Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6840,2,Mod(1,6840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6840, 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("6840.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6840 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6840.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: | \(54.6176749826\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1772.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 8 \) |
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 | \(0.654334\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6840.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.11309 | −1.55460 | −0.777301 | − | 0.629129i | \(-0.783412\pi\) | ||||
−0.777301 | + | 0.629129i | \(0.783412\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.11309 | 0.637121 | 0.318560 | − | 0.947903i | \(-0.396801\pi\) | ||||
0.318560 | + | 0.947903i | \(0.396801\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.80442 | 1.33251 | 0.666254 | − | 0.745725i | \(-0.267897\pi\) | ||||
0.666254 | + | 0.745725i | \(0.267897\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.691333 | 0.144153 | 0.0720764 | − | 0.997399i | \(-0.477037\pi\) | ||||
0.0720764 | + | 0.997399i | \(0.477037\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.11309 | −0.763782 | −0.381891 | − | 0.924207i | \(-0.624727\pi\) | ||||
−0.381891 | + | 0.924207i | \(0.624727\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.11309 | 0.695239 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.42176 | 0.562533 | 0.281267 | − | 0.959630i | \(-0.409245\pi\) | ||||
0.281267 | + | 0.959630i | \(0.409245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.42176 | −0.846736 | −0.423368 | − | 0.905958i | \(-0.639152\pi\) | ||||
−0.423368 | + | 0.905958i | \(0.639152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.80442 | −0.427671 | −0.213835 | − | 0.976870i | \(-0.568596\pi\) | ||||
−0.213835 | + | 0.976870i | \(0.568596\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.691333 | −0.100841 | −0.0504206 | − | 0.998728i | \(-0.516056\pi\) | ||||
−0.0504206 | + | 0.998728i | \(0.516056\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.91751 | 1.41679 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.69133 | 0.369683 | 0.184842 | − | 0.982768i | \(-0.440823\pi\) | ||||
0.184842 | + | 0.982768i | \(0.440823\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.11309 | −0.284929 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.53485 | −1.24133 | −0.620666 | − | 0.784075i | \(-0.713138\pi\) | ||||
−0.620666 | + | 0.784075i | \(0.713138\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.91751 | −0.373549 | −0.186775 | − | 0.982403i | \(-0.559803\pi\) | ||||
−0.186775 | + | 0.982403i | \(0.559803\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.80442 | −0.595915 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.60885 | −0.665648 | −0.332824 | − | 0.942989i | \(-0.608001\pi\) | ||||
−0.332824 | + | 0.942989i | \(0.608001\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.69133 | −0.990469 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1437 | 1.70380 | 0.851899 | − | 0.523705i | \(-0.175451\pi\) | ||||
0.851899 | + | 0.523705i | \(0.175451\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.22618 | −0.683412 | −0.341706 | − | 0.939807i | \(-0.611005\pi\) | ||||
−0.341706 | + | 0.939807i | \(0.611005\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.42176 | 0.150706 | 0.0753530 | − | 0.997157i | \(-0.475992\pi\) | ||||
0.0753530 | + | 0.997157i | \(0.475992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.7610 | −2.07152 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4218 | 1.56584 | 0.782921 | − | 0.622121i | \(-0.213729\pi\) | ||||
0.782921 | + | 0.622121i | \(0.213729\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.2262 | 1.01754 | 0.508772 | − | 0.860902i | \(-0.330100\pi\) | ||||
0.508772 | + | 0.860902i | \(0.330100\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4524 | 1.62110 | 0.810550 | − | 0.585670i | \(-0.199168\pi\) | ||||
0.810550 | + | 0.585670i | \(0.199168\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.4524 | −1.59051 | −0.795255 | − | 0.606275i | \(-0.792663\pi\) | ||||
−0.795255 | + | 0.606275i | \(0.792663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.53485 | −0.721708 | −0.360854 | − | 0.932622i | \(-0.617515\pi\) | ||||
−0.360854 | + | 0.932622i | \(0.617515\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.5348 | 1.64954 | 0.824770 | − | 0.565469i | \(-0.191305\pi\) | ||||
0.824770 | + | 0.565469i | \(0.191305\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.691333 | −0.0644671 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.4524 | 1.50819 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.53485 | −0.594077 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.83503 | −0.872718 | −0.436359 | − | 0.899773i | \(-0.643732\pi\) | ||||
−0.436359 | + | 0.899773i | \(0.643732\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.33927 | −0.553865 | −0.276932 | − | 0.960889i | \(-0.589318\pi\) | ||||
−0.276932 | + | 0.960889i | \(0.589318\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.11309 | −0.356650 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.30867 | −0.624422 | −0.312211 | − | 0.950013i | \(-0.601070\pi\) | ||||
−0.312211 | + | 0.950013i | \(0.601070\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.22618 | −0.697736 | −0.348868 | − | 0.937172i | \(-0.613434\pi\) | ||||
−0.348868 | + | 0.937172i | \(0.613434\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.1522 | 0.848968 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.11309 | 0.341574 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.38267 | 0.604812 | 0.302406 | − | 0.953179i | \(-0.402210\pi\) | ||||
0.302406 | + | 0.953179i | \(0.402210\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.38267 | −0.600793 | −0.300396 | − | 0.953814i | \(-0.597119\pi\) | ||||
−0.300396 | + | 0.953814i | \(0.597119\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.9175 | 1.03093 | 0.515465 | − | 0.856911i | \(-0.327619\pi\) | ||||
0.515465 | + | 0.856911i | \(0.327619\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.84352 | −0.224100 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.42176 | −0.424665 | −0.212332 | − | 0.977197i | \(-0.568106\pi\) | ||||
−0.212332 | + | 0.977197i | \(0.568106\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.9175 | 0.999587 | 0.499794 | − | 0.866145i | \(-0.333409\pi\) | ||||
0.499794 | + | 0.866145i | \(0.333409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.0825 | 0.775576 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.5348 | 1.02904 | 0.514518 | − | 0.857480i | \(-0.327971\pi\) | ||||
0.514518 | + | 0.857480i | \(0.327971\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.11309 | −0.310920 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.9175 | 0.816013 | 0.408007 | − | 0.912979i | \(-0.366224\pi\) | ||||
0.408007 | + | 0.912979i | \(0.366224\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.3699 | −1.29109 | −0.645546 | − | 0.763721i | \(-0.723370\pi\) | ||||
−0.645546 | + | 0.763721i | \(0.723370\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.42176 | −0.251573 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.45236 | −0.618098 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.730425 | −0.0528517 | −0.0264258 | − | 0.999651i | \(-0.508413\pi\) | ||||
−0.0264258 | + | 0.999651i | \(0.508413\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.4830 | 1.83430 | 0.917152 | − | 0.398537i | \(-0.130482\pi\) | ||||
0.917152 | + | 0.398537i | \(0.130482\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.7610 | 1.55041 | 0.775205 | − | 0.631710i | \(-0.217647\pi\) | ||||
0.775205 | + | 0.631710i | \(0.217647\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.60885 | 0.114048 | 0.0570241 | − | 0.998373i | \(-0.481839\pi\) | ||||
0.0570241 | + | 0.998373i | \(0.481839\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.9175 | 1.18738 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.42176 | 0.378672 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.11309 | 0.146166 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.83503 | 0.677071 | 0.338536 | − | 0.940954i | \(-0.390068\pi\) | ||||
0.338536 | + | 0.940954i | \(0.390068\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.80442 | 0.191260 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.22618 | 0.558430 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.2177 | −1.29272 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.8350 | 0.926462 | 0.463231 | − | 0.886238i | \(-0.346690\pi\) | ||||
0.463231 | + | 0.886238i | \(0.346690\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.3002 | −0.683647 | −0.341823 | − | 0.939764i | \(-0.611044\pi\) | ||||
−0.341823 | + | 0.939764i | \(0.611044\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.08249 | 0.600188 | 0.300094 | − | 0.953910i | \(-0.402982\pi\) | ||||
0.300094 | + | 0.953910i | \(0.402982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.5264 | 1.47575 | 0.737875 | − | 0.674937i | \(-0.235829\pi\) | ||||
0.737875 | + | 0.674937i | \(0.235829\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.691333 | 0.0450976 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.7219 | 1.53444 | 0.767222 | − | 0.641381i | \(-0.221638\pi\) | ||||
0.767222 | + | 0.641381i | \(0.221638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.2177 | 1.36675 | 0.683376 | − | 0.730067i | \(-0.260511\pi\) | ||||
0.683376 | + | 0.730067i | \(0.260511\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.91751 | −0.633607 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.80442 | 0.305698 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.1743 | 1.77835 | 0.889173 | − | 0.457571i | \(-0.151280\pi\) | ||||
0.889173 | + | 0.457571i | \(0.151280\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.46085 | 0.0918428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.3002 | −0.767264 | −0.383632 | − | 0.923486i | \(-0.625327\pi\) | ||||
−0.383632 | + | 0.923486i | \(0.625327\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.0740 | −0.874516 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.9175 | −0.796528 | −0.398264 | − | 0.917271i | \(-0.630387\pi\) | ||||
−0.398264 | + | 0.917271i | \(0.630387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.69133 | −0.165327 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.73042 | 0.410361 | 0.205181 | − | 0.978724i | \(-0.434222\pi\) | ||||
0.205181 | + | 0.978724i | \(0.434222\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.77382 | −0.472226 | −0.236113 | − | 0.971726i | \(-0.575874\pi\) | ||||
−0.236113 | + | 0.971726i | \(0.575874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.11309 | 0.127424 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.3087 | 0.919809 | 0.459904 | − | 0.887968i | \(-0.347884\pi\) | ||||
0.459904 | + | 0.887968i | \(0.347884\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4218 | −0.800675 | −0.400337 | − | 0.916368i | \(-0.631107\pi\) | ||||
−0.400337 | + | 0.916368i | \(0.631107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0306 | 0.893477 | 0.446738 | − | 0.894665i | \(-0.352585\pi\) | ||||
0.446738 | + | 0.894665i | \(0.352585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.3002 | 1.31634 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.08249 | 0.530604 | 0.265302 | − | 0.964165i | \(-0.414528\pi\) | ||||
0.265302 | + | 0.964165i | \(0.414528\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.53485 | 0.555140 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.32146 | 0.192085 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.5348 | 0.664858 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.91751 | 0.167056 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.2262 | 1.83925 | 0.919623 | − | 0.392803i | \(-0.128495\pi\) | ||||
0.919623 | + | 0.392803i | \(0.128495\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.7304 | 0.948695 | 0.474348 | − | 0.880338i | \(-0.342684\pi\) | ||||
0.474348 | + | 0.880338i | \(0.342684\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.6785 | −0.829680 | −0.414840 | − | 0.909894i | \(-0.636163\pi\) | ||||
−0.414840 | + | 0.909894i | \(0.636163\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.9090 | 1.00587 | 0.502936 | − | 0.864324i | \(-0.332253\pi\) | ||||
0.502936 | + | 0.864324i | \(0.332253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.69133 | −0.486621 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.00000 | −0.222566 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.80442 | 0.266501 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.84352 | 0.156768 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.92600 | −0.105863 | −0.0529313 | − | 0.998598i | \(-0.516856\pi\) | ||||
−0.0529313 | + | 0.998598i | \(0.516856\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.2568 | −0.940037 | −0.470019 | − | 0.882657i | \(-0.655753\pi\) | ||||
−0.470019 | + | 0.882657i | \(0.655753\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.22618 | −0.228861 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | −0.647939 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.6785 | 1.21745 | 0.608724 | − | 0.793382i | \(-0.291682\pi\) | ||||
0.608724 | + | 0.793382i | \(0.291682\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.61733 | 0.247160 | 0.123580 | − | 0.992335i | \(-0.460562\pi\) | ||||
0.123580 | + | 0.992335i | \(0.460562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.7610 | 1.26467 | 0.632336 | − | 0.774694i | \(-0.282096\pi\) | ||||
0.632336 | + | 0.774694i | \(0.282096\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.60885 | 0.297687 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.5042 | 0.659949 | 0.329974 | − | 0.943990i | \(-0.392960\pi\) | ||||
0.329974 | + | 0.943990i | \(0.392960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.73042 | −0.351325 | −0.175663 | − | 0.984450i | \(-0.556207\pi\) | ||||
−0.175663 | + | 0.984450i | \(0.556207\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.0697 | −0.574710 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.80442 | 0.455876 | 0.227938 | − | 0.973676i | \(-0.426802\pi\) | ||||
0.227938 | + | 0.973676i | \(0.426802\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.7610 | −1.01774 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.7610 | −1.63145 | −0.815727 | − | 0.578437i | \(-0.803663\pi\) | ||||
−0.815727 | + | 0.578437i | \(0.803663\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.0697 | −1.17881 | −0.589403 | − | 0.807839i | \(-0.700637\pi\) | ||||
−0.589403 | + | 0.807839i | \(0.700637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.69133 | 0.442951 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.0000 | 0.709828 | 0.354914 | − | 0.934899i | \(-0.384510\pi\) | ||||
0.354914 | + | 0.934899i | \(0.384510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.76533 | −0.139849 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1437 | −0.761962 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.5264 | 1.93358 | 0.966791 | − | 0.255567i | \(-0.0822622\pi\) | ||||
0.966791 | + | 0.255567i | \(0.0822622\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.1003 | −1.10364 | −0.551818 | − | 0.833964i | \(-0.686066\pi\) | ||||
−0.551818 | + | 0.833964i | \(0.686066\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.60885 | −0.478651 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.23048 | 0.358402 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.2262 | 1.49459 | 0.747294 | − | 0.664493i | \(-0.231353\pi\) | ||||
0.747294 | + | 0.664493i | \(0.231353\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 39.2177 | 1.92978 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.22618 | 0.305631 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.7219 | −0.572654 | −0.286327 | − | 0.958132i | \(-0.592434\pi\) | ||||
−0.286327 | + | 0.958132i | \(0.592434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.9787 | −1.50981 | −0.754905 | − | 0.655834i | \(-0.772317\pi\) | ||||
−0.754905 | + | 0.655834i | \(0.772317\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0000 | 0.580721 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.2959 | 0.929450 | 0.464725 | − | 0.885455i | \(-0.346153\pi\) | ||||
0.464725 | + | 0.885455i | \(0.346153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.4218 | −1.12558 | −0.562789 | − | 0.826601i | \(-0.690272\pi\) | ||||
−0.562789 | + | 0.826601i | \(0.690272\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.691333 | 0.0330709 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.85630 | −0.422688 | −0.211344 | − | 0.977412i | \(-0.567784\pi\) | ||||
−0.211344 | + | 0.977412i | \(0.567784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.23467 | 0.343729 | 0.171865 | − | 0.985121i | \(-0.445021\pi\) | ||||
0.171865 | + | 0.985121i | \(0.445021\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.42176 | −0.0673978 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.19558 | 0.0564227 | 0.0282114 | − | 0.999602i | \(-0.491019\pi\) | ||||
0.0282114 | + | 0.999602i | \(0.491019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4567 | −0.539473 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.7610 | 0.926411 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.9915 | 0.794829 | 0.397415 | − | 0.917639i | \(-0.369907\pi\) | ||||
0.397415 | + | 0.917639i | \(0.369907\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.6173 | 0.773946 | 0.386973 | − | 0.922091i | \(-0.373521\pi\) | ||||
0.386973 | + | 0.922091i | \(0.373521\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.1131 | −0.562943 | −0.281472 | − | 0.959570i | \(-0.590822\pi\) | ||||
−0.281472 | + | 0.959570i | \(0.590822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.6701 | −1.74316 | −0.871581 | − | 0.490251i | \(-0.836905\pi\) | ||||
−0.871581 | + | 0.490251i | \(0.836905\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.4524 | −0.759700 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.92600 | −0.272478 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 34.1131 | 1.55867 | 0.779333 | − | 0.626609i | \(-0.215558\pi\) | ||||
0.779333 | + | 0.626609i | \(0.215558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4396 | 0.749580 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.4218 | −0.700266 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.5136 | −1.74522 | −0.872608 | − | 0.488421i | \(-0.837573\pi\) | ||||
−0.872608 | + | 0.488421i | \(0.837573\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.49576 | −0.157761 | −0.0788806 | − | 0.996884i | \(-0.525135\pi\) | ||||
−0.0788806 | + | 0.996884i | \(0.525135\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.4524 | 0.740977 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23.0697 | 1.03482 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.2262 | −0.726384 | −0.363192 | − | 0.931714i | \(-0.618313\pi\) | ||||
−0.363192 | + | 0.931714i | \(0.618313\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.3699 | 1.48789 | 0.743945 | − | 0.668241i | \(-0.232953\pi\) | ||||
0.743945 | + | 0.668241i | \(0.232953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.2262 | −0.455059 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.5570 | −0.866847 | −0.433424 | − | 0.901190i | \(-0.642695\pi\) | ||||
−0.433424 | + | 0.901190i | \(0.642695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.6785 | −1.09171 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.4524 | −0.724978 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.46085 | −0.0642481 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.63945 | −0.203258 | −0.101629 | − | 0.994822i | \(-0.532405\pi\) | ||||
−0.101629 | + | 0.994822i | \(0.532405\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.8962 | −1.56963 | −0.784816 | − | 0.619728i | \(-0.787243\pi\) | ||||
−0.784816 | + | 0.619728i | \(0.787243\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000 | 0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5221 | −0.979220 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.0484 | −1.12828 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.4524 | 0.711298 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.9566 | 0.902665 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.53485 | 0.322757 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2262 | 1.03584 | 0.517918 | − | 0.855430i | \(-0.326707\pi\) | ||||
0.517918 | + | 0.855430i | \(0.326707\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.11309 | −0.175224 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −62.2874 | −2.64873 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00000 | −0.254228 | −0.127114 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127114 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.4736 | −0.569874 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.9175 | −1.89305 | −0.946524 | − | 0.322634i | \(-0.895432\pi\) | ||||
−0.946524 | + | 0.322634i | \(0.895432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.5348 | −0.737697 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.1956 | 0.720876 | 0.360438 | − | 0.932783i | \(-0.382627\pi\) | ||||
0.360438 | + | 0.932783i | \(0.382627\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.15648 | −0.0483974 | −0.0241987 | − | 0.999707i | \(-0.507703\pi\) | ||||
−0.0241987 | + | 0.999707i | \(0.507703\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.691333 | 0.0288306 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.5136 | −1.52008 | −0.760040 | − | 0.649876i | \(-0.774821\pi\) | ||||
−0.760040 | + | 0.649876i | \(0.774821\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.6088 | 1.06243 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.68703 | 0.235533 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.61733 | −0.190578 | −0.0952889 | − | 0.995450i | \(-0.530377\pi\) | ||||
−0.0952889 | + | 0.995450i | \(0.530377\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.00000 | −0.0824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.5961 | −1.05110 | −0.525552 | − | 0.850761i | \(-0.676141\pi\) | ||||
−0.525552 | + | 0.850761i | \(0.676141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.4524 | −0.674481 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.3571 | −1.85324 | −0.926620 | − | 0.375999i | \(-0.877300\pi\) | ||||
−0.926620 | + | 0.375999i | \(0.877300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.6088 | 0.636698 | 0.318349 | − | 0.947974i | \(-0.396872\pi\) | ||||
0.318349 | + | 0.947974i | \(0.396872\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.53485 | 0.265679 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.8962 | 1.61934 | 0.809669 | − | 0.586887i | \(-0.199647\pi\) | ||||
0.809669 | + | 0.586887i | \(0.199647\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.32146 | −0.134372 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.6828 | 0.471866 | 0.235933 | − | 0.971769i | \(-0.424185\pi\) | ||||
0.235933 | + | 0.971769i | \(0.424185\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.2874 | 1.05829 | 0.529145 | − | 0.848531i | \(-0.322513\pi\) | ||||
0.529145 | + | 0.848531i | \(0.322513\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.2959 | 0.936340 | 0.468170 | − | 0.883638i | \(-0.344913\pi\) | ||||
0.468170 | + | 0.883638i | \(0.344913\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.84782 | −0.234288 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.6870 | −0.545738 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.2347 | −0.845339 | −0.422669 | − | 0.906284i | \(-0.638907\pi\) | ||||
−0.422669 | + | 0.906284i | \(0.638907\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.83503 | 0.390291 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.6479 | 1.88788 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.7091 | 1.56842 | 0.784209 | − | 0.620497i | \(-0.213069\pi\) | ||||
0.784209 | + | 0.620497i | \(0.213069\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.8044 | 1.05706 | 0.528532 | − | 0.848914i | \(-0.322743\pi\) | ||||
0.528532 | + | 0.848914i | \(0.322743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.3002 | −0.404942 | −0.202471 | − | 0.979288i | \(-0.564897\pi\) | ||||
−0.202471 | + | 0.979288i | \(0.564897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.1480 | −0.790878 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.8563 | 0.659638 | 0.329819 | − | 0.944044i | \(-0.393012\pi\) | ||||
0.329819 | + | 0.944044i | \(0.393012\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.33927 | 0.247696 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.90903 | 0.0743651 | 0.0371826 | − | 0.999308i | \(-0.488162\pi\) | ||||
0.0371826 | + | 0.999308i | \(0.488162\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.30018 | 0.0894666 | 0.0447333 | − | 0.998999i | \(-0.485756\pi\) | ||||
0.0447333 | + | 0.998999i | \(0.485756\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.11309 | 0.159499 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.84352 | −0.110101 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.16497 | −0.237996 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.4745 | −1.25180 | −0.625900 | − | 0.779904i | \(-0.715268\pi\) | ||||
−0.625900 | + | 0.779904i | \(0.715268\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.07400 | 0.310309 | 0.155154 | − | 0.987890i | \(-0.450412\pi\) | ||||
0.155154 | + | 0.987890i | \(0.450412\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −63.4311 | −2.43426 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.6173 | −0.712372 | −0.356186 | − | 0.934415i | \(-0.615923\pi\) | ||||
−0.356186 | + | 0.934415i | \(0.615923\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.30867 | 0.279250 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.9303 | 0.492605 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.6088 | −0.974206 | −0.487103 | − | 0.873344i | \(-0.661946\pi\) | ||||
−0.487103 | + | 0.873344i | \(0.661946\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.22618 | 0.312037 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.6870 | 0.821455 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.765332 | −0.0289062 | −0.0144531 | − | 0.999896i | \(-0.504601\pi\) | ||||
−0.0144531 | + | 0.999896i | \(0.504601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.42176 | 0.129054 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −42.0612 | −1.58187 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.8222 | 1.34533 | 0.672666 | − | 0.739946i | \(-0.265149\pi\) | ||||
0.672666 | + | 0.739946i | \(0.265149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.38267 | −0.0517812 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.1522 | −0.379670 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.7916 | 0.849985 | 0.424992 | − | 0.905197i | \(-0.360277\pi\) | ||||
0.424992 | + | 0.905197i | \(0.360277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −67.6701 | −2.52016 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.11309 | −0.152756 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.6351 | 1.32163 | 0.660817 | − | 0.750547i | \(-0.270210\pi\) | ||||
0.660817 | + | 0.750547i | \(0.270210\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.2177 | 0.414901 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.6913 | 0.764252 | 0.382126 | − | 0.924110i | \(-0.375192\pi\) | ||||
0.382126 | + | 0.924110i | \(0.375192\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.45236 | 0.311347 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.2177 | −0.854077 | −0.427038 | − | 0.904234i | \(-0.640443\pi\) | ||||
−0.427038 | + | 0.904234i | \(0.640443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.06970 | −0.259362 | −0.129681 | − | 0.991556i | \(-0.541395\pi\) | ||||
−0.129681 | + | 0.991556i | \(0.541395\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.38267 | −0.270480 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 67.6701 | 2.47261 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.61733 | −0.314451 | −0.157225 | − | 0.987563i | \(-0.550255\pi\) | ||||
−0.157225 | + | 0.987563i | \(0.550255\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.38267 | 0.268683 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 47.9872 | 1.74412 | 0.872062 | − | 0.489395i | \(-0.162782\pi\) | ||||
0.872062 | + | 0.489395i | \(0.162782\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.0527 | 0.835661 | 0.417830 | − | 0.908525i | \(-0.362791\pi\) | ||||
0.417830 | + | 0.908525i | \(0.362791\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.9915 | 1.12197 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45.8094 | −1.65408 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.0697 | 1.33677 | 0.668384 | − | 0.743817i | \(-0.266986\pi\) | ||||
0.668384 | + | 0.743817i | \(0.266986\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.3087 | 0.910289 | 0.455145 | − | 0.890417i | \(-0.349588\pi\) | ||||
0.455145 | + | 0.890417i | \(0.349588\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.42176 | −0.194255 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.8520 | −0.424098 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.9175 | −0.461046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.9915 | −0.391805 | −0.195903 | − | 0.980623i | \(-0.562764\pi\) | ||||
−0.195903 | + | 0.980623i | \(0.562764\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −72.1224 | −2.56438 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0170 | −0.497757 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.69982 | 0.272742 | 0.136371 | − | 0.990658i | \(-0.456456\pi\) | ||||
0.136371 | + | 0.990658i | \(0.456456\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.76533 | 0.0978304 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.6785 | 0.447416 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.84352 | 0.100221 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.4524 | −0.789383 | −0.394692 | − | 0.918814i | \(-0.629149\pi\) | ||||
−0.394692 | + | 0.918814i | \(0.629149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.5051 | 1.87882 | 0.939409 | − | 0.342799i | \(-0.111375\pi\) | ||||
0.939409 | + | 0.342799i | \(0.111375\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.42176 | 0.189916 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.80442 | −0.0981144 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.62582 | −0.0567415 | −0.0283708 | − | 0.999597i | \(-0.509032\pi\) | ||||
−0.0283708 | + | 0.999597i | \(0.509032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.4958 | −1.02816 | −0.514079 | − | 0.857743i | \(-0.671866\pi\) | ||||
−0.514079 | + | 0.857743i | \(0.671866\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.91751 | 0.170999 | 0.0854994 | − | 0.996338i | \(-0.472751\pi\) | ||||
0.0854994 | + | 0.996338i | \(0.472751\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.9175 | −0.587570 | −0.293785 | − | 0.955872i | \(-0.594915\pi\) | ||||
−0.293785 | + | 0.955872i | \(0.594915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.6701 | −1.37449 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.9175 | −0.447029 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.8435 | 0.374360 | 0.187180 | − | 0.982326i | \(-0.440065\pi\) | ||||
0.187180 | + | 0.982326i | \(0.440065\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.0825 | −0.416637 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.0825 | −0.346848 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.8784 | 0.923554 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.36557 | 0.0810908 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.9175 | 0.990117 | 0.495058 | − | 0.868860i | \(-0.335147\pi\) | ||||
0.495058 | + | 0.868860i | \(0.335147\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.2917 | −0.932266 | −0.466133 | − | 0.884715i | \(-0.654353\pi\) | ||||
−0.466133 | + | 0.884715i | \(0.654353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.6173 | −0.362259 | −0.181129 | − | 0.983459i | \(-0.557975\pi\) | ||||
−0.181129 | + | 0.983459i | \(0.557975\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.61733 | 0.225257 | 0.112628 | − | 0.993637i | \(-0.464073\pi\) | ||||
0.112628 | + | 0.993637i | \(0.464073\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.5348 | −0.460199 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.0000 | 1.08553 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.2177 | 0.651167 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.11309 | 0.139048 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.4133 | 0.756842 | 0.378421 | − | 0.925634i | \(-0.376467\pi\) | ||||
0.378421 | + | 0.925634i | \(0.376467\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.5392 | 0.422455 | 0.211227 | − | 0.977437i | \(-0.432254\pi\) | ||||
0.211227 | + | 0.977437i | \(0.432254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.96091 | 0.267906 | 0.133953 | − | 0.990988i | \(-0.457233\pi\) | ||||
0.133953 | + | 0.990988i | \(0.457233\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.68703 | 0.190952 | 0.0954759 | − | 0.995432i | \(-0.469563\pi\) | ||||
0.0954759 | + | 0.995432i | \(0.469563\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.4524 | 1.35673 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.691333 | −0.0231346 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.9175 | −0.364932 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.22618 | 0.274359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.7653 | −0.358645 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17.3699 | 0.577394 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.6088 | 0.584692 | 0.292346 | − | 0.956313i | \(-0.405564\pi\) | ||||
0.292346 | + | 0.956313i | \(0.405564\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.2177 | 0.769237 | 0.384618 | − | 0.923076i | \(-0.374333\pi\) | ||||
0.384618 | + | 0.923076i | \(0.374333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.1565 | −0.435416 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 26.0740 | 0.861039 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.06970 | 0.233208 | 0.116604 | − | 0.993179i | \(-0.462799\pi\) | ||||
0.116604 | + | 0.993179i | \(0.462799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.9473 | −0.886980 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.42176 | 0.112507 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 52.9659 | 1.73776 | 0.868878 | − | 0.495026i | \(-0.164842\pi\) | ||||
0.868878 | + | 0.495026i | \(0.164842\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.91751 | 0.325033 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.45236 | 0.276422 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.75685 | 0.122731 | 0.0613654 | − | 0.998115i | \(-0.480455\pi\) | ||||
0.0613654 | + | 0.998115i | \(0.480455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.0178 | 0.424369 | 0.212184 | − | 0.977230i | \(-0.431942\pi\) | ||||
0.212184 | + | 0.977230i | \(0.431942\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.74824 | −0.122059 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.3912 | −0.662623 | −0.331312 | − | 0.943521i | \(-0.607491\pi\) | ||||
−0.331312 | + | 0.943521i | \(0.607491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.8265 | 0.935749 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.2746 | 1.56377 | 0.781884 | − | 0.623424i | \(-0.214259\pi\) | ||||
0.781884 | + | 0.623424i | \(0.214259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.730425 | 0.0236360 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.0612 | 0.970727 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.4830 | −0.820326 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.9396 | −0.930636 | −0.465318 | − | 0.885144i | \(-0.654060\pi\) | ||||
−0.465318 | + | 0.885144i | \(0.654060\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.92600 | 0.125991 | 0.0629957 | − | 0.998014i | \(-0.479935\pi\) | ||||
0.0629957 | + | 0.998014i | \(0.479935\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 33.8350 | 1.08470 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.30867 | 0.297811 | 0.148905 | − | 0.988851i | \(-0.452425\pi\) | ||||
0.148905 | + | 0.988851i | \(0.452425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.00430 | 0.0960179 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.8478 | 0.441677 | 0.220838 | − | 0.975310i | \(-0.429121\pi\) | ||||
0.220838 | + | 0.975310i | \(0.429121\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.7610 | −0.693364 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.93879 | −0.0616500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.5433 | 0.970241 | 0.485121 | − | 0.874447i | \(-0.338776\pi\) | ||||
0.485121 | + | 0.874447i | \(0.338776\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.60885 | −0.0510039 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.75254 | −0.213855 | −0.106928 | − | 0.994267i | \(-0.534101\pi\) | ||||
−0.106928 | + | 0.994267i | \(0.534101\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6840.2.a.bh.1.1 | 3 | ||
3.2 | odd | 2 | 2280.2.a.u.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 4560.2.a.bs.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2280.2.a.u.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
4560.2.a.bs.1.3 | 3 | 12.11 | even | 2 | |||
6840.2.a.bh.1.1 | 3 | 1.1 | even | 1 | trivial |