Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(4.04841538248\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.445042\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.445042 | −0.314692 | −0.157346 | − | 0.987544i | \(-0.550294\pi\) | ||||
−0.157346 | + | 0.987544i | \(0.550294\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.80194 | −0.900969 | ||||||||
\(5\) | 0.246980 | 0.110453 | 0.0552263 | − | 0.998474i | \(-0.482412\pi\) | ||||
0.0552263 | + | 0.998474i | \(0.482412\pi\) | |||||||
\(6\) | −0.445042 | −0.181688 | ||||||||
\(7\) | −1.75302 | −0.662579 | −0.331290 | − | 0.943529i | \(-0.607484\pi\) | ||||
−0.331290 | + | 0.943529i | \(0.607484\pi\) | |||||||
\(8\) | 1.69202 | 0.598220 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.109916 | −0.0347586 | ||||||||
\(11\) | −5.65279 | −1.70438 | −0.852191 | − | 0.523232i | \(-0.824726\pi\) | ||||
−0.852191 | + | 0.523232i | \(0.824726\pi\) | |||||||
\(12\) | −1.80194 | −0.520175 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.780167 | 0.208509 | ||||||||
\(15\) | 0.246980 | 0.0637699 | ||||||||
\(16\) | 2.85086 | 0.712714 | ||||||||
\(17\) | −3.80194 | −0.922105 | −0.461053 | − | 0.887373i | \(-0.652528\pi\) | ||||
−0.461053 | + | 0.887373i | \(0.652528\pi\) | |||||||
\(18\) | −0.445042 | −0.104897 | ||||||||
\(19\) | −5.58211 | −1.28062 | −0.640311 | − | 0.768115i | \(-0.721195\pi\) | ||||
−0.640311 | + | 0.768115i | \(0.721195\pi\) | |||||||
\(20\) | −0.445042 | −0.0995144 | ||||||||
\(21\) | −1.75302 | −0.382540 | ||||||||
\(22\) | 2.51573 | 0.536355 | ||||||||
\(23\) | 8.34481 | 1.74001 | 0.870007 | − | 0.493039i | \(-0.164114\pi\) | ||||
0.870007 | + | 0.493039i | \(0.164114\pi\) | |||||||
\(24\) | 1.69202 | 0.345382 | ||||||||
\(25\) | −4.93900 | −0.987800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.15883 | 0.596963 | ||||||||
\(29\) | −5.93900 | −1.10284 | −0.551422 | − | 0.834226i | \(-0.685915\pi\) | ||||
−0.551422 | + | 0.834226i | \(0.685915\pi\) | |||||||
\(30\) | −0.109916 | −0.0200679 | ||||||||
\(31\) | −5.26875 | −0.946295 | −0.473148 | − | 0.880983i | \(-0.656882\pi\) | ||||
−0.473148 | + | 0.880983i | \(0.656882\pi\) | |||||||
\(32\) | −4.65279 | −0.822505 | ||||||||
\(33\) | −5.65279 | −0.984025 | ||||||||
\(34\) | 1.69202 | 0.290179 | ||||||||
\(35\) | −0.432960 | −0.0731836 | ||||||||
\(36\) | −1.80194 | −0.300323 | ||||||||
\(37\) | −3.19806 | −0.525758 | −0.262879 | − | 0.964829i | \(-0.584672\pi\) | ||||
−0.262879 | + | 0.964829i | \(0.584672\pi\) | |||||||
\(38\) | 2.48427 | 0.403002 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.417895 | 0.0660750 | ||||||||
\(41\) | −0.445042 | −0.0695039 | −0.0347519 | − | 0.999396i | \(-0.511064\pi\) | ||||
−0.0347519 | + | 0.999396i | \(0.511064\pi\) | |||||||
\(42\) | 0.780167 | 0.120382 | ||||||||
\(43\) | 1.71379 | 0.261351 | 0.130675 | − | 0.991425i | \(-0.458285\pi\) | ||||
0.130675 | + | 0.991425i | \(0.458285\pi\) | |||||||
\(44\) | 10.1860 | 1.53559 | ||||||||
\(45\) | 0.246980 | 0.0368175 | ||||||||
\(46\) | −3.71379 | −0.547569 | ||||||||
\(47\) | 6.73556 | 0.982483 | 0.491241 | − | 0.871024i | \(-0.336543\pi\) | ||||
0.491241 | + | 0.871024i | \(0.336543\pi\) | |||||||
\(48\) | 2.85086 | 0.411485 | ||||||||
\(49\) | −3.92692 | −0.560988 | ||||||||
\(50\) | 2.19806 | 0.310853 | ||||||||
\(51\) | −3.80194 | −0.532378 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.06100 | −0.145739 | −0.0728697 | − | 0.997341i | \(-0.523216\pi\) | ||||
−0.0728697 | + | 0.997341i | \(0.523216\pi\) | |||||||
\(54\) | −0.445042 | −0.0605625 | ||||||||
\(55\) | −1.39612 | −0.188253 | ||||||||
\(56\) | −2.96615 | −0.396368 | ||||||||
\(57\) | −5.58211 | −0.739368 | ||||||||
\(58\) | 2.64310 | 0.347057 | ||||||||
\(59\) | 13.7017 | 1.78381 | 0.891905 | − | 0.452222i | \(-0.149369\pi\) | ||||
0.891905 | + | 0.452222i | \(0.149369\pi\) | |||||||
\(60\) | −0.445042 | −0.0574547 | ||||||||
\(61\) | −8.51573 | −1.09033 | −0.545164 | − | 0.838330i | \(-0.683533\pi\) | ||||
−0.545164 | + | 0.838330i | \(0.683533\pi\) | |||||||
\(62\) | 2.34481 | 0.297792 | ||||||||
\(63\) | −1.75302 | −0.220860 | ||||||||
\(64\) | −3.63102 | −0.453878 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.51573 | 0.309665 | ||||||||
\(67\) | −5.96077 | −0.728224 | −0.364112 | − | 0.931355i | \(-0.618627\pi\) | ||||
−0.364112 | + | 0.931355i | \(0.618627\pi\) | |||||||
\(68\) | 6.85086 | 0.830788 | ||||||||
\(69\) | 8.34481 | 1.00460 | ||||||||
\(70\) | 0.192685 | 0.0230303 | ||||||||
\(71\) | 5.71917 | 0.678740 | 0.339370 | − | 0.940653i | \(-0.389786\pi\) | ||||
0.339370 | + | 0.940653i | \(0.389786\pi\) | |||||||
\(72\) | 1.69202 | 0.199407 | ||||||||
\(73\) | −7.35690 | −0.861060 | −0.430530 | − | 0.902576i | \(-0.641673\pi\) | ||||
−0.430530 | + | 0.902576i | \(0.641673\pi\) | |||||||
\(74\) | 1.42327 | 0.165452 | ||||||||
\(75\) | −4.93900 | −0.570307 | ||||||||
\(76\) | 10.0586 | 1.15380 | ||||||||
\(77\) | 9.90946 | 1.12929 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.45473 | 0.501196 | 0.250598 | − | 0.968091i | \(-0.419373\pi\) | ||||
0.250598 | + | 0.968091i | \(0.419373\pi\) | |||||||
\(80\) | 0.704103 | 0.0787211 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.198062 | 0.0218723 | ||||||||
\(83\) | 10.1860 | 1.11806 | 0.559028 | − | 0.829149i | \(-0.311174\pi\) | ||||
0.559028 | + | 0.829149i | \(0.311174\pi\) | |||||||
\(84\) | 3.15883 | 0.344657 | ||||||||
\(85\) | −0.939001 | −0.101849 | ||||||||
\(86\) | −0.762709 | −0.0822450 | ||||||||
\(87\) | −5.93900 | −0.636728 | ||||||||
\(88\) | −9.56465 | −1.01959 | ||||||||
\(89\) | −0.137063 | −0.0145287 | −0.00726434 | − | 0.999974i | \(-0.502312\pi\) | ||||
−0.00726434 | + | 0.999974i | \(0.502312\pi\) | |||||||
\(90\) | −0.109916 | −0.0115862 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −15.0368 | −1.56770 | ||||||||
\(93\) | −5.26875 | −0.546344 | ||||||||
\(94\) | −2.99761 | −0.309180 | ||||||||
\(95\) | −1.37867 | −0.141448 | ||||||||
\(96\) | −4.65279 | −0.474874 | ||||||||
\(97\) | 13.6896 | 1.38997 | 0.694986 | − | 0.719024i | \(-0.255411\pi\) | ||||
0.694986 | + | 0.719024i | \(0.255411\pi\) | |||||||
\(98\) | 1.74764 | 0.176539 | ||||||||
\(99\) | −5.65279 | −0.568127 | ||||||||
\(100\) | 8.89977 | 0.889977 | ||||||||
\(101\) | −5.41119 | −0.538434 | −0.269217 | − | 0.963080i | \(-0.586765\pi\) | ||||
−0.269217 | + | 0.963080i | \(0.586765\pi\) | |||||||
\(102\) | 1.69202 | 0.167535 | ||||||||
\(103\) | 13.7560 | 1.35542 | 0.677710 | − | 0.735330i | \(-0.262973\pi\) | ||||
0.677710 | + | 0.735330i | \(0.262973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.432960 | −0.0422526 | ||||||||
\(106\) | 0.472189 | 0.0458630 | ||||||||
\(107\) | −12.8170 | −1.23907 | −0.619533 | − | 0.784970i | \(-0.712678\pi\) | ||||
−0.619533 | + | 0.784970i | \(0.712678\pi\) | |||||||
\(108\) | −1.80194 | −0.173392 | ||||||||
\(109\) | −12.1468 | −1.16345 | −0.581724 | − | 0.813386i | \(-0.697622\pi\) | ||||
−0.581724 | + | 0.813386i | \(0.697622\pi\) | |||||||
\(110\) | 0.621334 | 0.0592419 | ||||||||
\(111\) | −3.19806 | −0.303547 | ||||||||
\(112\) | −4.99761 | −0.472229 | ||||||||
\(113\) | −1.63773 | −0.154064 | −0.0770322 | − | 0.997029i | \(-0.524544\pi\) | ||||
−0.0770322 | + | 0.997029i | \(0.524544\pi\) | |||||||
\(114\) | 2.48427 | 0.232673 | ||||||||
\(115\) | 2.06100 | 0.192189 | ||||||||
\(116\) | 10.7017 | 0.993629 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.09783 | −0.561351 | ||||||||
\(119\) | 6.66487 | 0.610968 | ||||||||
\(120\) | 0.417895 | 0.0381484 | ||||||||
\(121\) | 20.9541 | 1.90492 | ||||||||
\(122\) | 3.78986 | 0.343117 | ||||||||
\(123\) | −0.445042 | −0.0401281 | ||||||||
\(124\) | 9.49396 | 0.852583 | ||||||||
\(125\) | −2.45473 | −0.219558 | ||||||||
\(126\) | 0.780167 | 0.0695028 | ||||||||
\(127\) | 10.7995 | 0.958305 | 0.479152 | − | 0.877732i | \(-0.340944\pi\) | ||||
0.479152 | + | 0.877732i | \(0.340944\pi\) | |||||||
\(128\) | 10.9215 | 0.965337 | ||||||||
\(129\) | 1.71379 | 0.150891 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.907542 | 0.0792923 | 0.0396462 | − | 0.999214i | \(-0.487377\pi\) | ||||
0.0396462 | + | 0.999214i | \(0.487377\pi\) | |||||||
\(132\) | 10.1860 | 0.886576 | ||||||||
\(133\) | 9.78554 | 0.848514 | ||||||||
\(134\) | 2.65279 | 0.229166 | ||||||||
\(135\) | 0.246980 | 0.0212566 | ||||||||
\(136\) | −6.43296 | −0.551622 | ||||||||
\(137\) | 9.54825 | 0.815762 | 0.407881 | − | 0.913035i | \(-0.366268\pi\) | ||||
0.407881 | + | 0.913035i | \(0.366268\pi\) | |||||||
\(138\) | −3.71379 | −0.316139 | ||||||||
\(139\) | −4.09246 | −0.347118 | −0.173559 | − | 0.984823i | \(-0.555527\pi\) | ||||
−0.173559 | + | 0.984823i | \(0.555527\pi\) | |||||||
\(140\) | 0.780167 | 0.0659362 | ||||||||
\(141\) | 6.73556 | 0.567237 | ||||||||
\(142\) | −2.54527 | −0.213594 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.85086 | 0.237571 | ||||||||
\(145\) | −1.46681 | −0.121812 | ||||||||
\(146\) | 3.27413 | 0.270969 | ||||||||
\(147\) | −3.92692 | −0.323887 | ||||||||
\(148\) | 5.76271 | 0.473692 | ||||||||
\(149\) | 15.3884 | 1.26066 | 0.630332 | − | 0.776326i | \(-0.282919\pi\) | ||||
0.630332 | + | 0.776326i | \(0.282919\pi\) | |||||||
\(150\) | 2.19806 | 0.179471 | ||||||||
\(151\) | 3.67456 | 0.299032 | 0.149516 | − | 0.988759i | \(-0.452228\pi\) | ||||
0.149516 | + | 0.988759i | \(0.452228\pi\) | |||||||
\(152\) | −9.44504 | −0.766094 | ||||||||
\(153\) | −3.80194 | −0.307368 | ||||||||
\(154\) | −4.41013 | −0.355378 | ||||||||
\(155\) | −1.30127 | −0.104521 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.87800 | −0.389307 | −0.194653 | − | 0.980872i | \(-0.562358\pi\) | ||||
−0.194653 | + | 0.980872i | \(0.562358\pi\) | |||||||
\(158\) | −1.98254 | −0.157723 | ||||||||
\(159\) | −1.06100 | −0.0841427 | ||||||||
\(160\) | −1.14914 | −0.0908479 | ||||||||
\(161\) | −14.6286 | −1.15290 | ||||||||
\(162\) | −0.445042 | −0.0349658 | ||||||||
\(163\) | −8.63102 | −0.676034 | −0.338017 | − | 0.941140i | \(-0.609756\pi\) | ||||
−0.338017 | + | 0.941140i | \(0.609756\pi\) | |||||||
\(164\) | 0.801938 | 0.0626208 | ||||||||
\(165\) | −1.39612 | −0.108688 | ||||||||
\(166\) | −4.53319 | −0.351844 | ||||||||
\(167\) | −9.46980 | −0.732795 | −0.366397 | − | 0.930458i | \(-0.619409\pi\) | ||||
−0.366397 | + | 0.930458i | \(0.619409\pi\) | |||||||
\(168\) | −2.96615 | −0.228843 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.417895 | 0.0320511 | ||||||||
\(171\) | −5.58211 | −0.426874 | ||||||||
\(172\) | −3.08815 | −0.235469 | ||||||||
\(173\) | 4.77479 | 0.363021 | 0.181510 | − | 0.983389i | \(-0.441901\pi\) | ||||
0.181510 | + | 0.983389i | \(0.441901\pi\) | |||||||
\(174\) | 2.64310 | 0.200373 | ||||||||
\(175\) | 8.65817 | 0.654496 | ||||||||
\(176\) | −16.1153 | −1.21474 | ||||||||
\(177\) | 13.7017 | 1.02988 | ||||||||
\(178\) | 0.0609989 | 0.00457206 | ||||||||
\(179\) | 3.43535 | 0.256770 | 0.128385 | − | 0.991724i | \(-0.459021\pi\) | ||||
0.128385 | + | 0.991724i | \(0.459021\pi\) | |||||||
\(180\) | −0.445042 | −0.0331715 | ||||||||
\(181\) | −13.4862 | −1.00242 | −0.501210 | − | 0.865326i | \(-0.667112\pi\) | ||||
−0.501210 | + | 0.865326i | \(0.667112\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.51573 | −0.629501 | ||||||||
\(184\) | 14.1196 | 1.04091 | ||||||||
\(185\) | −0.789856 | −0.0580714 | ||||||||
\(186\) | 2.34481 | 0.171930 | ||||||||
\(187\) | 21.4916 | 1.57162 | ||||||||
\(188\) | −12.1371 | −0.885186 | ||||||||
\(189\) | −1.75302 | −0.127513 | ||||||||
\(190\) | 0.613564 | 0.0445126 | ||||||||
\(191\) | −1.30127 | −0.0941569 | −0.0470784 | − | 0.998891i | \(-0.514991\pi\) | ||||
−0.0470784 | + | 0.998891i | \(0.514991\pi\) | |||||||
\(192\) | −3.63102 | −0.262046 | ||||||||
\(193\) | 9.19567 | 0.661919 | 0.330959 | − | 0.943645i | \(-0.392628\pi\) | ||||
0.330959 | + | 0.943645i | \(0.392628\pi\) | |||||||
\(194\) | −6.09246 | −0.437413 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.07606 | 0.505433 | ||||||||
\(197\) | −4.11231 | −0.292990 | −0.146495 | − | 0.989211i | \(-0.546799\pi\) | ||||
−0.146495 | + | 0.989211i | \(0.546799\pi\) | |||||||
\(198\) | 2.51573 | 0.178785 | ||||||||
\(199\) | −24.7724 | −1.75607 | −0.878034 | − | 0.478598i | \(-0.841145\pi\) | ||||
−0.878034 | + | 0.478598i | \(0.841145\pi\) | |||||||
\(200\) | −8.35690 | −0.590922 | ||||||||
\(201\) | −5.96077 | −0.420440 | ||||||||
\(202\) | 2.40821 | 0.169441 | ||||||||
\(203\) | 10.4112 | 0.730722 | ||||||||
\(204\) | 6.85086 | 0.479656 | ||||||||
\(205\) | −0.109916 | −0.00767688 | ||||||||
\(206\) | −6.12200 | −0.426540 | ||||||||
\(207\) | 8.34481 | 0.580005 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 31.5545 | 2.18267 | ||||||||
\(210\) | 0.192685 | 0.0132966 | ||||||||
\(211\) | −5.93900 | −0.408858 | −0.204429 | − | 0.978881i | \(-0.565534\pi\) | ||||
−0.204429 | + | 0.978881i | \(0.565534\pi\) | |||||||
\(212\) | 1.91185 | 0.131307 | ||||||||
\(213\) | 5.71917 | 0.391871 | ||||||||
\(214\) | 5.70410 | 0.389924 | ||||||||
\(215\) | 0.423272 | 0.0288669 | ||||||||
\(216\) | 1.69202 | 0.115127 | ||||||||
\(217\) | 9.23623 | 0.626996 | ||||||||
\(218\) | 5.40581 | 0.366128 | ||||||||
\(219\) | −7.35690 | −0.497133 | ||||||||
\(220\) | 2.51573 | 0.169610 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.42327 | 0.0955237 | ||||||||
\(223\) | −14.2010 | −0.950972 | −0.475486 | − | 0.879723i | \(-0.657728\pi\) | ||||
−0.475486 | + | 0.879723i | \(0.657728\pi\) | |||||||
\(224\) | 8.15644 | 0.544975 | ||||||||
\(225\) | −4.93900 | −0.329267 | ||||||||
\(226\) | 0.728857 | 0.0484829 | ||||||||
\(227\) | −16.0073 | −1.06244 | −0.531221 | − | 0.847233i | \(-0.678267\pi\) | ||||
−0.531221 | + | 0.847233i | \(0.678267\pi\) | |||||||
\(228\) | 10.0586 | 0.666147 | ||||||||
\(229\) | −1.84117 | −0.121668 | −0.0608339 | − | 0.998148i | \(-0.519376\pi\) | ||||
−0.0608339 | + | 0.998148i | \(0.519376\pi\) | |||||||
\(230\) | −0.917231 | −0.0604804 | ||||||||
\(231\) | 9.90946 | 0.651995 | ||||||||
\(232\) | −10.0489 | −0.659744 | ||||||||
\(233\) | −23.4252 | −1.53464 | −0.767318 | − | 0.641267i | \(-0.778409\pi\) | ||||
−0.767318 | + | 0.641267i | \(0.778409\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.66355 | 0.108518 | ||||||||
\(236\) | −24.6896 | −1.60716 | ||||||||
\(237\) | 4.45473 | 0.289366 | ||||||||
\(238\) | −2.96615 | −0.192267 | ||||||||
\(239\) | −14.6015 | −0.944491 | −0.472246 | − | 0.881467i | \(-0.656556\pi\) | ||||
−0.472246 | + | 0.881467i | \(0.656556\pi\) | |||||||
\(240\) | 0.704103 | 0.0454497 | ||||||||
\(241\) | −8.63102 | −0.555973 | −0.277987 | − | 0.960585i | \(-0.589667\pi\) | ||||
−0.277987 | + | 0.960585i | \(0.589667\pi\) | |||||||
\(242\) | −9.32544 | −0.599462 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 15.3448 | 0.982351 | ||||||||
\(245\) | −0.969869 | −0.0619627 | ||||||||
\(246\) | 0.198062 | 0.0126280 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8.91484 | −0.566093 | ||||||||
\(249\) | 10.1860 | 0.645510 | ||||||||
\(250\) | 1.09246 | 0.0690931 | ||||||||
\(251\) | −3.80194 | −0.239976 | −0.119988 | − | 0.992775i | \(-0.538286\pi\) | ||||
−0.119988 | + | 0.992775i | \(0.538286\pi\) | |||||||
\(252\) | 3.15883 | 0.198988 | ||||||||
\(253\) | −47.1715 | −2.96565 | ||||||||
\(254\) | −4.80625 | −0.301571 | ||||||||
\(255\) | −0.939001 | −0.0588025 | ||||||||
\(256\) | 2.40150 | 0.150094 | ||||||||
\(257\) | −20.5961 | −1.28475 | −0.642375 | − | 0.766391i | \(-0.722051\pi\) | ||||
−0.642375 | + | 0.766391i | \(0.722051\pi\) | |||||||
\(258\) | −0.762709 | −0.0474842 | ||||||||
\(259\) | 5.60627 | 0.348357 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.93900 | −0.367615 | ||||||||
\(262\) | −0.403894 | −0.0249527 | ||||||||
\(263\) | 0.332733 | 0.0205172 | 0.0102586 | − | 0.999947i | \(-0.496735\pi\) | ||||
0.0102586 | + | 0.999947i | \(0.496735\pi\) | |||||||
\(264\) | −9.56465 | −0.588663 | ||||||||
\(265\) | −0.262045 | −0.0160973 | ||||||||
\(266\) | −4.35498 | −0.267021 | ||||||||
\(267\) | −0.137063 | −0.00838814 | ||||||||
\(268\) | 10.7409 | 0.656107 | ||||||||
\(269\) | 27.3032 | 1.66471 | 0.832353 | − | 0.554247i | \(-0.186994\pi\) | ||||
0.832353 | + | 0.554247i | \(0.186994\pi\) | |||||||
\(270\) | −0.109916 | −0.00668929 | ||||||||
\(271\) | −27.9855 | −1.70000 | −0.850000 | − | 0.526783i | \(-0.823398\pi\) | ||||
−0.850000 | + | 0.526783i | \(0.823398\pi\) | |||||||
\(272\) | −10.8388 | −0.657197 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.24937 | −0.256714 | ||||||||
\(275\) | 27.9191 | 1.68359 | ||||||||
\(276\) | −15.0368 | −0.905111 | ||||||||
\(277\) | −2.10321 | −0.126370 | −0.0631849 | − | 0.998002i | \(-0.520126\pi\) | ||||
−0.0631849 | + | 0.998002i | \(0.520126\pi\) | |||||||
\(278\) | 1.82132 | 0.109235 | ||||||||
\(279\) | −5.26875 | −0.315432 | ||||||||
\(280\) | −0.732578 | −0.0437799 | ||||||||
\(281\) | −27.2349 | −1.62470 | −0.812349 | − | 0.583172i | \(-0.801811\pi\) | ||||
−0.812349 | + | 0.583172i | \(0.801811\pi\) | |||||||
\(282\) | −2.99761 | −0.178505 | ||||||||
\(283\) | 5.28382 | 0.314090 | 0.157045 | − | 0.987591i | \(-0.449803\pi\) | ||||
0.157045 | + | 0.987591i | \(0.449803\pi\) | |||||||
\(284\) | −10.3056 | −0.611524 | ||||||||
\(285\) | −1.37867 | −0.0816651 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.780167 | 0.0460518 | ||||||||
\(288\) | −4.65279 | −0.274168 | ||||||||
\(289\) | −2.54527 | −0.149722 | ||||||||
\(290\) | 0.652793 | 0.0383333 | ||||||||
\(291\) | 13.6896 | 0.802500 | ||||||||
\(292\) | 13.2567 | 0.775788 | ||||||||
\(293\) | −32.6625 | −1.90816 | −0.954081 | − | 0.299548i | \(-0.903164\pi\) | ||||
−0.954081 | + | 0.299548i | \(0.903164\pi\) | |||||||
\(294\) | 1.74764 | 0.101925 | ||||||||
\(295\) | 3.38404 | 0.197027 | ||||||||
\(296\) | −5.41119 | −0.314519 | ||||||||
\(297\) | −5.65279 | −0.328008 | ||||||||
\(298\) | −6.84846 | −0.396721 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 8.89977 | 0.513829 | ||||||||
\(301\) | −3.00431 | −0.173166 | ||||||||
\(302\) | −1.63533 | −0.0941029 | ||||||||
\(303\) | −5.41119 | −0.310865 | ||||||||
\(304\) | −15.9138 | −0.912717 | ||||||||
\(305\) | −2.10321 | −0.120430 | ||||||||
\(306\) | 1.69202 | 0.0967264 | ||||||||
\(307\) | 20.7614 | 1.18491 | 0.592457 | − | 0.805602i | \(-0.298158\pi\) | ||||
0.592457 | + | 0.805602i | \(0.298158\pi\) | |||||||
\(308\) | −17.8562 | −1.01745 | ||||||||
\(309\) | 13.7560 | 0.782552 | ||||||||
\(310\) | 0.579121 | 0.0328919 | ||||||||
\(311\) | −11.3013 | −0.640836 | −0.320418 | − | 0.947276i | \(-0.603823\pi\) | ||||
−0.320418 | + | 0.947276i | \(0.603823\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.27173 | −0.241453 | −0.120726 | − | 0.992686i | \(-0.538522\pi\) | ||||
−0.120726 | + | 0.992686i | \(0.538522\pi\) | |||||||
\(314\) | 2.17092 | 0.122512 | ||||||||
\(315\) | −0.432960 | −0.0243945 | ||||||||
\(316\) | −8.02715 | −0.451562 | ||||||||
\(317\) | −15.4776 | −0.869307 | −0.434653 | − | 0.900598i | \(-0.643129\pi\) | ||||
−0.434653 | + | 0.900598i | \(0.643129\pi\) | |||||||
\(318\) | 0.472189 | 0.0264790 | ||||||||
\(319\) | 33.5719 | 1.87967 | ||||||||
\(320\) | −0.896789 | −0.0501320 | ||||||||
\(321\) | −12.8170 | −0.715375 | ||||||||
\(322\) | 6.51035 | 0.362808 | ||||||||
\(323\) | 21.2228 | 1.18087 | ||||||||
\(324\) | −1.80194 | −0.100108 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.84117 | 0.212743 | ||||||||
\(327\) | −12.1468 | −0.671717 | ||||||||
\(328\) | −0.753020 | −0.0415786 | ||||||||
\(329\) | −11.8076 | −0.650973 | ||||||||
\(330\) | 0.621334 | 0.0342033 | ||||||||
\(331\) | −6.06829 | −0.333544 | −0.166772 | − | 0.985996i | \(-0.553334\pi\) | ||||
−0.166772 | + | 0.985996i | \(0.553334\pi\) | |||||||
\(332\) | −18.3545 | −1.00733 | ||||||||
\(333\) | −3.19806 | −0.175253 | ||||||||
\(334\) | 4.21446 | 0.230605 | ||||||||
\(335\) | −1.47219 | −0.0804343 | ||||||||
\(336\) | −4.99761 | −0.272642 | ||||||||
\(337\) | 12.1239 | 0.660432 | 0.330216 | − | 0.943905i | \(-0.392878\pi\) | ||||
0.330216 | + | 0.943905i | \(0.392878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.63773 | −0.0889491 | ||||||||
\(340\) | 1.69202 | 0.0917627 | ||||||||
\(341\) | 29.7832 | 1.61285 | ||||||||
\(342\) | 2.48427 | 0.134334 | ||||||||
\(343\) | 19.1551 | 1.03428 | ||||||||
\(344\) | 2.89977 | 0.156345 | ||||||||
\(345\) | 2.06100 | 0.110960 | ||||||||
\(346\) | −2.12498 | −0.114240 | ||||||||
\(347\) | 23.1497 | 1.24274 | 0.621371 | − | 0.783516i | \(-0.286576\pi\) | ||||
0.621371 | + | 0.783516i | \(0.286576\pi\) | |||||||
\(348\) | 10.7017 | 0.573672 | ||||||||
\(349\) | 22.1957 | 1.18811 | 0.594053 | − | 0.804426i | \(-0.297527\pi\) | ||||
0.594053 | + | 0.804426i | \(0.297527\pi\) | |||||||
\(350\) | −3.85325 | −0.205965 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.3013 | 1.40186 | ||||||||
\(353\) | 5.07069 | 0.269885 | 0.134943 | − | 0.990853i | \(-0.456915\pi\) | ||||
0.134943 | + | 0.990853i | \(0.456915\pi\) | |||||||
\(354\) | −6.09783 | −0.324096 | ||||||||
\(355\) | 1.41252 | 0.0749687 | ||||||||
\(356\) | 0.246980 | 0.0130899 | ||||||||
\(357\) | 6.66487 | 0.352743 | ||||||||
\(358\) | −1.52888 | −0.0808036 | ||||||||
\(359\) | 16.6746 | 0.880050 | 0.440025 | − | 0.897986i | \(-0.354970\pi\) | ||||
0.440025 | + | 0.897986i | \(0.354970\pi\) | |||||||
\(360\) | 0.417895 | 0.0220250 | ||||||||
\(361\) | 12.1599 | 0.639995 | ||||||||
\(362\) | 6.00192 | 0.315454 | ||||||||
\(363\) | 20.9541 | 1.09980 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.81700 | −0.0951063 | ||||||||
\(366\) | 3.78986 | 0.198099 | ||||||||
\(367\) | −1.17928 | −0.0615577 | −0.0307789 | − | 0.999526i | \(-0.509799\pi\) | ||||
−0.0307789 | + | 0.999526i | \(0.509799\pi\) | |||||||
\(368\) | 23.7899 | 1.24013 | ||||||||
\(369\) | −0.445042 | −0.0231680 | ||||||||
\(370\) | 0.351519 | 0.0182746 | ||||||||
\(371\) | 1.85995 | 0.0965639 | ||||||||
\(372\) | 9.49396 | 0.492239 | ||||||||
\(373\) | −30.0925 | −1.55813 | −0.779064 | − | 0.626944i | \(-0.784305\pi\) | ||||
−0.779064 | + | 0.626944i | \(0.784305\pi\) | |||||||
\(374\) | −9.56465 | −0.494576 | ||||||||
\(375\) | −2.45473 | −0.126762 | ||||||||
\(376\) | 11.3967 | 0.587741 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.780167 | 0.0401275 | ||||||||
\(379\) | 19.1631 | 0.984345 | 0.492172 | − | 0.870498i | \(-0.336203\pi\) | ||||
0.492172 | + | 0.870498i | \(0.336203\pi\) | |||||||
\(380\) | 2.48427 | 0.127440 | ||||||||
\(381\) | 10.7995 | 0.553277 | ||||||||
\(382\) | 0.579121 | 0.0296304 | ||||||||
\(383\) | 15.3884 | 0.786308 | 0.393154 | − | 0.919473i | \(-0.371384\pi\) | ||||
0.393154 | + | 0.919473i | \(0.371384\pi\) | |||||||
\(384\) | 10.9215 | 0.557338 | ||||||||
\(385\) | 2.44743 | 0.124733 | ||||||||
\(386\) | −4.09246 | −0.208301 | ||||||||
\(387\) | 1.71379 | 0.0871169 | ||||||||
\(388\) | −24.6679 | −1.25232 | ||||||||
\(389\) | −24.0315 | −1.21844 | −0.609222 | − | 0.793000i | \(-0.708518\pi\) | ||||
−0.609222 | + | 0.793000i | \(0.708518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.7265 | −1.60448 | ||||||||
\(392\) | −6.64443 | −0.335594 | ||||||||
\(393\) | 0.907542 | 0.0457794 | ||||||||
\(394\) | 1.83015 | 0.0922016 | ||||||||
\(395\) | 1.10023 | 0.0553585 | ||||||||
\(396\) | 10.1860 | 0.511865 | ||||||||
\(397\) | −29.6015 | −1.48566 | −0.742828 | − | 0.669482i | \(-0.766516\pi\) | ||||
−0.742828 | + | 0.669482i | \(0.766516\pi\) | |||||||
\(398\) | 11.0248 | 0.552621 | ||||||||
\(399\) | 9.78554 | 0.489890 | ||||||||
\(400\) | −14.0804 | −0.704019 | ||||||||
\(401\) | 21.1032 | 1.05384 | 0.526922 | − | 0.849914i | \(-0.323346\pi\) | ||||
0.526922 | + | 0.849914i | \(0.323346\pi\) | |||||||
\(402\) | 2.65279 | 0.132309 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 9.75063 | 0.485112 | ||||||||
\(405\) | 0.246980 | 0.0122725 | ||||||||
\(406\) | −4.63342 | −0.229953 | ||||||||
\(407\) | 18.0780 | 0.896092 | ||||||||
\(408\) | −6.43296 | −0.318479 | ||||||||
\(409\) | 36.0224 | 1.78119 | 0.890596 | − | 0.454796i | \(-0.150288\pi\) | ||||
0.890596 | + | 0.454796i | \(0.150288\pi\) | |||||||
\(410\) | 0.0489173 | 0.00241586 | ||||||||
\(411\) | 9.54825 | 0.470981 | ||||||||
\(412\) | −24.7875 | −1.22119 | ||||||||
\(413\) | −24.0194 | −1.18192 | ||||||||
\(414\) | −3.71379 | −0.182523 | ||||||||
\(415\) | 2.51573 | 0.123492 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.09246 | −0.200409 | ||||||||
\(418\) | −14.0431 | −0.686869 | ||||||||
\(419\) | 5.96854 | 0.291582 | 0.145791 | − | 0.989315i | \(-0.453427\pi\) | ||||
0.145791 | + | 0.989315i | \(0.453427\pi\) | |||||||
\(420\) | 0.780167 | 0.0380683 | ||||||||
\(421\) | 2.09544 | 0.102126 | 0.0510628 | − | 0.998695i | \(-0.483739\pi\) | ||||
0.0510628 | + | 0.998695i | \(0.483739\pi\) | |||||||
\(422\) | 2.64310 | 0.128664 | ||||||||
\(423\) | 6.73556 | 0.327494 | ||||||||
\(424\) | −1.79523 | −0.0871842 | ||||||||
\(425\) | 18.7778 | 0.910856 | ||||||||
\(426\) | −2.54527 | −0.123319 | ||||||||
\(427\) | 14.9282 | 0.722429 | ||||||||
\(428\) | 23.0954 | 1.11636 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.188374 | −0.00908418 | ||||||||
\(431\) | 2.88577 | 0.139003 | 0.0695014 | − | 0.997582i | \(-0.477859\pi\) | ||||
0.0695014 | + | 0.997582i | \(0.477859\pi\) | |||||||
\(432\) | 2.85086 | 0.137162 | ||||||||
\(433\) | −12.6485 | −0.607847 | −0.303924 | − | 0.952696i | \(-0.598297\pi\) | ||||
−0.303924 | + | 0.952696i | \(0.598297\pi\) | |||||||
\(434\) | −4.11051 | −0.197311 | ||||||||
\(435\) | −1.46681 | −0.0703283 | ||||||||
\(436\) | 21.8877 | 1.04823 | ||||||||
\(437\) | −46.5816 | −2.22830 | ||||||||
\(438\) | 3.27413 | 0.156444 | ||||||||
\(439\) | −10.9269 | −0.521513 | −0.260757 | − | 0.965405i | \(-0.583972\pi\) | ||||
−0.260757 | + | 0.965405i | \(0.583972\pi\) | |||||||
\(440\) | −2.36227 | −0.112617 | ||||||||
\(441\) | −3.92692 | −0.186996 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.2403 | −0.914133 | −0.457067 | − | 0.889433i | \(-0.651100\pi\) | ||||
−0.457067 | + | 0.889433i | \(0.651100\pi\) | |||||||
\(444\) | 5.76271 | 0.273486 | ||||||||
\(445\) | −0.0338518 | −0.00160473 | ||||||||
\(446\) | 6.32006 | 0.299264 | ||||||||
\(447\) | 15.3884 | 0.727844 | ||||||||
\(448\) | 6.36526 | 0.300730 | ||||||||
\(449\) | 28.8200 | 1.36010 | 0.680050 | − | 0.733166i | \(-0.261958\pi\) | ||||
0.680050 | + | 0.733166i | \(0.261958\pi\) | |||||||
\(450\) | 2.19806 | 0.103618 | ||||||||
\(451\) | 2.51573 | 0.118461 | ||||||||
\(452\) | 2.95108 | 0.138807 | ||||||||
\(453\) | 3.67456 | 0.172646 | ||||||||
\(454\) | 7.12392 | 0.334342 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.44504 | −0.442305 | ||||||||
\(457\) | 18.0707 | 0.845311 | 0.422656 | − | 0.906290i | \(-0.361098\pi\) | ||||
0.422656 | + | 0.906290i | \(0.361098\pi\) | |||||||
\(458\) | 0.819396 | 0.0382879 | ||||||||
\(459\) | −3.80194 | −0.177459 | ||||||||
\(460\) | −3.71379 | −0.173156 | ||||||||
\(461\) | 7.56763 | 0.352460 | 0.176230 | − | 0.984349i | \(-0.443610\pi\) | ||||
0.176230 | + | 0.984349i | \(0.443610\pi\) | |||||||
\(462\) | −4.41013 | −0.205178 | ||||||||
\(463\) | −35.3551 | −1.64309 | −0.821545 | − | 0.570143i | \(-0.806888\pi\) | ||||
−0.821545 | + | 0.570143i | \(0.806888\pi\) | |||||||
\(464\) | −16.9312 | −0.786013 | ||||||||
\(465\) | −1.30127 | −0.0603451 | ||||||||
\(466\) | 10.4252 | 0.482938 | ||||||||
\(467\) | 13.0000 | 0.601568 | 0.300784 | − | 0.953692i | \(-0.402752\pi\) | ||||
0.300784 | + | 0.953692i | \(0.402752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4494 | 0.482506 | ||||||||
\(470\) | −0.740348 | −0.0341497 | ||||||||
\(471\) | −4.87800 | −0.224766 | ||||||||
\(472\) | 23.1836 | 1.06711 | ||||||||
\(473\) | −9.68771 | −0.445441 | ||||||||
\(474\) | −1.98254 | −0.0910612 | ||||||||
\(475\) | 27.5700 | 1.26500 | ||||||||
\(476\) | −12.0097 | −0.550463 | ||||||||
\(477\) | −1.06100 | −0.0485798 | ||||||||
\(478\) | 6.49827 | 0.297224 | ||||||||
\(479\) | 25.5265 | 1.16633 | 0.583167 | − | 0.812352i | \(-0.301813\pi\) | ||||
0.583167 | + | 0.812352i | \(0.301813\pi\) | |||||||
\(480\) | −1.14914 | −0.0524510 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.84117 | 0.174960 | ||||||||
\(483\) | −14.6286 | −0.665626 | ||||||||
\(484\) | −37.7579 | −1.71627 | ||||||||
\(485\) | 3.38106 | 0.153526 | ||||||||
\(486\) | −0.445042 | −0.0201875 | ||||||||
\(487\) | −16.0073 | −0.725360 | −0.362680 | − | 0.931914i | \(-0.618138\pi\) | ||||
−0.362680 | + | 0.931914i | \(0.618138\pi\) | |||||||
\(488\) | −14.4088 | −0.652256 | ||||||||
\(489\) | −8.63102 | −0.390308 | ||||||||
\(490\) | 0.431632 | 0.0194992 | ||||||||
\(491\) | 20.7385 | 0.935917 | 0.467959 | − | 0.883750i | \(-0.344990\pi\) | ||||
0.467959 | + | 0.883750i | \(0.344990\pi\) | |||||||
\(492\) | 0.801938 | 0.0361541 | ||||||||
\(493\) | 22.5797 | 1.01694 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.39612 | −0.0627511 | ||||||||
\(496\) | −15.0204 | −0.674438 | ||||||||
\(497\) | −10.0258 | −0.449719 | ||||||||
\(498\) | −4.53319 | −0.203137 | ||||||||
\(499\) | 8.06770 | 0.361160 | 0.180580 | − | 0.983560i | \(-0.442203\pi\) | ||||
0.180580 | + | 0.983560i | \(0.442203\pi\) | |||||||
\(500\) | 4.42327 | 0.197815 | ||||||||
\(501\) | −9.46980 | −0.423079 | ||||||||
\(502\) | 1.69202 | 0.0755186 | ||||||||
\(503\) | −30.2422 | −1.34843 | −0.674216 | − | 0.738534i | \(-0.735518\pi\) | ||||
−0.674216 | + | 0.738534i | \(0.735518\pi\) | |||||||
\(504\) | −2.96615 | −0.132123 | ||||||||
\(505\) | −1.33645 | −0.0594714 | ||||||||
\(506\) | 20.9933 | 0.933266 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −19.4601 | −0.863403 | ||||||||
\(509\) | −16.0495 | −0.711382 | −0.355691 | − | 0.934604i | \(-0.615754\pi\) | ||||
−0.355691 | + | 0.934604i | \(0.615754\pi\) | |||||||
\(510\) | 0.417895 | 0.0185047 | ||||||||
\(511\) | 12.8968 | 0.570520 | ||||||||
\(512\) | −22.9119 | −1.01257 | ||||||||
\(513\) | −5.58211 | −0.246456 | ||||||||
\(514\) | 9.16613 | 0.404301 | ||||||||
\(515\) | 3.39745 | 0.149710 | ||||||||
\(516\) | −3.08815 | −0.135948 | ||||||||
\(517\) | −38.0747 | −1.67452 | ||||||||
\(518\) | −2.49502 | −0.109625 | ||||||||
\(519\) | 4.77479 | 0.209590 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.69309 | −0.117986 | −0.0589931 | − | 0.998258i | \(-0.518789\pi\) | ||||
−0.0589931 | + | 0.998258i | \(0.518789\pi\) | |||||||
\(522\) | 2.64310 | 0.115686 | ||||||||
\(523\) | 35.3957 | 1.54774 | 0.773872 | − | 0.633342i | \(-0.218317\pi\) | ||||
0.773872 | + | 0.633342i | \(0.218317\pi\) | |||||||
\(524\) | −1.63533 | −0.0714399 | ||||||||
\(525\) | 8.65817 | 0.377874 | ||||||||
\(526\) | −0.148080 | −0.00645659 | ||||||||
\(527\) | 20.0315 | 0.872584 | ||||||||
\(528\) | −16.1153 | −0.701328 | ||||||||
\(529\) | 46.6359 | 2.02765 | ||||||||
\(530\) | 0.116621 | 0.00506569 | ||||||||
\(531\) | 13.7017 | 0.594604 | ||||||||
\(532\) | −17.6329 | −0.764485 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.0609989 | 0.00263968 | ||||||||
\(535\) | −3.16554 | −0.136858 | ||||||||
\(536\) | −10.0858 | −0.435638 | ||||||||
\(537\) | 3.43535 | 0.148246 | ||||||||
\(538\) | −12.1511 | −0.523870 | ||||||||
\(539\) | 22.1981 | 0.956138 | ||||||||
\(540\) | −0.445042 | −0.0191516 | ||||||||
\(541\) | 34.7338 | 1.49332 | 0.746660 | − | 0.665205i | \(-0.231656\pi\) | ||||
0.746660 | + | 0.665205i | \(0.231656\pi\) | |||||||
\(542\) | 12.4547 | 0.534976 | ||||||||
\(543\) | −13.4862 | −0.578748 | ||||||||
\(544\) | 17.6896 | 0.758437 | ||||||||
\(545\) | −3.00000 | −0.128506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.1183 | −1.11674 | −0.558368 | − | 0.829593i | \(-0.688572\pi\) | ||||
−0.558368 | + | 0.829593i | \(0.688572\pi\) | |||||||
\(548\) | −17.2054 | −0.734976 | ||||||||
\(549\) | −8.51573 | −0.363442 | ||||||||
\(550\) | −12.4252 | −0.529812 | ||||||||
\(551\) | 33.1521 | 1.41233 | ||||||||
\(552\) | 14.1196 | 0.600970 | ||||||||
\(553\) | −7.80923 | −0.332082 | ||||||||
\(554\) | 0.936017 | 0.0397676 | ||||||||
\(555\) | −0.789856 | −0.0335275 | ||||||||
\(556\) | 7.37435 | 0.312742 | ||||||||
\(557\) | −24.7748 | −1.04974 | −0.524871 | − | 0.851182i | \(-0.675886\pi\) | ||||
−0.524871 | + | 0.851182i | \(0.675886\pi\) | |||||||
\(558\) | 2.34481 | 0.0992639 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.23431 | −0.0521590 | ||||||||
\(561\) | 21.4916 | 0.907375 | ||||||||
\(562\) | 12.1207 | 0.511280 | ||||||||
\(563\) | 5.26098 | 0.221724 | 0.110862 | − | 0.993836i | \(-0.464639\pi\) | ||||
0.110862 | + | 0.993836i | \(0.464639\pi\) | |||||||
\(564\) | −12.1371 | −0.511063 | ||||||||
\(565\) | −0.404485 | −0.0170168 | ||||||||
\(566\) | −2.35152 | −0.0988417 | ||||||||
\(567\) | −1.75302 | −0.0736199 | ||||||||
\(568\) | 9.67696 | 0.406036 | ||||||||
\(569\) | −33.7458 | −1.41470 | −0.707350 | − | 0.706864i | \(-0.750109\pi\) | ||||
−0.707350 | + | 0.706864i | \(0.750109\pi\) | |||||||
\(570\) | 0.613564 | 0.0256994 | ||||||||
\(571\) | 23.0887 | 0.966234 | 0.483117 | − | 0.875556i | \(-0.339505\pi\) | ||||
0.483117 | + | 0.875556i | \(0.339505\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.30127 | −0.0543615 | ||||||||
\(574\) | −0.347207 | −0.0144921 | ||||||||
\(575\) | −41.2150 | −1.71879 | ||||||||
\(576\) | −3.63102 | −0.151293 | ||||||||
\(577\) | −3.57002 | −0.148622 | −0.0743110 | − | 0.997235i | \(-0.523676\pi\) | ||||
−0.0743110 | + | 0.997235i | \(0.523676\pi\) | |||||||
\(578\) | 1.13275 | 0.0471162 | ||||||||
\(579\) | 9.19567 | 0.382159 | ||||||||
\(580\) | 2.64310 | 0.109749 | ||||||||
\(581\) | −17.8562 | −0.740801 | ||||||||
\(582\) | −6.09246 | −0.252541 | ||||||||
\(583\) | 5.99761 | 0.248396 | ||||||||
\(584\) | −12.4480 | −0.515103 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.5362 | 0.600484 | ||||||||
\(587\) | 11.4625 | 0.473108 | 0.236554 | − | 0.971618i | \(-0.423982\pi\) | ||||
0.236554 | + | 0.971618i | \(0.423982\pi\) | |||||||
\(588\) | 7.07606 | 0.291812 | ||||||||
\(589\) | 29.4107 | 1.21185 | ||||||||
\(590\) | −1.50604 | −0.0620027 | ||||||||
\(591\) | −4.11231 | −0.169158 | ||||||||
\(592\) | −9.11721 | −0.374715 | ||||||||
\(593\) | 21.8538 | 0.897430 | 0.448715 | − | 0.893675i | \(-0.351882\pi\) | ||||
0.448715 | + | 0.893675i | \(0.351882\pi\) | |||||||
\(594\) | 2.51573 | 0.103222 | ||||||||
\(595\) | 1.64609 | 0.0674830 | ||||||||
\(596\) | −27.7289 | −1.13582 | ||||||||
\(597\) | −24.7724 | −1.01387 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.0573 | 1.10553 | 0.552765 | − | 0.833337i | \(-0.313573\pi\) | ||||
0.552765 | + | 0.833337i | \(0.313573\pi\) | |||||||
\(600\) | −8.35690 | −0.341169 | ||||||||
\(601\) | 10.8780 | 0.443723 | 0.221861 | − | 0.975078i | \(-0.428787\pi\) | ||||
0.221861 | + | 0.975078i | \(0.428787\pi\) | |||||||
\(602\) | 1.33704 | 0.0544939 | ||||||||
\(603\) | −5.96077 | −0.242741 | ||||||||
\(604\) | −6.62133 | −0.269418 | ||||||||
\(605\) | 5.17523 | 0.210403 | ||||||||
\(606\) | 2.40821 | 0.0978267 | ||||||||
\(607\) | −29.6359 | −1.20289 | −0.601443 | − | 0.798916i | \(-0.705407\pi\) | ||||
−0.601443 | + | 0.798916i | \(0.705407\pi\) | |||||||
\(608\) | 25.9724 | 1.05332 | ||||||||
\(609\) | 10.4112 | 0.421883 | ||||||||
\(610\) | 0.936017 | 0.0378982 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.85086 | 0.276929 | ||||||||
\(613\) | −10.2343 | −0.413360 | −0.206680 | − | 0.978409i | \(-0.566266\pi\) | ||||
−0.206680 | + | 0.978409i | \(0.566266\pi\) | |||||||
\(614\) | −9.23968 | −0.372883 | ||||||||
\(615\) | −0.109916 | −0.00443225 | ||||||||
\(616\) | 16.7670 | 0.675563 | ||||||||
\(617\) | −26.2828 | −1.05810 | −0.529052 | − | 0.848590i | \(-0.677452\pi\) | ||||
−0.529052 | + | 0.848590i | \(0.677452\pi\) | |||||||
\(618\) | −6.12200 | −0.246263 | ||||||||
\(619\) | −29.0834 | −1.16896 | −0.584479 | − | 0.811408i | \(-0.698701\pi\) | ||||
−0.584479 | + | 0.811408i | \(0.698701\pi\) | |||||||
\(620\) | 2.34481 | 0.0941700 | ||||||||
\(621\) | 8.34481 | 0.334866 | ||||||||
\(622\) | 5.02954 | 0.201666 | ||||||||
\(623\) | 0.240275 | 0.00962641 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0887 | 0.963549 | ||||||||
\(626\) | 1.90110 | 0.0759833 | ||||||||
\(627\) | 31.5545 | 1.26016 | ||||||||
\(628\) | 8.78986 | 0.350753 | ||||||||
\(629\) | 12.1588 | 0.484804 | ||||||||
\(630\) | 0.192685 | 0.00767677 | ||||||||
\(631\) | −25.4480 | −1.01307 | −0.506535 | − | 0.862219i | \(-0.669074\pi\) | ||||
−0.506535 | + | 0.862219i | \(0.669074\pi\) | |||||||
\(632\) | 7.53750 | 0.299826 | ||||||||
\(633\) | −5.93900 | −0.236054 | ||||||||
\(634\) | 6.88816 | 0.273564 | ||||||||
\(635\) | 2.66727 | 0.105847 | ||||||||
\(636\) | 1.91185 | 0.0758099 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.9409 | −0.591517 | ||||||||
\(639\) | 5.71917 | 0.226247 | ||||||||
\(640\) | 2.69740 | 0.106624 | ||||||||
\(641\) | −26.7409 | −1.05620 | −0.528102 | − | 0.849181i | \(-0.677096\pi\) | ||||
−0.528102 | + | 0.849181i | \(0.677096\pi\) | |||||||
\(642\) | 5.70410 | 0.225123 | ||||||||
\(643\) | 32.9614 | 1.29987 | 0.649935 | − | 0.759990i | \(-0.274796\pi\) | ||||
0.649935 | + | 0.759990i | \(0.274796\pi\) | |||||||
\(644\) | 26.3599 | 1.03872 | ||||||||
\(645\) | 0.423272 | 0.0166663 | ||||||||
\(646\) | −9.44504 | −0.371610 | ||||||||
\(647\) | 34.4946 | 1.35612 | 0.678060 | − | 0.735006i | \(-0.262821\pi\) | ||||
0.678060 | + | 0.735006i | \(0.262821\pi\) | |||||||
\(648\) | 1.69202 | 0.0664689 | ||||||||
\(649\) | −77.4529 | −3.04029 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.23623 | 0.361996 | ||||||||
\(652\) | 15.5526 | 0.609085 | ||||||||
\(653\) | 36.1517 | 1.41472 | 0.707362 | − | 0.706852i | \(-0.249885\pi\) | ||||
0.707362 | + | 0.706852i | \(0.249885\pi\) | |||||||
\(654\) | 5.40581 | 0.211384 | ||||||||
\(655\) | 0.224144 | 0.00875805 | ||||||||
\(656\) | −1.26875 | −0.0495364 | ||||||||
\(657\) | −7.35690 | −0.287020 | ||||||||
\(658\) | 5.25487 | 0.204856 | ||||||||
\(659\) | −6.81700 | −0.265553 | −0.132776 | − | 0.991146i | \(-0.542389\pi\) | ||||
−0.132776 | + | 0.991146i | \(0.542389\pi\) | |||||||
\(660\) | 2.51573 | 0.0979246 | ||||||||
\(661\) | 10.8944 | 0.423743 | 0.211871 | − | 0.977298i | \(-0.432044\pi\) | ||||
0.211871 | + | 0.977298i | \(0.432044\pi\) | |||||||
\(662\) | 2.70065 | 0.104964 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.2349 | 0.668844 | ||||||||
\(665\) | 2.41683 | 0.0937206 | ||||||||
\(666\) | 1.42327 | 0.0551507 | ||||||||
\(667\) | −49.5599 | −1.91897 | ||||||||
\(668\) | 17.0640 | 0.660225 | ||||||||
\(669\) | −14.2010 | −0.549044 | ||||||||
\(670\) | 0.655186 | 0.0253120 | ||||||||
\(671\) | 48.1377 | 1.85833 | ||||||||
\(672\) | 8.15644 | 0.314642 | ||||||||
\(673\) | 20.7385 | 0.799412 | 0.399706 | − | 0.916643i | \(-0.369112\pi\) | ||||
0.399706 | + | 0.916643i | \(0.369112\pi\) | |||||||
\(674\) | −5.39565 | −0.207833 | ||||||||
\(675\) | −4.93900 | −0.190102 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5786 | −0.983067 | −0.491534 | − | 0.870859i | \(-0.663564\pi\) | ||||
−0.491534 | + | 0.870859i | \(0.663564\pi\) | |||||||
\(678\) | 0.728857 | 0.0279916 | ||||||||
\(679\) | −23.9982 | −0.920966 | ||||||||
\(680\) | −1.58881 | −0.0609281 | ||||||||
\(681\) | −16.0073 | −0.613401 | ||||||||
\(682\) | −13.2547 | −0.507551 | ||||||||
\(683\) | −21.6310 | −0.827688 | −0.413844 | − | 0.910348i | \(-0.635814\pi\) | ||||
−0.413844 | + | 0.910348i | \(0.635814\pi\) | |||||||
\(684\) | 10.0586 | 0.384600 | ||||||||
\(685\) | 2.35822 | 0.0901031 | ||||||||
\(686\) | −8.52483 | −0.325479 | ||||||||
\(687\) | −1.84117 | −0.0702449 | ||||||||
\(688\) | 4.88577 | 0.186268 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.917231 | −0.0349184 | ||||||||
\(691\) | −2.62996 | −0.100048 | −0.0500242 | − | 0.998748i | \(-0.515930\pi\) | ||||
−0.0500242 | + | 0.998748i | \(0.515930\pi\) | |||||||
\(692\) | −8.60388 | −0.327070 | ||||||||
\(693\) | 9.90946 | 0.376429 | ||||||||
\(694\) | −10.3026 | −0.391081 | ||||||||
\(695\) | −1.01075 | −0.0383401 | ||||||||
\(696\) | −10.0489 | −0.380903 | ||||||||
\(697\) | 1.69202 | 0.0640899 | ||||||||
\(698\) | −9.87800 | −0.373888 | ||||||||
\(699\) | −23.4252 | −0.886022 | ||||||||
\(700\) | −15.6015 | −0.589681 | ||||||||
\(701\) | 40.0925 | 1.51427 | 0.757136 | − | 0.653258i | \(-0.226598\pi\) | ||||
0.757136 | + | 0.653258i | \(0.226598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.8519 | 0.673298 | ||||||||
\(704\) | 20.5254 | 0.773581 | ||||||||
\(705\) | 1.66355 | 0.0626528 | ||||||||
\(706\) | −2.25667 | −0.0849308 | ||||||||
\(707\) | 9.48593 | 0.356755 | ||||||||
\(708\) | −24.6896 | −0.927893 | ||||||||
\(709\) | −23.2097 | −0.871657 | −0.435829 | − | 0.900030i | \(-0.643545\pi\) | ||||
−0.435829 | + | 0.900030i | \(0.643545\pi\) | |||||||
\(710\) | −0.628630 | −0.0235921 | ||||||||
\(711\) | 4.45473 | 0.167065 | ||||||||
\(712\) | −0.231914 | −0.00869135 | ||||||||
\(713\) | −43.9667 | −1.64657 | ||||||||
\(714\) | −2.96615 | −0.111005 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.19029 | −0.231342 | ||||||||
\(717\) | −14.6015 | −0.545302 | ||||||||
\(718\) | −7.42088 | −0.276945 | ||||||||
\(719\) | −26.0146 | −0.970181 | −0.485090 | − | 0.874464i | \(-0.661213\pi\) | ||||
−0.485090 | + | 0.874464i | \(0.661213\pi\) | |||||||
\(720\) | 0.704103 | 0.0262404 | ||||||||
\(721\) | −24.1146 | −0.898073 | ||||||||
\(722\) | −5.41166 | −0.201401 | ||||||||
\(723\) | −8.63102 | −0.320991 | ||||||||
\(724\) | 24.3013 | 0.903150 | ||||||||
\(725\) | 29.3327 | 1.08939 | ||||||||
\(726\) | −9.32544 | −0.346099 | ||||||||
\(727\) | −16.5472 | −0.613701 | −0.306851 | − | 0.951758i | \(-0.599275\pi\) | ||||
−0.306851 | + | 0.951758i | \(0.599275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.808643 | 0.0299292 | ||||||||
\(731\) | −6.51573 | −0.240993 | ||||||||
\(732\) | 15.3448 | 0.567161 | ||||||||
\(733\) | −18.8750 | −0.697165 | −0.348582 | − | 0.937278i | \(-0.613337\pi\) | ||||
−0.348582 | + | 0.937278i | \(0.613337\pi\) | |||||||
\(734\) | 0.524827 | 0.0193717 | ||||||||
\(735\) | −0.969869 | −0.0357742 | ||||||||
\(736\) | −38.8267 | −1.43117 | ||||||||
\(737\) | 33.6950 | 1.24117 | ||||||||
\(738\) | 0.198062 | 0.00729077 | ||||||||
\(739\) | −47.3239 | −1.74084 | −0.870419 | − | 0.492312i | \(-0.836152\pi\) | ||||
−0.870419 | + | 0.492312i | \(0.836152\pi\) | |||||||
\(740\) | 1.42327 | 0.0523205 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.827757 | −0.0303879 | ||||||||
\(743\) | 8.88769 | 0.326058 | 0.163029 | − | 0.986621i | \(-0.447874\pi\) | ||||
0.163029 | + | 0.986621i | \(0.447874\pi\) | |||||||
\(744\) | −8.91484 | −0.326834 | ||||||||
\(745\) | 3.80061 | 0.139244 | ||||||||
\(746\) | 13.3924 | 0.490331 | ||||||||
\(747\) | 10.1860 | 0.372686 | ||||||||
\(748\) | −38.7265 | −1.41598 | ||||||||
\(749\) | 22.4685 | 0.820980 | ||||||||
\(750\) | 1.09246 | 0.0398909 | ||||||||
\(751\) | 0.710808 | 0.0259377 | 0.0129689 | − | 0.999916i | \(-0.495872\pi\) | ||||
0.0129689 | + | 0.999916i | \(0.495872\pi\) | |||||||
\(752\) | 19.2021 | 0.700229 | ||||||||
\(753\) | −3.80194 | −0.138550 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.907542 | 0.0330288 | ||||||||
\(756\) | 3.15883 | 0.114886 | ||||||||
\(757\) | 9.78554 | 0.355662 | 0.177831 | − | 0.984061i | \(-0.443092\pi\) | ||||
0.177831 | + | 0.984061i | \(0.443092\pi\) | |||||||
\(758\) | −8.52840 | −0.309766 | ||||||||
\(759\) | −47.1715 | −1.71222 | ||||||||
\(760\) | −2.33273 | −0.0846171 | ||||||||
\(761\) | 18.8810 | 0.684435 | 0.342218 | − | 0.939621i | \(-0.388822\pi\) | ||||
0.342218 | + | 0.939621i | \(0.388822\pi\) | |||||||
\(762\) | −4.80625 | −0.174112 | ||||||||
\(763\) | 21.2935 | 0.770877 | ||||||||
\(764\) | 2.34481 | 0.0848324 | ||||||||
\(765\) | −0.939001 | −0.0339497 | ||||||||
\(766\) | −6.84846 | −0.247445 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.40150 | 0.0866567 | ||||||||
\(769\) | 12.4349 | 0.448413 | 0.224207 | − | 0.974542i | \(-0.428021\pi\) | ||||
0.224207 | + | 0.974542i | \(0.428021\pi\) | |||||||
\(770\) | −1.08921 | −0.0392524 | ||||||||
\(771\) | −20.5961 | −0.741751 | ||||||||
\(772\) | −16.5700 | −0.596368 | ||||||||
\(773\) | −45.6746 | −1.64280 | −0.821400 | − | 0.570353i | \(-0.806807\pi\) | ||||
−0.821400 | + | 0.570353i | \(0.806807\pi\) | |||||||
\(774\) | −0.762709 | −0.0274150 | ||||||||
\(775\) | 26.0224 | 0.934751 | ||||||||
\(776\) | 23.1631 | 0.831508 | ||||||||
\(777\) | 5.60627 | 0.201124 | ||||||||
\(778\) | 10.6950 | 0.383435 | ||||||||
\(779\) | 2.48427 | 0.0890082 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.3293 | −1.15683 | ||||||||
\(782\) | 14.1196 | 0.504916 | ||||||||
\(783\) | −5.93900 | −0.212243 | ||||||||
\(784\) | −11.1951 | −0.399824 | ||||||||
\(785\) | −1.20477 | −0.0430000 | ||||||||
\(786\) | −0.403894 | −0.0144064 | ||||||||
\(787\) | 4.51871 | 0.161075 | 0.0805374 | − | 0.996752i | \(-0.474336\pi\) | ||||
0.0805374 | + | 0.996752i | \(0.474336\pi\) | |||||||
\(788\) | 7.41013 | 0.263975 | ||||||||
\(789\) | 0.332733 | 0.0118456 | ||||||||
\(790\) | −0.489647 | −0.0174209 | ||||||||
\(791\) | 2.87097 | 0.102080 | ||||||||
\(792\) | −9.56465 | −0.339865 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.1739 | 0.467524 | ||||||||
\(795\) | −0.262045 | −0.00929378 | ||||||||
\(796\) | 44.6383 | 1.58216 | ||||||||
\(797\) | −28.7391 | −1.01799 | −0.508996 | − | 0.860769i | \(-0.669983\pi\) | ||||
−0.508996 | + | 0.860769i | \(0.669983\pi\) | |||||||
\(798\) | −4.35498 | −0.154165 | ||||||||
\(799\) | −25.6082 | −0.905953 | ||||||||
\(800\) | 22.9801 | 0.812471 | ||||||||
\(801\) | −0.137063 | −0.00484289 | ||||||||
\(802\) | −9.39181 | −0.331636 | ||||||||
\(803\) | 41.5870 | 1.46757 | ||||||||
\(804\) | 10.7409 | 0.378804 | ||||||||
\(805\) | −3.61297 | −0.127341 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.3032 | 0.961118 | ||||||||
\(808\) | −9.15585 | −0.322102 | ||||||||
\(809\) | 5.42891 | 0.190870 | 0.0954352 | − | 0.995436i | \(-0.469576\pi\) | ||||
0.0954352 | + | 0.995436i | \(0.469576\pi\) | |||||||
\(810\) | −0.109916 | −0.00386206 | ||||||||
\(811\) | −0.629104 | −0.0220908 | −0.0110454 | − | 0.999939i | \(-0.503516\pi\) | ||||
−0.0110454 | + | 0.999939i | \(0.503516\pi\) | |||||||
\(812\) | −18.7603 | −0.658358 | ||||||||
\(813\) | −27.9855 | −0.981495 | ||||||||
\(814\) | −8.04546 | −0.281993 | ||||||||
\(815\) | −2.13169 | −0.0746697 | ||||||||
\(816\) | −10.8388 | −0.379433 | ||||||||
\(817\) | −9.56657 | −0.334692 | ||||||||
\(818\) | −16.0315 | −0.560527 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.198062 | 0.00691663 | ||||||||
\(821\) | −36.2640 | −1.26562 | −0.632811 | − | 0.774307i | \(-0.718099\pi\) | ||||
−0.632811 | + | 0.774307i | \(0.718099\pi\) | |||||||
\(822\) | −4.24937 | −0.148214 | ||||||||
\(823\) | 41.7396 | 1.45495 | 0.727476 | − | 0.686133i | \(-0.240693\pi\) | ||||
0.727476 | + | 0.686133i | \(0.240693\pi\) | |||||||
\(824\) | 23.2755 | 0.810839 | ||||||||
\(825\) | 27.9191 | 0.972020 | ||||||||
\(826\) | 10.6896 | 0.371940 | ||||||||
\(827\) | −38.1997 | −1.32833 | −0.664167 | − | 0.747584i | \(-0.731214\pi\) | ||||
−0.664167 | + | 0.747584i | \(0.731214\pi\) | |||||||
\(828\) | −15.0368 | −0.522566 | ||||||||
\(829\) | 15.9788 | 0.554967 | 0.277484 | − | 0.960730i | \(-0.410500\pi\) | ||||
0.277484 | + | 0.960730i | \(0.410500\pi\) | |||||||
\(830\) | −1.11960 | −0.0388621 | ||||||||
\(831\) | −2.10321 | −0.0729596 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.9299 | 0.517290 | ||||||||
\(834\) | 1.82132 | 0.0630670 | ||||||||
\(835\) | −2.33885 | −0.0809391 | ||||||||
\(836\) | −56.8592 | −1.96652 | ||||||||
\(837\) | −5.26875 | −0.182115 | ||||||||
\(838\) | −2.65625 | −0.0917587 | ||||||||
\(839\) | 4.63879 | 0.160149 | 0.0800744 | − | 0.996789i | \(-0.474484\pi\) | ||||
0.0800744 | + | 0.996789i | \(0.474484\pi\) | |||||||
\(840\) | −0.732578 | −0.0252763 | ||||||||
\(841\) | 6.27173 | 0.216267 | ||||||||
\(842\) | −0.932559 | −0.0321381 | ||||||||
\(843\) | −27.2349 | −0.938020 | ||||||||
\(844\) | 10.7017 | 0.368368 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.99761 | −0.103060 | ||||||||
\(847\) | −36.7329 | −1.26216 | ||||||||
\(848\) | −3.02475 | −0.103870 | ||||||||
\(849\) | 5.28382 | 0.181340 | ||||||||
\(850\) | −8.35690 | −0.286639 | ||||||||
\(851\) | −26.6872 | −0.914827 | ||||||||
\(852\) | −10.3056 | −0.353064 | ||||||||
\(853\) | −18.3884 | −0.629605 | −0.314803 | − | 0.949157i | \(-0.601938\pi\) | ||||
−0.314803 | + | 0.949157i | \(0.601938\pi\) | |||||||
\(854\) | −6.64370 | −0.227343 | ||||||||
\(855\) | −1.37867 | −0.0471494 | ||||||||
\(856\) | −21.6866 | −0.741234 | ||||||||
\(857\) | 28.1849 | 0.962778 | 0.481389 | − | 0.876507i | \(-0.340132\pi\) | ||||
0.481389 | + | 0.876507i | \(0.340132\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.3957 | 1.13944 | 0.569722 | − | 0.821837i | \(-0.307051\pi\) | ||||
0.569722 | + | 0.821837i | \(0.307051\pi\) | |||||||
\(860\) | −0.762709 | −0.0260082 | ||||||||
\(861\) | 0.780167 | 0.0265880 | ||||||||
\(862\) | −1.28429 | −0.0437431 | ||||||||
\(863\) | 43.0640 | 1.46592 | 0.732958 | − | 0.680274i | \(-0.238139\pi\) | ||||
0.732958 | + | 0.680274i | \(0.238139\pi\) | |||||||
\(864\) | −4.65279 | −0.158291 | ||||||||
\(865\) | 1.17928 | 0.0400966 | ||||||||
\(866\) | 5.62910 | 0.191285 | ||||||||
\(867\) | −2.54527 | −0.0864419 | ||||||||
\(868\) | −16.6431 | −0.564904 | ||||||||
\(869\) | −25.1817 | −0.854230 | ||||||||
\(870\) | 0.652793 | 0.0221317 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −20.5526 | −0.695998 | ||||||||
\(873\) | 13.6896 | 0.463324 | ||||||||
\(874\) | 20.7308 | 0.701229 | ||||||||
\(875\) | 4.30319 | 0.145474 | ||||||||
\(876\) | 13.2567 | 0.447901 | ||||||||
\(877\) | 30.1702 | 1.01877 | 0.509387 | − | 0.860537i | \(-0.329872\pi\) | ||||
0.509387 | + | 0.860537i | \(0.329872\pi\) | |||||||
\(878\) | 4.86294 | 0.164116 | ||||||||
\(879\) | −32.6625 | −1.10168 | ||||||||
\(880\) | −3.98015 | −0.134171 | ||||||||
\(881\) | −3.56273 | −0.120031 | −0.0600157 | − | 0.998197i | \(-0.519115\pi\) | ||||
−0.0600157 | + | 0.998197i | \(0.519115\pi\) | |||||||
\(882\) | 1.74764 | 0.0588462 | ||||||||
\(883\) | −10.2088 | −0.343554 | −0.171777 | − | 0.985136i | \(-0.554951\pi\) | ||||
−0.171777 | + | 0.985136i | \(0.554951\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.38404 | 0.113753 | ||||||||
\(886\) | 8.56273 | 0.287670 | ||||||||
\(887\) | −9.33645 | −0.313487 | −0.156744 | − | 0.987639i | \(-0.550100\pi\) | ||||
−0.156744 | + | 0.987639i | \(0.550100\pi\) | |||||||
\(888\) | −5.41119 | −0.181588 | ||||||||
\(889\) | −18.9318 | −0.634953 | ||||||||
\(890\) | 0.0150655 | 0.000504996 0 | ||||||||
\(891\) | −5.65279 | −0.189376 | ||||||||
\(892\) | 25.5894 | 0.856797 | ||||||||
\(893\) | −37.5986 | −1.25819 | ||||||||
\(894\) | −6.84846 | −0.229047 | ||||||||
\(895\) | 0.848462 | 0.0283610 | ||||||||
\(896\) | −19.1457 | −0.639613 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.8261 | −0.428013 | ||||||||
\(899\) | 31.2911 | 1.04362 | ||||||||
\(900\) | 8.89977 | 0.296659 | ||||||||
\(901\) | 4.03385 | 0.134387 | ||||||||
\(902\) | −1.11960 | −0.0372788 | ||||||||
\(903\) | −3.00431 | −0.0999772 | ||||||||
\(904\) | −2.77107 | −0.0921644 | ||||||||
\(905\) | −3.33081 | −0.110720 | ||||||||
\(906\) | −1.63533 | −0.0543303 | ||||||||
\(907\) | −41.0804 | −1.36405 | −0.682026 | − | 0.731328i | \(-0.738901\pi\) | ||||
−0.682026 | + | 0.731328i | \(0.738901\pi\) | |||||||
\(908\) | 28.8442 | 0.957227 | ||||||||
\(909\) | −5.41119 | −0.179478 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.9705 | −0.628519 | −0.314260 | − | 0.949337i | \(-0.601756\pi\) | ||||
−0.314260 | + | 0.949337i | \(0.601756\pi\) | |||||||
\(912\) | −15.9138 | −0.526958 | ||||||||
\(913\) | −57.5792 | −1.90559 | ||||||||
\(914\) | −8.04221 | −0.266013 | ||||||||
\(915\) | −2.10321 | −0.0695300 | ||||||||
\(916\) | 3.31767 | 0.109619 | ||||||||
\(917\) | −1.59094 | −0.0525375 | ||||||||
\(918\) | 1.69202 | 0.0558450 | ||||||||
\(919\) | 29.0019 | 0.956685 | 0.478343 | − | 0.878173i | \(-0.341238\pi\) | ||||
0.478343 | + | 0.878173i | \(0.341238\pi\) | |||||||
\(920\) | 3.48725 | 0.114971 | ||||||||
\(921\) | 20.7614 | 0.684111 | ||||||||
\(922\) | −3.36791 | −0.110916 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −17.8562 | −0.587427 | ||||||||
\(925\) | 15.7952 | 0.519344 | ||||||||
\(926\) | 15.7345 | 0.517068 | ||||||||
\(927\) | 13.7560 | 0.451806 | ||||||||
\(928\) | 27.6329 | 0.907096 | ||||||||
\(929\) | 50.7211 | 1.66410 | 0.832052 | − | 0.554697i | \(-0.187166\pi\) | ||||
0.832052 | + | 0.554697i | \(0.187166\pi\) | |||||||
\(930\) | 0.579121 | 0.0189901 | ||||||||
\(931\) | 21.9205 | 0.718415 | ||||||||
\(932\) | 42.2107 | 1.38266 | ||||||||
\(933\) | −11.3013 | −0.369987 | ||||||||
\(934\) | −5.78554 | −0.189309 | ||||||||
\(935\) | 5.30798 | 0.173589 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.3051 | 1.67606 | 0.838032 | − | 0.545620i | \(-0.183706\pi\) | ||||
0.838032 | + | 0.545620i | \(0.183706\pi\) | |||||||
\(938\) | −4.65040 | −0.151841 | ||||||||
\(939\) | −4.27173 | −0.139403 | ||||||||
\(940\) | −2.99761 | −0.0977712 | ||||||||
\(941\) | 34.7036 | 1.13131 | 0.565653 | − | 0.824643i | \(-0.308624\pi\) | ||||
0.565653 | + | 0.824643i | \(0.308624\pi\) | |||||||
\(942\) | 2.17092 | 0.0707322 | ||||||||
\(943\) | −3.71379 | −0.120938 | ||||||||
\(944\) | 39.0616 | 1.27135 | ||||||||
\(945\) | −0.432960 | −0.0140842 | ||||||||
\(946\) | 4.31144 | 0.140177 | ||||||||
\(947\) | 13.0127 | 0.422855 | 0.211428 | − | 0.977394i | \(-0.432189\pi\) | ||||
0.211428 | + | 0.977394i | \(0.432189\pi\) | |||||||
\(948\) | −8.02715 | −0.260710 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −12.2698 | −0.398085 | ||||||||
\(951\) | −15.4776 | −0.501894 | ||||||||
\(952\) | 11.2771 | 0.365493 | ||||||||
\(953\) | 26.0151 | 0.842711 | 0.421355 | − | 0.906896i | \(-0.361555\pi\) | ||||
0.421355 | + | 0.906896i | \(0.361555\pi\) | |||||||
\(954\) | 0.472189 | 0.0152877 | ||||||||
\(955\) | −0.321388 | −0.0103999 | ||||||||
\(956\) | 26.3110 | 0.850957 | ||||||||
\(957\) | 33.5719 | 1.08523 | ||||||||
\(958\) | −11.3604 | −0.367036 | ||||||||
\(959\) | −16.7383 | −0.540507 | ||||||||
\(960\) | −0.896789 | −0.0289437 | ||||||||
\(961\) | −3.24027 | −0.104525 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.8170 | −0.413022 | ||||||||
\(964\) | 15.5526 | 0.500914 | ||||||||
\(965\) | 2.27114 | 0.0731107 | ||||||||
\(966\) | 6.51035 | 0.209467 | ||||||||
\(967\) | −36.6644 | −1.17905 | −0.589524 | − | 0.807751i | \(-0.700685\pi\) | ||||
−0.589524 | + | 0.807751i | \(0.700685\pi\) | |||||||
\(968\) | 35.4547 | 1.13956 | ||||||||
\(969\) | 21.2228 | 0.681775 | ||||||||
\(970\) | −1.50471 | −0.0483134 | ||||||||
\(971\) | −37.8465 | −1.21455 | −0.607277 | − | 0.794490i | \(-0.707738\pi\) | ||||
−0.607277 | + | 0.794490i | \(0.707738\pi\) | |||||||
\(972\) | −1.80194 | −0.0577972 | ||||||||
\(973\) | 7.17416 | 0.229993 | ||||||||
\(974\) | 7.12392 | 0.228265 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.2771 | −0.777091 | ||||||||
\(977\) | −28.8998 | −0.924586 | −0.462293 | − | 0.886727i | \(-0.652973\pi\) | ||||
−0.462293 | + | 0.886727i | \(0.652973\pi\) | |||||||
\(978\) | 3.84117 | 0.122827 | ||||||||
\(979\) | 0.774791 | 0.0247624 | ||||||||
\(980\) | 1.74764 | 0.0558264 | ||||||||
\(981\) | −12.1468 | −0.387816 | ||||||||
\(982\) | −9.22952 | −0.294526 | ||||||||
\(983\) | 19.3991 | 0.618735 | 0.309368 | − | 0.950942i | \(-0.399883\pi\) | ||||
0.309368 | + | 0.950942i | \(0.399883\pi\) | |||||||
\(984\) | −0.753020 | −0.0240054 | ||||||||
\(985\) | −1.01566 | −0.0323615 | ||||||||
\(986\) | −10.0489 | −0.320023 | ||||||||
\(987\) | −11.8076 | −0.375839 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14.3013 | 0.454754 | ||||||||
\(990\) | 0.621334 | 0.0197473 | ||||||||
\(991\) | −5.18300 | −0.164643 | −0.0823217 | − | 0.996606i | \(-0.526233\pi\) | ||||
−0.0823217 | + | 0.996606i | \(0.526233\pi\) | |||||||
\(992\) | 24.5144 | 0.778333 | ||||||||
\(993\) | −6.06829 | −0.192572 | ||||||||
\(994\) | 4.46191 | 0.141523 | ||||||||
\(995\) | −6.11828 | −0.193962 | ||||||||
\(996\) | −18.3545 | −0.581585 | ||||||||
\(997\) | −49.3642 | −1.56338 | −0.781690 | − | 0.623667i | \(-0.785642\pi\) | ||||
−0.781690 | + | 0.623667i | \(0.785642\pi\) | |||||||
\(998\) | −3.59047 | −0.113654 | ||||||||
\(999\) | −3.19806 | −0.101182 |
(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 | 507.2.a.j.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1521.2.a.q.1.2 | 3 | |||
4.3 | odd | 2 | 8112.2.a.by.1.3 | 3 | |||
13.2 | odd | 12 | 507.2.j.h.316.3 | 12 | |||
13.3 | even | 3 | 507.2.e.k.22.2 | 6 | |||
13.4 | even | 6 | 507.2.e.j.484.2 | 6 | |||
13.5 | odd | 4 | 507.2.b.g.337.4 | 6 | |||
13.6 | odd | 12 | 507.2.j.h.361.4 | 12 | |||
13.7 | odd | 12 | 507.2.j.h.361.3 | 12 | |||
13.8 | odd | 4 | 507.2.b.g.337.3 | 6 | |||
13.9 | even | 3 | 507.2.e.k.484.2 | 6 | |||
13.10 | even | 6 | 507.2.e.j.22.2 | 6 | |||
13.11 | odd | 12 | 507.2.j.h.316.4 | 12 | |||
13.12 | even | 2 | 507.2.a.k.1.2 | yes | 3 | ||
39.5 | even | 4 | 1521.2.b.m.1351.3 | 6 | |||
39.8 | even | 4 | 1521.2.b.m.1351.4 | 6 | |||
39.38 | odd | 2 | 1521.2.a.p.1.2 | 3 | |||
52.51 | odd | 2 | 8112.2.a.cf.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.j.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
507.2.a.k.1.2 | yes | 3 | 13.12 | even | 2 | ||
507.2.b.g.337.3 | 6 | 13.8 | odd | 4 | |||
507.2.b.g.337.4 | 6 | 13.5 | odd | 4 | |||
507.2.e.j.22.2 | 6 | 13.10 | even | 6 | |||
507.2.e.j.484.2 | 6 | 13.4 | even | 6 | |||
507.2.e.k.22.2 | 6 | 13.3 | even | 3 | |||
507.2.e.k.484.2 | 6 | 13.9 | even | 3 | |||
507.2.j.h.316.3 | 12 | 13.2 | odd | 12 | |||
507.2.j.h.316.4 | 12 | 13.11 | odd | 12 | |||
507.2.j.h.361.3 | 12 | 13.7 | odd | 12 | |||
507.2.j.h.361.4 | 12 | 13.6 | odd | 12 | |||
1521.2.a.p.1.2 | 3 | 39.38 | odd | 2 | |||
1521.2.a.q.1.2 | 3 | 3.2 | odd | 2 | |||
1521.2.b.m.1351.3 | 6 | 39.5 | even | 4 | |||
1521.2.b.m.1351.4 | 6 | 39.8 | even | 4 | |||
8112.2.a.by.1.3 | 3 | 4.3 | odd | 2 | |||
8112.2.a.cf.1.1 | 3 | 52.51 | odd | 2 |