Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, 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("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 5 x^{18} - 29 x^{17} + 165 x^{16} + 325 x^{15} - 2208 x^{14} - 1891 x^{13} + 15895 x^{12} + 6652 x^{11} - 67665 x^{10} - 17345 x^{9} + 174105 x^{8} + 41499 x^{7} + \cdots - 5628 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.02734\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 | ||||||||
\(3\) | −1.02734 | −0.593135 | −0.296568 | − | 0.955012i | \(-0.595842\pi\) | ||||
−0.296568 | + | 0.955012i | \(0.595842\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.96391 | 1.49822 | 0.749109 | − | 0.662447i | \(-0.230482\pi\) | ||||
0.749109 | + | 0.662447i | \(0.230482\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.94457 | −0.648191 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.133682 | −0.0403067 | −0.0201534 | − | 0.999797i | \(-0.506415\pi\) | ||||
−0.0201534 | + | 0.999797i | \(0.506415\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.05488 | 0.569922 | 0.284961 | − | 0.958539i | \(-0.408019\pi\) | ||||
0.284961 | + | 0.958539i | \(0.408019\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.02734 | −0.265258 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.43734 | 0.348606 | 0.174303 | − | 0.984692i | \(-0.444233\pi\) | ||||
0.174303 | + | 0.984692i | \(0.444233\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.44046 | −1.70696 | −0.853480 | − | 0.521126i | \(-0.825512\pi\) | ||||
−0.853480 | + | 0.521126i | \(0.825512\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.07229 | −0.888646 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.51346 | −1.35815 | −0.679075 | − | 0.734069i | \(-0.737619\pi\) | ||||
−0.679075 | + | 0.734069i | \(0.737619\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.07976 | 0.977600 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.69856 | 0.686806 | 0.343403 | − | 0.939188i | \(-0.388420\pi\) | ||||
0.343403 | + | 0.939188i | \(0.388420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.79194 | 1.21987 | 0.609934 | − | 0.792452i | \(-0.291196\pi\) | ||||
0.609934 | + | 0.792452i | \(0.291196\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.137337 | 0.0239073 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.96391 | 0.670023 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.7260 | −1.76335 | −0.881675 | − | 0.471858i | \(-0.843584\pi\) | ||||
−0.881675 | + | 0.471858i | \(0.843584\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.11106 | −0.338041 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.8991 | −1.85832 | −0.929161 | − | 0.369676i | \(-0.879469\pi\) | ||||
−0.929161 | + | 0.369676i | \(0.879469\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.64630 | −0.556056 | −0.278028 | − | 0.960573i | \(-0.589681\pi\) | ||||
−0.278028 | + | 0.960573i | \(0.589681\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.94457 | −0.289880 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.70849 | −0.978534 | −0.489267 | − | 0.872134i | \(-0.662736\pi\) | ||||
−0.489267 | + | 0.872134i | \(0.662736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.71260 | 1.24466 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.47664 | −0.206771 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.2211 | −1.54134 | −0.770670 | − | 0.637234i | \(-0.780078\pi\) | ||||
−0.770670 | + | 0.637234i | \(0.780078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.133682 | −0.0180257 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.64389 | 1.01246 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.753474 | −0.0980939 | −0.0490470 | − | 0.998796i | \(-0.515618\pi\) | ||||
−0.0490470 | + | 0.998796i | \(0.515618\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.95271 | 0.506093 | 0.253046 | − | 0.967454i | \(-0.418567\pi\) | ||||
0.253046 | + | 0.967454i | \(0.418567\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.70811 | −0.971131 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.05488 | 0.254877 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.858406 | 0.104871 | 0.0524355 | − | 0.998624i | \(-0.483302\pi\) | ||||
0.0524355 | + | 0.998624i | \(0.483302\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.69154 | 0.805566 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.58753 | 0.307083 | 0.153541 | − | 0.988142i | \(-0.450932\pi\) | ||||
0.153541 | + | 0.988142i | \(0.450932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.62749 | 1.00977 | 0.504886 | − | 0.863186i | \(-0.331535\pi\) | ||||
0.504886 | + | 0.863186i | \(0.331535\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.02734 | −0.118627 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.529905 | −0.0603883 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.1509 | −1.14207 | −0.571033 | − | 0.820927i | \(-0.693457\pi\) | ||||
−0.571033 | + | 0.820927i | \(0.693457\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.615076 | 0.0683418 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.7116 | −1.83433 | −0.917167 | − | 0.398504i | \(-0.869530\pi\) | ||||
−0.917167 | + | 0.398504i | \(0.869530\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.43734 | 0.155901 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.79968 | −0.407369 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.16458 | −0.653444 | −0.326722 | − | 0.945120i | \(-0.605944\pi\) | ||||
−0.326722 | + | 0.945120i | \(0.605944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.14538 | 0.853867 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.97763 | −0.723547 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.44046 | −0.763375 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.556936 | 0.0565482 | 0.0282741 | − | 0.999600i | \(-0.490999\pi\) | ||||
0.0282741 | + | 0.999600i | \(0.490999\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.259955 | 0.0261264 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.80987 | 0.379097 | 0.189548 | − | 0.981871i | \(-0.439298\pi\) | ||||
0.189548 | + | 0.981871i | \(0.439298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.50594 | 0.148384 | 0.0741922 | − | 0.997244i | \(-0.476362\pi\) | ||||
0.0741922 | + | 0.997244i | \(0.476362\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.07229 | −0.397414 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.03707 | −0.100258 | −0.0501288 | − | 0.998743i | \(-0.515963\pi\) | ||||
−0.0501288 | + | 0.998743i | \(0.515963\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.2279 | 1.07544 | 0.537721 | − | 0.843123i | \(-0.319286\pi\) | ||||
0.537721 | + | 0.843123i | \(0.319286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.0193 | 1.04590 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.67887 | −0.157935 | −0.0789675 | − | 0.996877i | \(-0.525162\pi\) | ||||
−0.0789675 | + | 0.996877i | \(0.525162\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.51346 | −0.607383 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.99587 | −0.369418 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.69749 | 0.522288 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9821 | −0.998375 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.2244 | 1.10224 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0216 | 0.889275 | 0.444637 | − | 0.895711i | \(-0.353333\pi\) | ||||
0.444637 | + | 0.895711i | \(0.353333\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.74599 | 0.329816 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.0967 | −1.31901 | −0.659503 | − | 0.751702i | \(-0.729233\pi\) | ||||
−0.659503 | + | 0.751702i | \(0.729233\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −29.4933 | −2.55740 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.07976 | 0.437196 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.54668 | 0.217578 | 0.108789 | − | 0.994065i | \(-0.465303\pi\) | ||||
0.108789 | + | 0.994065i | \(0.465303\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.1062 | −1.36611 | −0.683054 | − | 0.730368i | \(-0.739349\pi\) | ||||
−0.683054 | + | 0.730368i | \(0.739349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.89190 | 0.580403 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.274702 | −0.0229717 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.69856 | 0.307149 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.95080 | −0.738250 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.5893 | 1.85058 | 0.925292 | − | 0.379255i | \(-0.123820\pi\) | ||||
0.925292 | + | 0.379255i | \(0.123820\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.79501 | −0.225963 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.79194 | 0.545542 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.54438 | −0.362681 | −0.181340 | − | 0.983420i | \(-0.558044\pi\) | ||||
−0.181340 | + | 0.983420i | \(0.558044\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5279 | 0.914223 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25.8188 | −2.03480 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.4641 | −1.75952 | −0.879761 | − | 0.475416i | \(-0.842298\pi\) | ||||
−0.879761 | + | 0.475416i | \(0.842298\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.137337 | 0.0106917 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.9065 | 1.54041 | 0.770206 | − | 0.637795i | \(-0.220153\pi\) | ||||
0.770206 | + | 0.637795i | \(0.220153\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.77745 | −0.675189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.4685 | 1.10643 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6650 | 0.810842 | 0.405421 | − | 0.914130i | \(-0.367125\pi\) | ||||
0.405421 | + | 0.914130i | \(0.367125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.96391 | 0.299644 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.774074 | 0.0581830 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.0173 | 1.42142 | 0.710711 | − | 0.703484i | \(-0.248373\pi\) | ||||
0.710711 | + | 0.703484i | \(0.248373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.31287 | 0.0975850 | 0.0487925 | − | 0.998809i | \(-0.484463\pi\) | ||||
0.0487925 | + | 0.998809i | \(0.484463\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.06078 | −0.300181 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.7260 | −0.788594 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.192147 | −0.0140512 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20.1357 | 1.46466 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.03989 | 0.437031 | 0.218516 | − | 0.975833i | \(-0.429879\pi\) | ||||
0.218516 | + | 0.975833i | \(0.429879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.26958 | −0.163368 | −0.0816840 | − | 0.996658i | \(-0.526030\pi\) | ||||
−0.0816840 | + | 0.996658i | \(0.526030\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.11106 | −0.151176 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.3797 | 1.52324 | 0.761621 | − | 0.648023i | \(-0.224404\pi\) | ||||
0.761621 | + | 0.648023i | \(0.224404\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.8996 | 1.26887 | 0.634433 | − | 0.772978i | \(-0.281234\pi\) | ||||
0.634433 | + | 0.772978i | \(0.281234\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.881875 | −0.0622027 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.6608 | 1.02898 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8991 | −0.831067 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.6659 | 0.880340 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.994658 | 0.0688019 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.87449 | 0.335574 | 0.167787 | − | 0.985823i | \(-0.446338\pi\) | ||||
0.167787 | + | 0.985823i | \(0.446338\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.65827 | −0.182142 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.64630 | −0.248676 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.9227 | 1.82763 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.86337 | −0.598931 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.95357 | 0.198678 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.06676 | −0.138400 | −0.0692002 | − | 0.997603i | \(-0.522045\pi\) | ||||
−0.0692002 | + | 0.997603i | \(0.522045\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.94457 | −0.129638 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −27.3298 | −1.81394 | −0.906972 | − | 0.421191i | \(-0.861612\pi\) | ||||
−0.906972 | + | 0.421191i | \(0.861612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.24658 | −0.280622 | −0.140311 | − | 0.990107i | \(-0.544810\pi\) | ||||
−0.140311 | + | 0.990107i | \(0.544810\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.544393 | 0.0358184 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.54497 | 0.232239 | 0.116119 | − | 0.993235i | \(-0.462954\pi\) | ||||
0.116119 | + | 0.993235i | \(0.462954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.70849 | −0.437614 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.4284 | 0.677400 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.2406 | −0.985834 | −0.492917 | − | 0.870076i | \(-0.664069\pi\) | ||||
−0.492917 | + | 0.870076i | \(0.664069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.6270 | 1.32870 | 0.664351 | − | 0.747421i | \(-0.268708\pi\) | ||||
0.664351 | + | 0.747421i | \(0.268708\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.8712 | −1.01814 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.71260 | 0.556627 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.2893 | −0.972834 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.1685 | 1.08801 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.5890 | −1.80452 | −0.902259 | − | 0.431194i | \(-0.858093\pi\) | ||||
−0.902259 | + | 0.431194i | \(0.858093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.870734 | 0.0547426 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.47664 | −0.0924706 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.63056 | 0.413603 | 0.206801 | − | 0.978383i | \(-0.433695\pi\) | ||||
0.206801 | + | 0.978383i | \(0.433695\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −42.5171 | −2.64188 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.19212 | −0.445181 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5541 | −0.650791 | −0.325396 | − | 0.945578i | \(-0.605497\pi\) | ||||
−0.325396 | + | 0.945578i | \(0.605497\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.2211 | −0.689308 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.33312 | 0.387581 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −28.1483 | −1.71623 | −0.858116 | − | 0.513456i | \(-0.828365\pi\) | ||||
−0.858116 | + | 0.513456i | \(0.828365\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.01280 | 0.0615233 | 0.0307616 | − | 0.999527i | \(-0.490207\pi\) | ||||
0.0307616 | + | 0.999527i | \(0.490207\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.36807 | −0.506459 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.133682 | −0.00806135 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.3520 | 1.28292 | 0.641458 | − | 0.767158i | \(-0.278330\pi\) | ||||
0.641458 | + | 0.767158i | \(0.278330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.2074 | −0.790707 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.92765 | −0.532579 | −0.266290 | − | 0.963893i | \(-0.585798\pi\) | ||||
−0.266290 | + | 0.963893i | \(0.585798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.24757 | 0.371380 | 0.185690 | − | 0.982608i | \(-0.440548\pi\) | ||||
0.185690 | + | 0.982608i | \(0.440548\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.64389 | 0.452785 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −47.1668 | −2.78417 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.9341 | −0.878474 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.572162 | −0.0335408 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.327469 | 0.0191309 | 0.00956546 | − | 0.999954i | \(-0.496955\pi\) | ||||
0.00956546 | + | 0.999954i | \(0.496955\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.753474 | −0.0438689 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.679074 | −0.0394039 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.3844 | −0.774040 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.4536 | −0.833093 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.91404 | −0.224856 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.95271 | 0.226332 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.36459 | −0.420319 | −0.210160 | − | 0.977667i | \(-0.567398\pi\) | ||||
−0.210160 | + | 0.977667i | \(0.567398\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.54711 | −0.0880121 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0965 | −0.572522 | −0.286261 | − | 0.958152i | \(-0.592413\pi\) | ||||
−0.286261 | + | 0.958152i | \(0.592413\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.37945 | −0.304064 | −0.152032 | − | 0.988376i | \(-0.548582\pi\) | ||||
−0.152032 | + | 0.988376i | \(0.548582\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.70811 | −0.434303 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.47050 | −0.194923 | −0.0974614 | − | 0.995239i | \(-0.531072\pi\) | ||||
−0.0974614 | + | 0.995239i | \(0.531072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.494432 | −0.0276829 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.06543 | 0.0594663 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.6945 | −0.595056 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.05488 | 0.113984 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.5349 | −0.637882 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −26.5919 | −1.46606 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3616 | −0.899315 | −0.449657 | − | 0.893201i | \(-0.648454\pi\) | ||||
−0.449657 | + | 0.893201i | \(0.648454\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.8576 | 1.14299 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.858406 | 0.0468997 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.16717 | 0.281474 | 0.140737 | − | 0.990047i | \(-0.455053\pi\) | ||||
0.140737 | + | 0.990047i | \(0.455053\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.72477 | 0.0936768 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.907962 | −0.0491689 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.78858 | 0.366549 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.69154 | 0.360260 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.09030 | −0.219579 | −0.109790 | − | 0.993955i | \(-0.535018\pi\) | ||||
−0.109790 | + | 0.993955i | \(0.535018\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.4790 | 1.41739 | 0.708695 | − | 0.705515i | \(-0.249284\pi\) | ||||
0.708695 | + | 0.705515i | \(0.249284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.4383 | 0.557156 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.17028 | −0.0622879 | −0.0311440 | − | 0.999515i | \(-0.509915\pi\) | ||||
−0.0311440 | + | 0.999515i | \(0.509915\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.58753 | 0.137332 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.85326 | −0.309787 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.6986 | −0.722984 | −0.361492 | − | 0.932375i | \(-0.617732\pi\) | ||||
−0.361492 | + | 0.932375i | \(0.617732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.3605 | 1.91371 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.2824 | 0.592172 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.62749 | 0.451583 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.03348 | 0.471544 | 0.235772 | − | 0.971808i | \(-0.424238\pi\) | ||||
0.235772 | + | 0.971808i | \(0.424238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 23.1386 | 1.20455 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −44.4796 | −2.30926 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.8393 | −0.613013 | −0.306507 | − | 0.951868i | \(-0.599160\pi\) | ||||
−0.306507 | + | 0.951868i | \(0.599160\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.02734 | −0.0530516 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.60011 | 0.391426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.7124 | −1.42349 | −0.711744 | − | 0.702439i | \(-0.752094\pi\) | ||||
−0.711744 | + | 0.702439i | \(0.752094\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.2956 | −0.527460 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.5967 | −1.15464 | −0.577319 | − | 0.816519i | \(-0.695901\pi\) | ||||
−0.577319 | + | 0.816519i | \(0.695901\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.529905 | −0.0270065 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.09050 | 0.360430 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0430 | −0.712007 | −0.356004 | − | 0.934485i | \(-0.615861\pi\) | ||||
−0.356004 | + | 0.934485i | \(0.615861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.36205 | −0.473459 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.5095 | 0.782349 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.1509 | −0.510748 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.14697 | 0.157942 | 0.0789711 | − | 0.996877i | \(-0.474837\pi\) | ||||
0.0789711 | + | 0.996877i | \(0.474837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.2997 | 1.51688 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.3354 | 1.36506 | 0.682532 | − | 0.730856i | \(-0.260879\pi\) | ||||
0.682532 | + | 0.730856i | \(0.260879\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.9566 | 0.695230 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.615076 | 0.0305634 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.43388 | 0.0710749 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.9743 | −1.38324 | −0.691621 | − | 0.722261i | \(-0.743103\pi\) | ||||
−0.691621 | + | 0.722261i | \(0.743103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.61631 | −0.129053 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.98670 | −0.146966 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.7116 | −0.820339 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.5465 | 0.810287 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.3654 | −0.604091 | −0.302045 | − | 0.953294i | \(-0.597669\pi\) | ||||
−0.302045 | + | 0.953294i | \(0.597669\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.47148 | 0.461612 | 0.230806 | − | 0.973000i | \(-0.425864\pi\) | ||||
0.230806 | + | 0.973000i | \(0.425864\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.0451 | 0.634276 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.43734 | 0.0697212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.6682 | 0.758237 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.282212 | 0.0136253 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.0707 | −1.35212 | −0.676060 | − | 0.736847i | \(-0.736314\pi\) | ||||
−0.676060 | + | 0.736847i | \(0.736314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.360158 | −0.0173081 | −0.00865405 | − | 0.999963i | \(-0.502755\pi\) | ||||
−0.00865405 | + | 0.999963i | \(0.502755\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.79968 | −0.182181 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 48.4631 | 2.31831 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.13899 | 0.149816 | 0.0749078 | − | 0.997190i | \(-0.476134\pi\) | ||||
0.0749078 | + | 0.997190i | \(0.476134\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.9423 | −0.806775 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.0600 | 1.61824 | 0.809119 | − | 0.587644i | \(-0.199945\pi\) | ||||
0.809119 | + | 0.587644i | \(0.199945\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.16458 | −0.292229 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.2069 | −1.09765 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.2927 | −0.721709 | −0.360854 | − | 0.932622i | \(-0.617515\pi\) | ||||
−0.360854 | + | 0.932622i | \(0.617515\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.59069 | 0.0749029 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.02734 | −0.0482687 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.14538 | 0.381861 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.66399 | −0.124616 | −0.0623082 | − | 0.998057i | \(-0.519846\pi\) | ||||
−0.0623082 | + | 0.998057i | \(0.519846\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.30134 | 0.340797 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.9871 | −1.11719 | −0.558595 | − | 0.829440i | \(-0.688659\pi\) | ||||
−0.558595 | + | 0.829440i | \(0.688659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.0725 | 1.76938 | 0.884689 | − | 0.466181i | \(-0.154371\pi\) | ||||
0.884689 | + | 0.466181i | \(0.154371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.97763 | −0.323580 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.8268 | −1.75042 | −0.875208 | − | 0.483748i | \(-0.839275\pi\) | ||||
−0.875208 | + | 0.483748i | \(0.839275\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.40265 | 0.157120 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.66862 | 0.215119 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.487446 | 0.0224128 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.44046 | −0.341392 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.8203 | 0.999083 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.00495 | 0.274373 | 0.137187 | − | 0.990545i | \(-0.456194\pi\) | ||||
0.137187 | + | 0.990545i | \(0.456194\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.0408 | −1.00497 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26.5247 | 1.20691 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.556936 | 0.0252891 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.20663 | 0.0999917 | 0.0499959 | − | 0.998749i | \(-0.484079\pi\) | ||||
0.0499959 | + | 0.998749i | \(0.484079\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.0783 | 1.04363 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.98970 | −0.450829 | −0.225414 | − | 0.974263i | \(-0.572374\pi\) | ||||
−0.225414 | + | 0.974263i | \(0.572374\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.31609 | 0.239425 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.259955 | 0.0116841 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.2567 | 0.460077 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.2215 | −0.681409 | −0.340704 | − | 0.940171i | \(-0.610665\pi\) | ||||
−0.340704 | + | 0.940171i | \(0.610665\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.4508 | −0.913673 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.9678 | 0.756559 | 0.378279 | − | 0.925691i | \(-0.376516\pi\) | ||||
0.378279 | + | 0.925691i | \(0.376516\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.80987 | 0.169537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.01743 | 0.400478 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.68393 | 0.296260 | 0.148130 | − | 0.988968i | \(-0.452675\pi\) | ||||
0.148130 | + | 0.988968i | \(0.452675\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.1986 | 1.51286 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −37.7957 | −1.66872 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.50594 | 0.0663596 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.896806 | 0.0394415 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.9565 | −0.480939 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.08733 | 0.135259 | 0.0676293 | − | 0.997711i | \(-0.478456\pi\) | ||||
0.0676293 | + | 0.997711i | \(0.478456\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.7765 | −1.69558 | −0.847789 | − | 0.530334i | \(-0.822067\pi\) | ||||
−0.847789 | + | 0.530334i | \(0.822067\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.07229 | −0.177729 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.76233 | 0.425254 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4251 | 0.844571 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.46518 | 0.0635836 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.4512 | −1.05910 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.03707 | −0.0448365 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.5373 | −0.843095 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.16472 | −0.0501680 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.0182391 | 0.000784158 0 | 0.000392079 | − | 1.00000i | \(-0.499875\pi\) | ||||
0.000392079 | 1.00000i | \(0.499875\pi\) | ||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.34877 | −0.0578811 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.2279 | 0.480952 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.21039 | 0.351051 | 0.175526 | − | 0.984475i | \(-0.443838\pi\) | ||||
0.175526 | + | 0.984475i | \(0.443838\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.68633 | −0.328045 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.5190 | −1.17235 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −40.2373 | −1.71106 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.0193 | 0.467743 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.3446 | −0.607801 | −0.303901 | − | 0.952704i | \(-0.598289\pi\) | ||||
−0.303901 | + | 0.952704i | \(0.598289\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.49273 | −0.316909 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.197400 | 0.00833425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.8903 | −1.59689 | −0.798444 | − | 0.602069i | \(-0.794343\pi\) | ||||
−0.798444 | + | 0.602069i | \(0.794343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.67887 | −0.0706306 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.43811 | 0.102391 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.3786 | −0.980083 | −0.490041 | − | 0.871699i | \(-0.663018\pi\) | ||||
−0.490041 | + | 0.871699i | \(0.663018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.0058 | −1.54864 | −0.774321 | − | 0.632793i | \(-0.781909\pi\) | ||||
−0.774321 | + | 0.632793i | \(0.781909\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.20503 | −0.259219 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.51346 | −0.271630 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.2057 | 1.13259 | 0.566293 | − | 0.824204i | \(-0.308377\pi\) | ||||
0.566293 | + | 0.824204i | \(0.308377\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.33163 | 0.0968993 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −66.2432 | −2.74823 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.50007 | 0.0621264 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.99587 | −0.165209 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.7726 | 0.651004 | 0.325502 | − | 0.945541i | \(-0.394467\pi\) | ||||
0.325502 | + | 0.945541i | \(0.394467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −50.5352 | −2.08227 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.9642 | −0.903488 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.8998 | 1.51529 | 0.757647 | − | 0.652664i | \(-0.226349\pi\) | ||||
0.757647 | + | 0.652664i | \(0.226349\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.69749 | 0.233574 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.3889 | −0.752609 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.35830 | −0.0963574 | −0.0481787 | − | 0.998839i | \(-0.515342\pi\) | ||||
−0.0481787 | + | 0.998839i | \(0.515342\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.63950 | 0.311622 | 0.155811 | − | 0.987787i | \(-0.450201\pi\) | ||||
0.155811 | + | 0.987787i | \(0.450201\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.66923 | −0.0679764 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.9821 | −0.446487 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.10217 | −0.166502 | −0.0832510 | − | 0.996529i | \(-0.526530\pi\) | ||||
−0.0832510 | + | 0.996529i | \(0.526530\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.0616 | −0.610327 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.7852 | −0.557688 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.291089 | 0.0117570 | 0.00587849 | − | 0.999983i | \(-0.498129\pi\) | ||||
0.00587849 | + | 0.999983i | \(0.498129\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.2244 | 0.492935 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.8169 | 1.56271 | 0.781356 | − | 0.624086i | \(-0.214529\pi\) | ||||
0.781356 | + | 0.624086i | \(0.214529\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.1127 | 0.768203 | 0.384101 | − | 0.923291i | \(-0.374511\pi\) | ||||
0.384101 | + | 0.923291i | \(0.374511\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −33.0868 | −1.32773 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.4358 | −0.979001 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.02185 | −0.0408088 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.4170 | −0.614715 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9259 | 0.594190 | 0.297095 | − | 0.954848i | \(-0.403982\pi\) | ||||
0.297095 | + | 0.954848i | \(0.403982\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.00776 | −0.199041 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.0216 | 0.397696 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.9034 | 0.709357 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.03163 | −0.199048 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.7962 | 0.742404 | 0.371202 | − | 0.928552i | \(-0.378946\pi\) | ||||
0.371202 | + | 0.928552i | \(0.378946\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.4370 | −1.59468 | −0.797340 | − | 0.603531i | \(-0.793760\pi\) | ||||
−0.797340 | + | 0.603531i | \(0.793760\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.74599 | 0.147498 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.42847 | 0.0954728 | 0.0477364 | − | 0.998860i | \(-0.484799\pi\) | ||||
0.0477364 | + | 0.998860i | \(0.484799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.100726 | 0.00395385 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.6587 | −1.08403 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.12265 | 0.0439328 | 0.0219664 | − | 0.999759i | \(-0.493007\pi\) | ||||
0.0219664 | + | 0.999759i | \(0.493007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.0967 | −0.589878 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.7768 | −0.654524 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.1554 | 1.05782 | 0.528912 | − | 0.848676i | \(-0.322600\pi\) | ||||
0.528912 | + | 0.848676i | \(0.322600\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.7346 | −1.38992 | −0.694958 | − | 0.719050i | \(-0.744577\pi\) | ||||
−0.694958 | + | 0.719050i | \(0.744577\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.03432 | −0.117843 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −29.4933 | −1.14370 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.0904 | −0.932785 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.12326 | 0.0820901 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.528408 | −0.0203989 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.6470 | 0.410413 | 0.205207 | − | 0.978719i | \(-0.434213\pi\) | ||||
0.205207 | + | 0.978719i | \(0.434213\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.07976 | 0.195520 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.1032 | 0.426729 | 0.213364 | − | 0.976973i | \(-0.431558\pi\) | ||||
0.213364 | + | 0.976973i | \(0.431558\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.20764 | 0.0847216 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.0770 | 1.07591 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.9637 | −0.725626 | −0.362813 | − | 0.931862i | \(-0.618184\pi\) | ||||
−0.362813 | + | 0.931862i | \(0.618184\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.54668 | 0.0973036 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.36268 | 0.166447 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.0581 | −0.878444 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.8152 | 0.601639 | 0.300820 | − | 0.953681i | \(-0.402740\pi\) | ||||
0.300820 | + | 0.953681i | \(0.402740\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.03044 | 0.0391431 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.1062 | −0.610942 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.1030 | −0.647822 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.64189 | −0.137749 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.1451 | 1.85619 | 0.928093 | − | 0.372348i | \(-0.121447\pi\) | ||||
0.928093 | + | 0.372348i | \(0.121447\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 79.8067 | 3.00997 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.89190 | 0.259564 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.1020 | 0.567969 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.2932 | 0.461681 | 0.230840 | − | 0.972992i | \(-0.425852\pi\) | ||||
0.230840 | + | 0.972992i | \(0.425852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.7392 | 0.740277 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −44.2390 | −1.65676 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.274702 | −0.0102733 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.6573 | 0.584733 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.6066 | 0.544735 | 0.272368 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272368 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.96941 | 0.222312 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.1910 | −0.788100 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.69856 | 0.137361 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7835 | −0.511200 | −0.255600 | − | 0.966783i | \(-0.582273\pi\) | ||||
−0.255600 | + | 0.966783i | \(0.582273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.4599 | 0.535550 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.24098 | −0.193845 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.9036 | 1.36306 | 0.681532 | − | 0.731788i | \(-0.261314\pi\) | ||||
0.681532 | + | 0.731788i | \(0.261314\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.95080 | −0.330155 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.114754 | −0.00422701 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.6989 | 0.687849 | 0.343924 | − | 0.938997i | \(-0.388244\pi\) | ||||
0.343924 | + | 0.938997i | \(0.388244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.7073 | 0.577022 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −39.5144 | −1.44964 | −0.724822 | − | 0.688936i | \(-0.758078\pi\) | ||||
−0.724822 | + | 0.688936i | \(0.758078\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.5893 | 0.827606 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 32.4969 | 1.18900 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.11086 | −0.150208 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.1120 | 0.989332 | 0.494666 | − | 0.869083i | \(-0.335290\pi\) | ||||
0.494666 | + | 0.869083i | \(0.335290\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.3706 | 1.07032 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.5912 | 0.857436 | 0.428718 | − | 0.903438i | \(-0.358965\pi\) | ||||
0.428718 | + | 0.903438i | \(0.358965\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.894540 | −0.0324697 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.2953 | −1.71445 | −0.857227 | − | 0.514938i | \(-0.827815\pi\) | ||||
−0.857227 | + | 0.514938i | \(0.827815\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.5065 | 1.61124 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.79501 | −0.101054 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.54830 | −0.0559059 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.4354 | −1.09753 | −0.548765 | − | 0.835977i | \(-0.684902\pi\) | ||||
−0.548765 | + | 0.835977i | \(0.684902\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.81184 | −0.245322 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.2118 | −0.403260 | −0.201630 | − | 0.979462i | \(-0.564624\pi\) | ||||
−0.201630 | + | 0.979462i | \(0.564624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.79194 | 0.243974 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 43.6795 | 1.56699 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 88.5345 | 3.17208 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.345906 | −0.0123775 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.7878 | 0.671421 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.54438 | −0.162196 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.9000 | 0.495480 | 0.247740 | − | 0.968827i | \(-0.420312\pi\) | ||||
0.247740 | + | 0.968827i | \(0.420312\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.8426 | 0.386007 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.65490 | −0.236621 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.12236 | 0.288434 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11.5279 | 0.408853 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.8572 | 1.34097 | 0.670486 | − | 0.741923i | \(-0.266086\pi\) | ||||
0.670486 | + | 0.741923i | \(0.266086\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.64238 | −0.341123 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.9875 | 0.423556 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.15334 | −0.0407006 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.8188 | −0.909992 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.9179 | 1.01796 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.7911 | −0.871607 | −0.435804 | − | 0.900042i | \(-0.643536\pi\) | ||||
−0.435804 | + | 0.900042i | \(0.643536\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.7289 | 0.903463 | 0.451732 | − | 0.892154i | \(-0.350806\pi\) | ||||
0.451732 | + | 0.892154i | \(0.350806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.04049 | −0.0364916 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.4641 | −0.786882 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.1302 | 0.949165 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.8393 | −0.553469 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.07179 | −0.211907 | −0.105953 | − | 0.994371i | \(-0.533789\pi\) | ||||
−0.105953 | + | 0.994371i | \(0.533789\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0513 | 0.350367 | 0.175184 | − | 0.984536i | \(-0.443948\pi\) | ||||
0.175184 | + | 0.984536i | \(0.443948\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.137337 | 0.00478147 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.6283 | 0.543450 | 0.271725 | − | 0.962375i | \(-0.412406\pi\) | ||||
0.271725 | + | 0.962375i | \(0.412406\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.3019 | 1.57340 | 0.786700 | − | 0.617335i | \(-0.211788\pi\) | ||||
0.786700 | + | 0.617335i | \(0.211788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.9358 | −0.760943 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.5230 | 0.433895 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.9065 | 0.688893 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.5014 | 1.19254 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.1343 | 0.522494 | 0.261247 | − | 0.965272i | \(-0.415866\pi\) | ||||
0.261247 | + | 0.965272i | \(0.415866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.3206 | −0.528298 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.17174 | 0.315891 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.77745 | −0.301954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.5322 | −1.49578 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.41838 | −0.220278 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 69.8636 | 2.39489 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.6754 | 1.08455 | 0.542273 | − | 0.840202i | \(-0.317564\pi\) | ||||
0.542273 | + | 0.840202i | \(0.317564\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.4685 | 0.494813 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.3228 | 1.44572 | 0.722860 | − | 0.690995i | \(-0.242827\pi\) | ||||
0.722860 | + | 0.690995i | \(0.242827\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −56.6416 | −1.93259 | −0.966294 | − | 0.257443i | \(-0.917120\pi\) | ||||
−0.966294 | + | 0.257443i | \(0.917120\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 48.4564 | 1.65139 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.0497365 | −0.00169305 | −0.000846524 | − | 1.00000i | \(-0.500269\pi\) | ||||
−0.000846524 | 1.00000i | \(0.500269\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.6650 | 0.362620 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.3424 | 0.521054 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.35700 | 0.0460330 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.76392 | 0.0597683 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.08300 | −0.0366540 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.96391 | 0.134005 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −54.5613 | −1.84241 | −0.921203 | − | 0.389083i | \(-0.872792\pi\) | ||||
−0.921203 | + | 0.389083i | \(0.872792\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.336422 | −0.0113472 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.4965 | −0.993763 | −0.496881 | − | 0.867818i | \(-0.665522\pi\) | ||||
−0.496881 | + | 0.867818i | \(0.665522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.0908 | −1.24820 | −0.624102 | − | 0.781343i | \(-0.714535\pi\) | ||||
−0.624102 | + | 0.781343i | \(0.714535\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.774074 | 0.0260202 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −47.4882 | −1.59450 | −0.797250 | − | 0.603650i | \(-0.793713\pi\) | ||||
−0.797250 | + | 0.603650i | \(0.793713\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.7248 | 1.33233 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.0822248 | −0.00275464 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 49.9143 | 1.67032 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.0173 | 0.635679 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.7503 | 0.459110 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.1204 | 0.837812 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.1286 | −0.537321 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.8488 | 0.494137 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.31287 | 0.0436413 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.4378 | 0.446196 | 0.223098 | − | 0.974796i | \(-0.428383\pi\) | ||||
0.223098 | + | 0.974796i | \(0.428383\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.40857 | −0.245727 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.50824 | 0.281891 | 0.140945 | − | 0.990017i | \(-0.454986\pi\) | ||||
0.140945 | + | 0.990017i | \(0.454986\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.23404 | 0.0739360 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.06078 | −0.134245 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −59.8421 | −1.97616 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.1993 | −0.699300 | −0.349650 | − | 0.936880i | \(-0.613699\pi\) | ||||
−0.349650 | + | 0.936880i | \(0.613699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.56594 | 0.249306 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.31706 | 0.175013 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.7260 | −0.352670 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.92840 | −0.0961814 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.0555 | 0.690808 | 0.345404 | − | 0.938454i | \(-0.387742\pi\) | ||||
0.345404 | + | 0.938454i | \(0.387742\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −64.8257 | −2.12458 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.3726 | 0.339583 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.192147 | −0.00628388 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.3528 | 0.534222 | 0.267111 | − | 0.963666i | \(-0.413931\pi\) | ||||
0.267111 | + | 0.963666i | \(0.413931\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.52652 | 0.180351 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.7196 | −1.55561 | −0.777807 | − | 0.628503i | \(-0.783668\pi\) | ||||
−0.777807 | + | 0.628503i | \(0.783668\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 77.5040 | 2.52388 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.1357 | 0.655015 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.7202 | 0.933281 | 0.466641 | − | 0.884447i | \(-0.345464\pi\) | ||||
0.466641 | + | 0.884447i | \(0.345464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.7285 | 0.575491 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.56538 | 0.115616 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.5233 | −0.600029 | −0.300015 | − | 0.953935i | \(-0.596992\pi\) | ||||
−0.300015 | + | 0.953935i | \(0.596992\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.03989 | 0.195446 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.507950 | 0.0164197 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.0948 | 0.325979 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1304 | 0.488079 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.01666 | 0.0649860 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.26958 | −0.0730604 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.7628 | 1.34300 | 0.671501 | − | 0.741004i | \(-0.265650\pi\) | ||||
0.671501 | + | 0.741004i | \(0.265650\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.9869 | 0.352949 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.5280 | −1.33270 | −0.666348 | − | 0.745641i | \(-0.732143\pi\) | ||||
−0.666348 | + | 0.745641i | \(0.732143\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −63.8435 | −2.04673 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.11106 | −0.0676082 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.3955 | −0.332582 | −0.166291 | − | 0.986077i | \(-0.553179\pi\) | ||||
−0.166291 | + | 0.986077i | \(0.553179\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.824095 | 0.0263382 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.8335 | −0.697091 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54.5823 | 1.74091 | 0.870453 | − | 0.492251i | \(-0.163826\pi\) | ||||
0.870453 | + | 0.492251i | \(0.163826\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.3797 | 0.681215 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.3189 | 0.869570 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.7500 | 0.755208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.8329 | 0.693543 | 0.346772 | − | 0.937950i | \(-0.387278\pi\) | ||||
0.346772 | + | 0.937950i | \(0.387278\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.8089 | 0.533415 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.8996 | 0.567454 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.3450 | −1.59444 | −0.797221 | − | 0.603688i | \(-0.793697\pi\) | ||||
−0.797221 | + | 0.603688i | \(0.793697\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −54.4857 | −1.72385 |
(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 | 6040.2.a.p.1.9 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.p.1.9 | ✓ | 19 | 1.1 | even | 1 | trivial |