Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6864,2,Mod(1,6864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6864 = 2^{4} \cdot 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6864.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: | \(54.8093159474\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8468.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 3x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 429) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.89122\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6864.1 |
$q$-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 | ||||||||
\(5\) | −0.776183 | −0.347120 | −0.173560 | − | 0.984823i | \(-0.555527\pi\) | ||||
−0.173560 | + | 0.984823i | \(0.555527\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.69175 | −1.01739 | −0.508693 | − | 0.860948i | \(-0.669871\pi\) | ||||
−0.508693 | + | 0.860948i | \(0.669871\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.776183 | −0.200410 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.62136 | 0.635773 | 0.317886 | − | 0.948129i | \(-0.397027\pi\) | ||||
0.317886 | + | 0.948129i | \(0.397027\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.69175 | −1.53519 | −0.767596 | − | 0.640934i | \(-0.778547\pi\) | ||||
−0.767596 | + | 0.640934i | \(0.778547\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.69175 | −0.587388 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.02655 | 1.67365 | 0.836826 | − | 0.547469i | \(-0.184408\pi\) | ||||
0.836826 | + | 0.547469i | \(0.184408\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.39754 | −0.879508 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.09695 | −1.50357 | −0.751783 | − | 0.659411i | \(-0.770806\pi\) | ||||
−0.751783 | + | 0.659411i | \(0.770806\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.34106 | 1.13889 | 0.569444 | − | 0.822030i | \(-0.307158\pi\) | ||||
0.569444 | + | 0.822030i | \(0.307158\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.08929 | 0.353154 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.398941 | −0.0655854 | −0.0327927 | − | 0.999462i | \(-0.510440\pi\) | ||||
−0.0327927 | + | 0.999462i | \(0.510440\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.87313 | 1.07340 | 0.536701 | − | 0.843772i | \(-0.319670\pi\) | ||||
0.536701 | + | 0.843772i | \(0.319670\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.23786 | −1.10376 | −0.551882 | − | 0.833923i | \(-0.686090\pi\) | ||||
−0.551882 | + | 0.833923i | \(0.686090\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.776183 | −0.115707 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.53692 | 0.661778 | 0.330889 | − | 0.943670i | \(-0.392651\pi\) | ||||
0.330889 | + | 0.943670i | \(0.392651\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.245516 | 0.0350737 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.62136 | 0.367063 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.75448 | −0.378358 | −0.189179 | − | 0.981943i | \(-0.560583\pi\) | ||||
−0.189179 | + | 0.981943i | \(0.560583\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.776183 | −0.104660 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.69175 | −0.886344 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.8104 | −1.40739 | −0.703697 | − | 0.710500i | \(-0.748469\pi\) | ||||
−0.703697 | + | 0.710500i | \(0.748469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.02796 | −0.643764 | −0.321882 | − | 0.946780i | \(-0.604315\pi\) | ||||
−0.321882 | + | 0.946780i | \(0.604315\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.69175 | −0.339129 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.776183 | −0.0962736 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.95756 | 0.605663 | 0.302831 | − | 0.953044i | \(-0.402068\pi\) | ||||
0.302831 | + | 0.953044i | \(0.402068\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.02655 | 0.966284 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.96382 | 0.707775 | 0.353888 | − | 0.935288i | \(-0.384860\pi\) | ||||
0.353888 | + | 0.935288i | \(0.384860\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.79648 | 0.444344 | 0.222172 | − | 0.975007i | \(-0.428685\pi\) | ||||
0.222172 | + | 0.975007i | \(0.428685\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.39754 | −0.507784 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.69175 | −0.306753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.14564 | −0.241403 | −0.120702 | − | 0.992689i | \(-0.538514\pi\) | ||||
−0.120702 | + | 0.992689i | \(0.538514\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.73375 | −0.409832 | −0.204916 | − | 0.978780i | \(-0.565692\pi\) | ||||
−0.204916 | + | 0.978780i | \(0.565692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.03465 | −0.220689 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.09695 | −0.868084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.37724 | 0.251987 | 0.125994 | − | 0.992031i | \(-0.459788\pi\) | ||||
0.125994 | + | 0.992031i | \(0.459788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.69175 | −0.282172 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.34106 | 0.657538 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.19402 | 0.532895 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.8355 | −1.81093 | −0.905463 | − | 0.424426i | \(-0.860476\pi\) | ||||
−0.905463 | + | 0.424426i | \(0.860476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1096 | −1.10545 | −0.552723 | − | 0.833365i | \(-0.686411\pi\) | ||||
−0.552723 | + | 0.833365i | \(0.686411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.1814 | −1.00320 | −0.501601 | − | 0.865099i | \(-0.667255\pi\) | ||||
−0.501601 | + | 0.865099i | \(0.667255\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.08929 | 0.203894 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.06133 | −0.295950 | −0.147975 | − | 0.988991i | \(-0.547276\pi\) | ||||
−0.147975 | + | 0.988991i | \(0.547276\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.1800 | 1.26241 | 0.631207 | − | 0.775615i | \(-0.282560\pi\) | ||||
0.631207 | + | 0.775615i | \(0.282560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.398941 | −0.0378658 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.50074 | 0.423394 | 0.211697 | − | 0.977335i | \(-0.432101\pi\) | ||||
0.211697 | + | 0.977335i | \(0.432101\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.23007 | −0.580957 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.05604 | −0.646826 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.87313 | 0.619729 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.29421 | 0.652414 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.9687 | −1.77193 | −0.885967 | − | 0.463749i | \(-0.846504\pi\) | ||||
−0.885967 | + | 0.463749i | \(0.846504\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.23786 | −0.637258 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.92335 | −0.430155 | −0.215078 | − | 0.976597i | \(-0.569000\pi\) | ||||
−0.215078 | + | 0.976597i | \(0.569000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.0125 | 1.56188 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.776183 | −0.0668032 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.1876 | −1.12670 | −0.563348 | − | 0.826220i | \(-0.690487\pi\) | ||||
−0.563348 | + | 0.826220i | \(0.690487\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0203 | −0.934729 | −0.467365 | − | 0.884065i | \(-0.654797\pi\) | ||||
−0.467365 | + | 0.884065i | \(0.654797\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.53692 | 0.382078 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.28471 | 0.521917 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.245516 | 0.0202498 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.25663 | 0.676409 | 0.338205 | − | 0.941073i | \(-0.390180\pi\) | ||||
0.338205 | + | 0.941073i | \(0.390180\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.61510 | 0.294193 | 0.147096 | − | 0.989122i | \(-0.453007\pi\) | ||||
0.147096 | + | 0.989122i | \(0.453007\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.62136 | 0.211924 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.92182 | −0.395330 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0672 | 1.60153 | 0.800766 | − | 0.598977i | \(-0.204426\pi\) | ||||
0.800766 | + | 0.598977i | \(0.204426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.75448 | −0.218445 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.6055 | −1.70275 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.9827 | −1.40852 | −0.704258 | − | 0.709945i | \(-0.748720\pi\) | ||||
−0.704258 | + | 0.709945i | \(0.748720\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.776183 | −0.0604258 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.74626 | −0.754188 | −0.377094 | − | 0.926175i | \(-0.623077\pi\) | ||||
−0.377094 | + | 0.926175i | \(0.623077\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.69175 | −0.511731 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.9841 | −1.13922 | −0.569611 | − | 0.821915i | \(-0.692906\pi\) | ||||
−0.569611 | + | 0.821915i | \(0.692906\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.8371 | 0.894799 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.8104 | −0.812559 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.5273 | 1.08582 | 0.542911 | − | 0.839790i | \(-0.317322\pi\) | ||||
0.542911 | + | 0.839790i | \(0.317322\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.909310 | 0.0675885 | 0.0337942 | − | 0.999429i | \(-0.489241\pi\) | ||||
0.0337942 | + | 0.999429i | \(0.489241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.02796 | −0.371677 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.309651 | 0.0227660 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.62136 | 0.191693 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.69175 | −0.195796 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4448 | −0.900477 | −0.450238 | − | 0.892908i | \(-0.648661\pi\) | ||||
−0.450238 | + | 0.892908i | \(0.648661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3406 | 1.32019 | 0.660093 | − | 0.751184i | \(-0.270517\pi\) | ||||
0.660093 | + | 0.751184i | \(0.270517\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.776183 | −0.0555836 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.96535 | −0.567508 | −0.283754 | − | 0.958897i | \(-0.591580\pi\) | ||||
−0.283754 | + | 0.958897i | \(0.591580\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6415 | 1.03791 | 0.518955 | − | 0.854801i | \(-0.326321\pi\) | ||||
0.518955 | + | 0.854801i | \(0.326321\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.95756 | 0.349680 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.7950 | 1.52971 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.33481 | −0.372599 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.02655 | 0.557884 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.69175 | −0.462878 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.9716 | −1.03069 | −0.515344 | − | 0.856983i | \(-0.672336\pi\) | ||||
−0.515344 | + | 0.856983i | \(0.672336\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.96382 | 0.408634 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.61790 | 0.383138 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.0686 | −1.15869 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.79648 | 0.256542 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.62136 | 0.176332 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.2003 | 1.75450 | 0.877250 | − | 0.480033i | \(-0.159375\pi\) | ||||
0.877250 | + | 0.480033i | \(0.159375\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.39754 | −0.293169 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.2441 | −1.60914 | −0.804569 | − | 0.593859i | \(-0.797604\pi\) | ||||
−0.804569 | + | 0.593859i | \(0.797604\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.43954 | −0.425537 | −0.212768 | − | 0.977103i | \(-0.568248\pi\) | ||||
−0.212768 | + | 0.977103i | \(0.568248\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.69175 | −0.177104 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.0536 | −1.57580 | −0.787900 | − | 0.615803i | \(-0.788832\pi\) | ||||
−0.787900 | + | 0.615803i | \(0.788832\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.52148 | −0.229716 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.14564 | −0.139374 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.01391 | −0.324323 | −0.162162 | − | 0.986764i | \(-0.551847\pi\) | ||||
−0.162162 | + | 0.986764i | \(0.551847\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.9890 | −1.60968 | −0.804841 | − | 0.593491i | \(-0.797749\pi\) | ||||
−0.804841 | + | 0.593491i | \(0.797749\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.190565 | −0.0121748 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.69175 | −0.425786 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.73375 | −0.236617 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0406 | −1.13871 | −0.569356 | − | 0.822091i | \(-0.692807\pi\) | ||||
−0.569356 | + | 0.822091i | \(0.692807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.02655 | 0.504625 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.03465 | −0.127415 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.1298 | −1.31804 | −0.659019 | − | 0.752126i | \(-0.729028\pi\) | ||||
−0.659019 | + | 0.752126i | \(0.729028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.07385 | 0.0667257 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.09695 | −0.501188 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.8592 | −0.731271 | −0.365635 | − | 0.930758i | \(-0.619148\pi\) | ||||
−0.365635 | + | 0.930758i | \(0.619148\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.13798 | 0.131335 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.37724 | 0.145485 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.322165 | −0.0196427 | −0.00982136 | − | 0.999952i | \(-0.503126\pi\) | ||||
−0.00982136 | + | 0.999952i | \(0.503126\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.2944 | −1.59727 | −0.798636 | − | 0.601814i | \(-0.794445\pi\) | ||||
−0.798636 | + | 0.601814i | \(0.794445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.69175 | −0.162912 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.39754 | −0.265182 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.89247 | −0.534297 | −0.267148 | − | 0.963655i | \(-0.586081\pi\) | ||||
−0.267148 | + | 0.963655i | \(0.586081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.34106 | 0.379629 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.5833 | 1.40686 | 0.703432 | − | 0.710763i | \(-0.251650\pi\) | ||||
0.703432 | + | 0.710763i | \(0.251650\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.13754 | −0.483727 | −0.241863 | − | 0.970310i | \(-0.577759\pi\) | ||||
−0.241863 | + | 0.970310i | \(0.577759\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.19402 | 0.307667 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −18.5007 | −1.09206 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.1285 | −0.595793 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.8355 | −1.04554 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.8649 | 1.16052 | 0.580260 | − | 0.814431i | \(-0.302951\pi\) | ||||
0.580260 | + | 0.814431i | \(0.302951\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.39084 | 0.488534 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.02655 | 0.464188 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.4825 | 1.12295 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.1096 | −0.638229 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.90261 | 0.223463 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.3305 | 1.33154 | 0.665770 | − | 0.746157i | \(-0.268103\pi\) | ||||
0.665770 | + | 0.746157i | \(0.268103\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.1814 | −0.579198 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.43359 | 0.251406 | 0.125703 | − | 0.992068i | \(-0.459881\pi\) | ||||
0.125703 | + | 0.992068i | \(0.459881\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.4129 | −0.984233 | −0.492116 | − | 0.870529i | \(-0.663777\pi\) | ||||
−0.492116 | + | 0.870529i | \(0.663777\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.08929 | 0.117718 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.8752 | −1.73412 | −0.867062 | − | 0.498201i | \(-0.833994\pi\) | ||||
−0.867062 | + | 0.498201i | \(0.833994\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.09695 | −0.453342 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.06133 | −0.170867 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.5415 | −0.976033 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.39754 | −0.243932 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.1800 | 0.728855 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.2123 | −0.673284 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.72749 | −0.369776 | −0.184888 | − | 0.982760i | \(-0.559192\pi\) | ||||
−0.184888 | + | 0.982760i | \(0.559192\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.398941 | −0.0218618 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.84798 | −0.210237 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.06133 | −0.275708 | −0.137854 | − | 0.990453i | \(-0.544021\pi\) | ||||
−0.137854 | + | 0.990453i | \(0.544021\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.50074 | 0.244447 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.34106 | 0.343388 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.1814 | 0.981702 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.23007 | −0.335416 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.34303 | 0.233146 | 0.116573 | − | 0.993182i | \(-0.462809\pi\) | ||||
0.116573 | + | 0.993182i | \(0.462809\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.2779 | 1.08545 | 0.542725 | − | 0.839910i | \(-0.317393\pi\) | ||||
0.542725 | + | 0.839910i | \(0.317393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.5630 | −1.94605 | −0.973027 | − | 0.230691i | \(-0.925901\pi\) | ||||
−0.973027 | + | 0.230691i | \(0.925901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.62901 | −0.245683 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.05604 | −0.373445 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.8621 | 1.47051 | 0.735253 | − | 0.677793i | \(-0.237063\pi\) | ||||
0.735253 | + | 0.677793i | \(0.237063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.7795 | 1.35682 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.94676 | −0.154241 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4476 | −0.545362 | −0.272681 | − | 0.962104i | \(-0.587910\pi\) | ||||
−0.272681 | + | 0.962104i | \(0.587910\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.87313 | 0.357801 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.41438 | 0.384936 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.8842 | −0.926011 | −0.463006 | − | 0.886355i | \(-0.653229\pi\) | ||||
−0.463006 | + | 0.886355i | \(0.653229\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.29421 | 0.376671 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.09695 | −0.417014 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.6200 | 0.699610 | 0.349805 | − | 0.936822i | \(-0.386248\pi\) | ||||
0.349805 | + | 0.936822i | \(0.386248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.9687 | −1.02303 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.62901 | −0.236532 | −0.118266 | − | 0.992982i | \(-0.537733\pi\) | ||||
−0.118266 | + | 0.992982i | \(0.537733\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.08929 | 0.106480 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.23786 | −0.367921 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.34290 | 0.270896 | 0.135448 | − | 0.990784i | \(-0.456753\pi\) | ||||
0.135448 | + | 0.990784i | \(0.456753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.0405 | 1.06406 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.92335 | −0.248350 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.66541 | 0.0837958 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.0700 | 1.40879 | 0.704397 | − | 0.709806i | \(-0.251217\pi\) | ||||
0.704397 | + | 0.709806i | \(0.251217\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.0125 | 0.901754 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.3942 | 1.61769 | 0.808844 | − | 0.588023i | \(-0.200094\pi\) | ||||
0.808844 | + | 0.588023i | \(0.200094\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.34106 | 0.315871 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.776183 | −0.0385688 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.398941 | −0.0197748 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.4380 | −1.10949 | −0.554744 | − | 0.832021i | \(-0.687184\pi\) | ||||
−0.554744 | + | 0.832021i | \(0.687184\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.1876 | −0.650498 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 29.0989 | 1.43186 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.89807 | 0.142261 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.0203 | −0.539666 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.6113 | −1.98399 | −0.991996 | − | 0.126272i | \(-0.959699\pi\) | ||||
−0.991996 | + | 0.126272i | \(0.959699\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.67241 | −0.130245 | −0.0651227 | − | 0.997877i | \(-0.520744\pi\) | ||||
−0.0651227 | + | 0.997877i | \(0.520744\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.53692 | 0.220593 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.5275 | −0.559167 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.5340 | 0.654956 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.00000 | 0.0482805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.9972 | 1.25224 | 0.626121 | − | 0.779726i | \(-0.284642\pi\) | ||||
0.626121 | + | 0.779726i | \(0.284642\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.9765 | 0.911951 | 0.455975 | − | 0.889992i | \(-0.349291\pi\) | ||||
0.455975 | + | 0.889992i | \(0.349291\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.28471 | 0.301329 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −53.7117 | −2.56938 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.8586 | −0.804619 | −0.402310 | − | 0.915504i | \(-0.631792\pi\) | ||||
−0.402310 | + | 0.915504i | \(0.631792\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.245516 | 0.0116912 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.5105 | −1.63964 | −0.819821 | − | 0.572620i | \(-0.805927\pi\) | ||||
−0.819821 | + | 0.572620i | \(0.805927\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.84517 | −0.0874697 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.25663 | 0.390525 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.12363 | 0.241799 | 0.120899 | − | 0.992665i | \(-0.461422\pi\) | ||||
0.120899 | + | 0.992665i | \(0.461422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.87313 | 0.323643 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.61510 | 0.169852 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.08929 | 0.0979474 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9248 | −0.932045 | −0.466022 | − | 0.884773i | \(-0.654313\pi\) | ||||
−0.466022 | + | 0.884773i | \(0.654313\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.62136 | 0.122354 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.4661 | −0.487454 | −0.243727 | − | 0.969844i | \(-0.578370\pi\) | ||||
−0.243727 | + | 0.969844i | \(0.578370\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.5558 | 1.69889 | 0.849447 | − | 0.527675i | \(-0.176936\pi\) | ||||
0.849447 | + | 0.527675i | \(0.176936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.92182 | −0.228244 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.43079 | 0.112484 | 0.0562418 | − | 0.998417i | \(-0.482088\pi\) | ||||
0.0562418 | + | 0.998417i | \(0.482088\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.3445 | −0.616193 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.0672 | 0.924646 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.23786 | −0.332797 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.4272 | 1.35021 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.75448 | −0.126119 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.96535 | 0.0897990 | 0.0448995 | − | 0.998992i | \(-0.485703\pi\) | ||||
0.0448995 | + | 0.998992i | \(0.485703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.398941 | −0.0181901 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.6055 | −0.983083 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.8436 | 0.628608 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.4863 | −1.01895 | −0.509475 | − | 0.860486i | \(-0.670160\pi\) | ||||
−0.509475 | + | 0.860486i | \(0.670160\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.9827 | −0.813207 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.2914 | −0.780350 | −0.390175 | − | 0.920741i | \(-0.627586\pi\) | ||||
−0.390175 | + | 0.920741i | \(0.627586\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.2250 | −0.955926 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.776183 | −0.0348868 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0531 | −0.720080 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.71485 | −0.166299 | −0.0831497 | − | 0.996537i | \(-0.526498\pi\) | ||||
−0.0831497 | + | 0.996537i | \(0.526498\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.74626 | −0.435431 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.68064 | 0.342463 | 0.171231 | − | 0.985231i | \(-0.445225\pi\) | ||||
0.171231 | + | 0.985231i | \(0.445225\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.62307 | 0.383722 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.0035 | 1.28556 | 0.642778 | − | 0.766053i | \(-0.277782\pi\) | ||||
0.642778 | + | 0.766053i | \(0.277782\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.2192 | −0.452070 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.69175 | −0.295448 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.90261 | 0.348231 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.53692 | 0.199534 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.9841 | −0.657730 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.5973 | 1.42811 | 0.714056 | − | 0.700089i | \(-0.246856\pi\) | ||||
0.714056 | + | 0.700089i | \(0.246856\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7304 | 0.469207 | 0.234603 | − | 0.972091i | \(-0.424621\pi\) | ||||
0.234603 | + | 0.972091i | \(0.424621\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.8371 | 0.516612 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.6222 | 0.724074 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.4256 | 1.80111 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.8104 | −0.469131 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.87313 | 0.297708 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.37616 | 0.102730 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.5273 | 0.626899 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.245516 | 0.0105751 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.4910 | 0.537031 | 0.268516 | − | 0.963275i | \(-0.413467\pi\) | ||||
0.268516 | + | 0.963275i | \(0.413467\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.909310 | 0.0390222 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.2301 | −0.438208 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2377 | −0.608761 | −0.304381 | − | 0.952550i | \(-0.598450\pi\) | ||||
−0.304381 | + | 0.952550i | \(0.598450\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.02796 | −0.214588 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.1827 | 2.30826 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.77553 | 0.245600 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.309651 | 0.0131439 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.4633 | −1.20603 | −0.603014 | − | 0.797730i | \(-0.706034\pi\) | ||||
−0.603014 | + | 0.797730i | \(0.706034\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.23786 | −0.306129 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.62136 | 0.110674 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.8998 | 1.26013 | 0.630063 | − | 0.776544i | \(-0.283029\pi\) | ||||
0.630063 | + | 0.776544i | \(0.283029\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.49340 | −0.146968 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.69175 | −0.113043 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.5572 | 0.903726 | 0.451863 | − | 0.892087i | \(-0.350760\pi\) | ||||
0.451863 | + | 0.892087i | \(0.350760\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.0830 | 1.59372 | 0.796862 | − | 0.604162i | \(-0.206492\pi\) | ||||
0.796862 | + | 0.604162i | \(0.206492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.4448 | −0.519890 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35.2971 | −1.47199 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.7463 | 0.822048 | 0.411024 | − | 0.911625i | \(-0.365171\pi\) | ||||
0.411024 | + | 0.911625i | \(0.365171\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.3406 | 0.762210 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0503 | 0.416957 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.75448 | −0.114079 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.776183 | −0.0320912 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.48001 | 0.226184 | 0.113092 | − | 0.993585i | \(-0.463925\pi\) | ||||
0.113092 | + | 0.993585i | \(0.463925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.4328 | −1.74841 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.96535 | −0.327651 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.0670 | 1.44003 | 0.720015 | − | 0.693958i | \(-0.244135\pi\) | ||||
0.720015 | + | 0.693958i | \(0.244135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.47678 | 0.224526 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.6415 | 0.599238 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.3401 | −0.708497 | −0.354249 | − | 0.935151i | \(-0.615263\pi\) | ||||
−0.354249 | + | 0.935151i | \(0.615263\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0253 | 0.653685 | 0.326842 | − | 0.945079i | \(-0.394015\pi\) | ||||
0.326842 | + | 0.945079i | \(0.394015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.95756 | 0.201888 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.776183 | −0.0315563 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.2673 | 1.10675 | 0.553373 | − | 0.832934i | \(-0.313340\pi\) | ||||
0.553373 | + | 0.832934i | \(0.313340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.7950 | 0.883176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.53692 | 0.183544 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.92195 | −0.319965 | −0.159982 | − | 0.987120i | \(-0.551144\pi\) | ||||
−0.159982 | + | 0.987120i | \(0.551144\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.33481 | −0.215120 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.8293 | −1.16062 | −0.580312 | − | 0.814394i | \(-0.697069\pi\) | ||||
−0.580312 | + | 0.814394i | \(0.697069\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.75794 | −0.151044 | −0.0755222 | − | 0.997144i | \(-0.524062\pi\) | ||||
−0.0755222 | + | 0.997144i | \(0.524062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.02655 | 0.322095 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.39894 | −0.256368 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.3261 | 0.653042 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.69175 | −0.267243 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.04577 | −0.0416974 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.7525 | −0.587288 | −0.293644 | − | 0.955915i | \(-0.594868\pi\) | ||||
−0.293644 | + | 0.955915i | \(0.594868\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9716 | −0.595068 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.4993 | 0.615073 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.245516 | 0.00972768 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.96382 | 0.235925 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.5133 | −1.04721 | −0.523605 | − | 0.851961i | \(-0.675413\pi\) | ||||
−0.523605 | + | 0.851961i | \(0.675413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.7371 | 0.699482 | 0.349741 | − | 0.936846i | \(-0.386270\pi\) | ||||
0.349741 | + | 0.936846i | \(0.386270\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.61790 | 0.221205 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.2751 | 1.26886 | 0.634432 | − | 0.772978i | \(-0.281234\pi\) | ||||
0.634432 | + | 0.772978i | \(0.281234\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.8104 | −0.424345 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.0686 | −0.668969 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.25803 | −0.127497 | −0.0637483 | − | 0.997966i | \(-0.520305\pi\) | ||||
−0.0637483 | + | 0.997966i | \(0.520305\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.82142 | 0.149315 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.79648 | 0.148115 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.0368 | −1.52066 | −0.760329 | − | 0.649539i | \(-0.774962\pi\) | ||||
−0.760329 | + | 0.649539i | \(0.774962\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.9194 | −1.51379 | −0.756895 | − | 0.653537i | \(-0.773285\pi\) | ||||
−0.756895 | + | 0.653537i | \(0.773285\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.62136 | 0.101805 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.9810 | −0.542160 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −64.9906 | −2.51645 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 26.2003 | 1.01296 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.02796 | −0.194102 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.5466 | 1.33167 | 0.665837 | − | 0.746097i | \(-0.268074\pi\) | ||||
0.665837 | + | 0.746097i | \(0.268074\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.39754 | −0.169261 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.4362 | 0.977591 | 0.488796 | − | 0.872398i | \(-0.337436\pi\) | ||||
0.488796 | + | 0.872398i | \(0.337436\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 48.0088 | 1.84241 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.2441 | −0.929037 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.81027 | −0.375379 | −0.187690 | − | 0.982228i | \(-0.560100\pi\) | ||||
−0.187690 | + | 0.982228i | \(0.560100\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.2360 | 0.391098 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.43954 | −0.245684 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.75448 | −0.104937 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.32133 | 0.240475 | 0.120237 | − | 0.992745i | \(-0.461634\pi\) | ||||
0.120237 | + | 0.992745i | \(0.461634\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.69175 | −0.102251 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.55377 | 0.324463 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0169 | 0.682440 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24.0536 | −0.909789 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.4082 | 1.14850 | 0.574251 | − | 0.818679i | \(-0.305293\pi\) | ||||
0.574251 | + | 0.818679i | \(0.305293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.66961 | 0.100686 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.52148 | −0.132627 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.9042 | 1.12466 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.0014 | −1.42717 | −0.713586 | − | 0.700568i | \(-0.752930\pi\) | ||||
−0.713586 | + | 0.700568i | \(0.752930\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.14564 | −0.0804678 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 50.8969 | 1.90610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.776183 | −0.0290276 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.01391 | −0.187248 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.7670 | −1.29659 | −0.648295 | − | 0.761389i | \(-0.724518\pi\) | ||||
−0.648295 | + | 0.761389i | \(0.724518\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.4057 | 1.02064 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.9890 | −0.929350 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35.6067 | 1.32240 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.5746 | −1.02269 | −0.511343 | − | 0.859377i | \(-0.670852\pi\) | ||||
−0.511343 | + | 0.859377i | \(0.670852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.9730 | −0.701742 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5076 | 0.757464 | 0.378732 | − | 0.925506i | \(-0.376360\pi\) | ||||
0.378732 | + | 0.925506i | \(0.376360\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.190565 | −0.00702910 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.95756 | 0.182614 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.7241 | 1.09342 | 0.546710 | − | 0.837322i | \(-0.315880\pi\) | ||||
0.546710 | + | 0.837322i | \(0.315880\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.69175 | −0.245828 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.01986 | −0.184161 | −0.0920804 | − | 0.995752i | \(-0.529352\pi\) | ||||
−0.0920804 | + | 0.995752i | \(0.529352\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.40865 | −0.234795 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.73375 | −0.136611 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.24035 | 0.301096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.7309 | 0.647011 | 0.323506 | − | 0.946226i | \(-0.395139\pi\) | ||||
0.323506 | + | 0.946226i | \(0.395139\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.0406 | −0.657436 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.80598 | −0.102120 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.8369 | −1.19348 | −0.596740 | − | 0.802435i | \(-0.703537\pi\) | ||||
−0.596740 | + | 0.802435i | \(0.703537\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.02655 | 0.291345 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.7015 | 1.47543 | 0.737713 | − | 0.675114i | \(-0.235906\pi\) | ||||
0.737713 | + | 0.675114i | \(0.235906\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.4772 | −1.28436 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.03465 | −0.0735630 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.8104 | −0.390341 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.1712 | −1.12406 | −0.562032 | − | 0.827116i | \(-0.689980\pi\) | ||||
−0.562032 | + | 0.827116i | \(0.689980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.1298 | −0.760970 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.63553 | 0.346566 | 0.173283 | − | 0.984872i | \(-0.444563\pi\) | ||||
0.173283 | + | 0.984872i | \(0.444563\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −27.8851 | −1.00166 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.07385 | 0.0385241 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −45.9933 | −1.64788 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.96382 | 0.213402 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.09695 | −0.289361 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.5758 | −0.555923 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.7241 | 1.05955 | 0.529775 | − | 0.848138i | \(-0.322276\pi\) | ||||
0.529775 | + | 0.848138i | \(0.322276\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.8592 | −0.422199 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.1149 | −0.430755 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.02796 | −0.178548 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.13798 | 0.0758265 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.82571 | 0.170935 | 0.0854677 | − | 0.996341i | \(-0.472762\pi\) | ||||
0.0854677 | + | 0.996341i | \(0.472762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.8929 | 0.420741 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.37724 | 0.0839957 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.79648 | 0.133975 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.7698 | 0.591058 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.322165 | −0.0113407 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.6284 | −1.11200 | −0.555998 | − | 0.831183i | \(-0.687664\pi\) | ||||
−0.555998 | + | 0.831183i | \(0.687664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.2655 | 1.06276 | 0.531382 | − | 0.847132i | \(-0.321673\pi\) | ||||
0.531382 | + | 0.847132i | \(0.321673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.2944 | −0.922186 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.9579 | 0.488923 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 48.4339 | 1.69449 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.69175 | −0.0940573 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.9833 | −0.662521 | −0.331261 | − | 0.943539i | \(-0.607474\pi\) | ||||
−0.331261 | + | 0.943539i | \(0.607474\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.6234 | 0.858318 | 0.429159 | − | 0.903229i | \(-0.358810\pi\) | ||||
0.429159 | + | 0.903229i | \(0.358810\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.39754 | −0.153103 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.7784 | −0.826855 | −0.413427 | − | 0.910537i | \(-0.635668\pi\) | ||||
−0.413427 | + | 0.910537i | \(0.635668\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.5973 | 1.54893 | 0.774463 | − | 0.632619i | \(-0.218020\pi\) | ||||
0.774463 | + | 0.632619i | \(0.218020\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.89247 | −0.308476 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.643584 | 0.0222989 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.56488 | 0.261793 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.34106 | 0.219179 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.1090 | 0.763288 | 0.381644 | − | 0.924309i | \(-0.375358\pi\) | ||||
0.381644 | + | 0.924309i | \(0.375358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.5606 | 1.26071 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.5833 | 0.812253 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.776183 | −0.0267015 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.69175 | −0.0924896 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.13754 | −0.279280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.20212 | −0.109767 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.8689 | −0.611820 | −0.305910 | − | 0.952060i | \(-0.598961\pi\) | ||||
−0.305910 | + | 0.952060i | \(0.598961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.19402 | 0.177632 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.6521 | 0.398029 | 0.199014 | − | 0.979997i | \(-0.436226\pi\) | ||||
0.199014 | + | 0.979997i | \(0.436226\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.8576 | −1.80348 | −0.901740 | − | 0.432279i | \(-0.857710\pi\) | ||||
−0.901740 | + | 0.432279i | \(0.857710\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.5007 | −0.630504 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −51.1483 | −1.74111 | −0.870554 | − | 0.492072i | \(-0.836240\pi\) | ||||
−0.870554 | + | 0.492072i | \(0.836240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.6304 | 0.395446 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.1285 | −0.343981 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.14564 | −0.0727859 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.95756 | 0.167981 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.8355 | −0.603642 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −19.6342 | −0.663757 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.0125 | −0.945915 | −0.472958 | − | 0.881085i | \(-0.656814\pi\) | ||||
−0.472958 | + | 0.881085i | \(0.656814\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.8649 | 0.670027 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.2095 | 0.546111 | 0.273055 | − | 0.961998i | \(-0.411966\pi\) | ||||
0.273055 | + | 0.961998i | \(0.411966\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.4100 | 1.69643 | 0.848216 | − | 0.529650i | \(-0.177677\pi\) | ||||
0.848216 | + | 0.529650i | \(0.177677\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.39084 | 0.282055 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.4717 | −1.66110 | −0.830548 | − | 0.556947i | \(-0.811973\pi\) | ||||
−0.830548 | + | 0.556947i | \(0.811973\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 53.7507 | 1.80274 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.3600 | −1.01596 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.2758 | −0.376910 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.02655 | 0.267999 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −51.3432 | −1.71239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.22049 | −0.240549 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.4825 | 0.648337 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.705791 | −0.0234613 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 59.3623 | 1.97109 | 0.985547 | − | 0.169403i | \(-0.0541839\pi\) | ||||
0.985547 | + | 0.169403i | \(0.0541839\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.1096 | −0.368482 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.7337 | 0.786334 | 0.393167 | − | 0.919467i | \(-0.371379\pi\) | ||||
0.393167 | + | 0.919467i | \(0.371379\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.73375 | −0.123569 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.90261 | 0.129016 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.2524 | 0.437634 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.1293 | −1.22478 | −0.612392 | − | 0.790555i | \(-0.709792\pi\) | ||||
−0.612392 | + | 0.790555i | \(0.709792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.3305 | 0.768765 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.96382 | 0.196302 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.75436 | 0.0576829 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.1814 | −0.334400 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.10364 | −0.101827 | −0.0509136 | − | 0.998703i | \(-0.516213\pi\) | ||||
−0.0509136 | + | 0.998703i | \(0.516213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.64293 | −0.0538448 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.43359 | 0.145149 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.03465 | −0.0665403 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.1072 | 0.754880 | 0.377440 | − | 0.926034i | \(-0.376804\pi\) | ||||
0.377440 | + | 0.926034i | \(0.376804\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.4129 | −0.568247 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.36416 | 0.0444704 | 0.0222352 | − | 0.999753i | \(-0.492922\pi\) | ||||
0.0222352 | + | 0.999753i | \(0.492922\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.1676 | 1.79650 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.08929 | 0.0679646 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.6209 | 0.605098 | 0.302549 | − | 0.953134i | \(-0.402162\pi\) | ||||
0.302549 | + | 0.953134i | \(0.402162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.79648 | 0.123239 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.8752 | −1.00120 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.4237 | 0.629194 | 0.314597 | − | 0.949225i | \(-0.398131\pi\) | ||||
0.314597 | + | 0.949225i | \(0.398131\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.65947 | 0.312573 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.09695 | −0.261737 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.4978 | 1.14628 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.20907 | 0.297067 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.06133 | −0.0986501 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.2357 | −0.458263 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2413 | 0.329338 | 0.164669 | − | 0.986349i | \(-0.447344\pi\) | ||||
0.164669 | + | 0.986349i | \(0.447344\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.5415 | −0.563513 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.71822 | −0.279781 | −0.139890 | − | 0.990167i | \(-0.544675\pi\) | ||||
−0.139890 | + | 0.990167i | \(0.544675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.6639 | 0.950980 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.39754 | −0.140834 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56.9127 | −1.82080 | −0.910400 | − | 0.413730i | \(-0.864226\pi\) | ||||
−0.910400 | + | 0.413730i | \(0.864226\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.37724 | 0.0759770 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.1800 | 0.420804 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.1270 | −0.801425 | −0.400713 | − | 0.916204i | \(-0.631237\pi\) | ||||
−0.400713 | + | 0.916204i | \(0.631237\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.18257 | 0.196993 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.2123 | −0.388721 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −58.0951 | −1.84732 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.8268 | 0.407458 | 0.203729 | − | 0.979027i | \(-0.434694\pi\) | ||||
0.203729 | + | 0.979027i | \(0.434694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.72749 | −0.213490 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.3645 | −0.360279 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.62596 | 0.0831650 | 0.0415825 | − | 0.999135i | \(-0.486760\pi\) | ||||
0.0415825 | + | 0.999135i | \(0.486760\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.398941 | −0.0126219 |
(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 | 6864.2.a.bz.1.2 | 4 | ||
4.3 | odd | 2 | 429.2.a.h.1.4 | ✓ | 4 | ||
12.11 | even | 2 | 1287.2.a.m.1.1 | 4 | |||
44.43 | even | 2 | 4719.2.a.z.1.1 | 4 | |||
52.51 | odd | 2 | 5577.2.a.m.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.a.h.1.4 | ✓ | 4 | 4.3 | odd | 2 | ||
1287.2.a.m.1.1 | 4 | 12.11 | even | 2 | |||
4719.2.a.z.1.1 | 4 | 44.43 | even | 2 | |||
5577.2.a.m.1.1 | 4 | 52.51 | odd | 2 | |||
6864.2.a.bz.1.2 | 4 | 1.1 | even | 1 | trivial |