Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 19x^{5} + 19x^{4} - 35x^{3} - 10x^{2} + 18x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.85152\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.41642 | −1.52787 | −0.763934 | − | 0.645294i | \(-0.776735\pi\) | ||||
−0.763934 | + | 0.645294i | \(0.776735\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.05098 | 0.775198 | 0.387599 | − | 0.921828i | \(-0.373305\pi\) | ||||
0.387599 | + | 0.921828i | \(0.373305\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.14688 | 0.345796 | 0.172898 | − | 0.984940i | \(-0.444687\pi\) | ||||
0.172898 | + | 0.984940i | \(0.444687\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.51492 | −1.25221 | −0.626106 | − | 0.779738i | \(-0.715352\pi\) | ||||
−0.626106 | + | 0.779738i | \(0.715352\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.41642 | −0.882115 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.446852 | 0.108377 | 0.0541887 | − | 0.998531i | \(-0.482743\pi\) | ||||
0.0541887 | + | 0.998531i | \(0.482743\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.11134 | −0.484374 | −0.242187 | − | 0.970230i | \(-0.577865\pi\) | ||||
−0.242187 | + | 0.970230i | \(0.577865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.05098 | 0.447561 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.67190 | 1.33438 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.57178 | 1.18033 | 0.590163 | − | 0.807284i | \(-0.299063\pi\) | ||||
0.590163 | + | 0.807284i | \(0.299063\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.14688 | 0.199645 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.00700 | −1.18440 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.89567 | −0.804843 | −0.402421 | − | 0.915455i | \(-0.631831\pi\) | ||||
−0.402421 | + | 0.915455i | \(0.631831\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.51492 | −0.722965 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.92571 | 0.613093 | 0.306547 | − | 0.951856i | \(-0.400826\pi\) | ||||
0.306547 | + | 0.951856i | \(0.400826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.16338 | 0.482410 | 0.241205 | − | 0.970474i | \(-0.422457\pi\) | ||||
0.241205 | + | 0.970474i | \(0.422457\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.41642 | −0.509289 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.451968 | −0.0659262 | −0.0329631 | − | 0.999457i | \(-0.510494\pi\) | ||||
−0.0329631 | + | 0.999457i | \(0.510494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.79348 | −0.399068 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.446852 | 0.0625717 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.11866 | 0.565742 | 0.282871 | − | 0.959158i | \(-0.408713\pi\) | ||||
0.282871 | + | 0.959158i | \(0.408713\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.91820 | −0.528330 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.11134 | −0.279653 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.31529 | −0.822180 | −0.411090 | − | 0.911595i | \(-0.634852\pi\) | ||||
−0.411090 | + | 0.911595i | \(0.634852\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.75827 | −1.12138 | −0.560690 | − | 0.828025i | \(-0.689464\pi\) | ||||
−0.560690 | + | 0.828025i | \(0.689464\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.05098 | 0.258399 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.4248 | 1.91322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.6292 | −1.29856 | −0.649280 | − | 0.760549i | \(-0.724930\pi\) | ||||
−0.649280 | + | 0.760549i | \(0.724930\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3216 | 1.58099 | 0.790494 | − | 0.612469i | \(-0.209824\pi\) | ||||
0.790494 | + | 0.612469i | \(0.209824\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.6838 | −1.48452 | −0.742262 | − | 0.670110i | \(-0.766247\pi\) | ||||
−0.742262 | + | 0.670110i | \(0.766247\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.67190 | 0.770405 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.35222 | 0.268060 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.30778 | 0.259646 | 0.129823 | − | 0.991537i | \(-0.458559\pi\) | ||||
0.129823 | + | 0.991537i | \(0.458559\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.59898 | −0.504804 | −0.252402 | − | 0.967622i | \(-0.581221\pi\) | ||||
−0.252402 | + | 0.967622i | \(0.581221\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.52663 | −0.165586 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.8381 | 1.57284 | 0.786418 | − | 0.617695i | \(-0.211933\pi\) | ||||
0.786418 | + | 0.617695i | \(0.211933\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.26001 | −0.970713 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.57178 | 0.681462 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.21320 | 0.740059 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.14524 | 0.827024 | 0.413512 | − | 0.910499i | \(-0.364302\pi\) | ||||
0.413512 | + | 0.910499i | \(0.364302\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.14688 | 0.115265 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.8719 | −1.08180 | −0.540899 | − | 0.841088i | \(-0.681916\pi\) | ||||
−0.540899 | + | 0.841088i | \(0.681916\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.4916 | 1.42790 | 0.713950 | − | 0.700196i | \(-0.246904\pi\) | ||||
0.713950 | + | 0.700196i | \(0.246904\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.00700 | −0.683814 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.0590 | −1.06912 | −0.534558 | − | 0.845132i | \(-0.679522\pi\) | ||||
−0.534558 | + | 0.845132i | \(0.679522\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.38049 | −0.515358 | −0.257679 | − | 0.966231i | \(-0.582958\pi\) | ||||
−0.257679 | + | 0.966231i | \(0.582958\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.89567 | −0.464676 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.54011 | −0.238954 | −0.119477 | − | 0.992837i | \(-0.538122\pi\) | ||||
−0.119477 | + | 0.992837i | \(0.538122\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.41642 | −0.318582 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.51492 | −0.417404 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.916484 | 0.0840139 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.68468 | −0.880425 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.92571 | 0.353969 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.71192 | −0.510889 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.41710 | −0.658161 | −0.329080 | − | 0.944302i | \(-0.606739\pi\) | ||||
−0.329080 | + | 0.944302i | \(0.606739\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.16338 | 0.278520 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.83180 | −0.596897 | −0.298448 | − | 0.954426i | \(-0.596469\pi\) | ||||
−0.298448 | + | 0.954426i | \(0.596469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.33031 | −0.375486 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.41642 | −0.294038 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.7282 | −1.25832 | −0.629159 | − | 0.777276i | \(-0.716601\pi\) | ||||
−0.629159 | + | 0.777276i | \(0.716601\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.3372 | −1.72497 | −0.862487 | − | 0.506079i | \(-0.831095\pi\) | ||||
−0.862487 | + | 0.506079i | \(0.831095\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.451968 | −0.0380625 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.17805 | −0.433010 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.41642 | −0.283718 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.79348 | −0.230402 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.98828 | 0.162887 | 0.0814433 | − | 0.996678i | \(-0.474047\pi\) | ||||
0.0814433 | + | 0.996678i | \(0.474047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.688066 | −0.0559940 | −0.0279970 | − | 0.999608i | \(-0.508913\pi\) | ||||
−0.0279970 | + | 0.999608i | \(0.508913\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.446852 | 0.0361258 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.4519 | −1.80338 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.26724 | 0.579989 | 0.289994 | − | 0.957028i | \(-0.406347\pi\) | ||||
0.289994 | + | 0.957028i | \(0.406347\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.11866 | 0.326631 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.05098 | 0.161640 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.3903 | −1.67542 | −0.837711 | − | 0.546114i | \(-0.816106\pi\) | ||||
−0.837711 | + | 0.546114i | \(0.816106\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.91820 | −0.305032 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.78952 | 0.293242 | 0.146621 | − | 0.989193i | \(-0.453160\pi\) | ||||
0.146621 | + | 0.989193i | \(0.453160\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.38447 | 0.568036 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.11134 | −0.161458 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.3538 | 1.62350 | 0.811750 | − | 0.584005i | \(-0.198515\pi\) | ||||
0.811750 | + | 0.584005i | \(0.198515\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.6839 | 1.03441 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.31529 | −0.474686 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.0982 | −1.42746 | −0.713732 | − | 0.700418i | \(-0.752997\pi\) | ||||
−0.713732 | + | 0.700418i | \(0.752997\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7729 | 0.800747 | 0.400374 | − | 0.916352i | \(-0.368880\pi\) | ||||
0.400374 | + | 0.916352i | \(0.368880\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.75827 | −0.647430 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.7256 | 1.22969 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.512483 | 0.0374765 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.05098 | 0.149187 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.8685 | −1.00349 | −0.501746 | − | 0.865015i | \(-0.667309\pi\) | ||||
−0.501746 | + | 0.865015i | \(0.667309\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.4103 | 1.75709 | 0.878545 | − | 0.477659i | \(-0.158515\pi\) | ||||
0.878545 | + | 0.477659i | \(0.158515\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.4248 | 1.10460 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.9348 | −1.13531 | −0.567655 | − | 0.823267i | \(-0.692149\pi\) | ||||
−0.567655 | + | 0.823267i | \(0.692149\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.3201 | −1.58223 | −0.791115 | − | 0.611667i | \(-0.790499\pi\) | ||||
−0.791115 | + | 0.611667i | \(0.790499\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.6292 | −0.749724 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.05098 | 0.143951 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.4119 | −0.936725 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.42144 | −0.167494 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.36302 | −0.231520 | −0.115760 | − | 0.993277i | \(-0.536930\pi\) | ||||
−0.115760 | + | 0.993277i | \(0.536930\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.3216 | 0.912784 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.8074 | −0.737060 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.4786 | 0.914987 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.6838 | −0.857090 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.01750 | −0.135712 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.0725 | −1.07629 | −0.538147 | − | 0.842851i | \(-0.680875\pi\) | ||||
−0.538147 | + | 0.842851i | \(0.680875\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.67190 | 0.444794 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.1471 | 1.20447 | 0.602233 | − | 0.798320i | \(-0.294278\pi\) | ||||
0.602233 | + | 0.798320i | \(0.294278\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.11132 | −0.469929 | −0.234965 | − | 0.972004i | \(-0.575497\pi\) | ||||
−0.234965 | + | 0.972004i | \(0.575497\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.35222 | 0.154765 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.07312 | 0.201327 | 0.100663 | − | 0.994921i | \(-0.467903\pi\) | ||||
0.100663 | + | 0.994921i | \(0.467903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.54411 | 0.100727 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.30778 | 0.149906 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.61297 | 0.492442 | 0.246221 | − | 0.969214i | \(-0.420811\pi\) | ||||
0.246221 | + | 0.969214i | \(0.420811\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.4791 | −1.31917 | −0.659587 | − | 0.751629i | \(-0.729269\pi\) | ||||
−0.659587 | + | 0.751629i | \(0.729269\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.54368 | 0.609724 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.53251 | 0.606539 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.59898 | −0.291449 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.7623 | 0.679313 | 0.339656 | − | 0.940550i | \(-0.389689\pi\) | ||||
0.339656 | + | 0.940550i | \(0.389689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.14688 | 0.0721034 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.52663 | −0.0956014 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.2212 | −1.19899 | −0.599493 | − | 0.800380i | \(-0.704631\pi\) | ||||
−0.599493 | + | 0.800380i | \(0.704631\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.0409 | −0.623913 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.85390 | 0.545955 | 0.272978 | − | 0.962020i | \(-0.411992\pi\) | ||||
0.272978 | + | 0.962020i | \(0.411992\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.0711 | −0.864379 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.8381 | 0.908077 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.97519 | 0.608198 | 0.304099 | − | 0.952640i | \(-0.401645\pi\) | ||||
0.304099 | + | 0.952640i | \(0.401645\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.7260 | −0.894541 | −0.447270 | − | 0.894399i | \(-0.647604\pi\) | ||||
−0.447270 | + | 0.894399i | \(0.647604\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.26001 | −0.560441 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.65184 | 0.461423 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.848598 | 0.0509873 | 0.0254937 | − | 0.999675i | \(-0.491884\pi\) | ||||
0.0254937 | + | 0.999675i | \(0.491884\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.57178 | 0.393442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.8691 | −1.36426 | −0.682128 | − | 0.731233i | \(-0.738945\pi\) | ||||
−0.682128 | + | 0.731233i | \(0.738945\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.10218 | −0.481624 | −0.240812 | − | 0.970572i | \(-0.577414\pi\) | ||||
−0.240812 | + | 0.970572i | \(0.577414\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.21320 | 0.427273 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.05156 | 0.475268 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8003 | −0.988254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.14524 | 0.477482 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.6949 | 1.44269 | 0.721344 | − | 0.692577i | \(-0.243525\pi\) | ||||
0.721344 | + | 0.692577i | \(0.243525\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.5757 | 1.25618 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.14688 | 0.0665485 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.51492 | −0.261104 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.48803 | 0.373964 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.8719 | −0.624576 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.9219 | 1.71332 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.75138 | −0.442395 | −0.221197 | − | 0.975229i | \(-0.570997\pi\) | ||||
−0.221197 | + | 0.975229i | \(0.570997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.4916 | 0.824399 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.2388 | 0.637292 | 0.318646 | − | 0.947874i | \(-0.396772\pi\) | ||||
0.318646 | + | 0.947874i | \(0.396772\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3629 | 0.698794 | 0.349397 | − | 0.936975i | \(-0.386386\pi\) | ||||
0.349397 | + | 0.936975i | \(0.386386\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.00700 | −0.394800 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.5402 | −0.591994 | −0.295997 | − | 0.955189i | \(-0.595652\pi\) | ||||
−0.295997 | + | 0.955189i | \(0.595652\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.14688 | 0.0642127 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.0590 | −0.617254 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.943454 | −0.0524952 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −30.1231 | −1.67093 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.38049 | −0.297542 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.926977 | −0.0511059 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.4647 | −1.45463 | −0.727316 | − | 0.686303i | \(-0.759233\pi\) | ||||
−0.727316 | + | 0.686303i | \(0.759233\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.89567 | −0.268281 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 36.3137 | 1.98403 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.0080 | −1.30780 | −0.653901 | − | 0.756580i | \(-0.726869\pi\) | ||||
−0.653901 | + | 0.756580i | \(0.726869\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.54011 | −0.137960 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.53701 | 0.408152 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0862 | −1.08455 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.41642 | −0.183934 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.2863 | −0.766929 | −0.383465 | − | 0.923556i | \(-0.625269\pi\) | ||||
−0.383465 | + | 0.923556i | \(0.625269\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.7682 | 1.70051 | 0.850257 | − | 0.526368i | \(-0.176446\pi\) | ||||
0.850257 | + | 0.526368i | \(0.176446\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.51492 | −0.240988 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.4300 | 1.03416 | 0.517078 | − | 0.855938i | \(-0.327020\pi\) | ||||
0.517078 | + | 0.855938i | \(0.327020\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −45.5123 | −2.41554 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.916484 | 0.0485055 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.6319 | 0.719465 | 0.359733 | − | 0.933055i | \(-0.382868\pi\) | ||||
0.359733 | + | 0.933055i | \(0.382868\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5423 | −0.765382 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.68468 | −0.508314 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 43.3331 | 2.26816 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.1439 | −1.41690 | −0.708450 | − | 0.705761i | \(-0.750605\pi\) | ||||
−0.708450 | + | 0.705761i | \(0.750605\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.92571 | 0.204364 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.44730 | 0.438562 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 38.3540 | 1.98589 | 0.992947 | − | 0.118562i | \(-0.0378284\pi\) | ||||
0.992947 | + | 0.118562i | \(0.0378284\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.71192 | −0.294962 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.51492 | −0.232530 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.1885 | −1.80751 | −0.903757 | − | 0.428046i | \(-0.859202\pi\) | ||||
−0.903757 | + | 0.428046i | \(0.859202\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.41710 | −0.379989 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.7678 | −0.601307 | −0.300653 | − | 0.953733i | \(-0.597205\pi\) | ||||
−0.300653 | + | 0.953733i | \(0.597205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.03616 | −0.409561 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.16338 | 0.160803 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.4904 | −0.836096 | −0.418048 | − | 0.908425i | \(-0.637286\pi\) | ||||
−0.418048 | + | 0.908425i | \(0.637286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.446852 | 0.0225983 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.83180 | −0.344618 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.88434 | −0.396704 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.18614 | 0.360662 | 0.180331 | − | 0.983606i | \(-0.442283\pi\) | ||||
0.180331 | + | 0.983606i | \(0.442283\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.33031 | −0.216787 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.904789 | −0.0451830 | −0.0225915 | − | 0.999745i | \(-0.507192\pi\) | ||||
−0.0225915 | + | 0.999745i | \(0.507192\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.6710 | −1.47802 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.41642 | −0.169763 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.61472 | −0.278311 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.7504 | 1.76774 | 0.883872 | − | 0.467730i | \(-0.154928\pi\) | ||||
0.883872 | + | 0.467730i | \(0.154928\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.7282 | −0.726491 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.9525 | −0.637353 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.7120 | 0.771274 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.3372 | −0.995915 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.9086 | 1.90081 | 0.950404 | − | 0.311018i | \(-0.100670\pi\) | ||||
0.950404 | + | 0.311018i | \(0.100670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.3864 | −1.38347 | −0.691735 | − | 0.722151i | \(-0.743154\pi\) | ||||
−0.691735 | + | 0.722151i | \(0.743154\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.451968 | −0.0219754 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.98135 | 0.144617 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.9630 | −0.869292 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.17805 | −0.249998 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.922354 | −0.0444282 | −0.0222141 | − | 0.999753i | \(-0.507072\pi\) | ||||
−0.0222141 | + | 0.999753i | \(0.507072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.8030 | 0.567217 | 0.283608 | − | 0.958940i | \(-0.408468\pi\) | ||||
0.283608 | + | 0.958940i | \(0.408468\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.41642 | −0.163805 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.11134 | −0.100999 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.5722 | 1.02958 | 0.514791 | − | 0.857315i | \(-0.327869\pi\) | ||||
0.514791 | + | 0.857315i | \(0.327869\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.79348 | −0.133023 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.00039 | 0.380110 | 0.190055 | − | 0.981773i | \(-0.439133\pi\) | ||||
0.190055 | + | 0.981773i | \(0.439133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −50.6931 | −2.40309 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.98828 | 0.0940426 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.4319 | −0.728277 | −0.364138 | − | 0.931345i | \(-0.618637\pi\) | ||||
−0.364138 | + | 0.931345i | \(0.618637\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.50230 | 0.212005 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.688066 | −0.0323281 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 31.6360 | 1.48312 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.0563 | −1.63987 | −0.819933 | − | 0.572460i | \(-0.805989\pi\) | ||||
−0.819933 | + | 0.572460i | \(0.805989\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.446852 | 0.0208572 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.9727 | −1.62884 | −0.814420 | − | 0.580276i | \(-0.802945\pi\) | ||||
−0.814420 | + | 0.580276i | \(0.802945\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.9578 | −0.834569 | −0.417284 | − | 0.908776i | \(-0.637018\pi\) | ||||
−0.417284 | + | 0.908776i | \(0.637018\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −22.4519 | −1.04118 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.6365 | −1.04749 | −0.523747 | − | 0.851874i | \(-0.675466\pi\) | ||||
−0.523747 | + | 0.851874i | \(0.675466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.8002 | −1.00664 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.26724 | 0.334857 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.62800 | 0.166816 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0866 | −0.646339 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.11866 | 0.188581 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.26212 | 0.149050 | 0.0745250 | − | 0.997219i | \(-0.476256\pi\) | ||||
0.0745250 | + | 0.997219i | \(0.476256\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.1035 | 1.00783 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.05098 | 0.0933229 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −27.8275 | −1.26358 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.0283 | −1.63260 | −0.816300 | − | 0.577628i | \(-0.803978\pi\) | ||||
−0.816300 | + | 0.577628i | \(0.803978\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.3903 | −0.967305 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.4507 | −1.41935 | −0.709674 | − | 0.704530i | \(-0.751158\pi\) | ||||
−0.709674 | + | 0.704530i | \(0.751158\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.446852 | 0.0201252 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.91820 | −0.176110 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.3224 | 1.22558 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.5170 | 0.739402 | 0.369701 | − | 0.929151i | \(-0.379460\pi\) | ||||
0.369701 | + | 0.929151i | \(0.379460\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.78952 | 0.169303 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −30.9673 | −1.38076 | −0.690381 | − | 0.723446i | \(-0.742557\pi\) | ||||
−0.690381 | + | 0.723446i | \(0.742557\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 37.1430 | 1.65284 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.38447 | 0.327956 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14.5132 | −0.643287 | −0.321644 | − | 0.946861i | \(-0.604235\pi\) | ||||
−0.321644 | + | 0.946861i | \(0.604235\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.0142 | −1.15080 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.11134 | −0.0932178 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −49.5094 | −2.18164 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.518350 | −0.0227970 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.3538 | 0.937329 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.08813 | −0.179104 | −0.0895522 | − | 0.995982i | \(-0.528544\pi\) | ||||
−0.0895522 | + | 0.995982i | \(0.528544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.1992 | 0.926976 | 0.463488 | − | 0.886103i | \(-0.346598\pi\) | ||||
0.463488 | + | 0.886103i | \(0.346598\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.6839 | 0.597216 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.93661 | 0.127921 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.31529 | −0.274060 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.7243 | −0.767723 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.7822 | 1.63347 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.0982 | −0.824147 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.20377 | −0.137996 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.4030 | 0.533245 | 0.266622 | − | 0.963801i | \(-0.414092\pi\) | ||||
0.266622 | + | 0.963801i | \(0.414092\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.7729 | 0.462312 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.3820 | 0.787399 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8751 | 0.593255 | 0.296627 | − | 0.954993i | \(-0.404138\pi\) | ||||
0.296627 | + | 0.954993i | \(0.404138\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.75827 | −0.373794 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.11134 | −0.0899460 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.73321 | 0.201277 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.7256 | 0.709964 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.49572 | 0.402347 | 0.201173 | − | 0.979556i | \(-0.435525\pi\) | ||||
0.201173 | + | 0.979556i | \(0.435525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.2824 | −0.604080 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.512483 | 0.0216370 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.34046 | 0.267219 | 0.133609 | − | 0.991034i | \(-0.457343\pi\) | ||||
0.133609 | + | 0.991034i | \(0.457343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.67809 | 0.365090 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.05098 | 0.0861331 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.6377 | −0.487876 | −0.243938 | − | 0.969791i | \(-0.578439\pi\) | ||||
−0.243938 | + | 0.969791i | \(0.578439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.7525 | −1.07771 | −0.538854 | − | 0.842399i | \(-0.681143\pi\) | ||||
−0.538854 | + | 0.842399i | \(0.681143\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8685 | −0.579367 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.67190 | 0.278238 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.196347 | −0.00817405 | −0.00408702 | − | 0.999992i | \(-0.501301\pi\) | ||||
−0.00408702 | + | 0.999992i | \(0.501301\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.4103 | 1.01446 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.43243 | −0.391323 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.72359 | 0.195631 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.4248 | 0.637739 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.75537 | 0.155001 | 0.0775003 | − | 0.996992i | \(-0.475306\pi\) | ||||
0.0775003 | + | 0.996992i | \(0.475306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.8752 | −0.571719 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.9348 | −0.655471 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.7741 | −0.935219 | −0.467609 | − | 0.883935i | \(-0.654885\pi\) | ||||
−0.467609 | + | 0.883935i | \(0.654885\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.13109 | −0.128362 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.3201 | −0.913501 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.514422 | 0.0210187 | 0.0105093 | − | 0.999945i | \(-0.496655\pi\) | ||||
0.0105093 | + | 0.999945i | \(0.496655\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.2236 | −0.743358 | −0.371679 | − | 0.928361i | \(-0.621218\pi\) | ||||
−0.371679 | + | 0.928361i | \(0.621218\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.6292 | −0.432854 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.0869 | 1.34517 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.4283 | −0.504449 | −0.252224 | − | 0.967669i | \(-0.581162\pi\) | ||||
−0.252224 | + | 0.967669i | \(0.581162\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.05098 | 0.0831099 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.04060 | 0.0825537 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.1624 | −0.895131 | −0.447566 | − | 0.894251i | \(-0.647709\pi\) | ||||
−0.447566 | + | 0.894251i | \(0.647709\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13.4119 | −0.540819 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.4373 | −0.500705 | −0.250352 | − | 0.968155i | \(-0.580547\pi\) | ||||
−0.250352 | + | 0.968155i | \(0.580547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.1769 | 1.25311 | 0.626553 | − | 0.779379i | \(-0.284465\pi\) | ||||
0.626553 | + | 0.779379i | \(0.284465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.4327 | 1.21926 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.8452 | −0.553809 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.42144 | −0.0967030 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.18764 | −0.0872268 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1401 | −0.921191 | −0.460596 | − | 0.887610i | \(-0.652364\pi\) | ||||
−0.460596 | + | 0.887610i | \(0.652364\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.36302 | −0.133668 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.3399 | 1.00558 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6123 | 0.499718 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.3216 | 0.526996 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.5718 | 1.04952 | 0.524761 | − | 0.851250i | \(-0.324155\pi\) | ||||
0.524761 | + | 0.851250i | \(0.324155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.2684 | 0.562691 | 0.281345 | − | 0.959607i | \(-0.409219\pi\) | ||||
0.281345 | + | 0.959607i | \(0.409219\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.8074 | −0.425542 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.4489 | 0.843242 | 0.421621 | − | 0.906772i | \(-0.361461\pi\) | ||||
0.421621 | + | 0.906772i | \(0.361461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.24285 | −0.284307 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.4786 | 0.528268 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.4337 | −1.03443 | −0.517216 | − | 0.855855i | \(-0.673032\pi\) | ||||
−0.517216 | + | 0.855855i | \(0.673032\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.3403 | 0.911979 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.6838 | −0.494841 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.2186 | 1.02133 | 0.510666 | − | 0.859779i | \(-0.329399\pi\) | ||||
0.510666 | + | 0.859779i | \(0.329399\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.9343 | 1.16431 | 0.582154 | − | 0.813078i | \(-0.302210\pi\) | ||||
0.582154 | + | 0.813078i | \(0.302210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.01750 | −0.0783531 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.7941 | 0.573692 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.0725 | −0.621398 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.0446 | −0.387769 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.9988 | −0.423971 | −0.211986 | − | 0.977273i | \(-0.567993\pi\) | ||||
−0.211986 | + | 0.977273i | \(0.567993\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.67190 | 0.256802 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7102 | 0.949688 | 0.474844 | − | 0.880070i | \(-0.342504\pi\) | ||||
0.474844 | + | 0.880070i | \(0.342504\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.7057 | 0.641107 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.1471 | 0.695399 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.25274 | 0.315782 | 0.157891 | − | 0.987457i | \(-0.449530\pi\) | ||||
0.157891 | + | 0.987457i | \(0.449530\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 50.3178 | 1.92254 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.11132 | −0.271314 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.5954 | −0.708429 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.9738 | −0.417463 | −0.208732 | − | 0.977973i | \(-0.566934\pi\) | ||||
−0.208732 | + | 0.977973i | \(0.566934\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.35222 | 0.0893534 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 69.4802 | 2.63553 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.75421 | 0.0664455 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.07312 | 0.116236 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.2229 | −1.63251 | −0.816254 | − | 0.577694i | \(-0.803953\pi\) | ||||
−0.816254 | + | 0.577694i | \(0.803953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.3364 | 0.389845 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.54411 | 0.0581545 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.2981 | −0.838607 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.16787 | 0.269195 | 0.134598 | − | 0.990900i | \(-0.457026\pi\) | ||||
0.134598 | + | 0.990900i | \(0.457026\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.30778 | 0.0865485 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.57178 | 0.246115 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.6904 | 0.661582 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.61297 | 0.284312 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.57336 | 0.319732 | 0.159866 | − | 0.987139i | \(-0.448894\pi\) | ||||
0.159866 | + | 0.987139i | \(0.448894\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.7220 | 1.10691 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.4791 | −0.761625 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.67190 | 0.247788 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.72086 | −0.249263 | −0.124631 | − | 0.992203i | \(-0.539775\pi\) | ||||
−0.124631 | + | 0.992203i | \(0.539775\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.41356 | 0.0522824 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5994 | 0.908601 | 0.454301 | − | 0.890848i | \(-0.349889\pi\) | ||||
0.454301 | + | 0.890848i | \(0.349889\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.54368 | 0.352024 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.1903 | −0.449037 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.8595 | 0.840901 | 0.420450 | − | 0.907316i | \(-0.361872\pi\) | ||||
0.420450 | + | 0.907316i | \(0.361872\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.53251 | 0.350185 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.5707 | −0.938099 | −0.469050 | − | 0.883172i | \(-0.655403\pi\) | ||||
−0.469050 | + | 0.883172i | \(0.655403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.79280 | −0.248869 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.59898 | −0.168268 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.6818 | −0.828776 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.27611 | −0.265509 | −0.132754 | − | 0.991149i | \(-0.542382\pi\) | ||||
−0.132754 | + | 0.991149i | \(0.542382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.7623 | 0.392201 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.35072 | 0.0855514 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.9497 | 0.688738 | 0.344369 | − | 0.938834i | \(-0.388093\pi\) | ||||
0.344369 | + | 0.938834i | \(0.388093\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.14688 | 0.0416289 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.2163 | 0.406591 | 0.203295 | − | 0.979117i | \(-0.434835\pi\) | ||||
0.203295 | + | 0.979117i | \(0.434835\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.0353 | −0.399504 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.52663 | −0.0551955 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.5130 | 1.02954 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.2889 | −1.34467 | −0.672337 | − | 0.740245i | \(-0.734709\pi\) | ||||
−0.672337 | + | 0.740245i | \(0.734709\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.2212 | −0.692234 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 54.5495 | 1.96201 | 0.981005 | − | 0.193983i | \(-0.0621408\pi\) | ||||
0.981005 | + | 0.193983i | \(0.0621408\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.8463 | 1.57501 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.0409 | −0.360216 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.28850 | −0.296966 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.2783 | 0.546699 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.8279 | −0.886146 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.0718 | 0.965004 | 0.482502 | − | 0.875895i | \(-0.339728\pi\) | ||||
0.482502 | + | 0.875895i | \(0.339728\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.85390 | 0.315207 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.20973 | −0.185236 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.5428 | 1.40421 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.0711 | −0.499049 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.74869 | 0.168207 | 0.0841036 | − | 0.996457i | \(-0.473197\pi\) | ||||
0.0841036 | + | 0.996457i | \(0.473197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.201962 | −0.00714492 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.8381 | 0.524279 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.5467 | −0.513342 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.00700 | −0.246964 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.97519 | 0.351143 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.8430 | 1.01407 | 0.507033 | − | 0.861927i | \(-0.330742\pi\) | ||||
0.507033 | + | 0.861927i | \(0.330742\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.47894 | 0.122162 | 0.0610810 | − | 0.998133i | \(-0.480545\pi\) | ||||
0.0610810 | + | 0.998133i | \(0.480545\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.7260 | −0.516463 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 73.0783 | 2.55982 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.67895 | −0.233667 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.26001 | −0.323571 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.1095 | −1.19043 | −0.595216 | − | 0.803566i | \(-0.702933\pi\) | ||||
−0.595216 | + | 0.803566i | \(0.702933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.6176 | 1.55527 | 0.777636 | − | 0.628715i | \(-0.216419\pi\) | ||||
0.777636 | + | 0.628715i | \(0.216419\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.65184 | 0.266403 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0174 | 1.14813 | 0.574064 | − | 0.818810i | \(-0.305366\pi\) | ||||
0.574064 | + | 0.818810i | \(0.305366\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.4901 | −1.40628 | −0.703139 | − | 0.711052i | \(-0.748219\pi\) | ||||
−0.703139 | + | 0.711052i | \(0.748219\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.848598 | 0.0294376 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.24827 | −0.0432500 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.9466 | −0.448035 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.57178 | 0.227154 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.3358 | −1.42707 | −0.713536 | − | 0.700619i | \(-0.752907\pi\) | ||||
−0.713536 | + | 0.700619i | \(0.752907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.8691 | −0.787654 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.2284 | −0.867885 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.8631 | −0.682504 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.10218 | −0.278066 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.89567 | −0.167821 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.0312 | −0.446179 | −0.223090 | − | 0.974798i | \(-0.571614\pi\) | ||||
−0.223090 | + | 0.974798i | \(0.571614\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.21320 | 0.246686 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.49480 | −0.187699 | −0.0938494 | − | 0.995586i | \(-0.529917\pi\) | ||||
−0.0938494 | + | 0.995586i | \(0.529917\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.8403 | −0.745180 | −0.372590 | − | 0.927996i | \(-0.621530\pi\) | ||||
−0.372590 | + | 0.927996i | \(0.621530\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.05156 | 0.274396 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.67863 | 0.261384 | 0.130692 | − | 0.991423i | \(-0.458280\pi\) | ||||
0.130692 | + | 0.991423i | \(0.458280\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72.9535 | −2.48049 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8003 | −0.570569 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.64674 | 0.0897844 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47.9899 | 1.62607 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.14524 | 0.275675 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.7150 | −0.396040 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.3068 | 1.09092 | 0.545461 | − | 0.838136i | \(-0.316355\pi\) | ||||
0.545461 | + | 0.838136i | \(0.316355\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.6949 | 0.832937 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.7489 | −0.833812 | −0.416906 | − | 0.908950i | \(-0.636886\pi\) | ||||
−0.416906 | + | 0.908950i | \(0.636886\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.2435 | −0.782207 | −0.391103 | − | 0.920347i | \(-0.627907\pi\) | ||||
−0.391103 | + | 0.920347i | \(0.627907\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.5757 | 0.725258 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.2844 | 0.882544 | 0.441272 | − | 0.897374i | \(-0.354527\pi\) | ||||
0.441272 | + | 0.897374i | \(0.354527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.2123 | −0.510205 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.14688 | 0.0384218 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.954255 | 0.0319329 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 65.2473 | 2.18098 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.51492 | −0.150749 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.57178 | 0.219181 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.84043 | 0.0613136 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.48803 | 0.215908 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.8049 | −1.22344 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.1109 | 1.79672 | 0.898361 | − | 0.439258i | \(-0.144759\pi\) | ||||
0.898361 | + | 0.439258i | \(0.144759\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.8719 | −0.360599 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.6064 | −0.483932 | −0.241966 | − | 0.970285i | \(-0.577792\pi\) | ||||
−0.241966 | + | 0.970285i | \(0.577792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.27446 | −0.174559 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.9219 | 0.989187 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.0119 | −0.462713 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.49205 | −0.115192 | −0.0575961 | − | 0.998340i | \(-0.518344\pi\) | ||||
−0.0575961 | + | 0.998340i | \(0.518344\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.75138 | −0.255417 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −60.1461 | −1.97973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.6634 | −1.07397 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.4916 | 0.475967 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.6091 | −0.413690 | −0.206845 | − | 0.978374i | \(-0.566320\pi\) | ||||
−0.206845 | + | 0.978374i | \(0.566320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.89797 | 0.193298 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.2388 | 0.367941 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.75086 | −0.0572591 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.6562 | 0.707477 | 0.353739 | − | 0.935344i | \(-0.384910\pi\) | ||||
0.353739 | + | 0.935344i | \(0.384910\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.3629 | 0.403449 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.3084 | 1.44441 | 0.722206 | − | 0.691678i | \(-0.243128\pi\) | ||||
0.722206 | + | 0.691678i | \(0.243128\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.92571 | 0.127839 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.00700 | −0.227938 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.6519 | 1.87344 | 0.936718 | − | 0.350085i | \(-0.113847\pi\) | ||||
0.936718 | + | 0.350085i | \(0.113847\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 57.2662 | 1.85894 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.5402 | −0.341788 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.3695 | 0.465472 | 0.232736 | − | 0.972540i | \(-0.425232\pi\) | ||||
0.232736 | + | 0.972540i | \(0.425232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47.3807 | 1.53320 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.14688 | 0.0370732 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.2073 | −0.975446 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.1883 | 0.393172 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.0590 | −0.356372 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −83.3957 | −2.68460 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.7620 | 0.346082 | 0.173041 | − | 0.984915i | \(-0.444641\pi\) | ||||
0.173041 | + | 0.984915i | \(0.444641\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.943454 | −0.0303081 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.9320 | −0.992656 | −0.496328 | − | 0.868135i | \(-0.665319\pi\) | ||||
−0.496328 | + | 0.868135i | \(0.665319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.7111 | −1.33720 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30.1231 | −0.964711 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.4813 | 0.879204 | 0.439602 | − | 0.898193i | \(-0.355120\pi\) | ||||
0.439602 | + | 0.898193i | \(0.355120\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.0175 | 0.543880 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.38049 | −0.171786 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.6830 | 0.468316 | 0.234158 | − | 0.972199i | \(-0.424767\pi\) | ||||
0.234158 | + | 0.972199i | \(0.424767\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 54.4400 | 1.73460 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.926977 | −0.0295060 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.16338 | 0.100590 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.32406 | 0.264422 | 0.132211 | − | 0.991222i | \(-0.457792\pi\) | ||||
0.132211 | + | 0.991222i | \(0.457792\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26.4647 | −0.839832 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 76.2548 | 2.41744 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.9269 | 0.662762 | 0.331381 | − | 0.943497i | \(-0.392486\pi\) | ||||
0.331381 | + | 0.943497i | \(0.392486\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.89567 | −0.154892 |
(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 | 8004.2.a.d.1.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.d.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial |