Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 21 x^{10} + 116 x^{9} + 106 x^{8} - 774 x^{7} - 63 x^{6} + 2013 x^{5} - 417 x^{4} + \cdots - 375 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.09665\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | ||||||||
\(5\) | 1.09665 | 0.490436 | 0.245218 | − | 0.969468i | \(-0.421141\pi\) | ||||
0.245218 | + | 0.969468i | \(0.421141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.72925 | −1.03156 | −0.515779 | − | 0.856722i | \(-0.672497\pi\) | ||||
−0.515779 | + | 0.856722i | \(0.672497\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.09665 | −0.346790 | ||||||||
\(11\) | −4.35836 | −1.31409 | −0.657047 | − | 0.753850i | \(-0.728195\pi\) | ||||
−0.657047 | + | 0.753850i | \(0.728195\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.83892 | −1.06472 | −0.532362 | − | 0.846517i | \(-0.678696\pi\) | ||||
−0.532362 | + | 0.846517i | \(0.678696\pi\) | |||||||
\(14\) | 2.72925 | 0.729422 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.52192 | −1.09673 | −0.548364 | − | 0.836240i | \(-0.684749\pi\) | ||||
−0.548364 | + | 0.836240i | \(0.684749\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.46202 | −0.335411 | −0.167706 | − | 0.985837i | \(-0.553636\pi\) | ||||
−0.167706 | + | 0.985837i | \(0.553636\pi\) | |||||||
\(20\) | 1.09665 | 0.245218 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.35836 | 0.929205 | ||||||||
\(23\) | −2.47990 | −0.517094 | −0.258547 | − | 0.965999i | \(-0.583244\pi\) | ||||
−0.258547 | + | 0.965999i | \(0.583244\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.79736 | −0.759473 | ||||||||
\(26\) | 3.83892 | 0.752874 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.72925 | −0.515779 | ||||||||
\(29\) | 9.77560 | 1.81528 | 0.907642 | − | 0.419745i | \(-0.137881\pi\) | ||||
0.907642 | + | 0.419745i | \(0.137881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.816654 | −0.146675 | −0.0733377 | − | 0.997307i | \(-0.523365\pi\) | ||||
−0.0733377 | + | 0.997307i | \(0.523365\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.52192 | 0.775503 | ||||||||
\(35\) | −2.99302 | −0.505913 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.29988 | 0.542498 | 0.271249 | − | 0.962509i | \(-0.412563\pi\) | ||||
0.271249 | + | 0.962509i | \(0.412563\pi\) | |||||||
\(38\) | 1.46202 | 0.237172 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.09665 | −0.173395 | ||||||||
\(41\) | −6.03409 | −0.942366 | −0.471183 | − | 0.882035i | \(-0.656173\pi\) | ||||
−0.471183 | + | 0.882035i | \(0.656173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.88226 | 0.439540 | 0.219770 | − | 0.975552i | \(-0.429469\pi\) | ||||
0.219770 | + | 0.975552i | \(0.429469\pi\) | |||||||
\(44\) | −4.35836 | −0.657047 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.47990 | 0.365641 | ||||||||
\(47\) | −1.80668 | −0.263531 | −0.131765 | − | 0.991281i | \(-0.542065\pi\) | ||||
−0.131765 | + | 0.991281i | \(0.542065\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.448781 | 0.0641115 | ||||||||
\(50\) | 3.79736 | 0.537028 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.83892 | −0.532362 | ||||||||
\(53\) | 9.70841 | 1.33355 | 0.666776 | − | 0.745258i | \(-0.267674\pi\) | ||||
0.666776 | + | 0.745258i | \(0.267674\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.77958 | −0.644479 | ||||||||
\(56\) | 2.72925 | 0.364711 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.77560 | −1.28360 | ||||||||
\(59\) | −11.7716 | −1.53253 | −0.766265 | − | 0.642525i | \(-0.777887\pi\) | ||||
−0.766265 | + | 0.642525i | \(0.777887\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.5328 | −1.60466 | −0.802332 | − | 0.596878i | \(-0.796408\pi\) | ||||
−0.802332 | + | 0.596878i | \(0.796408\pi\) | |||||||
\(62\) | 0.816654 | 0.103715 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.20994 | −0.522179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.19967 | −1.12392 | −0.561959 | − | 0.827165i | \(-0.689952\pi\) | ||||
−0.561959 | + | 0.827165i | \(0.689952\pi\) | |||||||
\(68\) | −4.52192 | −0.548364 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.99302 | 0.357734 | ||||||||
\(71\) | −12.1052 | −1.43662 | −0.718310 | − | 0.695723i | \(-0.755084\pi\) | ||||
−0.718310 | + | 0.695723i | \(0.755084\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.35826 | −1.09530 | −0.547651 | − | 0.836707i | \(-0.684478\pi\) | ||||
−0.547651 | + | 0.836707i | \(0.684478\pi\) | |||||||
\(74\) | −3.29988 | −0.383604 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.46202 | −0.167706 | ||||||||
\(77\) | 11.8950 | 1.35556 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.85287 | 0.771008 | 0.385504 | − | 0.922706i | \(-0.374028\pi\) | ||||
0.385504 | + | 0.922706i | \(0.374028\pi\) | |||||||
\(80\) | 1.09665 | 0.122609 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.03409 | 0.666353 | ||||||||
\(83\) | 3.17103 | 0.348066 | 0.174033 | − | 0.984740i | \(-0.444320\pi\) | ||||
0.174033 | + | 0.984740i | \(0.444320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.95895 | −0.537874 | ||||||||
\(86\) | −2.88226 | −0.310802 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.35836 | 0.464602 | ||||||||
\(89\) | 12.3920 | 1.31355 | 0.656776 | − | 0.754085i | \(-0.271920\pi\) | ||||
0.656776 | + | 0.754085i | \(0.271920\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4774 | 1.09833 | ||||||||
\(92\) | −2.47990 | −0.258547 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.80668 | 0.186344 | ||||||||
\(95\) | −1.60332 | −0.164498 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.62366 | 0.672531 | 0.336266 | − | 0.941767i | \(-0.390836\pi\) | ||||
0.336266 | + | 0.941767i | \(0.390836\pi\) | |||||||
\(98\) | −0.448781 | −0.0453337 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.79736 | −0.379736 | ||||||||
\(101\) | 18.9994 | 1.89051 | 0.945256 | − | 0.326328i | \(-0.105812\pi\) | ||||
0.945256 | + | 0.326328i | \(0.105812\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.86431 | 0.282229 | 0.141114 | − | 0.989993i | \(-0.454931\pi\) | ||||
0.141114 | + | 0.989993i | \(0.454931\pi\) | |||||||
\(104\) | 3.83892 | 0.376437 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.70841 | −0.942964 | ||||||||
\(107\) | 16.8994 | 1.63372 | 0.816862 | − | 0.576833i | \(-0.195712\pi\) | ||||
0.816862 | + | 0.576833i | \(0.195712\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.752058 | 0.0720341 | 0.0360170 | − | 0.999351i | \(-0.488533\pi\) | ||||
0.0360170 | + | 0.999351i | \(0.488533\pi\) | |||||||
\(110\) | 4.77958 | 0.455715 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.72925 | −0.257889 | ||||||||
\(113\) | −14.1817 | −1.33410 | −0.667052 | − | 0.745011i | \(-0.732444\pi\) | ||||
−0.667052 | + | 0.745011i | \(0.732444\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.71957 | −0.253601 | ||||||||
\(116\) | 9.77560 | 0.907642 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.7716 | 1.08366 | ||||||||
\(119\) | 12.3414 | 1.13134 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.99528 | 0.726844 | ||||||||
\(122\) | 12.5328 | 1.13467 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.816654 | −0.0733377 | ||||||||
\(125\) | −9.64761 | −0.862908 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.60414 | 0.408551 | 0.204276 | − | 0.978913i | \(-0.434516\pi\) | ||||
0.204276 | + | 0.978913i | \(0.434516\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.20994 | 0.369236 | ||||||||
\(131\) | −0.536620 | −0.0468847 | −0.0234423 | − | 0.999725i | \(-0.507463\pi\) | ||||
−0.0234423 | + | 0.999725i | \(0.507463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.99022 | 0.345996 | ||||||||
\(134\) | 9.19967 | 0.794730 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.52192 | 0.387752 | ||||||||
\(137\) | 20.2425 | 1.72944 | 0.864718 | − | 0.502259i | \(-0.167497\pi\) | ||||
0.864718 | + | 0.502259i | \(0.167497\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.15773 | −0.267835 | −0.133918 | − | 0.990992i | \(-0.542756\pi\) | ||||
−0.133918 | + | 0.990992i | \(0.542756\pi\) | |||||||
\(140\) | −2.99302 | −0.252956 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.1052 | 1.01584 | ||||||||
\(143\) | 16.7314 | 1.39915 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.7204 | 0.890280 | ||||||||
\(146\) | 9.35826 | 0.774495 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.29988 | 0.271249 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24.1133 | −1.96231 | −0.981155 | − | 0.193222i | \(-0.938106\pi\) | ||||
−0.981155 | + | 0.193222i | \(0.938106\pi\) | |||||||
\(152\) | 1.46202 | 0.118586 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.8950 | −0.958529 | ||||||||
\(155\) | −0.895581 | −0.0719348 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.00350 | −0.479131 | −0.239566 | − | 0.970880i | \(-0.577005\pi\) | ||||
−0.239566 | + | 0.970880i | \(0.577005\pi\) | |||||||
\(158\) | −6.85287 | −0.545185 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.09665 | −0.0866976 | ||||||||
\(161\) | 6.76824 | 0.533412 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.2994 | −1.51165 | −0.755825 | − | 0.654774i | \(-0.772764\pi\) | ||||
−0.755825 | + | 0.654774i | \(0.772764\pi\) | |||||||
\(164\) | −6.03409 | −0.471183 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.17103 | −0.246120 | ||||||||
\(167\) | −16.5548 | −1.28105 | −0.640524 | − | 0.767938i | \(-0.721283\pi\) | ||||
−0.640524 | + | 0.767938i | \(0.721283\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.73730 | 0.133639 | ||||||||
\(170\) | 4.95895 | 0.380334 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.88226 | 0.219770 | ||||||||
\(173\) | −11.9508 | −0.908605 | −0.454302 | − | 0.890848i | \(-0.650111\pi\) | ||||
−0.454302 | + | 0.890848i | \(0.650111\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.3639 | 0.783440 | ||||||||
\(176\) | −4.35836 | −0.328524 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.3920 | −0.928822 | ||||||||
\(179\) | 18.9136 | 1.41367 | 0.706833 | − | 0.707380i | \(-0.250123\pi\) | ||||
0.706833 | + | 0.707380i | \(0.250123\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.8386 | 1.62325 | 0.811624 | − | 0.584181i | \(-0.198584\pi\) | ||||
0.811624 | + | 0.584181i | \(0.198584\pi\) | |||||||
\(182\) | −10.4774 | −0.776633 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.47990 | 0.182820 | ||||||||
\(185\) | 3.61881 | 0.266060 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.7082 | 1.44120 | ||||||||
\(188\) | −1.80668 | −0.131765 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.60332 | 0.116317 | ||||||||
\(191\) | 16.5320 | 1.19621 | 0.598105 | − | 0.801418i | \(-0.295920\pi\) | ||||
0.598105 | + | 0.801418i | \(0.295920\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8366 | 0.852014 | 0.426007 | − | 0.904720i | \(-0.359920\pi\) | ||||
0.426007 | + | 0.904720i | \(0.359920\pi\) | |||||||
\(194\) | −6.62366 | −0.475551 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.448781 | 0.0320558 | ||||||||
\(197\) | 17.0473 | 1.21457 | 0.607287 | − | 0.794483i | \(-0.292258\pi\) | ||||
0.607287 | + | 0.794483i | \(0.292258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.59160 | 0.325490 | 0.162745 | − | 0.986668i | \(-0.447965\pi\) | ||||
0.162745 | + | 0.986668i | \(0.447965\pi\) | |||||||
\(200\) | 3.79736 | 0.268514 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.9994 | −1.33679 | ||||||||
\(203\) | −26.6800 | −1.87257 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.61726 | −0.462170 | ||||||||
\(206\) | −2.86431 | −0.199566 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.83892 | −0.266181 | ||||||||
\(209\) | 6.37202 | 0.440762 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.98312 | 0.687267 | 0.343633 | − | 0.939104i | \(-0.388342\pi\) | ||||
0.343633 | + | 0.939104i | \(0.388342\pi\) | |||||||
\(212\) | 9.70841 | 0.666776 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.8994 | −1.15522 | ||||||||
\(215\) | 3.16082 | 0.215566 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.22885 | 0.151304 | ||||||||
\(218\) | −0.752058 | −0.0509358 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.77958 | −0.322239 | ||||||||
\(221\) | 17.3593 | 1.16771 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4741 | −0.835326 | −0.417663 | − | 0.908602i | \(-0.637151\pi\) | ||||
−0.417663 | + | 0.908602i | \(0.637151\pi\) | |||||||
\(224\) | 2.72925 | 0.182355 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.1817 | 0.943354 | ||||||||
\(227\) | 4.41661 | 0.293141 | 0.146570 | − | 0.989200i | \(-0.453176\pi\) | ||||
0.146570 | + | 0.989200i | \(0.453176\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.1109 | −1.39505 | −0.697524 | − | 0.716561i | \(-0.745715\pi\) | ||||
−0.697524 | + | 0.716561i | \(0.745715\pi\) | |||||||
\(230\) | 2.71957 | 0.179323 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.77560 | −0.641800 | ||||||||
\(233\) | −3.50298 | −0.229488 | −0.114744 | − | 0.993395i | \(-0.536605\pi\) | ||||
−0.114744 | + | 0.993395i | \(0.536605\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.98129 | −0.129245 | ||||||||
\(236\) | −11.7716 | −0.766265 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.3414 | −0.799976 | ||||||||
\(239\) | 27.2008 | 1.75947 | 0.879736 | − | 0.475463i | \(-0.157719\pi\) | ||||
0.879736 | + | 0.475463i | \(0.157719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.93758 | 0.446889 | 0.223444 | − | 0.974717i | \(-0.428270\pi\) | ||||
0.223444 | + | 0.974717i | \(0.428270\pi\) | |||||||
\(242\) | −7.99528 | −0.513956 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −12.5328 | −0.802332 | ||||||||
\(245\) | 0.492154 | 0.0314426 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.61259 | 0.357121 | ||||||||
\(248\) | 0.816654 | 0.0518576 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.64761 | 0.610168 | ||||||||
\(251\) | 18.5290 | 1.16954 | 0.584771 | − | 0.811199i | \(-0.301185\pi\) | ||||
0.584771 | + | 0.811199i | \(0.301185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.8083 | 0.679510 | ||||||||
\(254\) | −4.60414 | −0.288889 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.3360 | −1.76755 | −0.883776 | − | 0.467911i | \(-0.845007\pi\) | ||||
−0.883776 | + | 0.467911i | \(0.845007\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.00619 | −0.559618 | ||||||||
\(260\) | −4.20994 | −0.261089 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.536620 | 0.0331525 | ||||||||
\(263\) | 13.0188 | 0.802773 | 0.401386 | − | 0.915909i | \(-0.368528\pi\) | ||||
0.401386 | + | 0.915909i | \(0.368528\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6467 | 0.654022 | ||||||||
\(266\) | −3.99022 | −0.244656 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.19967 | −0.561959 | ||||||||
\(269\) | 27.1713 | 1.65666 | 0.828331 | − | 0.560239i | \(-0.189291\pi\) | ||||
0.828331 | + | 0.560239i | \(0.189291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.154348 | 0.00937599 | 0.00468800 | − | 0.999989i | \(-0.498508\pi\) | ||||
0.00468800 | + | 0.999989i | \(0.498508\pi\) | |||||||
\(272\) | −4.52192 | −0.274182 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.2425 | −1.22290 | ||||||||
\(275\) | 16.5503 | 0.998019 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.6038 | 1.71864 | 0.859319 | − | 0.511440i | \(-0.170888\pi\) | ||||
0.859319 | + | 0.511440i | \(0.170888\pi\) | |||||||
\(278\) | 3.15773 | 0.189388 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.99302 | 0.178867 | ||||||||
\(281\) | 5.48687 | 0.327319 | 0.163660 | − | 0.986517i | \(-0.447670\pi\) | ||||
0.163660 | + | 0.986517i | \(0.447670\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.3381 | 1.09008 | 0.545042 | − | 0.838408i | \(-0.316514\pi\) | ||||
0.545042 | + | 0.838408i | \(0.316514\pi\) | |||||||
\(284\) | −12.1052 | −0.718310 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.7314 | −0.989347 | ||||||||
\(287\) | 16.4685 | 0.972105 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.44778 | 0.202811 | ||||||||
\(290\) | −10.7204 | −0.629523 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.35826 | −0.547651 | ||||||||
\(293\) | 31.7560 | 1.85520 | 0.927602 | − | 0.373569i | \(-0.121866\pi\) | ||||
0.927602 | + | 0.373569i | \(0.121866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.9093 | −0.751607 | ||||||||
\(296\) | −3.29988 | −0.191802 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 9.52012 | 0.550563 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.86639 | −0.453411 | ||||||||
\(302\) | 24.1133 | 1.38756 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.46202 | −0.0838528 | ||||||||
\(305\) | −13.7441 | −0.786984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.4876 | −1.96831 | −0.984155 | − | 0.177310i | \(-0.943261\pi\) | ||||
−0.984155 | + | 0.177310i | \(0.943261\pi\) | |||||||
\(308\) | 11.8950 | 0.677782 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.895581 | 0.0508656 | ||||||||
\(311\) | 7.52575 | 0.426746 | 0.213373 | − | 0.976971i | \(-0.431555\pi\) | ||||
0.213373 | + | 0.976971i | \(0.431555\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.0840 | −1.58740 | −0.793700 | − | 0.608310i | \(-0.791848\pi\) | ||||
−0.793700 | + | 0.608310i | \(0.791848\pi\) | |||||||
\(314\) | 6.00350 | 0.338797 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.85287 | 0.385504 | ||||||||
\(317\) | 25.6207 | 1.43900 | 0.719501 | − | 0.694492i | \(-0.244371\pi\) | ||||
0.719501 | + | 0.694492i | \(0.244371\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −42.6056 | −2.38545 | ||||||||
\(320\) | 1.09665 | 0.0613044 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.76824 | −0.377180 | ||||||||
\(323\) | 6.61116 | 0.367855 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.5778 | 0.808630 | ||||||||
\(326\) | 19.2994 | 1.06890 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.03409 | 0.333177 | ||||||||
\(329\) | 4.93086 | 0.271847 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.31125 | 0.0720727 | 0.0360363 | − | 0.999350i | \(-0.488527\pi\) | ||||
0.0360363 | + | 0.999350i | \(0.488527\pi\) | |||||||
\(332\) | 3.17103 | 0.174033 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.5548 | 0.905838 | ||||||||
\(335\) | −10.0888 | −0.551210 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.4513 | −1.00511 | −0.502553 | − | 0.864547i | \(-0.667606\pi\) | ||||
−0.502553 | + | 0.864547i | \(0.667606\pi\) | |||||||
\(338\) | −1.73730 | −0.0944969 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.95895 | −0.268937 | ||||||||
\(341\) | 3.55927 | 0.192745 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8799 | 0.965423 | ||||||||
\(344\) | −2.88226 | −0.155401 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.9508 | 0.642481 | ||||||||
\(347\) | 7.23732 | 0.388520 | 0.194260 | − | 0.980950i | \(-0.437770\pi\) | ||||
0.194260 | + | 0.980950i | \(0.437770\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0951 | −0.861549 | −0.430774 | − | 0.902460i | \(-0.641760\pi\) | ||||
−0.430774 | + | 0.902460i | \(0.641760\pi\) | |||||||
\(350\) | −10.3639 | −0.553976 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.35836 | 0.232301 | ||||||||
\(353\) | −26.2451 | −1.39689 | −0.698443 | − | 0.715666i | \(-0.746123\pi\) | ||||
−0.698443 | + | 0.715666i | \(0.746123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.2751 | −0.704570 | ||||||||
\(356\) | 12.3920 | 0.656776 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.9136 | −0.999613 | ||||||||
\(359\) | −35.3204 | −1.86414 | −0.932071 | − | 0.362277i | \(-0.881999\pi\) | ||||
−0.932071 | + | 0.362277i | \(0.881999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8625 | −0.887499 | ||||||||
\(362\) | −21.8386 | −1.14781 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.4774 | 0.549163 | ||||||||
\(365\) | −10.2627 | −0.537175 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.7864 | 0.928443 | 0.464222 | − | 0.885719i | \(-0.346334\pi\) | ||||
0.464222 | + | 0.885719i | \(0.346334\pi\) | |||||||
\(368\) | −2.47990 | −0.129274 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.61881 | −0.188133 | ||||||||
\(371\) | −26.4966 | −1.37564 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.38565 | 0.278858 | 0.139429 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139429 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(374\) | −19.7082 | −1.01908 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.80668 | 0.0931722 | ||||||||
\(377\) | −37.5278 | −1.93278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.50892 | −0.128875 | −0.0644373 | − | 0.997922i | \(-0.520525\pi\) | ||||
−0.0644373 | + | 0.997922i | \(0.520525\pi\) | |||||||
\(380\) | −1.60332 | −0.0822488 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.5320 | −0.845849 | ||||||||
\(383\) | −13.1237 | −0.670591 | −0.335296 | − | 0.942113i | \(-0.608836\pi\) | ||||
−0.335296 | + | 0.942113i | \(0.608836\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.0446 | 0.664817 | ||||||||
\(386\) | −11.8366 | −0.602465 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.62366 | 0.336266 | ||||||||
\(389\) | 16.8554 | 0.854601 | 0.427301 | − | 0.904110i | \(-0.359465\pi\) | ||||
0.427301 | + | 0.904110i | \(0.359465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.2139 | 0.567111 | ||||||||
\(392\) | −0.448781 | −0.0226669 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.0473 | −0.858833 | ||||||||
\(395\) | 7.51518 | 0.378130 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.5551 | −1.43314 | −0.716571 | − | 0.697514i | \(-0.754289\pi\) | ||||
−0.716571 | + | 0.697514i | \(0.754289\pi\) | |||||||
\(398\) | −4.59160 | −0.230156 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.79736 | −0.189868 | ||||||||
\(401\) | −26.0083 | −1.29879 | −0.649397 | − | 0.760450i | \(-0.724979\pi\) | ||||
−0.649397 | + | 0.760450i | \(0.724979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.13507 | 0.156169 | ||||||||
\(404\) | 18.9994 | 0.945256 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26.6800 | 1.32411 | ||||||||
\(407\) | −14.3821 | −0.712893 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.62454 | 0.475903 | 0.237951 | − | 0.971277i | \(-0.423524\pi\) | ||||
0.237951 | + | 0.971277i | \(0.423524\pi\) | |||||||
\(410\) | 6.61726 | 0.326803 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.86431 | 0.141114 | ||||||||
\(413\) | 32.1275 | 1.58089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.47750 | 0.170704 | ||||||||
\(416\) | 3.83892 | 0.188219 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.37202 | −0.311666 | ||||||||
\(419\) | 17.5251 | 0.856157 | 0.428078 | − | 0.903742i | \(-0.359191\pi\) | ||||
0.428078 | + | 0.903742i | \(0.359191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.8934 | 1.55439 | 0.777195 | − | 0.629260i | \(-0.216642\pi\) | ||||
0.777195 | + | 0.629260i | \(0.216642\pi\) | |||||||
\(422\) | −9.98312 | −0.485971 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.70841 | −0.471482 | ||||||||
\(425\) | 17.1714 | 0.832935 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.2052 | 1.65530 | ||||||||
\(428\) | 16.8994 | 0.816862 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.16082 | −0.152428 | ||||||||
\(431\) | 6.40574 | 0.308553 | 0.154277 | − | 0.988028i | \(-0.450695\pi\) | ||||
0.154277 | + | 0.988028i | \(0.450695\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4910 | 0.600281 | 0.300141 | − | 0.953895i | \(-0.402966\pi\) | ||||
0.300141 | + | 0.953895i | \(0.402966\pi\) | |||||||
\(434\) | −2.22885 | −0.106988 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.752058 | 0.0360170 | ||||||||
\(437\) | 3.62567 | 0.173439 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.2958 | 1.49367 | 0.746834 | − | 0.665010i | \(-0.231573\pi\) | ||||
0.746834 | + | 0.665010i | \(0.231573\pi\) | |||||||
\(440\) | 4.77958 | 0.227858 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.3593 | −0.825698 | ||||||||
\(443\) | −39.4216 | −1.87298 | −0.936488 | − | 0.350700i | \(-0.885944\pi\) | ||||
−0.936488 | + | 0.350700i | \(0.885944\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5897 | 0.644213 | ||||||||
\(446\) | 12.4741 | 0.590665 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.72925 | −0.128945 | ||||||||
\(449\) | 3.51295 | 0.165787 | 0.0828933 | − | 0.996558i | \(-0.473584\pi\) | ||||
0.0828933 | + | 0.996558i | \(0.473584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.2987 | 1.23836 | ||||||||
\(452\) | −14.1817 | −0.667052 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.41661 | −0.207282 | ||||||||
\(455\) | 11.4900 | 0.538658 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0035 | 0.608278 | 0.304139 | − | 0.952628i | \(-0.401631\pi\) | ||||
0.304139 | + | 0.952628i | \(0.401631\pi\) | |||||||
\(458\) | 21.1109 | 0.986448 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.71957 | −0.126801 | ||||||||
\(461\) | 7.06541 | 0.329069 | 0.164534 | − | 0.986371i | \(-0.447388\pi\) | ||||
0.164534 | + | 0.986371i | \(0.447388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.9332 | −0.972847 | −0.486423 | − | 0.873723i | \(-0.661699\pi\) | ||||
−0.486423 | + | 0.873723i | \(0.661699\pi\) | |||||||
\(464\) | 9.77560 | 0.453821 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.50298 | 0.162272 | ||||||||
\(467\) | −28.2094 | −1.30538 | −0.652688 | − | 0.757627i | \(-0.726359\pi\) | ||||
−0.652688 | + | 0.757627i | \(0.726359\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.1082 | 1.15939 | ||||||||
\(470\) | 1.98129 | 0.0913899 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.7716 | 0.541831 | ||||||||
\(473\) | −12.5619 | −0.577597 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.55184 | 0.254736 | ||||||||
\(476\) | 12.3414 | 0.565669 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −27.2008 | −1.24413 | ||||||||
\(479\) | 19.7500 | 0.902399 | 0.451200 | − | 0.892423i | \(-0.350996\pi\) | ||||
0.451200 | + | 0.892423i | \(0.350996\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.6680 | −0.577611 | ||||||||
\(482\) | −6.93758 | −0.315998 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.99528 | 0.363422 | ||||||||
\(485\) | 7.26382 | 0.329833 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.8585 | −1.03582 | −0.517908 | − | 0.855437i | \(-0.673289\pi\) | ||||
−0.517908 | + | 0.855437i | \(0.673289\pi\) | |||||||
\(488\) | 12.5328 | 0.567334 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.492154 | −0.0222333 | ||||||||
\(491\) | −9.36712 | −0.422732 | −0.211366 | − | 0.977407i | \(-0.567791\pi\) | ||||
−0.211366 | + | 0.977407i | \(0.567791\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.2045 | −1.99087 | ||||||||
\(494\) | −5.61259 | −0.252522 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.816654 | −0.0366689 | ||||||||
\(497\) | 33.0380 | 1.48196 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.1322 | −0.453580 | −0.226790 | − | 0.973944i | \(-0.572823\pi\) | ||||
−0.226790 | + | 0.973944i | \(0.572823\pi\) | |||||||
\(500\) | −9.64761 | −0.431454 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.5290 | −0.826991 | ||||||||
\(503\) | −15.1255 | −0.674413 | −0.337206 | − | 0.941431i | \(-0.609482\pi\) | ||||
−0.337206 | + | 0.941431i | \(0.609482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.8357 | 0.927175 | ||||||||
\(506\) | −10.8083 | −0.480486 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.60414 | 0.204276 | ||||||||
\(509\) | 6.98576 | 0.309638 | 0.154819 | − | 0.987943i | \(-0.450521\pi\) | ||||
0.154819 | + | 0.987943i | \(0.450521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.5410 | 1.12987 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.3360 | 1.24985 | ||||||||
\(515\) | 3.14114 | 0.138415 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.87414 | 0.346304 | ||||||||
\(518\) | 9.00619 | 0.395709 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.20994 | 0.184618 | ||||||||
\(521\) | −40.9358 | −1.79343 | −0.896714 | − | 0.442611i | \(-0.854052\pi\) | ||||
−0.896714 | + | 0.442611i | \(0.854052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.9444 | −0.872109 | −0.436055 | − | 0.899920i | \(-0.643625\pi\) | ||||
−0.436055 | + | 0.899920i | \(0.643625\pi\) | |||||||
\(524\) | −0.536620 | −0.0234423 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.0188 | −0.567646 | ||||||||
\(527\) | 3.69285 | 0.160863 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8501 | −0.732614 | ||||||||
\(530\) | −10.6467 | −0.462463 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.99022 | 0.172998 | ||||||||
\(533\) | 23.1644 | 1.00336 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.5327 | 0.801237 | ||||||||
\(536\) | 9.19967 | 0.397365 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −27.1713 | −1.17144 | ||||||||
\(539\) | −1.95595 | −0.0842486 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.8738 | 1.19839 | 0.599195 | − | 0.800603i | \(-0.295487\pi\) | ||||
0.599195 | + | 0.800603i | \(0.295487\pi\) | |||||||
\(542\) | −0.154348 | −0.00662983 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.52192 | 0.193876 | ||||||||
\(545\) | 0.824742 | 0.0353281 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.04603 | 0.344023 | 0.172012 | − | 0.985095i | \(-0.444973\pi\) | ||||
0.172012 | + | 0.985095i | \(0.444973\pi\) | |||||||
\(548\) | 20.2425 | 0.864718 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −16.5503 | −0.705706 | ||||||||
\(551\) | −14.2922 | −0.608867 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.7032 | −0.795339 | ||||||||
\(554\) | −28.6038 | −1.21526 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.15773 | −0.133918 | ||||||||
\(557\) | 18.9214 | 0.801726 | 0.400863 | − | 0.916138i | \(-0.368710\pi\) | ||||
0.400863 | + | 0.916138i | \(0.368710\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.0648 | −0.467989 | ||||||||
\(560\) | −2.99302 | −0.126478 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.48687 | −0.231450 | ||||||||
\(563\) | −28.7214 | −1.21046 | −0.605232 | − | 0.796049i | \(-0.706920\pi\) | ||||
−0.605232 | + | 0.796049i | \(0.706920\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.5523 | −0.654292 | ||||||||
\(566\) | −18.3381 | −0.770806 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.1052 | 0.507922 | ||||||||
\(569\) | 27.6719 | 1.16007 | 0.580033 | − | 0.814593i | \(-0.303040\pi\) | ||||
0.580033 | + | 0.814593i | \(0.303040\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.38536 | 0.350916 | 0.175458 | − | 0.984487i | \(-0.443859\pi\) | ||||
0.175458 | + | 0.984487i | \(0.443859\pi\) | |||||||
\(572\) | 16.7314 | 0.699574 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.4685 | −0.687382 | ||||||||
\(575\) | 9.41707 | 0.392719 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.4251 | 1.43314 | 0.716568 | − | 0.697517i | \(-0.245712\pi\) | ||||
0.716568 | + | 0.697517i | \(0.245712\pi\) | |||||||
\(578\) | −3.44778 | −0.143409 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.7204 | 0.445140 | ||||||||
\(581\) | −8.65452 | −0.359050 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −42.3127 | −1.75241 | ||||||||
\(584\) | 9.35826 | 0.387248 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −31.7560 | −1.31183 | ||||||||
\(587\) | −38.9122 | −1.60608 | −0.803039 | − | 0.595927i | \(-0.796785\pi\) | ||||
−0.803039 | + | 0.595927i | \(0.796785\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.19397 | 0.0491966 | ||||||||
\(590\) | 12.9093 | 0.531467 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.29988 | 0.135624 | ||||||||
\(593\) | 9.78088 | 0.401653 | 0.200826 | − | 0.979627i | \(-0.435637\pi\) | ||||
0.200826 | + | 0.979627i | \(0.435637\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.5342 | 0.554848 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.52012 | −0.389307 | ||||||||
\(599\) | 37.3040 | 1.52420 | 0.762100 | − | 0.647459i | \(-0.224168\pi\) | ||||
0.762100 | + | 0.647459i | \(0.224168\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.1603 | 0.985520 | 0.492760 | − | 0.870165i | \(-0.335988\pi\) | ||||
0.492760 | + | 0.870165i | \(0.335988\pi\) | |||||||
\(602\) | 7.86639 | 0.320610 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.1133 | −0.981155 | ||||||||
\(605\) | 8.76800 | 0.356470 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.8379 | −1.73874 | −0.869369 | − | 0.494164i | \(-0.835474\pi\) | ||||
−0.869369 | + | 0.494164i | \(0.835474\pi\) | |||||||
\(608\) | 1.46202 | 0.0592929 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.7441 | 0.556482 | ||||||||
\(611\) | 6.93569 | 0.280588 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.7697 | 1.24278 | 0.621389 | − | 0.783502i | \(-0.286569\pi\) | ||||
0.621389 | + | 0.783502i | \(0.286569\pi\) | |||||||
\(614\) | 34.4876 | 1.39181 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.8950 | −0.479264 | ||||||||
\(617\) | 35.1120 | 1.41356 | 0.706778 | − | 0.707435i | \(-0.250148\pi\) | ||||
0.706778 | + | 0.707435i | \(0.250148\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.8156 | 0.876842 | 0.438421 | − | 0.898770i | \(-0.355538\pi\) | ||||
0.438421 | + | 0.898770i | \(0.355538\pi\) | |||||||
\(620\) | −0.895581 | −0.0359674 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.52575 | −0.301755 | ||||||||
\(623\) | −33.8209 | −1.35501 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.40680 | 0.336272 | ||||||||
\(626\) | 28.0840 | 1.12246 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.00350 | −0.239566 | ||||||||
\(629\) | −14.9218 | −0.594972 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1031 | −0.481815 | −0.240907 | − | 0.970548i | \(-0.577445\pi\) | ||||
−0.240907 | + | 0.970548i | \(0.577445\pi\) | |||||||
\(632\) | −6.85287 | −0.272592 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −25.6207 | −1.01753 | ||||||||
\(635\) | 5.04912 | 0.200368 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.72283 | −0.0682611 | ||||||||
\(638\) | 42.6056 | 1.68677 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.09665 | −0.0433488 | ||||||||
\(641\) | −13.1368 | −0.518873 | −0.259437 | − | 0.965760i | \(-0.583537\pi\) | ||||
−0.259437 | + | 0.965760i | \(0.583537\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.8722 | −0.468195 | −0.234097 | − | 0.972213i | \(-0.575213\pi\) | ||||
−0.234097 | + | 0.972213i | \(0.575213\pi\) | |||||||
\(644\) | 6.76824 | 0.266706 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.61116 | −0.260113 | ||||||||
\(647\) | −11.6314 | −0.457279 | −0.228639 | − | 0.973511i | \(-0.573428\pi\) | ||||
−0.228639 | + | 0.973511i | \(0.573428\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.3048 | 2.01389 | ||||||||
\(650\) | −14.5778 | −0.571788 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.2994 | −0.755825 | ||||||||
\(653\) | −47.2362 | −1.84850 | −0.924248 | − | 0.381793i | \(-0.875307\pi\) | ||||
−0.924248 | + | 0.381793i | \(0.875307\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.588483 | −0.0229939 | ||||||||
\(656\) | −6.03409 | −0.235591 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.93086 | −0.192225 | ||||||||
\(659\) | 43.1846 | 1.68223 | 0.841117 | − | 0.540853i | \(-0.181899\pi\) | ||||
0.841117 | + | 0.540853i | \(0.181899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.8820 | 1.59013 | 0.795063 | − | 0.606526i | \(-0.207438\pi\) | ||||
0.795063 | + | 0.606526i | \(0.207438\pi\) | |||||||
\(662\) | −1.31125 | −0.0509631 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.17103 | −0.123060 | ||||||||
\(665\) | 4.37587 | 0.169689 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.2425 | −0.938673 | ||||||||
\(668\) | −16.5548 | −0.640524 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0888 | 0.389764 | ||||||||
\(671\) | 54.6225 | 2.10868 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.77879 | −0.222756 | −0.111378 | − | 0.993778i | \(-0.535526\pi\) | ||||
−0.111378 | + | 0.993778i | \(0.535526\pi\) | |||||||
\(674\) | 18.4513 | 0.710717 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.73730 | 0.0668194 | ||||||||
\(677\) | −34.1968 | −1.31429 | −0.657146 | − | 0.753764i | \(-0.728236\pi\) | ||||
−0.657146 | + | 0.753764i | \(0.728236\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.0776 | −0.693755 | ||||||||
\(680\) | 4.95895 | 0.190167 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.55927 | −0.136292 | ||||||||
\(683\) | −6.45987 | −0.247180 | −0.123590 | − | 0.992333i | \(-0.539441\pi\) | ||||
−0.123590 | + | 0.992333i | \(0.539441\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.1989 | 0.848176 | ||||||||
\(686\) | −17.8799 | −0.682657 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.88226 | 0.109885 | ||||||||
\(689\) | −37.2698 | −1.41987 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.7970 | −0.524863 | −0.262432 | − | 0.964951i | \(-0.584524\pi\) | ||||
−0.262432 | + | 0.964951i | \(0.584524\pi\) | |||||||
\(692\) | −11.9508 | −0.454302 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.23732 | −0.274725 | ||||||||
\(695\) | −3.46292 | −0.131356 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.2857 | 1.03352 | ||||||||
\(698\) | 16.0951 | 0.609207 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.3639 | 0.391720 | ||||||||
\(701\) | 28.5634 | 1.07882 | 0.539412 | − | 0.842042i | \(-0.318646\pi\) | ||||
0.539412 | + | 0.842042i | \(0.318646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.82451 | −0.181960 | ||||||||
\(704\) | −4.35836 | −0.164262 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.2451 | 0.987748 | ||||||||
\(707\) | −51.8541 | −1.95017 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.6004 | −1.07411 | −0.537055 | − | 0.843547i | \(-0.680463\pi\) | ||||
−0.537055 | + | 0.843547i | \(0.680463\pi\) | |||||||
\(710\) | 13.2751 | 0.498206 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.3920 | −0.464411 | ||||||||
\(713\) | 2.02522 | 0.0758450 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.3484 | 0.686192 | ||||||||
\(716\) | 18.9136 | 0.706833 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35.3204 | 1.31815 | ||||||||
\(719\) | 18.5267 | 0.690931 | 0.345465 | − | 0.938432i | \(-0.387721\pi\) | ||||
0.345465 | + | 0.938432i | \(0.387721\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.81741 | −0.291135 | ||||||||
\(722\) | 16.8625 | 0.627557 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.8386 | 0.811624 | ||||||||
\(725\) | −37.1215 | −1.37866 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.9428 | −0.887989 | −0.443995 | − | 0.896029i | \(-0.646439\pi\) | ||||
−0.443995 | + | 0.896029i | \(0.646439\pi\) | |||||||
\(728\) | −10.4774 | −0.388317 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.2627 | 0.379840 | ||||||||
\(731\) | −13.0333 | −0.482056 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.7865 | −0.952444 | −0.476222 | − | 0.879325i | \(-0.657994\pi\) | ||||
−0.476222 | + | 0.879325i | \(0.657994\pi\) | |||||||
\(734\) | −17.7864 | −0.656508 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.47990 | 0.0914102 | ||||||||
\(737\) | 40.0955 | 1.47693 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.5497 | 0.903077 | 0.451538 | − | 0.892252i | \(-0.350875\pi\) | ||||
0.451538 | + | 0.892252i | \(0.350875\pi\) | |||||||
\(740\) | 3.61881 | 0.133030 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.4966 | 0.972722 | ||||||||
\(743\) | 9.44491 | 0.346500 | 0.173250 | − | 0.984878i | \(-0.444573\pi\) | ||||
0.173250 | + | 0.984878i | \(0.444573\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.09665 | 0.0401780 | ||||||||
\(746\) | −5.38565 | −0.197183 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 19.7082 | 0.720601 | ||||||||
\(749\) | −46.1226 | −1.68528 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0856 | 0.878895 | 0.439447 | − | 0.898268i | \(-0.355174\pi\) | ||||
0.439447 | + | 0.898268i | \(0.355174\pi\) | |||||||
\(752\) | −1.80668 | −0.0658827 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.5278 | 1.36668 | ||||||||
\(755\) | −26.4438 | −0.962387 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.5109 | 1.47240 | 0.736198 | − | 0.676767i | \(-0.236619\pi\) | ||||
0.736198 | + | 0.676767i | \(0.236619\pi\) | |||||||
\(758\) | 2.50892 | 0.0911281 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.60332 | 0.0581587 | ||||||||
\(761\) | −20.8544 | −0.755972 | −0.377986 | − | 0.925811i | \(-0.623383\pi\) | ||||
−0.377986 | + | 0.925811i | \(0.623383\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.05255 | −0.0743073 | ||||||||
\(764\) | 16.5320 | 0.598105 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.1237 | 0.474180 | ||||||||
\(767\) | 45.1902 | 1.63172 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.6339 | 1.64560 | 0.822800 | − | 0.568331i | \(-0.192411\pi\) | ||||
0.822800 | + | 0.568331i | \(0.192411\pi\) | |||||||
\(770\) | −13.0446 | −0.470097 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.8366 | 0.426007 | ||||||||
\(773\) | 12.8727 | 0.462997 | 0.231499 | − | 0.972835i | \(-0.425637\pi\) | ||||
0.231499 | + | 0.972835i | \(0.425637\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.10113 | 0.111396 | ||||||||
\(776\) | −6.62366 | −0.237776 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.8554 | −0.604294 | ||||||||
\(779\) | 8.82198 | 0.316080 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.7587 | 1.88785 | ||||||||
\(782\) | −11.2139 | −0.401008 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.448781 | 0.0160279 | ||||||||
\(785\) | −6.58372 | −0.234983 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.3025 | 1.75745 | 0.878723 | − | 0.477332i | \(-0.158396\pi\) | ||||
0.878723 | + | 0.477332i | \(0.158396\pi\) | |||||||
\(788\) | 17.0473 | 0.607287 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.51518 | −0.267378 | ||||||||
\(791\) | 38.7054 | 1.37621 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.1125 | 1.70853 | ||||||||
\(794\) | 28.5551 | 1.01338 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.59160 | 0.162745 | ||||||||
\(797\) | 4.83675 | 0.171326 | 0.0856632 | − | 0.996324i | \(-0.472699\pi\) | ||||
0.0856632 | + | 0.996324i | \(0.472699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.16965 | 0.289021 | ||||||||
\(800\) | 3.79736 | 0.134257 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.0083 | 0.918386 | ||||||||
\(803\) | 40.7866 | 1.43933 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.42238 | 0.261604 | ||||||||
\(806\) | −3.13507 | −0.110428 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −18.9994 | −0.668397 | ||||||||
\(809\) | −16.3692 | −0.575510 | −0.287755 | − | 0.957704i | \(-0.592909\pi\) | ||||
−0.287755 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.7722 | −1.36147 | −0.680737 | − | 0.732528i | \(-0.738340\pi\) | ||||
−0.680737 | + | 0.732528i | \(0.738340\pi\) | |||||||
\(812\) | −26.6800 | −0.936285 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.3821 | 0.504091 | ||||||||
\(815\) | −21.1647 | −0.741366 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.21393 | −0.147427 | ||||||||
\(818\) | −9.62454 | −0.336514 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.61726 | −0.231085 | ||||||||
\(821\) | 29.6576 | 1.03506 | 0.517529 | − | 0.855666i | \(-0.326852\pi\) | ||||
0.517529 | + | 0.855666i | \(0.326852\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.6906 | 1.03495 | 0.517474 | − | 0.855699i | \(-0.326872\pi\) | ||||
0.517474 | + | 0.855699i | \(0.326872\pi\) | |||||||
\(824\) | −2.86431 | −0.0997830 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −32.1275 | −1.11786 | ||||||||
\(827\) | −13.8789 | −0.482618 | −0.241309 | − | 0.970448i | \(-0.577577\pi\) | ||||
−0.241309 | + | 0.970448i | \(0.577577\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 39.1836 | 1.36090 | 0.680451 | − | 0.732793i | \(-0.261784\pi\) | ||||
0.680451 | + | 0.732793i | \(0.261784\pi\) | |||||||
\(830\) | −3.47750 | −0.120706 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.83892 | −0.133091 | ||||||||
\(833\) | −2.02935 | −0.0703129 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.1548 | −0.628271 | ||||||||
\(836\) | 6.37202 | 0.220381 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.5251 | −0.605394 | ||||||||
\(839\) | −4.43681 | −0.153176 | −0.0765879 | − | 0.997063i | \(-0.524403\pi\) | ||||
−0.0765879 | + | 0.997063i | \(0.524403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.5624 | 2.29526 | ||||||||
\(842\) | −31.8934 | −1.09912 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.98312 | 0.343633 | ||||||||
\(845\) | 1.90521 | 0.0655412 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.8211 | −0.749781 | ||||||||
\(848\) | 9.70841 | 0.333388 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.1714 | −0.588974 | ||||||||
\(851\) | −8.18337 | −0.280522 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.3902 | −1.82804 | −0.914022 | − | 0.405664i | \(-0.867040\pi\) | ||||
−0.914022 | + | 0.405664i | \(0.867040\pi\) | |||||||
\(854\) | −34.2052 | −1.17048 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.8994 | −0.577609 | ||||||||
\(857\) | 34.9541 | 1.19401 | 0.597004 | − | 0.802238i | \(-0.296358\pi\) | ||||
0.597004 | + | 0.802238i | \(0.296358\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.50093 | 0.290048 | 0.145024 | − | 0.989428i | \(-0.453674\pi\) | ||||
0.145024 | + | 0.989428i | \(0.453674\pi\) | |||||||
\(860\) | 3.16082 | 0.107783 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.40574 | −0.218180 | ||||||||
\(863\) | −20.3417 | −0.692440 | −0.346220 | − | 0.938153i | \(-0.612535\pi\) | ||||
−0.346220 | + | 0.938153i | \(0.612535\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.1058 | −0.445612 | ||||||||
\(866\) | −12.4910 | −0.424463 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.22885 | 0.0756521 | ||||||||
\(869\) | −29.8672 | −1.01318 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.3168 | 1.19666 | ||||||||
\(872\) | −0.752058 | −0.0254679 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.62567 | −0.122640 | ||||||||
\(875\) | 26.3307 | 0.890140 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.1783 | −0.377466 | −0.188733 | − | 0.982028i | \(-0.560438\pi\) | ||||
−0.188733 | + | 0.982028i | \(0.560438\pi\) | |||||||
\(878\) | −31.2958 | −1.05618 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.77958 | −0.161120 | ||||||||
\(881\) | 13.5491 | 0.456480 | 0.228240 | − | 0.973605i | \(-0.426703\pi\) | ||||
0.228240 | + | 0.973605i | \(0.426703\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.6753 | 1.06596 | 0.532979 | − | 0.846129i | \(-0.321073\pi\) | ||||
0.532979 | + | 0.846129i | \(0.321073\pi\) | |||||||
\(884\) | 17.3593 | 0.583856 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.4216 | 1.32439 | ||||||||
\(887\) | 2.92676 | 0.0982710 | 0.0491355 | − | 0.998792i | \(-0.484353\pi\) | ||||
0.0491355 | + | 0.998792i | \(0.484353\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.5658 | −0.421444 | ||||||||
\(890\) | −13.5897 | −0.455527 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.4741 | −0.417663 | ||||||||
\(893\) | 2.64140 | 0.0883912 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.7415 | 0.693312 | ||||||||
\(896\) | 2.72925 | 0.0911777 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.51295 | −0.117229 | ||||||||
\(899\) | −7.98329 | −0.266258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.9007 | −1.46254 | ||||||||
\(902\) | −26.2987 | −0.875651 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.1817 | 0.471677 | ||||||||
\(905\) | 23.9492 | 0.796098 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.72412 | −0.289680 | −0.144840 | − | 0.989455i | \(-0.546267\pi\) | ||||
−0.144840 | + | 0.989455i | \(0.546267\pi\) | |||||||
\(908\) | 4.41661 | 0.146570 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.4900 | −0.380889 | ||||||||
\(911\) | −18.4481 | −0.611214 | −0.305607 | − | 0.952158i | \(-0.598859\pi\) | ||||
−0.305607 | + | 0.952158i | \(0.598859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.8205 | −0.457391 | ||||||||
\(914\) | −13.0035 | −0.430118 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.1109 | −0.697524 | ||||||||
\(917\) | 1.46457 | 0.0483643 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.8809 | −1.11763 | −0.558814 | − | 0.829293i | \(-0.688743\pi\) | ||||
−0.558814 | + | 0.829293i | \(0.688743\pi\) | |||||||
\(920\) | 2.71957 | 0.0896616 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.06541 | −0.232687 | ||||||||
\(923\) | 46.4708 | 1.52960 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.5309 | −0.412012 | ||||||||
\(926\) | 20.9332 | 0.687906 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.77560 | −0.320900 | ||||||||
\(929\) | −6.69462 | −0.219643 | −0.109822 | − | 0.993951i | \(-0.535028\pi\) | ||||
−0.109822 | + | 0.993951i | \(0.535028\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.656128 | −0.0215037 | ||||||||
\(932\) | −3.50298 | −0.114744 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.2094 | 0.923040 | ||||||||
\(935\) | 21.6129 | 0.706817 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.4433 | 0.373836 | 0.186918 | − | 0.982375i | \(-0.440150\pi\) | ||||
0.186918 | + | 0.982375i | \(0.440150\pi\) | |||||||
\(938\) | −25.1082 | −0.819810 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.98129 | −0.0646225 | ||||||||
\(941\) | −30.0674 | −0.980171 | −0.490085 | − | 0.871674i | \(-0.663034\pi\) | ||||
−0.490085 | + | 0.871674i | \(0.663034\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.9639 | 0.487292 | ||||||||
\(944\) | −11.7716 | −0.383132 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.5619 | 0.408423 | ||||||||
\(947\) | 18.9500 | 0.615793 | 0.307896 | − | 0.951420i | \(-0.400375\pi\) | ||||
0.307896 | + | 0.951420i | \(0.400375\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.9256 | 1.16619 | ||||||||
\(950\) | −5.55184 | −0.180125 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.3414 | −0.399988 | ||||||||
\(953\) | 43.1005 | 1.39616 | 0.698081 | − | 0.716019i | \(-0.254038\pi\) | ||||
0.698081 | + | 0.716019i | \(0.254038\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.1297 | 0.586664 | ||||||||
\(956\) | 27.2008 | 0.879736 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −19.7500 | −0.638093 | ||||||||
\(959\) | −55.2468 | −1.78401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3331 | −0.978486 | ||||||||
\(962\) | 12.6680 | 0.408432 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.93758 | 0.223444 | ||||||||
\(965\) | 12.9805 | 0.417858 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 59.9741 | 1.92864 | 0.964319 | − | 0.264743i | \(-0.0852870\pi\) | ||||
0.964319 | + | 0.264743i | \(0.0852870\pi\) | |||||||
\(968\) | −7.99528 | −0.256978 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.26382 | −0.233227 | ||||||||
\(971\) | −22.6541 | −0.727006 | −0.363503 | − | 0.931593i | \(-0.618419\pi\) | ||||
−0.363503 | + | 0.931593i | \(0.618419\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.61822 | 0.276287 | ||||||||
\(974\) | 22.8585 | 0.732432 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.5328 | −0.401166 | ||||||||
\(977\) | −23.1749 | −0.741430 | −0.370715 | − | 0.928747i | \(-0.620887\pi\) | ||||
−0.370715 | + | 0.928747i | \(0.620887\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54.0089 | −1.72613 | ||||||||
\(980\) | 0.492154 | 0.0157213 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.36712 | 0.298917 | ||||||||
\(983\) | 24.3734 | 0.777390 | 0.388695 | − | 0.921367i | \(-0.372926\pi\) | ||||
0.388695 | + | 0.921367i | \(0.372926\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.6949 | 0.595670 | ||||||||
\(986\) | 44.2045 | 1.40776 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.61259 | 0.178560 | ||||||||
\(989\) | −7.14770 | −0.227284 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.73172 | 0.245606 | 0.122803 | − | 0.992431i | \(-0.460812\pi\) | ||||
0.122803 | + | 0.992431i | \(0.460812\pi\) | |||||||
\(992\) | 0.816654 | 0.0259288 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −33.0380 | −1.04790 | ||||||||
\(995\) | 5.03537 | 0.159632 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.46445 | 0.173061 | 0.0865305 | − | 0.996249i | \(-0.472422\pi\) | ||||
0.0865305 | + | 0.996249i | \(0.472422\pi\) | |||||||
\(998\) | 10.1322 | 0.320729 | ||||||||
\(999\) | 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 | 8046.2.a.l.1.8 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.m.1.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.l.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.m.1.5 | yes | 12 | 3.2 | odd | 2 |