Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2415,2,Mod(1,2415)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2415, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2415.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2415.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: | \(19.2838720881\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 16x^{8} + 30x^{7} + 87x^{6} - 143x^{5} - 196x^{4} + 244x^{3} + 160x^{2} - 89x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.90103\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2415.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90103 | −1.34423 | −0.672117 | − | 0.740445i | \(-0.734615\pi\) | ||||
−0.672117 | + | 0.740445i | \(0.734615\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.61393 | 0.806964 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.90103 | −0.776094 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.733935 | 0.259485 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.90103 | −0.601160 | ||||||||
\(11\) | 3.08250 | 0.929410 | 0.464705 | − | 0.885466i | \(-0.346160\pi\) | ||||
0.464705 | + | 0.885466i | \(0.346160\pi\) | |||||||
\(12\) | 1.61393 | 0.465901 | ||||||||
\(13\) | −4.36980 | −1.21197 | −0.605983 | − | 0.795478i | \(-0.707220\pi\) | ||||
−0.605983 | + | 0.795478i | \(0.707220\pi\) | |||||||
\(14\) | −1.90103 | −0.508073 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −4.62309 | −1.15577 | ||||||||
\(17\) | −3.91348 | −0.949157 | −0.474579 | − | 0.880213i | \(-0.657400\pi\) | ||||
−0.474579 | + | 0.880213i | \(0.657400\pi\) | |||||||
\(18\) | −1.90103 | −0.448078 | ||||||||
\(19\) | 0.209598 | 0.0480850 | 0.0240425 | − | 0.999711i | \(-0.492346\pi\) | ||||
0.0240425 | + | 0.999711i | \(0.492346\pi\) | |||||||
\(20\) | 1.61393 | 0.360885 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −5.85994 | −1.24934 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0.733935 | 0.149814 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.30714 | 1.62916 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.61393 | 0.305004 | ||||||||
\(29\) | 2.84119 | 0.527595 | 0.263798 | − | 0.964578i | \(-0.415025\pi\) | ||||
0.263798 | + | 0.964578i | \(0.415025\pi\) | |||||||
\(30\) | −1.90103 | −0.347080 | ||||||||
\(31\) | 9.13845 | 1.64131 | 0.820657 | − | 0.571421i | \(-0.193608\pi\) | ||||
0.820657 | + | 0.571421i | \(0.193608\pi\) | |||||||
\(32\) | 7.32078 | 1.29414 | ||||||||
\(33\) | 3.08250 | 0.536595 | ||||||||
\(34\) | 7.43965 | 1.27589 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.61393 | 0.268988 | ||||||||
\(37\) | 6.74648 | 1.10911 | 0.554557 | − | 0.832145i | \(-0.312888\pi\) | ||||
0.554557 | + | 0.832145i | \(0.312888\pi\) | |||||||
\(38\) | −0.398452 | −0.0646375 | ||||||||
\(39\) | −4.36980 | −0.699728 | ||||||||
\(40\) | 0.733935 | 0.116045 | ||||||||
\(41\) | −3.97914 | −0.621437 | −0.310719 | − | 0.950502i | \(-0.600570\pi\) | ||||
−0.310719 | + | 0.950502i | \(0.600570\pi\) | |||||||
\(42\) | −1.90103 | −0.293336 | ||||||||
\(43\) | 9.51553 | 1.45110 | 0.725552 | − | 0.688167i | \(-0.241584\pi\) | ||||
0.725552 | + | 0.688167i | \(0.241584\pi\) | |||||||
\(44\) | 4.97494 | 0.750000 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 1.90103 | 0.280292 | ||||||||
\(47\) | 7.70980 | 1.12459 | 0.562295 | − | 0.826937i | \(-0.309919\pi\) | ||||
0.562295 | + | 0.826937i | \(0.309919\pi\) | |||||||
\(48\) | −4.62309 | −0.667286 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.90103 | −0.268847 | ||||||||
\(51\) | −3.91348 | −0.547996 | ||||||||
\(52\) | −7.05255 | −0.978013 | ||||||||
\(53\) | −12.7231 | −1.74766 | −0.873829 | − | 0.486234i | \(-0.838370\pi\) | ||||
−0.873829 | + | 0.486234i | \(0.838370\pi\) | |||||||
\(54\) | −1.90103 | −0.258698 | ||||||||
\(55\) | 3.08250 | 0.415645 | ||||||||
\(56\) | 0.733935 | 0.0980762 | ||||||||
\(57\) | 0.209598 | 0.0277619 | ||||||||
\(58\) | −5.40119 | −0.709211 | ||||||||
\(59\) | 3.22294 | 0.419591 | 0.209796 | − | 0.977745i | \(-0.432720\pi\) | ||||
0.209796 | + | 0.977745i | \(0.432720\pi\) | |||||||
\(60\) | 1.61393 | 0.208357 | ||||||||
\(61\) | −1.71549 | −0.219646 | −0.109823 | − | 0.993951i | \(-0.535028\pi\) | ||||
−0.109823 | + | 0.993951i | \(0.535028\pi\) | |||||||
\(62\) | −17.3725 | −2.20631 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −4.67087 | −0.583859 | ||||||||
\(65\) | −4.36980 | −0.542007 | ||||||||
\(66\) | −5.85994 | −0.721309 | ||||||||
\(67\) | 4.68562 | 0.572440 | 0.286220 | − | 0.958164i | \(-0.407601\pi\) | ||||
0.286220 | + | 0.958164i | \(0.407601\pi\) | |||||||
\(68\) | −6.31607 | −0.765936 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −1.90103 | −0.227217 | ||||||||
\(71\) | 4.54168 | 0.538999 | 0.269499 | − | 0.963001i | \(-0.413142\pi\) | ||||
0.269499 | + | 0.963001i | \(0.413142\pi\) | |||||||
\(72\) | 0.733935 | 0.0864951 | ||||||||
\(73\) | −0.767751 | −0.0898585 | −0.0449292 | − | 0.998990i | \(-0.514306\pi\) | ||||
−0.0449292 | + | 0.998990i | \(0.514306\pi\) | |||||||
\(74\) | −12.8253 | −1.49091 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0.338276 | 0.0388029 | ||||||||
\(77\) | 3.08250 | 0.351284 | ||||||||
\(78\) | 8.30714 | 0.940599 | ||||||||
\(79\) | 6.64506 | 0.747628 | 0.373814 | − | 0.927504i | \(-0.378050\pi\) | ||||
0.373814 | + | 0.927504i | \(0.378050\pi\) | |||||||
\(80\) | −4.62309 | −0.516877 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.56448 | 0.835357 | ||||||||
\(83\) | −15.8348 | −1.73809 | −0.869047 | − | 0.494730i | \(-0.835267\pi\) | ||||
−0.869047 | + | 0.494730i | \(0.835267\pi\) | |||||||
\(84\) | 1.61393 | 0.176094 | ||||||||
\(85\) | −3.91348 | −0.424476 | ||||||||
\(86\) | −18.0893 | −1.95062 | ||||||||
\(87\) | 2.84119 | 0.304607 | ||||||||
\(88\) | 2.26236 | 0.241168 | ||||||||
\(89\) | 7.44650 | 0.789328 | 0.394664 | − | 0.918826i | \(-0.370861\pi\) | ||||
0.394664 | + | 0.918826i | \(0.370861\pi\) | |||||||
\(90\) | −1.90103 | −0.200387 | ||||||||
\(91\) | −4.36980 | −0.458080 | ||||||||
\(92\) | −1.61393 | −0.168264 | ||||||||
\(93\) | 9.13845 | 0.947613 | ||||||||
\(94\) | −14.6566 | −1.51171 | ||||||||
\(95\) | 0.209598 | 0.0215043 | ||||||||
\(96\) | 7.32078 | 0.747174 | ||||||||
\(97\) | 4.06148 | 0.412380 | 0.206190 | − | 0.978512i | \(-0.433893\pi\) | ||||
0.206190 | + | 0.978512i | \(0.433893\pi\) | |||||||
\(98\) | −1.90103 | −0.192033 | ||||||||
\(99\) | 3.08250 | 0.309803 | ||||||||
\(100\) | 1.61393 | 0.161393 | ||||||||
\(101\) | −10.3687 | −1.03173 | −0.515864 | − | 0.856670i | \(-0.672529\pi\) | ||||
−0.515864 | + | 0.856670i | \(0.672529\pi\) | |||||||
\(102\) | 7.43965 | 0.736635 | ||||||||
\(103\) | 9.76343 | 0.962020 | 0.481010 | − | 0.876715i | \(-0.340270\pi\) | ||||
0.481010 | + | 0.876715i | \(0.340270\pi\) | |||||||
\(104\) | −3.20715 | −0.314487 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 24.1871 | 2.34926 | ||||||||
\(107\) | 11.9192 | 1.15227 | 0.576134 | − | 0.817355i | \(-0.304560\pi\) | ||||
0.576134 | + | 0.817355i | \(0.304560\pi\) | |||||||
\(108\) | 1.61393 | 0.155300 | ||||||||
\(109\) | 16.2721 | 1.55859 | 0.779293 | − | 0.626660i | \(-0.215579\pi\) | ||||
0.779293 | + | 0.626660i | \(0.215579\pi\) | |||||||
\(110\) | −5.85994 | −0.558723 | ||||||||
\(111\) | 6.74648 | 0.640348 | ||||||||
\(112\) | −4.62309 | −0.436841 | ||||||||
\(113\) | −7.03810 | −0.662089 | −0.331045 | − | 0.943615i | \(-0.607401\pi\) | ||||
−0.331045 | + | 0.943615i | \(0.607401\pi\) | |||||||
\(114\) | −0.398452 | −0.0373185 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 4.58547 | 0.425750 | ||||||||
\(117\) | −4.36980 | −0.403988 | ||||||||
\(118\) | −6.12692 | −0.564028 | ||||||||
\(119\) | −3.91348 | −0.358748 | ||||||||
\(120\) | 0.733935 | 0.0669988 | ||||||||
\(121\) | −1.49818 | −0.136198 | ||||||||
\(122\) | 3.26121 | 0.295256 | ||||||||
\(123\) | −3.97914 | −0.358787 | ||||||||
\(124\) | 14.7488 | 1.32448 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.90103 | −0.169358 | ||||||||
\(127\) | −5.61942 | −0.498642 | −0.249321 | − | 0.968421i | \(-0.580208\pi\) | ||||
−0.249321 | + | 0.968421i | \(0.580208\pi\) | |||||||
\(128\) | −5.76208 | −0.509301 | ||||||||
\(129\) | 9.51553 | 0.837796 | ||||||||
\(130\) | 8.30714 | 0.728585 | ||||||||
\(131\) | −6.97507 | −0.609415 | −0.304707 | − | 0.952446i | \(-0.598559\pi\) | ||||
−0.304707 | + | 0.952446i | \(0.598559\pi\) | |||||||
\(132\) | 4.97494 | 0.433013 | ||||||||
\(133\) | 0.209598 | 0.0181744 | ||||||||
\(134\) | −8.90752 | −0.769492 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −2.87224 | −0.246292 | ||||||||
\(137\) | 9.50150 | 0.811768 | 0.405884 | − | 0.913925i | \(-0.366964\pi\) | ||||
0.405884 | + | 0.913925i | \(0.366964\pi\) | |||||||
\(138\) | 1.90103 | 0.161827 | ||||||||
\(139\) | 12.7424 | 1.08079 | 0.540397 | − | 0.841410i | \(-0.318274\pi\) | ||||
0.540397 | + | 0.841410i | \(0.318274\pi\) | |||||||
\(140\) | 1.61393 | 0.136402 | ||||||||
\(141\) | 7.70980 | 0.649282 | ||||||||
\(142\) | −8.63390 | −0.724540 | ||||||||
\(143\) | −13.4699 | −1.12641 | ||||||||
\(144\) | −4.62309 | −0.385258 | ||||||||
\(145\) | 2.84119 | 0.235948 | ||||||||
\(146\) | 1.45952 | 0.120791 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 10.8883 | 0.895016 | ||||||||
\(149\) | 5.60930 | 0.459532 | 0.229766 | − | 0.973246i | \(-0.426204\pi\) | ||||
0.229766 | + | 0.973246i | \(0.426204\pi\) | |||||||
\(150\) | −1.90103 | −0.155219 | ||||||||
\(151\) | 8.79336 | 0.715594 | 0.357797 | − | 0.933799i | \(-0.383528\pi\) | ||||
0.357797 | + | 0.933799i | \(0.383528\pi\) | |||||||
\(152\) | 0.153831 | 0.0124774 | ||||||||
\(153\) | −3.91348 | −0.316386 | ||||||||
\(154\) | −5.85994 | −0.472208 | ||||||||
\(155\) | 9.13845 | 0.734018 | ||||||||
\(156\) | −7.05255 | −0.564656 | ||||||||
\(157\) | −4.41110 | −0.352044 | −0.176022 | − | 0.984386i | \(-0.556323\pi\) | ||||
−0.176022 | + | 0.984386i | \(0.556323\pi\) | |||||||
\(158\) | −12.6325 | −1.00499 | ||||||||
\(159\) | −12.7231 | −1.00901 | ||||||||
\(160\) | 7.32078 | 0.578759 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −1.90103 | −0.149359 | ||||||||
\(163\) | 6.73572 | 0.527582 | 0.263791 | − | 0.964580i | \(-0.415027\pi\) | ||||
0.263791 | + | 0.964580i | \(0.415027\pi\) | |||||||
\(164\) | −6.42205 | −0.501478 | ||||||||
\(165\) | 3.08250 | 0.239973 | ||||||||
\(166\) | 30.1025 | 2.33640 | ||||||||
\(167\) | 2.01945 | 0.156269 | 0.0781347 | − | 0.996943i | \(-0.475104\pi\) | ||||
0.0781347 | + | 0.996943i | \(0.475104\pi\) | |||||||
\(168\) | 0.733935 | 0.0566243 | ||||||||
\(169\) | 6.09518 | 0.468860 | ||||||||
\(170\) | 7.43965 | 0.570595 | ||||||||
\(171\) | 0.209598 | 0.0160283 | ||||||||
\(172\) | 15.3574 | 1.17099 | ||||||||
\(173\) | −5.66981 | −0.431068 | −0.215534 | − | 0.976496i | \(-0.569149\pi\) | ||||
−0.215534 | + | 0.976496i | \(0.569149\pi\) | |||||||
\(174\) | −5.40119 | −0.409463 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −14.2507 | −1.07419 | ||||||||
\(177\) | 3.22294 | 0.242251 | ||||||||
\(178\) | −14.1561 | −1.06104 | ||||||||
\(179\) | 4.87447 | 0.364335 | 0.182168 | − | 0.983267i | \(-0.441689\pi\) | ||||
0.182168 | + | 0.983267i | \(0.441689\pi\) | |||||||
\(180\) | 1.61393 | 0.120295 | ||||||||
\(181\) | −11.3864 | −0.846348 | −0.423174 | − | 0.906048i | \(-0.639084\pi\) | ||||
−0.423174 | + | 0.906048i | \(0.639084\pi\) | |||||||
\(182\) | 8.30714 | 0.615766 | ||||||||
\(183\) | −1.71549 | −0.126813 | ||||||||
\(184\) | −0.733935 | −0.0541064 | ||||||||
\(185\) | 6.74648 | 0.496011 | ||||||||
\(186\) | −17.3725 | −1.27381 | ||||||||
\(187\) | −12.0633 | −0.882156 | ||||||||
\(188\) | 12.4431 | 0.907503 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −0.398452 | −0.0289068 | ||||||||
\(191\) | 22.0335 | 1.59429 | 0.797144 | − | 0.603790i | \(-0.206343\pi\) | ||||
0.797144 | + | 0.603790i | \(0.206343\pi\) | |||||||
\(192\) | −4.67087 | −0.337091 | ||||||||
\(193\) | −15.2006 | −1.09416 | −0.547081 | − | 0.837080i | \(-0.684261\pi\) | ||||
−0.547081 | + | 0.837080i | \(0.684261\pi\) | |||||||
\(194\) | −7.72100 | −0.554336 | ||||||||
\(195\) | −4.36980 | −0.312928 | ||||||||
\(196\) | 1.61393 | 0.115281 | ||||||||
\(197\) | 8.03612 | 0.572550 | 0.286275 | − | 0.958148i | \(-0.407583\pi\) | ||||
0.286275 | + | 0.958148i | \(0.407583\pi\) | |||||||
\(198\) | −5.85994 | −0.416448 | ||||||||
\(199\) | −25.5617 | −1.81202 | −0.906011 | − | 0.423254i | \(-0.860888\pi\) | ||||
−0.906011 | + | 0.423254i | \(0.860888\pi\) | |||||||
\(200\) | 0.733935 | 0.0518970 | ||||||||
\(201\) | 4.68562 | 0.330498 | ||||||||
\(202\) | 19.7113 | 1.38688 | ||||||||
\(203\) | 2.84119 | 0.199412 | ||||||||
\(204\) | −6.31607 | −0.442213 | ||||||||
\(205\) | −3.97914 | −0.277915 | ||||||||
\(206\) | −18.5606 | −1.29318 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 20.2020 | 1.40076 | ||||||||
\(209\) | 0.646086 | 0.0446907 | ||||||||
\(210\) | −1.90103 | −0.131184 | ||||||||
\(211\) | 11.9115 | 0.820023 | 0.410011 | − | 0.912080i | \(-0.365525\pi\) | ||||
0.410011 | + | 0.912080i | \(0.365525\pi\) | |||||||
\(212\) | −20.5342 | −1.41030 | ||||||||
\(213\) | 4.54168 | 0.311191 | ||||||||
\(214\) | −22.6587 | −1.54892 | ||||||||
\(215\) | 9.51553 | 0.648954 | ||||||||
\(216\) | 0.733935 | 0.0499379 | ||||||||
\(217\) | 9.13845 | 0.620358 | ||||||||
\(218\) | −30.9338 | −2.09510 | ||||||||
\(219\) | −0.767751 | −0.0518798 | ||||||||
\(220\) | 4.97494 | 0.335410 | ||||||||
\(221\) | 17.1011 | 1.15035 | ||||||||
\(222\) | −12.8253 | −0.860777 | ||||||||
\(223\) | 9.10602 | 0.609784 | 0.304892 | − | 0.952387i | \(-0.401380\pi\) | ||||
0.304892 | + | 0.952387i | \(0.401380\pi\) | |||||||
\(224\) | 7.32078 | 0.489140 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 13.3797 | 0.890003 | ||||||||
\(227\) | −6.99649 | −0.464373 | −0.232187 | − | 0.972671i | \(-0.574588\pi\) | ||||
−0.232187 | + | 0.972671i | \(0.574588\pi\) | |||||||
\(228\) | 0.338276 | 0.0224029 | ||||||||
\(229\) | 16.7572 | 1.10735 | 0.553675 | − | 0.832733i | \(-0.313225\pi\) | ||||
0.553675 | + | 0.832733i | \(0.313225\pi\) | |||||||
\(230\) | 1.90103 | 0.125350 | ||||||||
\(231\) | 3.08250 | 0.202814 | ||||||||
\(232\) | 2.08525 | 0.136903 | ||||||||
\(233\) | −20.2492 | −1.32657 | −0.663283 | − | 0.748368i | \(-0.730838\pi\) | ||||
−0.663283 | + | 0.748368i | \(0.730838\pi\) | |||||||
\(234\) | 8.30714 | 0.543055 | ||||||||
\(235\) | 7.70980 | 0.502932 | ||||||||
\(236\) | 5.20160 | 0.338595 | ||||||||
\(237\) | 6.64506 | 0.431643 | ||||||||
\(238\) | 7.43965 | 0.482241 | ||||||||
\(239\) | 22.1015 | 1.42963 | 0.714814 | − | 0.699314i | \(-0.246511\pi\) | ||||
0.714814 | + | 0.699314i | \(0.246511\pi\) | |||||||
\(240\) | −4.62309 | −0.298419 | ||||||||
\(241\) | 21.9020 | 1.41083 | 0.705416 | − | 0.708794i | \(-0.250760\pi\) | ||||
0.705416 | + | 0.708794i | \(0.250760\pi\) | |||||||
\(242\) | 2.84808 | 0.183082 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.76868 | −0.177247 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 7.56448 | 0.482294 | ||||||||
\(247\) | −0.915901 | −0.0582774 | ||||||||
\(248\) | 6.70703 | 0.425897 | ||||||||
\(249\) | −15.8348 | −1.00349 | ||||||||
\(250\) | −1.90103 | −0.120232 | ||||||||
\(251\) | −4.01352 | −0.253331 | −0.126666 | − | 0.991945i | \(-0.540427\pi\) | ||||
−0.126666 | + | 0.991945i | \(0.540427\pi\) | |||||||
\(252\) | 1.61393 | 0.101668 | ||||||||
\(253\) | −3.08250 | −0.193795 | ||||||||
\(254\) | 10.6827 | 0.670292 | ||||||||
\(255\) | −3.91348 | −0.245071 | ||||||||
\(256\) | 20.2957 | 1.26848 | ||||||||
\(257\) | 3.79537 | 0.236749 | 0.118374 | − | 0.992969i | \(-0.462232\pi\) | ||||
0.118374 | + | 0.992969i | \(0.462232\pi\) | |||||||
\(258\) | −18.0893 | −1.12619 | ||||||||
\(259\) | 6.74648 | 0.419206 | ||||||||
\(260\) | −7.05255 | −0.437381 | ||||||||
\(261\) | 2.84119 | 0.175865 | ||||||||
\(262\) | 13.2598 | 0.819196 | ||||||||
\(263\) | −5.72874 | −0.353249 | −0.176625 | − | 0.984278i | \(-0.556518\pi\) | ||||
−0.176625 | + | 0.984278i | \(0.556518\pi\) | |||||||
\(264\) | 2.26236 | 0.139238 | ||||||||
\(265\) | −12.7231 | −0.781576 | ||||||||
\(266\) | −0.398452 | −0.0244307 | ||||||||
\(267\) | 7.44650 | 0.455719 | ||||||||
\(268\) | 7.56225 | 0.461938 | ||||||||
\(269\) | −3.25219 | −0.198289 | −0.0991446 | − | 0.995073i | \(-0.531611\pi\) | ||||
−0.0991446 | + | 0.995073i | \(0.531611\pi\) | |||||||
\(270\) | −1.90103 | −0.115693 | ||||||||
\(271\) | 12.1949 | 0.740789 | 0.370394 | − | 0.928875i | \(-0.379223\pi\) | ||||
0.370394 | + | 0.928875i | \(0.379223\pi\) | |||||||
\(272\) | 18.0924 | 1.09701 | ||||||||
\(273\) | −4.36980 | −0.264473 | ||||||||
\(274\) | −18.0627 | −1.09121 | ||||||||
\(275\) | 3.08250 | 0.185882 | ||||||||
\(276\) | −1.61393 | −0.0971471 | ||||||||
\(277\) | −17.8849 | −1.07460 | −0.537301 | − | 0.843391i | \(-0.680556\pi\) | ||||
−0.537301 | + | 0.843391i | \(0.680556\pi\) | |||||||
\(278\) | −24.2237 | −1.45284 | ||||||||
\(279\) | 9.13845 | 0.547105 | ||||||||
\(280\) | 0.733935 | 0.0438610 | ||||||||
\(281\) | 27.6266 | 1.64807 | 0.824034 | − | 0.566541i | \(-0.191719\pi\) | ||||
0.824034 | + | 0.566541i | \(0.191719\pi\) | |||||||
\(282\) | −14.6566 | −0.872787 | ||||||||
\(283\) | −27.9862 | −1.66361 | −0.831803 | − | 0.555071i | \(-0.812691\pi\) | ||||
−0.831803 | + | 0.555071i | \(0.812691\pi\) | |||||||
\(284\) | 7.32995 | 0.434953 | ||||||||
\(285\) | 0.209598 | 0.0124155 | ||||||||
\(286\) | 25.6068 | 1.51416 | ||||||||
\(287\) | −3.97914 | −0.234881 | ||||||||
\(288\) | 7.32078 | 0.431381 | ||||||||
\(289\) | −1.68470 | −0.0991002 | ||||||||
\(290\) | −5.40119 | −0.317169 | ||||||||
\(291\) | 4.06148 | 0.238088 | ||||||||
\(292\) | −1.23910 | −0.0725126 | ||||||||
\(293\) | −23.8737 | −1.39471 | −0.697357 | − | 0.716724i | \(-0.745641\pi\) | ||||
−0.697357 | + | 0.716724i | \(0.745641\pi\) | |||||||
\(294\) | −1.90103 | −0.110871 | ||||||||
\(295\) | 3.22294 | 0.187647 | ||||||||
\(296\) | 4.95148 | 0.287799 | ||||||||
\(297\) | 3.08250 | 0.178865 | ||||||||
\(298\) | −10.6635 | −0.617718 | ||||||||
\(299\) | 4.36980 | 0.252712 | ||||||||
\(300\) | 1.61393 | 0.0931802 | ||||||||
\(301\) | 9.51553 | 0.548466 | ||||||||
\(302\) | −16.7165 | −0.961925 | ||||||||
\(303\) | −10.3687 | −0.595668 | ||||||||
\(304\) | −0.968990 | −0.0555754 | ||||||||
\(305\) | −1.71549 | −0.0982289 | ||||||||
\(306\) | 7.43965 | 0.425296 | ||||||||
\(307\) | 25.9704 | 1.48221 | 0.741105 | − | 0.671390i | \(-0.234302\pi\) | ||||
0.741105 | + | 0.671390i | \(0.234302\pi\) | |||||||
\(308\) | 4.97494 | 0.283473 | ||||||||
\(309\) | 9.76343 | 0.555422 | ||||||||
\(310\) | −17.3725 | −0.986692 | ||||||||
\(311\) | −2.17066 | −0.123087 | −0.0615434 | − | 0.998104i | \(-0.519602\pi\) | ||||
−0.0615434 | + | 0.998104i | \(0.519602\pi\) | |||||||
\(312\) | −3.20715 | −0.181569 | ||||||||
\(313\) | 30.0595 | 1.69906 | 0.849532 | − | 0.527537i | \(-0.176884\pi\) | ||||
0.849532 | + | 0.527537i | \(0.176884\pi\) | |||||||
\(314\) | 8.38566 | 0.473230 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 10.7247 | 0.603309 | ||||||||
\(317\) | −1.65752 | −0.0930954 | −0.0465477 | − | 0.998916i | \(-0.514822\pi\) | ||||
−0.0465477 | + | 0.998916i | \(0.514822\pi\) | |||||||
\(318\) | 24.1871 | 1.35635 | ||||||||
\(319\) | 8.75797 | 0.490352 | ||||||||
\(320\) | −4.67087 | −0.261110 | ||||||||
\(321\) | 11.9192 | 0.665263 | ||||||||
\(322\) | 1.90103 | 0.105940 | ||||||||
\(323\) | −0.820256 | −0.0456403 | ||||||||
\(324\) | 1.61393 | 0.0896627 | ||||||||
\(325\) | −4.36980 | −0.242393 | ||||||||
\(326\) | −12.8048 | −0.709194 | ||||||||
\(327\) | 16.2721 | 0.899850 | ||||||||
\(328\) | −2.92043 | −0.161254 | ||||||||
\(329\) | 7.70980 | 0.425055 | ||||||||
\(330\) | −5.85994 | −0.322579 | ||||||||
\(331\) | 20.7489 | 1.14046 | 0.570232 | − | 0.821483i | \(-0.306853\pi\) | ||||
0.570232 | + | 0.821483i | \(0.306853\pi\) | |||||||
\(332\) | −25.5562 | −1.40258 | ||||||||
\(333\) | 6.74648 | 0.369705 | ||||||||
\(334\) | −3.83903 | −0.210063 | ||||||||
\(335\) | 4.68562 | 0.256003 | ||||||||
\(336\) | −4.62309 | −0.252210 | ||||||||
\(337\) | −24.4181 | −1.33014 | −0.665068 | − | 0.746782i | \(-0.731598\pi\) | ||||
−0.665068 | + | 0.746782i | \(0.731598\pi\) | |||||||
\(338\) | −11.5871 | −0.630257 | ||||||||
\(339\) | −7.03810 | −0.382257 | ||||||||
\(340\) | −6.31607 | −0.342537 | ||||||||
\(341\) | 28.1693 | 1.52545 | ||||||||
\(342\) | −0.398452 | −0.0215458 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 6.98378 | 0.376540 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 10.7785 | 0.579456 | ||||||||
\(347\) | 9.13516 | 0.490401 | 0.245201 | − | 0.969472i | \(-0.421146\pi\) | ||||
0.245201 | + | 0.969472i | \(0.421146\pi\) | |||||||
\(348\) | 4.58547 | 0.245807 | ||||||||
\(349\) | 21.6578 | 1.15932 | 0.579658 | − | 0.814860i | \(-0.303186\pi\) | ||||
0.579658 | + | 0.814860i | \(0.303186\pi\) | |||||||
\(350\) | −1.90103 | −0.101615 | ||||||||
\(351\) | −4.36980 | −0.233243 | ||||||||
\(352\) | 22.5663 | 1.20279 | ||||||||
\(353\) | −19.4080 | −1.03298 | −0.516491 | − | 0.856293i | \(-0.672762\pi\) | ||||
−0.516491 | + | 0.856293i | \(0.672762\pi\) | |||||||
\(354\) | −6.12692 | −0.325642 | ||||||||
\(355\) | 4.54168 | 0.241048 | ||||||||
\(356\) | 12.0181 | 0.636959 | ||||||||
\(357\) | −3.91348 | −0.207123 | ||||||||
\(358\) | −9.26654 | −0.489752 | ||||||||
\(359\) | −20.2121 | −1.06675 | −0.533377 | − | 0.845878i | \(-0.679077\pi\) | ||||
−0.533377 | + | 0.845878i | \(0.679077\pi\) | |||||||
\(360\) | 0.733935 | 0.0386818 | ||||||||
\(361\) | −18.9561 | −0.997688 | ||||||||
\(362\) | 21.6460 | 1.13769 | ||||||||
\(363\) | −1.49818 | −0.0786338 | ||||||||
\(364\) | −7.05255 | −0.369654 | ||||||||
\(365\) | −0.767751 | −0.0401859 | ||||||||
\(366\) | 3.26121 | 0.170466 | ||||||||
\(367\) | −6.58805 | −0.343893 | −0.171947 | − | 0.985106i | \(-0.555006\pi\) | ||||
−0.171947 | + | 0.985106i | \(0.555006\pi\) | |||||||
\(368\) | 4.62309 | 0.240995 | ||||||||
\(369\) | −3.97914 | −0.207146 | ||||||||
\(370\) | −12.8253 | −0.666755 | ||||||||
\(371\) | −12.7231 | −0.660552 | ||||||||
\(372\) | 14.7488 | 0.764690 | ||||||||
\(373\) | −17.0919 | −0.884986 | −0.442493 | − | 0.896772i | \(-0.645906\pi\) | ||||
−0.442493 | + | 0.896772i | \(0.645906\pi\) | |||||||
\(374\) | 22.9327 | 1.18582 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 5.65849 | 0.291814 | ||||||||
\(377\) | −12.4154 | −0.639427 | ||||||||
\(378\) | −1.90103 | −0.0977786 | ||||||||
\(379\) | 13.0912 | 0.672449 | 0.336224 | − | 0.941782i | \(-0.390850\pi\) | ||||
0.336224 | + | 0.941782i | \(0.390850\pi\) | |||||||
\(380\) | 0.338276 | 0.0173532 | ||||||||
\(381\) | −5.61942 | −0.287891 | ||||||||
\(382\) | −41.8864 | −2.14309 | ||||||||
\(383\) | 11.9650 | 0.611382 | 0.305691 | − | 0.952131i | \(-0.401113\pi\) | ||||
0.305691 | + | 0.952131i | \(0.401113\pi\) | |||||||
\(384\) | −5.76208 | −0.294045 | ||||||||
\(385\) | 3.08250 | 0.157099 | ||||||||
\(386\) | 28.8968 | 1.47081 | ||||||||
\(387\) | 9.51553 | 0.483701 | ||||||||
\(388\) | 6.55493 | 0.332776 | ||||||||
\(389\) | −14.7054 | −0.745591 | −0.372796 | − | 0.927914i | \(-0.621601\pi\) | ||||
−0.372796 | + | 0.927914i | \(0.621601\pi\) | |||||||
\(390\) | 8.30714 | 0.420648 | ||||||||
\(391\) | 3.91348 | 0.197913 | ||||||||
\(392\) | 0.733935 | 0.0370693 | ||||||||
\(393\) | −6.97507 | −0.351846 | ||||||||
\(394\) | −15.2769 | −0.769640 | ||||||||
\(395\) | 6.64506 | 0.334349 | ||||||||
\(396\) | 4.97494 | 0.250000 | ||||||||
\(397\) | 36.3058 | 1.82213 | 0.911067 | − | 0.412258i | \(-0.135260\pi\) | ||||
0.911067 | + | 0.412258i | \(0.135260\pi\) | |||||||
\(398\) | 48.5937 | 2.43578 | ||||||||
\(399\) | 0.209598 | 0.0104930 | ||||||||
\(400\) | −4.62309 | −0.231155 | ||||||||
\(401\) | 28.9819 | 1.44729 | 0.723644 | − | 0.690173i | \(-0.242466\pi\) | ||||
0.723644 | + | 0.690173i | \(0.242466\pi\) | |||||||
\(402\) | −8.90752 | −0.444267 | ||||||||
\(403\) | −39.9332 | −1.98922 | ||||||||
\(404\) | −16.7344 | −0.832568 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −5.40119 | −0.268057 | ||||||||
\(407\) | 20.7961 | 1.03082 | ||||||||
\(408\) | −2.87224 | −0.142197 | ||||||||
\(409\) | 31.0744 | 1.53653 | 0.768264 | − | 0.640133i | \(-0.221121\pi\) | ||||
0.768264 | + | 0.640133i | \(0.221121\pi\) | |||||||
\(410\) | 7.56448 | 0.373583 | ||||||||
\(411\) | 9.50150 | 0.468674 | ||||||||
\(412\) | 15.7575 | 0.776316 | ||||||||
\(413\) | 3.22294 | 0.158591 | ||||||||
\(414\) | 1.90103 | 0.0934307 | ||||||||
\(415\) | −15.8348 | −0.777299 | ||||||||
\(416\) | −31.9904 | −1.56846 | ||||||||
\(417\) | 12.7424 | 0.623997 | ||||||||
\(418\) | −1.22823 | −0.0600747 | ||||||||
\(419\) | 18.8076 | 0.918811 | 0.459405 | − | 0.888227i | \(-0.348063\pi\) | ||||
0.459405 | + | 0.888227i | \(0.348063\pi\) | |||||||
\(420\) | 1.61393 | 0.0787516 | ||||||||
\(421\) | −21.3350 | −1.03980 | −0.519902 | − | 0.854226i | \(-0.674032\pi\) | ||||
−0.519902 | + | 0.854226i | \(0.674032\pi\) | |||||||
\(422\) | −22.6442 | −1.10230 | ||||||||
\(423\) | 7.70980 | 0.374863 | ||||||||
\(424\) | −9.33795 | −0.453491 | ||||||||
\(425\) | −3.91348 | −0.189831 | ||||||||
\(426\) | −8.63390 | −0.418314 | ||||||||
\(427\) | −1.71549 | −0.0830186 | ||||||||
\(428\) | 19.2367 | 0.929840 | ||||||||
\(429\) | −13.4699 | −0.650334 | ||||||||
\(430\) | −18.0893 | −0.872345 | ||||||||
\(431\) | −23.3085 | −1.12273 | −0.561365 | − | 0.827569i | \(-0.689723\pi\) | ||||
−0.561365 | + | 0.827569i | \(0.689723\pi\) | |||||||
\(432\) | −4.62309 | −0.222429 | ||||||||
\(433\) | −3.79975 | −0.182604 | −0.0913022 | − | 0.995823i | \(-0.529103\pi\) | ||||
−0.0913022 | + | 0.995823i | \(0.529103\pi\) | |||||||
\(434\) | −17.3725 | −0.833907 | ||||||||
\(435\) | 2.84119 | 0.136224 | ||||||||
\(436\) | 26.2620 | 1.25772 | ||||||||
\(437\) | −0.209598 | −0.0100264 | ||||||||
\(438\) | 1.45952 | 0.0697386 | ||||||||
\(439\) | −33.5648 | −1.60196 | −0.800979 | − | 0.598692i | \(-0.795687\pi\) | ||||
−0.800979 | + | 0.598692i | \(0.795687\pi\) | |||||||
\(440\) | 2.26236 | 0.107854 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −32.5098 | −1.54633 | ||||||||
\(443\) | 2.73658 | 0.130019 | 0.0650094 | − | 0.997885i | \(-0.479292\pi\) | ||||
0.0650094 | + | 0.997885i | \(0.479292\pi\) | |||||||
\(444\) | 10.8883 | 0.516738 | ||||||||
\(445\) | 7.44650 | 0.352998 | ||||||||
\(446\) | −17.3108 | −0.819692 | ||||||||
\(447\) | 5.60930 | 0.265311 | ||||||||
\(448\) | −4.67087 | −0.220678 | ||||||||
\(449\) | −5.40737 | −0.255189 | −0.127595 | − | 0.991826i | \(-0.540726\pi\) | ||||
−0.127595 | + | 0.991826i | \(0.540726\pi\) | |||||||
\(450\) | −1.90103 | −0.0896156 | ||||||||
\(451\) | −12.2657 | −0.577570 | ||||||||
\(452\) | −11.3590 | −0.534282 | ||||||||
\(453\) | 8.79336 | 0.413148 | ||||||||
\(454\) | 13.3006 | 0.624226 | ||||||||
\(455\) | −4.36980 | −0.204860 | ||||||||
\(456\) | 0.153831 | 0.00720380 | ||||||||
\(457\) | −12.5890 | −0.588888 | −0.294444 | − | 0.955669i | \(-0.595134\pi\) | ||||
−0.294444 | + | 0.955669i | \(0.595134\pi\) | |||||||
\(458\) | −31.8561 | −1.48854 | ||||||||
\(459\) | −3.91348 | −0.182665 | ||||||||
\(460\) | −1.61393 | −0.0752498 | ||||||||
\(461\) | −14.5901 | −0.679529 | −0.339764 | − | 0.940511i | \(-0.610347\pi\) | ||||
−0.339764 | + | 0.940511i | \(0.610347\pi\) | |||||||
\(462\) | −5.85994 | −0.272629 | ||||||||
\(463\) | 32.9600 | 1.53178 | 0.765890 | − | 0.642972i | \(-0.222299\pi\) | ||||
0.765890 | + | 0.642972i | \(0.222299\pi\) | |||||||
\(464\) | −13.1351 | −0.609780 | ||||||||
\(465\) | 9.13845 | 0.423785 | ||||||||
\(466\) | 38.4943 | 1.78322 | ||||||||
\(467\) | 4.16884 | 0.192911 | 0.0964554 | − | 0.995337i | \(-0.469249\pi\) | ||||
0.0964554 | + | 0.995337i | \(0.469249\pi\) | |||||||
\(468\) | −7.05255 | −0.326004 | ||||||||
\(469\) | 4.68562 | 0.216362 | ||||||||
\(470\) | −14.6566 | −0.676058 | ||||||||
\(471\) | −4.41110 | −0.203253 | ||||||||
\(472\) | 2.36543 | 0.108878 | ||||||||
\(473\) | 29.3316 | 1.34867 | ||||||||
\(474\) | −12.6325 | −0.580229 | ||||||||
\(475\) | 0.209598 | 0.00961701 | ||||||||
\(476\) | −6.31607 | −0.289497 | ||||||||
\(477\) | −12.7231 | −0.582552 | ||||||||
\(478\) | −42.0157 | −1.92176 | ||||||||
\(479\) | −36.1536 | −1.65190 | −0.825949 | − | 0.563745i | \(-0.809360\pi\) | ||||
−0.825949 | + | 0.563745i | \(0.809360\pi\) | |||||||
\(480\) | 7.32078 | 0.334146 | ||||||||
\(481\) | −29.4808 | −1.34421 | ||||||||
\(482\) | −41.6364 | −1.89649 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | −2.41795 | −0.109907 | ||||||||
\(485\) | 4.06148 | 0.184422 | ||||||||
\(486\) | −1.90103 | −0.0862326 | ||||||||
\(487\) | −39.3649 | −1.78379 | −0.891896 | − | 0.452240i | \(-0.850625\pi\) | ||||
−0.891896 | + | 0.452240i | \(0.850625\pi\) | |||||||
\(488\) | −1.25906 | −0.0569950 | ||||||||
\(489\) | 6.73572 | 0.304600 | ||||||||
\(490\) | −1.90103 | −0.0858799 | ||||||||
\(491\) | 16.1377 | 0.728284 | 0.364142 | − | 0.931344i | \(-0.381362\pi\) | ||||
0.364142 | + | 0.931344i | \(0.381362\pi\) | |||||||
\(492\) | −6.42205 | −0.289528 | ||||||||
\(493\) | −11.1189 | −0.500771 | ||||||||
\(494\) | 1.74116 | 0.0783384 | ||||||||
\(495\) | 3.08250 | 0.138548 | ||||||||
\(496\) | −42.2479 | −1.89699 | ||||||||
\(497\) | 4.54168 | 0.203722 | ||||||||
\(498\) | 30.1025 | 1.34892 | ||||||||
\(499\) | −12.0077 | −0.537539 | −0.268770 | − | 0.963205i | \(-0.586617\pi\) | ||||
−0.268770 | + | 0.963205i | \(0.586617\pi\) | |||||||
\(500\) | 1.61393 | 0.0721771 | ||||||||
\(501\) | 2.01945 | 0.0902222 | ||||||||
\(502\) | 7.62984 | 0.340536 | ||||||||
\(503\) | −14.0978 | −0.628588 | −0.314294 | − | 0.949326i | \(-0.601768\pi\) | ||||
−0.314294 | + | 0.949326i | \(0.601768\pi\) | |||||||
\(504\) | 0.733935 | 0.0326921 | ||||||||
\(505\) | −10.3687 | −0.461403 | ||||||||
\(506\) | 5.85994 | 0.260506 | ||||||||
\(507\) | 6.09518 | 0.270696 | ||||||||
\(508\) | −9.06933 | −0.402387 | ||||||||
\(509\) | −2.17861 | −0.0965653 | −0.0482826 | − | 0.998834i | \(-0.515375\pi\) | ||||
−0.0482826 | + | 0.998834i | \(0.515375\pi\) | |||||||
\(510\) | 7.43965 | 0.329433 | ||||||||
\(511\) | −0.767751 | −0.0339633 | ||||||||
\(512\) | −27.0586 | −1.19583 | ||||||||
\(513\) | 0.209598 | 0.00925397 | ||||||||
\(514\) | −7.21512 | −0.318245 | ||||||||
\(515\) | 9.76343 | 0.430228 | ||||||||
\(516\) | 15.3574 | 0.676071 | ||||||||
\(517\) | 23.7655 | 1.04520 | ||||||||
\(518\) | −12.8253 | −0.563511 | ||||||||
\(519\) | −5.66981 | −0.248877 | ||||||||
\(520\) | −3.20715 | −0.140643 | ||||||||
\(521\) | −29.3160 | −1.28436 | −0.642178 | − | 0.766555i | \(-0.721969\pi\) | ||||
−0.642178 | + | 0.766555i | \(0.721969\pi\) | |||||||
\(522\) | −5.40119 | −0.236404 | ||||||||
\(523\) | −5.47392 | −0.239358 | −0.119679 | − | 0.992813i | \(-0.538187\pi\) | ||||
−0.119679 | + | 0.992813i | \(0.538187\pi\) | |||||||
\(524\) | −11.2573 | −0.491776 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 10.8905 | 0.474849 | ||||||||
\(527\) | −35.7631 | −1.55787 | ||||||||
\(528\) | −14.2507 | −0.620182 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 24.1871 | 1.05062 | ||||||||
\(531\) | 3.22294 | 0.139864 | ||||||||
\(532\) | 0.338276 | 0.0146661 | ||||||||
\(533\) | 17.3881 | 0.753160 | ||||||||
\(534\) | −14.1561 | −0.612592 | ||||||||
\(535\) | 11.9192 | 0.515310 | ||||||||
\(536\) | 3.43894 | 0.148540 | ||||||||
\(537\) | 4.87447 | 0.210349 | ||||||||
\(538\) | 6.18251 | 0.266547 | ||||||||
\(539\) | 3.08250 | 0.132773 | ||||||||
\(540\) | 1.61393 | 0.0694524 | ||||||||
\(541\) | 24.1677 | 1.03905 | 0.519525 | − | 0.854455i | \(-0.326109\pi\) | ||||
0.519525 | + | 0.854455i | \(0.326109\pi\) | |||||||
\(542\) | −23.1830 | −0.995794 | ||||||||
\(543\) | −11.3864 | −0.488639 | ||||||||
\(544\) | −28.6497 | −1.22835 | ||||||||
\(545\) | 16.2721 | 0.697021 | ||||||||
\(546\) | 8.30714 | 0.355513 | ||||||||
\(547\) | 8.49967 | 0.363419 | 0.181710 | − | 0.983352i | \(-0.441837\pi\) | ||||
0.181710 | + | 0.983352i | \(0.441837\pi\) | |||||||
\(548\) | 15.3347 | 0.655068 | ||||||||
\(549\) | −1.71549 | −0.0732155 | ||||||||
\(550\) | −5.85994 | −0.249869 | ||||||||
\(551\) | 0.595507 | 0.0253694 | ||||||||
\(552\) | −0.733935 | −0.0312383 | ||||||||
\(553\) | 6.64506 | 0.282577 | ||||||||
\(554\) | 33.9999 | 1.44452 | ||||||||
\(555\) | 6.74648 | 0.286372 | ||||||||
\(556\) | 20.5653 | 0.872162 | ||||||||
\(557\) | −17.4128 | −0.737803 | −0.368902 | − | 0.929468i | \(-0.620266\pi\) | ||||
−0.368902 | + | 0.929468i | \(0.620266\pi\) | |||||||
\(558\) | −17.3725 | −0.735437 | ||||||||
\(559\) | −41.5810 | −1.75869 | ||||||||
\(560\) | −4.62309 | −0.195361 | ||||||||
\(561\) | −12.0633 | −0.509313 | ||||||||
\(562\) | −52.5192 | −2.21539 | ||||||||
\(563\) | −7.29010 | −0.307241 | −0.153620 | − | 0.988130i | \(-0.549093\pi\) | ||||
−0.153620 | + | 0.988130i | \(0.549093\pi\) | |||||||
\(564\) | 12.4431 | 0.523947 | ||||||||
\(565\) | −7.03810 | −0.296095 | ||||||||
\(566\) | 53.2027 | 2.23627 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 3.33330 | 0.139862 | ||||||||
\(569\) | −28.1750 | −1.18116 | −0.590578 | − | 0.806980i | \(-0.701100\pi\) | ||||
−0.590578 | + | 0.806980i | \(0.701100\pi\) | |||||||
\(570\) | −0.398452 | −0.0166893 | ||||||||
\(571\) | 32.1338 | 1.34476 | 0.672380 | − | 0.740206i | \(-0.265272\pi\) | ||||
0.672380 | + | 0.740206i | \(0.265272\pi\) | |||||||
\(572\) | −21.7395 | −0.908974 | ||||||||
\(573\) | 22.0335 | 0.920462 | ||||||||
\(574\) | 7.56448 | 0.315735 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | −4.67087 | −0.194620 | ||||||||
\(577\) | 12.3009 | 0.512095 | 0.256047 | − | 0.966664i | \(-0.417580\pi\) | ||||
0.256047 | + | 0.966664i | \(0.417580\pi\) | |||||||
\(578\) | 3.20268 | 0.133214 | ||||||||
\(579\) | −15.2006 | −0.631715 | ||||||||
\(580\) | 4.58547 | 0.190401 | ||||||||
\(581\) | −15.8348 | −0.656938 | ||||||||
\(582\) | −7.72100 | −0.320046 | ||||||||
\(583\) | −39.2191 | −1.62429 | ||||||||
\(584\) | −0.563479 | −0.0233169 | ||||||||
\(585\) | −4.36980 | −0.180669 | ||||||||
\(586\) | 45.3846 | 1.87482 | ||||||||
\(587\) | −19.9075 | −0.821671 | −0.410836 | − | 0.911709i | \(-0.634763\pi\) | ||||
−0.410836 | + | 0.911709i | \(0.634763\pi\) | |||||||
\(588\) | 1.61393 | 0.0665573 | ||||||||
\(589\) | 1.91540 | 0.0789226 | ||||||||
\(590\) | −6.12692 | −0.252241 | ||||||||
\(591\) | 8.03612 | 0.330562 | ||||||||
\(592\) | −31.1896 | −1.28188 | ||||||||
\(593\) | −1.27208 | −0.0522382 | −0.0261191 | − | 0.999659i | \(-0.508315\pi\) | ||||
−0.0261191 | + | 0.999659i | \(0.508315\pi\) | |||||||
\(594\) | −5.85994 | −0.240436 | ||||||||
\(595\) | −3.91348 | −0.160437 | ||||||||
\(596\) | 9.05301 | 0.370826 | ||||||||
\(597\) | −25.5617 | −1.04617 | ||||||||
\(598\) | −8.30714 | −0.339704 | ||||||||
\(599\) | −12.3041 | −0.502732 | −0.251366 | − | 0.967892i | \(-0.580880\pi\) | ||||
−0.251366 | + | 0.967892i | \(0.580880\pi\) | |||||||
\(600\) | 0.733935 | 0.0299628 | ||||||||
\(601\) | 29.9449 | 1.22148 | 0.610739 | − | 0.791832i | \(-0.290872\pi\) | ||||
0.610739 | + | 0.791832i | \(0.290872\pi\) | |||||||
\(602\) | −18.0893 | −0.737266 | ||||||||
\(603\) | 4.68562 | 0.190813 | ||||||||
\(604\) | 14.1919 | 0.577459 | ||||||||
\(605\) | −1.49818 | −0.0609095 | ||||||||
\(606\) | 19.7113 | 0.800718 | ||||||||
\(607\) | 3.66335 | 0.148691 | 0.0743454 | − | 0.997233i | \(-0.476313\pi\) | ||||
0.0743454 | + | 0.997233i | \(0.476313\pi\) | |||||||
\(608\) | 1.53442 | 0.0622290 | ||||||||
\(609\) | 2.84119 | 0.115131 | ||||||||
\(610\) | 3.26121 | 0.132043 | ||||||||
\(611\) | −33.6903 | −1.36296 | ||||||||
\(612\) | −6.31607 | −0.255312 | ||||||||
\(613\) | 13.7083 | 0.553672 | 0.276836 | − | 0.960917i | \(-0.410714\pi\) | ||||
0.276836 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(614\) | −49.3706 | −1.99244 | ||||||||
\(615\) | −3.97914 | −0.160454 | ||||||||
\(616\) | 2.26236 | 0.0911529 | ||||||||
\(617\) | 27.5979 | 1.11105 | 0.555525 | − | 0.831500i | \(-0.312517\pi\) | ||||
0.555525 | + | 0.831500i | \(0.312517\pi\) | |||||||
\(618\) | −18.5606 | −0.746618 | ||||||||
\(619\) | −32.6525 | −1.31241 | −0.656207 | − | 0.754581i | \(-0.727840\pi\) | ||||
−0.656207 | + | 0.754581i | \(0.727840\pi\) | |||||||
\(620\) | 14.7488 | 0.592326 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 4.12649 | 0.165457 | ||||||||
\(623\) | 7.44650 | 0.298338 | ||||||||
\(624\) | 20.2020 | 0.808727 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −57.1441 | −2.28394 | ||||||||
\(627\) | 0.646086 | 0.0258022 | ||||||||
\(628\) | −7.11921 | −0.284087 | ||||||||
\(629\) | −26.4022 | −1.05272 | ||||||||
\(630\) | −1.90103 | −0.0757390 | ||||||||
\(631\) | −26.2164 | −1.04366 | −0.521830 | − | 0.853050i | \(-0.674750\pi\) | ||||
−0.521830 | + | 0.853050i | \(0.674750\pi\) | |||||||
\(632\) | 4.87704 | 0.193998 | ||||||||
\(633\) | 11.9115 | 0.473440 | ||||||||
\(634\) | 3.15099 | 0.125142 | ||||||||
\(635\) | −5.61942 | −0.223000 | ||||||||
\(636\) | −20.5342 | −0.814235 | ||||||||
\(637\) | −4.36980 | −0.173138 | ||||||||
\(638\) | −16.6492 | −0.659148 | ||||||||
\(639\) | 4.54168 | 0.179666 | ||||||||
\(640\) | −5.76208 | −0.227766 | ||||||||
\(641\) | 1.61002 | 0.0635919 | 0.0317959 | − | 0.999494i | \(-0.489877\pi\) | ||||
0.0317959 | + | 0.999494i | \(0.489877\pi\) | |||||||
\(642\) | −22.6587 | −0.894269 | ||||||||
\(643\) | 16.6094 | 0.655011 | 0.327505 | − | 0.944849i | \(-0.393792\pi\) | ||||
0.327505 | + | 0.944849i | \(0.393792\pi\) | |||||||
\(644\) | −1.61393 | −0.0635977 | ||||||||
\(645\) | 9.51553 | 0.374674 | ||||||||
\(646\) | 1.55933 | 0.0613512 | ||||||||
\(647\) | −2.13466 | −0.0839220 | −0.0419610 | − | 0.999119i | \(-0.513361\pi\) | ||||
−0.0419610 | + | 0.999119i | \(0.513361\pi\) | |||||||
\(648\) | 0.733935 | 0.0288317 | ||||||||
\(649\) | 9.93472 | 0.389972 | ||||||||
\(650\) | 8.30714 | 0.325833 | ||||||||
\(651\) | 9.13845 | 0.358164 | ||||||||
\(652\) | 10.8710 | 0.425740 | ||||||||
\(653\) | 33.3242 | 1.30408 | 0.652039 | − | 0.758185i | \(-0.273914\pi\) | ||||
0.652039 | + | 0.758185i | \(0.273914\pi\) | |||||||
\(654\) | −30.9338 | −1.20961 | ||||||||
\(655\) | −6.97507 | −0.272539 | ||||||||
\(656\) | 18.3959 | 0.718240 | ||||||||
\(657\) | −0.767751 | −0.0299528 | ||||||||
\(658\) | −14.6566 | −0.571373 | ||||||||
\(659\) | −21.3629 | −0.832181 | −0.416091 | − | 0.909323i | \(-0.636600\pi\) | ||||
−0.416091 | + | 0.909323i | \(0.636600\pi\) | |||||||
\(660\) | 4.97494 | 0.193649 | ||||||||
\(661\) | −36.3297 | −1.41306 | −0.706530 | − | 0.707683i | \(-0.749741\pi\) | ||||
−0.706530 | + | 0.707683i | \(0.749741\pi\) | |||||||
\(662\) | −39.4444 | −1.53305 | ||||||||
\(663\) | 17.1011 | 0.664152 | ||||||||
\(664\) | −11.6217 | −0.451009 | ||||||||
\(665\) | 0.209598 | 0.00812786 | ||||||||
\(666\) | −12.8253 | −0.496970 | ||||||||
\(667\) | −2.84119 | −0.110011 | ||||||||
\(668\) | 3.25924 | 0.126104 | ||||||||
\(669\) | 9.10602 | 0.352059 | ||||||||
\(670\) | −8.90752 | −0.344127 | ||||||||
\(671\) | −5.28801 | −0.204142 | ||||||||
\(672\) | 7.32078 | 0.282405 | ||||||||
\(673\) | −46.2707 | −1.78360 | −0.891801 | − | 0.452427i | \(-0.850558\pi\) | ||||
−0.891801 | + | 0.452427i | \(0.850558\pi\) | |||||||
\(674\) | 46.4196 | 1.78801 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 9.83718 | 0.378353 | ||||||||
\(677\) | −49.3486 | −1.89662 | −0.948310 | − | 0.317345i | \(-0.897209\pi\) | ||||
−0.948310 | + | 0.317345i | \(0.897209\pi\) | |||||||
\(678\) | 13.3797 | 0.513843 | ||||||||
\(679\) | 4.06148 | 0.155865 | ||||||||
\(680\) | −2.87224 | −0.110145 | ||||||||
\(681\) | −6.99649 | −0.268106 | ||||||||
\(682\) | −53.5508 | −2.05057 | ||||||||
\(683\) | −31.0717 | −1.18893 | −0.594463 | − | 0.804123i | \(-0.702635\pi\) | ||||
−0.594463 | + | 0.804123i | \(0.702635\pi\) | |||||||
\(684\) | 0.338276 | 0.0129343 | ||||||||
\(685\) | 9.50150 | 0.363034 | ||||||||
\(686\) | −1.90103 | −0.0725818 | ||||||||
\(687\) | 16.7572 | 0.639329 | ||||||||
\(688\) | −43.9912 | −1.67715 | ||||||||
\(689\) | 55.5976 | 2.11810 | ||||||||
\(690\) | 1.90103 | 0.0723711 | ||||||||
\(691\) | −18.1085 | −0.688879 | −0.344440 | − | 0.938808i | \(-0.611931\pi\) | ||||
−0.344440 | + | 0.938808i | \(0.611931\pi\) | |||||||
\(692\) | −9.15067 | −0.347856 | ||||||||
\(693\) | 3.08250 | 0.117095 | ||||||||
\(694\) | −17.3663 | −0.659214 | ||||||||
\(695\) | 12.7424 | 0.483346 | ||||||||
\(696\) | 2.08525 | 0.0790410 | ||||||||
\(697\) | 15.5723 | 0.589842 | ||||||||
\(698\) | −41.1722 | −1.55839 | ||||||||
\(699\) | −20.2492 | −0.765894 | ||||||||
\(700\) | 1.61393 | 0.0610008 | ||||||||
\(701\) | 12.5359 | 0.473476 | 0.236738 | − | 0.971573i | \(-0.423922\pi\) | ||||
0.236738 | + | 0.971573i | \(0.423922\pi\) | |||||||
\(702\) | 8.30714 | 0.313533 | ||||||||
\(703\) | 1.41405 | 0.0533318 | ||||||||
\(704\) | −14.3980 | −0.542644 | ||||||||
\(705\) | 7.70980 | 0.290368 | ||||||||
\(706\) | 36.8952 | 1.38857 | ||||||||
\(707\) | −10.3687 | −0.389957 | ||||||||
\(708\) | 5.20160 | 0.195488 | ||||||||
\(709\) | 24.6520 | 0.925826 | 0.462913 | − | 0.886404i | \(-0.346804\pi\) | ||||
0.462913 | + | 0.886404i | \(0.346804\pi\) | |||||||
\(710\) | −8.63390 | −0.324024 | ||||||||
\(711\) | 6.64506 | 0.249209 | ||||||||
\(712\) | 5.46525 | 0.204819 | ||||||||
\(713\) | −9.13845 | −0.342238 | ||||||||
\(714\) | 7.43965 | 0.278422 | ||||||||
\(715\) | −13.4699 | −0.503747 | ||||||||
\(716\) | 7.86705 | 0.294005 | ||||||||
\(717\) | 22.1015 | 0.825397 | ||||||||
\(718\) | 38.4239 | 1.43397 | ||||||||
\(719\) | 3.39866 | 0.126749 | 0.0633743 | − | 0.997990i | \(-0.479814\pi\) | ||||
0.0633743 | + | 0.997990i | \(0.479814\pi\) | |||||||
\(720\) | −4.62309 | −0.172292 | ||||||||
\(721\) | 9.76343 | 0.363609 | ||||||||
\(722\) | 36.0361 | 1.34113 | ||||||||
\(723\) | 21.9020 | 0.814544 | ||||||||
\(724\) | −18.3769 | −0.682972 | ||||||||
\(725\) | 2.84119 | 0.105519 | ||||||||
\(726\) | 2.84808 | 0.105702 | ||||||||
\(727\) | −24.0284 | −0.891165 | −0.445583 | − | 0.895241i | \(-0.647003\pi\) | ||||
−0.445583 | + | 0.895241i | \(0.647003\pi\) | |||||||
\(728\) | −3.20715 | −0.118865 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.45952 | 0.0540193 | ||||||||
\(731\) | −37.2388 | −1.37733 | ||||||||
\(732\) | −2.76868 | −0.102334 | ||||||||
\(733\) | 19.0389 | 0.703218 | 0.351609 | − | 0.936147i | \(-0.385635\pi\) | ||||
0.351609 | + | 0.936147i | \(0.385635\pi\) | |||||||
\(734\) | 12.5241 | 0.462273 | ||||||||
\(735\) | 1.00000 | 0.0368856 | ||||||||
\(736\) | −7.32078 | −0.269848 | ||||||||
\(737\) | 14.4434 | 0.532031 | ||||||||
\(738\) | 7.56448 | 0.278452 | ||||||||
\(739\) | 10.8761 | 0.400083 | 0.200041 | − | 0.979787i | \(-0.435892\pi\) | ||||
0.200041 | + | 0.979787i | \(0.435892\pi\) | |||||||
\(740\) | 10.8883 | 0.400263 | ||||||||
\(741\) | −0.915901 | −0.0336465 | ||||||||
\(742\) | 24.1871 | 0.887937 | ||||||||
\(743\) | 31.0934 | 1.14071 | 0.570353 | − | 0.821400i | \(-0.306807\pi\) | ||||
0.570353 | + | 0.821400i | \(0.306807\pi\) | |||||||
\(744\) | 6.70703 | 0.245892 | ||||||||
\(745\) | 5.60930 | 0.205509 | ||||||||
\(746\) | 32.4923 | 1.18963 | ||||||||
\(747\) | −15.8348 | −0.579364 | ||||||||
\(748\) | −19.4693 | −0.711868 | ||||||||
\(749\) | 11.9192 | 0.435517 | ||||||||
\(750\) | −1.90103 | −0.0694159 | ||||||||
\(751\) | 0.377023 | 0.0137578 | 0.00687889 | − | 0.999976i | \(-0.497810\pi\) | ||||
0.00687889 | + | 0.999976i | \(0.497810\pi\) | |||||||
\(752\) | −35.6431 | −1.29977 | ||||||||
\(753\) | −4.01352 | −0.146261 | ||||||||
\(754\) | 23.6021 | 0.859539 | ||||||||
\(755\) | 8.79336 | 0.320023 | ||||||||
\(756\) | 1.61393 | 0.0586980 | ||||||||
\(757\) | −49.5370 | −1.80045 | −0.900227 | − | 0.435421i | \(-0.856599\pi\) | ||||
−0.900227 | + | 0.435421i | \(0.856599\pi\) | |||||||
\(758\) | −24.8868 | −0.903928 | ||||||||
\(759\) | −3.08250 | −0.111888 | ||||||||
\(760\) | 0.153831 | 0.00558004 | ||||||||
\(761\) | 23.1228 | 0.838201 | 0.419100 | − | 0.907940i | \(-0.362346\pi\) | ||||
0.419100 | + | 0.907940i | \(0.362346\pi\) | |||||||
\(762\) | 10.6827 | 0.386993 | ||||||||
\(763\) | 16.2721 | 0.589090 | ||||||||
\(764\) | 35.5605 | 1.28653 | ||||||||
\(765\) | −3.91348 | −0.141492 | ||||||||
\(766\) | −22.7458 | −0.821841 | ||||||||
\(767\) | −14.0836 | −0.508530 | ||||||||
\(768\) | 20.2957 | 0.732356 | ||||||||
\(769\) | 3.97204 | 0.143235 | 0.0716177 | − | 0.997432i | \(-0.477184\pi\) | ||||
0.0716177 | + | 0.997432i | \(0.477184\pi\) | |||||||
\(770\) | −5.85994 | −0.211178 | ||||||||
\(771\) | 3.79537 | 0.136687 | ||||||||
\(772\) | −24.5326 | −0.882949 | ||||||||
\(773\) | −15.7764 | −0.567438 | −0.283719 | − | 0.958907i | \(-0.591568\pi\) | ||||
−0.283719 | + | 0.958907i | \(0.591568\pi\) | |||||||
\(774\) | −18.0893 | −0.650208 | ||||||||
\(775\) | 9.13845 | 0.328263 | ||||||||
\(776\) | 2.98086 | 0.107007 | ||||||||
\(777\) | 6.74648 | 0.242029 | ||||||||
\(778\) | 27.9554 | 1.00225 | ||||||||
\(779\) | −0.834019 | −0.0298818 | ||||||||
\(780\) | −7.05255 | −0.252522 | ||||||||
\(781\) | 13.9998 | 0.500951 | ||||||||
\(782\) | −7.43965 | −0.266041 | ||||||||
\(783\) | 2.84119 | 0.101536 | ||||||||
\(784\) | −4.62309 | −0.165110 | ||||||||
\(785\) | −4.41110 | −0.157439 | ||||||||
\(786\) | 13.2598 | 0.472963 | ||||||||
\(787\) | 23.8046 | 0.848541 | 0.424271 | − | 0.905535i | \(-0.360531\pi\) | ||||
0.424271 | + | 0.905535i | \(0.360531\pi\) | |||||||
\(788\) | 12.9697 | 0.462027 | ||||||||
\(789\) | −5.72874 | −0.203948 | ||||||||
\(790\) | −12.6325 | −0.449444 | ||||||||
\(791\) | −7.03810 | −0.250246 | ||||||||
\(792\) | 2.26236 | 0.0803893 | ||||||||
\(793\) | 7.49637 | 0.266204 | ||||||||
\(794\) | −69.0185 | −2.44937 | ||||||||
\(795\) | −12.7231 | −0.451243 | ||||||||
\(796\) | −41.2548 | −1.46224 | ||||||||
\(797\) | 29.2994 | 1.03784 | 0.518918 | − | 0.854824i | \(-0.326335\pi\) | ||||
0.518918 | + | 0.854824i | \(0.326335\pi\) | |||||||
\(798\) | −0.398452 | −0.0141051 | ||||||||
\(799\) | −30.1721 | −1.06741 | ||||||||
\(800\) | 7.32078 | 0.258829 | ||||||||
\(801\) | 7.44650 | 0.263109 | ||||||||
\(802\) | −55.0956 | −1.94549 | ||||||||
\(803\) | −2.36660 | −0.0835153 | ||||||||
\(804\) | 7.56225 | 0.266700 | ||||||||
\(805\) | −1.00000 | −0.0352454 | ||||||||
\(806\) | 75.9144 | 2.67397 | ||||||||
\(807\) | −3.25219 | −0.114482 | ||||||||
\(808\) | −7.60998 | −0.267718 | ||||||||
\(809\) | −30.0197 | −1.05544 | −0.527718 | − | 0.849419i | \(-0.676952\pi\) | ||||
−0.527718 | + | 0.849419i | \(0.676952\pi\) | |||||||
\(810\) | −1.90103 | −0.0667955 | ||||||||
\(811\) | −8.04869 | −0.282628 | −0.141314 | − | 0.989965i | \(-0.545133\pi\) | ||||
−0.141314 | + | 0.989965i | \(0.545133\pi\) | |||||||
\(812\) | 4.58547 | 0.160919 | ||||||||
\(813\) | 12.1949 | 0.427695 | ||||||||
\(814\) | −39.5340 | −1.38567 | ||||||||
\(815\) | 6.73572 | 0.235942 | ||||||||
\(816\) | 18.0924 | 0.633359 | ||||||||
\(817\) | 1.99443 | 0.0697764 | ||||||||
\(818\) | −59.0734 | −2.06545 | ||||||||
\(819\) | −4.36980 | −0.152693 | ||||||||
\(820\) | −6.42205 | −0.224268 | ||||||||
\(821\) | −10.3262 | −0.360388 | −0.180194 | − | 0.983631i | \(-0.557673\pi\) | ||||
−0.180194 | + | 0.983631i | \(0.557673\pi\) | |||||||
\(822\) | −18.0627 | −0.630008 | ||||||||
\(823\) | −22.7733 | −0.793827 | −0.396914 | − | 0.917856i | \(-0.629919\pi\) | ||||
−0.396914 | + | 0.917856i | \(0.629919\pi\) | |||||||
\(824\) | 7.16573 | 0.249630 | ||||||||
\(825\) | 3.08250 | 0.107319 | ||||||||
\(826\) | −6.12692 | −0.213183 | ||||||||
\(827\) | −17.0953 | −0.594461 | −0.297230 | − | 0.954806i | \(-0.596063\pi\) | ||||
−0.297230 | + | 0.954806i | \(0.596063\pi\) | |||||||
\(828\) | −1.61393 | −0.0560879 | ||||||||
\(829\) | −23.9580 | −0.832097 | −0.416049 | − | 0.909342i | \(-0.636585\pi\) | ||||
−0.416049 | + | 0.909342i | \(0.636585\pi\) | |||||||
\(830\) | 30.1025 | 1.04487 | ||||||||
\(831\) | −17.8849 | −0.620422 | ||||||||
\(832\) | 20.4108 | 0.707617 | ||||||||
\(833\) | −3.91348 | −0.135594 | ||||||||
\(834\) | −24.2237 | −0.838797 | ||||||||
\(835\) | 2.01945 | 0.0698858 | ||||||||
\(836\) | 1.04274 | 0.0360638 | ||||||||
\(837\) | 9.13845 | 0.315871 | ||||||||
\(838\) | −35.7539 | −1.23510 | ||||||||
\(839\) | 9.81942 | 0.339004 | 0.169502 | − | 0.985530i | \(-0.445784\pi\) | ||||
0.169502 | + | 0.985530i | \(0.445784\pi\) | |||||||
\(840\) | 0.733935 | 0.0253232 | ||||||||
\(841\) | −20.9277 | −0.721643 | ||||||||
\(842\) | 40.5585 | 1.39774 | ||||||||
\(843\) | 27.6266 | 0.951512 | ||||||||
\(844\) | 19.2243 | 0.661729 | ||||||||
\(845\) | 6.09518 | 0.209681 | ||||||||
\(846\) | −14.6566 | −0.503904 | ||||||||
\(847\) | −1.49818 | −0.0514779 | ||||||||
\(848\) | 58.8202 | 2.01990 | ||||||||
\(849\) | −27.9862 | −0.960483 | ||||||||
\(850\) | 7.43965 | 0.255178 | ||||||||
\(851\) | −6.74648 | −0.231266 | ||||||||
\(852\) | 7.32995 | 0.251120 | ||||||||
\(853\) | −28.4065 | −0.972621 | −0.486311 | − | 0.873786i | \(-0.661658\pi\) | ||||
−0.486311 | + | 0.873786i | \(0.661658\pi\) | |||||||
\(854\) | 3.26121 | 0.111596 | ||||||||
\(855\) | 0.209598 | 0.00716809 | ||||||||
\(856\) | 8.74789 | 0.298997 | ||||||||
\(857\) | 52.0850 | 1.77919 | 0.889594 | − | 0.456752i | \(-0.150987\pi\) | ||||
0.889594 | + | 0.456752i | \(0.150987\pi\) | |||||||
\(858\) | 25.6068 | 0.874201 | ||||||||
\(859\) | −42.1751 | −1.43900 | −0.719498 | − | 0.694494i | \(-0.755628\pi\) | ||||
−0.719498 | + | 0.694494i | \(0.755628\pi\) | |||||||
\(860\) | 15.3574 | 0.523682 | ||||||||
\(861\) | −3.97914 | −0.135609 | ||||||||
\(862\) | 44.3102 | 1.50921 | ||||||||
\(863\) | −35.5510 | −1.21017 | −0.605085 | − | 0.796161i | \(-0.706861\pi\) | ||||
−0.605085 | + | 0.796161i | \(0.706861\pi\) | |||||||
\(864\) | 7.32078 | 0.249058 | ||||||||
\(865\) | −5.66981 | −0.192779 | ||||||||
\(866\) | 7.22346 | 0.245463 | ||||||||
\(867\) | −1.68470 | −0.0572155 | ||||||||
\(868\) | 14.7488 | 0.500607 | ||||||||
\(869\) | 20.4834 | 0.694853 | ||||||||
\(870\) | −5.40119 | −0.183118 | ||||||||
\(871\) | −20.4752 | −0.693777 | ||||||||
\(872\) | 11.9427 | 0.404430 | ||||||||
\(873\) | 4.06148 | 0.137460 | ||||||||
\(874\) | 0.398452 | 0.0134779 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −1.23910 | −0.0418652 | ||||||||
\(877\) | −12.2578 | −0.413917 | −0.206959 | − | 0.978350i | \(-0.566357\pi\) | ||||
−0.206959 | + | 0.978350i | \(0.566357\pi\) | |||||||
\(878\) | 63.8077 | 2.15341 | ||||||||
\(879\) | −23.8737 | −0.805239 | ||||||||
\(880\) | −14.2507 | −0.480391 | ||||||||
\(881\) | −5.90662 | −0.198999 | −0.0994996 | − | 0.995038i | \(-0.531724\pi\) | ||||
−0.0994996 | + | 0.995038i | \(0.531724\pi\) | |||||||
\(882\) | −1.90103 | −0.0640111 | ||||||||
\(883\) | 37.4513 | 1.26033 | 0.630167 | − | 0.776459i | \(-0.282986\pi\) | ||||
0.630167 | + | 0.776459i | \(0.282986\pi\) | |||||||
\(884\) | 27.6000 | 0.928288 | ||||||||
\(885\) | 3.22294 | 0.108338 | ||||||||
\(886\) | −5.20233 | −0.174776 | ||||||||
\(887\) | 6.18188 | 0.207567 | 0.103784 | − | 0.994600i | \(-0.466905\pi\) | ||||
0.103784 | + | 0.994600i | \(0.466905\pi\) | |||||||
\(888\) | 4.95148 | 0.166161 | ||||||||
\(889\) | −5.61942 | −0.188469 | ||||||||
\(890\) | −14.1561 | −0.474512 | ||||||||
\(891\) | 3.08250 | 0.103268 | ||||||||
\(892\) | 14.6965 | 0.492074 | ||||||||
\(893\) | 1.61596 | 0.0540759 | ||||||||
\(894\) | −10.6635 | −0.356640 | ||||||||
\(895\) | 4.87447 | 0.162936 | ||||||||
\(896\) | −5.76208 | −0.192498 | ||||||||
\(897\) | 4.36980 | 0.145903 | ||||||||
\(898\) | 10.2796 | 0.343034 | ||||||||
\(899\) | 25.9640 | 0.865949 | ||||||||
\(900\) | 1.61393 | 0.0537976 | ||||||||
\(901\) | 49.7917 | 1.65880 | ||||||||
\(902\) | 23.3175 | 0.776389 | ||||||||
\(903\) | 9.51553 | 0.316657 | ||||||||
\(904\) | −5.16551 | −0.171802 | ||||||||
\(905\) | −11.3864 | −0.378498 | ||||||||
\(906\) | −16.7165 | −0.555368 | ||||||||
\(907\) | −12.5773 | −0.417622 | −0.208811 | − | 0.977956i | \(-0.566959\pi\) | ||||
−0.208811 | + | 0.977956i | \(0.566959\pi\) | |||||||
\(908\) | −11.2918 | −0.374733 | ||||||||
\(909\) | −10.3687 | −0.343909 | ||||||||
\(910\) | 8.30714 | 0.275379 | ||||||||
\(911\) | −30.2652 | −1.00273 | −0.501365 | − | 0.865236i | \(-0.667169\pi\) | ||||
−0.501365 | + | 0.865236i | \(0.667169\pi\) | |||||||
\(912\) | −0.968990 | −0.0320865 | ||||||||
\(913\) | −48.8108 | −1.61540 | ||||||||
\(914\) | 23.9321 | 0.791603 | ||||||||
\(915\) | −1.71549 | −0.0567125 | ||||||||
\(916\) | 27.0450 | 0.893592 | ||||||||
\(917\) | −6.97507 | −0.230337 | ||||||||
\(918\) | 7.43965 | 0.245545 | ||||||||
\(919\) | 39.2049 | 1.29325 | 0.646625 | − | 0.762808i | \(-0.276180\pi\) | ||||
0.646625 | + | 0.762808i | \(0.276180\pi\) | |||||||
\(920\) | −0.733935 | −0.0241971 | ||||||||
\(921\) | 25.9704 | 0.855754 | ||||||||
\(922\) | 27.7363 | 0.913445 | ||||||||
\(923\) | −19.8463 | −0.653248 | ||||||||
\(924\) | 4.97494 | 0.163663 | ||||||||
\(925\) | 6.74648 | 0.221823 | ||||||||
\(926\) | −62.6580 | −2.05907 | ||||||||
\(927\) | 9.76343 | 0.320673 | ||||||||
\(928\) | 20.7997 | 0.682784 | ||||||||
\(929\) | 51.0030 | 1.67335 | 0.836677 | − | 0.547697i | \(-0.184495\pi\) | ||||
0.836677 | + | 0.547697i | \(0.184495\pi\) | |||||||
\(930\) | −17.3725 | −0.569667 | ||||||||
\(931\) | 0.209598 | 0.00686929 | ||||||||
\(932\) | −32.6807 | −1.07049 | ||||||||
\(933\) | −2.17066 | −0.0710642 | ||||||||
\(934\) | −7.92510 | −0.259317 | ||||||||
\(935\) | −12.0633 | −0.394512 | ||||||||
\(936\) | −3.20715 | −0.104829 | ||||||||
\(937\) | 45.8018 | 1.49628 | 0.748139 | − | 0.663542i | \(-0.230947\pi\) | ||||
0.748139 | + | 0.663542i | \(0.230947\pi\) | |||||||
\(938\) | −8.90752 | −0.290841 | ||||||||
\(939\) | 30.0595 | 0.980955 | ||||||||
\(940\) | 12.4431 | 0.405848 | ||||||||
\(941\) | 2.75338 | 0.0897576 | 0.0448788 | − | 0.998992i | \(-0.485710\pi\) | ||||
0.0448788 | + | 0.998992i | \(0.485710\pi\) | |||||||
\(942\) | 8.38566 | 0.273219 | ||||||||
\(943\) | 3.97914 | 0.129579 | ||||||||
\(944\) | −14.8999 | −0.484952 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | −55.7604 | −1.81293 | ||||||||
\(947\) | 16.0802 | 0.522538 | 0.261269 | − | 0.965266i | \(-0.415859\pi\) | ||||
0.261269 | + | 0.965266i | \(0.415859\pi\) | |||||||
\(948\) | 10.7247 | 0.348321 | ||||||||
\(949\) | 3.35492 | 0.108905 | ||||||||
\(950\) | −0.398452 | −0.0129275 | ||||||||
\(951\) | −1.65752 | −0.0537486 | ||||||||
\(952\) | −2.87224 | −0.0930897 | ||||||||
\(953\) | −30.6082 | −0.991497 | −0.495748 | − | 0.868466i | \(-0.665106\pi\) | ||||
−0.495748 | + | 0.868466i | \(0.665106\pi\) | |||||||
\(954\) | 24.1871 | 0.783087 | ||||||||
\(955\) | 22.0335 | 0.712987 | ||||||||
\(956\) | 35.6703 | 1.15366 | ||||||||
\(957\) | 8.75797 | 0.283105 | ||||||||
\(958\) | 68.7291 | 2.22054 | ||||||||
\(959\) | 9.50150 | 0.306819 | ||||||||
\(960\) | −4.67087 | −0.150752 | ||||||||
\(961\) | 52.5113 | 1.69391 | ||||||||
\(962\) | 56.0440 | 1.80693 | ||||||||
\(963\) | 11.9192 | 0.384090 | ||||||||
\(964\) | 35.3482 | 1.13849 | ||||||||
\(965\) | −15.2006 | −0.489324 | ||||||||
\(966\) | 1.90103 | 0.0611648 | ||||||||
\(967\) | 18.7317 | 0.602370 | 0.301185 | − | 0.953566i | \(-0.402618\pi\) | ||||
0.301185 | + | 0.953566i | \(0.402618\pi\) | |||||||
\(968\) | −1.09956 | −0.0353413 | ||||||||
\(969\) | −0.820256 | −0.0263504 | ||||||||
\(970\) | −7.72100 | −0.247906 | ||||||||
\(971\) | −23.1564 | −0.743124 | −0.371562 | − | 0.928408i | \(-0.621178\pi\) | ||||
−0.371562 | + | 0.928408i | \(0.621178\pi\) | |||||||
\(972\) | 1.61393 | 0.0517668 | ||||||||
\(973\) | 12.7424 | 0.408502 | ||||||||
\(974\) | 74.8340 | 2.39783 | ||||||||
\(975\) | −4.36980 | −0.139946 | ||||||||
\(976\) | 7.93088 | 0.253861 | ||||||||
\(977\) | 19.1370 | 0.612246 | 0.306123 | − | 0.951992i | \(-0.400968\pi\) | ||||
0.306123 | + | 0.951992i | \(0.400968\pi\) | |||||||
\(978\) | −12.8048 | −0.409453 | ||||||||
\(979\) | 22.9539 | 0.733609 | ||||||||
\(980\) | 1.61393 | 0.0515551 | ||||||||
\(981\) | 16.2721 | 0.519529 | ||||||||
\(982\) | −30.6783 | −0.978983 | ||||||||
\(983\) | 42.4715 | 1.35463 | 0.677315 | − | 0.735693i | \(-0.263143\pi\) | ||||
0.677315 | + | 0.735693i | \(0.263143\pi\) | |||||||
\(984\) | −2.92043 | −0.0930999 | ||||||||
\(985\) | 8.03612 | 0.256052 | ||||||||
\(986\) | 21.1374 | 0.673153 | ||||||||
\(987\) | 7.70980 | 0.245405 | ||||||||
\(988\) | −1.47820 | −0.0470278 | ||||||||
\(989\) | −9.51553 | −0.302576 | ||||||||
\(990\) | −5.85994 | −0.186241 | ||||||||
\(991\) | −5.46923 | −0.173736 | −0.0868679 | − | 0.996220i | \(-0.527686\pi\) | ||||
−0.0868679 | + | 0.996220i | \(0.527686\pi\) | |||||||
\(992\) | 66.9006 | 2.12410 | ||||||||
\(993\) | 20.7489 | 0.658448 | ||||||||
\(994\) | −8.63390 | −0.273851 | ||||||||
\(995\) | −25.5617 | −0.810361 | ||||||||
\(996\) | −25.5562 | −0.809780 | ||||||||
\(997\) | −6.14896 | −0.194740 | −0.0973698 | − | 0.995248i | \(-0.531043\pi\) | ||||
−0.0973698 | + | 0.995248i | \(0.531043\pi\) | |||||||
\(998\) | 22.8271 | 0.722578 | ||||||||
\(999\) | 6.74648 | 0.213449 |
(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 | 2415.2.a.w.1.2 | ✓ | 10 | |
3.2 | odd | 2 | 7245.2.a.bv.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2415.2.a.w.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
7245.2.a.bv.1.9 | 10 | 3.2 | odd | 2 |