Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, 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("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.52046292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 10x^{4} + 9x^{3} + 24x^{2} - 18x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 574) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.43859\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-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 | ||||||||
\(3\) | −2.30861 | −1.33288 | −0.666439 | − | 0.745559i | \(-0.732182\pi\) | ||||
−0.666439 | + | 0.745559i | \(0.732182\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.374437 | 0.167453 | 0.0837266 | − | 0.996489i | \(-0.473318\pi\) | ||||
0.0837266 | + | 0.996489i | \(0.473318\pi\) | |||||||
\(6\) | 2.30861 | 0.942487 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.32969 | 0.776564 | ||||||||
\(10\) | −0.374437 | −0.118407 | ||||||||
\(11\) | 2.34222 | 0.706205 | 0.353103 | − | 0.935585i | \(-0.385127\pi\) | ||||
0.353103 | + | 0.935585i | \(0.385127\pi\) | |||||||
\(12\) | −2.30861 | −0.666439 | ||||||||
\(13\) | −0.133679 | −0.0370759 | −0.0185379 | − | 0.999828i | \(-0.505901\pi\) | ||||
−0.0185379 | + | 0.999828i | \(0.505901\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.864429 | −0.223195 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.70413 | −0.413312 | −0.206656 | − | 0.978414i | \(-0.566258\pi\) | ||||
−0.206656 | + | 0.978414i | \(0.566258\pi\) | |||||||
\(18\) | −2.32969 | −0.549114 | ||||||||
\(19\) | −0.725210 | −0.166375 | −0.0831873 | − | 0.996534i | \(-0.526510\pi\) | ||||
−0.0831873 | + | 0.996534i | \(0.526510\pi\) | |||||||
\(20\) | 0.374437 | 0.0837266 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.34222 | −0.499363 | ||||||||
\(23\) | 0.678862 | 0.141553 | 0.0707763 | − | 0.997492i | \(-0.477452\pi\) | ||||
0.0707763 | + | 0.997492i | \(0.477452\pi\) | |||||||
\(24\) | 2.30861 | 0.471244 | ||||||||
\(25\) | −4.85980 | −0.971959 | ||||||||
\(26\) | 0.133679 | 0.0262166 | ||||||||
\(27\) | 1.54748 | 0.297812 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.81673 | 0.523053 | 0.261527 | − | 0.965196i | \(-0.415774\pi\) | ||||
0.261527 | + | 0.965196i | \(0.415774\pi\) | |||||||
\(30\) | 0.864429 | 0.157822 | ||||||||
\(31\) | −2.53866 | −0.455957 | −0.227978 | − | 0.973666i | \(-0.573212\pi\) | ||||
−0.227978 | + | 0.973666i | \(0.573212\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −5.40728 | −0.941286 | ||||||||
\(34\) | 1.70413 | 0.292256 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.32969 | 0.388282 | ||||||||
\(37\) | 9.14872 | 1.50404 | 0.752020 | − | 0.659140i | \(-0.229080\pi\) | ||||
0.752020 | + | 0.659140i | \(0.229080\pi\) | |||||||
\(38\) | 0.725210 | 0.117645 | ||||||||
\(39\) | 0.308613 | 0.0494176 | ||||||||
\(40\) | −0.374437 | −0.0592036 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.66821 | 1.01689 | 0.508446 | − | 0.861094i | \(-0.330220\pi\) | ||||
0.508446 | + | 0.861094i | \(0.330220\pi\) | |||||||
\(44\) | 2.34222 | 0.353103 | ||||||||
\(45\) | 0.872322 | 0.130038 | ||||||||
\(46\) | −0.678862 | −0.100093 | ||||||||
\(47\) | 3.99629 | 0.582919 | 0.291460 | − | 0.956583i | \(-0.405859\pi\) | ||||
0.291460 | + | 0.956583i | \(0.405859\pi\) | |||||||
\(48\) | −2.30861 | −0.333220 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.85980 | 0.687279 | ||||||||
\(51\) | 3.93418 | 0.550895 | ||||||||
\(52\) | −0.133679 | −0.0185379 | ||||||||
\(53\) | −1.22541 | −0.168324 | −0.0841618 | − | 0.996452i | \(-0.526821\pi\) | ||||
−0.0841618 | + | 0.996452i | \(0.526821\pi\) | |||||||
\(54\) | −1.54748 | −0.210585 | ||||||||
\(55\) | 0.877012 | 0.118256 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.67423 | 0.221757 | ||||||||
\(58\) | −2.81673 | −0.369855 | ||||||||
\(59\) | −13.6176 | −1.77286 | −0.886432 | − | 0.462859i | \(-0.846824\pi\) | ||||
−0.886432 | + | 0.462859i | \(0.846824\pi\) | |||||||
\(60\) | −0.864429 | −0.111597 | ||||||||
\(61\) | −1.22171 | −0.156424 | −0.0782119 | − | 0.996937i | \(-0.524921\pi\) | ||||
−0.0782119 | + | 0.996937i | \(0.524921\pi\) | |||||||
\(62\) | 2.53866 | 0.322410 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0500543 | −0.00620847 | ||||||||
\(66\) | 5.40728 | 0.665590 | ||||||||
\(67\) | 0.682971 | 0.0834382 | 0.0417191 | − | 0.999129i | \(-0.486717\pi\) | ||||
0.0417191 | + | 0.999129i | \(0.486717\pi\) | |||||||
\(68\) | −1.70413 | −0.206656 | ||||||||
\(69\) | −1.56723 | −0.188672 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.12528 | 0.964294 | 0.482147 | − | 0.876090i | \(-0.339857\pi\) | ||||
0.482147 | + | 0.876090i | \(0.339857\pi\) | |||||||
\(72\) | −2.32969 | −0.274557 | ||||||||
\(73\) | −2.89686 | −0.339052 | −0.169526 | − | 0.985526i | \(-0.554224\pi\) | ||||
−0.169526 | + | 0.985526i | \(0.554224\pi\) | |||||||
\(74\) | −9.14872 | −1.06352 | ||||||||
\(75\) | 11.2194 | 1.29550 | ||||||||
\(76\) | −0.725210 | −0.0831873 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.308613 | −0.0349435 | ||||||||
\(79\) | −13.0919 | −1.47296 | −0.736479 | − | 0.676461i | \(-0.763513\pi\) | ||||
−0.736479 | + | 0.676461i | \(0.763513\pi\) | |||||||
\(80\) | 0.374437 | 0.0418633 | ||||||||
\(81\) | −10.5616 | −1.17351 | ||||||||
\(82\) | 1.00000 | 0.110432 | ||||||||
\(83\) | −1.52221 | −0.167084 | −0.0835422 | − | 0.996504i | \(-0.526623\pi\) | ||||
−0.0835422 | + | 0.996504i | \(0.526623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.638089 | −0.0692104 | ||||||||
\(86\) | −6.66821 | −0.719051 | ||||||||
\(87\) | −6.50274 | −0.697166 | ||||||||
\(88\) | −2.34222 | −0.249681 | ||||||||
\(89\) | 8.52779 | 0.903943 | 0.451972 | − | 0.892032i | \(-0.350721\pi\) | ||||
0.451972 | + | 0.892032i | \(0.350721\pi\) | |||||||
\(90\) | −0.872322 | −0.0919509 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.678862 | 0.0707763 | ||||||||
\(93\) | 5.86078 | 0.607735 | ||||||||
\(94\) | −3.99629 | −0.412186 | ||||||||
\(95\) | −0.271545 | −0.0278600 | ||||||||
\(96\) | 2.30861 | 0.235622 | ||||||||
\(97\) | −1.74259 | −0.176933 | −0.0884664 | − | 0.996079i | \(-0.528197\pi\) | ||||
−0.0884664 | + | 0.996079i | \(0.528197\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.45665 | 0.548414 | ||||||||
\(100\) | −4.85980 | −0.485980 | ||||||||
\(101\) | −16.3793 | −1.62980 | −0.814901 | − | 0.579600i | \(-0.803209\pi\) | ||||
−0.814901 | + | 0.579600i | \(0.803209\pi\) | |||||||
\(102\) | −3.93418 | −0.389541 | ||||||||
\(103\) | 0.328088 | 0.0323275 | 0.0161637 | − | 0.999869i | \(-0.494855\pi\) | ||||
0.0161637 | + | 0.999869i | \(0.494855\pi\) | |||||||
\(104\) | 0.133679 | 0.0131083 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.22541 | 0.119023 | ||||||||
\(107\) | 1.47989 | 0.143066 | 0.0715332 | − | 0.997438i | \(-0.477211\pi\) | ||||
0.0715332 | + | 0.997438i | \(0.477211\pi\) | |||||||
\(108\) | 1.54748 | 0.148906 | ||||||||
\(109\) | 10.0351 | 0.961192 | 0.480596 | − | 0.876942i | \(-0.340420\pi\) | ||||
0.480596 | + | 0.876942i | \(0.340420\pi\) | |||||||
\(110\) | −0.877012 | −0.0836198 | ||||||||
\(111\) | −21.1208 | −2.00470 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.994747 | 0.0935779 | 0.0467890 | − | 0.998905i | \(-0.485101\pi\) | ||||
0.0467890 | + | 0.998905i | \(0.485101\pi\) | |||||||
\(114\) | −1.67423 | −0.156806 | ||||||||
\(115\) | 0.254191 | 0.0237034 | ||||||||
\(116\) | 2.81673 | 0.261527 | ||||||||
\(117\) | −0.311431 | −0.0287918 | ||||||||
\(118\) | 13.6176 | 1.25360 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.864429 | 0.0789112 | ||||||||
\(121\) | −5.51401 | −0.501274 | ||||||||
\(122\) | 1.22171 | 0.110608 | ||||||||
\(123\) | 2.30861 | 0.208161 | ||||||||
\(124\) | −2.53866 | −0.227978 | ||||||||
\(125\) | −3.69187 | −0.330211 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3765 | 1.36445 | 0.682223 | − | 0.731144i | \(-0.261013\pi\) | ||||
0.682223 | + | 0.731144i | \(0.261013\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −15.3943 | −1.35539 | ||||||||
\(130\) | 0.0500543 | 0.00439005 | ||||||||
\(131\) | 12.0702 | 1.05458 | 0.527288 | − | 0.849687i | \(-0.323209\pi\) | ||||
0.527288 | + | 0.849687i | \(0.323209\pi\) | |||||||
\(132\) | −5.40728 | −0.470643 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.682971 | −0.0589997 | ||||||||
\(135\) | 0.579433 | 0.0498696 | ||||||||
\(136\) | 1.70413 | 0.146128 | ||||||||
\(137\) | 6.61995 | 0.565580 | 0.282790 | − | 0.959182i | \(-0.408740\pi\) | ||||
0.282790 | + | 0.959182i | \(0.408740\pi\) | |||||||
\(138\) | 1.56723 | 0.133411 | ||||||||
\(139\) | −0.730250 | −0.0619390 | −0.0309695 | − | 0.999520i | \(-0.509859\pi\) | ||||
−0.0309695 | + | 0.999520i | \(0.509859\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.22590 | −0.776961 | ||||||||
\(142\) | −8.12528 | −0.681859 | ||||||||
\(143\) | −0.313105 | −0.0261832 | ||||||||
\(144\) | 2.32969 | 0.194141 | ||||||||
\(145\) | 1.05469 | 0.0875869 | ||||||||
\(146\) | 2.89686 | 0.239746 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.14872 | 0.752020 | ||||||||
\(149\) | 3.39341 | 0.277999 | 0.138999 | − | 0.990292i | \(-0.455611\pi\) | ||||
0.138999 | + | 0.990292i | \(0.455611\pi\) | |||||||
\(150\) | −11.2194 | −0.916059 | ||||||||
\(151\) | −15.9780 | −1.30027 | −0.650135 | − | 0.759819i | \(-0.725288\pi\) | ||||
−0.650135 | + | 0.759819i | \(0.725288\pi\) | |||||||
\(152\) | 0.725210 | 0.0588223 | ||||||||
\(153\) | −3.97010 | −0.320964 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.950567 | −0.0763514 | ||||||||
\(156\) | 0.308613 | 0.0247088 | ||||||||
\(157\) | 9.31987 | 0.743806 | 0.371903 | − | 0.928272i | \(-0.378705\pi\) | ||||
0.371903 | + | 0.928272i | \(0.378705\pi\) | |||||||
\(158\) | 13.0919 | 1.04154 | ||||||||
\(159\) | 2.82901 | 0.224355 | ||||||||
\(160\) | −0.374437 | −0.0296018 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 10.5616 | 0.829798 | ||||||||
\(163\) | 20.0824 | 1.57297 | 0.786487 | − | 0.617607i | \(-0.211898\pi\) | ||||
0.786487 | + | 0.617607i | \(0.211898\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | −2.02468 | −0.157621 | ||||||||
\(166\) | 1.52221 | 0.118146 | ||||||||
\(167\) | 2.04253 | 0.158056 | 0.0790278 | − | 0.996872i | \(-0.474818\pi\) | ||||
0.0790278 | + | 0.996872i | \(0.474818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9821 | −0.998625 | ||||||||
\(170\) | 0.638089 | 0.0489392 | ||||||||
\(171\) | −1.68952 | −0.129201 | ||||||||
\(172\) | 6.66821 | 0.508446 | ||||||||
\(173\) | −9.56918 | −0.727531 | −0.363766 | − | 0.931491i | \(-0.618509\pi\) | ||||
−0.363766 | + | 0.931491i | \(0.618509\pi\) | |||||||
\(174\) | 6.50274 | 0.492971 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.34222 | 0.176551 | ||||||||
\(177\) | 31.4378 | 2.36301 | ||||||||
\(178\) | −8.52779 | −0.639185 | ||||||||
\(179\) | 9.97650 | 0.745678 | 0.372839 | − | 0.927896i | \(-0.378384\pi\) | ||||
0.372839 | + | 0.927896i | \(0.378384\pi\) | |||||||
\(180\) | 0.872322 | 0.0650191 | ||||||||
\(181\) | −24.3936 | −1.81316 | −0.906581 | − | 0.422032i | \(-0.861317\pi\) | ||||
−0.906581 | + | 0.422032i | \(0.861317\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.82045 | 0.208494 | ||||||||
\(184\) | −0.678862 | −0.0500464 | ||||||||
\(185\) | 3.42561 | 0.251856 | ||||||||
\(186\) | −5.86078 | −0.429733 | ||||||||
\(187\) | −3.99144 | −0.291883 | ||||||||
\(188\) | 3.99629 | 0.291460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.271545 | 0.0197000 | ||||||||
\(191\) | 4.44946 | 0.321952 | 0.160976 | − | 0.986958i | \(-0.448536\pi\) | ||||
0.160976 | + | 0.986958i | \(0.448536\pi\) | |||||||
\(192\) | −2.30861 | −0.166610 | ||||||||
\(193\) | −11.2662 | −0.810956 | −0.405478 | − | 0.914105i | \(-0.632895\pi\) | ||||
−0.405478 | + | 0.914105i | \(0.632895\pi\) | |||||||
\(194\) | 1.74259 | 0.125110 | ||||||||
\(195\) | 0.115556 | 0.00827513 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.60076 | 0.399037 | 0.199519 | − | 0.979894i | \(-0.436062\pi\) | ||||
0.199519 | + | 0.979894i | \(0.436062\pi\) | |||||||
\(198\) | −5.45665 | −0.387787 | ||||||||
\(199\) | 5.73582 | 0.406601 | 0.203301 | − | 0.979116i | \(-0.434833\pi\) | ||||
0.203301 | + | 0.979116i | \(0.434833\pi\) | |||||||
\(200\) | 4.85980 | 0.343640 | ||||||||
\(201\) | −1.57672 | −0.111213 | ||||||||
\(202\) | 16.3793 | 1.15244 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.93418 | 0.275447 | ||||||||
\(205\) | −0.374437 | −0.0261518 | ||||||||
\(206\) | −0.328088 | −0.0228590 | ||||||||
\(207\) | 1.58154 | 0.109925 | ||||||||
\(208\) | −0.133679 | −0.00926897 | ||||||||
\(209\) | −1.69860 | −0.117495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.41074 | 0.510176 | 0.255088 | − | 0.966918i | \(-0.417896\pi\) | ||||
0.255088 | + | 0.966918i | \(0.417896\pi\) | |||||||
\(212\) | −1.22541 | −0.0841618 | ||||||||
\(213\) | −18.7581 | −1.28529 | ||||||||
\(214\) | −1.47989 | −0.101163 | ||||||||
\(215\) | 2.49682 | 0.170282 | ||||||||
\(216\) | −1.54748 | −0.105293 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0351 | −0.679665 | ||||||||
\(219\) | 6.68774 | 0.451916 | ||||||||
\(220\) | 0.877012 | 0.0591282 | ||||||||
\(221\) | 0.227806 | 0.0153239 | ||||||||
\(222\) | 21.1208 | 1.41754 | ||||||||
\(223\) | 1.69048 | 0.113203 | 0.0566015 | − | 0.998397i | \(-0.481974\pi\) | ||||
0.0566015 | + | 0.998397i | \(0.481974\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.3218 | −0.754789 | ||||||||
\(226\) | −0.994747 | −0.0661696 | ||||||||
\(227\) | 7.85873 | 0.521602 | 0.260801 | − | 0.965393i | \(-0.416013\pi\) | ||||
0.260801 | + | 0.965393i | \(0.416013\pi\) | |||||||
\(228\) | 1.67423 | 0.110879 | ||||||||
\(229\) | −16.2972 | −1.07695 | −0.538475 | − | 0.842642i | \(-0.680999\pi\) | ||||
−0.538475 | + | 0.842642i | \(0.680999\pi\) | |||||||
\(230\) | −0.254191 | −0.0167608 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.81673 | −0.184927 | ||||||||
\(233\) | 9.03314 | 0.591781 | 0.295890 | − | 0.955222i | \(-0.404384\pi\) | ||||
0.295890 | + | 0.955222i | \(0.404384\pi\) | |||||||
\(234\) | 0.311431 | 0.0203589 | ||||||||
\(235\) | 1.49636 | 0.0976117 | ||||||||
\(236\) | −13.6176 | −0.886432 | ||||||||
\(237\) | 30.2242 | 1.96327 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.20554 | −0.0779796 | −0.0389898 | − | 0.999240i | \(-0.512414\pi\) | ||||
−0.0389898 | + | 0.999240i | \(0.512414\pi\) | |||||||
\(240\) | −0.864429 | −0.0557987 | ||||||||
\(241\) | 17.6334 | 1.13587 | 0.567933 | − | 0.823075i | \(-0.307743\pi\) | ||||
0.567933 | + | 0.823075i | \(0.307743\pi\) | |||||||
\(242\) | 5.51401 | 0.354454 | ||||||||
\(243\) | 19.7402 | 1.26634 | ||||||||
\(244\) | −1.22171 | −0.0782119 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.30861 | −0.147192 | ||||||||
\(247\) | 0.0969453 | 0.00616848 | ||||||||
\(248\) | 2.53866 | 0.161205 | ||||||||
\(249\) | 3.51419 | 0.222703 | ||||||||
\(250\) | 3.69187 | 0.233494 | ||||||||
\(251\) | 7.98132 | 0.503776 | 0.251888 | − | 0.967756i | \(-0.418948\pi\) | ||||
0.251888 | + | 0.967756i | \(0.418948\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.59004 | 0.0999652 | ||||||||
\(254\) | −15.3765 | −0.964809 | ||||||||
\(255\) | 1.47310 | 0.0922491 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.3379 | 0.769616 | 0.384808 | − | 0.922997i | \(-0.374268\pi\) | ||||
0.384808 | + | 0.922997i | \(0.374268\pi\) | |||||||
\(258\) | 15.3943 | 0.958408 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.0500543 | −0.00310423 | ||||||||
\(261\) | 6.56211 | 0.406185 | ||||||||
\(262\) | −12.0702 | −0.745698 | ||||||||
\(263\) | 24.8075 | 1.52969 | 0.764847 | − | 0.644212i | \(-0.222815\pi\) | ||||
0.764847 | + | 0.644212i | \(0.222815\pi\) | |||||||
\(264\) | 5.40728 | 0.332795 | ||||||||
\(265\) | −0.458840 | −0.0281863 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.6874 | −1.20485 | ||||||||
\(268\) | 0.682971 | 0.0417191 | ||||||||
\(269\) | −0.0721853 | −0.00440122 | −0.00220061 | − | 0.999998i | \(-0.500700\pi\) | ||||
−0.00220061 | + | 0.999998i | \(0.500700\pi\) | |||||||
\(270\) | −0.579433 | −0.0352631 | ||||||||
\(271\) | 21.7890 | 1.32359 | 0.661793 | − | 0.749687i | \(-0.269796\pi\) | ||||
0.661793 | + | 0.749687i | \(0.269796\pi\) | |||||||
\(272\) | −1.70413 | −0.103328 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.61995 | −0.399926 | ||||||||
\(275\) | −11.3827 | −0.686403 | ||||||||
\(276\) | −1.56723 | −0.0943361 | ||||||||
\(277\) | −6.50956 | −0.391122 | −0.195561 | − | 0.980692i | \(-0.562653\pi\) | ||||
−0.195561 | + | 0.980692i | \(0.562653\pi\) | |||||||
\(278\) | 0.730250 | 0.0437975 | ||||||||
\(279\) | −5.91430 | −0.354080 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.2833 | 1.68724 | 0.843621 | − | 0.536939i | \(-0.180419\pi\) | ||||
0.843621 | + | 0.536939i | \(0.180419\pi\) | |||||||
\(282\) | 9.22590 | 0.549394 | ||||||||
\(283\) | 21.3545 | 1.26939 | 0.634696 | − | 0.772762i | \(-0.281125\pi\) | ||||
0.634696 | + | 0.772762i | \(0.281125\pi\) | |||||||
\(284\) | 8.12528 | 0.482147 | ||||||||
\(285\) | 0.626893 | 0.0371339 | ||||||||
\(286\) | 0.313105 | 0.0185143 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.32969 | −0.137278 | ||||||||
\(289\) | −14.0959 | −0.829173 | ||||||||
\(290\) | −1.05469 | −0.0619333 | ||||||||
\(291\) | 4.02295 | 0.235830 | ||||||||
\(292\) | −2.89686 | −0.169526 | ||||||||
\(293\) | 7.82803 | 0.457319 | 0.228659 | − | 0.973507i | \(-0.426566\pi\) | ||||
0.228659 | + | 0.973507i | \(0.426566\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.09894 | −0.296872 | ||||||||
\(296\) | −9.14872 | −0.531758 | ||||||||
\(297\) | 3.62453 | 0.210317 | ||||||||
\(298\) | −3.39341 | −0.196575 | ||||||||
\(299\) | −0.0907495 | −0.00524818 | ||||||||
\(300\) | 11.2194 | 0.647752 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 15.9780 | 0.919430 | ||||||||
\(303\) | 37.8135 | 2.17233 | ||||||||
\(304\) | −0.725210 | −0.0415937 | ||||||||
\(305\) | −0.457452 | −0.0261936 | ||||||||
\(306\) | 3.97010 | 0.226956 | ||||||||
\(307\) | 23.9521 | 1.36702 | 0.683510 | − | 0.729941i | \(-0.260453\pi\) | ||||
0.683510 | + | 0.729941i | \(0.260453\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.757428 | −0.0430886 | ||||||||
\(310\) | 0.950567 | 0.0539886 | ||||||||
\(311\) | 14.4749 | 0.820797 | 0.410399 | − | 0.911906i | \(-0.365390\pi\) | ||||
0.410399 | + | 0.911906i | \(0.365390\pi\) | |||||||
\(312\) | −0.308613 | −0.0174718 | ||||||||
\(313\) | −14.2889 | −0.807655 | −0.403828 | − | 0.914835i | \(-0.632320\pi\) | ||||
−0.403828 | + | 0.914835i | \(0.632320\pi\) | |||||||
\(314\) | −9.31987 | −0.525951 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.0919 | −0.736479 | ||||||||
\(317\) | 2.19881 | 0.123498 | 0.0617488 | − | 0.998092i | \(-0.480332\pi\) | ||||
0.0617488 | + | 0.998092i | \(0.480332\pi\) | |||||||
\(318\) | −2.82901 | −0.158643 | ||||||||
\(319\) | 6.59739 | 0.369383 | ||||||||
\(320\) | 0.374437 | 0.0209316 | ||||||||
\(321\) | −3.41649 | −0.190690 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.23585 | 0.0687647 | ||||||||
\(324\) | −10.5616 | −0.586756 | ||||||||
\(325\) | 0.649652 | 0.0360362 | ||||||||
\(326\) | −20.0824 | −1.11226 | ||||||||
\(327\) | −23.1672 | −1.28115 | ||||||||
\(328\) | 1.00000 | 0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.02468 | 0.111455 | ||||||||
\(331\) | 22.2134 | 1.22096 | 0.610478 | − | 0.792033i | \(-0.290977\pi\) | ||||
0.610478 | + | 0.792033i | \(0.290977\pi\) | |||||||
\(332\) | −1.52221 | −0.0835422 | ||||||||
\(333\) | 21.3137 | 1.16798 | ||||||||
\(334\) | −2.04253 | −0.111762 | ||||||||
\(335\) | 0.255729 | 0.0139720 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8724 | 0.810149 | 0.405075 | − | 0.914284i | \(-0.367246\pi\) | ||||
0.405075 | + | 0.914284i | \(0.367246\pi\) | |||||||
\(338\) | 12.9821 | 0.706135 | ||||||||
\(339\) | −2.29649 | −0.124728 | ||||||||
\(340\) | −0.638089 | −0.0346052 | ||||||||
\(341\) | −5.94609 | −0.321999 | ||||||||
\(342\) | 1.68952 | 0.0913587 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.66821 | −0.359526 | ||||||||
\(345\) | −0.586828 | −0.0315938 | ||||||||
\(346\) | 9.56918 | 0.514442 | ||||||||
\(347\) | 5.22478 | 0.280481 | 0.140240 | − | 0.990117i | \(-0.455212\pi\) | ||||
0.140240 | + | 0.990117i | \(0.455212\pi\) | |||||||
\(348\) | −6.50274 | −0.348583 | ||||||||
\(349\) | 23.4754 | 1.25661 | 0.628305 | − | 0.777967i | \(-0.283749\pi\) | ||||
0.628305 | + | 0.777967i | \(0.283749\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.206865 | −0.0110417 | ||||||||
\(352\) | −2.34222 | −0.124841 | ||||||||
\(353\) | 5.25312 | 0.279595 | 0.139798 | − | 0.990180i | \(-0.455355\pi\) | ||||
0.139798 | + | 0.990180i | \(0.455355\pi\) | |||||||
\(354\) | −31.4378 | −1.67090 | ||||||||
\(355\) | 3.04240 | 0.161474 | ||||||||
\(356\) | 8.52779 | 0.451972 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.97650 | −0.527274 | ||||||||
\(359\) | 10.0526 | 0.530557 | 0.265278 | − | 0.964172i | \(-0.414536\pi\) | ||||
0.265278 | + | 0.964172i | \(0.414536\pi\) | |||||||
\(360\) | −0.872322 | −0.0459754 | ||||||||
\(361\) | −18.4741 | −0.972319 | ||||||||
\(362\) | 24.3936 | 1.28210 | ||||||||
\(363\) | 12.7297 | 0.668137 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.08469 | −0.0567754 | ||||||||
\(366\) | −2.82045 | −0.147427 | ||||||||
\(367\) | −4.93946 | −0.257837 | −0.128919 | − | 0.991655i | \(-0.541151\pi\) | ||||
−0.128919 | + | 0.991655i | \(0.541151\pi\) | |||||||
\(368\) | 0.678862 | 0.0353881 | ||||||||
\(369\) | −2.32969 | −0.121279 | ||||||||
\(370\) | −3.42561 | −0.178089 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.86078 | 0.303867 | ||||||||
\(373\) | −19.0600 | −0.986889 | −0.493444 | − | 0.869777i | \(-0.664262\pi\) | ||||
−0.493444 | + | 0.869777i | \(0.664262\pi\) | |||||||
\(374\) | 3.99144 | 0.206393 | ||||||||
\(375\) | 8.52310 | 0.440131 | ||||||||
\(376\) | −3.99629 | −0.206093 | ||||||||
\(377\) | −0.376537 | −0.0193927 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8915 | −1.07312 | −0.536562 | − | 0.843861i | \(-0.680277\pi\) | ||||
−0.536562 | + | 0.843861i | \(0.680277\pi\) | |||||||
\(380\) | −0.271545 | −0.0139300 | ||||||||
\(381\) | −35.4984 | −1.81864 | ||||||||
\(382\) | −4.44946 | −0.227654 | ||||||||
\(383\) | 36.0739 | 1.84329 | 0.921645 | − | 0.388034i | \(-0.126846\pi\) | ||||
0.921645 | + | 0.388034i | \(0.126846\pi\) | |||||||
\(384\) | 2.30861 | 0.117811 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.2662 | 0.573433 | ||||||||
\(387\) | 15.5349 | 0.789682 | ||||||||
\(388\) | −1.74259 | −0.0884664 | ||||||||
\(389\) | 35.0407 | 1.77663 | 0.888317 | − | 0.459230i | \(-0.151875\pi\) | ||||
0.888317 | + | 0.459230i | \(0.151875\pi\) | |||||||
\(390\) | −0.115556 | −0.00585140 | ||||||||
\(391\) | −1.15687 | −0.0585054 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.8654 | −1.40562 | ||||||||
\(394\) | −5.60076 | −0.282162 | ||||||||
\(395\) | −4.90210 | −0.246651 | ||||||||
\(396\) | 5.45665 | 0.274207 | ||||||||
\(397\) | −21.3240 | −1.07022 | −0.535111 | − | 0.844782i | \(-0.679730\pi\) | ||||
−0.535111 | + | 0.844782i | \(0.679730\pi\) | |||||||
\(398\) | −5.73582 | −0.287511 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.85980 | −0.242990 | ||||||||
\(401\) | 2.72976 | 0.136318 | 0.0681590 | − | 0.997674i | \(-0.478287\pi\) | ||||
0.0681590 | + | 0.997674i | \(0.478287\pi\) | |||||||
\(402\) | 1.57672 | 0.0786395 | ||||||||
\(403\) | 0.339365 | 0.0169050 | ||||||||
\(404\) | −16.3793 | −0.814901 | ||||||||
\(405\) | −3.95465 | −0.196508 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.4283 | 1.06216 | ||||||||
\(408\) | −3.93418 | −0.194771 | ||||||||
\(409\) | 20.4532 | 1.01135 | 0.505673 | − | 0.862725i | \(-0.331244\pi\) | ||||
0.505673 | + | 0.862725i | \(0.331244\pi\) | |||||||
\(410\) | 0.374437 | 0.0184921 | ||||||||
\(411\) | −15.2829 | −0.753850 | ||||||||
\(412\) | 0.328088 | 0.0161637 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.58154 | −0.0777285 | ||||||||
\(415\) | −0.569971 | −0.0279788 | ||||||||
\(416\) | 0.133679 | 0.00655415 | ||||||||
\(417\) | 1.68587 | 0.0825572 | ||||||||
\(418\) | 1.69860 | 0.0830813 | ||||||||
\(419\) | 7.57172 | 0.369903 | 0.184951 | − | 0.982748i | \(-0.440787\pi\) | ||||
0.184951 | + | 0.982748i | \(0.440787\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.0012 | 0.584903 | 0.292451 | − | 0.956280i | \(-0.405529\pi\) | ||||
0.292451 | + | 0.956280i | \(0.405529\pi\) | |||||||
\(422\) | −7.41074 | −0.360749 | ||||||||
\(423\) | 9.31014 | 0.452674 | ||||||||
\(424\) | 1.22541 | 0.0595114 | ||||||||
\(425\) | 8.28173 | 0.401723 | ||||||||
\(426\) | 18.7581 | 0.908835 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.47989 | 0.0715332 | ||||||||
\(429\) | 0.722839 | 0.0348990 | ||||||||
\(430\) | −2.49682 | −0.120407 | ||||||||
\(431\) | 13.7132 | 0.660543 | 0.330271 | − | 0.943886i | \(-0.392860\pi\) | ||||
0.330271 | + | 0.943886i | \(0.392860\pi\) | |||||||
\(432\) | 1.54748 | 0.0744531 | ||||||||
\(433\) | 23.7704 | 1.14233 | 0.571167 | − | 0.820834i | \(-0.306491\pi\) | ||||
0.571167 | + | 0.820834i | \(0.306491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.43486 | −0.116743 | ||||||||
\(436\) | 10.0351 | 0.480596 | ||||||||
\(437\) | −0.492318 | −0.0235508 | ||||||||
\(438\) | −6.68774 | −0.319553 | ||||||||
\(439\) | 19.3393 | 0.923014 | 0.461507 | − | 0.887137i | \(-0.347309\pi\) | ||||
0.461507 | + | 0.887137i | \(0.347309\pi\) | |||||||
\(440\) | −0.877012 | −0.0418099 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.227806 | −0.0108356 | ||||||||
\(443\) | 32.4468 | 1.54159 | 0.770797 | − | 0.637080i | \(-0.219858\pi\) | ||||
0.770797 | + | 0.637080i | \(0.219858\pi\) | |||||||
\(444\) | −21.1208 | −1.00235 | ||||||||
\(445\) | 3.19311 | 0.151368 | ||||||||
\(446\) | −1.69048 | −0.0800466 | ||||||||
\(447\) | −7.83406 | −0.370539 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.8167 | 0.510472 | 0.255236 | − | 0.966879i | \(-0.417847\pi\) | ||||
0.255236 | + | 0.966879i | \(0.417847\pi\) | |||||||
\(450\) | 11.3218 | 0.533717 | ||||||||
\(451\) | −2.34222 | −0.110291 | ||||||||
\(452\) | 0.994747 | 0.0467890 | ||||||||
\(453\) | 36.8870 | 1.73310 | ||||||||
\(454\) | −7.85873 | −0.368829 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.67423 | −0.0784030 | ||||||||
\(457\) | −14.6183 | −0.683816 | −0.341908 | − | 0.939733i | \(-0.611073\pi\) | ||||
−0.341908 | + | 0.939733i | \(0.611073\pi\) | |||||||
\(458\) | 16.2972 | 0.761519 | ||||||||
\(459\) | −2.63710 | −0.123089 | ||||||||
\(460\) | 0.254191 | 0.0118517 | ||||||||
\(461\) | −21.3560 | −0.994650 | −0.497325 | − | 0.867564i | \(-0.665684\pi\) | ||||
−0.497325 | + | 0.867564i | \(0.665684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.3519 | 0.806412 | 0.403206 | − | 0.915109i | \(-0.367896\pi\) | ||||
0.403206 | + | 0.915109i | \(0.367896\pi\) | |||||||
\(464\) | 2.81673 | 0.130763 | ||||||||
\(465\) | 2.19449 | 0.101767 | ||||||||
\(466\) | −9.03314 | −0.418452 | ||||||||
\(467\) | 10.3452 | 0.478720 | 0.239360 | − | 0.970931i | \(-0.423062\pi\) | ||||
0.239360 | + | 0.970931i | \(0.423062\pi\) | |||||||
\(468\) | −0.311431 | −0.0143959 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.49636 | −0.0690219 | ||||||||
\(471\) | −21.5160 | −0.991403 | ||||||||
\(472\) | 13.6176 | 0.626802 | ||||||||
\(473\) | 15.6184 | 0.718135 | ||||||||
\(474\) | −30.2242 | −1.38824 | ||||||||
\(475\) | 3.52438 | 0.161709 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.85484 | −0.130714 | ||||||||
\(478\) | 1.20554 | 0.0551399 | ||||||||
\(479\) | 37.8835 | 1.73094 | 0.865471 | − | 0.500959i | \(-0.167019\pi\) | ||||
0.865471 | + | 0.500959i | \(0.167019\pi\) | |||||||
\(480\) | 0.864429 | 0.0394556 | ||||||||
\(481\) | −1.22299 | −0.0557636 | ||||||||
\(482\) | −17.6334 | −0.803179 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.51401 | −0.250637 | ||||||||
\(485\) | −0.652488 | −0.0296279 | ||||||||
\(486\) | −19.7402 | −0.895435 | ||||||||
\(487\) | −18.9378 | −0.858152 | −0.429076 | − | 0.903268i | \(-0.641161\pi\) | ||||
−0.429076 | + | 0.903268i | \(0.641161\pi\) | |||||||
\(488\) | 1.22171 | 0.0553042 | ||||||||
\(489\) | −46.3625 | −2.09658 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.3032 | 0.961398 | 0.480699 | − | 0.876886i | \(-0.340383\pi\) | ||||
0.480699 | + | 0.876886i | \(0.340383\pi\) | |||||||
\(492\) | 2.30861 | 0.104080 | ||||||||
\(493\) | −4.80007 | −0.216184 | ||||||||
\(494\) | −0.0969453 | −0.00436178 | ||||||||
\(495\) | 2.04317 | 0.0918336 | ||||||||
\(496\) | −2.53866 | −0.113989 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.51419 | −0.157475 | ||||||||
\(499\) | −27.3251 | −1.22324 | −0.611621 | − | 0.791151i | \(-0.709482\pi\) | ||||
−0.611621 | + | 0.791151i | \(0.709482\pi\) | |||||||
\(500\) | −3.69187 | −0.165105 | ||||||||
\(501\) | −4.71541 | −0.210669 | ||||||||
\(502\) | −7.98132 | −0.356224 | ||||||||
\(503\) | −32.9508 | −1.46920 | −0.734601 | − | 0.678500i | \(-0.762630\pi\) | ||||
−0.734601 | + | 0.678500i | \(0.762630\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.13301 | −0.272915 | ||||||||
\(506\) | −1.59004 | −0.0706860 | ||||||||
\(507\) | 29.9707 | 1.33105 | ||||||||
\(508\) | 15.3765 | 0.682223 | ||||||||
\(509\) | 5.72873 | 0.253921 | 0.126961 | − | 0.991908i | \(-0.459478\pi\) | ||||
0.126961 | + | 0.991908i | \(0.459478\pi\) | |||||||
\(510\) | −1.47310 | −0.0652299 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.12225 | −0.0495484 | ||||||||
\(514\) | −12.3379 | −0.544201 | ||||||||
\(515\) | 0.122848 | 0.00541334 | ||||||||
\(516\) | −15.3943 | −0.677697 | ||||||||
\(517\) | 9.36019 | 0.411661 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.0915 | 0.969711 | ||||||||
\(520\) | 0.0500543 | 0.00219503 | ||||||||
\(521\) | 26.4083 | 1.15697 | 0.578484 | − | 0.815694i | \(-0.303644\pi\) | ||||
0.578484 | + | 0.815694i | \(0.303644\pi\) | |||||||
\(522\) | −6.56211 | −0.287216 | ||||||||
\(523\) | 4.18053 | 0.182802 | 0.0914008 | − | 0.995814i | \(-0.470866\pi\) | ||||
0.0914008 | + | 0.995814i | \(0.470866\pi\) | |||||||
\(524\) | 12.0702 | 0.527288 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.8075 | −1.08166 | ||||||||
\(527\) | 4.32621 | 0.188452 | ||||||||
\(528\) | −5.40728 | −0.235321 | ||||||||
\(529\) | −22.5391 | −0.979963 | ||||||||
\(530\) | 0.458840 | 0.0199307 | ||||||||
\(531\) | −31.7249 | −1.37674 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.133679 | 0.00579028 | ||||||||
\(534\) | 19.6874 | 0.851955 | ||||||||
\(535\) | 0.554125 | 0.0239569 | ||||||||
\(536\) | −0.682971 | −0.0294999 | ||||||||
\(537\) | −23.0319 | −0.993899 | ||||||||
\(538\) | 0.0721853 | 0.00311213 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.579433 | 0.0249348 | ||||||||
\(541\) | −20.2919 | −0.872419 | −0.436209 | − | 0.899845i | \(-0.643679\pi\) | ||||
−0.436209 | + | 0.899845i | \(0.643679\pi\) | |||||||
\(542\) | −21.7890 | −0.935917 | ||||||||
\(543\) | 56.3154 | 2.41672 | ||||||||
\(544\) | 1.70413 | 0.0730640 | ||||||||
\(545\) | 3.75752 | 0.160955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4553 | 1.08839 | 0.544195 | − | 0.838959i | \(-0.316835\pi\) | ||||
0.544195 | + | 0.838959i | \(0.316835\pi\) | |||||||
\(548\) | 6.61995 | 0.282790 | ||||||||
\(549\) | −2.84621 | −0.121473 | ||||||||
\(550\) | 11.3827 | 0.485360 | ||||||||
\(551\) | −2.04272 | −0.0870228 | ||||||||
\(552\) | 1.56723 | 0.0667057 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.50956 | 0.276565 | ||||||||
\(555\) | −7.90842 | −0.335694 | ||||||||
\(556\) | −0.730250 | −0.0309695 | ||||||||
\(557\) | −3.05327 | −0.129371 | −0.0646855 | − | 0.997906i | \(-0.520604\pi\) | ||||
−0.0646855 | + | 0.997906i | \(0.520604\pi\) | |||||||
\(558\) | 5.91430 | 0.250372 | ||||||||
\(559\) | −0.891399 | −0.0377021 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.21470 | 0.389045 | ||||||||
\(562\) | −28.2833 | −1.19306 | ||||||||
\(563\) | −41.3768 | −1.74382 | −0.871912 | − | 0.489663i | \(-0.837120\pi\) | ||||
−0.871912 | + | 0.489663i | \(0.837120\pi\) | |||||||
\(564\) | −9.22590 | −0.388480 | ||||||||
\(565\) | 0.372470 | 0.0156699 | ||||||||
\(566\) | −21.3545 | −0.897596 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.12528 | −0.340929 | ||||||||
\(569\) | −3.02824 | −0.126950 | −0.0634752 | − | 0.997983i | \(-0.520218\pi\) | ||||
−0.0634752 | + | 0.997983i | \(0.520218\pi\) | |||||||
\(570\) | −0.626893 | −0.0262577 | ||||||||
\(571\) | −9.63737 | −0.403311 | −0.201656 | − | 0.979456i | \(-0.564632\pi\) | ||||
−0.201656 | + | 0.979456i | \(0.564632\pi\) | |||||||
\(572\) | −0.313105 | −0.0130916 | ||||||||
\(573\) | −10.2721 | −0.429122 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.29913 | −0.137583 | ||||||||
\(576\) | 2.32969 | 0.0970706 | ||||||||
\(577\) | 26.5826 | 1.10665 | 0.553323 | − | 0.832967i | \(-0.313359\pi\) | ||||
0.553323 | + | 0.832967i | \(0.313359\pi\) | |||||||
\(578\) | 14.0959 | 0.586314 | ||||||||
\(579\) | 26.0092 | 1.08091 | ||||||||
\(580\) | 1.05469 | 0.0437935 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −4.02295 | −0.166757 | ||||||||
\(583\) | −2.87019 | −0.118871 | ||||||||
\(584\) | 2.89686 | 0.119873 | ||||||||
\(585\) | −0.116611 | −0.00482128 | ||||||||
\(586\) | −7.82803 | −0.323373 | ||||||||
\(587\) | 35.2886 | 1.45652 | 0.728259 | − | 0.685302i | \(-0.240330\pi\) | ||||
0.728259 | + | 0.685302i | \(0.240330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.84106 | 0.0758596 | ||||||||
\(590\) | 5.09894 | 0.209920 | ||||||||
\(591\) | −12.9300 | −0.531868 | ||||||||
\(592\) | 9.14872 | 0.376010 | ||||||||
\(593\) | −26.0103 | −1.06812 | −0.534058 | − | 0.845448i | \(-0.679334\pi\) | ||||
−0.534058 | + | 0.845448i | \(0.679334\pi\) | |||||||
\(594\) | −3.62453 | −0.148716 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.39341 | 0.138999 | ||||||||
\(597\) | −13.2418 | −0.541950 | ||||||||
\(598\) | 0.0907495 | 0.00371102 | ||||||||
\(599\) | 38.6365 | 1.57865 | 0.789323 | − | 0.613978i | \(-0.210432\pi\) | ||||
0.789323 | + | 0.613978i | \(0.210432\pi\) | |||||||
\(600\) | −11.2194 | −0.458030 | ||||||||
\(601\) | −36.0703 | −1.47134 | −0.735669 | − | 0.677341i | \(-0.763132\pi\) | ||||
−0.735669 | + | 0.677341i | \(0.763132\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.59111 | 0.0647952 | ||||||||
\(604\) | −15.9780 | −0.650135 | ||||||||
\(605\) | −2.06465 | −0.0839399 | ||||||||
\(606\) | −37.8135 | −1.53607 | ||||||||
\(607\) | −24.7841 | −1.00596 | −0.502978 | − | 0.864299i | \(-0.667762\pi\) | ||||
−0.502978 | + | 0.864299i | \(0.667762\pi\) | |||||||
\(608\) | 0.725210 | 0.0294112 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.457452 | 0.0185217 | ||||||||
\(611\) | −0.534220 | −0.0216122 | ||||||||
\(612\) | −3.97010 | −0.160482 | ||||||||
\(613\) | 34.6013 | 1.39753 | 0.698766 | − | 0.715350i | \(-0.253733\pi\) | ||||
0.698766 | + | 0.715350i | \(0.253733\pi\) | |||||||
\(614\) | −23.9521 | −0.966629 | ||||||||
\(615\) | 0.864429 | 0.0348571 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.4565 | 1.66897 | 0.834487 | − | 0.551027i | \(-0.185764\pi\) | ||||
0.834487 | + | 0.551027i | \(0.185764\pi\) | |||||||
\(618\) | 0.757428 | 0.0304682 | ||||||||
\(619\) | 25.1330 | 1.01018 | 0.505091 | − | 0.863066i | \(-0.331459\pi\) | ||||
0.505091 | + | 0.863066i | \(0.331459\pi\) | |||||||
\(620\) | −0.950567 | −0.0381757 | ||||||||
\(621\) | 1.05052 | 0.0421561 | ||||||||
\(622\) | −14.4749 | −0.580391 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.308613 | 0.0123544 | ||||||||
\(625\) | 22.9166 | 0.916665 | ||||||||
\(626\) | 14.2889 | 0.571098 | ||||||||
\(627\) | 3.92141 | 0.156606 | ||||||||
\(628\) | 9.31987 | 0.371903 | ||||||||
\(629\) | −15.5906 | −0.621638 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.3032 | −1.40540 | −0.702699 | − | 0.711487i | \(-0.748022\pi\) | ||||
−0.702699 | + | 0.711487i | \(0.748022\pi\) | |||||||
\(632\) | 13.0919 | 0.520769 | ||||||||
\(633\) | −17.1085 | −0.680003 | ||||||||
\(634\) | −2.19881 | −0.0873260 | ||||||||
\(635\) | 5.75753 | 0.228481 | ||||||||
\(636\) | 2.82901 | 0.112177 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.59739 | −0.261193 | ||||||||
\(639\) | 18.9294 | 0.748836 | ||||||||
\(640\) | −0.374437 | −0.0148009 | ||||||||
\(641\) | −34.9140 | −1.37902 | −0.689509 | − | 0.724277i | \(-0.742174\pi\) | ||||
−0.689509 | + | 0.724277i | \(0.742174\pi\) | |||||||
\(642\) | 3.41649 | 0.134838 | ||||||||
\(643\) | −28.9500 | −1.14168 | −0.570838 | − | 0.821063i | \(-0.693382\pi\) | ||||
−0.570838 | + | 0.821063i | \(0.693382\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.76419 | −0.226965 | ||||||||
\(646\) | −1.23585 | −0.0486240 | ||||||||
\(647\) | −14.7297 | −0.579085 | −0.289542 | − | 0.957165i | \(-0.593503\pi\) | ||||
−0.289542 | + | 0.957165i | \(0.593503\pi\) | |||||||
\(648\) | 10.5616 | 0.414899 | ||||||||
\(649\) | −31.8955 | −1.25201 | ||||||||
\(650\) | −0.649652 | −0.0254815 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.0824 | 0.786487 | ||||||||
\(653\) | −37.6229 | −1.47230 | −0.736149 | − | 0.676820i | \(-0.763358\pi\) | ||||
−0.736149 | + | 0.676820i | \(0.763358\pi\) | |||||||
\(654\) | 23.1672 | 0.905911 | ||||||||
\(655\) | 4.51951 | 0.176592 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | −6.74881 | −0.263296 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.2994 | −0.595979 | −0.297989 | − | 0.954569i | \(-0.596316\pi\) | ||||
−0.297989 | + | 0.954569i | \(0.596316\pi\) | |||||||
\(660\) | −2.02468 | −0.0788106 | ||||||||
\(661\) | 26.3758 | 1.02590 | 0.512949 | − | 0.858419i | \(-0.328553\pi\) | ||||
0.512949 | + | 0.858419i | \(0.328553\pi\) | |||||||
\(662\) | −22.2134 | −0.863346 | ||||||||
\(663\) | −0.525916 | −0.0204249 | ||||||||
\(664\) | 1.52221 | 0.0590732 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.3137 | −0.825889 | ||||||||
\(667\) | 1.91217 | 0.0740395 | ||||||||
\(668\) | 2.04253 | 0.0790278 | ||||||||
\(669\) | −3.90267 | −0.150886 | ||||||||
\(670\) | −0.255729 | −0.00987969 | ||||||||
\(671\) | −2.86151 | −0.110467 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.4518 | 0.441433 | 0.220717 | − | 0.975338i | \(-0.429160\pi\) | ||||
0.220717 | + | 0.975338i | \(0.429160\pi\) | |||||||
\(674\) | −14.8724 | −0.572862 | ||||||||
\(675\) | −7.52043 | −0.289462 | ||||||||
\(676\) | −12.9821 | −0.499313 | ||||||||
\(677\) | −32.1448 | −1.23543 | −0.617713 | − | 0.786404i | \(-0.711941\pi\) | ||||
−0.617713 | + | 0.786404i | \(0.711941\pi\) | |||||||
\(678\) | 2.29649 | 0.0881960 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.638089 | 0.0244696 | ||||||||
\(681\) | −18.1428 | −0.695232 | ||||||||
\(682\) | 5.94609 | 0.227688 | ||||||||
\(683\) | −26.2292 | −1.00363 | −0.501815 | − | 0.864975i | \(-0.667334\pi\) | ||||
−0.501815 | + | 0.864975i | \(0.667334\pi\) | |||||||
\(684\) | −1.68952 | −0.0646003 | ||||||||
\(685\) | 2.47875 | 0.0947082 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.6239 | 1.43544 | ||||||||
\(688\) | 6.66821 | 0.254223 | ||||||||
\(689\) | 0.163812 | 0.00624074 | ||||||||
\(690\) | 0.586828 | 0.0223402 | ||||||||
\(691\) | −20.2617 | −0.770791 | −0.385396 | − | 0.922751i | \(-0.625935\pi\) | ||||
−0.385396 | + | 0.922751i | \(0.625935\pi\) | |||||||
\(692\) | −9.56918 | −0.363766 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.22478 | −0.198330 | ||||||||
\(695\) | −0.273432 | −0.0103719 | ||||||||
\(696\) | 6.50274 | 0.246486 | ||||||||
\(697\) | 1.70413 | 0.0645485 | ||||||||
\(698\) | −23.4754 | −0.888557 | ||||||||
\(699\) | −20.8540 | −0.788772 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.932833 | 0.0352326 | 0.0176163 | − | 0.999845i | \(-0.494392\pi\) | ||||
0.0176163 | + | 0.999845i | \(0.494392\pi\) | |||||||
\(702\) | 0.206865 | 0.00780763 | ||||||||
\(703\) | −6.63475 | −0.250234 | ||||||||
\(704\) | 2.34222 | 0.0882757 | ||||||||
\(705\) | −3.45451 | −0.130104 | ||||||||
\(706\) | −5.25312 | −0.197704 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 31.4378 | 1.18151 | ||||||||
\(709\) | −52.6076 | −1.97572 | −0.987860 | − | 0.155346i | \(-0.950351\pi\) | ||||
−0.987860 | + | 0.155346i | \(0.950351\pi\) | |||||||
\(710\) | −3.04240 | −0.114179 | ||||||||
\(711\) | −30.5002 | −1.14385 | ||||||||
\(712\) | −8.52779 | −0.319592 | ||||||||
\(713\) | −1.72340 | −0.0645418 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.117238 | −0.00438445 | ||||||||
\(716\) | 9.97650 | 0.372839 | ||||||||
\(717\) | 2.78312 | 0.103937 | ||||||||
\(718\) | −10.0526 | −0.375160 | ||||||||
\(719\) | 2.08372 | 0.0777098 | 0.0388549 | − | 0.999245i | \(-0.487629\pi\) | ||||
0.0388549 | + | 0.999245i | \(0.487629\pi\) | |||||||
\(720\) | 0.872322 | 0.0325095 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.4741 | 0.687534 | ||||||||
\(723\) | −40.7087 | −1.51397 | ||||||||
\(724\) | −24.3936 | −0.906581 | ||||||||
\(725\) | −13.6887 | −0.508387 | ||||||||
\(726\) | −12.7297 | −0.472444 | ||||||||
\(727\) | 40.7427 | 1.51106 | 0.755532 | − | 0.655112i | \(-0.227379\pi\) | ||||
0.755532 | + | 0.655112i | \(0.227379\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.8877 | −0.514360 | ||||||||
\(730\) | 1.08469 | 0.0401463 | ||||||||
\(731\) | −11.3635 | −0.420294 | ||||||||
\(732\) | 2.82045 | 0.104247 | ||||||||
\(733\) | 2.54040 | 0.0938320 | 0.0469160 | − | 0.998899i | \(-0.485061\pi\) | ||||
0.0469160 | + | 0.998899i | \(0.485061\pi\) | |||||||
\(734\) | 4.93946 | 0.182319 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.678862 | −0.0250232 | ||||||||
\(737\) | 1.59967 | 0.0589245 | ||||||||
\(738\) | 2.32969 | 0.0857572 | ||||||||
\(739\) | −0.495193 | −0.0182160 | −0.00910798 | − | 0.999959i | \(-0.502899\pi\) | ||||
−0.00910798 | + | 0.999959i | \(0.502899\pi\) | |||||||
\(740\) | 3.42561 | 0.125928 | ||||||||
\(741\) | −0.223809 | −0.00822184 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.8689 | −1.02241 | −0.511205 | − | 0.859459i | \(-0.670801\pi\) | ||||
−0.511205 | + | 0.859459i | \(0.670801\pi\) | |||||||
\(744\) | −5.86078 | −0.214867 | ||||||||
\(745\) | 1.27062 | 0.0465518 | ||||||||
\(746\) | 19.0600 | 0.697836 | ||||||||
\(747\) | −3.54628 | −0.129752 | ||||||||
\(748\) | −3.99144 | −0.145942 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.52310 | −0.311219 | ||||||||
\(751\) | −17.3440 | −0.632893 | −0.316446 | − | 0.948610i | \(-0.602490\pi\) | ||||
−0.316446 | + | 0.948610i | \(0.602490\pi\) | |||||||
\(752\) | 3.99629 | 0.145730 | ||||||||
\(753\) | −18.4258 | −0.671473 | ||||||||
\(754\) | 0.376537 | 0.0137127 | ||||||||
\(755\) | −5.98274 | −0.217734 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.664377 | 0.0241472 | 0.0120736 | − | 0.999927i | \(-0.496157\pi\) | ||||
0.0120736 | + | 0.999927i | \(0.496157\pi\) | |||||||
\(758\) | 20.8915 | 0.758813 | ||||||||
\(759\) | −3.67079 | −0.133241 | ||||||||
\(760\) | 0.271545 | 0.00984998 | ||||||||
\(761\) | −34.3582 | −1.24548 | −0.622742 | − | 0.782427i | \(-0.713981\pi\) | ||||
−0.622742 | + | 0.782427i | \(0.713981\pi\) | |||||||
\(762\) | 35.4984 | 1.28597 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.44946 | 0.160976 | ||||||||
\(765\) | −1.48655 | −0.0537464 | ||||||||
\(766\) | −36.0739 | −1.30340 | ||||||||
\(767\) | 1.82039 | 0.0657305 | ||||||||
\(768\) | −2.30861 | −0.0833049 | ||||||||
\(769\) | 14.2112 | 0.512468 | 0.256234 | − | 0.966615i | \(-0.417518\pi\) | ||||
0.256234 | + | 0.966615i | \(0.417518\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.4834 | −1.02580 | ||||||||
\(772\) | −11.2662 | −0.405478 | ||||||||
\(773\) | 50.5040 | 1.81650 | 0.908252 | − | 0.418423i | \(-0.137417\pi\) | ||||
0.908252 | + | 0.418423i | \(0.137417\pi\) | |||||||
\(774\) | −15.5349 | −0.558390 | ||||||||
\(775\) | 12.3374 | 0.443171 | ||||||||
\(776\) | 1.74259 | 0.0625552 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −35.0407 | −1.25627 | ||||||||
\(779\) | 0.725210 | 0.0259834 | ||||||||
\(780\) | 0.115556 | 0.00413757 | ||||||||
\(781\) | 19.0312 | 0.680989 | ||||||||
\(782\) | 1.15687 | 0.0413696 | ||||||||
\(783\) | 4.35883 | 0.155772 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.48970 | 0.124553 | ||||||||
\(786\) | 27.8654 | 0.993924 | ||||||||
\(787\) | 26.3396 | 0.938906 | 0.469453 | − | 0.882957i | \(-0.344451\pi\) | ||||
0.469453 | + | 0.882957i | \(0.344451\pi\) | |||||||
\(788\) | 5.60076 | 0.199519 | ||||||||
\(789\) | −57.2708 | −2.03890 | ||||||||
\(790\) | 4.90210 | 0.174409 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.45665 | −0.193894 | ||||||||
\(793\) | 0.163317 | 0.00579955 | ||||||||
\(794\) | 21.3240 | 0.756761 | ||||||||
\(795\) | 1.05928 | 0.0375689 | ||||||||
\(796\) | 5.73582 | 0.203301 | ||||||||
\(797\) | 11.4534 | 0.405700 | 0.202850 | − | 0.979210i | \(-0.434980\pi\) | ||||
0.202850 | + | 0.979210i | \(0.434980\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.81020 | −0.240928 | ||||||||
\(800\) | 4.85980 | 0.171820 | ||||||||
\(801\) | 19.8671 | 0.701970 | ||||||||
\(802\) | −2.72976 | −0.0963913 | ||||||||
\(803\) | −6.78509 | −0.239441 | ||||||||
\(804\) | −1.57672 | −0.0556065 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.339365 | −0.0119536 | ||||||||
\(807\) | 0.166648 | 0.00586629 | ||||||||
\(808\) | 16.3793 | 0.576222 | ||||||||
\(809\) | 16.2845 | 0.572532 | 0.286266 | − | 0.958150i | \(-0.407586\pi\) | ||||
0.286266 | + | 0.958150i | \(0.407586\pi\) | |||||||
\(810\) | 3.95465 | 0.138952 | ||||||||
\(811\) | 23.4547 | 0.823607 | 0.411804 | − | 0.911273i | \(-0.364899\pi\) | ||||
0.411804 | + | 0.911273i | \(0.364899\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −50.3023 | −1.76418 | ||||||||
\(814\) | −21.4283 | −0.751061 | ||||||||
\(815\) | 7.51958 | 0.263399 | ||||||||
\(816\) | 3.93418 | 0.137724 | ||||||||
\(817\) | −4.83585 | −0.169185 | ||||||||
\(818\) | −20.4532 | −0.715130 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.374437 | −0.0130759 | ||||||||
\(821\) | 32.6342 | 1.13894 | 0.569470 | − | 0.822012i | \(-0.307148\pi\) | ||||
0.569470 | + | 0.822012i | \(0.307148\pi\) | |||||||
\(822\) | 15.2829 | 0.533052 | ||||||||
\(823\) | 8.23017 | 0.286886 | 0.143443 | − | 0.989659i | \(-0.454183\pi\) | ||||
0.143443 | + | 0.989659i | \(0.454183\pi\) | |||||||
\(824\) | −0.328088 | −0.0114295 | ||||||||
\(825\) | 26.2783 | 0.914892 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.3662 | −1.78618 | −0.893089 | − | 0.449879i | \(-0.851467\pi\) | ||||
−0.893089 | + | 0.449879i | \(0.851467\pi\) | |||||||
\(828\) | 1.58154 | 0.0549623 | ||||||||
\(829\) | −42.0898 | −1.46184 | −0.730920 | − | 0.682463i | \(-0.760909\pi\) | ||||
−0.730920 | + | 0.682463i | \(0.760909\pi\) | |||||||
\(830\) | 0.569971 | 0.0197840 | ||||||||
\(831\) | 15.0281 | 0.521318 | ||||||||
\(832\) | −0.133679 | −0.00463448 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.68587 | −0.0583767 | ||||||||
\(835\) | 0.764798 | 0.0264669 | ||||||||
\(836\) | −1.69860 | −0.0587474 | ||||||||
\(837\) | −3.92852 | −0.135790 | ||||||||
\(838\) | −7.57172 | −0.261561 | ||||||||
\(839\) | 10.2124 | 0.352572 | 0.176286 | − | 0.984339i | \(-0.443592\pi\) | ||||
0.176286 | + | 0.984339i | \(0.443592\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0660 | −0.726415 | ||||||||
\(842\) | −12.0012 | −0.413589 | ||||||||
\(843\) | −65.2953 | −2.24889 | ||||||||
\(844\) | 7.41074 | 0.255088 | ||||||||
\(845\) | −4.86098 | −0.167223 | ||||||||
\(846\) | −9.31014 | −0.320089 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.22541 | −0.0420809 | ||||||||
\(849\) | −49.2993 | −1.69195 | ||||||||
\(850\) | −8.28173 | −0.284061 | ||||||||
\(851\) | 6.21072 | 0.212901 | ||||||||
\(852\) | −18.7581 | −0.642643 | ||||||||
\(853\) | −32.3872 | −1.10892 | −0.554459 | − | 0.832211i | \(-0.687075\pi\) | ||||
−0.554459 | + | 0.832211i | \(0.687075\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.632617 | −0.0216351 | ||||||||
\(856\) | −1.47989 | −0.0505816 | ||||||||
\(857\) | 55.8370 | 1.90735 | 0.953677 | − | 0.300831i | \(-0.0972642\pi\) | ||||
0.953677 | + | 0.300831i | \(0.0972642\pi\) | |||||||
\(858\) | −0.722839 | −0.0246773 | ||||||||
\(859\) | −7.27325 | −0.248160 | −0.124080 | − | 0.992272i | \(-0.539598\pi\) | ||||
−0.124080 | + | 0.992272i | \(0.539598\pi\) | |||||||
\(860\) | 2.49682 | 0.0851409 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.7132 | −0.467074 | ||||||||
\(863\) | 13.0836 | 0.445369 | 0.222685 | − | 0.974891i | \(-0.428518\pi\) | ||||
0.222685 | + | 0.974891i | \(0.428518\pi\) | |||||||
\(864\) | −1.54748 | −0.0526463 | ||||||||
\(865\) | −3.58305 | −0.121827 | ||||||||
\(866\) | −23.7704 | −0.807753 | ||||||||
\(867\) | 32.5421 | 1.10519 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.6642 | −1.04021 | ||||||||
\(870\) | 2.43486 | 0.0825496 | ||||||||
\(871\) | −0.0912989 | −0.00309354 | ||||||||
\(872\) | −10.0351 | −0.339833 | ||||||||
\(873\) | −4.05969 | −0.137400 | ||||||||
\(874\) | 0.492318 | 0.0166529 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.68774 | 0.225958 | ||||||||
\(877\) | 43.5882 | 1.47187 | 0.735935 | − | 0.677052i | \(-0.236743\pi\) | ||||
0.735935 | + | 0.677052i | \(0.236743\pi\) | |||||||
\(878\) | −19.3393 | −0.652669 | ||||||||
\(879\) | −18.0719 | −0.609550 | ||||||||
\(880\) | 0.877012 | 0.0295641 | ||||||||
\(881\) | 21.2788 | 0.716901 | 0.358451 | − | 0.933549i | \(-0.383305\pi\) | ||||
0.358451 | + | 0.933549i | \(0.383305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.1393 | −0.610435 | −0.305218 | − | 0.952283i | \(-0.598729\pi\) | ||||
−0.305218 | + | 0.952283i | \(0.598729\pi\) | |||||||
\(884\) | 0.227806 | 0.00766195 | ||||||||
\(885\) | 11.7715 | 0.395694 | ||||||||
\(886\) | −32.4468 | −1.09007 | ||||||||
\(887\) | 45.6323 | 1.53218 | 0.766092 | − | 0.642731i | \(-0.222199\pi\) | ||||
0.766092 | + | 0.642731i | \(0.222199\pi\) | |||||||
\(888\) | 21.1208 | 0.708769 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.19311 | −0.107033 | ||||||||
\(891\) | −24.7376 | −0.828741 | ||||||||
\(892\) | 1.69048 | 0.0566015 | ||||||||
\(893\) | −2.89815 | −0.0969830 | ||||||||
\(894\) | 7.83406 | 0.262010 | ||||||||
\(895\) | 3.73557 | 0.124866 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.209506 | 0.00699519 | ||||||||
\(898\) | −10.8167 | −0.360958 | ||||||||
\(899\) | −7.15071 | −0.238490 | ||||||||
\(900\) | −11.3218 | −0.377395 | ||||||||
\(901\) | 2.08827 | 0.0695702 | ||||||||
\(902\) | 2.34222 | 0.0779873 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.994747 | −0.0330848 | ||||||||
\(905\) | −9.13385 | −0.303620 | ||||||||
\(906\) | −36.8870 | −1.22549 | ||||||||
\(907\) | −39.6445 | −1.31637 | −0.658187 | − | 0.752855i | \(-0.728676\pi\) | ||||
−0.658187 | + | 0.752855i | \(0.728676\pi\) | |||||||
\(908\) | 7.85873 | 0.260801 | ||||||||
\(909\) | −38.1588 | −1.26565 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.2850 | −0.771468 | −0.385734 | − | 0.922610i | \(-0.626052\pi\) | ||||
−0.385734 | + | 0.922610i | \(0.626052\pi\) | |||||||
\(912\) | 1.67423 | 0.0554393 | ||||||||
\(913\) | −3.56535 | −0.117996 | ||||||||
\(914\) | 14.6183 | 0.483531 | ||||||||
\(915\) | 1.05608 | 0.0349129 | ||||||||
\(916\) | −16.2972 | −0.538475 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.63710 | 0.0870374 | ||||||||
\(919\) | 39.5032 | 1.30309 | 0.651544 | − | 0.758610i | \(-0.274121\pi\) | ||||
0.651544 | + | 0.758610i | \(0.274121\pi\) | |||||||
\(920\) | −0.254191 | −0.00838042 | ||||||||
\(921\) | −55.2962 | −1.82207 | ||||||||
\(922\) | 21.3560 | 0.703323 | ||||||||
\(923\) | −1.08618 | −0.0357520 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.4609 | −1.46187 | ||||||||
\(926\) | −17.3519 | −0.570220 | ||||||||
\(927\) | 0.764345 | 0.0251044 | ||||||||
\(928\) | −2.81673 | −0.0924636 | ||||||||
\(929\) | 41.4690 | 1.36055 | 0.680277 | − | 0.732955i | \(-0.261859\pi\) | ||||
0.680277 | + | 0.732955i | \(0.261859\pi\) | |||||||
\(930\) | −2.19449 | −0.0719602 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.03314 | 0.295890 | ||||||||
\(933\) | −33.4170 | −1.09402 | ||||||||
\(934\) | −10.3452 | −0.338506 | ||||||||
\(935\) | −1.49454 | −0.0488768 | ||||||||
\(936\) | 0.311431 | 0.0101794 | ||||||||
\(937\) | 32.0902 | 1.04834 | 0.524170 | − | 0.851613i | \(-0.324375\pi\) | ||||
0.524170 | + | 0.851613i | \(0.324375\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.9875 | 1.07651 | ||||||||
\(940\) | 1.49636 | 0.0488058 | ||||||||
\(941\) | −17.0335 | −0.555275 | −0.277638 | − | 0.960686i | \(-0.589551\pi\) | ||||
−0.277638 | + | 0.960686i | \(0.589551\pi\) | |||||||
\(942\) | 21.5160 | 0.701028 | ||||||||
\(943\) | −0.678862 | −0.0221068 | ||||||||
\(944\) | −13.6176 | −0.443216 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.6184 | −0.507798 | ||||||||
\(947\) | −26.5551 | −0.862923 | −0.431462 | − | 0.902131i | \(-0.642002\pi\) | ||||
−0.431462 | + | 0.902131i | \(0.642002\pi\) | |||||||
\(948\) | 30.2242 | 0.981636 | ||||||||
\(949\) | 0.387250 | 0.0125707 | ||||||||
\(950\) | −3.52438 | −0.114346 | ||||||||
\(951\) | −5.07621 | −0.164607 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.2798 | −1.11043 | −0.555215 | − | 0.831707i | \(-0.687364\pi\) | ||||
−0.555215 | + | 0.831707i | \(0.687364\pi\) | |||||||
\(954\) | 2.85484 | 0.0924289 | ||||||||
\(955\) | 1.66604 | 0.0539118 | ||||||||
\(956\) | −1.20554 | −0.0389898 | ||||||||
\(957\) | −15.2308 | −0.492343 | ||||||||
\(958\) | −37.8835 | −1.22396 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.864429 | −0.0278993 | ||||||||
\(961\) | −24.5552 | −0.792104 | ||||||||
\(962\) | 1.22299 | 0.0394308 | ||||||||
\(963\) | 3.44769 | 0.111100 | ||||||||
\(964\) | 17.6334 | 0.567933 | ||||||||
\(965\) | −4.21847 | −0.135797 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.5935 | −1.49835 | −0.749173 | − | 0.662375i | \(-0.769549\pi\) | ||||
−0.749173 | + | 0.662375i | \(0.769549\pi\) | |||||||
\(968\) | 5.51401 | 0.177227 | ||||||||
\(969\) | −2.85311 | −0.0916550 | ||||||||
\(970\) | 0.652488 | 0.0209501 | ||||||||
\(971\) | 2.67921 | 0.0859800 | 0.0429900 | − | 0.999076i | \(-0.486312\pi\) | ||||
0.0429900 | + | 0.999076i | \(0.486312\pi\) | |||||||
\(972\) | 19.7402 | 0.633168 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 18.9378 | 0.606805 | ||||||||
\(975\) | −1.49980 | −0.0480319 | ||||||||
\(976\) | −1.22171 | −0.0391059 | ||||||||
\(977\) | −47.8723 | −1.53157 | −0.765786 | − | 0.643096i | \(-0.777650\pi\) | ||||
−0.765786 | + | 0.643096i | \(0.777650\pi\) | |||||||
\(978\) | 46.3625 | 1.48251 | ||||||||
\(979\) | 19.9739 | 0.638370 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.3788 | 0.746427 | ||||||||
\(982\) | −21.3032 | −0.679811 | ||||||||
\(983\) | 13.1498 | 0.419414 | 0.209707 | − | 0.977764i | \(-0.432749\pi\) | ||||
0.209707 | + | 0.977764i | \(0.432749\pi\) | |||||||
\(984\) | −2.30861 | −0.0735959 | ||||||||
\(985\) | 2.09713 | 0.0668201 | ||||||||
\(986\) | 4.80007 | 0.152865 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0969453 | 0.00308424 | ||||||||
\(989\) | 4.52679 | 0.143944 | ||||||||
\(990\) | −2.04317 | −0.0649362 | ||||||||
\(991\) | 54.2881 | 1.72452 | 0.862260 | − | 0.506467i | \(-0.169049\pi\) | ||||
0.862260 | + | 0.506467i | \(0.169049\pi\) | |||||||
\(992\) | 2.53866 | 0.0806025 | ||||||||
\(993\) | −51.2820 | −1.62739 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.14770 | 0.0680867 | ||||||||
\(996\) | 3.51419 | 0.111352 | ||||||||
\(997\) | −8.22418 | −0.260462 | −0.130231 | − | 0.991484i | \(-0.541572\pi\) | ||||
−0.130231 | + | 0.991484i | \(0.541572\pi\) | |||||||
\(998\) | 27.3251 | 0.864962 | ||||||||
\(999\) | 14.1574 | 0.447922 |
(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 | 4018.2.a.bn.1.2 | 6 | ||
7.3 | odd | 6 | 574.2.e.g.247.2 | yes | 12 | ||
7.5 | odd | 6 | 574.2.e.g.165.2 | ✓ | 12 | ||
7.6 | odd | 2 | 4018.2.a.bo.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
574.2.e.g.165.2 | ✓ | 12 | 7.5 | odd | 6 | ||
574.2.e.g.247.2 | yes | 12 | 7.3 | odd | 6 | ||
4018.2.a.bn.1.2 | 6 | 1.1 | even | 1 | trivial | ||
4018.2.a.bo.1.5 | 6 | 7.6 | odd | 2 |