Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4014,2,Mod(1,4014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4014.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4014 = 2 \cdot 3^{2} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4014.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: | \(32.0519513713\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 18x^{5} - 8x^{4} + 51x^{3} + 47x^{2} - 2x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1338) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.369925\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4014.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.69148 | −1.20367 | −0.601834 | − | 0.798621i | \(-0.705563\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.17419 | 0.821767 | 0.410884 | − | 0.911688i | \(-0.365220\pi\) | ||||
0.410884 | + | 0.911688i | \(0.365220\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.69148 | 0.851122 | ||||||||
\(11\) | 2.79991 | 0.844206 | 0.422103 | − | 0.906548i | \(-0.361292\pi\) | ||||
0.422103 | + | 0.906548i | \(0.361292\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.60736 | 1.55520 | 0.777601 | − | 0.628758i | \(-0.216436\pi\) | ||||
0.777601 | + | 0.628758i | \(0.216436\pi\) | |||||||
\(14\) | −2.17419 | −0.581077 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.05158 | 0.982654 | 0.491327 | − | 0.870975i | \(-0.336512\pi\) | ||||
0.491327 | + | 0.870975i | \(0.336512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.43987 | 0.789160 | 0.394580 | − | 0.918861i | \(-0.370890\pi\) | ||||
0.394580 | + | 0.918861i | \(0.370890\pi\) | |||||||
\(20\) | −2.69148 | −0.601834 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.79991 | −0.596944 | ||||||||
\(23\) | 0.907338 | 0.189193 | 0.0945965 | − | 0.995516i | \(-0.469844\pi\) | ||||
0.0945965 | + | 0.995516i | \(0.469844\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.24408 | 0.448816 | ||||||||
\(26\) | −5.60736 | −1.09969 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.17419 | 0.410884 | ||||||||
\(29\) | −3.53306 | −0.656073 | −0.328036 | − | 0.944665i | \(-0.606387\pi\) | ||||
−0.328036 | + | 0.944665i | \(0.606387\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.49443 | 0.448012 | 0.224006 | − | 0.974588i | \(-0.428086\pi\) | ||||
0.224006 | + | 0.974588i | \(0.428086\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.05158 | −0.694841 | ||||||||
\(35\) | −5.85180 | −0.989135 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.44606 | 0.730928 | 0.365464 | − | 0.930826i | \(-0.380910\pi\) | ||||
0.365464 | + | 0.930826i | \(0.380910\pi\) | |||||||
\(38\) | −3.43987 | −0.558021 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.69148 | 0.425561 | ||||||||
\(41\) | 10.8990 | 1.70214 | 0.851071 | − | 0.525050i | \(-0.175953\pi\) | ||||
0.851071 | + | 0.525050i | \(0.175953\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.91186 | −1.20655 | −0.603274 | − | 0.797534i | \(-0.706137\pi\) | ||||
−0.603274 | + | 0.797534i | \(0.706137\pi\) | |||||||
\(44\) | 2.79991 | 0.422103 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.907338 | −0.133780 | ||||||||
\(47\) | 13.4073 | 1.95566 | 0.977829 | − | 0.209406i | \(-0.0671531\pi\) | ||||
0.977829 | + | 0.209406i | \(0.0671531\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.27289 | −0.324698 | ||||||||
\(50\) | −2.24408 | −0.317361 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.60736 | 0.777601 | ||||||||
\(53\) | −13.1947 | −1.81243 | −0.906213 | − | 0.422822i | \(-0.861039\pi\) | ||||
−0.906213 | + | 0.422822i | \(0.861039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.53592 | −1.01614 | ||||||||
\(56\) | −2.17419 | −0.290539 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.53306 | 0.463913 | ||||||||
\(59\) | −11.3491 | −1.47752 | −0.738762 | − | 0.673966i | \(-0.764589\pi\) | ||||
−0.738762 | + | 0.673966i | \(0.764589\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.466941 | 0.0597857 | 0.0298928 | − | 0.999553i | \(-0.490483\pi\) | ||||
0.0298928 | + | 0.999553i | \(0.490483\pi\) | |||||||
\(62\) | −2.49443 | −0.316792 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −15.0921 | −1.87195 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.52324 | 0.796940 | 0.398470 | − | 0.917181i | \(-0.369541\pi\) | ||||
0.398470 | + | 0.917181i | \(0.369541\pi\) | |||||||
\(68\) | 4.05158 | 0.491327 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.85180 | 0.699424 | ||||||||
\(71\) | −2.84960 | −0.338186 | −0.169093 | − | 0.985600i | \(-0.554084\pi\) | ||||
−0.169093 | + | 0.985600i | \(0.554084\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.29281 | 0.502435 | 0.251218 | − | 0.967931i | \(-0.419169\pi\) | ||||
0.251218 | + | 0.967931i | \(0.419169\pi\) | |||||||
\(74\) | −4.44606 | −0.516844 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.43987 | 0.394580 | ||||||||
\(77\) | 6.08755 | 0.693741 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.97329 | −0.897065 | −0.448533 | − | 0.893766i | \(-0.648053\pi\) | ||||
−0.448533 | + | 0.893766i | \(0.648053\pi\) | |||||||
\(80\) | −2.69148 | −0.300917 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.8990 | −1.20360 | ||||||||
\(83\) | 1.80391 | 0.198005 | 0.0990024 | − | 0.995087i | \(-0.468435\pi\) | ||||
0.0990024 | + | 0.995087i | \(0.468435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9048 | −1.18279 | ||||||||
\(86\) | 7.91186 | 0.853158 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.79991 | −0.298472 | ||||||||
\(89\) | −10.9572 | −1.16146 | −0.580730 | − | 0.814096i | \(-0.697233\pi\) | ||||
−0.580730 | + | 0.814096i | \(0.697233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.1915 | 1.27801 | ||||||||
\(92\) | 0.907338 | 0.0945965 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.4073 | −1.38286 | ||||||||
\(95\) | −9.25835 | −0.949887 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.3978 | 1.66495 | 0.832473 | − | 0.554066i | \(-0.186924\pi\) | ||||
0.832473 | + | 0.554066i | \(0.186924\pi\) | |||||||
\(98\) | 2.27289 | 0.229596 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.24408 | 0.224408 | ||||||||
\(101\) | −3.53689 | −0.351933 | −0.175967 | − | 0.984396i | \(-0.556305\pi\) | ||||
−0.175967 | + | 0.984396i | \(0.556305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.03869 | −0.496477 | −0.248239 | − | 0.968699i | \(-0.579852\pi\) | ||||
−0.248239 | + | 0.968699i | \(0.579852\pi\) | |||||||
\(104\) | −5.60736 | −0.549847 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.1947 | 1.28158 | ||||||||
\(107\) | 8.32832 | 0.805129 | 0.402565 | − | 0.915392i | \(-0.368119\pi\) | ||||
0.402565 | + | 0.915392i | \(0.368119\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.72745 | 0.261242 | 0.130621 | − | 0.991432i | \(-0.458303\pi\) | ||||
0.130621 | + | 0.991432i | \(0.458303\pi\) | |||||||
\(110\) | 7.53592 | 0.718522 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.17419 | 0.205442 | ||||||||
\(113\) | −13.6313 | −1.28233 | −0.641165 | − | 0.767403i | \(-0.721548\pi\) | ||||
−0.641165 | + | 0.767403i | \(0.721548\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.44208 | −0.227725 | ||||||||
\(116\) | −3.53306 | −0.328036 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.3491 | 1.04477 | ||||||||
\(119\) | 8.80892 | 0.807513 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.16049 | −0.287317 | ||||||||
\(122\) | −0.466941 | −0.0422749 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.49443 | 0.224006 | ||||||||
\(125\) | 7.41751 | 0.663443 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6128 | −1.20794 | −0.603969 | − | 0.797008i | \(-0.706415\pi\) | ||||
−0.603969 | + | 0.797008i | \(0.706415\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.0921 | 1.32367 | ||||||||
\(131\) | 17.7178 | 1.54801 | 0.774004 | − | 0.633181i | \(-0.218251\pi\) | ||||
0.774004 | + | 0.633181i | \(0.218251\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.47894 | 0.648506 | ||||||||
\(134\) | −6.52324 | −0.563522 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.05158 | −0.347420 | ||||||||
\(137\) | 15.2395 | 1.30200 | 0.650998 | − | 0.759079i | \(-0.274351\pi\) | ||||
0.650998 | + | 0.759079i | \(0.274351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.87274 | −0.413300 | −0.206650 | − | 0.978415i | \(-0.566256\pi\) | ||||
−0.206650 | + | 0.978415i | \(0.566256\pi\) | |||||||
\(140\) | −5.85180 | −0.494567 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.84960 | 0.239133 | ||||||||
\(143\) | 15.7001 | 1.31291 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.50917 | 0.789693 | ||||||||
\(146\) | −4.29281 | −0.355275 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.44606 | 0.365464 | ||||||||
\(149\) | 14.5888 | 1.19516 | 0.597579 | − | 0.801810i | \(-0.296129\pi\) | ||||
0.597579 | + | 0.801810i | \(0.296129\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6330 | 1.02806 | 0.514028 | − | 0.857773i | \(-0.328153\pi\) | ||||
0.514028 | + | 0.857773i | \(0.328153\pi\) | |||||||
\(152\) | −3.43987 | −0.279010 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.08755 | −0.490549 | ||||||||
\(155\) | −6.71371 | −0.539258 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0602 | −0.962507 | −0.481254 | − | 0.876581i | \(-0.659818\pi\) | ||||
−0.481254 | + | 0.876581i | \(0.659818\pi\) | |||||||
\(158\) | 7.97329 | 0.634321 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.69148 | 0.212780 | ||||||||
\(161\) | 1.97273 | 0.155473 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.156053 | 0.0122230 | 0.00611149 | − | 0.999981i | \(-0.498055\pi\) | ||||
0.00611149 | + | 0.999981i | \(0.498055\pi\) | |||||||
\(164\) | 10.8990 | 0.851071 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.80391 | −0.140011 | ||||||||
\(167\) | −1.39325 | −0.107813 | −0.0539065 | − | 0.998546i | \(-0.517167\pi\) | ||||
−0.0539065 | + | 0.998546i | \(0.517167\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.4425 | 1.41865 | ||||||||
\(170\) | 10.9048 | 0.836358 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.91186 | −0.603274 | ||||||||
\(173\) | 16.6528 | 1.26609 | 0.633043 | − | 0.774117i | \(-0.281806\pi\) | ||||
0.633043 | + | 0.774117i | \(0.281806\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.87906 | 0.368822 | ||||||||
\(176\) | 2.79991 | 0.211051 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.9572 | 0.821277 | ||||||||
\(179\) | 12.9554 | 0.968331 | 0.484165 | − | 0.874977i | \(-0.339123\pi\) | ||||
0.484165 | + | 0.874977i | \(0.339123\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.76887 | −0.651785 | −0.325892 | − | 0.945407i | \(-0.605665\pi\) | ||||
−0.325892 | + | 0.945407i | \(0.605665\pi\) | |||||||
\(182\) | −12.1915 | −0.903692 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.907338 | −0.0668898 | ||||||||
\(185\) | −11.9665 | −0.879794 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3441 | 0.829562 | ||||||||
\(188\) | 13.4073 | 0.977829 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.25835 | 0.671672 | ||||||||
\(191\) | −2.78928 | −0.201825 | −0.100912 | − | 0.994895i | \(-0.532176\pi\) | ||||
−0.100912 | + | 0.994895i | \(0.532176\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.6058 | −0.835402 | −0.417701 | − | 0.908585i | \(-0.637164\pi\) | ||||
−0.417701 | + | 0.908585i | \(0.637164\pi\) | |||||||
\(194\) | −16.3978 | −1.17729 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.27289 | −0.162349 | ||||||||
\(197\) | −20.5331 | −1.46293 | −0.731463 | − | 0.681881i | \(-0.761162\pi\) | ||||
−0.731463 | + | 0.681881i | \(0.761162\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.9919 | 1.27541 | 0.637706 | − | 0.770280i | \(-0.279883\pi\) | ||||
0.637706 | + | 0.770280i | \(0.279883\pi\) | |||||||
\(200\) | −2.24408 | −0.158680 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.53689 | 0.248855 | ||||||||
\(203\) | −7.68155 | −0.539139 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29.3346 | −2.04881 | ||||||||
\(206\) | 5.03869 | 0.351062 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.60736 | 0.388800 | ||||||||
\(209\) | 9.63134 | 0.666214 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.08882 | −0.212643 | −0.106321 | − | 0.994332i | \(-0.533907\pi\) | ||||
−0.106321 | + | 0.994332i | \(0.533907\pi\) | |||||||
\(212\) | −13.1947 | −0.906213 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.32832 | −0.569312 | ||||||||
\(215\) | 21.2946 | 1.45228 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.42336 | 0.368162 | ||||||||
\(218\) | −2.72745 | −0.184726 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.53592 | −0.508072 | ||||||||
\(221\) | 22.7187 | 1.52822 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | −2.17419 | −0.145269 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.6313 | 0.906744 | ||||||||
\(227\) | 19.8177 | 1.31535 | 0.657675 | − | 0.753302i | \(-0.271540\pi\) | ||||
0.657675 | + | 0.753302i | \(0.271540\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.3745 | −1.67680 | −0.838398 | − | 0.545058i | \(-0.816508\pi\) | ||||
−0.838398 | + | 0.545058i | \(0.816508\pi\) | |||||||
\(230\) | 2.44208 | 0.161026 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.53306 | 0.231957 | ||||||||
\(233\) | −8.41472 | −0.551266 | −0.275633 | − | 0.961263i | \(-0.588888\pi\) | ||||
−0.275633 | + | 0.961263i | \(0.588888\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.0855 | −2.35396 | ||||||||
\(236\) | −11.3491 | −0.738762 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.80892 | −0.570998 | ||||||||
\(239\) | 28.9489 | 1.87255 | 0.936273 | − | 0.351272i | \(-0.114251\pi\) | ||||
0.936273 | + | 0.351272i | \(0.114251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.56905 | 0.165487 | 0.0827435 | − | 0.996571i | \(-0.473632\pi\) | ||||
0.0827435 | + | 0.996571i | \(0.473632\pi\) | |||||||
\(242\) | 3.16049 | 0.203164 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.466941 | 0.0298928 | ||||||||
\(245\) | 6.11744 | 0.390829 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.2886 | 1.22730 | ||||||||
\(248\) | −2.49443 | −0.158396 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.41751 | −0.469125 | ||||||||
\(251\) | −14.7729 | −0.932456 | −0.466228 | − | 0.884665i | \(-0.654387\pi\) | ||||
−0.466228 | + | 0.884665i | \(0.654387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.54047 | 0.159718 | ||||||||
\(254\) | 13.6128 | 0.854140 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.3220 | 1.26765 | 0.633827 | − | 0.773475i | \(-0.281483\pi\) | ||||
0.633827 | + | 0.773475i | \(0.281483\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.66659 | 0.600653 | ||||||||
\(260\) | −15.0921 | −0.935973 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.7178 | −1.09461 | ||||||||
\(263\) | 13.9440 | 0.859826 | 0.429913 | − | 0.902870i | \(-0.358544\pi\) | ||||
0.429913 | + | 0.902870i | \(0.358544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.5132 | 2.18156 | ||||||||
\(266\) | −7.47894 | −0.458563 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.52324 | 0.398470 | ||||||||
\(269\) | 1.33483 | 0.0813862 | 0.0406931 | − | 0.999172i | \(-0.487043\pi\) | ||||
0.0406931 | + | 0.999172i | \(0.487043\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0818 | 1.09839 | 0.549197 | − | 0.835693i | \(-0.314934\pi\) | ||||
0.549197 | + | 0.835693i | \(0.314934\pi\) | |||||||
\(272\) | 4.05158 | 0.245663 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.2395 | −0.920650 | ||||||||
\(275\) | 6.28323 | 0.378893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.92461 | 0.416059 | 0.208030 | − | 0.978123i | \(-0.433295\pi\) | ||||
0.208030 | + | 0.978123i | \(0.433295\pi\) | |||||||
\(278\) | 4.87274 | 0.292247 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.85180 | 0.349712 | ||||||||
\(281\) | −8.16492 | −0.487078 | −0.243539 | − | 0.969891i | \(-0.578308\pi\) | ||||
−0.243539 | + | 0.969891i | \(0.578308\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9290 | −0.827993 | −0.413996 | − | 0.910279i | \(-0.635867\pi\) | ||||
−0.413996 | + | 0.910279i | \(0.635867\pi\) | |||||||
\(284\) | −2.84960 | −0.169093 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.7001 | −0.928368 | ||||||||
\(287\) | 23.6966 | 1.39877 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.584665 | −0.0343921 | ||||||||
\(290\) | −9.50917 | −0.558398 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.29281 | 0.251218 | ||||||||
\(293\) | 22.2675 | 1.30088 | 0.650439 | − | 0.759558i | \(-0.274585\pi\) | ||||
0.650439 | + | 0.759558i | \(0.274585\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.5459 | 1.77845 | ||||||||
\(296\) | −4.44606 | −0.258422 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.5888 | −0.845105 | ||||||||
\(299\) | 5.08777 | 0.294233 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.2019 | −0.991502 | ||||||||
\(302\) | −12.6330 | −0.726946 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.43987 | 0.197290 | ||||||||
\(305\) | −1.25676 | −0.0719621 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.05512 | −0.459730 | −0.229865 | − | 0.973222i | \(-0.573829\pi\) | ||||
−0.229865 | + | 0.973222i | \(0.573829\pi\) | |||||||
\(308\) | 6.08755 | 0.346870 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.71371 | 0.381313 | ||||||||
\(311\) | −5.19327 | −0.294483 | −0.147242 | − | 0.989101i | \(-0.547040\pi\) | ||||
−0.147242 | + | 0.989101i | \(0.547040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.77635 | 0.100405 | 0.0502025 | − | 0.998739i | \(-0.484013\pi\) | ||||
0.0502025 | + | 0.998739i | \(0.484013\pi\) | |||||||
\(314\) | 12.0602 | 0.680595 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.97329 | −0.448533 | ||||||||
\(317\) | −16.7624 | −0.941470 | −0.470735 | − | 0.882275i | \(-0.656011\pi\) | ||||
−0.470735 | + | 0.882275i | \(0.656011\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.89226 | −0.553860 | ||||||||
\(320\) | −2.69148 | −0.150458 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.97273 | −0.109936 | ||||||||
\(323\) | 13.9369 | 0.775471 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.5834 | 0.697999 | ||||||||
\(326\) | −0.156053 | −0.00864295 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.8990 | −0.601798 | ||||||||
\(329\) | 29.1501 | 1.60710 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.10572 | −0.170706 | −0.0853530 | − | 0.996351i | \(-0.527202\pi\) | ||||
−0.0853530 | + | 0.996351i | \(0.527202\pi\) | |||||||
\(332\) | 1.80391 | 0.0990024 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.39325 | 0.0762353 | ||||||||
\(335\) | −17.5572 | −0.959251 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.0670 | 0.875225 | 0.437613 | − | 0.899164i | \(-0.355824\pi\) | ||||
0.437613 | + | 0.899164i | \(0.355824\pi\) | |||||||
\(338\) | −18.4425 | −1.00314 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.9048 | −0.591394 | ||||||||
\(341\) | 6.98418 | 0.378214 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1610 | −1.08859 | ||||||||
\(344\) | 7.91186 | 0.426579 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.6528 | −0.895258 | ||||||||
\(347\) | −20.1398 | −1.08116 | −0.540580 | − | 0.841293i | \(-0.681795\pi\) | ||||
−0.540580 | + | 0.841293i | \(0.681795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.6684 | 1.64164 | 0.820821 | − | 0.571186i | \(-0.193516\pi\) | ||||
0.820821 | + | 0.571186i | \(0.193516\pi\) | |||||||
\(350\) | −4.87906 | −0.260797 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.79991 | −0.149236 | ||||||||
\(353\) | −26.7829 | −1.42551 | −0.712755 | − | 0.701413i | \(-0.752553\pi\) | ||||
−0.712755 | + | 0.701413i | \(0.752553\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.66966 | 0.407063 | ||||||||
\(356\) | −10.9572 | −0.580730 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.9554 | −0.684713 | ||||||||
\(359\) | −9.32994 | −0.492415 | −0.246208 | − | 0.969217i | \(-0.579185\pi\) | ||||
−0.246208 | + | 0.969217i | \(0.579185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.16729 | −0.377226 | ||||||||
\(362\) | 8.76887 | 0.460881 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.1915 | 0.639007 | ||||||||
\(365\) | −11.5540 | −0.604765 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.3737 | −1.01130 | −0.505649 | − | 0.862739i | \(-0.668747\pi\) | ||||
−0.505649 | + | 0.862739i | \(0.668747\pi\) | |||||||
\(368\) | 0.907338 | 0.0472983 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.9665 | 0.622108 | ||||||||
\(371\) | −28.6877 | −1.48939 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.5202 | −1.26961 | −0.634805 | − | 0.772672i | \(-0.718920\pi\) | ||||
−0.634805 | + | 0.772672i | \(0.718920\pi\) | |||||||
\(374\) | −11.3441 | −0.586589 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.4073 | −0.691429 | ||||||||
\(377\) | −19.8111 | −1.02033 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.5623 | 1.41578 | 0.707889 | − | 0.706323i | \(-0.249647\pi\) | ||||
0.707889 | + | 0.706323i | \(0.249647\pi\) | |||||||
\(380\) | −9.25835 | −0.474943 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.78928 | 0.142712 | ||||||||
\(383\) | 21.8176 | 1.11483 | 0.557414 | − | 0.830235i | \(-0.311794\pi\) | ||||
0.557414 | + | 0.830235i | \(0.311794\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.3845 | −0.835033 | ||||||||
\(386\) | 11.6058 | 0.590718 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.3978 | 0.832473 | ||||||||
\(389\) | 16.2181 | 0.822290 | 0.411145 | − | 0.911570i | \(-0.365129\pi\) | ||||
0.411145 | + | 0.911570i | \(0.365129\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.67616 | 0.185911 | ||||||||
\(392\) | 2.27289 | 0.114798 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.5331 | 1.03444 | ||||||||
\(395\) | 21.4600 | 1.07977 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.66612 | 0.0836200 | 0.0418100 | − | 0.999126i | \(-0.486688\pi\) | ||||
0.0418100 | + | 0.999126i | \(0.486688\pi\) | |||||||
\(398\) | −17.9919 | −0.901852 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.24408 | 0.112204 | ||||||||
\(401\) | 33.0190 | 1.64889 | 0.824446 | − | 0.565940i | \(-0.191487\pi\) | ||||
0.824446 | + | 0.565940i | \(0.191487\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.9871 | 0.696749 | ||||||||
\(404\) | −3.53689 | −0.175967 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.68155 | 0.381229 | ||||||||
\(407\) | 12.4486 | 0.617053 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.0353 | 1.63349 | 0.816744 | − | 0.577000i | \(-0.195777\pi\) | ||||
0.816744 | + | 0.577000i | \(0.195777\pi\) | |||||||
\(410\) | 29.3346 | 1.44873 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.03869 | −0.248239 | ||||||||
\(413\) | −24.6751 | −1.21418 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.85519 | −0.238332 | ||||||||
\(416\) | −5.60736 | −0.274923 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.63134 | −0.471084 | ||||||||
\(419\) | 8.61709 | 0.420972 | 0.210486 | − | 0.977597i | \(-0.432495\pi\) | ||||
0.210486 | + | 0.977597i | \(0.432495\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.7662 | −0.670922 | −0.335461 | − | 0.942054i | \(-0.608892\pi\) | ||||
−0.335461 | + | 0.942054i | \(0.608892\pi\) | |||||||
\(422\) | 3.08882 | 0.150361 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.1947 | 0.640789 | ||||||||
\(425\) | 9.09208 | 0.441030 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.01522 | 0.0491299 | ||||||||
\(428\) | 8.32832 | 0.402565 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −21.2946 | −1.02692 | ||||||||
\(431\) | −7.17551 | −0.345632 | −0.172816 | − | 0.984954i | \(-0.555287\pi\) | ||||
−0.172816 | + | 0.984954i | \(0.555287\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.4852 | 0.551944 | 0.275972 | − | 0.961166i | \(-0.411000\pi\) | ||||
0.275972 | + | 0.961166i | \(0.411000\pi\) | |||||||
\(434\) | −5.42336 | −0.260330 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.72745 | 0.130621 | ||||||||
\(437\) | 3.12112 | 0.149304 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.6077 | −0.506279 | −0.253139 | − | 0.967430i | \(-0.581463\pi\) | ||||
−0.253139 | + | 0.967430i | \(0.581463\pi\) | |||||||
\(440\) | 7.53592 | 0.359261 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −22.7187 | −1.08062 | ||||||||
\(443\) | 23.6850 | 1.12531 | 0.562654 | − | 0.826693i | \(-0.309780\pi\) | ||||
0.562654 | + | 0.826693i | \(0.309780\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.4911 | 1.39801 | ||||||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.17419 | 0.102721 | ||||||||
\(449\) | −26.0448 | −1.22913 | −0.614565 | − | 0.788866i | \(-0.710668\pi\) | ||||
−0.614565 | + | 0.788866i | \(0.710668\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.5163 | 1.43696 | ||||||||
\(452\) | −13.6313 | −0.641165 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.8177 | −0.930093 | ||||||||
\(455\) | −32.8131 | −1.53830 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.4587 | 0.910237 | 0.455119 | − | 0.890431i | \(-0.349597\pi\) | ||||
0.455119 | + | 0.890431i | \(0.349597\pi\) | |||||||
\(458\) | 25.3745 | 1.18567 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.44208 | −0.113863 | ||||||||
\(461\) | 1.34885 | 0.0628221 | 0.0314110 | − | 0.999507i | \(-0.490000\pi\) | ||||
0.0314110 | + | 0.999507i | \(0.490000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.2142 | −0.892958 | −0.446479 | − | 0.894794i | \(-0.647322\pi\) | ||||
−0.446479 | + | 0.894794i | \(0.647322\pi\) | |||||||
\(464\) | −3.53306 | −0.164018 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.41472 | 0.389804 | ||||||||
\(467\) | −30.1602 | −1.39565 | −0.697824 | − | 0.716269i | \(-0.745848\pi\) | ||||
−0.697824 | + | 0.716269i | \(0.745848\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.1828 | 0.654899 | ||||||||
\(470\) | 36.0855 | 1.66450 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.3491 | 0.522384 | ||||||||
\(473\) | −22.1525 | −1.01857 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.71934 | 0.354188 | ||||||||
\(476\) | 8.80892 | 0.403756 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.9489 | −1.32409 | ||||||||
\(479\) | −10.4392 | −0.476979 | −0.238490 | − | 0.971145i | \(-0.576652\pi\) | ||||
−0.238490 | + | 0.971145i | \(0.576652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.9307 | 1.13674 | ||||||||
\(482\) | −2.56905 | −0.117017 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.16049 | −0.143658 | ||||||||
\(485\) | −44.1344 | −2.00404 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.5437 | 0.840297 | 0.420149 | − | 0.907455i | \(-0.361978\pi\) | ||||
0.420149 | + | 0.907455i | \(0.361978\pi\) | |||||||
\(488\) | −0.466941 | −0.0211374 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.11744 | −0.276358 | ||||||||
\(491\) | −17.6989 | −0.798739 | −0.399370 | − | 0.916790i | \(-0.630771\pi\) | ||||
−0.399370 | + | 0.916790i | \(0.630771\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.3145 | −0.644692 | ||||||||
\(494\) | −19.2886 | −0.867835 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.49443 | 0.112003 | ||||||||
\(497\) | −6.19559 | −0.277910 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.78926 | −0.124864 | −0.0624321 | − | 0.998049i | \(-0.519886\pi\) | ||||
−0.0624321 | + | 0.998049i | \(0.519886\pi\) | |||||||
\(500\) | 7.41751 | 0.331721 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.7729 | 0.659346 | ||||||||
\(503\) | 26.2160 | 1.16892 | 0.584458 | − | 0.811424i | \(-0.301307\pi\) | ||||
0.584458 | + | 0.811424i | \(0.301307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.51947 | 0.423611 | ||||||||
\(506\) | −2.54047 | −0.112938 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.6128 | −0.603969 | ||||||||
\(509\) | −1.95494 | −0.0866510 | −0.0433255 | − | 0.999061i | \(-0.513795\pi\) | ||||
−0.0433255 | + | 0.999061i | \(0.513795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.33339 | 0.412885 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20.3220 | −0.896367 | ||||||||
\(515\) | 13.5616 | 0.597593 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.5393 | 1.65098 | ||||||||
\(518\) | −9.66659 | −0.424726 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.0921 | 0.661833 | ||||||||
\(521\) | −23.9402 | −1.04884 | −0.524420 | − | 0.851459i | \(-0.675718\pi\) | ||||
−0.524420 | + | 0.851459i | \(0.675718\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.6405 | 1.47100 | 0.735498 | − | 0.677527i | \(-0.236948\pi\) | ||||
0.735498 | + | 0.677527i | \(0.236948\pi\) | |||||||
\(524\) | 17.7178 | 0.774004 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.9440 | −0.607989 | ||||||||
\(527\) | 10.1064 | 0.440241 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1767 | −0.964206 | ||||||||
\(530\) | −35.5132 | −1.54259 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.47894 | 0.324253 | ||||||||
\(533\) | 61.1148 | 2.64718 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.4155 | −0.969108 | ||||||||
\(536\) | −6.52324 | −0.281761 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.33483 | −0.0575487 | ||||||||
\(539\) | −6.36389 | −0.274112 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.9644 | −1.24528 | −0.622638 | − | 0.782510i | \(-0.713939\pi\) | ||||
−0.622638 | + | 0.782510i | \(0.713939\pi\) | |||||||
\(542\) | −18.0818 | −0.776681 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.05158 | −0.173710 | ||||||||
\(545\) | −7.34088 | −0.314449 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.6631 | 1.73863 | 0.869314 | − | 0.494260i | \(-0.164561\pi\) | ||||
0.869314 | + | 0.494260i | \(0.164561\pi\) | |||||||
\(548\) | 15.2395 | 0.650998 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.28323 | −0.267918 | ||||||||
\(551\) | −12.1533 | −0.517747 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.3355 | −0.737179 | ||||||||
\(554\) | −6.92461 | −0.294198 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.87274 | −0.206650 | ||||||||
\(557\) | −33.3538 | −1.41325 | −0.706624 | − | 0.707590i | \(-0.749783\pi\) | ||||
−0.706624 | + | 0.707590i | \(0.749783\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −44.3647 | −1.87643 | ||||||||
\(560\) | −5.85180 | −0.247284 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.16492 | 0.344416 | ||||||||
\(563\) | −19.0344 | −0.802205 | −0.401102 | − | 0.916033i | \(-0.631373\pi\) | ||||
−0.401102 | + | 0.916033i | \(0.631373\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.6885 | 1.54350 | ||||||||
\(566\) | 13.9290 | 0.585479 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.84960 | 0.119567 | ||||||||
\(569\) | 36.6564 | 1.53672 | 0.768358 | − | 0.640020i | \(-0.221074\pi\) | ||||
0.768358 | + | 0.640020i | \(0.221074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.9181 | −1.16833 | −0.584167 | − | 0.811633i | \(-0.698579\pi\) | ||||
−0.584167 | + | 0.811633i | \(0.698579\pi\) | |||||||
\(572\) | 15.7001 | 0.656455 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −23.6966 | −0.989076 | ||||||||
\(575\) | 2.03614 | 0.0849128 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.9442 | 0.747028 | 0.373514 | − | 0.927624i | \(-0.378153\pi\) | ||||
0.373514 | + | 0.927624i | \(0.378153\pi\) | |||||||
\(578\) | 0.584665 | 0.0243189 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.50917 | 0.394847 | ||||||||
\(581\) | 3.92205 | 0.162714 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.9439 | −1.53006 | ||||||||
\(584\) | −4.29281 | −0.177638 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.2675 | −0.919860 | ||||||||
\(587\) | 26.5520 | 1.09592 | 0.547960 | − | 0.836505i | \(-0.315405\pi\) | ||||
0.547960 | + | 0.836505i | \(0.315405\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.58051 | 0.353554 | ||||||||
\(590\) | −30.5459 | −1.25755 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.44606 | 0.182732 | ||||||||
\(593\) | 13.9180 | 0.571543 | 0.285771 | − | 0.958298i | \(-0.407750\pi\) | ||||
0.285771 | + | 0.958298i | \(0.407750\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.7091 | −0.971977 | ||||||||
\(596\) | 14.5888 | 0.597579 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.08777 | −0.208054 | ||||||||
\(599\) | 3.31413 | 0.135412 | 0.0677059 | − | 0.997705i | \(-0.478432\pi\) | ||||
0.0677059 | + | 0.997705i | \(0.478432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.4692 | 0.998118 | 0.499059 | − | 0.866568i | \(-0.333679\pi\) | ||||
0.499059 | + | 0.866568i | \(0.333679\pi\) | |||||||
\(602\) | 17.2019 | 0.701098 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.6330 | 0.514028 | ||||||||
\(605\) | 8.50639 | 0.345834 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.4463 | 1.51990 | 0.759950 | − | 0.649981i | \(-0.225223\pi\) | ||||
0.759950 | + | 0.649981i | \(0.225223\pi\) | |||||||
\(608\) | −3.43987 | −0.139505 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.25676 | 0.0508849 | ||||||||
\(611\) | 75.1796 | 3.04144 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.8819 | −0.722241 | −0.361121 | − | 0.932519i | \(-0.617606\pi\) | ||||
−0.361121 | + | 0.932519i | \(0.617606\pi\) | |||||||
\(614\) | 8.05512 | 0.325078 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.08755 | −0.245274 | ||||||||
\(617\) | −6.14776 | −0.247500 | −0.123750 | − | 0.992313i | \(-0.539492\pi\) | ||||
−0.123750 | + | 0.992313i | \(0.539492\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.3510 | −0.858169 | −0.429085 | − | 0.903264i | \(-0.641164\pi\) | ||||
−0.429085 | + | 0.903264i | \(0.641164\pi\) | |||||||
\(620\) | −6.71371 | −0.269629 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.19327 | 0.208231 | ||||||||
\(623\) | −23.8231 | −0.954451 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.1845 | −1.24738 | ||||||||
\(626\) | −1.77635 | −0.0709971 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.0602 | −0.481254 | ||||||||
\(629\) | 18.0136 | 0.718249 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.9747 | −1.63118 | −0.815589 | − | 0.578632i | \(-0.803587\pi\) | ||||
−0.815589 | + | 0.578632i | \(0.803587\pi\) | |||||||
\(632\) | 7.97329 | 0.317161 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.7624 | 0.665720 | ||||||||
\(635\) | 36.6385 | 1.45395 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.7449 | −0.504971 | ||||||||
\(638\) | 9.89226 | 0.391638 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.69148 | 0.106390 | ||||||||
\(641\) | 31.0690 | 1.22715 | 0.613575 | − | 0.789636i | \(-0.289731\pi\) | ||||
0.613575 | + | 0.789636i | \(0.289731\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.6129 | 1.12838 | 0.564192 | − | 0.825643i | \(-0.309188\pi\) | ||||
0.564192 | + | 0.825643i | \(0.309188\pi\) | |||||||
\(644\) | 1.97273 | 0.0777363 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.9369 | −0.548341 | ||||||||
\(647\) | −46.2606 | −1.81869 | −0.909346 | − | 0.416042i | \(-0.863417\pi\) | ||||
−0.909346 | + | 0.416042i | \(0.863417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.7764 | −1.24733 | ||||||||
\(650\) | −12.5834 | −0.493560 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.156053 | 0.00611149 | ||||||||
\(653\) | 39.3565 | 1.54014 | 0.770068 | − | 0.637961i | \(-0.220222\pi\) | ||||
0.770068 | + | 0.637961i | \(0.220222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −47.6870 | −1.86329 | ||||||||
\(656\) | 10.8990 | 0.425536 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −29.1501 | −1.13639 | ||||||||
\(659\) | 19.6764 | 0.766485 | 0.383242 | − | 0.923648i | \(-0.374807\pi\) | ||||
0.383242 | + | 0.923648i | \(0.374807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.9951 | 1.51673 | 0.758366 | − | 0.651829i | \(-0.225998\pi\) | ||||
0.758366 | + | 0.651829i | \(0.225998\pi\) | |||||||
\(662\) | 3.10572 | 0.120707 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.80391 | −0.0700053 | ||||||||
\(665\) | −20.1294 | −0.780586 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.20568 | −0.124124 | ||||||||
\(668\) | −1.39325 | −0.0539065 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.5572 | 0.678293 | ||||||||
\(671\) | 1.30739 | 0.0504714 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.3800 | 0.824139 | 0.412069 | − | 0.911152i | \(-0.364806\pi\) | ||||
0.412069 | + | 0.911152i | \(0.364806\pi\) | |||||||
\(674\) | −16.0670 | −0.618878 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.4425 | 0.709326 | ||||||||
\(677\) | −21.4801 | −0.825548 | −0.412774 | − | 0.910833i | \(-0.635440\pi\) | ||||
−0.412774 | + | 0.910833i | \(0.635440\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.6520 | 1.36820 | ||||||||
\(680\) | 10.9048 | 0.418179 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.98418 | −0.267438 | ||||||||
\(683\) | −43.7953 | −1.67578 | −0.837890 | − | 0.545839i | \(-0.816211\pi\) | ||||
−0.837890 | + | 0.545839i | \(0.816211\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41.0168 | −1.56717 | ||||||||
\(686\) | 20.1610 | 0.769752 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.91186 | −0.301637 | ||||||||
\(689\) | −73.9872 | −2.81869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.1162 | −0.537007 | −0.268504 | − | 0.963279i | \(-0.586529\pi\) | ||||
−0.268504 | + | 0.963279i | \(0.586529\pi\) | |||||||
\(692\) | 16.6528 | 0.633043 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.1398 | 0.764495 | ||||||||
\(695\) | 13.1149 | 0.497476 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 44.1583 | 1.67262 | ||||||||
\(698\) | −30.6684 | −1.16082 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.87906 | 0.184411 | ||||||||
\(701\) | 45.2816 | 1.71026 | 0.855132 | − | 0.518411i | \(-0.173476\pi\) | ||||
0.855132 | + | 0.518411i | \(0.173476\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2939 | 0.576819 | ||||||||
\(704\) | 2.79991 | 0.105526 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.7829 | 1.00799 | ||||||||
\(707\) | −7.68987 | −0.289207 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.5070 | −0.695046 | −0.347523 | − | 0.937671i | \(-0.612977\pi\) | ||||
−0.347523 | + | 0.937671i | \(0.612977\pi\) | |||||||
\(710\) | −7.66966 | −0.287837 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.9572 | 0.410638 | ||||||||
\(713\) | 2.26329 | 0.0847608 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.2566 | −1.58031 | ||||||||
\(716\) | 12.9554 | 0.484165 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.32994 | 0.348190 | ||||||||
\(719\) | −25.6525 | −0.956675 | −0.478338 | − | 0.878176i | \(-0.658760\pi\) | ||||
−0.478338 | + | 0.878176i | \(0.658760\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.9551 | −0.407989 | ||||||||
\(722\) | 7.16729 | 0.266739 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.76887 | −0.325892 | ||||||||
\(725\) | −7.92846 | −0.294456 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.95897 | 0.221006 | 0.110503 | − | 0.993876i | \(-0.464754\pi\) | ||||
0.110503 | + | 0.993876i | \(0.464754\pi\) | |||||||
\(728\) | −12.1915 | −0.451846 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.5540 | 0.427633 | ||||||||
\(731\) | −32.0556 | −1.18562 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.21396 | −0.192582 | −0.0962910 | − | 0.995353i | \(-0.530698\pi\) | ||||
−0.0962910 | + | 0.995353i | \(0.530698\pi\) | |||||||
\(734\) | 19.3737 | 0.715096 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.907338 | −0.0334449 | ||||||||
\(737\) | 18.2645 | 0.672781 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.06983 | −0.260068 | −0.130034 | − | 0.991510i | \(-0.541509\pi\) | ||||
−0.130034 | + | 0.991510i | \(0.541509\pi\) | |||||||
\(740\) | −11.9665 | −0.439897 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 28.6877 | 1.05316 | ||||||||
\(743\) | −12.7178 | −0.466572 | −0.233286 | − | 0.972408i | \(-0.574948\pi\) | ||||
−0.233286 | + | 0.972408i | \(0.574948\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −39.2654 | −1.43857 | ||||||||
\(746\) | 24.5202 | 0.897750 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.3441 | 0.414781 | ||||||||
\(749\) | 18.1074 | 0.661629 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.0917 | 1.02508 | 0.512541 | − | 0.858663i | \(-0.328704\pi\) | ||||
0.512541 | + | 0.858663i | \(0.328704\pi\) | |||||||
\(752\) | 13.4073 | 0.488914 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.8111 | 0.721479 | ||||||||
\(755\) | −34.0014 | −1.23744 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.4644 | −0.489373 | −0.244687 | − | 0.969602i | \(-0.578685\pi\) | ||||
−0.244687 | + | 0.969602i | \(0.578685\pi\) | |||||||
\(758\) | −27.5623 | −1.00111 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.25835 | 0.335836 | ||||||||
\(761\) | −8.48297 | −0.307508 | −0.153754 | − | 0.988109i | \(-0.549136\pi\) | ||||
−0.153754 | + | 0.988109i | \(0.549136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.93000 | 0.214680 | ||||||||
\(764\) | −2.78928 | −0.100912 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.8176 | −0.788303 | ||||||||
\(767\) | −63.6384 | −2.29785 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.5298 | 1.75003 | 0.875015 | − | 0.484096i | \(-0.160851\pi\) | ||||
0.875015 | + | 0.484096i | \(0.160851\pi\) | |||||||
\(770\) | 16.3845 | 0.590458 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.6058 | −0.417701 | ||||||||
\(773\) | −30.8916 | −1.11109 | −0.555546 | − | 0.831486i | \(-0.687491\pi\) | ||||
−0.555546 | + | 0.831486i | \(0.687491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.59769 | 0.201075 | ||||||||
\(776\) | −16.3978 | −0.588647 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.2181 | −0.581447 | ||||||||
\(779\) | 37.4913 | 1.34326 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.97864 | −0.285498 | ||||||||
\(782\) | −3.67616 | −0.131459 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.27289 | −0.0811746 | ||||||||
\(785\) | 32.4598 | 1.15854 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.2345 | −0.400465 | −0.200233 | − | 0.979748i | \(-0.564170\pi\) | ||||
−0.200233 | + | 0.979748i | \(0.564170\pi\) | |||||||
\(788\) | −20.5331 | −0.731463 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.4600 | −0.763512 | ||||||||
\(791\) | −29.6372 | −1.05378 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.61831 | 0.0929788 | ||||||||
\(794\) | −1.66612 | −0.0591283 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.9919 | 0.637706 | ||||||||
\(797\) | −24.3923 | −0.864020 | −0.432010 | − | 0.901869i | \(-0.642195\pi\) | ||||
−0.432010 | + | 0.901869i | \(0.642195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.3209 | 1.92173 | ||||||||
\(800\) | −2.24408 | −0.0793402 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −33.0190 | −1.16594 | ||||||||
\(803\) | 12.0195 | 0.424159 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.30956 | −0.187137 | ||||||||
\(806\) | −13.9871 | −0.492676 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.53689 | 0.124427 | ||||||||
\(809\) | 29.6845 | 1.04365 | 0.521825 | − | 0.853052i | \(-0.325251\pi\) | ||||
0.521825 | + | 0.853052i | \(0.325251\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.60658 | −0.0564146 | −0.0282073 | − | 0.999602i | \(-0.508980\pi\) | ||||
−0.0282073 | + | 0.999602i | \(0.508980\pi\) | |||||||
\(812\) | −7.68155 | −0.269570 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.4486 | −0.436323 | ||||||||
\(815\) | −0.420013 | −0.0147124 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.2158 | −0.952160 | ||||||||
\(818\) | −33.0353 | −1.15505 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29.3346 | −1.02441 | ||||||||
\(821\) | −21.5725 | −0.752884 | −0.376442 | − | 0.926440i | \(-0.622853\pi\) | ||||
−0.376442 | + | 0.926440i | \(0.622853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.3535 | 1.05806 | 0.529029 | − | 0.848604i | \(-0.322556\pi\) | ||||
0.529029 | + | 0.848604i | \(0.322556\pi\) | |||||||
\(824\) | 5.03869 | 0.175531 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.6751 | 0.858556 | ||||||||
\(827\) | 6.69089 | 0.232665 | 0.116333 | − | 0.993210i | \(-0.462886\pi\) | ||||
0.116333 | + | 0.993210i | \(0.462886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.3700 | −0.742209 | −0.371105 | − | 0.928591i | \(-0.621021\pi\) | ||||
−0.371105 | + | 0.928591i | \(0.621021\pi\) | |||||||
\(830\) | 4.85519 | 0.168526 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.60736 | 0.194400 | ||||||||
\(833\) | −9.20880 | −0.319066 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.74991 | 0.129771 | ||||||||
\(836\) | 9.63134 | 0.333107 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.61709 | −0.297672 | ||||||||
\(839\) | 25.5944 | 0.883618 | 0.441809 | − | 0.897109i | \(-0.354337\pi\) | ||||
0.441809 | + | 0.897109i | \(0.354337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.5175 | −0.569569 | ||||||||
\(842\) | 13.7662 | 0.474413 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.08882 | −0.106321 | ||||||||
\(845\) | −49.6376 | −1.70759 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.87150 | −0.236108 | ||||||||
\(848\) | −13.1947 | −0.453106 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.09208 | −0.311856 | ||||||||
\(851\) | 4.03408 | 0.138286 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.1839 | 1.30739 | 0.653696 | − | 0.756757i | \(-0.273217\pi\) | ||||
0.653696 | + | 0.756757i | \(0.273217\pi\) | |||||||
\(854\) | −1.01522 | −0.0347401 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.32832 | −0.284656 | ||||||||
\(857\) | 2.35315 | 0.0803820 | 0.0401910 | − | 0.999192i | \(-0.487203\pi\) | ||||
0.0401910 | + | 0.999192i | \(0.487203\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.4562 | −1.34623 | −0.673115 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673115 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(860\) | 21.2946 | 0.726141 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.17551 | 0.244399 | ||||||||
\(863\) | −37.5791 | −1.27921 | −0.639604 | − | 0.768704i | \(-0.720902\pi\) | ||||
−0.639604 | + | 0.768704i | \(0.720902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.8206 | −1.52395 | ||||||||
\(866\) | −11.4852 | −0.390283 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.42336 | 0.184081 | ||||||||
\(869\) | −22.3245 | −0.757308 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.5781 | 1.23940 | ||||||||
\(872\) | −2.72745 | −0.0923630 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.12112 | −0.105574 | ||||||||
\(875\) | 16.1271 | 0.545195 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.7077 | −0.631714 | −0.315857 | − | 0.948807i | \(-0.602292\pi\) | ||||
−0.315857 | + | 0.948807i | \(0.602292\pi\) | |||||||
\(878\) | 10.6077 | 0.357993 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.53592 | −0.254036 | ||||||||
\(881\) | 25.8200 | 0.869897 | 0.434949 | − | 0.900455i | \(-0.356767\pi\) | ||||
0.434949 | + | 0.900455i | \(0.356767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.2777 | 0.581442 | 0.290721 | − | 0.956808i | \(-0.406105\pi\) | ||||
0.290721 | + | 0.956808i | \(0.406105\pi\) | |||||||
\(884\) | 22.7187 | 0.764112 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.6850 | −0.795713 | ||||||||
\(887\) | −58.1805 | −1.95351 | −0.976754 | − | 0.214362i | \(-0.931233\pi\) | ||||
−0.976754 | + | 0.214362i | \(0.931233\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.5968 | −0.992643 | ||||||||
\(890\) | −29.4911 | −0.988544 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.00000 | −0.0334825 | ||||||||
\(893\) | 46.1194 | 1.54333 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.8692 | −1.16555 | ||||||||
\(896\) | −2.17419 | −0.0726347 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.0448 | 0.869126 | ||||||||
\(899\) | −8.81296 | −0.293929 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.4593 | −1.78099 | ||||||||
\(902\) | −30.5163 | −1.01608 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.6313 | 0.453372 | ||||||||
\(905\) | 23.6012 | 0.784532 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3120 | 0.442019 | 0.221009 | − | 0.975272i | \(-0.429065\pi\) | ||||
0.221009 | + | 0.975272i | \(0.429065\pi\) | |||||||
\(908\) | 19.8177 | 0.657675 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 32.8131 | 1.08775 | ||||||||
\(911\) | −26.5194 | −0.878626 | −0.439313 | − | 0.898334i | \(-0.644778\pi\) | ||||
−0.439313 | + | 0.898334i | \(0.644778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.05079 | 0.167157 | ||||||||
\(914\) | −19.4587 | −0.643635 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −25.3745 | −0.838398 | ||||||||
\(917\) | 38.5218 | 1.27210 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.1795 | −0.929555 | −0.464777 | − | 0.885428i | \(-0.653866\pi\) | ||||
−0.464777 | + | 0.885428i | \(0.653866\pi\) | |||||||
\(920\) | 2.44208 | 0.0805131 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.34885 | −0.0444219 | ||||||||
\(923\) | −15.9788 | −0.525947 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.97731 | 0.328052 | ||||||||
\(926\) | 19.2142 | 0.631417 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.53306 | 0.115978 | ||||||||
\(929\) | 2.20228 | 0.0722544 | 0.0361272 | − | 0.999347i | \(-0.488498\pi\) | ||||
0.0361272 | + | 0.999347i | \(0.488498\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.81844 | −0.256239 | ||||||||
\(932\) | −8.41472 | −0.275633 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 30.1602 | 0.986872 | ||||||||
\(935\) | −30.5324 | −0.998517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.5251 | 0.376507 | 0.188254 | − | 0.982120i | \(-0.439717\pi\) | ||||
0.188254 | + | 0.982120i | \(0.439717\pi\) | |||||||
\(938\) | −14.1828 | −0.463084 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −36.0855 | −1.17698 | ||||||||
\(941\) | −30.5023 | −0.994345 | −0.497173 | − | 0.867652i | \(-0.665628\pi\) | ||||
−0.497173 | + | 0.867652i | \(0.665628\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.88910 | 0.322033 | ||||||||
\(944\) | −11.3491 | −0.369381 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.1525 | 0.720241 | ||||||||
\(947\) | −19.5995 | −0.636899 | −0.318450 | − | 0.947940i | \(-0.603162\pi\) | ||||
−0.318450 | + | 0.947940i | \(0.603162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.0713 | 0.781388 | ||||||||
\(950\) | −7.71934 | −0.250449 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.80892 | −0.285499 | ||||||||
\(953\) | 9.62406 | 0.311754 | 0.155877 | − | 0.987776i | \(-0.450180\pi\) | ||||
0.155877 | + | 0.987776i | \(0.450180\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.50729 | 0.242930 | ||||||||
\(956\) | 28.9489 | 0.936273 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.4392 | 0.337275 | ||||||||
\(959\) | 33.1336 | 1.06994 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.7778 | −0.799285 | ||||||||
\(962\) | −24.9307 | −0.803797 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.56905 | 0.0827435 | ||||||||
\(965\) | 31.2367 | 1.00555 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.2488 | −1.00489 | −0.502447 | − | 0.864608i | \(-0.667567\pi\) | ||||
−0.502447 | + | 0.864608i | \(0.667567\pi\) | |||||||
\(968\) | 3.16049 | 0.101582 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 44.1344 | 1.41707 | ||||||||
\(971\) | −34.3885 | −1.10358 | −0.551789 | − | 0.833984i | \(-0.686055\pi\) | ||||
−0.551789 | + | 0.833984i | \(0.686055\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.5943 | −0.339637 | ||||||||
\(974\) | −18.5437 | −0.594180 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.466941 | 0.0149464 | ||||||||
\(977\) | −14.9389 | −0.477939 | −0.238970 | − | 0.971027i | \(-0.576810\pi\) | ||||
−0.238970 | + | 0.971027i | \(0.576810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.6792 | −0.980512 | ||||||||
\(980\) | 6.11744 | 0.195414 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.6989 | 0.564794 | ||||||||
\(983\) | −58.4046 | −1.86282 | −0.931409 | − | 0.363975i | \(-0.881419\pi\) | ||||
−0.931409 | + | 0.363975i | \(0.881419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.2646 | 1.76088 | ||||||||
\(986\) | 14.3145 | 0.455866 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19.2886 | 0.613652 | ||||||||
\(989\) | −7.17873 | −0.228270 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.49611 | 0.174590 | 0.0872949 | − | 0.996183i | \(-0.472178\pi\) | ||||
0.0872949 | + | 0.996183i | \(0.472178\pi\) | |||||||
\(992\) | −2.49443 | −0.0791981 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.19559 | 0.196512 | ||||||||
\(995\) | −48.4249 | −1.53517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.0412 | 1.07809 | 0.539047 | − | 0.842275i | \(-0.318784\pi\) | ||||
0.539047 | + | 0.842275i | \(0.318784\pi\) | |||||||
\(998\) | 2.78926 | 0.0882924 | ||||||||
\(999\) | 0 | 0 |
(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 | 4014.2.a.v.1.3 | 7 | ||
3.2 | odd | 2 | 1338.2.a.j.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1338.2.a.j.1.5 | ✓ | 7 | 3.2 | odd | 2 | ||
4014.2.a.v.1.3 | 7 | 1.1 | even | 1 | trivial |