Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1932) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.61803 | 0.723607 | 0.361803 | − | 0.932254i | \(-0.382161\pi\) | ||||
0.361803 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.23607 | 1.27722 | 0.638611 | − | 0.769529i | \(-0.279509\pi\) | ||||
0.638611 | + | 0.769529i | \(0.279509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.61803 | 0.726112 | 0.363056 | − | 0.931767i | \(-0.381733\pi\) | ||||
0.363056 | + | 0.931767i | \(0.381733\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.61803 | 0.417775 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23607 | 0.542326 | 0.271163 | − | 0.962533i | \(-0.412592\pi\) | ||||
0.271163 | + | 0.962533i | \(0.412592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.47214 | 1.25539 | 0.627697 | − | 0.778458i | \(-0.283998\pi\) | ||||
0.627697 | + | 0.778458i | \(0.283998\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.38197 | −0.476393 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.47214 | −0.644759 | −0.322380 | − | 0.946610i | \(-0.604483\pi\) | ||||
−0.322380 | + | 0.946610i | \(0.604483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.23607 | 1.12003 | 0.560015 | − | 0.828482i | \(-0.310795\pi\) | ||||
0.560015 | + | 0.828482i | \(0.310795\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.23607 | 0.737405 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.61803 | 0.273498 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.47214 | 0.570816 | 0.285408 | − | 0.958406i | \(-0.407871\pi\) | ||||
0.285408 | + | 0.958406i | \(0.407871\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.61803 | 0.419221 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.47214 | −0.229909 | −0.114955 | − | 0.993371i | \(-0.536672\pi\) | ||||
−0.114955 | + | 0.993371i | \(0.536672\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.56231 | −1.15324 | −0.576620 | − | 0.817012i | \(-0.695629\pi\) | ||||
−0.576620 | + | 0.817012i | \(0.695629\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.61803 | 0.241202 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.23607 | 0.763759 | 0.381880 | − | 0.924212i | \(-0.375277\pi\) | ||||
0.381880 | + | 0.924212i | \(0.375277\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.23607 | 0.313112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.09017 | 0.561828 | 0.280914 | − | 0.959733i | \(-0.409362\pi\) | ||||
0.280914 | + | 0.959733i | \(0.409362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.85410 | 0.924207 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.47214 | 0.724802 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.61803 | 0.731406 | 0.365703 | − | 0.930732i | \(-0.380829\pi\) | ||||
0.365703 | + | 0.930732i | \(0.380829\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3262 | −1.32214 | −0.661070 | − | 0.750325i | \(-0.729897\pi\) | ||||
−0.661070 | + | 0.750325i | \(0.729897\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.23607 | 0.525420 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.61803 | 0.686352 | 0.343176 | − | 0.939271i | \(-0.388497\pi\) | ||||
0.343176 | + | 0.939271i | \(0.388497\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.14590 | 0.492028 | 0.246014 | − | 0.969266i | \(-0.420879\pi\) | ||||
0.246014 | + | 0.969266i | \(0.420879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.9443 | −1.86614 | −0.933068 | − | 0.359700i | \(-0.882879\pi\) | ||||
−0.933068 | + | 0.359700i | \(0.882879\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.38197 | −0.275046 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.23607 | 0.482745 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.76393 | 0.423475 | 0.211738 | − | 0.977327i | \(-0.432088\pi\) | ||||
0.211738 | + | 0.977327i | \(0.432088\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.94427 | −1.09153 | −0.545763 | − | 0.837940i | \(-0.683760\pi\) | ||||
−0.545763 | + | 0.837940i | \(0.683760\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.61803 | 0.392431 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.47214 | −0.372252 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.85410 | 0.408534 | 0.204267 | − | 0.978915i | \(-0.434519\pi\) | ||||
0.204267 | + | 0.978915i | \(0.434519\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.61803 | 0.274445 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.23607 | 0.646650 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.85410 | 0.908412 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.23607 | 0.430108 | 0.215054 | − | 0.976602i | \(-0.431007\pi\) | ||||
0.215054 | + | 0.976602i | \(0.431007\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.23607 | 0.425741 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.61803 | −0.360008 | −0.180004 | − | 0.983666i | \(-0.557611\pi\) | ||||
−0.180004 | + | 0.983666i | \(0.557611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.94427 | −0.881305 | −0.440653 | − | 0.897678i | \(-0.645253\pi\) | ||||
−0.440653 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.61803 | 0.157904 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.6180 | 1.21983 | 0.609916 | − | 0.792466i | \(-0.291203\pi\) | ||||
0.609916 | + | 0.792466i | \(0.291203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.38197 | −0.419716 | −0.209858 | − | 0.977732i | \(-0.567300\pi\) | ||||
−0.209858 | + | 0.977732i | \(0.567300\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.47214 | 0.329561 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5623 | −1.18176 | −0.590881 | − | 0.806759i | \(-0.701220\pi\) | ||||
−0.590881 | + | 0.806759i | \(0.701220\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.61803 | −0.150882 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.61803 | 0.242037 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.23607 | 0.204980 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.94427 | 0.631297 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.47214 | −0.132738 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.9443 | −1.06833 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.8541 | 1.22935 | 0.614676 | − | 0.788779i | \(-0.289287\pi\) | ||||
0.614676 | + | 0.788779i | \(0.289287\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.56231 | −0.665824 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.9443 | −1.56780 | −0.783899 | − | 0.620888i | \(-0.786772\pi\) | ||||
−0.783899 | + | 0.620888i | \(0.786772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.47214 | 0.474494 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.61803 | 0.139258 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.23607 | 0.361912 | 0.180956 | − | 0.983491i | \(-0.442081\pi\) | ||||
0.180956 | + | 0.983491i | \(0.442081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0344 | −1.44484 | −0.722421 | − | 0.691453i | \(-0.756971\pi\) | ||||
−0.722421 | + | 0.691453i | \(0.756971\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.23607 | 0.440956 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.0902 | 0.927407 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.61803 | −0.466552 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.6525 | −1.36422 | −0.682112 | − | 0.731248i | \(-0.738938\pi\) | ||||
−0.682112 | + | 0.731248i | \(0.738938\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.7082 | 1.27832 | 0.639158 | − | 0.769076i | \(-0.279283\pi\) | ||||
0.639158 | + | 0.769076i | \(0.279283\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.23607 | 0.180775 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0902 | 0.810462 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7639 | −1.01867 | −0.509336 | − | 0.860568i | \(-0.670109\pi\) | ||||
−0.509336 | + | 0.860568i | \(0.670109\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.09017 | 0.324372 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.5623 | 1.29726 | 0.648630 | − | 0.761104i | \(-0.275342\pi\) | ||||
0.648630 | + | 0.761104i | \(0.275342\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.85410 | 0.533591 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.8885 | −1.61640 | −0.808202 | − | 0.588905i | \(-0.799559\pi\) | ||||
−0.808202 | + | 0.588905i | \(0.799559\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.14590 | −0.472761 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.47214 | 0.418465 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.05573 | 0.156294 | 0.0781471 | − | 0.996942i | \(-0.475100\pi\) | ||||
0.0781471 | + | 0.996942i | \(0.475100\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.38197 | −0.180060 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.61803 | 0.422277 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −21.7984 | −1.62929 | −0.814643 | − | 0.579962i | \(-0.803067\pi\) | ||||
−0.814643 | + | 0.579962i | \(0.803067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.236068 | 0.0175468 | 0.00877340 | − | 0.999962i | \(-0.497207\pi\) | ||||
0.00877340 | + | 0.999962i | \(0.497207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.3262 | −0.763337 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.61803 | 0.413046 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.47214 | 0.692671 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.1246 | 1.38381 | 0.691904 | − | 0.721989i | \(-0.256772\pi\) | ||||
0.691904 | + | 0.721989i | \(0.256772\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.7082 | −1.27466 | −0.637332 | − | 0.770589i | \(-0.719962\pi\) | ||||
−0.637332 | + | 0.770589i | \(0.719962\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.23607 | 0.303351 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.61803 | −0.614009 | −0.307005 | − | 0.951708i | \(-0.599327\pi\) | ||||
−0.307005 | + | 0.951708i | \(0.599327\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.3262 | 1.51178 | 0.755888 | − | 0.654700i | \(-0.227205\pi\) | ||||
0.755888 | + | 0.654700i | \(0.227205\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.61803 | 0.396266 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.47214 | −0.243696 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.38197 | −0.166364 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.1803 | 1.60342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.23607 | −0.153937 | −0.0769686 | − | 0.997034i | \(-0.524524\pi\) | ||||
−0.0769686 | + | 0.997034i | \(0.524524\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.14590 | 0.284072 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.2361 | −0.834493 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.23607 | 0.423332 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.9443 | −1.07741 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.85410 | 0.393790 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.2148 | 1.68851 | 0.844253 | − | 0.535944i | \(-0.180044\pi\) | ||||
0.844253 | + | 0.535944i | \(0.180044\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.38197 | −0.158798 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.0902 | 0.669708 | 0.334854 | − | 0.942270i | \(-0.391313\pi\) | ||||
0.334854 | + | 0.942270i | \(0.391313\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3820 | 0.818223 | 0.409112 | − | 0.912484i | \(-0.365839\pi\) | ||||
0.409112 | + | 0.912484i | \(0.365839\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.23607 | 0.278713 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.09017 | 0.136932 | 0.0684658 | − | 0.997653i | \(-0.478190\pi\) | ||||
0.0684658 | + | 0.997653i | \(0.478190\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.47214 | 0.552661 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.76393 | 0.244494 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.03444 | −0.455020 | −0.227510 | − | 0.973776i | \(-0.573058\pi\) | ||||
−0.227510 | + | 0.973776i | \(0.573058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.2918 | −0.727369 | −0.363684 | − | 0.931522i | \(-0.618481\pi\) | ||||
−0.363684 | + | 0.931522i | \(0.618481\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.61803 | 0.103372 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.3262 | 0.911557 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.94427 | −0.630193 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.180340 | 0.0113830 | 0.00569148 | − | 0.999984i | \(-0.498188\pi\) | ||||
0.00569148 | + | 0.999984i | \(0.498188\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.23607 | −0.266319 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.61803 | 0.226570 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.2918 | 0.766741 | 0.383371 | − | 0.923595i | \(-0.374763\pi\) | ||||
0.383371 | + | 0.923595i | \(0.374763\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.47214 | 0.215748 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.47214 | −0.214920 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.94427 | −0.613190 | −0.306595 | − | 0.951840i | \(-0.599190\pi\) | ||||
−0.306595 | + | 0.951840i | \(0.599190\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.61803 | 0.406543 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.85410 | 0.235867 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.0902 | 1.40783 | 0.703916 | − | 0.710283i | \(-0.251433\pi\) | ||||
0.703916 | + | 0.710283i | \(0.251433\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.3607 | −1.90503 | −0.952513 | − | 0.304499i | \(-0.901511\pi\) | ||||
−0.952513 | + | 0.304499i | \(0.901511\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.61803 | 0.158451 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.0902 | −0.608460 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.61803 | 0.517807 | 0.258904 | − | 0.965903i | \(-0.416639\pi\) | ||||
0.258904 | + | 0.965903i | \(0.416639\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.23607 | 0.373344 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.6525 | 1.35133 | 0.675667 | − | 0.737207i | \(-0.263856\pi\) | ||||
0.675667 | + | 0.737207i | \(0.263856\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.90983 | 0.470191 | 0.235095 | − | 0.971972i | \(-0.424460\pi\) | ||||
0.235095 | + | 0.971972i | \(0.424460\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.85410 | 0.524472 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.47214 | −0.0868974 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0000 | −0.705882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.23607 | 0.248323 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.9443 | 1.45726 | 0.728630 | − | 0.684908i | \(-0.240157\pi\) | ||||
0.728630 | + | 0.684908i | \(0.240157\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.09017 | 0.529250 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.23607 | 0.245802 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.61803 | −0.151405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.56231 | −0.435884 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.61803 | −0.207851 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.7082 | −0.956709 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.2361 | −0.584203 | −0.292102 | − | 0.956387i | \(-0.594355\pi\) | ||||
−0.292102 | + | 0.956387i | \(0.594355\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.94427 | −0.508822 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30.9787 | −1.75664 | −0.878321 | − | 0.478072i | \(-0.841336\pi\) | ||||
−0.878321 | + | 0.478072i | \(0.841336\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.47214 | −0.139733 | −0.0698667 | − | 0.997556i | \(-0.522257\pi\) | ||||
−0.0698667 | + | 0.997556i | \(0.522257\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.61803 | 0.0911659 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.96556 | 0.278894 | 0.139447 | − | 0.990230i | \(-0.455468\pi\) | ||||
0.139447 | + | 0.990230i | \(0.455468\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.7082 | −0.823501 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.6180 | 0.704270 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.2361 | 0.680833 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.23607 | −0.345915 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.38197 | −0.242323 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.23607 | 0.288674 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.9443 | −1.04127 | −0.520636 | − | 0.853779i | \(-0.674305\pi\) | ||||
−0.520636 | + | 0.853779i | \(0.674305\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.47214 | 0.190272 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.09017 | 0.496649 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.56231 | 0.302998 | 0.151499 | − | 0.988457i | \(-0.451590\pi\) | ||||
0.151499 | + | 0.988457i | \(0.451590\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.5623 | −0.682291 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.4164 | 1.43053 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.61803 | −0.0871120 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.18034 | 0.170730 | 0.0853648 | − | 0.996350i | \(-0.472794\pi\) | ||||
0.0853648 | + | 0.996350i | \(0.472794\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.9098 | 0.637519 | 0.318759 | − | 0.947836i | \(-0.396734\pi\) | ||||
0.318759 | + | 0.947836i | \(0.396734\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.61803 | 0.139740 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.9443 | 1.38087 | 0.690437 | − | 0.723392i | \(-0.257418\pi\) | ||||
0.690437 | + | 0.723392i | \(0.257418\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.70820 | 0.356034 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.23607 | 0.118345 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.32624 | 0.386664 | 0.193332 | − | 0.981133i | \(-0.438071\pi\) | ||||
0.193332 | + | 0.981133i | \(0.438071\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.9443 | 0.576014 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.94427 | 0.364480 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.7984 | −1.35035 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7984 | −0.668070 | −0.334035 | − | 0.942561i | \(-0.608410\pi\) | ||||
−0.334035 | + | 0.942561i | \(0.608410\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.47214 | −0.0766363 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.09017 | 0.212351 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.05573 | 0.417110 | 0.208555 | − | 0.978011i | \(-0.433124\pi\) | ||||
0.208555 | + | 0.978011i | \(0.433124\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.9443 | −0.616800 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.09017 | −0.468168 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.8328 | 1.37831 | 0.689155 | − | 0.724614i | \(-0.257982\pi\) | ||||
0.689155 | + | 0.724614i | \(0.257982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.8541 | 0.709767 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.47214 | −0.484004 | −0.242002 | − | 0.970276i | \(-0.577804\pi\) | ||||
−0.242002 | + | 0.970276i | \(0.577804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.85410 | 0.349317 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.56231 | −0.384414 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.4164 | 1.33937 | 0.669683 | − | 0.742648i | \(-0.266430\pi\) | ||||
0.669683 | + | 0.742648i | \(0.266430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.23607 | −0.113083 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.9443 | −0.905169 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.09017 | 0.306430 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.81966 | 0.292080 | 0.146040 | − | 0.989279i | \(-0.453347\pi\) | ||||
0.146040 | + | 0.989279i | \(0.453347\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.47214 | 0.273949 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.3607 | 1.66595 | 0.832976 | − | 0.553308i | \(-0.186635\pi\) | ||||
0.832976 | + | 0.553308i | \(0.186635\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.3262 | 0.813268 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.61803 | 0.0804008 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.7082 | 0.729059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.236068 | 0.0116728 | 0.00583641 | − | 0.999983i | \(-0.498142\pi\) | ||||
0.00583641 | + | 0.999983i | \(0.498142\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.23607 | 0.208950 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.61803 | 0.276445 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0902 | −0.789835 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.0344 | −0.834180 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.2148 | 0.547878 | 0.273939 | − | 0.961747i | \(-0.411673\pi\) | ||||
0.273939 | + | 0.961747i | \(0.411673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.5066 | −0.999429 | −0.499715 | − | 0.866190i | \(-0.666562\pi\) | ||||
−0.499715 | + | 0.866190i | \(0.666562\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.23607 | 0.254586 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.32624 | −0.258360 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.3262 | −0.499722 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.0902 | 0.535438 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.43769 | 0.117420 | 0.0587098 | − | 0.998275i | \(-0.481301\pi\) | ||||
0.0587098 | + | 0.998275i | \(0.481301\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.2918 | −0.494592 | −0.247296 | − | 0.968940i | \(-0.579542\pi\) | ||||
−0.247296 | + | 0.968940i | \(0.579542\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.61803 | −0.269364 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.47214 | −0.261768 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.1803 | −1.39270 | −0.696351 | − | 0.717702i | \(-0.745194\pi\) | ||||
−0.696351 | + | 0.717702i | \(0.745194\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.8885 | −1.03996 | −0.519978 | − | 0.854180i | \(-0.674060\pi\) | ||||
−0.519978 | + | 0.854180i | \(0.674060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.23607 | 0.295618 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.6525 | −0.787635 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.09017 | −0.0986412 | −0.0493206 | − | 0.998783i | \(-0.515706\pi\) | ||||
−0.0493206 | + | 0.998783i | \(0.515706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.23607 | −0.293645 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.7082 | 0.738036 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.23607 | 0.198590 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.85410 | 0.133509 | 0.0667546 | − | 0.997769i | \(-0.478736\pi\) | ||||
0.0667546 | + | 0.997769i | \(0.478736\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.23607 | 0.104371 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.56231 | −0.212488 | −0.106244 | − | 0.994340i | \(-0.533882\pi\) | ||||
−0.106244 | + | 0.994340i | \(0.533882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.11146 | 0.0516537 | 0.0258269 | − | 0.999666i | \(-0.491778\pi\) | ||||
0.0258269 | + | 0.999666i | \(0.491778\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.0902 | 0.467920 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.4164 | 0.574563 | 0.287281 | − | 0.957846i | \(-0.407249\pi\) | ||||
0.287281 | + | 0.957846i | \(0.407249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.61803 | 0.259417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.7639 | −0.588131 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.0344 | −1.47295 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.0344 | −0.598061 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.09017 | 0.187276 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.1803 | 0.693607 | 0.346804 | − | 0.937938i | \(-0.387267\pi\) | ||||
0.346804 | + | 0.937938i | \(0.387267\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.09017 | 0.414476 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.85410 | 0.311229 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.4721 | −1.33551 | −0.667755 | − | 0.744381i | \(-0.732745\pi\) | ||||
−0.667755 | + | 0.744381i | \(0.732745\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.5623 | 0.748973 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.85410 | −0.264192 | −0.132096 | − | 0.991237i | \(-0.542171\pi\) | ||||
−0.132096 | + | 0.991237i | \(0.542171\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.76393 | −0.349670 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.85410 | 0.308069 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.14590 | 0.185969 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.2705 | −1.44463 | −0.722313 | − | 0.691566i | \(-0.756921\pi\) | ||||
−0.722313 | + | 0.691566i | \(0.756921\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.8885 | −0.933231 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.5623 | 1.09518 | 0.547590 | − | 0.836747i | \(-0.315546\pi\) | ||||
0.547590 | + | 0.836747i | \(0.315546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.85410 | −0.260504 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.14590 | −0.272949 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7082 | 0.696254 | 0.348127 | − | 0.937447i | \(-0.386818\pi\) | ||||
0.348127 | + | 0.937447i | \(0.386818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.9443 | −0.705333 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.47214 | 0.241601 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.4721 | −0.637719 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.1803 | 0.975490 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.05573 | 0.0902364 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.472136 | −0.0206847 | −0.0103423 | − | 0.999947i | \(-0.503292\pi\) | ||||
−0.0103423 | + | 0.999947i | \(0.503292\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.41641 | −0.411751 | −0.205875 | − | 0.978578i | \(-0.566004\pi\) | ||||
−0.205875 | + | 0.978578i | \(0.566004\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.38197 | −0.103958 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.9443 | 0.607422 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.61803 | 0.243802 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.85410 | −0.166940 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.4164 | 0.882678 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −21.7984 | −0.940669 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.23607 | 0.182460 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.7082 | −0.675348 | −0.337674 | − | 0.941263i | \(-0.609640\pi\) | ||||
−0.337674 | + | 0.941263i | \(0.609640\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.236068 | 0.0101306 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.09017 | −0.303710 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.09017 | 0.345911 | 0.172955 | − | 0.984930i | \(-0.444668\pi\) | ||||
0.172955 | + | 0.984930i | \(0.444668\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.3262 | −0.440713 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.0000 | −0.809427 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.76393 | 0.160059 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.61803 | 0.238472 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.6525 | −1.12930 | −0.564651 | − | 0.825330i | \(-0.690989\pi\) | ||||
−0.564651 | + | 0.825330i | \(0.690989\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.7984 | −0.837382 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.47214 | 0.399914 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.506578 | −0.0213497 | −0.0106749 | − | 0.999943i | \(-0.503398\pi\) | ||||
−0.0106749 | + | 0.999943i | \(0.503398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.3262 | −0.855131 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.5279 | 0.734806 | 0.367403 | − | 0.930062i | \(-0.380247\pi\) | ||||
0.367403 | + | 0.930062i | \(0.380247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.7082 | −0.699217 | −0.349608 | − | 0.936896i | \(-0.613685\pi\) | ||||
−0.349608 | + | 0.936896i | \(0.613685\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.1246 | 0.798942 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.38197 | 0.0993348 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.0557 | −0.543517 | −0.271759 | − | 0.962365i | \(-0.587605\pi\) | ||||
−0.271759 | + | 0.962365i | \(0.587605\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.7082 | −0.735928 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.94427 | −0.412558 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.3262 | 0.717579 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.23607 | 0.175140 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0344 | −0.496715 | −0.248357 | − | 0.968668i | \(-0.579891\pi\) | ||||
−0.248357 | + | 0.968668i | \(0.579891\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.1246 | 1.40608 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.61803 | −0.354499 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.23607 | 0.297150 | 0.148575 | − | 0.988901i | \(-0.452531\pi\) | ||||
0.148575 | + | 0.988901i | \(0.452531\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.61803 | 0.148325 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 21.3262 | 0.872825 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.3951 | 1.48706 | 0.743532 | − | 0.668700i | \(-0.233149\pi\) | ||||
0.743532 | + | 0.668700i | \(0.233149\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.6869 | −1.04779 | −0.523896 | − | 0.851782i | \(-0.675522\pi\) | ||||
−0.523896 | + | 0.851782i | \(0.675522\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.61803 | 0.228784 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.2361 | 0.456811 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.6312 | 1.52740 | 0.763701 | − | 0.645570i | \(-0.223380\pi\) | ||||
0.763701 | + | 0.645570i | \(0.223380\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.47214 | −0.140698 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.7082 | 0.554575 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.2361 | −0.898106 | −0.449053 | − | 0.893505i | \(-0.648239\pi\) | ||||
−0.449053 | + | 0.893505i | \(0.648239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.38197 | −0.0960501 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0902 | −1.09061 | −0.545305 | − | 0.838238i | \(-0.683586\pi\) | ||||
−0.545305 | + | 0.838238i | \(0.683586\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0344 | 0.885639 | 0.442819 | − | 0.896611i | \(-0.353978\pi\) | ||||
0.442819 | + | 0.896611i | \(0.353978\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.85410 | 0.154411 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.41641 | −0.296656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.1803 | 0.925734 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.76393 | 0.309568 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.527864 | 0.0210139 | 0.0105070 | − | 0.999945i | \(-0.496655\pi\) | ||||
0.0105070 | + | 0.999945i | \(0.496655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.23607 | −0.0888757 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.4164 | 0.889568 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.61803 | 0.103730 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.14590 | 0.164009 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.1459 | −1.11170 | −0.555848 | − | 0.831284i | \(-0.687606\pi\) | ||||
−0.555848 | + | 0.831284i | \(0.687606\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.9787 | 1.06394 | 0.531968 | − | 0.846764i | \(-0.321453\pi\) | ||||
0.531968 | + | 0.846764i | \(0.321453\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.2361 | −0.481795 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.0902 | 1.65474 | 0.827368 | − | 0.561661i | \(-0.189837\pi\) | ||||
0.827368 | + | 0.561661i | \(0.189837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23.7984 | 0.934168 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.23607 | 0.244411 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0344 | 0.744875 | 0.372438 | − | 0.928057i | \(-0.378522\pi\) | ||||
0.372438 | + | 0.928057i | \(0.378522\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.0344 | −1.13447 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.9443 | −0.622045 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.0689 | −0.664909 | −0.332455 | − | 0.943119i | \(-0.607877\pi\) | ||||
−0.332455 | + | 0.943119i | \(0.607877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.1803 | −1.21277 | −0.606387 | − | 0.795169i | \(-0.707382\pi\) | ||||
−0.606387 | + | 0.795169i | \(0.707382\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.85410 | 0.227354 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.85410 | 0.343347 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.47214 | 0.134442 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.2148 | 0.974860 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −43.7426 | −1.68867 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.58359 | −0.292326 | −0.146163 | − | 0.989261i | \(-0.546692\pi\) | ||||
−0.146163 | + | 0.989261i | \(0.546692\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.38197 | −0.0916819 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.9787 | 0.960010 | 0.480005 | − | 0.877266i | \(-0.340635\pi\) | ||||
0.480005 | + | 0.877266i | \(0.340635\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.23607 | 0.162565 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0902 | 0.386656 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.2361 | 0.774312 | 0.387156 | − | 0.922014i | \(-0.373458\pi\) | ||||
0.387156 | + | 0.922014i | \(0.373458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.85410 | 0.261882 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.3820 | 0.472401 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.7082 | 0.407950 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.5623 | 0.668102 | 0.334051 | − | 0.942555i | \(-0.391584\pi\) | ||||
0.334051 | + | 0.942555i | \(0.391584\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.23607 | 0.160915 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27.5623 | −1.04550 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.29180 | −0.124686 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.09017 | 0.0790575 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.21478 | 0.196960 | 0.0984798 | − | 0.995139i | \(-0.468602\pi\) | ||||
0.0984798 | + | 0.995139i | \(0.468602\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 19.0000 | 0.716599 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.47214 | 0.319079 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.61803 | −0.136070 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.2705 | −0.949054 | −0.474527 | − | 0.880241i | \(-0.657381\pi\) | ||||
−0.474527 | + | 0.880241i | \(0.657381\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.76393 | 0.141158 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.23607 | −0.233543 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.9443 | 0.671078 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.03444 | −0.262706 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.23607 | 0.232566 | 0.116283 | − | 0.993216i | \(-0.462902\pi\) | ||||
0.116283 | + | 0.993216i | \(0.462902\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.94427 | −0.333102 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.2918 | −0.419946 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.27051 | 0.307159 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.5279 | −1.35474 | −0.677372 | − | 0.735641i | \(-0.736881\pi\) | ||||
−0.677372 | + | 0.735641i | \(0.736881\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.9098 | −0.625433 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.59675 | 0.280592 | 0.140296 | − | 0.990110i | \(-0.455195\pi\) | ||||
0.140296 | + | 0.990110i | \(0.455195\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.61803 | 0.0596821 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.7984 | 0.876624 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5967 | 0.904806 | 0.452403 | − | 0.891814i | \(-0.350567\pi\) | ||||
0.452403 | + | 0.891814i | \(0.350567\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.3262 | 0.526288 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.7984 | 1.97367 | 0.986835 | − | 0.161727i | \(-0.0517066\pi\) | ||||
0.986835 | + | 0.161727i | \(0.0517066\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.9443 | −0.987162 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.94427 | −0.363842 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.6180 | 0.461053 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.96556 | 0.327158 | 0.163579 | − | 0.986530i | \(-0.447696\pi\) | ||||
0.163579 | + | 0.986530i | \(0.447696\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.180340 | 0.00657195 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.4164 | 0.924998 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.0000 | 1.27210 | 0.636048 | − | 0.771649i | \(-0.280568\pi\) | ||||
0.636048 | + | 0.771649i | \(0.280568\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.23607 | −0.153760 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.8328 | −1.55269 | −0.776344 | − | 0.630309i | \(-0.782928\pi\) | ||||
−0.776344 | + | 0.630309i | \(0.782928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.38197 | −0.158638 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.61803 | 0.130810 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.7082 | 0.531082 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.81966 | 0.281984 | 0.140992 | − | 0.990011i | \(-0.454971\pi\) | ||||
0.140992 | + | 0.990011i | \(0.454971\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.2918 | 0.442678 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.4721 | 0.556494 | 0.278247 | − | 0.960510i | \(-0.410247\pi\) | ||||
0.278247 | + | 0.960510i | \(0.410247\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.8541 | −0.533575 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.47214 | 0.124562 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.05573 | −0.288626 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.5623 | 0.628429 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.47214 | −0.124084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.6525 | −0.737118 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.4508 | −1.37062 | −0.685312 | − | 0.728249i | \(-0.740334\pi\) | ||||
−0.685312 | + | 0.728249i | \(0.740334\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.94427 | −0.354025 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.5623 | −0.446664 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.0344 | −0.960021 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.61803 | 0.234717 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.5410 | −1.36519 | −0.682596 | − | 0.730795i | \(-0.739149\pi\) | ||||
−0.682596 | + | 0.730795i | \(0.739149\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.7082 | 0.414206 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.85410 | 0.136178 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −67.5410 | −2.38347 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.61803 | −0.0570282 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.0902 | 0.812812 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.6180 | 0.654575 | 0.327288 | − | 0.944925i | \(-0.393865\pi\) | ||||
0.327288 | + | 0.944925i | \(0.393865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.4164 | −1.13829 | −0.569147 | − | 0.822236i | \(-0.692726\pi\) | ||||
−0.569147 | + | 0.822236i | \(0.692726\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.3607 | −1.09987 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.7984 | 0.938706 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.3820 | −1.44777 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.61803 | 0.0914815 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.875388 | 0.0305513 | 0.0152756 | − | 0.999883i | \(-0.495137\pi\) | ||||
0.0152756 | + | 0.999883i | \(0.495137\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.7295 | −0.548296 | −0.274148 | − | 0.961688i | \(-0.588396\pi\) | ||||
−0.274148 | + | 0.961688i | \(0.588396\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.0902 | −0.351295 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.43769 | 0.119540 | 0.0597702 | − | 0.998212i | \(-0.480963\pi\) | ||||
0.0597702 | + | 0.998212i | \(0.480963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.1246 | 0.698957 | 0.349478 | − | 0.936944i | \(-0.386359\pi\) | ||||
0.349478 | + | 0.936944i | \(0.386359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.61803 | 0.298956 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.23607 | 0.0774752 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.7984 | −1.16964 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.23607 | 0.215550 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.9230 | −1.03306 | −0.516528 | − | 0.856270i | \(-0.672776\pi\) | ||||
−0.516528 | + | 0.856270i | \(0.672776\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.9443 | −0.584285 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.6525 | 0.780193 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.94427 | −0.342093 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.94427 | 0.238608 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.90983 | 0.271465 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.47214 | −0.119023 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.65248 | 0.0908190 | 0.0454095 | − | 0.998968i | \(-0.485541\pi\) | ||||
0.0454095 | + | 0.998968i | \(0.485541\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.85410 | 0.302804 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.1246 | 1.40479 | 0.702395 | − | 0.711787i | \(-0.252114\pi\) | ||||
0.702395 | + | 0.711787i | \(0.252114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.94427 | −0.100457 | −0.0502286 | − | 0.998738i | \(-0.515995\pi\) | ||||
−0.0502286 | + | 0.998738i | \(0.515995\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.47214 | −0.0501703 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.1246 | 1.26374 | 0.631868 | − | 0.775076i | \(-0.282288\pi\) | ||||
0.631868 | + | 0.775076i | \(0.282288\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.32624 | 0.113095 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0000 | −0.407541 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.9443 | 0.540872 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.7082 | 0.498368 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.23607 | 0.143369 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.9443 | −0.403790 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.1935 | 1.72868 | 0.864341 | − | 0.502907i | \(-0.167736\pi\) | ||||
0.864341 | + | 0.502907i | \(0.167736\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.9443 | 0.841349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.2918 | −0.751030 | −0.375515 | − | 0.926816i | \(-0.622534\pi\) | ||||
−0.375515 | + | 0.926816i | \(0.622534\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.74265 | −0.327866 | −0.163933 | − | 0.986471i | \(-0.552418\pi\) | ||||
−0.163933 | + | 0.986471i | \(0.552418\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.09017 | 0.305563 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.437694 | 0.0146963 | 0.00734816 | − | 0.999973i | \(-0.497661\pi\) | ||||
0.00734816 | + | 0.999973i | \(0.497661\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.8541 | 0.464652 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.23607 | 0.141914 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.6525 | 0.958819 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −35.2705 | −1.17896 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.61803 | −0.0874136 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.6525 | −0.722151 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.14590 | 0.304694 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.56231 | −0.251658 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.381966 | 0.0126970 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.0344 | −1.56175 | −0.780877 | − | 0.624685i | \(-0.785227\pi\) | ||||
−0.780877 | + | 0.624685i | \(0.785227\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.61803 | −0.120003 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.5410 | 1.14440 | 0.572198 | − | 0.820116i | \(-0.306091\pi\) | ||||
0.572198 | + | 0.820116i | \(0.306091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.1246 | −1.39412 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.7082 | −0.552356 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.9443 | −0.592572 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.4164 | −0.673475 | −0.336738 | − | 0.941599i | \(-0.609324\pi\) | ||||
−0.336738 | + | 0.941599i | \(0.609324\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.2361 | −0.337290 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.8541 | 0.357267 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.27051 | −0.271933 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.94427 | −0.293768 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.50658 | 0.246283 | 0.123141 | − | 0.992389i | \(-0.460703\pi\) | ||||
0.123141 | + | 0.992389i | \(0.460703\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.47214 | 0.179342 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.9787 | −1.01420 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.3262 | 0.501222 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.5279 | 0.735953 | 0.367977 | − | 0.929835i | \(-0.380051\pi\) | ||||
0.367977 | + | 0.929835i | \(0.380051\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.47214 | −0.0806751 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.0000 | 0.912774 | 0.456387 | − | 0.889781i | \(-0.349143\pi\) | ||||
0.456387 | + | 0.889781i | \(0.349143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.47214 | 0.0479393 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.61803 | 0.0526346 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −59.8885 | −1.94612 | −0.973058 | − | 0.230560i | \(-0.925944\pi\) | ||||
−0.973058 | + | 0.230560i | \(0.925944\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.7426 | −1.35502 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.96556 | 0.161019 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.5623 | −1.08719 | −0.543595 | − | 0.839348i | \(-0.682937\pi\) | ||||
−0.543595 | + | 0.839348i | \(0.682937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.9443 | 1.00133 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.7082 | −0.475449 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.23607 | 0.136790 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.88854 | 0.254469 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.6180 | 0.406610 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.6525 | −0.922356 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.52786 | −0.242080 | −0.121040 | − | 0.992648i | \(-0.538623\pi\) | ||||
−0.121040 | + | 0.992648i | \(0.538623\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.2361 | 0.393079 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.6738 | 0.438812 | 0.219406 | − | 0.975634i | \(-0.429588\pi\) | ||||
0.219406 | + | 0.975634i | \(0.429588\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.0344 | −0.546099 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.23607 | −0.199714 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −57.0902 | −1.82648 | −0.913238 | − | 0.407426i | \(-0.866426\pi\) | ||||
−0.913238 | + | 0.407426i | \(0.866426\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.3262 | 0.521789 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.38197 | −0.139905 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.7771 | 1.55575 | 0.777874 | − | 0.628421i | \(-0.216298\pi\) | ||||
0.777874 | + | 0.628421i | \(0.216298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.9443 | −0.444301 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.23607 | 0.166666 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.56231 | 0.240467 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.1591 | −1.87925 | −0.939625 | − | 0.342207i | \(-0.888826\pi\) | ||||
−0.939625 | + | 0.342207i | \(0.888826\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.9443 | −0.601178 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 34.5066 | 1.09393 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1246 | 0.890715 | 0.445358 | − | 0.895353i | \(-0.353077\pi\) | ||||
0.445358 | + | 0.895353i | \(0.353077\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.47214 | 0.109854 |
(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 | 7728.2.a.bo.1.2 | 2 | ||
4.3 | odd | 2 | 1932.2.a.d.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 5796.2.a.i.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.a.d.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
5796.2.a.i.1.1 | 2 | 12.11 | even | 2 | |||
7728.2.a.bo.1.2 | 2 | 1.1 | even | 1 | trivial |