Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4284,2,Mod(1,4284)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4284, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4284.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4284.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: | \(34.2079122259\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 476) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4284.1 |
$q$-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 | ||||||||
\(5\) | −2.30278 | −1.02983 | −0.514916 | − | 0.857240i | \(-0.672177\pi\) | ||||
−0.514916 | + | 0.857240i | \(0.672177\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60555 | 0.722650 | 0.361325 | − | 0.932440i | \(-0.382325\pi\) | ||||
0.361325 | + | 0.932440i | \(0.382325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.39445 | 0.319908 | 0.159954 | − | 0.987124i | \(-0.448865\pi\) | ||||
0.159954 | + | 0.987124i | \(0.448865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.302776 | 0.0605551 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.21110 | 0.967677 | 0.483839 | − | 0.875157i | \(-0.339242\pi\) | ||||
0.483839 | + | 0.875157i | \(0.339242\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.69722 | 0.664041 | 0.332021 | − | 0.943272i | \(-0.392270\pi\) | ||||
0.332021 | + | 0.943272i | \(0.392270\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.30278 | 0.389240 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8167 | −1.94265 | −0.971323 | − | 0.237764i | \(-0.923586\pi\) | ||||
−0.971323 | + | 0.237764i | \(0.923586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.51388 | −1.01730 | −0.508648 | − | 0.860974i | \(-0.669855\pi\) | ||||
−0.508648 | + | 0.860974i | \(0.669855\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.697224 | −0.106326 | −0.0531629 | − | 0.998586i | \(-0.516930\pi\) | ||||
−0.0531629 | + | 0.998586i | \(0.516930\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.60555 | −0.671789 | −0.335894 | − | 0.941900i | \(-0.609039\pi\) | ||||
−0.335894 | + | 0.941900i | \(0.609039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.30278 | −0.591032 | −0.295516 | − | 0.955338i | \(-0.595492\pi\) | ||||
−0.295516 | + | 0.955338i | \(0.595492\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.21110 | 1.24202 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.00000 | 1.04151 | 0.520756 | − | 0.853706i | \(-0.325650\pi\) | ||||
0.520756 | + | 0.853706i | \(0.325650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.51388 | −0.321869 | −0.160935 | − | 0.986965i | \(-0.551451\pi\) | ||||
−0.160935 | + | 0.986965i | \(0.551451\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.00000 | −0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.30278 | 0.770007 | 0.385003 | − | 0.922915i | \(-0.374200\pi\) | ||||
0.385003 | + | 0.922915i | \(0.374200\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6056 | 1.25865 | 0.629324 | − | 0.777143i | \(-0.283332\pi\) | ||||
0.629324 | + | 0.777143i | \(0.283332\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.5139 | −1.23056 | −0.615278 | − | 0.788310i | \(-0.710956\pi\) | ||||
−0.615278 | + | 0.788310i | \(0.710956\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.60555 | 0.518165 | 0.259083 | − | 0.965855i | \(-0.416580\pi\) | ||||
0.259083 | + | 0.965855i | \(0.416580\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2111 | 1.23058 | 0.615289 | − | 0.788301i | \(-0.289039\pi\) | ||||
0.615289 | + | 0.788301i | \(0.289039\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.30278 | −0.249771 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.8167 | 1.46456 | 0.732281 | − | 0.681002i | \(-0.238456\pi\) | ||||
0.732281 | + | 0.681002i | \(0.238456\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.60555 | −0.273136 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.21110 | −0.329452 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.69722 | −0.984604 | −0.492302 | − | 0.870424i | \(-0.663844\pi\) | ||||
−0.492302 | + | 0.870424i | \(0.663844\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.39445 | 0.536768 | 0.268384 | − | 0.963312i | \(-0.413510\pi\) | ||||
0.268384 | + | 0.963312i | \(0.413510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.60555 | −0.251888 | −0.125944 | − | 0.992037i | \(-0.540196\pi\) | ||||
−0.125944 | + | 0.992037i | \(0.540196\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.2111 | 1.84009 | 0.920045 | − | 0.391813i | \(-0.128152\pi\) | ||||
0.920045 | + | 0.391813i | \(0.128152\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.6056 | 1.56212 | 0.781059 | − | 0.624457i | \(-0.214680\pi\) | ||||
0.781059 | + | 0.624457i | \(0.214680\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.21110 | 0.858940 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8167 | 0.967471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.51388 | −0.311806 | −0.155903 | − | 0.987772i | \(-0.549829\pi\) | ||||
−0.155903 | + | 0.987772i | \(0.549829\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.21110 | −0.455296 | −0.227648 | − | 0.973743i | \(-0.573104\pi\) | ||||
−0.227648 | + | 0.973743i | \(0.573104\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.39445 | −0.120914 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.11943 | 0.608254 | 0.304127 | − | 0.952632i | \(-0.401635\pi\) | ||||
0.304127 | + | 0.952632i | \(0.401635\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.51388 | −0.806957 | −0.403478 | − | 0.914989i | \(-0.632199\pi\) | ||||
−0.403478 | + | 0.914989i | \(0.632199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.4222 | −0.871549 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | −0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.697224 | 0.0571188 | 0.0285594 | − | 0.999592i | \(-0.490908\pi\) | ||||
0.0285594 | + | 0.999592i | \(0.490908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3028 | 1.24532 | 0.622661 | − | 0.782492i | \(-0.286052\pi\) | ||||
0.622661 | + | 0.782492i | \(0.286052\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.51388 | −0.683851 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.60555 | 0.674039 | 0.337019 | − | 0.941498i | \(-0.390581\pi\) | ||||
0.337019 | + | 0.941498i | \(0.390581\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.1194 | 1.01521 | 0.507606 | − | 0.861589i | \(-0.330531\pi\) | ||||
0.507606 | + | 0.861589i | \(0.330531\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.21110 | −0.477777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.7250 | 0.891434 | 0.445717 | − | 0.895174i | \(-0.352949\pi\) | ||||
0.445717 | + | 0.895174i | \(0.352949\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.302776 | −0.0228877 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.51388 | 0.636357 | 0.318179 | − | 0.948031i | \(-0.396929\pi\) | ||||
0.318179 | + | 0.948031i | \(0.396929\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 27.2111 | 2.00060 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.7250 | −1.49961 | −0.749803 | − | 0.661661i | \(-0.769852\pi\) | ||||
−0.749803 | + | 0.661661i | \(0.769852\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.0278 | 1.51361 | 0.756806 | − | 0.653640i | \(-0.226759\pi\) | ||||
0.756806 | + | 0.653640i | \(0.226759\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.605551 | −0.0431437 | −0.0215719 | − | 0.999767i | \(-0.506867\pi\) | ||||
−0.0215719 | + | 0.999767i | \(0.506867\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.3028 | 0.943009 | 0.471504 | − | 0.881864i | \(-0.343711\pi\) | ||||
0.471504 | + | 0.881864i | \(0.343711\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.21110 | −0.365748 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.0000 | 1.04765 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.57779 | −0.385824 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.8167 | 1.91498 | 0.957489 | − | 0.288471i | \(-0.0931468\pi\) | ||||
0.957489 | + | 0.288471i | \(0.0931468\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.60555 | 0.109498 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.69722 | −0.250984 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.60555 | 0.175268 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.81665 | −0.523442 | −0.261721 | − | 0.965144i | \(-0.584290\pi\) | ||||
−0.261721 | + | 0.965144i | \(0.584290\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.9083 | −0.856756 | −0.428378 | − | 0.903600i | \(-0.640915\pi\) | ||||
−0.428378 | + | 0.903600i | \(0.640915\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.2111 | 0.873014 | 0.436507 | − | 0.899701i | \(-0.356215\pi\) | ||||
0.436507 | + | 0.899701i | \(0.356215\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.3944 | −1.27057 | −0.635286 | − | 0.772277i | \(-0.719118\pi\) | ||||
−0.635286 | + | 0.772277i | \(0.719118\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.6056 | 0.691830 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.11943 | 0.460518 | 0.230259 | − | 0.973129i | \(-0.426043\pi\) | ||||
0.230259 | + | 0.973129i | \(0.426043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.48612 | −0.546639 | −0.273320 | − | 0.961923i | \(-0.588122\pi\) | ||||
−0.273320 | + | 0.961923i | \(0.588122\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.30278 | −0.147119 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.63331 | 0.231182 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.8167 | 1.50329 | 0.751647 | − | 0.659566i | \(-0.229260\pi\) | ||||
0.751647 | + | 0.659566i | \(0.229260\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.0000 | 1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.4222 | −1.52342 | −0.761708 | − | 0.647921i | \(-0.775639\pi\) | ||||
−0.761708 | + | 0.647921i | \(0.775639\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.8167 | 0.734251 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4222 | −0.642661 | −0.321330 | − | 0.946967i | \(-0.604130\pi\) | ||||
−0.321330 | + | 0.946967i | \(0.604130\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.90833 | 0.608664 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.2111 | −1.65909 | −0.829545 | − | 0.558440i | \(-0.811400\pi\) | ||||
−0.829545 | + | 0.558440i | \(0.811400\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4222 | 1.11907 | 0.559535 | − | 0.828807i | \(-0.310980\pi\) | ||||
0.559535 | + | 0.828807i | \(0.310980\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.21110 | −0.0730322 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.4222 | 1.82789 | 0.913947 | − | 0.405835i | \(-0.133019\pi\) | ||||
0.913947 | + | 0.405835i | \(0.133019\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.11943 | −0.365055 | −0.182527 | − | 0.983201i | \(-0.558428\pi\) | ||||
−0.182527 | + | 0.983201i | \(0.558428\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.3305 | −1.14908 | −0.574540 | − | 0.818476i | \(-0.694819\pi\) | ||||
−0.574540 | + | 0.818476i | \(0.694819\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.51388 | 0.384502 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.21110 | −0.187595 | −0.0937973 | − | 0.995591i | \(-0.529901\pi\) | ||||
−0.0937973 | + | 0.995591i | \(0.529901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.4222 | −1.07258 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.4222 | −0.602732 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.697224 | 0.0401873 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.78890 | 0.331471 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.7250 | −0.834977 | −0.417489 | − | 0.908682i | \(-0.637090\pi\) | ||||
−0.417489 | + | 0.908682i | \(0.637090\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.90833 | −0.390482 | −0.195241 | − | 0.980755i | \(-0.562549\pi\) | ||||
−0.195241 | + | 0.980755i | \(0.562549\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.63331 | −0.541060 | −0.270530 | − | 0.962711i | \(-0.587199\pi\) | ||||
−0.270530 | + | 0.962711i | \(0.587199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.8444 | −1.16706 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.39445 | 0.0775892 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.788897 | 0.0437602 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.60555 | 0.253912 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.7250 | −1.57887 | −0.789434 | − | 0.613836i | \(-0.789626\pi\) | ||||
−0.789434 | + | 0.613836i | \(0.789626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.5139 | −0.792978 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4222 | 0.785628 | 0.392814 | − | 0.919618i | \(-0.371502\pi\) | ||||
0.392814 | + | 0.919618i | \(0.371502\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.7889 | −0.800864 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.8444 | 1.65581 | 0.827907 | − | 0.560865i | \(-0.189531\pi\) | ||||
0.827907 | + | 0.560865i | \(0.189531\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4222 | −0.557888 | −0.278944 | − | 0.960307i | \(-0.589984\pi\) | ||||
−0.278944 | + | 0.960307i | \(0.589984\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.0000 | 0.851594 | 0.425797 | − | 0.904819i | \(-0.359994\pi\) | ||||
0.425797 | + | 0.904819i | \(0.359994\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.4222 | −1.29620 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 19.5139 | 1.02990 | 0.514952 | − | 0.857219i | \(-0.327810\pi\) | ||||
0.514952 | + | 0.857219i | \(0.327810\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0555 | −0.897659 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.2111 | 1.26727 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.90833 | −0.204013 | −0.102007 | − | 0.994784i | \(-0.532526\pi\) | ||||
−0.102007 | + | 0.994784i | \(0.532526\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.30278 | 0.223389 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.3305 | 1.25979 | 0.629894 | − | 0.776681i | \(-0.283098\pi\) | ||||
0.629894 | + | 0.776681i | \(0.283098\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.5778 | 0.699292 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.4222 | 1.97362 | 0.986808 | − | 0.161895i | \(-0.0517605\pi\) | ||||
0.986808 | + | 0.161895i | \(0.0517605\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.4222 | 1.55450 | 0.777251 | − | 0.629191i | \(-0.216614\pi\) | ||||
0.777251 | + | 0.629191i | \(0.216614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.21110 | −0.469441 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.72498 | −0.138162 | −0.0690810 | − | 0.997611i | \(-0.522007\pi\) | ||||
−0.0690810 | + | 0.997611i | \(0.522007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.6056 | −0.533623 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9083 | −1.14974 | −0.574868 | − | 0.818246i | \(-0.694947\pi\) | ||||
−0.574868 | + | 0.818246i | \(0.694947\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.60555 | 0.229990 | 0.114995 | − | 0.993366i | \(-0.463315\pi\) | ||||
0.114995 | + | 0.993366i | \(0.463315\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.63331 | 0.479869 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 47.2666 | 2.34292 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8167 | 0.782083 | 0.391042 | − | 0.920373i | \(-0.372115\pi\) | ||||
0.391042 | + | 0.920373i | \(0.372115\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.8167 | −1.26729 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.51388 | −0.464783 | −0.232392 | − | 0.972622i | \(-0.574655\pi\) | ||||
−0.232392 | + | 0.972622i | \(0.574655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.9083 | 1.06775 | 0.533873 | − | 0.845565i | \(-0.320736\pi\) | ||||
0.533873 | + | 0.845565i | \(0.320736\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.302776 | 0.0146868 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.51388 | 0.121655 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.8444 | −1.38939 | −0.694693 | − | 0.719306i | \(-0.744460\pi\) | ||||
−0.694693 | + | 0.719306i | \(0.744460\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.6056 | −0.701898 | −0.350949 | − | 0.936395i | \(-0.614141\pi\) | ||||
−0.350949 | + | 0.936395i | \(0.614141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.57779 | −0.266822 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.9083 | 1.52290 | 0.761451 | − | 0.648223i | \(-0.224487\pi\) | ||||
0.761451 | + | 0.648223i | \(0.224487\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.7889 | 0.892687 | 0.446344 | − | 0.894862i | \(-0.352726\pi\) | ||||
0.446344 | + | 0.894862i | \(0.352726\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.8167 | −1.50825 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.0278 | −1.46429 | −0.732145 | − | 0.681149i | \(-0.761481\pi\) | ||||
−0.732145 | + | 0.681149i | \(0.761481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.0555 | 1.22691 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.00000 | 0.281284 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.09167 | −0.144622 | −0.0723112 | − | 0.997382i | \(-0.523037\pi\) | ||||
−0.0723112 | + | 0.997382i | \(0.523037\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.6056 | −1.42544 | −0.712721 | − | 0.701447i | \(-0.752538\pi\) | ||||
−0.712721 | + | 0.701447i | \(0.752538\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7250 | 1.19554 | 0.597771 | − | 0.801667i | \(-0.296053\pi\) | ||||
0.597771 | + | 0.801667i | \(0.296053\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.39445 | 0.434723 | 0.217362 | − | 0.976091i | \(-0.430255\pi\) | ||||
0.217362 | + | 0.976091i | \(0.430255\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.30278 | −0.291035 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.78890 | 0.128234 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.422205 | 0.0193721 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.9083 | −1.27516 | −0.637582 | − | 0.770382i | \(-0.720065\pi\) | ||||
−0.637582 | + | 0.770382i | \(0.720065\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.7889 | −1.40385 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.3305 | 1.01398 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.0000 | −1.26880 | −0.634401 | − | 0.773004i | \(-0.718753\pi\) | ||||
−0.634401 | + | 0.773004i | \(0.718753\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.48612 | 0.202456 | 0.101228 | − | 0.994863i | \(-0.467723\pi\) | ||||
0.101228 | + | 0.994863i | \(0.467723\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.21110 | 0.234696 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.6056 | −0.475724 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.7889 | −0.662042 | −0.331021 | − | 0.943623i | \(-0.607393\pi\) | ||||
−0.331021 | + | 0.943623i | \(0.607393\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.88057 | 0.262202 | 0.131101 | − | 0.991369i | \(-0.458149\pi\) | ||||
0.131101 | + | 0.991369i | \(0.458149\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4222 | −0.552781 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.605551 | 0.0268406 | 0.0134203 | − | 0.999910i | \(-0.495728\pi\) | ||||
0.0134203 | + | 0.999910i | \(0.495728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.5139 | 0.465107 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.2389 | −1.42061 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.4222 | 0.810208 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.5139 | 0.811108 | 0.405554 | − | 0.914071i | \(-0.367079\pi\) | ||||
0.405554 | + | 0.914071i | \(0.367079\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.0555 | −1.48914 | −0.744572 | − | 0.667542i | \(-0.767346\pi\) | ||||
−0.744572 | + | 0.667542i | \(0.767346\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.69722 | 0.161054 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.9722 | −0.735149 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | 0.259403 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.00000 | 0.171973 | 0.0859867 | − | 0.996296i | \(-0.472596\pi\) | ||||
0.0859867 | + | 0.996296i | \(0.472596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.2389 | −1.89498 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00000 | 0.0855138 | 0.0427569 | − | 0.999086i | \(-0.486386\pi\) | ||||
0.0427569 | + | 0.999086i | \(0.486386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.26662 | 0.309568 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.60555 | −0.195848 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.2111 | 1.49194 | 0.745971 | − | 0.665978i | \(-0.231986\pi\) | ||||
0.745971 | + | 0.665978i | \(0.231986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.81665 | −0.0768363 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.2389 | −1.60872 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.11943 | 0.130773 | 0.0653866 | − | 0.997860i | \(-0.479172\pi\) | ||||
0.0653866 | + | 0.997860i | \(0.479172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.4500 | 0.813956 | 0.406978 | − | 0.913438i | \(-0.366583\pi\) | ||||
0.406978 | + | 0.913438i | \(0.366583\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.21110 | −0.0505065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.8167 | −1.24128 | −0.620642 | − | 0.784094i | \(-0.713128\pi\) | ||||
−0.620642 | + | 0.784094i | \(0.713128\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.2111 | −0.465115 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.2111 | 0.712811 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.6056 | 0.767933 | 0.383967 | − | 0.923347i | \(-0.374558\pi\) | ||||
0.383967 | + | 0.923347i | \(0.374558\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.15559 | 0.212432 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.8167 | −1.79933 | −0.899667 | − | 0.436576i | \(-0.856191\pi\) | ||||
−0.899667 | + | 0.436576i | \(0.856191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.30278 | 0.0944046 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.72498 | 0.233916 | 0.116958 | − | 0.993137i | \(-0.462686\pi\) | ||||
0.116958 | + | 0.993137i | \(0.462686\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.2666 | −1.68330 | −0.841650 | − | 0.540023i | \(-0.818415\pi\) | ||||
−0.841650 | + | 0.540023i | \(0.818415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.5139 | −0.468106 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.3305 | −1.59638 | −0.798189 | − | 0.602408i | \(-0.794208\pi\) | ||||
−0.798189 | + | 0.602408i | \(0.794208\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | −0.485468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.7250 | 0.433178 | 0.216589 | − | 0.976263i | \(-0.430507\pi\) | ||||
0.216589 | + | 0.976263i | \(0.430507\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.6333 | 1.43454 | 0.717271 | − | 0.696794i | \(-0.245391\pi\) | ||||
0.717271 | + | 0.696794i | \(0.245391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.7889 | 0.915963 | 0.457982 | − | 0.888962i | \(-0.348573\pi\) | ||||
0.457982 | + | 0.888962i | \(0.348573\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.8167 | −0.553553 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.4222 | −1.05689 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.8167 | −0.471161 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.1194 | −0.641704 | −0.320852 | − | 0.947129i | \(-0.603969\pi\) | ||||
−0.320852 | + | 0.947129i | \(0.603969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.09167 | 0.321108 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.60555 | 0.103236 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.366692 | −0.0144835 | −0.00724174 | − | 0.999974i | \(-0.502305\pi\) | ||||
−0.00724174 | + | 0.999974i | \(0.502305\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.1194 | 1.30610 | 0.653051 | − | 0.757314i | \(-0.273489\pi\) | ||||
0.653051 | + | 0.757314i | \(0.273489\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.63331 | −0.300096 | −0.150048 | − | 0.988679i | \(-0.547943\pi\) | ||||
−0.150048 | + | 0.988679i | \(0.547943\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.0000 | −1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.5778 | −0.453074 | −0.226537 | − | 0.974003i | \(-0.572740\pi\) | ||||
−0.226537 | + | 0.974003i | \(0.572740\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000 | 0.468879 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.11943 | 0.160470 | 0.0802351 | − | 0.996776i | \(-0.474433\pi\) | ||||
0.0802351 | + | 0.996776i | \(0.474433\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.0278 | 1.20684 | 0.603420 | − | 0.797424i | \(-0.293804\pi\) | ||||
0.603420 | + | 0.797424i | \(0.293804\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.21110 | 0.124521 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.8444 | −0.807099 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0555 | 0.388189 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.0278 | 1.11894 | 0.559469 | − | 0.828851i | \(-0.311005\pi\) | ||||
0.559469 | + | 0.828851i | \(0.311005\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.69722 | 0.372145 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.6056 | −0.788450 | −0.394225 | − | 0.919014i | \(-0.628987\pi\) | ||||
−0.394225 | + | 0.919014i | \(0.628987\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.3944 | −0.626400 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.2111 | −0.427109 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.9361 | 1.70945 | 0.854725 | − | 0.519082i | \(-0.173726\pi\) | ||||
0.854725 | + | 0.519082i | \(0.173726\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.9083 | 0.831030 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.51388 | −0.246731 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.4222 | 1.52673 | 0.763363 | − | 0.645970i | \(-0.223547\pi\) | ||||
0.763363 | + | 0.645970i | \(0.223547\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.4777 | −0.621469 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.39445 | −0.202879 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.2389 | 1.73654 | 0.868268 | − | 0.496095i | \(-0.165233\pi\) | ||||
0.868268 | + | 0.496095i | \(0.165233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.7889 | −0.553849 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | 0.897549 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.3028 | −0.496110 | −0.248055 | − | 0.968746i | \(-0.579791\pi\) | ||||
−0.248055 | + | 0.968746i | \(0.579791\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.57779 | 0.0585978 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.4222 | 0.534890 | 0.267445 | − | 0.963573i | \(-0.413821\pi\) | ||||
0.267445 | + | 0.963573i | \(0.413821\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.697224 | −0.0257878 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.2389 | −1.26464 | −0.632321 | − | 0.774707i | \(-0.717897\pi\) | ||||
−0.632321 | + | 0.774707i | \(0.717897\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.2111 | −0.928663 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.3305 | 0.600728 | 0.300364 | − | 0.953825i | \(-0.402892\pi\) | ||||
0.300364 | + | 0.953825i | \(0.402892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.3944 | 1.00500 | 0.502502 | − | 0.864576i | \(-0.332413\pi\) | ||||
0.502502 | + | 0.864576i | \(0.332413\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.60555 | −0.0588228 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.60555 | 0.0952048 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.6056 | 0.387002 | 0.193501 | − | 0.981100i | \(-0.438016\pi\) | ||||
0.193501 | + | 0.981100i | \(0.438016\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35.2389 | −1.28247 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.3028 | −0.410806 | −0.205403 | − | 0.978677i | \(-0.565851\pi\) | ||||
−0.205403 | + | 0.978677i | \(0.565851\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.238859 | −0.00865863 | −0.00432931 | − | 0.999991i | \(-0.501378\pi\) | ||||
−0.00432931 | + | 0.999991i | \(0.501378\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.2111 | −0.695489 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.8444 | 0.752648 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.0555 | 1.30020 | 0.650098 | − | 0.759851i | \(-0.274728\pi\) | ||||
0.650098 | + | 0.759851i | \(0.274728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.0278 | 0.684381 | 0.342190 | − | 0.939631i | \(-0.388831\pi\) | ||||
0.342190 | + | 0.939631i | \(0.388831\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.11943 | 0.0402111 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.08327 | −0.325442 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.4222 | −1.51799 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.60555 | −0.164379 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.5778 | 0.769165 | 0.384583 | − | 0.923091i | \(-0.374345\pi\) | ||||
0.384583 | + | 0.923091i | \(0.374345\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.6056 | −0.590425 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.55004 | −0.232599 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.0555 | 0.852090 | 0.426045 | − | 0.904702i | \(-0.359907\pi\) | ||||
0.426045 | + | 0.904702i | \(0.359907\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.60555 | −0.162933 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 42.0555 | 1.48411 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.21110 | −0.324649 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.81665 | −0.0638701 | −0.0319351 | − | 0.999490i | \(-0.510167\pi\) | ||||
−0.0319351 | + | 0.999490i | \(0.510167\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.5139 | −0.790569 | −0.395285 | − | 0.918559i | \(-0.629354\pi\) | ||||
−0.395285 | + | 0.918559i | \(0.629354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.8167 | −0.694147 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.972244 | −0.0340145 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.2389 | −1.47415 | −0.737073 | − | 0.675813i | \(-0.763793\pi\) | ||||
−0.737073 | + | 0.675813i | \(0.763793\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.3944 | −1.09434 | −0.547171 | − | 0.837021i | \(-0.684295\pi\) | ||||
−0.547171 | + | 0.837021i | \(0.684295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.7889 | −1.07063 | −0.535317 | − | 0.844651i | \(-0.679808\pi\) | ||||
−0.535317 | + | 0.844651i | \(0.679808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.2389 | 1.18916 | 0.594582 | − | 0.804035i | \(-0.297317\pi\) | ||||
0.594582 | + | 0.804035i | \(0.297317\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.00000 | 0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.2111 | −1.04550 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.4222 | 0.359814 | 0.179907 | − | 0.983684i | \(-0.442420\pi\) | ||||
0.179907 | + | 0.983684i | \(0.442420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.84441 | −0.0636004 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.3028 | 0.492030 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.00000 | −0.171802 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.2666 | 1.62028 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.9638 | −1.26266 | −0.631330 | − | 0.775514i | \(-0.717491\pi\) | ||||
−0.631330 | + | 0.775514i | \(0.717491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.3944 | −1.61708 | −0.808539 | − | 0.588443i | \(-0.799741\pi\) | ||||
−0.808539 | + | 0.588443i | \(0.799741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.3583 | 1.78230 | 0.891148 | − | 0.453712i | \(-0.149900\pi\) | ||||
0.891148 | + | 0.453712i | \(0.149900\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.0000 | −0.918028 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.4222 | −0.624931 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.4222 | 0.556445 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.8167 | −0.365670 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.60555 | −0.290589 | −0.145294 | − | 0.989388i | \(-0.546413\pi\) | ||||
−0.145294 | + | 0.989388i | \(0.546413\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.1194 | −0.408314 | −0.204157 | − | 0.978938i | \(-0.565445\pi\) | ||||
−0.204157 | + | 0.978938i | \(0.565445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.9083 | 0.770927 | 0.385463 | − | 0.922723i | \(-0.374042\pi\) | ||||
0.385463 | + | 0.922723i | \(0.374042\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 48.7805 | 1.63789 | 0.818944 | − | 0.573873i | \(-0.194560\pi\) | ||||
0.818944 | + | 0.573873i | \(0.194560\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.51388 | 0.117852 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.42221 | −0.214911 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.6056 | −0.655341 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.2666 | 0.642578 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.30278 | −0.143346 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.8167 | 0.459281 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.7889 | 0.424648 | 0.212324 | − | 0.977199i | \(-0.431897\pi\) | ||||
0.212324 | + | 0.977199i | \(0.431897\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.81665 | −0.192714 | −0.0963572 | − | 0.995347i | \(-0.530719\pi\) | ||||
−0.0963572 | + | 0.995347i | \(0.530719\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.8444 | −1.48413 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.21110 | 0.172086 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.3583 | −1.62818 | −0.814090 | − | 0.580739i | \(-0.802764\pi\) | ||||
−0.814090 | + | 0.580739i | \(0.802764\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.6333 | 0.909561 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.57779 | −0.117637 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.9083 | −1.53901 | −0.769506 | − | 0.638639i | \(-0.779498\pi\) | ||||
−0.769506 | + | 0.638639i | \(0.779498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.39445 | 0.0457012 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.21110 | 0.301235 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.7889 | −0.744481 | −0.372240 | − | 0.928136i | \(-0.621410\pi\) | ||||
−0.372240 | + | 0.928136i | \(0.621410\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.3028 | 1.21604 | 0.608018 | − | 0.793923i | \(-0.291965\pi\) | ||||
0.608018 | + | 0.793923i | \(0.291965\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.0555 | 0.848484 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.8444 | 1.06730 | 0.533650 | − | 0.845705i | \(-0.320820\pi\) | ||||
0.533650 | + | 0.845705i | \(0.320820\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.3944 | −0.889261 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.3583 | −1.76084 | −0.880419 | − | 0.474197i | \(-0.842738\pi\) | ||||
−0.880419 | + | 0.474197i | \(0.842738\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47.7250 | 1.54434 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.11943 | −0.229898 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3305 | −0.559049 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48.4222 | −1.55877 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.51388 | 0.273788 | 0.136894 | − | 0.990586i | \(-0.456288\pi\) | ||||
0.136894 | + | 0.990586i | \(0.456288\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.2111 | −0.552331 | −0.276165 | − | 0.961110i | \(-0.589064\pi\) | ||||
−0.276165 | + | 0.961110i | \(0.589064\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.51388 | 0.305001 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.3028 | 0.393601 | 0.196800 | − | 0.980444i | \(-0.436945\pi\) | ||||
0.196800 | + | 0.980444i | \(0.436945\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −55.2666 | −1.76633 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.7805 | 1.81102 | 0.905508 | − | 0.424329i | \(-0.139490\pi\) | ||||
0.905508 | + | 0.424329i | \(0.139490\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.39445 | 0.0444308 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.78890 | 0.0886818 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.21110 | 0.102004 | 0.0510020 | − | 0.998699i | \(-0.483759\pi\) | ||||
0.0510020 | + | 0.998699i | \(0.483759\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.6333 | −0.971141 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49.3028 | −1.56143 | −0.780717 | − | 0.624884i | \(-0.785146\pi\) | ||||
−0.780717 | + | 0.624884i | \(0.785146\pi\) | |||||||
\(998\) | 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 | 4284.2.a.l.1.1 | 2 | ||
3.2 | odd | 2 | 476.2.a.c.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 1904.2.a.k.1.1 | 2 | |||
21.20 | even | 2 | 3332.2.a.k.1.1 | 2 | |||
24.5 | odd | 2 | 7616.2.a.t.1.1 | 2 | |||
24.11 | even | 2 | 7616.2.a.o.1.2 | 2 | |||
51.50 | odd | 2 | 8092.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
476.2.a.c.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
1904.2.a.k.1.1 | 2 | 12.11 | even | 2 | |||
3332.2.a.k.1.1 | 2 | 21.20 | even | 2 | |||
4284.2.a.l.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7616.2.a.o.1.2 | 2 | 24.11 | even | 2 | |||
7616.2.a.t.1.1 | 2 | 24.5 | odd | 2 | |||
8092.2.a.l.1.1 | 2 | 51.50 | odd | 2 |