Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7168,2,Mod(1,7168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7168, 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("7168.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7168 = 2^{10} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7168.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: | \(57.2367681689\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.9433055232.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 6x^{6} + 32x^{5} + 9x^{4} - 76x^{3} - 4x^{2} + 48x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1792) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.38887\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7168.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.09974 | −1.21228 | −0.606142 | − | 0.795356i | \(-0.707284\pi\) | ||||
−0.606142 | + | 0.795356i | \(0.707284\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.59647 | 1.16118 | 0.580589 | − | 0.814196i | \(-0.302822\pi\) | ||||
0.580589 | + | 0.814196i | \(0.302822\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.40890 | 0.469633 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.454591 | −0.137064 | −0.0685322 | − | 0.997649i | \(-0.521832\pi\) | ||||
−0.0685322 | + | 0.997649i | \(0.521832\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.53068 | 1.81128 | 0.905642 | − | 0.424044i | \(-0.139390\pi\) | ||||
0.905642 | + | 0.424044i | \(0.139390\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.45192 | −1.40768 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.84172 | 0.446682 | 0.223341 | − | 0.974740i | \(-0.428304\pi\) | ||||
0.223341 | + | 0.974740i | \(0.428304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.50056 | −1.26191 | −0.630957 | − | 0.775818i | \(-0.717338\pi\) | ||||
−0.630957 | + | 0.775818i | \(0.717338\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.09974 | −0.458200 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.88497 | −1.22710 | −0.613550 | − | 0.789656i | \(-0.710259\pi\) | ||||
−0.613550 | + | 0.789656i | \(0.710259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.74168 | 0.348336 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.34090 | 0.642956 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.69134 | −1.61394 | −0.806970 | − | 0.590592i | \(-0.798894\pi\) | ||||
−0.806970 | + | 0.590592i | \(0.798894\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.69821 | 1.02343 | 0.511714 | − | 0.859156i | \(-0.329011\pi\) | ||||
0.511714 | + | 0.859156i | \(0.329011\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.954522 | 0.166161 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.59647 | 0.438884 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.35999 | 0.387980 | 0.193990 | − | 0.981003i | \(-0.437857\pi\) | ||||
0.193990 | + | 0.981003i | \(0.437857\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.7127 | −2.19579 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.7333 | 1.67626 | 0.838132 | − | 0.545468i | \(-0.183648\pi\) | ||||
0.838132 | + | 0.545468i | \(0.183648\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.753925 | 0.114972 | 0.0574862 | − | 0.998346i | \(-0.481691\pi\) | ||||
0.0574862 | + | 0.998346i | \(0.481691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.65817 | 0.545327 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.465401 | 0.0678856 | 0.0339428 | − | 0.999424i | \(-0.489194\pi\) | ||||
0.0339428 | + | 0.999424i | \(0.489194\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.86712 | −0.541505 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.881386 | 0.121068 | 0.0605338 | − | 0.998166i | \(-0.480720\pi\) | ||||
0.0605338 | + | 0.998166i | \(0.480720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18033 | −0.159156 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.5497 | 1.52980 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3546 | 1.34806 | 0.674030 | − | 0.738704i | \(-0.264562\pi\) | ||||
0.674030 | + | 0.738704i | \(0.264562\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.7092 | 1.37118 | 0.685589 | − | 0.727989i | \(-0.259545\pi\) | ||||
0.685589 | + | 0.727989i | \(0.259545\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.40890 | 0.177504 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.9567 | 2.10322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.71619 | 1.06485 | 0.532426 | − | 0.846477i | \(-0.321281\pi\) | ||||
0.532426 | + | 0.846477i | \(0.321281\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 12.3569 | 1.48759 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.162532 | −0.0192890 | −0.00964452 | − | 0.999953i | \(-0.503070\pi\) | ||||
−0.00964452 | + | 0.999953i | \(0.503070\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.49118 | −0.408612 | −0.204306 | − | 0.978907i | \(-0.565494\pi\) | ||||
−0.204306 | + | 0.978907i | \(0.565494\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.65707 | −0.422283 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.454591 | −0.0518054 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.28703 | −0.932363 | −0.466182 | − | 0.884689i | \(-0.654371\pi\) | ||||
−0.466182 | + | 0.884689i | \(0.654371\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2417 | −1.24908 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.55356 | −0.390054 | −0.195027 | − | 0.980798i | \(-0.562479\pi\) | ||||
−0.195027 | + | 0.980798i | \(0.562479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.78197 | 0.518677 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.2495 | 1.95655 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.60040 | 0.169642 | 0.0848209 | − | 0.996396i | \(-0.472968\pi\) | ||||
0.0848209 | + | 0.996396i | \(0.472968\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.53068 | 0.684601 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.9647 | −1.24069 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14.2821 | −1.46531 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.88621 | −0.902258 | −0.451129 | − | 0.892459i | \(-0.648979\pi\) | ||||
−0.451129 | + | 0.892459i | \(0.648979\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.640472 | −0.0643699 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8668 | 1.37980 | 0.689901 | − | 0.723904i | \(-0.257654\pi\) | ||||
0.689901 | + | 0.723904i | \(0.257654\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.3236 | −1.41135 | −0.705674 | − | 0.708537i | \(-0.749356\pi\) | ||||
−0.705674 | + | 0.708537i | \(0.749356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.45192 | −0.532052 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.1314 | 1.46280 | 0.731401 | − | 0.681947i | \(-0.238867\pi\) | ||||
0.731401 | + | 0.681947i | \(0.238867\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.4465 | −1.00059 | −0.500296 | − | 0.865854i | \(-0.666776\pi\) | ||||
−0.500296 | + | 0.865854i | \(0.666776\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.95537 | −0.470343 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.05995 | −0.758217 | −0.379108 | − | 0.925352i | \(-0.623769\pi\) | ||||
−0.379108 | + | 0.925352i | \(0.623769\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.2802 | −1.42488 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.20105 | 0.850638 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.84172 | 0.168830 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7933 | −0.981213 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.5372 | −2.03211 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.46014 | −0.756698 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.367471 | 0.0326078 | 0.0163039 | − | 0.999867i | \(-0.494810\pi\) | ||||
0.0163039 | + | 0.999867i | \(0.494810\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.58304 | −0.139379 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.1642 | 1.15016 | 0.575081 | − | 0.818096i | \(-0.304970\pi\) | ||||
0.575081 | + | 0.818096i | \(0.304970\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.50056 | −0.476959 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.67456 | 0.746587 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.85872 | 0.585980 | 0.292990 | − | 0.956115i | \(-0.405350\pi\) | ||||
0.292990 | + | 0.956115i | \(0.405350\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.8721 | 1.93998 | 0.969991 | − | 0.243141i | \(-0.0781777\pi\) | ||||
0.969991 | + | 0.243141i | \(0.0781777\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.977219 | −0.0822967 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.96879 | −0.248262 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.5668 | −1.87407 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.09974 | −0.173183 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.4973 | 1.76112 | 0.880562 | − | 0.473931i | \(-0.157165\pi\) | ||||
0.880562 | + | 0.473931i | \(0.157165\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.76306 | 0.387612 | 0.193806 | − | 0.981040i | \(-0.437917\pi\) | ||||
0.193806 | + | 0.981040i | \(0.437917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.59479 | 0.209776 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.7952 | 1.18838 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.6718 | 1.33055 | 0.665277 | − | 0.746596i | \(-0.268313\pi\) | ||||
0.665277 | + | 0.746596i | \(0.268313\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.85068 | −0.146768 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.88497 | −0.463800 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.6908 | −1.07234 | −0.536171 | − | 0.844109i | \(-0.680130\pi\) | ||||
−0.536171 | + | 0.844109i | \(0.680130\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.47839 | 0.192942 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.1916 | −1.02079 | −0.510397 | − | 0.859939i | \(-0.670501\pi\) | ||||
−0.510397 | + | 0.859939i | \(0.670501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 29.6497 | 2.28075 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.74972 | −0.592636 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.06309 | 0.689054 | 0.344527 | − | 0.938776i | \(-0.388039\pi\) | ||||
0.344527 | + | 0.938776i | \(0.388039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.74168 | 0.131659 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.7420 | −1.63423 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.8125 | 0.957653 | 0.478826 | − | 0.877910i | \(-0.341062\pi\) | ||||
0.478826 | + | 0.877910i | \(0.341062\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.3980 | −1.44184 | −0.720920 | − | 0.693019i | \(-0.756280\pi\) | ||||
−0.720920 | + | 0.693019i | \(0.756280\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.4866 | −1.66226 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.12766 | 0.450515 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.837227 | −0.0612241 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.34090 | 0.243015 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.2622 | −1.39376 | −0.696882 | − | 0.717186i | \(-0.745430\pi\) | ||||
−0.696882 | + | 0.717186i | \(0.745430\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.38323 | −0.171549 | −0.0857744 | − | 0.996315i | \(-0.527336\pi\) | ||||
−0.0857744 | + | 0.996315i | \(0.527336\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −35.6047 | −2.54971 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.71532 | 0.620941 | 0.310470 | − | 0.950583i | \(-0.399513\pi\) | ||||
0.310470 | + | 0.950583i | \(0.399513\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.33136 | 0.661483 | 0.330741 | − | 0.943721i | \(-0.392701\pi\) | ||||
0.330741 | + | 0.943721i | \(0.392701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.3017 | −1.29090 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.69134 | −0.610012 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27.8688 | 1.94644 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.29132 | −0.576286 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.50050 | 0.172963 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.3470 | −1.88264 | −0.941321 | − | 0.337513i | \(-0.890414\pi\) | ||||
−0.941321 | + | 0.337513i | \(0.890414\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.341275 | 0.0233838 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.95755 | 0.133504 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.69821 | 0.386819 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.33057 | 0.495354 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0277 | 0.809067 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.2604 | 1.28977 | 0.644886 | − | 0.764279i | \(-0.276905\pi\) | ||||
0.644886 | + | 0.764279i | \(0.276905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.45385 | 0.163590 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.530703 | 0.0352240 | 0.0176120 | − | 0.999845i | \(-0.494394\pi\) | ||||
0.0176120 | + | 0.999845i | \(0.494394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.2167 | −0.873382 | −0.436691 | − | 0.899612i | \(-0.643850\pi\) | ||||
−0.436691 | + | 0.899612i | \(0.643850\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.954522 | 0.0628029 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.8761 | 0.909055 | 0.454527 | − | 0.890733i | \(-0.349808\pi\) | ||||
0.454527 | + | 0.890733i | \(0.349808\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.20840 | 0.0788274 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 17.4006 | 1.13029 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.2148 | 0.984165 | 0.492082 | − | 0.870549i | \(-0.336236\pi\) | ||||
0.492082 | + | 0.870549i | \(0.336236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.2964 | 1.82273 | 0.911364 | − | 0.411601i | \(-0.135030\pi\) | ||||
0.911364 | + | 0.411601i | \(0.135030\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5819 | 0.871281 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.59647 | 0.165883 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −35.9223 | −2.28568 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.46154 | 0.472856 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.6157 | −0.796295 | −0.398147 | − | 0.917321i | \(-0.630347\pi\) | ||||
−0.398147 | + | 0.917321i | \(0.630347\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.67525 | 0.168192 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.0409 | −0.628784 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.4810 | −1.71422 | −0.857110 | − | 0.515133i | \(-0.827742\pi\) | ||||
−0.857110 | + | 0.515133i | \(0.827742\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.35999 | 0.146643 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.2452 | −0.757959 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.9308 | −0.920674 | −0.460337 | − | 0.887744i | \(-0.652271\pi\) | ||||
−0.460337 | + | 0.887744i | \(0.652271\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.28850 | 0.140581 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.36042 | −0.205654 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.00645316 | −0.000393456 0 | −0.000196728 | − | 1.00000i | \(-0.500063\pi\) | ||||
−0.000196728 | 1.00000i | \(0.500063\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.74567 | 0.349025 | 0.174512 | − | 0.984655i | \(-0.444165\pi\) | ||||
0.174512 | + | 0.984655i | \(0.444165\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.7127 | −0.829931 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.791752 | −0.0477445 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.9643 | −0.959203 | −0.479602 | − | 0.877486i | \(-0.659219\pi\) | ||||
−0.479602 | + | 0.877486i | \(0.659219\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.02819 | 0.480635 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.71094 | 0.579306 | 0.289653 | − | 0.957132i | \(-0.406460\pi\) | ||||
0.289653 | + | 0.957132i | \(0.406460\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.8953 | −1.06377 | −0.531884 | − | 0.846817i | \(-0.678516\pi\) | ||||
−0.531884 | + | 0.846817i | \(0.678516\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 29.9886 | 1.77637 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.7333 | 0.633568 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.6081 | −0.800475 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.6587 | 1.09379 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.28175 | 0.0748807 | 0.0374403 | − | 0.999299i | \(-0.488080\pi\) | ||||
0.0374403 | + | 0.999299i | \(0.488080\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.8856 | 1.56534 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.51874 | −0.0881263 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38.4328 | −2.22263 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.753925 | 0.0434555 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.1167 | −1.67271 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.8063 | 1.59218 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9201 | 1.19398 | 0.596988 | − | 0.802251i | \(-0.296364\pi\) | ||||
0.596988 | + | 0.802251i | \(0.296364\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.0758 | 1.71095 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.6043 | 0.658022 | 0.329011 | − | 0.944326i | \(-0.393285\pi\) | ||||
0.329011 | + | 0.944326i | \(0.393285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.5621 | 1.04919 | 0.524596 | − | 0.851351i | \(-0.324216\pi\) | ||||
0.524596 | + | 0.851351i | \(0.324216\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.65817 | 0.206114 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4666 | 1.26185 | 0.630924 | − | 0.775845i | \(-0.282676\pi\) | ||||
0.630924 | + | 0.775845i | \(0.282676\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.95100 | 0.221214 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31.7719 | −1.77333 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.1305 | −0.563674 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.3744 | 0.630936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.9349 | 1.21300 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.465401 | 0.0256584 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.77317 | −0.427252 | −0.213626 | − | 0.976915i | \(-0.568527\pi\) | ||||
−0.213626 | + | 0.976915i | \(0.568527\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.32499 | 0.182208 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.6314 | 1.23648 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.73515 | 0.148993 | 0.0744966 | − | 0.997221i | \(-0.476265\pi\) | ||||
0.0744966 | + | 0.997221i | \(0.476265\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.9238 | 0.919174 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.59035 | −0.140275 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 32.0843 | 1.72736 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.3848 | 1.89956 | 0.949779 | − | 0.312922i | \(-0.101308\pi\) | ||||
0.949779 | + | 0.312922i | \(0.101308\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.3409 | 0.660596 | 0.330298 | − | 0.943877i | \(-0.392851\pi\) | ||||
0.330298 | + | 0.943877i | \(0.392851\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.8183 | 1.16458 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.2643 | −1.18501 | −0.592504 | − | 0.805567i | \(-0.701861\pi\) | ||||
−0.592504 | + | 0.805567i | \(0.701861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.422011 | −0.0223980 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.86712 | −0.204670 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.3142 | 0.966588 | 0.483294 | − | 0.875458i | \(-0.339440\pi\) | ||||
0.483294 | + | 0.875458i | \(0.339440\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.2561 | 0.592427 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.6632 | 1.18951 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.06477 | −0.474472 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.3398 | 1.00953 | 0.504764 | − | 0.863257i | \(-0.331580\pi\) | ||||
0.504764 | + | 0.863257i | \(0.331580\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.1222 | 0.787228 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.881386 | 0.0457593 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.97146 | 0.412747 | 0.206373 | − | 0.978473i | \(-0.433834\pi\) | ||||
0.206373 | + | 0.978473i | \(0.433834\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.7641 | 0.917333 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −56.7603 | −2.92330 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.58476 | 0.235503 | 0.117752 | − | 0.993043i | \(-0.462431\pi\) | ||||
0.117752 | + | 0.993043i | \(0.462431\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.771592 | −0.0395299 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.39804 | 0.275827 | 0.137913 | − | 0.990444i | \(-0.455960\pi\) | ||||
0.137913 | + | 0.990444i | \(0.455960\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.18033 | −0.0601554 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.06220 | 0.0539948 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.1427 | 1.12268 | 0.561340 | − | 0.827586i | \(-0.310286\pi\) | ||||
0.561340 | + | 0.827586i | \(0.310286\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8384 | −0.548123 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.6414 | −1.39432 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.5171 | −1.08264 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.17580 | 0.159389 | 0.0796945 | − | 0.996819i | \(-0.474606\pi\) | ||||
0.0796945 | + | 0.996819i | \(0.474606\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.5497 | 0.578209 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.3307 | −0.965331 | −0.482665 | − | 0.875805i | \(-0.660331\pi\) | ||||
−0.482665 | + | 0.875805i | \(0.660331\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 37.2131 | 1.85372 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −29.1888 | −1.45040 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.07283 | −0.0531783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.497591 | 0.0246043 | 0.0123021 | − | 0.999924i | \(-0.496084\pi\) | ||||
0.0123021 | + | 0.999924i | \(0.496084\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.4015 | −0.710375 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.3546 | 0.509519 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.22673 | −0.452922 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −48.0253 | −2.35181 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.96496 | 0.242554 | 0.121277 | − | 0.992619i | \(-0.461301\pi\) | ||||
0.121277 | + | 0.992619i | \(0.461301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.91040 | 0.0931073 | 0.0465537 | − | 0.998916i | \(-0.485176\pi\) | ||||
0.0465537 | + | 0.998916i | \(0.485176\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.655702 | 0.0318813 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.20768 | 0.155595 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.7092 | 0.518256 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.23367 | 0.300964 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.6166 | 0.944896 | 0.472448 | − | 0.881358i | \(-0.343370\pi\) | ||||
0.472448 | + | 0.881358i | \(0.343370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.76217 | 0.132741 | 0.0663706 | − | 0.997795i | \(-0.478858\pi\) | ||||
0.0663706 | + | 0.997795i | \(0.478858\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 47.3844 | 2.27191 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 32.3706 | 1.54850 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.05296 | −0.145710 | −0.0728550 | − | 0.997343i | \(-0.523211\pi\) | ||||
−0.0728550 | + | 0.997343i | \(0.523211\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.40890 | 0.0670904 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.93814 | 0.0920836 | 0.0460418 | − | 0.998940i | \(-0.485339\pi\) | ||||
0.0460418 | + | 0.998940i | \(0.485339\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.15539 | 0.196985 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −45.1386 | −2.13498 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.6173 | 1.82246 | 0.911232 | − | 0.411894i | \(-0.135133\pi\) | ||||
0.911232 | + | 0.411894i | \(0.135133\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.87927 | −0.229756 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.0012 | −0.469896 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.9567 | 0.794944 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.0959 | −1.68849 | −0.844247 | − | 0.535955i | \(-0.819952\pi\) | ||||
−0.844247 | + | 0.535955i | \(0.819952\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.15298 | 0.287197 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.07115 | −0.282762 | −0.141381 | − | 0.989955i | \(-0.545154\pi\) | ||||
−0.141381 | + | 0.989955i | \(0.545154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.38348 | −0.157243 | −0.0786217 | − | 0.996905i | \(-0.525052\pi\) | ||||
−0.0786217 | + | 0.996905i | \(0.525052\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −31.0661 | −1.44066 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.7940 | −1.42498 | −0.712489 | − | 0.701683i | \(-0.752432\pi\) | ||||
−0.712489 | + | 0.701683i | \(0.752432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.71619 | 0.402476 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.0064 | −1.61301 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.342727 | −0.0157586 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.58022 | −0.439570 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.24178 | 0.0568573 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.74054 | −0.307983 | −0.153992 | − | 0.988072i | \(-0.549213\pi\) | ||||
−0.153992 | + | 0.988072i | \(0.549213\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.4123 | 0.702743 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.3569 | 0.562258 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −23.0728 | −1.04768 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.4472 | 1.37970 | 0.689848 | − | 0.723954i | \(-0.257677\pi\) | ||||
0.689848 | + | 0.723954i | \(0.257677\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28.7470 | 1.29998 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.7806 | 0.712166 | 0.356083 | − | 0.934454i | \(-0.384112\pi\) | ||||
0.356083 | + | 0.934454i | \(0.384112\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.0070 | −0.720918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.66297 | −0.0747449 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.162532 | −0.00729057 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.6859 | −1.10509 | −0.552547 | − | 0.833482i | \(-0.686344\pi\) | ||||
−0.552547 | + | 0.833482i | \(0.686344\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.6988 | 1.23749 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.7354 | 1.19207 | 0.596035 | − | 0.802958i | \(-0.296742\pi\) | ||||
0.596035 | + | 0.802958i | \(0.296742\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0049 | 1.60220 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −62.2566 | −2.76491 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.4609 | −0.862588 | −0.431294 | − | 0.902212i | \(-0.641943\pi\) | ||||
−0.431294 | + | 0.902212i | \(0.641943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.49118 | −0.154441 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18.3768 | −0.811355 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37.1909 | −1.63883 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.211567 | −0.00930470 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.0301 | −0.835330 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.5859 | 1.60286 | 0.801428 | − | 0.598091i | \(-0.204074\pi\) | ||||
0.801428 | + | 0.598091i | \(0.204074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.68929 | −0.248775 | −0.124388 | − | 0.992234i | \(-0.539697\pi\) | ||||
−0.124388 | + | 0.992234i | \(0.539697\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.65707 | −0.159608 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.4945 | 0.457147 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.6328 | 0.505776 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.5886 | 0.633093 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 70.0958 | 3.03619 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39.2882 | 1.69858 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.9029 | −1.16095 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.454591 | −0.0195806 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.3799 | 1.09117 | 0.545584 | − | 0.838056i | \(-0.316308\pi\) | ||||
0.545584 | + | 0.838056i | \(0.316308\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 40.7306 | 1.74792 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27.1241 | −1.16187 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.7752 | 1.14482 | 0.572412 | − | 0.819966i | \(-0.306008\pi\) | ||||
0.572412 | + | 0.819966i | \(0.306008\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.0882 | 0.643950 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47.8072 | 2.03665 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.28703 | −0.352400 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.8665 | −0.546152 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.9236 | 1.81873 | 0.909366 | − | 0.415998i | \(-0.136568\pi\) | ||||
0.909366 | + | 0.415998i | \(0.136568\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.92364 | 0.208248 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.75796 | 0.0742210 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.7662 | 1.08592 | 0.542958 | − | 0.839760i | \(-0.317304\pi\) | ||||
0.542958 | + | 0.839760i | \(0.317304\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.9275 | −0.880425 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.2417 | −0.472107 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −40.3261 | −1.69056 | −0.845279 | − | 0.534325i | \(-0.820566\pi\) | ||||
−0.845279 | + | 0.534325i | \(0.820566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.6720 | −1.07434 | −0.537169 | − | 0.843475i | \(-0.680506\pi\) | ||||
−0.537169 | + | 0.843475i | \(0.680506\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 40.4456 | 1.68964 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.2497 | −0.427444 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.8535 | 1.20119 | 0.600594 | − | 0.799554i | \(-0.294931\pi\) | ||||
0.600594 | + | 0.799554i | \(0.294931\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.00416 | 0.207966 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.55356 | −0.147427 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.400670 | −0.0165941 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.8903 | 0.987743 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 31.1230 | 1.28458 | 0.642292 | − | 0.766460i | \(-0.277984\pi\) | ||||
0.642292 | + | 0.766460i | \(0.277984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −31.3433 | −1.29148 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.2999 | −0.752757 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.6606 | −1.01269 | −0.506344 | − | 0.862331i | \(-0.669004\pi\) | ||||
−0.506344 | + | 0.862331i | \(0.669004\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.78197 | 0.196042 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.5934 | −0.801905 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.8236 | −0.442239 | −0.221120 | − | 0.975247i | \(-0.570971\pi\) | ||||
−0.221120 | + | 0.975247i | \(0.570971\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.6417 | 0.678828 | 0.339414 | − | 0.940637i | \(-0.389771\pi\) | ||||
0.339414 | + | 0.940637i | \(0.389771\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.2802 | 0.500089 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.0247 | −1.13936 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.3716 | 0.908037 | 0.454019 | − | 0.890992i | \(-0.349990\pi\) | ||||
0.454019 | + | 0.890992i | \(0.349990\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.2495 | 0.739508 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.03938 | 0.122960 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.2891 | 1.86960 | 0.934800 | − | 0.355175i | \(-0.115579\pi\) | ||||
0.934800 | + | 0.355175i | \(0.115579\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −58.5172 | −2.35964 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.37531 | 0.135885 | 0.0679424 | − | 0.997689i | \(-0.478357\pi\) | ||||
0.0679424 | + | 0.997689i | \(0.478357\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.05532 | 0.203190 | 0.101595 | − | 0.994826i | \(-0.467605\pi\) | ||||
0.101595 | + | 0.994826i | \(0.467605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.6611 | −0.788972 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.60040 | 0.0641186 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6750 | −1.22700 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.25040 | −0.209681 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.34644 | 0.173304 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.2089 | −1.24241 | −0.621204 | − | 0.783649i | \(-0.713356\pi\) | ||||
−0.621204 | + | 0.783649i | \(0.713356\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 57.4214 | 2.28230 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.954129 | 0.0378634 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.53068 | 0.258755 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.228991 | −0.00905876 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.7829 | 1.01836 | 0.509182 | − | 0.860659i | \(-0.329948\pi\) | ||||
0.509182 | + | 0.860659i | \(0.329948\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.57885 | −0.101700 | −0.0508500 | − | 0.998706i | \(-0.516193\pi\) | ||||
−0.0508500 | + | 0.998706i | \(0.516193\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.11033 | −0.161844 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.0909 | 0.396713 | 0.198356 | − | 0.980130i | \(-0.436440\pi\) | ||||
0.198356 | + | 0.980130i | \(0.436440\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.70713 | −0.184771 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.9647 | −0.468935 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.6009 | −0.767041 | −0.383520 | − | 0.923532i | \(-0.625288\pi\) | ||||
−0.383520 | + | 0.923532i | \(0.625288\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.1805 | 1.33554 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.91872 | −0.191898 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.6681 | −0.766162 | −0.383081 | − | 0.923715i | \(-0.625137\pi\) | ||||
−0.383081 | + | 0.923715i | \(0.625137\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.60575 | 0.0624564 | 0.0312282 | − | 0.999512i | \(-0.490058\pi\) | ||||
0.0312282 | + | 0.999512i | \(0.490058\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.2549 | −0.980820 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.2821 | −0.553834 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 51.1482 | 1.98047 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −40.4418 | −1.56357 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.86832 | −0.187939 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.91726 | 0.382282 | 0.191141 | − | 0.981563i | \(-0.438781\pi\) | ||||
0.191141 | + | 0.981563i | \(0.438781\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.81878 | 0.223965 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.2883 | −0.895042 | −0.447521 | − | 0.894273i | \(-0.647693\pi\) | ||||
−0.447521 | + | 0.894273i | \(0.647693\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.88621 | −0.341021 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.11434 | −0.0427015 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.80039 | 0.298474 | 0.149237 | − | 0.988801i | \(-0.452318\pi\) | ||||
0.149237 | + | 0.988801i | \(0.452318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.8085 | 0.680428 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.7515 | 1.05879 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.75605 | 0.219288 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0204 | 1.67462 | 0.837308 | − | 0.546732i | \(-0.184128\pi\) | ||||
0.837308 | + | 0.546732i | \(0.184128\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.640472 | −0.0243295 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 59.3867 | 2.25267 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.7677 | 0.748756 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.1362 | −1.10203 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.7777 | −1.16246 | −0.581229 | − | 0.813740i | \(-0.697428\pi\) | ||||
−0.581229 | + | 0.813740i | \(0.697428\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.9813 | −0.489598 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.53732 | −0.0955612 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.8668 | 0.521516 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.3503 | −0.689159 | −0.344580 | − | 0.938757i | \(-0.611979\pi\) | ||||
−0.344580 | + | 0.938757i | \(0.611979\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.6756 | −0.437868 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33.5338 | −1.25585 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.70838 | −0.288277 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −31.9471 | −1.19309 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.4527 | 1.35946 | 0.679728 | − | 0.733464i | \(-0.262098\pi\) | ||||
0.679728 | + | 0.733464i | \(0.262098\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.3236 | −0.533439 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −59.4149 | −2.20966 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.1375 | −0.562194 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.9281 | 1.40668 | 0.703338 | − | 0.710855i | \(-0.251692\pi\) | ||||
0.703338 | + | 0.710855i | \(0.251692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.20661 | 0.192838 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.38852 | 0.0513561 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.2291 | −0.673306 | −0.336653 | − | 0.941629i | \(-0.609295\pi\) | ||||
−0.336653 | + | 0.941629i | \(0.609295\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.45192 | −0.201097 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.96230 | −0.145953 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.2720 | 0.414645 | 0.207323 | − | 0.978273i | \(-0.433525\pi\) | ||||
0.207323 | + | 0.978273i | \(0.433525\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 75.4275 | 2.77090 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −41.0385 | −1.50556 | −0.752779 | − | 0.658273i | \(-0.771287\pi\) | ||||
−0.752779 | + | 0.658273i | \(0.771287\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.8171 | 2.04498 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.00660 | −0.183182 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1314 | 0.552888 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8700 | −0.615594 | −0.307797 | − | 0.951452i | \(-0.599592\pi\) | ||||
−0.307797 | + | 0.951452i | \(0.599592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.4896 | 0.965336 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.3672 | 0.450087 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.6915 | −1.11550 | −0.557750 | − | 0.830009i | \(-0.688335\pi\) | ||||
−0.557750 | + | 0.830009i | \(0.688335\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.61733 | −0.203896 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.35285 | −0.302791 | −0.151395 | − | 0.988473i | \(-0.548377\pi\) | ||||
−0.151395 | + | 0.988473i | \(0.548377\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.4465 | −0.378188 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.73731 | 0.243588 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 67.6229 | 2.44172 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.8388 | −0.787527 | −0.393764 | − | 0.919212i | \(-0.628827\pi\) | ||||
−0.393764 | + | 0.919212i | \(0.628827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 57.7030 | 2.07812 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.26946 | −0.333399 | −0.166700 | − | 0.986008i | \(-0.553311\pi\) | ||||
−0.166700 | + | 0.986008i | \(0.553311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.92446 | 0.356497 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.95537 | −0.177773 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −59.0392 | −2.11530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0738857 | 0.00264384 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.0369 | −1.03769 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43.2879 | 1.54501 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.2810 | −0.901170 | −0.450585 | − | 0.892733i | \(-0.648785\pi\) | ||||
−0.450585 | + | 0.892733i | \(0.648785\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.3508 | 1.11612 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.05995 | −0.286579 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 69.9386 | 2.48359 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.80524 | −0.170424 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.6248 | 0.801410 | 0.400705 | − | 0.916207i | \(-0.368765\pi\) | ||||
0.400705 | + | 0.916207i | \(0.368765\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.857136 | 0.0303233 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.25480 | 0.0796694 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.58706 | 0.0560062 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.2802 | −0.538555 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0135499 | 0.000476981 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.5401 | 0.476046 | 0.238023 | − | 0.971260i | \(-0.423501\pi\) | ||||
0.238023 | + | 0.971260i | \(0.423501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.11986 | 0.0744384 | 0.0372192 | − | 0.999307i | \(-0.488150\pi\) | ||||
0.0372192 | + | 0.999307i | \(0.488150\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.0644 | −0.423117 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.5477 | −1.24518 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.14701 | −0.145085 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.20105 | 0.321511 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.815513 | −0.0284616 | −0.0142308 | − | 0.999899i | \(-0.504530\pi\) | ||||
−0.0142308 | + | 0.999899i | \(0.504530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.8651 | 0.518164 | 0.259082 | − | 0.965855i | \(-0.416580\pi\) | ||||
0.259082 | + | 0.965855i | \(0.416580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.66247 | 0.0578799 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.9223 | 1.11005 | 0.555023 | − | 0.831835i | \(-0.312709\pi\) | ||||
0.555023 | + | 0.831835i | \(0.312709\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8241 | −0.757983 | −0.378992 | − | 0.925400i | \(-0.623729\pi\) | ||||
−0.378992 | + | 0.925400i | \(0.623729\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.5209 | 1.16283 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.84172 | 0.0638117 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.2516 | −1.18532 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.0371 | 0.658019 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.1968 | −1.28418 | −0.642089 | − | 0.766630i | \(-0.721932\pi\) | ||||
−0.642089 | + | 0.766630i | \(0.721932\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.5393 | 1.60480 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.3904 | −0.702284 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 76.9848 | 2.64836 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.7933 | −0.370864 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37.5755 | 1.28959 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.8885 | −0.476091 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.7608 | −1.08747 | −0.543735 | − | 0.839257i | \(-0.682990\pi\) | ||||
−0.543735 | + | 0.839257i | \(0.682990\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.1220 | −0.688156 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.6664 | −1.62825 | −0.814126 | − | 0.580688i | \(-0.802784\pi\) | ||||
−0.814126 | + | 0.580688i | \(0.802784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.6231 | 1.07897 | 0.539484 | − | 0.841996i | \(-0.318620\pi\) | ||||
0.539484 | + | 0.841996i | \(0.318620\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −22.5372 | −0.768064 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.01295 | −0.204683 | −0.102342 | − | 0.994749i | \(-0.532633\pi\) | ||||
−0.102342 | + | 0.994749i | \(0.532633\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.5321 | 0.800115 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.5734 | 0.970404 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.76721 | 0.127794 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.9226 | 1.92875 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.5198 | −0.423730 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.46014 | −0.286005 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.6592 | −0.359937 | −0.179968 | − | 0.983672i | \(-0.557600\pi\) | ||||
−0.179968 | + | 0.983672i | \(0.557600\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.69134 | −0.0907766 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.6023 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.3704 | −0.719170 | −0.359585 | − | 0.933112i | \(-0.617082\pi\) | ||||
−0.359585 | + | 0.933112i | \(0.617082\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −56.4527 | −1.89764 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 56.3410 | 1.89175 | 0.945873 | − | 0.324537i | \(-0.105208\pi\) | ||||
0.945873 | + | 0.324537i | \(0.105208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.367471 | 0.0123246 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.11037 | 0.171204 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.55996 | −0.0856658 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 33.2674 | 1.11201 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 80.6988 | 2.69446 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −49.5250 | −1.65175 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.62326 | 0.0540787 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.58304 | −0.0526804 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −50.3663 | −1.67423 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.40527 | 0.245888 | 0.122944 | − | 0.992414i | \(-0.460766\pi\) | ||||
0.122944 | + | 0.992414i | \(0.460766\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.5370 | 0.648000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0494 | −0.929319 | −0.464660 | − | 0.885489i | \(-0.653823\pi\) | ||||
−0.464660 | + | 0.885489i | \(0.653823\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.61542 | 0.0534625 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −58.3859 | −1.93018 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1642 | 0.434721 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.2282 | 1.19506 | 0.597529 | − | 0.801847i | \(-0.296149\pi\) | ||||
0.597529 | + | 0.801847i | \(0.296149\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.9268 | −1.44744 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.06145 | −0.0349379 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.11036 | 0.135148 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.1805 | −0.662815 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.6482 | 0.546210 | 0.273105 | − | 0.961984i | \(-0.411949\pi\) | ||||
0.273105 | + | 0.961984i | \(0.411949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.50056 | −0.180273 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.3661 | −0.797710 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.17384 | −0.0710922 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.4319 | −0.536807 | −0.268403 | − | 0.963307i | \(-0.586496\pi\) | ||||
−0.268403 | + | 0.963307i | \(0.586496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −38.9755 | −1.27192 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.5679 | 0.540099 | 0.270049 | − | 0.962846i | \(-0.412960\pi\) | ||||
0.270049 | + | 0.962846i | \(0.412960\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −63.1652 | −2.05694 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.67456 | 0.282183 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.7431 | −0.576574 | −0.288287 | − | 0.957544i | \(-0.593086\pi\) | ||||
−0.288287 | + | 0.957544i | \(0.593086\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.7998 | −0.740113 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.1739 | −1.52972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.9557 | 0.711213 | 0.355607 | − | 0.934636i | \(-0.384274\pi\) | ||||
0.355607 | + | 0.934636i | \(0.384274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −50.0138 | −1.61841 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.29607 | −0.268174 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.85872 | 0.221480 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.46955 | 0.0474047 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.3185 | 0.686980 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.18800 | −0.199199 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.2420 | 0.715255 | 0.357628 | − | 0.933864i | \(-0.383586\pi\) | ||||
0.357628 | + | 0.933864i | \(0.383586\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.2713 | 0.683333 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.5681 | 0.852612 | 0.426306 | − | 0.904579i | \(-0.359815\pi\) | ||||
0.426306 | + | 0.904579i | \(0.359815\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.8721 | 0.733244 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −23.8832 | −0.764873 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.54985 | −0.305527 | −0.152763 | − | 0.988263i | \(-0.548817\pi\) | ||||
−0.152763 | + | 0.988263i | \(0.548817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.727526 | −0.0232518 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.7180 | −0.469911 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.65760 | 0.180449 | 0.0902247 | − | 0.995921i | \(-0.471241\pi\) | ||||
0.0902247 | + | 0.995921i | \(0.471241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.6291 | 0.721023 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.977219 | −0.0311052 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.43682 | −0.141083 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62.8260 | −1.99573 | −0.997867 | − | 0.0652866i | \(-0.979204\pi\) | ||||
−0.997867 | + | 0.0652866i | \(0.979204\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.3216 | 0.517951 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.2287 | 0.768100 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.14444 | 0.257937 | 0.128969 | − | 0.991649i | \(-0.458833\pi\) | ||||
0.128969 | + | 0.991649i | \(0.458833\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.88449 | 0.249454 |
(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 | 7168.2.a.bf.1.2 | 8 | ||
4.3 | odd | 2 | 7168.2.a.be.1.7 | 8 | |||
8.3 | odd | 2 | 7168.2.a.ba.1.2 | 8 | |||
8.5 | even | 2 | 7168.2.a.bb.1.7 | 8 | |||
32.3 | odd | 8 | 1792.2.m.f.1345.8 | yes | 16 | ||
32.5 | even | 8 | 1792.2.m.e.449.8 | ✓ | 16 | ||
32.11 | odd | 8 | 1792.2.m.f.449.8 | yes | 16 | ||
32.13 | even | 8 | 1792.2.m.e.1345.8 | yes | 16 | ||
32.19 | odd | 8 | 1792.2.m.g.1345.1 | yes | 16 | ||
32.21 | even | 8 | 1792.2.m.h.449.1 | yes | 16 | ||
32.27 | odd | 8 | 1792.2.m.g.449.1 | yes | 16 | ||
32.29 | even | 8 | 1792.2.m.h.1345.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1792.2.m.e.449.8 | ✓ | 16 | 32.5 | even | 8 | ||
1792.2.m.e.1345.8 | yes | 16 | 32.13 | even | 8 | ||
1792.2.m.f.449.8 | yes | 16 | 32.11 | odd | 8 | ||
1792.2.m.f.1345.8 | yes | 16 | 32.3 | odd | 8 | ||
1792.2.m.g.449.1 | yes | 16 | 32.27 | odd | 8 | ||
1792.2.m.g.1345.1 | yes | 16 | 32.19 | odd | 8 | ||
1792.2.m.h.449.1 | yes | 16 | 32.21 | even | 8 | ||
1792.2.m.h.1345.1 | yes | 16 | 32.29 | even | 8 | ||
7168.2.a.ba.1.2 | 8 | 8.3 | odd | 2 | |||
7168.2.a.bb.1.7 | 8 | 8.5 | even | 2 | |||
7168.2.a.be.1.7 | 8 | 4.3 | odd | 2 | |||
7168.2.a.bf.1.2 | 8 | 1.1 | even | 1 | trivial |