Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, 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("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.39528.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} - 2x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.87063\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.24049 | 1.89640 | 0.948202 | − | 0.317668i | \(-0.102900\pi\) | ||||
0.948202 | + | 0.317668i | \(0.102900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.74125 | 1.73105 | 0.865526 | − | 0.500864i | \(-0.166984\pi\) | ||||
0.865526 | + | 0.500864i | \(0.166984\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.06174 | 1.68122 | 0.840612 | − | 0.541638i | \(-0.182196\pi\) | ||||
0.840612 | + | 0.541638i | \(0.182196\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.56098 | 0.621128 | 0.310564 | − | 0.950552i | \(-0.399482\pi\) | ||||
0.310564 | + | 0.950552i | \(0.399482\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.74125 | −1.77596 | −0.887982 | − | 0.459878i | \(-0.847893\pi\) | ||||
−0.887982 | + | 0.459878i | \(0.847893\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.67951 | 0.350203 | 0.175101 | − | 0.984550i | \(-0.443975\pi\) | ||||
0.175101 | + | 0.984550i | \(0.443975\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.9817 | 2.59635 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.24049 | 0.973134 | 0.486567 | − | 0.873643i | \(-0.338249\pi\) | ||||
0.486567 | + | 0.873643i | \(0.338249\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.24049 | −0.941219 | −0.470610 | − | 0.882341i | \(-0.655966\pi\) | ||||
−0.470610 | + | 0.882341i | \(0.655966\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.24049 | −0.716773 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.98174 | −1.31219 | −0.656095 | − | 0.754678i | \(-0.727793\pi\) | ||||
−0.656095 | + | 0.754678i | \(0.727793\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.24049 | 0.349905 | 0.174953 | − | 0.984577i | \(-0.444023\pi\) | ||||
0.174953 | + | 0.984577i | \(0.444023\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.92000 | 0.902792 | 0.451396 | − | 0.892324i | \(-0.350926\pi\) | ||||
0.451396 | + | 0.892324i | \(0.350926\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.62271 | 0.966022 | 0.483011 | − | 0.875614i | \(-0.339543\pi\) | ||||
0.483011 | + | 0.875614i | \(0.339543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.85826 | 0.392613 | 0.196306 | − | 0.980543i | \(-0.437105\pi\) | ||||
0.196306 | + | 0.980543i | \(0.437105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 24.3457 | 3.28277 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.48098 | 0.973940 | 0.486970 | − | 0.873419i | \(-0.338102\pi\) | ||||
0.486970 | + | 0.873419i | \(0.338102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.2222 | −1.56490 | −0.782448 | − | 0.622716i | \(-0.786029\pi\) | ||||
−0.782448 | + | 0.622716i | \(0.786029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 25.7047 | 3.18828 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.16049 | −0.996962 | −0.498481 | − | 0.866901i | \(-0.666109\pi\) | ||||
−0.498481 | + | 0.866901i | \(0.666109\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.32049 | 0.275391 | 0.137696 | − | 0.990475i | \(-0.456030\pi\) | ||||
0.137696 | + | 0.990475i | \(0.456030\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00152 | −0.117220 | −0.0586098 | − | 0.998281i | \(-0.518667\pi\) | ||||
−0.0586098 | + | 0.998281i | \(0.518667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.74125 | −0.654276 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.59951 | 0.855012 | 0.427506 | − | 0.904013i | \(-0.359392\pi\) | ||||
0.427506 | + | 0.904013i | \(0.359392\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.9817 | −1.53470 | −0.767348 | − | 0.641231i | \(-0.778424\pi\) | ||||
−0.767348 | + | 0.641231i | \(0.778424\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.8598 | 1.17791 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.8030 | −1.25111 | −0.625557 | − | 0.780178i | \(-0.715128\pi\) | ||||
−0.625557 | + | 0.780178i | \(0.715128\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.06174 | −0.635443 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −32.8267 | −3.36795 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.61777 | 0.367329 | 0.183665 | − | 0.982989i | \(-0.441204\pi\) | ||||
0.183665 | + | 0.982989i | \(0.441204\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.48250 | −0.943544 | −0.471772 | − | 0.881721i | \(-0.656385\pi\) | ||||
−0.471772 | + | 0.881721i | \(0.656385\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −20.1037 | −1.98088 | −0.990438 | − | 0.137961i | \(-0.955945\pi\) | ||||
−0.990438 | + | 0.137961i | \(0.955945\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.98174 | −0.189816 | −0.0949080 | − | 0.995486i | \(-0.530256\pi\) | ||||
−0.0949080 | + | 0.995486i | \(0.530256\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.74125 | 0.163803 | 0.0819015 | − | 0.996640i | \(-0.473901\pi\) | ||||
0.0819015 | + | 0.996640i | \(0.473901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.12195 | 0.664125 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.56098 | −0.234764 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.9620 | 1.99654 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 33.8465 | 3.02732 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.7230 | −1.04025 | −0.520123 | − | 0.854091i | \(-0.674114\pi\) | ||||
−0.520123 | + | 0.854091i | \(0.674114\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.50229 | −0.655478 | −0.327739 | − | 0.944768i | \(-0.606287\pi\) | ||||
−0.327739 | + | 0.944768i | \(0.606287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.74125 | 0.671252 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7413 | −1.00312 | −0.501561 | − | 0.865122i | \(-0.667241\pi\) | ||||
−0.501561 | + | 0.865122i | \(0.667241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.902774 | 0.0765723 | 0.0382861 | − | 0.999267i | \(-0.487810\pi\) | ||||
0.0382861 | + | 0.999267i | \(0.487810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 34.8020 | 2.91029 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.2222 | 1.84546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.24201 | 0.675212 | 0.337606 | − | 0.941288i | \(-0.390383\pi\) | ||||
0.337606 | + | 0.941288i | \(0.390383\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.3624 | 1.08742 | 0.543710 | − | 0.839273i | \(-0.317019\pi\) | ||||
0.543710 | + | 0.839273i | \(0.317019\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.2222 | −1.78493 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.0237 | −1.19902 | −0.599510 | − | 0.800367i | \(-0.704638\pi\) | ||||
−0.599510 | + | 0.800367i | \(0.704638\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.67951 | −0.132364 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.08152 | −0.0847115 | −0.0423557 | − | 0.999103i | \(-0.513486\pi\) | ||||
−0.0423557 | + | 0.999103i | \(0.513486\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.6242 | 1.20904 | 0.604520 | − | 0.796590i | \(-0.293365\pi\) | ||||
0.604520 | + | 0.796590i | \(0.293365\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.7447 | 1.82651 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.9635 | −0.909566 | −0.454783 | − | 0.890602i | \(-0.650283\pi\) | ||||
−0.454783 | + | 0.890602i | \(0.650283\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.9817 | −0.981327 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.22070 | −0.240727 | −0.120363 | − | 0.992730i | \(-0.538406\pi\) | ||||
−0.120363 | + | 0.992730i | \(0.538406\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.19854 | 0.0890865 | 0.0445433 | − | 0.999007i | \(-0.485817\pi\) | ||||
0.0445433 | + | 0.999007i | \(0.485817\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −33.8465 | −2.48844 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7032 | 1.07520 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.0015 | −1.37490 | −0.687451 | − | 0.726231i | \(-0.741270\pi\) | ||||
−0.687451 | + | 0.726231i | \(0.741270\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0015 | 0.863889 | 0.431944 | − | 0.901900i | \(-0.357828\pi\) | ||||
0.431944 | + | 0.901900i | \(0.357828\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.09875 | −0.149530 | −0.0747649 | − | 0.997201i | \(-0.523821\pi\) | ||||
−0.0747649 | + | 0.997201i | \(0.523821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8598 | 0.840718 | 0.420359 | − | 0.907358i | \(-0.361904\pi\) | ||||
0.420359 | + | 0.907358i | \(0.361904\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.24049 | −0.367810 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.50076 | 0.663562 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −44.4445 | −3.07429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.92494 | −0.339047 | −0.169523 | − | 0.985526i | \(-0.554223\pi\) | ||||
−0.169523 | + | 0.985526i | \(0.554223\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.1037 | 1.71206 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.24049 | 0.355748 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.5240 | 1.04425 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.62082 | −0.108538 | −0.0542692 | − | 0.998526i | \(-0.517283\pi\) | ||||
−0.0542692 | + | 0.998526i | \(0.517283\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.9437 | 1.19096 | 0.595482 | − | 0.803368i | \(-0.296961\pi\) | ||||
0.595482 | + | 0.803368i | \(0.296961\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1220 | 1.13145 | 0.565725 | − | 0.824594i | \(-0.308596\pi\) | ||||
0.565725 | + | 0.824594i | \(0.308596\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.8617 | −0.908109 | −0.454054 | − | 0.890974i | \(-0.650023\pi\) | ||||
−0.454054 | + | 0.890974i | \(0.650023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.0835 | 1.83197 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.57820 | −0.619562 | −0.309781 | − | 0.950808i | \(-0.600256\pi\) | ||||
−0.309781 | + | 0.950808i | \(0.600256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.58125 | −0.617183 | −0.308591 | − | 0.951195i | \(-0.599858\pi\) | ||||
−0.308591 | + | 0.951195i | \(0.599858\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.24049 | 0.270915 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −46.9254 | −2.98579 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.9437 | −1.19572 | −0.597858 | − | 0.801602i | \(-0.703981\pi\) | ||||
−0.597858 | + | 0.801602i | \(0.703981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.64250 | 0.606219 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.35750 | −0.521327 | −0.260663 | − | 0.965430i | \(-0.583941\pi\) | ||||
−0.260663 | + | 0.965430i | \(0.583941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.98174 | 0.495961 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.5412 | −1.20496 | −0.602481 | − | 0.798133i | \(-0.705821\pi\) | ||||
−0.602481 | + | 0.798133i | \(0.705821\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1204 | 0.744552 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7610 | 0.899996 | 0.449998 | − | 0.893029i | \(-0.351425\pi\) | ||||
0.449998 | + | 0.893029i | \(0.351425\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.8598 | −0.720431 | −0.360215 | − | 0.932869i | \(-0.617297\pi\) | ||||
−0.360215 | + | 0.932869i | \(0.617297\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 74.5314 | 4.49441 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.98326 | −0.299415 | −0.149708 | − | 0.988730i | \(-0.547833\pi\) | ||||
−0.149708 | + | 0.988730i | \(0.547833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.00152 | 0.0597459 | 0.0298730 | − | 0.999554i | \(-0.490490\pi\) | ||||
0.0298730 | + | 0.999554i | \(0.490490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.90125 | 0.469681 | 0.234840 | − | 0.972034i | \(-0.424543\pi\) | ||||
0.234840 | + | 0.972034i | \(0.424543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.24049 | −0.132252 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4414 | −0.614200 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.00341485 | −0.000199498 0 | −9.97490e−5 | − | 1.00000i | \(-0.500032\pi\) | ||||
−9.97490e−5 | 1.00000i | \(0.500032\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.7230 | 1.84698 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.1808 | 0.588769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.92000 | −0.341223 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −51.8282 | −2.96767 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.9604 | −1.36749 | −0.683747 | − | 0.729719i | \(-0.739651\pi\) | ||||
−0.683747 | + | 0.729719i | \(0.739651\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.97869 | 0.225611 | 0.112805 | − | 0.993617i | \(-0.464016\pi\) | ||||
0.112805 | + | 0.993617i | \(0.464016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.2005 | 1.59399 | 0.796995 | − | 0.603986i | \(-0.206422\pi\) | ||||
0.796995 | + | 0.603986i | \(0.206422\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.0015 | 0.954901 | 0.477450 | − | 0.878659i | \(-0.341561\pi\) | ||||
0.477450 | + | 0.878659i | \(0.341561\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 30.0870 | 1.68455 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.8252 | −1.10310 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 78.6919 | 4.36504 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.62271 | −0.365122 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.95652 | −0.107540 | −0.0537701 | − | 0.998553i | \(-0.517124\pi\) | ||||
−0.0537701 | + | 0.998553i | \(0.517124\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −34.6045 | −1.89064 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.2089 | −1.64558 | −0.822792 | − | 0.568343i | \(-0.807585\pi\) | ||||
−0.822792 | + | 0.568343i | \(0.807585\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.0870 | −1.62930 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.9882 | 1.28775 | 0.643877 | − | 0.765129i | \(-0.277325\pi\) | ||||
0.643877 | + | 0.765129i | \(0.277325\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.2855 | 1.56762 | 0.783808 | − | 0.621003i | \(-0.213275\pi\) | ||||
0.783808 | + | 0.621003i | \(0.213275\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.0420 | −0.800602 | −0.400301 | − | 0.916384i | \(-0.631094\pi\) | ||||
−0.400301 | + | 0.916384i | \(0.631094\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.84000 | 0.522253 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.9990 | 1.00273 | 0.501363 | − | 0.865237i | \(-0.332832\pi\) | ||||
0.501363 | + | 0.865237i | \(0.332832\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.9270 | 2.15405 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.24695 | −0.222296 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.8583 | 0.775595 | 0.387797 | − | 0.921745i | \(-0.373236\pi\) | ||||
0.387797 | + | 0.921745i | \(0.373236\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.85826 | −0.148394 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.1006 | 0.885438 | 0.442719 | − | 0.896660i | \(-0.354014\pi\) | ||||
0.442719 | + | 0.896660i | \(0.354014\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 31.7665 | 1.63606 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.3609 | 1.04587 | 0.522935 | − | 0.852373i | \(-0.324837\pi\) | ||||
0.522935 | + | 0.852373i | \(0.324837\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.1067 | 1.58948 | 0.794740 | − | 0.606950i | \(-0.207607\pi\) | ||||
0.794740 | + | 0.606950i | \(0.207607\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.3457 | −1.24077 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.5797 | −0.536413 | −0.268207 | − | 0.963361i | \(-0.586431\pi\) | ||||
−0.268207 | + | 0.963361i | \(0.586431\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.30119 | 0.217521 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 32.2256 | 1.62145 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.35598 | 0.0680545 | 0.0340272 | − | 0.999421i | \(-0.489167\pi\) | ||||
0.0340272 | + | 0.999421i | \(0.489167\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.23555 | −0.461201 | −0.230601 | − | 0.973048i | \(-0.574069\pi\) | ||||
−0.230601 | + | 0.973048i | \(0.574069\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.7665 | −1.58240 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −45.8252 | −2.27147 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.87957 | 0.488513 | 0.244257 | − | 0.969711i | \(-0.421456\pi\) | ||||
0.244257 | + | 0.969711i | \(0.421456\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.48098 | −0.368115 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −59.2894 | −2.91040 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.23555 | 0.109214 | 0.0546069 | − | 0.998508i | \(-0.482609\pi\) | ||||
0.0546069 | + | 0.998508i | \(0.482609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.83695 | 0.0895276 | 0.0447638 | − | 0.998998i | \(-0.485746\pi\) | ||||
0.0447638 | + | 0.998998i | \(0.485746\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33.2459 | 1.61266 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.2222 | 0.591475 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.517500 | 0.0249271 | 0.0124635 | − | 0.999922i | \(-0.496033\pi\) | ||||
0.0124635 | + | 0.999922i | \(0.496033\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.0607 | −1.01211 | −0.506056 | − | 0.862500i | \(-0.668897\pi\) | ||||
−0.506056 | + | 0.862500i | \(0.668897\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −13.0015 | −0.621947 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.61967 | −0.268212 | −0.134106 | − | 0.990967i | \(-0.542816\pi\) | ||||
−0.134106 | + | 0.990967i | \(0.542816\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.7443 | −1.03310 | −0.516551 | − | 0.856256i | \(-0.672784\pi\) | ||||
−0.516551 | + | 0.856256i | \(0.672784\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −50.0504 | −2.37262 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.77777 | −0.0838983 | −0.0419492 | − | 0.999120i | \(-0.513357\pi\) | ||||
−0.0419492 | + | 0.999120i | \(0.513357\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.8632 | 0.605704 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.7047 | −1.20506 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.7462 | −0.549464 | −0.274732 | − | 0.961521i | \(-0.588589\pi\) | ||||
−0.274732 | + | 0.961521i | \(0.588589\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.5980 | 0.586747 | 0.293373 | − | 0.955998i | \(-0.405222\pi\) | ||||
0.293373 | + | 0.955998i | \(0.405222\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.5615 | −0.769677 | −0.384838 | − | 0.922984i | \(-0.625743\pi\) | ||||
−0.384838 | + | 0.922984i | \(0.625743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.7264 | −0.820280 | −0.410140 | − | 0.912023i | \(-0.634520\pi\) | ||||
−0.410140 | + | 0.912023i | \(0.634520\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.16049 | 0.376816 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.9882 | 1.56278 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −100.495 | −4.61102 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 42.0291 | 1.92036 | 0.960180 | − | 0.279383i | \(-0.0901300\pi\) | ||||
0.960180 | + | 0.279383i | \(0.0901300\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.3832 | −2.20608 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.3411 | 0.696605 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.9604 | 0.723236 | 0.361618 | − | 0.932326i | \(-0.382224\pi\) | ||||
0.361618 | + | 0.932326i | \(0.382224\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.4311 | −1.77950 | −0.889751 | − | 0.456446i | \(-0.849122\pi\) | ||||
−0.889751 | + | 0.456446i | \(0.849122\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4208 | 0.604441 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.32049 | −0.104088 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.3229 | 1.13361 | 0.566804 | − | 0.823853i | \(-0.308180\pi\) | ||||
0.566804 | + | 0.823853i | \(0.308180\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.1417 | 0.541373 | 0.270687 | − | 0.962668i | \(-0.412749\pi\) | ||||
0.270687 | + | 0.962668i | \(0.412749\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.2104 | −1.78934 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.4859 | 1.57289 | 0.786443 | − | 0.617663i | \(-0.211920\pi\) | ||||
0.786443 | + | 0.617663i | \(0.211920\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.00152 | 0.0443048 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −85.2495 | −3.75654 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.0227 | 1.67223 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.7699 | 1.39186 | 0.695932 | − | 0.718108i | \(-0.254992\pi\) | ||||
0.695932 | + | 0.718108i | \(0.254992\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.97680 | −0.392528 | −0.196264 | − | 0.980551i | \(-0.562881\pi\) | ||||
−0.196264 | + | 0.980551i | \(0.562881\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.4208 | −0.584618 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1792 | −0.877358 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.5813 | 0.588269 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.9620 | 0.733329 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.74125 | 0.247293 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.5816 | −0.841879 | −0.420940 | − | 0.907089i | \(-0.638300\pi\) | ||||
−0.420940 | + | 0.907089i | \(0.638300\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.40354 | −0.359968 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.8480 | 1.91756 | 0.958781 | − | 0.284147i | \(-0.0917104\pi\) | ||||
0.958781 | + | 0.284147i | \(0.0917104\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.5679 | −1.72825 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.59951 | −0.323164 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.57326 | 0.0666613 | 0.0333306 | − | 0.999444i | \(-0.489389\pi\) | ||||
0.0333306 | + | 0.999444i | \(0.489389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.8855 | 1.51779 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.4231 | 0.987168 | 0.493584 | − | 0.869698i | \(-0.335687\pi\) | ||||
0.493584 | + | 0.869698i | \(0.335687\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.38375 | 0.310637 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.3255 | −1.14555 | −0.572773 | − | 0.819714i | \(-0.694132\pi\) | ||||
−0.572773 | + | 0.819714i | \(0.694132\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.1304 | −1.42831 | −0.714157 | − | 0.699986i | \(-0.753190\pi\) | ||||
−0.714157 | + | 0.699986i | \(0.753190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 21.8030 | 0.909247 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.35750 | 0.181405 | 0.0907026 | − | 0.995878i | \(-0.471089\pi\) | ||||
0.0907026 | + | 0.995878i | \(0.471089\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.9817 | 0.580060 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.4100 | 0.679633 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.2287 | 0.546006 | 0.273003 | − | 0.962013i | \(-0.411983\pi\) | ||||
0.273003 | + | 0.962013i | \(0.411983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 40.5679 | 1.67157 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.2405 | −0.913307 | −0.456654 | − | 0.889645i | \(-0.650952\pi\) | ||||
−0.456654 | + | 0.889645i | \(0.650952\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.8598 | −0.445208 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.70119 | 0.314662 | 0.157331 | − | 0.987546i | \(-0.449711\pi\) | ||||
0.157331 | + | 0.987546i | \(0.449711\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.1872 | −1.84323 | −0.921613 | − | 0.388111i | \(-0.873128\pi\) | ||||
−0.921613 | + | 0.388111i | \(0.873128\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 93.1294 | 3.78625 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.4494 | 0.667660 | 0.333830 | − | 0.942633i | \(-0.391659\pi\) | ||||
0.333830 | + | 0.942633i | \(0.391659\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40.1452 | 1.62410 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.5634 | 1.11327 | 0.556637 | − | 0.830756i | \(-0.312092\pi\) | ||||
0.556637 | + | 0.830756i | \(0.312092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.48402 | −0.341554 | −0.170777 | − | 0.985310i | \(-0.554628\pi\) | ||||
−0.170777 | + | 0.985310i | \(0.554628\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.5896 | −1.47066 | −0.735330 | − | 0.677709i | \(-0.762973\pi\) | ||||
−0.735330 | + | 0.677709i | \(0.762973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.8030 | 0.472877 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 78.6168 | 3.14467 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.4410 | −0.815038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.7976 | 0.429844 | 0.214922 | − | 0.976631i | \(-0.431050\pi\) | ||||
0.214922 | + | 0.976631i | \(0.431050\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −49.7112 | −1.97273 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.06174 | 0.240175 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.2696 | 1.51156 | 0.755779 | − | 0.654826i | \(-0.227258\pi\) | ||||
0.755779 | + | 0.654826i | \(0.227258\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.8499 | −1.41378 | −0.706891 | − | 0.707323i | \(-0.749903\pi\) | ||||
−0.706891 | + | 0.707323i | \(0.749903\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.4810 | 1.04107 | 0.520537 | − | 0.853839i | \(-0.325732\pi\) | ||||
0.520537 | + | 0.853839i | \(0.325732\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42.9502 | 1.68594 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.00646 | −0.0393859 | −0.0196930 | − | 0.999806i | \(-0.506269\pi\) | ||||
−0.0196930 | + | 0.999806i | \(0.506269\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.8134 | −1.24305 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.2485 | 0.438178 | 0.219089 | − | 0.975705i | \(-0.429691\pi\) | ||||
0.219089 | + | 0.975705i | \(0.429691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.2192 | −0.553062 | −0.276531 | − | 0.961005i | \(-0.589185\pi\) | ||||
−0.276531 | + | 0.961005i | \(0.589185\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.8267 | 1.27296 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.80146 | 0.340794 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −70.1709 | −2.70892 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.2302 | 1.24238 | 0.621192 | − | 0.783659i | \(-0.286649\pi\) | ||||
0.621192 | + | 0.783659i | \(0.286649\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.5710 | 1.86673 | 0.933367 | − | 0.358923i | \(-0.116856\pi\) | ||||
0.933367 | + | 0.358923i | \(0.116856\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.61777 | −0.138837 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −10.2222 | −0.391143 | −0.195571 | − | 0.980689i | \(-0.562656\pi\) | ||||
−0.195571 | + | 0.980689i | \(0.562656\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49.7886 | −1.90233 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.3260 | 0.660069 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.2207 | −1.18769 | −0.593846 | − | 0.804579i | \(-0.702391\pi\) | ||||
−0.593846 | + | 0.804579i | \(0.702391\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.82820 | 0.145212 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.73784 | 0.217336 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.3822 | 0.694287 | 0.347144 | − | 0.937812i | \(-0.387152\pi\) | ||||
0.347144 | + | 0.937812i | \(0.387152\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 61.7886 | 2.33040 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.48250 | 0.356626 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 46.5466 | 1.74809 | 0.874047 | − | 0.485841i | \(-0.161486\pi\) | ||||
0.874047 | + | 0.485841i | \(0.161486\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.80146 | −0.329617 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 147.577 | 5.51908 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.6998 | 1.66702 | 0.833510 | − | 0.552504i | \(-0.186328\pi\) | ||||
0.833510 | + | 0.552504i | \(0.186328\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.1037 | 0.748701 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 68.0306 | 2.52659 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.5285 | −0.835537 | −0.417769 | − | 0.908553i | \(-0.637188\pi\) | ||||
−0.417769 | + | 0.908553i | \(0.637188\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.1610 | 0.560749 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.92189 | −0.329538 | −0.164769 | − | 0.986332i | \(-0.552688\pi\) | ||||
−0.164769 | + | 0.986332i | \(0.552688\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −46.8514 | −1.72579 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.6770 | −0.503115 | −0.251557 | − | 0.967842i | \(-0.580943\pi\) | ||||
−0.251557 | + | 0.967842i | \(0.580943\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.7417 | 0.944373 | 0.472186 | − | 0.881499i | \(-0.343465\pi\) | ||||
0.472186 | + | 0.881499i | \(0.343465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.9502 | 1.28047 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.5329 | 1.73450 | 0.867251 | − | 0.497872i | \(-0.165885\pi\) | ||||
0.867251 | + | 0.497872i | \(0.165885\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 56.6633 | 2.06219 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.57479 | −0.275310 | −0.137655 | − | 0.990480i | \(-0.543957\pi\) | ||||
−0.137655 | + | 0.990480i | \(0.543957\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.2874 | −0.880417 | −0.440208 | − | 0.897896i | \(-0.645095\pi\) | ||||
−0.440208 | + | 0.897896i | \(0.645095\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.98174 | 0.0717437 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 45.3477 | 1.63741 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.35902 | 0.0490077 | 0.0245038 | − | 0.999700i | \(-0.492199\pi\) | ||||
0.0245038 | + | 0.999700i | \(0.492199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.2024 | −0.762599 | −0.381299 | − | 0.924452i | \(-0.624523\pi\) | ||||
−0.381299 | + | 0.924452i | \(0.624523\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −68.0306 | −2.44373 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.3442 | −0.621420 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.3225 | 0.476717 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −63.7078 | −2.27383 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.1990 | 1.32600 | 0.663001 | − | 0.748618i | \(-0.269282\pi\) | ||||
0.663001 | + | 0.748618i | \(0.269282\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.74125 | −0.0619117 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −74.0879 | −2.63094 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.2875 | −1.21453 | −0.607263 | − | 0.794501i | \(-0.707732\pi\) | ||||
−0.607263 | + | 0.794501i | \(0.707732\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.9606 | 0.600023 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.75000 | −0.202913 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.12195 | −0.251016 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11.2424 | −0.395261 | −0.197630 | − | 0.980277i | \(-0.563325\pi\) | ||||
−0.197630 | + | 0.980277i | \(0.563325\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.8997 | −0.382741 | −0.191371 | − | 0.981518i | \(-0.561293\pi\) | ||||
−0.191371 | + | 0.981518i | \(0.561293\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.58619 | −0.160647 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.8282 | −1.60333 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.5497 | −1.45009 | −0.725047 | − | 0.688700i | \(-0.758182\pi\) | ||||
−0.725047 | + | 0.688700i | \(0.758182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.3999 | 0.955102 | 0.477551 | − | 0.878604i | \(-0.341525\pi\) | ||||
0.477551 | + | 0.878604i | \(0.341525\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.1003 | 1.15101 | 0.575505 | − | 0.817798i | \(-0.304806\pi\) | ||||
0.575505 | + | 0.817798i | \(0.304806\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.4623 | −0.849612 | −0.424806 | − | 0.905284i | \(-0.639658\pi\) | ||||
−0.424806 | + | 0.905284i | \(0.639658\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.56098 | 0.0887325 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 66.2544 | 2.29283 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.1792 | −1.24905 | −0.624523 | − | 0.781006i | \(-0.714707\pi\) | ||||
−0.624523 | + | 0.781006i | \(0.714707\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.53729 | −0.0530099 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 100.689 | 3.46381 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.9620 | −0.754622 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.4054 | −0.459532 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.1605 | −0.621803 | −0.310902 | − | 0.950442i | \(-0.600631\pi\) | ||||
−0.310902 | + | 0.950442i | \(0.600631\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.4499 | −1.21094 | −0.605472 | − | 0.795866i | \(-0.707016\pi\) | ||||
−0.605472 | + | 0.795866i | \(0.707016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.2036 | −1.16701 | −0.583506 | − | 0.812109i | \(-0.698319\pi\) | ||||
−0.583506 | + | 0.812109i | \(0.698319\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.91354 | −0.0651376 | −0.0325688 | − | 0.999469i | \(-0.510369\pi\) | ||||
−0.0325688 | + | 0.999469i | \(0.510369\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.7310 | −1.72490 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.6307 | 1.48007 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.4667 | −1.67612 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −33.8465 | −1.14422 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.6237 | 1.57437 | 0.787185 | − | 0.616717i | \(-0.211538\pi\) | ||||
0.787185 | + | 0.616717i | \(0.211538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.6795 | −0.663020 | −0.331510 | − | 0.943452i | \(-0.607558\pi\) | ||||
−0.331510 | + | 0.943452i | \(0.607558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.83305 | 0.0616870 | 0.0308435 | − | 0.999524i | \(-0.490181\pi\) | ||||
0.0308435 | + | 0.999524i | \(0.490181\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 47.6648 | 1.60043 | 0.800213 | − | 0.599715i | \(-0.204719\pi\) | ||||
0.800213 | + | 0.599715i | \(0.204719\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.7230 | 0.393176 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −51.2681 | −1.71562 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.6573 | −0.456515 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.4627 | −0.915933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.31994 | 0.243863 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.08238 | 0.168944 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.0805 | −0.998806 | −0.499403 | − | 0.866370i | \(-0.666447\pi\) | ||||
−0.499403 | + | 0.866370i | \(0.666447\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41.5843 | −1.37775 | −0.688875 | − | 0.724880i | \(-0.741895\pi\) | ||||
−0.688875 | + | 0.724880i | \(0.741895\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −80.2727 | −2.65664 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.50229 | 0.247747 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19.0820 | −0.629458 | −0.314729 | − | 0.949182i | \(-0.601914\pi\) | ||||
−0.314729 | + | 0.949182i | \(0.601914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.0662 | 0.462994 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −103.617 | −3.40690 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.9684 | −1.54098 | −0.770492 | − | 0.637450i | \(-0.779989\pi\) | ||||
−0.770492 | + | 0.637450i | \(0.779989\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.74125 | −0.253709 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 62.3487 | 2.03902 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.7397 | −0.350852 | −0.175426 | − | 0.984493i | \(-0.556130\pi\) | ||||
−0.175426 | + | 0.984493i | \(0.556130\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.2024 | −1.14757 | −0.573783 | − | 0.819007i | \(-0.694525\pi\) | ||||
−0.573783 | + | 0.819007i | \(0.694525\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.76293 | 0.122538 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.7196 | 0.640800 | 0.320400 | − | 0.947282i | \(-0.396183\pi\) | ||||
0.320400 | + | 0.947282i | \(0.396183\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.07098 | −0.197072 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.0870 | 1.36333 | 0.681665 | − | 0.731664i | \(-0.261256\pi\) | ||||
0.681665 | + | 0.731664i | \(0.261256\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −80.5757 | −2.60737 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.7413 | 0.379145 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.53729 | −0.114106 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 50.8923 | 1.63828 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.87500 | 0.221085 | 0.110543 | − | 0.993871i | \(-0.464741\pi\) | ||||
0.110543 | + | 0.993871i | \(0.464741\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.9718 | 1.15439 | 0.577195 | − | 0.816606i | \(-0.304147\pi\) | ||||
0.577195 | + | 0.816606i | \(0.304147\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.902774 | −0.0289416 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.6014 | −0.339169 | −0.169584 | − | 0.985516i | \(-0.554243\pi\) | ||||
−0.169584 | + | 0.985516i | \(0.554243\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −67.7639 | −2.16574 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.3027 | −1.15788 | −0.578938 | − | 0.815371i | \(-0.696533\pi\) | ||||
−0.578938 | + | 0.815371i | \(0.696533\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.89973 | −0.283569 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.94271 | 0.316160 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.0049 | −0.476648 | −0.238324 | − | 0.971186i | \(-0.576598\pi\) | ||||
−0.238324 | + | 0.971186i | \(0.576598\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50.2913 | 1.59434 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.6677 | −1.19295 | −0.596474 | − | 0.802632i | \(-0.703432\pi\) | ||||
−0.596474 | + | 0.802632i | \(0.703432\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.a.bs.1.4 | yes | 4 | |
3.2 | odd | 2 | 6048.2.a.bk.1.1 | ✓ | 4 | ||
4.3 | odd | 2 | 6048.2.a.bt.1.4 | yes | 4 | ||
12.11 | even | 2 | 6048.2.a.bp.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bk.1.1 | ✓ | 4 | 3.2 | odd | 2 | ||
6048.2.a.bp.1.1 | yes | 4 | 12.11 | even | 2 | ||
6048.2.a.bs.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
6048.2.a.bt.1.4 | yes | 4 | 4.3 | odd | 2 |