Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.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: | \(21.8470699930\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 171) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.04374\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −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 | \(-0.352023\pi\) | ||||
0.448319 | + | 0.893874i | \(0.352023\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.20979 | 0.666276 | 0.333138 | − | 0.942878i | \(-0.391893\pi\) | ||||
0.333138 | + | 0.942878i | \(0.391893\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −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 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.01082 | −0.210770 | −0.105385 | − | 0.994432i | \(-0.533607\pi\) | ||||
−0.105385 | + | 0.994432i | \(0.533607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.37228 | 1.07446 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 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 | \(-0.640104\pi\) | ||||
−0.426074 | + | 0.904688i | \(0.640104\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.64018 | −1.29143 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.7446 | 1.76640 | 0.883198 | − | 0.469001i | \(-0.155386\pi\) | ||||
0.883198 | + | 0.469001i | \(0.155386\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −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 | \(-0.178016\pi\) | ||||
0.847651 | + | 0.530554i | \(0.178016\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.23142 | 0.617216 | 0.308608 | − | 0.951189i | \(-0.400137\pi\) | ||||
0.308608 | + | 0.951189i | \(0.400137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.37228 | −0.196040 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 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 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.8608 | −1.41395 | −0.706976 | − | 0.707237i | \(-0.749941\pi\) | ||||
−0.706976 | + | 0.707237i | \(0.749941\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.11684 | −0.655145 | −0.327572 | − | 0.944826i | \(-0.606231\pi\) | ||||
−0.327572 | + | 0.944826i | \(0.606231\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.44121 | −0.798933 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.02163 | −0.239924 | −0.119962 | − | 0.992779i | \(-0.538277\pi\) | ||||
−0.119962 | + | 0.992779i | \(0.538277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.11684 | −0.598881 | −0.299441 | − | 0.954115i | \(-0.596800\pi\) | ||||
−0.299441 | + | 0.954115i | \(0.596800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.24224 | 0.597408 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.8716 | 1.30308 | 0.651538 | − | 0.758616i | \(-0.274124\pi\) | ||||
0.651538 | + | 0.758616i | \(0.274124\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.3723 | 1.12503 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.22060 | 0.330427 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.48913 | 0.760405 | 0.380203 | − | 0.924903i | \(-0.375854\pi\) | ||||
0.380203 | + | 0.924903i | \(0.375854\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 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 | \(-0.383646\pi\) | ||||
0.357450 | + | 0.933932i | \(0.383646\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.41957 | −0.427256 | −0.213628 | − | 0.976915i | \(-0.568528\pi\) | ||||
−0.213628 | + | 0.976915i | \(0.568528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.25544 | 0.503380 | 0.251690 | − | 0.967808i | \(-0.419014\pi\) | ||||
0.251690 | + | 0.967808i | \(0.419014\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −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 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.64018 | −0.700374 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.11684 | −0.556077 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.19897 | −0.107239 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.7446 | 1.13090 | 0.565449 | − | 0.824784i | \(-0.308703\pi\) | ||||
0.565449 | + | 0.824784i | \(0.308703\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.0922 | 1.31861 | 0.659306 | − | 0.751875i | \(-0.270850\pi\) | ||||
0.659306 | + | 0.751875i | \(0.270850\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.37228 | −0.205703 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 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 | \(-0.542199\pi\) | ||||
−0.132184 | + | 0.991225i | \(0.542199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.41957 | 0.369583 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.25544 | −0.270349 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 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 | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.2804 | 1.22735 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.39794 | −0.188984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.4891 | 1.68316 | 0.841579 | − | 0.540134i | \(-0.181626\pi\) | ||||
0.841579 | + | 0.540134i | \(0.181626\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.44121 | 0.498435 | 0.249218 | − | 0.968447i | \(-0.419827\pi\) | ||||
0.249218 | + | 0.968447i | \(0.419827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −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 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.41957 | 0.330334 | 0.165167 | − | 0.986266i | \(-0.447184\pi\) | ||||
0.165167 | + | 0.986266i | \(0.447184\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.4891 | 1.44862 | 0.724308 | − | 0.689477i | \(-0.242160\pi\) | ||||
0.724308 | + | 0.689477i | \(0.242160\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −34.6040 | −2.54413 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.11684 | −0.520435 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.5334 | 1.55810 | 0.779051 | − | 0.626960i | \(-0.215701\pi\) | ||||
0.779051 | + | 0.626960i | \(0.215701\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.2337 | 1.16853 | 0.584263 | − | 0.811564i | \(-0.301384\pi\) | ||||
0.584263 | + | 0.811564i | \(0.301384\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −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 | \(-0.509966\pi\) | ||||
−0.0313026 | + | 0.999510i | \(0.509966\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.39794 | 0.168302 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.4891 | 1.22149 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.20979 | −0.152854 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −35.8029 | −2.44174 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2554 | −0.764069 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.44121 | −0.433282 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.3236 | −1.28255 | −0.641277 | − | 0.767310i | \(-0.721595\pi\) | ||||
−0.641277 | + | 0.767310i | \(0.721595\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.6277 | 1.03271 | 0.516354 | − | 0.856375i | \(-0.327289\pi\) | ||||
0.516354 | + | 0.856375i | \(0.327289\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −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 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6943 | 0.821123 | 0.410562 | − | 0.911833i | \(-0.365333\pi\) | ||||
0.410562 | + | 0.911833i | \(0.365333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.2337 | −1.56103 | −0.780515 | − | 0.625138i | \(-0.785043\pi\) | ||||
−0.780515 | + | 0.625138i | \(0.785043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.41957 | 0.282356 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | −0.127257 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.9313 | −1.51053 | −0.755266 | − | 0.655418i | \(-0.772493\pi\) | ||||
−0.755266 | + | 0.655418i | \(0.772493\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.23369 | −0.140431 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 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 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.0706 | −0.805966 | −0.402983 | − | 0.915208i | \(-0.632027\pi\) | ||||
−0.402983 | + | 0.915208i | \(0.632027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.7228 | −1.94872 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 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 | \(-0.781836\pi\) | ||||
−0.774177 | + | 0.632969i | \(0.781836\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.8716 | 0.715884 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.11684 | 0.547778 | 0.273889 | − | 0.961761i | \(-0.411690\pi\) | ||||
0.273889 | + | 0.961761i | \(0.411690\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 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 | \(-0.560653\pi\) | ||||
−0.189396 | + | 0.981901i | \(0.560653\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.8824 | −0.760425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.62772 | −0.389866 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −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 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.02163 | −0.116914 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.3723 | 1.52007 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.4793 | 0.943603 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.4891 | −1.45474 | −0.727371 | − | 0.686245i | \(-0.759258\pi\) | ||||
−0.727371 | + | 0.686245i | \(0.759258\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.6943 | −0.719825 | −0.359913 | − | 0.932986i | \(-0.617194\pi\) | ||||
−0.359913 | + | 0.932986i | \(0.617194\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.48913 | 0.423310 | 0.211655 | − | 0.977344i | \(-0.432115\pi\) | ||||
0.211655 | + | 0.977344i | \(0.432115\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −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 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.22060 | 0.179199 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.7446 | 0.596001 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.0381 | 0.553419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.9783 | −1.04314 | −0.521569 | − | 0.853209i | \(-0.674653\pi\) | ||||
−0.521569 | + | 0.853209i | \(0.674653\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.8824 | −0.703841 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.4845 | −0.567766 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.8614 | −1.07242 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.3942 | −1.73901 | −0.869505 | − | 0.493924i | \(-0.835562\pi\) | ||||
−0.869505 | + | 0.493924i | \(0.835562\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.8614 | 0.956099 | 0.478050 | − | 0.878333i | \(-0.341344\pi\) | ||||
0.478050 | + | 0.878333i | \(0.341344\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 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 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.60773 | 0.243187 | 0.121593 | − | 0.992580i | \(-0.461200\pi\) | ||||
0.121593 | + | 0.992580i | \(0.461200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.4793 | 0.862567 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.3669 | 1.21315 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.2337 | −1.25477 | −0.627386 | − | 0.778708i | \(-0.715875\pi\) | ||||
−0.627386 | + | 0.778708i | \(0.715875\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.02163 | 0.104119 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.7446 | −1.47651 | −0.738255 | − | 0.674522i | \(-0.764350\pi\) | ||||
−0.738255 | + | 0.674522i | \(0.764350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.3020 | 0.884090 | 0.442045 | − | 0.896993i | \(-0.354253\pi\) | ||||
0.442045 | + | 0.896993i | \(0.354253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.8832 | −0.860445 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 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 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.8824 | −0.648184 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.1168 | −0.859070 | −0.429535 | − | 0.903050i | \(-0.641322\pi\) | ||||
−0.429535 | + | 0.903050i | \(0.641322\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 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 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.7432 | 1.17691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.48913 | 0.370313 | 0.185157 | − | 0.982709i | \(-0.440721\pi\) | ||||
0.185157 | + | 0.982709i | \(0.440721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −25.7648 | −1.26780 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.2337 | −1.87682 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.8716 | −0.579965 | −0.289983 | − | 0.957032i | \(-0.593650\pi\) | ||||
−0.289983 | + | 0.957032i | \(0.593650\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.97825 | −0.437573 | −0.218787 | − | 0.975773i | \(-0.570210\pi\) | ||||
−0.218787 | + | 0.975773i | \(0.570210\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.3020 | −0.839269 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.1386 | −0.587428 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.1844 | 1.45393 | 0.726966 | − | 0.686674i | \(-0.240930\pi\) | ||||
0.726966 | + | 0.686674i | \(0.240930\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.0000 | −1.05725 | −0.528626 | − | 0.848855i | \(-0.677293\pi\) | ||||
−0.528626 | + | 0.848855i | \(0.677293\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.01082 | 0.0483539 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.2337 | 0.870246 | 0.435123 | − | 0.900371i | \(-0.356705\pi\) | ||||
0.435123 | + | 0.900371i | \(0.356705\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.9746 | 1.32911 | 0.664557 | − | 0.747238i | \(-0.268620\pi\) | ||||
0.664557 | + | 0.747238i | \(0.268620\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.7228 | −1.50381 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 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 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15.2804 | −0.716354 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.37228 | −0.391639 | −0.195819 | − | 0.980640i | \(-0.562737\pi\) | ||||
−0.195819 | + | 0.980640i | \(0.562737\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −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 | \(-0.482444\pi\) | ||||
0.0551246 | + | 0.998479i | \(0.482444\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.4374 | 1.68612 | 0.843062 | − | 0.537816i | \(-0.180751\pi\) | ||||
0.843062 | + | 0.537816i | \(0.180751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.48913 | 0.438167 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 24.5659 | 1.12954 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.37228 | −0.246497 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.5932 | −1.53491 | −0.767455 | − | 0.641103i | \(-0.778477\pi\) | ||||
−0.767455 | + | 0.641103i | \(0.778477\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.4891 | 0.979820 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.1195 | −1.09521 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.01082 | 0.0456175 | 0.0228087 | − | 0.999740i | \(-0.492739\pi\) | ||||
0.0228087 | + | 0.999740i | \(0.492739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.25544 | −0.146618 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.79588 | −0.215125 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.1168 | 0.497658 | 0.248829 | − | 0.968547i | \(-0.419954\pi\) | ||||
0.248829 | + | 0.968547i | \(0.419954\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.5715 | 1.40770 | 0.703852 | − | 0.710346i | \(-0.251462\pi\) | ||||
0.703852 | + | 0.710346i | \(0.251462\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −41.4891 | −1.84624 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.3669 | −1.02967 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.35053 | 0.411236 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 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 | \(-0.369478\pi\) | ||||
0.398652 | + | 0.917102i | \(0.369478\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.2804 | 0.665623 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.9783 | −0.955576 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.8608 | −0.470433 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.2337 | 0.615376 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.03245 | −0.130617 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.1168 | 0.907884 | 0.453942 | − | 0.891031i | \(-0.350017\pi\) | ||||
0.453942 | + | 0.891031i | \(0.350017\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.9257 | −0.725016 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.2337 | −0.950644 | −0.475322 | − | 0.879812i | \(-0.657668\pi\) | ||||
−0.475322 | + | 0.879812i | \(0.657668\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.01082 | −0.0430622 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.48913 | 0.403519 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −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 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.6472 | 1.62879 | 0.814393 | − | 0.580313i | \(-0.197070\pi\) | ||||
0.814393 | + | 0.580313i | \(0.197070\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.2337 | 1.60850 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 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 | \(-0.516731\pi\) | ||||
−0.0525384 | + | 0.998619i | \(0.516731\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.43039 | −0.226463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.1168 | −1.71172 | −0.855858 | − | 0.517210i | \(-0.826970\pi\) | ||||
−0.855858 | + | 0.517210i | \(0.826970\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.1628 | 1.16839 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.7663 | 0.901469 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.83348 | 0.0756758 | 0.0378379 | − | 0.999284i | \(-0.487953\pi\) | ||||
0.0378379 | + | 0.999284i | \(0.487953\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.74456 | 0.195496 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 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 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.8824 | −0.526361 | −0.263181 | − | 0.964747i | \(-0.584771\pi\) | ||||
−0.263181 | + | 0.964747i | \(0.584771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.2554 | −1.03019 | −0.515095 | − | 0.857133i | \(-0.672244\pi\) | ||||
−0.515095 | + | 0.857133i | \(0.672244\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.6999 | 0.800916 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.7446 | −1.16671 | −0.583353 | − | 0.812219i | \(-0.698260\pi\) | ||||
−0.583353 | + | 0.812219i | \(0.698260\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.46284 | 0.342370 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.60597 | 0.105254 | 0.0526271 | − | 0.998614i | \(-0.483241\pi\) | ||||
0.0526271 | + | 0.998614i | \(0.483241\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 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 | \(-0.544787\pi\) | ||||
−0.140240 | + | 0.990118i | \(0.544787\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.3669 | 0.936174 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.0000 | −0.920000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.6040 | −1.37975 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.1168 | −0.601792 | −0.300896 | − | 0.953657i | \(-0.597286\pi\) | ||||
−0.300896 | + | 0.953657i | \(0.597286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −41.0452 | −1.62883 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.74456 | −0.108744 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −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 | \(-0.256537\pi\) | ||||
0.692437 | + | 0.721479i | \(0.256537\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.1138 | 0.672814 | 0.336407 | − | 0.941717i | \(-0.390788\pi\) | ||||
0.336407 | + | 0.941717i | \(0.390788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 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 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.2371 | −0.437735 | −0.218867 | − | 0.975755i | \(-0.570236\pi\) | ||||
−0.218867 | + | 0.975755i | \(0.570236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.74456 | −0.262333 | −0.131167 | − | 0.991360i | \(-0.541872\pi\) | ||||
−0.131167 | + | 0.991360i | \(0.541872\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.64018 | 0.296273 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.02175 | −0.0395623 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.3071 | −0.436507 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.2554 | −0.973526 | −0.486763 | − | 0.873534i | \(-0.661822\pi\) | ||||
−0.486763 | + | 0.873534i | \(0.661822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 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 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.2277 | −1.30968 | −0.654842 | − | 0.755765i | \(-0.727265\pi\) | ||||
−0.654842 | + | 0.755765i | \(0.727265\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.8397 | −1.48399 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.6999 | 0.750507 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.1168 | −1.03157 | −0.515787 | − | 0.856717i | \(-0.672500\pi\) | ||||
−0.515787 | + | 0.856717i | \(0.672500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.0381 | 0.380767 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.4891 | 0.662448 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −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 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 30.5607 | 1.14935 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.0000 | 1.42712 | 0.713560 | − | 0.700594i | \(-0.247082\pi\) | ||||
0.713560 | + | 0.700594i | \(0.247082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.79588 | 0.179607 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.2337 | −0.532310 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.8354 | 1.44832 | 0.724158 | − | 0.689634i | \(-0.242229\pi\) | ||||
0.724158 | + | 0.689634i | \(0.242229\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.2119 | 0.641006 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.43039 | 0.201680 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.3505 | 1.38525 | 0.692627 | − | 0.721296i | \(-0.256453\pi\) | ||||
0.692627 | + | 0.721296i | \(0.256453\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.8029 | −1.32422 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.4674 | 0.682108 | 0.341054 | − | 0.940044i | \(-0.389216\pi\) | ||||
0.341054 | + | 0.940044i | \(0.389216\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.83915 | 0.325594 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.1168 | −0.997509 | −0.498755 | − | 0.866743i | \(-0.666209\pi\) | ||||
−0.498755 | + | 0.866743i | \(0.666209\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.5391 | −1.04700 | −0.523498 | − | 0.852027i | \(-0.675373\pi\) | ||||
−0.523498 | + | 0.852027i | \(0.675373\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −66.0951 | −2.42154 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.4845 | −0.383094 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.4674 | −0.892827 | −0.446414 | − | 0.894827i | \(-0.647299\pi\) | ||||
−0.446414 | + | 0.894827i | \(0.647299\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.8824 | −0.468839 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.11684 | −0.185975 | −0.0929874 | − | 0.995667i | \(-0.529642\pi\) | ||||
−0.0929874 | + | 0.995667i | \(0.529642\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 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 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.7216 | −0.784320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.88316 | 0.248213 | 0.124106 | − | 0.992269i | \(-0.460394\pi\) | ||||
0.124106 | + | 0.992269i | \(0.460394\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 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 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.43039 | 0.194564 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.46738 | −0.159855 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.44121 | −0.229896 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.9565 | 1.78076 | 0.890378 | − | 0.455221i | \(-0.150440\pi\) | ||||
0.890378 | + | 0.455221i | \(0.150440\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −28.1628 | −1.00135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2337 | −0.363409 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −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 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.3071 | −0.399020 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.72281 | 0.272193 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −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 | \(-0.276800\pi\) | ||||
0.645138 | + | 0.764066i | \(0.276800\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −69.2079 | −2.42425 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.1168 | −0.388929 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −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 | \(-0.547925\pi\) | ||||
−0.149993 | + | 0.988687i | \(0.547925\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.5391 | 0.992401 | 0.496200 | − | 0.868208i | \(-0.334728\pi\) | ||||
0.496200 | + | 0.868208i | \(0.334728\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.25544 | −0.0436031 | −0.0218016 | − | 0.999762i | \(-0.506940\pi\) | ||||
−0.0218016 | + | 0.999762i | \(0.506940\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.41957 | 0.153129 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −20.7446 | −0.717895 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.1844 | −1.04208 | −0.521041 | − | 0.853532i | \(-0.674456\pi\) | ||||
−0.521041 | + | 0.853532i | \(0.674456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.9783 | −0.964767 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.9854 | 0.997129 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.5109 | −0.498600 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.8608 | −0.372303 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.4674 | −1.31710 | −0.658549 | − | 0.752538i | \(-0.728829\pi\) | ||||
−0.658549 | + | 0.752538i | \(0.728829\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −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 | \(-0.516933\pi\) | ||||
−0.0531727 | + | 0.998585i | \(0.516933\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.9040 | 0.507340 | 0.253670 | − | 0.967291i | \(-0.418362\pi\) | ||||
0.253670 | + | 0.967291i | \(0.418362\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.25544 | 0.110688 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.83915 | 0.299847 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | 0.271070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.84429 | −0.0961547 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −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 | \(-0.516701\pi\) | ||||
−0.0524451 | + | 0.998624i | \(0.516701\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.7216 | −0.729338 | −0.364669 | − | 0.931137i | \(-0.618818\pi\) | ||||
−0.364669 | + | 0.931137i | \(0.618818\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.2337 | 1.01401 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.23142 | −0.141599 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2337 | −0.475780 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.79588 | −0.159952 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.7228 | −1.05684 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −62.7667 | −2.08644 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.2554 | −0.772184 | −0.386092 | − | 0.922460i | \(-0.626175\pi\) | ||||
−0.386092 | + | 0.922460i | \(0.626175\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.0019 | 1.22593 | 0.612964 | − | 0.790111i | \(-0.289977\pi\) | ||||
0.612964 | + | 0.790111i | \(0.289977\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.2337 | 0.868208 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 35.8029 | 1.18232 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.9783 | −0.626035 | −0.313017 | − | 0.949747i | \(-0.601340\pi\) | ||||
−0.313017 | + | 0.949747i | \(0.601340\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.04326 | −0.133086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 57.7228 | 1.89791 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 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 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 22.9205 | 0.749581 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.11684 | −0.167160 | −0.0835800 | − | 0.996501i | \(-0.526635\pi\) | ||||
−0.0835800 | + | 0.996501i | \(0.526635\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 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 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.84996 | 0.320081 | 0.160040 | − | 0.987110i | \(-0.448838\pi\) | ||||
0.160040 | + | 0.987110i | \(0.448838\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.2337 | −0.332200 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 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 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28.6091 | 0.923837 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.48913 | −0.273843 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −52.2823 | −1.68303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.00000 | −0.257263 | −0.128631 | − | 0.991692i | \(-0.541058\pi\) | ||||
−0.128631 | + | 0.991692i | \(0.541058\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.5296 | 1.65366 | 0.826832 | − | 0.562448i | \(-0.190140\pi\) | ||||
0.826832 | + | 0.562448i | \(0.190140\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.39403 | −0.237042 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −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 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.2823 | −1.66755 | −0.833773 | − | 0.552108i | \(-0.813824\pi\) | ||||
−0.833773 | + | 0.552108i | \(0.813824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 76.4674 | 2.43645 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.2371 | −0.357319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.84429 | 0.0901702 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.3505 | −0.612837 | −0.306419 | − | 0.951897i | \(-0.599131\pi\) | ||||
−0.306419 | + | 0.951897i | \(0.599131\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2736.2.a.bf.1.1 | 4 | ||
3.2 | odd | 2 | inner | 2736.2.a.bf.1.4 | 4 | ||
4.3 | odd | 2 | 171.2.a.e.1.4 | yes | 4 | ||
12.11 | even | 2 | 171.2.a.e.1.1 | ✓ | 4 | ||
20.19 | odd | 2 | 4275.2.a.bp.1.1 | 4 | |||
28.27 | even | 2 | 8379.2.a.bw.1.4 | 4 | |||
60.59 | even | 2 | 4275.2.a.bp.1.4 | 4 | |||
76.75 | even | 2 | 3249.2.a.bf.1.1 | 4 | |||
84.83 | odd | 2 | 8379.2.a.bw.1.1 | 4 | |||
228.227 | odd | 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 | 12.11 | even | 2 | ||
171.2.a.e.1.4 | yes | 4 | 4.3 | odd | 2 | ||
2736.2.a.bf.1.1 | 4 | 1.1 | even | 1 | trivial | ||
2736.2.a.bf.1.4 | 4 | 3.2 | odd | 2 | inner | ||
3249.2.a.bf.1.1 | 4 | 76.75 | even | 2 | |||
3249.2.a.bf.1.4 | 4 | 228.227 | odd | 2 | |||
4275.2.a.bp.1.1 | 4 | 20.19 | odd | 2 | |||
4275.2.a.bp.1.4 | 4 | 60.59 | even | 2 | |||
8379.2.a.bw.1.1 | 4 | 84.83 | odd | 2 | |||
8379.2.a.bw.1.4 | 4 | 28.27 | even | 2 |