Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,2,Mod(1,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.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: | \(1.36544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.13068.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 6x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.328543\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 171.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.71519 | 1.91993 | 0.959966 | − | 0.280116i | \(-0.0903729\pi\) | ||||
0.959966 | + | 0.280116i | \(0.0903729\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.37228 | 2.68614 | ||||||||
\(5\) | −3.22060 | −1.44030 | −0.720149 | − | 0.693820i | \(-0.755926\pi\) | ||||
−0.720149 | + | 0.693820i | \(0.755926\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.37228 | −0.896638 | −0.448319 | − | 0.893874i | \(-0.647977\pi\) | ||||
−0.448319 | + | 0.893874i | \(0.647977\pi\) | |||||||
\(8\) | 9.15640 | 3.23728 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.74456 | −2.76527 | ||||||||
\(11\) | −2.20979 | −0.666276 | −0.333138 | − | 0.942878i | \(-0.608107\pi\) | ||||
−0.333138 | + | 0.942878i | \(0.608107\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −6.44121 | −1.72148 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.1168 | 3.52921 | ||||||||
\(17\) | −3.22060 | −0.781111 | −0.390555 | − | 0.920579i | \(-0.627717\pi\) | ||||
−0.390555 | + | 0.920579i | \(0.627717\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −17.3020 | −3.86884 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.00000 | −1.27920 | ||||||||
\(23\) | 1.01082 | 0.210770 | 0.105385 | − | 0.994432i | \(-0.466393\pi\) | ||||
0.105385 | + | 0.994432i | \(0.466393\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.37228 | 1.07446 | ||||||||
\(26\) | 5.43039 | 1.06499 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −12.7446 | −2.40850 | ||||||||
\(29\) | 1.01082 | 0.187704 | 0.0938519 | − | 0.995586i | \(-0.470082\pi\) | ||||
0.0938519 | + | 0.995586i | \(0.470082\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.74456 | 0.852149 | 0.426074 | − | 0.904688i | \(-0.359896\pi\) | ||||
0.426074 | + | 0.904688i | \(0.359896\pi\) | |||||||
\(32\) | 20.0172 | 3.53857 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.74456 | −1.49968 | ||||||||
\(35\) | 7.64018 | 1.29143 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.7446 | 1.76640 | 0.883198 | − | 0.469001i | \(-0.155386\pi\) | ||||
0.883198 | + | 0.469001i | \(0.155386\pi\) | |||||||
\(38\) | 2.71519 | 0.440463 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −29.4891 | −4.66264 | ||||||||
\(41\) | −5.43039 | −0.848084 | −0.424042 | − | 0.905642i | \(-0.639389\pi\) | ||||
−0.424042 | + | 0.905642i | \(0.639389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.1168 | −1.69530 | −0.847651 | − | 0.530554i | \(-0.821984\pi\) | ||||
−0.847651 | + | 0.530554i | \(0.821984\pi\) | |||||||
\(44\) | −11.8716 | −1.78971 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.74456 | 0.404664 | ||||||||
\(47\) | −4.23142 | −0.617216 | −0.308608 | − | 0.951189i | \(-0.599863\pi\) | ||||
−0.308608 | + | 0.951189i | \(0.599863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.37228 | −0.196040 | ||||||||
\(50\) | 14.5868 | 2.06288 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.7446 | 1.49000 | ||||||||
\(53\) | 9.84996 | 1.35300 | 0.676498 | − | 0.736444i | \(-0.263497\pi\) | ||||
0.676498 | + | 0.736444i | \(0.263497\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.11684 | 0.959635 | ||||||||
\(56\) | −21.7216 | −2.90267 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.74456 | 0.360379 | ||||||||
\(59\) | 10.8608 | 1.41395 | 0.706976 | − | 0.707237i | \(-0.250059\pi\) | ||||
0.706976 | + | 0.707237i | \(0.250059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.11684 | −0.655145 | −0.327572 | − | 0.944826i | \(-0.606231\pi\) | ||||
−0.327572 | + | 0.944826i | \(0.606231\pi\) | |||||||
\(62\) | 12.8824 | 1.63607 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 26.1168 | 3.26461 | ||||||||
\(65\) | −6.44121 | −0.798933 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −17.3020 | −2.09817 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 20.7446 | 2.47945 | ||||||||
\(71\) | 2.02163 | 0.239924 | 0.119962 | − | 0.992779i | \(-0.461723\pi\) | ||||
0.119962 | + | 0.992779i | \(0.461723\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.11684 | −0.598881 | −0.299441 | − | 0.954115i | \(-0.596800\pi\) | ||||
−0.299441 | + | 0.954115i | \(0.596800\pi\) | |||||||
\(74\) | 29.1736 | 3.39136 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.37228 | 0.616243 | ||||||||
\(77\) | 5.24224 | 0.597408 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | −45.4647 | −5.08311 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.7446 | −1.62826 | ||||||||
\(83\) | −11.8716 | −1.30308 | −0.651538 | − | 0.758616i | \(-0.725876\pi\) | ||||
−0.651538 | + | 0.758616i | \(0.725876\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.3723 | 1.12503 | ||||||||
\(86\) | −30.1844 | −3.25487 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −20.2337 | −2.15692 | ||||||||
\(89\) | 9.84996 | 1.04409 | 0.522047 | − | 0.852917i | \(-0.325169\pi\) | ||||
0.522047 | + | 0.852917i | \(0.325169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.74456 | −0.497365 | ||||||||
\(92\) | 5.43039 | 0.566157 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11.4891 | −1.18501 | ||||||||
\(95\) | −3.22060 | −0.330427 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.48913 | 0.760405 | 0.380203 | − | 0.924903i | \(-0.375854\pi\) | ||||
0.380203 | + | 0.924903i | \(0.375854\pi\) | |||||||
\(98\) | −3.72601 | −0.376384 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 28.8614 | 2.88614 | ||||||||
\(101\) | 12.8824 | 1.28185 | 0.640924 | − | 0.767604i | \(-0.278551\pi\) | ||||
0.640924 | + | 0.767604i | \(0.278551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.25544 | −0.714899 | −0.357450 | − | 0.933932i | \(-0.616354\pi\) | ||||
−0.357450 | + | 0.933932i | \(0.616354\pi\) | |||||||
\(104\) | 18.3128 | 1.79572 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 26.7446 | 2.59766 | ||||||||
\(107\) | 4.41957 | 0.427256 | 0.213628 | − | 0.976915i | \(-0.431472\pi\) | ||||
0.213628 | + | 0.976915i | \(0.431472\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.25544 | 0.503380 | 0.251690 | − | 0.967808i | \(-0.419014\pi\) | ||||
0.251690 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(110\) | 19.3236 | 1.84243 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −33.4891 | −3.16442 | ||||||||
\(113\) | −11.8716 | −1.11679 | −0.558393 | − | 0.829577i | \(-0.688582\pi\) | ||||
−0.558393 | + | 0.829577i | \(0.688582\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.25544 | −0.303571 | ||||||||
\(116\) | 5.43039 | 0.504199 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 29.4891 | 2.71469 | ||||||||
\(119\) | 7.64018 | 0.700374 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.11684 | −0.556077 | ||||||||
\(122\) | −13.8932 | −1.25783 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 25.4891 | 2.28899 | ||||||||
\(125\) | −1.19897 | −0.107239 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.7446 | −1.13090 | −0.565449 | − | 0.824784i | \(-0.691297\pi\) | ||||
−0.565449 | + | 0.824784i | \(0.691297\pi\) | |||||||
\(128\) | 30.8780 | 2.72925 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −17.4891 | −1.53390 | ||||||||
\(131\) | −15.0922 | −1.31861 | −0.659306 | − | 0.751875i | \(-0.729150\pi\) | ||||
−0.659306 | + | 0.751875i | \(0.729150\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.37228 | −0.205703 | ||||||||
\(134\) | −10.8608 | −0.938228 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −29.4891 | −2.52867 | ||||||||
\(137\) | 12.0597 | 1.03033 | 0.515167 | − | 0.857090i | \(-0.327730\pi\) | ||||
0.515167 | + | 0.857090i | \(0.327730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.11684 | 0.264367 | 0.132184 | − | 0.991225i | \(-0.457801\pi\) | ||||
0.132184 | + | 0.991225i | \(0.457801\pi\) | |||||||
\(140\) | 41.0452 | 3.46895 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.48913 | 0.460637 | ||||||||
\(143\) | −4.41957 | −0.369583 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.25544 | −0.270349 | ||||||||
\(146\) | −13.8932 | −1.14981 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 57.7228 | 4.74479 | ||||||||
\(149\) | 20.5226 | 1.68128 | 0.840638 | − | 0.541598i | \(-0.182180\pi\) | ||||
0.840638 | + | 0.541598i | \(0.182180\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | −0.325515 | −0.162758 | − | 0.986666i | \(-0.552039\pi\) | ||||
−0.162758 | + | 0.986666i | \(0.552039\pi\) | |||||||
\(152\) | 9.15640 | 0.742682 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.2337 | 1.14698 | ||||||||
\(155\) | −15.2804 | −1.22735 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | −10.8608 | −0.864037 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −64.4674 | −5.09659 | ||||||||
\(161\) | −2.39794 | −0.188984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −21.4891 | −1.68316 | −0.841579 | − | 0.540134i | \(-0.818374\pi\) | ||||
−0.841579 | + | 0.540134i | \(0.818374\pi\) | |||||||
\(164\) | −29.1736 | −2.27807 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −32.2337 | −2.50182 | ||||||||
\(167\) | −6.44121 | −0.498435 | −0.249218 | − | 0.968447i | \(-0.580173\pi\) | ||||
−0.249218 | + | 0.968447i | \(0.580173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 28.1628 | 2.15999 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −59.7228 | −4.55382 | ||||||||
\(173\) | −1.01082 | −0.0768509 | −0.0384255 | − | 0.999261i | \(-0.512234\pi\) | ||||
−0.0384255 | + | 0.999261i | \(0.512234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.7446 | −0.963398 | ||||||||
\(176\) | −31.1952 | −2.35143 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 26.7446 | 2.00459 | ||||||||
\(179\) | −4.41957 | −0.330334 | −0.165167 | − | 0.986266i | \(-0.552816\pi\) | ||||
−0.165167 | + | 0.986266i | \(0.552816\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.4891 | 1.44862 | 0.724308 | − | 0.689477i | \(-0.242160\pi\) | ||||
0.724308 | + | 0.689477i | \(0.242160\pi\) | |||||||
\(182\) | −12.8824 | −0.954908 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.25544 | 0.682320 | ||||||||
\(185\) | −34.6040 | −2.54413 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.11684 | 0.520435 | ||||||||
\(188\) | −22.7324 | −1.65793 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.74456 | −0.634397 | ||||||||
\(191\) | −21.5334 | −1.55810 | −0.779051 | − | 0.626960i | \(-0.784299\pi\) | ||||
−0.779051 | + | 0.626960i | \(0.784299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.2337 | 1.16853 | 0.584263 | − | 0.811564i | \(-0.301384\pi\) | ||||
0.584263 | + | 0.811564i | \(0.301384\pi\) | |||||||
\(194\) | 20.3344 | 1.45993 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −7.37228 | −0.526592 | ||||||||
\(197\) | −23.7432 | −1.69163 | −0.845816 | − | 0.533475i | \(-0.820886\pi\) | ||||
−0.845816 | + | 0.533475i | \(0.820886\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.883156 | 0.0626053 | 0.0313026 | − | 0.999510i | \(-0.490034\pi\) | ||||
0.0313026 | + | 0.999510i | \(0.490034\pi\) | |||||||
\(200\) | 49.1908 | 3.47831 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 34.9783 | 2.46106 | ||||||||
\(203\) | −2.39794 | −0.168302 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.4891 | 1.22149 | ||||||||
\(206\) | −19.6999 | −1.37256 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 28.2337 | 1.95765 | ||||||||
\(209\) | −2.20979 | −0.152854 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 52.9168 | 3.63434 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 35.8029 | 2.44174 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2554 | −0.764069 | ||||||||
\(218\) | 14.2695 | 0.966455 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 38.2337 | 2.57771 | ||||||||
\(221\) | −6.44121 | −0.433282 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | −47.4864 | −3.17282 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32.2337 | −2.14415 | ||||||||
\(227\) | 19.3236 | 1.28255 | 0.641277 | − | 0.767310i | \(-0.278405\pi\) | ||||
0.641277 | + | 0.767310i | \(0.278405\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.6277 | 1.03271 | 0.516354 | − | 0.856375i | \(-0.327289\pi\) | ||||
0.516354 | + | 0.856375i | \(0.327289\pi\) | |||||||
\(230\) | −8.83915 | −0.582836 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.25544 | 0.607649 | ||||||||
\(233\) | −7.64018 | −0.500525 | −0.250262 | − | 0.968178i | \(-0.580517\pi\) | ||||
−0.250262 | + | 0.968178i | \(0.580517\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.6277 | 0.888974 | ||||||||
\(236\) | 58.3472 | 3.79808 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 20.7446 | 1.34467 | ||||||||
\(239\) | −12.6943 | −0.821123 | −0.410562 | − | 0.911833i | \(-0.634667\pi\) | ||||
−0.410562 | + | 0.911833i | \(0.634667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.2337 | −1.56103 | −0.780515 | − | 0.625138i | \(-0.785043\pi\) | ||||
−0.780515 | + | 0.625138i | \(0.785043\pi\) | |||||||
\(242\) | −16.6084 | −1.06763 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −27.4891 | −1.75981 | ||||||||
\(245\) | 4.41957 | 0.282356 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000 | 0.127257 | ||||||||
\(248\) | 43.4431 | 2.75864 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.25544 | −0.205892 | ||||||||
\(251\) | 23.9313 | 1.51053 | 0.755266 | − | 0.655418i | \(-0.227507\pi\) | ||||
0.755266 | + | 0.655418i | \(0.227507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.23369 | −0.140431 | ||||||||
\(254\) | −34.6040 | −2.17125 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 31.6060 | 1.97537 | ||||||||
\(257\) | 5.43039 | 0.338738 | 0.169369 | − | 0.985553i | \(-0.445827\pi\) | ||||
0.169369 | + | 0.985553i | \(0.445827\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.4891 | −1.58382 | ||||||||
\(260\) | −34.6040 | −2.14605 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −40.9783 | −2.53164 | ||||||||
\(263\) | 13.0706 | 0.805966 | 0.402983 | − | 0.915208i | \(-0.367973\pi\) | ||||
0.402983 | + | 0.915208i | \(0.367973\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.7228 | −1.94872 | ||||||||
\(266\) | −6.44121 | −0.394936 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.4891 | −1.31266 | ||||||||
\(269\) | 7.82833 | 0.477302 | 0.238651 | − | 0.971105i | \(-0.423295\pi\) | ||||
0.238651 | + | 0.971105i | \(0.423295\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.4891 | 1.54835 | 0.774177 | − | 0.632969i | \(-0.218164\pi\) | ||||
0.774177 | + | 0.632969i | \(0.218164\pi\) | |||||||
\(272\) | −45.4647 | −2.75671 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.7446 | 1.97817 | ||||||||
\(275\) | −11.8716 | −0.715884 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.11684 | 0.547778 | 0.273889 | − | 0.961761i | \(-0.411690\pi\) | ||||
0.273889 | + | 0.961761i | \(0.411690\pi\) | |||||||
\(278\) | 8.46284 | 0.507567 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 69.9565 | 4.18070 | ||||||||
\(281\) | 24.7540 | 1.47670 | 0.738350 | − | 0.674418i | \(-0.235605\pi\) | ||||
0.738350 | + | 0.674418i | \(0.235605\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.37228 | 0.378793 | 0.189396 | − | 0.981901i | \(-0.439347\pi\) | ||||
0.189396 | + | 0.981901i | \(0.439347\pi\) | |||||||
\(284\) | 10.8608 | 0.644469 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.0000 | −0.709575 | ||||||||
\(287\) | 12.8824 | 0.760425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.62772 | −0.389866 | ||||||||
\(290\) | −8.83915 | −0.519053 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −27.4891 | −1.60868 | ||||||||
\(293\) | −25.1303 | −1.46813 | −0.734064 | − | 0.679080i | \(-0.762379\pi\) | ||||
−0.734064 | + | 0.679080i | \(0.762379\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −34.9783 | −2.03651 | ||||||||
\(296\) | 98.3815 | 5.71831 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 55.7228 | 3.22794 | ||||||||
\(299\) | 2.02163 | 0.116914 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.3723 | 1.52007 | ||||||||
\(302\) | −10.8608 | −0.624968 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.1168 | 0.809657 | ||||||||
\(305\) | 16.4793 | 0.943603 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4891 | 1.45474 | 0.727371 | − | 0.686245i | \(-0.240742\pi\) | ||||
0.727371 | + | 0.686245i | \(0.240742\pi\) | |||||||
\(308\) | 28.1628 | 1.60472 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −41.4891 | −2.35642 | ||||||||
\(311\) | 12.6943 | 0.719825 | 0.359913 | − | 0.932986i | \(-0.382806\pi\) | ||||
0.359913 | + | 0.932986i | \(0.382806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.48913 | 0.423310 | 0.211655 | − | 0.977344i | \(-0.432115\pi\) | ||||
0.211655 | + | 0.977344i | \(0.432115\pi\) | |||||||
\(314\) | 5.43039 | 0.306455 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −21.4891 | −1.20886 | ||||||||
\(317\) | −12.2479 | −0.687911 | −0.343955 | − | 0.938986i | \(-0.611767\pi\) | ||||
−0.343955 | + | 0.938986i | \(0.611767\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.23369 | −0.125063 | ||||||||
\(320\) | −84.1120 | −4.70200 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.51087 | −0.362837 | ||||||||
\(323\) | −3.22060 | −0.179199 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.7446 | 0.596001 | ||||||||
\(326\) | −58.3472 | −3.23155 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −49.7228 | −2.74548 | ||||||||
\(329\) | 10.0381 | 0.553419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9783 | 1.04314 | 0.521569 | − | 0.853209i | \(-0.325347\pi\) | ||||
0.521569 | + | 0.853209i | \(0.325347\pi\) | |||||||
\(332\) | −63.7775 | −3.50025 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.4891 | −0.956962 | ||||||||
\(335\) | 12.8824 | 0.703841 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | −24.4368 | −1.32918 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 55.7228 | 3.02199 | ||||||||
\(341\) | −10.4845 | −0.567766 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8614 | 1.07242 | ||||||||
\(344\) | −101.790 | −5.48816 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.74456 | −0.147549 | ||||||||
\(347\) | 32.3942 | 1.73901 | 0.869505 | − | 0.493924i | \(-0.164438\pi\) | ||||
0.869505 | + | 0.493924i | \(0.164438\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8614 | 0.956099 | 0.478050 | − | 0.878333i | \(-0.341344\pi\) | ||||
0.478050 | + | 0.878333i | \(0.341344\pi\) | |||||||
\(350\) | −34.6040 | −1.84966 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −44.2337 | −2.35766 | ||||||||
\(353\) | 14.9040 | 0.793262 | 0.396631 | − | 0.917978i | \(-0.370179\pi\) | ||||
0.396631 | + | 0.917978i | \(0.370179\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.51087 | −0.345561 | ||||||||
\(356\) | 52.9168 | 2.80458 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −4.60773 | −0.243187 | −0.121593 | − | 0.992580i | \(-0.538800\pi\) | ||||
−0.121593 | + | 0.992580i | \(0.538800\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 52.9168 | 2.78124 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −25.4891 | −1.33599 | ||||||||
\(365\) | 16.4793 | 0.862567 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 14.2695 | 0.743851 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −93.9565 | −4.88457 | ||||||||
\(371\) | −23.3669 | −1.21315 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.2337 | −1.25477 | −0.627386 | − | 0.778708i | \(-0.715875\pi\) | ||||
−0.627386 | + | 0.778708i | \(0.715875\pi\) | |||||||
\(374\) | 19.3236 | 0.999200 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −38.7446 | −1.99810 | ||||||||
\(377\) | 2.02163 | 0.104119 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.7446 | 1.47651 | 0.738255 | − | 0.674522i | \(-0.235650\pi\) | ||||
0.738255 | + | 0.674522i | \(0.235650\pi\) | |||||||
\(380\) | −17.3020 | −0.887573 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −58.4674 | −2.99145 | ||||||||
\(383\) | −17.3020 | −0.884090 | −0.442045 | − | 0.896993i | \(-0.645747\pi\) | ||||
−0.442045 | + | 0.896993i | \(0.645747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.8832 | −0.860445 | ||||||||
\(386\) | 44.0776 | 2.24349 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 40.2337 | 2.04256 | ||||||||
\(389\) | 12.0597 | 0.611454 | 0.305727 | − | 0.952119i | \(-0.401101\pi\) | ||||
0.305727 | + | 0.952119i | \(0.401101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.25544 | −0.164635 | ||||||||
\(392\) | −12.5652 | −0.634636 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −64.4674 | −3.24782 | ||||||||
\(395\) | 12.8824 | 0.648184 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.1168 | −0.859070 | −0.429535 | − | 0.903050i | \(-0.641322\pi\) | ||||
−0.429535 | + | 0.903050i | \(0.641322\pi\) | |||||||
\(398\) | 2.39794 | 0.120198 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 75.8397 | 3.79198 | ||||||||
\(401\) | 3.40876 | 0.170225 | 0.0851126 | − | 0.996371i | \(-0.472875\pi\) | ||||
0.0851126 | + | 0.996371i | \(0.472875\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.48913 | 0.472687 | ||||||||
\(404\) | 69.2079 | 3.44322 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.51087 | −0.323129 | ||||||||
\(407\) | −23.7432 | −1.17691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.48913 | 0.370313 | 0.185157 | − | 0.982709i | \(-0.440721\pi\) | ||||
0.185157 | + | 0.982709i | \(0.440721\pi\) | |||||||
\(410\) | 47.4864 | 2.34519 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −38.9783 | −1.92032 | ||||||||
\(413\) | −25.7648 | −1.26780 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.2337 | 1.87682 | ||||||||
\(416\) | 40.0344 | 1.96285 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.00000 | −0.293470 | ||||||||
\(419\) | 11.8716 | 0.579965 | 0.289983 | − | 0.957032i | \(-0.406350\pi\) | ||||
0.289983 | + | 0.957032i | \(0.406350\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.97825 | −0.437573 | −0.218787 | − | 0.975773i | \(-0.570210\pi\) | ||||
−0.218787 | + | 0.975773i | \(0.570210\pi\) | |||||||
\(422\) | −10.8608 | −0.528694 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 90.1902 | 4.38002 | ||||||||
\(425\) | −17.3020 | −0.839269 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.1386 | 0.587428 | ||||||||
\(428\) | 23.7432 | 1.14767 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 97.2119 | 4.68798 | ||||||||
\(431\) | −30.1844 | −1.45393 | −0.726966 | − | 0.686674i | \(-0.759070\pi\) | ||||
−0.726966 | + | 0.686674i | \(0.759070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0000 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(434\) | −30.5607 | −1.46696 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 28.2337 | 1.35215 | ||||||||
\(437\) | 1.01082 | 0.0483539 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.2337 | −0.870246 | −0.435123 | − | 0.900371i | \(-0.643295\pi\) | ||||
−0.435123 | + | 0.900371i | \(0.643295\pi\) | |||||||
\(440\) | 65.1647 | 3.10660 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.4891 | −0.831873 | ||||||||
\(443\) | −27.9746 | −1.32911 | −0.664557 | − | 0.747238i | \(-0.731380\pi\) | ||||
−0.664557 | + | 0.747238i | \(0.731380\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.7228 | −1.50381 | ||||||||
\(446\) | −10.8608 | −0.514273 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −61.9565 | −2.92717 | ||||||||
\(449\) | 22.3561 | 1.05505 | 0.527524 | − | 0.849540i | \(-0.323120\pi\) | ||||
0.527524 | + | 0.849540i | \(0.323120\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.0000 | 0.565058 | ||||||||
\(452\) | −63.7775 | −2.99984 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 52.4674 | 2.46242 | ||||||||
\(455\) | 15.2804 | 0.716354 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.37228 | −0.391639 | −0.195819 | − | 0.980640i | \(-0.562737\pi\) | ||||
−0.195819 | + | 0.980640i | \(0.562737\pi\) | |||||||
\(458\) | 42.4323 | 1.98273 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17.4891 | −0.815435 | ||||||||
\(461\) | −26.9638 | −1.25583 | −0.627914 | − | 0.778282i | \(-0.716091\pi\) | ||||
−0.627914 | + | 0.778282i | \(0.716091\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.37228 | −0.110249 | −0.0551246 | − | 0.998479i | \(-0.517556\pi\) | ||||
−0.0551246 | + | 0.998479i | \(0.517556\pi\) | |||||||
\(464\) | 14.2695 | 0.662447 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.7446 | −0.960973 | ||||||||
\(467\) | −36.4374 | −1.68612 | −0.843062 | − | 0.537816i | \(-0.819249\pi\) | ||||
−0.843062 | + | 0.537816i | \(0.819249\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.48913 | 0.438167 | ||||||||
\(470\) | 37.0019 | 1.70677 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 99.4456 | 4.57736 | ||||||||
\(473\) | 24.5659 | 1.12954 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.37228 | 0.246497 | ||||||||
\(476\) | 41.0452 | 1.88130 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −34.4674 | −1.57650 | ||||||||
\(479\) | 33.5932 | 1.53491 | 0.767455 | − | 0.641103i | \(-0.221523\pi\) | ||||
0.767455 | + | 0.641103i | \(0.221523\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.4891 | 0.979820 | ||||||||
\(482\) | −65.7992 | −2.99707 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −32.8614 | −1.49370 | ||||||||
\(485\) | −24.1195 | −1.09521 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | 0.362515 | 0.181257 | − | 0.983436i | \(-0.441983\pi\) | ||||
0.181257 | + | 0.983436i | \(0.441983\pi\) | |||||||
\(488\) | −46.8519 | −2.12088 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.0000 | 0.542105 | ||||||||
\(491\) | −1.01082 | −0.0456175 | −0.0228087 | − | 0.999740i | \(-0.507261\pi\) | ||||
−0.0228087 | + | 0.999740i | \(0.507261\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.25544 | −0.146618 | ||||||||
\(494\) | 5.43039 | 0.244325 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 66.9783 | 3.00741 | ||||||||
\(497\) | −4.79588 | −0.215125 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.1168 | −0.497658 | −0.248829 | − | 0.968547i | \(-0.580046\pi\) | ||||
−0.248829 | + | 0.968547i | \(0.580046\pi\) | |||||||
\(500\) | −6.44121 | −0.288059 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 64.9783 | 2.90012 | ||||||||
\(503\) | −31.5715 | −1.40770 | −0.703852 | − | 0.710346i | \(-0.748538\pi\) | ||||
−0.703852 | + | 0.710346i | \(0.748538\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −41.4891 | −1.84624 | ||||||||
\(506\) | −6.06490 | −0.269618 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −68.4674 | −3.03775 | ||||||||
\(509\) | 24.7540 | 1.09720 | 0.548601 | − | 0.836084i | \(-0.315161\pi\) | ||||
0.548601 | + | 0.836084i | \(0.315161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.1386 | 0.536980 | ||||||||
\(512\) | 24.0604 | 1.06333 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.7446 | 0.650355 | ||||||||
\(515\) | 23.3669 | 1.02967 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.35053 | 0.411236 | ||||||||
\(518\) | −69.2079 | −3.04082 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −58.9783 | −2.58637 | ||||||||
\(521\) | 16.2912 | 0.713729 | 0.356864 | − | 0.934156i | \(-0.383846\pi\) | ||||
0.356864 | + | 0.934156i | \(0.383846\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.2337 | −0.797304 | −0.398652 | − | 0.917102i | \(-0.630522\pi\) | ||||
−0.398652 | + | 0.917102i | \(0.630522\pi\) | |||||||
\(524\) | −81.0795 | −3.54198 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.4891 | 1.54740 | ||||||||
\(527\) | −15.2804 | −0.665623 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9783 | −0.955576 | ||||||||
\(530\) | −86.1336 | −3.74140 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.7446 | −0.552547 | ||||||||
\(533\) | −10.8608 | −0.470433 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.2337 | −0.615376 | ||||||||
\(536\) | −36.6256 | −1.58198 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.2554 | 0.916387 | ||||||||
\(539\) | 3.03245 | 0.130617 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.1168 | 0.907884 | 0.453942 | − | 0.891031i | \(-0.350017\pi\) | ||||
0.453942 | + | 0.891031i | \(0.350017\pi\) | |||||||
\(542\) | 69.2079 | 2.97274 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −64.4674 | −2.76402 | ||||||||
\(545\) | −16.9257 | −0.725016 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.2337 | 0.950644 | 0.475322 | − | 0.879812i | \(-0.342332\pi\) | ||||
0.475322 | + | 0.879812i | \(0.342332\pi\) | |||||||
\(548\) | 64.7884 | 2.76762 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −32.2337 | −1.37445 | ||||||||
\(551\) | 1.01082 | 0.0430622 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.48913 | 0.403519 | ||||||||
\(554\) | 24.7540 | 1.05170 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.7446 | 0.710128 | ||||||||
\(557\) | −20.5226 | −0.869570 | −0.434785 | − | 0.900534i | \(-0.643176\pi\) | ||||
−0.434785 | + | 0.900534i | \(0.643176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.2337 | −0.940385 | ||||||||
\(560\) | 107.855 | 4.55771 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 67.2119 | 2.83516 | ||||||||
\(563\) | −38.6472 | −1.62879 | −0.814393 | − | 0.580313i | \(-0.802930\pi\) | ||||
−0.814393 | + | 0.580313i | \(0.802930\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.2337 | 1.60850 | ||||||||
\(566\) | 17.3020 | 0.727257 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.5109 | 0.776699 | ||||||||
\(569\) | 3.03245 | 0.127127 | 0.0635634 | − | 0.997978i | \(-0.479753\pi\) | ||||
0.0635634 | + | 0.997978i | \(0.479753\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.51087 | 0.105077 | 0.0525384 | − | 0.998619i | \(-0.483269\pi\) | ||||
0.0525384 | + | 0.998619i | \(0.483269\pi\) | |||||||
\(572\) | −23.7432 | −0.992753 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 34.9783 | 1.45996 | ||||||||
\(575\) | 5.43039 | 0.226463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.1168 | −1.71172 | −0.855858 | − | 0.517210i | \(-0.826970\pi\) | ||||
−0.855858 | + | 0.517210i | \(0.826970\pi\) | |||||||
\(578\) | −17.9955 | −0.748516 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −17.4891 | −0.726196 | ||||||||
\(581\) | 28.1628 | 1.16839 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.7663 | −0.901469 | ||||||||
\(584\) | −46.8519 | −1.93874 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −68.2337 | −2.81871 | ||||||||
\(587\) | −1.83348 | −0.0756758 | −0.0378379 | − | 0.999284i | \(-0.512047\pi\) | ||||
−0.0378379 | + | 0.999284i | \(0.512047\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.74456 | 0.195496 | ||||||||
\(590\) | −94.9728 | −3.90997 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 151.679 | 6.23398 | ||||||||
\(593\) | 4.04326 | 0.166037 | 0.0830185 | − | 0.996548i | \(-0.473544\pi\) | ||||
0.0830185 | + | 0.996548i | \(0.473544\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.6060 | −1.00875 | ||||||||
\(596\) | 110.253 | 4.51614 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.48913 | 0.224467 | ||||||||
\(599\) | 12.8824 | 0.526361 | 0.263181 | − | 0.964747i | \(-0.415229\pi\) | ||||
0.263181 | + | 0.964747i | \(0.415229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.2554 | −1.03019 | −0.515095 | − | 0.857133i | \(-0.672244\pi\) | ||||
−0.515095 | + | 0.857133i | \(0.672244\pi\) | |||||||
\(602\) | 71.6059 | 2.91844 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.4891 | −0.874380 | ||||||||
\(605\) | 19.6999 | 0.800916 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.7446 | 1.16671 | 0.583353 | − | 0.812219i | \(-0.301740\pi\) | ||||
0.583353 | + | 0.812219i | \(0.301740\pi\) | |||||||
\(608\) | 20.0172 | 0.811804 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 44.7446 | 1.81165 | ||||||||
\(611\) | −8.46284 | −0.342370 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.60597 | 0.105254 | 0.0526271 | − | 0.998614i | \(-0.483241\pi\) | ||||
0.0526271 | + | 0.998614i | \(0.483241\pi\) | |||||||
\(614\) | 69.2079 | 2.79300 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.0000 | 1.93398 | ||||||||
\(617\) | 3.22060 | 0.129657 | 0.0648283 | − | 0.997896i | \(-0.479350\pi\) | ||||
0.0648283 | + | 0.997896i | \(0.479350\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.97825 | 0.280480 | 0.140240 | − | 0.990118i | \(-0.455213\pi\) | ||||
0.140240 | + | 0.990118i | \(0.455213\pi\) | |||||||
\(620\) | −82.0903 | −3.29683 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 34.4674 | 1.38202 | ||||||||
\(623\) | −23.3669 | −0.936174 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | −0.920000 | ||||||||
\(626\) | 20.3344 | 0.812727 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.7446 | 0.428755 | ||||||||
\(629\) | −34.6040 | −1.37975 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.1168 | 0.601792 | 0.300896 | − | 0.953657i | \(-0.402714\pi\) | ||||
0.300896 | + | 0.953657i | \(0.402714\pi\) | |||||||
\(632\) | −36.6256 | −1.45689 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −33.2554 | −1.32074 | ||||||||
\(635\) | 41.0452 | 1.62883 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.74456 | −0.108744 | ||||||||
\(638\) | −6.06490 | −0.240112 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −99.4456 | −3.93093 | ||||||||
\(641\) | −24.7540 | −0.977724 | −0.488862 | − | 0.872361i | \(-0.662588\pi\) | ||||
−0.488862 | + | 0.872361i | \(0.662588\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.1168 | −1.38487 | −0.692437 | − | 0.721479i | \(-0.743463\pi\) | ||||
−0.692437 | + | 0.721479i | \(0.743463\pi\) | |||||||
\(644\) | −12.8824 | −0.507638 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.74456 | −0.344050 | ||||||||
\(647\) | −17.1138 | −0.672814 | −0.336407 | − | 0.941717i | \(-0.609212\pi\) | ||||
−0.336407 | + | 0.941717i | \(0.609212\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 29.1736 | 1.14428 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −115.446 | −4.52120 | ||||||||
\(653\) | 14.0814 | 0.551047 | 0.275524 | − | 0.961294i | \(-0.411149\pi\) | ||||
0.275524 | + | 0.961294i | \(0.411149\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 48.6060 | 1.89919 | ||||||||
\(656\) | −76.6600 | −2.99307 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 27.2554 | 1.06253 | ||||||||
\(659\) | 11.2371 | 0.437735 | 0.218867 | − | 0.975755i | \(-0.429764\pi\) | ||||
0.218867 | + | 0.975755i | \(0.429764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.74456 | −0.262333 | −0.131167 | − | 0.991360i | \(-0.541872\pi\) | ||||
−0.131167 | + | 0.991360i | \(0.541872\pi\) | |||||||
\(662\) | 51.5296 | 2.00276 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −108.701 | −4.21842 | ||||||||
\(665\) | 7.64018 | 0.296273 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.02175 | 0.0395623 | ||||||||
\(668\) | −34.6040 | −1.33887 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 34.9783 | 1.35133 | ||||||||
\(671\) | 11.3071 | 0.436507 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.2554 | −0.973526 | −0.486763 | − | 0.873534i | \(-0.661822\pi\) | ||||
−0.486763 | + | 0.873534i | \(0.661822\pi\) | |||||||
\(674\) | 38.0127 | 1.46420 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −48.3505 | −1.85964 | ||||||||
\(677\) | 44.4539 | 1.70850 | 0.854252 | − | 0.519860i | \(-0.174016\pi\) | ||||
0.854252 | + | 0.519860i | \(0.174016\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.7663 | −0.681808 | ||||||||
\(680\) | 94.9728 | 3.64204 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28.4674 | −1.09007 | ||||||||
\(683\) | 34.2277 | 1.30968 | 0.654842 | − | 0.755765i | \(-0.272735\pi\) | ||||
0.654842 | + | 0.755765i | \(0.272735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.8397 | −1.48399 | ||||||||
\(686\) | 53.9276 | 2.05896 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −156.935 | −5.98308 | ||||||||
\(689\) | 19.6999 | 0.750507 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.1168 | 1.03157 | 0.515787 | − | 0.856717i | \(-0.327500\pi\) | ||||
0.515787 | + | 0.856717i | \(0.327500\pi\) | |||||||
\(692\) | −5.43039 | −0.206432 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 87.9565 | 3.33878 | ||||||||
\(695\) | −10.0381 | −0.380767 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.4891 | 0.662448 | ||||||||
\(698\) | 48.4972 | 1.83565 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −68.4674 | −2.58782 | ||||||||
\(701\) | −30.5607 | −1.15426 | −0.577131 | − | 0.816652i | \(-0.695828\pi\) | ||||
−0.577131 | + | 0.816652i | \(0.695828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.7446 | 0.405239 | ||||||||
\(704\) | −57.7126 | −2.17513 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.4674 | 1.52301 | ||||||||
\(707\) | −30.5607 | −1.14935 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.0000 | 1.42712 | 0.713560 | − | 0.700594i | \(-0.247082\pi\) | ||||
0.713560 | + | 0.700594i | \(0.247082\pi\) | |||||||
\(710\) | −17.6783 | −0.663454 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 90.1902 | 3.38002 | ||||||||
\(713\) | 4.79588 | 0.179607 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.2337 | 0.532310 | ||||||||
\(716\) | −23.7432 | −0.887325 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.5109 | −0.466902 | ||||||||
\(719\) | −38.8354 | −1.44832 | −0.724158 | − | 0.689634i | \(-0.757771\pi\) | ||||
−0.724158 | + | 0.689634i | \(0.757771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2119 | 0.641006 | ||||||||
\(722\) | 2.71519 | 0.101049 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 104.701 | 3.89118 | ||||||||
\(725\) | 5.43039 | 0.201680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.3505 | −1.38525 | −0.692627 | − | 0.721296i | \(-0.743547\pi\) | ||||
−0.692627 | + | 0.721296i | \(0.743547\pi\) | |||||||
\(728\) | −43.4431 | −1.61011 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 44.7446 | 1.65607 | ||||||||
\(731\) | 35.8029 | 1.32422 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.4674 | 0.682108 | 0.341054 | − | 0.940044i | \(-0.389216\pi\) | ||||
0.341054 | + | 0.940044i | \(0.389216\pi\) | |||||||
\(734\) | 21.7216 | 0.801757 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.2337 | 0.745824 | ||||||||
\(737\) | 8.83915 | 0.325594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.1168 | 0.997509 | 0.498755 | − | 0.866743i | \(-0.333791\pi\) | ||||
0.498755 | + | 0.866743i | \(0.333791\pi\) | |||||||
\(740\) | −185.902 | −6.83390 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −63.4456 | −2.32916 | ||||||||
\(743\) | 28.5391 | 1.04700 | 0.523498 | − | 0.852027i | \(-0.324627\pi\) | ||||
0.523498 | + | 0.852027i | \(0.324627\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −66.0951 | −2.42154 | ||||||||
\(746\) | −65.7992 | −2.40908 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 38.2337 | 1.39796 | ||||||||
\(749\) | −10.4845 | −0.383094 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.4674 | 0.892827 | 0.446414 | − | 0.894827i | \(-0.352701\pi\) | ||||
0.446414 | + | 0.894827i | \(0.352701\pi\) | |||||||
\(752\) | −59.7343 | −2.17829 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.48913 | 0.199902 | ||||||||
\(755\) | 12.8824 | 0.468839 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.11684 | −0.185975 | −0.0929874 | − | 0.995667i | \(-0.529642\pi\) | ||||
−0.0929874 | + | 0.995667i | \(0.529642\pi\) | |||||||
\(758\) | 78.0471 | 2.83480 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −29.4891 | −1.06968 | ||||||||
\(761\) | 0.822662 | 0.0298215 | 0.0149107 | − | 0.999889i | \(-0.495254\pi\) | ||||
0.0149107 | + | 0.999889i | \(0.495254\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.4674 | −0.451349 | ||||||||
\(764\) | −115.683 | −4.18528 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −46.9783 | −1.69739 | ||||||||
\(767\) | 21.7216 | 0.784320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.88316 | 0.248213 | 0.124106 | − | 0.992269i | \(-0.460394\pi\) | ||||
0.124106 | + | 0.992269i | \(0.460394\pi\) | |||||||
\(770\) | −45.8411 | −1.65200 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 87.2119 | 3.13883 | ||||||||
\(773\) | 5.43039 | 0.195318 | 0.0976588 | − | 0.995220i | \(-0.468865\pi\) | ||||
0.0976588 | + | 0.995220i | \(0.468865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.4891 | 0.915596 | ||||||||
\(776\) | 68.5734 | 2.46164 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.7446 | 1.17395 | ||||||||
\(779\) | −5.43039 | −0.194564 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.46738 | −0.159855 | ||||||||
\(782\) | −8.83915 | −0.316087 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.3723 | −0.691867 | ||||||||
\(785\) | −6.44121 | −0.229896 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.9565 | −1.78076 | −0.890378 | − | 0.455221i | \(-0.849560\pi\) | ||||
−0.890378 | + | 0.455221i | \(0.849560\pi\) | |||||||
\(788\) | −127.555 | −4.54396 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 34.9783 | 1.24447 | ||||||||
\(791\) | 28.1628 | 1.00135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2337 | −0.363409 | ||||||||
\(794\) | −46.4756 | −1.64936 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.74456 | 0.168167 | ||||||||
\(797\) | −7.45202 | −0.263964 | −0.131982 | − | 0.991252i | \(-0.542134\pi\) | ||||
−0.131982 | + | 0.991252i | \(0.542134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.6277 | 0.482114 | ||||||||
\(800\) | 107.538 | 3.80204 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.25544 | 0.326821 | ||||||||
\(803\) | 11.3071 | 0.399020 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.72281 | 0.272193 | ||||||||
\(806\) | 25.7648 | 0.907527 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 117.957 | 4.14970 | ||||||||
\(809\) | −3.59691 | −0.126461 | −0.0632303 | − | 0.997999i | \(-0.520140\pi\) | ||||
−0.0632303 | + | 0.997999i | \(0.520140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.7446 | −1.29028 | −0.645138 | − | 0.764066i | \(-0.723200\pi\) | ||||
−0.645138 | + | 0.764066i | \(0.723200\pi\) | |||||||
\(812\) | −12.8824 | −0.452084 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −64.4674 | −2.25958 | ||||||||
\(815\) | 69.2079 | 2.42425 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.1168 | −0.388929 | ||||||||
\(818\) | 20.3344 | 0.710977 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 93.9565 | 3.28110 | ||||||||
\(821\) | −29.3617 | −1.02473 | −0.512366 | − | 0.858767i | \(-0.671231\pi\) | ||||
−0.512366 | + | 0.858767i | \(0.671231\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.60597 | 0.299985 | 0.149993 | − | 0.988687i | \(-0.452075\pi\) | ||||
0.149993 | + | 0.988687i | \(0.452075\pi\) | |||||||
\(824\) | −66.4337 | −2.31433 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −69.9565 | −2.43410 | ||||||||
\(827\) | −28.5391 | −0.992401 | −0.496200 | − | 0.868208i | \(-0.665272\pi\) | ||||
−0.496200 | + | 0.868208i | \(0.665272\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.25544 | −0.0436031 | −0.0218016 | − | 0.999762i | \(-0.506940\pi\) | ||||
−0.0218016 | + | 0.999762i | \(0.506940\pi\) | |||||||
\(830\) | 103.812 | 3.60336 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 52.2337 | 1.81088 | ||||||||
\(833\) | 4.41957 | 0.153129 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.7446 | 0.717895 | ||||||||
\(836\) | −11.8716 | −0.410588 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 32.2337 | 1.11349 | ||||||||
\(839\) | 30.1844 | 1.04208 | 0.521041 | − | 0.853532i | \(-0.325544\pi\) | ||||
0.521041 | + | 0.853532i | \(0.325544\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9783 | −0.964767 | ||||||||
\(842\) | −24.3777 | −0.840111 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.4891 | −0.739686 | ||||||||
\(845\) | 28.9854 | 0.997129 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.5109 | 0.498600 | ||||||||
\(848\) | 139.050 | 4.77501 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −46.9783 | −1.61134 | ||||||||
\(851\) | 10.8608 | 0.372303 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.4674 | −1.31710 | −0.658549 | − | 0.752538i | \(-0.728829\pi\) | ||||
−0.658549 | + | 0.752538i | \(0.728829\pi\) | |||||||
\(854\) | 32.9586 | 1.12782 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 40.4674 | 1.38315 | ||||||||
\(857\) | −35.2385 | −1.20372 | −0.601862 | − | 0.798600i | \(-0.705574\pi\) | ||||
−0.601862 | + | 0.798600i | \(0.705574\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.11684 | 0.106345 | 0.0531727 | − | 0.998585i | \(-0.483067\pi\) | ||||
0.0531727 | + | 0.998585i | \(0.483067\pi\) | |||||||
\(860\) | 192.343 | 6.55886 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −81.9565 | −2.79145 | ||||||||
\(863\) | −14.9040 | −0.507340 | −0.253670 | − | 0.967291i | \(-0.581638\pi\) | ||||
−0.253670 | + | 0.967291i | \(0.581638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.25544 | 0.110688 | ||||||||
\(866\) | −59.7343 | −2.02985 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −60.4674 | −2.05240 | ||||||||
\(869\) | 8.83915 | 0.299847 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | 48.1209 | 1.62958 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.74456 | 0.0928362 | ||||||||
\(875\) | 2.84429 | 0.0961547 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | −49.5080 | −1.67081 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 100.467 | 3.38675 | ||||||||
\(881\) | −0.822662 | −0.0277162 | −0.0138581 | − | 0.999904i | \(-0.504411\pi\) | ||||
−0.0138581 | + | 0.999904i | \(0.504411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.11684 | 0.104890 | 0.0524451 | − | 0.998624i | \(-0.483299\pi\) | ||||
0.0524451 | + | 0.998624i | \(0.483299\pi\) | |||||||
\(884\) | −34.6040 | −1.16386 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −75.9565 | −2.55181 | ||||||||
\(887\) | 21.7216 | 0.729338 | 0.364669 | − | 0.931137i | \(-0.381182\pi\) | ||||
0.364669 | + | 0.931137i | \(0.381182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.2337 | 1.01401 | ||||||||
\(890\) | −86.1336 | −2.88721 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −21.4891 | −0.719509 | ||||||||
\(893\) | −4.23142 | −0.141599 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.2337 | 0.475780 | ||||||||
\(896\) | −73.2512 | −2.44715 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 60.7011 | 2.02562 | ||||||||
\(899\) | 4.79588 | 0.159952 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.7228 | −1.05684 | ||||||||
\(902\) | 32.5823 | 1.08487 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −108.701 | −3.61534 | ||||||||
\(905\) | −62.7667 | −2.08644 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.2554 | 0.772184 | 0.386092 | − | 0.922460i | \(-0.373825\pi\) | ||||
0.386092 | + | 0.922460i | \(0.373825\pi\) | |||||||
\(908\) | 103.812 | 3.44512 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41.4891 | 1.37535 | ||||||||
\(911\) | −37.0019 | −1.22593 | −0.612964 | − | 0.790111i | \(-0.710023\pi\) | ||||
−0.612964 | + | 0.790111i | \(0.710023\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.2337 | 0.868208 | ||||||||
\(914\) | −22.7324 | −0.751920 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 83.9565 | 2.77400 | ||||||||
\(917\) | 35.8029 | 1.18232 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.9783 | 0.626035 | 0.313017 | − | 0.949747i | \(-0.398660\pi\) | ||||
0.313017 | + | 0.949747i | \(0.398660\pi\) | |||||||
\(920\) | −29.8081 | −0.982743 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −73.2119 | −2.41111 | ||||||||
\(923\) | 4.04326 | 0.133086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 57.7228 | 1.89791 | ||||||||
\(926\) | −6.44121 | −0.211671 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 20.2337 | 0.664203 | ||||||||
\(929\) | 4.79588 | 0.157348 | 0.0786739 | − | 0.996900i | \(-0.474931\pi\) | ||||
0.0786739 | + | 0.996900i | \(0.474931\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.37228 | −0.0449747 | ||||||||
\(932\) | −41.0452 | −1.34448 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −98.9348 | −3.23724 | ||||||||
\(935\) | −22.9205 | −0.749581 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.11684 | −0.167160 | −0.0835800 | − | 0.996501i | \(-0.526635\pi\) | ||||
−0.0835800 | + | 0.996501i | \(0.526635\pi\) | |||||||
\(938\) | 25.7648 | 0.841251 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 73.2119 | 2.38791 | ||||||||
\(941\) | 24.7540 | 0.806957 | 0.403479 | − | 0.914989i | \(-0.367801\pi\) | ||||
0.403479 | + | 0.914989i | \(0.367801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.48913 | −0.178751 | ||||||||
\(944\) | 153.320 | 4.99014 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 66.7011 | 2.16864 | ||||||||
\(947\) | −9.84996 | −0.320081 | −0.160040 | − | 0.987110i | \(-0.551162\pi\) | ||||
−0.160040 | + | 0.987110i | \(0.551162\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.2337 | −0.332200 | ||||||||
\(950\) | 14.5868 | 0.473258 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 69.9565 | 2.26730 | ||||||||
\(953\) | 9.47365 | 0.306882 | 0.153441 | − | 0.988158i | \(-0.450965\pi\) | ||||
0.153441 | + | 0.988158i | \(0.450965\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 69.3505 | 2.24413 | ||||||||
\(956\) | −68.1971 | −2.20565 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 91.2119 | 2.94692 | ||||||||
\(959\) | −28.6091 | −0.923837 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.48913 | −0.273843 | ||||||||
\(962\) | 58.3472 | 1.88119 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −130.190 | −4.19314 | ||||||||
\(965\) | −52.2823 | −1.68303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | −56.0083 | −1.80017 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −65.4891 | −2.10273 | ||||||||
\(971\) | −51.5296 | −1.65366 | −0.826832 | − | 0.562448i | \(-0.809860\pi\) | ||||
−0.826832 | + | 0.562448i | \(0.809860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.39403 | −0.237042 | ||||||||
\(974\) | 21.7216 | 0.696004 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −72.2337 | −2.31214 | ||||||||
\(977\) | −20.7107 | −0.662595 | −0.331298 | − | 0.943526i | \(-0.607486\pi\) | ||||
−0.331298 | + | 0.943526i | \(0.607486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.7663 | −0.695654 | ||||||||
\(980\) | 23.7432 | 0.758448 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.74456 | −0.0875825 | ||||||||
\(983\) | 52.2823 | 1.66755 | 0.833773 | − | 0.552108i | \(-0.186176\pi\) | ||||
0.833773 | + | 0.552108i | \(0.186176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 76.4674 | 2.43645 | ||||||||
\(986\) | −8.83915 | −0.281496 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.7446 | 0.341830 | ||||||||
\(989\) | −11.2371 | −0.357319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | 94.9728 | 3.01539 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −13.0217 | −0.413025 | ||||||||
\(995\) | −2.84429 | −0.0901702 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.3505 | −0.612837 | −0.306419 | − | 0.951897i | \(-0.599131\pi\) | ||||
−0.306419 | + | 0.951897i | \(0.599131\pi\) | |||||||
\(998\) | −30.1844 | −0.955470 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 171.2.a.e.1.4 | yes | 4 | |
3.2 | odd | 2 | inner | 171.2.a.e.1.1 | ✓ | 4 | |
4.3 | odd | 2 | 2736.2.a.bf.1.1 | 4 | |||
5.4 | even | 2 | 4275.2.a.bp.1.1 | 4 | |||
7.6 | odd | 2 | 8379.2.a.bw.1.4 | 4 | |||
12.11 | even | 2 | 2736.2.a.bf.1.4 | 4 | |||
15.14 | odd | 2 | 4275.2.a.bp.1.4 | 4 | |||
19.18 | odd | 2 | 3249.2.a.bf.1.1 | 4 | |||
21.20 | even | 2 | 8379.2.a.bw.1.1 | 4 | |||
57.56 | even | 2 | 3249.2.a.bf.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.a.e.1.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
171.2.a.e.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
2736.2.a.bf.1.1 | 4 | 4.3 | odd | 2 | |||
2736.2.a.bf.1.4 | 4 | 12.11 | even | 2 | |||
3249.2.a.bf.1.1 | 4 | 19.18 | odd | 2 | |||
3249.2.a.bf.1.4 | 4 | 57.56 | even | 2 | |||
4275.2.a.bp.1.1 | 4 | 5.4 | even | 2 | |||
4275.2.a.bp.1.4 | 4 | 15.14 | odd | 2 | |||
8379.2.a.bw.1.1 | 4 | 21.20 | even | 2 | |||
8379.2.a.bw.1.4 | 4 | 7.6 | odd | 2 |