Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4560,2,Mod(1,4560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4560, 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("4560.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4560 = 2^{4} \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4560.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(36.4117833217\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 2280) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4560.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.38776 | −1.65842 | −0.829208 | − | 0.558940i | \(-0.811208\pi\) | ||||
−0.829208 | + | 0.558940i | \(0.811208\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.38776 | −1.92598 | −0.962990 | − | 0.269536i | \(-0.913130\pi\) | ||||
−0.962990 | + | 0.269536i | \(0.913130\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.13536 | −0.314892 | −0.157446 | − | 0.987528i | \(-0.550326\pi\) | ||||
−0.157446 | + | 0.987528i | \(0.550326\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.72928 | 0.419412 | 0.209706 | − | 0.977764i | \(-0.432749\pi\) | ||||
0.209706 | + | 0.977764i | \(0.432749\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.38776 | −0.957487 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.52311 | −0.317591 | −0.158796 | − | 0.987311i | \(-0.550761\pi\) | ||||
−0.158796 | + | 0.987311i | \(0.550761\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.65847 | 1.23645 | 0.618224 | − | 0.786002i | \(-0.287853\pi\) | ||||
0.618224 | + | 0.786002i | \(0.287853\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.72928 | 0.669799 | 0.334899 | − | 0.942254i | \(-0.391298\pi\) | ||||
0.334899 | + | 0.942254i | \(0.391298\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.38776 | −1.11197 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.38776 | 0.741666 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.59392 | −0.755236 | −0.377618 | − | 0.925961i | \(-0.623257\pi\) | ||||
−0.377618 | + | 0.925961i | \(0.623257\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.13536 | −0.181803 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.64015 | −1.50554 | −0.752769 | − | 0.658284i | \(-0.771282\pi\) | ||||
−0.752769 | + | 0.658284i | \(0.771282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.59392 | −0.395569 | −0.197785 | − | 0.980245i | \(-0.563375\pi\) | ||||
−0.197785 | + | 0.980245i | \(0.563375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.52311 | 1.38909 | 0.694544 | − | 0.719450i | \(-0.255606\pi\) | ||||
0.694544 | + | 0.719450i | \(0.255606\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.2524 | 1.75034 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.72928 | 0.242148 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5231 | 1.58282 | 0.791411 | − | 0.611285i | \(-0.209347\pi\) | ||||
0.791411 | + | 0.611285i | \(0.209347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.38776 | 0.861325 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.9817 | −1.95045 | −0.975224 | − | 0.221219i | \(-0.928996\pi\) | ||||
−0.975224 | + | 0.221219i | \(0.928996\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.79383 | −0.229677 | −0.114838 | − | 0.993384i | \(-0.536635\pi\) | ||||
−0.114838 | + | 0.993384i | \(0.536635\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.38776 | −0.552805 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.13536 | 0.140824 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.04623 | 0.860834 | 0.430417 | − | 0.902630i | \(-0.358367\pi\) | ||||
0.430417 | + | 0.902630i | \(0.358367\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.52311 | −0.183361 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.31695 | 1.10572 | 0.552859 | − | 0.833275i | \(-0.313537\pi\) | ||||
0.552859 | + | 0.833275i | \(0.313537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.50479 | −0.995411 | −0.497705 | − | 0.867346i | \(-0.665824\pi\) | ||||
−0.497705 | + | 0.867346i | \(0.665824\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 28.0279 | 3.19408 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.25240 | 1.04098 | 0.520488 | − | 0.853869i | \(-0.325750\pi\) | ||||
0.520488 | + | 0.853869i | \(0.325750\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.04623 | −0.992953 | −0.496476 | − | 0.868050i | \(-0.665373\pi\) | ||||
−0.496476 | + | 0.868050i | \(0.665373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.72928 | −0.187567 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.65847 | 0.713863 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.5939 | 1.12295 | 0.561477 | − | 0.827492i | \(-0.310233\pi\) | ||||
0.561477 | + | 0.827492i | \(0.310233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.98168 | 0.522222 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.72928 | 0.386709 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.59392 | −0.466442 | −0.233221 | − | 0.972424i | \(-0.574927\pi\) | ||||
−0.233221 | + | 0.972424i | \(0.574927\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.38776 | −0.641994 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.22449 | 0.121841 | 0.0609206 | − | 0.998143i | \(-0.480596\pi\) | ||||
0.0609206 | + | 0.998143i | \(0.480596\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.04623 | 0.694286 | 0.347143 | − | 0.937812i | \(-0.387152\pi\) | ||||
0.347143 | + | 0.937812i | \(0.387152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.38776 | 0.428201 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.45856 | 0.334352 | 0.167176 | − | 0.985927i | \(-0.446535\pi\) | ||||
0.167176 | + | 0.985927i | \(0.446535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9817 | 1.24342 | 0.621710 | − | 0.783248i | \(-0.286438\pi\) | ||||
0.621710 | + | 0.783248i | \(0.286438\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.59392 | −0.436036 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.7938 | 1.29761 | 0.648807 | − | 0.760953i | \(-0.275268\pi\) | ||||
0.648807 | + | 0.760953i | \(0.275268\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.52311 | 0.142031 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.13536 | −0.104964 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.58767 | −0.695560 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 29.8034 | 2.70940 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.64015 | −0.869223 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.04623 | −0.625252 | −0.312626 | − | 0.949876i | \(-0.601209\pi\) | ||||
−0.312626 | + | 0.949876i | \(0.601209\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.59392 | −0.228382 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.117037 | 0.0102256 | 0.00511279 | − | 0.999987i | \(-0.498373\pi\) | ||||
0.00511279 | + | 0.999987i | \(0.498373\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.38776 | 0.380467 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.2524 | 0.961357 | 0.480679 | − | 0.876897i | \(-0.340390\pi\) | ||||
0.480679 | + | 0.876897i | \(0.340390\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3169 | −1.12953 | −0.564764 | − | 0.825252i | \(-0.691033\pi\) | ||||
−0.564764 | + | 0.825252i | \(0.691033\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.52311 | 0.801991 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.25240 | 0.606476 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.65847 | −0.552956 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.2524 | 1.01056 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.0000 | 1.14692 | 0.573462 | − | 0.819232i | \(-0.305600\pi\) | ||||
0.573462 | + | 0.819232i | \(0.305600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2341 | −0.832837 | −0.416419 | − | 0.909173i | \(-0.636715\pi\) | ||||
−0.416419 | + | 0.909173i | \(0.636715\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.72928 | 0.139804 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.72928 | −0.299543 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.0279 | 0.959931 | 0.479966 | − | 0.877287i | \(-0.340649\pi\) | ||||
0.479966 | + | 0.877287i | \(0.340649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5231 | 0.913842 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.68305 | 0.526698 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.4157 | 1.12912 | 0.564561 | − | 0.825391i | \(-0.309046\pi\) | ||||
0.564561 | + | 0.825391i | \(0.309046\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.38776 | 0.497286 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.79383 | 0.293576 | 0.146788 | − | 0.989168i | \(-0.453107\pi\) | ||||
0.146788 | + | 0.989168i | \(0.453107\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7110 | −0.900843 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.2986 | −0.935047 | −0.467524 | − | 0.883981i | \(-0.654854\pi\) | ||||
−0.467524 | + | 0.883981i | \(0.654854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.38776 | −0.331683 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.9817 | −1.12609 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.02791 | 0.151573 | 0.0757864 | − | 0.997124i | \(-0.475853\pi\) | ||||
0.0757864 | + | 0.997124i | \(0.475853\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.5231 | −1.30248 | −0.651241 | − | 0.758871i | \(-0.725751\pi\) | ||||
−0.651241 | + | 0.758871i | \(0.725751\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.79383 | −0.132604 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.59392 | 0.337752 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.0462 | −0.807780 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.38776 | −0.319162 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3878 | 0.751632 | 0.375816 | − | 0.926694i | \(-0.377363\pi\) | ||||
0.375816 | + | 0.926694i | \(0.377363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.13536 | 0.0817249 | 0.0408625 | − | 0.999165i | \(-0.486989\pi\) | ||||
0.0408625 | + | 0.999165i | \(0.486989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.13536 | 0.0813048 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.5693 | 1.03802 | 0.519011 | − | 0.854767i | \(-0.326300\pi\) | ||||
0.519011 | + | 0.854767i | \(0.326300\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.18785 | −0.651309 | −0.325655 | − | 0.945489i | \(-0.605585\pi\) | ||||
−0.325655 | + | 0.945489i | \(0.605585\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.04623 | 0.497003 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −29.2158 | −2.05054 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.64015 | 0.673297 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.52311 | −0.105864 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.38776 | 0.441850 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5048 | 0.998551 | 0.499276 | − | 0.866443i | \(-0.333600\pi\) | ||||
0.499276 | + | 0.866443i | \(0.333600\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.31695 | 0.638387 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.59392 | 0.176904 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.3632 | −1.11080 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.50479 | −0.574701 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.96336 | −0.132070 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4586 | 1.30304 | 0.651521 | − | 0.758631i | \(-0.274131\pi\) | ||||
0.651521 | + | 0.758631i | \(0.274131\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.2524 | 0.746848 | 0.373424 | − | 0.927661i | \(-0.378184\pi\) | ||||
0.373424 | + | 0.927661i | \(0.378184\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2062 | 0.674443 | 0.337221 | − | 0.941425i | \(-0.390513\pi\) | ||||
0.337221 | + | 0.941425i | \(0.390513\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 28.0279 | 1.84410 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.3449 | −1.92245 | −0.961223 | − | 0.275774i | \(-0.911066\pi\) | ||||
−0.961223 | + | 0.275774i | \(0.911066\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.52311 | −0.621219 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.25240 | 0.601008 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.1170 | −1.30126 | −0.650631 | − | 0.759394i | \(-0.725496\pi\) | ||||
−0.650631 | + | 0.759394i | \(0.725496\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.55102 | 0.228741 | 0.114371 | − | 0.993438i | \(-0.463515\pi\) | ||||
0.114371 | + | 0.993438i | \(0.463515\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.2524 | −0.782777 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.13536 | 0.0722412 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.04623 | −0.573281 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.836734 | 0.0528142 | 0.0264071 | − | 0.999651i | \(-0.491593\pi\) | ||||
0.0264071 | + | 0.999651i | \(0.491593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.72928 | 0.611675 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.72928 | −0.108292 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.2986 | 1.01668 | 0.508340 | − | 0.861156i | \(-0.330259\pi\) | ||||
0.508340 | + | 0.861156i | \(0.330259\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.1570 | 1.25250 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.65847 | 0.412149 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.206167 | 0.0127128 | 0.00635641 | − | 0.999980i | \(-0.497977\pi\) | ||||
0.00635641 | + | 0.999980i | \(0.497977\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.5231 | −0.707859 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.5939 | 0.648338 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.7509 | −1.50909 | −0.754545 | − | 0.656248i | \(-0.772143\pi\) | ||||
−0.754545 | + | 0.656248i | \(0.772143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.3265 | −1.11326 | −0.556629 | − | 0.830761i | \(-0.687905\pi\) | ||||
−0.556629 | + | 0.830761i | \(0.687905\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.98168 | 0.301505 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.38776 | −0.385196 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.25240 | 0.435754 | 0.217877 | − | 0.975976i | \(-0.430087\pi\) | ||||
0.217877 | + | 0.975976i | \(0.430087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.72928 | 0.223266 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.4061 | 1.03836 | 0.519180 | − | 0.854665i | \(-0.326238\pi\) | ||||
0.519180 | + | 0.854665i | \(0.326238\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.32320 | 0.256988 | 0.128494 | − | 0.991710i | \(-0.458986\pi\) | ||||
0.128494 | + | 0.991710i | \(0.458986\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00000 | 0.0592349 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 42.2986 | 2.49681 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0096 | −0.824093 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.59392 | −0.269301 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.2524 | 1.00790 | 0.503948 | − | 0.863734i | \(-0.331880\pi\) | ||||
0.503948 | + | 0.863734i | \(0.331880\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.9817 | 0.872267 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.38776 | −0.370655 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.72928 | 0.100007 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.3815 | 0.656019 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.22449 | 0.0703451 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.79383 | 0.102715 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.31695 | 0.303454 | 0.151727 | − | 0.988422i | \(-0.451517\pi\) | ||||
0.151727 | + | 0.988422i | \(0.451517\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.04623 | 0.400846 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.65847 | 0.490977 | 0.245488 | − | 0.969400i | \(-0.421052\pi\) | ||||
0.245488 | + | 0.969400i | \(0.421052\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.7389 | −1.39832 | −0.699162 | − | 0.714964i | \(-0.746443\pi\) | ||||
−0.699162 | + | 0.714964i | \(0.746443\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.38776 | 0.247222 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.0279 | −1.01255 | −0.506274 | − | 0.862373i | \(-0.668978\pi\) | ||||
−0.506274 | + | 0.862373i | \(0.668978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.5327 | −2.38137 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.45856 | 0.193038 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.72928 | −0.0962198 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.13536 | −0.0629784 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.9817 | 0.717888 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −41.7851 | −2.30369 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9817 | −0.713538 | −0.356769 | − | 0.934193i | \(-0.616122\pi\) | ||||
−0.356769 | + | 0.934193i | \(0.616122\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.59392 | −0.251745 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.04623 | −0.384977 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.8646 | −0.809729 | −0.404864 | − | 0.914377i | \(-0.632681\pi\) | ||||
−0.404864 | + | 0.914377i | \(0.632681\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.7938 | 0.749178 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.8217 | −1.29002 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −23.0462 | −1.24438 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.52311 | 0.0820017 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.5048 | 1.53022 | 0.765109 | − | 0.643901i | \(-0.222685\pi\) | ||||
0.765109 | + | 0.643901i | \(0.222685\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.5048 | −1.31171 | −0.655856 | − | 0.754886i | \(-0.727692\pi\) | ||||
−0.655856 | + | 0.754886i | \(0.727692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.13536 | −0.0606010 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.206167 | 0.0109732 | 0.00548659 | − | 0.999985i | \(-0.498254\pi\) | ||||
0.00548659 | + | 0.999985i | \(0.498254\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.31695 | −0.494492 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.58767 | −0.401582 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.6122 | −1.14065 | −0.570325 | − | 0.821419i | \(-0.693183\pi\) | ||||
−0.570325 | + | 0.821419i | \(0.693183\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.8034 | 1.56427 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.50479 | 0.445161 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.3973 | −1.11693 | −0.558466 | − | 0.829527i | \(-0.688610\pi\) | ||||
−0.558466 | + | 0.829527i | \(0.688610\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.64015 | −0.501846 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −50.5606 | −2.62498 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.67680 | −0.0868212 | −0.0434106 | − | 0.999057i | \(-0.513822\pi\) | ||||
−0.0434106 | + | 0.999057i | \(0.513822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.55976 | −0.389347 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.01832 | −0.360507 | −0.180253 | − | 0.983620i | \(-0.557692\pi\) | ||||
−0.180253 | + | 0.983620i | \(0.557692\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.04623 | −0.360989 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.5972 | 1.46125 | 0.730626 | − | 0.682778i | \(-0.239229\pi\) | ||||
0.730626 | + | 0.682778i | \(0.239229\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.0279 | −1.42843 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.59392 | −0.131856 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.6339 | 1.24899 | 0.624494 | − | 0.781030i | \(-0.285305\pi\) | ||||
0.624494 | + | 0.781030i | \(0.285305\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.63389 | −0.133202 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.117037 | 0.00590374 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.25240 | −0.465539 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8401 | −0.544047 | −0.272024 | − | 0.962291i | \(-0.587693\pi\) | ||||
−0.272024 | + | 0.962291i | \(0.587693\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.38776 | 0.219663 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.6864 | 0.833278 | 0.416639 | − | 0.909072i | \(-0.363208\pi\) | ||||
0.416639 | + | 0.909072i | \(0.363208\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.23407 | −0.210914 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.3449 | 1.45457 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.3265 | 1.20287 | 0.601435 | − | 0.798922i | \(-0.294596\pi\) | ||||
0.601435 | + | 0.798922i | \(0.294596\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.2524 | 0.555040 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 65.7359 | 3.23465 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.04623 | 0.444062 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.3169 | −0.652134 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.6681 | 0.667728 | 0.333864 | − | 0.942621i | \(-0.391647\pi\) | ||||
0.333864 | + | 0.942621i | \(0.391647\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.7938 | −0.769744 | −0.384872 | − | 0.922970i | \(-0.625754\pi\) | ||||
−0.384872 | + | 0.922970i | \(0.625754\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.52311 | 0.463030 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.72928 | 0.0838825 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.87090 | 0.380899 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.25240 | 0.350149 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.7389 | 1.48064 | 0.740320 | − | 0.672255i | \(-0.234674\pi\) | ||||
0.740320 | + | 0.672255i | \(0.234674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.0525 | 1.15589 | 0.577944 | − | 0.816076i | \(-0.303855\pi\) | ||||
0.577944 | + | 0.816076i | \(0.303855\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.65847 | −0.319249 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.52311 | 0.0728604 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.38150 | −0.447754 | −0.223877 | − | 0.974617i | \(-0.571871\pi\) | ||||
−0.223877 | + | 0.974617i | \(0.571871\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.2524 | 0.583447 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.1974 | −1.71979 | −0.859896 | − | 0.510469i | \(-0.829472\pi\) | ||||
−0.859896 | + | 0.510469i | \(0.829472\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.5939 | −0.502200 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0000 | 0.662177 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.3328 | 1.38430 | 0.692150 | − | 0.721754i | \(-0.256664\pi\) | ||||
0.692150 | + | 0.721754i | \(0.256664\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 61.5789 | 2.89964 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.2341 | −0.480839 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.98168 | −0.233545 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.1974 | −1.50613 | −0.753066 | − | 0.657945i | \(-0.771426\pi\) | ||||
−0.753066 | + | 0.657945i | \(0.771426\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.72928 | 0.0807160 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.6339 | −0.774718 | −0.387359 | − | 0.921929i | \(-0.626613\pi\) | ||||
−0.387359 | + | 0.921929i | \(0.626613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.2095 | 1.49690 | 0.748451 | − | 0.663190i | \(-0.230798\pi\) | ||||
0.748451 | + | 0.663190i | \(0.230798\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.72928 | −0.172941 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.81215 | −0.407778 | −0.203889 | − | 0.978994i | \(-0.565358\pi\) | ||||
−0.203889 | + | 0.978994i | \(0.565358\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.9171 | −1.42762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0279 | 0.554217 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.5693 | 0.761859 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.5231 | 0.527607 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.30488 | −0.0596216 | −0.0298108 | − | 0.999556i | \(-0.509490\pi\) | ||||
−0.0298108 | + | 0.999556i | \(0.509490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.21575 | 0.237818 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.68305 | 0.304089 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.59392 | 0.208599 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.3632 | 1.10400 | 0.552000 | − | 0.833844i | \(-0.313865\pi\) | ||||
0.552000 | + | 0.833844i | \(0.313865\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.4157 | 0.651899 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.7605 | −1.79437 | −0.897183 | − | 0.441658i | \(-0.854390\pi\) | ||||
−0.897183 | + | 0.441658i | \(0.854390\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5144 | 0.518581 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.38776 | 0.287108 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −40.8805 | −1.83374 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −42.3265 | −1.89480 | −0.947398 | − | 0.320058i | \(-0.896298\pi\) | ||||
−0.947398 | + | 0.320058i | \(0.896298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.79383 | 0.169496 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.8959 | 1.73428 | 0.867141 | − | 0.498063i | \(-0.165955\pi\) | ||||
0.867141 | + | 0.498063i | \(0.165955\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.22449 | −0.0544891 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.7110 | −0.520102 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.4340 | 0.506802 | 0.253401 | − | 0.967361i | \(-0.418451\pi\) | ||||
0.253401 | + | 0.967361i | \(0.418451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 37.3169 | 1.65080 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.04623 | −0.310494 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −60.8313 | −2.67536 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.2986 | −0.539850 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.5910 | 1.82213 | 0.911067 | − | 0.412258i | \(-0.135260\pi\) | ||||
0.911067 | + | 0.412258i | \(0.135260\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.8313 | 1.43561 | 0.717807 | − | 0.696242i | \(-0.245146\pi\) | ||||
0.717807 | + | 0.696242i | \(0.245146\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.38776 | −0.191497 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.44898 | 0.280922 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6801 | −0.899136 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.9817 | −0.650149 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.9450 | 0.474082 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.45856 | −0.149527 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.02791 | 0.0875106 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −78.2653 | −3.37113 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.0924575 | −0.00397506 | −0.00198753 | − | 0.999998i | \(-0.500633\pi\) | ||||
−0.00198753 | + | 0.999998i | \(0.500633\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.5231 | −0.751989 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.9817 | −0.556074 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.77551 | −0.375214 | −0.187607 | − | 0.982244i | \(-0.560073\pi\) | ||||
−0.187607 | + | 0.982244i | \(0.560073\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.79383 | −0.0765589 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.65847 | −0.283661 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.5972 | −1.72637 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.59392 | 0.195001 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.5606 | −1.88809 | −0.944047 | − | 0.329812i | \(-0.893015\pi\) | ||||
−0.944047 | + | 0.329812i | \(0.893015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.94503 | 0.124562 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.0462 | −0.466372 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.6743 | 1.54564 | 0.772819 | − | 0.634626i | \(-0.218846\pi\) | ||||
0.772819 | + | 0.634626i | \(0.218846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.7938 | −0.580311 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.38776 | −0.184268 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22.5939 | −0.947187 | −0.473593 | − | 0.880744i | \(-0.657043\pi\) | ||||
−0.473593 | + | 0.880744i | \(0.657043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.1050 | −0.673972 | −0.336986 | − | 0.941510i | \(-0.609408\pi\) | ||||
−0.336986 | + | 0.941510i | \(0.609408\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.3878 | 0.433955 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.52311 | −0.0635183 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.32653 | 0.346638 | 0.173319 | − | 0.984866i | \(-0.444551\pi\) | ||||
0.173319 | + | 0.984866i | \(0.444551\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.13536 | 0.0471839 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.6926 | 1.64673 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −73.6068 | −3.04848 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.13536 | 0.0469413 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.9508 | 1.07111 | 0.535553 | − | 0.844502i | \(-0.320103\pi\) | ||||
0.535553 | + | 0.844502i | \(0.320103\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.72928 | −0.153662 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.5693 | 0.599303 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.38150 | 0.303122 | 0.151561 | − | 0.988448i | \(-0.451570\pi\) | ||||
0.151561 | + | 0.988448i | \(0.451570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.58767 | 0.311064 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.18785 | −0.376033 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.4219 | 1.03871 | 0.519356 | − | 0.854558i | \(-0.326172\pi\) | ||||
0.519356 | + | 0.854558i | \(0.326172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.8217 | 1.05329 | 0.526645 | − | 0.850085i | \(-0.323450\pi\) | ||||
0.526645 | + | 0.850085i | \(0.323450\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.04623 | 0.286945 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −29.8034 | −1.21168 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.31695 | −0.215808 | −0.107904 | − | 0.994161i | \(-0.534414\pi\) | ||||
−0.107904 | + | 0.994161i | \(0.534414\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.2158 | −1.18388 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.8122 | −0.437413 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.4498 | −1.51258 | −0.756292 | − | 0.654234i | \(-0.772991\pi\) | ||||
−0.756292 | + | 0.654234i | \(0.772991\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.64015 | 0.388728 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.2341 | 1.45873 | 0.729364 | − | 0.684125i | \(-0.239816\pi\) | ||||
0.729364 | + | 0.684125i | \(0.239816\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.7293 | −1.51647 | −0.758234 | − | 0.651983i | \(-0.773938\pi\) | ||||
−0.758234 | + | 0.651983i | \(0.773938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.52311 | −0.0611205 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −46.4835 | −1.86232 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.38776 | 0.255102 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.94419 | −0.316755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.4586 | 0.774633 | 0.387317 | − | 0.921947i | \(-0.373402\pi\) | ||||
0.387317 | + | 0.921947i | \(0.373402\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.5048 | 0.576514 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.04623 | 0.279621 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.9109 | −0.551169 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.31695 | 0.368573 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.1912 | 1.70595 | 0.852974 | − | 0.521953i | \(-0.174796\pi\) | ||||
0.852974 | + | 0.521953i | \(0.174796\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.4157 | −0.726243 | −0.363121 | − | 0.931742i | \(-0.618289\pi\) | ||||
−0.363121 | + | 0.931742i | \(0.618289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.59392 | 0.102136 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.2986 | −0.719393 | −0.359697 | − | 0.933069i | \(-0.617120\pi\) | ||||
−0.359697 | + | 0.933069i | \(0.617120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 95.6993 | 3.75653 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.3632 | −0.641323 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.1570 | −0.554007 | −0.277003 | − | 0.960869i | \(-0.589341\pi\) | ||||
−0.277003 | + | 0.960869i | \(0.589341\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.117037 | −0.00457301 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.50479 | −0.331804 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.3544 | 1.57199 | 0.785993 | − | 0.618236i | \(-0.212152\pi\) | ||||
0.785993 | + | 0.618236i | \(0.212152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.0837 | −1.87024 | −0.935120 | − | 0.354331i | \(-0.884709\pi\) | ||||
−0.935120 | + | 0.354331i | \(0.884709\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.96336 | −0.0762504 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.38776 | −0.170150 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.1416 | −0.392685 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.4586 | 0.752312 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4586 | 0.442353 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.86464 | −0.110424 | −0.0552119 | − | 0.998475i | \(-0.517583\pi\) | ||||
−0.0552119 | + | 0.998475i | \(0.517583\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 33.4865 | 1.28699 | 0.643495 | − | 0.765450i | \(-0.277484\pi\) | ||||
0.643495 | + | 0.765450i | \(0.277484\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.1570 | 0.773555 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.2524 | 0.431193 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.5972 | 1.24730 | 0.623650 | − | 0.781704i | \(-0.285649\pi\) | ||||
0.623650 | + | 0.781704i | \(0.285649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2524 | −0.429932 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.2062 | 0.389390 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.0829 | −0.498418 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.3728 | 1.11739 | 0.558696 | − | 0.829372i | \(-0.311302\pi\) | ||||
0.558696 | + | 0.829372i | \(0.311302\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.0279 | 1.06469 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.3169 | 0.505141 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.6705 | −0.631442 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.3449 | −1.10992 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.4952 | 0.434168 | 0.217084 | − | 0.976153i | \(-0.430345\pi\) | ||||
0.217084 | + | 0.976153i | \(0.430345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.59392 | 0.173263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.52311 | −0.358661 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.37276 | −0.202063 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.7572 | −1.19267 | −0.596333 | − | 0.802737i | \(-0.703376\pi\) | ||||
−0.596333 | + | 0.802737i | \(0.703376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.25240 | 0.346992 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.68012 | −0.212722 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.25240 | −0.271224 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.1170 | −0.751285 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.4802 | 0.912958 | 0.456479 | − | 0.889734i | \(-0.349110\pi\) | ||||
0.456479 | + | 0.889734i | \(0.349110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.9171 | −1.15141 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.55102 | 0.132064 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.65847 | 0.247289 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.4340 | 0.869118 | 0.434559 | − | 0.900643i | \(-0.356904\pi\) | ||||
0.434559 | + | 0.900643i | \(0.356904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.48562 | −0.165907 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.8863 | 1.69485 | 0.847424 | − | 0.530916i | \(-0.178152\pi\) | ||||
0.847424 | + | 0.530916i | \(0.178152\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.2524 | −0.451936 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −45.0096 | −1.65795 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.1020 | 1.14411 | 0.572054 | − | 0.820216i | \(-0.306147\pi\) | ||||
0.572054 | + | 0.820216i | \(0.306147\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.13536 | 0.0417085 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.5048 | −0.532129 | −0.266065 | − | 0.963955i | \(-0.585723\pi\) | ||||
−0.266065 | + | 0.963955i | \(0.585723\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.0000 | −0.512920 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.04623 | −0.330984 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.1753 | −0.554495 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.4094 | 1.80297 | 0.901487 | − | 0.432805i | \(-0.142476\pi\) | ||||
0.901487 | + | 0.432805i | \(0.142476\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.836734 | 0.0304923 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.2341 | 0.372456 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1108 | 0.912667 | 0.456333 | − | 0.889809i | \(-0.349162\pi\) | ||||
0.456333 | + | 0.889809i | \(0.349162\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.72928 | 0.353151 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.00000 | 0.217500 | 0.108750 | − | 0.994069i | \(-0.465315\pi\) | ||||
0.108750 | + | 0.994069i | \(0.465315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −56.9604 | −2.06211 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.72928 | −0.0625223 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.0096 | 0.614181 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.9634 | 0.575653 | 0.287827 | − | 0.957683i | \(-0.407067\pi\) | ||||
0.287827 | + | 0.957683i | \(0.407067\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.2986 | 0.586981 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.6522 | 0.562971 | 0.281486 | − | 0.959565i | \(-0.409173\pi\) | ||||
0.281486 | + | 0.959565i | \(0.409173\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.72928 | 0.133960 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.1570 | 0.723129 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.64015 | 0.345394 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −59.5144 | −2.12959 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.65847 | 0.237954 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.0279 | −0.429294 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −38.4556 | −1.37080 | −0.685398 | − | 0.728169i | \(-0.740372\pi\) | ||||
−0.685398 | + | 0.728169i | \(0.740372\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.206167 | 0.00733975 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −60.5240 | −2.15198 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.03664 | 0.0723234 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.5231 | −0.408683 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.2986 | 1.00239 | 0.501194 | − | 0.865335i | \(-0.332894\pi\) | ||||
0.501194 | + | 0.865335i | \(0.332894\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.4681 | 0.582601 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.5939 | 0.374318 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.3265 | 1.91714 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.68305 | −0.235547 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.7509 | −0.871274 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.0925 | 1.26894 | 0.634472 | − | 0.772946i | \(-0.281218\pi\) | ||||
0.634472 | + | 0.772946i | \(0.281218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.05581 | 0.282878 | 0.141439 | − | 0.989947i | \(-0.454827\pi\) | ||||
0.141439 | + | 0.989947i | \(0.454827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.3265 | −0.642740 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.4157 | −0.504959 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.59392 | 0.0907499 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.98168 | 0.174074 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.9142 | −1.67222 | −0.836108 | − | 0.548564i | \(-0.815175\pi\) | ||||
−0.836108 | + | 0.548564i | \(0.815175\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.1633 | 0.458843 | 0.229421 | − | 0.973327i | \(-0.426317\pi\) | ||||
0.229421 | + | 0.973327i | \(0.426317\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.38776 | −0.222393 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.2524 | 0.808565 | 0.404283 | − | 0.914634i | \(-0.367521\pi\) | ||||
0.404283 | + | 0.914634i | \(0.367521\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.3478 | −0.359393 | −0.179697 | − | 0.983722i | \(-0.557512\pi\) | ||||
−0.179697 | + | 0.983722i | \(0.557512\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.25240 | 0.251583 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.1878 | 0.734115 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.79383 | −0.131291 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.72928 | 0.128903 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.1512 | −1.07546 | −0.537729 | − | 0.843117i | \(-0.680718\pi\) | ||||
−0.537729 | + | 0.843117i | \(0.680718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3353 | 0.528802 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.4061 | 0.599497 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.7110 | 0.402869 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −130.770 | −4.49331 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.32320 | 0.148372 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.99707 | 0.239856 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.07414 | 0.242214 | 0.121107 | − | 0.992639i | \(-0.461356\pi\) | ||||
0.121107 | + | 0.992639i | \(0.461356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.4769 | −1.24603 | −0.623013 | − | 0.782211i | \(-0.714092\pi\) | ||||
−0.623013 | + | 0.782211i | \(0.714092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.58767 | −0.122410 | −0.0612048 | − | 0.998125i | \(-0.519494\pi\) | ||||
−0.0612048 | + | 0.998125i | \(0.519494\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 42.2986 | 1.44153 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.5972 | 0.973462 | 0.486731 | − | 0.873552i | \(-0.338189\pi\) | ||||
0.486731 | + | 0.873552i | \(0.338189\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.2986 | 0.418166 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.0096 | −0.475790 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −59.1020 | −2.00490 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.59392 | −0.155481 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.38776 | 0.148333 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.6402 | 0.528130 | 0.264065 | − | 0.964505i | \(-0.414937\pi\) | ||||
0.264065 | + | 0.964505i | \(0.414937\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.2524 | 0.581909 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.7851 | −1.60992 | −0.804960 | − | 0.593329i | \(-0.797813\pi\) | ||||
−0.804960 | + | 0.593329i | \(0.797813\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.09871 | −0.306196 | −0.153098 | − | 0.988211i | \(-0.548925\pi\) | ||||
−0.153098 | + | 0.988211i | \(0.548925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.9817 | 0.503604 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.5510 | 1.39515 | 0.697573 | − | 0.716513i | \(-0.254263\pi\) | ||||
0.697573 | + | 0.716513i | \(0.254263\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.9171 | 1.03693 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.38776 | −0.213998 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.52311 | −0.318679 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.02791 | −0.0677854 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.72928 | 0.0577390 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.8313 | 0.828171 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.9267 | 0.663855 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 11.3815 | 0.378753 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.5231 | 0.582488 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.775511 | −0.0257504 | −0.0128752 | − | 0.999917i | \(-0.504098\pi\) | ||||
−0.0128752 | + | 0.999917i | \(0.504098\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.22449 | 0.0406138 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.90754 | 0.195726 | 0.0978628 | − | 0.995200i | \(-0.468799\pi\) | ||||
0.0978628 | + | 0.995200i | \(0.468799\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57.7851 | 1.91241 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.79383 | 0.0593023 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.513530 | −0.0169582 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.1483 | 1.25840 | 0.629198 | − | 0.777245i | \(-0.283384\pi\) | ||||
0.629198 | + | 0.777245i | \(0.283384\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.31695 | 0.175199 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.5781 | −0.348182 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.59392 | −0.151047 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.04623 | 0.231429 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.2341 | −0.991948 | −0.495974 | − | 0.868337i | \(-0.665189\pi\) | ||||
−0.495974 | + | 0.868337i | \(0.665189\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.2524 | −0.401556 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.65847 | 0.283466 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.0462 | 0.361250 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.6926 | 0.708668 | 0.354334 | − | 0.935119i | \(-0.384708\pi\) | ||||
0.354334 | + | 0.935119i | \(0.384708\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −24.7389 | −0.807322 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.08039 | −0.133017 | −0.0665085 | − | 0.997786i | \(-0.521186\pi\) | ||||
−0.0665085 | + | 0.997786i | \(0.521186\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.6831 | 0.478146 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.38776 | 0.142734 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.5606 | −0.928095 | −0.464047 | − | 0.885810i | \(-0.653603\pi\) | ||||
−0.464047 | + | 0.885810i | \(0.653603\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.65599 | 0.313447 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0279 | −0.584595 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.8401 | 1.19337 | 0.596683 | − | 0.802477i | \(-0.296485\pi\) | ||||
0.596683 | + | 0.802477i | \(0.296485\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.3878 | −0.336140 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −42.5327 | −1.37489 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −49.3728 | −1.59433 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.0925 | −0.551370 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.45856 | 0.111451 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.13536 | −0.0365485 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.1999 | −0.746059 | −0.373029 | − | 0.927820i | \(-0.621681\pi\) | ||||
−0.373029 | + | 0.927820i | \(0.621681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.72928 | −0.0555525 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.79383 | 0.0575668 | 0.0287834 | − | 0.999586i | \(-0.490837\pi\) | ||||
0.0287834 | + | 0.999586i | \(0.490837\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 58.4315 | 1.87323 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.13536 | −0.0363606 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.4961 | 1.61551 | 0.807756 | − | 0.589517i | \(-0.200682\pi\) | ||||
0.807756 | + | 0.589517i | \(0.200682\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −67.6714 | −2.16279 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.9817 | 0.414473 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.8034 | −1.04627 | −0.523133 | − | 0.852251i | \(-0.675237\pi\) | ||||
−0.523133 | + | 0.852251i | \(0.675237\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.5693 | −0.464218 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −41.7851 | −1.33003 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.95084 | 0.125629 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.4277 | −1.03010 | −0.515050 | − | 0.857160i | \(-0.672227\pi\) | ||||
−0.515050 | + | 0.857160i | \(0.672227\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.9817 | −0.411961 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.18785 | 0.291274 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.93545 | 0.187978 | 0.0939888 | − | 0.995573i | \(-0.470038\pi\) | ||||
0.0939888 | + | 0.995573i | \(0.470038\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.59392 | −0.145345 |
(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 | 4560.2.a.bt.1.1 | 3 | ||
4.3 | odd | 2 | 2280.2.a.r.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 6840.2.a.bk.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.r.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
4560.2.a.bt.1.1 | 3 | 1.1 | even | 1 | trivial | ||
6840.2.a.bk.1.3 | 3 | 12.11 | even | 2 |