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: | 4.4.22896.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 9x^{2} - 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.398683\) 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 | ||||||||
\(5\) | 4.38773 | 1.96225 | 0.981127 | − | 0.193367i | \(-0.0619407\pi\) | ||||
0.981127 | + | 0.193367i | \(0.0619407\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.59037 | 1.08254 | 0.541268 | − | 0.840850i | \(-0.317944\pi\) | ||||
0.541268 | + | 0.840850i | \(0.317944\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.797366 | 0.221150 | 0.110575 | − | 0.993868i | \(-0.464731\pi\) | ||||
0.110575 | + | 0.993868i | \(0.464731\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.295993 | 0.0717889 | 0.0358944 | − | 0.999356i | \(-0.488572\pi\) | ||||
0.0358944 | + | 0.999356i | \(0.488572\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.704007 | 0.161510 | 0.0807551 | − | 0.996734i | \(-0.474267\pi\) | ||||
0.0807551 | + | 0.996734i | \(0.474267\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.86446 | −1.63985 | −0.819926 | − | 0.572469i | \(-0.805986\pi\) | ||||
−0.819926 | + | 0.572469i | \(0.805986\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.2522 | 2.85044 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.50137 | 0.835884 | 0.417942 | − | 0.908474i | \(-0.362752\pi\) | ||||
0.417942 | + | 0.908474i | \(0.362752\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50137 | −0.269654 | −0.134827 | − | 0.990869i | \(-0.543048\pi\) | ||||
−0.134827 | + | 0.990869i | \(0.543048\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.38773 | 0.741662 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.202634 | −0.0333128 | −0.0166564 | − | 0.999861i | \(-0.505302\pi\) | ||||
−0.0166564 | + | 0.999861i | \(0.505302\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.66182 | −1.35275 | −0.676375 | − | 0.736558i | \(-0.736450\pi\) | ||||
−0.676375 | + | 0.736558i | \(0.736450\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.79737 | −0.426594 | −0.213297 | − | 0.976987i | \(-0.568420\pi\) | ||||
−0.213297 | + | 0.976987i | \(0.568420\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.27409 | 1.20690 | 0.603450 | − | 0.797401i | \(-0.293792\pi\) | ||||
0.603450 | + | 0.797401i | \(0.293792\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.7536 | 2.12421 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.27409 | 1.07719 | 0.538597 | − | 0.842563i | \(-0.318954\pi\) | ||||
0.538597 | + | 0.842563i | \(0.318954\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9562 | 1.53083 | 0.765417 | − | 0.643535i | \(-0.222533\pi\) | ||||
0.765417 | + | 0.643535i | \(0.222533\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.49863 | 0.433951 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.3455 | 1.63042 | 0.815209 | − | 0.579167i | \(-0.196622\pi\) | ||||
0.815209 | + | 0.579167i | \(0.196622\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.79300 | −0.806181 | −0.403090 | − | 0.915160i | \(-0.632064\pi\) | ||||
−0.403090 | + | 0.915160i | \(0.632064\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.20538 | 0.726285 | 0.363142 | − | 0.931734i | \(-0.381704\pi\) | ||||
0.363142 | + | 0.931734i | \(0.381704\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.59037 | 0.409160 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.7536 | −1.65991 | −0.829953 | − | 0.557834i | \(-0.811633\pi\) | ||||
−0.829953 | + | 0.557834i | \(0.811633\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.6443 | −1.60742 | −0.803710 | − | 0.595022i | \(-0.797143\pi\) | ||||
−0.803710 | + | 0.595022i | \(0.797143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.29874 | 0.140868 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.66182 | −0.494152 | −0.247076 | − | 0.968996i | \(-0.579470\pi\) | ||||
−0.247076 | + | 0.968996i | \(0.579470\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.797366 | 0.0835867 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.08899 | 0.316924 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.54818 | −0.867936 | −0.433968 | − | 0.900928i | \(-0.642887\pi\) | ||||
−0.433968 | + | 0.900928i | \(0.642887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.29599 | 0.825482 | 0.412741 | − | 0.910848i | \(-0.364571\pi\) | ||||
0.412741 | + | 0.910848i | \(0.364571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.04681 | −0.891408 | −0.445704 | − | 0.895180i | \(-0.647047\pi\) | ||||
−0.445704 | + | 0.895180i | \(0.647047\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8847 | −1.05227 | −0.526134 | − | 0.850402i | \(-0.676359\pi\) | ||||
−0.526134 | + | 0.850402i | \(0.676359\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.45482 | 0.618260 | 0.309130 | − | 0.951020i | \(-0.399962\pi\) | ||||
0.309130 | + | 0.951020i | \(0.399962\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1807 | 1.05179 | 0.525897 | − | 0.850548i | \(-0.323730\pi\) | ||||
0.525897 | + | 0.850548i | \(0.323730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −34.5071 | −3.21781 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.295993 | 0.0271337 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.89072 | 0.171884 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 40.5961 | 3.63103 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.3483 | 1.27320 | 0.636602 | − | 0.771192i | \(-0.280339\pi\) | ||||
0.636602 | + | 0.771192i | \(0.280339\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.2768 | 1.50948 | 0.754742 | − | 0.656022i | \(-0.227762\pi\) | ||||
0.754742 | + | 0.656022i | \(0.227762\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.704007 | 0.0610451 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.31191 | 0.453827 | 0.226914 | − | 0.973915i | \(-0.427137\pi\) | ||||
0.226914 | + | 0.973915i | \(0.427137\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.9534 | −0.929059 | −0.464530 | − | 0.885558i | \(-0.653777\pi\) | ||||
−0.464530 | + | 0.885558i | \(0.653777\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.86283 | 0.239402 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.7508 | 1.64022 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3674 | 1.09510 | 0.547552 | − | 0.836772i | \(-0.315560\pi\) | ||||
0.547552 | + | 0.836772i | \(0.315560\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.95619 | −0.810224 | −0.405112 | − | 0.914267i | \(-0.632767\pi\) | ||||
−0.405112 | + | 0.914267i | \(0.632767\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.58762 | −0.529130 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.80011 | −0.782134 | −0.391067 | − | 0.920362i | \(-0.627894\pi\) | ||||
−0.391067 | + | 0.920362i | \(0.627894\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.86446 | −0.619806 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.38935 | 0.422127 | 0.211063 | − | 0.977472i | \(-0.432307\pi\) | ||||
0.211063 | + | 0.977472i | \(0.432307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.1807 | 1.17472 | 0.587360 | − | 0.809326i | \(-0.300167\pi\) | ||||
0.587360 | + | 0.809326i | \(0.300167\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3642 | −0.951093 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.6837 | 0.964326 | 0.482163 | − | 0.876082i | \(-0.339851\pi\) | ||||
0.482163 | + | 0.876082i | \(0.339851\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.2522 | 1.07736 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.0715 | −1.27598 | −0.637990 | − | 0.770044i | \(-0.720234\pi\) | ||||
−0.637990 | + | 0.770044i | \(0.720234\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.3642 | −1.58799 | −0.793995 | − | 0.607925i | \(-0.792002\pi\) | ||||
−0.793995 | + | 0.607925i | \(0.792002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.889104 | −0.0653682 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.06272 | 0.0777141 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.31902 | 0.312513 | 0.156257 | − | 0.987716i | \(-0.450057\pi\) | ||||
0.156257 | + | 0.987716i | \(0.450057\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.14291 | −0.586140 | −0.293070 | − | 0.956091i | \(-0.594677\pi\) | ||||
−0.293070 | + | 0.956091i | \(0.594677\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.32364 | −0.664282 | −0.332141 | − | 0.943230i | \(-0.607771\pi\) | ||||
−0.332141 | + | 0.943230i | \(0.607771\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.3483 | −1.22979 | −0.614894 | − | 0.788610i | \(-0.710801\pi\) | ||||
−0.614894 | + | 0.788610i | \(0.710801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.50137 | 0.315934 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −38.0057 | −2.65444 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.52764 | 0.174841 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.9589 | 1.58056 | 0.790279 | − | 0.612747i | \(-0.209935\pi\) | ||||
0.790279 | + | 0.612747i | \(0.209935\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.2741 | −0.837086 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.50137 | −0.101920 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.236015 | 0.0158761 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.79737 | −0.120361 | −0.0601803 | − | 0.998188i | \(-0.519168\pi\) | ||||
−0.0601803 | + | 0.998188i | \(0.519168\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.1835 | −0.808646 | −0.404323 | − | 0.914616i | \(-0.632493\pi\) | ||||
−0.404323 | + | 0.914616i | \(0.632493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.1457 | −1.52951 | −0.764754 | − | 0.644322i | \(-0.777140\pi\) | ||||
−0.764754 | + | 0.644322i | \(0.777140\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.7289 | −0.768387 | −0.384193 | − | 0.923253i | \(-0.625520\pi\) | ||||
−0.384193 | + | 0.923253i | \(0.625520\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.3045 | 2.36824 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.4822 | −1.13083 | −0.565415 | − | 0.824806i | \(-0.691284\pi\) | ||||
−0.565415 | + | 0.824806i | \(0.691284\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.7508 | 1.40109 | 0.700547 | − | 0.713607i | \(-0.252940\pi\) | ||||
0.700547 | + | 0.713607i | \(0.252940\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.38773 | 0.280322 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.561351 | 0.0357179 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5975 | −0.668907 | −0.334453 | − | 0.942412i | \(-0.608552\pi\) | ||||
−0.334453 | + | 0.942412i | \(0.608552\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.2363 | −1.77520 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.9578 | 1.30731 | 0.653656 | − | 0.756792i | \(-0.273234\pi\) | ||||
0.653656 | + | 0.756792i | \(0.273234\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.202634 | −0.0125911 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.27846 | 0.140496 | 0.0702478 | − | 0.997530i | \(-0.477621\pi\) | ||||
0.0702478 | + | 0.997530i | \(0.477621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.5509 | 1.07814 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.8672 | 1.02841 | 0.514206 | − | 0.857667i | \(-0.328087\pi\) | ||||
0.514206 | + | 0.857667i | \(0.328087\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.81328 | −0.353132 | −0.176566 | − | 0.984289i | \(-0.556499\pi\) | ||||
−0.176566 | + | 0.984289i | \(0.556499\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 51.1706 | 3.08570 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.1588 | −0.970890 | −0.485445 | − | 0.874267i | \(-0.661342\pi\) | ||||
−0.485445 | + | 0.874267i | \(0.661342\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.86608 | 0.290286 | 0.145143 | − | 0.989411i | \(-0.453636\pi\) | ||||
0.145143 | + | 0.989411i | \(0.453636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.5509 | −1.28107 | −0.640535 | − | 0.767929i | \(-0.721287\pi\) | ||||
−0.640535 | + | 0.767929i | \(0.721287\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.66182 | −0.511291 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9124 | −0.994846 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.3978 | −1.36692 | −0.683458 | − | 0.729990i | \(-0.739525\pi\) | ||||
−0.683458 | + | 0.729990i | \(0.739525\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.3045 | 2.11373 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.27085 | −0.362653 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.79737 | −0.161237 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 52.4606 | 3.00388 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.0189 | 1.94156 | 0.970781 | − | 0.239967i | \(-0.0771366\pi\) | ||||
0.970781 | + | 0.239967i | \(0.0771366\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.5977 | −1.22470 | −0.612348 | − | 0.790589i | \(-0.709775\pi\) | ||||
−0.612348 | + | 0.790589i | \(0.709775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.34280 | −0.471563 | −0.235781 | − | 0.971806i | \(-0.575765\pi\) | ||||
−0.235781 | + | 0.971806i | \(0.575765\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.0901 | 1.29687 | 0.648435 | − | 0.761270i | \(-0.275424\pi\) | ||||
0.648435 | + | 0.761270i | \(0.275424\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.1616 | 0.904874 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.208381 | 0.0115946 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.3642 | 0.630373 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.27409 | 0.456165 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.0991 | −1.65440 | −0.827198 | − | 0.561910i | \(-0.810067\pi\) | ||||
−0.827198 | + | 0.561910i | \(0.810067\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 58.5567 | 3.19929 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.3615 | 1.38153 | 0.690763 | − | 0.723081i | \(-0.257275\pi\) | ||||
0.690763 | + | 0.723081i | \(0.257275\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.39048 | −0.291911 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.43454 | −0.452790 | −0.226395 | − | 0.974036i | \(-0.572694\pi\) | ||||
−0.226395 | + | 0.974036i | \(0.572694\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.5947 | −1.04888 | −0.524441 | − | 0.851447i | \(-0.675726\pi\) | ||||
−0.524441 | + | 0.851447i | \(0.675726\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.7111 | 0.995892 | 0.497946 | − | 0.867208i | \(-0.334088\pi\) | ||||
0.497946 | + | 0.867208i | \(0.334088\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −29.8059 | −1.58193 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.02216 | 0.370615 | 0.185308 | − | 0.982681i | \(-0.440672\pi\) | ||||
0.185308 | + | 0.982681i | \(0.440672\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5044 | −0.973914 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.2275 | 1.42515 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.4912 | −1.01743 | −0.508716 | − | 0.860934i | \(-0.669880\pi\) | ||||
−0.508716 | + | 0.860934i | \(0.669880\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.0085 | 1.29489 | 0.647445 | − | 0.762112i | \(-0.275837\pi\) | ||||
0.647445 | + | 0.762112i | \(0.275837\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.58924 | 0.184855 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.3921 | 0.842005 | 0.421003 | − | 0.907059i | \(-0.361678\pi\) | ||||
0.421003 | + | 0.907059i | \(0.361678\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.2798 | −0.678568 | −0.339284 | − | 0.940684i | \(-0.610185\pi\) | ||||
−0.339284 | + | 0.940684i | \(0.610185\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.7536 | 0.802876 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.5537 | −1.14352 | −0.571758 | − | 0.820422i | \(-0.693738\pi\) | ||||
−0.571758 | + | 0.820422i | \(0.693738\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.32783 | −0.117723 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −64.7347 | −3.25715 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.3149 | −1.77240 | −0.886202 | − | 0.463299i | \(-0.846666\pi\) | ||||
−0.886202 | + | 0.463299i | \(0.846666\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.8218 | 1.78885 | 0.894427 | − | 0.447214i | \(-0.147584\pi\) | ||||
0.894427 | + | 0.447214i | \(0.147584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.19714 | −0.0596340 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.727531 | −0.0360624 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.9430 | −1.08501 | −0.542506 | − | 0.840052i | \(-0.682525\pi\) | ||||
−0.542506 | + | 0.840052i | \(0.682525\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.27409 | 0.407141 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −64.2552 | −3.15416 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.67636 | 0.130749 | 0.0653743 | − | 0.997861i | \(-0.479176\pi\) | ||||
0.0653743 | + | 0.997861i | \(0.479176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.93479 | 0.386718 | 0.193359 | − | 0.981128i | \(-0.438062\pi\) | ||||
0.193359 | + | 0.981128i | \(0.438062\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.21855 | 0.204630 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.9562 | 0.578601 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.13280 | −0.150902 | −0.0754508 | − | 0.997150i | \(-0.524040\pi\) | ||||
−0.0754508 | + | 0.997150i | \(0.524040\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.1561 | 1.25698 | 0.628491 | − | 0.777817i | \(-0.283673\pi\) | ||||
0.628491 | + | 0.777817i | \(0.283673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.53663 | −0.264853 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.18397 | 0.438327 | 0.219164 | − | 0.975688i | \(-0.429667\pi\) | ||||
0.219164 | + | 0.975688i | \(0.429667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.1353 | 1.81186 | 0.905931 | − | 0.423424i | \(-0.139172\pi\) | ||||
0.905931 | + | 0.423424i | \(0.139172\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.4548 | −0.969652 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4140 | 0.491467 | 0.245734 | − | 0.969337i | \(-0.420971\pi\) | ||||
0.245734 | + | 0.969337i | \(0.420971\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.0991 | −1.46440 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.49863 | 0.164018 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.1457 | −0.661706 | −0.330853 | − | 0.943682i | \(-0.607336\pi\) | ||||
−0.330853 | + | 0.943682i | \(0.607336\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.91101 | −0.228728 | −0.114364 | − | 0.993439i | \(-0.536483\pi\) | ||||
−0.114364 | + | 0.993439i | \(0.536483\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.59473 | 0.167061 | 0.0835307 | − | 0.996505i | \(-0.473380\pi\) | ||||
0.0835307 | + | 0.996505i | \(0.473380\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.0463 | 1.06646 | 0.533228 | − | 0.845972i | \(-0.320979\pi\) | ||||
0.533228 | + | 0.845972i | \(0.320979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.3455 | 0.616240 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.0436 | −0.461804 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0336 | 0.460375 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.7404 | 0.582123 | 0.291062 | − | 0.956704i | \(-0.405992\pi\) | ||||
0.291062 | + | 0.956704i | \(0.405992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.161574 | −0.00736712 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −37.5071 | −1.70311 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.1150 | 1.31933 | 0.659664 | − | 0.751561i | \(-0.270699\pi\) | ||||
0.659664 | + | 0.751561i | \(0.270699\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.2155 | 1.40874 | 0.704368 | − | 0.709835i | \(-0.251231\pi\) | ||||
0.704368 | + | 0.709835i | \(0.251231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.33238 | 0.0600072 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.79300 | −0.304708 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.1588 | 1.30533 | 0.652664 | − | 0.757647i | \(-0.273651\pi\) | ||||
0.652664 | + | 0.757647i | \(0.273651\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.8337 | 0.795168 | 0.397584 | − | 0.917566i | \(-0.369849\pi\) | ||||
0.397584 | + | 0.917566i | \(0.369849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.4006 | 1.61980 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.65471 | −0.250641 | −0.125320 | − | 0.992116i | \(-0.539996\pi\) | ||||
−0.125320 | + | 0.992116i | \(0.539996\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.20538 | 0.274510 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −39.6950 | −1.74917 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.7070 | 1.30651 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00162 | −0.394368 | −0.197184 | − | 0.980366i | \(-0.563180\pi\) | ||||
−0.197184 | + | 0.980366i | \(0.563180\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.9589 | −0.610382 | −0.305191 | − | 0.952291i | \(-0.598720\pi\) | ||||
−0.305191 | + | 0.952291i | \(0.598720\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.444396 | −0.0193582 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.8497 | 1.68912 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.90664 | −0.299160 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −47.7593 | −2.06481 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.59037 | 0.154648 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.24919 | −0.0537067 | −0.0268533 | − | 0.999639i | \(-0.508549\pi\) | ||||
−0.0268533 | + | 0.999639i | \(0.508549\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 28.3220 | 1.21318 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.6911 | 0.799173 | 0.399587 | − | 0.916695i | \(-0.369154\pi\) | ||||
0.399587 | + | 0.916695i | \(0.369154\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.16900 | 0.135004 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.7536 | −0.627385 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.2388 | −1.78971 | −0.894857 | − | 0.446353i | \(-0.852723\pi\) | ||||
−0.894857 | + | 0.446353i | \(0.852723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.23052 | −0.0943411 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.0030 | 0.843026 | 0.421513 | − | 0.906822i | \(-0.361499\pi\) | ||||
0.421513 | + | 0.906822i | \(0.361499\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 49.0580 | 2.06389 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.36470 | 0.350667 | 0.175333 | − | 0.984509i | \(-0.443900\pi\) | ||||
0.175333 | + | 0.984509i | \(0.443900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7695 | −0.827327 | −0.413663 | − | 0.910430i | \(-0.635751\pi\) | ||||
−0.413663 | + | 0.910430i | \(0.635751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −112.086 | −4.67430 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.1867 | 0.507340 | 0.253670 | − | 0.967291i | \(-0.418362\pi\) | ||||
0.253670 | + | 0.967291i | \(0.418362\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.6443 | −0.607547 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.3615 | 0.594791 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.54219 | −0.393848 | −0.196924 | − | 0.980419i | \(-0.563095\pi\) | ||||
−0.196924 | + | 0.980419i | \(0.563095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.05698 | −0.0435520 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.1002 | 1.23607 | 0.618034 | − | 0.786151i | \(-0.287929\pi\) | ||||
0.618034 | + | 0.786151i | \(0.287929\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.29874 | 0.0532431 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.0101 | 1.59391 | 0.796955 | − | 0.604039i | \(-0.206443\pi\) | ||||
0.796955 | + | 0.604039i | \(0.206443\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.20263 | 0.130638 | 0.0653191 | − | 0.997864i | \(-0.479193\pi\) | ||||
0.0653191 | + | 0.997864i | \(0.479193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.29599 | 0.337280 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.1429 | 0.898753 | 0.449377 | − | 0.893342i | \(-0.351646\pi\) | ||||
0.449377 | + | 0.893342i | \(0.351646\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.59748 | 0.266905 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.50137 | 0.0606399 | 0.0303199 | − | 0.999540i | \(-0.490347\pi\) | ||||
0.0303199 | + | 0.999540i | \(0.490347\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.2275 | −0.452004 | −0.226002 | − | 0.974127i | \(-0.572566\pi\) | ||||
−0.226002 | + | 0.974127i | \(0.572566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.09911 | 0.285337 | 0.142669 | − | 0.989771i | \(-0.454432\pi\) | ||||
0.142669 | + | 0.989771i | \(0.454432\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.66182 | −0.186772 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 106.864 | 4.27456 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.0599783 | −0.00239149 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.7098 | −1.85949 | −0.929743 | − | 0.368209i | \(-0.879971\pi\) | ||||
−0.929743 | + | 0.368209i | \(0.879971\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 62.9565 | 2.49835 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.797366 | 0.0315928 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.13693 | 0.123901 | 0.0619505 | − | 0.998079i | \(-0.480268\pi\) | ||||
0.0619505 | + | 0.998079i | \(0.480268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.2522 | 1.15359 | 0.576797 | − | 0.816888i | \(-0.304302\pi\) | ||||
0.576797 | + | 0.816888i | \(0.304302\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.37320 | 0.250556 | 0.125278 | − | 0.992122i | \(-0.460018\pi\) | ||||
0.125278 | + | 0.992122i | \(0.460018\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.7070 | 1.16610 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.0901 | −0.433990 | −0.216995 | − | 0.976173i | \(-0.569626\pi\) | ||||
−0.216995 | + | 0.976173i | \(0.569626\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 75.8061 | 2.96199 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.9633 | −1.36198 | −0.680989 | − | 0.732294i | \(-0.738450\pi\) | ||||
−0.680989 | + | 0.732294i | \(0.738450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.2524 | −1.37116 | −0.685581 | − | 0.727997i | \(-0.740452\pi\) | ||||
−0.685581 | + | 0.727997i | \(0.740452\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.08899 | 0.119786 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.4008 | −1.37073 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.9271 | 1.65718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.14291 | −0.159698 | −0.0798488 | − | 0.996807i | \(-0.525444\pi\) | ||||
−0.0798488 | + | 0.996807i | \(0.525444\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.5306 | −0.558458 | −0.279229 | − | 0.960225i | \(-0.590079\pi\) | ||||
−0.279229 | + | 0.960225i | \(0.590079\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.54818 | −0.328049 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.0422 | −0.881685 | −0.440842 | − | 0.897585i | \(-0.645320\pi\) | ||||
−0.440842 | + | 0.897585i | \(0.645320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.3072 | 0.890524 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.18946 | 0.121509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.3587 | −0.964691 | −0.482346 | − | 0.875981i | \(-0.660215\pi\) | ||||
−0.482346 | + | 0.875981i | \(0.660215\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −48.0608 | −1.82305 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.56384 | −0.0971124 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.1459 | 1.28967 | 0.644837 | − | 0.764320i | \(-0.276925\pi\) | ||||
0.644837 | + | 0.764320i | \(0.276925\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.142656 | −0.00538037 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.29599 | 0.312003 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.9301 | −1.49961 | −0.749803 | − | 0.661661i | \(-0.769852\pi\) | ||||
−0.749803 | + | 0.661661i | \(0.769852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.8075 | 0.442194 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.5614 | 0.469768 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.49539 | −0.204943 | −0.102472 | − | 0.994736i | \(-0.532675\pi\) | ||||
−0.102472 | + | 0.994736i | \(0.532675\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.04681 | −0.336921 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 64.1544 | 2.38263 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.5564 | 1.31871 | 0.659357 | − | 0.751830i | \(-0.270828\pi\) | ||||
0.659357 | + | 0.751830i | \(0.270828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.828001 | −0.0306247 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.7536 | −1.28365 | −0.641826 | − | 0.766850i | \(-0.721823\pi\) | ||||
−0.641826 | + | 0.766850i | \(0.721823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 47.9154 | 1.76499 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.8367 | −1.75970 | −0.879852 | − | 0.475248i | \(-0.842358\pi\) | ||||
−0.879852 | + | 0.475248i | \(0.842358\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.5717 | −0.644643 | −0.322322 | − | 0.946630i | \(-0.604463\pi\) | ||||
−0.322322 | + | 0.946630i | \(0.604463\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 58.6528 | 2.14887 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.8847 | −0.397720 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.7508 | −0.939661 | −0.469830 | − | 0.882757i | \(-0.655685\pi\) | ||||
−0.469830 | + | 0.882757i | \(0.655685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.6851 | −1.58986 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.21580 | 0.189572 | 0.0947858 | − | 0.995498i | \(-0.469783\pi\) | ||||
0.0947858 | + | 0.995498i | \(0.469783\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.0655 | −0.944873 | −0.472436 | − | 0.881365i | \(-0.656625\pi\) | ||||
−0.472436 | + | 0.881365i | \(0.656625\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.45482 | 0.233680 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.59748 | 0.238221 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.9896 | 0.612660 | 0.306330 | − | 0.951925i | \(-0.400899\pi\) | ||||
0.306330 | + | 0.951925i | \(0.400899\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.8396 | −0.569709 | −0.284855 | − | 0.958571i | \(-0.591945\pi\) | ||||
−0.284855 | + | 0.958571i | \(0.591945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.3978 | −0.768633 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.09798 | −0.218483 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.3894 | −0.872720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43.0003 | −1.53474 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.7376 | −0.988740 | −0.494370 | − | 0.869252i | \(-0.664601\pi\) | ||||
−0.494370 | + | 0.869252i | \(0.664601\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.1807 | 0.397541 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.53346 | 0.338543 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.5192 | 0.762248 | 0.381124 | − | 0.924524i | \(-0.375537\pi\) | ||||
0.381124 | + | 0.924524i | \(0.375537\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.44907 | 0.0866420 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.2796 | 0.786229 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34.5071 | −1.21622 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.90939 | 0.278079 | 0.139040 | − | 0.990287i | \(-0.455598\pi\) | ||||
0.139040 | + | 0.990287i | \(0.455598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.5947 | 0.933867 | 0.466934 | − | 0.884292i | \(-0.345359\pi\) | ||||
0.466934 | + | 0.884292i | \(0.345359\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.6470 | 0.828319 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.96936 | −0.0688993 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.7757 | −1.24858 | −0.624291 | − | 0.781192i | \(-0.714612\pi\) | ||||
−0.624291 | + | 0.781192i | \(0.714612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00549 | 0.279054 | 0.139527 | − | 0.990218i | \(-0.455442\pi\) | ||||
0.139527 | + | 0.990218i | \(0.455442\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.60927 | −0.264600 | −0.132300 | − | 0.991210i | \(-0.542236\pi\) | ||||
−0.132300 | + | 0.991210i | \(0.542236\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.2081 | −0.806051 | −0.403026 | − | 0.915189i | \(-0.632041\pi\) | ||||
−0.403026 | + | 0.915189i | \(0.632041\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.295993 | 0.0102556 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 66.6090 | 2.30510 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.9121 | 0.860062 | 0.430031 | − | 0.902814i | \(-0.358503\pi\) | ||||
0.430031 | + | 0.902814i | \(0.358503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.73764 | −0.301298 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −54.2508 | −1.86629 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.89072 | 0.0649661 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.59361 | 0.0546281 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.7376 | −0.675804 | −0.337902 | − | 0.941181i | \(-0.609717\pi\) | ||||
−0.337902 | + | 0.941181i | \(0.609717\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.2916 | 0.761467 | 0.380734 | − | 0.924685i | \(-0.375671\pi\) | ||||
0.380734 | + | 0.924685i | \(0.375671\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.1646 | 0.858604 | 0.429302 | − | 0.903161i | \(-0.358760\pi\) | ||||
0.429302 | + | 0.903161i | \(0.358760\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.7625 | −1.76202 | −0.881009 | − | 0.473100i | \(-0.843135\pi\) | ||||
−0.881009 | + | 0.473100i | \(0.843135\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55.6528 | 1.89225 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.9707 | −1.79691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.6413 | 0.360566 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40.5961 | 1.37240 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 58.7464 | 1.98372 | 0.991862 | − | 0.127315i | \(-0.0406358\pi\) | ||||
0.991862 | + | 0.127315i | \(0.0406358\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.1284 | −1.89101 | −0.945507 | − | 0.325603i | \(-0.894433\pi\) | ||||
−0.945507 | + | 0.325603i | \(0.894433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.14017 | 0.307591 | 0.153796 | − | 0.988103i | \(-0.450850\pi\) | ||||
0.153796 | + | 0.988103i | \(0.450850\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.4083 | 1.55824 | 0.779119 | − | 0.626877i | \(-0.215667\pi\) | ||||
0.779119 | + | 0.626877i | \(0.215667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.3483 | 0.481226 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.82502 | 0.194927 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −74.9050 | −2.50380 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.75824 | −0.225400 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.18397 | 0.0394438 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −93.7404 | −3.11604 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.1867 | −0.935925 | −0.467962 | − | 0.883748i | \(-0.655012\pi\) | ||||
−0.467962 | + | 0.883748i | \(0.655012\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.1235 | −1.32935 | −0.664675 | − | 0.747132i | \(-0.731430\pi\) | ||||
−0.664675 | + | 0.747132i | \(0.731430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.5783 | −1.74009 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.2768 | 0.570531 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.6445 | 0.582040 | 0.291020 | − | 0.956717i | \(-0.406005\pi\) | ||||
0.291020 | + | 0.956717i | \(0.406005\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.41651 | −0.178286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.88798 | −0.0949562 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.3924 | 0.701860 | 0.350930 | − | 0.936402i | \(-0.385865\pi\) | ||||
0.350930 | + | 0.936402i | \(0.385865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.704007 | 0.0230729 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.66295 | 0.152495 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.0580 | −1.53732 | −0.768660 | − | 0.639658i | \(-0.779076\pi\) | ||||
−0.768660 | + | 0.639658i | \(0.779076\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.0668 | −0.523764 | −0.261882 | − | 0.965100i | \(-0.584343\pi\) | ||||
−0.261882 | + | 0.965100i | \(0.584343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 68.1205 | 2.21831 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.4838 | 0.860609 | 0.430305 | − | 0.902684i | \(-0.358406\pi\) | ||||
0.430305 | + | 0.902684i | \(0.358406\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.94796 | 0.160618 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.8337 | −0.577692 | −0.288846 | − | 0.957376i | \(-0.593272\pi\) | ||||
−0.288846 | + | 0.957376i | \(0.593272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.9507 | 0.613230 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.31191 | 0.171530 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.7459 | −0.927286 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.7289 | −1.15015 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.4113 | 0.913645 | 0.456822 | − | 0.889558i | \(-0.348987\pi\) | ||||
0.456822 | + | 0.889558i | \(0.348987\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.0550 | −0.611505 | −0.305753 | − | 0.952111i | \(-0.598908\pi\) | ||||
−0.305753 | + | 0.952111i | \(0.598908\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.9534 | −0.351151 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.1046 | −1.41103 | −0.705516 | − | 0.708694i | \(-0.749284\pi\) | ||||
−0.705516 | + | 0.708694i | \(0.749284\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.7376 | −0.534937 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −47.7867 | −1.52416 | −0.762080 | − | 0.647483i | \(-0.775821\pi\) | ||||
−0.762080 | + | 0.647483i | \(0.775821\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.9096 | −1.30349 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.9998 | 0.699552 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.6161 | −0.654893 | −0.327447 | − | 0.944870i | \(-0.606188\pi\) | ||||
−0.327447 | + | 0.944870i | \(0.606188\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −76.1196 | −2.41315 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.8160 | 0.532569 | 0.266284 | − | 0.963894i | \(-0.414204\pi\) | ||||
0.266284 | + | 0.963894i | \(0.414204\pi\) | |||||||
\(998\) | 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.bv.1.4 | yes | 4 | |
3.2 | odd | 2 | 6048.2.a.bo.1.1 | yes | 4 | ||
4.3 | odd | 2 | 6048.2.a.br.1.4 | yes | 4 | ||
12.11 | even | 2 | 6048.2.a.bm.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bm.1.1 | ✓ | 4 | 12.11 | even | 2 | ||
6048.2.a.bo.1.1 | yes | 4 | 3.2 | odd | 2 | ||
6048.2.a.br.1.4 | yes | 4 | 4.3 | odd | 2 | ||
6048.2.a.bv.1.4 | yes | 4 | 1.1 | even | 1 | trivial |