Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1380,2,Mod(1,1380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1380.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: | \(11.0193554789\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 16x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.20905\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1380.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.20905 | 1.59087 | 0.795436 | − | 0.606038i | \(-0.207242\pi\) | ||||
0.795436 | + | 0.606038i | \(0.207242\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.75353 | 0.830219 | 0.415110 | − | 0.909771i | \(-0.363743\pi\) | ||||
0.415110 | + | 0.909771i | \(0.363743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.753525 | −0.208990 | −0.104495 | − | 0.994525i | \(-0.533323\pi\) | ||||
−0.104495 | + | 0.994525i | \(0.533323\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.96257 | −1.20360 | −0.601801 | − | 0.798646i | \(-0.705550\pi\) | ||||
−0.601801 | + | 0.798646i | \(0.705550\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.75353 | 1.09053 | 0.545267 | − | 0.838263i | \(-0.316428\pi\) | ||||
0.545267 | + | 0.838263i | \(0.316428\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.20905 | 0.918490 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.96257 | 0.921527 | 0.460764 | − | 0.887523i | \(-0.347576\pi\) | ||||
0.460764 | + | 0.887523i | \(0.347576\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.209050 | −0.0375464 | −0.0187732 | − | 0.999824i | \(-0.505976\pi\) | ||||
−0.0187732 | + | 0.999824i | \(0.505976\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.75353 | 0.479327 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.20905 | −0.711459 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.71610 | −0.939721 | −0.469861 | − | 0.882741i | \(-0.655696\pi\) | ||||
−0.469861 | + | 0.882741i | \(0.655696\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.753525 | −0.120661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.38067 | −1.46502 | −0.732508 | − | 0.680759i | \(-0.761650\pi\) | ||||
−0.732508 | + | 0.680759i | \(0.761650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.4181 | 1.89374 | 0.946871 | − | 0.321613i | \(-0.104225\pi\) | ||||
0.946871 | + | 0.321613i | \(0.104225\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.17162 | 1.04609 | 0.523044 | − | 0.852305i | \(-0.324796\pi\) | ||||
0.523044 | + | 0.852305i | \(0.324796\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.7161 | 1.53087 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.96257 | −0.694899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.38067 | −1.28853 | −0.644267 | − | 0.764800i | \(-0.722838\pi\) | ||||
−0.644267 | + | 0.764800i | \(0.722838\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.75353 | −0.371285 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.75353 | 0.629620 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.96257 | −0.646072 | −0.323036 | − | 0.946387i | \(-0.604704\pi\) | ||||
−0.323036 | + | 0.946387i | \(0.604704\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.17162 | −0.662159 | −0.331079 | − | 0.943603i | \(-0.607413\pi\) | ||||
−0.331079 | + | 0.943603i | \(0.607413\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.20905 | 0.530290 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.753525 | 0.0934633 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.209050 | −0.0255395 | −0.0127697 | − | 0.999918i | \(-0.504065\pi\) | ||||
−0.0127697 | + | 0.999918i | \(0.504065\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.38067 | 1.11328 | 0.556641 | − | 0.830753i | \(-0.312090\pi\) | ||||
0.556641 | + | 0.830753i | \(0.312090\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2606 | 1.20091 | 0.600455 | − | 0.799659i | \(-0.294986\pi\) | ||||
0.600455 | + | 0.799659i | \(0.294986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.5897 | 1.32077 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.41810 | −0.272057 | −0.136029 | − | 0.990705i | \(-0.543434\pi\) | ||||
−0.136029 | + | 0.990705i | \(0.543434\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.45552 | 0.598822 | 0.299411 | − | 0.954124i | \(-0.403210\pi\) | ||||
0.299411 | + | 0.954124i | \(0.403210\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.96257 | 0.538267 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.96257 | 0.532044 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.91105 | 0.520570 | 0.260285 | − | 0.965532i | \(-0.416183\pi\) | ||||
0.260285 | + | 0.965532i | \(0.416183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.17162 | −0.332477 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.209050 | −0.0216775 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.75353 | −0.487701 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3432 | 1.05020 | 0.525099 | − | 0.851041i | \(-0.324028\pi\) | ||||
0.525099 | + | 0.851041i | \(0.324028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.75353 | 0.276740 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.8877 | 1.48138 | 0.740692 | − | 0.671845i | \(-0.234498\pi\) | ||||
0.740692 | + | 0.671845i | \(0.234498\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.9251 | 1.76622 | 0.883109 | − | 0.469168i | \(-0.155446\pi\) | ||||
0.883109 | + | 0.469168i | \(0.155446\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.20905 | −0.410761 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.4696 | −1.59218 | −0.796089 | − | 0.605179i | \(-0.793102\pi\) | ||||
−0.796089 | + | 0.605179i | \(0.793102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.26058 | −0.599654 | −0.299827 | − | 0.953994i | \(-0.596929\pi\) | ||||
−0.299827 | + | 0.953994i | \(0.596929\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.71610 | −0.542548 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.38067 | −0.882460 | −0.441230 | − | 0.897394i | \(-0.645458\pi\) | ||||
−0.441230 | + | 0.897394i | \(0.645458\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.753525 | −0.0696634 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −20.8877 | −1.91477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.41810 | −0.310736 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.38067 | −0.845827 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.0827 | −1.95952 | −0.979760 | − | 0.200175i | \(-0.935849\pi\) | ||||
−0.979760 | + | 0.200175i | \(0.935849\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4181 | 1.09335 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.58190 | −0.138211 | −0.0691056 | − | 0.997609i | \(-0.522015\pi\) | ||||
−0.0691056 | + | 0.997609i | \(0.522015\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.0078 | 1.73490 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.91105 | −0.419579 | −0.209790 | − | 0.977747i | \(-0.567278\pi\) | ||||
−0.209790 | + | 0.977747i | \(0.567278\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1342 | 1.19885 | 0.599424 | − | 0.800432i | \(-0.295397\pi\) | ||||
0.599424 | + | 0.800432i | \(0.295397\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.17162 | 0.603960 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.07485 | −0.173508 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.96257 | −0.412119 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.7161 | 0.883849 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.24647 | 0.265962 | 0.132981 | − | 0.991119i | \(-0.457545\pi\) | ||||
0.132981 | + | 0.991119i | \(0.457545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.418100 | 0.0340245 | 0.0170122 | − | 0.999855i | \(-0.494585\pi\) | ||||
0.0170122 | + | 0.999855i | \(0.494585\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.96257 | −0.401200 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.209050 | 0.0167913 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.0452 | −1.67959 | −0.839797 | − | 0.542901i | \(-0.817326\pi\) | ||||
−0.839797 | + | 0.542901i | \(0.817326\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.38067 | −0.743936 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.20905 | 0.331720 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.43220 | −0.582135 | −0.291067 | − | 0.956703i | \(-0.594010\pi\) | ||||
−0.291067 | + | 0.956703i | \(0.594010\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.75353 | −0.214362 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.1716 | −1.48354 | −0.741772 | − | 0.670652i | \(-0.766015\pi\) | ||||
−0.741772 | + | 0.670652i | \(0.766015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.4322 | −0.956323 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.75353 | 0.363511 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.20905 | 0.318174 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.96257 | −0.373010 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.8503 | 1.03522 | 0.517610 | − | 0.855617i | \(-0.326822\pi\) | ||||
0.517610 | + | 0.855617i | \(0.326822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9110 | 0.959671 | 0.479835 | − | 0.877359i | \(-0.340696\pi\) | ||||
0.479835 | + | 0.877359i | \(0.340696\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.17162 | −0.382297 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.71610 | 0.420256 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.6646 | −0.999253 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.20905 | 0.306163 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.15752 | −0.590258 | −0.295129 | − | 0.955457i | \(-0.595363\pi\) | ||||
−0.295129 | + | 0.955457i | \(0.595363\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.7613 | −1.20651 | −0.603254 | − | 0.797549i | \(-0.706130\pi\) | ||||
−0.603254 | + | 0.797549i | \(0.706130\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.753525 | 0.0539611 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.9110 | −0.777380 | −0.388690 | − | 0.921369i | \(-0.627072\pi\) | ||||
−0.388690 | + | 0.921369i | \(0.627072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.49295 | −0.318497 | −0.159248 | − | 0.987239i | \(-0.550907\pi\) | ||||
−0.159248 | + | 0.987239i | \(0.550907\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.209050 | −0.0147452 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.8877 | 1.46603 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.38067 | 0.655175 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.0890 | 0.905382 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.71610 | 0.668884 | 0.334442 | − | 0.942416i | \(-0.391452\pi\) | ||||
0.334442 | + | 0.942416i | \(0.391452\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.38067 | 0.642753 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.4181 | −0.846907 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.879901 | −0.0597316 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.2606 | 0.693345 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.73942 | 0.251541 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.4322 | −1.30128 | −0.650638 | − | 0.759388i | \(-0.725499\pi\) | ||||
−0.650638 | + | 0.759388i | \(0.725499\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.985900 | −0.0654365 | −0.0327182 | − | 0.999465i | \(-0.510416\pi\) | ||||
−0.0327182 | + | 0.999465i | \(0.510416\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.08895 | 0.204124 | 0.102062 | − | 0.994778i | \(-0.467456\pi\) | ||||
0.102062 | + | 0.994778i | \(0.467456\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.5897 | 0.762548 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.83620 | 0.578879 | 0.289439 | − | 0.957196i | \(-0.406531\pi\) | ||||
0.289439 | + | 0.957196i | \(0.406531\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.17162 | −0.467825 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.41810 | −0.157072 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.3807 | −1.38300 | −0.691500 | − | 0.722376i | \(-0.743050\pi\) | ||||
−0.691500 | + | 0.722376i | \(0.743050\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.2606 | 1.43393 | 0.716965 | − | 0.697109i | \(-0.245531\pi\) | ||||
0.716965 | + | 0.697109i | \(0.245531\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.7161 | −0.684627 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.58190 | −0.227911 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.45552 | 0.345730 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.59600 | −0.416336 | −0.208168 | − | 0.978093i | \(-0.566750\pi\) | ||||
−0.208168 | + | 0.978093i | \(0.566750\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.75353 | 0.173113 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.96257 | 0.310768 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.1857 | −1.13439 | −0.567197 | − | 0.823582i | \(-0.691972\pi\) | ||||
−0.567197 | + | 0.823582i | \(0.691972\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.0593 | −1.49498 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.96257 | 0.307176 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.3807 | −0.948413 | −0.474207 | − | 0.880414i | \(-0.657265\pi\) | ||||
−0.474207 | + | 0.880414i | \(0.657265\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.38067 | 0.576250 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.91105 | 0.300551 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.544475 | 0.0331972 | 0.0165986 | − | 0.999862i | \(-0.494716\pi\) | ||||
0.0165986 | + | 0.999862i | \(0.494716\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.2090 | −0.741647 | −0.370823 | − | 0.928703i | \(-0.620925\pi\) | ||||
−0.370823 | + | 0.928703i | \(0.620925\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.17162 | −0.191955 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.75353 | 0.166044 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.0141 | −1.26261 | −0.631307 | − | 0.775533i | \(-0.717481\pi\) | ||||
−0.631307 | + | 0.775533i | \(0.717481\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.209050 | −0.0125155 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.1857 | −1.44280 | −0.721400 | − | 0.692519i | \(-0.756501\pi\) | ||||
−0.721400 | + | 0.692519i | \(0.756501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.1201 | 0.898797 | 0.449398 | − | 0.893331i | \(-0.351638\pi\) | ||||
0.449398 | + | 0.893331i | \(0.351638\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.75353 | −0.281575 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −39.4837 | −2.33065 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.62715 | 0.448656 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3432 | 0.606332 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.4696 | 0.611642 | 0.305821 | − | 0.952089i | \(-0.401069\pi\) | ||||
0.305821 | + | 0.952089i | \(0.401069\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.96257 | 0.288932 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.75353 | 0.159776 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.753525 | −0.0435775 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 52.2684 | 3.01270 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.8877 | 0.855277 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.17162 | 0.296126 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.1575 | −0.693867 | −0.346933 | − | 0.937890i | \(-0.612777\pi\) | ||||
−0.346933 | + | 0.937890i | \(0.612777\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.9251 | 1.01973 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.4181 | −1.95167 | −0.975836 | − | 0.218506i | \(-0.929882\pi\) | ||||
−0.975836 | + | 0.218506i | \(0.929882\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.5664 | 1.67119 | 0.835596 | − | 0.549345i | \(-0.185123\pi\) | ||||
0.835596 | + | 0.549345i | \(0.185123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.20905 | −0.237153 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.66457 | 0.0934918 | 0.0467459 | − | 0.998907i | \(-0.485115\pi\) | ||||
0.0467459 | + | 0.998907i | \(0.485115\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.6646 | 0.765069 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.4696 | −0.919245 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.5897 | −1.31257 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.753525 | −0.0417981 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.26058 | −0.346211 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.1857 | 1.66419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.12010 | 0.171496 | 0.0857481 | − | 0.996317i | \(-0.472672\pi\) | ||||
0.0857481 | + | 0.996317i | \(0.472672\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.71610 | −0.313240 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.209050 | 0.0114216 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5819 | −0.630906 | −0.315453 | − | 0.948941i | \(-0.602157\pi\) | ||||
−0.315453 | + | 0.948941i | \(0.602157\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.38067 | −0.509488 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.575624 | −0.0311718 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.6412 | 0.844548 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.3432 | 1.41418 | 0.707090 | − | 0.707124i | \(-0.250008\pi\) | ||||
0.707090 | + | 0.707124i | \(0.250008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.22315 | 0.493704 | 0.246852 | − | 0.969053i | \(-0.420604\pi\) | ||||
0.246852 | + | 0.969053i | \(0.420604\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.753525 | −0.0402202 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.1857 | −0.967928 | −0.483964 | − | 0.875088i | \(-0.660804\pi\) | ||||
−0.483964 | + | 0.875088i | \(0.660804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.38067 | −0.497875 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20.8877 | −1.10550 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.17162 | 0.378504 | 0.189252 | − | 0.981929i | \(-0.439394\pi\) | ||||
0.189252 | + | 0.981929i | \(0.439394\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.59600 | 0.189263 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.41810 | −0.179404 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.2606 | −0.537063 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.5664 | 0.916959 | 0.458479 | − | 0.888705i | \(-0.348394\pi\) | ||||
0.458479 | + | 0.888705i | \(0.348394\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.38067 | −0.488338 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −39.4837 | −2.04989 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.6724 | −1.74349 | −0.871745 | − | 0.489959i | \(-0.837012\pi\) | ||||
−0.871745 | + | 0.489959i | \(0.837012\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.73942 | −0.192590 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.4181 | 0.946074 | 0.473037 | − | 0.881043i | \(-0.343158\pi\) | ||||
0.473037 | + | 0.881043i | \(0.343158\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.0827 | −1.13133 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.7847 | −1.06205 | −0.531024 | − | 0.847357i | \(-0.678192\pi\) | ||||
−0.531024 | + | 0.847357i | \(0.678192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.5897 | −0.590667 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.4181 | 0.631247 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.5212 | 1.14187 | 0.570934 | − | 0.820996i | \(-0.306581\pi\) | ||||
0.570934 | + | 0.820996i | \(0.306581\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.96257 | −0.250968 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.58190 | −0.0797963 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.41810 | 0.121668 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.4040 | −0.773105 | −0.386552 | − | 0.922267i | \(-0.626334\pi\) | ||||
−0.386552 | + | 0.922267i | \(0.626334\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.0078 | 1.00164 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.5212 | −0.525401 | −0.262701 | − | 0.964877i | \(-0.584613\pi\) | ||||
−0.262701 | + | 0.964877i | \(0.584613\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.157524 | 0.00784684 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.7394 | −0.780174 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.0593 | −1.28855 | −0.644276 | − | 0.764793i | \(-0.722841\pi\) | ||||
−0.644276 | + | 0.764793i | \(0.722841\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.91105 | −0.242244 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −20.8877 | −1.02782 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.45552 | −0.267801 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.1342 | 0.692155 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.73942 | −0.182683 | −0.0913414 | − | 0.995820i | \(-0.529115\pi\) | ||||
−0.0913414 | + | 0.995820i | \(0.529115\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.09677 | −0.150928 | −0.0754638 | − | 0.997149i | \(-0.524044\pi\) | ||||
−0.0754638 | + | 0.997149i | \(0.524044\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.17162 | 0.348696 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.96257 | −0.240720 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.7676 | −1.05341 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.07485 | −0.100175 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.1653 | −1.74202 | −0.871012 | − | 0.491262i | \(-0.836536\pi\) | ||||
−0.871012 | + | 0.491262i | \(0.836536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6271 | −0.799050 | −0.399525 | − | 0.916722i | \(-0.630825\pi\) | ||||
−0.399525 | + | 0.916722i | \(0.630825\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.96257 | −0.237937 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.75353 | 0.227392 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.7613 | 1.84998 | 0.924989 | − | 0.379994i | \(-0.124074\pi\) | ||||
0.924989 | + | 0.379994i | \(0.124074\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.7161 | 0.510290 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.5149 | 1.59234 | 0.796170 | − | 0.605073i | \(-0.206856\pi\) | ||||
0.796170 | + | 0.605073i | \(0.206856\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.91105 | −0.232806 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.24647 | 0.153553 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.9018 | −0.656068 | −0.328034 | − | 0.944666i | \(-0.606386\pi\) | ||||
−0.328034 | + | 0.944666i | \(0.606386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.8299 | −1.21628 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.418100 | 0.0196440 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.17162 | 0.148688 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.28390 | −0.106836 | −0.0534182 | − | 0.998572i | \(-0.517012\pi\) | ||||
−0.0534182 | + | 0.998572i | \(0.517012\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.96257 | −0.231633 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.34325 | 0.388584 | 0.194292 | − | 0.980944i | \(-0.437759\pi\) | ||||
0.194292 | + | 0.980944i | \(0.437759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.6928 | −1.28699 | −0.643496 | − | 0.765449i | \(-0.722517\pi\) | ||||
−0.643496 | + | 0.765449i | \(0.722517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.209050 | 0.00969445 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.53037 | 0.348464 | 0.174232 | − | 0.984705i | \(-0.444256\pi\) | ||||
0.174232 | + | 0.984705i | \(0.444256\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.879901 | −0.0406300 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.0452 | −0.969714 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 34.1935 | 1.57222 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.75353 | 0.218107 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.38067 | −0.429512 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.1857 | −0.830927 | −0.415463 | − | 0.909610i | \(-0.636381\pi\) | ||||
−0.415463 | + | 0.909610i | \(0.636381\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.30722 | 0.196393 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.20905 | 0.191518 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.3432 | −0.469663 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.2606 | −1.09935 | −0.549676 | − | 0.835378i | \(-0.685249\pi\) | ||||
−0.549676 | + | 0.835378i | \(0.685249\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.43220 | −0.336096 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.8877 | 0.671874 | 0.335937 | − | 0.941885i | \(-0.390947\pi\) | ||||
0.335937 | + | 0.941885i | \(0.390947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.6271 | −1.10915 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.75353 | −0.123762 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 39.4837 | 1.77109 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.312101 | −0.0139716 | −0.00698578 | − | 0.999976i | \(-0.502224\pi\) | ||||
−0.00698578 | + | 0.999976i | \(0.502224\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.1716 | −0.856525 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.8877 | 0.931338 | 0.465669 | − | 0.884959i | \(-0.345814\pi\) | ||||
0.465669 | + | 0.884959i | \(0.345814\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.8877 | −0.662495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.4322 | −0.552133 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.9251 | 1.23776 | 0.618880 | − | 0.785485i | \(-0.287587\pi\) | ||||
0.618880 | + | 0.785485i | \(0.287587\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.1873 | 1.91049 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.75353 | 0.209873 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17.9251 | −0.789876 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.7472 | 0.868483 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.0360 | 1.40352 | 0.701762 | − | 0.712412i | \(-0.252397\pi\) | ||||
0.701762 | + | 0.712412i | \(0.252397\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.8644 | 1.69942 | 0.849711 | − | 0.527249i | \(-0.176777\pi\) | ||||
0.849711 | + | 0.527249i | \(0.176777\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.20905 | 0.183698 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.03743 | 0.0451909 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.96257 | −0.215357 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.06857 | 0.306174 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.4696 | 0.712044 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.8503 | 0.597685 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.5071 | 1.27096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.07485 | 0.175191 | 0.0875957 | − | 0.996156i | \(-0.472082\pi\) | ||||
0.0875957 | + | 0.996156i | \(0.472082\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.9110 | 0.554066 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.26058 | 0.268174 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.17162 | −0.220720 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.5897 | 1.00496 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.1779 | −0.432808 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.71610 | 0.242635 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.63343 | 0.0692105 | 0.0346052 | − | 0.999401i | \(-0.488983\pi\) | ||||
0.0346052 | + | 0.999401i | \(0.488983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.35735 | −0.395774 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.6646 | −0.576919 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.2310 | −0.979069 | −0.489534 | − | 0.871984i | \(-0.662833\pi\) | ||||
−0.489534 | + | 0.871984i | \(0.662833\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.38067 | 0.394648 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.20905 | 0.176763 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.3291 | 0.894164 | 0.447082 | − | 0.894493i | \(-0.352463\pi\) | ||||
0.447082 | + | 0.894493i | \(0.352463\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.18573 | −0.175167 | −0.0875836 | − | 0.996157i | \(-0.527914\pi\) | ||||
−0.0875836 | + | 0.996157i | \(0.527914\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.15752 | −0.340785 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5678 | 0.439943 | 0.219972 | − | 0.975506i | \(-0.429404\pi\) | ||||
0.219972 | + | 0.975506i | \(0.429404\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.7613 | −0.696578 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.9626 | 0.952648 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.8299 | −1.06977 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.753525 | 0.0311544 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.4181 | 1.17294 | 0.586470 | − | 0.809971i | \(-0.300517\pi\) | ||||
0.586470 | + | 0.809971i | \(0.300517\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.993723 | −0.0409457 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.9110 | −0.448821 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.9937 | 1.19063 | 0.595315 | − | 0.803493i | \(-0.297027\pi\) | ||||
0.595315 | + | 0.803493i | \(0.297027\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.8877 | 0.856313 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.49295 | −0.183884 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.10305 | −0.249364 | −0.124682 | − | 0.992197i | \(-0.539791\pi\) | ||||
−0.124682 | + | 0.992197i | \(0.539791\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.3885 | −1.19878 | −0.599391 | − | 0.800456i | \(-0.704590\pi\) | ||||
−0.599391 | + | 0.800456i | \(0.704590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.209050 | −0.00851316 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.41810 | 0.138966 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.58972 | −0.145702 | −0.0728512 | − | 0.997343i | \(-0.523210\pi\) | ||||
−0.0728512 | + | 0.997343i | \(0.523210\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.8877 | 0.846413 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.40400 | −0.218622 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.4040 | −0.864499 | −0.432250 | − | 0.901754i | \(-0.642280\pi\) | ||||
−0.432250 | + | 0.901754i | \(0.642280\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.38067 | 0.378265 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.2917 | 1.30002 | 0.650008 | − | 0.759927i | \(-0.274766\pi\) | ||||
0.650008 | + | 0.759927i | \(0.274766\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.1046 | 1.89329 | 0.946647 | − | 0.322273i | \(-0.104447\pi\) | ||||
0.946647 | + | 0.322273i | \(0.104447\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.6709 | 0.828160 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.0890 | 0.522722 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.3666 | 1.13105 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5149 | 0.936112 | 0.468056 | − | 0.883699i | \(-0.344954\pi\) | ||||
0.468056 | + | 0.883699i | \(0.344954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.71610 | 0.386180 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.0827 | 0.876324 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.07485 | −0.319937 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.38067 | 0.371094 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.67867 | −0.263792 | −0.131896 | − | 0.991264i | \(-0.542106\pi\) | ||||
−0.131896 | + | 0.991264i | \(0.542106\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.1201 | 1.06951 | 0.534756 | − | 0.845006i | \(-0.320403\pi\) | ||||
0.534756 | + | 0.845006i | \(0.320403\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.4181 | −0.488962 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.7394 | −1.09055 | −0.545275 | − | 0.838257i | \(-0.683575\pi\) | ||||
−0.545275 | + | 0.838257i | \(0.683575\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.6646 | −0.536381 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.879901 | −0.0344860 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.75353 | −0.107754 | −0.0538769 | − | 0.998548i | \(-0.517158\pi\) | ||||
−0.0538769 | + | 0.998548i | \(0.517158\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.58190 | 0.0618100 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.2606 | 0.400303 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.5897 | 0.451472 | 0.225736 | − | 0.974189i | \(-0.427521\pi\) | ||||
0.225736 | + | 0.974189i | \(0.427521\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.3432 | 1.10242 | 0.551212 | − | 0.834365i | \(-0.314165\pi\) | ||||
0.551212 | + | 0.834365i | \(0.314165\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.73942 | 0.145227 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.0078 | −0.775870 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.96257 | 0.192152 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.4322 | −0.751292 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.2402 | −0.549737 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.0360 | −1.85165 | −0.925826 | − | 0.377949i | \(-0.876629\pi\) | ||||
−0.925826 | + | 0.377949i | \(0.876629\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.51627 | 0.0967083 | 0.0483541 | − | 0.998830i | \(-0.484602\pi\) | ||||
0.0483541 | + | 0.998830i | \(0.484602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.5353 | 1.67073 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.985900 | −0.0377798 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.84248 | −0.147028 | −0.0735141 | − | 0.997294i | \(-0.523421\pi\) | ||||
−0.0735141 | + | 0.997294i | \(0.523421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.91105 | 0.187642 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.08895 | 0.117851 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.06857 | 0.269291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.59600 | 0.0987565 | 0.0493783 | − | 0.998780i | \(-0.484276\pi\) | ||||
0.0493783 | + | 0.998780i | \(0.484276\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.5897 | 0.440257 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.1342 | −0.536141 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.5523 | 1.76329 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.83620 | 0.334216 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.5897 | 1.57082 | 0.785411 | − | 0.618974i | \(-0.212452\pi\) | ||||
0.785411 | + | 0.618974i | \(0.212452\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.1716 | −1.02480 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.17162 | −0.270099 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 62.6632 | 2.35669 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −53.1716 | −1.99690 | −0.998451 | − | 0.0556356i | \(-0.982281\pi\) | ||||
−0.998451 | + | 0.0556356i | \(0.982281\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.41810 | −0.0906858 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.209050 | −0.00782898 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.07485 | 0.0775950 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.3807 | −0.798476 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.3807 | 1.69241 | 0.846207 | − | 0.532855i | \(-0.178881\pi\) | ||||
0.846207 | + | 0.532855i | \(0.178881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 75.4478 | 2.80982 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.2606 | 0.827880 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.96257 | 0.184305 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.4026 | −1.72098 | −0.860489 | − | 0.509470i | \(-0.829842\pi\) | ||||
−0.860489 | + | 0.509470i | \(0.829842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −61.6257 | −2.27931 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.8051 | 0.842324 | 0.421162 | − | 0.906985i | \(-0.361622\pi\) | ||||
0.421162 | + | 0.906985i | \(0.361622\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.7161 | −0.395269 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.575624 | −0.0212034 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5241 | −0.607849 | −0.303924 | − | 0.952696i | \(-0.598297\pi\) | ||||
−0.303924 | + | 0.952696i | \(0.598297\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.58190 | −0.131584 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.8503 | 1.60871 | 0.804356 | − | 0.594148i | \(-0.202511\pi\) | ||||
0.804356 | + | 0.594148i | \(0.202511\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.24647 | −0.118942 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.45552 | 0.199607 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −69.3215 | −2.53295 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.73942 | 0.209435 | 0.104717 | − | 0.994502i | \(-0.466606\pi\) | ||||
0.104717 | + | 0.994502i | \(0.466606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.59600 | −0.240372 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.418100 | −0.0152162 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.86580 | −0.358579 | −0.179289 | − | 0.983796i | \(-0.557380\pi\) | ||||
−0.179289 | + | 0.983796i | \(0.557380\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.75353 | 0.0999466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.69418 | 0.170164 | 0.0850819 | − | 0.996374i | \(-0.472885\pi\) | ||||
0.0850819 | + | 0.996374i | \(0.472885\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.3511 | −0.953973 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.96257 | 0.179422 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.73942 | 0.135023 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.5431 | 1.64233 | 0.821163 | − | 0.570694i | \(-0.193326\pi\) | ||||
0.821163 | + | 0.570694i | \(0.193326\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.1857 | −0.654943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.4929 | 0.449340 | 0.224670 | − | 0.974435i | \(-0.427870\pi\) | ||||
0.224670 | + | 0.974435i | \(0.427870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.209050 | −0.00750929 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.0593 | −0.863124 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −44.5913 | −1.59765 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.8299 | 0.924267 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.96257 | 0.177348 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.0452 | 0.751137 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.71610 | −0.203757 | −0.101878 | − | 0.994797i | \(-0.532485\pi\) | ||||
−0.101878 | + | 0.994797i | \(0.532485\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.3807 | −0.547567 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.4837 | −1.40388 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.89695 | 0.138385 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.38067 | 0.332698 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.48373 | −0.335931 | −0.167965 | − | 0.985793i | \(-0.553720\pi\) | ||||
−0.167965 | + | 0.985793i | \(0.553720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.5897 | −1.25907 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.91105 | 0.173523 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.2528 | 0.997018 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.20905 | −0.148350 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.544475 | 0.0191664 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.0672 | 1.76027 | 0.880134 | − | 0.474725i | \(-0.157453\pi\) | ||||
0.880134 | + | 0.474725i | \(0.157453\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.14830 | −0.321240 | −0.160620 | − | 0.987016i | \(-0.551349\pi\) | ||||
−0.160620 | + | 0.987016i | \(0.551349\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.2090 | −0.428190 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.43220 | 0.260339 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59.0297 | 2.06519 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.17162 | −0.110826 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.91105 | −0.171397 | −0.0856984 | − | 0.996321i | \(-0.527312\pi\) | ||||
−0.0856984 | + | 0.996321i | \(0.527312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.7006 | 0.826151 | 0.413075 | − | 0.910697i | \(-0.364455\pi\) | ||||
0.413075 | + | 0.910697i | \(0.364455\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.75353 | 0.0958654 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.1405 | 0.456939 | 0.228470 | − | 0.973551i | \(-0.426628\pi\) | ||||
0.228470 | + | 0.973551i | \(0.426628\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.6412 | −1.58519 | −0.792593 | − | 0.609751i | \(-0.791269\pi\) | ||||
−0.792593 | + | 0.609751i | \(0.791269\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.0141 | −0.728971 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −53.1794 | −1.84256 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.1716 | 0.663461 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.209050 | −0.00722582 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.40400 | −0.186567 | −0.0932834 | − | 0.995640i | \(-0.529736\pi\) | ||||
−0.0932834 | + | 0.995640i | \(0.529736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.37285 | −0.150788 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.1857 | −0.833001 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4322 | 0.427681 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.3870 | −0.494341 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.1201 | 0.518920 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.71610 | −0.195945 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.0297 | −1.81570 | −0.907852 | − | 0.419291i | \(-0.862279\pi\) | ||||
−0.907852 | + | 0.419291i | \(0.862279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.75353 | −0.162567 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.4463 | −0.493476 | −0.246738 | − | 0.969082i | \(-0.579359\pi\) | ||||
−0.246738 | + | 0.969082i | \(0.579359\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.8658 | 0.473095 | 0.236548 | − | 0.971620i | \(-0.423984\pi\) | ||||
0.236548 | + | 0.971620i | \(0.423984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.4837 | −1.34560 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.5834 | 1.78996 | 0.894981 | − | 0.446105i | \(-0.147189\pi\) | ||||
0.894981 | + | 0.446105i | \(0.147189\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.62715 | 0.259032 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.65830 | −0.225867 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.157524 | 0.00533751 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.3432 | 0.350066 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.20905 | −0.142292 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.3291 | −0.855305 | −0.427652 | − | 0.903943i | \(-0.640659\pi\) | ||||
−0.427652 | + | 0.903943i | \(0.640659\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.4696 | 0.353132 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.2606 | 0.480451 | 0.240225 | − | 0.970717i | \(-0.422779\pi\) | ||||
0.240225 | + | 0.970717i | \(0.422779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.6320 | 1.36738 | 0.683688 | − | 0.729774i | \(-0.260375\pi\) | ||||
0.683688 | + | 0.729774i | \(0.260375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.96257 | 0.166815 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.9534 | −0.669968 | −0.334984 | − | 0.942224i | \(-0.608731\pi\) | ||||
−0.334984 | + | 0.942224i | \(0.608731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −92.9471 | −3.11734 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.75353 | 0.0922466 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.0905 | 1.14080 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.8503 | −0.462964 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.753525 | −0.0251595 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.03743 | −0.0346001 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.5523 | 1.55088 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 52.2684 | 1.73938 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.9110 | −0.429178 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.8814 | −0.992197 | −0.496099 | − | 0.868266i | \(-0.665235\pi\) | ||||
−0.496099 | + | 0.868266i | \(0.665235\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.8877 | 0.493795 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.8644 | 0.625005 | 0.312503 | − | 0.949917i | \(-0.398833\pi\) | ||||
0.312503 | + | 0.949917i | \(0.398833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.0219 | 0.497153 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.17162 | 0.170969 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.65830 | −0.219876 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.2402 | 0.535715 | 0.267857 | − | 0.963459i | \(-0.413684\pi\) | ||||
0.267857 | + | 0.963459i | \(0.413684\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.1575 | −0.400604 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.06857 | −0.232665 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.71610 | −0.187944 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.9251 | 0.588739 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.3340 | 0.962418 | 0.481209 | − | 0.876606i | \(-0.340198\pi\) | ||||
0.481209 | + | 0.876606i | \(0.340198\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.9393 | 1.66947 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34.4181 | −1.12680 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.6646 | 0.446879 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.3573 | −1.35109 | −0.675543 | − | 0.737321i | \(-0.736091\pi\) | ||||
−0.675543 | + | 0.737321i | \(0.736091\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.5664 | 0.964863 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.4259 | 1.64384 | 0.821919 | − | 0.569604i | \(-0.192904\pi\) | ||||
0.821919 | + | 0.569604i | \(0.192904\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.38067 | −0.305477 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.20905 | −0.136920 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.50705 | 0.178955 | 0.0894775 | − | 0.995989i | \(-0.471480\pi\) | ||||
0.0894775 | + | 0.995989i | \(0.471480\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.73160 | −0.250978 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.66457 | 0.0539775 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.864400 | 0.0280007 | 0.0140003 | − | 0.999902i | \(-0.495543\pi\) | ||||
0.0140003 | + | 0.999902i | \(0.495543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.15752 | 0.263971 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.6646 | 0.441713 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.6709 | −0.667497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9563 | −0.998590 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.4696 | −0.530726 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.7613 | 0.539567 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.7535 | 0.345810 | 0.172905 | − | 0.984939i | \(-0.444685\pi\) | ||||
0.172905 | + | 0.984939i | \(0.444685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.5897 | −0.757811 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.1794 | 1.12896 | 0.564481 | − | 0.825446i | \(-0.309076\pi\) | ||||
0.564481 | + | 0.825446i | \(0.309076\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 59.4915 | 1.90721 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.753525 | −0.0241321 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.9767 | 0.511139 | 0.255570 | − | 0.966791i | \(-0.417737\pi\) | ||||
0.255570 | + | 0.966791i | \(0.417737\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.5227 | 0.432187 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.26058 | −0.199885 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −57.2592 | −1.82628 | −0.913142 | − | 0.407642i | \(-0.866351\pi\) | ||||
−0.913142 | + | 0.407642i | \(0.866351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.9110 | 0.347655 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30.1857 | 0.960822 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.4181 | 0.394873 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.8799 | 0.409144 | 0.204572 | − | 0.978852i | \(-0.434420\pi\) | ||||
0.204572 | + | 0.978852i | \(0.434420\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.12010 | 0.0990134 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.49295 | 0.142436 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.7754 | −1.25970 | −0.629851 | − | 0.776716i | \(-0.716884\pi\) | ||||
−0.629851 | + | 0.776716i | \(0.716884\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.71610 | −0.180849 |
(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 | 1380.2.a.j.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 4140.2.a.s.1.3 | 3 | |||
4.3 | odd | 2 | 5520.2.a.bv.1.1 | 3 | |||
5.2 | odd | 4 | 6900.2.f.r.6349.3 | 6 | |||
5.3 | odd | 4 | 6900.2.f.r.6349.4 | 6 | |||
5.4 | even | 2 | 6900.2.a.x.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1380.2.a.j.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
4140.2.a.s.1.3 | 3 | 3.2 | odd | 2 | |||
5520.2.a.bv.1.1 | 3 | 4.3 | odd | 2 | |||
6900.2.a.x.1.1 | 3 | 5.4 | even | 2 | |||
6900.2.f.r.6349.3 | 6 | 5.2 | odd | 4 | |||
6900.2.f.r.6349.4 | 6 | 5.3 | odd | 4 |