Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3192,2,Mod(1,3192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3192, 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("3192.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3192 = 2^{3} \cdot 3 \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3192.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: | \(25.4882483252\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.135076.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 5x^{3} + 4x^{2} + 4x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.94486\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3192.1 |
$q$-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 | ||||||||
\(5\) | −3.88971 | −1.73953 | −0.869766 | − | 0.493464i | \(-0.835730\pi\) | ||||
−0.869766 | + | 0.493464i | \(0.835730\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.21056 | 0.968021 | 0.484010 | − | 0.875062i | \(-0.339180\pi\) | ||||
0.484010 | + | 0.875062i | \(0.339180\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.39794 | 1.49712 | 0.748559 | − | 0.663068i | \(-0.230746\pi\) | ||||
0.748559 | + | 0.663068i | \(0.230746\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.88971 | 1.00432 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.41108 | −1.06984 | −0.534922 | − | 0.844902i | \(-0.679659\pi\) | ||||
−0.534922 | + | 0.844902i | \(0.679659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.39794 | −0.708519 | −0.354259 | − | 0.935147i | \(-0.615267\pi\) | ||||
−0.354259 | + | 0.935147i | \(0.615267\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.1299 | 2.02597 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.28765 | −1.35328 | −0.676641 | − | 0.736313i | \(-0.736565\pi\) | ||||
−0.676641 | + | 0.736313i | \(0.736565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.187375 | 0.0336535 | 0.0168268 | − | 0.999858i | \(-0.494644\pi\) | ||||
0.0168268 | + | 0.999858i | \(0.494644\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.21056 | −0.558887 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.88971 | −0.657481 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.60850 | −0.757633 | −0.378816 | − | 0.925472i | \(-0.623669\pi\) | ||||
−0.378816 | + | 0.925472i | \(0.623669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.39794 | −0.864362 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.77943 | −1.52729 | −0.763645 | − | 0.645637i | \(-0.776592\pi\) | ||||
−0.763645 | + | 0.645637i | \(0.776592\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.88971 | −0.579844 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.45071 | 0.649203 | 0.324602 | − | 0.945851i | \(-0.394770\pi\) | ||||
0.324602 | + | 0.945851i | \(0.394770\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.41108 | 0.617674 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.2876 | 1.55048 | 0.775239 | − | 0.631668i | \(-0.217629\pi\) | ||||
0.775239 | + | 0.631668i | \(0.217629\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.4882 | −1.68390 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.77156 | −0.751394 | −0.375697 | − | 0.926743i | \(-0.622597\pi\) | ||||
−0.375697 | + | 0.926743i | \(0.622597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −20.9964 | −2.60429 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.48173 | 0.303191 | 0.151596 | − | 0.988443i | \(-0.451559\pi\) | ||||
0.151596 | + | 0.988443i | \(0.451559\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.39794 | 0.409064 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4175 | 1.47369 | 0.736844 | − | 0.676063i | \(-0.236315\pi\) | ||||
0.736844 | + | 0.676063i | \(0.236315\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.08714 | −0.478363 | −0.239181 | − | 0.970975i | \(-0.576879\pi\) | ||||
−0.239181 | + | 0.970975i | \(0.576879\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.1299 | −1.16970 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.21056 | 0.365878 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.68920 | 0.302558 | 0.151279 | − | 0.988491i | \(-0.451661\pi\) | ||||
0.151279 | + | 0.988491i | \(0.451661\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.92935 | 0.431302 | 0.215651 | − | 0.976470i | \(-0.430813\pi\) | ||||
0.215651 | + | 0.976470i | \(0.430813\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.1578 | 1.86103 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.28765 | 0.781318 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.70874 | 0.287126 | 0.143563 | − | 0.989641i | \(-0.454144\pi\) | ||||
0.143563 | + | 0.989641i | \(0.454144\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.39794 | 0.565858 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.187375 | −0.0194299 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.88971 | −0.399076 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.227011 | −0.0230495 | −0.0115248 | − | 0.999934i | \(-0.503669\pi\) | ||||
−0.0115248 | + | 0.999934i | \(0.503669\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.21056 | 0.322674 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.6691 | 1.95715 | 0.978576 | − | 0.205885i | \(-0.0660073\pi\) | ||||
0.978576 | + | 0.205885i | \(0.0660073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.7219 | −1.45059 | −0.725297 | − | 0.688436i | \(-0.758297\pi\) | ||||
−0.725297 | + | 0.688436i | \(0.758297\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.88971 | 0.379597 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.95366 | 0.865583 | 0.432792 | − | 0.901494i | \(-0.357529\pi\) | ||||
0.432792 | + | 0.901494i | \(0.357529\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5921 | 1.30188 | 0.650941 | − | 0.759128i | \(-0.274374\pi\) | ||||
0.650941 | + | 0.759128i | \(0.274374\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.60850 | 0.437419 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.35047 | 0.785546 | 0.392773 | − | 0.919635i | \(-0.371516\pi\) | ||||
0.392773 | + | 0.919635i | \(0.371516\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.2170 | 1.23249 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.39794 | 0.499039 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.41108 | −0.404363 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.692290 | −0.0629355 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.77943 | 0.881781 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −19.9537 | −1.78471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.70565 | −0.506294 | −0.253147 | − | 0.967428i | \(-0.581466\pi\) | ||||
−0.253147 | + | 0.967428i | \(0.581466\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3505 | −0.904325 | −0.452163 | − | 0.891936i | \(-0.649347\pi\) | ||||
−0.452163 | + | 0.891936i | \(0.649347\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.88971 | 0.334773 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.7959 | 1.43497 | 0.717484 | − | 0.696575i | \(-0.245294\pi\) | ||||
0.717484 | + | 0.696575i | \(0.245294\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.3469 | −1.38652 | −0.693261 | − | 0.720686i | \(-0.743827\pi\) | ||||
−0.693261 | + | 0.720686i | \(0.743827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.45071 | −0.374818 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.3304 | 1.44924 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 28.3469 | 2.35408 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.82907 | 0.395613 | 0.197807 | − | 0.980241i | \(-0.436618\pi\) | ||||
0.197807 | + | 0.980241i | \(0.436618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.2645 | 1.73048 | 0.865240 | − | 0.501358i | \(-0.167166\pi\) | ||||
0.865240 | + | 0.501358i | \(0.167166\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.41108 | −0.356614 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.728835 | −0.0585414 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.1377 | 1.84659 | 0.923296 | − | 0.384090i | \(-0.125485\pi\) | ||||
0.923296 | + | 0.384090i | \(0.125485\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.2876 | −0.895169 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.39794 | −0.267795 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.27117 | 0.569522 | 0.284761 | − | 0.958599i | \(-0.408086\pi\) | ||||
0.284761 | + | 0.958599i | \(0.408086\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.4882 | 0.972202 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.12986 | −0.551725 | −0.275863 | − | 0.961197i | \(-0.588964\pi\) | ||||
−0.275863 | + | 0.961197i | \(0.588964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.1377 | 1.24136 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.08349 | −0.234433 | −0.117217 | − | 0.993106i | \(-0.537397\pi\) | ||||
−0.117217 | + | 0.993106i | \(0.537397\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.1299 | 0.765746 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.77156 | 0.433817 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.3669 | 0.999091 | 0.499545 | − | 0.866288i | \(-0.333500\pi\) | ||||
0.499545 | + | 0.866288i | \(0.333500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.15305 | 0.606012 | 0.303006 | − | 0.952989i | \(-0.402010\pi\) | ||||
0.303006 | + | 0.952989i | \(0.402010\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.9257 | 1.31793 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.1620 | −1.03563 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.5722 | −1.12677 | −0.563383 | − | 0.826196i | \(-0.690500\pi\) | ||||
−0.563383 | + | 0.826196i | \(0.690500\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.95727 | 0.644759 | 0.322379 | − | 0.946611i | \(-0.395517\pi\) | ||||
0.322379 | + | 0.946611i | \(0.395517\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.9964 | 1.50359 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.52923 | 0.322694 | 0.161347 | − | 0.986898i | \(-0.448416\pi\) | ||||
0.161347 | + | 0.986898i | \(0.448416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.08714 | −0.431506 | −0.215753 | − | 0.976448i | \(-0.569221\pi\) | ||||
−0.215753 | + | 0.976448i | \(0.569221\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.48173 | −0.175048 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.28765 | −0.511493 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 38.0392 | 2.65677 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.39794 | −0.236173 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.21056 | 0.222079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.5574 | 1.62176 | 0.810880 | − | 0.585212i | \(-0.198989\pi\) | ||||
0.810880 | + | 0.585212i | \(0.198989\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.4175 | −0.850834 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.187375 | 0.0127198 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.08714 | 0.276183 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.8107 | −1.60168 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.27648 | 0.487269 | 0.243635 | − | 0.969867i | \(-0.421660\pi\) | ||||
0.243635 | + | 0.969867i | \(0.421660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.1299 | 0.675324 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.4619 | −0.694380 | −0.347190 | − | 0.937795i | \(-0.612864\pi\) | ||||
−0.347190 | + | 0.937795i | \(0.612864\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.20055 | −0.277580 | −0.138790 | − | 0.990322i | \(-0.544321\pi\) | ||||
−0.138790 | + | 0.990322i | \(0.544321\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.21056 | −0.211239 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.40468 | −0.0920233 | −0.0460117 | − | 0.998941i | \(-0.514651\pi\) | ||||
−0.0460117 | + | 0.998941i | \(0.514651\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.3120 | −1.12931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.68920 | −0.174682 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.2994 | −1.31306 | −0.656528 | − | 0.754301i | \(-0.727976\pi\) | ||||
−0.656528 | + | 0.754301i | \(0.727976\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6245 | −1.52179 | −0.760893 | − | 0.648878i | \(-0.775239\pi\) | ||||
−0.760893 | + | 0.648878i | \(0.775239\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.88971 | −0.248505 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.39794 | 0.343463 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.92935 | −0.249012 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.82380 | 0.115117 | 0.0575585 | − | 0.998342i | \(-0.481668\pi\) | ||||
0.0575585 | + | 0.998342i | \(0.481668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.9093 | −0.685861 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.1578 | −1.07446 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.72883 | −0.419733 | −0.209867 | − | 0.977730i | \(-0.567303\pi\) | ||||
−0.209867 | + | 0.977730i | \(0.567303\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.60850 | −0.286358 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.28765 | −0.451094 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.4371 | −0.828566 | −0.414283 | − | 0.910148i | \(-0.635968\pi\) | ||||
−0.414283 | + | 0.910148i | \(0.635968\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −43.9057 | −2.69711 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.70874 | −0.165772 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8666 | 0.967401 | 0.483701 | − | 0.875234i | \(-0.339292\pi\) | ||||
0.483701 | + | 0.875234i | \(0.339292\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.667979 | −0.0405768 | −0.0202884 | − | 0.999794i | \(-0.506458\pi\) | ||||
−0.0202884 | + | 0.999794i | \(0.506458\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.39794 | −0.326698 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 32.5226 | 1.96118 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.8501 | 1.49310 | 0.746549 | − | 0.665330i | \(-0.231709\pi\) | ||||
0.746549 | + | 0.665330i | \(0.231709\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.187375 | 0.0112178 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0671 | 0.660206 | 0.330103 | − | 0.943945i | \(-0.392916\pi\) | ||||
0.330103 | + | 0.943945i | \(0.392916\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.0306 | −1.72569 | −0.862844 | − | 0.505470i | \(-0.831319\pi\) | ||||
−0.862844 | + | 0.505470i | \(0.831319\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.88971 | 0.230407 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.77943 | −0.577261 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.45760 | 0.144565 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.227011 | 0.0133076 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.8830 | 0.635792 | 0.317896 | − | 0.948126i | \(-0.397024\pi\) | ||||
0.317896 | + | 0.948126i | \(0.397024\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.4497 | 1.30707 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.21056 | −0.186296 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.3419 | −1.06074 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.6691 | −1.12996 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.3383 | −1.33635 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.77156 | 0.557693 | 0.278846 | − | 0.960336i | \(-0.410048\pi\) | ||||
0.278846 | + | 0.960336i | \(0.410048\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.7219 | 0.837500 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.4307 | 1.49875 | 0.749373 | − | 0.662148i | \(-0.230355\pi\) | ||||
0.749373 | + | 0.662148i | \(0.230355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.7873 | 0.892350 | 0.446175 | − | 0.894946i | \(-0.352786\pi\) | ||||
0.446175 | + | 0.894946i | \(0.352786\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.88971 | −0.219160 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.1707 | 1.35756 | 0.678780 | − | 0.734342i | \(-0.262509\pi\) | ||||
0.678780 | + | 0.734342i | \(0.262509\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.3975 | −1.31001 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.95366 | −0.499745 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.41108 | −0.245439 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 54.6804 | 3.03312 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.5921 | −0.751642 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.45071 | 0.245376 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.32398 | −0.402562 | −0.201281 | − | 0.979534i | \(-0.564510\pi\) | ||||
−0.201281 | + | 0.979534i | \(0.564510\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.60850 | −0.252544 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.65321 | −0.527411 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.73670 | −0.475918 | −0.237959 | − | 0.971275i | \(-0.576478\pi\) | ||||
−0.237959 | + | 0.971275i | \(0.576478\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.35047 | −0.453535 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.601579 | 0.0325773 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.2170 | −0.711579 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.1179 | −0.704205 | −0.352102 | − | 0.935961i | \(-0.614533\pi\) | ||||
−0.352102 | + | 0.935961i | \(0.614533\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.08910 | −0.486529 | −0.243264 | − | 0.969960i | \(-0.578218\pi\) | ||||
−0.243264 | + | 0.969960i | \(0.578218\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.39794 | −0.288121 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 35.7494 | 1.90275 | 0.951373 | − | 0.308041i | \(-0.0996735\pi\) | ||||
0.951373 | + | 0.308041i | \(0.0996735\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −48.3006 | −2.56353 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.41108 | 0.233459 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.5357 | −1.08383 | −0.541915 | − | 0.840433i | \(-0.682301\pi\) | ||||
−0.541915 | + | 0.840433i | \(0.682301\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.692290 | 0.0363358 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.8978 | 0.832128 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.85870 | 0.410221 | 0.205110 | − | 0.978739i | \(-0.434245\pi\) | ||||
0.205110 | + | 0.978739i | \(0.434245\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.77943 | −0.509097 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.2876 | 0.586026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8126 | 0.922303 | 0.461151 | − | 0.887321i | \(-0.347437\pi\) | ||||
0.461151 | + | 0.887321i | \(0.347437\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.9537 | 1.03040 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −39.3383 | −2.02602 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.06425 | −0.0546668 | −0.0273334 | − | 0.999626i | \(-0.508702\pi\) | ||||
−0.0273334 | + | 0.999626i | \(0.508702\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.70565 | 0.292309 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.7009 | 1.05777 | 0.528884 | − | 0.848694i | \(-0.322610\pi\) | ||||
0.528884 | + | 0.848694i | \(0.322610\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.4882 | −0.636456 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.0260 | 1.62379 | 0.811893 | − | 0.583807i | \(-0.198437\pi\) | ||||
0.811893 | + | 0.583807i | \(0.198437\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.9886 | 0.758004 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.3505 | 0.522112 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.4602 | −0.526310 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.6381 | 0.885232 | 0.442616 | − | 0.896711i | \(-0.354050\pi\) | ||||
0.442616 | + | 0.896711i | \(0.354050\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.00000 | −0.0500626 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.23341 | −0.161469 | −0.0807345 | − | 0.996736i | \(-0.525727\pi\) | ||||
−0.0807345 | + | 0.996736i | \(0.525727\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.01144 | 0.0503833 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.88971 | −0.193281 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.7959 | −0.733404 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.9523 | −1.87662 | −0.938309 | − | 0.345797i | \(-0.887609\pi\) | ||||
−0.938309 | + | 0.345797i | \(0.887609\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.7959 | −0.828479 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.77156 | −0.284000 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.2840 | −0.750264 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.3469 | 0.800509 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.7016 | 1.35331 | 0.676655 | − | 0.736301i | \(-0.263429\pi\) | ||||
0.676655 | + | 0.736301i | \(0.263429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8054 | 0.672834 | 0.336417 | − | 0.941713i | \(-0.390785\pi\) | ||||
0.336417 | + | 0.941713i | \(0.390785\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.45071 | 0.216401 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −44.6836 | −2.16747 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.3304 | −0.836720 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.40106 | −0.452833 | −0.226417 | − | 0.974031i | \(-0.572701\pi\) | ||||
−0.226417 | + | 0.974031i | \(0.572701\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 36.9236 | 1.77443 | 0.887217 | − | 0.461352i | \(-0.152635\pi\) | ||||
0.887217 | + | 0.461352i | \(0.152635\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −28.3469 | −1.35913 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.39794 | −0.162545 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.9040 | 0.520418 | 0.260209 | − | 0.965552i | \(-0.416208\pi\) | ||||
0.260209 | + | 0.965552i | \(0.416208\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.1704 | 1.57598 | 0.787988 | − | 0.615691i | \(-0.211123\pi\) | ||||
0.787988 | + | 0.615691i | \(0.211123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.5362 | −0.499465 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.82907 | −0.228407 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.3711 | −1.33892 | −0.669458 | − | 0.742850i | \(-0.733474\pi\) | ||||
−0.669458 | + | 0.742850i | \(0.733474\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.3975 | −1.47845 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.2645 | −0.999093 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.9964 | −0.984328 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.70015 | −0.0795298 | −0.0397649 | − | 0.999209i | \(-0.512661\pi\) | ||||
−0.0397649 | + | 0.999209i | \(0.512661\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.41108 | 0.205891 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.7221 | −1.01170 | −0.505850 | − | 0.862621i | \(-0.668821\pi\) | ||||
−0.505850 | + | 0.862621i | \(0.668821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.8186 | 0.642204 | 0.321102 | − | 0.947045i | \(-0.395947\pi\) | ||||
0.321102 | + | 0.947045i | \(0.395947\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.728835 | 0.0337989 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.4481 | 1.54779 | 0.773896 | − | 0.633312i | \(-0.218305\pi\) | ||||
0.773896 | + | 0.633312i | \(0.218305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.48173 | 0.114596 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.1377 | −1.06613 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.1299 | 0.464790 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.2876 | 0.516826 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.2039 | −0.831756 | −0.415878 | − | 0.909421i | \(-0.636526\pi\) | ||||
−0.415878 | + | 0.909421i | \(0.636526\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.8764 | −1.13427 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.39794 | 0.154611 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.883009 | 0.0400954 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.03105 | −0.227979 | −0.113989 | − | 0.993482i | \(-0.536363\pi\) | ||||
−0.113989 | + | 0.993482i | \(0.536363\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.27117 | −0.328813 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.3063 | 0.465116 | 0.232558 | − | 0.972583i | \(-0.425290\pi\) | ||||
0.232558 | + | 0.972583i | \(0.425290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.1464 | 1.44780 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.4882 | −0.561301 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.4175 | 0.557002 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 40.3006 | 1.80410 | 0.902050 | − | 0.431631i | \(-0.142062\pi\) | ||||
0.902050 | + | 0.431631i | \(0.142062\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.12986 | 0.318539 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.7133 | 0.477682 | 0.238841 | − | 0.971059i | \(-0.423233\pi\) | ||||
0.238841 | + | 0.971059i | \(0.423233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −76.5073 | −3.40453 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.1377 | −0.716702 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.8429 | 1.10114 | 0.550571 | − | 0.834788i | \(-0.314410\pi\) | ||||
0.550571 | + | 0.834788i | \(0.314410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.08714 | −0.180804 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 57.2640 | 2.52335 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.2893 | 0.628442 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.08349 | 0.135350 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.0934 | 0.880307 | 0.440154 | − | 0.897922i | \(-0.354924\pi\) | ||||
0.440154 | + | 0.897922i | \(0.354924\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.313894 | −0.0137256 | −0.00686281 | − | 0.999976i | \(-0.502185\pi\) | ||||
−0.00686281 | + | 0.999976i | \(0.502185\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.1299 | −0.442103 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.826525 | −0.0360040 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4540 | −0.498001 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.77156 | −0.250465 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −52.7887 | −2.28653 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.8272 | −1.50571 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.3669 | −0.576825 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.21056 | 0.138289 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.1749 | −1.21133 | −0.605667 | − | 0.795718i | \(-0.707094\pi\) | ||||
−0.605667 | + | 0.795718i | \(0.707094\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.15305 | −0.349881 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −52.8692 | −2.26467 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.89928 | 0.423262 | 0.211631 | − | 0.977350i | \(-0.432122\pi\) | ||||
0.211631 | + | 0.977350i | \(0.432122\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.28765 | −0.310464 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.68920 | 0.114356 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.9257 | −0.760905 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.6477 | 1.12910 | 0.564549 | − | 0.825400i | \(-0.309050\pi\) | ||||
0.564549 | + | 0.825400i | \(0.309050\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.1620 | 0.597922 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.0871 | −1.09944 | −0.549721 | − | 0.835348i | \(-0.685266\pi\) | ||||
−0.549721 | + | 0.835348i | \(0.685266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.4809 | −1.36648 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.1726 | −1.72605 | −0.863023 | − | 0.505164i | \(-0.831432\pi\) | ||||
−0.863023 | + | 0.505164i | \(0.831432\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.7052 | 1.24312 | 0.621561 | − | 0.783366i | \(-0.286499\pi\) | ||||
0.621561 | + | 0.783366i | \(0.286499\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.5722 | 0.650538 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.4206 | −1.43544 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.8094 | −0.866305 | −0.433152 | − | 0.901321i | \(-0.642599\pi\) | ||||
−0.433152 | + | 0.901321i | \(0.642599\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.95727 | −0.372251 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.92935 | 0.163017 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.2397 | 1.50090 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20.9964 | −0.868095 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.6887 | −0.647541 | −0.323771 | − | 0.946136i | \(-0.604951\pi\) | ||||
−0.323771 | + | 0.946136i | \(0.604951\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.187375 | 0.00772065 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.52923 | −0.186307 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.8786 | 0.528860 | 0.264430 | − | 0.964405i | \(-0.414816\pi\) | ||||
0.264430 | + | 0.964405i | \(0.414816\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.1578 | 0.703402 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.08714 | 0.249130 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.2196 | 1.60247 | 0.801236 | − | 0.598349i | \(-0.204176\pi\) | ||||
0.801236 | + | 0.598349i | \(0.204176\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.7757 | 1.82644 | 0.913219 | − | 0.407470i | \(-0.133589\pi\) | ||||
0.913219 | + | 0.407470i | \(0.133589\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.48173 | 0.101064 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.69281 | 0.109478 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.5842 | −0.876075 | −0.438038 | − | 0.898957i | \(-0.644326\pi\) | ||||
−0.438038 | + | 0.898957i | \(0.644326\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.28765 | 0.295310 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.0247 | 0.971934 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.91651 | 0.360134 | 0.180067 | − | 0.983654i | \(-0.442368\pi\) | ||||
0.180067 | + | 0.983654i | \(0.442368\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −38.0392 | −1.53389 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.97997 | 0.321262 | 0.160631 | − | 0.987015i | \(-0.448647\pi\) | ||||
0.160631 | + | 0.987015i | \(0.448647\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −48.9484 | −1.96740 | −0.983702 | − | 0.179807i | \(-0.942453\pi\) | ||||
−0.983702 | + | 0.179807i | \(0.942453\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.39794 | 0.136355 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.70874 | 0.108523 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 26.9648 | 1.07859 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.21056 | −0.128218 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.3284 | 0.810548 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.7873 | 0.708101 | 0.354050 | − | 0.935226i | \(-0.384804\pi\) | ||||
0.354050 | + | 0.935226i | \(0.384804\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.5574 | −0.936324 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.1933 | 0.880715 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.39794 | 0.213874 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.4175 | 0.491229 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −47.3548 | −1.87040 | −0.935200 | − | 0.354119i | \(-0.884781\pi\) | ||||
−0.935200 | + | 0.354119i | \(0.884781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.6180 | 1.24689 | 0.623447 | − | 0.781866i | \(-0.285732\pi\) | ||||
0.623447 | + | 0.781866i | \(0.285732\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.8541 | 1.44888 | 0.724441 | − | 0.689336i | \(-0.242098\pi\) | ||||
0.724441 | + | 0.689336i | \(0.242098\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.5300 | −0.727365 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.187375 | −0.00734380 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.2239 | −0.674024 | −0.337012 | − | 0.941500i | \(-0.609416\pi\) | ||||
−0.337012 | + | 0.941500i | \(0.609416\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.2604 | 1.57310 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.08714 | −0.159454 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.2939 | −1.76440 | −0.882200 | − | 0.470875i | \(-0.843938\pi\) | ||||
−0.882200 | + | 0.470875i | \(0.843938\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.7862 | 1.15855 | 0.579274 | − | 0.815133i | \(-0.303336\pi\) | ||||
0.579274 | + | 0.815133i | \(0.303336\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.8107 | 0.924732 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.88971 | −0.150837 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.7630 | 0.958826 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.27648 | −0.281325 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.2634 | 0.743654 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.3390 | 0.475634 | 0.237817 | − | 0.971310i | \(-0.423568\pi\) | ||||
0.237817 | + | 0.971310i | \(0.423568\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.1299 | −0.389899 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.1134 | −0.849888 | −0.424944 | − | 0.905220i | \(-0.639706\pi\) | ||||
−0.424944 | + | 0.905220i | \(0.639706\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.227011 | −0.00871190 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.4619 | 0.400900 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.10362 | −0.310076 | −0.155038 | − | 0.987908i | \(-0.549550\pi\) | ||||
−0.155038 | + | 0.987908i | \(0.549550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −65.3311 | −2.49617 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.20055 | 0.160261 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 60.9300 | 2.32125 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.94343 | 0.264141 | 0.132070 | − | 0.991240i | \(-0.457838\pi\) | ||||
0.132070 | + | 0.991240i | \(0.457838\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.21056 | 0.121959 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 63.5846 | 2.41190 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.1378 | 1.63396 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.40468 | 0.0531297 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.5329 | −0.813285 | −0.406643 | − | 0.913587i | \(-0.633301\pi\) | ||||
−0.406643 | + | 0.913587i | \(0.633301\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.60850 | −0.173813 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.3120 | 0.652007 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.6691 | 0.739734 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.7686 | −1.45599 | −0.727993 | − | 0.685584i | \(-0.759547\pi\) | ||||
−0.727993 | + | 0.685584i | \(0.759547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.68920 | 0.100853 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.636688 | −0.0238442 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −67.4103 | −2.52100 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.2994 | 0.758094 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.7725 | −1.37138 | −0.685692 | − | 0.727892i | \(-0.740500\pi\) | ||||
−0.685692 | + | 0.727892i | \(0.740500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.7219 | −0.548273 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23.6245 | 0.878603 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −73.8229 | −2.74171 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.2853 | 0.789427 | 0.394714 | − | 0.918804i | \(-0.370844\pi\) | ||||
0.394714 | + | 0.918804i | \(0.370844\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.13845 | 0.226729 | 0.113364 | − | 0.993553i | \(-0.463837\pi\) | ||||
0.113364 | + | 0.993553i | \(0.463837\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.88971 | 0.143474 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.96774 | 0.293496 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.89946 | 0.290586 | 0.145293 | − | 0.989389i | \(-0.453587\pi\) | ||||
0.145293 | + | 0.989389i | \(0.453587\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.39794 | −0.198298 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.80306 | 0.286267 | 0.143133 | − | 0.989703i | \(-0.454282\pi\) | ||||
0.143133 | + | 0.989703i | \(0.454282\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.7837 | −0.688182 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.92935 | 0.143767 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.95366 | 0.327160 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.19505 | 0.153080 | 0.0765399 | − | 0.997067i | \(-0.475613\pi\) | ||||
0.0765399 | + | 0.997067i | \(0.475613\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.82380 | −0.0664628 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −82.7128 | −3.01023 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.7036 | −1.95189 | −0.975944 | − | 0.218019i | \(-0.930040\pi\) | ||||
−0.975944 | + | 0.218019i | \(0.930040\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.9093 | 0.395982 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.55602 | −0.346406 | −0.173203 | − | 0.984886i | \(-0.555412\pi\) | ||||
−0.173203 | + | 0.984886i | \(0.555412\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.5921 | 0.492065 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.1578 | 0.620342 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.1545 | −1.12493 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.1819 | 1.41294 | 0.706468 | − | 0.707745i | \(-0.250288\pi\) | ||||
0.706468 | + | 0.707745i | \(0.250288\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.72883 | 0.242333 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0079 | 0.863503 | 0.431751 | − | 0.901993i | \(-0.357896\pi\) | ||||
0.431751 | + | 0.901993i | \(0.357896\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.89808 | 0.0681811 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.60850 | 0.165329 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.77943 | −0.350384 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.8672 | 1.42656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.28765 | 0.260439 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −89.9991 | −3.21221 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.5795 | −1.12569 | −0.562844 | − | 0.826563i | \(-0.690293\pi\) | ||||
−0.562844 | + | 0.826563i | \(0.690293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.4371 | 0.478373 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.35047 | 0.296909 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.3876 | 1.15012 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 43.9057 | 1.55718 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.9415 | −1.55649 | −0.778243 | − | 0.627963i | \(-0.783889\pi\) | ||||
−0.778243 | + | 0.627963i | \(0.783889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.6324 | −0.694546 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.70874 | 0.0957086 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.1220 | −0.463065 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.2170 | 0.465838 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.8666 | −0.558529 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.9862 | 1.05426 | 0.527129 | − | 0.849786i | \(-0.323269\pi\) | ||||
0.527129 | + | 0.849786i | \(0.323269\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.2495 | −1.51870 | −0.759348 | − | 0.650684i | \(-0.774482\pi\) | ||||
−0.759348 | + | 0.650684i | \(0.774482\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.667979 | 0.0234270 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.2827 | −0.990701 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.39794 | 0.188619 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.7141 | 0.932327 | 0.466163 | − | 0.884699i | \(-0.345636\pi\) | ||||
0.466163 | + | 0.884699i | \(0.345636\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.3860 | −1.19862 | −0.599311 | − | 0.800517i | \(-0.704559\pi\) | ||||
−0.599311 | + | 0.800517i | \(0.704559\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32.5226 | −1.13229 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.9941 | −1.56460 | −0.782298 | − | 0.622904i | \(-0.785953\pi\) | ||||
−0.782298 | + | 0.622904i | \(0.785953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.4814 | 0.641886 | 0.320943 | − | 0.947098i | \(-0.396000\pi\) | ||||
0.320943 | + | 0.947098i | \(0.396000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.8501 | −0.862041 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.41108 | −0.152835 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.7331 | 0.959744 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.187375 | −0.00647662 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.79062 | −0.130867 | −0.0654334 | − | 0.997857i | \(-0.520843\pi\) | ||||
−0.0654334 | + | 0.997857i | \(0.520843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.1098 | 0.831374 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.0671 | −0.381170 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −62.7711 | −2.15939 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.692290 | −0.0237874 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 29.0306 | 0.996326 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.6594 | 0.536797 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2268 | 0.761032 | 0.380516 | − | 0.924774i | \(-0.375746\pi\) | ||||
0.380516 | + | 0.924774i | \(0.375746\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.88971 | −0.133025 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.8593 | 1.63484 | 0.817422 | − | 0.576039i | \(-0.195403\pi\) | ||||
0.817422 | + | 0.576039i | \(0.195403\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.1825 | 1.54161 | 0.770803 | − | 0.637073i | \(-0.219855\pi\) | ||||
0.770803 | + | 0.637073i | \(0.219855\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.77943 | 0.333282 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −57.7815 | −1.96690 | −0.983452 | − | 0.181169i | \(-0.942012\pi\) | ||||
−0.983452 | + | 0.181169i | \(0.942012\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.9939 | 0.407804 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.45760 | −0.0834644 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.63384 | 0.292883 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.3962 | 0.453913 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.227011 | −0.00768318 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.9537 | −0.674558 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.69062 | 0.158391 | 0.0791955 | − | 0.996859i | \(-0.474765\pi\) | ||||
0.0791955 | + | 0.996859i | \(0.474765\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.8830 | −0.367075 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.6008 | 1.06466 | 0.532329 | − | 0.846537i | \(-0.321317\pi\) | ||||
0.532329 | + | 0.846537i | \(0.321317\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.3294 | −1.79468 | −0.897339 | − | 0.441341i | \(-0.854503\pi\) | ||||
−0.897339 | + | 0.441341i | \(0.854503\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.4497 | −0.754639 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −54.7883 | −1.83961 | −0.919805 | − | 0.392375i | \(-0.871654\pi\) | ||||
−0.919805 | + | 0.392375i | \(0.871654\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.70565 | −0.191361 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.21056 | 0.107558 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.45071 | 0.148937 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.9935 | −1.73795 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.3419 | 0.612417 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.36552 | −0.0455427 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49.7907 | −1.65877 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.7130 | −1.05418 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.2313 | −1.10343 | −0.551714 | − | 0.834034i | \(-0.686026\pi\) | ||||
−0.551714 | + | 0.834034i | \(0.686026\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.6691 | 0.652384 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.8193 | 1.84938 | 0.924689 | − | 0.380724i | \(-0.124325\pi\) | ||||
0.924689 | + | 0.380724i | \(0.124325\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.6154 | 0.417509 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.3383 | 0.771540 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3505 | −0.341803 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.7495 | −0.816411 | −0.408205 | − | 0.912890i | \(-0.633845\pi\) | ||||
−0.408205 | + | 0.912890i | \(0.633845\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.77156 | −0.321984 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.0290 | 2.20629 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.6835 | −1.53494 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.7219 | −0.483531 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.4232 | 0.702873 | 0.351437 | − | 0.936212i | \(-0.385693\pi\) | ||||
0.351437 | + | 0.936212i | \(0.385693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.4307 | −0.865302 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 55.0863 | 1.80151 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.68246 | −0.283644 | −0.141822 | − | 0.989892i | \(-0.545296\pi\) | ||||
−0.141822 | + | 0.989892i | \(0.545296\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.7873 | −0.515199 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.10977 | −0.0361774 | −0.0180887 | − | 0.999836i | \(-0.505758\pi\) | ||||
−0.0180887 | + | 0.999836i | \(0.505758\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.2299 | 1.08211 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.88971 | 0.126532 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.5890 | 0.799034 | 0.399517 | − | 0.916726i | \(-0.369178\pi\) | ||||
0.399517 | + | 0.916726i | \(0.369178\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.0621 | −0.716166 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.1707 | −0.783787 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.5773 | −1.70315 | −0.851573 | − | 0.524236i | \(-0.824351\pi\) | ||||
−0.851573 | + | 0.524236i | \(0.824351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60.5714 | 1.96004 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.3975 | 0.756332 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.7959 | 0.542367 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9649 | −0.998867 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.95366 | 0.288528 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.8412 | −1.12158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.7190 | −0.569805 | −0.284902 | − | 0.958557i | \(-0.591961\pi\) | ||||
−0.284902 | + | 0.958557i | \(0.591961\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.41108 | 0.141704 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.8300 | −0.604284 | −0.302142 | − | 0.953263i | \(-0.597702\pi\) | ||||
−0.302142 | + | 0.953263i | \(0.597702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.3469 | −0.524056 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −54.6804 | −1.75117 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.3840 | −0.780114 | −0.390057 | − | 0.920791i | \(-0.627545\pi\) | ||||
−0.390057 | + | 0.920791i | \(0.627545\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.69658 | 0.277944 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.5921 | 0.433961 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.6388 | 1.83839 | 0.919196 | − | 0.393801i | \(-0.128840\pi\) | ||||
0.919196 | + | 0.393801i | \(0.128840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.6174 | −0.561337 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.45071 | −0.141668 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.6557 | 0.529086 | 0.264543 | − | 0.964374i | \(-0.414779\pi\) | ||||
0.264543 | + | 0.964374i | \(0.414779\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.32398 | 0.232419 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.6772 | 0.750618 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.8780 | 0.534532 | 0.267266 | − | 0.963623i | \(-0.413880\pi\) | ||||
0.267266 | + | 0.963623i | \(0.413880\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.60850 | 0.145806 |
(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 | 3192.2.a.ba.1.1 | ✓ | 5 | |
3.2 | odd | 2 | 9576.2.a.co.1.5 | 5 | |||
4.3 | odd | 2 | 6384.2.a.ce.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3192.2.a.ba.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
6384.2.a.ce.1.1 | 5 | 4.3 | odd | 2 | |||
9576.2.a.co.1.5 | 5 | 3.2 | odd | 2 |