Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.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: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.69202 | −0.756695 | −0.378348 | − | 0.925664i | \(-0.623508\pi\) | ||||
−0.378348 | + | 0.925664i | \(0.623508\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.69202 | 0.535064 | ||||||||
\(11\) | −3.15883 | −0.952424 | −0.476212 | − | 0.879330i | \(-0.657991\pi\) | ||||
−0.476212 | + | 0.879330i | \(0.657991\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 1.69202 | 0.436878 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.74094 | 1.87745 | 0.938727 | − | 0.344662i | \(-0.112007\pi\) | ||||
0.938727 | + | 0.344662i | \(0.112007\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −3.15883 | −0.724686 | −0.362343 | − | 0.932045i | \(-0.618023\pi\) | ||||
−0.362343 | + | 0.932045i | \(0.618023\pi\) | |||||||
\(20\) | −1.69202 | −0.378348 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 3.15883 | 0.673466 | ||||||||
\(23\) | 7.89977 | 1.64722 | 0.823608 | − | 0.567159i | \(-0.191958\pi\) | ||||
0.823608 | + | 0.567159i | \(0.191958\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −2.13706 | −0.427413 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −4.96077 | −0.921192 | −0.460596 | − | 0.887610i | \(-0.652364\pi\) | ||||
−0.460596 | + | 0.887610i | \(0.652364\pi\) | |||||||
\(30\) | −1.69202 | −0.308919 | ||||||||
\(31\) | −4.82908 | −0.867329 | −0.433665 | − | 0.901074i | \(-0.642780\pi\) | ||||
−0.433665 | + | 0.901074i | \(0.642780\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.15883 | 0.549882 | ||||||||
\(34\) | −7.74094 | −1.32756 | ||||||||
\(35\) | −1.69202 | −0.286004 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.185981 | 0.0305750 | 0.0152875 | − | 0.999883i | \(-0.495134\pi\) | ||||
0.0152875 | + | 0.999883i | \(0.495134\pi\) | |||||||
\(38\) | 3.15883 | 0.512430 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.69202 | 0.267532 | ||||||||
\(41\) | −0.978230 | −0.152774 | −0.0763869 | − | 0.997078i | \(-0.524338\pi\) | ||||
−0.0763869 | + | 0.997078i | \(0.524338\pi\) | |||||||
\(42\) | 1.00000 | 0.154303 | ||||||||
\(43\) | −8.19806 | −1.25019 | −0.625096 | − | 0.780548i | \(-0.714940\pi\) | ||||
−0.625096 | + | 0.780548i | \(0.714940\pi\) | |||||||
\(44\) | −3.15883 | −0.476212 | ||||||||
\(45\) | −1.69202 | −0.252232 | ||||||||
\(46\) | −7.89977 | −1.16476 | ||||||||
\(47\) | −2.78017 | −0.405529 | −0.202765 | − | 0.979228i | \(-0.564993\pi\) | ||||
−0.202765 | + | 0.979228i | \(0.564993\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.13706 | 0.302226 | ||||||||
\(51\) | −7.74094 | −1.08395 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.652793 | −0.0896680 | −0.0448340 | − | 0.998994i | \(-0.514276\pi\) | ||||
−0.0448340 | + | 0.998994i | \(0.514276\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 5.34481 | 0.720695 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 3.15883 | 0.418398 | ||||||||
\(58\) | 4.96077 | 0.651381 | ||||||||
\(59\) | 4.80194 | 0.625159 | 0.312580 | − | 0.949892i | \(-0.398807\pi\) | ||||
0.312580 | + | 0.949892i | \(0.398807\pi\) | |||||||
\(60\) | 1.69202 | 0.218439 | ||||||||
\(61\) | 3.21983 | 0.412257 | 0.206129 | − | 0.978525i | \(-0.433913\pi\) | ||||
0.206129 | + | 0.978525i | \(0.433913\pi\) | |||||||
\(62\) | 4.82908 | 0.613294 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.15883 | −0.388826 | ||||||||
\(67\) | 4.52111 | 0.552341 | 0.276171 | − | 0.961109i | \(-0.410935\pi\) | ||||
0.276171 | + | 0.961109i | \(0.410935\pi\) | |||||||
\(68\) | 7.74094 | 0.938727 | ||||||||
\(69\) | −7.89977 | −0.951021 | ||||||||
\(70\) | 1.69202 | 0.202235 | ||||||||
\(71\) | 1.20775 | 0.143334 | 0.0716668 | − | 0.997429i | \(-0.477168\pi\) | ||||
0.0716668 | + | 0.997429i | \(0.477168\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 14.1564 | 1.65689 | 0.828443 | − | 0.560073i | \(-0.189227\pi\) | ||||
0.828443 | + | 0.560073i | \(0.189227\pi\) | |||||||
\(74\) | −0.185981 | −0.0216198 | ||||||||
\(75\) | 2.13706 | 0.246767 | ||||||||
\(76\) | −3.15883 | −0.362343 | ||||||||
\(77\) | −3.15883 | −0.359982 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.33944 | −0.825751 | −0.412876 | − | 0.910787i | \(-0.635476\pi\) | ||||
−0.412876 | + | 0.910787i | \(0.635476\pi\) | |||||||
\(80\) | −1.69202 | −0.189174 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.978230 | 0.108027 | ||||||||
\(83\) | 8.32304 | 0.913573 | 0.456786 | − | 0.889576i | \(-0.349000\pi\) | ||||
0.456786 | + | 0.889576i | \(0.349000\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | −13.0978 | −1.42066 | ||||||||
\(86\) | 8.19806 | 0.884020 | ||||||||
\(87\) | 4.96077 | 0.531851 | ||||||||
\(88\) | 3.15883 | 0.336733 | ||||||||
\(89\) | −13.5526 | −1.43657 | −0.718285 | − | 0.695749i | \(-0.755072\pi\) | ||||
−0.718285 | + | 0.695749i | \(0.755072\pi\) | |||||||
\(90\) | 1.69202 | 0.178355 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.89977 | 0.823608 | ||||||||
\(93\) | 4.82908 | 0.500753 | ||||||||
\(94\) | 2.78017 | 0.286752 | ||||||||
\(95\) | 5.34481 | 0.548366 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.83340 | 0.795361 | 0.397680 | − | 0.917524i | \(-0.369815\pi\) | ||||
0.397680 | + | 0.917524i | \(0.369815\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −3.15883 | −0.317475 | ||||||||
\(100\) | −2.13706 | −0.213706 | ||||||||
\(101\) | 15.2228 | 1.51473 | 0.757363 | − | 0.652994i | \(-0.226487\pi\) | ||||
0.757363 | + | 0.652994i | \(0.226487\pi\) | |||||||
\(102\) | 7.74094 | 0.766467 | ||||||||
\(103\) | −11.6528 | −1.14818 | −0.574092 | − | 0.818791i | \(-0.694645\pi\) | ||||
−0.574092 | + | 0.818791i | \(0.694645\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.69202 | 0.165124 | ||||||||
\(106\) | 0.652793 | 0.0634048 | ||||||||
\(107\) | 14.5797 | 1.40947 | 0.704737 | − | 0.709469i | \(-0.251065\pi\) | ||||
0.704737 | + | 0.709469i | \(0.251065\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −6.29590 | −0.603038 | −0.301519 | − | 0.953460i | \(-0.597494\pi\) | ||||
−0.301519 | + | 0.953460i | \(0.597494\pi\) | |||||||
\(110\) | −5.34481 | −0.509608 | ||||||||
\(111\) | −0.185981 | −0.0176525 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 15.1860 | 1.42858 | 0.714288 | − | 0.699851i | \(-0.246750\pi\) | ||||
0.714288 | + | 0.699851i | \(0.246750\pi\) | |||||||
\(114\) | −3.15883 | −0.295852 | ||||||||
\(115\) | −13.3666 | −1.24644 | ||||||||
\(116\) | −4.96077 | −0.460596 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.80194 | −0.442054 | ||||||||
\(119\) | 7.74094 | 0.709611 | ||||||||
\(120\) | −1.69202 | −0.154460 | ||||||||
\(121\) | −1.02177 | −0.0928882 | ||||||||
\(122\) | −3.21983 | −0.291510 | ||||||||
\(123\) | 0.978230 | 0.0882040 | ||||||||
\(124\) | −4.82908 | −0.433665 | ||||||||
\(125\) | 12.0761 | 1.08012 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 11.8629 | 1.05267 | 0.526333 | − | 0.850279i | \(-0.323567\pi\) | ||||
0.526333 | + | 0.850279i | \(0.323567\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.19806 | 0.721799 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.56465 | −0.136704 | −0.0683519 | − | 0.997661i | \(-0.521774\pi\) | ||||
−0.0683519 | + | 0.997661i | \(0.521774\pi\) | |||||||
\(132\) | 3.15883 | 0.274941 | ||||||||
\(133\) | −3.15883 | −0.273906 | ||||||||
\(134\) | −4.52111 | −0.390564 | ||||||||
\(135\) | 1.69202 | 0.145626 | ||||||||
\(136\) | −7.74094 | −0.663780 | ||||||||
\(137\) | −20.5700 | −1.75742 | −0.878708 | − | 0.477360i | \(-0.841594\pi\) | ||||
−0.878708 | + | 0.477360i | \(0.841594\pi\) | |||||||
\(138\) | 7.89977 | 0.672473 | ||||||||
\(139\) | −22.5308 | −1.91104 | −0.955519 | − | 0.294931i | \(-0.904703\pi\) | ||||
−0.955519 | + | 0.294931i | \(0.904703\pi\) | |||||||
\(140\) | −1.69202 | −0.143002 | ||||||||
\(141\) | 2.78017 | 0.234132 | ||||||||
\(142\) | −1.20775 | −0.101352 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.39373 | 0.697061 | ||||||||
\(146\) | −14.1564 | −1.17160 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0.185981 | 0.0152875 | ||||||||
\(149\) | 1.60925 | 0.131835 | 0.0659175 | − | 0.997825i | \(-0.479003\pi\) | ||||
0.0659175 | + | 0.997825i | \(0.479003\pi\) | |||||||
\(150\) | −2.13706 | −0.174490 | ||||||||
\(151\) | −13.1709 | −1.07183 | −0.535917 | − | 0.844271i | \(-0.680034\pi\) | ||||
−0.535917 | + | 0.844271i | \(0.680034\pi\) | |||||||
\(152\) | 3.15883 | 0.256215 | ||||||||
\(153\) | 7.74094 | 0.625818 | ||||||||
\(154\) | 3.15883 | 0.254546 | ||||||||
\(155\) | 8.17092 | 0.656304 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.61596 | −0.208776 | −0.104388 | − | 0.994537i | \(-0.533288\pi\) | ||||
−0.104388 | + | 0.994537i | \(0.533288\pi\) | |||||||
\(158\) | 7.33944 | 0.583894 | ||||||||
\(159\) | 0.652793 | 0.0517698 | ||||||||
\(160\) | 1.69202 | 0.133766 | ||||||||
\(161\) | 7.89977 | 0.622589 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −0.853248 | −0.0668315 | −0.0334158 | − | 0.999442i | \(-0.510639\pi\) | ||||
−0.0334158 | + | 0.999442i | \(0.510639\pi\) | |||||||
\(164\) | −0.978230 | −0.0763869 | ||||||||
\(165\) | −5.34481 | −0.416093 | ||||||||
\(166\) | −8.32304 | −0.645993 | ||||||||
\(167\) | −14.8944 | −1.15256 | −0.576281 | − | 0.817251i | \(-0.695497\pi\) | ||||
−0.576281 | + | 0.817251i | \(0.695497\pi\) | |||||||
\(168\) | 1.00000 | 0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 13.0978 | 1.00456 | ||||||||
\(171\) | −3.15883 | −0.241562 | ||||||||
\(172\) | −8.19806 | −0.625096 | ||||||||
\(173\) | −7.28621 | −0.553960 | −0.276980 | − | 0.960876i | \(-0.589334\pi\) | ||||
−0.276980 | + | 0.960876i | \(0.589334\pi\) | |||||||
\(174\) | −4.96077 | −0.376075 | ||||||||
\(175\) | −2.13706 | −0.161547 | ||||||||
\(176\) | −3.15883 | −0.238106 | ||||||||
\(177\) | −4.80194 | −0.360936 | ||||||||
\(178\) | 13.5526 | 1.01581 | ||||||||
\(179\) | −4.10992 | −0.307190 | −0.153595 | − | 0.988134i | \(-0.549085\pi\) | ||||
−0.153595 | + | 0.988134i | \(0.549085\pi\) | |||||||
\(180\) | −1.69202 | −0.126116 | ||||||||
\(181\) | −8.63640 | −0.641939 | −0.320969 | − | 0.947090i | \(-0.604009\pi\) | ||||
−0.320969 | + | 0.947090i | \(0.604009\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.21983 | −0.238017 | ||||||||
\(184\) | −7.89977 | −0.582379 | ||||||||
\(185\) | −0.314683 | −0.0231360 | ||||||||
\(186\) | −4.82908 | −0.354086 | ||||||||
\(187\) | −24.4523 | −1.78813 | ||||||||
\(188\) | −2.78017 | −0.202765 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −5.34481 | −0.387754 | ||||||||
\(191\) | 26.9922 | 1.95309 | 0.976545 | − | 0.215315i | \(-0.0690779\pi\) | ||||
0.976545 | + | 0.215315i | \(0.0690779\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −16.2174 | −1.16736 | −0.583678 | − | 0.811985i | \(-0.698387\pi\) | ||||
−0.583678 | + | 0.811985i | \(0.698387\pi\) | |||||||
\(194\) | −7.83340 | −0.562405 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 21.6625 | 1.54339 | 0.771694 | − | 0.635994i | \(-0.219410\pi\) | ||||
0.771694 | + | 0.635994i | \(0.219410\pi\) | |||||||
\(198\) | 3.15883 | 0.224489 | ||||||||
\(199\) | −8.81700 | −0.625021 | −0.312510 | − | 0.949914i | \(-0.601170\pi\) | ||||
−0.312510 | + | 0.949914i | \(0.601170\pi\) | |||||||
\(200\) | 2.13706 | 0.151113 | ||||||||
\(201\) | −4.52111 | −0.318894 | ||||||||
\(202\) | −15.2228 | −1.07107 | ||||||||
\(203\) | −4.96077 | −0.348178 | ||||||||
\(204\) | −7.74094 | −0.541974 | ||||||||
\(205\) | 1.65519 | 0.115603 | ||||||||
\(206\) | 11.6528 | 0.811889 | ||||||||
\(207\) | 7.89977 | 0.549072 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.97823 | 0.690209 | ||||||||
\(210\) | −1.69202 | −0.116761 | ||||||||
\(211\) | 0.753020 | 0.0518401 | 0.0259200 | − | 0.999664i | \(-0.491748\pi\) | ||||
0.0259200 | + | 0.999664i | \(0.491748\pi\) | |||||||
\(212\) | −0.652793 | −0.0448340 | ||||||||
\(213\) | −1.20775 | −0.0827537 | ||||||||
\(214\) | −14.5797 | −0.996649 | ||||||||
\(215\) | 13.8713 | 0.946015 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.82908 | −0.327820 | ||||||||
\(218\) | 6.29590 | 0.426412 | ||||||||
\(219\) | −14.1564 | −0.956604 | ||||||||
\(220\) | 5.34481 | 0.360347 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.185981 | 0.0124822 | ||||||||
\(223\) | 2.14377 | 0.143557 | 0.0717787 | − | 0.997421i | \(-0.477132\pi\) | ||||
0.0717787 | + | 0.997421i | \(0.477132\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −2.13706 | −0.142471 | ||||||||
\(226\) | −15.1860 | −1.01016 | ||||||||
\(227\) | −21.3327 | −1.41590 | −0.707952 | − | 0.706261i | \(-0.750381\pi\) | ||||
−0.707952 | + | 0.706261i | \(0.750381\pi\) | |||||||
\(228\) | 3.15883 | 0.209199 | ||||||||
\(229\) | 15.3502 | 1.01437 | 0.507185 | − | 0.861837i | \(-0.330686\pi\) | ||||
0.507185 | + | 0.861837i | \(0.330686\pi\) | |||||||
\(230\) | 13.3666 | 0.881366 | ||||||||
\(231\) | 3.15883 | 0.207836 | ||||||||
\(232\) | 4.96077 | 0.325691 | ||||||||
\(233\) | 23.1468 | 1.51639 | 0.758197 | − | 0.652025i | \(-0.226080\pi\) | ||||
0.758197 | + | 0.652025i | \(0.226080\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.70410 | 0.306862 | ||||||||
\(236\) | 4.80194 | 0.312580 | ||||||||
\(237\) | 7.33944 | 0.476748 | ||||||||
\(238\) | −7.74094 | −0.501771 | ||||||||
\(239\) | 17.8538 | 1.15487 | 0.577434 | − | 0.816437i | \(-0.304054\pi\) | ||||
0.577434 | + | 0.816437i | \(0.304054\pi\) | |||||||
\(240\) | 1.69202 | 0.109220 | ||||||||
\(241\) | −16.4179 | −1.05757 | −0.528785 | − | 0.848756i | \(-0.677352\pi\) | ||||
−0.528785 | + | 0.848756i | \(0.677352\pi\) | |||||||
\(242\) | 1.02177 | 0.0656819 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 3.21983 | 0.206129 | ||||||||
\(245\) | −1.69202 | −0.108099 | ||||||||
\(246\) | −0.978230 | −0.0623696 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.82908 | 0.306647 | ||||||||
\(249\) | −8.32304 | −0.527451 | ||||||||
\(250\) | −12.0761 | −0.763757 | ||||||||
\(251\) | −23.9124 | −1.50934 | −0.754670 | − | 0.656104i | \(-0.772203\pi\) | ||||
−0.754670 | + | 0.656104i | \(0.772203\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −24.9541 | −1.56885 | ||||||||
\(254\) | −11.8629 | −0.744347 | ||||||||
\(255\) | 13.0978 | 0.820218 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.77479 | 0.547356 | 0.273678 | − | 0.961821i | \(-0.411760\pi\) | ||||
0.273678 | + | 0.961821i | \(0.411760\pi\) | |||||||
\(258\) | −8.19806 | −0.510389 | ||||||||
\(259\) | 0.185981 | 0.0115563 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.96077 | −0.307064 | ||||||||
\(262\) | 1.56465 | 0.0966642 | ||||||||
\(263\) | 6.78448 | 0.418349 | 0.209174 | − | 0.977878i | \(-0.432922\pi\) | ||||
0.209174 | + | 0.977878i | \(0.432922\pi\) | |||||||
\(264\) | −3.15883 | −0.194413 | ||||||||
\(265\) | 1.10454 | 0.0678513 | ||||||||
\(266\) | 3.15883 | 0.193681 | ||||||||
\(267\) | 13.5526 | 0.829404 | ||||||||
\(268\) | 4.52111 | 0.276171 | ||||||||
\(269\) | −5.13706 | −0.313212 | −0.156606 | − | 0.987661i | \(-0.550055\pi\) | ||||
−0.156606 | + | 0.987661i | \(0.550055\pi\) | |||||||
\(270\) | −1.69202 | −0.102973 | ||||||||
\(271\) | 25.7995 | 1.56721 | 0.783605 | − | 0.621259i | \(-0.213378\pi\) | ||||
0.783605 | + | 0.621259i | \(0.213378\pi\) | |||||||
\(272\) | 7.74094 | 0.469363 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.5700 | 1.24268 | ||||||||
\(275\) | 6.75063 | 0.407078 | ||||||||
\(276\) | −7.89977 | −0.475510 | ||||||||
\(277\) | 19.9976 | 1.20154 | 0.600770 | − | 0.799422i | \(-0.294861\pi\) | ||||
0.600770 | + | 0.799422i | \(0.294861\pi\) | |||||||
\(278\) | 22.5308 | 1.35131 | ||||||||
\(279\) | −4.82908 | −0.289110 | ||||||||
\(280\) | 1.69202 | 0.101118 | ||||||||
\(281\) | −18.5851 | −1.10869 | −0.554347 | − | 0.832286i | \(-0.687032\pi\) | ||||
−0.554347 | + | 0.832286i | \(0.687032\pi\) | |||||||
\(282\) | −2.78017 | −0.165557 | ||||||||
\(283\) | −4.35152 | −0.258671 | −0.129335 | − | 0.991601i | \(-0.541284\pi\) | ||||
−0.129335 | + | 0.991601i | \(0.541284\pi\) | |||||||
\(284\) | 1.20775 | 0.0716668 | ||||||||
\(285\) | −5.34481 | −0.316599 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.978230 | −0.0577431 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 42.9221 | 2.52483 | ||||||||
\(290\) | −8.39373 | −0.492897 | ||||||||
\(291\) | −7.83340 | −0.459202 | ||||||||
\(292\) | 14.1564 | 0.828443 | ||||||||
\(293\) | −7.14138 | −0.417204 | −0.208602 | − | 0.978001i | \(-0.566891\pi\) | ||||
−0.208602 | + | 0.978001i | \(0.566891\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −8.12498 | −0.473055 | ||||||||
\(296\) | −0.185981 | −0.0108099 | ||||||||
\(297\) | 3.15883 | 0.183294 | ||||||||
\(298\) | −1.60925 | −0.0932215 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.13706 | 0.123383 | ||||||||
\(301\) | −8.19806 | −0.472528 | ||||||||
\(302\) | 13.1709 | 0.757901 | ||||||||
\(303\) | −15.2228 | −0.874528 | ||||||||
\(304\) | −3.15883 | −0.181172 | ||||||||
\(305\) | −5.44803 | −0.311953 | ||||||||
\(306\) | −7.74094 | −0.442520 | ||||||||
\(307\) | 3.13467 | 0.178905 | 0.0894525 | − | 0.995991i | \(-0.471488\pi\) | ||||
0.0894525 | + | 0.995991i | \(0.471488\pi\) | |||||||
\(308\) | −3.15883 | −0.179991 | ||||||||
\(309\) | 11.6528 | 0.662904 | ||||||||
\(310\) | −8.17092 | −0.464077 | ||||||||
\(311\) | −32.7875 | −1.85921 | −0.929603 | − | 0.368562i | \(-0.879850\pi\) | ||||
−0.929603 | + | 0.368562i | \(0.879850\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.5985 | 0.655586 | 0.327793 | − | 0.944750i | \(-0.393695\pi\) | ||||
0.327793 | + | 0.944750i | \(0.393695\pi\) | |||||||
\(314\) | 2.61596 | 0.147627 | ||||||||
\(315\) | −1.69202 | −0.0953346 | ||||||||
\(316\) | −7.33944 | −0.412876 | ||||||||
\(317\) | 3.71810 | 0.208830 | 0.104415 | − | 0.994534i | \(-0.466703\pi\) | ||||
0.104415 | + | 0.994534i | \(0.466703\pi\) | |||||||
\(318\) | −0.652793 | −0.0366068 | ||||||||
\(319\) | 15.6703 | 0.877366 | ||||||||
\(320\) | −1.69202 | −0.0945869 | ||||||||
\(321\) | −14.5797 | −0.813760 | ||||||||
\(322\) | −7.89977 | −0.440237 | ||||||||
\(323\) | −24.4523 | −1.36056 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.853248 | 0.0472570 | ||||||||
\(327\) | 6.29590 | 0.348164 | ||||||||
\(328\) | 0.978230 | 0.0540137 | ||||||||
\(329\) | −2.78017 | −0.153276 | ||||||||
\(330\) | 5.34481 | 0.294222 | ||||||||
\(331\) | −15.8532 | −0.871373 | −0.435687 | − | 0.900098i | \(-0.643494\pi\) | ||||
−0.435687 | + | 0.900098i | \(0.643494\pi\) | |||||||
\(332\) | 8.32304 | 0.456786 | ||||||||
\(333\) | 0.185981 | 0.0101917 | ||||||||
\(334\) | 14.8944 | 0.814985 | ||||||||
\(335\) | −7.64981 | −0.417954 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | −26.2597 | −1.43045 | −0.715227 | − | 0.698892i | \(-0.753677\pi\) | ||||
−0.715227 | + | 0.698892i | \(0.753677\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.1860 | −0.824789 | ||||||||
\(340\) | −13.0978 | −0.710330 | ||||||||
\(341\) | 15.2543 | 0.826065 | ||||||||
\(342\) | 3.15883 | 0.170810 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 8.19806 | 0.442010 | ||||||||
\(345\) | 13.3666 | 0.719633 | ||||||||
\(346\) | 7.28621 | 0.391709 | ||||||||
\(347\) | −16.3099 | −0.875561 | −0.437781 | − | 0.899082i | \(-0.644235\pi\) | ||||
−0.437781 | + | 0.899082i | \(0.644235\pi\) | |||||||
\(348\) | 4.96077 | 0.265925 | ||||||||
\(349\) | −34.3937 | −1.84105 | −0.920527 | − | 0.390679i | \(-0.872240\pi\) | ||||
−0.920527 | + | 0.390679i | \(0.872240\pi\) | |||||||
\(350\) | 2.13706 | 0.114231 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.15883 | 0.168366 | ||||||||
\(353\) | −16.3284 | −0.869074 | −0.434537 | − | 0.900654i | \(-0.643088\pi\) | ||||
−0.434537 | + | 0.900654i | \(0.643088\pi\) | |||||||
\(354\) | 4.80194 | 0.255220 | ||||||||
\(355\) | −2.04354 | −0.108460 | ||||||||
\(356\) | −13.5526 | −0.718285 | ||||||||
\(357\) | −7.74094 | −0.409694 | ||||||||
\(358\) | 4.10992 | 0.217216 | ||||||||
\(359\) | 21.0248 | 1.10964 | 0.554822 | − | 0.831969i | \(-0.312786\pi\) | ||||
0.554822 | + | 0.831969i | \(0.312786\pi\) | |||||||
\(360\) | 1.69202 | 0.0891774 | ||||||||
\(361\) | −9.02177 | −0.474830 | ||||||||
\(362\) | 8.63640 | 0.453919 | ||||||||
\(363\) | 1.02177 | 0.0536290 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.9530 | −1.25376 | ||||||||
\(366\) | 3.21983 | 0.168303 | ||||||||
\(367\) | −23.0858 | −1.20507 | −0.602533 | − | 0.798094i | \(-0.705842\pi\) | ||||
−0.602533 | + | 0.798094i | \(0.705842\pi\) | |||||||
\(368\) | 7.89977 | 0.411804 | ||||||||
\(369\) | −0.978230 | −0.0509246 | ||||||||
\(370\) | 0.314683 | 0.0163596 | ||||||||
\(371\) | −0.652793 | −0.0338913 | ||||||||
\(372\) | 4.82908 | 0.250376 | ||||||||
\(373\) | −16.6189 | −0.860496 | −0.430248 | − | 0.902711i | \(-0.641574\pi\) | ||||
−0.430248 | + | 0.902711i | \(0.641574\pi\) | |||||||
\(374\) | 24.4523 | 1.26440 | ||||||||
\(375\) | −12.0761 | −0.623605 | ||||||||
\(376\) | 2.78017 | 0.143376 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000 | 0.0514344 | ||||||||
\(379\) | 16.4131 | 0.843085 | 0.421542 | − | 0.906809i | \(-0.361489\pi\) | ||||
0.421542 | + | 0.906809i | \(0.361489\pi\) | |||||||
\(380\) | 5.34481 | 0.274183 | ||||||||
\(381\) | −11.8629 | −0.607757 | ||||||||
\(382\) | −26.9922 | −1.38104 | ||||||||
\(383\) | −0.241603 | −0.0123453 | −0.00617266 | − | 0.999981i | \(-0.501965\pi\) | ||||
−0.00617266 | + | 0.999981i | \(0.501965\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 5.34481 | 0.272397 | ||||||||
\(386\) | 16.2174 | 0.825446 | ||||||||
\(387\) | −8.19806 | −0.416731 | ||||||||
\(388\) | 7.83340 | 0.397680 | ||||||||
\(389\) | −28.5042 | −1.44522 | −0.722611 | − | 0.691255i | \(-0.757058\pi\) | ||||
−0.722611 | + | 0.691255i | \(0.757058\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61.1517 | 3.09257 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 1.56465 | 0.0789260 | ||||||||
\(394\) | −21.6625 | −1.09134 | ||||||||
\(395\) | 12.4185 | 0.624842 | ||||||||
\(396\) | −3.15883 | −0.158737 | ||||||||
\(397\) | −13.8009 | −0.692646 | −0.346323 | − | 0.938115i | \(-0.612570\pi\) | ||||
−0.346323 | + | 0.938115i | \(0.612570\pi\) | |||||||
\(398\) | 8.81700 | 0.441956 | ||||||||
\(399\) | 3.15883 | 0.158139 | ||||||||
\(400\) | −2.13706 | −0.106853 | ||||||||
\(401\) | 20.3134 | 1.01440 | 0.507200 | − | 0.861828i | \(-0.330680\pi\) | ||||
0.507200 | + | 0.861828i | \(0.330680\pi\) | |||||||
\(402\) | 4.52111 | 0.225492 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 15.2228 | 0.757363 | ||||||||
\(405\) | −1.69202 | −0.0840772 | ||||||||
\(406\) | 4.96077 | 0.246199 | ||||||||
\(407\) | −0.587482 | −0.0291204 | ||||||||
\(408\) | 7.74094 | 0.383234 | ||||||||
\(409\) | 21.0683 | 1.04176 | 0.520880 | − | 0.853630i | \(-0.325604\pi\) | ||||
0.520880 | + | 0.853630i | \(0.325604\pi\) | |||||||
\(410\) | −1.65519 | −0.0817438 | ||||||||
\(411\) | 20.5700 | 1.01464 | ||||||||
\(412\) | −11.6528 | −0.574092 | ||||||||
\(413\) | 4.80194 | 0.236288 | ||||||||
\(414\) | −7.89977 | −0.388253 | ||||||||
\(415\) | −14.0828 | −0.691296 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.5308 | 1.10334 | ||||||||
\(418\) | −9.97823 | −0.488051 | ||||||||
\(419\) | −0.486663 | −0.0237751 | −0.0118875 | − | 0.999929i | \(-0.503784\pi\) | ||||
−0.0118875 | + | 0.999929i | \(0.503784\pi\) | |||||||
\(420\) | 1.69202 | 0.0825622 | ||||||||
\(421\) | −26.4644 | −1.28980 | −0.644898 | − | 0.764268i | \(-0.723100\pi\) | ||||
−0.644898 | + | 0.764268i | \(0.723100\pi\) | |||||||
\(422\) | −0.753020 | −0.0366565 | ||||||||
\(423\) | −2.78017 | −0.135176 | ||||||||
\(424\) | 0.652793 | 0.0317024 | ||||||||
\(425\) | −16.5429 | −0.802447 | ||||||||
\(426\) | 1.20775 | 0.0585157 | ||||||||
\(427\) | 3.21983 | 0.155819 | ||||||||
\(428\) | 14.5797 | 0.704737 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.8713 | −0.668933 | ||||||||
\(431\) | −17.2476 | −0.830786 | −0.415393 | − | 0.909642i | \(-0.636356\pi\) | ||||
−0.415393 | + | 0.909642i | \(0.636356\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 2.78687 | 0.133929 | 0.0669643 | − | 0.997755i | \(-0.478669\pi\) | ||||
0.0669643 | + | 0.997755i | \(0.478669\pi\) | |||||||
\(434\) | 4.82908 | 0.231803 | ||||||||
\(435\) | −8.39373 | −0.402449 | ||||||||
\(436\) | −6.29590 | −0.301519 | ||||||||
\(437\) | −24.9541 | −1.19371 | ||||||||
\(438\) | 14.1564 | 0.676421 | ||||||||
\(439\) | −21.4808 | −1.02522 | −0.512612 | − | 0.858621i | \(-0.671322\pi\) | ||||
−0.512612 | + | 0.858621i | \(0.671322\pi\) | |||||||
\(440\) | −5.34481 | −0.254804 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.85623 | 0.468284 | 0.234142 | − | 0.972202i | \(-0.424772\pi\) | ||||
0.234142 | + | 0.972202i | \(0.424772\pi\) | |||||||
\(444\) | −0.185981 | −0.00882625 | ||||||||
\(445\) | 22.9312 | 1.08704 | ||||||||
\(446\) | −2.14377 | −0.101510 | ||||||||
\(447\) | −1.60925 | −0.0761150 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −10.8358 | −0.511373 | −0.255686 | − | 0.966760i | \(-0.582301\pi\) | ||||
−0.255686 | + | 0.966760i | \(0.582301\pi\) | |||||||
\(450\) | 2.13706 | 0.100742 | ||||||||
\(451\) | 3.09006 | 0.145505 | ||||||||
\(452\) | 15.1860 | 0.714288 | ||||||||
\(453\) | 13.1709 | 0.618824 | ||||||||
\(454\) | 21.3327 | 1.00119 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.15883 | −0.147926 | ||||||||
\(457\) | 15.5386 | 0.726863 | 0.363432 | − | 0.931621i | \(-0.381605\pi\) | ||||
0.363432 | + | 0.931621i | \(0.381605\pi\) | |||||||
\(458\) | −15.3502 | −0.717267 | ||||||||
\(459\) | −7.74094 | −0.361316 | ||||||||
\(460\) | −13.3666 | −0.623220 | ||||||||
\(461\) | 5.55389 | 0.258671 | 0.129335 | − | 0.991601i | \(-0.458716\pi\) | ||||
0.129335 | + | 0.991601i | \(0.458716\pi\) | |||||||
\(462\) | −3.15883 | −0.146962 | ||||||||
\(463\) | −8.29291 | −0.385404 | −0.192702 | − | 0.981257i | \(-0.561725\pi\) | ||||
−0.192702 | + | 0.981257i | \(0.561725\pi\) | |||||||
\(464\) | −4.96077 | −0.230298 | ||||||||
\(465\) | −8.17092 | −0.378917 | ||||||||
\(466\) | −23.1468 | −1.07225 | ||||||||
\(467\) | −22.7071 | −1.05076 | −0.525379 | − | 0.850868i | \(-0.676077\pi\) | ||||
−0.525379 | + | 0.850868i | \(0.676077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.52111 | 0.208765 | ||||||||
\(470\) | −4.70410 | −0.216984 | ||||||||
\(471\) | 2.61596 | 0.120537 | ||||||||
\(472\) | −4.80194 | −0.221027 | ||||||||
\(473\) | 25.8963 | 1.19071 | ||||||||
\(474\) | −7.33944 | −0.337112 | ||||||||
\(475\) | 6.75063 | 0.309740 | ||||||||
\(476\) | 7.74094 | 0.354805 | ||||||||
\(477\) | −0.652793 | −0.0298893 | ||||||||
\(478\) | −17.8538 | −0.816616 | ||||||||
\(479\) | −22.9245 | −1.04745 | −0.523724 | − | 0.851888i | \(-0.675458\pi\) | ||||
−0.523724 | + | 0.851888i | \(0.675458\pi\) | |||||||
\(480\) | −1.69202 | −0.0772299 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 16.4179 | 0.747815 | ||||||||
\(483\) | −7.89977 | −0.359452 | ||||||||
\(484\) | −1.02177 | −0.0464441 | ||||||||
\(485\) | −13.2543 | −0.601846 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −7.97525 | −0.361393 | −0.180696 | − | 0.983539i | \(-0.557835\pi\) | ||||
−0.180696 | + | 0.983539i | \(0.557835\pi\) | |||||||
\(488\) | −3.21983 | −0.145755 | ||||||||
\(489\) | 0.853248 | 0.0385852 | ||||||||
\(490\) | 1.69202 | 0.0764377 | ||||||||
\(491\) | −25.0116 | −1.12876 | −0.564379 | − | 0.825516i | \(-0.690884\pi\) | ||||
−0.564379 | + | 0.825516i | \(0.690884\pi\) | |||||||
\(492\) | 0.978230 | 0.0441020 | ||||||||
\(493\) | −38.4010 | −1.72950 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.34481 | 0.240232 | ||||||||
\(496\) | −4.82908 | −0.216832 | ||||||||
\(497\) | 1.20775 | 0.0541750 | ||||||||
\(498\) | 8.32304 | 0.372965 | ||||||||
\(499\) | −11.7168 | −0.524515 | −0.262257 | − | 0.964998i | \(-0.584467\pi\) | ||||
−0.262257 | + | 0.964998i | \(0.584467\pi\) | |||||||
\(500\) | 12.0761 | 0.540058 | ||||||||
\(501\) | 14.8944 | 0.665433 | ||||||||
\(502\) | 23.9124 | 1.06726 | ||||||||
\(503\) | 6.62133 | 0.295231 | 0.147615 | − | 0.989045i | \(-0.452840\pi\) | ||||
0.147615 | + | 0.989045i | \(0.452840\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −25.7573 | −1.14619 | ||||||||
\(506\) | 24.9541 | 1.10934 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.8629 | 0.526333 | ||||||||
\(509\) | −33.6728 | −1.49252 | −0.746259 | − | 0.665655i | \(-0.768152\pi\) | ||||
−0.746259 | + | 0.665655i | \(0.768152\pi\) | |||||||
\(510\) | −13.0978 | −0.579982 | ||||||||
\(511\) | 14.1564 | 0.626244 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.15883 | 0.139466 | ||||||||
\(514\) | −8.77479 | −0.387039 | ||||||||
\(515\) | 19.7168 | 0.868825 | ||||||||
\(516\) | 8.19806 | 0.360900 | ||||||||
\(517\) | 8.78209 | 0.386236 | ||||||||
\(518\) | −0.185981 | −0.00817152 | ||||||||
\(519\) | 7.28621 | 0.319829 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.73125 | −0.294901 | −0.147451 | − | 0.989069i | \(-0.547107\pi\) | ||||
−0.147451 | + | 0.989069i | \(0.547107\pi\) | |||||||
\(522\) | 4.96077 | 0.217127 | ||||||||
\(523\) | 4.01938 | 0.175755 | 0.0878776 | − | 0.996131i | \(-0.471992\pi\) | ||||
0.0878776 | + | 0.996131i | \(0.471992\pi\) | |||||||
\(524\) | −1.56465 | −0.0683519 | ||||||||
\(525\) | 2.13706 | 0.0932691 | ||||||||
\(526\) | −6.78448 | −0.295817 | ||||||||
\(527\) | −37.3817 | −1.62837 | ||||||||
\(528\) | 3.15883 | 0.137471 | ||||||||
\(529\) | 39.4064 | 1.71332 | ||||||||
\(530\) | −1.10454 | −0.0479781 | ||||||||
\(531\) | 4.80194 | 0.208386 | ||||||||
\(532\) | −3.15883 | −0.136953 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −13.5526 | −0.586477 | ||||||||
\(535\) | −24.6692 | −1.06654 | ||||||||
\(536\) | −4.52111 | −0.195282 | ||||||||
\(537\) | 4.10992 | 0.177356 | ||||||||
\(538\) | 5.13706 | 0.221475 | ||||||||
\(539\) | −3.15883 | −0.136061 | ||||||||
\(540\) | 1.69202 | 0.0728130 | ||||||||
\(541\) | −44.8286 | −1.92733 | −0.963666 | − | 0.267109i | \(-0.913932\pi\) | ||||
−0.963666 | + | 0.267109i | \(0.913932\pi\) | |||||||
\(542\) | −25.7995 | −1.10819 | ||||||||
\(543\) | 8.63640 | 0.370623 | ||||||||
\(544\) | −7.74094 | −0.331890 | ||||||||
\(545\) | 10.6528 | 0.456316 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.5603 | −1.30667 | −0.653333 | − | 0.757071i | \(-0.726630\pi\) | ||||
−0.653333 | + | 0.757071i | \(0.726630\pi\) | |||||||
\(548\) | −20.5700 | −0.878708 | ||||||||
\(549\) | 3.21983 | 0.137419 | ||||||||
\(550\) | −6.75063 | −0.287848 | ||||||||
\(551\) | 15.6703 | 0.667575 | ||||||||
\(552\) | 7.89977 | 0.336237 | ||||||||
\(553\) | −7.33944 | −0.312105 | ||||||||
\(554\) | −19.9976 | −0.849617 | ||||||||
\(555\) | 0.314683 | 0.0133576 | ||||||||
\(556\) | −22.5308 | −0.955519 | ||||||||
\(557\) | −44.0277 | −1.86552 | −0.932758 | − | 0.360504i | \(-0.882605\pi\) | ||||
−0.932758 | + | 0.360504i | \(0.882605\pi\) | |||||||
\(558\) | 4.82908 | 0.204431 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.69202 | −0.0715010 | ||||||||
\(561\) | 24.4523 | 1.03238 | ||||||||
\(562\) | 18.5851 | 0.783965 | ||||||||
\(563\) | −30.7138 | −1.29443 | −0.647216 | − | 0.762307i | \(-0.724067\pi\) | ||||
−0.647216 | + | 0.762307i | \(0.724067\pi\) | |||||||
\(564\) | 2.78017 | 0.117066 | ||||||||
\(565\) | −25.6950 | −1.08100 | ||||||||
\(566\) | 4.35152 | 0.182908 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −1.20775 | −0.0506761 | ||||||||
\(569\) | 35.8963 | 1.50485 | 0.752426 | − | 0.658677i | \(-0.228884\pi\) | ||||
0.752426 | + | 0.658677i | \(0.228884\pi\) | |||||||
\(570\) | 5.34481 | 0.223870 | ||||||||
\(571\) | −30.2218 | −1.26474 | −0.632370 | − | 0.774666i | \(-0.717918\pi\) | ||||
−0.632370 | + | 0.774666i | \(0.717918\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.9922 | −1.12762 | ||||||||
\(574\) | 0.978230 | 0.0408305 | ||||||||
\(575\) | −16.8823 | −0.704041 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −10.6799 | −0.444612 | −0.222306 | − | 0.974977i | \(-0.571358\pi\) | ||||
−0.222306 | + | 0.974977i | \(0.571358\pi\) | |||||||
\(578\) | −42.9221 | −1.78533 | ||||||||
\(579\) | 16.2174 | 0.673974 | ||||||||
\(580\) | 8.39373 | 0.348531 | ||||||||
\(581\) | 8.32304 | 0.345298 | ||||||||
\(582\) | 7.83340 | 0.324705 | ||||||||
\(583\) | 2.06206 | 0.0854020 | ||||||||
\(584\) | −14.1564 | −0.585798 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.14138 | 0.295007 | ||||||||
\(587\) | −5.42865 | −0.224064 | −0.112032 | − | 0.993705i | \(-0.535736\pi\) | ||||
−0.112032 | + | 0.993705i | \(0.535736\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 15.2543 | 0.628541 | ||||||||
\(590\) | 8.12498 | 0.334500 | ||||||||
\(591\) | −21.6625 | −0.891075 | ||||||||
\(592\) | 0.185981 | 0.00764376 | ||||||||
\(593\) | −12.3037 | −0.505251 | −0.252626 | − | 0.967564i | \(-0.581294\pi\) | ||||
−0.252626 | + | 0.967564i | \(0.581294\pi\) | |||||||
\(594\) | −3.15883 | −0.129609 | ||||||||
\(595\) | −13.0978 | −0.536959 | ||||||||
\(596\) | 1.60925 | 0.0659175 | ||||||||
\(597\) | 8.81700 | 0.360856 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.9487 | −1.75484 | −0.877418 | − | 0.479727i | \(-0.840736\pi\) | ||||
−0.877418 | + | 0.479727i | \(0.840736\pi\) | |||||||
\(600\) | −2.13706 | −0.0872452 | ||||||||
\(601\) | 6.95348 | 0.283638 | 0.141819 | − | 0.989893i | \(-0.454705\pi\) | ||||
0.141819 | + | 0.989893i | \(0.454705\pi\) | |||||||
\(602\) | 8.19806 | 0.334128 | ||||||||
\(603\) | 4.52111 | 0.184114 | ||||||||
\(604\) | −13.1709 | −0.535917 | ||||||||
\(605\) | 1.72886 | 0.0702880 | ||||||||
\(606\) | 15.2228 | 0.618385 | ||||||||
\(607\) | 4.25129 | 0.172555 | 0.0862773 | − | 0.996271i | \(-0.472503\pi\) | ||||
0.0862773 | + | 0.996271i | \(0.472503\pi\) | |||||||
\(608\) | 3.15883 | 0.128108 | ||||||||
\(609\) | 4.96077 | 0.201021 | ||||||||
\(610\) | 5.44803 | 0.220584 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.74094 | 0.312909 | ||||||||
\(613\) | 9.09113 | 0.367187 | 0.183594 | − | 0.983002i | \(-0.441227\pi\) | ||||
0.183594 | + | 0.983002i | \(0.441227\pi\) | |||||||
\(614\) | −3.13467 | −0.126505 | ||||||||
\(615\) | −1.65519 | −0.0667435 | ||||||||
\(616\) | 3.15883 | 0.127273 | ||||||||
\(617\) | −12.2067 | −0.491423 | −0.245711 | − | 0.969343i | \(-0.579022\pi\) | ||||
−0.245711 | + | 0.969343i | \(0.579022\pi\) | |||||||
\(618\) | −11.6528 | −0.468744 | ||||||||
\(619\) | −49.1183 | −1.97423 | −0.987115 | − | 0.160012i | \(-0.948847\pi\) | ||||
−0.987115 | + | 0.160012i | \(0.948847\pi\) | |||||||
\(620\) | 8.17092 | 0.328152 | ||||||||
\(621\) | −7.89977 | −0.317007 | ||||||||
\(622\) | 32.7875 | 1.31466 | ||||||||
\(623\) | −13.5526 | −0.542972 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.74764 | −0.389906 | ||||||||
\(626\) | −11.5985 | −0.463569 | ||||||||
\(627\) | −9.97823 | −0.398492 | ||||||||
\(628\) | −2.61596 | −0.104388 | ||||||||
\(629\) | 1.43967 | 0.0574032 | ||||||||
\(630\) | 1.69202 | 0.0674117 | ||||||||
\(631\) | 16.4620 | 0.655343 | 0.327671 | − | 0.944792i | \(-0.393736\pi\) | ||||
0.327671 | + | 0.944792i | \(0.393736\pi\) | |||||||
\(632\) | 7.33944 | 0.291947 | ||||||||
\(633\) | −0.753020 | −0.0299299 | ||||||||
\(634\) | −3.71810 | −0.147665 | ||||||||
\(635\) | −20.0723 | −0.796547 | ||||||||
\(636\) | 0.652793 | 0.0258849 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −15.6703 | −0.620391 | ||||||||
\(639\) | 1.20775 | 0.0477779 | ||||||||
\(640\) | 1.69202 | 0.0668830 | ||||||||
\(641\) | 43.0428 | 1.70009 | 0.850044 | − | 0.526711i | \(-0.176575\pi\) | ||||
0.850044 | + | 0.526711i | \(0.176575\pi\) | |||||||
\(642\) | 14.5797 | 0.575415 | ||||||||
\(643\) | 20.3220 | 0.801421 | 0.400710 | − | 0.916205i | \(-0.368763\pi\) | ||||
0.400710 | + | 0.916205i | \(0.368763\pi\) | |||||||
\(644\) | 7.89977 | 0.311295 | ||||||||
\(645\) | −13.8713 | −0.546182 | ||||||||
\(646\) | 24.4523 | 0.962064 | ||||||||
\(647\) | 11.0049 | 0.432647 | 0.216324 | − | 0.976322i | \(-0.430593\pi\) | ||||
0.216324 | + | 0.976322i | \(0.430593\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −15.1685 | −0.595417 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.82908 | 0.189267 | ||||||||
\(652\) | −0.853248 | −0.0334158 | ||||||||
\(653\) | −17.9355 | −0.701872 | −0.350936 | − | 0.936399i | \(-0.614137\pi\) | ||||
−0.350936 | + | 0.936399i | \(0.614137\pi\) | |||||||
\(654\) | −6.29590 | −0.246189 | ||||||||
\(655\) | 2.64742 | 0.103443 | ||||||||
\(656\) | −0.978230 | −0.0381935 | ||||||||
\(657\) | 14.1564 | 0.552295 | ||||||||
\(658\) | 2.78017 | 0.108382 | ||||||||
\(659\) | 29.1594 | 1.13589 | 0.567945 | − | 0.823067i | \(-0.307739\pi\) | ||||
0.567945 | + | 0.823067i | \(0.307739\pi\) | |||||||
\(660\) | −5.34481 | −0.208047 | ||||||||
\(661\) | 34.5217 | 1.34274 | 0.671369 | − | 0.741123i | \(-0.265707\pi\) | ||||
0.671369 | + | 0.741123i | \(0.265707\pi\) | |||||||
\(662\) | 15.8532 | 0.616154 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.32304 | −0.322997 | ||||||||
\(665\) | 5.34481 | 0.207263 | ||||||||
\(666\) | −0.185981 | −0.00720660 | ||||||||
\(667\) | −39.1890 | −1.51740 | ||||||||
\(668\) | −14.8944 | −0.576281 | ||||||||
\(669\) | −2.14377 | −0.0828829 | ||||||||
\(670\) | 7.64981 | 0.295538 | ||||||||
\(671\) | −10.1709 | −0.392644 | ||||||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −9.46203 | −0.364734 | −0.182367 | − | 0.983231i | \(-0.558376\pi\) | ||||
−0.182367 | + | 0.983231i | \(0.558376\pi\) | |||||||
\(674\) | 26.2597 | 1.01148 | ||||||||
\(675\) | 2.13706 | 0.0822556 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.1438 | −0.658889 | −0.329444 | − | 0.944175i | \(-0.606861\pi\) | ||||
−0.329444 | + | 0.944175i | \(0.606861\pi\) | |||||||
\(678\) | 15.1860 | 0.583214 | ||||||||
\(679\) | 7.83340 | 0.300618 | ||||||||
\(680\) | 13.0978 | 0.502279 | ||||||||
\(681\) | 21.3327 | 0.817472 | ||||||||
\(682\) | −15.2543 | −0.584116 | ||||||||
\(683\) | 21.0339 | 0.804838 | 0.402419 | − | 0.915456i | \(-0.368170\pi\) | ||||
0.402419 | + | 0.915456i | \(0.368170\pi\) | |||||||
\(684\) | −3.15883 | −0.120781 | ||||||||
\(685\) | 34.8049 | 1.32983 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −15.3502 | −0.585646 | ||||||||
\(688\) | −8.19806 | −0.312548 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −13.3666 | −0.508857 | ||||||||
\(691\) | 9.23490 | 0.351312 | 0.175656 | − | 0.984452i | \(-0.443795\pi\) | ||||
0.175656 | + | 0.984452i | \(0.443795\pi\) | |||||||
\(692\) | −7.28621 | −0.276980 | ||||||||
\(693\) | −3.15883 | −0.119994 | ||||||||
\(694\) | 16.3099 | 0.619115 | ||||||||
\(695\) | 38.1226 | 1.44607 | ||||||||
\(696\) | −4.96077 | −0.188038 | ||||||||
\(697\) | −7.57242 | −0.286826 | ||||||||
\(698\) | 34.3937 | 1.30182 | ||||||||
\(699\) | −23.1468 | −0.875491 | ||||||||
\(700\) | −2.13706 | −0.0807734 | ||||||||
\(701\) | −17.2989 | −0.653370 | −0.326685 | − | 0.945133i | \(-0.605932\pi\) | ||||
−0.326685 | + | 0.945133i | \(0.605932\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.587482 | −0.0221573 | ||||||||
\(704\) | −3.15883 | −0.119053 | ||||||||
\(705\) | −4.70410 | −0.177167 | ||||||||
\(706\) | 16.3284 | 0.614528 | ||||||||
\(707\) | 15.2228 | 0.572513 | ||||||||
\(708\) | −4.80194 | −0.180468 | ||||||||
\(709\) | −19.2911 | −0.724493 | −0.362246 | − | 0.932082i | \(-0.617990\pi\) | ||||
−0.362246 | + | 0.932082i | \(0.617990\pi\) | |||||||
\(710\) | 2.04354 | 0.0766927 | ||||||||
\(711\) | −7.33944 | −0.275250 | ||||||||
\(712\) | 13.5526 | 0.507904 | ||||||||
\(713\) | −38.1487 | −1.42868 | ||||||||
\(714\) | 7.74094 | 0.289697 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.10992 | −0.153595 | ||||||||
\(717\) | −17.8538 | −0.666764 | ||||||||
\(718\) | −21.0248 | −0.784637 | ||||||||
\(719\) | −3.61165 | −0.134692 | −0.0673458 | − | 0.997730i | \(-0.521453\pi\) | ||||
−0.0673458 | + | 0.997730i | \(0.521453\pi\) | |||||||
\(720\) | −1.69202 | −0.0630579 | ||||||||
\(721\) | −11.6528 | −0.433973 | ||||||||
\(722\) | 9.02177 | 0.335756 | ||||||||
\(723\) | 16.4179 | 0.610588 | ||||||||
\(724\) | −8.63640 | −0.320969 | ||||||||
\(725\) | 10.6015 | 0.393729 | ||||||||
\(726\) | −1.02177 | −0.0379215 | ||||||||
\(727\) | −18.6614 | −0.692114 | −0.346057 | − | 0.938214i | \(-0.612480\pi\) | ||||
−0.346057 | + | 0.938214i | \(0.612480\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 23.9530 | 0.886540 | ||||||||
\(731\) | −63.4607 | −2.34718 | ||||||||
\(732\) | −3.21983 | −0.119008 | ||||||||
\(733\) | 41.8872 | 1.54714 | 0.773570 | − | 0.633711i | \(-0.218469\pi\) | ||||
0.773570 | + | 0.633711i | \(0.218469\pi\) | |||||||
\(734\) | 23.0858 | 0.852111 | ||||||||
\(735\) | 1.69202 | 0.0624112 | ||||||||
\(736\) | −7.89977 | −0.291189 | ||||||||
\(737\) | −14.2814 | −0.526063 | ||||||||
\(738\) | 0.978230 | 0.0360091 | ||||||||
\(739\) | 46.7622 | 1.72018 | 0.860088 | − | 0.510145i | \(-0.170408\pi\) | ||||
0.860088 | + | 0.510145i | \(0.170408\pi\) | |||||||
\(740\) | −0.314683 | −0.0115680 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.652793 | 0.0239648 | ||||||||
\(743\) | 13.3260 | 0.488885 | 0.244442 | − | 0.969664i | \(-0.421395\pi\) | ||||
0.244442 | + | 0.969664i | \(0.421395\pi\) | |||||||
\(744\) | −4.82908 | −0.177043 | ||||||||
\(745\) | −2.72289 | −0.0997589 | ||||||||
\(746\) | 16.6189 | 0.608463 | ||||||||
\(747\) | 8.32304 | 0.304524 | ||||||||
\(748\) | −24.4523 | −0.894066 | ||||||||
\(749\) | 14.5797 | 0.532731 | ||||||||
\(750\) | 12.0761 | 0.440956 | ||||||||
\(751\) | 21.8888 | 0.798732 | 0.399366 | − | 0.916792i | \(-0.369230\pi\) | ||||
0.399366 | + | 0.916792i | \(0.369230\pi\) | |||||||
\(752\) | −2.78017 | −0.101382 | ||||||||
\(753\) | 23.9124 | 0.871418 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.2855 | 0.811051 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 12.6974 | 0.461495 | 0.230747 | − | 0.973014i | \(-0.425883\pi\) | ||||
0.230747 | + | 0.973014i | \(0.425883\pi\) | |||||||
\(758\) | −16.4131 | −0.596151 | ||||||||
\(759\) | 24.9541 | 0.905775 | ||||||||
\(760\) | −5.34481 | −0.193877 | ||||||||
\(761\) | 53.5096 | 1.93972 | 0.969861 | − | 0.243659i | \(-0.0783477\pi\) | ||||
0.969861 | + | 0.243659i | \(0.0783477\pi\) | |||||||
\(762\) | 11.8629 | 0.429749 | ||||||||
\(763\) | −6.29590 | −0.227927 | ||||||||
\(764\) | 26.9922 | 0.976545 | ||||||||
\(765\) | −13.0978 | −0.473553 | ||||||||
\(766\) | 0.241603 | 0.00872946 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −22.2892 | −0.803769 | −0.401884 | − | 0.915690i | \(-0.631645\pi\) | ||||
−0.401884 | + | 0.915690i | \(0.631645\pi\) | |||||||
\(770\) | −5.34481 | −0.192614 | ||||||||
\(771\) | −8.77479 | −0.316016 | ||||||||
\(772\) | −16.2174 | −0.583678 | ||||||||
\(773\) | 32.3726 | 1.16436 | 0.582180 | − | 0.813060i | \(-0.302200\pi\) | ||||
0.582180 | + | 0.813060i | \(0.302200\pi\) | |||||||
\(774\) | 8.19806 | 0.294673 | ||||||||
\(775\) | 10.3201 | 0.370708 | ||||||||
\(776\) | −7.83340 | −0.281203 | ||||||||
\(777\) | −0.185981 | −0.00667202 | ||||||||
\(778\) | 28.5042 | 1.02193 | ||||||||
\(779\) | 3.09006 | 0.110713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.81508 | −0.136514 | ||||||||
\(782\) | −61.1517 | −2.18678 | ||||||||
\(783\) | 4.96077 | 0.177284 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 4.42626 | 0.157980 | ||||||||
\(786\) | −1.56465 | −0.0558091 | ||||||||
\(787\) | −31.0984 | −1.10854 | −0.554270 | − | 0.832337i | \(-0.687002\pi\) | ||||
−0.554270 | + | 0.832337i | \(0.687002\pi\) | |||||||
\(788\) | 21.6625 | 0.771694 | ||||||||
\(789\) | −6.78448 | −0.241534 | ||||||||
\(790\) | −12.4185 | −0.441830 | ||||||||
\(791\) | 15.1860 | 0.539951 | ||||||||
\(792\) | 3.15883 | 0.112244 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.8009 | 0.489775 | ||||||||
\(795\) | −1.10454 | −0.0391740 | ||||||||
\(796\) | −8.81700 | −0.312510 | ||||||||
\(797\) | −23.1997 | −0.821776 | −0.410888 | − | 0.911686i | \(-0.634781\pi\) | ||||
−0.410888 | + | 0.911686i | \(0.634781\pi\) | |||||||
\(798\) | −3.15883 | −0.111821 | ||||||||
\(799\) | −21.5211 | −0.761362 | ||||||||
\(800\) | 2.13706 | 0.0755566 | ||||||||
\(801\) | −13.5526 | −0.478856 | ||||||||
\(802\) | −20.3134 | −0.717290 | ||||||||
\(803\) | −44.7178 | −1.57806 | ||||||||
\(804\) | −4.52111 | −0.159447 | ||||||||
\(805\) | −13.3666 | −0.471110 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.13706 | 0.180833 | ||||||||
\(808\) | −15.2228 | −0.535537 | ||||||||
\(809\) | −5.47948 | −0.192648 | −0.0963242 | − | 0.995350i | \(-0.530709\pi\) | ||||
−0.0963242 | + | 0.995350i | \(0.530709\pi\) | |||||||
\(810\) | 1.69202 | 0.0594516 | ||||||||
\(811\) | −52.0592 | −1.82805 | −0.914023 | − | 0.405663i | \(-0.867041\pi\) | ||||
−0.914023 | + | 0.405663i | \(0.867041\pi\) | |||||||
\(812\) | −4.96077 | −0.174089 | ||||||||
\(813\) | −25.7995 | −0.904830 | ||||||||
\(814\) | 0.587482 | 0.0205912 | ||||||||
\(815\) | 1.44371 | 0.0505711 | ||||||||
\(816\) | −7.74094 | −0.270987 | ||||||||
\(817\) | 25.8963 | 0.905997 | ||||||||
\(818\) | −21.0683 | −0.736636 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.65519 | 0.0578016 | ||||||||
\(821\) | −2.61655 | −0.0913182 | −0.0456591 | − | 0.998957i | \(-0.514539\pi\) | ||||
−0.0456591 | + | 0.998957i | \(0.514539\pi\) | |||||||
\(822\) | −20.5700 | −0.717462 | ||||||||
\(823\) | 50.4596 | 1.75891 | 0.879456 | − | 0.475980i | \(-0.157907\pi\) | ||||
0.879456 | + | 0.475980i | \(0.157907\pi\) | |||||||
\(824\) | 11.6528 | 0.405944 | ||||||||
\(825\) | −6.75063 | −0.235027 | ||||||||
\(826\) | −4.80194 | −0.167081 | ||||||||
\(827\) | −2.91079 | −0.101218 | −0.0506090 | − | 0.998719i | \(-0.516116\pi\) | ||||
−0.0506090 | + | 0.998719i | \(0.516116\pi\) | |||||||
\(828\) | 7.89977 | 0.274536 | ||||||||
\(829\) | −6.09724 | −0.211766 | −0.105883 | − | 0.994379i | \(-0.533767\pi\) | ||||
−0.105883 | + | 0.994379i | \(0.533767\pi\) | |||||||
\(830\) | 14.0828 | 0.488820 | ||||||||
\(831\) | −19.9976 | −0.693709 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.74094 | 0.268208 | ||||||||
\(834\) | −22.5308 | −0.780178 | ||||||||
\(835\) | 25.2016 | 0.872139 | ||||||||
\(836\) | 9.97823 | 0.345104 | ||||||||
\(837\) | 4.82908 | 0.166918 | ||||||||
\(838\) | 0.486663 | 0.0168115 | ||||||||
\(839\) | 4.22654 | 0.145916 | 0.0729581 | − | 0.997335i | \(-0.476756\pi\) | ||||
0.0729581 | + | 0.997335i | \(0.476756\pi\) | |||||||
\(840\) | −1.69202 | −0.0583803 | ||||||||
\(841\) | −4.39075 | −0.151405 | ||||||||
\(842\) | 26.4644 | 0.912024 | ||||||||
\(843\) | 18.5851 | 0.640104 | ||||||||
\(844\) | 0.753020 | 0.0259200 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.78017 | 0.0955841 | ||||||||
\(847\) | −1.02177 | −0.0351084 | ||||||||
\(848\) | −0.652793 | −0.0224170 | ||||||||
\(849\) | 4.35152 | 0.149344 | ||||||||
\(850\) | 16.5429 | 0.567416 | ||||||||
\(851\) | 1.46921 | 0.0503637 | ||||||||
\(852\) | −1.20775 | −0.0413769 | ||||||||
\(853\) | −42.0538 | −1.43990 | −0.719948 | − | 0.694028i | \(-0.755834\pi\) | ||||
−0.719948 | + | 0.694028i | \(0.755834\pi\) | |||||||
\(854\) | −3.21983 | −0.110180 | ||||||||
\(855\) | 5.34481 | 0.182789 | ||||||||
\(856\) | −14.5797 | −0.498324 | ||||||||
\(857\) | −40.6039 | −1.38700 | −0.693501 | − | 0.720456i | \(-0.743933\pi\) | ||||
−0.693501 | + | 0.720456i | \(0.743933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.53643 | 0.154781 | 0.0773906 | − | 0.997001i | \(-0.475341\pi\) | ||||
0.0773906 | + | 0.997001i | \(0.475341\pi\) | |||||||
\(860\) | 13.8713 | 0.473007 | ||||||||
\(861\) | 0.978230 | 0.0333380 | ||||||||
\(862\) | 17.2476 | 0.587455 | ||||||||
\(863\) | −27.8592 | −0.948339 | −0.474169 | − | 0.880434i | \(-0.657252\pi\) | ||||
−0.474169 | + | 0.880434i | \(0.657252\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 12.3284 | 0.419179 | ||||||||
\(866\) | −2.78687 | −0.0947018 | ||||||||
\(867\) | −42.9221 | −1.45771 | ||||||||
\(868\) | −4.82908 | −0.163910 | ||||||||
\(869\) | 23.1841 | 0.786465 | ||||||||
\(870\) | 8.39373 | 0.284574 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.29590 | 0.213206 | ||||||||
\(873\) | 7.83340 | 0.265120 | ||||||||
\(874\) | 24.9541 | 0.844084 | ||||||||
\(875\) | 12.0761 | 0.408245 | ||||||||
\(876\) | −14.1564 | −0.478302 | ||||||||
\(877\) | 45.6892 | 1.54281 | 0.771407 | − | 0.636343i | \(-0.219554\pi\) | ||||
0.771407 | + | 0.636343i | \(0.219554\pi\) | |||||||
\(878\) | 21.4808 | 0.724942 | ||||||||
\(879\) | 7.14138 | 0.240873 | ||||||||
\(880\) | 5.34481 | 0.180174 | ||||||||
\(881\) | 17.2935 | 0.582633 | 0.291316 | − | 0.956627i | \(-0.405907\pi\) | ||||
0.291316 | + | 0.956627i | \(0.405907\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 41.8179 | 1.40728 | 0.703641 | − | 0.710555i | \(-0.251556\pi\) | ||||
0.703641 | + | 0.710555i | \(0.251556\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.12498 | 0.273118 | ||||||||
\(886\) | −9.85623 | −0.331127 | ||||||||
\(887\) | −11.4196 | −0.383431 | −0.191715 | − | 0.981451i | \(-0.561405\pi\) | ||||
−0.191715 | + | 0.981451i | \(0.561405\pi\) | |||||||
\(888\) | 0.185981 | 0.00624110 | ||||||||
\(889\) | 11.8629 | 0.397870 | ||||||||
\(890\) | −22.9312 | −0.768657 | ||||||||
\(891\) | −3.15883 | −0.105825 | ||||||||
\(892\) | 2.14377 | 0.0717787 | ||||||||
\(893\) | 8.78209 | 0.293881 | ||||||||
\(894\) | 1.60925 | 0.0538214 | ||||||||
\(895\) | 6.95407 | 0.232449 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.8358 | 0.361595 | ||||||||
\(899\) | 23.9560 | 0.798977 | ||||||||
\(900\) | −2.13706 | −0.0712354 | ||||||||
\(901\) | −5.05323 | −0.168347 | ||||||||
\(902\) | −3.09006 | −0.102888 | ||||||||
\(903\) | 8.19806 | 0.272814 | ||||||||
\(904\) | −15.1860 | −0.505078 | ||||||||
\(905\) | 14.6130 | 0.485752 | ||||||||
\(906\) | −13.1709 | −0.437574 | ||||||||
\(907\) | −31.6396 | −1.05058 | −0.525289 | − | 0.850924i | \(-0.676043\pi\) | ||||
−0.525289 | + | 0.850924i | \(0.676043\pi\) | |||||||
\(908\) | −21.3327 | −0.707952 | ||||||||
\(909\) | 15.2228 | 0.504909 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.5875 | 0.483305 | 0.241652 | − | 0.970363i | \(-0.422311\pi\) | ||||
0.241652 | + | 0.970363i | \(0.422311\pi\) | |||||||
\(912\) | 3.15883 | 0.104599 | ||||||||
\(913\) | −26.2911 | −0.870109 | ||||||||
\(914\) | −15.5386 | −0.513970 | ||||||||
\(915\) | 5.44803 | 0.180106 | ||||||||
\(916\) | 15.3502 | 0.507185 | ||||||||
\(917\) | −1.56465 | −0.0516692 | ||||||||
\(918\) | 7.74094 | 0.255489 | ||||||||
\(919\) | −47.3019 | −1.56034 | −0.780172 | − | 0.625565i | \(-0.784869\pi\) | ||||
−0.780172 | + | 0.625565i | \(0.784869\pi\) | |||||||
\(920\) | 13.3666 | 0.440683 | ||||||||
\(921\) | −3.13467 | −0.103291 | ||||||||
\(922\) | −5.55389 | −0.182908 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.15883 | 0.103918 | ||||||||
\(925\) | −0.397452 | −0.0130682 | ||||||||
\(926\) | 8.29291 | 0.272522 | ||||||||
\(927\) | −11.6528 | −0.382728 | ||||||||
\(928\) | 4.96077 | 0.162845 | ||||||||
\(929\) | 40.5526 | 1.33049 | 0.665243 | − | 0.746627i | \(-0.268328\pi\) | ||||
0.665243 | + | 0.746627i | \(0.268328\pi\) | |||||||
\(930\) | 8.17092 | 0.267935 | ||||||||
\(931\) | −3.15883 | −0.103527 | ||||||||
\(932\) | 23.1468 | 0.758197 | ||||||||
\(933\) | 32.7875 | 1.07341 | ||||||||
\(934\) | 22.7071 | 0.742999 | ||||||||
\(935\) | 41.3739 | 1.35307 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.7186 | 0.611509 | 0.305755 | − | 0.952110i | \(-0.401091\pi\) | ||||
0.305755 | + | 0.952110i | \(0.401091\pi\) | |||||||
\(938\) | −4.52111 | −0.147619 | ||||||||
\(939\) | −11.5985 | −0.378503 | ||||||||
\(940\) | 4.70410 | 0.153431 | ||||||||
\(941\) | −27.2285 | −0.887622 | −0.443811 | − | 0.896120i | \(-0.646374\pi\) | ||||
−0.443811 | + | 0.896120i | \(0.646374\pi\) | |||||||
\(942\) | −2.61596 | −0.0852325 | ||||||||
\(943\) | −7.72779 | −0.251652 | ||||||||
\(944\) | 4.80194 | 0.156290 | ||||||||
\(945\) | 1.69202 | 0.0550415 | ||||||||
\(946\) | −25.8963 | −0.841962 | ||||||||
\(947\) | −51.9963 | −1.68965 | −0.844826 | − | 0.535041i | \(-0.820296\pi\) | ||||
−0.844826 | + | 0.535041i | \(0.820296\pi\) | |||||||
\(948\) | 7.33944 | 0.238374 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.75063 | −0.219019 | ||||||||
\(951\) | −3.71810 | −0.120568 | ||||||||
\(952\) | −7.74094 | −0.250885 | ||||||||
\(953\) | −37.5265 | −1.21560 | −0.607801 | − | 0.794089i | \(-0.707948\pi\) | ||||
−0.607801 | + | 0.794089i | \(0.707948\pi\) | |||||||
\(954\) | 0.652793 | 0.0211349 | ||||||||
\(955\) | −45.6714 | −1.47789 | ||||||||
\(956\) | 17.8538 | 0.577434 | ||||||||
\(957\) | −15.6703 | −0.506547 | ||||||||
\(958\) | 22.9245 | 0.740658 | ||||||||
\(959\) | −20.5700 | −0.664241 | ||||||||
\(960\) | 1.69202 | 0.0546098 | ||||||||
\(961\) | −7.67994 | −0.247740 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.5797 | 0.469825 | ||||||||
\(964\) | −16.4179 | −0.528785 | ||||||||
\(965\) | 27.4403 | 0.883333 | ||||||||
\(966\) | 7.89977 | 0.254171 | ||||||||
\(967\) | −49.0786 | −1.57826 | −0.789130 | − | 0.614226i | \(-0.789468\pi\) | ||||
−0.789130 | + | 0.614226i | \(0.789468\pi\) | |||||||
\(968\) | 1.02177 | 0.0328409 | ||||||||
\(969\) | 24.4523 | 0.785522 | ||||||||
\(970\) | 13.2543 | 0.425569 | ||||||||
\(971\) | −37.6746 | −1.20903 | −0.604517 | − | 0.796592i | \(-0.706634\pi\) | ||||
−0.604517 | + | 0.796592i | \(0.706634\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −22.5308 | −0.722304 | ||||||||
\(974\) | 7.97525 | 0.255543 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.21983 | 0.103064 | ||||||||
\(977\) | −10.0852 | −0.322653 | −0.161326 | − | 0.986901i | \(-0.551577\pi\) | ||||
−0.161326 | + | 0.986901i | \(0.551577\pi\) | |||||||
\(978\) | −0.853248 | −0.0272839 | ||||||||
\(979\) | 42.8103 | 1.36822 | ||||||||
\(980\) | −1.69202 | −0.0540496 | ||||||||
\(981\) | −6.29590 | −0.201013 | ||||||||
\(982\) | 25.0116 | 0.798152 | ||||||||
\(983\) | 24.1299 | 0.769624 | 0.384812 | − | 0.922995i | \(-0.374266\pi\) | ||||
0.384812 | + | 0.922995i | \(0.374266\pi\) | |||||||
\(984\) | −0.978230 | −0.0311848 | ||||||||
\(985\) | −36.6534 | −1.16787 | ||||||||
\(986\) | 38.4010 | 1.22294 | ||||||||
\(987\) | 2.78017 | 0.0884937 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −64.7628 | −2.05934 | ||||||||
\(990\) | −5.34481 | −0.169869 | ||||||||
\(991\) | −39.6553 | −1.25969 | −0.629846 | − | 0.776720i | \(-0.716882\pi\) | ||||
−0.629846 | + | 0.776720i | \(0.716882\pi\) | |||||||
\(992\) | 4.82908 | 0.153324 | ||||||||
\(993\) | 15.8532 | 0.503088 | ||||||||
\(994\) | −1.20775 | −0.0383075 | ||||||||
\(995\) | 14.9186 | 0.472950 | ||||||||
\(996\) | −8.32304 | −0.263726 | ||||||||
\(997\) | −29.5394 | −0.935523 | −0.467761 | − | 0.883855i | \(-0.654939\pi\) | ||||
−0.467761 | + | 0.883855i | \(0.654939\pi\) | |||||||
\(998\) | 11.7168 | 0.370888 | ||||||||
\(999\) | −0.185981 | −0.00588417 |
(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 | 7098.2.a.cd.1.1 | ✓ | 3 | |
13.12 | even | 2 | 7098.2.a.ci.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7098.2.a.cd.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
7098.2.a.ci.1.3 | yes | 3 | 13.12 | even | 2 |