Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.113481.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 9x^{2} + 3x + 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 574) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.31920\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.07936 | −1.82435 | −0.912173 | − | 0.409805i | \(-0.865597\pi\) | ||||
−0.912173 | + | 0.409805i | \(0.865597\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 4.07936 | 1.29001 | ||||||||
\(11\) | −1.94052 | −0.585089 | −0.292544 | − | 0.956252i | \(-0.594502\pi\) | ||||
−0.292544 | + | 0.956252i | \(0.594502\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 4.70068 | 1.30374 | 0.651868 | − | 0.758333i | \(-0.273986\pi\) | ||||
0.651868 | + | 0.758333i | \(0.273986\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.07936 | −1.05329 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.440968 | 0.106950 | 0.0534752 | − | 0.998569i | \(-0.482970\pi\) | ||||
0.0534752 | + | 0.998569i | \(0.482970\pi\) | |||||||
\(18\) | 2.00000 | 0.471405 | ||||||||
\(19\) | 4.01707 | 0.921580 | 0.460790 | − | 0.887509i | \(-0.347566\pi\) | ||||
0.460790 | + | 0.887509i | \(0.347566\pi\) | |||||||
\(20\) | −4.07936 | −0.912173 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.94052 | 0.413720 | ||||||||
\(23\) | 4.39856 | 0.917163 | 0.458582 | − | 0.888652i | \(-0.348358\pi\) | ||||
0.458582 | + | 0.888652i | \(0.348358\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 11.6412 | 2.32824 | ||||||||
\(26\) | −4.70068 | −0.921880 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.37868 | −0.813100 | −0.406550 | − | 0.913628i | \(-0.633268\pi\) | ||||
−0.406550 | + | 0.913628i | \(0.633268\pi\) | |||||||
\(30\) | 4.07936 | 0.744786 | ||||||||
\(31\) | −6.06229 | −1.08882 | −0.544410 | − | 0.838819i | \(-0.683246\pi\) | ||||
−0.544410 | + | 0.838819i | \(0.683246\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.94052 | −0.337801 | ||||||||
\(34\) | −0.440968 | −0.0756253 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 5.95759 | 0.979422 | 0.489711 | − | 0.871885i | \(-0.337102\pi\) | ||||
0.489711 | + | 0.871885i | \(0.337102\pi\) | |||||||
\(38\) | −4.01707 | −0.651655 | ||||||||
\(39\) | 4.70068 | 0.752712 | ||||||||
\(40\) | 4.07936 | 0.645004 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.45804 | −0.527346 | −0.263673 | − | 0.964612i | \(-0.584934\pi\) | ||||
−0.263673 | + | 0.964612i | \(0.584934\pi\) | |||||||
\(44\) | −1.94052 | −0.292544 | ||||||||
\(45\) | 8.15873 | 1.21623 | ||||||||
\(46\) | −4.39856 | −0.648532 | ||||||||
\(47\) | −1.69788 | −0.247661 | −0.123830 | − | 0.992303i | \(-0.539518\pi\) | ||||
−0.123830 | + | 0.992303i | \(0.539518\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −11.6412 | −1.64631 | ||||||||
\(51\) | 0.440968 | 0.0617478 | ||||||||
\(52\) | 4.70068 | 0.651868 | ||||||||
\(53\) | 3.31920 | 0.455927 | 0.227963 | − | 0.973670i | \(-0.426793\pi\) | ||||
0.227963 | + | 0.973670i | \(0.426793\pi\) | |||||||
\(54\) | 5.00000 | 0.680414 | ||||||||
\(55\) | 7.91608 | 1.06740 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.01707 | 0.532074 | ||||||||
\(58\) | 4.37868 | 0.574949 | ||||||||
\(59\) | 9.41564 | 1.22581 | 0.612906 | − | 0.790156i | \(-0.290001\pi\) | ||||
0.612906 | + | 0.790156i | \(0.290001\pi\) | |||||||
\(60\) | −4.07936 | −0.526644 | ||||||||
\(61\) | 10.8423 | 1.38822 | 0.694110 | − | 0.719869i | \(-0.255798\pi\) | ||||
0.694110 | + | 0.719869i | \(0.255798\pi\) | |||||||
\(62\) | 6.06229 | 0.769911 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −19.1758 | −2.37847 | ||||||||
\(66\) | 1.94052 | 0.238861 | ||||||||
\(67\) | −4.01988 | −0.491107 | −0.245553 | − | 0.969383i | \(-0.578970\pi\) | ||||
−0.245553 | + | 0.969383i | \(0.578970\pi\) | |||||||
\(68\) | 0.440968 | 0.0534752 | ||||||||
\(69\) | 4.39856 | 0.529525 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.12087 | −0.370380 | −0.185190 | − | 0.982703i | \(-0.559290\pi\) | ||||
−0.185190 | + | 0.982703i | \(0.559290\pi\) | |||||||
\(72\) | 2.00000 | 0.235702 | ||||||||
\(73\) | −9.01707 | −1.05537 | −0.527684 | − | 0.849441i | \(-0.676940\pi\) | ||||
−0.527684 | + | 0.849441i | \(0.676940\pi\) | |||||||
\(74\) | −5.95759 | −0.692556 | ||||||||
\(75\) | 11.6412 | 1.34421 | ||||||||
\(76\) | 4.01707 | 0.460790 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.70068 | −0.532248 | ||||||||
\(79\) | −16.7800 | −1.88790 | −0.943951 | − | 0.330084i | \(-0.892923\pi\) | ||||
−0.943951 | + | 0.330084i | \(0.892923\pi\) | |||||||
\(80\) | −4.07936 | −0.456087 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.00000 | 0.110432 | ||||||||
\(83\) | −2.43726 | −0.267524 | −0.133762 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133762 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.79887 | −0.195115 | ||||||||
\(86\) | 3.45804 | 0.372890 | ||||||||
\(87\) | −4.37868 | −0.469444 | ||||||||
\(88\) | 1.94052 | 0.206860 | ||||||||
\(89\) | 5.01707 | 0.531809 | 0.265904 | − | 0.963999i | \(-0.414329\pi\) | ||||
0.265904 | + | 0.963999i | \(0.414329\pi\) | |||||||
\(90\) | −8.15873 | −0.860005 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.39856 | 0.458582 | ||||||||
\(93\) | −6.06229 | −0.628630 | ||||||||
\(94\) | 1.69788 | 0.175123 | ||||||||
\(95\) | −16.3871 | −1.68128 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 15.5402 | 1.57787 | 0.788935 | − | 0.614477i | \(-0.210633\pi\) | ||||
0.788935 | + | 0.614477i | \(0.210633\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.88104 | 0.390059 | ||||||||
\(100\) | 11.6412 | 1.16412 | ||||||||
\(101\) | −13.7178 | −1.36497 | −0.682484 | − | 0.730901i | \(-0.739100\pi\) | ||||
−0.682484 | + | 0.730901i | \(0.739100\pi\) | |||||||
\(102\) | −0.440968 | −0.0436623 | ||||||||
\(103\) | 18.9803 | 1.87018 | 0.935092 | − | 0.354406i | \(-0.115317\pi\) | ||||
0.935092 | + | 0.354406i | \(0.115317\pi\) | |||||||
\(104\) | −4.70068 | −0.460940 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.31920 | −0.322389 | ||||||||
\(107\) | −7.25691 | −0.701552 | −0.350776 | − | 0.936459i | \(-0.614082\pi\) | ||||
−0.350776 | + | 0.936459i | \(0.614082\pi\) | |||||||
\(108\) | −5.00000 | −0.481125 | ||||||||
\(109\) | 2.53740 | 0.243039 | 0.121520 | − | 0.992589i | \(-0.461223\pi\) | ||||
0.121520 | + | 0.992589i | \(0.461223\pi\) | |||||||
\(110\) | −7.91608 | −0.754769 | ||||||||
\(111\) | 5.95759 | 0.565470 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.68080 | −0.534405 | −0.267202 | − | 0.963640i | \(-0.586099\pi\) | ||||
−0.267202 | + | 0.963640i | \(0.586099\pi\) | |||||||
\(114\) | −4.01707 | −0.376233 | ||||||||
\(115\) | −17.9433 | −1.67322 | ||||||||
\(116\) | −4.37868 | −0.406550 | ||||||||
\(117\) | −9.40137 | −0.869157 | ||||||||
\(118\) | −9.41564 | −0.866779 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.07936 | 0.372393 | ||||||||
\(121\) | −7.23438 | −0.657671 | ||||||||
\(122\) | −10.8423 | −0.981619 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | −6.06229 | −0.544410 | ||||||||
\(125\) | −27.0919 | −2.42317 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.3986 | −1.27767 | −0.638833 | − | 0.769346i | \(-0.720582\pi\) | ||||
−0.638833 | + | 0.769346i | \(0.720582\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.45804 | −0.304464 | ||||||||
\(130\) | 19.1758 | 1.68183 | ||||||||
\(131\) | −10.3419 | −0.903575 | −0.451788 | − | 0.892126i | \(-0.649213\pi\) | ||||
−0.451788 | + | 0.892126i | \(0.649213\pi\) | |||||||
\(132\) | −1.94052 | −0.168901 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.01988 | 0.347265 | ||||||||
\(135\) | 20.3968 | 1.75548 | ||||||||
\(136\) | −0.440968 | −0.0378127 | ||||||||
\(137\) | −1.33346 | −0.113925 | −0.0569627 | − | 0.998376i | \(-0.518142\pi\) | ||||
−0.0569627 | + | 0.998376i | \(0.518142\pi\) | |||||||
\(138\) | −4.39856 | −0.374430 | ||||||||
\(139\) | −2.24545 | −0.190457 | −0.0952284 | − | 0.995455i | \(-0.530358\pi\) | ||||
−0.0952284 | + | 0.995455i | \(0.530358\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.69788 | −0.142987 | ||||||||
\(142\) | 3.12087 | 0.261898 | ||||||||
\(143\) | −9.12177 | −0.762801 | ||||||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | 17.8622 | 1.48338 | ||||||||
\(146\) | 9.01707 | 0.746258 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.95759 | 0.489711 | ||||||||
\(149\) | −12.4165 | −1.01720 | −0.508601 | − | 0.861002i | \(-0.669837\pi\) | ||||
−0.508601 | + | 0.861002i | \(0.669837\pi\) | |||||||
\(150\) | −11.6412 | −0.950500 | ||||||||
\(151\) | −11.9613 | −0.973397 | −0.486698 | − | 0.873570i | \(-0.661799\pi\) | ||||
−0.486698 | + | 0.873570i | \(0.661799\pi\) | |||||||
\(152\) | −4.01707 | −0.325828 | ||||||||
\(153\) | −0.881935 | −0.0713002 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 24.7303 | 1.98638 | ||||||||
\(156\) | 4.70068 | 0.376356 | ||||||||
\(157\) | 8.56184 | 0.683309 | 0.341655 | − | 0.939826i | \(-0.389013\pi\) | ||||
0.341655 | + | 0.939826i | \(0.389013\pi\) | |||||||
\(158\) | 16.7800 | 1.33495 | ||||||||
\(159\) | 3.31920 | 0.263230 | ||||||||
\(160\) | 4.07936 | 0.322502 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −20.1200 | −1.57592 | −0.787961 | − | 0.615725i | \(-0.788863\pi\) | ||||
−0.787961 | + | 0.615725i | \(0.788863\pi\) | |||||||
\(164\) | −1.00000 | −0.0780869 | ||||||||
\(165\) | 7.91608 | 0.616266 | ||||||||
\(166\) | 2.43726 | 0.189168 | ||||||||
\(167\) | 19.0794 | 1.47641 | 0.738203 | − | 0.674579i | \(-0.235675\pi\) | ||||
0.738203 | + | 0.674579i | \(0.235675\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.09644 | 0.699726 | ||||||||
\(170\) | 1.79887 | 0.137967 | ||||||||
\(171\) | −8.03415 | −0.614387 | ||||||||
\(172\) | −3.45804 | −0.263673 | ||||||||
\(173\) | −23.6838 | −1.80064 | −0.900322 | − | 0.435224i | \(-0.856669\pi\) | ||||
−0.900322 | + | 0.435224i | \(0.856669\pi\) | |||||||
\(174\) | 4.37868 | 0.331947 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.94052 | −0.146272 | ||||||||
\(177\) | 9.41564 | 0.707722 | ||||||||
\(178\) | −5.01707 | −0.376046 | ||||||||
\(179\) | −10.7178 | −0.801083 | −0.400541 | − | 0.916279i | \(-0.631178\pi\) | ||||
−0.400541 | + | 0.916279i | \(0.631178\pi\) | |||||||
\(180\) | 8.15873 | 0.608116 | ||||||||
\(181\) | −19.2381 | −1.42996 | −0.714978 | − | 0.699147i | \(-0.753563\pi\) | ||||
−0.714978 | + | 0.699147i | \(0.753563\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.8423 | 0.801489 | ||||||||
\(184\) | −4.39856 | −0.324266 | ||||||||
\(185\) | −24.3032 | −1.78681 | ||||||||
\(186\) | 6.06229 | 0.444509 | ||||||||
\(187\) | −0.855706 | −0.0625754 | ||||||||
\(188\) | −1.69788 | −0.123830 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 16.3871 | 1.18885 | ||||||||
\(191\) | −2.13884 | −0.154761 | −0.0773807 | − | 0.997002i | \(-0.524656\pi\) | ||||
−0.0773807 | + | 0.997002i | \(0.524656\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 14.9217 | 1.07409 | 0.537044 | − | 0.843554i | \(-0.319541\pi\) | ||||
0.537044 | + | 0.843554i | \(0.319541\pi\) | |||||||
\(194\) | −15.5402 | −1.11572 | ||||||||
\(195\) | −19.1758 | −1.37321 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.2524 | −1.58541 | −0.792707 | − | 0.609602i | \(-0.791329\pi\) | ||||
−0.792707 | + | 0.609602i | \(0.791329\pi\) | |||||||
\(198\) | −3.88104 | −0.275813 | ||||||||
\(199\) | 1.48248 | 0.105090 | 0.0525450 | − | 0.998619i | \(-0.483267\pi\) | ||||
0.0525450 | + | 0.998619i | \(0.483267\pi\) | |||||||
\(200\) | −11.6412 | −0.823157 | ||||||||
\(201\) | −4.01988 | −0.283541 | ||||||||
\(202\) | 13.7178 | 0.965178 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.440968 | 0.0308739 | ||||||||
\(205\) | 4.07936 | 0.284915 | ||||||||
\(206\) | −18.9803 | −1.32242 | ||||||||
\(207\) | −8.79712 | −0.611442 | ||||||||
\(208\) | 4.70068 | 0.325934 | ||||||||
\(209\) | −7.79521 | −0.539206 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8226 | −1.64002 | −0.820008 | − | 0.572351i | \(-0.806031\pi\) | ||||
−0.820008 | + | 0.572351i | \(0.806031\pi\) | |||||||
\(212\) | 3.31920 | 0.227963 | ||||||||
\(213\) | −3.12087 | −0.213839 | ||||||||
\(214\) | 7.25691 | 0.496072 | ||||||||
\(215\) | 14.1066 | 0.962063 | ||||||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.53740 | −0.171855 | ||||||||
\(219\) | −9.01707 | −0.609317 | ||||||||
\(220\) | 7.91608 | 0.533702 | ||||||||
\(221\) | 2.07285 | 0.139435 | ||||||||
\(222\) | −5.95759 | −0.399847 | ||||||||
\(223\) | 6.91608 | 0.463135 | 0.231568 | − | 0.972819i | \(-0.425615\pi\) | ||||
0.231568 | + | 0.972819i | \(0.425615\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23.2824 | −1.55216 | ||||||||
\(226\) | 5.68080 | 0.377881 | ||||||||
\(227\) | 21.1606 | 1.40448 | 0.702240 | − | 0.711940i | \(-0.252183\pi\) | ||||
0.702240 | + | 0.711940i | \(0.252183\pi\) | |||||||
\(228\) | 4.01707 | 0.266037 | ||||||||
\(229\) | −17.8709 | −1.18094 | −0.590470 | − | 0.807060i | \(-0.701058\pi\) | ||||
−0.590470 | + | 0.807060i | \(0.701058\pi\) | |||||||
\(230\) | 17.9433 | 1.18315 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.37868 | 0.287474 | ||||||||
\(233\) | −19.8847 | −1.30269 | −0.651346 | − | 0.758780i | \(-0.725796\pi\) | ||||
−0.651346 | + | 0.758780i | \(0.725796\pi\) | |||||||
\(234\) | 9.40137 | 0.614587 | ||||||||
\(235\) | 6.92625 | 0.451819 | ||||||||
\(236\) | 9.41564 | 0.612906 | ||||||||
\(237\) | −16.7800 | −1.08998 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.61396 | −0.621875 | −0.310938 | − | 0.950430i | \(-0.600643\pi\) | ||||
−0.310938 | + | 0.950430i | \(0.600643\pi\) | |||||||
\(240\) | −4.07936 | −0.263322 | ||||||||
\(241\) | −12.1587 | −0.783212 | −0.391606 | − | 0.920133i | \(-0.628080\pi\) | ||||
−0.391606 | + | 0.920133i | \(0.628080\pi\) | |||||||
\(242\) | 7.23438 | 0.465044 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 10.8423 | 0.694110 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.00000 | 0.0637577 | ||||||||
\(247\) | 18.8830 | 1.20150 | ||||||||
\(248\) | 6.06229 | 0.384956 | ||||||||
\(249\) | −2.43726 | −0.154455 | ||||||||
\(250\) | 27.0919 | 1.71344 | ||||||||
\(251\) | −21.7234 | −1.37117 | −0.685584 | − | 0.727994i | \(-0.740453\pi\) | ||||
−0.685584 | + | 0.727994i | \(0.740453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.53549 | −0.536622 | ||||||||
\(254\) | 14.3986 | 0.903446 | ||||||||
\(255\) | −1.79887 | −0.112649 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.4697 | 1.58875 | 0.794377 | − | 0.607425i | \(-0.207797\pi\) | ||||
0.794377 | + | 0.607425i | \(0.207797\pi\) | |||||||
\(258\) | 3.45804 | 0.215288 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −19.1758 | −1.18923 | ||||||||
\(261\) | 8.75736 | 0.542067 | ||||||||
\(262\) | 10.3419 | 0.638924 | ||||||||
\(263\) | 0.982926 | 0.0606098 | 0.0303049 | − | 0.999541i | \(-0.490352\pi\) | ||||
0.0303049 | + | 0.999541i | \(0.490352\pi\) | |||||||
\(264\) | 1.94052 | 0.119431 | ||||||||
\(265\) | −13.5402 | −0.831769 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.01707 | 0.307040 | ||||||||
\(268\) | −4.01988 | −0.245553 | ||||||||
\(269\) | −16.5800 | −1.01090 | −0.505450 | − | 0.862856i | \(-0.668673\pi\) | ||||
−0.505450 | + | 0.862856i | \(0.668673\pi\) | |||||||
\(270\) | −20.3968 | −1.24131 | ||||||||
\(271\) | 0.900754 | 0.0547169 | 0.0273585 | − | 0.999626i | \(-0.491290\pi\) | ||||
0.0273585 | + | 0.999626i | \(0.491290\pi\) | |||||||
\(272\) | 0.440968 | 0.0267376 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.33346 | 0.0805575 | ||||||||
\(275\) | −22.5900 | −1.36223 | ||||||||
\(276\) | 4.39856 | 0.264762 | ||||||||
\(277\) | 22.7811 | 1.36878 | 0.684392 | − | 0.729114i | \(-0.260068\pi\) | ||||
0.684392 | + | 0.729114i | \(0.260068\pi\) | |||||||
\(278\) | 2.24545 | 0.134673 | ||||||||
\(279\) | 12.1246 | 0.725880 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.3940 | 1.33591 | 0.667957 | − | 0.744200i | \(-0.267169\pi\) | ||||
0.667957 | + | 0.744200i | \(0.267169\pi\) | |||||||
\(282\) | 1.69788 | 0.101107 | ||||||||
\(283\) | −8.25601 | −0.490769 | −0.245384 | − | 0.969426i | \(-0.578914\pi\) | ||||
−0.245384 | + | 0.969426i | \(0.578914\pi\) | |||||||
\(284\) | −3.12087 | −0.185190 | ||||||||
\(285\) | −16.3871 | −0.970688 | ||||||||
\(286\) | 9.12177 | 0.539382 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.00000 | 0.117851 | ||||||||
\(289\) | −16.8055 | −0.988562 | ||||||||
\(290\) | −17.8622 | −1.04891 | ||||||||
\(291\) | 15.5402 | 0.910983 | ||||||||
\(292\) | −9.01707 | −0.527684 | ||||||||
\(293\) | 22.0938 | 1.29073 | 0.645367 | − | 0.763873i | \(-0.276705\pi\) | ||||
0.645367 | + | 0.763873i | \(0.276705\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.4098 | −2.23630 | ||||||||
\(296\) | −5.95759 | −0.346278 | ||||||||
\(297\) | 9.70260 | 0.563002 | ||||||||
\(298\) | 12.4165 | 0.719270 | ||||||||
\(299\) | 20.6762 | 1.19574 | ||||||||
\(300\) | 11.6412 | 0.672105 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.9613 | 0.688295 | ||||||||
\(303\) | −13.7178 | −0.788065 | ||||||||
\(304\) | 4.01707 | 0.230395 | ||||||||
\(305\) | −44.2298 | −2.53259 | ||||||||
\(306\) | 0.881935 | 0.0504169 | ||||||||
\(307\) | 14.3382 | 0.818323 | 0.409162 | − | 0.912462i | \(-0.365821\pi\) | ||||
0.409162 | + | 0.912462i | \(0.365821\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.9803 | 1.07975 | ||||||||
\(310\) | −24.7303 | −1.40459 | ||||||||
\(311\) | −11.3049 | −0.641044 | −0.320522 | − | 0.947241i | \(-0.603858\pi\) | ||||
−0.320522 | + | 0.947241i | \(0.603858\pi\) | |||||||
\(312\) | −4.70068 | −0.266124 | ||||||||
\(313\) | −18.6196 | −1.05244 | −0.526220 | − | 0.850348i | \(-0.676391\pi\) | ||||
−0.526220 | + | 0.850348i | \(0.676391\pi\) | |||||||
\(314\) | −8.56184 | −0.483173 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.7800 | −0.943951 | ||||||||
\(317\) | −5.65547 | −0.317643 | −0.158821 | − | 0.987307i | \(-0.550769\pi\) | ||||
−0.158821 | + | 0.987307i | \(0.550769\pi\) | |||||||
\(318\) | −3.31920 | −0.186131 | ||||||||
\(319\) | 8.49691 | 0.475736 | ||||||||
\(320\) | −4.07936 | −0.228043 | ||||||||
\(321\) | −7.25691 | −0.405041 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.77140 | 0.0985633 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 54.7216 | 3.03541 | ||||||||
\(326\) | 20.1200 | 1.11435 | ||||||||
\(327\) | 2.53740 | 0.140319 | ||||||||
\(328\) | 1.00000 | 0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.91608 | −0.435766 | ||||||||
\(331\) | 29.4448 | 1.61843 | 0.809217 | − | 0.587509i | \(-0.199891\pi\) | ||||
0.809217 | + | 0.587509i | \(0.199891\pi\) | |||||||
\(332\) | −2.43726 | −0.133762 | ||||||||
\(333\) | −11.9152 | −0.652948 | ||||||||
\(334\) | −19.0794 | −1.04398 | ||||||||
\(335\) | 16.3986 | 0.895949 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.2266 | −1.37418 | −0.687091 | − | 0.726571i | \(-0.741113\pi\) | ||||
−0.687091 | + | 0.726571i | \(0.741113\pi\) | |||||||
\(338\) | −9.09644 | −0.494781 | ||||||||
\(339\) | −5.68080 | −0.308539 | ||||||||
\(340\) | −1.79887 | −0.0975573 | ||||||||
\(341\) | 11.7640 | 0.637056 | ||||||||
\(342\) | 8.03415 | 0.434437 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.45804 | 0.186445 | ||||||||
\(345\) | −17.9433 | −0.966036 | ||||||||
\(346\) | 23.6838 | 1.27325 | ||||||||
\(347\) | 25.6113 | 1.37489 | 0.687444 | − | 0.726238i | \(-0.258733\pi\) | ||||
0.687444 | + | 0.726238i | \(0.258733\pi\) | |||||||
\(348\) | −4.37868 | −0.234722 | ||||||||
\(349\) | −8.25601 | −0.441934 | −0.220967 | − | 0.975281i | \(-0.570921\pi\) | ||||
−0.220967 | + | 0.975281i | \(0.570921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.5034 | −1.25452 | ||||||||
\(352\) | 1.94052 | 0.103430 | ||||||||
\(353\) | 26.8423 | 1.42867 | 0.714337 | − | 0.699802i | \(-0.246729\pi\) | ||||
0.714337 | + | 0.699802i | \(0.246729\pi\) | |||||||
\(354\) | −9.41564 | −0.500435 | ||||||||
\(355\) | 12.7312 | 0.675701 | ||||||||
\(356\) | 5.01707 | 0.265904 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.7178 | 0.566451 | ||||||||
\(359\) | 0.384295 | 0.0202823 | 0.0101412 | − | 0.999949i | \(-0.496772\pi\) | ||||
0.0101412 | + | 0.999949i | \(0.496772\pi\) | |||||||
\(360\) | −8.15873 | −0.430003 | ||||||||
\(361\) | −2.86312 | −0.150690 | ||||||||
\(362\) | 19.2381 | 1.01113 | ||||||||
\(363\) | −7.23438 | −0.379707 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 36.7839 | 1.92536 | ||||||||
\(366\) | −10.8423 | −0.566738 | ||||||||
\(367\) | 13.1841 | 0.688202 | 0.344101 | − | 0.938933i | \(-0.388184\pi\) | ||||
0.344101 | + | 0.938933i | \(0.388184\pi\) | |||||||
\(368\) | 4.39856 | 0.229291 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 24.3032 | 1.26346 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.06229 | −0.314315 | ||||||||
\(373\) | 22.7718 | 1.17908 | 0.589539 | − | 0.807740i | \(-0.299309\pi\) | ||||
0.589539 | + | 0.807740i | \(0.299309\pi\) | |||||||
\(374\) | 0.855706 | 0.0442475 | ||||||||
\(375\) | −27.0919 | −1.39902 | ||||||||
\(376\) | 1.69788 | 0.0875613 | ||||||||
\(377\) | −20.5828 | −1.06007 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.1870 | 1.60197 | 0.800985 | − | 0.598684i | \(-0.204310\pi\) | ||||
0.800985 | + | 0.598684i | \(0.204310\pi\) | |||||||
\(380\) | −16.3871 | −0.840641 | ||||||||
\(381\) | −14.3986 | −0.737661 | ||||||||
\(382\) | 2.13884 | 0.109433 | ||||||||
\(383\) | −26.4933 | −1.35374 | −0.676871 | − | 0.736102i | \(-0.736665\pi\) | ||||
−0.676871 | + | 0.736102i | \(0.736665\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.9217 | −0.759495 | ||||||||
\(387\) | 6.91608 | 0.351564 | ||||||||
\(388\) | 15.5402 | 0.788935 | ||||||||
\(389\) | −25.3741 | −1.28652 | −0.643260 | − | 0.765648i | \(-0.722418\pi\) | ||||
−0.643260 | + | 0.765648i | \(0.722418\pi\) | |||||||
\(390\) | 19.1758 | 0.971004 | ||||||||
\(391\) | 1.93962 | 0.0980909 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.3419 | −0.521679 | ||||||||
\(394\) | 22.2524 | 1.12106 | ||||||||
\(395\) | 68.4519 | 3.44419 | ||||||||
\(396\) | 3.88104 | 0.195030 | ||||||||
\(397\) | −20.2409 | −1.01586 | −0.507931 | − | 0.861398i | \(-0.669589\pi\) | ||||
−0.507931 | + | 0.861398i | \(0.669589\pi\) | |||||||
\(398\) | −1.48248 | −0.0743099 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.6412 | 0.582060 | ||||||||
\(401\) | 24.1769 | 1.20733 | 0.603667 | − | 0.797236i | \(-0.293705\pi\) | ||||
0.603667 | + | 0.797236i | \(0.293705\pi\) | |||||||
\(402\) | 4.01988 | 0.200494 | ||||||||
\(403\) | −28.4969 | −1.41953 | ||||||||
\(404\) | −13.7178 | −0.682484 | ||||||||
\(405\) | −4.07936 | −0.202705 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.5608 | −0.573049 | ||||||||
\(408\) | −0.440968 | −0.0218311 | ||||||||
\(409\) | −0.369133 | −0.0182525 | −0.00912624 | − | 0.999958i | \(-0.502905\pi\) | ||||
−0.00912624 | + | 0.999958i | \(0.502905\pi\) | |||||||
\(410\) | −4.07936 | −0.201465 | ||||||||
\(411\) | −1.33346 | −0.0657749 | ||||||||
\(412\) | 18.9803 | 0.935092 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.79712 | 0.432355 | ||||||||
\(415\) | 9.94248 | 0.488057 | ||||||||
\(416\) | −4.70068 | −0.230470 | ||||||||
\(417\) | −2.24545 | −0.109960 | ||||||||
\(418\) | 7.79521 | 0.381276 | ||||||||
\(419\) | 23.1427 | 1.13060 | 0.565298 | − | 0.824887i | \(-0.308761\pi\) | ||||
0.565298 | + | 0.824887i | \(0.308761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.35790 | 0.163654 | 0.0818270 | − | 0.996647i | \(-0.473925\pi\) | ||||
0.0818270 | + | 0.996647i | \(0.473925\pi\) | |||||||
\(422\) | 23.8226 | 1.15967 | ||||||||
\(423\) | 3.39575 | 0.165107 | ||||||||
\(424\) | −3.31920 | −0.161194 | ||||||||
\(425\) | 5.13339 | 0.249006 | ||||||||
\(426\) | 3.12087 | 0.151207 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.25691 | −0.350776 | ||||||||
\(429\) | −9.12177 | −0.440403 | ||||||||
\(430\) | −14.1066 | −0.680281 | ||||||||
\(431\) | −14.4267 | −0.694910 | −0.347455 | − | 0.937697i | \(-0.612954\pi\) | ||||
−0.347455 | + | 0.937697i | \(0.612954\pi\) | |||||||
\(432\) | −5.00000 | −0.240563 | ||||||||
\(433\) | −17.0172 | −0.817796 | −0.408898 | − | 0.912580i | \(-0.634087\pi\) | ||||
−0.408898 | + | 0.912580i | \(0.634087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.8622 | 0.856428 | ||||||||
\(436\) | 2.53740 | 0.121520 | ||||||||
\(437\) | 17.6693 | 0.845239 | ||||||||
\(438\) | 9.01707 | 0.430852 | ||||||||
\(439\) | 6.95198 | 0.331800 | 0.165900 | − | 0.986143i | \(-0.446947\pi\) | ||||
0.165900 | + | 0.986143i | \(0.446947\pi\) | |||||||
\(440\) | −7.91608 | −0.377384 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.07285 | −0.0985954 | ||||||||
\(443\) | −6.93861 | −0.329663 | −0.164832 | − | 0.986322i | \(-0.552708\pi\) | ||||
−0.164832 | + | 0.986322i | \(0.552708\pi\) | |||||||
\(444\) | 5.95759 | 0.282735 | ||||||||
\(445\) | −20.4665 | −0.970204 | ||||||||
\(446\) | −6.91608 | −0.327486 | ||||||||
\(447\) | −12.4165 | −0.587282 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.34363 | −0.299375 | −0.149687 | − | 0.988733i | \(-0.547827\pi\) | ||||
−0.149687 | + | 0.988733i | \(0.547827\pi\) | |||||||
\(450\) | 23.2824 | 1.09754 | ||||||||
\(451\) | 1.94052 | 0.0913755 | ||||||||
\(452\) | −5.68080 | −0.267202 | ||||||||
\(453\) | −11.9613 | −0.561991 | ||||||||
\(454\) | −21.1606 | −0.993118 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.01707 | −0.188117 | ||||||||
\(457\) | −0.102054 | −0.00477390 | −0.00238695 | − | 0.999997i | \(-0.500760\pi\) | ||||
−0.00238695 | + | 0.999997i | \(0.500760\pi\) | |||||||
\(458\) | 17.8709 | 0.835051 | ||||||||
\(459\) | −2.20484 | −0.102913 | ||||||||
\(460\) | −17.9433 | −0.836612 | ||||||||
\(461\) | 32.0692 | 1.49361 | 0.746806 | − | 0.665042i | \(-0.231587\pi\) | ||||
0.746806 | + | 0.665042i | \(0.231587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.6907 | −1.42632 | −0.713158 | − | 0.701003i | \(-0.752736\pi\) | ||||
−0.713158 | + | 0.701003i | \(0.752736\pi\) | |||||||
\(464\) | −4.37868 | −0.203275 | ||||||||
\(465\) | 24.7303 | 1.14684 | ||||||||
\(466\) | 19.8847 | 0.921143 | ||||||||
\(467\) | 16.2852 | 0.753590 | 0.376795 | − | 0.926297i | \(-0.377026\pi\) | ||||
0.376795 | + | 0.926297i | \(0.377026\pi\) | |||||||
\(468\) | −9.40137 | −0.434578 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.92625 | −0.319484 | ||||||||
\(471\) | 8.56184 | 0.394509 | ||||||||
\(472\) | −9.41564 | −0.433390 | ||||||||
\(473\) | 6.71040 | 0.308544 | ||||||||
\(474\) | 16.7800 | 0.770733 | ||||||||
\(475\) | 46.7636 | 2.14566 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.63840 | −0.303951 | ||||||||
\(478\) | 9.61396 | 0.439732 | ||||||||
\(479\) | −18.9208 | −0.864514 | −0.432257 | − | 0.901751i | \(-0.642283\pi\) | ||||
−0.432257 | + | 0.901751i | \(0.642283\pi\) | |||||||
\(480\) | 4.07936 | 0.186197 | ||||||||
\(481\) | 28.0048 | 1.27691 | ||||||||
\(482\) | 12.1587 | 0.553815 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.23438 | −0.328836 | ||||||||
\(485\) | −63.3942 | −2.87858 | ||||||||
\(486\) | −16.0000 | −0.725775 | ||||||||
\(487\) | −31.0190 | −1.40560 | −0.702802 | − | 0.711385i | \(-0.748068\pi\) | ||||
−0.702802 | + | 0.711385i | \(0.748068\pi\) | |||||||
\(488\) | −10.8423 | −0.490810 | ||||||||
\(489\) | −20.1200 | −0.909859 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.5780 | −0.657897 | −0.328948 | − | 0.944348i | \(-0.606694\pi\) | ||||
−0.328948 | + | 0.944348i | \(0.606694\pi\) | |||||||
\(492\) | −1.00000 | −0.0450835 | ||||||||
\(493\) | −1.93086 | −0.0869614 | ||||||||
\(494\) | −18.8830 | −0.849586 | ||||||||
\(495\) | −15.8322 | −0.711603 | ||||||||
\(496\) | −6.06229 | −0.272205 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.43726 | 0.109216 | ||||||||
\(499\) | 34.7266 | 1.55457 | 0.777287 | − | 0.629146i | \(-0.216595\pi\) | ||||
0.777287 | + | 0.629146i | \(0.216595\pi\) | |||||||
\(500\) | −27.0919 | −1.21159 | ||||||||
\(501\) | 19.0794 | 0.852403 | ||||||||
\(502\) | 21.7234 | 0.969562 | ||||||||
\(503\) | −15.5498 | −0.693329 | −0.346665 | − | 0.937989i | \(-0.612686\pi\) | ||||
−0.346665 | + | 0.937989i | \(0.612686\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 55.9597 | 2.49017 | ||||||||
\(506\) | 8.53549 | 0.379449 | ||||||||
\(507\) | 9.09644 | 0.403987 | ||||||||
\(508\) | −14.3986 | −0.638833 | ||||||||
\(509\) | −28.8793 | −1.28005 | −0.640026 | − | 0.768353i | \(-0.721076\pi\) | ||||
−0.640026 | + | 0.768353i | \(0.721076\pi\) | |||||||
\(510\) | 1.79887 | 0.0796552 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −20.0854 | −0.886791 | ||||||||
\(514\) | −25.4697 | −1.12342 | ||||||||
\(515\) | −77.4275 | −3.41186 | ||||||||
\(516\) | −3.45804 | −0.152232 | ||||||||
\(517\) | 3.29476 | 0.144903 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.6838 | −1.03960 | ||||||||
\(520\) | 19.1758 | 0.840914 | ||||||||
\(521\) | −25.7009 | −1.12597 | −0.562987 | − | 0.826465i | \(-0.690348\pi\) | ||||
−0.562987 | + | 0.826465i | \(0.690348\pi\) | |||||||
\(522\) | −8.75736 | −0.383299 | ||||||||
\(523\) | −25.3391 | −1.10800 | −0.554000 | − | 0.832516i | \(-0.686899\pi\) | ||||
−0.554000 | + | 0.832516i | \(0.686899\pi\) | |||||||
\(524\) | −10.3419 | −0.451788 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.982926 | −0.0428576 | ||||||||
\(527\) | −2.67327 | −0.116450 | ||||||||
\(528\) | −1.94052 | −0.0844503 | ||||||||
\(529\) | −3.65266 | −0.158811 | ||||||||
\(530\) | 13.5402 | 0.588149 | ||||||||
\(531\) | −18.8313 | −0.817208 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.70068 | −0.203609 | ||||||||
\(534\) | −5.01707 | −0.217110 | ||||||||
\(535\) | 29.6036 | 1.27987 | ||||||||
\(536\) | 4.01988 | 0.173632 | ||||||||
\(537\) | −10.7178 | −0.462505 | ||||||||
\(538\) | 16.5800 | 0.714814 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 20.3968 | 0.877739 | ||||||||
\(541\) | 3.62588 | 0.155889 | 0.0779443 | − | 0.996958i | \(-0.475164\pi\) | ||||
0.0779443 | + | 0.996958i | \(0.475164\pi\) | |||||||
\(542\) | −0.900754 | −0.0386907 | ||||||||
\(543\) | −19.2381 | −0.825585 | ||||||||
\(544\) | −0.440968 | −0.0189063 | ||||||||
\(545\) | −10.3510 | −0.443388 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.5979 | −1.09449 | −0.547245 | − | 0.836973i | \(-0.684323\pi\) | ||||
−0.547245 | + | 0.836973i | \(0.684323\pi\) | |||||||
\(548\) | −1.33346 | −0.0569627 | ||||||||
\(549\) | −21.6847 | −0.925479 | ||||||||
\(550\) | 22.5900 | 0.963240 | ||||||||
\(551\) | −17.5895 | −0.749337 | ||||||||
\(552\) | −4.39856 | −0.187215 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22.7811 | −0.967877 | ||||||||
\(555\) | −24.3032 | −1.03161 | ||||||||
\(556\) | −2.24545 | −0.0952284 | ||||||||
\(557\) | −20.8064 | −0.881597 | −0.440799 | − | 0.897606i | \(-0.645305\pi\) | ||||
−0.440799 | + | 0.897606i | \(0.645305\pi\) | |||||||
\(558\) | −12.1246 | −0.513274 | ||||||||
\(559\) | −16.2552 | −0.687520 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.855706 | −0.0361279 | ||||||||
\(562\) | −22.3940 | −0.944634 | ||||||||
\(563\) | 4.18035 | 0.176181 | 0.0880905 | − | 0.996112i | \(-0.471924\pi\) | ||||
0.0880905 | + | 0.996112i | \(0.471924\pi\) | |||||||
\(564\) | −1.69788 | −0.0714935 | ||||||||
\(565\) | 23.1741 | 0.974940 | ||||||||
\(566\) | 8.25601 | 0.347026 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.12087 | 0.130949 | ||||||||
\(569\) | 22.3313 | 0.936178 | 0.468089 | − | 0.883681i | \(-0.344943\pi\) | ||||
0.468089 | + | 0.883681i | \(0.344943\pi\) | |||||||
\(570\) | 16.3871 | 0.686380 | ||||||||
\(571\) | 0.540213 | 0.0226072 | 0.0113036 | − | 0.999936i | \(-0.496402\pi\) | ||||
0.0113036 | + | 0.999936i | \(0.496402\pi\) | |||||||
\(572\) | −9.12177 | −0.381400 | ||||||||
\(573\) | −2.13884 | −0.0893515 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 51.2045 | 2.13538 | ||||||||
\(576\) | −2.00000 | −0.0833333 | ||||||||
\(577\) | −34.1976 | −1.42367 | −0.711833 | − | 0.702349i | \(-0.752135\pi\) | ||||
−0.711833 | + | 0.702349i | \(0.752135\pi\) | |||||||
\(578\) | 16.8055 | 0.699019 | ||||||||
\(579\) | 14.9217 | 0.620125 | ||||||||
\(580\) | 17.8622 | 0.741688 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −15.5402 | −0.644163 | ||||||||
\(583\) | −6.44097 | −0.266758 | ||||||||
\(584\) | 9.01707 | 0.373129 | ||||||||
\(585\) | 38.3516 | 1.58564 | ||||||||
\(586\) | −22.0938 | −0.912686 | ||||||||
\(587\) | 28.7424 | 1.18633 | 0.593163 | − | 0.805082i | \(-0.297879\pi\) | ||||
0.593163 | + | 0.805082i | \(0.297879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.3527 | −1.00343 | ||||||||
\(590\) | 38.4098 | 1.58131 | ||||||||
\(591\) | −22.2524 | −0.915340 | ||||||||
\(592\) | 5.95759 | 0.244856 | ||||||||
\(593\) | 6.60340 | 0.271169 | 0.135585 | − | 0.990766i | \(-0.456709\pi\) | ||||
0.135585 | + | 0.990766i | \(0.456709\pi\) | |||||||
\(594\) | −9.70260 | −0.398102 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.4165 | −0.508601 | ||||||||
\(597\) | 1.48248 | 0.0606738 | ||||||||
\(598\) | −20.6762 | −0.845515 | ||||||||
\(599\) | 16.2363 | 0.663399 | 0.331700 | − | 0.943385i | \(-0.392378\pi\) | ||||
0.331700 | + | 0.943385i | \(0.392378\pi\) | |||||||
\(600\) | −11.6412 | −0.475250 | ||||||||
\(601\) | 13.7519 | 0.560952 | 0.280476 | − | 0.959861i | \(-0.409508\pi\) | ||||
0.280476 | + | 0.959861i | \(0.409508\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.03977 | 0.327405 | ||||||||
\(604\) | −11.9613 | −0.486698 | ||||||||
\(605\) | 29.5117 | 1.19982 | ||||||||
\(606\) | 13.7178 | 0.557246 | ||||||||
\(607\) | −39.0984 | −1.58695 | −0.793477 | − | 0.608600i | \(-0.791732\pi\) | ||||
−0.793477 | + | 0.608600i | \(0.791732\pi\) | |||||||
\(608\) | −4.01707 | −0.162914 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 44.2298 | 1.79081 | ||||||||
\(611\) | −7.98118 | −0.322884 | ||||||||
\(612\) | −0.881935 | −0.0356501 | ||||||||
\(613\) | 40.8010 | 1.64794 | 0.823968 | − | 0.566636i | \(-0.191755\pi\) | ||||
0.823968 | + | 0.566636i | \(0.191755\pi\) | |||||||
\(614\) | −14.3382 | −0.578642 | ||||||||
\(615\) | 4.07936 | 0.164496 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.41929 | 0.137656 | 0.0688278 | − | 0.997629i | \(-0.478074\pi\) | ||||
0.0688278 | + | 0.997629i | \(0.478074\pi\) | |||||||
\(618\) | −18.9803 | −0.763499 | ||||||||
\(619\) | −7.17686 | −0.288463 | −0.144231 | − | 0.989544i | \(-0.546071\pi\) | ||||
−0.144231 | + | 0.989544i | \(0.546071\pi\) | |||||||
\(620\) | 24.7303 | 0.993192 | ||||||||
\(621\) | −21.9928 | −0.882541 | ||||||||
\(622\) | 11.3049 | 0.453286 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.70068 | 0.188178 | ||||||||
\(625\) | 52.3116 | 2.09246 | ||||||||
\(626\) | 18.6196 | 0.744188 | ||||||||
\(627\) | −7.79521 | −0.311311 | ||||||||
\(628\) | 8.56184 | 0.341655 | ||||||||
\(629\) | 2.62711 | 0.104750 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.4156 | 1.17102 | 0.585509 | − | 0.810666i | \(-0.300895\pi\) | ||||
0.585509 | + | 0.810666i | \(0.300895\pi\) | |||||||
\(632\) | 16.7800 | 0.667474 | ||||||||
\(633\) | −23.8226 | −0.946864 | ||||||||
\(634\) | 5.65547 | 0.224607 | ||||||||
\(635\) | 58.7370 | 2.33091 | ||||||||
\(636\) | 3.31920 | 0.131615 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8.49691 | −0.336396 | ||||||||
\(639\) | 6.24175 | 0.246920 | ||||||||
\(640\) | 4.07936 | 0.161251 | ||||||||
\(641\) | −27.0361 | −1.06786 | −0.533931 | − | 0.845528i | \(-0.679286\pi\) | ||||
−0.533931 | + | 0.845528i | \(0.679286\pi\) | |||||||
\(642\) | 7.25691 | 0.286407 | ||||||||
\(643\) | −15.9105 | −0.627448 | −0.313724 | − | 0.949514i | \(-0.601577\pi\) | ||||
−0.313724 | + | 0.949514i | \(0.601577\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.1066 | 0.555447 | ||||||||
\(646\) | −1.77140 | −0.0696948 | ||||||||
\(647\) | −2.40227 | −0.0944428 | −0.0472214 | − | 0.998884i | \(-0.515037\pi\) | ||||
−0.0472214 | + | 0.998884i | \(0.515037\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −18.2712 | −0.717208 | ||||||||
\(650\) | −54.7216 | −2.14636 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.1200 | −0.787961 | ||||||||
\(653\) | 18.2297 | 0.713382 | 0.356691 | − | 0.934222i | \(-0.383905\pi\) | ||||
0.356691 | + | 0.934222i | \(0.383905\pi\) | |||||||
\(654\) | −2.53740 | −0.0992204 | ||||||||
\(655\) | 42.1883 | 1.64843 | ||||||||
\(656\) | −1.00000 | −0.0390434 | ||||||||
\(657\) | 18.0341 | 0.703579 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.41372 | 0.210889 | 0.105444 | − | 0.994425i | \(-0.466374\pi\) | ||||
0.105444 | + | 0.994425i | \(0.466374\pi\) | |||||||
\(660\) | 7.91608 | 0.308133 | ||||||||
\(661\) | −39.6518 | −1.54228 | −0.771138 | − | 0.636668i | \(-0.780312\pi\) | ||||
−0.771138 | + | 0.636668i | \(0.780312\pi\) | |||||||
\(662\) | −29.4448 | −1.14441 | ||||||||
\(663\) | 2.07285 | 0.0805028 | ||||||||
\(664\) | 2.43726 | 0.0945841 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.9152 | 0.461704 | ||||||||
\(667\) | −19.2599 | −0.745746 | ||||||||
\(668\) | 19.0794 | 0.738203 | ||||||||
\(669\) | 6.91608 | 0.267391 | ||||||||
\(670\) | −16.3986 | −0.633532 | ||||||||
\(671\) | −21.0398 | −0.812231 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.21450 | −0.123910 | −0.0619550 | − | 0.998079i | \(-0.519734\pi\) | ||||
−0.0619550 | + | 0.998079i | \(0.519734\pi\) | |||||||
\(674\) | 25.2266 | 0.971694 | ||||||||
\(675\) | −58.2060 | −2.24035 | ||||||||
\(676\) | 9.09644 | 0.349863 | ||||||||
\(677\) | 15.6998 | 0.603394 | 0.301697 | − | 0.953404i | \(-0.402447\pi\) | ||||
0.301697 | + | 0.953404i | \(0.402447\pi\) | |||||||
\(678\) | 5.68080 | 0.218170 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.79887 | 0.0689834 | ||||||||
\(681\) | 21.1606 | 0.810877 | ||||||||
\(682\) | −11.7640 | −0.450466 | ||||||||
\(683\) | 25.3014 | 0.968133 | 0.484066 | − | 0.875031i | \(-0.339159\pi\) | ||||
0.484066 | + | 0.875031i | \(0.339159\pi\) | |||||||
\(684\) | −8.03415 | −0.307193 | ||||||||
\(685\) | 5.43968 | 0.207840 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.8709 | −0.681816 | ||||||||
\(688\) | −3.45804 | −0.131837 | ||||||||
\(689\) | 15.6025 | 0.594408 | ||||||||
\(690\) | 17.9433 | 0.683091 | ||||||||
\(691\) | 39.1902 | 1.49087 | 0.745433 | − | 0.666580i | \(-0.232243\pi\) | ||||
0.745433 | + | 0.666580i | \(0.232243\pi\) | |||||||
\(692\) | −23.6838 | −0.900322 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.6113 | −0.972192 | ||||||||
\(695\) | 9.16001 | 0.347459 | ||||||||
\(696\) | 4.37868 | 0.165973 | ||||||||
\(697\) | −0.440968 | −0.0167028 | ||||||||
\(698\) | 8.25601 | 0.312495 | ||||||||
\(699\) | −19.8847 | −0.752110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0748 | 0.380520 | 0.190260 | − | 0.981734i | \(-0.439067\pi\) | ||||
0.190260 | + | 0.981734i | \(0.439067\pi\) | |||||||
\(702\) | 23.5034 | 0.887080 | ||||||||
\(703\) | 23.9321 | 0.902616 | ||||||||
\(704\) | −1.94052 | −0.0731361 | ||||||||
\(705\) | 6.92625 | 0.260858 | ||||||||
\(706\) | −26.8423 | −1.01022 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.41564 | 0.353861 | ||||||||
\(709\) | −38.4537 | −1.44416 | −0.722079 | − | 0.691811i | \(-0.756813\pi\) | ||||
−0.722079 | + | 0.691811i | \(0.756813\pi\) | |||||||
\(710\) | −12.7312 | −0.477793 | ||||||||
\(711\) | 33.5601 | 1.25860 | ||||||||
\(712\) | −5.01707 | −0.188023 | ||||||||
\(713\) | −26.6653 | −0.998625 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 37.2110 | 1.39161 | ||||||||
\(716\) | −10.7178 | −0.400541 | ||||||||
\(717\) | −9.61396 | −0.359040 | ||||||||
\(718\) | −0.384295 | −0.0143418 | ||||||||
\(719\) | 2.43637 | 0.0908611 | 0.0454306 | − | 0.998967i | \(-0.485534\pi\) | ||||
0.0454306 | + | 0.998967i | \(0.485534\pi\) | |||||||
\(720\) | 8.15873 | 0.304058 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.86312 | 0.106554 | ||||||||
\(723\) | −12.1587 | −0.452188 | ||||||||
\(724\) | −19.2381 | −0.714978 | ||||||||
\(725\) | −50.9731 | −1.89309 | ||||||||
\(726\) | 7.23438 | 0.268493 | ||||||||
\(727\) | −28.8804 | −1.07111 | −0.535557 | − | 0.844499i | \(-0.679898\pi\) | ||||
−0.535557 | + | 0.844499i | \(0.679898\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | −36.7839 | −1.36143 | ||||||||
\(731\) | −1.52488 | −0.0563999 | ||||||||
\(732\) | 10.8423 | 0.400744 | ||||||||
\(733\) | −51.7612 | −1.91184 | −0.955922 | − | 0.293620i | \(-0.905140\pi\) | ||||
−0.955922 | + | 0.293620i | \(0.905140\pi\) | |||||||
\(734\) | −13.1841 | −0.486632 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.39856 | −0.162133 | ||||||||
\(737\) | 7.80066 | 0.287341 | ||||||||
\(738\) | −2.00000 | −0.0736210 | ||||||||
\(739\) | 22.5951 | 0.831176 | 0.415588 | − | 0.909553i | \(-0.363576\pi\) | ||||
0.415588 | + | 0.909553i | \(0.363576\pi\) | |||||||
\(740\) | −24.3032 | −0.893403 | ||||||||
\(741\) | 18.8830 | 0.693684 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.6291 | −0.940241 | −0.470121 | − | 0.882602i | \(-0.655790\pi\) | ||||
−0.470121 | + | 0.882602i | \(0.655790\pi\) | |||||||
\(744\) | 6.06229 | 0.222254 | ||||||||
\(745\) | 50.6515 | 1.85573 | ||||||||
\(746\) | −22.7718 | −0.833734 | ||||||||
\(747\) | 4.87453 | 0.178350 | ||||||||
\(748\) | −0.855706 | −0.0312877 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 27.0919 | 0.989256 | ||||||||
\(751\) | −18.3751 | −0.670518 | −0.335259 | − | 0.942126i | \(-0.608824\pi\) | ||||
−0.335259 | + | 0.942126i | \(0.608824\pi\) | |||||||
\(752\) | −1.69788 | −0.0619152 | ||||||||
\(753\) | −21.7234 | −0.791644 | ||||||||
\(754\) | 20.5828 | 0.749581 | ||||||||
\(755\) | 48.7945 | 1.77581 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.8133 | 1.81050 | 0.905248 | − | 0.424883i | \(-0.139685\pi\) | ||||
0.905248 | + | 0.424883i | \(0.139685\pi\) | |||||||
\(758\) | −31.1870 | −1.13276 | ||||||||
\(759\) | −8.53549 | −0.309819 | ||||||||
\(760\) | 16.3871 | 0.594423 | ||||||||
\(761\) | 13.8893 | 0.503487 | 0.251743 | − | 0.967794i | \(-0.418996\pi\) | ||||
0.251743 | + | 0.967794i | \(0.418996\pi\) | |||||||
\(762\) | 14.3986 | 0.521605 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.13884 | −0.0773807 | ||||||||
\(765\) | 3.59773 | 0.130076 | ||||||||
\(766\) | 26.4933 | 0.957240 | ||||||||
\(767\) | 44.2599 | 1.59813 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −7.76562 | −0.280035 | −0.140018 | − | 0.990149i | \(-0.544716\pi\) | ||||
−0.140018 | + | 0.990149i | \(0.544716\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.4697 | 0.917268 | ||||||||
\(772\) | 14.9217 | 0.537044 | ||||||||
\(773\) | 33.3345 | 1.19896 | 0.599480 | − | 0.800390i | \(-0.295374\pi\) | ||||
0.599480 | + | 0.800390i | \(0.295374\pi\) | |||||||
\(774\) | −6.91608 | −0.248593 | ||||||||
\(775\) | −70.5723 | −2.53503 | ||||||||
\(776\) | −15.5402 | −0.557861 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.3741 | 0.909706 | ||||||||
\(779\) | −4.01707 | −0.143927 | ||||||||
\(780\) | −19.1758 | −0.686604 | ||||||||
\(781\) | 6.05612 | 0.216705 | ||||||||
\(782\) | −1.93962 | −0.0693608 | ||||||||
\(783\) | 21.8934 | 0.782406 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.9269 | −1.24659 | ||||||||
\(786\) | 10.3419 | 0.368883 | ||||||||
\(787\) | 23.0605 | 0.822020 | 0.411010 | − | 0.911631i | \(-0.365176\pi\) | ||||
0.411010 | + | 0.911631i | \(0.365176\pi\) | |||||||
\(788\) | −22.2524 | −0.792707 | ||||||||
\(789\) | 0.982926 | 0.0349931 | ||||||||
\(790\) | −68.4519 | −2.43541 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.88104 | −0.137907 | ||||||||
\(793\) | 50.9664 | 1.80987 | ||||||||
\(794\) | 20.2409 | 0.718323 | ||||||||
\(795\) | −13.5402 | −0.480222 | ||||||||
\(796\) | 1.48248 | 0.0525450 | ||||||||
\(797\) | −55.2752 | −1.95795 | −0.978974 | − | 0.203984i | \(-0.934611\pi\) | ||||
−0.978974 | + | 0.203984i | \(0.934611\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.748708 | −0.0264874 | ||||||||
\(800\) | −11.6412 | −0.411579 | ||||||||
\(801\) | −10.0341 | −0.354539 | ||||||||
\(802\) | −24.1769 | −0.853715 | ||||||||
\(803\) | 17.4978 | 0.617484 | ||||||||
\(804\) | −4.01988 | −0.141770 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28.4969 | 1.00376 | ||||||||
\(807\) | −16.5800 | −0.583643 | ||||||||
\(808\) | 13.7178 | 0.482589 | ||||||||
\(809\) | 27.0605 | 0.951398 | 0.475699 | − | 0.879608i | \(-0.342195\pi\) | ||||
0.475699 | + | 0.879608i | \(0.342195\pi\) | |||||||
\(810\) | 4.07936 | 0.143334 | ||||||||
\(811\) | −28.0614 | −0.985370 | −0.492685 | − | 0.870208i | \(-0.663985\pi\) | ||||
−0.492685 | + | 0.870208i | \(0.663985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.900754 | 0.0315908 | ||||||||
\(814\) | 11.5608 | 0.405207 | ||||||||
\(815\) | 82.0769 | 2.87503 | ||||||||
\(816\) | 0.440968 | 0.0154370 | ||||||||
\(817\) | −13.8912 | −0.485992 | ||||||||
\(818\) | 0.369133 | 0.0129065 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.07936 | 0.142458 | ||||||||
\(821\) | 1.96641 | 0.0686281 | 0.0343141 | − | 0.999411i | \(-0.489075\pi\) | ||||
0.0343141 | + | 0.999411i | \(0.489075\pi\) | |||||||
\(822\) | 1.33346 | 0.0465099 | ||||||||
\(823\) | −23.4278 | −0.816641 | −0.408320 | − | 0.912839i | \(-0.633885\pi\) | ||||
−0.408320 | + | 0.912839i | \(0.633885\pi\) | |||||||
\(824\) | −18.9803 | −0.661210 | ||||||||
\(825\) | −22.5900 | −0.786482 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −35.6449 | −1.23949 | −0.619747 | − | 0.784801i | \(-0.712765\pi\) | ||||
−0.619747 | + | 0.784801i | \(0.712765\pi\) | |||||||
\(828\) | −8.79712 | −0.305721 | ||||||||
\(829\) | 22.0945 | 0.767375 | 0.383687 | − | 0.923463i | \(-0.374654\pi\) | ||||
0.383687 | + | 0.923463i | \(0.374654\pi\) | |||||||
\(830\) | −9.94248 | −0.345108 | ||||||||
\(831\) | 22.7811 | 0.790268 | ||||||||
\(832\) | 4.70068 | 0.162967 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.24545 | 0.0777536 | ||||||||
\(835\) | −77.8317 | −2.69348 | ||||||||
\(836\) | −7.79521 | −0.269603 | ||||||||
\(837\) | 30.3114 | 1.04772 | ||||||||
\(838\) | −23.1427 | −0.799452 | ||||||||
\(839\) | 14.2759 | 0.492860 | 0.246430 | − | 0.969161i | \(-0.420742\pi\) | ||||
0.246430 | + | 0.969161i | \(0.420742\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.82718 | −0.338868 | ||||||||
\(842\) | −3.35790 | −0.115721 | ||||||||
\(843\) | 22.3940 | 0.771291 | ||||||||
\(844\) | −23.8226 | −0.820008 | ||||||||
\(845\) | −37.1077 | −1.27654 | ||||||||
\(846\) | −3.39575 | −0.116748 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.31920 | 0.113982 | ||||||||
\(849\) | −8.25601 | −0.283346 | ||||||||
\(850\) | −5.13339 | −0.176074 | ||||||||
\(851\) | 26.2048 | 0.898290 | ||||||||
\(852\) | −3.12087 | −0.106919 | ||||||||
\(853\) | 31.3715 | 1.07414 | 0.537070 | − | 0.843538i | \(-0.319531\pi\) | ||||
0.537070 | + | 0.843538i | \(0.319531\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 32.7742 | 1.12085 | ||||||||
\(856\) | 7.25691 | 0.248036 | ||||||||
\(857\) | 37.9251 | 1.29550 | 0.647748 | − | 0.761855i | \(-0.275711\pi\) | ||||
0.647748 | + | 0.761855i | \(0.275711\pi\) | |||||||
\(858\) | 9.12177 | 0.311412 | ||||||||
\(859\) | 37.0493 | 1.26411 | 0.632053 | − | 0.774925i | \(-0.282212\pi\) | ||||
0.632053 | + | 0.774925i | \(0.282212\pi\) | |||||||
\(860\) | 14.1066 | 0.481031 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.4267 | 0.491375 | ||||||||
\(863\) | −34.6451 | −1.17933 | −0.589666 | − | 0.807647i | \(-0.700741\pi\) | ||||
−0.589666 | + | 0.807647i | \(0.700741\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | 96.6147 | 3.28500 | ||||||||
\(866\) | 17.0172 | 0.578269 | ||||||||
\(867\) | −16.8055 | −0.570746 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 32.5620 | 1.10459 | ||||||||
\(870\) | −17.8622 | −0.605586 | ||||||||
\(871\) | −18.8962 | −0.640273 | ||||||||
\(872\) | −2.53740 | −0.0859274 | ||||||||
\(873\) | −31.0804 | −1.05191 | ||||||||
\(874\) | −17.6693 | −0.597675 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.01707 | −0.304659 | ||||||||
\(877\) | 32.4202 | 1.09475 | 0.547376 | − | 0.836887i | \(-0.315627\pi\) | ||||
0.547376 | + | 0.836887i | \(0.315627\pi\) | |||||||
\(878\) | −6.95198 | −0.234618 | ||||||||
\(879\) | 22.0938 | 0.745205 | ||||||||
\(880\) | 7.91608 | 0.266851 | ||||||||
\(881\) | −1.96496 | −0.0662010 | −0.0331005 | − | 0.999452i | \(-0.510538\pi\) | ||||
−0.0331005 | + | 0.999452i | \(0.510538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.8577 | 1.07210 | 0.536048 | − | 0.844188i | \(-0.319917\pi\) | ||||
0.536048 | + | 0.844188i | \(0.319917\pi\) | |||||||
\(884\) | 2.07285 | 0.0697175 | ||||||||
\(885\) | −38.4098 | −1.29113 | ||||||||
\(886\) | 6.93861 | 0.233107 | ||||||||
\(887\) | −42.1401 | −1.41493 | −0.707463 | − | 0.706751i | \(-0.750160\pi\) | ||||
−0.707463 | + | 0.706751i | \(0.750160\pi\) | |||||||
\(888\) | −5.95759 | −0.199924 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 20.4665 | 0.686038 | ||||||||
\(891\) | −1.94052 | −0.0650098 | ||||||||
\(892\) | 6.91608 | 0.231568 | ||||||||
\(893\) | −6.82049 | −0.228239 | ||||||||
\(894\) | 12.4165 | 0.415271 | ||||||||
\(895\) | 43.7216 | 1.46145 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.6762 | 0.690360 | ||||||||
\(898\) | 6.34363 | 0.211690 | ||||||||
\(899\) | 26.5448 | 0.885319 | ||||||||
\(900\) | −23.2824 | −0.776080 | ||||||||
\(901\) | 1.46366 | 0.0487615 | ||||||||
\(902\) | −1.94052 | −0.0646122 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.68080 | 0.188941 | ||||||||
\(905\) | 78.4792 | 2.60874 | ||||||||
\(906\) | 11.9613 | 0.397388 | ||||||||
\(907\) | 48.2194 | 1.60110 | 0.800550 | − | 0.599266i | \(-0.204541\pi\) | ||||
0.800550 | + | 0.599266i | \(0.204541\pi\) | |||||||
\(908\) | 21.1606 | 0.702240 | ||||||||
\(909\) | 27.4355 | 0.909979 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.5650 | −0.383167 | −0.191583 | − | 0.981476i | \(-0.561362\pi\) | ||||
−0.191583 | + | 0.981476i | \(0.561362\pi\) | |||||||
\(912\) | 4.01707 | 0.133019 | ||||||||
\(913\) | 4.72956 | 0.156525 | ||||||||
\(914\) | 0.102054 | 0.00337566 | ||||||||
\(915\) | −44.2298 | −1.46219 | ||||||||
\(916\) | −17.8709 | −0.590470 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.20484 | 0.0727705 | ||||||||
\(919\) | 10.6555 | 0.351492 | 0.175746 | − | 0.984436i | \(-0.443766\pi\) | ||||
0.175746 | + | 0.984436i | \(0.443766\pi\) | |||||||
\(920\) | 17.9433 | 0.591574 | ||||||||
\(921\) | 14.3382 | 0.472459 | ||||||||
\(922\) | −32.0692 | −1.05614 | ||||||||
\(923\) | −14.6702 | −0.482877 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 69.3536 | 2.28033 | ||||||||
\(926\) | 30.6907 | 1.00856 | ||||||||
\(927\) | −37.9606 | −1.24679 | ||||||||
\(928\) | 4.37868 | 0.143737 | ||||||||
\(929\) | −0.941368 | −0.0308853 | −0.0154426 | − | 0.999881i | \(-0.504916\pi\) | ||||
−0.0154426 | + | 0.999881i | \(0.504916\pi\) | |||||||
\(930\) | −24.7303 | −0.810938 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −19.8847 | −0.651346 | ||||||||
\(933\) | −11.3049 | −0.370107 | ||||||||
\(934\) | −16.2852 | −0.532869 | ||||||||
\(935\) | 3.49074 | 0.114159 | ||||||||
\(936\) | 9.40137 | 0.307293 | ||||||||
\(937\) | 22.1066 | 0.722191 | 0.361096 | − | 0.932529i | \(-0.382403\pi\) | ||||
0.361096 | + | 0.932529i | \(0.382403\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.6196 | −0.607627 | ||||||||
\(940\) | 6.92625 | 0.225909 | ||||||||
\(941\) | −3.80359 | −0.123993 | −0.0619967 | − | 0.998076i | \(-0.519747\pi\) | ||||
−0.0619967 | + | 0.998076i | \(0.519747\pi\) | |||||||
\(942\) | −8.56184 | −0.278960 | ||||||||
\(943\) | −4.39856 | −0.143237 | ||||||||
\(944\) | 9.41564 | 0.306453 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.71040 | −0.218174 | ||||||||
\(947\) | −32.3212 | −1.05030 | −0.525148 | − | 0.851011i | \(-0.675990\pi\) | ||||
−0.525148 | + | 0.851011i | \(0.675990\pi\) | |||||||
\(948\) | −16.7800 | −0.544991 | ||||||||
\(949\) | −42.3864 | −1.37592 | ||||||||
\(950\) | −46.7636 | −1.51721 | ||||||||
\(951\) | −5.65547 | −0.183391 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.2882 | −1.69378 | −0.846890 | − | 0.531768i | \(-0.821528\pi\) | ||||
−0.846890 | + | 0.531768i | \(0.821528\pi\) | |||||||
\(954\) | 6.63840 | 0.214926 | ||||||||
\(955\) | 8.72512 | 0.282338 | ||||||||
\(956\) | −9.61396 | −0.310938 | ||||||||
\(957\) | 8.49691 | 0.274666 | ||||||||
\(958\) | 18.9208 | 0.611303 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4.07936 | −0.131661 | ||||||||
\(961\) | 5.75135 | 0.185527 | ||||||||
\(962\) | −28.0048 | −0.902910 | ||||||||
\(963\) | 14.5138 | 0.467701 | ||||||||
\(964\) | −12.1587 | −0.391606 | ||||||||
\(965\) | −60.8710 | −1.95951 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.0071 | −0.868489 | −0.434244 | − | 0.900795i | \(-0.642985\pi\) | ||||
−0.434244 | + | 0.900795i | \(0.642985\pi\) | |||||||
\(968\) | 7.23438 | 0.232522 | ||||||||
\(969\) | 1.77140 | 0.0569056 | ||||||||
\(970\) | 63.3942 | 2.03546 | ||||||||
\(971\) | 43.1053 | 1.38331 | 0.691657 | − | 0.722226i | \(-0.256881\pi\) | ||||
0.691657 | + | 0.722226i | \(0.256881\pi\) | |||||||
\(972\) | 16.0000 | 0.513200 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31.0190 | 0.993912 | ||||||||
\(975\) | 54.7216 | 1.75249 | ||||||||
\(976\) | 10.8423 | 0.347055 | ||||||||
\(977\) | −36.4611 | −1.16649 | −0.583246 | − | 0.812295i | \(-0.698218\pi\) | ||||
−0.583246 | + | 0.812295i | \(0.698218\pi\) | |||||||
\(978\) | 20.1200 | 0.643367 | ||||||||
\(979\) | −9.73573 | −0.311155 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.07481 | −0.162026 | ||||||||
\(982\) | 14.5780 | 0.465203 | ||||||||
\(983\) | −45.2441 | −1.44306 | −0.721531 | − | 0.692382i | \(-0.756561\pi\) | ||||
−0.721531 | + | 0.692382i | \(0.756561\pi\) | |||||||
\(984\) | 1.00000 | 0.0318788 | ||||||||
\(985\) | 90.7754 | 2.89235 | ||||||||
\(986\) | 1.93086 | 0.0614910 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.8830 | 0.600748 | ||||||||
\(989\) | −15.2104 | −0.483663 | ||||||||
\(990\) | 15.8322 | 0.503179 | ||||||||
\(991\) | 5.77314 | 0.183390 | 0.0916950 | − | 0.995787i | \(-0.470772\pi\) | ||||
0.0916950 | + | 0.995787i | \(0.470772\pi\) | |||||||
\(992\) | 6.06229 | 0.192478 | ||||||||
\(993\) | 29.4448 | 0.934404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.04757 | −0.191721 | ||||||||
\(996\) | −2.43726 | −0.0772276 | ||||||||
\(997\) | −1.26253 | −0.0399846 | −0.0199923 | − | 0.999800i | \(-0.506364\pi\) | ||||
−0.0199923 | + | 0.999800i | \(0.506364\pi\) | |||||||
\(998\) | −34.7266 | −1.09925 | ||||||||
\(999\) | −29.7880 | −0.942450 |
(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 | 4018.2.a.bk.1.1 | 4 | ||
7.2 | even | 3 | 574.2.e.f.165.4 | ✓ | 8 | ||
7.4 | even | 3 | 574.2.e.f.247.4 | yes | 8 | ||
7.6 | odd | 2 | 4018.2.a.bi.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
574.2.e.f.165.4 | ✓ | 8 | 7.2 | even | 3 | ||
574.2.e.f.247.4 | yes | 8 | 7.4 | even | 3 | ||
4018.2.a.bi.1.4 | 4 | 7.6 | odd | 2 | |||
4018.2.a.bk.1.1 | 4 | 1.1 | even | 1 | trivial |