Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2475,2,Mod(1,2475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2475.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2475.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: | \(19.7629745003\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2475.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53919 | −1.08837 | −0.544185 | − | 0.838965i | \(-0.683161\pi\) | ||||
−0.544185 | + | 0.838965i | \(0.683161\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.369102 | 0.184551 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.290725 | 0.109884 | 0.0549418 | − | 0.998490i | \(-0.482503\pi\) | ||||
0.0549418 | + | 0.998490i | \(0.482503\pi\) | |||||||
\(8\) | 2.51026 | 0.887511 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.97107 | 1.93343 | 0.966714 | − | 0.255861i | \(-0.0823590\pi\) | ||||
0.966714 | + | 0.255861i | \(0.0823590\pi\) | |||||||
\(14\) | −0.447480 | −0.119594 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.60197 | −1.15049 | ||||||||
\(17\) | −4.78765 | −1.16118 | −0.580588 | − | 0.814197i | \(-0.697177\pi\) | ||||
−0.580588 | + | 0.814197i | \(0.697177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.75872 | 1.77997 | 0.889987 | − | 0.455987i | \(-0.150714\pi\) | ||||
0.889987 | + | 0.455987i | \(0.150714\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.53919 | −0.328156 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −10.7298 | −2.10429 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.107307 | 0.0202791 | ||||||||
\(29\) | 7.41855 | 1.37759 | 0.688795 | − | 0.724956i | \(-0.258140\pi\) | ||||
0.688795 | + | 0.724956i | \(0.258140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.34017 | 1.13873 | 0.569364 | − | 0.822085i | \(-0.307189\pi\) | ||||
0.569364 | + | 0.822085i | \(0.307189\pi\) | |||||||
\(32\) | 2.06278 | 0.364651 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.36910 | 1.26379 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.41855 | −0.562006 | −0.281003 | − | 0.959707i | \(-0.590667\pi\) | ||||
−0.281003 | + | 0.959707i | \(0.590667\pi\) | |||||||
\(38\) | −11.9421 | −1.93727 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.41855 | 1.15858 | 0.579291 | − | 0.815120i | \(-0.303329\pi\) | ||||
0.579291 | + | 0.815120i | \(0.303329\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.290725 | 0.0443351 | 0.0221675 | − | 0.999754i | \(-0.492943\pi\) | ||||
0.0221675 | + | 0.999754i | \(0.492943\pi\) | |||||||
\(44\) | 0.369102 | 0.0556443 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.15676 | 0.907764 | ||||||||
\(47\) | −5.26180 | −0.767512 | −0.383756 | − | 0.923435i | \(-0.625370\pi\) | ||||
−0.383756 | + | 0.923435i | \(0.625370\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91548 | −0.987926 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.57304 | 0.356816 | ||||||||
\(53\) | −5.75872 | −0.791022 | −0.395511 | − | 0.918461i | \(-0.629432\pi\) | ||||
−0.395511 | + | 0.918461i | \(0.629432\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.729794 | 0.0975229 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.4186 | −1.49933 | ||||||||
\(59\) | −3.60197 | −0.468936 | −0.234468 | − | 0.972124i | \(-0.575335\pi\) | ||||
−0.234468 | + | 0.972124i | \(0.575335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.68035 | −0.855331 | −0.427665 | − | 0.903937i | \(-0.640664\pi\) | ||||
−0.427665 | + | 0.903937i | \(0.640664\pi\) | |||||||
\(62\) | −9.75872 | −1.23936 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.02893 | 0.753616 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.15676 | 0.752167 | 0.376084 | − | 0.926586i | \(-0.377271\pi\) | ||||
0.376084 | + | 0.926586i | \(0.377271\pi\) | |||||||
\(68\) | −1.76713 | −0.214296 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.07838 | 0.602693 | 0.301346 | − | 0.953515i | \(-0.402564\pi\) | ||||
0.301346 | + | 0.953515i | \(0.402564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.12783 | −0.132002 | −0.0660010 | − | 0.997820i | \(-0.521024\pi\) | ||||
−0.0660010 | + | 0.997820i | \(0.521024\pi\) | |||||||
\(74\) | 5.26180 | 0.611671 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.86376 | 0.328496 | ||||||||
\(77\) | 0.290725 | 0.0331311 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.921622 | −0.103691 | −0.0518453 | − | 0.998655i | \(-0.516510\pi\) | ||||
−0.0518453 | + | 0.998655i | \(0.516510\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.4186 | −1.26097 | ||||||||
\(83\) | −1.70928 | −0.187617 | −0.0938087 | − | 0.995590i | \(-0.529904\pi\) | ||||
−0.0938087 | + | 0.995590i | \(0.529904\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.447480 | −0.0482530 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.51026 | 0.267595 | ||||||||
\(89\) | −4.34017 | −0.460057 | −0.230029 | − | 0.973184i | \(-0.573882\pi\) | ||||
−0.230029 | + | 0.973184i | \(0.573882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.02666 | 0.212452 | ||||||||
\(92\) | −1.47641 | −0.153926 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.09890 | 0.835337 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.68035 | 0.475217 | 0.237609 | − | 0.971361i | \(-0.423636\pi\) | ||||
0.237609 | + | 0.971361i | \(0.423636\pi\) | |||||||
\(98\) | 10.6442 | 1.07523 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.58145 | 0.853886 | 0.426943 | − | 0.904279i | \(-0.359590\pi\) | ||||
0.426943 | + | 0.904279i | \(0.359590\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.73820 | 0.663935 | 0.331968 | − | 0.943291i | \(-0.392288\pi\) | ||||
0.331968 | + | 0.943291i | \(0.392288\pi\) | |||||||
\(104\) | 17.4992 | 1.71594 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.86376 | 0.860925 | ||||||||
\(107\) | −12.2329 | −1.18260 | −0.591298 | − | 0.806453i | \(-0.701384\pi\) | ||||
−0.591298 | + | 0.806453i | \(0.701384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.31351 | −0.604725 | −0.302362 | − | 0.953193i | \(-0.597775\pi\) | ||||
−0.302362 | + | 0.953193i | \(0.597775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.33791 | −0.126420 | ||||||||
\(113\) | 16.4969 | 1.55190 | 0.775950 | − | 0.630794i | \(-0.217271\pi\) | ||||
0.775950 | + | 0.630794i | \(0.217271\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.73820 | 0.254236 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.54411 | 0.510377 | ||||||||
\(119\) | −1.39189 | −0.127594 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 10.2823 | 0.930917 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.34017 | 0.210154 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.87217 | 0.432336 | 0.216168 | − | 0.976356i | \(-0.430644\pi\) | ||||
0.216168 | + | 0.976356i | \(0.430644\pi\) | |||||||
\(128\) | −13.4052 | −1.18487 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.68035 | 0.758405 | 0.379203 | − | 0.925314i | \(-0.376198\pi\) | ||||
0.379203 | + | 0.925314i | \(0.376198\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.25565 | 0.195590 | ||||||||
\(134\) | −9.47641 | −0.818637 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.0183 | −1.03056 | ||||||||
\(137\) | 12.5958 | 1.07613 | 0.538067 | − | 0.842902i | \(-0.319155\pi\) | ||||
0.538067 | + | 0.842902i | \(0.319155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.91548 | −0.841020 | −0.420510 | − | 0.907288i | \(-0.638149\pi\) | ||||
−0.420510 | + | 0.907288i | \(0.638149\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.81658 | −0.655953 | ||||||||
\(143\) | 6.97107 | 0.582950 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.73594 | 0.143667 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.26180 | −0.103719 | ||||||||
\(149\) | 1.26180 | 0.103370 | 0.0516851 | − | 0.998663i | \(-0.483541\pi\) | ||||
0.0516851 | + | 0.998663i | \(0.483541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.60197 | 0.130366 | 0.0651832 | − | 0.997873i | \(-0.479237\pi\) | ||||
0.0651832 | + | 0.997873i | \(0.479237\pi\) | |||||||
\(152\) | 19.4764 | 1.57975 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.447480 | −0.0360590 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.10504 | −0.567044 | −0.283522 | − | 0.958966i | \(-0.591503\pi\) | ||||
−0.283522 | + | 0.958966i | \(0.591503\pi\) | |||||||
\(158\) | 1.41855 | 0.112854 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.16290 | −0.0916492 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.9360 | −1.79649 | −0.898243 | − | 0.439499i | \(-0.855156\pi\) | ||||
−0.898243 | + | 0.439499i | \(0.855156\pi\) | |||||||
\(164\) | 2.73820 | 0.213818 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.63090 | 0.204197 | ||||||||
\(167\) | −4.81432 | −0.372543 | −0.186271 | − | 0.982498i | \(-0.559640\pi\) | ||||
−0.186271 | + | 0.982498i | \(0.559640\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 35.5958 | 2.73814 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.107307 | 0.00818209 | ||||||||
\(173\) | 12.8865 | 0.979746 | 0.489873 | − | 0.871794i | \(-0.337043\pi\) | ||||
0.489873 | + | 0.871794i | \(0.337043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.60197 | −0.346886 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.68035 | 0.500713 | ||||||||
\(179\) | −1.84324 | −0.137771 | −0.0688853 | − | 0.997625i | \(-0.521944\pi\) | ||||
−0.0688853 | + | 0.997625i | \(0.521944\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.2823 | 0.764278 | 0.382139 | − | 0.924105i | \(-0.375187\pi\) | ||||
0.382139 | + | 0.924105i | \(0.375187\pi\) | |||||||
\(182\) | −3.11942 | −0.231226 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.0410 | −0.740235 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.78765 | −0.350108 | ||||||||
\(188\) | −1.94214 | −0.141645 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.5174 | 0.833373 | 0.416687 | − | 0.909050i | \(-0.363191\pi\) | ||||
0.416687 | + | 0.909050i | \(0.363191\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.86603 | 0.278283 | 0.139141 | − | 0.990273i | \(-0.455566\pi\) | ||||
0.139141 | + | 0.990273i | \(0.455566\pi\) | |||||||
\(194\) | −7.20394 | −0.517212 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.55252 | −0.182323 | ||||||||
\(197\) | 8.57304 | 0.610804 | 0.305402 | − | 0.952224i | \(-0.401209\pi\) | ||||
0.305402 | + | 0.952224i | \(0.401209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.31351 | 0.589329 | 0.294665 | − | 0.955601i | \(-0.404792\pi\) | ||||
0.294665 | + | 0.955601i | \(0.404792\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.2085 | −0.929345 | ||||||||
\(203\) | 2.15676 | 0.151375 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.3714 | −0.722608 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −32.0806 | −2.22439 | ||||||||
\(209\) | 7.75872 | 0.536682 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.9155 | 1.78410 | 0.892048 | − | 0.451941i | \(-0.149268\pi\) | ||||
0.892048 | + | 0.451941i | \(0.149268\pi\) | |||||||
\(212\) | −2.12556 | −0.145984 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.8287 | 1.28710 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.84324 | 0.125128 | ||||||||
\(218\) | 9.71769 | 0.658165 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −33.3751 | −2.24505 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.62863 | −0.644781 | −0.322390 | − | 0.946607i | \(-0.604486\pi\) | ||||
−0.322390 | + | 0.946607i | \(0.604486\pi\) | |||||||
\(224\) | 0.599701 | 0.0400692 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.3919 | −1.68904 | ||||||||
\(227\) | 18.3896 | 1.22056 | 0.610281 | − | 0.792185i | \(-0.291057\pi\) | ||||
0.610281 | + | 0.792185i | \(0.291057\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.1506 | 1.13334 | 0.566672 | − | 0.823943i | \(-0.308231\pi\) | ||||
0.566672 | + | 0.823943i | \(0.308231\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.6225 | 1.22263 | ||||||||
\(233\) | 4.10731 | 0.269079 | 0.134539 | − | 0.990908i | \(-0.457045\pi\) | ||||
0.134539 | + | 0.990908i | \(0.457045\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.32950 | −0.0865428 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.14238 | 0.138870 | ||||||||
\(239\) | 4.36683 | 0.282467 | 0.141234 | − | 0.989976i | \(-0.454893\pi\) | ||||
0.141234 | + | 0.989976i | \(0.454893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.20394 | −0.335215 | −0.167608 | − | 0.985854i | \(-0.553604\pi\) | ||||
−0.167608 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(242\) | −1.53919 | −0.0989428 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.46573 | −0.157852 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 54.0866 | 3.44145 | ||||||||
\(248\) | 15.9155 | 1.01063 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.28231 | 0.522775 | 0.261388 | − | 0.965234i | \(-0.415820\pi\) | ||||
0.261388 | + | 0.965234i | \(0.415820\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | −7.49920 | −0.470541 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.57531 | 0.535957 | ||||||||
\(257\) | −11.0205 | −0.687441 | −0.343721 | − | 0.939072i | \(-0.611687\pi\) | ||||
−0.343721 | + | 0.939072i | \(0.611687\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.993857 | −0.0617553 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.3607 | −0.825426 | ||||||||
\(263\) | 2.97107 | 0.183204 | 0.0916020 | − | 0.995796i | \(-0.470801\pi\) | ||||
0.0916020 | + | 0.995796i | \(0.470801\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.47187 | −0.212874 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.27247 | 0.138813 | ||||||||
\(269\) | 15.8432 | 0.965980 | 0.482990 | − | 0.875626i | \(-0.339551\pi\) | ||||
0.482990 | + | 0.875626i | \(0.339551\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.28231 | −0.381623 | −0.190812 | − | 0.981627i | \(-0.561112\pi\) | ||||
−0.190812 | + | 0.981627i | \(0.561112\pi\) | |||||||
\(272\) | 22.0326 | 1.33592 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.3874 | −1.17123 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.12783 | 0.308101 | 0.154051 | − | 0.988063i | \(-0.450768\pi\) | ||||
0.154051 | + | 0.988063i | \(0.450768\pi\) | |||||||
\(278\) | 15.2618 | 0.915342 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.8888 | −1.30578 | −0.652889 | − | 0.757454i | \(-0.726443\pi\) | ||||
−0.652889 | + | 0.757454i | \(0.726443\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.9649 | 1.54345 | 0.771727 | − | 0.635954i | \(-0.219393\pi\) | ||||
0.771727 | + | 0.635954i | \(0.219393\pi\) | |||||||
\(284\) | 1.87444 | 0.111228 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.7298 | −0.634466 | ||||||||
\(287\) | 2.15676 | 0.127309 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.92162 | 0.348331 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.416283 | −0.0243611 | ||||||||
\(293\) | −10.4163 | −0.608526 | −0.304263 | − | 0.952588i | \(-0.598410\pi\) | ||||
−0.304263 | + | 0.952588i | \(0.598410\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.58145 | −0.498787 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.94214 | −0.112505 | ||||||||
\(299\) | −27.8843 | −1.61259 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.0845208 | 0.00487170 | ||||||||
\(302\) | −2.46573 | −0.141887 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −35.7054 | −2.04785 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.0700 | −1.65911 | −0.829555 | − | 0.558425i | \(-0.811406\pi\) | ||||
−0.829555 | + | 0.558425i | \(0.811406\pi\) | |||||||
\(308\) | 0.107307 | 0.00611439 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.44521 | −0.308770 | −0.154385 | − | 0.988011i | \(-0.549340\pi\) | ||||
−0.154385 | + | 0.988011i | \(0.549340\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.0928 | 1.41833 | 0.709163 | − | 0.705044i | \(-0.249073\pi\) | ||||
0.709163 | + | 0.705044i | \(0.249073\pi\) | |||||||
\(314\) | 10.9360 | 0.617154 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.340173 | −0.0191362 | ||||||||
\(317\) | −21.1773 | −1.18943 | −0.594717 | − | 0.803935i | \(-0.702736\pi\) | ||||
−0.594717 | + | 0.803935i | \(0.702736\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.41855 | 0.415359 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.78992 | 0.0997484 | ||||||||
\(323\) | −37.1461 | −2.06686 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 35.3028 | 1.95524 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 18.6225 | 1.02825 | ||||||||
\(329\) | −1.52973 | −0.0843369 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.70701 | −0.368650 | −0.184325 | − | 0.982865i | \(-0.559010\pi\) | ||||
−0.184325 | + | 0.982865i | \(0.559010\pi\) | |||||||
\(332\) | −0.630898 | −0.0346250 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.41014 | 0.405465 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7503 | 1.29376 | 0.646881 | − | 0.762591i | \(-0.276073\pi\) | ||||
0.646881 | + | 0.762591i | \(0.276073\pi\) | |||||||
\(338\) | −54.7887 | −2.98011 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.34017 | 0.343340 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.04557 | −0.218440 | ||||||||
\(344\) | 0.729794 | 0.0393479 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.8348 | −1.06633 | ||||||||
\(347\) | 31.1689 | 1.67323 | 0.836616 | − | 0.547790i | \(-0.184531\pi\) | ||||
0.836616 | + | 0.547790i | \(0.184531\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0472 | 0.591342 | 0.295671 | − | 0.955290i | \(-0.404457\pi\) | ||||
0.295671 | + | 0.955290i | \(0.404457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.06278 | 0.109947 | ||||||||
\(353\) | 27.4329 | 1.46011 | 0.730054 | − | 0.683390i | \(-0.239495\pi\) | ||||
0.730054 | + | 0.683390i | \(0.239495\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.60197 | −0.0849041 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.83710 | 0.149945 | ||||||||
\(359\) | 19.1506 | 1.01073 | 0.505365 | − | 0.862905i | \(-0.331358\pi\) | ||||
0.505365 | + | 0.862905i | \(0.331358\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.1978 | 2.16830 | ||||||||
\(362\) | −15.8264 | −0.831818 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.748046 | 0.0392083 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.5692 | −0.760504 | −0.380252 | − | 0.924883i | \(-0.624163\pi\) | ||||
−0.380252 | + | 0.924883i | \(0.624163\pi\) | |||||||
\(368\) | 18.4079 | 0.959577 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.67420 | −0.0869203 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.81432 | −0.456388 | −0.228194 | − | 0.973616i | \(-0.573282\pi\) | ||||
−0.228194 | + | 0.973616i | \(0.573282\pi\) | |||||||
\(374\) | 7.36910 | 0.381047 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.2085 | −0.681175 | ||||||||
\(377\) | 51.7152 | 2.66347 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.5174 | −1.20801 | −0.604005 | − | 0.796980i | \(-0.706429\pi\) | ||||
−0.604005 | + | 0.796980i | \(0.706429\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.7275 | −0.907019 | ||||||||
\(383\) | 19.3028 | 0.986329 | 0.493164 | − | 0.869936i | \(-0.335840\pi\) | ||||
0.493164 | + | 0.869936i | \(0.335840\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.95055 | −0.302875 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.72753 | 0.0877019 | ||||||||
\(389\) | 20.0410 | 1.01612 | 0.508060 | − | 0.861321i | \(-0.330363\pi\) | ||||
0.508060 | + | 0.861321i | \(0.330363\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.1506 | 0.968488 | ||||||||
\(392\) | −17.3596 | −0.876795 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.1955 | −0.664781 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.3607 | −1.67433 | −0.837163 | − | 0.546954i | \(-0.815787\pi\) | ||||
−0.837163 | + | 0.546954i | \(0.815787\pi\) | |||||||
\(398\) | −12.7961 | −0.641409 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.6475 | 1.88003 | 0.940014 | − | 0.341135i | \(-0.110811\pi\) | ||||
0.940014 | + | 0.341135i | \(0.110811\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.1978 | 2.20165 | ||||||||
\(404\) | 3.16743 | 0.157586 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.31965 | −0.164752 | ||||||||
\(407\) | −3.41855 | −0.169451 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.2039 | −1.24625 | −0.623127 | − | 0.782120i | \(-0.714138\pi\) | ||||
−0.623127 | + | 0.782120i | \(0.714138\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.48709 | 0.122530 | ||||||||
\(413\) | −1.04718 | −0.0515284 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 14.3798 | 0.705027 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.9421 | −0.584109 | ||||||||
\(419\) | −17.8432 | −0.871700 | −0.435850 | − | 0.900019i | \(-0.643552\pi\) | ||||
−0.435850 | + | 0.900019i | \(0.643552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.8120 | −0.575684 | −0.287842 | − | 0.957678i | \(-0.592938\pi\) | ||||
−0.287842 | + | 0.957678i | \(0.592938\pi\) | |||||||
\(422\) | −39.8888 | −1.94176 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.4559 | −0.702040 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.94214 | −0.0939868 | ||||||||
\(428\) | −4.51518 | −0.218249 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6803 | −0.803464 | −0.401732 | − | 0.915757i | \(-0.631592\pi\) | ||||
−0.401732 | + | 0.915757i | \(0.631592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.3135 | −1.36066 | −0.680330 | − | 0.732906i | \(-0.738164\pi\) | ||||
−0.680330 | + | 0.732906i | \(0.738164\pi\) | |||||||
\(434\) | −2.83710 | −0.136185 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.33033 | −0.111603 | ||||||||
\(437\) | −31.0349 | −1.48460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.4452 | −1.30989 | −0.654944 | − | 0.755677i | \(-0.727308\pi\) | ||||
−0.654944 | + | 0.755677i | \(0.727308\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 51.3705 | 2.44345 | ||||||||
\(443\) | −0.412408 | −0.0195941 | −0.00979704 | − | 0.999952i | \(-0.503119\pi\) | ||||
−0.00979704 | + | 0.999952i | \(0.503119\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.8203 | 0.701761 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.75276 | 0.0828100 | ||||||||
\(449\) | −1.33403 | −0.0629568 | −0.0314784 | − | 0.999504i | \(-0.510022\pi\) | ||||
−0.0314784 | + | 0.999504i | \(0.510022\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.41855 | 0.349326 | ||||||||
\(452\) | 6.08906 | 0.286405 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28.3051 | −1.32842 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.6514 | 0.545030 | 0.272515 | − | 0.962151i | \(-0.412145\pi\) | ||||
0.272515 | + | 0.962151i | \(0.412145\pi\) | |||||||
\(458\) | −26.3980 | −1.23350 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.05786 | 0.0958440 | 0.0479220 | − | 0.998851i | \(-0.484740\pi\) | ||||
0.0479220 | + | 0.998851i | \(0.484740\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.7792 | 1.33748 | 0.668742 | − | 0.743494i | \(-0.266833\pi\) | ||||
0.668742 | + | 0.743494i | \(0.266833\pi\) | |||||||
\(464\) | −34.1399 | −1.58491 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.32192 | −0.292857 | ||||||||
\(467\) | −1.84324 | −0.0852952 | −0.0426476 | − | 0.999090i | \(-0.513579\pi\) | ||||
−0.0426476 | + | 0.999090i | \(0.513579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.78992 | 0.0826509 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.04187 | −0.416186 | ||||||||
\(473\) | 0.290725 | 0.0133675 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.513749 | −0.0235477 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.72138 | −0.307429 | ||||||||
\(479\) | −26.8371 | −1.22622 | −0.613109 | − | 0.789998i | \(-0.710081\pi\) | ||||
−0.613109 | + | 0.789998i | \(0.710081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.8310 | −1.08660 | ||||||||
\(482\) | 8.00984 | 0.364838 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.369102 | 0.0167774 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5646 | 1.29439 | 0.647193 | − | 0.762326i | \(-0.275943\pi\) | ||||
0.647193 | + | 0.762326i | \(0.275943\pi\) | |||||||
\(488\) | −16.7694 | −0.759115 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.9877 | −1.17281 | −0.586405 | − | 0.810018i | \(-0.699457\pi\) | ||||
−0.586405 | + | 0.810018i | \(0.699457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.5174 | −1.59963 | ||||||||
\(494\) | −83.2495 | −3.74557 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.1773 | −1.31010 | ||||||||
\(497\) | 1.47641 | 0.0662260 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.5174 | −1.23185 | −0.615925 | − | 0.787805i | \(-0.711218\pi\) | ||||
−0.615925 | + | 0.787805i | \(0.711218\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.7480 | −0.568973 | ||||||||
\(503\) | −22.6576 | −1.01025 | −0.505125 | − | 0.863046i | \(-0.668554\pi\) | ||||
−0.505125 | + | 0.863046i | \(0.668554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.15676 | 0.273701 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.79833 | 0.0797880 | ||||||||
\(509\) | 27.8432 | 1.23413 | 0.617065 | − | 0.786912i | \(-0.288322\pi\) | ||||
0.617065 | + | 0.786912i | \(0.288322\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.327887 | −0.0145049 | ||||||||
\(512\) | 13.6114 | 0.601546 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.9627 | 0.748191 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.26180 | −0.231413 | ||||||||
\(518\) | 1.52973 | 0.0672126 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.7009 | −1.30122 | −0.650609 | − | 0.759413i | \(-0.725486\pi\) | ||||
−0.650609 | + | 0.759413i | \(0.725486\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.7565 | 1.08252 | 0.541262 | − | 0.840854i | \(-0.317947\pi\) | ||||
0.541262 | + | 0.840854i | \(0.317947\pi\) | |||||||
\(524\) | 3.20394 | 0.139965 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.57304 | −0.199394 | ||||||||
\(527\) | −30.3545 | −1.32226 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.832567 | 0.0360963 | ||||||||
\(533\) | 51.7152 | 2.24004 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 15.4551 | 0.667557 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.3857 | −1.05134 | ||||||||
\(539\) | −6.91548 | −0.297871 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5236 | −0.538431 | −0.269216 | − | 0.963080i | \(-0.586764\pi\) | ||||
−0.269216 | + | 0.963080i | \(0.586764\pi\) | |||||||
\(542\) | 9.66967 | 0.415348 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.87587 | −0.423425 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.2784 | −0.610502 | −0.305251 | − | 0.952272i | \(-0.598740\pi\) | ||||
−0.305251 | + | 0.952272i | \(0.598740\pi\) | |||||||
\(548\) | 4.64915 | 0.198602 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 57.5585 | 2.45207 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.267938 | −0.0113939 | ||||||||
\(554\) | −7.89269 | −0.335328 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.65983 | −0.155211 | ||||||||
\(557\) | 3.57918 | 0.151655 | 0.0758274 | − | 0.997121i | \(-0.475840\pi\) | ||||
0.0758274 | + | 0.997121i | \(0.475840\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.02666 | 0.0857187 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 33.6910 | 1.42117 | ||||||||
\(563\) | −28.9588 | −1.22047 | −0.610234 | − | 0.792222i | \(-0.708924\pi\) | ||||
−0.610234 | + | 0.792222i | \(0.708924\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −39.9649 | −1.67985 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.7480 | 0.534896 | ||||||||
\(569\) | 25.8264 | 1.08270 | 0.541350 | − | 0.840797i | \(-0.317913\pi\) | ||||
0.541350 | + | 0.840797i | \(0.317913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.1194 | 0.716425 | 0.358213 | − | 0.933640i | \(-0.383386\pi\) | ||||
0.358213 | + | 0.933640i | \(0.383386\pi\) | |||||||
\(572\) | 2.57304 | 0.107584 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.31965 | −0.138560 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.5692 | 0.939567 | 0.469783 | − | 0.882782i | \(-0.344332\pi\) | ||||
0.469783 | + | 0.882782i | \(0.344332\pi\) | |||||||
\(578\) | −9.11450 | −0.379113 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.496928 | −0.0206161 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.75872 | −0.238502 | ||||||||
\(584\) | −2.83114 | −0.117153 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.0326 | 0.662302 | ||||||||
\(587\) | −3.63317 | −0.149957 | −0.0749784 | − | 0.997185i | \(-0.523889\pi\) | ||||
−0.0749784 | + | 0.997185i | \(0.523889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.1917 | 2.02691 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 15.7321 | 0.646584 | ||||||||
\(593\) | −12.3051 | −0.505310 | −0.252655 | − | 0.967556i | \(-0.581304\pi\) | ||||
−0.252655 | + | 0.967556i | \(0.581304\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.465732 | 0.0190771 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 42.9192 | 1.75510 | ||||||||
\(599\) | −19.6865 | −0.804368 | −0.402184 | − | 0.915559i | \(-0.631749\pi\) | ||||
−0.402184 | + | 0.915559i | \(0.631749\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.8843 | 1.05584 | 0.527921 | − | 0.849294i | \(-0.322972\pi\) | ||||
0.527921 | + | 0.849294i | \(0.322972\pi\) | |||||||
\(602\) | −0.130094 | −0.00530222 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.591290 | 0.0240593 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.5357 | −1.68588 | −0.842941 | − | 0.538006i | \(-0.819178\pi\) | ||||
−0.842941 | + | 0.538006i | \(0.819178\pi\) | |||||||
\(608\) | 16.0045 | 0.649070 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.6803 | −1.48393 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.6453 | −0.833855 | −0.416927 | − | 0.908940i | \(-0.636893\pi\) | ||||
−0.416927 | + | 0.908940i | \(0.636893\pi\) | |||||||
\(614\) | 44.7442 | 1.80573 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.729794 | 0.0294042 | ||||||||
\(617\) | −8.69472 | −0.350036 | −0.175018 | − | 0.984565i | \(-0.555998\pi\) | ||||
−0.175018 | + | 0.984565i | \(0.555998\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.65368 | 0.106661 | 0.0533303 | − | 0.998577i | \(-0.483016\pi\) | ||||
0.0533303 | + | 0.998577i | \(0.483016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.38121 | 0.336056 | ||||||||
\(623\) | −1.26180 | −0.0505528 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −38.6225 | −1.54367 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.62249 | −0.104649 | ||||||||
\(629\) | 16.3668 | 0.652588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.6393 | −0.423544 | −0.211772 | − | 0.977319i | \(-0.567923\pi\) | ||||
−0.211772 | + | 0.977319i | \(0.567923\pi\) | |||||||
\(632\) | −2.31351 | −0.0920265 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 32.5958 | 1.29455 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −48.2083 | −1.91008 | ||||||||
\(638\) | −11.4186 | −0.452065 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.8576 | 1.41629 | 0.708145 | − | 0.706067i | \(-0.249532\pi\) | ||||
0.708145 | + | 0.706067i | \(0.249532\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.2146 | 0.481697 | 0.240849 | − | 0.970563i | \(-0.422574\pi\) | ||||
0.240849 | + | 0.970563i | \(0.422574\pi\) | |||||||
\(644\) | −0.429229 | −0.0169140 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 57.1748 | 2.24951 | ||||||||
\(647\) | −25.9421 | −1.01989 | −0.509945 | − | 0.860207i | \(-0.670334\pi\) | ||||
−0.509945 | + | 0.860207i | \(0.670334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.60197 | −0.141390 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.46573 | −0.331544 | ||||||||
\(653\) | 14.3402 | 0.561174 | 0.280587 | − | 0.959829i | \(-0.409471\pi\) | ||||
0.280587 | + | 0.959829i | \(0.409471\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −34.1399 | −1.33294 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.35455 | 0.0917899 | ||||||||
\(659\) | −6.52359 | −0.254123 | −0.127062 | − | 0.991895i | \(-0.540555\pi\) | ||||
−0.127062 | + | 0.991895i | \(0.540555\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.16290 | 0.123022 | 0.0615112 | − | 0.998106i | \(-0.480408\pi\) | ||||
0.0615112 | + | 0.998106i | \(0.480408\pi\) | |||||||
\(662\) | 10.3234 | 0.401228 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.29072 | −0.166512 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.6742 | −1.14899 | ||||||||
\(668\) | −1.77698 | −0.0687532 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.68035 | −0.257892 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.4885 | −0.712680 | −0.356340 | − | 0.934356i | \(-0.615976\pi\) | ||||
−0.356340 | + | 0.934356i | \(0.615976\pi\) | |||||||
\(674\) | −36.5562 | −1.40809 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.1385 | 0.505327 | ||||||||
\(677\) | −15.0966 | −0.580211 | −0.290105 | − | 0.956995i | \(-0.593690\pi\) | ||||
−0.290105 | + | 0.956995i | \(0.593690\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.36069 | 0.0522186 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.75872 | −0.373681 | ||||||||
\(683\) | 12.4657 | 0.476988 | 0.238494 | − | 0.971144i | \(-0.423346\pi\) | ||||
0.238494 | + | 0.971144i | \(0.423346\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.22690 | 0.237744 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.33791 | −0.0510072 | ||||||||
\(689\) | −40.1445 | −1.52938 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7214 | −1.16870 | −0.584348 | − | 0.811503i | \(-0.698650\pi\) | ||||
−0.584348 | + | 0.811503i | \(0.698650\pi\) | |||||||
\(692\) | 4.75646 | 0.180813 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −47.9748 | −1.82110 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.5174 | −1.34532 | ||||||||
\(698\) | −17.0037 | −0.643599 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.9955 | −0.679679 | −0.339840 | − | 0.940483i | \(-0.610373\pi\) | ||||
−0.339840 | + | 0.940483i | \(0.610373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26.5236 | −1.00036 | ||||||||
\(704\) | 6.02893 | 0.227224 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −42.2245 | −1.58914 | ||||||||
\(707\) | 2.49484 | 0.0938281 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.5897 | 0.885929 | 0.442965 | − | 0.896539i | \(-0.353927\pi\) | ||||
0.442965 | + | 0.896539i | \(0.353927\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.8950 | −0.408306 | ||||||||
\(713\) | −25.3607 | −0.949765 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.680346 | −0.0254257 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.4764 | −1.10005 | ||||||||
\(719\) | −24.5646 | −0.916106 | −0.458053 | − | 0.888925i | \(-0.651453\pi\) | ||||
−0.458053 | + | 0.888925i | \(0.651453\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.95896 | 0.0729556 | ||||||||
\(722\) | −63.4112 | −2.35992 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.79523 | 0.141048 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.51130 | 0.315667 | 0.157833 | − | 0.987466i | \(-0.449549\pi\) | ||||
0.157833 | + | 0.987466i | \(0.449549\pi\) | |||||||
\(728\) | 5.08745 | 0.188553 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.39189 | −0.0514809 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.8615 | −1.10296 | −0.551480 | − | 0.834188i | \(-0.685937\pi\) | ||||
−0.551480 | + | 0.834188i | \(0.685937\pi\) | |||||||
\(734\) | 22.4247 | 0.827711 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.25112 | −0.304140 | ||||||||
\(737\) | 6.15676 | 0.226787 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.7526 | −1.35197 | −0.675983 | − | 0.736917i | \(-0.736281\pi\) | ||||
−0.675983 | + | 0.736917i | \(0.736281\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.57691 | 0.0946015 | ||||||||
\(743\) | 2.17501 | 0.0797933 | 0.0398966 | − | 0.999204i | \(-0.487297\pi\) | ||||
0.0398966 | + | 0.999204i | \(0.487297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.5669 | 0.496719 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.76713 | −0.0646128 | ||||||||
\(749\) | −3.55640 | −0.129948 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.4580 | −1.62229 | −0.811147 | − | 0.584842i | \(-0.801157\pi\) | ||||
−0.811147 | + | 0.584842i | \(0.801157\pi\) | |||||||
\(752\) | 24.2146 | 0.883016 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −79.5995 | −2.89884 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.4247 | −0.960422 | −0.480211 | − | 0.877153i | \(-0.659440\pi\) | ||||
−0.480211 | + | 0.877153i | \(0.659440\pi\) | |||||||
\(758\) | 36.1978 | 1.31476 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.6163 | 1.00109 | 0.500546 | − | 0.865710i | \(-0.333133\pi\) | ||||
0.500546 | + | 0.865710i | \(0.333133\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.83549 | −0.0664493 | ||||||||
\(764\) | 4.25112 | 0.153800 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −29.7107 | −1.07349 | ||||||||
\(767\) | −25.1096 | −0.906654 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.8432 | 1.00405 | 0.502027 | − | 0.864852i | \(-0.332588\pi\) | ||||
0.502027 | + | 0.864852i | \(0.332588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.42696 | 0.0513575 | ||||||||
\(773\) | 18.0267 | 0.648374 | 0.324187 | − | 0.945993i | \(-0.394909\pi\) | ||||
0.324187 | + | 0.945993i | \(0.394909\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.7489 | 0.421760 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30.8469 | −1.10592 | ||||||||
\(779\) | 57.5585 | 2.06225 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.07838 | 0.181719 | ||||||||
\(782\) | −29.4764 | −1.05407 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 31.8248 | 1.13660 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.6391 | 1.27040 | 0.635199 | − | 0.772349i | \(-0.280918\pi\) | ||||
0.635199 | + | 0.772349i | \(0.280918\pi\) | |||||||
\(788\) | 3.16433 | 0.112725 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.79606 | 0.170528 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.5692 | −1.65372 | ||||||||
\(794\) | 51.3484 | 1.82229 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.06854 | 0.108761 | ||||||||
\(797\) | 4.97948 | 0.176382 | 0.0881911 | − | 0.996104i | \(-0.471891\pi\) | ||||
0.0881911 | + | 0.996104i | \(0.471891\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.1917 | 0.891217 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −57.9467 | −2.04617 | ||||||||
\(803\) | −1.12783 | −0.0398001 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −68.0288 | −2.39621 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 21.5417 | 0.757833 | ||||||||
\(809\) | −31.6697 | −1.11345 | −0.556723 | − | 0.830698i | \(-0.687942\pi\) | ||||
−0.556723 | + | 0.830698i | \(0.687942\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.7998 | −0.765493 | −0.382747 | − | 0.923853i | \(-0.625022\pi\) | ||||
−0.382747 | + | 0.923853i | \(0.625022\pi\) | |||||||
\(812\) | 0.796064 | 0.0279364 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.26180 | 0.184426 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.25565 | 0.0789153 | ||||||||
\(818\) | 38.7936 | 1.35639 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.9360 | 0.381669 | 0.190834 | − | 0.981622i | \(-0.438881\pi\) | ||||
0.190834 | + | 0.981622i | \(0.438881\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.9709 | 1.60244 | 0.801222 | − | 0.598367i | \(-0.204183\pi\) | ||||
0.801222 | + | 0.598367i | \(0.204183\pi\) | |||||||
\(824\) | 16.9146 | 0.589249 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.61181 | 0.0560820 | ||||||||
\(827\) | 22.9711 | 0.798782 | 0.399391 | − | 0.916781i | \(-0.369222\pi\) | ||||
0.399391 | + | 0.916781i | \(0.369222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.1543 | −1.67247 | −0.836234 | − | 0.548373i | \(-0.815248\pi\) | ||||
−0.836234 | + | 0.548373i | \(0.815248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 42.0281 | 1.45706 | ||||||||
\(833\) | 33.1089 | 1.14716 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.86376 | 0.0990453 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.4641 | 0.948732 | ||||||||
\(839\) | 17.9278 | 0.618935 | 0.309468 | − | 0.950910i | \(-0.399849\pi\) | ||||
0.309468 | + | 0.950910i | \(0.399849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.0349 | 0.897755 | ||||||||
\(842\) | 18.1810 | 0.626558 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.56547 | 0.329257 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.290725 | 0.00998942 | ||||||||
\(848\) | 26.5015 | 0.910064 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.6742 | 0.468746 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.54799 | −0.326917 | −0.163458 | − | 0.986550i | \(-0.552265\pi\) | ||||
−0.163458 | + | 0.986550i | \(0.552265\pi\) | |||||||
\(854\) | 2.98932 | 0.102292 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.7077 | −1.04957 | ||||||||
\(857\) | −10.5776 | −0.361323 | −0.180662 | − | 0.983545i | \(-0.557824\pi\) | ||||
−0.180662 | + | 0.983545i | \(0.557824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.3340 | −1.06910 | −0.534552 | − | 0.845136i | \(-0.679520\pi\) | ||||
−0.534552 | + | 0.845136i | \(0.679520\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.6742 | 0.874467 | ||||||||
\(863\) | −56.7792 | −1.93279 | −0.966394 | − | 0.257066i | \(-0.917244\pi\) | ||||
−0.966394 | + | 0.257066i | \(0.917244\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 43.5798 | 1.48090 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.680346 | 0.0230924 | ||||||||
\(869\) | −0.921622 | −0.0312639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.9192 | 1.45426 | ||||||||
\(872\) | −15.8486 | −0.536700 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 47.7686 | 1.61580 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.87832 | 0.198497 | 0.0992483 | − | 0.995063i | \(-0.468356\pi\) | ||||
0.0992483 | + | 0.995063i | \(0.468356\pi\) | |||||||
\(878\) | 42.2434 | 1.42564 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.21008 | −0.276605 | −0.138302 | − | 0.990390i | \(-0.544165\pi\) | ||||
−0.138302 | + | 0.990390i | \(0.544165\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.0349 | −0.909797 | −0.454898 | − | 0.890543i | \(-0.650324\pi\) | ||||
−0.454898 | + | 0.890543i | \(0.650324\pi\) | |||||||
\(884\) | −12.3188 | −0.414327 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.634773 | 0.0213256 | ||||||||
\(887\) | 48.7442 | 1.63667 | 0.818335 | − | 0.574742i | \(-0.194898\pi\) | ||||
0.818335 | + | 0.574742i | \(0.194898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.41646 | 0.0475066 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.55395 | −0.118995 | ||||||||
\(893\) | −40.8248 | −1.36615 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.89723 | −0.130197 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.05332 | 0.0685203 | ||||||||
\(899\) | 47.0349 | 1.56870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.5708 | 0.918516 | ||||||||
\(902\) | −11.4186 | −0.380196 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41.4116 | 1.37733 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.4657 | −1.07801 | −0.539003 | − | 0.842304i | \(-0.681199\pi\) | ||||
−0.539003 | + | 0.842304i | \(0.681199\pi\) | |||||||
\(908\) | 6.78765 | 0.225256 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.84939 | 0.160667 | 0.0803337 | − | 0.996768i | \(-0.474401\pi\) | ||||
0.0803337 | + | 0.996768i | \(0.474401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.70928 | −0.0565688 | ||||||||
\(914\) | −17.9337 | −0.593195 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.33033 | 0.209160 | ||||||||
\(917\) | 2.52359 | 0.0833363 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.3980 | −0.474947 | −0.237474 | − | 0.971394i | \(-0.576319\pi\) | ||||
−0.237474 | + | 0.971394i | \(0.576319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.16743 | −0.104314 | ||||||||
\(923\) | 35.4017 | 1.16526 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −44.2967 | −1.45568 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.3028 | 0.502340 | ||||||||
\(929\) | 11.1629 | 0.366243 | 0.183121 | − | 0.983090i | \(-0.441380\pi\) | ||||
0.183121 | + | 0.983090i | \(0.441380\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −53.6553 | −1.75848 | ||||||||
\(932\) | 1.51602 | 0.0496588 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.83710 | 0.0928328 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.6453 | 1.58917 | 0.794586 | − | 0.607152i | \(-0.207688\pi\) | ||||
0.794586 | + | 0.607152i | \(0.207688\pi\) | |||||||
\(938\) | −2.75503 | −0.0899548 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.4124 | −0.535029 | −0.267515 | − | 0.963554i | \(-0.586202\pi\) | ||||
−0.267515 | + | 0.963554i | \(0.586202\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.6742 | −0.966325 | ||||||||
\(944\) | 16.5761 | 0.539508 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.447480 | −0.0145488 | ||||||||
\(947\) | 45.7198 | 1.48569 | 0.742847 | − | 0.669462i | \(-0.233475\pi\) | ||||
0.742847 | + | 0.669462i | \(0.233475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.86216 | −0.255216 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.49400 | −0.113241 | ||||||||
\(953\) | 26.4619 | 0.857184 | 0.428592 | − | 0.903498i | \(-0.359010\pi\) | ||||
0.428592 | + | 0.903498i | \(0.359010\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.61181 | 0.0521296 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 41.3074 | 1.33458 | ||||||||
\(959\) | 3.66192 | 0.118249 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.19779 | 0.296703 | ||||||||
\(962\) | 36.6803 | 1.18262 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.92079 | −0.0618643 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.5464 | 1.62546 | 0.812731 | − | 0.582639i | \(-0.197980\pi\) | ||||
0.812731 | + | 0.582639i | \(0.197980\pi\) | |||||||
\(968\) | 2.51026 | 0.0806828 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.3074 | 1.83908 | 0.919540 | − | 0.392995i | \(-0.128561\pi\) | ||||
0.919540 | + | 0.392995i | \(0.128561\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.88267 | −0.0924143 | ||||||||
\(974\) | −43.9664 | −1.40877 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 30.7427 | 0.984051 | ||||||||
\(977\) | 45.7875 | 1.46487 | 0.732436 | − | 0.680836i | \(-0.238384\pi\) | ||||
0.732436 | + | 0.680836i | \(0.238384\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.34017 | −0.138713 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 40.0000 | 1.27645 | ||||||||
\(983\) | −55.0805 | −1.75679 | −0.878397 | − | 0.477932i | \(-0.841387\pi\) | ||||
−0.878397 | + | 0.477932i | \(0.841387\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 54.6681 | 1.74099 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19.9635 | 0.635123 | ||||||||
\(989\) | −1.16290 | −0.0369780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.6947 | 1.29271 | 0.646355 | − | 0.763037i | \(-0.276292\pi\) | ||||
0.646355 | + | 0.763037i | \(0.276292\pi\) | |||||||
\(992\) | 13.0784 | 0.415239 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.27247 | −0.0720785 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.7610 | −1.03755 | −0.518775 | − | 0.854911i | \(-0.673612\pi\) | ||||
−0.518775 | + | 0.854911i | \(0.673612\pi\) | |||||||
\(998\) | 42.3545 | 1.34071 | ||||||||
\(999\) | 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 | 2475.2.a.y.1.2 | 3 | ||
3.2 | odd | 2 | 825.2.a.n.1.2 | 3 | |||
5.2 | odd | 4 | 495.2.c.d.199.2 | 6 | |||
5.3 | odd | 4 | 495.2.c.d.199.5 | 6 | |||
5.4 | even | 2 | 2475.2.a.be.1.2 | 3 | |||
15.2 | even | 4 | 165.2.c.a.34.5 | yes | 6 | ||
15.8 | even | 4 | 165.2.c.a.34.2 | ✓ | 6 | ||
15.14 | odd | 2 | 825.2.a.h.1.2 | 3 | |||
33.32 | even | 2 | 9075.2.a.cc.1.2 | 3 | |||
60.23 | odd | 4 | 2640.2.d.i.529.6 | 6 | |||
60.47 | odd | 4 | 2640.2.d.i.529.3 | 6 | |||
165.32 | odd | 4 | 1815.2.c.d.364.2 | 6 | |||
165.98 | odd | 4 | 1815.2.c.d.364.5 | 6 | |||
165.164 | even | 2 | 9075.2.a.ck.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.c.a.34.2 | ✓ | 6 | 15.8 | even | 4 | ||
165.2.c.a.34.5 | yes | 6 | 15.2 | even | 4 | ||
495.2.c.d.199.2 | 6 | 5.2 | odd | 4 | |||
495.2.c.d.199.5 | 6 | 5.3 | odd | 4 | |||
825.2.a.h.1.2 | 3 | 15.14 | odd | 2 | |||
825.2.a.n.1.2 | 3 | 3.2 | odd | 2 | |||
1815.2.c.d.364.2 | 6 | 165.32 | odd | 4 | |||
1815.2.c.d.364.5 | 6 | 165.98 | odd | 4 | |||
2475.2.a.y.1.2 | 3 | 1.1 | even | 1 | trivial | ||
2475.2.a.be.1.2 | 3 | 5.4 | even | 2 | |||
2640.2.d.i.529.3 | 6 | 60.47 | odd | 4 | |||
2640.2.d.i.529.6 | 6 | 60.23 | odd | 4 | |||
9075.2.a.cc.1.2 | 3 | 33.32 | even | 2 | |||
9075.2.a.ck.1.2 | 3 | 165.164 | even | 2 |