Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,2,Mod(1,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, 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("810.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.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: | \(6.46788256372\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.73205 | 1.41058 | 0.705291 | − | 0.708918i | \(-0.250816\pi\) | ||||
0.705291 | + | 0.708918i | \(0.250816\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.73205 | 1.03508 | 0.517542 | − | 0.855658i | \(-0.326847\pi\) | ||||
0.517542 | + | 0.855658i | \(0.326847\pi\) | |||||||
\(14\) | −3.73205 | −0.997433 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.92820 | −1.81885 | −0.909427 | − | 0.415863i | \(-0.863480\pi\) | ||||
−0.909427 | + | 0.415863i | \(0.863480\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.46410 | −0.738549 | ||||||||
\(23\) | −0.464102 | −0.0967719 | −0.0483859 | − | 0.998829i | \(-0.515408\pi\) | ||||
−0.0483859 | + | 0.998829i | \(0.515408\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.73205 | −0.731915 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.73205 | 0.705291 | ||||||||
\(29\) | 6.92820 | 1.28654 | 0.643268 | − | 0.765641i | \(-0.277578\pi\) | ||||
0.643268 | + | 0.765641i | \(0.277578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.46410 | 0.981382 | 0.490691 | − | 0.871334i | \(-0.336744\pi\) | ||||
0.490691 | + | 0.871334i | \(0.336744\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.46410 | 0.594089 | ||||||||
\(35\) | −3.73205 | −0.630832 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | 7.92820 | 1.28612 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −5.19615 | −0.811503 | −0.405751 | − | 0.913984i | \(-0.632990\pi\) | ||||
−0.405751 | + | 0.913984i | \(0.632990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.46410 | −0.223273 | −0.111637 | − | 0.993749i | \(-0.535609\pi\) | ||||
−0.111637 | + | 0.993749i | \(0.535609\pi\) | |||||||
\(44\) | 3.46410 | 0.522233 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.464102 | 0.0684280 | ||||||||
\(47\) | 6.46410 | 0.942886 | 0.471443 | − | 0.881897i | \(-0.343733\pi\) | ||||
0.471443 | + | 0.881897i | \(0.343733\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.73205 | 0.517542 | ||||||||
\(53\) | 12.4641 | 1.71208 | 0.856038 | − | 0.516913i | \(-0.172919\pi\) | ||||
0.856038 | + | 0.516913i | \(0.172919\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | −0.467099 | ||||||||
\(56\) | −3.73205 | −0.498716 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.92820 | −0.909718 | ||||||||
\(59\) | −8.66025 | −1.12747 | −0.563735 | − | 0.825956i | \(-0.690636\pi\) | ||||
−0.563735 | + | 0.825956i | \(0.690636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.39230 | −1.07452 | −0.537262 | − | 0.843415i | \(-0.680541\pi\) | ||||
−0.537262 | + | 0.843415i | \(0.680541\pi\) | |||||||
\(62\) | −5.46410 | −0.693942 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.73205 | −0.462904 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | −3.46410 | −0.420084 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.73205 | 0.446065 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.39230 | 0.748163 | 0.374081 | − | 0.927396i | \(-0.377958\pi\) | ||||
0.374081 | + | 0.927396i | \(0.377958\pi\) | |||||||
\(74\) | −8.00000 | −0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.92820 | −0.909427 | ||||||||
\(77\) | 12.9282 | 1.47331 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.39230 | 0.719190 | 0.359595 | − | 0.933108i | \(-0.382915\pi\) | ||||
0.359595 | + | 0.933108i | \(0.382915\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.19615 | 0.573819 | ||||||||
\(83\) | 8.53590 | 0.936937 | 0.468468 | − | 0.883480i | \(-0.344806\pi\) | ||||
0.468468 | + | 0.883480i | \(0.344806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410 | 0.375735 | ||||||||
\(86\) | 1.46410 | 0.157878 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.46410 | −0.369274 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9282 | 1.46007 | ||||||||
\(92\) | −0.464102 | −0.0483859 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.46410 | −0.666721 | ||||||||
\(95\) | 7.92820 | 0.813416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.07180 | 0.108824 | 0.0544122 | − | 0.998519i | \(-0.482671\pi\) | ||||
0.0544122 | + | 0.998519i | \(0.482671\pi\) | |||||||
\(98\) | −6.92820 | −0.699854 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.46410 | 0.941713 | 0.470857 | − | 0.882210i | \(-0.343945\pi\) | ||||
0.470857 | + | 0.882210i | \(0.343945\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.1962 | −1.49732 | −0.748661 | − | 0.662953i | \(-0.769303\pi\) | ||||
−0.748661 | + | 0.662953i | \(0.769303\pi\) | |||||||
\(104\) | −3.73205 | −0.365958 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.4641 | −1.21062 | ||||||||
\(107\) | 8.53590 | 0.825196 | 0.412598 | − | 0.910913i | \(-0.364621\pi\) | ||||
0.412598 | + | 0.910913i | \(0.364621\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.8564 | −1.71033 | −0.855167 | − | 0.518353i | \(-0.826545\pi\) | ||||
−0.855167 | + | 0.518353i | \(0.826545\pi\) | |||||||
\(110\) | 3.46410 | 0.330289 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.73205 | 0.352646 | ||||||||
\(113\) | 12.9282 | 1.21618 | 0.608092 | − | 0.793867i | \(-0.291935\pi\) | ||||
0.608092 | + | 0.793867i | \(0.291935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.464102 | 0.0432777 | ||||||||
\(116\) | 6.92820 | 0.643268 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.66025 | 0.797241 | ||||||||
\(119\) | −12.9282 | −1.18513 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.39230 | 0.759804 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.46410 | 0.490691 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.1962 | −1.34844 | −0.674220 | − | 0.738530i | \(-0.735520\pi\) | ||||
−0.674220 | + | 0.738530i | \(0.735520\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.73205 | 0.327323 | ||||||||
\(131\) | 13.7321 | 1.19977 | 0.599887 | − | 0.800084i | \(-0.295212\pi\) | ||||
0.599887 | + | 0.800084i | \(0.295212\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −29.5885 | −2.56564 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | 0.297044 | ||||||||
\(137\) | −10.3923 | −0.887875 | −0.443937 | − | 0.896058i | \(-0.646419\pi\) | ||||
−0.443937 | + | 0.896058i | \(0.646419\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0000 | −1.10265 | −0.551323 | − | 0.834292i | \(-0.685877\pi\) | ||||
−0.551323 | + | 0.834292i | \(0.685877\pi\) | |||||||
\(140\) | −3.73205 | −0.315416 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 12.9282 | 1.08111 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.92820 | −0.575356 | ||||||||
\(146\) | −6.39230 | −0.529031 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3923 | 1.49674 | 0.748372 | − | 0.663279i | \(-0.230836\pi\) | ||||
0.748372 | + | 0.663279i | \(0.230836\pi\) | |||||||
\(152\) | 7.92820 | 0.643062 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.9282 | −1.04178 | ||||||||
\(155\) | −5.46410 | −0.438887 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.1244 | 1.12725 | 0.563623 | − | 0.826032i | \(-0.309407\pi\) | ||||
0.563623 | + | 0.826032i | \(0.309407\pi\) | |||||||
\(158\) | −6.39230 | −0.508544 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −1.73205 | −0.136505 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.85641 | 0.772013 | 0.386007 | − | 0.922496i | \(-0.373854\pi\) | ||||
0.386007 | + | 0.922496i | \(0.373854\pi\) | |||||||
\(164\) | −5.19615 | −0.405751 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.53590 | −0.662514 | ||||||||
\(167\) | 6.92820 | 0.536120 | 0.268060 | − | 0.963402i | \(-0.413617\pi\) | ||||
0.268060 | + | 0.963402i | \(0.413617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.928203 | 0.0714002 | ||||||||
\(170\) | −3.46410 | −0.265684 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.46410 | −0.111637 | ||||||||
\(173\) | −20.3205 | −1.54494 | −0.772470 | − | 0.635051i | \(-0.780979\pi\) | ||||
−0.772470 | + | 0.635051i | \(0.780979\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.73205 | 0.282117 | ||||||||
\(176\) | 3.46410 | 0.261116 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.0000 | 0.899438 | ||||||||
\(179\) | 12.1244 | 0.906217 | 0.453108 | − | 0.891455i | \(-0.350315\pi\) | ||||
0.453108 | + | 0.891455i | \(0.350315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.5359 | −0.931786 | −0.465893 | − | 0.884841i | \(-0.654267\pi\) | ||||
−0.465893 | + | 0.884841i | \(0.654267\pi\) | |||||||
\(182\) | −13.9282 | −1.03243 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.464102 | 0.0342140 | ||||||||
\(185\) | −8.00000 | −0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | 6.46410 | 0.471443 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.92820 | −0.575172 | ||||||||
\(191\) | 2.53590 | 0.183491 | 0.0917456 | − | 0.995782i | \(-0.470755\pi\) | ||||
0.0917456 | + | 0.995782i | \(0.470755\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.0000 | −1.15171 | −0.575853 | − | 0.817554i | \(-0.695330\pi\) | ||||
−0.575853 | + | 0.817554i | \(0.695330\pi\) | |||||||
\(194\) | −1.07180 | −0.0769505 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.92820 | 0.494872 | ||||||||
\(197\) | −11.5359 | −0.821899 | −0.410949 | − | 0.911658i | \(-0.634803\pi\) | ||||
−0.410949 | + | 0.911658i | \(0.634803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.2487 | −1.57717 | −0.788585 | − | 0.614926i | \(-0.789186\pi\) | ||||
−0.788585 | + | 0.614926i | \(0.789186\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.46410 | −0.665892 | ||||||||
\(203\) | 25.8564 | 1.81476 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.19615 | 0.362915 | ||||||||
\(206\) | 15.1962 | 1.05877 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.73205 | 0.258771 | ||||||||
\(209\) | −27.4641 | −1.89973 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.85641 | −0.609700 | −0.304850 | − | 0.952400i | \(-0.598606\pi\) | ||||
−0.304850 | + | 0.952400i | \(0.598606\pi\) | |||||||
\(212\) | 12.4641 | 0.856038 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.53590 | −0.583502 | ||||||||
\(215\) | 1.46410 | 0.0998509 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.3923 | 1.38432 | ||||||||
\(218\) | 17.8564 | 1.20939 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.46410 | −0.233550 | ||||||||
\(221\) | −12.9282 | −0.869645 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5359 | −0.839466 | −0.419733 | − | 0.907648i | \(-0.637876\pi\) | ||||
−0.419733 | + | 0.907648i | \(0.637876\pi\) | |||||||
\(224\) | −3.73205 | −0.249358 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.9282 | −0.859971 | ||||||||
\(227\) | 16.3923 | 1.08800 | 0.543998 | − | 0.839087i | \(-0.316910\pi\) | ||||
0.543998 | + | 0.839087i | \(0.316910\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.8564 | 1.44431 | 0.722156 | − | 0.691730i | \(-0.243151\pi\) | ||||
0.722156 | + | 0.691730i | \(0.243151\pi\) | |||||||
\(230\) | −0.464102 | −0.0306020 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.92820 | −0.454859 | ||||||||
\(233\) | −12.0000 | −0.786146 | −0.393073 | − | 0.919507i | \(-0.628588\pi\) | ||||
−0.393073 | + | 0.919507i | \(0.628588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.46410 | −0.421671 | ||||||||
\(236\) | −8.66025 | −0.563735 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.9282 | 0.838011 | ||||||||
\(239\) | −8.53590 | −0.552141 | −0.276071 | − | 0.961137i | \(-0.589032\pi\) | ||||
−0.276071 | + | 0.961137i | \(0.589032\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.9282 | −1.09044 | −0.545221 | − | 0.838293i | \(-0.683554\pi\) | ||||
−0.545221 | + | 0.838293i | \(0.683554\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.39230 | −0.537262 | ||||||||
\(245\) | −6.92820 | −0.442627 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.5885 | −1.88267 | ||||||||
\(248\) | −5.46410 | −0.346971 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −12.1244 | −0.765283 | −0.382641 | − | 0.923897i | \(-0.624985\pi\) | ||||
−0.382641 | + | 0.923897i | \(0.624985\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.60770 | −0.101075 | ||||||||
\(254\) | 15.1962 | 0.953491 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −31.8564 | −1.98715 | −0.993574 | − | 0.113184i | \(-0.963895\pi\) | ||||
−0.993574 | + | 0.113184i | \(0.963895\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.8564 | 1.85519 | ||||||||
\(260\) | −3.73205 | −0.231452 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.7321 | −0.848369 | ||||||||
\(263\) | −8.32051 | −0.513065 | −0.256532 | − | 0.966536i | \(-0.582580\pi\) | ||||
−0.256532 | + | 0.966536i | \(0.582580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.4641 | −0.765664 | ||||||||
\(266\) | 29.5885 | 1.81418 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000 | 0.488678 | ||||||||
\(269\) | −12.9282 | −0.788246 | −0.394123 | − | 0.919058i | \(-0.628952\pi\) | ||||
−0.394123 | + | 0.919058i | \(0.628952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0000 | 0.850439 | 0.425220 | − | 0.905090i | \(-0.360197\pi\) | ||||
0.425220 | + | 0.905090i | \(0.360197\pi\) | |||||||
\(272\) | −3.46410 | −0.210042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.3923 | 0.627822 | ||||||||
\(275\) | 3.46410 | 0.208893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.2679 | 0.737110 | 0.368555 | − | 0.929606i | \(-0.379853\pi\) | ||||
0.368555 | + | 0.929606i | \(0.379853\pi\) | |||||||
\(278\) | 13.0000 | 0.779688 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.73205 | 0.223033 | ||||||||
\(281\) | 7.05256 | 0.420720 | 0.210360 | − | 0.977624i | \(-0.432536\pi\) | ||||
0.210360 | + | 0.977624i | \(0.432536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.32051 | −0.197384 | −0.0986919 | − | 0.995118i | \(-0.531466\pi\) | ||||
−0.0986919 | + | 0.995118i | \(0.531466\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.9282 | −0.764461 | ||||||||
\(287\) | −19.3923 | −1.14469 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 6.92820 | 0.406838 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.39230 | 0.374081 | ||||||||
\(293\) | 7.39230 | 0.431863 | 0.215932 | − | 0.976409i | \(-0.430721\pi\) | ||||
0.215932 | + | 0.976409i | \(0.430721\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.66025 | 0.504219 | ||||||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.0000 | 1.04271 | ||||||||
\(299\) | −1.73205 | −0.100167 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.46410 | −0.314946 | ||||||||
\(302\) | −18.3923 | −1.05836 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.92820 | −0.454714 | ||||||||
\(305\) | 8.39230 | 0.480542 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3923 | 0.707266 | 0.353633 | − | 0.935384i | \(-0.384946\pi\) | ||||
0.353633 | + | 0.935384i | \(0.384946\pi\) | |||||||
\(308\) | 12.9282 | 0.736653 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.46410 | 0.310340 | ||||||||
\(311\) | 8.53590 | 0.484026 | 0.242013 | − | 0.970273i | \(-0.422192\pi\) | ||||
0.242013 | + | 0.970273i | \(0.422192\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.32051 | −0.187686 | −0.0938431 | − | 0.995587i | \(-0.529915\pi\) | ||||
−0.0938431 | + | 0.995587i | \(0.529915\pi\) | |||||||
\(314\) | −14.1244 | −0.797084 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.39230 | 0.359595 | ||||||||
\(317\) | −17.5359 | −0.984914 | −0.492457 | − | 0.870337i | \(-0.663901\pi\) | ||||
−0.492457 | + | 0.870337i | \(0.663901\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0000 | 1.34374 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.73205 | 0.0965234 | ||||||||
\(323\) | 27.4641 | 1.52814 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.73205 | 0.207017 | ||||||||
\(326\) | −9.85641 | −0.545896 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.19615 | 0.286910 | ||||||||
\(329\) | 24.1244 | 1.33002 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 8.53590 | 0.468468 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.92820 | −0.379094 | ||||||||
\(335\) | −8.00000 | −0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.07180 | 0.385225 | 0.192613 | − | 0.981275i | \(-0.438304\pi\) | ||||
0.192613 | + | 0.981275i | \(0.438304\pi\) | |||||||
\(338\) | −0.928203 | −0.0504876 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.46410 | 0.187867 | ||||||||
\(341\) | 18.9282 | 1.02502 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.267949 | −0.0144679 | ||||||||
\(344\) | 1.46410 | 0.0789391 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.3205 | 1.09244 | ||||||||
\(347\) | −14.7846 | −0.793679 | −0.396840 | − | 0.917888i | \(-0.629893\pi\) | ||||
−0.396840 | + | 0.917888i | \(0.629893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | −3.73205 | −0.199487 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.46410 | −0.184637 | ||||||||
\(353\) | 22.3923 | 1.19182 | 0.595911 | − | 0.803050i | \(-0.296791\pi\) | ||||
0.595911 | + | 0.803050i | \(0.296791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.00000 | −0.318447 | ||||||||
\(356\) | −12.0000 | −0.635999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.1244 | −0.640792 | ||||||||
\(359\) | −8.53590 | −0.450507 | −0.225254 | − | 0.974300i | \(-0.572321\pi\) | ||||
−0.225254 | + | 0.974300i | \(0.572321\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.8564 | 2.30823 | ||||||||
\(362\) | 12.5359 | 0.658872 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 13.9282 | 0.730036 | ||||||||
\(365\) | −6.39230 | −0.334589 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.39230 | 0.333676 | 0.166838 | − | 0.985984i | \(-0.446644\pi\) | ||||
0.166838 | + | 0.985984i | \(0.446644\pi\) | |||||||
\(368\) | −0.464102 | −0.0241930 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.00000 | 0.415900 | ||||||||
\(371\) | 46.5167 | 2.41502 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.9282 | −0.565841 | −0.282920 | − | 0.959143i | \(-0.591303\pi\) | ||||
−0.282920 | + | 0.959143i | \(0.591303\pi\) | |||||||
\(374\) | 12.0000 | 0.620505 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.46410 | −0.333361 | ||||||||
\(377\) | 25.8564 | 1.33167 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.8564 | 1.89319 | 0.946593 | − | 0.322430i | \(-0.104500\pi\) | ||||
0.946593 | + | 0.322430i | \(0.104500\pi\) | |||||||
\(380\) | 7.92820 | 0.406708 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.53590 | −0.129748 | ||||||||
\(383\) | −6.46410 | −0.330300 | −0.165150 | − | 0.986268i | \(-0.552811\pi\) | ||||
−0.165150 | + | 0.986268i | \(0.552811\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.9282 | −0.658882 | ||||||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.07180 | 0.0544122 | ||||||||
\(389\) | 23.3205 | 1.18240 | 0.591198 | − | 0.806526i | \(-0.298655\pi\) | ||||
0.591198 | + | 0.806526i | \(0.298655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.60770 | 0.0813046 | ||||||||
\(392\) | −6.92820 | −0.349927 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.5359 | 0.581170 | ||||||||
\(395\) | −6.39230 | −0.321632 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.85641 | 0.494679 | 0.247339 | − | 0.968929i | \(-0.420444\pi\) | ||||
0.247339 | + | 0.968929i | \(0.420444\pi\) | |||||||
\(398\) | 22.2487 | 1.11523 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −39.5885 | −1.97695 | −0.988477 | − | 0.151374i | \(-0.951630\pi\) | ||||
−0.988477 | + | 0.151374i | \(0.951630\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.3923 | 1.01581 | ||||||||
\(404\) | 9.46410 | 0.470857 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −25.8564 | −1.28323 | ||||||||
\(407\) | 27.7128 | 1.37367 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.9282 | −0.688705 | −0.344353 | − | 0.938840i | \(-0.611902\pi\) | ||||
−0.344353 | + | 0.938840i | \(0.611902\pi\) | |||||||
\(410\) | −5.19615 | −0.256620 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.1962 | −0.748661 | ||||||||
\(413\) | −32.3205 | −1.59039 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.53590 | −0.419011 | ||||||||
\(416\) | −3.73205 | −0.182979 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 27.4641 | 1.34331 | ||||||||
\(419\) | −3.46410 | −0.169232 | −0.0846162 | − | 0.996414i | \(-0.526966\pi\) | ||||
−0.0846162 | + | 0.996414i | \(0.526966\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.60770 | 0.468250 | 0.234125 | − | 0.972206i | \(-0.424777\pi\) | ||||
0.234125 | + | 0.972206i | \(0.424777\pi\) | |||||||
\(422\) | 8.85641 | 0.431123 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.4641 | −0.605310 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.3205 | −1.51571 | ||||||||
\(428\) | 8.53590 | 0.412598 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.46410 | −0.0706052 | ||||||||
\(431\) | −28.3923 | −1.36761 | −0.683805 | − | 0.729665i | \(-0.739676\pi\) | ||||
−0.683805 | + | 0.729665i | \(0.739676\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.92820 | 0.140720 | 0.0703602 | − | 0.997522i | \(-0.477585\pi\) | ||||
0.0703602 | + | 0.997522i | \(0.477585\pi\) | |||||||
\(434\) | −20.3923 | −0.978862 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.8564 | −0.855167 | ||||||||
\(437\) | 3.67949 | 0.176014 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.3923 | 0.877817 | 0.438908 | − | 0.898532i | \(-0.355365\pi\) | ||||
0.438908 | + | 0.898532i | \(0.355365\pi\) | |||||||
\(440\) | 3.46410 | 0.165145 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.9282 | 0.614932 | ||||||||
\(443\) | −31.8564 | −1.51354 | −0.756772 | − | 0.653679i | \(-0.773225\pi\) | ||||
−0.756772 | + | 0.653679i | \(0.773225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.0000 | 0.568855 | ||||||||
\(446\) | 12.5359 | 0.593592 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.73205 | 0.176323 | ||||||||
\(449\) | −32.9090 | −1.55307 | −0.776535 | − | 0.630074i | \(-0.783025\pi\) | ||||
−0.776535 | + | 0.630074i | \(0.783025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | 12.9282 | 0.608092 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.3923 | −0.769329 | ||||||||
\(455\) | −13.9282 | −0.652964 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.3923 | −0.953912 | −0.476956 | − | 0.878927i | \(-0.658260\pi\) | ||||
−0.476956 | + | 0.878927i | \(0.658260\pi\) | |||||||
\(458\) | −21.8564 | −1.02128 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.464102 | 0.0216388 | ||||||||
\(461\) | 8.78461 | 0.409140 | 0.204570 | − | 0.978852i | \(-0.434420\pi\) | ||||
0.204570 | + | 0.978852i | \(0.434420\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.80385 | −0.223254 | −0.111627 | − | 0.993750i | \(-0.535606\pi\) | ||||
−0.111627 | + | 0.993750i | \(0.535606\pi\) | |||||||
\(464\) | 6.92820 | 0.321634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0000 | 0.555889 | ||||||||
\(467\) | 6.00000 | 0.277647 | 0.138823 | − | 0.990317i | \(-0.455668\pi\) | ||||
0.138823 | + | 0.990317i | \(0.455668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.8564 | 1.37864 | ||||||||
\(470\) | 6.46410 | 0.298167 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.66025 | 0.398621 | ||||||||
\(473\) | −5.07180 | −0.233201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.92820 | −0.363771 | ||||||||
\(476\) | −12.9282 | −0.592563 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.53590 | 0.390423 | ||||||||
\(479\) | 12.9282 | 0.590705 | 0.295352 | − | 0.955388i | \(-0.404563\pi\) | ||||
0.295352 | + | 0.955388i | \(0.404563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.8564 | 1.36133 | ||||||||
\(482\) | 16.9282 | 0.771059 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −1.07180 | −0.0486678 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.4449 | −1.24365 | −0.621823 | − | 0.783158i | \(-0.713608\pi\) | ||||
−0.621823 | + | 0.783158i | \(0.713608\pi\) | |||||||
\(488\) | 8.39230 | 0.379902 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.92820 | 0.312984 | ||||||||
\(491\) | −12.1244 | −0.547165 | −0.273582 | − | 0.961849i | \(-0.588209\pi\) | ||||
−0.273582 | + | 0.961849i | \(0.588209\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.0000 | −1.08091 | ||||||||
\(494\) | 29.5885 | 1.33125 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.46410 | 0.245345 | ||||||||
\(497\) | 22.3923 | 1.00443 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.78461 | −0.169422 | −0.0847112 | − | 0.996406i | \(-0.526997\pi\) | ||||
−0.0847112 | + | 0.996406i | \(0.526997\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.1244 | 0.541136 | ||||||||
\(503\) | −5.07180 | −0.226140 | −0.113070 | − | 0.993587i | \(-0.536068\pi\) | ||||
−0.113070 | + | 0.993587i | \(0.536068\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.46410 | −0.421147 | ||||||||
\(506\) | 1.60770 | 0.0714708 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.1962 | −0.674220 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.8564 | 1.05535 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 31.8564 | 1.40513 | ||||||||
\(515\) | 15.1962 | 0.669622 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.3923 | 0.984812 | ||||||||
\(518\) | −29.8564 | −1.31182 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.73205 | 0.163661 | ||||||||
\(521\) | −17.1962 | −0.753377 | −0.376689 | − | 0.926340i | \(-0.622937\pi\) | ||||
−0.376689 | + | 0.926340i | \(0.622937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.00000 | 0.0874539 | 0.0437269 | − | 0.999044i | \(-0.486077\pi\) | ||||
0.0437269 | + | 0.999044i | \(0.486077\pi\) | |||||||
\(524\) | 13.7321 | 0.599887 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.32051 | 0.362791 | ||||||||
\(527\) | −18.9282 | −0.824525 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7846 | −0.990635 | ||||||||
\(530\) | 12.4641 | 0.541406 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −29.5885 | −1.28282 | ||||||||
\(533\) | −19.3923 | −0.839974 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.53590 | −0.369039 | ||||||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 12.9282 | 0.557374 | ||||||||
\(539\) | 24.0000 | 1.03375 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.9282 | 1.15773 | 0.578867 | − | 0.815422i | \(-0.303495\pi\) | ||||
0.578867 | + | 0.815422i | \(0.303495\pi\) | |||||||
\(542\) | −14.0000 | −0.601351 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.46410 | 0.148522 | ||||||||
\(545\) | 17.8564 | 0.764884 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.3923 | 0.529857 | 0.264928 | − | 0.964268i | \(-0.414652\pi\) | ||||
0.264928 | + | 0.964268i | \(0.414652\pi\) | |||||||
\(548\) | −10.3923 | −0.443937 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.46410 | −0.147710 | ||||||||
\(551\) | −54.9282 | −2.34002 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.8564 | 1.01448 | ||||||||
\(554\) | −12.2679 | −0.521215 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.0000 | −0.551323 | ||||||||
\(557\) | 22.1769 | 0.939666 | 0.469833 | − | 0.882755i | \(-0.344314\pi\) | ||||
0.469833 | + | 0.882755i | \(0.344314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.46410 | −0.231107 | ||||||||
\(560\) | −3.73205 | −0.157708 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.05256 | −0.297494 | ||||||||
\(563\) | 13.8564 | 0.583978 | 0.291989 | − | 0.956422i | \(-0.405683\pi\) | ||||
0.291989 | + | 0.956422i | \(0.405683\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.9282 | −0.543894 | ||||||||
\(566\) | 3.32051 | 0.139571 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | −12.1244 | −0.508279 | −0.254140 | − | 0.967168i | \(-0.581792\pi\) | ||||
−0.254140 | + | 0.967168i | \(0.581792\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.9282 | 0.624726 | 0.312363 | − | 0.949963i | \(-0.398880\pi\) | ||||
0.312363 | + | 0.949963i | \(0.398880\pi\) | |||||||
\(572\) | 12.9282 | 0.540555 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19.3923 | 0.809419 | ||||||||
\(575\) | −0.464102 | −0.0193544 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.7846 | −1.03180 | −0.515898 | − | 0.856650i | \(-0.672542\pi\) | ||||
−0.515898 | + | 0.856650i | \(0.672542\pi\) | |||||||
\(578\) | 5.00000 | 0.207973 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.92820 | −0.287678 | ||||||||
\(581\) | 31.8564 | 1.32163 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.1769 | 1.78821 | ||||||||
\(584\) | −6.39230 | −0.264515 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.39230 | −0.305373 | ||||||||
\(587\) | 22.3923 | 0.924229 | 0.462115 | − | 0.886820i | \(-0.347091\pi\) | ||||
0.462115 | + | 0.886820i | \(0.347091\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43.3205 | −1.78499 | ||||||||
\(590\) | −8.66025 | −0.356537 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.00000 | 0.328798 | ||||||||
\(593\) | 3.46410 | 0.142254 | 0.0711268 | − | 0.997467i | \(-0.477341\pi\) | ||||
0.0711268 | + | 0.997467i | \(0.477341\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.9282 | 0.530005 | ||||||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.73205 | 0.0708288 | ||||||||
\(599\) | 18.0000 | 0.735460 | 0.367730 | − | 0.929933i | \(-0.380135\pi\) | ||||
0.367730 | + | 0.929933i | \(0.380135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.92820 | 0.241816 | 0.120908 | − | 0.992664i | \(-0.461419\pi\) | ||||
0.120908 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(602\) | 5.46410 | 0.222700 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.3923 | 0.748372 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.1769 | 1.10308 | 0.551538 | − | 0.834149i | \(-0.314041\pi\) | ||||
0.551538 | + | 0.834149i | \(0.314041\pi\) | |||||||
\(608\) | 7.92820 | 0.321531 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.39230 | −0.339794 | ||||||||
\(611\) | 24.1244 | 0.975967 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.9808 | −0.483898 | −0.241949 | − | 0.970289i | \(-0.577787\pi\) | ||||
−0.241949 | + | 0.970289i | \(0.577787\pi\) | |||||||
\(614\) | −12.3923 | −0.500113 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.9282 | −0.520892 | ||||||||
\(617\) | −22.3923 | −0.901480 | −0.450740 | − | 0.892655i | \(-0.648840\pi\) | ||||
−0.450740 | + | 0.892655i | \(0.648840\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.7846 | −0.634437 | −0.317219 | − | 0.948352i | \(-0.602749\pi\) | ||||
−0.317219 | + | 0.948352i | \(0.602749\pi\) | |||||||
\(620\) | −5.46410 | −0.219444 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.53590 | −0.342258 | ||||||||
\(623\) | −44.7846 | −1.79426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.32051 | 0.132714 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.1244 | 0.563623 | ||||||||
\(629\) | −27.7128 | −1.10498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.7128 | −0.784755 | −0.392377 | − | 0.919804i | \(-0.628347\pi\) | ||||
−0.392377 | + | 0.919804i | \(0.628347\pi\) | |||||||
\(632\) | −6.39230 | −0.254272 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17.5359 | 0.696439 | ||||||||
\(635\) | 15.1962 | 0.603041 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.8564 | 1.02447 | ||||||||
\(638\) | −24.0000 | −0.950169 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 3.21539 | 0.127000 | 0.0635001 | − | 0.997982i | \(-0.479774\pi\) | ||||
0.0635001 | + | 0.997982i | \(0.479774\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.392305 | 0.0154710 | 0.00773550 | − | 0.999970i | \(-0.497538\pi\) | ||||
0.00773550 | + | 0.999970i | \(0.497538\pi\) | |||||||
\(644\) | −1.73205 | −0.0682524 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27.4641 | −1.08056 | ||||||||
\(647\) | −22.6410 | −0.890110 | −0.445055 | − | 0.895503i | \(-0.646816\pi\) | ||||
−0.445055 | + | 0.895503i | \(0.646816\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.0000 | −1.17760 | ||||||||
\(650\) | −3.73205 | −0.146383 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.85641 | 0.386007 | ||||||||
\(653\) | 12.9282 | 0.505920 | 0.252960 | − | 0.967477i | \(-0.418596\pi\) | ||||
0.252960 | + | 0.967477i | \(0.418596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.7321 | −0.536556 | ||||||||
\(656\) | −5.19615 | −0.202876 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.1244 | −0.940465 | ||||||||
\(659\) | 4.94744 | 0.192725 | 0.0963625 | − | 0.995346i | \(-0.469279\pi\) | ||||
0.0963625 | + | 0.995346i | \(0.469279\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.6077 | −0.451487 | −0.225744 | − | 0.974187i | \(-0.572481\pi\) | ||||
−0.225744 | + | 0.974187i | \(0.572481\pi\) | |||||||
\(662\) | −8.00000 | −0.310929 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.53590 | −0.331257 | ||||||||
\(665\) | 29.5885 | 1.14739 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.21539 | −0.124500 | ||||||||
\(668\) | 6.92820 | 0.268060 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.00000 | 0.309067 | ||||||||
\(671\) | −29.0718 | −1.12230 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.1769 | 1.51016 | 0.755080 | − | 0.655633i | \(-0.227598\pi\) | ||||
0.755080 | + | 0.655633i | \(0.227598\pi\) | |||||||
\(674\) | −7.07180 | −0.272395 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.928203 | 0.0357001 | ||||||||
\(677\) | −15.2487 | −0.586056 | −0.293028 | − | 0.956104i | \(-0.594663\pi\) | ||||
−0.293028 | + | 0.956104i | \(0.594663\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000 | 0.153506 | ||||||||
\(680\) | −3.46410 | −0.132842 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −18.9282 | −0.724798 | ||||||||
\(683\) | 21.7128 | 0.830818 | 0.415409 | − | 0.909635i | \(-0.363639\pi\) | ||||
0.415409 | + | 0.909635i | \(0.363639\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.3923 | 0.397070 | ||||||||
\(686\) | 0.267949 | 0.0102303 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.46410 | −0.0558184 | ||||||||
\(689\) | 46.5167 | 1.77214 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.7846 | −1.51348 | −0.756739 | − | 0.653717i | \(-0.773209\pi\) | ||||
−0.756739 | + | 0.653717i | \(0.773209\pi\) | |||||||
\(692\) | −20.3205 | −0.772470 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.7846 | 0.561216 | ||||||||
\(695\) | 13.0000 | 0.493118 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | 0.681799 | ||||||||
\(698\) | −2.00000 | −0.0757011 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.73205 | 0.141058 | ||||||||
\(701\) | −41.3205 | −1.56065 | −0.780327 | − | 0.625372i | \(-0.784947\pi\) | ||||
−0.780327 | + | 0.625372i | \(0.784947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −63.4256 | −2.39214 | ||||||||
\(704\) | 3.46410 | 0.130558 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.3923 | −0.842746 | ||||||||
\(707\) | 35.3205 | 1.32836 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.3205 | −0.800708 | −0.400354 | − | 0.916360i | \(-0.631113\pi\) | ||||
−0.400354 | + | 0.916360i | \(0.631113\pi\) | |||||||
\(710\) | 6.00000 | 0.225176 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.0000 | 0.449719 | ||||||||
\(713\) | −2.53590 | −0.0949701 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.9282 | −0.483487 | ||||||||
\(716\) | 12.1244 | 0.453108 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.53590 | 0.318557 | ||||||||
\(719\) | 35.5692 | 1.32651 | 0.663254 | − | 0.748394i | \(-0.269175\pi\) | ||||
0.663254 | + | 0.748394i | \(0.269175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −56.7128 | −2.11210 | ||||||||
\(722\) | −43.8564 | −1.63217 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.5359 | −0.465893 | ||||||||
\(725\) | 6.92820 | 0.257307 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.8038 | −1.06828 | −0.534138 | − | 0.845397i | \(-0.679364\pi\) | ||||
−0.534138 | + | 0.845397i | \(0.679364\pi\) | |||||||
\(728\) | −13.9282 | −0.516214 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.39230 | 0.236590 | ||||||||
\(731\) | 5.07180 | 0.187587 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.0000 | −0.590973 | −0.295487 | − | 0.955347i | \(-0.595482\pi\) | ||||
−0.295487 | + | 0.955347i | \(0.595482\pi\) | |||||||
\(734\) | −6.39230 | −0.235944 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.464102 | 0.0171070 | ||||||||
\(737\) | 27.7128 | 1.02081 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.5692 | 1.38201 | 0.691003 | − | 0.722852i | \(-0.257169\pi\) | ||||
0.691003 | + | 0.722852i | \(0.257169\pi\) | |||||||
\(740\) | −8.00000 | −0.294086 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −46.5167 | −1.70768 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0000 | 0.659469 | ||||||||
\(746\) | 10.9282 | 0.400110 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.0000 | −0.438763 | ||||||||
\(749\) | 31.8564 | 1.16401 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.7846 | 0.831422 | 0.415711 | − | 0.909497i | \(-0.363533\pi\) | ||||
0.415711 | + | 0.909497i | \(0.363533\pi\) | |||||||
\(752\) | 6.46410 | 0.235722 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −25.8564 | −0.941635 | ||||||||
\(755\) | −18.3923 | −0.669365 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.80385 | 0.319981 | 0.159991 | − | 0.987119i | \(-0.448854\pi\) | ||||
0.159991 | + | 0.987119i | \(0.448854\pi\) | |||||||
\(758\) | −36.8564 | −1.33868 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.92820 | −0.287586 | ||||||||
\(761\) | 13.7321 | 0.497786 | 0.248893 | − | 0.968531i | \(-0.419933\pi\) | ||||
0.248893 | + | 0.968531i | \(0.419933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −66.6410 | −2.41257 | ||||||||
\(764\) | 2.53590 | 0.0917456 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.46410 | 0.233557 | ||||||||
\(767\) | −32.3205 | −1.16703 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.0718 | −0.976234 | −0.488117 | − | 0.872778i | \(-0.662316\pi\) | ||||
−0.488117 | + | 0.872778i | \(0.662316\pi\) | |||||||
\(770\) | 12.9282 | 0.465900 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.0000 | −0.575853 | ||||||||
\(773\) | 24.9282 | 0.896605 | 0.448303 | − | 0.893882i | \(-0.352029\pi\) | ||||
0.448303 | + | 0.893882i | \(0.352029\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.46410 | 0.196276 | ||||||||
\(776\) | −1.07180 | −0.0384753 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.3205 | −0.836081 | ||||||||
\(779\) | 41.1962 | 1.47601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.7846 | 0.743732 | ||||||||
\(782\) | −1.60770 | −0.0574911 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.92820 | 0.247436 | ||||||||
\(785\) | −14.1244 | −0.504120 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.0000 | −1.21197 | −0.605985 | − | 0.795476i | \(-0.707221\pi\) | ||||
−0.605985 | + | 0.795476i | \(0.707221\pi\) | |||||||
\(788\) | −11.5359 | −0.410949 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.39230 | 0.227428 | ||||||||
\(791\) | 48.2487 | 1.71553 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.3205 | −1.11222 | ||||||||
\(794\) | −9.85641 | −0.349791 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.2487 | −0.788585 | ||||||||
\(797\) | −16.1436 | −0.571835 | −0.285918 | − | 0.958254i | \(-0.592298\pi\) | ||||
−0.285918 | + | 0.958254i | \(0.592298\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22.3923 | −0.792183 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 39.5885 | 1.39792 | ||||||||
\(803\) | 22.1436 | 0.781430 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.73205 | 0.0610468 | ||||||||
\(806\) | −20.3923 | −0.718288 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.46410 | −0.332946 | ||||||||
\(809\) | 51.5885 | 1.81375 | 0.906877 | − | 0.421396i | \(-0.138460\pi\) | ||||
0.906877 | + | 0.421396i | \(0.138460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.14359 | −0.0752717 | −0.0376359 | − | 0.999292i | \(-0.511983\pi\) | ||||
−0.0376359 | + | 0.999292i | \(0.511983\pi\) | |||||||
\(812\) | 25.8564 | 0.907382 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.7128 | −0.971334 | ||||||||
\(815\) | −9.85641 | −0.345255 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.6077 | 0.406102 | ||||||||
\(818\) | 13.9282 | 0.486988 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.19615 | 0.181458 | ||||||||
\(821\) | −41.3205 | −1.44210 | −0.721048 | − | 0.692885i | \(-0.756339\pi\) | ||||
−0.721048 | + | 0.692885i | \(0.756339\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.3205 | 0.882617 | 0.441309 | − | 0.897355i | \(-0.354514\pi\) | ||||
0.441309 | + | 0.897355i | \(0.354514\pi\) | |||||||
\(824\) | 15.1962 | 0.529383 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 32.3205 | 1.12457 | ||||||||
\(827\) | −56.1051 | −1.95097 | −0.975483 | − | 0.220075i | \(-0.929370\pi\) | ||||
−0.975483 | + | 0.220075i | \(0.929370\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.5692 | 1.30483 | 0.652416 | − | 0.757861i | \(-0.273755\pi\) | ||||
0.652416 | + | 0.757861i | \(0.273755\pi\) | |||||||
\(830\) | 8.53590 | 0.296285 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.73205 | 0.129386 | ||||||||
\(833\) | −24.0000 | −0.831551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.92820 | −0.239760 | ||||||||
\(836\) | −27.4641 | −0.949866 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.46410 | 0.119665 | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | −9.60770 | −0.331103 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.85641 | −0.304850 | ||||||||
\(845\) | −0.928203 | −0.0319312 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.73205 | 0.128235 | ||||||||
\(848\) | 12.4641 | 0.428019 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.46410 | 0.118818 | ||||||||
\(851\) | −3.71281 | −0.127274 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.21539 | −0.247050 | −0.123525 | − | 0.992341i | \(-0.539420\pi\) | ||||
−0.123525 | + | 0.992341i | \(0.539420\pi\) | |||||||
\(854\) | 31.3205 | 1.07177 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.53590 | −0.291751 | ||||||||
\(857\) | −45.7128 | −1.56152 | −0.780760 | − | 0.624831i | \(-0.785168\pi\) | ||||
−0.780760 | + | 0.624831i | \(0.785168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.7846 | 1.80099 | 0.900494 | − | 0.434869i | \(-0.143205\pi\) | ||||
0.900494 | + | 0.434869i | \(0.143205\pi\) | |||||||
\(860\) | 1.46410 | 0.0499255 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.3923 | 0.967046 | ||||||||
\(863\) | −9.67949 | −0.329494 | −0.164747 | − | 0.986336i | \(-0.552681\pi\) | ||||
−0.164747 | + | 0.986336i | \(0.552681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.3205 | 0.690918 | ||||||||
\(866\) | −2.92820 | −0.0995044 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.3923 | 0.692160 | ||||||||
\(869\) | 22.1436 | 0.751170 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.8564 | 1.01165 | ||||||||
\(872\) | 17.8564 | 0.604694 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.67949 | −0.124461 | ||||||||
\(875\) | −3.73205 | −0.126166 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.4449 | −0.926747 | −0.463374 | − | 0.886163i | \(-0.653361\pi\) | ||||
−0.463374 | + | 0.886163i | \(0.653361\pi\) | |||||||
\(878\) | −18.3923 | −0.620710 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.46410 | −0.116775 | ||||||||
\(881\) | −29.5692 | −0.996212 | −0.498106 | − | 0.867116i | \(-0.665971\pi\) | ||||
−0.498106 | + | 0.867116i | \(0.665971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.4641 | 0.789630 | 0.394815 | − | 0.918761i | \(-0.370809\pi\) | ||||
0.394815 | + | 0.918761i | \(0.370809\pi\) | |||||||
\(884\) | −12.9282 | −0.434823 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.8564 | 1.07024 | ||||||||
\(887\) | 53.1051 | 1.78310 | 0.891548 | − | 0.452927i | \(-0.149620\pi\) | ||||
0.891548 | + | 0.452927i | \(0.149620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −56.7128 | −1.90209 | ||||||||
\(890\) | −12.0000 | −0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.5359 | −0.419733 | ||||||||
\(893\) | −51.2487 | −1.71497 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1244 | −0.405273 | ||||||||
\(896\) | −3.73205 | −0.124679 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32.9090 | 1.09819 | ||||||||
\(899\) | 37.8564 | 1.26258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.1769 | −1.43843 | ||||||||
\(902\) | 18.0000 | 0.599334 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.9282 | −0.429986 | ||||||||
\(905\) | 12.5359 | 0.416707 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.5692 | −0.915421 | −0.457710 | − | 0.889101i | \(-0.651330\pi\) | ||||
−0.457710 | + | 0.889101i | \(0.651330\pi\) | |||||||
\(908\) | 16.3923 | 0.543998 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.9282 | 0.461715 | ||||||||
\(911\) | 46.3923 | 1.53705 | 0.768523 | − | 0.639822i | \(-0.220992\pi\) | ||||
0.768523 | + | 0.639822i | \(0.220992\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 29.5692 | 0.978598 | ||||||||
\(914\) | 20.3923 | 0.674517 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.8564 | 0.722156 | ||||||||
\(917\) | 51.2487 | 1.69238 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.7846 | 0.553673 | 0.276837 | − | 0.960917i | \(-0.410714\pi\) | ||||
0.276837 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(920\) | −0.464102 | −0.0153010 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.78461 | −0.289306 | ||||||||
\(923\) | 22.3923 | 0.737052 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 4.80385 | 0.157864 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.92820 | −0.227429 | ||||||||
\(929\) | 30.9282 | 1.01472 | 0.507361 | − | 0.861734i | \(-0.330621\pi\) | ||||
0.507361 | + | 0.861734i | \(0.330621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54.9282 | −1.80020 | ||||||||
\(932\) | −12.0000 | −0.393073 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.00000 | −0.196326 | ||||||||
\(935\) | 12.0000 | 0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.14359 | 0.200702 | 0.100351 | − | 0.994952i | \(-0.468003\pi\) | ||||
0.100351 | + | 0.994952i | \(0.468003\pi\) | |||||||
\(938\) | −29.8564 | −0.974846 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.46410 | −0.210836 | ||||||||
\(941\) | 5.32051 | 0.173444 | 0.0867218 | − | 0.996233i | \(-0.472361\pi\) | ||||
0.0867218 | + | 0.996233i | \(0.472361\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.41154 | 0.0785306 | ||||||||
\(944\) | −8.66025 | −0.281867 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.07180 | 0.164898 | ||||||||
\(947\) | −14.5359 | −0.472353 | −0.236177 | − | 0.971710i | \(-0.575894\pi\) | ||||
−0.236177 | + | 0.971710i | \(0.575894\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.8564 | 0.774412 | ||||||||
\(950\) | 7.92820 | 0.257225 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.9282 | 0.419005 | ||||||||
\(953\) | −18.2487 | −0.591134 | −0.295567 | − | 0.955322i | \(-0.595509\pi\) | ||||
−0.295567 | + | 0.955322i | \(0.595509\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.53590 | −0.0820597 | ||||||||
\(956\) | −8.53590 | −0.276071 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.9282 | −0.417691 | ||||||||
\(959\) | −38.7846 | −1.25242 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | −29.8564 | −0.962609 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.9282 | −0.545221 | ||||||||
\(965\) | 16.0000 | 0.515058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.39230 | 0.205563 | 0.102781 | − | 0.994704i | \(-0.467226\pi\) | ||||
0.102781 | + | 0.994704i | \(0.467226\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.07180 | 0.0344133 | ||||||||
\(971\) | 43.3013 | 1.38960 | 0.694802 | − | 0.719201i | \(-0.255492\pi\) | ||||
0.694802 | + | 0.719201i | \(0.255492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.5167 | −1.55537 | ||||||||
\(974\) | 27.4449 | 0.879390 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.39230 | −0.268631 | ||||||||
\(977\) | 42.0000 | 1.34370 | 0.671850 | − | 0.740688i | \(-0.265500\pi\) | ||||
0.671850 | + | 0.740688i | \(0.265500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.5692 | −1.32856 | ||||||||
\(980\) | −6.92820 | −0.221313 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.1244 | 0.386904 | ||||||||
\(983\) | 36.4974 | 1.16409 | 0.582043 | − | 0.813158i | \(-0.302253\pi\) | ||||
0.582043 | + | 0.813158i | \(0.302253\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.5359 | 0.367564 | ||||||||
\(986\) | 24.0000 | 0.764316 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29.5885 | −0.941334 | ||||||||
\(989\) | 0.679492 | 0.0216066 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.2154 | 0.356269 | 0.178134 | − | 0.984006i | \(-0.442994\pi\) | ||||
0.178134 | + | 0.984006i | \(0.442994\pi\) | |||||||
\(992\) | −5.46410 | −0.173485 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.3923 | −0.710241 | ||||||||
\(995\) | 22.2487 | 0.705332 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.19615 | −0.101223 | −0.0506116 | − | 0.998718i | \(-0.516117\pi\) | ||||
−0.0506116 | + | 0.998718i | \(0.516117\pi\) | |||||||
\(998\) | 3.78461 | 0.119800 | ||||||||
\(999\) | 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 | 810.2.a.j.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 810.2.a.l.1.2 | yes | 2 | ||
4.3 | odd | 2 | 6480.2.a.bb.1.1 | 2 | |||
5.2 | odd | 4 | 4050.2.c.z.649.2 | 4 | |||
5.3 | odd | 4 | 4050.2.c.z.649.3 | 4 | |||
5.4 | even | 2 | 4050.2.a.bt.1.1 | 2 | |||
9.2 | odd | 6 | 810.2.e.m.271.1 | 4 | |||
9.4 | even | 3 | 810.2.e.n.541.1 | 4 | |||
9.5 | odd | 6 | 810.2.e.m.541.1 | 4 | |||
9.7 | even | 3 | 810.2.e.n.271.1 | 4 | |||
12.11 | even | 2 | 6480.2.a.bj.1.1 | 2 | |||
15.2 | even | 4 | 4050.2.c.x.649.4 | 4 | |||
15.8 | even | 4 | 4050.2.c.x.649.1 | 4 | |||
15.14 | odd | 2 | 4050.2.a.bk.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
810.2.a.j.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
810.2.a.l.1.2 | yes | 2 | 3.2 | odd | 2 | ||
810.2.e.m.271.1 | 4 | 9.2 | odd | 6 | |||
810.2.e.m.541.1 | 4 | 9.5 | odd | 6 | |||
810.2.e.n.271.1 | 4 | 9.7 | even | 3 | |||
810.2.e.n.541.1 | 4 | 9.4 | even | 3 | |||
4050.2.a.bk.1.1 | 2 | 15.14 | odd | 2 | |||
4050.2.a.bt.1.1 | 2 | 5.4 | even | 2 | |||
4050.2.c.x.649.1 | 4 | 15.8 | even | 4 | |||
4050.2.c.x.649.4 | 4 | 15.2 | even | 4 | |||
4050.2.c.z.649.2 | 4 | 5.2 | odd | 4 | |||
4050.2.c.z.649.3 | 4 | 5.3 | odd | 4 | |||
6480.2.a.bb.1.1 | 2 | 4.3 | odd | 2 | |||
6480.2.a.bj.1.1 | 2 | 12.11 | even | 2 |