Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | ||||||||
\(3\) | −0.478839 | −0.276458 | −0.138229 | − | 0.990400i | \(-0.544141\pi\) | ||||
−0.138229 | + | 0.990400i | \(0.544141\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.59155 | 0.601550 | 0.300775 | − | 0.953695i | \(-0.402755\pi\) | ||||
0.300775 | + | 0.953695i | \(0.402755\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.77071 | −0.923571 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.51847 | −1.96539 | −0.982697 | − | 0.185221i | \(-0.940700\pi\) | ||||
−0.982697 | + | 0.185221i | \(0.940700\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.37511 | −0.936086 | −0.468043 | − | 0.883706i | \(-0.655041\pi\) | ||||
−0.468043 | + | 0.883706i | \(0.655041\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.478839 | 0.123636 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.23762 | −0.785237 | −0.392619 | − | 0.919701i | \(-0.628431\pi\) | ||||
−0.392619 | + | 0.919701i | \(0.628431\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.00948756 | −0.00217660 | −0.00108830 | − | 0.999999i | \(-0.500346\pi\) | ||||
−0.00108830 | + | 0.999999i | \(0.500346\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.762097 | −0.166303 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.46543 | 1.76516 | 0.882582 | − | 0.470158i | \(-0.155803\pi\) | ||||
0.882582 | + | 0.470158i | \(0.155803\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.76324 | 0.531787 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.667812 | 0.124010 | 0.0620048 | − | 0.998076i | \(-0.480251\pi\) | ||||
0.0620048 | + | 0.998076i | \(0.480251\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.17937 | −0.391426 | −0.195713 | − | 0.980661i | \(-0.562702\pi\) | ||||
−0.195713 | + | 0.980661i | \(0.562702\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.12130 | 0.543349 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.59155 | −0.269021 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.25603 | −1.52168 | −0.760841 | − | 0.648938i | \(-0.775213\pi\) | ||||
−0.760841 | + | 0.648938i | \(0.775213\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.61613 | 0.258789 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.04803 | −0.788369 | −0.394185 | − | 0.919031i | \(-0.628973\pi\) | ||||
−0.394185 | + | 0.919031i | \(0.628973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.75194 | −0.877163 | −0.438582 | − | 0.898691i | \(-0.644519\pi\) | ||||
−0.438582 | + | 0.898691i | \(0.644519\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.77071 | 0.413033 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.87332 | 0.564982 | 0.282491 | − | 0.959270i | \(-0.408839\pi\) | ||||
0.282491 | + | 0.959270i | \(0.408839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.46697 | −0.638138 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.55030 | 0.217085 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.05072 | 0.419049 | 0.209525 | − | 0.977803i | \(-0.432808\pi\) | ||||
0.209525 | + | 0.977803i | \(0.432808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.51847 | 0.878951 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.00454302 | 0.000601738 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.2701 | −1.33705 | −0.668524 | − | 0.743690i | \(-0.733074\pi\) | ||||
−0.668524 | + | 0.743690i | \(0.733074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.0510 | −1.67101 | −0.835505 | − | 0.549483i | \(-0.814825\pi\) | ||||
−0.835505 | + | 0.549483i | \(0.814825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.40973 | −0.555574 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.37511 | 0.418630 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.12502 | 0.259612 | 0.129806 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129806 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.05358 | −0.487994 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.04241 | 0.361067 | 0.180534 | − | 0.983569i | \(-0.442218\pi\) | ||||
0.180534 | + | 0.983569i | \(0.442218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.95988 | 0.229387 | 0.114693 | − | 0.993401i | \(-0.463411\pi\) | ||||
0.114693 | + | 0.993401i | \(0.463411\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.478839 | −0.0552916 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.3745 | −1.18228 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.09588 | 0.910857 | 0.455429 | − | 0.890272i | \(-0.349486\pi\) | ||||
0.455429 | + | 0.890272i | \(0.349486\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.98899 | 0.776554 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.98216 | −0.217570 | −0.108785 | − | 0.994065i | \(-0.534696\pi\) | ||||
−0.108785 | + | 0.994065i | \(0.534696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.23762 | 0.351169 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.319775 | −0.0342835 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.89121 | −1.04847 | −0.524233 | − | 0.851575i | \(-0.675648\pi\) | ||||
−0.524233 | + | 0.851575i | \(0.675648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.37165 | −0.563102 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.04357 | 0.108213 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.00948756 | 0.000973403 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.02485 | 0.307127 | 0.153564 | − | 0.988139i | \(-0.450925\pi\) | ||||
0.153564 | + | 0.988139i | \(0.450925\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.0608 | 1.81518 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.6742 | −1.16162 | −0.580812 | − | 0.814038i | \(-0.697265\pi\) | ||||
−0.580812 | + | 0.814038i | \(0.697265\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.03823 | −0.792031 | −0.396015 | − | 0.918244i | \(-0.629607\pi\) | ||||
−0.396015 | + | 0.918244i | \(0.629607\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.762097 | 0.0743731 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.8919 | 1.92302 | 0.961511 | − | 0.274766i | \(-0.0886004\pi\) | ||||
0.961511 | + | 0.274766i | \(0.0886004\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5363 | 1.29654 | 0.648270 | − | 0.761410i | \(-0.275493\pi\) | ||||
0.648270 | + | 0.761410i | \(0.275493\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.43215 | 0.420681 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.38594 | 0.694810 | 0.347405 | − | 0.937715i | \(-0.387063\pi\) | ||||
0.347405 | + | 0.937715i | \(0.387063\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.46543 | −0.789405 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.35145 | 0.864542 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.15283 | −0.472359 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.4905 | 2.86277 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.41719 | 0.217951 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.93979 | 0.172128 | 0.0860642 | − | 0.996290i | \(-0.472571\pi\) | ||||
0.0860642 | + | 0.996290i | \(0.472571\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.75426 | 0.242499 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.2579 | −1.07098 | −0.535490 | − | 0.844541i | \(-0.679873\pi\) | ||||
−0.535490 | + | 0.844541i | \(0.679873\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0150999 | −0.00130933 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.76324 | −0.237822 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.3710 | 1.05693 | 0.528463 | − | 0.848956i | \(-0.322768\pi\) | ||||
0.528463 | + | 0.848956i | \(0.322768\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.21075 | 0.187513 | 0.0937565 | − | 0.995595i | \(-0.470112\pi\) | ||||
0.0937565 | + | 0.995595i | \(0.470112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.85470 | −0.156194 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.0005 | 1.83978 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.667812 | −0.0554588 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.13896 | 0.176418 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.91615 | 0.238900 | 0.119450 | − | 0.992840i | \(-0.461887\pi\) | ||||
0.119450 | + | 0.992840i | \(0.461887\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.1186 | −1.71861 | −0.859303 | − | 0.511466i | \(-0.829102\pi\) | ||||
−0.859303 | + | 0.511466i | \(0.829102\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.97050 | 0.725222 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.17937 | 0.175051 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3435 | −0.905314 | −0.452657 | − | 0.891685i | \(-0.649524\pi\) | ||||
−0.452657 | + | 0.891685i | \(0.649524\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.46081 | −0.115849 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.4732 | 1.06183 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0049 | 1.09695 | 0.548473 | − | 0.836168i | \(-0.315209\pi\) | ||||
0.548473 | + | 0.836168i | \(0.315209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.12130 | −0.242993 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.315144 | 0.0243866 | 0.0121933 | − | 0.999926i | \(-0.496119\pi\) | ||||
0.0121933 | + | 0.999926i | \(0.496119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.60865 | −0.123743 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0262873 | 0.00201024 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.9627 | 1.36568 | 0.682840 | − | 0.730568i | \(-0.260744\pi\) | ||||
0.682840 | + | 0.730568i | \(0.260744\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.59155 | 0.120310 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.91771 | 0.369638 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.5698 | −0.939514 | −0.469757 | − | 0.882796i | \(-0.655659\pi\) | ||||
−0.469757 | + | 0.882796i | \(0.655659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.08922 | 0.526938 | 0.263469 | − | 0.964668i | \(-0.415133\pi\) | ||||
0.263469 | + | 0.964668i | \(0.415133\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.24934 | 0.461964 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.25603 | 0.680517 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.1043 | 1.54330 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.39784 | 0.319896 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9385 | 1.22563 | 0.612815 | − | 0.790227i | \(-0.290037\pi\) | ||||
0.612815 | + | 0.790227i | \(0.290037\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.43727 | 0.319402 | 0.159701 | − | 0.987165i | \(-0.448947\pi\) | ||||
0.159701 | + | 0.987165i | \(0.448947\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.61613 | −0.115734 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.0520 | −1.42864 | −0.714321 | − | 0.699818i | \(-0.753265\pi\) | ||||
−0.714321 | + | 0.699818i | \(0.753265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0566 | 1.70532 | 0.852662 | − | 0.522463i | \(-0.174987\pi\) | ||||
0.852662 | + | 0.522463i | \(0.174987\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.01754 | −0.0717720 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.06286 | 0.0745980 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.04803 | 0.352569 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −23.4553 | −1.63025 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0618444 | 0.00427787 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.6275 | 1.83311 | 0.916555 | − | 0.399908i | \(-0.130958\pi\) | ||||
0.916555 | + | 0.399908i | \(0.130958\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.45683 | −0.0998200 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.75194 | 0.392279 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.46858 | −0.235462 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.938469 | −0.0634158 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.9273 | 0.735050 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5388 | 0.839661 | 0.419831 | − | 0.907602i | \(-0.362089\pi\) | ||||
0.419831 | + | 0.907602i | \(0.362089\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.77071 | −0.184714 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.9761 | 0.861257 | 0.430628 | − | 0.902529i | \(-0.358292\pi\) | ||||
0.430628 | + | 0.902529i | \(0.358292\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.8603 | −1.70890 | −0.854448 | − | 0.519537i | \(-0.826105\pi\) | ||||
−0.854448 | + | 0.519537i | \(0.826105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.96771 | 0.326851 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.6146 | 1.21948 | 0.609741 | − | 0.792601i | \(-0.291274\pi\) | ||||
0.609741 | + | 0.792601i | \(0.291274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.87332 | −0.252668 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.87663 | −0.251814 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.5495 | −0.811762 | −0.405881 | − | 0.913926i | \(-0.633035\pi\) | ||||
−0.405881 | + | 0.913926i | \(0.633035\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.8773 | 1.02275 | 0.511374 | − | 0.859358i | \(-0.329137\pi\) | ||||
0.511374 | + | 0.859358i | \(0.329137\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.6363 | −0.746471 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.46697 | 0.285384 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0320215 | 0.00203748 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.949135 | 0.0601490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23.9721 | 1.51311 | 0.756554 | − | 0.653931i | \(-0.226881\pi\) | ||||
0.756554 | + | 0.653931i | \(0.226881\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −55.1817 | −3.46924 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.55030 | −0.0970834 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.06832 | 0.316153 | 0.158077 | − | 0.987427i | \(-0.449471\pi\) | ||||
0.158077 | + | 0.987427i | \(0.449471\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.7314 | −0.915367 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.85032 | −0.114532 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.2226 | −0.692016 | −0.346008 | − | 0.938232i | \(-0.612463\pi\) | ||||
−0.346008 | + | 0.938232i | \(0.612463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.05072 | −0.187404 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.73630 | 0.289857 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.0188 | 0.671826 | 0.335913 | − | 0.941893i | \(-0.390955\pi\) | ||||
0.335913 | + | 0.941893i | \(0.390955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.62774 | −0.159624 | −0.0798120 | − | 0.996810i | \(-0.525432\pi\) | ||||
−0.0798120 | + | 0.996810i | \(0.525432\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.57216 | 0.155674 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.51847 | −0.393079 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.3754 | 1.28433 | 0.642163 | − | 0.766569i | \(-0.278037\pi\) | ||||
0.642163 | + | 0.766569i | \(0.278037\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.03841 | 0.361510 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.70369 | 0.578873 | 0.289437 | − | 0.957197i | \(-0.406532\pi\) | ||||
0.289437 | + | 0.957197i | \(0.406532\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.1599 | −1.25783 | −0.628914 | − | 0.777475i | \(-0.716500\pi\) | ||||
−0.628914 | + | 0.777475i | \(0.716500\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.00454302 | −0.000269105 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.03419 | −0.474243 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.51785 | −0.383403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.44842 | −0.0849078 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −22.1188 | −1.29219 | −0.646096 | − | 0.763256i | \(-0.723599\pi\) | ||||
−0.646096 | + | 0.763256i | \(0.723599\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2701 | 0.597946 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.0121 | −1.04517 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −28.5717 | −1.65235 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.15451 | −0.527657 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.59006 | 0.321140 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.0510 | 0.747298 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.5312 | −0.829340 | −0.414670 | − | 0.909972i | \(-0.636103\pi\) | ||||
−0.414670 | + | 0.909972i | \(0.636103\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.84902 | 0.218963 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.7278 | −1.00525 | −0.502625 | − | 0.864505i | \(-0.667632\pi\) | ||||
−0.502625 | + | 0.864505i | \(0.667632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.5951 | 1.44672 | 0.723360 | − | 0.690471i | \(-0.242597\pi\) | ||||
0.723360 | + | 0.690471i | \(0.242597\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.40973 | 0.248460 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.4433 | 0.923546 | 0.461773 | − | 0.886998i | \(-0.347213\pi\) | ||||
0.461773 | + | 0.886998i | \(0.347213\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.35312 | −0.243728 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.52502 | −0.531635 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0307171 | 0.00170914 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.37511 | −0.187217 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.48171 | −0.358439 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.16459 | 0.339865 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.06819 | −0.388503 | −0.194251 | − | 0.980952i | \(-0.562228\pi\) | ||||
−0.194251 | + | 0.980952i | \(0.562228\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.6458 | 1.40538 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.12502 | −0.116102 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.49664 | −0.0815274 | −0.0407637 | − | 0.999169i | \(-0.512979\pi\) | ||||
−0.0407637 | + | 0.999169i | \(0.512979\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.53668 | −0.192086 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.2062 | 0.769307 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.2503 | −0.985421 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.05358 | 0.218238 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.1701 | 1.08279 | 0.541395 | − | 0.840768i | \(-0.317896\pi\) | ||||
0.541395 | + | 0.840768i | \(0.317896\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.25271 | −0.0670563 | −0.0335281 | − | 0.999438i | \(-0.510674\pi\) | ||||
−0.0335281 | + | 0.999438i | \(0.510674\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.32625 | −0.497798 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.07028 | 0.0569654 | 0.0284827 | − | 0.999594i | \(-0.490932\pi\) | ||||
0.0284827 | + | 0.999594i | \(0.490932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.04241 | −0.161474 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.46738 | 0.130587 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.35021 | −0.387929 | −0.193965 | − | 0.981009i | \(-0.562135\pi\) | ||||
−0.193965 | + | 0.981009i | \(0.562135\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9999 | −0.999995 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.0789 | −0.791437 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.95988 | −0.102585 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.5066 | −1.69683 | −0.848417 | − | 0.529329i | \(-0.822444\pi\) | ||||
−0.848417 | + | 0.529329i | \(0.822444\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.9866 | 0.728115 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.85538 | 0.252079 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.5269 | −0.855729 | −0.427864 | − | 0.903843i | \(-0.640734\pi\) | ||||
−0.427864 | + | 0.903843i | \(0.640734\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.478839 | 0.0247272 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.25394 | −0.116084 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.95294 | −0.408515 | −0.204258 | − | 0.978917i | \(-0.565478\pi\) | ||||
−0.204258 | + | 0.978917i | \(0.565478\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.928848 | −0.0475863 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.3368 | 1.80563 | 0.902813 | − | 0.430033i | \(-0.141498\pi\) | ||||
0.902813 | + | 0.430033i | \(0.141498\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.3745 | 0.528733 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.9370 | 0.810122 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.32277 | −0.269875 | −0.134937 | − | 0.990854i | \(-0.543083\pi\) | ||||
−0.134937 | + | 0.990854i | \(0.543083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.4078 | −1.38607 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.86958 | 0.296081 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.09588 | −0.407348 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.276063 | −0.0138552 | −0.00692761 | − | 0.999976i | \(-0.502205\pi\) | ||||
−0.00692761 | + | 0.999976i | \(0.502205\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.00723044 | 0.000361975 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.35561 | 0.366409 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.98899 | −0.347286 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 60.3352 | 2.99070 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.42243 | 0.465909 | 0.232955 | − | 0.972488i | \(-0.425161\pi\) | ||||
0.232955 | + | 0.972488i | \(0.425161\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.92373 | −0.292196 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.3453 | −0.804301 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.98216 | 0.0973002 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.05859 | −0.0518395 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.3124 | −0.943473 | −0.471737 | − | 0.881739i | \(-0.656373\pi\) | ||||
−0.471737 | + | 0.881739i | \(0.656373\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.8066 | 1.55016 | 0.775079 | − | 0.631865i | \(-0.217710\pi\) | ||||
0.775079 | + | 0.631865i | \(0.217710\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.7319 | −0.521801 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.23762 | −0.157047 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.7713 | −1.00520 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.5347 | −0.508621 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.3343 | 1.12398 | 0.561988 | − | 0.827145i | \(-0.310037\pi\) | ||||
0.561988 | + | 0.827145i | \(0.310037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.3387 | −1.74632 | −0.873162 | − | 0.487429i | \(-0.837935\pi\) | ||||
−0.873162 | + | 0.487429i | \(0.837935\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.319775 | 0.0153320 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.0803163 | −0.00384205 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.5069 | −1.02647 | −0.513234 | − | 0.858249i | \(-0.671553\pi\) | ||||
−0.513234 | + | 0.858249i | \(0.671553\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.3767 | 0.589366 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.38206 | −0.303221 | −0.151610 | − | 0.988440i | \(-0.548446\pi\) | ||||
−0.151610 | + | 0.988440i | \(0.548446\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.89121 | 0.468888 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.39637 | −0.0660459 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.6905 | 0.693288 | 0.346644 | − | 0.937997i | \(-0.387321\pi\) | ||||
0.346644 | + | 0.937997i | \(0.387321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.9054 | 1.54946 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.1124 | 0.475123 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.37165 | 0.251827 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.1232 | −0.473544 | −0.236772 | − | 0.971565i | \(-0.576089\pi\) | ||||
−0.236772 | + | 0.971565i | \(0.576089\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.94632 | −0.417579 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.3021 | 1.55103 | 0.775516 | − | 0.631328i | \(-0.217490\pi\) | ||||
0.775516 | + | 0.631328i | \(0.217490\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.3006 | 1.50113 | 0.750567 | − | 0.660794i | \(-0.229780\pi\) | ||||
0.750567 | + | 0.660794i | \(0.229780\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.04357 | −0.0483943 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.2767 | 1.67869 | 0.839343 | − | 0.543602i | \(-0.182940\pi\) | ||||
0.839343 | + | 0.543602i | \(0.182940\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.38208 | 0.156170 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.43174 | 0.250281 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.4939 | 1.72397 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.00948756 | −0.000435319 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.45268 | −0.387022 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.42794 | 0.202318 | 0.101159 | − | 0.994870i | \(-0.467745\pi\) | ||||
0.101159 | + | 0.994870i | \(0.467745\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.2401 | 1.42443 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.45148 | −0.293553 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.02485 | −0.137351 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1553 | 0.732066 | 0.366033 | − | 0.930602i | \(-0.380716\pi\) | ||||
0.366033 | + | 0.930602i | \(0.380716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.70609 | −0.303260 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.4388 | 1.28343 | 0.641713 | − | 0.766945i | \(-0.278224\pi\) | ||||
0.641713 | + | 0.766945i | \(0.278224\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.16212 | −0.0973770 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.0608 | −0.811773 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.84215 | 0.217200 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −41.8276 | −1.87246 | −0.936231 | − | 0.351385i | \(-0.885711\pi\) | ||||
−0.936231 | + | 0.351385i | \(0.885711\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.150903 | −0.00674186 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.8979 | −0.708854 | −0.354427 | − | 0.935084i | \(-0.615324\pi\) | ||||
−0.354427 | + | 0.935084i | \(0.615324\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.6742 | 0.519494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.770287 | 0.0342097 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.5133 | 1.13086 | 0.565428 | − | 0.824798i | \(-0.308711\pi\) | ||||
0.565428 | + | 0.824798i | \(0.308711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.11925 | 0.137988 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0262165 | −0.00115748 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.03823 | 0.354207 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.2482 | −1.11041 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.60126 | −0.377554 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3889 | 0.761822 | 0.380911 | − | 0.924612i | \(-0.375610\pi\) | ||||
0.380911 | + | 0.924612i | \(0.375610\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.27388 | −0.0557031 | −0.0278516 | − | 0.999612i | \(-0.508867\pi\) | ||||
−0.0278516 | + | 0.999612i | \(0.508867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.762097 | −0.0332606 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.05596 | 0.307362 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.6635 | 2.11581 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.4554 | 1.23486 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.0376 | 0.737982 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.8919 | −0.860002 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.01894 | 0.259736 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.1178 | 1.25419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.532136 | −0.0228783 | −0.0114392 | − | 0.999935i | \(-0.503641\pi\) | ||||
−0.0114392 | + | 0.999935i | \(0.503641\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.39460 | −0.145676 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.5363 | −0.579831 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.1102 | 0.774335 | 0.387167 | − | 0.922009i | \(-0.373454\pi\) | ||||
0.387167 | + | 0.922009i | \(0.373454\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.1606 | 1.54330 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.00633591 | −0.000269919 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.8850 | 0.547926 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.43215 | −0.188134 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.4203 | −0.738124 | −0.369062 | − | 0.929405i | \(-0.620321\pi\) | ||||
−0.369062 | + | 0.929405i | \(0.620321\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.4134 | 0.821100 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.1056 | −0.426658 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.1757 | 1.52463 | 0.762313 | − | 0.647209i | \(-0.224064\pi\) | ||||
0.762313 | + | 0.647209i | \(0.224064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.38594 | −0.310729 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.1233 | 0.467136 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.3021 | 0.431886 | 0.215943 | − | 0.976406i | \(-0.430718\pi\) | ||||
0.215943 | + | 0.976406i | \(0.430718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.62701 | −0.319180 | −0.159590 | − | 0.987183i | \(-0.551017\pi\) | ||||
−0.159590 | + | 0.987183i | \(0.551017\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.11084 | −0.338835 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.46543 | 0.353033 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.9812 | −1.20650 | −0.603252 | − | 0.797551i | \(-0.706129\pi\) | ||||
−0.603252 | + | 0.797551i | \(0.706129\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.12474 | −0.0883012 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.15470 | −0.130879 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.8861 | −0.823596 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.35145 | −0.386635 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.7378 | 1.18613 | 0.593067 | − | 0.805153i | \(-0.297917\pi\) | ||||
0.593067 | + | 0.805153i | \(0.297917\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0206769 | 0.000851977 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.60167 | 0.394960 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.6436 | −1.42264 | −0.711321 | − | 0.702868i | \(-0.751903\pi\) | ||||
−0.711321 | + | 0.702868i | \(0.751903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.15283 | 0.211245 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.5192 | −0.471451 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.821286 | 0.0335568 | 0.0167784 | − | 0.999859i | \(-0.494659\pi\) | ||||
0.0167784 | + | 0.999859i | \(0.494659\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.98090 | 0.162384 | 0.0811921 | − | 0.996698i | \(-0.474127\pi\) | ||||
0.0811921 | + | 0.996698i | \(0.474127\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.88782 | −0.239771 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31.4905 | −1.28027 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.0648 | 0.692638 | 0.346319 | − | 0.938117i | \(-0.387432\pi\) | ||||
0.346319 | + | 0.938117i | \(0.387432\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.508938 | −0.0206232 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0729 | −0.528872 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.0452 | −0.930785 | −0.465393 | − | 0.885104i | \(-0.654087\pi\) | ||||
−0.465393 | + | 0.885104i | \(0.654087\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.41719 | −0.0974707 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.88644 | −0.357755 | −0.178877 | − | 0.983871i | \(-0.557247\pi\) | ||||
−0.178877 | + | 0.983871i | \(0.557247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.1230 | −0.447072 | −0.223536 | − | 0.974696i | \(-0.571760\pi\) | ||||
−0.223536 | + | 0.974696i | \(0.571760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 23.3921 | 0.938691 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.7424 | −0.630704 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0296135 | −0.00118265 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.9675 | 1.19488 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.7216 | −1.78034 | −0.890169 | − | 0.455631i | \(-0.849414\pi\) | ||||
−0.890169 | + | 0.455631i | \(0.849414\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.7503 | −0.506778 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.93979 | −0.0769782 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.0765 | 0.597352 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.42964 | −0.333471 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.3811 | 0.805006 | 0.402503 | − | 0.915419i | \(-0.368140\pi\) | ||||
0.402503 | + | 0.915419i | \(0.368140\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.3474 | −1.15735 | −0.578674 | − | 0.815559i | \(-0.696430\pi\) | ||||
−0.578674 | + | 0.815559i | \(0.696430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.75426 | −0.108449 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.25165 | 0.0492073 | 0.0246037 | − | 0.999697i | \(-0.492168\pi\) | ||||
0.0246037 | + | 0.999697i | \(0.492168\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 66.9451 | 2.62783 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.66089 | 0.0650955 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.3003 | 1.26401 | 0.632004 | − | 0.774965i | \(-0.282232\pi\) | ||||
0.632004 | + | 0.774965i | \(0.282232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.2579 | 0.478957 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.43027 | −0.211855 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.2366 | −1.29471 | −0.647357 | − | 0.762187i | \(-0.724126\pi\) | ||||
−0.647357 | + | 0.762187i | \(0.724126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.6990 | −0.416143 | −0.208072 | − | 0.978114i | \(-0.566719\pi\) | ||||
−0.208072 | + | 0.978114i | \(0.566719\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.23242 | −0.203210 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.0150999 | 0.000585550 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.65332 | 0.218897 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.00408 | −0.232131 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 85.0726 | 3.28419 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.79966 | 0.107919 | 0.0539596 | − | 0.998543i | \(-0.482816\pi\) | ||||
0.0539596 | + | 0.998543i | \(0.482816\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.76324 | 0.106357 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.7940 | −0.453279 | −0.226639 | − | 0.973979i | \(-0.572774\pi\) | ||||
−0.226639 | + | 0.973979i | \(0.572774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.81420 | 0.184752 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.21349 | −0.238101 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −45.2908 | −1.73300 | −0.866502 | − | 0.499174i | \(-0.833637\pi\) | ||||
−0.866502 | + | 0.499174i | \(0.833637\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.3710 | −0.472672 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.3829 | 0.472438 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.2965 | −0.392266 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.5846 | −0.668951 | −0.334476 | − | 0.942404i | \(-0.608559\pi\) | ||||
−0.334476 | + | 0.942404i | \(0.608559\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 28.7447 | 1.09192 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.21075 | −0.0838584 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.3436 | 0.619057 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.91339 | −0.337136 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.5026 | −0.661062 | −0.330531 | − | 0.943795i | \(-0.607228\pi\) | ||||
−0.330531 | + | 0.943795i | \(0.607228\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0878172 | 0.00331209 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.85470 | 0.0698521 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.5800 | −0.698775 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.7252 | 0.966128 | 0.483064 | − | 0.875585i | \(-0.339524\pi\) | ||||
0.483064 | + | 0.875585i | \(0.339524\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.4314 | −0.841241 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.4493 | −0.690932 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.0005 | −0.822774 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.00921 | 0.224418 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.7240 | 0.511818 | 0.255909 | − | 0.966701i | \(-0.417625\pi\) | ||||
0.255909 | + | 0.966701i | \(0.417625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.7933 | −0.476446 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.60269 | −0.282747 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.667812 | 0.0248019 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.8546 | −1.73774 | −0.868870 | − | 0.495041i | \(-0.835153\pi\) | ||||
−0.868870 | + | 0.495041i | \(0.835153\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.3950 | −0.570186 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.6226 | 0.688781 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.3702 | 0.604647 | 0.302324 | − | 0.953205i | \(-0.402238\pi\) | ||||
0.302324 | + | 0.953205i | \(0.402238\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.13896 | −0.0788967 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.8519 | −0.510241 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.25605 | −0.156561 | −0.0782806 | − | 0.996931i | \(-0.524943\pi\) | ||||
−0.0782806 | + | 0.996931i | \(0.524943\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0153332 | −0.000563278 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.9608 | 0.695605 | 0.347802 | − | 0.937568i | \(-0.386928\pi\) | ||||
0.347802 | + | 0.937568i | \(0.386928\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.91615 | −0.106839 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.49199 | 0.200941 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.6590 | 1.15679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.7461 | 1.08545 | 0.542724 | − | 0.839911i | \(-0.317393\pi\) | ||||
0.542724 | + | 0.839911i | \(0.317393\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.4788 | −0.418311 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.1186 | 0.768584 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.3794 | 1.61300 | 0.806499 | − | 0.591235i | \(-0.201360\pi\) | ||||
0.806499 | + | 0.591235i | \(0.201360\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 26.4232 | 0.959100 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.37209 | −0.267238 | −0.133619 | − | 0.991033i | \(-0.542660\pi\) | ||||
−0.133619 | + | 0.991033i | \(0.542660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.5437 | 0.779934 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.97050 | −0.324329 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.6626 | 1.25159 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.3210 | 1.70644 | 0.853219 | − | 0.521553i | \(-0.174647\pi\) | ||||
0.853219 | + | 0.521553i | \(0.174647\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.42691 | −0.0874031 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.2867 | −1.23321 | −0.616604 | − | 0.787274i | \(-0.711492\pi\) | ||||
−0.616604 | + | 0.787274i | \(0.711492\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.17937 | −0.0782853 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.05400 | 0.253061 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0478935 | 0.00171596 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.8319 | −0.709640 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.84533 | 0.0659467 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.3435 | 0.404869 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.4729 | 0.943656 | 0.471828 | − | 0.881691i | \(-0.343594\pi\) | ||||
0.471828 | + | 0.881691i | \(0.343594\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.37383 | 0.191314 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.7551 | 0.417963 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.0485 | 1.56421 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.46081 | 0.0518095 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.2108 | 0.467950 | 0.233975 | − | 0.972243i | \(-0.424827\pi\) | ||||
0.233975 | + | 0.972243i | \(0.424827\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.5403 | −0.443645 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.4057 | 0.968333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.7754 | −0.450835 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.4732 | −0.474867 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.27622 | −0.185732 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.69076 | 0.0594441 | 0.0297220 | − | 0.999558i | \(-0.490538\pi\) | ||||
0.0297220 | + | 0.999558i | \(0.490538\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.2707 | 1.34386 | 0.671932 | − | 0.740613i | \(-0.265465\pi\) | ||||
0.671932 | + | 0.740613i | \(0.265465\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.25827 | 0.0441294 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.0049 | −0.490569 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0545719 | 0.00190923 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.8833 | 0.520065 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.0505 | 0.909170 | 0.454585 | − | 0.890703i | \(-0.349788\pi\) | ||||
0.454585 | + | 0.890703i | \(0.349788\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −46.9913 | −1.63801 | −0.819007 | − | 0.573783i | \(-0.805475\pi\) | ||||
−0.819007 | + | 0.573783i | \(0.805475\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.12130 | 0.108670 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.23256 | 0.216727 | 0.108364 | − | 0.994111i | \(-0.465439\pi\) | ||||
0.108364 | + | 0.994111i | \(0.465439\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.9160 | 0.622247 | 0.311124 | − | 0.950369i | \(-0.399295\pi\) | ||||
0.311124 | + | 0.950369i | \(0.399295\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.2354 | −0.355062 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.4623 | 0.501090 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.315144 | −0.0109060 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.02213 | −0.208155 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −40.6949 | −1.40495 | −0.702473 | − | 0.711711i | \(-0.747921\pi\) | ||||
−0.702473 | + | 0.711711i | \(0.747921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5540 | −0.984622 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.64651 | −0.160034 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.60865 | 0.0553394 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50.1187 | 1.72210 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.1322 | 0.347737 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −78.3563 | −2.68602 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.9318 | −1.43572 | −0.717859 | − | 0.696188i | \(-0.754878\pi\) | ||||
−0.717859 | + | 0.696188i | \(0.754878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.0262873 | −0.000899007 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.5473 | −0.496927 | −0.248464 | − | 0.968641i | \(-0.579926\pi\) | ||||
−0.248464 | + | 0.968641i | \(0.579926\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.4475 | 0.902378 | 0.451189 | − | 0.892428i | \(-0.351000\pi\) | ||||
0.451189 | + | 0.892428i | \(0.351000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.84709 | 0.131108 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −55.3001 | −1.88244 | −0.941218 | − | 0.337798i | \(-0.890318\pi\) | ||||
−0.941218 | + | 0.337798i | \(0.890318\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.9627 | −0.610751 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.12100 | 0.105995 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.7728 | −1.79019 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.17217 | −0.243020 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.38099 | −0.283654 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.59155 | −0.0538042 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.509653 | 0.0172098 | 0.00860489 | − | 0.999963i | \(-0.497261\pi\) | ||||
0.00860489 | + | 0.999963i | \(0.497261\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.5913 | 0.357237 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.6582 | 1.57195 | 0.785977 | − | 0.618256i | \(-0.212161\pi\) | ||||
0.785977 | + | 0.618256i | \(0.212161\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.1322 | −1.11499 | −0.557494 | − | 0.830181i | \(-0.688237\pi\) | ||||
−0.557494 | + | 0.830181i | \(0.688237\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.91771 | −0.165307 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.4172 | 1.05489 | 0.527443 | − | 0.849590i | \(-0.323151\pi\) | ||||
0.527443 | + | 0.849590i | \(0.323151\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.08727 | 0.103544 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −45.5575 | −1.52623 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0367484 | −0.00122974 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.5698 | 0.420164 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.6813 | 0.456804 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.45541 | −0.0485406 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.87707 | −0.329053 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.38354 | 0.145875 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.08922 | −0.235654 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.89124 | −0.328433 | −0.164217 | − | 0.986424i | \(-0.552510\pi\) | ||||
−0.164217 | + | 0.986424i | \(0.552510\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.3458 | 1.07284 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.8943 | 1.12297 | 0.561485 | − | 0.827487i | \(-0.310230\pi\) | ||||
0.561485 | + | 0.827487i | \(0.310230\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.9206 | 0.427611 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.24934 | −0.206597 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.5091 | −0.644248 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.3342 | −0.670762 | −0.335381 | − | 0.942083i | \(-0.608865\pi\) | ||||
−0.335381 | + | 0.942083i | \(0.608865\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.95812 | 0.229278 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.2685 | −0.337990 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.25603 | −0.304336 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.2716 | 0.731496 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.07264 | −0.264855 | −0.132427 | − | 0.991193i | \(-0.542277\pi\) | ||||
−0.132427 | + | 0.991193i | \(0.542277\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0423806 | 0.00138897 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.48875 | 0.277909 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.1043 | −0.690185 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.9023 | 1.07487 | 0.537436 | − | 0.843304i | \(-0.319393\pi\) | ||||
0.537436 | + | 0.843304i | \(0.319393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.2559 | −0.399957 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.8664 | 0.484629 | 0.242315 | − | 0.970198i | \(-0.422093\pi\) | ||||
0.242315 | + | 0.970198i | \(0.422093\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −42.7337 | −1.39160 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.39784 | −0.143062 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.5736 | 0.441082 | 0.220541 | − | 0.975378i | \(-0.429218\pi\) | ||||
0.220541 | + | 0.975378i | \(0.429218\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.61481 | −0.214726 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.87369 | −0.255322 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.3361 | −1.33901 | −0.669504 | − | 0.742808i | \(-0.733493\pi\) | ||||
−0.669504 | + | 0.742808i | \(0.733493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.9385 | −0.548118 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.08444 | 0.0673805 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.6891 | 0.635794 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.2503 | −0.846785 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −55.1147 | −1.77605 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.43727 | −0.142841 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.5352 | −0.981946 | −0.490973 | − | 0.871175i | \(-0.663359\pi\) | ||||
−0.490973 | + | 0.871175i | \(0.663359\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0147085 | −0.000472507 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.0974 | 1.19051 | 0.595256 | − | 0.803536i | \(-0.297051\pi\) | ||||
0.595256 | + | 0.803536i | \(0.297051\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.51851 | 0.112798 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.61613 | 0.0517577 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.96666 | −0.158898 | −0.0794488 | − | 0.996839i | \(-0.525316\pi\) | ||||
−0.0794488 | + | 0.996839i | \(0.525316\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64.4756 | 2.06065 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.5052 | −1.19745 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.46334 | 0.0785684 | 0.0392842 | − | 0.999228i | \(-0.487492\pi\) | ||||
0.0392842 | + | 0.999228i | \(0.487492\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0520 | 0.638909 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.95185 | −0.0939584 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.6927 | −1.54834 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.5590 | 0.907206 | 0.453603 | − | 0.891204i | \(-0.350138\pi\) | ||||
0.453603 | + | 0.891204i | \(0.350138\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.38453 | 0.107405 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.0566 | −0.762644 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.5746 | −0.999977 | −0.499989 | − | 0.866032i | \(-0.666662\pi\) | ||||
−0.499989 | + | 0.866032i | \(0.666662\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.5767 | −0.809210 |
(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 | 8020.2.a.e.1.17 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.e.1.17 | ✓ | 35 | 1.1 | even | 1 | trivial |