Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,2,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(4.24005634733\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 2.23607 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.38197 | −0.900299 | −0.450149 | − | 0.892953i | \(-0.648629\pi\) | ||||
−0.450149 | + | 0.892953i | \(0.648629\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.38197 | −0.437016 | ||||||||
\(11\) | −2.23607 | −0.674200 | −0.337100 | − | 0.941469i | \(-0.609446\pi\) | ||||
−0.337100 | + | 0.941469i | \(0.609446\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.23607 | −1.72957 | −0.864787 | − | 0.502139i | \(-0.832547\pi\) | ||||
−0.864787 | + | 0.502139i | \(0.832547\pi\) | |||||||
\(14\) | 1.47214 | 0.393445 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −1.85410 | −0.449686 | −0.224843 | − | 0.974395i | \(-0.572187\pi\) | ||||
−0.224843 | + | 0.974395i | \(0.572187\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.09017 | 0.708934 | 0.354467 | − | 0.935069i | \(-0.384662\pi\) | ||||
0.354467 | + | 0.935069i | \(0.384662\pi\) | |||||||
\(20\) | −3.61803 | −0.809017 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.38197 | 0.294636 | ||||||||
\(23\) | 4.61803 | 0.962927 | 0.481463 | − | 0.876466i | \(-0.340105\pi\) | ||||
0.481463 | + | 0.876466i | \(0.340105\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.85410 | 0.755852 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.85410 | 0.728357 | ||||||||
\(29\) | −6.38197 | −1.18510 | −0.592551 | − | 0.805533i | \(-0.701879\pi\) | ||||
−0.592551 | + | 0.805533i | \(0.701879\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.5623 | −1.89705 | −0.948523 | − | 0.316708i | \(-0.897422\pi\) | ||||
−0.948523 | + | 0.316708i | \(0.897422\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.14590 | 0.196520 | ||||||||
\(35\) | −5.32624 | −0.900299 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.145898 | −0.0239855 | −0.0119927 | − | 0.999928i | \(-0.503818\pi\) | ||||
−0.0119927 | + | 0.999928i | \(0.503818\pi\) | |||||||
\(38\) | −1.90983 | −0.309815 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.00000 | 0.790569 | ||||||||
\(41\) | −8.09017 | −1.26347 | −0.631736 | − | 0.775183i | \(-0.717657\pi\) | ||||
−0.631736 | + | 0.775183i | \(0.717657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.70820 | −1.32799 | −0.663994 | − | 0.747738i | \(-0.731140\pi\) | ||||
−0.663994 | + | 0.747738i | \(0.731140\pi\) | |||||||
\(44\) | 3.61803 | 0.545439 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.85410 | −0.420814 | ||||||||
\(47\) | 10.8541 | 1.58323 | 0.791617 | − | 0.611018i | \(-0.209240\pi\) | ||||
0.791617 | + | 0.611018i | \(0.209240\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.32624 | −0.189463 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.0902 | 1.39925 | ||||||||
\(53\) | −6.23607 | −0.856590 | −0.428295 | − | 0.903639i | \(-0.640886\pi\) | ||||
−0.428295 | + | 0.903639i | \(0.640886\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | −5.32624 | −0.711748 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.94427 | 0.517908 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.14590 | −0.402791 | −0.201395 | − | 0.979510i | \(-0.564548\pi\) | ||||
−0.201395 | + | 0.979510i | \(0.564548\pi\) | |||||||
\(62\) | 6.52786 | 0.829040 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | −13.9443 | −1.72957 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7082 | 1.30822 | 0.654108 | − | 0.756401i | \(-0.273044\pi\) | ||||
0.654108 | + | 0.756401i | \(0.273044\pi\) | |||||||
\(68\) | 3.00000 | 0.363803 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.29180 | 0.393445 | ||||||||
\(71\) | 7.94427 | 0.942812 | 0.471406 | − | 0.881916i | \(-0.343747\pi\) | ||||
0.471406 | + | 0.881916i | \(0.343747\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.854102 | 0.0999651 | 0.0499825 | − | 0.998750i | \(-0.484083\pi\) | ||||
0.0499825 | + | 0.998750i | \(0.484083\pi\) | |||||||
\(74\) | 0.0901699 | 0.0104820 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.00000 | −0.573539 | ||||||||
\(77\) | 5.32624 | 0.606981 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00000 | −0.337526 | −0.168763 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168763 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(80\) | 4.14590 | 0.463525 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.00000 | 0.552158 | ||||||||
\(83\) | 1.61803 | 0.177602 | 0.0888012 | − | 0.996049i | \(-0.471696\pi\) | ||||
0.0888012 | + | 0.996049i | \(0.471696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.14590 | −0.449686 | ||||||||
\(86\) | 5.38197 | 0.580352 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.00000 | −0.533002 | ||||||||
\(89\) | 13.7984 | 1.46262 | 0.731312 | − | 0.682043i | \(-0.238908\pi\) | ||||
0.731312 | + | 0.682043i | \(0.238908\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.8541 | 1.55713 | ||||||||
\(92\) | −7.47214 | −0.779024 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.70820 | −0.691898 | ||||||||
\(95\) | 6.90983 | 0.708934 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | 0.304604 | 0.152302 | − | 0.988334i | \(-0.451331\pi\) | ||||
0.152302 | + | 0.988334i | \(0.451331\pi\) | |||||||
\(98\) | 0.819660 | 0.0827982 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.70820 | −0.368980 | −0.184490 | − | 0.982834i | \(-0.559063\pi\) | ||||
−0.184490 | + | 0.982834i | \(0.559063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.23607 | −0.318859 | −0.159430 | − | 0.987209i | \(-0.550966\pi\) | ||||
−0.159430 | + | 0.987209i | \(0.550966\pi\) | |||||||
\(104\) | −13.9443 | −1.36735 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.85410 | 0.374343 | ||||||||
\(107\) | −0.909830 | −0.0879566 | −0.0439783 | − | 0.999032i | \(-0.514003\pi\) | ||||
−0.0439783 | + | 0.999032i | \(0.514003\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.14590 | −0.397105 | −0.198553 | − | 0.980090i | \(-0.563624\pi\) | ||||
−0.198553 | + | 0.980090i | \(0.563624\pi\) | |||||||
\(110\) | 3.09017 | 0.294636 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.41641 | −0.417311 | ||||||||
\(113\) | 9.00000 | 0.846649 | 0.423324 | − | 0.905978i | \(-0.360863\pi\) | ||||
0.423324 | + | 0.905978i | \(0.360863\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.3262 | 0.962927 | ||||||||
\(116\) | 10.3262 | 0.958767 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.618034 | −0.0568946 | ||||||||
\(119\) | 4.41641 | 0.404851 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.00000 | −0.545455 | ||||||||
\(122\) | 1.94427 | 0.176026 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17.0902 | 1.53474 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9443 | 1.41483 | 0.707413 | − | 0.706801i | \(-0.249862\pi\) | ||||
0.707413 | + | 0.706801i | \(0.249862\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.61803 | 0.755852 | ||||||||
\(131\) | 20.6525 | 1.80442 | 0.902208 | − | 0.431302i | \(-0.141946\pi\) | ||||
0.902208 | + | 0.431302i | \(0.141946\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.36068 | −0.638252 | ||||||||
\(134\) | −6.61803 | −0.571711 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.14590 | −0.355508 | ||||||||
\(137\) | −12.2361 | −1.04540 | −0.522699 | − | 0.852517i | \(-0.675075\pi\) | ||||
−0.522699 | + | 0.852517i | \(0.675075\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7639 | 0.997804 | 0.498902 | − | 0.866658i | \(-0.333737\pi\) | ||||
0.498902 | + | 0.866658i | \(0.333737\pi\) | |||||||
\(140\) | 8.61803 | 0.728357 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.90983 | −0.412024 | ||||||||
\(143\) | 13.9443 | 1.16608 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.2705 | −1.18510 | ||||||||
\(146\) | −0.527864 | −0.0436863 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.236068 | 0.0194047 | ||||||||
\(149\) | −19.0902 | −1.56393 | −0.781964 | − | 0.623324i | \(-0.785782\pi\) | ||||
−0.781964 | + | 0.623324i | \(0.785782\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.56231 | 0.208517 | 0.104259 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104259 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(152\) | 6.90983 | 0.560461 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.29180 | −0.265260 | ||||||||
\(155\) | −23.6180 | −1.89705 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000 | 0.718278 | 0.359139 | − | 0.933284i | \(-0.383070\pi\) | ||||
0.359139 | + | 0.933284i | \(0.383070\pi\) | |||||||
\(158\) | 1.85410 | 0.147504 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.5623 | −0.993137 | ||||||||
\(161\) | −11.0000 | −0.866921 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.5623 | −1.45391 | −0.726956 | − | 0.686684i | \(-0.759066\pi\) | ||||
−0.726956 | + | 0.686684i | \(0.759066\pi\) | |||||||
\(164\) | 13.0902 | 1.02217 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.00000 | −0.0776151 | ||||||||
\(167\) | −7.03444 | −0.544341 | −0.272171 | − | 0.962249i | \(-0.587742\pi\) | ||||
−0.272171 | + | 0.962249i | \(0.587742\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.8885 | 1.99143 | ||||||||
\(170\) | 2.56231 | 0.196520 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.0902 | 1.07437 | ||||||||
\(173\) | −12.3820 | −0.941383 | −0.470692 | − | 0.882298i | \(-0.655996\pi\) | ||||
−0.470692 | + | 0.882298i | \(0.655996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.14590 | −0.312509 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.52786 | −0.639190 | ||||||||
\(179\) | 0.527864 | 0.0394544 | 0.0197272 | − | 0.999805i | \(-0.493720\pi\) | ||||
0.0197272 | + | 0.999805i | \(0.493720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.2705 | 1.65535 | 0.827677 | − | 0.561205i | \(-0.189662\pi\) | ||||
0.827677 | + | 0.561205i | \(0.189662\pi\) | |||||||
\(182\) | −9.18034 | −0.680492 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.3262 | 0.761260 | ||||||||
\(185\) | −0.326238 | −0.0239855 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.14590 | 0.303178 | ||||||||
\(188\) | −17.5623 | −1.28086 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.27051 | −0.309815 | ||||||||
\(191\) | −16.4164 | −1.18785 | −0.593925 | − | 0.804521i | \(-0.702422\pi\) | ||||
−0.593925 | + | 0.804521i | \(0.702422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00000 | 0.575853 | 0.287926 | − | 0.957653i | \(-0.407034\pi\) | ||||
0.287926 | + | 0.957653i | \(0.407034\pi\) | |||||||
\(194\) | −1.85410 | −0.133117 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.14590 | 0.153278 | ||||||||
\(197\) | 20.6525 | 1.47143 | 0.735714 | − | 0.677292i | \(-0.236847\pi\) | ||||
0.735714 | + | 0.677292i | \(0.236847\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5623 | −1.17407 | −0.587035 | − | 0.809561i | \(-0.699705\pi\) | ||||
−0.587035 | + | 0.809561i | \(0.699705\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.29180 | 0.161250 | ||||||||
\(203\) | 15.2016 | 1.06694 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.0902 | −1.26347 | ||||||||
\(206\) | 2.00000 | 0.139347 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.5623 | −0.801702 | ||||||||
\(209\) | −6.90983 | −0.477963 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.14590 | −0.147730 | −0.0738649 | − | 0.997268i | \(-0.523533\pi\) | ||||
−0.0738649 | + | 0.997268i | \(0.523533\pi\) | |||||||
\(212\) | 10.0902 | 0.692996 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.562306 | 0.0384384 | ||||||||
\(215\) | −19.4721 | −1.32799 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.1591 | 1.70791 | ||||||||
\(218\) | 2.56231 | 0.173541 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.09017 | 0.545439 | ||||||||
\(221\) | 11.5623 | 0.777765 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.52786 | −0.638033 | −0.319016 | − | 0.947749i | \(-0.603353\pi\) | ||||
−0.319016 | + | 0.947749i | \(0.603353\pi\) | |||||||
\(224\) | 13.3820 | 0.894120 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.56231 | −0.369999 | ||||||||
\(227\) | 22.1459 | 1.46987 | 0.734937 | − | 0.678135i | \(-0.237211\pi\) | ||||
0.734937 | + | 0.678135i | \(0.237211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.14590 | −0.604378 | −0.302189 | − | 0.953248i | \(-0.597717\pi\) | ||||
−0.302189 | + | 0.953248i | \(0.597717\pi\) | |||||||
\(230\) | −6.38197 | −0.420814 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.2705 | −0.936905 | ||||||||
\(233\) | 8.29180 | 0.543214 | 0.271607 | − | 0.962408i | \(-0.412445\pi\) | ||||
0.271607 | + | 0.962408i | \(0.412445\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.2705 | 1.58323 | ||||||||
\(236\) | −1.61803 | −0.105325 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.72949 | −0.176927 | ||||||||
\(239\) | 1.47214 | 0.0952246 | 0.0476123 | − | 0.998866i | \(-0.484839\pi\) | ||||
0.0476123 | + | 0.998866i | \(0.484839\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.4164 | −1.50838 | −0.754192 | − | 0.656654i | \(-0.771971\pi\) | ||||
−0.754192 | + | 0.656654i | \(0.771971\pi\) | |||||||
\(242\) | 3.70820 | 0.238372 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.09017 | 0.325865 | ||||||||
\(245\) | −2.96556 | −0.189463 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.2705 | −1.22615 | ||||||||
\(248\) | −23.6180 | −1.49975 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.90983 | 0.437016 | ||||||||
\(251\) | −15.1803 | −0.958175 | −0.479087 | − | 0.877767i | \(-0.659032\pi\) | ||||
−0.479087 | + | 0.877767i | \(0.659032\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.3262 | −0.649205 | ||||||||
\(254\) | −9.85410 | −0.618301 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 19.4164 | 1.21116 | 0.605581 | − | 0.795784i | \(-0.292941\pi\) | ||||
0.605581 | + | 0.795784i | \(0.292941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.347524 | 0.0215941 | ||||||||
\(260\) | 22.5623 | 1.39925 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.7639 | −0.788558 | ||||||||
\(263\) | −1.61803 | −0.0997722 | −0.0498861 | − | 0.998755i | \(-0.515886\pi\) | ||||
−0.0498861 | + | 0.998755i | \(0.515886\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.9443 | −0.856590 | ||||||||
\(266\) | 4.54915 | 0.278926 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17.3262 | −1.05837 | ||||||||
\(269\) | 11.4721 | 0.699468 | 0.349734 | − | 0.936849i | \(-0.386272\pi\) | ||||
0.349734 | + | 0.936849i | \(0.386272\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.76393 | −0.471625 | −0.235813 | − | 0.971799i | \(-0.575775\pi\) | ||||
−0.235813 | + | 0.971799i | \(0.575775\pi\) | |||||||
\(272\) | −3.43769 | −0.208441 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.56231 | 0.456856 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.47214 | −0.328789 | −0.164394 | − | 0.986395i | \(-0.552567\pi\) | ||||
−0.164394 | + | 0.986395i | \(0.552567\pi\) | |||||||
\(278\) | −7.27051 | −0.436056 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.9098 | −0.711748 | ||||||||
\(281\) | −9.70820 | −0.579143 | −0.289571 | − | 0.957156i | \(-0.593513\pi\) | ||||
−0.289571 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.2705 | −1.38329 | −0.691644 | − | 0.722238i | \(-0.743113\pi\) | ||||
−0.691644 | + | 0.722238i | \(0.743113\pi\) | |||||||
\(284\) | −12.8541 | −0.762751 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.61803 | −0.509595 | ||||||||
\(287\) | 19.2705 | 1.13750 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.5623 | −0.797783 | ||||||||
\(290\) | 8.81966 | 0.517908 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.38197 | −0.0808734 | ||||||||
\(293\) | −19.3820 | −1.13231 | −0.566153 | − | 0.824300i | \(-0.691569\pi\) | ||||
−0.566153 | + | 0.824300i | \(0.691569\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.23607 | 0.130189 | ||||||||
\(296\) | −0.326238 | −0.0189622 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.7984 | 0.683461 | ||||||||
\(299\) | −28.7984 | −1.66545 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.7426 | 1.19559 | ||||||||
\(302\) | −1.58359 | −0.0911255 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.72949 | 0.328609 | ||||||||
\(305\) | −7.03444 | −0.402791 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.8885 | −1.47754 | −0.738769 | − | 0.673959i | \(-0.764592\pi\) | ||||
−0.738769 | + | 0.673959i | \(0.764592\pi\) | |||||||
\(308\) | −8.61803 | −0.491058 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.5967 | 0.829040 | ||||||||
\(311\) | −27.4508 | −1.55659 | −0.778297 | − | 0.627896i | \(-0.783916\pi\) | ||||
−0.778297 | + | 0.627896i | \(0.783916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.7984 | −1.17559 | −0.587797 | − | 0.809009i | \(-0.700005\pi\) | ||||
−0.587797 | + | 0.809009i | \(0.700005\pi\) | |||||||
\(314\) | −5.56231 | −0.313899 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.85410 | 0.273065 | ||||||||
\(317\) | 29.1803 | 1.63893 | 0.819466 | − | 0.573128i | \(-0.194270\pi\) | ||||
0.819466 | + | 0.573128i | \(0.194270\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.2705 | 0.798995 | ||||||||
\(320\) | −0.527864 | −0.0295085 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.79837 | 0.378859 | ||||||||
\(323\) | −5.72949 | −0.318797 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.4721 | 0.635383 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −18.0902 | −0.998863 | ||||||||
\(329\) | −25.8541 | −1.42538 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.1246 | −0.611464 | −0.305732 | − | 0.952118i | \(-0.598901\pi\) | ||||
−0.305732 | + | 0.952118i | \(0.598901\pi\) | |||||||
\(332\) | −2.61803 | −0.143683 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.34752 | 0.237886 | ||||||||
\(335\) | 23.9443 | 1.30822 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.9098 | −0.812190 | −0.406095 | − | 0.913831i | \(-0.633110\pi\) | ||||
−0.406095 | + | 0.913831i | \(0.633110\pi\) | |||||||
\(338\) | −16.0000 | −0.870285 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.70820 | 0.363803 | ||||||||
\(341\) | 23.6180 | 1.27899 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8328 | 1.07087 | ||||||||
\(344\) | −19.4721 | −1.04987 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.65248 | 0.411400 | ||||||||
\(347\) | −31.0344 | −1.66602 | −0.833008 | − | 0.553261i | \(-0.813383\pi\) | ||||
−0.833008 | + | 0.553261i | \(0.813383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.0000 | −1.44528 | −0.722638 | − | 0.691226i | \(-0.757071\pi\) | ||||
−0.722638 | + | 0.691226i | \(0.757071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.5623 | 0.669573 | ||||||||
\(353\) | 16.0344 | 0.853427 | 0.426714 | − | 0.904387i | \(-0.359671\pi\) | ||||
0.426714 | + | 0.904387i | \(0.359671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.7639 | 0.942812 | ||||||||
\(356\) | −22.3262 | −1.18329 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.326238 | −0.0172422 | ||||||||
\(359\) | 21.8885 | 1.15523 | 0.577617 | − | 0.816308i | \(-0.303983\pi\) | ||||
0.577617 | + | 0.816308i | \(0.303983\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.45085 | −0.497413 | ||||||||
\(362\) | −13.7639 | −0.723416 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.0344 | −1.25975 | ||||||||
\(365\) | 1.90983 | 0.0999651 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.8328 | 1.55726 | 0.778630 | − | 0.627483i | \(-0.215915\pi\) | ||||
0.778630 | + | 0.627483i | \(0.215915\pi\) | |||||||
\(368\) | 8.56231 | 0.446341 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.201626 | 0.0104820 | ||||||||
\(371\) | 14.8541 | 0.771187 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.3262 | 1.77735 | 0.888673 | − | 0.458542i | \(-0.151628\pi\) | ||||
0.888673 | + | 0.458542i | \(0.151628\pi\) | |||||||
\(374\) | −2.56231 | −0.132494 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.2705 | 1.25166 | ||||||||
\(377\) | 39.7984 | 2.04972 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4164 | 1.15145 | 0.575727 | − | 0.817642i | \(-0.304719\pi\) | ||||
0.575727 | + | 0.817642i | \(0.304719\pi\) | |||||||
\(380\) | −11.1803 | −0.573539 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.1459 | 0.519109 | ||||||||
\(383\) | 18.2361 | 0.931820 | 0.465910 | − | 0.884832i | \(-0.345727\pi\) | ||||
0.465910 | + | 0.884832i | \(0.345727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.9098 | 0.606981 | ||||||||
\(386\) | −4.94427 | −0.251657 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.85410 | −0.246430 | ||||||||
\(389\) | −32.4721 | −1.64640 | −0.823201 | − | 0.567750i | \(-0.807814\pi\) | ||||
−0.823201 | + | 0.567750i | \(0.807814\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.56231 | −0.433014 | ||||||||
\(392\) | −2.96556 | −0.149783 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.7639 | −0.643038 | ||||||||
\(395\) | −6.70820 | −0.337526 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.00000 | 0.150566 | 0.0752828 | − | 0.997162i | \(-0.476014\pi\) | ||||
0.0752828 | + | 0.997162i | \(0.476014\pi\) | |||||||
\(398\) | 10.2361 | 0.513088 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0902 | 0.853442 | 0.426721 | − | 0.904383i | \(-0.359669\pi\) | ||||
0.426721 | + | 0.904383i | \(0.359669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 65.8673 | 3.28108 | ||||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.39512 | −0.466272 | ||||||||
\(407\) | 0.326238 | 0.0161710 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.5836 | −0.523325 | −0.261662 | − | 0.965159i | \(-0.584271\pi\) | ||||
−0.261662 | + | 0.965159i | \(0.584271\pi\) | |||||||
\(410\) | 11.1803 | 0.552158 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.23607 | 0.257963 | ||||||||
\(413\) | −2.38197 | −0.117209 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.61803 | 0.177602 | ||||||||
\(416\) | 35.0344 | 1.71770 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.27051 | 0.208877 | ||||||||
\(419\) | 31.3050 | 1.52935 | 0.764673 | − | 0.644418i | \(-0.222900\pi\) | ||||
0.764673 | + | 0.644418i | \(0.222900\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.00000 | 0.0487370 | 0.0243685 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243685 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(422\) | 1.32624 | 0.0645603 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.9443 | −0.677194 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.49342 | 0.362632 | ||||||||
\(428\) | 1.47214 | 0.0711584 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.0344 | 0.580352 | ||||||||
\(431\) | −12.3820 | −0.596418 | −0.298209 | − | 0.954501i | \(-0.596389\pi\) | ||||
−0.298209 | + | 0.954501i | \(0.596389\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.67376 | 0.176550 | 0.0882749 | − | 0.996096i | \(-0.471865\pi\) | ||||
0.0882749 | + | 0.996096i | \(0.471865\pi\) | |||||||
\(434\) | −15.5492 | −0.746383 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.70820 | 0.321265 | ||||||||
\(437\) | 14.2705 | 0.682651 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.6180 | −1.65223 | −0.826114 | − | 0.563503i | \(-0.809453\pi\) | ||||
−0.826114 | + | 0.563503i | \(0.809453\pi\) | |||||||
\(440\) | −11.1803 | −0.533002 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.14590 | −0.339896 | ||||||||
\(443\) | −3.38197 | −0.160682 | −0.0803410 | − | 0.996767i | \(-0.525601\pi\) | ||||
−0.0803410 | + | 0.996767i | \(0.525601\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.8541 | 1.46262 | ||||||||
\(446\) | 5.88854 | 0.278831 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.562306 | 0.0265665 | ||||||||
\(449\) | −6.88854 | −0.325090 | −0.162545 | − | 0.986701i | \(-0.551970\pi\) | ||||
−0.162545 | + | 0.986701i | \(0.551970\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.0902 | 0.851833 | ||||||||
\(452\) | −14.5623 | −0.684953 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.6869 | −0.642359 | ||||||||
\(455\) | 33.2148 | 1.55713 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.6869 | 1.57581 | 0.787904 | − | 0.615798i | \(-0.211166\pi\) | ||||
0.787904 | + | 0.615798i | \(0.211166\pi\) | |||||||
\(458\) | 5.65248 | 0.264123 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.7082 | −0.779024 | ||||||||
\(461\) | −23.7426 | −1.10581 | −0.552903 | − | 0.833246i | \(-0.686480\pi\) | ||||
−0.552903 | + | 0.833246i | \(0.686480\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.14590 | 0.192676 | 0.0963381 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963381 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(464\) | −11.8328 | −0.549325 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.12461 | −0.237393 | ||||||||
\(467\) | −14.8328 | −0.686381 | −0.343190 | − | 0.939266i | \(-0.611508\pi\) | ||||
−0.343190 | + | 0.939266i | \(0.611508\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −25.5066 | −1.17778 | ||||||||
\(470\) | −15.0000 | −0.691898 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.23607 | 0.102923 | ||||||||
\(473\) | 19.4721 | 0.895330 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.14590 | −0.327532 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.909830 | −0.0416147 | ||||||||
\(479\) | 14.9098 | 0.681248 | 0.340624 | − | 0.940200i | \(-0.389362\pi\) | ||||
0.340624 | + | 0.940200i | \(0.389362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.909830 | 0.0414847 | ||||||||
\(482\) | 14.4721 | 0.659188 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.70820 | 0.441282 | ||||||||
\(485\) | 6.70820 | 0.304604 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.74265 | −0.260224 | −0.130112 | − | 0.991499i | \(-0.541534\pi\) | ||||
−0.130112 | + | 0.991499i | \(0.541534\pi\) | |||||||
\(488\) | −7.03444 | −0.318434 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.83282 | 0.0827982 | ||||||||
\(491\) | 11.5066 | 0.519285 | 0.259642 | − | 0.965705i | \(-0.416395\pi\) | ||||
0.259642 | + | 0.965705i | \(0.416395\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.8328 | 0.532923 | ||||||||
\(494\) | 11.9098 | 0.535849 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.5836 | −0.879329 | ||||||||
\(497\) | −18.9230 | −0.848812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.4164 | −0.645367 | −0.322684 | − | 0.946507i | \(-0.604585\pi\) | ||||
−0.322684 | + | 0.946507i | \(0.604585\pi\) | |||||||
\(500\) | 18.0902 | 0.809017 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.38197 | 0.418738 | ||||||||
\(503\) | −3.79837 | −0.169361 | −0.0846806 | − | 0.996408i | \(-0.526987\pi\) | ||||
−0.0846806 | + | 0.996408i | \(0.526987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.29180 | −0.368980 | ||||||||
\(506\) | 6.38197 | 0.283713 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −25.7984 | −1.14462 | ||||||||
\(509\) | −34.9230 | −1.54793 | −0.773967 | − | 0.633226i | \(-0.781730\pi\) | ||||
−0.773967 | + | 0.633226i | \(0.781730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.03444 | −0.0899984 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.0000 | −0.529297 | ||||||||
\(515\) | −7.23607 | −0.318859 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.2705 | −1.06742 | ||||||||
\(518\) | −0.214782 | −0.00943697 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −31.1803 | −1.36735 | ||||||||
\(521\) | −23.5066 | −1.02984 | −0.514921 | − | 0.857238i | \(-0.672179\pi\) | ||||
−0.514921 | + | 0.857238i | \(0.672179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0557 | 0.614614 | 0.307307 | − | 0.951610i | \(-0.400572\pi\) | ||||
0.307307 | + | 0.951610i | \(0.400572\pi\) | |||||||
\(524\) | −33.4164 | −1.45980 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.00000 | 0.0436021 | ||||||||
\(527\) | 19.5836 | 0.853075 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.67376 | −0.0727723 | ||||||||
\(530\) | 8.61803 | 0.374343 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.9098 | 0.516357 | ||||||||
\(533\) | 50.4508 | 2.18527 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.03444 | −0.0879566 | ||||||||
\(536\) | 23.9443 | 1.03424 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.09017 | −0.305679 | ||||||||
\(539\) | 2.96556 | 0.127736 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.1246 | −1.12318 | −0.561592 | − | 0.827414i | \(-0.689811\pi\) | ||||
−0.561592 | + | 0.827414i | \(0.689811\pi\) | |||||||
\(542\) | 4.79837 | 0.206108 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.4164 | 0.446600 | ||||||||
\(545\) | −9.27051 | −0.397105 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.4377 | 0.531797 | 0.265899 | − | 0.964001i | \(-0.414331\pi\) | ||||
0.265899 | + | 0.964001i | \(0.414331\pi\) | |||||||
\(548\) | 19.7984 | 0.845745 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.7214 | −0.840158 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.14590 | 0.303874 | ||||||||
\(554\) | 3.38197 | 0.143686 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.0344 | −0.807240 | ||||||||
\(557\) | 25.4164 | 1.07693 | 0.538464 | − | 0.842649i | \(-0.319005\pi\) | ||||
0.538464 | + | 0.842649i | \(0.319005\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 54.3050 | 2.29685 | ||||||||
\(560\) | −9.87539 | −0.417311 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.00000 | 0.253095 | ||||||||
\(563\) | 20.5967 | 0.868049 | 0.434025 | − | 0.900901i | \(-0.357093\pi\) | ||||
0.434025 | + | 0.900901i | \(0.357093\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.1246 | 0.846649 | ||||||||
\(566\) | 14.3820 | 0.604519 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17.7639 | 0.745358 | ||||||||
\(569\) | 11.5066 | 0.482381 | 0.241190 | − | 0.970478i | \(-0.422462\pi\) | ||||
0.241190 | + | 0.970478i | \(0.422462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.58359 | 0.0662713 | 0.0331356 | − | 0.999451i | \(-0.489451\pi\) | ||||
0.0331356 | + | 0.999451i | \(0.489451\pi\) | |||||||
\(572\) | −22.5623 | −0.943377 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11.9098 | −0.497107 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5279 | 0.521542 | 0.260771 | − | 0.965401i | \(-0.416023\pi\) | ||||
0.260771 | + | 0.965401i | \(0.416023\pi\) | |||||||
\(578\) | 8.38197 | 0.348644 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 23.0902 | 0.958767 | ||||||||
\(581\) | −3.85410 | −0.159895 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.9443 | 0.577513 | ||||||||
\(584\) | 1.90983 | 0.0790293 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.9787 | 0.494836 | ||||||||
\(587\) | 15.3607 | 0.634003 | 0.317002 | − | 0.948425i | \(-0.397324\pi\) | ||||
0.317002 | + | 0.948425i | \(0.397324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.6393 | −1.34488 | ||||||||
\(590\) | −1.38197 | −0.0568946 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.270510 | −0.0111179 | ||||||||
\(593\) | −16.0902 | −0.660744 | −0.330372 | − | 0.943851i | \(-0.607174\pi\) | ||||
−0.330372 | + | 0.943851i | \(0.607174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.87539 | 0.404851 | ||||||||
\(596\) | 30.8885 | 1.26524 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 17.7984 | 0.727830 | ||||||||
\(599\) | −2.65248 | −0.108377 | −0.0541886 | − | 0.998531i | \(-0.517257\pi\) | ||||
−0.0541886 | + | 0.998531i | \(0.517257\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.3820 | 0.953770 | 0.476885 | − | 0.878966i | \(-0.341766\pi\) | ||||
0.476885 | + | 0.878966i | \(0.341766\pi\) | |||||||
\(602\) | −12.8197 | −0.522490 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.14590 | −0.168694 | ||||||||
\(605\) | −13.4164 | −0.545455 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.6525 | −0.554137 | −0.277068 | − | 0.960850i | \(-0.589363\pi\) | ||||
−0.277068 | + | 0.960850i | \(0.589363\pi\) | |||||||
\(608\) | −17.3607 | −0.704069 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.34752 | 0.176026 | ||||||||
\(611\) | −67.6869 | −2.73832 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.6525 | −1.56116 | −0.780579 | − | 0.625057i | \(-0.785076\pi\) | ||||
−0.780579 | + | 0.625057i | \(0.785076\pi\) | |||||||
\(614\) | 16.0000 | 0.645707 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.9098 | 0.479861 | ||||||||
\(617\) | −22.1459 | −0.891560 | −0.445780 | − | 0.895142i | \(-0.647074\pi\) | ||||
−0.445780 | + | 0.895142i | \(0.647074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.1246 | 0.487329 | 0.243665 | − | 0.969860i | \(-0.421650\pi\) | ||||
0.243665 | + | 0.969860i | \(0.421650\pi\) | |||||||
\(620\) | 38.2148 | 1.53474 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16.9656 | 0.680257 | ||||||||
\(623\) | −32.8673 | −1.31680 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 12.8541 | 0.513753 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.5623 | −0.581099 | ||||||||
\(629\) | 0.270510 | 0.0107859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −40.4164 | −1.60895 | −0.804476 | − | 0.593985i | \(-0.797554\pi\) | ||||
−0.804476 | + | 0.593985i | \(0.797554\pi\) | |||||||
\(632\) | −6.70820 | −0.266838 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.0344 | −0.716239 | ||||||||
\(635\) | 35.6525 | 1.41483 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.27051 | 0.327690 | ||||||||
\(638\) | −8.81966 | −0.349174 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 25.4508 | 1.00603 | ||||||||
\(641\) | 27.9443 | 1.10373 | 0.551866 | − | 0.833933i | \(-0.313916\pi\) | ||||
0.551866 | + | 0.833933i | \(0.313916\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.8541 | −0.782969 | −0.391485 | − | 0.920185i | \(-0.628038\pi\) | ||||
−0.391485 | + | 0.920185i | \(0.628038\pi\) | |||||||
\(644\) | 17.7984 | 0.701354 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.54102 | 0.139320 | ||||||||
\(647\) | −44.9443 | −1.76694 | −0.883471 | − | 0.468486i | \(-0.844800\pi\) | ||||
−0.883471 | + | 0.468486i | \(0.844800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.23607 | −0.0877733 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30.0344 | 1.17624 | ||||||||
\(653\) | −40.0902 | −1.56885 | −0.784425 | − | 0.620224i | \(-0.787042\pi\) | ||||
−0.784425 | + | 0.620224i | \(0.787042\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.1803 | 1.80442 | ||||||||
\(656\) | −15.0000 | −0.585652 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 15.9787 | 0.622915 | ||||||||
\(659\) | −1.85410 | −0.0722256 | −0.0361128 | − | 0.999348i | \(-0.511498\pi\) | ||||
−0.0361128 | + | 0.999348i | \(0.511498\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7426 | 1.19575 | 0.597875 | − | 0.801589i | \(-0.296012\pi\) | ||||
0.597875 | + | 0.801589i | \(0.296012\pi\) | |||||||
\(662\) | 6.87539 | 0.267220 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.61803 | 0.140407 | ||||||||
\(665\) | −16.4590 | −0.638252 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.4721 | −1.14117 | ||||||||
\(668\) | 11.3820 | 0.440381 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.7984 | −0.571711 | ||||||||
\(671\) | 7.03444 | 0.271562 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.47214 | −0.326577 | −0.163288 | − | 0.986578i | \(-0.552210\pi\) | ||||
−0.163288 | + | 0.986578i | \(0.552210\pi\) | |||||||
\(674\) | 9.21478 | 0.354940 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −41.8885 | −1.61110 | ||||||||
\(677\) | 27.8197 | 1.06920 | 0.534598 | − | 0.845106i | \(-0.320463\pi\) | ||||
0.534598 | + | 0.845106i | \(0.320463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.14590 | −0.274234 | ||||||||
\(680\) | −9.27051 | −0.355508 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.5967 | −0.558938 | ||||||||
\(683\) | −39.0000 | −1.49229 | −0.746147 | − | 0.665782i | \(-0.768098\pi\) | ||||
−0.746147 | + | 0.665782i | \(0.768098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.3607 | −1.04540 | ||||||||
\(686\) | −12.2574 | −0.467988 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16.1459 | −0.615557 | ||||||||
\(689\) | 38.8885 | 1.48154 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.1246 | 1.33620 | 0.668102 | − | 0.744070i | \(-0.267107\pi\) | ||||
0.668102 | + | 0.744070i | \(0.267107\pi\) | |||||||
\(692\) | 20.0344 | 0.761595 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19.1803 | 0.728076 | ||||||||
\(695\) | 26.3050 | 0.997804 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.0000 | 0.568166 | ||||||||
\(698\) | 16.6869 | 0.631609 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.2016 | −0.687466 | −0.343733 | − | 0.939067i | \(-0.611692\pi\) | ||||
−0.343733 | + | 0.939067i | \(0.611692\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.450850 | −0.0170041 | ||||||||
\(704\) | 0.527864 | 0.0198946 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.90983 | −0.372961 | ||||||||
\(707\) | 8.83282 | 0.332192 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.7082 | −1.04060 | −0.520302 | − | 0.853983i | \(-0.674181\pi\) | ||||
−0.520302 | + | 0.853983i | \(0.674181\pi\) | |||||||
\(710\) | −10.9787 | −0.412024 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 30.8541 | 1.15631 | ||||||||
\(713\) | −48.7771 | −1.82672 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.1803 | 1.16608 | ||||||||
\(716\) | −0.854102 | −0.0319193 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.5279 | −0.504855 | ||||||||
\(719\) | −14.6180 | −0.545161 | −0.272580 | − | 0.962133i | \(-0.587877\pi\) | ||||
−0.272580 | + | 0.962133i | \(0.587877\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.70820 | 0.287069 | ||||||||
\(722\) | 5.84095 | 0.217378 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −36.0344 | −1.33921 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.0000 | 0.964287 | 0.482143 | − | 0.876092i | \(-0.339858\pi\) | ||||
0.482143 | + | 0.876092i | \(0.339858\pi\) | |||||||
\(728\) | 33.2148 | 1.23102 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.18034 | −0.0436863 | ||||||||
\(731\) | 16.1459 | 0.597178 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.5279 | 0.758214 | 0.379107 | − | 0.925353i | \(-0.376231\pi\) | ||||
0.379107 | + | 0.925353i | \(0.376231\pi\) | |||||||
\(734\) | −18.4377 | −0.680548 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25.9443 | −0.956319 | ||||||||
\(737\) | −23.9443 | −0.881999 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.1033 | 1.76951 | 0.884755 | − | 0.466057i | \(-0.154326\pi\) | ||||
0.884755 | + | 0.466057i | \(0.154326\pi\) | |||||||
\(740\) | 0.527864 | 0.0194047 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.18034 | −0.337021 | ||||||||
\(743\) | 24.6180 | 0.903148 | 0.451574 | − | 0.892234i | \(-0.350863\pi\) | ||||
0.451574 | + | 0.892234i | \(0.350863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −42.6869 | −1.56393 | ||||||||
\(746\) | −21.2148 | −0.776728 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.70820 | −0.245276 | ||||||||
\(749\) | 2.16718 | 0.0791872 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.87539 | −0.177905 | −0.0889527 | − | 0.996036i | \(-0.528352\pi\) | ||||
−0.0889527 | + | 0.996036i | \(0.528352\pi\) | |||||||
\(752\) | 20.1246 | 0.733869 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −24.5967 | −0.895761 | ||||||||
\(755\) | 5.72949 | 0.208517 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −41.3820 | −1.50405 | −0.752027 | − | 0.659133i | \(-0.770924\pi\) | ||||
−0.752027 | + | 0.659133i | \(0.770924\pi\) | |||||||
\(758\) | −13.8541 | −0.503204 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.4508 | 0.560461 | ||||||||
\(761\) | −30.7082 | −1.11317 | −0.556586 | − | 0.830790i | \(-0.687889\pi\) | ||||
−0.556586 | + | 0.830790i | \(0.687889\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.87539 | 0.357513 | ||||||||
\(764\) | 26.5623 | 0.960991 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.2705 | −0.407220 | ||||||||
\(767\) | −6.23607 | −0.225171 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.9787 | 0.395903 | 0.197951 | − | 0.980212i | \(-0.436571\pi\) | ||||
0.197951 | + | 0.980212i | \(0.436571\pi\) | |||||||
\(770\) | −7.36068 | −0.265260 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.9443 | −0.465875 | ||||||||
\(773\) | −28.6525 | −1.03056 | −0.515279 | − | 0.857023i | \(-0.672312\pi\) | ||||
−0.515279 | + | 0.857023i | \(0.672312\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.70820 | 0.240810 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.0689 | 0.719504 | ||||||||
\(779\) | −25.0000 | −0.895718 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.7639 | −0.635643 | ||||||||
\(782\) | 5.29180 | 0.189234 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.45898 | −0.0878207 | ||||||||
\(785\) | 20.1246 | 0.718278 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.29180 | −0.152986 | −0.0764930 | − | 0.997070i | \(-0.524372\pi\) | ||||
−0.0764930 | + | 0.997070i | \(0.524372\pi\) | |||||||
\(788\) | −33.4164 | −1.19041 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4.14590 | 0.147504 | ||||||||
\(791\) | −21.4377 | −0.762237 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.6180 | 0.696657 | ||||||||
\(794\) | −1.85410 | −0.0657996 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.7984 | 0.949843 | ||||||||
\(797\) | 1.23607 | 0.0437838 | 0.0218919 | − | 0.999760i | \(-0.493031\pi\) | ||||
0.0218919 | + | 0.999760i | \(0.493031\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.1246 | −0.711958 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.5623 | −0.372968 | ||||||||
\(803\) | −1.90983 | −0.0673964 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.5967 | −0.866921 | ||||||||
\(806\) | −40.7082 | −1.43389 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.29180 | −0.291704 | ||||||||
\(809\) | −7.67376 | −0.269795 | −0.134898 | − | 0.990860i | \(-0.543071\pi\) | ||||
−0.134898 | + | 0.990860i | \(0.543071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6525 | 0.514518 | 0.257259 | − | 0.966342i | \(-0.417181\pi\) | ||||
0.257259 | + | 0.966342i | \(0.417181\pi\) | |||||||
\(812\) | −24.5967 | −0.863177 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.201626 | −0.00706699 | ||||||||
\(815\) | −41.5066 | −1.45391 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.9098 | −0.941456 | ||||||||
\(818\) | 6.54102 | 0.228701 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 29.2705 | 1.02217 | ||||||||
\(821\) | 40.9230 | 1.42822 | 0.714111 | − | 0.700032i | \(-0.246831\pi\) | ||||
0.714111 | + | 0.700032i | \(0.246831\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.2918 | 0.393607 | 0.196804 | − | 0.980443i | \(-0.436944\pi\) | ||||
0.196804 | + | 0.980443i | \(0.436944\pi\) | |||||||
\(824\) | −7.23607 | −0.252080 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.47214 | 0.0512222 | ||||||||
\(827\) | 2.81966 | 0.0980492 | 0.0490246 | − | 0.998798i | \(-0.484389\pi\) | ||||
0.0490246 | + | 0.998798i | \(0.484389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.6869 | −1.58677 | −0.793386 | − | 0.608719i | \(-0.791684\pi\) | ||||
−0.793386 | + | 0.608719i | \(0.791684\pi\) | |||||||
\(830\) | −2.23607 | −0.0776151 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.47214 | 0.0510371 | ||||||||
\(833\) | 2.45898 | 0.0851986 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.7295 | −0.544341 | ||||||||
\(836\) | 11.1803 | 0.386680 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19.3475 | −0.668349 | ||||||||
\(839\) | 24.8197 | 0.856870 | 0.428435 | − | 0.903573i | \(-0.359065\pi\) | ||||
0.428435 | + | 0.903573i | \(0.359065\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.7295 | 0.404465 | ||||||||
\(842\) | −0.618034 | −0.0212989 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.47214 | 0.119516 | ||||||||
\(845\) | 57.8885 | 1.99143 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.2918 | 0.491072 | ||||||||
\(848\) | −11.5623 | −0.397051 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.673762 | −0.0230963 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.96556 | −0.135778 | −0.0678891 | − | 0.997693i | \(-0.521626\pi\) | ||||
−0.0678891 | + | 0.997693i | \(0.521626\pi\) | |||||||
\(854\) | −4.63119 | −0.158476 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.03444 | −0.0695358 | ||||||||
\(857\) | 28.7771 | 0.983007 | 0.491503 | − | 0.870876i | \(-0.336448\pi\) | ||||
0.491503 | + | 0.870876i | \(0.336448\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.5279 | 0.529804 | 0.264902 | − | 0.964275i | \(-0.414660\pi\) | ||||
0.264902 | + | 0.964275i | \(0.414660\pi\) | |||||||
\(860\) | 31.5066 | 1.07437 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.65248 | 0.260644 | ||||||||
\(863\) | −19.2016 | −0.653631 | −0.326815 | − | 0.945088i | \(-0.605976\pi\) | ||||
−0.326815 | + | 0.945088i | \(0.605976\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.6869 | −0.941383 | ||||||||
\(866\) | −2.27051 | −0.0771551 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −40.7082 | −1.38173 | ||||||||
\(869\) | 6.70820 | 0.227560 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −66.7771 | −2.26266 | ||||||||
\(872\) | −9.27051 | −0.313939 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.81966 | −0.298329 | ||||||||
\(875\) | 26.6312 | 0.900299 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.1115 | −0.544045 | −0.272023 | − | 0.962291i | \(-0.587693\pi\) | ||||
−0.272023 | + | 0.962291i | \(0.587693\pi\) | |||||||
\(878\) | 21.3951 | 0.722050 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.27051 | −0.312509 | ||||||||
\(881\) | 15.7082 | 0.529223 | 0.264611 | − | 0.964355i | \(-0.414756\pi\) | ||||
0.264611 | + | 0.964355i | \(0.414756\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.4164 | −0.788025 | −0.394012 | − | 0.919105i | \(-0.628913\pi\) | ||||
−0.394012 | + | 0.919105i | \(0.628913\pi\) | |||||||
\(884\) | −18.7082 | −0.629225 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.09017 | 0.0702206 | ||||||||
\(887\) | 22.5279 | 0.756412 | 0.378206 | − | 0.925722i | \(-0.376541\pi\) | ||||
0.378206 | + | 0.925722i | \(0.376541\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.9787 | −1.27377 | ||||||||
\(890\) | −19.0689 | −0.639190 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.4164 | 0.516180 | ||||||||
\(893\) | 33.5410 | 1.12241 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.18034 | 0.0394544 | ||||||||
\(896\) | −27.1115 | −0.905730 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.25735 | 0.142070 | ||||||||
\(899\) | 67.4083 | 2.24819 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.5623 | 0.385196 | ||||||||
\(902\) | −11.1803 | −0.372265 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 20.1246 | 0.669335 | ||||||||
\(905\) | 49.7984 | 1.65535 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.9443 | −0.662239 | −0.331119 | − | 0.943589i | \(-0.607426\pi\) | ||||
−0.331119 | + | 0.943589i | \(0.607426\pi\) | |||||||
\(908\) | −35.8328 | −1.18915 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −20.5279 | −0.680492 | ||||||||
\(911\) | 45.1033 | 1.49434 | 0.747170 | − | 0.664633i | \(-0.231412\pi\) | ||||
0.747170 | + | 0.664633i | \(0.231412\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.61803 | −0.119739 | ||||||||
\(914\) | −20.8197 | −0.688653 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.7984 | 0.488952 | ||||||||
\(917\) | −49.1935 | −1.62451 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.5967 | −0.448515 | −0.224258 | − | 0.974530i | \(-0.571996\pi\) | ||||
−0.224258 | + | 0.974530i | \(0.571996\pi\) | |||||||
\(920\) | 23.0902 | 0.761260 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.6738 | 0.483255 | ||||||||
\(923\) | −49.5410 | −1.63066 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.56231 | −0.0842026 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 35.8541 | 1.17697 | ||||||||
\(929\) | 48.7082 | 1.59806 | 0.799032 | − | 0.601288i | \(-0.205346\pi\) | ||||
0.799032 | + | 0.601288i | \(0.205346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.09830 | −0.134316 | ||||||||
\(932\) | −13.4164 | −0.439469 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9.16718 | 0.299959 | ||||||||
\(935\) | 9.27051 | 0.303178 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.7214 | 1.68966 | 0.844832 | − | 0.535032i | \(-0.179701\pi\) | ||||
0.844832 | + | 0.535032i | \(0.179701\pi\) | |||||||
\(938\) | 15.7639 | 0.514711 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −39.2705 | −1.28086 | ||||||||
\(941\) | −40.3050 | −1.31390 | −0.656952 | − | 0.753932i | \(-0.728155\pi\) | ||||
−0.656952 | + | 0.753932i | \(0.728155\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −37.3607 | −1.21663 | ||||||||
\(944\) | 1.85410 | 0.0603459 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0344 | −0.391273 | ||||||||
\(947\) | −25.0344 | −0.813510 | −0.406755 | − | 0.913537i | \(-0.633340\pi\) | ||||
−0.406755 | + | 0.913537i | \(0.633340\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.32624 | −0.172897 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.87539 | 0.320063 | ||||||||
\(953\) | −4.94427 | −0.160161 | −0.0800803 | − | 0.996788i | \(-0.525518\pi\) | ||||
−0.0800803 | + | 0.996788i | \(0.525518\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.7082 | −1.18785 | ||||||||
\(956\) | −2.38197 | −0.0770383 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.21478 | −0.297716 | ||||||||
\(959\) | 29.1459 | 0.941170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 80.5623 | 2.59878 | ||||||||
\(962\) | −0.562306 | −0.0181295 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37.8885 | 1.22031 | ||||||||
\(965\) | 17.8885 | 0.575853 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2705 | 0.491066 | 0.245533 | − | 0.969388i | \(-0.421037\pi\) | ||||
0.245533 | + | 0.969388i | \(0.421037\pi\) | |||||||
\(968\) | −13.4164 | −0.431220 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.14590 | −0.133117 | ||||||||
\(971\) | −46.7984 | −1.50183 | −0.750916 | − | 0.660398i | \(-0.770388\pi\) | ||||
−0.750916 | + | 0.660398i | \(0.770388\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.0213 | −0.898321 | ||||||||
\(974\) | 3.54915 | 0.113722 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.83282 | −0.186704 | ||||||||
\(977\) | 20.8885 | 0.668284 | 0.334142 | − | 0.942523i | \(-0.391554\pi\) | ||||
0.334142 | + | 0.942523i | \(0.391554\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.8541 | −0.986101 | ||||||||
\(980\) | 4.79837 | 0.153278 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.11146 | −0.226936 | ||||||||
\(983\) | 9.40325 | 0.299917 | 0.149959 | − | 0.988692i | \(-0.452086\pi\) | ||||
0.149959 | + | 0.988692i | \(0.452086\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.1803 | 1.47143 | ||||||||
\(986\) | −7.31308 | −0.232896 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 31.1803 | 0.991979 | ||||||||
\(989\) | −40.2148 | −1.27876 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.7426 | 0.754210 | 0.377105 | − | 0.926171i | \(-0.376920\pi\) | ||||
0.377105 | + | 0.926171i | \(0.376920\pi\) | |||||||
\(992\) | 59.3394 | 1.88403 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.6950 | 0.370944 | ||||||||
\(995\) | −37.0344 | −1.17407 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.2148 | 1.68533 | 0.842665 | − | 0.538439i | \(-0.180986\pi\) | ||||
0.842665 | + | 0.538439i | \(0.180986\pi\) | |||||||
\(998\) | 8.90983 | 0.282036 | ||||||||
\(999\) | 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 | 531.2.a.b.1.1 | 2 | ||
3.2 | odd | 2 | 177.2.a.b.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 8496.2.a.bb.1.2 | 2 | |||
12.11 | even | 2 | 2832.2.a.o.1.1 | 2 | |||
15.14 | odd | 2 | 4425.2.a.t.1.1 | 2 | |||
21.20 | even | 2 | 8673.2.a.k.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.2.a.b.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
531.2.a.b.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2832.2.a.o.1.1 | 2 | 12.11 | even | 2 | |||
4425.2.a.t.1.1 | 2 | 15.14 | odd | 2 | |||
8496.2.a.bb.1.2 | 2 | 4.3 | odd | 2 | |||
8673.2.a.k.1.2 | 2 | 21.20 | even | 2 |