Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2592,2,Mod(1,2592)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2592, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2592.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2592 = 2^{5} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2592.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: | \(20.6972242039\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13068.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 288) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.04374\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2592.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.37228 | −1.06092 | −0.530458 | − | 0.847711i | \(-0.677980\pi\) | ||||
−0.530458 | + | 0.847711i | \(0.677980\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.20979 | 0.835221 | 0.417610 | − | 0.908626i | \(-0.362868\pi\) | ||||
0.417610 | + | 0.908626i | \(0.362868\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.93580 | 1.78971 | 0.894855 | − | 0.446357i | \(-0.147279\pi\) | ||||
0.894855 | + | 0.446357i | \(0.147279\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.37228 | 1.21265 | 0.606326 | − | 0.795216i | \(-0.292643\pi\) | ||||
0.606326 | + | 0.795216i | \(0.292643\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.37228 | −0.817898 | −0.408949 | − | 0.912557i | \(-0.634105\pi\) | ||||
−0.408949 | + | 0.912557i | \(0.634105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.72601 | −0.854805 | −0.427403 | − | 0.904061i | \(-0.640571\pi\) | ||||
−0.427403 | + | 0.904061i | \(0.640571\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.20979 | −0.460772 | −0.230386 | − | 0.973099i | \(-0.573999\pi\) | ||||
−0.230386 | + | 0.973099i | \(0.573999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.627719 | 0.125544 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.372281 | −0.0691309 | −0.0345655 | − | 0.999402i | \(-0.511005\pi\) | ||||
−0.0345655 | + | 0.999402i | \(0.511005\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.66181 | 1.73531 | 0.867656 | − | 0.497165i | \(-0.165626\pi\) | ||||
0.867656 | + | 0.497165i | \(0.165626\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.24224 | −0.886099 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | −0.0780869 | − | 0.996947i | \(-0.524881\pi\) | ||||
−0.0780869 | + | 0.996947i | \(0.524881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.93580 | 0.905201 | 0.452600 | − | 0.891714i | \(-0.350496\pi\) | ||||
0.452600 | + | 0.891714i | \(0.350496\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.20979 | −0.322330 | −0.161165 | − | 0.986927i | \(-0.551525\pi\) | ||||
−0.161165 | + | 0.986927i | \(0.551525\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.11684 | −0.302406 | ||||||||
\(50\) | 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 | ||||||||
\(55\) | −14.0814 | −1.89873 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.3554 | −1.34815 | −0.674077 | − | 0.738661i | \(-0.735458\pi\) | ||||
−0.674077 | + | 0.738661i | \(0.735458\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.1168 | 1.93551 | 0.967757 | − | 0.251887i | \(-0.0810510\pi\) | ||||
0.967757 | + | 0.251887i | \(0.0810510\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.3723 | −1.28652 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.3554 | −1.26511 | −0.632555 | − | 0.774516i | \(-0.717994\pi\) | ||||
−0.632555 | + | 0.774516i | \(0.717994\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.41957 | −0.524507 | −0.262253 | − | 0.964999i | \(-0.584466\pi\) | ||||
−0.262253 | + | 0.964999i | \(0.584466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.62772 | 0.541634 | 0.270817 | − | 0.962631i | \(-0.412706\pi\) | ||||
0.270817 | + | 0.962631i | \(0.412706\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.1168 | 1.49480 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.66181 | −1.08704 | −0.543519 | − | 0.839397i | \(-0.682908\pi\) | ||||
−0.543519 | + | 0.839397i | \(0.682908\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.0814 | 1.54563 | 0.772816 | − | 0.634630i | \(-0.218847\pi\) | ||||
0.772816 | + | 0.634630i | \(0.218847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.25544 | −0.133076 | −0.0665380 | − | 0.997784i | \(-0.521195\pi\) | ||||
−0.0665380 | + | 0.997784i | \(0.521195\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.66181 | 1.01283 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.83915 | 0.906877 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.00000 | 0.913812 | 0.456906 | − | 0.889515i | \(-0.348958\pi\) | ||||
0.456906 | + | 0.889515i | \(0.348958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.1168 | 1.50418 | 0.752091 | − | 0.659059i | \(-0.229045\pi\) | ||||
0.752091 | + | 0.659059i | \(0.229045\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.20979 | −0.217737 | −0.108868 | − | 0.994056i | \(-0.534723\pi\) | ||||
−0.108868 | + | 0.994056i | \(0.534723\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.72601 | 0.360207 | 0.180104 | − | 0.983648i | \(-0.442357\pi\) | ||||
0.180104 | + | 0.983648i | \(0.442357\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.4891 | 1.67515 | 0.837577 | − | 0.546319i | \(-0.183971\pi\) | ||||
0.837577 | + | 0.546319i | \(0.183971\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.6277 | −1.09384 | −0.546922 | − | 0.837184i | \(-0.684201\pi\) | ||||
−0.546922 | + | 0.837184i | \(0.684201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.24224 | 0.488841 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.45202 | −0.683126 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.2337 | 2.20306 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.3723 | 0.927725 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.45202 | 0.661260 | 0.330630 | − | 0.943760i | \(-0.392739\pi\) | ||||
0.330630 | + | 0.943760i | \(0.392739\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.66181 | 0.844156 | 0.422078 | − | 0.906560i | \(-0.361301\pi\) | ||||
0.422078 | + | 0.906560i | \(0.361301\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.23369 | −0.713951 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.4891 | 1.06702 | 0.533509 | − | 0.845794i | \(-0.320873\pi\) | ||||
0.533509 | + | 0.845794i | \(0.320873\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.90335 | 0.246259 | 0.123129 | − | 0.992391i | \(-0.460707\pi\) | ||||
0.123129 | + | 0.992391i | \(0.460707\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.9530 | 2.17030 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.883156 | 0.0733421 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6277 | 0.952580 | 0.476290 | − | 0.879288i | \(-0.341981\pi\) | ||||
0.476290 | + | 0.879288i | \(0.341981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.20979 | −0.179830 | −0.0899149 | − | 0.995949i | \(-0.528660\pi\) | ||||
−0.0899149 | + | 0.995949i | \(0.528660\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.9205 | −1.84102 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.11684 | −0.248751 | −0.124376 | − | 0.992235i | \(-0.539693\pi\) | ||||
−0.124376 | + | 0.992235i | \(0.539693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.88316 | −0.384847 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.83915 | 0.692335 | 0.346168 | − | 0.938173i | \(-0.387483\pi\) | ||||
0.346168 | + | 0.938173i | \(0.387483\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.66181 | 0.747653 | 0.373827 | − | 0.927499i | \(-0.378046\pi\) | ||||
0.373827 | + | 0.927499i | \(0.378046\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.11684 | 0.470526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.372281 | 0.0283040 | 0.0141520 | − | 0.999900i | \(-0.495495\pi\) | ||||
0.0141520 | + | 0.999900i | \(0.495495\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.38712 | 0.104857 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.83915 | −0.660669 | −0.330334 | − | 0.943864i | \(-0.607162\pi\) | ||||
−0.330334 | + | 0.943864i | \(0.607162\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.23369 | −0.612005 | −0.306003 | − | 0.952031i | \(-0.598992\pi\) | ||||
−0.306003 | + | 0.952031i | \(0.598992\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.48913 | −0.697654 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.0172 | −1.46380 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.1138 | −1.23831 | −0.619157 | − | 0.785268i | \(-0.712525\pi\) | ||||
−0.619157 | + | 0.785268i | \(0.712525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | 0.0719816 | 0.0359908 | − | 0.999352i | \(-0.488541\pi\) | ||||
0.0359908 | + | 0.999352i | \(0.488541\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.744563 | −0.0530479 | −0.0265239 | − | 0.999648i | \(-0.508444\pi\) | ||||
−0.0265239 | + | 0.999648i | \(0.508444\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.7107 | 1.46815 | 0.734073 | − | 0.679071i | \(-0.237617\pi\) | ||||
0.734073 | + | 0.679071i | \(0.237617\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.822662 | −0.0577396 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.37228 | 0.165687 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.1168 | −1.52985 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.24224 | −0.360890 | −0.180445 | − | 0.983585i | \(-0.557754\pi\) | ||||
−0.180445 | + | 0.983585i | \(0.557754\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0814 | −0.960342 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.3505 | 1.44937 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.7446 | −0.991827 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.20979 | 0.147978 | 0.0739891 | − | 0.997259i | \(-0.476427\pi\) | ||||
0.0739891 | + | 0.997259i | \(0.476427\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.96825 | −0.595243 | −0.297622 | − | 0.954684i | \(-0.596193\pi\) | ||||
−0.297622 | + | 0.954684i | \(0.596193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.37228 | −0.288928 | −0.144464 | − | 0.989510i | \(-0.546146\pi\) | ||||
−0.144464 | + | 0.989510i | \(0.546146\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.86141 | −0.187457 | −0.0937285 | − | 0.995598i | \(-0.529879\pi\) | ||||
−0.0937285 | + | 0.995598i | \(0.529879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.24224 | 0.341966 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.1138 | −1.10700 | −0.553501 | − | 0.832849i | \(-0.686708\pi\) | ||||
−0.553501 | + | 0.832849i | \(0.686708\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.255437 | 0.0164542 | 0.00822708 | − | 0.999966i | \(-0.497381\pi\) | ||||
0.00822708 | + | 0.999966i | \(0.497381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.02175 | 0.320828 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.2912 | −1.03658 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1780 | 0.705551 | 0.352776 | − | 0.935708i | \(-0.385238\pi\) | ||||
0.352776 | + | 0.935708i | \(0.385238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.1168 | −0.824649 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.48913 | 0.404781 | 0.202390 | − | 0.979305i | \(-0.435129\pi\) | ||||
0.202390 | + | 0.979305i | \(0.435129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.83915 | 0.549238 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.1138 | 1.05528 | 0.527642 | − | 0.849467i | \(-0.323076\pi\) | ||||
0.527642 | + | 0.849467i | \(0.323076\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.48913 | −0.582912 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.48913 | −0.578562 | −0.289281 | − | 0.957244i | \(-0.593416\pi\) | ||||
−0.289281 | + | 0.957244i | \(0.593416\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.9040 | 0.905356 | 0.452678 | − | 0.891674i | \(-0.350469\pi\) | ||||
0.452678 | + | 0.891674i | \(0.350469\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.72601 | 0.224687 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.1168 | 0.788115 | 0.394057 | − | 0.919086i | \(-0.371071\pi\) | ||||
0.394057 | + | 0.919086i | \(0.371071\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.8614 | −1.54276 | −0.771381 | − | 0.636373i | \(-0.780434\pi\) | ||||
−0.771381 | + | 0.636373i | \(0.780434\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.24224 | 0.311619 | 0.155809 | − | 0.987787i | \(-0.450201\pi\) | ||||
0.155809 | + | 0.987787i | \(0.450201\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.20979 | −0.130440 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.62772 | −0.331042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.3723 | 1.19016 | 0.595081 | − | 0.803666i | \(-0.297120\pi\) | ||||
0.595081 | + | 0.803666i | \(0.297120\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.5659 | 1.43028 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.66181 | −0.558757 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.1168 | 0.756042 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −35.8614 | −2.05342 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.8563 | −1.64692 | −0.823459 | − | 0.567376i | \(-0.807959\pi\) | ||||
−0.823459 | + | 0.567376i | \(0.807959\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.6943 | 0.719825 | 0.359913 | − | 0.932986i | \(-0.382806\pi\) | ||||
0.359913 | + | 0.932986i | \(0.382806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.2337 | 1.08715 | 0.543576 | − | 0.839360i | \(-0.317070\pi\) | ||||
0.543576 | + | 0.839360i | \(0.317070\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.37228 | −0.470234 | −0.235117 | − | 0.971967i | \(-0.575547\pi\) | ||||
−0.235117 | + | 0.971967i | \(0.575547\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.20979 | −0.123724 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.5652 | 0.699144 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.74456 | 0.152241 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.88316 | −0.269217 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.4050 | −1.83610 | −0.918052 | − | 0.396459i | \(-0.870239\pi\) | ||||
−0.918052 | + | 0.396459i | \(0.870239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.5659 | 1.34218 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.00000 | −0.490261 | −0.245131 | − | 0.969490i | \(-0.578831\pi\) | ||||
−0.245131 | + | 0.969490i | \(0.578831\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 57.3505 | 3.10571 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1463 | −1.08780 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3554 | 0.555905 | 0.277953 | − | 0.960595i | \(-0.410344\pi\) | ||||
0.277953 | + | 0.960595i | \(0.410344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.1168 | −1.23742 | −0.618708 | − | 0.785621i | \(-0.712344\pi\) | ||||
−0.618708 | + | 0.785621i | \(0.712344\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.2337 | 1.02371 | 0.511853 | − | 0.859073i | \(-0.328959\pi\) | ||||
0.511853 | + | 0.859073i | \(0.328959\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.4845 | 0.556458 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.3561 | −1.17991 | −0.589954 | − | 0.807437i | \(-0.700854\pi\) | ||||
−0.589954 | + | 0.807437i | \(0.700854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.11684 | −0.269308 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.9783 | −0.574628 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.3401 | −1.42714 | −0.713571 | − | 0.700583i | \(-0.752923\pi\) | ||||
−0.713571 | + | 0.700583i | \(0.752923\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.83915 | 0.458906 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.1168 | −0.886277 | −0.443138 | − | 0.896453i | \(-0.646135\pi\) | ||||
−0.443138 | + | 0.896453i | \(0.646135\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.62772 | −0.0838318 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.14558 | −0.418411 | −0.209205 | − | 0.977872i | \(-0.567088\pi\) | ||||
−0.209205 | + | 0.977872i | \(0.567088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.9205 | −1.17118 | −0.585592 | − | 0.810606i | \(-0.699138\pi\) | ||||
−0.585592 | + | 0.810606i | \(0.699138\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.1168 | −1.58586 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.3505 | 0.981111 | 0.490555 | − | 0.871410i | \(-0.336794\pi\) | ||||
0.490555 | + | 0.871410i | \(0.336794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.45202 | 0.376865 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.9205 | 1.15326 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00000 | −0.200754 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.9783 | −1.39717 | −0.698584 | − | 0.715528i | \(-0.746186\pi\) | ||||
−0.698584 | + | 0.715528i | \(0.746186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 42.2441 | 2.10433 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.7432 | 1.17691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.2554 | −0.902673 | −0.451337 | − | 0.892354i | \(-0.649053\pi\) | ||||
−0.451337 | + | 0.892354i | \(0.649053\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.8832 | −1.12601 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −33.4050 | −1.63979 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.24224 | 0.256100 | 0.128050 | − | 0.991768i | \(-0.459128\pi\) | ||||
0.128050 | + | 0.991768i | \(0.459128\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.3723 | −1.09036 | −0.545179 | − | 0.838320i | \(-0.683538\pi\) | ||||
−0.545179 | + | 0.838320i | \(0.683538\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.11684 | −0.102682 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.4050 | 1.61658 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.45202 | −0.358951 | −0.179476 | − | 0.983762i | \(-0.557440\pi\) | ||||
−0.179476 | + | 0.983762i | \(0.557440\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.1168 | −0.870640 | −0.435320 | − | 0.900276i | \(-0.643365\pi\) | ||||
−0.435320 | + | 0.900276i | \(0.643365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.23369 | 0.393871 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.9205 | 1.09394 | 0.546969 | − | 0.837153i | \(-0.315782\pi\) | ||||
0.546969 | + | 0.837153i | \(0.315782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.96825 | 0.426094 | 0.213047 | − | 0.977042i | \(-0.431661\pi\) | ||||
0.213047 | + | 0.977042i | \(0.431661\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.97825 | 0.141183 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.1168 | 0.854987 | 0.427493 | − | 0.904018i | \(-0.359397\pi\) | ||||
0.427493 | + | 0.904018i | \(0.359397\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.93580 | −0.279506 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.9205 | −1.07453 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.9783 | −1.21521 | −0.607606 | − | 0.794239i | \(-0.707870\pi\) | ||||
−0.607606 | + | 0.794239i | \(0.707870\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.1168 | 1.35611 | 0.678053 | − | 0.735013i | \(-0.262824\pi\) | ||||
0.678053 | + | 0.735013i | \(0.262824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −37.8246 | −1.75786 | −0.878928 | − | 0.476954i | \(-0.841741\pi\) | ||||
−0.878928 | + | 0.476954i | \(0.841741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.3083 | −1.68015 | −0.840075 | − | 0.542470i | \(-0.817489\pi\) | ||||
−0.840075 | + | 0.542470i | \(0.817489\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.8832 | −1.05665 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.2337 | 1.62005 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.33889 | −0.107315 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.20979 | 0.100968 | 0.0504839 | − | 0.998725i | \(-0.483924\pi\) | ||||
0.0504839 | + | 0.998725i | \(0.483924\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.4891 | 0.797435 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.3505 | −0.969478 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.45202 | 0.337683 | 0.168842 | − | 0.985643i | \(-0.445997\pi\) | ||||
0.168842 | + | 0.985643i | \(0.445997\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.129100 | −0.00582621 | −0.00291310 | − | 0.999996i | \(-0.500927\pi\) | ||||
−0.00291310 | + | 0.999996i | \(0.500927\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.25544 | 0.0565421 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.76631 | −0.438079 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.2594 | 1.13077 | 0.565383 | − | 0.824828i | \(-0.308728\pi\) | ||||
0.565383 | + | 0.824828i | \(0.308728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.4845 | −0.467479 | −0.233740 | − | 0.972299i | \(-0.575096\pi\) | ||||
−0.233740 | + | 0.972299i | \(0.575096\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.8614 | −1.59581 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.3505 | 0.591752 | 0.295876 | − | 0.955226i | \(-0.404388\pi\) | ||||
0.295876 | + | 0.955226i | \(0.404388\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.2263 | 0.452384 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.24224 | 0.231000 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.1168 | −0.576878 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3505 | 0.716330 | 0.358165 | − | 0.933658i | \(-0.383403\pi\) | ||||
0.358165 | + | 0.933658i | \(0.383403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.3236 | −0.844963 | −0.422481 | − | 0.906372i | \(-0.638841\pi\) | ||||
−0.422481 | + | 0.906372i | \(0.638841\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.5823 | −1.41931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1168 | −0.787689 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.37228 | −0.189385 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.83915 | −0.382150 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.5652 | −0.541220 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.74456 | 0.375958 | 0.187979 | − | 0.982173i | \(-0.439806\pi\) | ||||
0.187979 | + | 0.982173i | \(0.439806\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.4891 | −1.77720 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.51622 | 0.0648291 | 0.0324145 | − | 0.999475i | \(-0.489680\pi\) | ||||
0.0324145 | + | 0.999475i | \(0.489680\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.38712 | 0.0590935 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.3505 | −0.907917 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.7446 | 0.794233 | 0.397116 | − | 0.917768i | \(-0.370011\pi\) | ||||
0.397116 | + | 0.917768i | \(0.370011\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.9530 | 1.09769 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.2270 | −0.936755 | −0.468377 | − | 0.883528i | \(-0.655161\pi\) | ||||
−0.468377 | + | 0.883528i | \(0.655161\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.5842 | 1.16048 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.7446 | 1.66618 | 0.833089 | − | 0.553138i | \(-0.186570\pi\) | ||||
0.833089 | + | 0.553138i | \(0.186570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.129100 | −0.00540267 | −0.00270134 | − | 0.999996i | \(-0.500860\pi\) | ||||
−0.00270134 | + | 0.999996i | \(0.500860\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.38712 | −0.0578471 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.1168 | 0.754214 | 0.377107 | − | 0.926170i | \(-0.376919\pi\) | ||||
0.377107 | + | 0.926170i | \(0.376919\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.1168 | 1.29094 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.7432 | 0.983342 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.7425 | 0.484665 | 0.242332 | − | 0.970193i | \(-0.422088\pi\) | ||||
0.242332 | + | 0.970193i | \(0.422088\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0000 | −1.48335 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.7228 | 0.727789 | 0.363894 | − | 0.931440i | \(-0.381447\pi\) | ||||
0.363894 | + | 0.931440i | \(0.381447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.6783 | 0.724739 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.3401 | 1.11709 | 0.558543 | − | 0.829476i | \(-0.311361\pi\) | ||||
0.558543 | + | 0.829476i | \(0.311361\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.76631 | −0.112840 | −0.0564201 | − | 0.998407i | \(-0.517969\pi\) | ||||
−0.0564201 | + | 0.998407i | \(0.517969\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −57.4891 | −2.33727 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.8246 | 1.53525 | 0.767626 | − | 0.640898i | \(-0.221438\pi\) | ||||
0.767626 | + | 0.640898i | \(0.221438\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.66181 | −0.390875 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.4674 | 1.47290 | 0.736452 | − | 0.676490i | \(-0.236500\pi\) | ||||
0.736452 | + | 0.676490i | \(0.236500\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 37.7446 | 1.51954 | 0.759769 | − | 0.650193i | \(-0.225312\pi\) | ||||
0.759769 | + | 0.650193i | \(0.225312\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.51622 | 0.0609422 | 0.0304711 | − | 0.999536i | \(-0.490299\pi\) | ||||
0.0304711 | + | 0.999536i | \(0.490299\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.77425 | −0.111148 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.7446 | −1.10978 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.4891 | −0.537847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.6783 | −0.701542 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.25544 | −0.366714 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.7446 | −0.542878 | −0.271439 | − | 0.962456i | \(-0.587499\pi\) | ||||
−0.271439 | + | 0.962456i | \(0.587499\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.8074 | −0.702255 | −0.351127 | − | 0.936328i | \(-0.614202\pi\) | ||||
−0.351127 | + | 0.936328i | \(0.614202\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.0344 | 1.57391 | 0.786956 | − | 0.617009i | \(-0.211656\pi\) | ||||
0.786956 | + | 0.617009i | \(0.211656\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −61.4674 | −2.41281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.1168 | −1.60903 | −0.804513 | − | 0.593935i | \(-0.797574\pi\) | ||||
−0.804513 | + | 0.593935i | \(0.797574\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.9205 | −0.895579 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.7597 | −1.23718 | −0.618591 | − | 0.785713i | \(-0.712296\pi\) | ||||
−0.618591 | + | 0.785713i | \(0.712296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.11684 | −0.121231 | −0.0606156 | − | 0.998161i | \(-0.519306\pi\) | ||||
−0.0606156 | + | 0.998161i | \(0.519306\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.5326 | 0.757443 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.822662 | 0.0318536 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 89.7305 | 3.46401 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3505 | 0.900097 | 0.450048 | − | 0.893004i | \(-0.351407\pi\) | ||||
0.450048 | + | 0.893004i | \(0.351407\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.35053 | −0.0519052 | −0.0259526 | − | 0.999663i | \(-0.508262\pi\) | ||||
−0.0259526 | + | 0.999663i | \(0.508262\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.8881 | 0.763234 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.3083 | 1.38930 | 0.694650 | − | 0.719348i | \(-0.255559\pi\) | ||||
0.694650 | + | 0.719348i | \(0.255559\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.6277 | −1.13202 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17.4891 | 0.666283 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.6637 | −1.77517 | −0.887586 | − | 0.460643i | \(-0.847619\pi\) | ||||
−0.887586 | + | 0.460643i | \(0.847619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.88756 | −0.261260 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.37228 | 0.127734 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.7446 | −1.31228 | −0.656142 | − | 0.754637i | \(-0.727813\pi\) | ||||
−0.656142 | + | 0.754637i | \(0.727813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.9040 | −0.562117 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33.4050 | 1.25632 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.6060 | −0.473427 | −0.236714 | − | 0.971579i | \(-0.576070\pi\) | ||||
−0.236714 | + | 0.971579i | \(0.576070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.3505 | −0.799584 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −61.5678 | −2.30250 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.5823 | 1.21512 | 0.607558 | − | 0.794275i | \(-0.292149\pi\) | ||||
0.607558 | + | 0.794275i | \(0.292149\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.88316 | −0.181858 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.233688 | −0.00867895 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.7921 | −1.29037 | −0.645184 | − | 0.764027i | \(-0.723219\pi\) | ||||
−0.645184 | + | 0.764027i | \(0.723219\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.0172 | −0.740362 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.8832 | 0.845209 | 0.422604 | − | 0.906314i | \(-0.361116\pi\) | ||||
0.422604 | + | 0.906314i | \(0.361116\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −61.4674 | −2.26418 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.5976 | 0.573767 | 0.286884 | − | 0.957965i | \(-0.407381\pi\) | ||||
0.286884 | + | 0.957965i | \(0.407381\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.5983 | −1.01248 | −0.506242 | − | 0.862392i | \(-0.668966\pi\) | ||||
−0.506242 | + | 0.862392i | \(0.668966\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.5842 | −1.01061 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.23369 | 0.300852 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.9205 | 0.836382 | 0.418191 | − | 0.908359i | \(-0.362664\pi\) | ||||
0.418191 | + | 0.908359i | \(0.362664\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.24224 | 0.190784 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.4674 | −1.25274 | −0.626369 | − | 0.779527i | \(-0.715460\pi\) | ||||
−0.626369 | + | 0.779527i | \(0.715460\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.3723 | −0.738495 | −0.369247 | − | 0.929331i | \(-0.620384\pi\) | ||||
−0.369247 | + | 0.929331i | \(0.620384\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.6472 | 1.39912 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45.2766 | −1.63484 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.8832 | −0.536700 | −0.268350 | − | 0.963321i | \(-0.586478\pi\) | ||||
−0.268350 | + | 0.963321i | \(0.586478\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.7446 | 0.674195 | 0.337098 | − | 0.941470i | \(-0.390555\pi\) | ||||
0.337098 | + | 0.941470i | \(0.390555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.06490 | 0.217858 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.72601 | 0.133498 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.2337 | −0.938715 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.39403 | 0.263904 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.2441 | −1.50584 | −0.752921 | − | 0.658111i | \(-0.771356\pi\) | ||||
−0.752921 | + | 0.658111i | \(0.771356\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.6948 | −0.913601 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66.0951 | 2.34711 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −46.0951 | −1.63277 | −0.816386 | − | 0.577507i | \(-0.804026\pi\) | ||||
−0.816386 | + | 0.577507i | \(0.804026\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.45202 | 0.263634 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.4692 | 0.969367 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.5842 | 0.408290 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.6277 | 0.443967 | 0.221983 | − | 0.975050i | \(-0.428747\pi\) | ||||
0.221983 | + | 0.975050i | \(0.428747\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.5341 | 1.17754 | 0.588771 | − | 0.808300i | \(-0.299612\pi\) | ||||
0.588771 | + | 0.808300i | \(0.299612\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.9689 | −0.734510 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.1168 | −0.773770 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.37228 | −0.292195 | −0.146097 | − | 0.989270i | \(-0.546671\pi\) | ||||
−0.146097 | + | 0.989270i | \(0.546671\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.9205 | −0.798959 | −0.399480 | − | 0.916742i | \(-0.630809\pi\) | ||||
−0.399480 | + | 0.916742i | \(0.630809\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.83915 | −0.307367 | −0.153684 | − | 0.988120i | \(-0.549114\pi\) | ||||
−0.153684 | + | 0.988120i | \(0.549114\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.23369 | −0.285968 | −0.142984 | − | 0.989725i | \(-0.545670\pi\) | ||||
−0.142984 | + | 0.989725i | \(0.545670\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.13859 | 0.247338 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.9205 | −0.793198 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.66181 | −0.333563 | −0.166781 | − | 0.985994i | \(-0.553337\pi\) | ||||
−0.166781 | + | 0.985994i | \(0.553337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8614 | −0.995221 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.5109 | −0.499189 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 53.5513 | 1.84004 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.83915 | −0.303002 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.1168 | −0.723027 | −0.361513 | − | 0.932367i | \(-0.617740\pi\) | ||||
−0.361513 | + | 0.932367i | \(0.617740\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.0951 | 1.50626 | 0.753130 | − | 0.657872i | \(-0.228543\pi\) | ||||
0.753130 | + | 0.657872i | \(0.228543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.8074 | −0.607580 | −0.303790 | − | 0.952739i | \(-0.598252\pi\) | ||||
−0.303790 | + | 0.952739i | \(0.598252\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.6783 | −0.601776 | −0.300888 | − | 0.953659i | \(-0.597283\pi\) | ||||
−0.300888 | + | 0.953659i | \(0.597283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.883156 | −0.0300282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −57.3505 | −1.94548 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.2766 | −1.53414 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.9205 | 0.774855 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.3505 | −0.450815 | −0.225408 | − | 0.974265i | \(-0.572371\pi\) | ||||
−0.225408 | + | 0.974265i | \(0.572371\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.23369 | −0.142637 | −0.0713183 | − | 0.997454i | \(-0.522721\pi\) | ||||
−0.0713183 | + | 0.997454i | \(0.522721\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.4043 | 0.720312 | 0.360156 | − | 0.932892i | \(-0.382723\pi\) | ||||
0.360156 | + | 0.932892i | \(0.382723\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.9205 | 0.769596 | 0.384798 | − | 0.923001i | \(-0.374271\pi\) | ||||
0.384798 | + | 0.923001i | \(0.374271\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.4674 | 0.552298 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.23369 | 0.275530 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.9689 | 0.700914 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.59691 | −0.119964 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.4891 | −0.449388 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.5326 | 0.649286 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.2919 | 0.939416 | 0.469708 | − | 0.882822i | \(-0.344359\pi\) | ||||
0.469708 | + | 0.882822i | \(0.344359\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.7286 | −1.74698 | −0.873488 | − | 0.486845i | \(-0.838148\pi\) | ||||
−0.873488 | + | 0.486845i | \(0.838148\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 83.5842 | 2.76623 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.3505 | 0.705057 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.1303 | −0.828973 | −0.414486 | − | 0.910056i | \(-0.636039\pi\) | ||||
−0.414486 | + | 0.910056i | \(0.636039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19.3236 | −0.636045 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.51087 | 0.0825571 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.3723 | −1.19334 | −0.596668 | − | 0.802488i | \(-0.703509\pi\) | ||||
−0.596668 | + | 0.802488i | \(0.703509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.88738 | 0.258499 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 47.4864 | 1.55297 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.2337 | 0.399657 | 0.199829 | − | 0.979831i | \(-0.435961\pi\) | ||||
0.199829 | + | 0.979831i | \(0.435961\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.0951 | 1.50266 | 0.751329 | − | 0.659928i | \(-0.229413\pi\) | ||||
0.751329 | + | 0.659928i | \(0.229413\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.20979 | 0.0719605 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.0986 | −1.10805 | −0.554027 | − | 0.832499i | \(-0.686910\pi\) | ||||
−0.554027 | + | 0.832499i | \(0.686910\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.2337 | 0.656813 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.6060 | 1.02382 | 0.511909 | − | 0.859040i | \(-0.328939\pi\) | ||||
0.511909 | + | 0.859040i | \(0.328939\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.5988 | 1.31375 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27.5983 | 0.891196 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.3505 | 2.01131 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.37228 | −0.0763664 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.5983 | −0.887501 | −0.443751 | − | 0.896150i | \(-0.646352\pi\) | ||||
−0.443751 | + | 0.896150i | \(0.646352\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −49.1317 | −1.57671 | −0.788356 | − | 0.615220i | \(-0.789067\pi\) | ||||
−0.788356 | + | 0.615220i | \(0.789067\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.41578 | 0.205680 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.7663 | −0.344445 | −0.172222 | − | 0.985058i | \(-0.555095\pi\) | ||||
−0.172222 | + | 0.985058i | \(0.555095\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.45202 | −0.238168 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.5988 | −1.29490 | −0.647451 | − | 0.762107i | \(-0.724165\pi\) | ||||
−0.647451 | + | 0.762107i | \(0.724165\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.76631 | 0.0562794 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.1168 | −0.417091 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.4864 | −1.50845 | −0.754227 | − | 0.656613i | \(-0.771988\pi\) | ||||
−0.754227 | + | 0.656613i | \(0.771988\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49.1317 | −1.55758 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.3505 | 1.30958 | 0.654792 | − | 0.755809i | \(-0.272756\pi\) | ||||
0.654792 | + | 0.755809i | \(0.272756\pi\) | |||||||
\(998\) | 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 | 2592.2.a.x.1.2 | 4 | ||
3.2 | odd | 2 | 2592.2.a.u.1.4 | 4 | |||
4.3 | odd | 2 | inner | 2592.2.a.x.1.1 | 4 | ||
8.3 | odd | 2 | 5184.2.a.cc.1.3 | 4 | |||
8.5 | even | 2 | 5184.2.a.cc.1.4 | 4 | |||
9.2 | odd | 6 | 288.2.i.f.193.1 | yes | 8 | ||
9.4 | even | 3 | 864.2.i.f.289.3 | 8 | |||
9.5 | odd | 6 | 288.2.i.f.97.1 | ✓ | 8 | ||
9.7 | even | 3 | 864.2.i.f.577.3 | 8 | |||
12.11 | even | 2 | 2592.2.a.u.1.3 | 4 | |||
24.5 | odd | 2 | 5184.2.a.cf.1.2 | 4 | |||
24.11 | even | 2 | 5184.2.a.cf.1.1 | 4 | |||
36.7 | odd | 6 | 864.2.i.f.577.4 | 8 | |||
36.11 | even | 6 | 288.2.i.f.193.4 | yes | 8 | ||
36.23 | even | 6 | 288.2.i.f.97.4 | yes | 8 | ||
36.31 | odd | 6 | 864.2.i.f.289.4 | 8 | |||
72.5 | odd | 6 | 576.2.i.n.385.4 | 8 | |||
72.11 | even | 6 | 576.2.i.n.193.1 | 8 | |||
72.13 | even | 6 | 1728.2.i.n.1153.1 | 8 | |||
72.29 | odd | 6 | 576.2.i.n.193.4 | 8 | |||
72.43 | odd | 6 | 1728.2.i.n.577.2 | 8 | |||
72.59 | even | 6 | 576.2.i.n.385.1 | 8 | |||
72.61 | even | 6 | 1728.2.i.n.577.1 | 8 | |||
72.67 | odd | 6 | 1728.2.i.n.1153.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.f.97.1 | ✓ | 8 | 9.5 | odd | 6 | ||
288.2.i.f.97.4 | yes | 8 | 36.23 | even | 6 | ||
288.2.i.f.193.1 | yes | 8 | 9.2 | odd | 6 | ||
288.2.i.f.193.4 | yes | 8 | 36.11 | even | 6 | ||
576.2.i.n.193.1 | 8 | 72.11 | even | 6 | |||
576.2.i.n.193.4 | 8 | 72.29 | odd | 6 | |||
576.2.i.n.385.1 | 8 | 72.59 | even | 6 | |||
576.2.i.n.385.4 | 8 | 72.5 | odd | 6 | |||
864.2.i.f.289.3 | 8 | 9.4 | even | 3 | |||
864.2.i.f.289.4 | 8 | 36.31 | odd | 6 | |||
864.2.i.f.577.3 | 8 | 9.7 | even | 3 | |||
864.2.i.f.577.4 | 8 | 36.7 | odd | 6 | |||
1728.2.i.n.577.1 | 8 | 72.61 | even | 6 | |||
1728.2.i.n.577.2 | 8 | 72.43 | odd | 6 | |||
1728.2.i.n.1153.1 | 8 | 72.13 | even | 6 | |||
1728.2.i.n.1153.2 | 8 | 72.67 | odd | 6 | |||
2592.2.a.u.1.3 | 4 | 12.11 | even | 2 | |||
2592.2.a.u.1.4 | 4 | 3.2 | odd | 2 | |||
2592.2.a.x.1.1 | 4 | 4.3 | odd | 2 | inner | ||
2592.2.a.x.1.2 | 4 | 1.1 | even | 1 | trivial | ||
5184.2.a.cc.1.3 | 4 | 8.3 | odd | 2 | |||
5184.2.a.cc.1.4 | 4 | 8.5 | even | 2 | |||
5184.2.a.cf.1.1 | 4 | 24.11 | even | 2 | |||
5184.2.a.cf.1.2 | 4 | 24.5 | odd | 2 |