Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1000,2,Mod(1,1000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1000, 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("1000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1000.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: | \(7.98504020213\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10025.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 11x^{2} + 10x + 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.03989\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1000.1 |
$q$-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 | ||||||||
\(3\) | −2.65792 | −1.53455 | −0.767275 | − | 0.641318i | \(-0.778388\pi\) | ||||
−0.767275 | + | 0.641318i | \(0.778388\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.68257 | −1.76985 | −0.884923 | − | 0.465738i | \(-0.845789\pi\) | ||||
−0.884923 | + | 0.465738i | \(0.845789\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.06454 | 1.35485 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0398855 | −0.0120259 | −0.00601297 | − | 0.999982i | \(-0.501914\pi\) | ||||
−0.00601297 | + | 0.999982i | \(0.501914\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.02465 | 0.284187 | 0.142093 | − | 0.989853i | \(-0.454617\pi\) | ||||
0.142093 | + | 0.989853i | \(0.454617\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.95852 | −1.20262 | −0.601309 | − | 0.799016i | \(-0.705354\pi\) | ||||
−0.601309 | + | 0.799016i | \(0.705354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.21924 | −1.88562 | −0.942812 | − | 0.333326i | \(-0.891829\pi\) | ||||
−0.942812 | + | 0.333326i | \(0.891829\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.4459 | 2.71592 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.15471 | 0.866316 | 0.433158 | − | 0.901318i | \(-0.357399\pi\) | ||||
0.433158 | + | 0.901318i | \(0.357399\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.82945 | −0.544528 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.878753 | −0.163180 | −0.0815901 | − | 0.996666i | \(-0.526000\pi\) | ||||
−0.0815901 | + | 0.996666i | \(0.526000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.45690 | 0.980088 | 0.490044 | − | 0.871698i | \(-0.336981\pi\) | ||||
0.490044 | + | 0.871698i | \(0.336981\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.106013 | 0.0184544 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.51202 | 1.56377 | 0.781883 | − | 0.623425i | \(-0.214259\pi\) | ||||
0.781883 | + | 0.623425i | \(0.214259\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.72344 | −0.436099 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.28378 | −0.825188 | −0.412594 | − | 0.910915i | \(-0.635377\pi\) | ||||
−0.412594 | + | 0.910915i | \(0.635377\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.95852 | 1.36616 | 0.683081 | − | 0.730343i | \(-0.260640\pi\) | ||||
0.683081 | + | 0.730343i | \(0.260640\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.09017 | −1.32594 | −0.662969 | − | 0.748647i | \(-0.730704\pi\) | ||||
−0.662969 | + | 0.748647i | \(0.730704\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.9265 | 2.13235 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.1794 | 1.84548 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.18095 | −0.162216 | −0.0811078 | − | 0.996705i | \(-0.525846\pi\) | ||||
−0.0811078 | + | 0.996705i | \(0.525846\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 21.8461 | 2.89358 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.34049 | 1.21603 | 0.608014 | − | 0.793926i | \(-0.291966\pi\) | ||||
0.608014 | + | 0.793926i | \(0.291966\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.57815 | 0.330098 | 0.165049 | − | 0.986285i | \(-0.447222\pi\) | ||||
0.165049 | + | 0.986285i | \(0.447222\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −19.0325 | −2.39787 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.46015 | 1.03357 | 0.516786 | − | 0.856115i | \(-0.327128\pi\) | ||||
0.516786 | + | 0.856115i | \(0.327128\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.0429 | −1.32941 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0383 | 1.78472 | 0.892359 | − | 0.451327i | \(-0.149049\pi\) | ||||
0.892359 | + | 0.451327i | \(0.149049\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.58597 | −0.419706 | −0.209853 | − | 0.977733i | \(-0.567299\pi\) | ||||
−0.209853 | + | 0.977733i | \(0.567299\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.186767 | 0.0212840 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2439 | −1.15253 | −0.576264 | − | 0.817264i | \(-0.695490\pi\) | ||||
−0.576264 | + | 0.817264i | \(0.695490\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.67315 | −0.519239 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.65890 | 1.06020 | 0.530101 | − | 0.847934i | \(-0.322154\pi\) | ||||
0.530101 | + | 0.847934i | \(0.322154\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.33565 | 0.250408 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.759096 | 0.0804640 | 0.0402320 | − | 0.999190i | \(-0.487190\pi\) | ||||
0.0402320 | + | 0.999190i | \(0.487190\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.79800 | −0.502967 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.5040 | −1.50400 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.67217 | 0.677456 | 0.338728 | − | 0.940884i | \(-0.390003\pi\) | ||||
0.338728 | + | 0.940884i | \(0.390003\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.162116 | −0.0162933 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.5597 | 1.15024 | 0.575118 | − | 0.818070i | \(-0.304956\pi\) | ||||
0.575118 | + | 0.818070i | \(0.304956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.3829 | −1.02306 | −0.511531 | − | 0.859265i | \(-0.670922\pi\) | ||||
−0.511531 | + | 0.859265i | \(0.670922\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.94329 | −0.574559 | −0.287280 | − | 0.957847i | \(-0.592751\pi\) | ||||
−0.287280 | + | 0.957847i | \(0.592751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.17936 | −0.879223 | −0.439611 | − | 0.898188i | \(-0.644884\pi\) | ||||
−0.439611 | + | 0.898188i | \(0.644884\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −25.2822 | −2.39968 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9249 | 1.40401 | 0.702007 | − | 0.712170i | \(-0.252288\pi\) | ||||
0.702007 | + | 0.712170i | \(0.252288\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.16473 | 0.385029 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23.2186 | 2.12845 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9984 | −0.999855 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.0439 | 1.26629 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.68416 | −0.593123 | −0.296562 | − | 0.955014i | \(-0.595840\pi\) | ||||
−0.296562 | + | 0.955014i | \(0.595840\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.8110 | −2.09644 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.552515 | 0.0482734 | 0.0241367 | − | 0.999709i | \(-0.492316\pi\) | ||||
0.0241367 | + | 0.999709i | \(0.492316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 38.4872 | 3.33726 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.95168 | 0.593922 | 0.296961 | − | 0.954890i | \(-0.404027\pi\) | ||||
0.296961 | + | 0.954890i | \(0.404027\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.19300 | 0.610102 | 0.305051 | − | 0.952336i | \(-0.401326\pi\) | ||||
0.305051 | + | 0.952336i | \(0.401326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.1609 | 2.03472 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0408687 | −0.00341761 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −39.6733 | −3.27220 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.22182 | 0.755481 | 0.377740 | − | 0.925912i | \(-0.376701\pi\) | ||||
0.377740 | + | 0.925912i | \(0.376701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.09501 | 0.251868 | 0.125934 | − | 0.992039i | \(-0.459807\pi\) | ||||
0.125934 | + | 0.992039i | \(0.459807\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.1541 | −1.62936 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.39463 | −0.191112 | −0.0955560 | − | 0.995424i | \(-0.530463\pi\) | ||||
−0.0955560 | + | 0.995424i | \(0.530463\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.13886 | 0.248928 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.4547 | −1.53325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.59240 | −0.516357 | −0.258178 | − | 0.966097i | \(-0.583122\pi\) | ||||
−0.258178 | + | 0.966097i | \(0.583122\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.24548 | −0.173761 | −0.0868804 | − | 0.996219i | \(-0.527690\pi\) | ||||
−0.0868804 | + | 0.996219i | \(0.527690\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.9501 | −0.919238 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −33.4074 | −2.55473 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.0782 | −0.766230 | −0.383115 | − | 0.923701i | \(-0.625149\pi\) | ||||
−0.383115 | + | 0.923701i | \(0.625149\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −24.8263 | −1.86606 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.0256 | 0.824095 | 0.412047 | − | 0.911162i | \(-0.364814\pi\) | ||||
0.412047 | + | 0.911162i | \(0.364814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.8950 | −0.958476 | −0.479238 | − | 0.877685i | \(-0.659087\pi\) | ||||
−0.479238 | + | 0.877685i | \(0.659087\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.85251 | −0.506552 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.197773 | 0.0144626 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.2491 | 0.963731 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6032 | −1.20136 | −0.600682 | − | 0.799488i | \(-0.705104\pi\) | ||||
−0.600682 | + | 0.799488i | \(0.705104\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.98477 | 0.358811 | 0.179406 | − | 0.983775i | \(-0.442583\pi\) | ||||
0.179406 | + | 0.983775i | \(0.442583\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.95528 | −0.566790 | −0.283395 | − | 0.959003i | \(-0.591461\pi\) | ||||
−0.283395 | + | 0.959003i | \(0.591461\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.26329 | −0.302217 | −0.151108 | − | 0.988517i | \(-0.548284\pi\) | ||||
−0.151108 | + | 0.988517i | \(0.548284\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.4864 | −1.58607 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.11482 | 0.288804 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.8870 | 1.17372 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.327829 | 0.0226764 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.6315 | 1.42033 | 0.710165 | − | 0.704035i | \(-0.248620\pi\) | ||||
0.710165 | + | 0.704035i | \(0.248620\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −39.9706 | −2.73874 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.5523 | −1.73460 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.53123 | 0.644061 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.08075 | −0.341769 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.79482 | 0.388050 | 0.194025 | − | 0.980997i | \(-0.437846\pi\) | ||||
0.194025 | + | 0.980997i | \(0.437846\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.95754 | 0.660905 | 0.330453 | − | 0.943823i | \(-0.392799\pi\) | ||||
0.330453 | + | 0.943823i | \(0.392799\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.91142 | −0.126310 | −0.0631551 | − | 0.998004i | \(-0.520116\pi\) | ||||
−0.0631551 | + | 0.998004i | \(0.520116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.496411 | −0.0326614 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.74650 | −0.179929 | −0.0899646 | − | 0.995945i | \(-0.528675\pi\) | ||||
−0.0899646 | + | 0.995945i | \(0.528675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.2274 | 1.76861 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.8189 | −1.08792 | −0.543961 | − | 0.839111i | \(-0.683076\pi\) | ||||
−0.543961 | + | 0.839111i | \(0.683076\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.69879 | 0.109429 | 0.0547143 | − | 0.998502i | \(-0.482575\pi\) | ||||
0.0547143 | + | 0.998502i | \(0.482575\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.9092 | 1.34133 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.42185 | −0.535870 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −25.6726 | −1.62693 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.25270 | −0.520906 | −0.260453 | − | 0.965487i | \(-0.583872\pi\) | ||||
−0.260453 | + | 0.965487i | \(0.583872\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.165713 | −0.0104183 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.6824 | 1.53964 | 0.769822 | − | 0.638258i | \(-0.220345\pi\) | ||||
0.769822 | + | 0.638258i | \(0.220345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −44.5407 | −2.76762 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.57172 | −0.221084 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0759 | −0.744633 | −0.372317 | − | 0.928106i | \(-0.621436\pi\) | ||||
−0.372317 | + | 0.928106i | \(0.621436\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.01762 | −0.123476 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.3577 | 1.05832 | 0.529160 | − | 0.848522i | \(-0.322507\pi\) | ||||
0.529160 | + | 0.848522i | \(0.322507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.40302 | −0.449701 | −0.224851 | − | 0.974393i | \(-0.572189\pi\) | ||||
−0.224851 | + | 0.974393i | \(0.572189\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.7527 | 0.771828 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.3208 | −1.10079 | −0.550395 | − | 0.834904i | \(-0.685523\pi\) | ||||
−0.550395 | + | 0.834904i | \(0.685523\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.1798 | 1.32787 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.3539 | −1.21421 | −0.607105 | − | 0.794621i | \(-0.707669\pi\) | ||||
−0.607105 | + | 0.794621i | \(0.707669\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.33149 | −0.198036 | −0.0990182 | − | 0.995086i | \(-0.531570\pi\) | ||||
−0.0990182 | + | 0.995086i | \(0.531570\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.7417 | 1.46045 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.58696 | 0.446292 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.7341 | −1.03959 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.3525 | 1.48111 | 0.740556 | − | 0.671995i | \(-0.234562\pi\) | ||||
0.740556 | + | 0.671995i | \(0.234562\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.112854 | 0.00654846 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.25712 | 0.246196 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.9489 | −2.41790 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −30.7248 | −1.76510 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.2611 | 1.09929 | 0.549644 | − | 0.835399i | \(-0.314763\pi\) | ||||
0.549644 | + | 0.835399i | \(0.314763\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.5970 | 1.56994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.6626 | 1.68201 | 0.841005 | − | 0.541028i | \(-0.181965\pi\) | ||||
0.841005 | + | 0.541028i | \(0.181965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.5759 | 0.880405 | 0.440202 | − | 0.897899i | \(-0.354907\pi\) | ||||
0.440202 | + | 0.897899i | \(0.354907\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.2994 | 1.81412 | 0.907058 | − | 0.421005i | \(-0.138323\pi\) | ||||
0.907058 | + | 0.421005i | \(0.138323\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0350495 | 0.00196240 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.7968 | 0.881690 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 40.7553 | 2.26769 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.3980 | 1.34921 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 42.5654 | 2.34670 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.3804 | 1.12021 | 0.560103 | − | 0.828423i | \(-0.310761\pi\) | ||||
0.560103 | + | 0.828423i | \(0.310761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 38.6620 | 2.11866 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.85795 | 0.264630 | 0.132315 | − | 0.991208i | \(-0.457759\pi\) | ||||
0.132315 | + | 0.991208i | \(0.457759\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −39.6691 | −2.15453 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.217651 | −0.0117865 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −37.1162 | −2.00409 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.5630 | 1.42598 | 0.712988 | − | 0.701177i | \(-0.247342\pi\) | ||||
0.712988 | + | 0.701177i | \(0.247342\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.01622 | 0.214983 | 0.107492 | − | 0.994206i | \(-0.465718\pi\) | ||||
0.107492 | + | 0.994206i | \(0.465718\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.89920 | −0.154748 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.1038 | −1.22969 | −0.614846 | − | 0.788647i | \(-0.710782\pi\) | ||||
−0.614846 | + | 0.788647i | \(0.710782\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −61.7133 | −3.26621 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.2611 | 1.22767 | 0.613837 | − | 0.789433i | \(-0.289625\pi\) | ||||
0.613837 | + | 0.789433i | \(0.289625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.5559 | 2.55558 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.2329 | 1.53433 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.305184 | 0.0159305 | 0.00796523 | − | 0.999968i | \(-0.497465\pi\) | ||||
0.00796523 | + | 0.999968i | \(0.497465\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.4761 | −1.11800 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.52987 | 0.287097 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.97859 | −0.361338 | −0.180669 | − | 0.983544i | \(-0.557826\pi\) | ||||
−0.180669 | + | 0.983544i | \(0.557826\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.900414 | −0.0463737 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.8509 | 1.43061 | 0.715303 | − | 0.698815i | \(-0.246289\pi\) | ||||
0.715303 | + | 0.698815i | \(0.246289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.7660 | 0.910178 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.54707 | −0.385637 | −0.192819 | − | 0.981234i | \(-0.561763\pi\) | ||||
−0.192819 | + | 0.981234i | \(0.561763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 36.4122 | 1.85094 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.4831 | 0.582218 | 0.291109 | − | 0.956690i | \(-0.405976\pi\) | ||||
0.291109 | + | 0.956690i | \(0.405976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.6012 | −1.04185 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.46854 | −0.0740780 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.39077 | −0.220367 | −0.110183 | − | 0.993911i | \(-0.535144\pi\) | ||||
−0.110183 | + | 0.993911i | \(0.535144\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −102.296 | −5.12120 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.31883 | −0.465360 | −0.232680 | − | 0.972553i | \(-0.574749\pi\) | ||||
−0.232680 | + | 0.972553i | \(0.574749\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.59142 | 0.278528 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.379392 | −0.0188058 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.7657 | −1.12569 | −0.562846 | − | 0.826562i | \(-0.690294\pi\) | ||||
−0.562846 | + | 0.826562i | \(0.690294\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.4770 | −0.911404 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −43.7375 | −2.15218 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.1184 | −0.936233 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.1849 | 0.888391 | 0.444196 | − | 0.895930i | \(-0.353489\pi\) | ||||
0.444196 | + | 0.895930i | \(0.353489\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.6177 | −0.712424 | −0.356212 | − | 0.934405i | \(-0.615932\pi\) | ||||
−0.356212 | + | 0.934405i | \(0.615932\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.9473 | −1.79644 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0724 | −0.584222 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.108626 | 0.00524450 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.73641 | 0.468986 | 0.234493 | − | 0.972118i | \(-0.424657\pi\) | ||||
0.234493 | + | 0.972118i | \(0.424657\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1544 | −0.968558 | −0.484279 | − | 0.874914i | \(-0.660918\pi\) | ||||
−0.484279 | + | 0.874914i | \(0.660918\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −34.1485 | −1.63355 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.93773 | 0.426574 | 0.213287 | − | 0.976990i | \(-0.431583\pi\) | ||||
0.213287 | + | 0.976990i | \(0.431583\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 60.6691 | 2.88901 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.43390 | −0.210661 | −0.105331 | − | 0.994437i | \(-0.533590\pi\) | ||||
−0.105331 | + | 0.994437i | \(0.533590\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −24.5108 | −1.15932 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.3645 | 1.81053 | 0.905267 | − | 0.424843i | \(-0.139671\pi\) | ||||
0.905267 | + | 0.424843i | \(0.139671\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.210746 | 0.00992365 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.22628 | −0.386504 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.8529 | 1.49002 | 0.745009 | − | 0.667055i | \(-0.232445\pi\) | ||||
0.745009 | + | 0.667055i | \(0.232445\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.0299 | 0.654860 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.4680 | 1.65191 | 0.825954 | − | 0.563737i | \(-0.190637\pi\) | ||||
0.825954 | + | 0.563737i | \(0.190637\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.845101 | 0.0392752 | 0.0196376 | − | 0.999807i | \(-0.493749\pi\) | ||||
0.0196376 | + | 0.999807i | \(0.493749\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.7848 | −0.637884 | −0.318942 | − | 0.947774i | \(-0.603328\pi\) | ||||
−0.318942 | + | 0.947774i | \(0.603328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.6152 | −1.82926 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.36473 | 0.293271 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.357315 | −0.0164294 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.80000 | −0.219777 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.08075 | 0.323528 | 0.161764 | − | 0.986829i | \(-0.448282\pi\) | ||||
0.161764 | + | 0.986829i | \(0.448282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.74650 | 0.444402 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 51.7090 | 2.35284 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.3059 | −1.14672 | −0.573359 | − | 0.819304i | \(-0.694360\pi\) | ||||
−0.573359 | + | 0.819304i | \(0.694360\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.5221 | 0.792375 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4890 | 1.10517 | 0.552587 | − | 0.833455i | \(-0.313641\pi\) | ||||
0.552587 | + | 0.833455i | \(0.313641\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.35732 | 0.196244 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −70.4179 | −3.15867 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.14230 | 0.140669 | 0.0703344 | − | 0.997523i | \(-0.477593\pi\) | ||||
0.0703344 | + | 0.997523i | \(0.477593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.96831 | 0.266645 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.7790 | 0.926489 | 0.463244 | − | 0.886231i | \(-0.346685\pi\) | ||||
0.463244 | + | 0.886231i | \(0.346685\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.7624 | 1.41062 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.9139 | −1.23726 | −0.618630 | − | 0.785682i | \(-0.712312\pi\) | ||||
−0.618630 | + | 0.785682i | \(0.712312\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.7916 | 0.742815 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23.2559 | 1.02678 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.362566 | 0.0159456 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.7870 | 1.17582 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0675 | 1.05442 | 0.527209 | − | 0.849736i | \(-0.323239\pi\) | ||||
0.527209 | + | 0.849736i | \(0.323239\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.1150 | −1.75411 | −0.877053 | − | 0.480393i | \(-0.840494\pi\) | ||||
−0.877053 | + | 0.480393i | \(0.840494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.0582 | −1.17867 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.73842 | −0.249496 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 37.9648 | 1.64753 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.41403 | −0.234508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.3052 | −1.26461 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.595350 | −0.0256435 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.9359 | −1.24405 | −0.622027 | − | 0.782996i | \(-0.713690\pi\) | ||||
−0.622027 | + | 0.782996i | \(0.713690\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.2738 | 1.47083 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9290 | 1.10865 | 0.554323 | − | 0.832302i | \(-0.312977\pi\) | ||||
0.554323 | + | 0.832302i | \(0.312977\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.4790 | 0.447232 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.22268 | 0.307697 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 47.9677 | 2.03980 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.7002 | −0.580496 | −0.290248 | − | 0.956952i | \(-0.593738\pi\) | ||||
−0.290248 | + | 0.956952i | \(0.593738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.17936 | 0.388245 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.525666 | −0.0221936 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.8866 | −1.04885 | −0.524423 | − | 0.851458i | \(-0.675719\pi\) | ||||
−0.524423 | + | 0.851458i | \(0.675719\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.8824 | 0.918973 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.2649 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.04643 | −0.294884 | −0.147442 | − | 0.989071i | \(-0.547104\pi\) | ||||
−0.147442 | + | 0.989071i | \(0.547104\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 44.1299 | 1.84355 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.86295 | 0.0775556 | 0.0387778 | − | 0.999248i | \(-0.487654\pi\) | ||||
0.0387778 | + | 0.999248i | \(0.487654\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.2491 | −0.550614 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.2285 | −1.87639 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0471027 | 0.00195079 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.9871 | −0.742409 | −0.371204 | − | 0.928551i | \(-0.621055\pi\) | ||||
−0.371204 | + | 0.928551i | \(0.621055\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44.8516 | −1.84808 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.1445 | 0.869768 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −29.1161 | −1.19565 | −0.597827 | − | 0.801625i | \(-0.703969\pi\) | ||||
−0.597827 | + | 0.801625i | \(0.703969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.3315 | 0.463767 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.0913 | 1.18864 | 0.594318 | − | 0.804230i | \(-0.297422\pi\) | ||||
0.594318 | + | 0.804230i | \(0.297422\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.3954 | 1.32144 | 0.660718 | − | 0.750634i | \(-0.270252\pi\) | ||||
0.660718 | + | 0.750634i | \(0.270252\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 34.3866 | 1.40033 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0239 | 0.772154 | 0.386077 | − | 0.922467i | \(-0.373830\pi\) | ||||
0.386077 | + | 0.922467i | \(0.373830\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.9369 | −0.443184 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.31425 | −0.376814 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.03474 | −0.0821823 | −0.0410911 | − | 0.999155i | \(-0.513083\pi\) | ||||
−0.0410911 | + | 0.999155i | \(0.513083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.73728 | 0.392008 | 0.196004 | − | 0.980603i | \(-0.437203\pi\) | ||||
0.196004 | + | 0.980603i | \(0.437203\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.1593 | 1.25240 | 0.626200 | − | 0.779662i | \(-0.284609\pi\) | ||||
0.626200 | + | 0.779662i | \(0.284609\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.7555 | −0.471734 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.55452 | −0.142409 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.871343 | −0.0347981 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −47.1656 | −1.88061 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.6829 | 1.14185 | 0.570925 | − | 0.821002i | \(-0.306585\pi\) | ||||
0.570925 | + | 0.821002i | \(0.306585\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −54.8368 | −2.17957 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.2944 | 0.605987 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 61.1237 | 2.41802 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.3152 | 0.881399 | 0.440699 | − | 0.897655i | \(-0.354731\pi\) | ||||
0.440699 | + | 0.897655i | \(0.354731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.8046 | −1.45143 | −0.725716 | − | 0.687994i | \(-0.758491\pi\) | ||||
−0.725716 | + | 0.687994i | \(0.758491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 49.8385 | 1.95935 | 0.979676 | − | 0.200584i | \(-0.0642841\pi\) | ||||
0.979676 | + | 0.200584i | \(0.0642841\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.372550 | −0.0146239 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 67.9160 | 2.66184 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.8293 | −0.619447 | −0.309723 | − | 0.950827i | \(-0.600236\pi\) | ||||
−0.309723 | + | 0.950827i | \(0.600236\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.5753 | −0.568637 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.1311 | −0.394651 | −0.197325 | − | 0.980338i | \(-0.563226\pi\) | ||||
−0.197325 | + | 0.980338i | \(0.563226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.7912 | −1.11985 | −0.559924 | − | 0.828544i | \(-0.689170\pi\) | ||||
−0.559924 | + | 0.828544i | \(0.689170\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.5042 | 0.524461 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.65096 | −0.141366 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.4022 | −0.595482 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.102831 | −0.00396974 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.6035 | 0.794205 | 0.397103 | − | 0.917774i | \(-0.370016\pi\) | ||||
0.397103 | + | 0.917774i | \(0.370016\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.5265 | 1.13479 | 0.567397 | − | 0.823444i | \(-0.307951\pi\) | ||||
0.567397 | + | 0.823444i | \(0.307951\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31.2429 | −1.19899 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.4663 | −1.01419 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.62067 | 0.138541 | 0.0692706 | − | 0.997598i | \(-0.477933\pi\) | ||||
0.0692706 | + | 0.997598i | \(0.477933\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.08040 | 0.193829 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.21006 | −0.0460996 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.34306 | 0.165218 | 0.0826090 | − | 0.996582i | \(-0.473675\pi\) | ||||
0.0826090 | + | 0.996582i | \(0.473675\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.759120 | 0.0288366 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.1997 | 0.992386 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.29997 | 0.276110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15.6469 | −0.590976 | −0.295488 | − | 0.955346i | \(-0.595482\pi\) | ||||
−0.295488 | + | 0.955346i | \(0.595482\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −78.1816 | −2.94868 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −54.1293 | −2.03574 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.6054 | −0.398296 | −0.199148 | − | 0.979969i | \(-0.563817\pi\) | ||||
−0.199148 | + | 0.979969i | \(0.563817\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.6367 | −1.56150 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.6718 | 0.849066 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 44.7032 | 1.66947 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.6068 | −1.06685 | −0.533427 | − | 0.845846i | \(-0.679096\pi\) | ||||
−0.533427 | + | 0.845846i | \(0.679096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.6189 | 1.81066 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.51524 | −0.167924 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.410174 | −0.0152125 | −0.00760625 | − | 0.999971i | \(-0.502421\pi\) | ||||
−0.00760625 | + | 0.999971i | \(0.502421\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.5556 | −1.53910 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.4211 | −1.64297 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.18559 | −0.265406 | −0.132703 | − | 0.991156i | \(-0.542366\pi\) | ||||
−0.132703 | + | 0.991156i | \(0.542366\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.337437 | −0.0124297 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.5555 | −1.67579 | −0.837894 | − | 0.545834i | \(-0.816213\pi\) | ||||
−0.837894 | + | 0.545834i | \(0.816213\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22.3846 | 0.822319 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.8535 | −0.434864 | −0.217432 | − | 0.976075i | \(-0.569768\pi\) | ||||
−0.217432 | + | 0.976075i | \(0.569768\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.2590 | 1.43641 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.8299 | 1.01688 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.674433 | 0.0246104 | 0.0123052 | − | 0.999924i | \(-0.496083\pi\) | ||||
0.0123052 | + | 0.999924i | \(0.496083\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.9350 | 0.799356 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.41666 | 0.124181 | 0.0620904 | − | 0.998071i | \(-0.480223\pi\) | ||||
0.0620904 | + | 0.998071i | \(0.480223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.440451 | 0.0159874 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.1930 | −0.949496 | −0.474748 | − | 0.880122i | \(-0.657461\pi\) | ||||
−0.474748 | + | 0.880122i | \(0.657461\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.9830 | 1.55609 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.57074 | 0.345579 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.1742 | 0.547195 | 0.273597 | − | 0.961844i | \(-0.411786\pi\) | ||||
0.273597 | + | 0.961844i | \(0.411786\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −65.6038 | −2.36266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29.0032 | −1.04317 | −0.521587 | − | 0.853198i | \(-0.674660\pi\) | ||||
−0.521587 | + | 0.853198i | \(0.674660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 118.386 | 4.24706 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 43.4287 | 1.55599 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.599810 | −0.0214629 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.48639 | 0.0888562 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.2660 | 0.686758 | 0.343379 | − | 0.939197i | \(-0.388429\pi\) | ||||
0.343379 | + | 0.939197i | \(0.388429\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.0968 | 1.14268 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −69.8868 | −2.48489 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.64170 | 0.0938096 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.54279 | −0.0546483 | −0.0273242 | − | 0.999627i | \(-0.508699\pi\) | ||||
−0.0273242 | + | 0.999627i | \(0.508699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.0738 | 1.59460 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.08537 | 0.109016 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.143028 | 0.00504736 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −46.1354 | −1.62404 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.7800 | 1.29312 | 0.646558 | − | 0.762865i | \(-0.276208\pi\) | ||||
0.646558 | + | 0.762865i | \(0.276208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.4212 | −0.611743 | −0.305871 | − | 0.952073i | \(-0.598948\pi\) | ||||
−0.305871 | + | 0.952073i | \(0.598948\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.6766 | 0.690090 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −73.6323 | −2.57607 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.5016 | −0.681442 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.6670 | 0.651484 | 0.325742 | − | 0.945459i | \(-0.394386\pi\) | ||||
0.325742 | + | 0.945459i | \(0.394386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.4544 | −1.37530 | −0.687648 | − | 0.726044i | \(-0.741357\pi\) | ||||
−0.687648 | + | 0.726044i | \(0.741357\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.1204 | −0.908297 | −0.454148 | − | 0.890926i | \(-0.650056\pi\) | ||||
−0.454148 | + | 0.890926i | \(0.650056\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.81880 | −0.341021 | −0.170510 | − | 0.985356i | \(-0.554542\pi\) | ||||
−0.170510 | + | 0.985356i | \(0.554542\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 48.6952 | 1.68922 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −74.0132 | −2.56441 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.4400 | −0.533686 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.9336 | 0.481042 | 0.240521 | − | 0.970644i | \(-0.422682\pi\) | ||||
0.240521 | + | 0.970644i | \(0.422682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.2278 | −0.973372 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 54.0990 | 1.86327 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 51.5008 | 1.76959 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.85483 | 0.303897 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.5197 | 1.35472 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1138 | 0.620205 | 0.310102 | − | 0.950703i | \(-0.399637\pi\) | ||||
0.310102 | + | 0.950703i | \(0.399637\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.72704 | 0.332269 | 0.166135 | − | 0.986103i | \(-0.446871\pi\) | ||||
0.166135 | + | 0.986103i | \(0.446871\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.7910 | 0.572902 | 0.286451 | − | 0.958095i | \(-0.407524\pi\) | ||||
0.286451 | + | 0.958095i | \(0.407524\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −65.7613 | −2.24114 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.06190 | 0.104228 | 0.0521141 | − | 0.998641i | \(-0.483404\pi\) | ||||
0.0521141 | + | 0.998641i | \(0.483404\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.1655 | −0.684857 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.408583 | 0.0138602 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.66869 | 0.293727 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.1193 | 0.917849 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.7836 | −0.735580 | −0.367790 | − | 0.929909i | \(-0.619886\pi\) | ||||
−0.367790 | + | 0.929909i | \(0.619886\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −67.3850 | −2.27284 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.4065 | 1.59717 | 0.798583 | − | 0.601885i | \(-0.205584\pi\) | ||||
0.798583 | + | 0.601885i | \(0.205584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.8303 | 0.566384 | 0.283192 | − | 0.959063i | \(-0.408607\pi\) | ||||
0.283192 | + | 0.959063i | \(0.408607\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.25584 | −0.0421671 | −0.0210835 | − | 0.999778i | \(-0.506712\pi\) | ||||
−0.0210835 | + | 0.999778i | \(0.506712\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.2991 | 1.04974 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.186391 | 0.00624434 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 74.7143 | 2.50022 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.3151 | −0.377800 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.79527 | −0.159931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.85576 | 0.195084 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 111.497 | 3.71038 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.0199 | −0.930385 | −0.465192 | − | 0.885210i | \(-0.654015\pi\) | ||||
−0.465192 | + | 0.885210i | \(0.654015\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 46.9849 | 1.55839 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.7419 | −0.687210 | −0.343605 | − | 0.939114i | \(-0.611648\pi\) | ||||
−0.343605 | + | 0.939114i | \(0.611648\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.385250 | −0.0127499 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.58719 | −0.0854365 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.224493 | −0.00740534 | −0.00370267 | − | 0.999993i | \(-0.501179\pi\) | ||||
−0.00370267 | + | 0.999993i | \(0.501179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −51.1944 | −1.68691 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.4090 | 0.507193 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42.2019 | −1.38609 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.2747 | −1.09171 | −0.545854 | − | 0.837880i | \(-0.683795\pi\) | ||||
−0.545854 | + | 0.837880i | \(0.683795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −122.684 | −4.02081 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −78.8407 | −2.58113 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.4776 | 0.603636 | 0.301818 | − | 0.953366i | \(-0.402406\pi\) | ||||
0.301818 | + | 0.953366i | \(0.402406\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.3996 | −1.35103 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.3752 | −0.436018 | −0.218009 | − | 0.975947i | \(-0.569956\pi\) | ||||
−0.218009 | + | 0.975947i | \(0.569956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.9525 | −0.714873 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.0656 | −1.20447 | −0.602235 | − | 0.798319i | \(-0.705723\pi\) | ||||
−0.602235 | + | 0.798319i | \(0.705723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.67437 | −0.119275 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −85.8493 | −2.78385 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.8429 | 0.901920 | 0.450960 | − | 0.892544i | \(-0.351082\pi\) | ||||
0.450960 | + | 0.892544i | \(0.351082\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0931588 | −0.00301140 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.5517 | −1.05115 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.22223 | −0.0394268 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.1567 | −0.778439 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −54.0629 | −1.73855 | −0.869274 | − | 0.494331i | \(-0.835413\pi\) | ||||
−0.869274 | + | 0.494331i | \(0.835413\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −108.324 | −3.47988 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.4131 | 1.71411 | 0.857054 | − | 0.515227i | \(-0.172292\pi\) | ||||
0.857054 | + | 0.515227i | \(0.172292\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.6817 | −1.07979 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.7391 | 1.30336 | 0.651679 | − | 0.758494i | \(-0.274065\pi\) | ||||
0.651679 | + | 0.758494i | \(0.274065\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0302769 | −0.000967655 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.3098 | −1.19121 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.22306 | −0.198485 | −0.0992423 | − | 0.995063i | \(-0.531642\pi\) | ||||
−0.0992423 | + | 0.995063i | \(0.531642\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −113.135 | −3.60114 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 37.2200 | 1.18353 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.7894 | −0.882759 | −0.441379 | − | 0.897321i | \(-0.645511\pi\) | ||||
−0.441379 | + | 0.897321i | \(0.645511\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −54.1694 | −1.71901 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.56549 | 0.271272 | 0.135636 | − | 0.990759i | \(-0.456692\pi\) | ||||
0.135636 | + | 0.990759i | \(0.456692\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −26.9138 | −0.851515 |
(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 | 1000.2.a.f.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 9000.2.a.q.1.1 | 4 | |||
4.3 | odd | 2 | 2000.2.a.q.1.4 | 4 | |||
5.2 | odd | 4 | 1000.2.c.c.249.7 | 8 | |||
5.3 | odd | 4 | 1000.2.c.c.249.2 | 8 | |||
5.4 | even | 2 | 1000.2.a.g.1.4 | yes | 4 | ||
8.3 | odd | 2 | 8000.2.a.be.1.1 | 4 | |||
8.5 | even | 2 | 8000.2.a.bn.1.4 | 4 | |||
15.14 | odd | 2 | 9000.2.a.bb.1.4 | 4 | |||
20.3 | even | 4 | 2000.2.c.i.1249.7 | 8 | |||
20.7 | even | 4 | 2000.2.c.i.1249.2 | 8 | |||
20.19 | odd | 2 | 2000.2.a.n.1.1 | 4 | |||
40.19 | odd | 2 | 8000.2.a.bo.1.4 | 4 | |||
40.29 | even | 2 | 8000.2.a.bd.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1000.2.a.f.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1000.2.a.g.1.4 | yes | 4 | 5.4 | even | 2 | ||
1000.2.c.c.249.2 | 8 | 5.3 | odd | 4 | |||
1000.2.c.c.249.7 | 8 | 5.2 | odd | 4 | |||
2000.2.a.n.1.1 | 4 | 20.19 | odd | 2 | |||
2000.2.a.q.1.4 | 4 | 4.3 | odd | 2 | |||
2000.2.c.i.1249.2 | 8 | 20.7 | even | 4 | |||
2000.2.c.i.1249.7 | 8 | 20.3 | even | 4 | |||
8000.2.a.bd.1.1 | 4 | 40.29 | even | 2 | |||
8000.2.a.be.1.1 | 4 | 8.3 | odd | 2 | |||
8000.2.a.bn.1.4 | 4 | 8.5 | even | 2 | |||
8000.2.a.bo.1.4 | 4 | 40.19 | odd | 2 | |||
9000.2.a.q.1.1 | 4 | 3.2 | odd | 2 | |||
9000.2.a.bb.1.4 | 4 | 15.14 | odd | 2 |