Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.23607 | −1.29099 | −0.645497 | − | 0.763763i | \(-0.723350\pi\) | ||||
−0.645497 | + | 0.763763i | \(0.723350\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.23607 | 0.912871 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.23607 | −0.645497 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 2.23607 | 0.577350 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.23607 | −0.299791 | −0.149895 | − | 0.988702i | \(-0.547894\pi\) | ||||
−0.149895 | + | 0.988702i | \(0.547894\pi\) | |||||||
\(18\) | −2.00000 | −0.471405 | ||||||||
\(19\) | −2.23607 | −0.512989 | −0.256495 | − | 0.966546i | \(-0.582568\pi\) | ||||
−0.256495 | + | 0.966546i | \(0.582568\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −2.23607 | −0.487950 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.76393 | −0.784834 | −0.392417 | − | 0.919787i | \(-0.628361\pi\) | ||||
−0.392417 | + | 0.919787i | \(0.628361\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | −2.23607 | −0.408248 | ||||||||
\(31\) | −5.23607 | −0.940426 | −0.470213 | − | 0.882553i | \(-0.655823\pi\) | ||||
−0.470213 | + | 0.882553i | \(0.655823\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.23607 | 0.211984 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 2.00000 | 0.333333 | ||||||||
\(37\) | 8.94427 | 1.47043 | 0.735215 | − | 0.677834i | \(-0.237081\pi\) | ||||
0.735215 | + | 0.677834i | \(0.237081\pi\) | |||||||
\(38\) | 2.23607 | 0.362738 | ||||||||
\(39\) | −2.23607 | −0.358057 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −7.23607 | −1.13008 | −0.565042 | − | 0.825062i | \(-0.691140\pi\) | ||||
−0.565042 | + | 0.825062i | \(0.691140\pi\) | |||||||
\(42\) | 2.23607 | 0.345033 | ||||||||
\(43\) | 3.23607 | 0.493496 | 0.246748 | − | 0.969080i | \(-0.420638\pi\) | ||||
0.246748 | + | 0.969080i | \(0.420638\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 3.76393 | 0.554962 | ||||||||
\(47\) | 7.70820 | 1.12436 | 0.562179 | − | 0.827016i | \(-0.309963\pi\) | ||||
0.562179 | + | 0.827016i | \(0.309963\pi\) | |||||||
\(48\) | −2.23607 | −0.322749 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 2.76393 | 0.387028 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −5.70820 | −0.784082 | −0.392041 | − | 0.919948i | \(-0.628231\pi\) | ||||
−0.392041 | + | 0.919948i | \(0.628231\pi\) | |||||||
\(54\) | −2.23607 | −0.304290 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | −4.47214 | −0.587220 | ||||||||
\(59\) | 4.70820 | 0.612956 | 0.306478 | − | 0.951878i | \(-0.400849\pi\) | ||||
0.306478 | + | 0.951878i | \(0.400849\pi\) | |||||||
\(60\) | 2.23607 | 0.288675 | ||||||||
\(61\) | −3.52786 | −0.451697 | −0.225848 | − | 0.974162i | \(-0.572515\pi\) | ||||
−0.225848 | + | 0.974162i | \(0.572515\pi\) | |||||||
\(62\) | 5.23607 | 0.664981 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.23607 | −0.884026 | −0.442013 | − | 0.897009i | \(-0.645736\pi\) | ||||
−0.442013 | + | 0.897009i | \(0.645736\pi\) | |||||||
\(68\) | −1.23607 | −0.149895 | ||||||||
\(69\) | 8.41641 | 1.01322 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −1.52786 | −0.181324 | −0.0906621 | − | 0.995882i | \(-0.528898\pi\) | ||||
−0.0906621 | + | 0.995882i | \(0.528898\pi\) | |||||||
\(72\) | −2.00000 | −0.235702 | ||||||||
\(73\) | −7.23607 | −0.846918 | −0.423459 | − | 0.905915i | \(-0.639184\pi\) | ||||
−0.423459 | + | 0.905915i | \(0.639184\pi\) | |||||||
\(74\) | −8.94427 | −1.03975 | ||||||||
\(75\) | −2.23607 | −0.258199 | ||||||||
\(76\) | −2.23607 | −0.256495 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.23607 | 0.253185 | ||||||||
\(79\) | 10.2361 | 1.15165 | 0.575824 | − | 0.817574i | \(-0.304681\pi\) | ||||
0.575824 | + | 0.817574i | \(0.304681\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 7.23607 | 0.799090 | ||||||||
\(83\) | −0.236068 | −0.0259118 | −0.0129559 | − | 0.999916i | \(-0.504124\pi\) | ||||
−0.0129559 | + | 0.999916i | \(0.504124\pi\) | |||||||
\(84\) | −2.23607 | −0.243975 | ||||||||
\(85\) | 1.23607 | 0.134070 | ||||||||
\(86\) | −3.23607 | −0.348954 | ||||||||
\(87\) | −10.0000 | −1.07211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.2361 | −1.82702 | −0.913510 | − | 0.406817i | \(-0.866639\pi\) | ||||
−0.913510 | + | 0.406817i | \(0.866639\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | −3.76393 | −0.392417 | ||||||||
\(93\) | 11.7082 | 1.21408 | ||||||||
\(94\) | −7.70820 | −0.795041 | ||||||||
\(95\) | 2.23607 | 0.229416 | ||||||||
\(96\) | 2.23607 | 0.228218 | ||||||||
\(97\) | 3.52786 | 0.358200 | 0.179100 | − | 0.983831i | \(-0.442681\pi\) | ||||
0.179100 | + | 0.983831i | \(0.442681\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.00000 | −0.0995037 | −0.0497519 | − | 0.998762i | \(-0.515843\pi\) | ||||
−0.0497519 | + | 0.998762i | \(0.515843\pi\) | |||||||
\(102\) | −2.76393 | −0.273670 | ||||||||
\(103\) | 14.1803 | 1.39723 | 0.698615 | − | 0.715498i | \(-0.253800\pi\) | ||||
0.698615 | + | 0.715498i | \(0.253800\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 2.23607 | 0.218218 | ||||||||
\(106\) | 5.70820 | 0.554430 | ||||||||
\(107\) | −2.47214 | −0.238990 | −0.119495 | − | 0.992835i | \(-0.538128\pi\) | ||||
−0.119495 | + | 0.992835i | \(0.538128\pi\) | |||||||
\(108\) | 2.23607 | 0.215166 | ||||||||
\(109\) | −3.70820 | −0.355182 | −0.177591 | − | 0.984104i | \(-0.556830\pi\) | ||||
−0.177591 | + | 0.984104i | \(0.556830\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.0000 | −1.89832 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −1.00000 | −0.0940721 | −0.0470360 | − | 0.998893i | \(-0.514978\pi\) | ||||
−0.0470360 | + | 0.998893i | \(0.514978\pi\) | |||||||
\(114\) | −5.00000 | −0.468293 | ||||||||
\(115\) | 3.76393 | 0.350988 | ||||||||
\(116\) | 4.47214 | 0.415227 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | −4.70820 | −0.433425 | ||||||||
\(119\) | −1.23607 | −0.113310 | ||||||||
\(120\) | −2.23607 | −0.204124 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.52786 | 0.319398 | ||||||||
\(123\) | 16.1803 | 1.45893 | ||||||||
\(124\) | −5.23607 | −0.470213 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 6.23607 | 0.553362 | 0.276681 | − | 0.960962i | \(-0.410766\pi\) | ||||
0.276681 | + | 0.960962i | \(0.410766\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.23607 | −0.637100 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | −3.18034 | −0.277868 | −0.138934 | − | 0.990302i | \(-0.544368\pi\) | ||||
−0.138934 | + | 0.990302i | \(0.544368\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.23607 | −0.193892 | ||||||||
\(134\) | 7.23607 | 0.625101 | ||||||||
\(135\) | −2.23607 | −0.192450 | ||||||||
\(136\) | 1.23607 | 0.105992 | ||||||||
\(137\) | 13.4721 | 1.15100 | 0.575501 | − | 0.817801i | \(-0.304807\pi\) | ||||
0.575501 | + | 0.817801i | \(0.304807\pi\) | |||||||
\(138\) | −8.41641 | −0.716452 | ||||||||
\(139\) | 4.23607 | 0.359299 | 0.179649 | − | 0.983731i | \(-0.442504\pi\) | ||||
0.179649 | + | 0.983731i | \(0.442504\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −17.2361 | −1.45154 | ||||||||
\(142\) | 1.52786 | 0.128216 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.00000 | 0.166667 | ||||||||
\(145\) | −4.47214 | −0.371391 | ||||||||
\(146\) | 7.23607 | 0.598861 | ||||||||
\(147\) | −2.23607 | −0.184428 | ||||||||
\(148\) | 8.94427 | 0.735215 | ||||||||
\(149\) | 4.00000 | 0.327693 | 0.163846 | − | 0.986486i | \(-0.447610\pi\) | ||||
0.163846 | + | 0.986486i | \(0.447610\pi\) | |||||||
\(150\) | 2.23607 | 0.182574 | ||||||||
\(151\) | 12.2361 | 0.995757 | 0.497879 | − | 0.867247i | \(-0.334113\pi\) | ||||
0.497879 | + | 0.867247i | \(0.334113\pi\) | |||||||
\(152\) | 2.23607 | 0.181369 | ||||||||
\(153\) | −2.47214 | −0.199860 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.23607 | 0.420571 | ||||||||
\(156\) | −2.23607 | −0.179029 | ||||||||
\(157\) | 8.52786 | 0.680598 | 0.340299 | − | 0.940317i | \(-0.389472\pi\) | ||||
0.340299 | + | 0.940317i | \(0.389472\pi\) | |||||||
\(158\) | −10.2361 | −0.814338 | ||||||||
\(159\) | 12.7639 | 1.01225 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −3.76393 | −0.296639 | ||||||||
\(162\) | 11.0000 | 0.864242 | ||||||||
\(163\) | −6.00000 | −0.469956 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(164\) | −7.23607 | −0.565042 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.236068 | 0.0183224 | ||||||||
\(167\) | 1.70820 | 0.132185 | 0.0660924 | − | 0.997814i | \(-0.478947\pi\) | ||||
0.0660924 | + | 0.997814i | \(0.478947\pi\) | |||||||
\(168\) | 2.23607 | 0.172516 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −1.23607 | −0.0948021 | ||||||||
\(171\) | −4.47214 | −0.341993 | ||||||||
\(172\) | 3.23607 | 0.246748 | ||||||||
\(173\) | 19.8885 | 1.51210 | 0.756049 | − | 0.654515i | \(-0.227127\pi\) | ||||
0.756049 | + | 0.654515i | \(0.227127\pi\) | |||||||
\(174\) | 10.0000 | 0.758098 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.5279 | −0.791323 | ||||||||
\(178\) | 17.2361 | 1.29190 | ||||||||
\(179\) | −11.2361 | −0.839823 | −0.419912 | − | 0.907565i | \(-0.637939\pi\) | ||||
−0.419912 | + | 0.907565i | \(0.637939\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | 7.00000 | 0.520306 | 0.260153 | − | 0.965567i | \(-0.416227\pi\) | ||||
0.260153 | + | 0.965567i | \(0.416227\pi\) | |||||||
\(182\) | −1.00000 | −0.0741249 | ||||||||
\(183\) | 7.88854 | 0.583138 | ||||||||
\(184\) | 3.76393 | 0.277481 | ||||||||
\(185\) | −8.94427 | −0.657596 | ||||||||
\(186\) | −11.7082 | −0.858487 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.70820 | 0.562179 | ||||||||
\(189\) | 2.23607 | 0.162650 | ||||||||
\(190\) | −2.23607 | −0.162221 | ||||||||
\(191\) | 25.1803 | 1.82199 | 0.910993 | − | 0.412422i | \(-0.135317\pi\) | ||||
0.910993 | + | 0.412422i | \(0.135317\pi\) | |||||||
\(192\) | −2.23607 | −0.161374 | ||||||||
\(193\) | 7.94427 | 0.571841 | 0.285921 | − | 0.958253i | \(-0.407701\pi\) | ||||
0.285921 | + | 0.958253i | \(0.407701\pi\) | |||||||
\(194\) | −3.52786 | −0.253286 | ||||||||
\(195\) | 2.23607 | 0.160128 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −7.52786 | −0.536338 | −0.268169 | − | 0.963372i | \(-0.586419\pi\) | ||||
−0.268169 | + | 0.963372i | \(0.586419\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.47214 | −0.317021 | −0.158511 | − | 0.987357i | \(-0.550669\pi\) | ||||
−0.158511 | + | 0.987357i | \(0.550669\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 16.1803 | 1.14127 | ||||||||
\(202\) | 1.00000 | 0.0703598 | ||||||||
\(203\) | 4.47214 | 0.313882 | ||||||||
\(204\) | 2.76393 | 0.193514 | ||||||||
\(205\) | 7.23607 | 0.505389 | ||||||||
\(206\) | −14.1803 | −0.987991 | ||||||||
\(207\) | −7.52786 | −0.523223 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −2.23607 | −0.154303 | ||||||||
\(211\) | 3.52786 | 0.242868 | 0.121434 | − | 0.992599i | \(-0.461251\pi\) | ||||
0.121434 | + | 0.992599i | \(0.461251\pi\) | |||||||
\(212\) | −5.70820 | −0.392041 | ||||||||
\(213\) | 3.41641 | 0.234088 | ||||||||
\(214\) | 2.47214 | 0.168992 | ||||||||
\(215\) | −3.23607 | −0.220698 | ||||||||
\(216\) | −2.23607 | −0.152145 | ||||||||
\(217\) | −5.23607 | −0.355447 | ||||||||
\(218\) | 3.70820 | 0.251151 | ||||||||
\(219\) | 16.1803 | 1.09337 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.23607 | −0.0831469 | ||||||||
\(222\) | 20.0000 | 1.34231 | ||||||||
\(223\) | −8.18034 | −0.547796 | −0.273898 | − | 0.961759i | \(-0.588313\pi\) | ||||
−0.273898 | + | 0.961759i | \(0.588313\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | 1.00000 | 0.0665190 | ||||||||
\(227\) | −7.41641 | −0.492244 | −0.246122 | − | 0.969239i | \(-0.579156\pi\) | ||||
−0.246122 | + | 0.969239i | \(0.579156\pi\) | |||||||
\(228\) | 5.00000 | 0.331133 | ||||||||
\(229\) | 6.94427 | 0.458890 | 0.229445 | − | 0.973322i | \(-0.426309\pi\) | ||||
0.229445 | + | 0.973322i | \(0.426309\pi\) | |||||||
\(230\) | −3.76393 | −0.248186 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.47214 | −0.293610 | ||||||||
\(233\) | 10.4164 | 0.682402 | 0.341201 | − | 0.939990i | \(-0.389166\pi\) | ||||
0.341201 | + | 0.939990i | \(0.389166\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | −7.70820 | −0.502828 | ||||||||
\(236\) | 4.70820 | 0.306478 | ||||||||
\(237\) | −22.8885 | −1.48677 | ||||||||
\(238\) | 1.23607 | 0.0801224 | ||||||||
\(239\) | 10.7082 | 0.692656 | 0.346328 | − | 0.938113i | \(-0.387428\pi\) | ||||
0.346328 | + | 0.938113i | \(0.387428\pi\) | |||||||
\(240\) | 2.23607 | 0.144338 | ||||||||
\(241\) | −22.3607 | −1.44038 | −0.720189 | − | 0.693778i | \(-0.755945\pi\) | ||||
−0.720189 | + | 0.693778i | \(0.755945\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.8885 | 1.14755 | ||||||||
\(244\) | −3.52786 | −0.225848 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −16.1803 | −1.03162 | ||||||||
\(247\) | −2.23607 | −0.142278 | ||||||||
\(248\) | 5.23607 | 0.332491 | ||||||||
\(249\) | 0.527864 | 0.0334520 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −29.8885 | −1.88655 | −0.943274 | − | 0.332015i | \(-0.892272\pi\) | ||||
−0.943274 | + | 0.332015i | \(0.892272\pi\) | |||||||
\(252\) | 2.00000 | 0.125988 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.23607 | −0.391286 | ||||||||
\(255\) | −2.76393 | −0.173084 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.76393 | −0.297166 | −0.148583 | − | 0.988900i | \(-0.547471\pi\) | ||||
−0.148583 | + | 0.988900i | \(0.547471\pi\) | |||||||
\(258\) | 7.23607 | 0.450498 | ||||||||
\(259\) | 8.94427 | 0.555770 | ||||||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | 8.94427 | 0.553637 | ||||||||
\(262\) | 3.18034 | 0.196482 | ||||||||
\(263\) | 7.65248 | 0.471872 | 0.235936 | − | 0.971769i | \(-0.424184\pi\) | ||||
0.235936 | + | 0.971769i | \(0.424184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.70820 | 0.350652 | ||||||||
\(266\) | 2.23607 | 0.137102 | ||||||||
\(267\) | 38.5410 | 2.35867 | ||||||||
\(268\) | −7.23607 | −0.442013 | ||||||||
\(269\) | −27.8328 | −1.69700 | −0.848498 | − | 0.529198i | \(-0.822493\pi\) | ||||
−0.848498 | + | 0.529198i | \(0.822493\pi\) | |||||||
\(270\) | 2.23607 | 0.136083 | ||||||||
\(271\) | 7.41641 | 0.450515 | 0.225257 | − | 0.974299i | \(-0.427678\pi\) | ||||
0.225257 | + | 0.974299i | \(0.427678\pi\) | |||||||
\(272\) | −1.23607 | −0.0749476 | ||||||||
\(273\) | −2.23607 | −0.135333 | ||||||||
\(274\) | −13.4721 | −0.813881 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.41641 | 0.506608 | ||||||||
\(277\) | 23.5967 | 1.41779 | 0.708896 | − | 0.705313i | \(-0.249194\pi\) | ||||
0.708896 | + | 0.705313i | \(0.249194\pi\) | |||||||
\(278\) | −4.23607 | −0.254062 | ||||||||
\(279\) | −10.4721 | −0.626950 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 25.8328 | 1.54106 | 0.770528 | − | 0.637406i | \(-0.219992\pi\) | ||||
0.770528 | + | 0.637406i | \(0.219992\pi\) | |||||||
\(282\) | 17.2361 | 1.02639 | ||||||||
\(283\) | 26.2361 | 1.55957 | 0.779786 | − | 0.626046i | \(-0.215328\pi\) | ||||
0.779786 | + | 0.626046i | \(0.215328\pi\) | |||||||
\(284\) | −1.52786 | −0.0906621 | ||||||||
\(285\) | −5.00000 | −0.296174 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.23607 | −0.427132 | ||||||||
\(288\) | −2.00000 | −0.117851 | ||||||||
\(289\) | −15.4721 | −0.910126 | ||||||||
\(290\) | 4.47214 | 0.262613 | ||||||||
\(291\) | −7.88854 | −0.462435 | ||||||||
\(292\) | −7.23607 | −0.423459 | ||||||||
\(293\) | −5.00000 | −0.292103 | −0.146052 | − | 0.989277i | \(-0.546657\pi\) | ||||
−0.146052 | + | 0.989277i | \(0.546657\pi\) | |||||||
\(294\) | 2.23607 | 0.130410 | ||||||||
\(295\) | −4.70820 | −0.274122 | ||||||||
\(296\) | −8.94427 | −0.519875 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.00000 | −0.231714 | ||||||||
\(299\) | −3.76393 | −0.217674 | ||||||||
\(300\) | −2.23607 | −0.129099 | ||||||||
\(301\) | 3.23607 | 0.186524 | ||||||||
\(302\) | −12.2361 | −0.704107 | ||||||||
\(303\) | 2.23607 | 0.128459 | ||||||||
\(304\) | −2.23607 | −0.128247 | ||||||||
\(305\) | 3.52786 | 0.202005 | ||||||||
\(306\) | 2.47214 | 0.141323 | ||||||||
\(307\) | 11.4164 | 0.651569 | 0.325784 | − | 0.945444i | \(-0.394372\pi\) | ||||
0.325784 | + | 0.945444i | \(0.394372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −31.7082 | −1.80382 | ||||||||
\(310\) | −5.23607 | −0.297389 | ||||||||
\(311\) | −27.1246 | −1.53810 | −0.769048 | − | 0.639191i | \(-0.779269\pi\) | ||||
−0.769048 | + | 0.639191i | \(0.779269\pi\) | |||||||
\(312\) | 2.23607 | 0.126592 | ||||||||
\(313\) | 19.5279 | 1.10378 | 0.551890 | − | 0.833917i | \(-0.313907\pi\) | ||||
0.551890 | + | 0.833917i | \(0.313907\pi\) | |||||||
\(314\) | −8.52786 | −0.481255 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 10.2361 | 0.575824 | ||||||||
\(317\) | 0.652476 | 0.0366467 | 0.0183233 | − | 0.999832i | \(-0.494167\pi\) | ||||
0.0183233 | + | 0.999832i | \(0.494167\pi\) | |||||||
\(318\) | −12.7639 | −0.715766 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 5.52786 | 0.308535 | ||||||||
\(322\) | 3.76393 | 0.209756 | ||||||||
\(323\) | 2.76393 | 0.153789 | ||||||||
\(324\) | −11.0000 | −0.611111 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 6.00000 | 0.332309 | ||||||||
\(327\) | 8.29180 | 0.458537 | ||||||||
\(328\) | 7.23607 | 0.399545 | ||||||||
\(329\) | 7.70820 | 0.424967 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.7082 | −1.19319 | −0.596595 | − | 0.802542i | \(-0.703480\pi\) | ||||
−0.596595 | + | 0.802542i | \(0.703480\pi\) | |||||||
\(332\) | −0.236068 | −0.0129559 | ||||||||
\(333\) | 17.8885 | 0.980286 | ||||||||
\(334\) | −1.70820 | −0.0934688 | ||||||||
\(335\) | 7.23607 | 0.395349 | ||||||||
\(336\) | −2.23607 | −0.121988 | ||||||||
\(337\) | −2.88854 | −0.157349 | −0.0786745 | − | 0.996900i | \(-0.525069\pi\) | ||||
−0.0786745 | + | 0.996900i | \(0.525069\pi\) | |||||||
\(338\) | 12.0000 | 0.652714 | ||||||||
\(339\) | 2.23607 | 0.121447 | ||||||||
\(340\) | 1.23607 | 0.0670352 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.47214 | 0.241825 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.23607 | −0.174477 | ||||||||
\(345\) | −8.41641 | −0.453124 | ||||||||
\(346\) | −19.8885 | −1.06921 | ||||||||
\(347\) | −6.00000 | −0.322097 | −0.161048 | − | 0.986947i | \(-0.551488\pi\) | ||||
−0.161048 | + | 0.986947i | \(0.551488\pi\) | |||||||
\(348\) | −10.0000 | −0.536056 | ||||||||
\(349\) | 0.416408 | 0.0222898 | 0.0111449 | − | 0.999938i | \(-0.496452\pi\) | ||||
0.0111449 | + | 0.999938i | \(0.496452\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 2.23607 | 0.119352 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.76393 | −0.253559 | −0.126779 | − | 0.991931i | \(-0.540464\pi\) | ||||
−0.126779 | + | 0.991931i | \(0.540464\pi\) | |||||||
\(354\) | 10.5279 | 0.559550 | ||||||||
\(355\) | 1.52786 | 0.0810906 | ||||||||
\(356\) | −17.2361 | −0.913510 | ||||||||
\(357\) | 2.76393 | 0.146283 | ||||||||
\(358\) | 11.2361 | 0.593845 | ||||||||
\(359\) | 16.0000 | 0.844448 | 0.422224 | − | 0.906492i | \(-0.361250\pi\) | ||||
0.422224 | + | 0.906492i | \(0.361250\pi\) | |||||||
\(360\) | 2.00000 | 0.105409 | ||||||||
\(361\) | −14.0000 | −0.736842 | ||||||||
\(362\) | −7.00000 | −0.367912 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.00000 | 0.0524142 | ||||||||
\(365\) | 7.23607 | 0.378753 | ||||||||
\(366\) | −7.88854 | −0.412341 | ||||||||
\(367\) | 8.18034 | 0.427010 | 0.213505 | − | 0.976942i | \(-0.431512\pi\) | ||||
0.213505 | + | 0.976942i | \(0.431512\pi\) | |||||||
\(368\) | −3.76393 | −0.196209 | ||||||||
\(369\) | −14.4721 | −0.753389 | ||||||||
\(370\) | 8.94427 | 0.464991 | ||||||||
\(371\) | −5.70820 | −0.296355 | ||||||||
\(372\) | 11.7082 | 0.607042 | ||||||||
\(373\) | −5.52786 | −0.286222 | −0.143111 | − | 0.989707i | \(-0.545711\pi\) | ||||
−0.143111 | + | 0.989707i | \(0.545711\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.23607 | 0.115470 | ||||||||
\(376\) | −7.70820 | −0.397520 | ||||||||
\(377\) | 4.47214 | 0.230327 | ||||||||
\(378\) | −2.23607 | −0.115011 | ||||||||
\(379\) | 11.4164 | 0.586421 | 0.293211 | − | 0.956048i | \(-0.405276\pi\) | ||||
0.293211 | + | 0.956048i | \(0.405276\pi\) | |||||||
\(380\) | 2.23607 | 0.114708 | ||||||||
\(381\) | −13.9443 | −0.714387 | ||||||||
\(382\) | −25.1803 | −1.28834 | ||||||||
\(383\) | −17.2361 | −0.880722 | −0.440361 | − | 0.897821i | \(-0.645150\pi\) | ||||
−0.440361 | + | 0.897821i | \(0.645150\pi\) | |||||||
\(384\) | 2.23607 | 0.114109 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.94427 | −0.404353 | ||||||||
\(387\) | 6.47214 | 0.328997 | ||||||||
\(388\) | 3.52786 | 0.179100 | ||||||||
\(389\) | −18.2918 | −0.927431 | −0.463715 | − | 0.885984i | \(-0.653484\pi\) | ||||
−0.463715 | + | 0.885984i | \(0.653484\pi\) | |||||||
\(390\) | −2.23607 | −0.113228 | ||||||||
\(391\) | 4.65248 | 0.235286 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 7.11146 | 0.358726 | ||||||||
\(394\) | 7.52786 | 0.379248 | ||||||||
\(395\) | −10.2361 | −0.515032 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.00000 | 0.301131 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(398\) | 4.47214 | 0.224168 | ||||||||
\(399\) | 5.00000 | 0.250313 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −28.8328 | −1.43984 | −0.719921 | − | 0.694056i | \(-0.755822\pi\) | ||||
−0.719921 | + | 0.694056i | \(0.755822\pi\) | |||||||
\(402\) | −16.1803 | −0.807002 | ||||||||
\(403\) | −5.23607 | −0.260827 | ||||||||
\(404\) | −1.00000 | −0.0497519 | ||||||||
\(405\) | 11.0000 | 0.546594 | ||||||||
\(406\) | −4.47214 | −0.221948 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −2.76393 | −0.136835 | ||||||||
\(409\) | 11.5279 | 0.570016 | 0.285008 | − | 0.958525i | \(-0.408004\pi\) | ||||
0.285008 | + | 0.958525i | \(0.408004\pi\) | |||||||
\(410\) | −7.23607 | −0.357364 | ||||||||
\(411\) | −30.1246 | −1.48594 | ||||||||
\(412\) | 14.1803 | 0.698615 | ||||||||
\(413\) | 4.70820 | 0.231676 | ||||||||
\(414\) | 7.52786 | 0.369974 | ||||||||
\(415\) | 0.236068 | 0.0115881 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −9.47214 | −0.463852 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.2361 | −1.37942 | −0.689711 | − | 0.724085i | \(-0.742262\pi\) | ||||
−0.689711 | + | 0.724085i | \(0.742262\pi\) | |||||||
\(420\) | 2.23607 | 0.109109 | ||||||||
\(421\) | −3.05573 | −0.148927 | −0.0744635 | − | 0.997224i | \(-0.523724\pi\) | ||||
−0.0744635 | + | 0.997224i | \(0.523724\pi\) | |||||||
\(422\) | −3.52786 | −0.171734 | ||||||||
\(423\) | 15.4164 | 0.749571 | ||||||||
\(424\) | 5.70820 | 0.277215 | ||||||||
\(425\) | −1.23607 | −0.0599581 | ||||||||
\(426\) | −3.41641 | −0.165526 | ||||||||
\(427\) | −3.52786 | −0.170725 | ||||||||
\(428\) | −2.47214 | −0.119495 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.23607 | 0.156057 | ||||||||
\(431\) | −33.6525 | −1.62098 | −0.810491 | − | 0.585751i | \(-0.800800\pi\) | ||||
−0.810491 | + | 0.585751i | \(0.800800\pi\) | |||||||
\(432\) | 2.23607 | 0.107583 | ||||||||
\(433\) | −12.6525 | −0.608039 | −0.304020 | − | 0.952666i | \(-0.598329\pi\) | ||||
−0.304020 | + | 0.952666i | \(0.598329\pi\) | |||||||
\(434\) | 5.23607 | 0.251339 | ||||||||
\(435\) | 10.0000 | 0.479463 | ||||||||
\(436\) | −3.70820 | −0.177591 | ||||||||
\(437\) | 8.41641 | 0.402611 | ||||||||
\(438\) | −16.1803 | −0.773127 | ||||||||
\(439\) | 15.1246 | 0.721858 | 0.360929 | − | 0.932593i | \(-0.382460\pi\) | ||||
0.360929 | + | 0.932593i | \(0.382460\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | 1.23607 | 0.0587938 | ||||||||
\(443\) | −24.3607 | −1.15741 | −0.578705 | − | 0.815537i | \(-0.696442\pi\) | ||||
−0.578705 | + | 0.815537i | \(0.696442\pi\) | |||||||
\(444\) | −20.0000 | −0.949158 | ||||||||
\(445\) | 17.2361 | 0.817068 | ||||||||
\(446\) | 8.18034 | 0.387350 | ||||||||
\(447\) | −8.94427 | −0.423050 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 23.8328 | 1.12474 | 0.562370 | − | 0.826886i | \(-0.309890\pi\) | ||||
0.562370 | + | 0.826886i | \(0.309890\pi\) | |||||||
\(450\) | −2.00000 | −0.0942809 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −1.00000 | −0.0470360 | ||||||||
\(453\) | −27.3607 | −1.28552 | ||||||||
\(454\) | 7.41641 | 0.348069 | ||||||||
\(455\) | −1.00000 | −0.0468807 | ||||||||
\(456\) | −5.00000 | −0.234146 | ||||||||
\(457\) | −36.4164 | −1.70349 | −0.851744 | − | 0.523958i | \(-0.824455\pi\) | ||||
−0.851744 | + | 0.523958i | \(0.824455\pi\) | |||||||
\(458\) | −6.94427 | −0.324485 | ||||||||
\(459\) | −2.76393 | −0.129009 | ||||||||
\(460\) | 3.76393 | 0.175494 | ||||||||
\(461\) | −23.8885 | −1.11260 | −0.556300 | − | 0.830981i | \(-0.687780\pi\) | ||||
−0.556300 | + | 0.830981i | \(0.687780\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.7082 | 0.497652 | 0.248826 | − | 0.968548i | \(-0.419955\pi\) | ||||
0.248826 | + | 0.968548i | \(0.419955\pi\) | |||||||
\(464\) | 4.47214 | 0.207614 | ||||||||
\(465\) | −11.7082 | −0.542955 | ||||||||
\(466\) | −10.4164 | −0.482531 | ||||||||
\(467\) | −2.81966 | −0.130478 | −0.0652392 | − | 0.997870i | \(-0.520781\pi\) | ||||
−0.0652392 | + | 0.997870i | \(0.520781\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −7.23607 | −0.334131 | ||||||||
\(470\) | 7.70820 | 0.355553 | ||||||||
\(471\) | −19.0689 | −0.878648 | ||||||||
\(472\) | −4.70820 | −0.216713 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 22.8885 | 1.05131 | ||||||||
\(475\) | −2.23607 | −0.102598 | ||||||||
\(476\) | −1.23607 | −0.0566551 | ||||||||
\(477\) | −11.4164 | −0.522721 | ||||||||
\(478\) | −10.7082 | −0.489782 | ||||||||
\(479\) | −27.5967 | −1.26093 | −0.630464 | − | 0.776219i | \(-0.717135\pi\) | ||||
−0.630464 | + | 0.776219i | \(0.717135\pi\) | |||||||
\(480\) | −2.23607 | −0.102062 | ||||||||
\(481\) | 8.94427 | 0.407824 | ||||||||
\(482\) | 22.3607 | 1.01850 | ||||||||
\(483\) | 8.41641 | 0.382960 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.52786 | −0.160192 | ||||||||
\(486\) | −17.8885 | −0.811441 | ||||||||
\(487\) | 2.23607 | 0.101326 | 0.0506630 | − | 0.998716i | \(-0.483867\pi\) | ||||
0.0506630 | + | 0.998716i | \(0.483867\pi\) | |||||||
\(488\) | 3.52786 | 0.159699 | ||||||||
\(489\) | 13.4164 | 0.606711 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 31.2361 | 1.40966 | 0.704832 | − | 0.709374i | \(-0.251022\pi\) | ||||
0.704832 | + | 0.709374i | \(0.251022\pi\) | |||||||
\(492\) | 16.1803 | 0.729466 | ||||||||
\(493\) | −5.52786 | −0.248962 | ||||||||
\(494\) | 2.23607 | 0.100605 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.23607 | −0.235106 | ||||||||
\(497\) | −1.52786 | −0.0685341 | ||||||||
\(498\) | −0.527864 | −0.0236542 | ||||||||
\(499\) | 26.8328 | 1.20120 | 0.600601 | − | 0.799549i | \(-0.294928\pi\) | ||||
0.600601 | + | 0.799549i | \(0.294928\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −3.81966 | −0.170650 | ||||||||
\(502\) | 29.8885 | 1.33399 | ||||||||
\(503\) | 25.5967 | 1.14130 | 0.570651 | − | 0.821192i | \(-0.306691\pi\) | ||||
0.570651 | + | 0.821192i | \(0.306691\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 1.00000 | 0.0444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 26.8328 | 1.19169 | ||||||||
\(508\) | 6.23607 | 0.276681 | ||||||||
\(509\) | 28.8885 | 1.28046 | 0.640231 | − | 0.768182i | \(-0.278839\pi\) | ||||
0.640231 | + | 0.768182i | \(0.278839\pi\) | |||||||
\(510\) | 2.76393 | 0.122389 | ||||||||
\(511\) | −7.23607 | −0.320105 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.00000 | −0.220755 | ||||||||
\(514\) | 4.76393 | 0.210128 | ||||||||
\(515\) | −14.1803 | −0.624860 | ||||||||
\(516\) | −7.23607 | −0.318550 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −8.94427 | −0.392989 | ||||||||
\(519\) | −44.4721 | −1.95211 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | −1.05573 | −0.0462523 | −0.0231261 | − | 0.999733i | \(-0.507362\pi\) | ||||
−0.0231261 | + | 0.999733i | \(0.507362\pi\) | |||||||
\(522\) | −8.94427 | −0.391480 | ||||||||
\(523\) | −35.6525 | −1.55897 | −0.779487 | − | 0.626418i | \(-0.784520\pi\) | ||||
−0.779487 | + | 0.626418i | \(0.784520\pi\) | |||||||
\(524\) | −3.18034 | −0.138934 | ||||||||
\(525\) | −2.23607 | −0.0975900 | ||||||||
\(526\) | −7.65248 | −0.333664 | ||||||||
\(527\) | 6.47214 | 0.281931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.83282 | −0.384035 | ||||||||
\(530\) | −5.70820 | −0.247949 | ||||||||
\(531\) | 9.41641 | 0.408637 | ||||||||
\(532\) | −2.23607 | −0.0969458 | ||||||||
\(533\) | −7.23607 | −0.313429 | ||||||||
\(534\) | −38.5410 | −1.66783 | ||||||||
\(535\) | 2.47214 | 0.106880 | ||||||||
\(536\) | 7.23607 | 0.312551 | ||||||||
\(537\) | 25.1246 | 1.08421 | ||||||||
\(538\) | 27.8328 | 1.19996 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.23607 | −0.0962250 | ||||||||
\(541\) | −35.3050 | −1.51788 | −0.758939 | − | 0.651161i | \(-0.774282\pi\) | ||||
−0.758939 | + | 0.651161i | \(0.774282\pi\) | |||||||
\(542\) | −7.41641 | −0.318562 | ||||||||
\(543\) | −15.6525 | −0.671712 | ||||||||
\(544\) | 1.23607 | 0.0529960 | ||||||||
\(545\) | 3.70820 | 0.158842 | ||||||||
\(546\) | 2.23607 | 0.0956949 | ||||||||
\(547\) | 6.65248 | 0.284439 | 0.142220 | − | 0.989835i | \(-0.454576\pi\) | ||||
0.142220 | + | 0.989835i | \(0.454576\pi\) | |||||||
\(548\) | 13.4721 | 0.575501 | ||||||||
\(549\) | −7.05573 | −0.301131 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.0000 | −0.426014 | ||||||||
\(552\) | −8.41641 | −0.358226 | ||||||||
\(553\) | 10.2361 | 0.435282 | ||||||||
\(554\) | −23.5967 | −1.00253 | ||||||||
\(555\) | 20.0000 | 0.848953 | ||||||||
\(556\) | 4.23607 | 0.179649 | ||||||||
\(557\) | −31.1246 | −1.31879 | −0.659396 | − | 0.751796i | \(-0.729188\pi\) | ||||
−0.659396 | + | 0.751796i | \(0.729188\pi\) | |||||||
\(558\) | 10.4721 | 0.443321 | ||||||||
\(559\) | 3.23607 | 0.136871 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.8328 | −1.08969 | ||||||||
\(563\) | −36.5967 | −1.54237 | −0.771185 | − | 0.636612i | \(-0.780335\pi\) | ||||
−0.771185 | + | 0.636612i | \(0.780335\pi\) | |||||||
\(564\) | −17.2361 | −0.725769 | ||||||||
\(565\) | 1.00000 | 0.0420703 | ||||||||
\(566\) | −26.2361 | −1.10278 | ||||||||
\(567\) | −11.0000 | −0.461957 | ||||||||
\(568\) | 1.52786 | 0.0641078 | ||||||||
\(569\) | 7.47214 | 0.313248 | 0.156624 | − | 0.987658i | \(-0.449939\pi\) | ||||
0.156624 | + | 0.987658i | \(0.449939\pi\) | |||||||
\(570\) | 5.00000 | 0.209427 | ||||||||
\(571\) | 36.3607 | 1.52165 | 0.760824 | − | 0.648959i | \(-0.224795\pi\) | ||||
0.760824 | + | 0.648959i | \(0.224795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −56.3050 | −2.35217 | ||||||||
\(574\) | 7.23607 | 0.302028 | ||||||||
\(575\) | −3.76393 | −0.156967 | ||||||||
\(576\) | 2.00000 | 0.0833333 | ||||||||
\(577\) | −35.0132 | −1.45762 | −0.728808 | − | 0.684718i | \(-0.759925\pi\) | ||||
−0.728808 | + | 0.684718i | \(0.759925\pi\) | |||||||
\(578\) | 15.4721 | 0.643556 | ||||||||
\(579\) | −17.7639 | −0.738244 | ||||||||
\(580\) | −4.47214 | −0.185695 | ||||||||
\(581\) | −0.236068 | −0.00979375 | ||||||||
\(582\) | 7.88854 | 0.326991 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 7.23607 | 0.299431 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 5.00000 | 0.206548 | ||||||||
\(587\) | −23.0689 | −0.952155 | −0.476077 | − | 0.879403i | \(-0.657942\pi\) | ||||
−0.476077 | + | 0.879403i | \(0.657942\pi\) | |||||||
\(588\) | −2.23607 | −0.0922139 | ||||||||
\(589\) | 11.7082 | 0.482428 | ||||||||
\(590\) | 4.70820 | 0.193834 | ||||||||
\(591\) | 16.8328 | 0.692410 | ||||||||
\(592\) | 8.94427 | 0.367607 | ||||||||
\(593\) | 36.9443 | 1.51712 | 0.758560 | − | 0.651604i | \(-0.225903\pi\) | ||||
0.758560 | + | 0.651604i | \(0.225903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.23607 | 0.0506738 | ||||||||
\(596\) | 4.00000 | 0.163846 | ||||||||
\(597\) | 10.0000 | 0.409273 | ||||||||
\(598\) | 3.76393 | 0.153919 | ||||||||
\(599\) | 27.0689 | 1.10600 | 0.553002 | − | 0.833180i | \(-0.313482\pi\) | ||||
0.553002 | + | 0.833180i | \(0.313482\pi\) | |||||||
\(600\) | 2.23607 | 0.0912871 | ||||||||
\(601\) | 26.6525 | 1.08718 | 0.543589 | − | 0.839352i | \(-0.317065\pi\) | ||||
0.543589 | + | 0.839352i | \(0.317065\pi\) | |||||||
\(602\) | −3.23607 | −0.131892 | ||||||||
\(603\) | −14.4721 | −0.589351 | ||||||||
\(604\) | 12.2361 | 0.497879 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.23607 | −0.0908341 | ||||||||
\(607\) | 21.0557 | 0.854626 | 0.427313 | − | 0.904104i | \(-0.359460\pi\) | ||||
0.427313 | + | 0.904104i | \(0.359460\pi\) | |||||||
\(608\) | 2.23607 | 0.0906845 | ||||||||
\(609\) | −10.0000 | −0.405220 | ||||||||
\(610\) | −3.52786 | −0.142839 | ||||||||
\(611\) | 7.70820 | 0.311841 | ||||||||
\(612\) | −2.47214 | −0.0999302 | ||||||||
\(613\) | 0.875388 | 0.0353566 | 0.0176783 | − | 0.999844i | \(-0.494373\pi\) | ||||
0.0176783 | + | 0.999844i | \(0.494373\pi\) | |||||||
\(614\) | −11.4164 | −0.460729 | ||||||||
\(615\) | −16.1803 | −0.652454 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.8885 | −1.76689 | −0.883443 | − | 0.468538i | \(-0.844781\pi\) | ||||
−0.883443 | + | 0.468538i | \(0.844781\pi\) | |||||||
\(618\) | 31.7082 | 1.27549 | ||||||||
\(619\) | −47.5410 | −1.91083 | −0.955417 | − | 0.295258i | \(-0.904594\pi\) | ||||
−0.955417 | + | 0.295258i | \(0.904594\pi\) | |||||||
\(620\) | 5.23607 | 0.210286 | ||||||||
\(621\) | −8.41641 | −0.337739 | ||||||||
\(622\) | 27.1246 | 1.08760 | ||||||||
\(623\) | −17.2361 | −0.690548 | ||||||||
\(624\) | −2.23607 | −0.0895144 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −19.5279 | −0.780490 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.52786 | 0.340299 | ||||||||
\(629\) | −11.0557 | −0.440821 | ||||||||
\(630\) | 2.00000 | 0.0796819 | ||||||||
\(631\) | −16.3607 | −0.651308 | −0.325654 | − | 0.945489i | \(-0.605585\pi\) | ||||
−0.325654 | + | 0.945489i | \(0.605585\pi\) | |||||||
\(632\) | −10.2361 | −0.407169 | ||||||||
\(633\) | −7.88854 | −0.313541 | ||||||||
\(634\) | −0.652476 | −0.0259131 | ||||||||
\(635\) | −6.23607 | −0.247471 | ||||||||
\(636\) | 12.7639 | 0.506123 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.05573 | −0.120883 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −23.8328 | −0.941340 | −0.470670 | − | 0.882309i | \(-0.655988\pi\) | ||||
−0.470670 | + | 0.882309i | \(0.655988\pi\) | |||||||
\(642\) | −5.52786 | −0.218167 | ||||||||
\(643\) | 6.11146 | 0.241012 | 0.120506 | − | 0.992713i | \(-0.461548\pi\) | ||||
0.120506 | + | 0.992713i | \(0.461548\pi\) | |||||||
\(644\) | −3.76393 | −0.148320 | ||||||||
\(645\) | 7.23607 | 0.284920 | ||||||||
\(646\) | −2.76393 | −0.108745 | ||||||||
\(647\) | −9.23607 | −0.363107 | −0.181554 | − | 0.983381i | \(-0.558113\pi\) | ||||
−0.181554 | + | 0.983381i | \(0.558113\pi\) | |||||||
\(648\) | 11.0000 | 0.432121 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | 11.7082 | 0.458881 | ||||||||
\(652\) | −6.00000 | −0.234978 | ||||||||
\(653\) | 26.2918 | 1.02888 | 0.514439 | − | 0.857527i | \(-0.328000\pi\) | ||||
0.514439 | + | 0.857527i | \(0.328000\pi\) | |||||||
\(654\) | −8.29180 | −0.324235 | ||||||||
\(655\) | 3.18034 | 0.124266 | ||||||||
\(656\) | −7.23607 | −0.282521 | ||||||||
\(657\) | −14.4721 | −0.564612 | ||||||||
\(658\) | −7.70820 | −0.300497 | ||||||||
\(659\) | −20.7639 | −0.808848 | −0.404424 | − | 0.914572i | \(-0.632528\pi\) | ||||
−0.404424 | + | 0.914572i | \(0.632528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.41641 | 0.171778 | 0.0858892 | − | 0.996305i | \(-0.472627\pi\) | ||||
0.0858892 | + | 0.996305i | \(0.472627\pi\) | |||||||
\(662\) | 21.7082 | 0.843713 | ||||||||
\(663\) | 2.76393 | 0.107342 | ||||||||
\(664\) | 0.236068 | 0.00916121 | ||||||||
\(665\) | 2.23607 | 0.0867110 | ||||||||
\(666\) | −17.8885 | −0.693167 | ||||||||
\(667\) | −16.8328 | −0.651769 | ||||||||
\(668\) | 1.70820 | 0.0660924 | ||||||||
\(669\) | 18.2918 | 0.707202 | ||||||||
\(670\) | −7.23607 | −0.279554 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.23607 | 0.0862582 | ||||||||
\(673\) | −10.0557 | −0.387620 | −0.193810 | − | 0.981039i | \(-0.562085\pi\) | ||||
−0.193810 | + | 0.981039i | \(0.562085\pi\) | |||||||
\(674\) | 2.88854 | 0.111263 | ||||||||
\(675\) | 2.23607 | 0.0860663 | ||||||||
\(676\) | −12.0000 | −0.461538 | ||||||||
\(677\) | −45.8328 | −1.76150 | −0.880749 | − | 0.473583i | \(-0.842960\pi\) | ||||
−0.880749 | + | 0.473583i | \(0.842960\pi\) | |||||||
\(678\) | −2.23607 | −0.0858757 | ||||||||
\(679\) | 3.52786 | 0.135387 | ||||||||
\(680\) | −1.23607 | −0.0474010 | ||||||||
\(681\) | 16.5836 | 0.635485 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.36068 | −0.243385 | −0.121692 | − | 0.992568i | \(-0.538832\pi\) | ||||
−0.121692 | + | 0.992568i | \(0.538832\pi\) | |||||||
\(684\) | −4.47214 | −0.170996 | ||||||||
\(685\) | −13.4721 | −0.514744 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −15.5279 | −0.592425 | ||||||||
\(688\) | 3.23607 | 0.123374 | ||||||||
\(689\) | −5.70820 | −0.217465 | ||||||||
\(690\) | 8.41641 | 0.320407 | ||||||||
\(691\) | −40.0000 | −1.52167 | −0.760836 | − | 0.648944i | \(-0.775211\pi\) | ||||
−0.760836 | + | 0.648944i | \(0.775211\pi\) | |||||||
\(692\) | 19.8885 | 0.756049 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.00000 | 0.227757 | ||||||||
\(695\) | −4.23607 | −0.160683 | ||||||||
\(696\) | 10.0000 | 0.379049 | ||||||||
\(697\) | 8.94427 | 0.338788 | ||||||||
\(698\) | −0.416408 | −0.0157613 | ||||||||
\(699\) | −23.2918 | −0.880977 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −17.5967 | −0.664620 | −0.332310 | − | 0.943170i | \(-0.607828\pi\) | ||||
−0.332310 | + | 0.943170i | \(0.607828\pi\) | |||||||
\(702\) | −2.23607 | −0.0843949 | ||||||||
\(703\) | −20.0000 | −0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.2361 | 0.649148 | ||||||||
\(706\) | 4.76393 | 0.179293 | ||||||||
\(707\) | −1.00000 | −0.0376089 | ||||||||
\(708\) | −10.5279 | −0.395661 | ||||||||
\(709\) | 19.0557 | 0.715653 | 0.357826 | − | 0.933788i | \(-0.383518\pi\) | ||||
0.357826 | + | 0.933788i | \(0.383518\pi\) | |||||||
\(710\) | −1.52786 | −0.0573397 | ||||||||
\(711\) | 20.4721 | 0.767765 | ||||||||
\(712\) | 17.2361 | 0.645949 | ||||||||
\(713\) | 19.7082 | 0.738078 | ||||||||
\(714\) | −2.76393 | −0.103438 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.2361 | −0.419912 | ||||||||
\(717\) | −23.9443 | −0.894215 | ||||||||
\(718\) | −16.0000 | −0.597115 | ||||||||
\(719\) | 6.83282 | 0.254821 | 0.127411 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127411 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | 14.1803 | 0.528103 | ||||||||
\(722\) | 14.0000 | 0.521026 | ||||||||
\(723\) | 50.0000 | 1.85952 | ||||||||
\(724\) | 7.00000 | 0.260153 | ||||||||
\(725\) | 4.47214 | 0.166091 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.3050 | −1.45774 | −0.728870 | − | 0.684652i | \(-0.759954\pi\) | ||||
−0.728870 | + | 0.684652i | \(0.759954\pi\) | |||||||
\(728\) | −1.00000 | −0.0370625 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | −7.23607 | −0.267819 | ||||||||
\(731\) | −4.00000 | −0.147945 | ||||||||
\(732\) | 7.88854 | 0.291569 | ||||||||
\(733\) | −48.4164 | −1.78830 | −0.894150 | − | 0.447767i | \(-0.852220\pi\) | ||||
−0.894150 | + | 0.447767i | \(0.852220\pi\) | |||||||
\(734\) | −8.18034 | −0.301942 | ||||||||
\(735\) | 2.23607 | 0.0824786 | ||||||||
\(736\) | 3.76393 | 0.138740 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 14.4721 | 0.532727 | ||||||||
\(739\) | 18.0689 | 0.664675 | 0.332337 | − | 0.943161i | \(-0.392163\pi\) | ||||
0.332337 | + | 0.943161i | \(0.392163\pi\) | |||||||
\(740\) | −8.94427 | −0.328798 | ||||||||
\(741\) | 5.00000 | 0.183680 | ||||||||
\(742\) | 5.70820 | 0.209555 | ||||||||
\(743\) | 28.0000 | 1.02722 | 0.513610 | − | 0.858024i | \(-0.328308\pi\) | ||||
0.513610 | + | 0.858024i | \(0.328308\pi\) | |||||||
\(744\) | −11.7082 | −0.429244 | ||||||||
\(745\) | −4.00000 | −0.146549 | ||||||||
\(746\) | 5.52786 | 0.202389 | ||||||||
\(747\) | −0.472136 | −0.0172746 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.47214 | −0.0903299 | ||||||||
\(750\) | −2.23607 | −0.0816497 | ||||||||
\(751\) | −11.1803 | −0.407976 | −0.203988 | − | 0.978973i | \(-0.565390\pi\) | ||||
−0.203988 | + | 0.978973i | \(0.565390\pi\) | |||||||
\(752\) | 7.70820 | 0.281089 | ||||||||
\(753\) | 66.8328 | 2.43552 | ||||||||
\(754\) | −4.47214 | −0.162866 | ||||||||
\(755\) | −12.2361 | −0.445316 | ||||||||
\(756\) | 2.23607 | 0.0813250 | ||||||||
\(757\) | −42.6525 | −1.55023 | −0.775115 | − | 0.631820i | \(-0.782308\pi\) | ||||
−0.775115 | + | 0.631820i | \(0.782308\pi\) | |||||||
\(758\) | −11.4164 | −0.414663 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.23607 | −0.0811107 | ||||||||
\(761\) | −30.5410 | −1.10711 | −0.553556 | − | 0.832812i | \(-0.686729\pi\) | ||||
−0.553556 | + | 0.832812i | \(0.686729\pi\) | |||||||
\(762\) | 13.9443 | 0.505148 | ||||||||
\(763\) | −3.70820 | −0.134246 | ||||||||
\(764\) | 25.1803 | 0.910993 | ||||||||
\(765\) | 2.47214 | 0.0893803 | ||||||||
\(766\) | 17.2361 | 0.622764 | ||||||||
\(767\) | 4.70820 | 0.170003 | ||||||||
\(768\) | −2.23607 | −0.0806872 | ||||||||
\(769\) | −12.0000 | −0.432731 | −0.216366 | − | 0.976312i | \(-0.569420\pi\) | ||||
−0.216366 | + | 0.976312i | \(0.569420\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6525 | 0.383640 | ||||||||
\(772\) | 7.94427 | 0.285921 | ||||||||
\(773\) | −27.9443 | −1.00509 | −0.502543 | − | 0.864552i | \(-0.667602\pi\) | ||||
−0.502543 | + | 0.864552i | \(0.667602\pi\) | |||||||
\(774\) | −6.47214 | −0.232636 | ||||||||
\(775\) | −5.23607 | −0.188085 | ||||||||
\(776\) | −3.52786 | −0.126643 | ||||||||
\(777\) | −20.0000 | −0.717496 | ||||||||
\(778\) | 18.2918 | 0.655793 | ||||||||
\(779\) | 16.1803 | 0.579721 | ||||||||
\(780\) | 2.23607 | 0.0800641 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.65248 | −0.166372 | ||||||||
\(783\) | 10.0000 | 0.357371 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −8.52786 | −0.304373 | ||||||||
\(786\) | −7.11146 | −0.253657 | ||||||||
\(787\) | −31.7771 | −1.13273 | −0.566365 | − | 0.824154i | \(-0.691651\pi\) | ||||
−0.566365 | + | 0.824154i | \(0.691651\pi\) | |||||||
\(788\) | −7.52786 | −0.268169 | ||||||||
\(789\) | −17.1115 | −0.609184 | ||||||||
\(790\) | 10.2361 | 0.364183 | ||||||||
\(791\) | −1.00000 | −0.0355559 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.52786 | −0.125278 | ||||||||
\(794\) | −6.00000 | −0.212932 | ||||||||
\(795\) | −12.7639 | −0.452690 | ||||||||
\(796\) | −4.47214 | −0.158511 | ||||||||
\(797\) | 28.8885 | 1.02328 | 0.511642 | − | 0.859199i | \(-0.329037\pi\) | ||||
0.511642 | + | 0.859199i | \(0.329037\pi\) | |||||||
\(798\) | −5.00000 | −0.176998 | ||||||||
\(799\) | −9.52786 | −0.337072 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −34.4721 | −1.21801 | ||||||||
\(802\) | 28.8328 | 1.01812 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 16.1803 | 0.570637 | ||||||||
\(805\) | 3.76393 | 0.132661 | ||||||||
\(806\) | 5.23607 | 0.184433 | ||||||||
\(807\) | 62.2361 | 2.19081 | ||||||||
\(808\) | 1.00000 | 0.0351799 | ||||||||
\(809\) | −1.63932 | −0.0576354 | −0.0288177 | − | 0.999585i | \(-0.509174\pi\) | ||||
−0.0288177 | + | 0.999585i | \(0.509174\pi\) | |||||||
\(810\) | −11.0000 | −0.386501 | ||||||||
\(811\) | 2.47214 | 0.0868084 | 0.0434042 | − | 0.999058i | \(-0.486180\pi\) | ||||
0.0434042 | + | 0.999058i | \(0.486180\pi\) | |||||||
\(812\) | 4.47214 | 0.156941 | ||||||||
\(813\) | −16.5836 | −0.581612 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | 0.210171 | ||||||||
\(816\) | 2.76393 | 0.0967570 | ||||||||
\(817\) | −7.23607 | −0.253158 | ||||||||
\(818\) | −11.5279 | −0.403062 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | 7.23607 | 0.252694 | ||||||||
\(821\) | 13.0557 | 0.455648 | 0.227824 | − | 0.973702i | \(-0.426839\pi\) | ||||
0.227824 | + | 0.973702i | \(0.426839\pi\) | |||||||
\(822\) | 30.1246 | 1.05072 | ||||||||
\(823\) | 16.3607 | 0.570297 | 0.285149 | − | 0.958483i | \(-0.407957\pi\) | ||||
0.285149 | + | 0.958483i | \(0.407957\pi\) | |||||||
\(824\) | −14.1803 | −0.493996 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.70820 | −0.163819 | ||||||||
\(827\) | 12.1803 | 0.423552 | 0.211776 | − | 0.977318i | \(-0.432075\pi\) | ||||
0.211776 | + | 0.977318i | \(0.432075\pi\) | |||||||
\(828\) | −7.52786 | −0.261611 | ||||||||
\(829\) | −11.9443 | −0.414842 | −0.207421 | − | 0.978252i | \(-0.566507\pi\) | ||||
−0.207421 | + | 0.978252i | \(0.566507\pi\) | |||||||
\(830\) | −0.236068 | −0.00819404 | ||||||||
\(831\) | −52.7639 | −1.83036 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −1.23607 | −0.0428272 | ||||||||
\(834\) | 9.47214 | 0.327993 | ||||||||
\(835\) | −1.70820 | −0.0591148 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.7082 | −0.404695 | ||||||||
\(838\) | 28.2361 | 0.975399 | ||||||||
\(839\) | −13.5967 | −0.469412 | −0.234706 | − | 0.972066i | \(-0.575413\pi\) | ||||
−0.234706 | + | 0.972066i | \(0.575413\pi\) | |||||||
\(840\) | −2.23607 | −0.0771517 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 3.05573 | 0.105307 | ||||||||
\(843\) | −57.7639 | −1.98950 | ||||||||
\(844\) | 3.52786 | 0.121434 | ||||||||
\(845\) | 12.0000 | 0.412813 | ||||||||
\(846\) | −15.4164 | −0.530027 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.70820 | −0.196021 | ||||||||
\(849\) | −58.6656 | −2.01340 | ||||||||
\(850\) | 1.23607 | 0.0423968 | ||||||||
\(851\) | −33.6656 | −1.15404 | ||||||||
\(852\) | 3.41641 | 0.117044 | ||||||||
\(853\) | 3.47214 | 0.118884 | 0.0594418 | − | 0.998232i | \(-0.481068\pi\) | ||||
0.0594418 | + | 0.998232i | \(0.481068\pi\) | |||||||
\(854\) | 3.52786 | 0.120721 | ||||||||
\(855\) | 4.47214 | 0.152944 | ||||||||
\(856\) | 2.47214 | 0.0844959 | ||||||||
\(857\) | 10.8328 | 0.370042 | 0.185021 | − | 0.982735i | \(-0.440765\pi\) | ||||
0.185021 | + | 0.982735i | \(0.440765\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.944272 | 0.0322181 | 0.0161091 | − | 0.999870i | \(-0.494872\pi\) | ||||
0.0161091 | + | 0.999870i | \(0.494872\pi\) | |||||||
\(860\) | −3.23607 | −0.110349 | ||||||||
\(861\) | 16.1803 | 0.551425 | ||||||||
\(862\) | 33.6525 | 1.14621 | ||||||||
\(863\) | −56.7214 | −1.93082 | −0.965409 | − | 0.260741i | \(-0.916033\pi\) | ||||
−0.965409 | + | 0.260741i | \(0.916033\pi\) | |||||||
\(864\) | −2.23607 | −0.0760726 | ||||||||
\(865\) | −19.8885 | −0.676231 | ||||||||
\(866\) | 12.6525 | 0.429949 | ||||||||
\(867\) | 34.5967 | 1.17497 | ||||||||
\(868\) | −5.23607 | −0.177724 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −10.0000 | −0.339032 | ||||||||
\(871\) | −7.23607 | −0.245185 | ||||||||
\(872\) | 3.70820 | 0.125576 | ||||||||
\(873\) | 7.05573 | 0.238800 | ||||||||
\(874\) | −8.41641 | −0.284689 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 16.1803 | 0.546683 | ||||||||
\(877\) | −51.9574 | −1.75448 | −0.877239 | − | 0.480054i | \(-0.840617\pi\) | ||||
−0.877239 | + | 0.480054i | \(0.840617\pi\) | |||||||
\(878\) | −15.1246 | −0.510431 | ||||||||
\(879\) | 11.1803 | 0.377104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.94427 | −0.166577 | −0.0832884 | − | 0.996525i | \(-0.526542\pi\) | ||||
−0.0832884 | + | 0.996525i | \(0.526542\pi\) | |||||||
\(882\) | −2.00000 | −0.0673435 | ||||||||
\(883\) | −22.4721 | −0.756248 | −0.378124 | − | 0.925755i | \(-0.623431\pi\) | ||||
−0.378124 | + | 0.925755i | \(0.623431\pi\) | |||||||
\(884\) | −1.23607 | −0.0415735 | ||||||||
\(885\) | 10.5279 | 0.353890 | ||||||||
\(886\) | 24.3607 | 0.818413 | ||||||||
\(887\) | 5.23607 | 0.175810 | 0.0879050 | − | 0.996129i | \(-0.471983\pi\) | ||||
0.0879050 | + | 0.996129i | \(0.471983\pi\) | |||||||
\(888\) | 20.0000 | 0.671156 | ||||||||
\(889\) | 6.23607 | 0.209151 | ||||||||
\(890\) | −17.2361 | −0.577754 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.18034 | −0.273898 | ||||||||
\(893\) | −17.2361 | −0.576783 | ||||||||
\(894\) | 8.94427 | 0.299141 | ||||||||
\(895\) | 11.2361 | 0.375580 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 8.41641 | 0.281016 | ||||||||
\(898\) | −23.8328 | −0.795311 | ||||||||
\(899\) | −23.4164 | −0.780981 | ||||||||
\(900\) | 2.00000 | 0.0666667 | ||||||||
\(901\) | 7.05573 | 0.235060 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.23607 | −0.240801 | ||||||||
\(904\) | 1.00000 | 0.0332595 | ||||||||
\(905\) | −7.00000 | −0.232688 | ||||||||
\(906\) | 27.3607 | 0.908998 | ||||||||
\(907\) | 40.3607 | 1.34015 | 0.670077 | − | 0.742291i | \(-0.266261\pi\) | ||||
0.670077 | + | 0.742291i | \(0.266261\pi\) | |||||||
\(908\) | −7.41641 | −0.246122 | ||||||||
\(909\) | −2.00000 | −0.0663358 | ||||||||
\(910\) | 1.00000 | 0.0331497 | ||||||||
\(911\) | −43.6525 | −1.44627 | −0.723136 | − | 0.690706i | \(-0.757300\pi\) | ||||
−0.723136 | + | 0.690706i | \(0.757300\pi\) | |||||||
\(912\) | 5.00000 | 0.165567 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 36.4164 | 1.20455 | ||||||||
\(915\) | −7.88854 | −0.260787 | ||||||||
\(916\) | 6.94427 | 0.229445 | ||||||||
\(917\) | −3.18034 | −0.105024 | ||||||||
\(918\) | 2.76393 | 0.0912234 | ||||||||
\(919\) | 12.9443 | 0.426992 | 0.213496 | − | 0.976944i | \(-0.431515\pi\) | ||||
0.213496 | + | 0.976944i | \(0.431515\pi\) | |||||||
\(920\) | −3.76393 | −0.124093 | ||||||||
\(921\) | −25.5279 | −0.841172 | ||||||||
\(922\) | 23.8885 | 0.786727 | ||||||||
\(923\) | −1.52786 | −0.0502903 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.94427 | 0.294086 | ||||||||
\(926\) | −10.7082 | −0.351893 | ||||||||
\(927\) | 28.3607 | 0.931487 | ||||||||
\(928\) | −4.47214 | −0.146805 | ||||||||
\(929\) | −42.8328 | −1.40530 | −0.702650 | − | 0.711536i | \(-0.748000\pi\) | ||||
−0.702650 | + | 0.711536i | \(0.748000\pi\) | |||||||
\(930\) | 11.7082 | 0.383927 | ||||||||
\(931\) | −2.23607 | −0.0732842 | ||||||||
\(932\) | 10.4164 | 0.341201 | ||||||||
\(933\) | 60.6525 | 1.98567 | ||||||||
\(934\) | 2.81966 | 0.0922621 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | 20.4721 | 0.668796 | 0.334398 | − | 0.942432i | \(-0.391467\pi\) | ||||
0.334398 | + | 0.942432i | \(0.391467\pi\) | |||||||
\(938\) | 7.23607 | 0.236266 | ||||||||
\(939\) | −43.6656 | −1.42497 | ||||||||
\(940\) | −7.70820 | −0.251414 | ||||||||
\(941\) | −55.8885 | −1.82191 | −0.910957 | − | 0.412501i | \(-0.864655\pi\) | ||||
−0.910957 | + | 0.412501i | \(0.864655\pi\) | |||||||
\(942\) | 19.0689 | 0.621298 | ||||||||
\(943\) | 27.2361 | 0.886928 | ||||||||
\(944\) | 4.70820 | 0.153239 | ||||||||
\(945\) | −2.23607 | −0.0727393 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.0689 | 0.327195 | 0.163597 | − | 0.986527i | \(-0.447690\pi\) | ||||
0.163597 | + | 0.986527i | \(0.447690\pi\) | |||||||
\(948\) | −22.8885 | −0.743385 | ||||||||
\(949\) | −7.23607 | −0.234893 | ||||||||
\(950\) | 2.23607 | 0.0725476 | ||||||||
\(951\) | −1.45898 | −0.0473107 | ||||||||
\(952\) | 1.23607 | 0.0400612 | ||||||||
\(953\) | 24.8885 | 0.806219 | 0.403110 | − | 0.915152i | \(-0.367929\pi\) | ||||
0.403110 | + | 0.915152i | \(0.367929\pi\) | |||||||
\(954\) | 11.4164 | 0.369620 | ||||||||
\(955\) | −25.1803 | −0.814817 | ||||||||
\(956\) | 10.7082 | 0.346328 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.5967 | 0.891610 | ||||||||
\(959\) | 13.4721 | 0.435038 | ||||||||
\(960\) | 2.23607 | 0.0721688 | ||||||||
\(961\) | −3.58359 | −0.115600 | ||||||||
\(962\) | −8.94427 | −0.288375 | ||||||||
\(963\) | −4.94427 | −0.159327 | ||||||||
\(964\) | −22.3607 | −0.720189 | ||||||||
\(965\) | −7.94427 | −0.255735 | ||||||||
\(966\) | −8.41641 | −0.270793 | ||||||||
\(967\) | 55.1935 | 1.77490 | 0.887452 | − | 0.460901i | \(-0.152474\pi\) | ||||
0.887452 | + | 0.460901i | \(0.152474\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.18034 | −0.198541 | ||||||||
\(970\) | 3.52786 | 0.113273 | ||||||||
\(971\) | −16.1246 | −0.517463 | −0.258732 | − | 0.965949i | \(-0.583305\pi\) | ||||
−0.258732 | + | 0.965949i | \(0.583305\pi\) | |||||||
\(972\) | 17.8885 | 0.573775 | ||||||||
\(973\) | 4.23607 | 0.135802 | ||||||||
\(974\) | −2.23607 | −0.0716482 | ||||||||
\(975\) | −2.23607 | −0.0716115 | ||||||||
\(976\) | −3.52786 | −0.112924 | ||||||||
\(977\) | −45.9443 | −1.46989 | −0.734944 | − | 0.678128i | \(-0.762791\pi\) | ||||
−0.734944 | + | 0.678128i | \(0.762791\pi\) | |||||||
\(978\) | −13.4164 | −0.429009 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −7.41641 | −0.236788 | ||||||||
\(982\) | −31.2361 | −0.996783 | ||||||||
\(983\) | 43.1935 | 1.37766 | 0.688829 | − | 0.724924i | \(-0.258125\pi\) | ||||
0.688829 | + | 0.724924i | \(0.258125\pi\) | |||||||
\(984\) | −16.1803 | −0.515810 | ||||||||
\(985\) | 7.52786 | 0.239858 | ||||||||
\(986\) | 5.52786 | 0.176043 | ||||||||
\(987\) | −17.2361 | −0.548630 | ||||||||
\(988\) | −2.23607 | −0.0711388 | ||||||||
\(989\) | −12.1803 | −0.387312 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.2918 | 0.612824 | 0.306412 | − | 0.951899i | \(-0.400871\pi\) | ||||
0.306412 | + | 0.951899i | \(0.400871\pi\) | |||||||
\(992\) | 5.23607 | 0.166245 | ||||||||
\(993\) | 48.5410 | 1.54040 | ||||||||
\(994\) | 1.52786 | 0.0484609 | ||||||||
\(995\) | 4.47214 | 0.141776 | ||||||||
\(996\) | 0.527864 | 0.0167260 | ||||||||
\(997\) | −59.8328 | −1.89492 | −0.947462 | − | 0.319868i | \(-0.896361\pi\) | ||||
−0.947462 | + | 0.319868i | \(0.896361\pi\) | |||||||
\(998\) | −26.8328 | −0.849378 | ||||||||
\(999\) | 20.0000 | 0.632772 |
(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 | 8470.2.a.bn.1.1 | ✓ | 2 | |
11.10 | odd | 2 | 8470.2.a.by.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.bn.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
8470.2.a.by.1.1 | yes | 2 | 11.10 | odd | 2 |