\) | |||||||
\(882\) | −15.3861 | −0.518076 | ||||||||
\(883\) | −11.6171 | −0.390947 | −0.195473 | − | 0.980709i | \(-0.562624\pi\) | ||||
−0.195473 | + | 0.980709i | \(0.562624\pi\) | |||||||
\(884\) | −3.81150 | −0.128194 | ||||||||
\(885\) | 4.26030 | 0.143208 | ||||||||
\(886\) | −30.3841 | −1.02077 | ||||||||
\(887\) | −22.5487 | −0.757111 | −0.378555 | − | 0.925579i | \(-0.623579\pi\) | ||||
−0.378555 | + | 0.925579i | \(0.623579\pi\) | |||||||
\(888\) | −1.41465 | −0.0474725 | ||||||||
\(889\) | −22.2512 | −0.746282 | ||||||||
\(890\) | 31.8515 | 1.06766 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.4375 | −0.818230 | ||||||||
\(893\) | 1.96711 | 0.0658269 | ||||||||
\(894\) | −1.95718 | −0.0654580 | ||||||||
\(895\) | −38.6236 | −1.29104 | ||||||||
\(896\) | 1.35199 | 0.0451668 | ||||||||
\(897\) | 0.174899 | 0.00583971 | ||||||||
\(898\) | −3.34155 | −0.111509 | ||||||||
\(899\) | −0.479184 | −0.0159817 | ||||||||
\(900\) | −13.2897 | −0.442990 | ||||||||
\(901\) | 15.9699 | 0.532034 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.35225 | 0.0450000 | ||||||||
\(904\) | 12.5601 | 0.417743 | ||||||||
\(905\) | −10.6245 | −0.353171 | ||||||||
\(906\) | 0.576921 | 0.0191669 | ||||||||
\(907\) | 18.3913 | 0.610672 | 0.305336 | − | 0.952245i | \(-0.401231\pi\) | ||||
0.305336 | + | 0.952245i | \(0.401231\pi\) | |||||||
\(908\) | 23.2524 | 0.771659 | ||||||||
\(909\) | 49.4041 | 1.63863 | ||||||||
\(910\) | 2.19124 | 0.0726389 | ||||||||
\(911\) | 47.2453 | 1.56531 | 0.782654 | − | 0.622458i | \(-0.213866\pi\) | ||||
0.782654 | + | 0.622458i | \(0.213866\pi\) | |||||||
\(912\) | 0.158731 | 0.00525610 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 29.3880 | 0.972068 | ||||||||
\(915\) | −3.11947 | −0.103126 | ||||||||
\(916\) | −1.94364 | −0.0642197 | ||||||||
\(917\) | 20.4922 | 0.676712 | ||||||||
\(918\) | −6.86244 | −0.226494 | ||||||||
\(919\) | 9.79492 | 0.323105 | 0.161552 | − | 0.986864i | \(-0.448350\pi\) | ||||
0.161552 | + | 0.986864i | \(0.448350\pi\) | |||||||
\(920\) | −6.43637 | −0.212201 | ||||||||
\(921\) | 3.01271 | 0.0992721 | ||||||||
\(922\) | −1.74308 | −0.0574053 | ||||||||
\(923\) | −1.95626 | −0.0643910 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.8148 | 1.30910 | ||||||||
\(926\) | 31.2015 | 1.02535 | ||||||||
\(927\) | 18.7665 | 0.616371 | ||||||||
\(928\) | −0.277873 | −0.00912164 | ||||||||
\(929\) | 22.9921 | 0.754346 | 0.377173 | − | 0.926143i | \(-0.376896\pi\) | ||||
0.377173 | + | 0.926143i | \(0.376896\pi\) | |||||||
\(930\) | 0.842233 | 0.0276179 | ||||||||
\(931\) | −5.17213 | −0.169510 | ||||||||
\(932\) | −5.46260 | −0.178933 | ||||||||
\(933\) | 1.98027 | 0.0648311 | ||||||||
\(934\) | −26.0733 | −0.853144 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.56697 | 0.0512179 | ||||||||
\(937\) | −36.6455 | −1.19716 | −0.598578 | − | 0.801065i | \(-0.704267\pi\) | ||||
−0.598578 | + | 0.801065i | \(0.704267\pi\) | |||||||
\(938\) | −1.37904 | −0.0450274 | ||||||||
\(939\) | −2.90067 | −0.0946599 | ||||||||
\(940\) | 6.05264 | 0.197415 | ||||||||
\(941\) | 14.2908 | 0.465868 | 0.232934 | − | 0.972493i | \(-0.425167\pi\) | ||||
0.232934 | + | 0.972493i | \(0.425167\pi\) | |||||||
\(942\) | 0.138342 | 0.00450741 | ||||||||
\(943\) | 17.5160 | 0.570399 | ||||||||
\(944\) | 8.72295 | 0.283908 | ||||||||
\(945\) | 3.94524 | 0.128339 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.0452 | 1.59375 | 0.796877 | − | 0.604142i | \(-0.206484\pi\) | ||||
0.796877 | + | 0.604142i | \(0.206484\pi\) | |||||||
\(948\) | −1.19591 | −0.0388414 | ||||||||
\(949\) | −0.906851 | −0.0294376 | ||||||||
\(950\) | −4.46742 | −0.144942 | ||||||||
\(951\) | −2.09255 | −0.0678556 | ||||||||
\(952\) | −9.78288 | −0.317065 | ||||||||
\(953\) | 9.95579 | 0.322500 | 0.161250 | − | 0.986914i | \(-0.448447\pi\) | ||||
0.161250 | + | 0.986914i | \(0.448447\pi\) | |||||||
\(954\) | −6.56547 | −0.212565 | ||||||||
\(955\) | 65.6055 | 2.12294 | ||||||||
\(956\) | 16.1582 | 0.522595 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −29.3946 | −0.949695 | ||||||||
\(959\) | 7.38237 | 0.238389 | ||||||||
\(960\) | 0.488401 | 0.0157631 | ||||||||
\(961\) | −28.0262 | −0.904071 | ||||||||
\(962\) | −4.69450 | −0.151357 | ||||||||
\(963\) | 39.2671 | 1.26537 | ||||||||
\(964\) | 17.9215 | 0.577212 | ||||||||
\(965\) | −72.1605 | −2.32293 | ||||||||
\(966\) | 0.448910 | 0.0144434 | ||||||||
\(967\) | 12.0203 | 0.386546 | 0.193273 | − | 0.981145i | \(-0.438090\pi\) | ||||
0.193273 | + | 0.981145i | \(0.438090\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.14856 | −0.0368972 | ||||||||
\(970\) | 32.1294 | 1.03161 | ||||||||
\(971\) | 51.9013 | 1.66559 | 0.832796 | − | 0.553580i | \(-0.186739\pi\) | ||||
0.832796 | + | 0.553580i | \(0.186739\pi\) | |||||||
\(972\) | 4.23784 | 0.135929 | ||||||||
\(973\) | −12.4781 | −0.400029 | ||||||||
\(974\) | −43.0919 | −1.38075 | ||||||||
\(975\) | 0.373524 | 0.0119624 | ||||||||
\(976\) | −6.38710 | −0.204446 | ||||||||
\(977\) | −28.7379 | −0.919407 | −0.459703 | − | 0.888073i | \(-0.652044\pi\) | ||||
−0.459703 | + | 0.888073i | \(0.652044\pi\) | |||||||
\(978\) | 1.22790 | 0.0392638 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −15.9142 | −0.508361 | ||||||||
\(981\) | 13.3079 | 0.424890 | ||||||||
\(982\) | −29.5401 | −0.942662 | ||||||||
\(983\) | 36.7856 | 1.17328 | 0.586639 | − | 0.809849i | \(-0.300451\pi\) | ||||
0.586639 | + | 0.809849i | \(0.300451\pi\) | |||||||
\(984\) | −1.32914 | −0.0423714 | ||||||||
\(985\) | 23.9878 | 0.764315 | ||||||||
\(986\) | 2.01067 | 0.0640328 | ||||||||
\(987\) | −0.422146 | −0.0134371 | ||||||||
\(988\) | 0.526746 | 0.0167580 | ||||||||
\(989\) | −13.1810 | −0.419131 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.5095 | −1.89038 | −0.945191 | − | 0.326517i | \(-0.894125\pi\) | ||||
−0.945191 | + | 0.326517i | \(0.894125\pi\) | |||||||
\(992\) | 1.72447 | 0.0547519 | ||||||||
\(993\) | 0.586069 | 0.0185983 | ||||||||
\(994\) | −5.02108 | −0.159259 | ||||||||
\(995\) | −29.1778 | −0.924999 | ||||||||
\(996\) | −1.03126 | −0.0326768 | ||||||||
\(997\) | 27.5241 | 0.871697 | 0.435848 | − | 0.900020i | \(-0.356448\pi\) | ||||
0.435848 | + | 0.900020i | \(0.356448\pi\) | |||||||
\(998\) | 27.8915 | 0.882889 | ||||||||
\(999\) | −8.45226 | −0.267418 |
(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 | 4598.2.a.bx.1.4 | 8 | ||
11.7 | odd | 10 | 418.2.f.f.115.3 | ✓ | 16 | ||
11.8 | odd | 10 | 418.2.f.f.229.3 | yes | 16 | ||
11.10 | odd | 2 | 4598.2.a.ca.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.f.f.115.3 | ✓ | 16 | 11.7 | odd | 10 | ||
418.2.f.f.229.3 | yes | 16 | 11.8 | odd | 10 | ||
4598.2.a.bx.1.4 | 8 | 1.1 | even | 1 | trivial | ||
4598.2.a.ca.1.4 | 8 | 11.10 | odd | 2 |