Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9450,2,Mod(1,9450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9450.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: | \(75.4586299101\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.29150 | 1.59545 | 0.797724 | − | 0.603023i | \(-0.206037\pi\) | ||||
0.797724 | + | 0.603023i | \(0.206037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.64575 | 1.28850 | 0.644250 | − | 0.764815i | \(-0.277170\pi\) | ||||
0.644250 | + | 0.764815i | \(0.277170\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | 0.121268 | − | 0.992620i | \(-0.461304\pi\) | ||||
0.121268 | + | 0.992620i | \(0.461304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.29150 | −1.44337 | −0.721685 | − | 0.692222i | \(-0.756632\pi\) | ||||
−0.721685 | + | 0.692222i | \(0.756632\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.29150 | −1.12815 | ||||||||
\(23\) | −1.64575 | −0.343163 | −0.171581 | − | 0.985170i | \(-0.554888\pi\) | ||||
−0.171581 | + | 0.985170i | \(0.554888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.64575 | −0.911107 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −10.6458 | −1.97687 | −0.988433 | − | 0.151657i | \(-0.951539\pi\) | ||||
−0.988433 | + | 0.151657i | \(0.951539\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.29150 | −1.30959 | −0.654796 | − | 0.755805i | \(-0.727246\pi\) | ||||
−0.654796 | + | 0.755805i | \(0.727246\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.64575 | 1.58575 | 0.792876 | − | 0.609383i | \(-0.208583\pi\) | ||||
0.792876 | + | 0.609383i | \(0.208583\pi\) | |||||||
\(38\) | 6.29150 | 1.02062 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.29150 | 1.13874 | 0.569371 | − | 0.822081i | \(-0.307187\pi\) | ||||
0.569371 | + | 0.822081i | \(0.307187\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.354249 | −0.0540224 | −0.0270112 | − | 0.999635i | \(-0.508599\pi\) | ||||
−0.0270112 | + | 0.999635i | \(0.508599\pi\) | |||||||
\(44\) | 5.29150 | 0.797724 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.64575 | 0.242653 | ||||||||
\(47\) | −0.645751 | −0.0941925 | −0.0470963 | − | 0.998890i | \(-0.514997\pi\) | ||||
−0.0470963 | + | 0.998890i | \(0.514997\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.64575 | 0.644250 | ||||||||
\(53\) | −2.64575 | −0.363422 | −0.181711 | − | 0.983352i | \(-0.558164\pi\) | ||||
−0.181711 | + | 0.983352i | \(0.558164\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.6458 | 1.39786 | ||||||||
\(59\) | −13.2915 | −1.73041 | −0.865203 | − | 0.501422i | \(-0.832811\pi\) | ||||
−0.865203 | + | 0.501422i | \(0.832811\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.64575 | 0.338754 | 0.169377 | − | 0.985551i | \(-0.445824\pi\) | ||||
0.169377 | + | 0.985551i | \(0.445824\pi\) | |||||||
\(62\) | 7.29150 | 0.926022 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.93725 | −0.603182 | −0.301591 | − | 0.953437i | \(-0.597518\pi\) | ||||
−0.301591 | + | 0.953437i | \(0.597518\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.2915 | −1.34005 | −0.670027 | − | 0.742336i | \(-0.733718\pi\) | ||||
−0.670027 | + | 0.742336i | \(0.733718\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.29150 | 0.619324 | 0.309662 | − | 0.950847i | \(-0.399784\pi\) | ||||
0.309662 | + | 0.950847i | \(0.399784\pi\) | |||||||
\(74\) | −9.64575 | −1.12130 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.29150 | −0.721685 | ||||||||
\(77\) | −5.29150 | −0.603023 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9373 | −1.79308 | −0.896541 | − | 0.442962i | \(-0.853928\pi\) | ||||
−0.896541 | + | 0.442962i | \(0.853928\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.29150 | −0.805212 | ||||||||
\(83\) | −3.64575 | −0.400173 | −0.200087 | − | 0.979778i | \(-0.564122\pi\) | ||||
−0.200087 | + | 0.979778i | \(0.564122\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.354249 | 0.0381996 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.29150 | −0.564076 | ||||||||
\(89\) | −1.00000 | −0.106000 | −0.0529999 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529999 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.64575 | −0.487007 | ||||||||
\(92\) | −1.64575 | −0.171581 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.645751 | 0.0666042 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9373 | 1.31358 | 0.656790 | − | 0.754074i | \(-0.271914\pi\) | ||||
0.656790 | + | 0.754074i | \(0.271914\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.9373 | −1.68532 | −0.842660 | − | 0.538446i | \(-0.819012\pi\) | ||||
−0.842660 | + | 0.538446i | \(0.819012\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.8745 | −1.76123 | −0.880614 | − | 0.473835i | \(-0.842869\pi\) | ||||
−0.880614 | + | 0.473835i | \(0.842869\pi\) | |||||||
\(104\) | −4.64575 | −0.455553 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.64575 | 0.256978 | ||||||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.64575 | −0.157634 | −0.0788172 | − | 0.996889i | \(-0.525114\pi\) | ||||
−0.0788172 | + | 0.996889i | \(0.525114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −8.58301 | −0.807421 | −0.403711 | − | 0.914887i | \(-0.632280\pi\) | ||||
−0.403711 | + | 0.914887i | \(0.632280\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −10.6458 | −0.988433 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.2915 | 1.22358 | ||||||||
\(119\) | −1.00000 | −0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.0000 | 1.54545 | ||||||||
\(122\) | −2.64575 | −0.239535 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.29150 | −0.654796 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6458 | 1.29960 | 0.649800 | − | 0.760105i | \(-0.274853\pi\) | ||||
0.649800 | + | 0.760105i | \(0.274853\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.9373 | −1.65456 | −0.827278 | − | 0.561793i | \(-0.810112\pi\) | ||||
−0.827278 | + | 0.561793i | \(0.810112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.29150 | 0.545542 | ||||||||
\(134\) | 4.93725 | 0.426514 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −7.64575 | −0.653221 | −0.326610 | − | 0.945159i | \(-0.605906\pi\) | ||||
−0.326610 | + | 0.945159i | \(0.605906\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.58301 | 0.388725 | 0.194363 | − | 0.980930i | \(-0.437736\pi\) | ||||
0.194363 | + | 0.980930i | \(0.437736\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.2915 | 0.947562 | ||||||||
\(143\) | 24.5830 | 2.05573 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.29150 | −0.437928 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.64575 | 0.792876 | ||||||||
\(149\) | 14.5203 | 1.18955 | 0.594773 | − | 0.803894i | \(-0.297242\pi\) | ||||
0.594773 | + | 0.803894i | \(0.297242\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2288 | 1.07654 | 0.538270 | − | 0.842772i | \(-0.319078\pi\) | ||||
0.538270 | + | 0.842772i | \(0.319078\pi\) | |||||||
\(152\) | 6.29150 | 0.510308 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.29150 | 0.426401 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.64575 | −0.530389 | −0.265194 | − | 0.964195i | \(-0.585436\pi\) | ||||
−0.265194 | + | 0.964195i | \(0.585436\pi\) | |||||||
\(158\) | 15.9373 | 1.26790 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.64575 | 0.129703 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.8745 | −1.55669 | −0.778346 | − | 0.627836i | \(-0.783941\pi\) | ||||
−0.778346 | + | 0.627836i | \(0.783941\pi\) | |||||||
\(164\) | 7.29150 | 0.569371 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.64575 | 0.282965 | ||||||||
\(167\) | 25.1660 | 1.94740 | 0.973702 | − | 0.227825i | \(-0.0731613\pi\) | ||||
0.973702 | + | 0.227825i | \(0.0731613\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.58301 | 0.660231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.354249 | −0.0270112 | ||||||||
\(173\) | −3.64575 | −0.277181 | −0.138591 | − | 0.990350i | \(-0.544257\pi\) | ||||
−0.138591 | + | 0.990350i | \(0.544257\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.29150 | 0.398862 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.00000 | 0.0749532 | ||||||||
\(179\) | −3.58301 | −0.267806 | −0.133903 | − | 0.990994i | \(-0.542751\pi\) | ||||
−0.133903 | + | 0.990994i | \(0.542751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3542 | 1.28993 | 0.644966 | − | 0.764212i | \(-0.276872\pi\) | ||||
0.644966 | + | 0.764212i | \(0.276872\pi\) | |||||||
\(182\) | 4.64575 | 0.344366 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.64575 | 0.121326 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.29150 | 0.386953 | ||||||||
\(188\) | −0.645751 | −0.0470963 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.58301 | 0.476330 | 0.238165 | − | 0.971225i | \(-0.423454\pi\) | ||||
0.238165 | + | 0.971225i | \(0.423454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.8745 | −1.21465 | −0.607327 | − | 0.794452i | \(-0.707758\pi\) | ||||
−0.607327 | + | 0.794452i | \(0.707758\pi\) | |||||||
\(194\) | −12.9373 | −0.928841 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −18.6458 | −1.32845 | −0.664227 | − | 0.747531i | \(-0.731239\pi\) | ||||
−0.664227 | + | 0.747531i | \(0.731239\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.5203 | 1.38375 | 0.691877 | − | 0.722015i | \(-0.256784\pi\) | ||||
0.691877 | + | 0.722015i | \(0.256784\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 16.9373 | 1.19170 | ||||||||
\(203\) | 10.6458 | 0.747185 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.8745 | 1.24538 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.64575 | 0.322125 | ||||||||
\(209\) | −33.2915 | −2.30282 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.2915 | 1.74114 | 0.870569 | − | 0.492046i | \(-0.163751\pi\) | ||||
0.870569 | + | 0.492046i | \(0.163751\pi\) | |||||||
\(212\) | −2.64575 | −0.181711 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | 0.410152 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.29150 | 0.494979 | ||||||||
\(218\) | 1.64575 | 0.111464 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.64575 | 0.312507 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.5203 | 1.44110 | 0.720552 | − | 0.693401i | \(-0.243889\pi\) | ||||
0.720552 | + | 0.693401i | \(0.243889\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.58301 | 0.570933 | ||||||||
\(227\) | −6.35425 | −0.421746 | −0.210873 | − | 0.977513i | \(-0.567631\pi\) | ||||
−0.210873 | + | 0.977513i | \(0.567631\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.5203 | 0.827362 | 0.413681 | − | 0.910422i | \(-0.364243\pi\) | ||||
0.413681 | + | 0.910422i | \(0.364243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.6458 | 0.698928 | ||||||||
\(233\) | 1.64575 | 0.107817 | 0.0539084 | − | 0.998546i | \(-0.482832\pi\) | ||||
0.0539084 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.2915 | −0.865203 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.00000 | 0.0648204 | ||||||||
\(239\) | −14.3542 | −0.928499 | −0.464250 | − | 0.885704i | \(-0.653676\pi\) | ||||
−0.464250 | + | 0.885704i | \(0.653676\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9373 | −0.833362 | −0.416681 | − | 0.909053i | \(-0.636807\pi\) | ||||
−0.416681 | + | 0.909053i | \(0.636807\pi\) | |||||||
\(242\) | −17.0000 | −1.09280 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.64575 | 0.169377 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.2288 | −1.85978 | ||||||||
\(248\) | 7.29150 | 0.463011 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.87451 | 0.244557 | 0.122278 | − | 0.992496i | \(-0.460980\pi\) | ||||
0.122278 | + | 0.992496i | \(0.460980\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.70850 | −0.547499 | ||||||||
\(254\) | −14.6458 | −0.918956 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.29150 | −0.142940 | −0.0714700 | − | 0.997443i | \(-0.522769\pi\) | ||||
−0.0714700 | + | 0.997443i | \(0.522769\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.64575 | −0.599358 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.9373 | 1.16995 | ||||||||
\(263\) | 19.8745 | 1.22551 | 0.612757 | − | 0.790271i | \(-0.290060\pi\) | ||||
0.612757 | + | 0.790271i | \(0.290060\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.29150 | −0.385757 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.93725 | −0.301591 | ||||||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.2915 | −0.928893 | −0.464446 | − | 0.885601i | \(-0.653747\pi\) | ||||
−0.464446 | + | 0.885601i | \(0.653747\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.64575 | 0.461897 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7085 | 0.883748 | 0.441874 | − | 0.897077i | \(-0.354314\pi\) | ||||
0.441874 | + | 0.897077i | \(0.354314\pi\) | |||||||
\(278\) | −4.58301 | −0.274870 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5203 | −0.806551 | −0.403276 | − | 0.915079i | \(-0.632128\pi\) | ||||
−0.403276 | + | 0.915079i | \(0.632128\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1660 | 0.723194 | 0.361597 | − | 0.932334i | \(-0.382232\pi\) | ||||
0.361597 | + | 0.932334i | \(0.382232\pi\) | |||||||
\(284\) | −11.2915 | −0.670027 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.5830 | −1.45362 | ||||||||
\(287\) | −7.29150 | −0.430404 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.29150 | 0.309662 | ||||||||
\(293\) | 31.5203 | 1.84143 | 0.920717 | − | 0.390232i | \(-0.127605\pi\) | ||||
0.920717 | + | 0.390232i | \(0.127605\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.64575 | −0.560648 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.5203 | −0.841136 | ||||||||
\(299\) | −7.64575 | −0.442165 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.354249 | 0.0204186 | ||||||||
\(302\) | −13.2288 | −0.761229 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.29150 | −0.360842 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.2915 | −0.986878 | −0.493439 | − | 0.869780i | \(-0.664260\pi\) | ||||
−0.493439 | + | 0.869780i | \(0.664260\pi\) | |||||||
\(308\) | −5.29150 | −0.301511 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.2915 | 1.20733 | 0.603665 | − | 0.797238i | \(-0.293706\pi\) | ||||
0.603665 | + | 0.797238i | \(0.293706\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.2288 | −0.691210 | −0.345605 | − | 0.938380i | \(-0.612326\pi\) | ||||
−0.345605 | + | 0.938380i | \(0.612326\pi\) | |||||||
\(314\) | 6.64575 | 0.375041 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.9373 | −0.896541 | ||||||||
\(317\) | −29.9373 | −1.68144 | −0.840722 | − | 0.541467i | \(-0.817869\pi\) | ||||
−0.840722 | + | 0.541467i | \(0.817869\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −56.3320 | −3.15399 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.64575 | −0.0917141 | ||||||||
\(323\) | −6.29150 | −0.350069 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.8745 | 1.10075 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.29150 | −0.402606 | ||||||||
\(329\) | 0.645751 | 0.0356014 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.64575 | −0.530178 | −0.265089 | − | 0.964224i | \(-0.585401\pi\) | ||||
−0.265089 | + | 0.964224i | \(0.585401\pi\) | |||||||
\(332\) | −3.64575 | −0.200087 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.1660 | −1.37702 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.1660 | 1.42535 | 0.712677 | − | 0.701493i | \(-0.247483\pi\) | ||||
0.712677 | + | 0.701493i | \(0.247483\pi\) | |||||||
\(338\) | −8.58301 | −0.466854 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −38.5830 | −2.08939 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.354249 | 0.0190998 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.64575 | 0.195997 | ||||||||
\(347\) | −9.70850 | −0.521179 | −0.260590 | − | 0.965450i | \(-0.583917\pi\) | ||||
−0.260590 | + | 0.965450i | \(0.583917\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.35425 | −0.500721 | −0.250361 | − | 0.968153i | \(-0.580549\pi\) | ||||
−0.250361 | + | 0.968153i | \(0.580549\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.29150 | −0.282038 | ||||||||
\(353\) | −16.4575 | −0.875945 | −0.437973 | − | 0.898988i | \(-0.644303\pi\) | ||||
−0.437973 | + | 0.898988i | \(0.644303\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.00000 | −0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.58301 | 0.189368 | ||||||||
\(359\) | −32.5830 | −1.71967 | −0.859833 | − | 0.510576i | \(-0.829432\pi\) | ||||
−0.859833 | + | 0.510576i | \(0.829432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.5830 | 1.08332 | ||||||||
\(362\) | −17.3542 | −0.912119 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.64575 | −0.243504 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.937254 | −0.0489243 | −0.0244621 | − | 0.999701i | \(-0.507787\pi\) | ||||
−0.0244621 | + | 0.999701i | \(0.507787\pi\) | |||||||
\(368\) | −1.64575 | −0.0857907 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.64575 | 0.137361 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.8745 | 1.23618 | 0.618088 | − | 0.786109i | \(-0.287908\pi\) | ||||
0.618088 | + | 0.786109i | \(0.287908\pi\) | |||||||
\(374\) | −5.29150 | −0.273617 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.645751 | 0.0333021 | ||||||||
\(377\) | −49.4575 | −2.54719 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.22876 | −0.114484 | −0.0572418 | − | 0.998360i | \(-0.518231\pi\) | ||||
−0.0572418 | + | 0.998360i | \(0.518231\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.58301 | −0.336816 | ||||||||
\(383\) | 27.2915 | 1.39453 | 0.697265 | − | 0.716813i | \(-0.254400\pi\) | ||||
0.697265 | + | 0.716813i | \(0.254400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.8745 | 0.858890 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.9373 | 0.656790 | ||||||||
\(389\) | 34.3948 | 1.74388 | 0.871942 | − | 0.489609i | \(-0.162861\pi\) | ||||
0.871942 | + | 0.489609i | \(0.162861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.64575 | −0.0832292 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.6458 | 0.939359 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.52026 | −0.226865 | −0.113433 | − | 0.993546i | \(-0.536185\pi\) | ||||
−0.113433 | + | 0.993546i | \(0.536185\pi\) | |||||||
\(398\) | −19.5203 | −0.978462 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.9373 | 1.24531 | 0.622654 | − | 0.782498i | \(-0.286055\pi\) | ||||
0.622654 | + | 0.782498i | \(0.286055\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.8745 | −1.68741 | ||||||||
\(404\) | −16.9373 | −0.842660 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.6458 | −0.528340 | ||||||||
\(407\) | 51.0405 | 2.52998 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.22876 | −0.406886 | −0.203443 | − | 0.979087i | \(-0.565213\pi\) | ||||
−0.203443 | + | 0.979087i | \(0.565213\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.8745 | −0.880614 | ||||||||
\(413\) | 13.2915 | 0.654032 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.64575 | −0.227777 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 33.2915 | 1.62834 | ||||||||
\(419\) | −22.3542 | −1.09208 | −0.546038 | − | 0.837760i | \(-0.683865\pi\) | ||||
−0.546038 | + | 0.837760i | \(0.683865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.58301 | −0.223362 | −0.111681 | − | 0.993744i | \(-0.535623\pi\) | ||||
−0.111681 | + | 0.993744i | \(0.535623\pi\) | |||||||
\(422\) | −25.2915 | −1.23117 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.64575 | 0.128489 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.64575 | −0.128037 | ||||||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.8745 | −1.63168 | −0.815839 | − | 0.578279i | \(-0.803724\pi\) | ||||
−0.815839 | + | 0.578279i | \(0.803724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.708497 | −0.0340482 | −0.0170241 | − | 0.999855i | \(-0.505419\pi\) | ||||
−0.0170241 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(434\) | −7.29150 | −0.350003 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.64575 | −0.0788172 | ||||||||
\(437\) | 10.3542 | 0.495311 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.0627 | −0.718906 | −0.359453 | − | 0.933163i | \(-0.617037\pi\) | ||||
−0.359453 | + | 0.933163i | \(0.617037\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.64575 | −0.220976 | ||||||||
\(443\) | −12.4170 | −0.589949 | −0.294975 | − | 0.955505i | \(-0.595311\pi\) | ||||
−0.294975 | + | 0.955505i | \(0.595311\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −21.5203 | −1.01901 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −8.22876 | −0.388339 | −0.194170 | − | 0.980968i | \(-0.562201\pi\) | ||||
−0.194170 | + | 0.980968i | \(0.562201\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.5830 | 1.81680 | ||||||||
\(452\) | −8.58301 | −0.403711 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.35425 | 0.298220 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.8745 | −1.81847 | −0.909236 | − | 0.416280i | \(-0.863334\pi\) | ||||
−0.909236 | + | 0.416280i | \(0.863334\pi\) | |||||||
\(458\) | −12.5203 | −0.585033 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.52026 | −0.163955 | −0.0819774 | − | 0.996634i | \(-0.526124\pi\) | ||||
−0.0819774 | + | 0.996634i | \(0.526124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.64575 | 0.308854 | 0.154427 | − | 0.988004i | \(-0.450647\pi\) | ||||
0.154427 | + | 0.988004i | \(0.450647\pi\) | |||||||
\(464\) | −10.6458 | −0.494217 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.64575 | −0.0762380 | ||||||||
\(467\) | −28.7085 | −1.32847 | −0.664235 | − | 0.747523i | \(-0.731243\pi\) | ||||
−0.664235 | + | 0.747523i | \(0.731243\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.93725 | 0.227981 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.2915 | 0.611791 | ||||||||
\(473\) | −1.87451 | −0.0861900 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.00000 | −0.0458349 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.3542 | 0.656548 | ||||||||
\(479\) | −7.35425 | −0.336024 | −0.168012 | − | 0.985785i | \(-0.553735\pi\) | ||||
−0.168012 | + | 0.985785i | \(0.553735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.8118 | 2.04324 | ||||||||
\(482\) | 12.9373 | 0.589276 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.0000 | 0.772727 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.708497 | −0.0321051 | −0.0160525 | − | 0.999871i | \(-0.505110\pi\) | ||||
−0.0160525 | + | 0.999871i | \(0.505110\pi\) | |||||||
\(488\) | −2.64575 | −0.119768 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.8745 | −0.581018 | −0.290509 | − | 0.956872i | \(-0.593825\pi\) | ||||
−0.290509 | + | 0.956872i | \(0.593825\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.6458 | −0.479461 | ||||||||
\(494\) | 29.2288 | 1.31506 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.29150 | −0.327398 | ||||||||
\(497\) | 11.2915 | 0.506493 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0627 | 0.584769 | 0.292384 | − | 0.956301i | \(-0.405551\pi\) | ||||
0.292384 | + | 0.956301i | \(0.405551\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.87451 | −0.172928 | ||||||||
\(503\) | −2.70850 | −0.120766 | −0.0603830 | − | 0.998175i | \(-0.519232\pi\) | ||||
−0.0603830 | + | 0.998175i | \(0.519232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8.70850 | 0.387140 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.6458 | 0.649800 | ||||||||
\(509\) | 7.52026 | 0.333330 | 0.166665 | − | 0.986014i | \(-0.446700\pi\) | ||||
0.166665 | + | 0.986014i | \(0.446700\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.29150 | −0.234082 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.29150 | 0.101074 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.41699 | −0.150279 | ||||||||
\(518\) | 9.64575 | 0.423810 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.5830 | −1.29605 | −0.648027 | − | 0.761617i | \(-0.724406\pi\) | ||||
−0.648027 | + | 0.761617i | \(0.724406\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.7490 | 1.16965 | 0.584826 | − | 0.811158i | \(-0.301163\pi\) | ||||
0.584826 | + | 0.811158i | \(0.301163\pi\) | |||||||
\(524\) | −18.9373 | −0.827278 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.8745 | −0.866570 | ||||||||
\(527\) | −7.29150 | −0.317623 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2915 | −0.882239 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.29150 | 0.272771 | ||||||||
\(533\) | 33.8745 | 1.46727 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.93725 | 0.213257 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.00000 | 0.258678 | ||||||||
\(539\) | 5.29150 | 0.227921 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.6458 | −0.586677 | −0.293338 | − | 0.956009i | \(-0.594766\pi\) | ||||
−0.293338 | + | 0.956009i | \(0.594766\pi\) | |||||||
\(542\) | 15.2915 | 0.656826 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | −7.64575 | −0.326610 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 66.9778 | 2.85335 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.9373 | 0.677721 | ||||||||
\(554\) | −14.7085 | −0.624904 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.58301 | 0.194363 | ||||||||
\(557\) | 4.52026 | 0.191530 | 0.0957648 | − | 0.995404i | \(-0.469470\pi\) | ||||
0.0957648 | + | 0.995404i | \(0.469470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.64575 | −0.0696079 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.5203 | 0.570318 | ||||||||
\(563\) | 23.0627 | 0.971979 | 0.485989 | − | 0.873965i | \(-0.338459\pi\) | ||||
0.485989 | + | 0.873965i | \(0.338459\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12.1660 | −0.511376 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.2915 | 0.473781 | ||||||||
\(569\) | −37.1660 | −1.55808 | −0.779040 | − | 0.626974i | \(-0.784293\pi\) | ||||
−0.779040 | + | 0.626974i | \(0.784293\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.5830 | 0.526582 | 0.263291 | − | 0.964716i | \(-0.415192\pi\) | ||||
0.263291 | + | 0.964716i | \(0.415192\pi\) | |||||||
\(572\) | 24.5830 | 1.02787 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.29150 | 0.304341 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.0000 | 0.666089 | 0.333044 | − | 0.942911i | \(-0.391924\pi\) | ||||
0.333044 | + | 0.942911i | \(0.391924\pi\) | |||||||
\(578\) | 16.0000 | 0.665512 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.64575 | 0.151251 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.0000 | −0.579821 | ||||||||
\(584\) | −5.29150 | −0.218964 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.5203 | −1.30209 | ||||||||
\(587\) | −31.5203 | −1.30098 | −0.650490 | − | 0.759515i | \(-0.725436\pi\) | ||||
−0.650490 | + | 0.759515i | \(0.725436\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.8745 | 1.89023 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.64575 | 0.396438 | ||||||||
\(593\) | 15.0000 | 0.615976 | 0.307988 | − | 0.951390i | \(-0.400344\pi\) | ||||
0.307988 | + | 0.951390i | \(0.400344\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.5203 | 0.594773 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.64575 | 0.312658 | ||||||||
\(599\) | −38.8118 | −1.58581 | −0.792903 | − | 0.609348i | \(-0.791431\pi\) | ||||
−0.792903 | + | 0.609348i | \(0.791431\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.2915 | −0.623753 | −0.311877 | − | 0.950123i | \(-0.600958\pi\) | ||||
−0.311877 | + | 0.950123i | \(0.600958\pi\) | |||||||
\(602\) | −0.354249 | −0.0144381 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.2288 | 0.538270 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.811762 | 0.0329484 | 0.0164742 | − | 0.999864i | \(-0.494756\pi\) | ||||
0.0164742 | + | 0.999864i | \(0.494756\pi\) | |||||||
\(608\) | 6.29150 | 0.255154 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.00000 | −0.121367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.9373 | −0.926427 | −0.463213 | − | 0.886247i | \(-0.653304\pi\) | ||||
−0.463213 | + | 0.886247i | \(0.653304\pi\) | |||||||
\(614\) | 17.2915 | 0.697828 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.29150 | 0.213201 | ||||||||
\(617\) | 5.06275 | 0.203818 | 0.101909 | − | 0.994794i | \(-0.467505\pi\) | ||||
0.101909 | + | 0.994794i | \(0.467505\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.2915 | −0.853711 | ||||||||
\(623\) | 1.00000 | 0.0400642 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.2288 | 0.488759 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.64575 | −0.265194 | ||||||||
\(629\) | 9.64575 | 0.384601 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.8118 | −1.10717 | −0.553584 | − | 0.832793i | \(-0.686740\pi\) | ||||
−0.553584 | + | 0.832793i | \(0.686740\pi\) | |||||||
\(632\) | 15.9373 | 0.633950 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.9373 | 1.18896 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.64575 | 0.184071 | ||||||||
\(638\) | 56.3320 | 2.23021 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.2915 | −1.39393 | −0.696965 | − | 0.717105i | \(-0.745467\pi\) | ||||
−0.696965 | + | 0.717105i | \(0.745467\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.29150 | −0.0903680 | −0.0451840 | − | 0.998979i | \(-0.514387\pi\) | ||||
−0.0451840 | + | 0.998979i | \(0.514387\pi\) | |||||||
\(644\) | 1.64575 | 0.0648517 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.29150 | 0.247536 | ||||||||
\(647\) | −11.3542 | −0.446382 | −0.223191 | − | 0.974775i | \(-0.571647\pi\) | ||||
−0.223191 | + | 0.974775i | \(0.571647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −70.3320 | −2.76077 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.8745 | −0.778346 | ||||||||
\(653\) | 27.8118 | 1.08836 | 0.544179 | − | 0.838969i | \(-0.316841\pi\) | ||||
0.544179 | + | 0.838969i | \(0.316841\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.29150 | 0.284685 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.645751 | −0.0251740 | ||||||||
\(659\) | 5.58301 | 0.217483 | 0.108742 | − | 0.994070i | \(-0.465318\pi\) | ||||
0.108742 | + | 0.994070i | \(0.465318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.16601 | −0.123144 | −0.0615718 | − | 0.998103i | \(-0.519611\pi\) | ||||
−0.0615718 | + | 0.998103i | \(0.519611\pi\) | |||||||
\(662\) | 9.64575 | 0.374893 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.64575 | 0.141483 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.5203 | 0.678387 | ||||||||
\(668\) | 25.1660 | 0.973702 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.0000 | 0.540464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.5830 | −1.02470 | −0.512350 | − | 0.858777i | \(-0.671225\pi\) | ||||
−0.512350 | + | 0.858777i | \(0.671225\pi\) | |||||||
\(674\) | −26.1660 | −1.00788 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.58301 | 0.330116 | ||||||||
\(677\) | 9.29150 | 0.357101 | 0.178551 | − | 0.983931i | \(-0.442859\pi\) | ||||
0.178551 | + | 0.983931i | \(0.442859\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.9373 | −0.496486 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 38.5830 | 1.47742 | ||||||||
\(683\) | −2.58301 | −0.0988359 | −0.0494180 | − | 0.998778i | \(-0.515737\pi\) | ||||
−0.0494180 | + | 0.998778i | \(0.515737\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.354249 | −0.0135056 | ||||||||
\(689\) | −12.2915 | −0.468269 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.7085 | −0.863872 | −0.431936 | − | 0.901904i | \(-0.642169\pi\) | ||||
−0.431936 | + | 0.901904i | \(0.642169\pi\) | |||||||
\(692\) | −3.64575 | −0.138591 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.70850 | 0.368530 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.29150 | 0.276185 | ||||||||
\(698\) | 9.35425 | 0.354064 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.2915 | −0.502013 | −0.251007 | − | 0.967985i | \(-0.580762\pi\) | ||||
−0.251007 | + | 0.967985i | \(0.580762\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −60.6863 | −2.28883 | ||||||||
\(704\) | 5.29150 | 0.199431 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.4575 | 0.619387 | ||||||||
\(707\) | 16.9373 | 0.636991 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.87451 | 0.0703986 | 0.0351993 | − | 0.999380i | \(-0.488793\pi\) | ||||
0.0351993 | + | 0.999380i | \(0.488793\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.00000 | 0.0374766 | ||||||||
\(713\) | 12.0000 | 0.449404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.58301 | −0.133903 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32.5830 | 1.21599 | ||||||||
\(719\) | 28.6458 | 1.06831 | 0.534153 | − | 0.845388i | \(-0.320631\pi\) | ||||
0.534153 | + | 0.845388i | \(0.320631\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.8745 | 0.665681 | ||||||||
\(722\) | −20.5830 | −0.766020 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.3542 | 0.644966 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.6458 | −0.951148 | −0.475574 | − | 0.879676i | \(-0.657760\pi\) | ||||
−0.475574 | + | 0.879676i | \(0.657760\pi\) | |||||||
\(728\) | 4.64575 | 0.172183 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.354249 | −0.0131024 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.8118 | −1.39661 | −0.698305 | − | 0.715801i | \(-0.746062\pi\) | ||||
−0.698305 | + | 0.715801i | \(0.746062\pi\) | |||||||
\(734\) | 0.937254 | 0.0345947 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.64575 | 0.0606632 | ||||||||
\(737\) | −26.1255 | −0.962345 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.3320 | 1.77792 | 0.888961 | − | 0.457983i | \(-0.151428\pi\) | ||||
0.888961 | + | 0.457983i | \(0.151428\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.64575 | −0.0971286 | ||||||||
\(743\) | −49.7490 | −1.82511 | −0.912557 | − | 0.408949i | \(-0.865895\pi\) | ||||
−0.912557 | + | 0.408949i | \(0.865895\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.8745 | −0.874108 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.29150 | 0.193476 | ||||||||
\(749\) | 6.00000 | 0.219235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5830 | −0.824066 | −0.412033 | − | 0.911169i | \(-0.635181\pi\) | ||||
−0.412033 | + | 0.911169i | \(0.635181\pi\) | |||||||
\(752\) | −0.645751 | −0.0235481 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 49.4575 | 1.80114 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.8118 | −1.04718 | −0.523591 | − | 0.851970i | \(-0.675408\pi\) | ||||
−0.523591 | + | 0.851970i | \(0.675408\pi\) | |||||||
\(758\) | 2.22876 | 0.0809521 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.83399 | −0.0664821 | −0.0332410 | − | 0.999447i | \(-0.510583\pi\) | ||||
−0.0332410 | + | 0.999447i | \(0.510583\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.64575 | 0.0595802 | ||||||||
\(764\) | 6.58301 | 0.238165 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.2915 | −0.986082 | ||||||||
\(767\) | −61.7490 | −2.22963 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.0000 | −1.15395 | −0.576975 | − | 0.816762i | \(-0.695767\pi\) | ||||
−0.576975 | + | 0.816762i | \(0.695767\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −16.8745 | −0.607327 | ||||||||
\(773\) | 25.1660 | 0.905158 | 0.452579 | − | 0.891724i | \(-0.350504\pi\) | ||||
0.452579 | + | 0.891724i | \(0.350504\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.9373 | −0.464420 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.3948 | −1.23311 | ||||||||
\(779\) | −45.8745 | −1.64362 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −59.7490 | −2.13799 | ||||||||
\(782\) | 1.64575 | 0.0588519 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.4170 | −0.692141 | −0.346071 | − | 0.938208i | \(-0.612484\pi\) | ||||
−0.346071 | + | 0.938208i | \(0.612484\pi\) | |||||||
\(788\) | −18.6458 | −0.664227 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.58301 | 0.305177 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.2915 | 0.436484 | ||||||||
\(794\) | 4.52026 | 0.160418 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.5203 | 0.691877 | ||||||||
\(797\) | 3.18824 | 0.112933 | 0.0564666 | − | 0.998404i | \(-0.482017\pi\) | ||||
0.0564666 | + | 0.998404i | \(0.482017\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.645751 | −0.0228450 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.9373 | −0.880565 | ||||||||
\(803\) | 28.0000 | 0.988099 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 33.8745 | 1.19318 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.9373 | 0.595851 | ||||||||
\(809\) | 24.5830 | 0.864292 | 0.432146 | − | 0.901804i | \(-0.357756\pi\) | ||||
0.432146 | + | 0.901804i | \(0.357756\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.1660 | 0.532551 | 0.266275 | − | 0.963897i | \(-0.414207\pi\) | ||||
0.266275 | + | 0.963897i | \(0.414207\pi\) | |||||||
\(812\) | 10.6458 | 0.373593 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −51.0405 | −1.78897 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.22876 | 0.0779743 | ||||||||
\(818\) | 8.22876 | 0.287712 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.2288 | 1.64829 | 0.824147 | − | 0.566375i | \(-0.191655\pi\) | ||||
0.824147 | + | 0.566375i | \(0.191655\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.0405 | 0.733426 | 0.366713 | − | 0.930334i | \(-0.380483\pi\) | ||||
0.366713 | + | 0.930334i | \(0.380483\pi\) | |||||||
\(824\) | 17.8745 | 0.622688 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.2915 | −0.462471 | ||||||||
\(827\) | −22.4170 | −0.779515 | −0.389758 | − | 0.920917i | \(-0.627441\pi\) | ||||
−0.389758 | + | 0.920917i | \(0.627441\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.6458 | 0.439205 | 0.219603 | − | 0.975589i | \(-0.429524\pi\) | ||||
0.219603 | + | 0.975589i | \(0.429524\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.64575 | 0.161062 | ||||||||
\(833\) | 1.00000 | 0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −33.2915 | −1.15141 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.3542 | 0.772215 | ||||||||
\(839\) | −2.18824 | −0.0755464 | −0.0377732 | − | 0.999286i | \(-0.512026\pi\) | ||||
−0.0377732 | + | 0.999286i | \(0.512026\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 84.3320 | 2.90800 | ||||||||
\(842\) | 4.58301 | 0.157941 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 25.2915 | 0.870569 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.0000 | −0.584127 | ||||||||
\(848\) | −2.64575 | −0.0908555 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.8745 | −0.544171 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.3320 | −1.03855 | −0.519274 | − | 0.854608i | \(-0.673798\pi\) | ||||
−0.519274 | + | 0.854608i | \(0.673798\pi\) | |||||||
\(854\) | 2.64575 | 0.0905357 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | 0.205076 | ||||||||
\(857\) | 23.7085 | 0.809867 | 0.404933 | − | 0.914346i | \(-0.367295\pi\) | ||||
0.404933 | + | 0.914346i | \(0.367295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.3320 | 1.71731 | 0.858653 | − | 0.512557i | \(-0.171302\pi\) | ||||
0.858653 | + | 0.512557i | \(0.171302\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.8745 | 1.15377 | ||||||||
\(863\) | −35.6458 | −1.21340 | −0.606698 | − | 0.794933i | \(-0.707506\pi\) | ||||
−0.606698 | + | 0.794933i | \(0.707506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.708497 | 0.0240757 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.29150 | 0.247490 | ||||||||
\(869\) | −84.3320 | −2.86077 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.9373 | −0.777199 | ||||||||
\(872\) | 1.64575 | 0.0557322 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.3542 | −0.350238 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.8745 | −0.873720 | −0.436860 | − | 0.899529i | \(-0.643909\pi\) | ||||
−0.436860 | + | 0.899529i | \(0.643909\pi\) | |||||||
\(878\) | 15.0627 | 0.508343 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.8745 | 1.57924 | 0.789621 | − | 0.613595i | \(-0.210277\pi\) | ||||
0.789621 | + | 0.613595i | \(0.210277\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.7085 | −0.696896 | −0.348448 | − | 0.937328i | \(-0.613291\pi\) | ||||
−0.348448 | + | 0.937328i | \(0.613291\pi\) | |||||||
\(884\) | 4.64575 | 0.156254 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.4170 | 0.417157 | ||||||||
\(887\) | 18.1255 | 0.608594 | 0.304297 | − | 0.952577i | \(-0.401578\pi\) | ||||
0.304297 | + | 0.952577i | \(0.401578\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.6458 | −0.491203 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.5203 | 0.720552 | ||||||||
\(893\) | 4.06275 | 0.135955 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.22876 | 0.274597 | ||||||||
\(899\) | 77.6235 | 2.58889 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.64575 | −0.0881428 | ||||||||
\(902\) | −38.5830 | −1.28467 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.58301 | 0.285467 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7085 | −0.421979 | −0.210989 | − | 0.977488i | \(-0.567669\pi\) | ||||
−0.210989 | + | 0.977488i | \(0.567669\pi\) | |||||||
\(908\) | −6.35425 | −0.210873 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.1660 | −0.436209 | −0.218105 | − | 0.975925i | \(-0.569987\pi\) | ||||
−0.218105 | + | 0.975925i | \(0.569987\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.2915 | −0.638456 | ||||||||
\(914\) | 38.8745 | 1.28585 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.5203 | 0.413681 | ||||||||
\(917\) | 18.9373 | 0.625363 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.0405 | 1.61770 | 0.808849 | − | 0.588017i | \(-0.200091\pi\) | ||||
0.808849 | + | 0.588017i | \(0.200091\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.52026 | 0.115934 | ||||||||
\(923\) | −52.4575 | −1.72666 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.64575 | −0.218393 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.6458 | 0.349464 | ||||||||
\(929\) | −10.8745 | −0.356781 | −0.178391 | − | 0.983960i | \(-0.557089\pi\) | ||||
−0.178391 | + | 0.983960i | \(0.557089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.29150 | −0.206196 | ||||||||
\(932\) | 1.64575 | 0.0539084 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.7085 | 0.939371 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.2288 | 0.530170 | 0.265085 | − | 0.964225i | \(-0.414600\pi\) | ||||
0.265085 | + | 0.964225i | \(0.414600\pi\) | |||||||
\(938\) | −4.93725 | −0.161207 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.6458 | −0.510037 | −0.255018 | − | 0.966936i | \(-0.582082\pi\) | ||||
−0.255018 | + | 0.966936i | \(0.582082\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0000 | −0.390774 | ||||||||
\(944\) | −13.2915 | −0.432602 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.87451 | 0.0609455 | ||||||||
\(947\) | 18.7085 | 0.607944 | 0.303972 | − | 0.952681i | \(-0.401687\pi\) | ||||
0.303972 | + | 0.952681i | \(0.401687\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.5830 | 0.797998 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.00000 | 0.0324102 | ||||||||
\(953\) | −18.1033 | −0.586422 | −0.293211 | − | 0.956048i | \(-0.594724\pi\) | ||||
−0.293211 | + | 0.956048i | \(0.594724\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.3542 | −0.464250 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.35425 | 0.237605 | ||||||||
\(959\) | 7.64575 | 0.246894 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.1660 | 0.715033 | ||||||||
\(962\) | −44.8118 | −1.44479 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.9373 | −0.416681 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.8118 | 1.47321 | 0.736603 | − | 0.676325i | \(-0.236428\pi\) | ||||
0.736603 | + | 0.676325i | \(0.236428\pi\) | |||||||
\(968\) | −17.0000 | −0.546401 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.77124 | −0.121025 | −0.0605125 | − | 0.998167i | \(-0.519273\pi\) | ||||
−0.0605125 | + | 0.998167i | \(0.519273\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.58301 | −0.146924 | ||||||||
\(974\) | 0.708497 | 0.0227017 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.64575 | 0.0846884 | ||||||||
\(977\) | 22.9373 | 0.733828 | 0.366914 | − | 0.930255i | \(-0.380414\pi\) | ||||
0.366914 | + | 0.930255i | \(0.380414\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.29150 | −0.169117 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.8745 | 0.410842 | ||||||||
\(983\) | 13.4797 | 0.429937 | 0.214968 | − | 0.976621i | \(-0.431035\pi\) | ||||
0.214968 | + | 0.976621i | \(0.431035\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.6458 | 0.339030 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −29.2288 | −0.929891 | ||||||||
\(989\) | 0.583005 | 0.0185385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.9373 | −1.07805 | −0.539026 | − | 0.842289i | \(-0.681208\pi\) | ||||
−0.539026 | + | 0.842289i | \(0.681208\pi\) | |||||||
\(992\) | 7.29150 | 0.231505 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.2915 | −0.358145 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.4575 | −1.59801 | −0.799003 | − | 0.601327i | \(-0.794639\pi\) | ||||
−0.799003 | + | 0.601327i | \(0.794639\pi\) | |||||||
\(998\) | −13.0627 | −0.413494 | ||||||||
\(999\) | 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 | 9450.2.a.ec.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9450.2.a.eq.1.1 | yes | 2 | ||
5.4 | even | 2 | 9450.2.a.et.1.2 | yes | 2 | ||
15.14 | odd | 2 | 9450.2.a.ej.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9450.2.a.ec.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9450.2.a.ej.1.1 | yes | 2 | 15.14 | odd | 2 | ||
9450.2.a.eq.1.1 | yes | 2 | 3.2 | odd | 2 | ||
9450.2.a.et.1.2 | yes | 2 | 5.4 | even | 2 |