Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 55 x^{16} + 288 x^{15} + 1222 x^{14} - 6888 x^{13} - 13745 x^{12} + 88434 x^{11} + 76571 x^{10} - 655793 x^{9} - 114554 x^{8} + 2789438 x^{7} + \cdots - 115488 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.235801\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(5\) | 0.235801 | 0.105453 | 0.0527267 | − | 0.998609i | \(-0.483209\pi\) | ||||
0.0527267 | + | 0.998609i | \(0.483209\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32081 | 0.499219 | 0.249609 | − | 0.968347i | \(-0.419698\pi\) | ||||
0.249609 | + | 0.968347i | \(0.419698\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.55746 | 0.469593 | 0.234797 | − | 0.972045i | \(-0.424558\pi\) | ||||
0.234797 | + | 0.972045i | \(0.424558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.66795 | −1.01731 | −0.508653 | − | 0.860972i | \(-0.669856\pi\) | ||||
−0.508653 | + | 0.860972i | \(0.669856\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.235801 | 0.0608835 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.58826 | −0.627745 | −0.313872 | − | 0.949465i | \(-0.601626\pi\) | ||||
−0.313872 | + | 0.949465i | \(0.601626\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.45355 | −0.333468 | −0.166734 | − | 0.986002i | \(-0.553322\pi\) | ||||
−0.166734 | + | 0.986002i | \(0.553322\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.32081 | 0.288224 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.94440 | −0.988880 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.25177 | 1.12285 | 0.561425 | − | 0.827527i | \(-0.310253\pi\) | ||||
0.561425 | + | 0.827527i | \(0.310253\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.55746 | 0.271120 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.311448 | 0.0526443 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.15202 | −1.50458 | −0.752291 | − | 0.658831i | \(-0.771051\pi\) | ||||
−0.752291 | + | 0.658831i | \(0.771051\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.66795 | −0.587342 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.1000 | 1.73353 | 0.866764 | − | 0.498719i | \(-0.166196\pi\) | ||||
0.866764 | + | 0.498719i | \(0.166196\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.13805 | 1.39354 | 0.696770 | − | 0.717295i | \(-0.254620\pi\) | ||||
0.696770 | + | 0.717295i | \(0.254620\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.235801 | 0.0351511 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.96289 | 1.16151 | 0.580753 | − | 0.814080i | \(-0.302758\pi\) | ||||
0.580753 | + | 0.814080i | \(0.302758\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.25546 | −0.750781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.58826 | −0.362429 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.80551 | −0.797448 | −0.398724 | − | 0.917071i | \(-0.630547\pi\) | ||||
−0.398724 | + | 0.917071i | \(0.630547\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.367252 | 0.0495202 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.45355 | −0.192528 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.27926 | 0.687301 | 0.343650 | − | 0.939098i | \(-0.388337\pi\) | ||||
0.343650 | + | 0.939098i | \(0.388337\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9066 | 1.65252 | 0.826260 | − | 0.563289i | \(-0.190464\pi\) | ||||
0.826260 | + | 0.563289i | \(0.190464\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.32081 | 0.166406 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.864906 | −0.107278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0629591 | −0.00769167 | −0.00384584 | − | 0.999993i | \(-0.501224\pi\) | ||||
−0.00384584 | + | 0.999993i | \(0.501224\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.10433 | 0.131060 | 0.0655298 | − | 0.997851i | \(-0.479126\pi\) | ||||
0.0655298 | + | 0.997851i | \(0.479126\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.3233 | 1.44233 | 0.721166 | − | 0.692763i | \(-0.243607\pi\) | ||||
0.721166 | + | 0.692763i | \(0.243607\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.94440 | −0.570930 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.05711 | 0.234430 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5754 | 1.41484 | 0.707422 | − | 0.706792i | \(-0.249858\pi\) | ||||
0.707422 | + | 0.706792i | \(0.249858\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.0990 | 1.21827 | 0.609137 | − | 0.793065i | \(-0.291516\pi\) | ||||
0.609137 | + | 0.793065i | \(0.291516\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.610314 | −0.0661978 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.93825 | 1.05345 | 0.526726 | − | 0.850035i | \(-0.323419\pi\) | ||||
0.526726 | + | 0.850035i | \(0.323419\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.84466 | −0.507858 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.25177 | 0.648278 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.342749 | −0.0351653 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.659173 | −0.0669289 | −0.0334645 | − | 0.999440i | \(-0.510654\pi\) | ||||
−0.0334645 | + | 0.999440i | \(0.510654\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.55746 | 0.156531 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.8646 | −1.67809 | −0.839043 | − | 0.544065i | \(-0.816884\pi\) | ||||
−0.839043 | + | 0.544065i | \(0.816884\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4751 | −1.22921 | −0.614604 | − | 0.788836i | \(-0.710684\pi\) | ||||
−0.614604 | + | 0.788836i | \(0.710684\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.311448 | 0.0303942 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.7008 | 1.71120 | 0.855598 | − | 0.517640i | \(-0.173189\pi\) | ||||
0.855598 | + | 0.517640i | \(0.173189\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0712 | 1.73090 | 0.865452 | − | 0.500992i | \(-0.167032\pi\) | ||||
0.865452 | + | 0.500992i | \(0.167032\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.15202 | −0.868671 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.31581 | −0.500069 | −0.250035 | − | 0.968237i | \(-0.580442\pi\) | ||||
−0.250035 | + | 0.968237i | \(0.580442\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.235801 | −0.0219886 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.66795 | −0.339102 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.41859 | −0.313382 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.57430 | −0.779482 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.1000 | 1.00085 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.34490 | −0.209734 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.1025 | 1.60634 | 0.803170 | − | 0.595750i | \(-0.203145\pi\) | ||||
0.803170 | + | 0.595750i | \(0.203145\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.13805 | 0.804561 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.1033 | 1.49432 | 0.747162 | − | 0.664642i | \(-0.231416\pi\) | ||||
0.747162 | + | 0.664642i | \(0.231416\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.91986 | −0.166473 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.235801 | 0.0202945 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.30297 | −0.282192 | −0.141096 | − | 0.989996i | \(-0.545063\pi\) | ||||
−0.141096 | + | 0.989996i | \(0.545063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.61502 | 0.476260 | 0.238130 | − | 0.971233i | \(-0.423466\pi\) | ||||
0.238130 | + | 0.971233i | \(0.423466\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.96289 | 0.670596 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.71270 | −0.477720 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.235801 | 0.0195822 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.25546 | −0.433463 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.57546 | −0.702529 | −0.351265 | − | 0.936276i | \(-0.614248\pi\) | ||||
−0.351265 | + | 0.936276i | \(0.614248\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.96597 | −0.159988 | −0.0799942 | − | 0.996795i | \(-0.525490\pi\) | ||||
−0.0799942 | + | 0.996795i | \(0.525490\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.58826 | −0.209248 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.47417 | 0.118408 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.8057 | 1.74029 | 0.870143 | − | 0.492799i | \(-0.164026\pi\) | ||||
0.870143 | + | 0.492799i | \(0.164026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.80551 | −0.460407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.32081 | −0.104094 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.957364 | −0.0749865 | −0.0374933 | − | 0.999297i | \(-0.511937\pi\) | ||||
−0.0374933 | + | 0.999297i | \(0.511937\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.367252 | 0.0285905 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.43303 | 0.729950 | 0.364975 | − | 0.931017i | \(-0.381078\pi\) | ||||
0.364975 | + | 0.931017i | \(0.381078\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.453852 | 0.0349117 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.45355 | −0.111156 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.93746 | −0.755531 | −0.377765 | − | 0.925901i | \(-0.623307\pi\) | ||||
−0.377765 | + | 0.925901i | \(0.623307\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.53060 | −0.493667 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.27926 | 0.396813 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.78781 | 0.582088 | 0.291044 | − | 0.956710i | \(-0.405997\pi\) | ||||
0.291044 | + | 0.956710i | \(0.405997\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6621 | 1.31282 | 0.656408 | − | 0.754406i | \(-0.272075\pi\) | ||||
0.656408 | + | 0.754406i | \(0.272075\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.9066 | 0.954083 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.15805 | −0.158663 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.03112 | −0.294785 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.32081 | 0.0960747 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.3446 | −1.18265 | −0.591326 | − | 0.806433i | \(-0.701395\pi\) | ||||
−0.591326 | + | 0.806433i | \(0.701395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.95073 | −0.212398 | −0.106199 | − | 0.994345i | \(-0.533868\pi\) | ||||
−0.106199 | + | 0.994345i | \(0.533868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.864906 | −0.0619372 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.66843 | −0.546353 | −0.273177 | − | 0.961964i | \(-0.588074\pi\) | ||||
−0.273177 | + | 0.961964i | \(0.588074\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.25025 | −0.0886278 | −0.0443139 | − | 0.999018i | \(-0.514110\pi\) | ||||
−0.0443139 | + | 0.999018i | \(0.514110\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.0629591 | −0.00444079 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.32081 | 0.0927026 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.61739 | 0.182806 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.26386 | −0.156594 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.0844 | −1.24498 | −0.622489 | − | 0.782628i | \(-0.713878\pi\) | ||||
−0.622489 | + | 0.782628i | \(0.713878\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.10433 | 0.0756673 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.15476 | 0.146953 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.25739 | 0.560548 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.3233 | 0.832730 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.49360 | 0.638609 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.9030 | −1.46674 | −0.733368 | − | 0.679832i | \(-0.762053\pi\) | ||||
−0.733368 | + | 0.679832i | \(0.762053\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.94440 | −0.329627 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.7643 | −1.04631 | −0.523155 | − | 0.852237i | \(-0.675245\pi\) | ||||
−0.523155 | + | 0.852237i | \(0.675245\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.580742 | −0.0383765 | −0.0191883 | − | 0.999816i | \(-0.506108\pi\) | ||||
−0.0191883 | + | 0.999816i | \(0.506108\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.05711 | 0.135348 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.02325 | −0.329084 | −0.164542 | − | 0.986370i | \(-0.552615\pi\) | ||||
−0.164542 | + | 0.986370i | \(0.552615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.87766 | 0.122485 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.5754 | 0.816860 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.5493 | −1.13517 | −0.567585 | − | 0.823315i | \(-0.692122\pi\) | ||||
−0.567585 | + | 0.823315i | \(0.692122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.66197 | 0.493551 | 0.246776 | − | 0.969073i | \(-0.420629\pi\) | ||||
0.246776 | + | 0.969073i | \(0.420629\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.23924 | −0.0791723 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.33155 | 0.339239 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.0990 | 0.703371 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.51257 | −0.474189 | −0.237095 | − | 0.971487i | \(-0.576195\pi\) | ||||
−0.237095 | + | 0.971487i | \(0.576195\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.55746 | −0.0979169 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.610314 | −0.0382193 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.3787 | −1.77022 | −0.885108 | − | 0.465386i | \(-0.845916\pi\) | ||||
−0.885108 | + | 0.465386i | \(0.845916\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.0881 | −0.751116 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.3465 | −0.637990 | −0.318995 | − | 0.947756i | \(-0.603345\pi\) | ||||
−0.318995 | + | 0.947756i | \(0.603345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.36894 | −0.0840936 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.93825 | 0.608211 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.0699 | 1.65048 | 0.825241 | − | 0.564781i | \(-0.191039\pi\) | ||||
0.825241 | + | 0.564781i | \(0.191039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.5819 | 1.91847 | 0.959233 | − | 0.282615i | \(-0.0912019\pi\) | ||||
0.959233 | + | 0.282615i | \(0.0912019\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.84466 | −0.293212 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.70072 | −0.464371 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.186204 | −0.0111879 | −0.00559395 | − | 0.999984i | \(-0.501781\pi\) | ||||
−0.00559395 | + | 0.999984i | \(0.501781\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.25177 | 0.374284 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.3180 | 1.21207 | 0.606035 | − | 0.795438i | \(-0.292759\pi\) | ||||
0.606035 | + | 0.795438i | \(0.292759\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.11388 | −0.125657 | −0.0628284 | − | 0.998024i | \(-0.520012\pi\) | ||||
−0.0628284 | + | 0.998024i | \(0.520012\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.342749 | −0.0203027 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.6610 | 0.865410 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3009 | −0.605937 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.659173 | −0.0386414 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.9170 | −0.929881 | −0.464940 | − | 0.885342i | \(-0.653924\pi\) | ||||
−0.464940 | + | 0.885342i | \(0.653924\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.24485 | 0.0724782 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.55746 | 0.0903732 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.66795 | 0.212123 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0696 | 0.695681 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.8646 | −0.968843 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.04339 | 0.174264 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.5322 | 1.22891 | 0.614454 | − | 0.788953i | \(-0.289376\pi\) | ||||
0.614454 | + | 0.788953i | \(0.289376\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4751 | −0.709684 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.6621 | 1.28505 | 0.642526 | − | 0.766264i | \(-0.277887\pi\) | ||||
0.642526 | + | 0.766264i | \(0.277887\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.15436 | −0.404389 | −0.202194 | − | 0.979345i | \(-0.564807\pi\) | ||||
−0.202194 | + | 0.979345i | \(0.564807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.311448 | 0.0175481 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.26223 | −0.183225 | −0.0916125 | − | 0.995795i | \(-0.529202\pi\) | ||||
−0.0916125 | + | 0.995795i | \(0.529202\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.55746 | 0.0872013 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.7008 | 0.987960 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.76217 | 0.209333 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.1358 | 1.00599 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.0712 | 0.999337 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.5175 | 0.579846 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.35489 | 0.129437 | 0.0647183 | − | 0.997904i | \(-0.479385\pi\) | ||||
0.0647183 | + | 0.997904i | \(0.479385\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.15202 | −0.501527 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.0148458 | −0.000811113 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.47977 | 0.135081 | 0.0675407 | − | 0.997717i | \(-0.478485\pi\) | ||||
0.0675407 | + | 0.997717i | \(0.478485\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.31581 | −0.288715 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.73690 | 0.527283 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1871 | −0.874023 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.235801 | −0.0126951 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.2901 | 0.767132 | 0.383566 | − | 0.923514i | \(-0.374696\pi\) | ||||
0.383566 | + | 0.923514i | \(0.374696\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.3138 | −0.605614 | −0.302807 | − | 0.953052i | \(-0.597924\pi\) | ||||
−0.302807 | + | 0.953052i | \(0.597924\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.66795 | −0.195781 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.17924 | −0.435337 | −0.217669 | − | 0.976023i | \(-0.569845\pi\) | ||||
−0.217669 | + | 0.976023i | \(0.569845\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.260402 | 0.0138207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.41859 | −0.180931 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.6446 | 0.720134 | 0.360067 | − | 0.932926i | \(-0.382754\pi\) | ||||
0.360067 | + | 0.932926i | \(0.382754\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8872 | −0.888799 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.57430 | −0.450034 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.90584 | 0.152099 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.14678 | 0.216460 | 0.108230 | − | 0.994126i | \(-0.465482\pi\) | ||||
0.108230 | + | 0.994126i | \(0.465482\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.1000 | 0.577843 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.66797 | −0.398101 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.5238 | −1.01090 | −0.505451 | − | 0.862855i | \(-0.668674\pi\) | ||||
−0.505451 | + | 0.862855i | \(0.668674\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.34490 | −0.121090 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.66795 | −0.188909 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2083 | 1.14076 | 0.570381 | − | 0.821380i | \(-0.306796\pi\) | ||||
0.570381 | + | 0.821380i | \(0.306796\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.1025 | 0.927421 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.3785 | −0.836902 | −0.418451 | − | 0.908239i | \(-0.637427\pi\) | ||||
−0.418451 | + | 0.908239i | \(0.637427\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.485069 | 0.0247214 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.13805 | 0.464513 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.61686 | −0.436892 | −0.218446 | − | 0.975849i | \(-0.570099\pi\) | ||||
−0.218446 | + | 0.975849i | \(0.570099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58826 | 0.130894 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.1033 | 0.862749 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.96529 | 0.149200 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.7894 | −1.14377 | −0.571885 | − | 0.820334i | \(-0.693787\pi\) | ||||
−0.571885 | + | 0.820334i | \(0.693787\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.91986 | −0.0961134 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.6941 | −0.633916 | −0.316958 | − | 0.948440i | \(-0.602661\pi\) | ||||
−0.316958 | + | 0.948440i | \(0.602661\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.9312 | −1.14228 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.235801 | 0.0117170 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.2539 | −0.706541 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.3119 | 1.20215 | 0.601073 | − | 0.799194i | \(-0.294740\pi\) | ||||
0.601073 | + | 0.799194i | \(0.294740\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.30297 | −0.162924 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.97289 | 0.343113 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.61716 | 0.128471 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.61502 | 0.274969 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.9676 | −1.07319 | −0.536594 | − | 0.843840i | \(-0.680289\pi\) | ||||
−0.536594 | + | 0.843840i | \(0.680289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.4023 | 0.994348 | 0.497174 | − | 0.867651i | \(-0.334371\pi\) | ||||
0.497174 | + | 0.867651i | \(0.334371\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.96289 | 0.387169 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.7974 | 0.620764 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.0471 | 0.824969 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.71270 | −0.275812 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.8642 | −0.667817 | −0.333909 | − | 0.942605i | \(-0.608368\pi\) | ||||
−0.333909 | + | 0.942605i | \(0.608368\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.17070 | −0.344602 | −0.172301 | − | 0.985044i | \(-0.555120\pi\) | ||||
−0.172301 | + | 0.985044i | \(0.555120\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.235801 | 0.0113058 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.45355 | 0.0695328 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.7238 | 0.941365 | 0.470683 | − | 0.882303i | \(-0.344008\pi\) | ||||
0.470683 | + | 0.882303i | \(0.344008\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.25546 | −0.250260 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.56265 | 0.454335 | 0.227167 | − | 0.973856i | \(-0.427054\pi\) | ||||
0.227167 | + | 0.973856i | \(0.427054\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.34345 | 0.111090 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.57546 | −0.405605 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.47592 | −0.400003 | −0.200002 | − | 0.979796i | \(-0.564095\pi\) | ||||
−0.200002 | + | 0.979796i | \(0.564095\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.2878 | 0.814053 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.96597 | −0.0923694 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.14238 | −0.0535554 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.53016 | 0.445802 | 0.222901 | − | 0.974841i | \(-0.428447\pi\) | ||||
0.222901 | + | 0.974841i | \(0.428447\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.58826 | −0.120810 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.60871 | 0.121500 | 0.0607498 | − | 0.998153i | \(-0.480651\pi\) | ||||
0.0607498 | + | 0.998153i | \(0.480651\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0415 | 0.838461 | 0.419230 | − | 0.907880i | \(-0.362300\pi\) | ||||
0.419230 | + | 0.907880i | \(0.362300\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.47417 | 0.0683631 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.51586 | 0.162695 | 0.0813473 | − | 0.996686i | \(-0.474078\pi\) | ||||
0.0813473 | + | 0.996686i | \(0.474078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.0831569 | −0.00383983 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.8057 | 1.00475 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.2322 | 0.654397 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.18694 | 0.329759 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.80551 | −0.265816 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.603449 | −0.0275723 | −0.0137861 | − | 0.999905i | \(-0.504388\pi\) | ||||
−0.0137861 | + | 0.999905i | \(0.504388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.5691 | 1.53062 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.32081 | −0.0600989 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.155434 | −0.00705788 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.61982 | 0.299973 | 0.149986 | − | 0.988688i | \(-0.452077\pi\) | ||||
0.149986 | + | 0.988688i | \(0.452077\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.957364 | −0.0432935 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6882 | −0.707998 | −0.353999 | − | 0.935246i | \(-0.615178\pi\) | ||||
−0.353999 | + | 0.935246i | \(0.615178\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.58826 | −0.116569 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.367252 | 0.0165067 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.45861 | 0.0654274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.0720 | −0.853779 | −0.426890 | − | 0.904304i | \(-0.640391\pi\) | ||||
−0.426890 | + | 0.904304i | \(0.640391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.43303 | 0.421437 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.50381 | −0.334578 | −0.167289 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167289 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.97668 | −0.176960 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.453852 | 0.0201563 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.7328 | 1.31789 | 0.658943 | − | 0.752193i | \(-0.271004\pi\) | ||||
0.658943 | + | 0.752193i | \(0.271004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.2767 | 0.720039 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.45355 | −0.0641759 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.94164 | −0.129624 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4019 | 0.545436 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.93746 | −0.436206 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.14188 | 0.0500268 | 0.0250134 | − | 0.999687i | \(-0.492037\pi\) | ||||
0.0250134 | + | 0.999687i | \(0.492037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.9260 | 0.696395 | 0.348197 | − | 0.937421i | \(-0.386794\pi\) | ||||
0.348197 | + | 0.937421i | \(0.386794\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.53060 | −0.285019 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.1812 | −0.704864 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.27926 | 0.229100 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.7142 | −1.76353 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.17386 | 0.180452 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.78781 | 0.336069 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.18520 | −0.352561 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.79768 | −0.421235 | −0.210618 | − | 0.977569i | \(-0.567547\pi\) | ||||
−0.210618 | + | 0.977569i | \(0.567547\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.6621 | 0.757955 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.26120 | 0.182530 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.9607 | 0.554161 | 0.277081 | − | 0.960847i | \(-0.410633\pi\) | ||||
0.277081 | + | 0.960847i | \(0.410633\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.9066 | 0.550840 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.45355 | −0.0619234 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.6097 | 0.706316 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.15805 | −0.0916043 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.0755 | 0.554026 | 0.277013 | − | 0.960866i | \(-0.410656\pi\) | ||||
0.277013 | + | 0.960866i | \(0.410656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.5179 | −1.41766 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.03112 | −0.170194 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.8969 | −1.13357 | −0.566785 | − | 0.823865i | \(-0.691813\pi\) | ||||
−0.566785 | + | 0.823865i | \(0.691813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.25347 | −0.0527340 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.32081 | 0.0554688 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.4961 | −0.649631 | −0.324816 | − | 0.945777i | \(-0.605302\pi\) | ||||
−0.324816 | + | 0.945777i | \(0.605302\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.7800 | 0.953312 | 0.476656 | − | 0.879090i | \(-0.341849\pi\) | ||||
0.476656 | + | 0.879090i | \(0.341849\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.3446 | −0.682804 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.94440 | 0.206196 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.6151 | 1.60757 | 0.803785 | − | 0.594920i | \(-0.202816\pi\) | ||||
0.803785 | + | 0.594920i | \(0.202816\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.95073 | −0.122628 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.6597 | 0.608185 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.04187 | −0.374476 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.864906 | −0.0357595 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.48452 | 0.391468 | 0.195734 | − | 0.980657i | \(-0.437291\pi\) | ||||
0.195734 | + | 0.980657i | \(0.437291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.08727 | −0.374434 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.66843 | −0.315437 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.4436 | 0.962714 | 0.481357 | − | 0.876525i | \(-0.340144\pi\) | ||||
0.481357 | + | 0.876525i | \(0.340144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.806108 | −0.0330472 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.25025 | −0.0511693 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.2702 | −1.80883 | −0.904416 | − | 0.426651i | \(-0.859693\pi\) | ||||
−0.904416 | + | 0.426651i | \(0.859693\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.15420 | −0.332617 | −0.166308 | − | 0.986074i | \(-0.553185\pi\) | ||||
−0.166308 | + | 0.986074i | \(0.553185\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0629591 | −0.00256389 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.02183 | −0.0821990 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.4638 | −0.952366 | −0.476183 | − | 0.879346i | \(-0.657980\pi\) | ||||
−0.476183 | + | 0.879346i | \(0.657980\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.32081 | 0.0535219 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.2075 | −1.18161 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.1828 | −0.976735 | −0.488367 | − | 0.872638i | \(-0.662407\pi\) | ||||
−0.488367 | + | 0.872638i | \(0.662407\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.61739 | 0.105543 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.9245 | 0.600839 | 0.300420 | − | 0.953807i | \(-0.402873\pi\) | ||||
0.300420 | + | 0.953807i | \(0.402873\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.0985 | 1.45092 | 0.725460 | − | 0.688264i | \(-0.241627\pi\) | ||||
0.725460 | + | 0.688264i | \(0.241627\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.1265 | 0.525903 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.1691 | 0.966762 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.26386 | −0.0904097 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.6878 | 0.944493 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.8935 | 0.831758 | 0.415879 | − | 0.909420i | \(-0.363474\pi\) | ||||
0.415879 | + | 0.909420i | \(0.363474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.0844 | −0.718788 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.26859 | 0.169394 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.2768 | 0.763774 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.10433 | 0.0436865 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.4373 | −0.886218 | −0.443109 | − | 0.896468i | \(-0.646125\pi\) | ||||
−0.443109 | + | 0.896468i | \(0.646125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.1046 | −0.635103 | −0.317552 | − | 0.948241i | \(-0.602861\pi\) | ||||
−0.317552 | + | 0.948241i | \(0.602861\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.15476 | 0.0848436 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.9830 | −1.57189 | −0.785947 | − | 0.618294i | \(-0.787824\pi\) | ||||
−0.785947 | + | 0.618294i | \(0.787824\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.22225 | 0.322752 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.25739 | 0.323633 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.3654 | 1.30569 | 0.652845 | − | 0.757492i | \(-0.273575\pi\) | ||||
0.652845 | + | 0.757492i | \(0.273575\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.03298 | 0.157582 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.3233 | 0.480777 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.8932 | 0.774930 | 0.387465 | − | 0.921884i | \(-0.373351\pi\) | ||||
0.387465 | + | 0.921884i | \(0.373351\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.4777 | 1.14655 | 0.573274 | − | 0.819363i | \(-0.305673\pi\) | ||||
0.573274 | + | 0.819363i | \(0.305673\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.49360 | 0.368701 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.452706 | −0.0175552 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.9030 | −0.846821 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.1016 | 0.776012 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.1505 | 1.12367 | 0.561835 | − | 0.827249i | \(-0.310095\pi\) | ||||
0.561835 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.94440 | −0.190310 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.9708 | −1.19031 | −0.595153 | − | 0.803612i | \(-0.702909\pi\) | ||||
−0.595153 | + | 0.803612i | \(0.702909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.870642 | −0.0334122 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.7643 | −0.604088 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.0933 | −0.539266 | −0.269633 | − | 0.962963i | \(-0.586902\pi\) | ||||
−0.269633 | + | 0.962963i | \(0.586902\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.778844 | −0.0297581 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.580742 | −0.0221567 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.2943 | 0.811249 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.2834 | −1.53245 | −0.766227 | − | 0.642570i | \(-0.777868\pi\) | ||||
−0.766227 | + | 0.642570i | \(0.777868\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.05711 | 0.0781433 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.32403 | 0.0502232 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.7296 | −1.08821 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.02325 | −0.189997 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.9405 | 1.16861 | 0.584303 | − | 0.811536i | \(-0.301368\pi\) | ||||
0.584303 | + | 0.811536i | \(0.301368\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.3029 | 0.501729 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.87766 | 0.0707167 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.2749 | −0.837732 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −52.0684 | −1.95547 | −0.977735 | − | 0.209842i | \(-0.932705\pi\) | ||||
−0.977735 | + | 0.209842i | \(0.932705\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.5754 | 0.471614 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.25177 | −0.234131 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.34706 | −0.0503772 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.5493 | −0.655390 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.53680 | −0.206488 | −0.103244 | − | 0.994656i | \(-0.532922\pi\) | ||||
−0.103244 | + | 0.994656i | \(0.532922\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.4772 | −0.613644 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.66197 | 0.284952 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.94440 | −0.183630 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.0694 | 0.447628 | 0.223814 | − | 0.974632i | \(-0.428149\pi\) | ||||
0.223814 | + | 0.974632i | \(0.428149\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.6516 | −0.874787 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.7033 | 0.801629 | 0.400815 | − | 0.916159i | \(-0.368727\pi\) | ||||
0.400815 | + | 0.916159i | \(0.368727\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.23924 | −0.0457102 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0980565 | −0.00361196 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.73830 | 0.358229 | 0.179115 | − | 0.983828i | \(-0.442677\pi\) | ||||
0.179115 | + | 0.983828i | \(0.442677\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.33155 | 0.195860 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.6942 | −0.392333 | −0.196166 | − | 0.980571i | \(-0.562849\pi\) | ||||
−0.196166 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.02210 | −0.0740841 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.0990 | 0.406091 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 23.3793 | 0.854262 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.4957 | −1.62367 | −0.811836 | − | 0.583886i | \(-0.801532\pi\) | ||||
−0.811836 | + | 0.583886i | \(0.801532\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.51257 | −0.273773 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.463578 | −0.0168713 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.9527 | −0.507118 | −0.253559 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253559 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.55746 | −0.0565324 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.28775 | 0.264181 | 0.132090 | − | 0.991238i | \(-0.457831\pi\) | ||||
0.132090 | + | 0.991238i | \(0.457831\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.8686 | 0.864100 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.610314 | −0.0220659 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.3640 | −0.699195 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.5824 | 0.886463 | 0.443232 | − | 0.896407i | \(-0.353832\pi\) | ||||
0.443232 | + | 0.896407i | \(0.353832\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.3787 | −1.02203 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.30187 | 0.262630 | 0.131315 | − | 0.991341i | \(-0.458080\pi\) | ||||
0.131315 | + | 0.991341i | \(0.458080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.9112 | −1.11036 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.0881 | −0.433657 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.1344 | −0.578075 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.71995 | 0.0615447 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.14181 | 0.183519 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.6152 | 1.69730 | 0.848650 | − | 0.528955i | \(-0.177416\pi\) | ||||
0.848650 | + | 0.528955i | \(0.177416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.3465 | −0.368344 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.02117 | −0.249644 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47.3407 | −1.68112 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.36894 | −0.0485515 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.7331 | −0.805246 | −0.402623 | − | 0.915366i | \(-0.631901\pi\) | ||||
−0.402623 | + | 0.915366i | \(0.631901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.6100 | −0.729130 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.93825 | 0.351151 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.1931 | 0.677309 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.311448 | −0.0109771 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.0699 | 0.952906 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.7281 | 0.517812 | 0.258906 | − | 0.965903i | \(-0.416638\pi\) | ||||
0.258906 | + | 0.965903i | \(0.416638\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.2811 | 0.396133 | 0.198067 | − | 0.980189i | \(-0.436534\pi\) | ||||
0.198067 | + | 0.980189i | \(0.436534\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 31.5819 | 1.10763 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.225747 | −0.00790758 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.2826 | −0.464700 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.84466 | −0.169286 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.1945 | 1.40280 | 0.701399 | − | 0.712769i | \(-0.252559\pi\) | ||||
0.701399 | + | 0.712769i | \(0.252559\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.7569 | 1.31612 | 0.658061 | − | 0.752964i | \(-0.271377\pi\) | ||||
0.658061 | + | 0.752964i | \(0.271377\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.70072 | −0.268105 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.9301 | −0.727810 | −0.363905 | − | 0.931436i | \(-0.618557\pi\) | ||||
−0.363905 | + | 0.931436i | \(0.618557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.4034 | −1.33380 | −0.666902 | − | 0.745145i | \(-0.732380\pi\) | ||||
−0.666902 | + | 0.745145i | \(0.732380\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.186204 | −0.00645934 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.6025 | 0.471299 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.22432 | 0.0769757 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.25177 | 0.216093 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.5390 | 1.15790 | 0.578948 | − | 0.815365i | \(-0.303464\pi\) | ||||
0.578948 | + | 0.815365i | \(0.303464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.3180 | 0.699789 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.107019 | 0.00368155 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.3250 | −0.389132 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.11388 | −0.0725480 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.15202 | 0.313727 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.62422 | 0.329527 | 0.164764 | − | 0.986333i | \(-0.447314\pi\) | ||||
0.164764 | + | 0.986333i | \(0.447314\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.342749 | −0.0117218 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −36.5360 | −1.24804 | −0.624022 | − | 0.781406i | \(-0.714503\pi\) | ||||
−0.624022 | + | 0.781406i | \(0.714503\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0505 | −1.19591 | −0.597954 | − | 0.801530i | \(-0.704020\pi\) | ||||
−0.597954 | + | 0.801530i | \(0.704020\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.6610 | 0.499645 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.83740 | −0.198708 | −0.0993538 | − | 0.995052i | \(-0.531678\pi\) | ||||
−0.0993538 | + | 0.995052i | \(0.531678\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.34326 | −0.0796733 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.3009 | −0.349838 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.5857 | 0.664401 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.230931 | 0.00782479 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.659173 | −0.0223096 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.09716 | −0.104703 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −48.6139 | −1.64157 | −0.820787 | − | 0.571234i | \(-0.806465\pi\) | ||||
−0.820787 | + | 0.571234i | \(0.806465\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.9170 | −0.536867 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.6969 | −1.00051 | −0.500256 | − | 0.865877i | \(-0.666761\pi\) | ||||
−0.500256 | + | 0.865877i | \(0.666761\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.2019 | −0.646196 | −0.323098 | − | 0.946366i | \(-0.604724\pi\) | ||||
−0.323098 | + | 0.946366i | \(0.604724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.24485 | 0.0418453 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.9751 | −1.10720 | −0.553598 | − | 0.832784i | \(-0.686746\pi\) | ||||
−0.553598 | + | 0.832784i | \(0.686746\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.9100 | 0.801915 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.55746 | 0.0521770 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.5745 | −0.387325 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.83637 | 0.0613832 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.66795 | 0.122469 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.25177 | 0.208508 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.0262 | 0.500594 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0696 | 0.401652 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.16475 | 0.138441 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.11525 | −0.0370312 | −0.0185156 | − | 0.999829i | \(-0.505894\pi\) | ||||
−0.0185156 | + | 0.999829i | \(0.505894\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.8646 | −0.559362 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.7434 | 0.389076 | 0.194538 | − | 0.980895i | \(-0.437679\pi\) | ||||
0.194538 | + | 0.980895i | \(0.437679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.2863 | 0.572093 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.04339 | 0.100611 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.5902 | 0.745995 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.976902 | −0.0322250 | −0.0161125 | − | 0.999870i | \(-0.505129\pi\) | ||||
−0.0161125 | + | 0.999870i | \(0.505129\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.5322 | 0.709511 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.05062 | −0.133328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.2512 | 1.48785 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.4751 | −0.409736 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.8871 | 0.783710 | 0.391855 | − | 0.920027i | \(-0.371833\pi\) | ||||
0.391855 | + | 0.920027i | \(0.371833\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.63909 | 0.250361 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.6621 | 0.741925 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.950542 | −0.0310860 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.19928 | −0.169853 | −0.0849265 | − | 0.996387i | \(-0.527066\pi\) | ||||
−0.0849265 | + | 0.996387i | \(0.527066\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.15436 | −0.233474 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.5399 | −1.02817 | −0.514085 | − | 0.857739i | \(-0.671869\pi\) | ||||
−0.514085 | + | 0.857739i | \(0.671869\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.1000 | −0.361465 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.311448 | 0.0101314 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.9817 | 1.26673 | 0.633367 | − | 0.773851i | \(-0.281672\pi\) | ||||
0.633367 | + | 0.773851i | \(0.281672\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.2012 | −1.46729 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.26223 | −0.105785 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.4546 | −0.856948 | −0.428474 | − | 0.903554i | \(-0.640949\pi\) | ||||
−0.428474 | + | 0.903554i | \(0.640949\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.85406 | −0.124715 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.55746 | 0.0503457 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.36260 | −0.140876 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.08459 | 0.260793 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.7008 | 0.570399 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.695785 | −0.0223981 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.6669 | −1.50071 | −0.750353 | − | 0.661037i | \(-0.770117\pi\) | ||||
−0.750353 | + | 0.661037i | \(0.770117\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.76217 | 0.120858 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.19172 | −0.262885 | −0.131442 | − | 0.991324i | \(-0.541961\pi\) | ||||
−0.131442 | + | 0.991324i | \(0.541961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.41637 | 0.237758 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.1358 | 0.580810 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.54176 | 0.209289 | 0.104645 | − | 0.994510i | \(-0.466629\pi\) | ||||
0.104645 | + | 0.994510i | \(0.466629\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.4785 | 0.494694 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0712 | 0.576968 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.2203 | −0.676823 | −0.338411 | − | 0.940998i | \(-0.609890\pi\) | ||||
−0.338411 | + | 0.940998i | \(0.609890\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.80822 | −0.0576148 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.5175 | 0.334774 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.13805 | −0.290573 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0972 | 0.574878 | 0.287439 | − | 0.957799i | \(-0.407196\pi\) | ||||
0.287439 | + | 0.957799i | \(0.407196\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.35489 | 0.0747302 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.294810 | −0.00934610 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0807050 | 0.00255595 | 0.00127798 | − | 0.999999i | \(-0.499593\pi\) | ||||
0.00127798 | + | 0.999999i | \(0.499593\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.15202 | −0.289557 |
(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 | 8004.2.a.k.1.9 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.k.1.9 | ✓ | 18 | 1.1 | even | 1 | trivial |