Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8029,2,Mod(1,8029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8029, 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("8029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8029 = 7 \cdot 31 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8029.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: | \(64.1118877829\) |
Analytic rank: | \(0\) |
Dimension: | \(70\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 8029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.70672 | −1.91394 | −0.956969 | − | 0.290191i | \(-0.906281\pi\) | ||||
−0.956969 | + | 0.290191i | \(0.906281\pi\) | |||||||
\(3\) | 2.12991 | 1.22971 | 0.614853 | − | 0.788642i | \(-0.289215\pi\) | ||||
0.614853 | + | 0.788642i | \(0.289215\pi\) | |||||||
\(4\) | 5.32631 | 2.66316 | ||||||||
\(5\) | −2.23028 | −0.997413 | −0.498707 | − | 0.866771i | \(-0.666191\pi\) | ||||
−0.498707 | + | 0.866771i | \(0.666191\pi\) | |||||||
\(6\) | −5.76507 | −2.35358 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −9.00339 | −3.18318 | ||||||||
\(9\) | 1.53652 | 0.512175 | ||||||||
\(10\) | 6.03675 | 1.90899 | ||||||||
\(11\) | 4.95603 | 1.49430 | 0.747150 | − | 0.664655i | \(-0.231421\pi\) | ||||
0.747150 | + | 0.664655i | \(0.231421\pi\) | |||||||
\(12\) | 11.3446 | 3.27490 | ||||||||
\(13\) | −5.36363 | −1.48760 | −0.743802 | − | 0.668400i | \(-0.766980\pi\) | ||||
−0.743802 | + | 0.668400i | \(0.766980\pi\) | |||||||
\(14\) | −2.70672 | −0.723400 | ||||||||
\(15\) | −4.75031 | −1.22652 | ||||||||
\(16\) | 13.7170 | 3.42925 | ||||||||
\(17\) | 6.72943 | 1.63213 | 0.816063 | − | 0.577962i | \(-0.196152\pi\) | ||||
0.816063 | + | 0.577962i | \(0.196152\pi\) | |||||||
\(18\) | −4.15894 | −0.980271 | ||||||||
\(19\) | −0.773178 | −0.177379 | −0.0886896 | − | 0.996059i | \(-0.528268\pi\) | ||||
−0.0886896 | + | 0.996059i | \(0.528268\pi\) | |||||||
\(20\) | −11.8792 | −2.65627 | ||||||||
\(21\) | 2.12991 | 0.464785 | ||||||||
\(22\) | −13.4146 | −2.86000 | ||||||||
\(23\) | −6.47732 | −1.35061 | −0.675307 | − | 0.737537i | \(-0.735989\pi\) | ||||
−0.675307 | + | 0.737537i | \(0.735989\pi\) | |||||||
\(24\) | −19.1764 | −3.91437 | ||||||||
\(25\) | −0.0258357 | −0.00516714 | ||||||||
\(26\) | 14.5178 | 2.84718 | ||||||||
\(27\) | −3.11707 | −0.599881 | ||||||||
\(28\) | 5.32631 | 1.00658 | ||||||||
\(29\) | 5.18642 | 0.963094 | 0.481547 | − | 0.876420i | \(-0.340075\pi\) | ||||
0.481547 | + | 0.876420i | \(0.340075\pi\) | |||||||
\(30\) | 12.8577 | 2.34749 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −19.1212 | −3.38019 | ||||||||
\(33\) | 10.5559 | 1.83755 | ||||||||
\(34\) | −18.2147 | −3.12379 | ||||||||
\(35\) | −2.23028 | −0.376987 | ||||||||
\(36\) | 8.18402 | 1.36400 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 2.09277 | 0.339493 | ||||||||
\(39\) | −11.4241 | −1.82931 | ||||||||
\(40\) | 20.0801 | 3.17494 | ||||||||
\(41\) | −9.63660 | −1.50498 | −0.752492 | − | 0.658602i | \(-0.771148\pi\) | ||||
−0.752492 | + | 0.658602i | \(0.771148\pi\) | |||||||
\(42\) | −5.76507 | −0.889569 | ||||||||
\(43\) | −1.75577 | −0.267752 | −0.133876 | − | 0.990998i | \(-0.542742\pi\) | ||||
−0.133876 | + | 0.990998i | \(0.542742\pi\) | |||||||
\(44\) | 26.3974 | 3.97956 | ||||||||
\(45\) | −3.42689 | −0.510850 | ||||||||
\(46\) | 17.5323 | 2.58499 | ||||||||
\(47\) | −5.65376 | −0.824686 | −0.412343 | − | 0.911029i | \(-0.635289\pi\) | ||||
−0.412343 | + | 0.911029i | \(0.635289\pi\) | |||||||
\(48\) | 29.2160 | 4.21697 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.0699299 | 0.00988958 | ||||||||
\(51\) | 14.3331 | 2.00704 | ||||||||
\(52\) | −28.5684 | −3.96172 | ||||||||
\(53\) | 1.55771 | 0.213968 | 0.106984 | − | 0.994261i | \(-0.465881\pi\) | ||||
0.106984 | + | 0.994261i | \(0.465881\pi\) | |||||||
\(54\) | 8.43703 | 1.14813 | ||||||||
\(55\) | −11.0534 | −1.49044 | ||||||||
\(56\) | −9.00339 | −1.20313 | ||||||||
\(57\) | −1.64680 | −0.218124 | ||||||||
\(58\) | −14.0382 | −1.84330 | ||||||||
\(59\) | −1.15151 | −0.149914 | −0.0749572 | − | 0.997187i | \(-0.523882\pi\) | ||||
−0.0749572 | + | 0.997187i | \(0.523882\pi\) | |||||||
\(60\) | −25.3016 | −3.26643 | ||||||||
\(61\) | −5.88076 | −0.752954 | −0.376477 | − | 0.926426i | \(-0.622865\pi\) | ||||
−0.376477 | + | 0.926426i | \(0.622865\pi\) | |||||||
\(62\) | −2.70672 | −0.343753 | ||||||||
\(63\) | 1.53652 | 0.193584 | ||||||||
\(64\) | 24.3218 | 3.04022 | ||||||||
\(65\) | 11.9624 | 1.48376 | ||||||||
\(66\) | −28.5719 | −3.51696 | ||||||||
\(67\) | 6.84298 | 0.836003 | 0.418002 | − | 0.908446i | \(-0.362731\pi\) | ||||
0.418002 | + | 0.908446i | \(0.362731\pi\) | |||||||
\(68\) | 35.8431 | 4.34661 | ||||||||
\(69\) | −13.7961 | −1.66086 | ||||||||
\(70\) | 6.03675 | 0.721529 | ||||||||
\(71\) | 14.3450 | 1.70244 | 0.851219 | − | 0.524811i | \(-0.175864\pi\) | ||||
0.851219 | + | 0.524811i | \(0.175864\pi\) | |||||||
\(72\) | −13.8339 | −1.63034 | ||||||||
\(73\) | 11.7703 | 1.37761 | 0.688804 | − | 0.724948i | \(-0.258136\pi\) | ||||
0.688804 | + | 0.724948i | \(0.258136\pi\) | |||||||
\(74\) | −2.70672 | −0.314649 | ||||||||
\(75\) | −0.0550277 | −0.00635406 | ||||||||
\(76\) | −4.11819 | −0.472389 | ||||||||
\(77\) | 4.95603 | 0.564793 | ||||||||
\(78\) | 30.9217 | 3.50119 | ||||||||
\(79\) | 12.1352 | 1.36532 | 0.682661 | − | 0.730735i | \(-0.260823\pi\) | ||||
0.682661 | + | 0.730735i | \(0.260823\pi\) | |||||||
\(80\) | −30.5928 | −3.42038 | ||||||||
\(81\) | −11.2487 | −1.24985 | ||||||||
\(82\) | 26.0835 | 2.88044 | ||||||||
\(83\) | 15.9764 | 1.75364 | 0.876821 | − | 0.480818i | \(-0.159660\pi\) | ||||
0.876821 | + | 0.480818i | \(0.159660\pi\) | |||||||
\(84\) | 11.3446 | 1.23780 | ||||||||
\(85\) | −15.0085 | −1.62790 | ||||||||
\(86\) | 4.75236 | 0.512460 | ||||||||
\(87\) | 11.0466 | 1.18432 | ||||||||
\(88\) | −44.6211 | −4.75663 | ||||||||
\(89\) | 17.2589 | 1.82944 | 0.914721 | − | 0.404087i | \(-0.132411\pi\) | ||||
0.914721 | + | 0.404087i | \(0.132411\pi\) | |||||||
\(90\) | 9.27561 | 0.977735 | ||||||||
\(91\) | −5.36363 | −0.562262 | ||||||||
\(92\) | −34.5002 | −3.59690 | ||||||||
\(93\) | 2.12991 | 0.220862 | ||||||||
\(94\) | 15.3031 | 1.57840 | ||||||||
\(95\) | 1.72441 | 0.176920 | ||||||||
\(96\) | −40.7266 | −4.15664 | ||||||||
\(97\) | −5.29694 | −0.537822 | −0.268911 | − | 0.963165i | \(-0.586664\pi\) | ||||
−0.268911 | + | 0.963165i | \(0.586664\pi\) | |||||||
\(98\) | −2.70672 | −0.273420 | ||||||||
\(99\) | 7.61507 | 0.765343 | ||||||||
\(100\) | −0.137609 | −0.0137609 | ||||||||
\(101\) | 15.0260 | 1.49514 | 0.747571 | − | 0.664182i | \(-0.231220\pi\) | ||||
0.747571 | + | 0.664182i | \(0.231220\pi\) | |||||||
\(102\) | −38.7956 | −3.84134 | ||||||||
\(103\) | −5.50726 | −0.542646 | −0.271323 | − | 0.962488i | \(-0.587461\pi\) | ||||
−0.271323 | + | 0.962488i | \(0.587461\pi\) | |||||||
\(104\) | 48.2909 | 4.73531 | ||||||||
\(105\) | −4.75031 | −0.463583 | ||||||||
\(106\) | −4.21628 | −0.409521 | ||||||||
\(107\) | −0.513430 | −0.0496352 | −0.0248176 | − | 0.999692i | \(-0.507900\pi\) | ||||
−0.0248176 | + | 0.999692i | \(0.507900\pi\) | |||||||
\(108\) | −16.6025 | −1.59758 | ||||||||
\(109\) | −15.1299 | −1.44918 | −0.724589 | − | 0.689181i | \(-0.757971\pi\) | ||||
−0.724589 | + | 0.689181i | \(0.757971\pi\) | |||||||
\(110\) | 29.9183 | 2.85260 | ||||||||
\(111\) | 2.12991 | 0.202162 | ||||||||
\(112\) | 13.7170 | 1.29613 | ||||||||
\(113\) | −5.68137 | −0.534458 | −0.267229 | − | 0.963633i | \(-0.586108\pi\) | ||||
−0.267229 | + | 0.963633i | \(0.586108\pi\) | |||||||
\(114\) | 4.45743 | 0.417476 | ||||||||
\(115\) | 14.4463 | 1.34712 | ||||||||
\(116\) | 27.6245 | 2.56487 | ||||||||
\(117\) | −8.24136 | −0.761914 | ||||||||
\(118\) | 3.11682 | 0.286927 | ||||||||
\(119\) | 6.72943 | 0.616886 | ||||||||
\(120\) | 42.7689 | 3.90425 | ||||||||
\(121\) | 13.5623 | 1.23293 | ||||||||
\(122\) | 15.9175 | 1.44111 | ||||||||
\(123\) | −20.5251 | −1.85069 | ||||||||
\(124\) | 5.32631 | 0.478317 | ||||||||
\(125\) | 11.2090 | 1.00257 | ||||||||
\(126\) | −4.15894 | −0.370508 | ||||||||
\(127\) | −6.27201 | −0.556551 | −0.278276 | − | 0.960501i | \(-0.589763\pi\) | ||||
−0.278276 | + | 0.960501i | \(0.589763\pi\) | |||||||
\(128\) | −27.5897 | −2.43861 | ||||||||
\(129\) | −3.73963 | −0.329256 | ||||||||
\(130\) | −32.3789 | −2.83982 | ||||||||
\(131\) | 3.63621 | 0.317697 | 0.158848 | − | 0.987303i | \(-0.449222\pi\) | ||||
0.158848 | + | 0.987303i | \(0.449222\pi\) | |||||||
\(132\) | 56.2241 | 4.89368 | ||||||||
\(133\) | −0.773178 | −0.0670431 | ||||||||
\(134\) | −18.5220 | −1.60006 | ||||||||
\(135\) | 6.95196 | 0.598329 | ||||||||
\(136\) | −60.5877 | −5.19535 | ||||||||
\(137\) | 12.4841 | 1.06659 | 0.533296 | − | 0.845929i | \(-0.320953\pi\) | ||||
0.533296 | + | 0.845929i | \(0.320953\pi\) | |||||||
\(138\) | 37.3422 | 3.17878 | ||||||||
\(139\) | 9.06042 | 0.768495 | 0.384248 | − | 0.923230i | \(-0.374461\pi\) | ||||
0.384248 | + | 0.923230i | \(0.374461\pi\) | |||||||
\(140\) | −11.8792 | −1.00397 | ||||||||
\(141\) | −12.0420 | −1.01412 | ||||||||
\(142\) | −38.8278 | −3.25836 | ||||||||
\(143\) | −26.5824 | −2.22293 | ||||||||
\(144\) | 21.0765 | 1.75638 | ||||||||
\(145\) | −11.5672 | −0.960602 | ||||||||
\(146\) | −31.8588 | −2.63665 | ||||||||
\(147\) | 2.12991 | 0.175672 | ||||||||
\(148\) | 5.32631 | 0.437820 | ||||||||
\(149\) | 7.36512 | 0.603374 | 0.301687 | − | 0.953407i | \(-0.402450\pi\) | ||||
0.301687 | + | 0.953407i | \(0.402450\pi\) | |||||||
\(150\) | 0.148945 | 0.0121613 | ||||||||
\(151\) | −4.98815 | −0.405930 | −0.202965 | − | 0.979186i | \(-0.565058\pi\) | ||||
−0.202965 | + | 0.979186i | \(0.565058\pi\) | |||||||
\(152\) | 6.96123 | 0.564630 | ||||||||
\(153\) | 10.3399 | 0.835935 | ||||||||
\(154\) | −13.4146 | −1.08098 | ||||||||
\(155\) | −2.23028 | −0.179141 | ||||||||
\(156\) | −60.8482 | −4.87175 | ||||||||
\(157\) | −2.80030 | −0.223488 | −0.111744 | − | 0.993737i | \(-0.535644\pi\) | ||||
−0.111744 | + | 0.993737i | \(0.535644\pi\) | |||||||
\(158\) | −32.8467 | −2.61314 | ||||||||
\(159\) | 3.31778 | 0.263117 | ||||||||
\(160\) | 42.6458 | 3.37145 | ||||||||
\(161\) | −6.47732 | −0.510484 | ||||||||
\(162\) | 30.4470 | 2.39214 | ||||||||
\(163\) | −22.3849 | −1.75332 | −0.876661 | − | 0.481108i | \(-0.840235\pi\) | ||||
−0.876661 | + | 0.481108i | \(0.840235\pi\) | |||||||
\(164\) | −51.3275 | −4.00801 | ||||||||
\(165\) | −23.5427 | −1.83280 | ||||||||
\(166\) | −43.2437 | −3.35636 | ||||||||
\(167\) | 6.99214 | 0.541068 | 0.270534 | − | 0.962710i | \(-0.412800\pi\) | ||||
0.270534 | + | 0.962710i | \(0.412800\pi\) | |||||||
\(168\) | −19.1764 | −1.47949 | ||||||||
\(169\) | 15.7686 | 1.21297 | ||||||||
\(170\) | 40.6239 | 3.11571 | ||||||||
\(171\) | −1.18801 | −0.0908492 | ||||||||
\(172\) | −9.35177 | −0.713065 | ||||||||
\(173\) | 0.859556 | 0.0653509 | 0.0326754 | − | 0.999466i | \(-0.489597\pi\) | ||||
0.0326754 | + | 0.999466i | \(0.489597\pi\) | |||||||
\(174\) | −29.9001 | −2.26672 | ||||||||
\(175\) | −0.0258357 | −0.00195299 | ||||||||
\(176\) | 67.9819 | 5.12433 | ||||||||
\(177\) | −2.45262 | −0.184351 | ||||||||
\(178\) | −46.7150 | −3.50144 | ||||||||
\(179\) | 7.00339 | 0.523458 | 0.261729 | − | 0.965141i | \(-0.415707\pi\) | ||||
0.261729 | + | 0.965141i | \(0.415707\pi\) | |||||||
\(180\) | −18.2527 | −1.36047 | ||||||||
\(181\) | −18.0941 | −1.34493 | −0.672463 | − | 0.740131i | \(-0.734764\pi\) | ||||
−0.672463 | + | 0.740131i | \(0.734764\pi\) | |||||||
\(182\) | 14.5178 | 1.07613 | ||||||||
\(183\) | −12.5255 | −0.925911 | ||||||||
\(184\) | 58.3178 | 4.29925 | ||||||||
\(185\) | −2.23028 | −0.163974 | ||||||||
\(186\) | −5.76507 | −0.422715 | ||||||||
\(187\) | 33.3513 | 2.43889 | ||||||||
\(188\) | −30.1137 | −2.19627 | ||||||||
\(189\) | −3.11707 | −0.226734 | ||||||||
\(190\) | −4.66748 | −0.338615 | ||||||||
\(191\) | 0.494943 | 0.0358129 | 0.0179064 | − | 0.999840i | \(-0.494300\pi\) | ||||
0.0179064 | + | 0.999840i | \(0.494300\pi\) | |||||||
\(192\) | 51.8033 | 3.73858 | ||||||||
\(193\) | 17.7276 | 1.27606 | 0.638030 | − | 0.770012i | \(-0.279750\pi\) | ||||
0.638030 | + | 0.770012i | \(0.279750\pi\) | |||||||
\(194\) | 14.3373 | 1.02936 | ||||||||
\(195\) | 25.4789 | 1.82458 | ||||||||
\(196\) | 5.32631 | 0.380451 | ||||||||
\(197\) | −11.4738 | −0.817477 | −0.408739 | − | 0.912651i | \(-0.634031\pi\) | ||||
−0.408739 | + | 0.912651i | \(0.634031\pi\) | |||||||
\(198\) | −20.6118 | −1.46482 | ||||||||
\(199\) | −0.363320 | −0.0257551 | −0.0128775 | − | 0.999917i | \(-0.504099\pi\) | ||||
−0.0128775 | + | 0.999917i | \(0.504099\pi\) | |||||||
\(200\) | 0.232609 | 0.0164479 | ||||||||
\(201\) | 14.5749 | 1.02804 | ||||||||
\(202\) | −40.6711 | −2.86161 | ||||||||
\(203\) | 5.18642 | 0.364015 | ||||||||
\(204\) | 76.3426 | 5.34505 | ||||||||
\(205\) | 21.4923 | 1.50109 | ||||||||
\(206\) | 14.9066 | 1.03859 | ||||||||
\(207\) | −9.95256 | −0.691751 | ||||||||
\(208\) | −73.5730 | −5.10137 | ||||||||
\(209\) | −3.83190 | −0.265058 | ||||||||
\(210\) | 12.8577 | 0.887268 | ||||||||
\(211\) | −13.6345 | −0.938639 | −0.469320 | − | 0.883028i | \(-0.655501\pi\) | ||||
−0.469320 | + | 0.883028i | \(0.655501\pi\) | |||||||
\(212\) | 8.29685 | 0.569830 | ||||||||
\(213\) | 30.5536 | 2.09350 | ||||||||
\(214\) | 1.38971 | 0.0949986 | ||||||||
\(215\) | 3.91586 | 0.267059 | ||||||||
\(216\) | 28.0642 | 1.90953 | ||||||||
\(217\) | 1.00000 | 0.0678844 | ||||||||
\(218\) | 40.9523 | 2.77364 | ||||||||
\(219\) | 25.0697 | 1.69405 | ||||||||
\(220\) | −58.8737 | −3.96926 | ||||||||
\(221\) | −36.0942 | −2.42796 | ||||||||
\(222\) | −5.76507 | −0.386926 | ||||||||
\(223\) | 17.0743 | 1.14338 | 0.571689 | − | 0.820471i | \(-0.306288\pi\) | ||||
0.571689 | + | 0.820471i | \(0.306288\pi\) | |||||||
\(224\) | −19.1212 | −1.27759 | ||||||||
\(225\) | −0.0396972 | −0.00264648 | ||||||||
\(226\) | 15.3778 | 1.02292 | ||||||||
\(227\) | 18.4559 | 1.22496 | 0.612482 | − | 0.790485i | \(-0.290171\pi\) | ||||
0.612482 | + | 0.790485i | \(0.290171\pi\) | |||||||
\(228\) | −8.77138 | −0.580899 | ||||||||
\(229\) | 9.95185 | 0.657637 | 0.328818 | − | 0.944393i | \(-0.393350\pi\) | ||||
0.328818 | + | 0.944393i | \(0.393350\pi\) | |||||||
\(230\) | −39.1019 | −2.57830 | ||||||||
\(231\) | 10.5559 | 0.694528 | ||||||||
\(232\) | −46.6954 | −3.06570 | ||||||||
\(233\) | −25.6279 | −1.67894 | −0.839471 | − | 0.543404i | \(-0.817135\pi\) | ||||
−0.839471 | + | 0.543404i | \(0.817135\pi\) | |||||||
\(234\) | 22.3070 | 1.45826 | ||||||||
\(235\) | 12.6095 | 0.822552 | ||||||||
\(236\) | −6.13333 | −0.399246 | ||||||||
\(237\) | 25.8470 | 1.67894 | ||||||||
\(238\) | −18.2147 | −1.18068 | ||||||||
\(239\) | −4.12222 | −0.266644 | −0.133322 | − | 0.991073i | \(-0.542564\pi\) | ||||
−0.133322 | + | 0.991073i | \(0.542564\pi\) | |||||||
\(240\) | −65.1600 | −4.20606 | ||||||||
\(241\) | 9.40872 | 0.606069 | 0.303034 | − | 0.952980i | \(-0.402000\pi\) | ||||
0.303034 | + | 0.952980i | \(0.402000\pi\) | |||||||
\(242\) | −36.7093 | −2.35976 | ||||||||
\(243\) | −14.6074 | −0.937068 | ||||||||
\(244\) | −31.3228 | −2.00523 | ||||||||
\(245\) | −2.23028 | −0.142488 | ||||||||
\(246\) | 55.5556 | 3.54210 | ||||||||
\(247\) | 4.14704 | 0.263870 | ||||||||
\(248\) | −9.00339 | −0.571716 | ||||||||
\(249\) | 34.0284 | 2.15646 | ||||||||
\(250\) | −30.3397 | −1.91885 | ||||||||
\(251\) | 22.5330 | 1.42227 | 0.711136 | − | 0.703055i | \(-0.248181\pi\) | ||||
0.711136 | + | 0.703055i | \(0.248181\pi\) | |||||||
\(252\) | 8.18402 | 0.515545 | ||||||||
\(253\) | −32.1018 | −2.01822 | ||||||||
\(254\) | 16.9766 | 1.06520 | ||||||||
\(255\) | −31.9669 | −2.00184 | ||||||||
\(256\) | 26.0340 | 1.62712 | ||||||||
\(257\) | −6.85995 | −0.427912 | −0.213956 | − | 0.976843i | \(-0.568635\pi\) | ||||
−0.213956 | + | 0.976843i | \(0.568635\pi\) | |||||||
\(258\) | 10.1221 | 0.630175 | ||||||||
\(259\) | 1.00000 | 0.0621370 | ||||||||
\(260\) | 63.7156 | 3.95148 | ||||||||
\(261\) | 7.96906 | 0.493273 | ||||||||
\(262\) | −9.84218 | −0.608052 | ||||||||
\(263\) | 0.0615964 | 0.00379820 | 0.00189910 | − | 0.999998i | \(-0.499395\pi\) | ||||
0.00189910 | + | 0.999998i | \(0.499395\pi\) | |||||||
\(264\) | −95.0391 | −5.84925 | ||||||||
\(265\) | −3.47413 | −0.213414 | ||||||||
\(266\) | 2.09277 | 0.128316 | ||||||||
\(267\) | 36.7600 | 2.24967 | ||||||||
\(268\) | 36.4479 | 2.22641 | ||||||||
\(269\) | 11.1217 | 0.678104 | 0.339052 | − | 0.940768i | \(-0.389894\pi\) | ||||
0.339052 | + | 0.940768i | \(0.389894\pi\) | |||||||
\(270\) | −18.8170 | −1.14516 | ||||||||
\(271\) | −26.3793 | −1.60243 | −0.801216 | − | 0.598376i | \(-0.795813\pi\) | ||||
−0.801216 | + | 0.598376i | \(0.795813\pi\) | |||||||
\(272\) | 92.3076 | 5.59697 | ||||||||
\(273\) | −11.4241 | −0.691416 | ||||||||
\(274\) | −33.7910 | −2.04139 | ||||||||
\(275\) | −0.128043 | −0.00772126 | ||||||||
\(276\) | −73.4825 | −4.42313 | ||||||||
\(277\) | −5.30262 | −0.318603 | −0.159302 | − | 0.987230i | \(-0.550924\pi\) | ||||
−0.159302 | + | 0.987230i | \(0.550924\pi\) | |||||||
\(278\) | −24.5240 | −1.47085 | ||||||||
\(279\) | 1.53652 | 0.0919893 | ||||||||
\(280\) | 20.0801 | 1.20002 | ||||||||
\(281\) | 30.9459 | 1.84607 | 0.923037 | − | 0.384710i | \(-0.125699\pi\) | ||||
0.923037 | + | 0.384710i | \(0.125699\pi\) | |||||||
\(282\) | 32.5943 | 1.94096 | ||||||||
\(283\) | 13.2330 | 0.786622 | 0.393311 | − | 0.919405i | \(-0.371330\pi\) | ||||
0.393311 | + | 0.919405i | \(0.371330\pi\) | |||||||
\(284\) | 76.4059 | 4.53386 | ||||||||
\(285\) | 3.67283 | 0.217560 | ||||||||
\(286\) | 71.9509 | 4.25455 | ||||||||
\(287\) | −9.63660 | −0.568830 | ||||||||
\(288\) | −29.3803 | −1.73125 | ||||||||
\(289\) | 28.2853 | 1.66384 | ||||||||
\(290\) | 31.3091 | 1.83853 | ||||||||
\(291\) | −11.2820 | −0.661363 | ||||||||
\(292\) | 62.6922 | 3.66879 | ||||||||
\(293\) | −4.32958 | −0.252937 | −0.126468 | − | 0.991971i | \(-0.540364\pi\) | ||||
−0.126468 | + | 0.991971i | \(0.540364\pi\) | |||||||
\(294\) | −5.76507 | −0.336226 | ||||||||
\(295\) | 2.56820 | 0.149527 | ||||||||
\(296\) | −9.00339 | −0.523311 | ||||||||
\(297\) | −15.4483 | −0.896403 | ||||||||
\(298\) | −19.9353 | −1.15482 | ||||||||
\(299\) | 34.7420 | 2.00918 | ||||||||
\(300\) | −0.293095 | −0.0169219 | ||||||||
\(301\) | −1.75577 | −0.101201 | ||||||||
\(302\) | 13.5015 | 0.776925 | ||||||||
\(303\) | 32.0040 | 1.83858 | ||||||||
\(304\) | −10.6057 | −0.608278 | ||||||||
\(305\) | 13.1158 | 0.751006 | ||||||||
\(306\) | −27.9873 | −1.59993 | ||||||||
\(307\) | 13.1072 | 0.748066 | 0.374033 | − | 0.927415i | \(-0.377975\pi\) | ||||
0.374033 | + | 0.927415i | \(0.377975\pi\) | |||||||
\(308\) | 26.3974 | 1.50413 | ||||||||
\(309\) | −11.7300 | −0.667295 | ||||||||
\(310\) | 6.03675 | 0.342864 | ||||||||
\(311\) | 10.7239 | 0.608095 | 0.304048 | − | 0.952657i | \(-0.401662\pi\) | ||||
0.304048 | + | 0.952657i | \(0.401662\pi\) | |||||||
\(312\) | 102.855 | 5.82304 | ||||||||
\(313\) | −18.7665 | −1.06074 | −0.530372 | − | 0.847765i | \(-0.677948\pi\) | ||||
−0.530372 | + | 0.847765i | \(0.677948\pi\) | |||||||
\(314\) | 7.57961 | 0.427742 | ||||||||
\(315\) | −3.42689 | −0.193083 | ||||||||
\(316\) | 64.6361 | 3.63607 | ||||||||
\(317\) | 16.0499 | 0.901453 | 0.450726 | − | 0.892662i | \(-0.351165\pi\) | ||||
0.450726 | + | 0.892662i | \(0.351165\pi\) | |||||||
\(318\) | −8.98030 | −0.503590 | ||||||||
\(319\) | 25.7041 | 1.43915 | ||||||||
\(320\) | −54.2445 | −3.03236 | ||||||||
\(321\) | −1.09356 | −0.0610366 | ||||||||
\(322\) | 17.5323 | 0.977035 | ||||||||
\(323\) | −5.20305 | −0.289505 | ||||||||
\(324\) | −59.9139 | −3.32855 | ||||||||
\(325\) | 0.138573 | 0.00768666 | ||||||||
\(326\) | 60.5897 | 3.35575 | ||||||||
\(327\) | −32.2253 | −1.78206 | ||||||||
\(328\) | 86.7621 | 4.79063 | ||||||||
\(329\) | −5.65376 | −0.311702 | ||||||||
\(330\) | 63.7234 | 3.50786 | ||||||||
\(331\) | 15.6915 | 0.862481 | 0.431240 | − | 0.902237i | \(-0.358076\pi\) | ||||
0.431240 | + | 0.902237i | \(0.358076\pi\) | |||||||
\(332\) | 85.0955 | 4.67022 | ||||||||
\(333\) | 1.53652 | 0.0842011 | ||||||||
\(334\) | −18.9257 | −1.03557 | ||||||||
\(335\) | −15.2618 | −0.833840 | ||||||||
\(336\) | 29.2160 | 1.59386 | ||||||||
\(337\) | −9.17039 | −0.499543 | −0.249771 | − | 0.968305i | \(-0.580355\pi\) | ||||
−0.249771 | + | 0.968305i | \(0.580355\pi\) | |||||||
\(338\) | −42.6810 | −2.32154 | ||||||||
\(339\) | −12.1008 | −0.657226 | ||||||||
\(340\) | −79.9402 | −4.33537 | ||||||||
\(341\) | 4.95603 | 0.268384 | ||||||||
\(342\) | 3.21560 | 0.173880 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 15.8079 | 0.852302 | ||||||||
\(345\) | 30.7693 | 1.65656 | ||||||||
\(346\) | −2.32658 | −0.125077 | ||||||||
\(347\) | 0.489439 | 0.0262745 | 0.0131372 | − | 0.999914i | \(-0.495818\pi\) | ||||
0.0131372 | + | 0.999914i | \(0.495818\pi\) | |||||||
\(348\) | 58.8378 | 3.15403 | ||||||||
\(349\) | 6.72850 | 0.360169 | 0.180084 | − | 0.983651i | \(-0.442363\pi\) | ||||
0.180084 | + | 0.983651i | \(0.442363\pi\) | |||||||
\(350\) | 0.0699299 | 0.00373791 | ||||||||
\(351\) | 16.7188 | 0.892385 | ||||||||
\(352\) | −94.7656 | −5.05102 | ||||||||
\(353\) | −20.8092 | −1.10756 | −0.553780 | − | 0.832663i | \(-0.686815\pi\) | ||||
−0.553780 | + | 0.832663i | \(0.686815\pi\) | |||||||
\(354\) | 6.63856 | 0.352835 | ||||||||
\(355\) | −31.9934 | −1.69803 | ||||||||
\(356\) | 91.9264 | 4.87209 | ||||||||
\(357\) | 14.3331 | 0.758588 | ||||||||
\(358\) | −18.9562 | −1.00187 | ||||||||
\(359\) | −18.8235 | −0.993466 | −0.496733 | − | 0.867903i | \(-0.665467\pi\) | ||||
−0.496733 | + | 0.867903i | \(0.665467\pi\) | |||||||
\(360\) | 30.8536 | 1.62613 | ||||||||
\(361\) | −18.4022 | −0.968537 | ||||||||
\(362\) | 48.9757 | 2.57410 | ||||||||
\(363\) | 28.8865 | 1.51615 | ||||||||
\(364\) | −28.5684 | −1.49739 | ||||||||
\(365\) | −26.2511 | −1.37404 | ||||||||
\(366\) | 33.9030 | 1.77214 | ||||||||
\(367\) | 36.3530 | 1.89761 | 0.948806 | − | 0.315860i | \(-0.102293\pi\) | ||||
0.948806 | + | 0.315860i | \(0.102293\pi\) | |||||||
\(368\) | −88.8494 | −4.63159 | ||||||||
\(369\) | −14.8069 | −0.770815 | ||||||||
\(370\) | 6.03675 | 0.313835 | ||||||||
\(371\) | 1.55771 | 0.0808722 | ||||||||
\(372\) | 11.3446 | 0.588189 | ||||||||
\(373\) | −32.0232 | −1.65810 | −0.829049 | − | 0.559176i | \(-0.811118\pi\) | ||||
−0.829049 | + | 0.559176i | \(0.811118\pi\) | |||||||
\(374\) | −90.2725 | −4.66788 | ||||||||
\(375\) | 23.8743 | 1.23286 | ||||||||
\(376\) | 50.9030 | 2.62512 | ||||||||
\(377\) | −27.8181 | −1.43270 | ||||||||
\(378\) | 8.43703 | 0.433954 | ||||||||
\(379\) | 33.0848 | 1.69945 | 0.849727 | − | 0.527223i | \(-0.176767\pi\) | ||||
0.849727 | + | 0.527223i | \(0.176767\pi\) | |||||||
\(380\) | 9.18473 | 0.471167 | ||||||||
\(381\) | −13.3588 | −0.684394 | ||||||||
\(382\) | −1.33967 | −0.0685436 | ||||||||
\(383\) | 30.8149 | 1.57457 | 0.787284 | − | 0.616591i | \(-0.211487\pi\) | ||||
0.787284 | + | 0.616591i | \(0.211487\pi\) | |||||||
\(384\) | −58.7637 | −2.99877 | ||||||||
\(385\) | −11.0534 | −0.563332 | ||||||||
\(386\) | −47.9835 | −2.44230 | ||||||||
\(387\) | −2.69778 | −0.137136 | ||||||||
\(388\) | −28.2132 | −1.43231 | ||||||||
\(389\) | −8.22603 | −0.417076 | −0.208538 | − | 0.978014i | \(-0.566871\pi\) | ||||
−0.208538 | + | 0.978014i | \(0.566871\pi\) | |||||||
\(390\) | −68.9642 | −3.49214 | ||||||||
\(391\) | −43.5887 | −2.20437 | ||||||||
\(392\) | −9.00339 | −0.454740 | ||||||||
\(393\) | 7.74480 | 0.390674 | ||||||||
\(394\) | 31.0564 | 1.56460 | ||||||||
\(395\) | −27.0650 | −1.36179 | ||||||||
\(396\) | 40.5603 | 2.03823 | ||||||||
\(397\) | 10.5592 | 0.529952 | 0.264976 | − | 0.964255i | \(-0.414636\pi\) | ||||
0.264976 | + | 0.964255i | \(0.414636\pi\) | |||||||
\(398\) | 0.983405 | 0.0492936 | ||||||||
\(399\) | −1.64680 | −0.0824432 | ||||||||
\(400\) | −0.354388 | −0.0177194 | ||||||||
\(401\) | 26.9031 | 1.34348 | 0.671739 | − | 0.740788i | \(-0.265548\pi\) | ||||
0.671739 | + | 0.740788i | \(0.265548\pi\) | |||||||
\(402\) | −39.4502 | −1.96760 | ||||||||
\(403\) | −5.36363 | −0.267182 | ||||||||
\(404\) | 80.0331 | 3.98180 | ||||||||
\(405\) | 25.0877 | 1.24662 | ||||||||
\(406\) | −14.0382 | −0.696703 | ||||||||
\(407\) | 4.95603 | 0.245662 | ||||||||
\(408\) | −129.046 | −6.38875 | ||||||||
\(409\) | 16.9620 | 0.838716 | 0.419358 | − | 0.907821i | \(-0.362255\pi\) | ||||
0.419358 | + | 0.907821i | \(0.362255\pi\) | |||||||
\(410\) | −58.1737 | −2.87299 | ||||||||
\(411\) | 26.5901 | 1.31159 | ||||||||
\(412\) | −29.3334 | −1.44515 | ||||||||
\(413\) | −1.15151 | −0.0566623 | ||||||||
\(414\) | 26.9388 | 1.32397 | ||||||||
\(415\) | −35.6320 | −1.74910 | ||||||||
\(416\) | 102.559 | 5.02839 | ||||||||
\(417\) | 19.2979 | 0.945022 | ||||||||
\(418\) | 10.3719 | 0.507304 | ||||||||
\(419\) | 32.4084 | 1.58326 | 0.791628 | − | 0.611003i | \(-0.209234\pi\) | ||||
0.791628 | + | 0.611003i | \(0.209234\pi\) | |||||||
\(420\) | −25.3016 | −1.23459 | ||||||||
\(421\) | 27.1769 | 1.32452 | 0.662260 | − | 0.749274i | \(-0.269597\pi\) | ||||
0.662260 | + | 0.749274i | \(0.269597\pi\) | |||||||
\(422\) | 36.9048 | 1.79650 | ||||||||
\(423\) | −8.68714 | −0.422383 | ||||||||
\(424\) | −14.0247 | −0.681098 | ||||||||
\(425\) | −0.173860 | −0.00843343 | ||||||||
\(426\) | −82.6998 | −4.00682 | ||||||||
\(427\) | −5.88076 | −0.284590 | ||||||||
\(428\) | −2.73469 | −0.132186 | ||||||||
\(429\) | −56.6181 | −2.73355 | ||||||||
\(430\) | −10.5991 | −0.511135 | ||||||||
\(431\) | −16.4070 | −0.790295 | −0.395148 | − | 0.918618i | \(-0.629307\pi\) | ||||
−0.395148 | + | 0.918618i | \(0.629307\pi\) | |||||||
\(432\) | −42.7569 | −2.05714 | ||||||||
\(433\) | −6.13627 | −0.294890 | −0.147445 | − | 0.989070i | \(-0.547105\pi\) | ||||
−0.147445 | + | 0.989070i | \(0.547105\pi\) | |||||||
\(434\) | −2.70672 | −0.129927 | ||||||||
\(435\) | −24.6371 | −1.18126 | ||||||||
\(436\) | −80.5865 | −3.85939 | ||||||||
\(437\) | 5.00812 | 0.239571 | ||||||||
\(438\) | −67.8565 | −3.24231 | ||||||||
\(439\) | 34.6611 | 1.65429 | 0.827143 | − | 0.561992i | \(-0.189965\pi\) | ||||
0.827143 | + | 0.561992i | \(0.189965\pi\) | |||||||
\(440\) | 99.5177 | 4.74432 | ||||||||
\(441\) | 1.53652 | 0.0731679 | ||||||||
\(442\) | 97.6968 | 4.64696 | ||||||||
\(443\) | −3.48138 | −0.165406 | −0.0827028 | − | 0.996574i | \(-0.526355\pi\) | ||||
−0.0827028 | + | 0.996574i | \(0.526355\pi\) | |||||||
\(444\) | 11.3446 | 0.538390 | ||||||||
\(445\) | −38.4923 | −1.82471 | ||||||||
\(446\) | −46.2152 | −2.18835 | ||||||||
\(447\) | 15.6871 | 0.741972 | ||||||||
\(448\) | 24.3218 | 1.14910 | ||||||||
\(449\) | −15.9861 | −0.754429 | −0.377214 | − | 0.926126i | \(-0.623118\pi\) | ||||
−0.377214 | + | 0.926126i | \(0.623118\pi\) | |||||||
\(450\) | 0.107449 | 0.00506520 | ||||||||
\(451\) | −47.7593 | −2.24890 | ||||||||
\(452\) | −30.2607 | −1.42335 | ||||||||
\(453\) | −10.6243 | −0.499175 | ||||||||
\(454\) | −49.9550 | −2.34450 | ||||||||
\(455\) | 11.9624 | 0.560807 | ||||||||
\(456\) | 14.8268 | 0.694328 | ||||||||
\(457\) | 13.8833 | 0.649433 | 0.324716 | − | 0.945811i | \(-0.394731\pi\) | ||||
0.324716 | + | 0.945811i | \(0.394731\pi\) | |||||||
\(458\) | −26.9368 | −1.25868 | ||||||||
\(459\) | −20.9761 | −0.979082 | ||||||||
\(460\) | 76.9453 | 3.58759 | ||||||||
\(461\) | −10.7269 | −0.499599 | −0.249800 | − | 0.968298i | \(-0.580365\pi\) | ||||
−0.249800 | + | 0.968298i | \(0.580365\pi\) | |||||||
\(462\) | −28.5719 | −1.32928 | ||||||||
\(463\) | −0.581977 | −0.0270467 | −0.0135234 | − | 0.999909i | \(-0.504305\pi\) | ||||
−0.0135234 | + | 0.999909i | \(0.504305\pi\) | |||||||
\(464\) | 71.1421 | 3.30269 | ||||||||
\(465\) | −4.75031 | −0.220290 | ||||||||
\(466\) | 69.3676 | 3.21339 | ||||||||
\(467\) | −15.8538 | −0.733625 | −0.366812 | − | 0.930295i | \(-0.619551\pi\) | ||||
−0.366812 | + | 0.930295i | \(0.619551\pi\) | |||||||
\(468\) | −43.8961 | −2.02910 | ||||||||
\(469\) | 6.84298 | 0.315979 | ||||||||
\(470\) | −34.1303 | −1.57431 | ||||||||
\(471\) | −5.96439 | −0.274824 | ||||||||
\(472\) | 10.3675 | 0.477205 | ||||||||
\(473\) | −8.70164 | −0.400102 | ||||||||
\(474\) | −69.9605 | −3.21339 | ||||||||
\(475\) | 0.0199756 | 0.000916543 0 | ||||||||
\(476\) | 35.8431 | 1.64286 | ||||||||
\(477\) | 2.39346 | 0.109589 | ||||||||
\(478\) | 11.1577 | 0.510340 | ||||||||
\(479\) | −19.7766 | −0.903616 | −0.451808 | − | 0.892115i | \(-0.649221\pi\) | ||||
−0.451808 | + | 0.892115i | \(0.649221\pi\) | |||||||
\(480\) | 90.8318 | 4.14589 | ||||||||
\(481\) | −5.36363 | −0.244561 | ||||||||
\(482\) | −25.4667 | −1.15998 | ||||||||
\(483\) | −13.7961 | −0.627745 | ||||||||
\(484\) | 72.2370 | 3.28350 | ||||||||
\(485\) | 11.8137 | 0.536431 | ||||||||
\(486\) | 39.5382 | 1.79349 | ||||||||
\(487\) | 21.3885 | 0.969207 | 0.484604 | − | 0.874734i | \(-0.338964\pi\) | ||||
0.484604 | + | 0.874734i | \(0.338964\pi\) | |||||||
\(488\) | 52.9467 | 2.39679 | ||||||||
\(489\) | −47.6779 | −2.15607 | ||||||||
\(490\) | 6.03675 | 0.272712 | ||||||||
\(491\) | −41.6324 | −1.87884 | −0.939422 | − | 0.342762i | \(-0.888638\pi\) | ||||
−0.939422 | + | 0.342762i | \(0.888638\pi\) | |||||||
\(492\) | −109.323 | −4.92867 | ||||||||
\(493\) | 34.9017 | 1.57189 | ||||||||
\(494\) | −11.2249 | −0.505031 | ||||||||
\(495\) | −16.9838 | −0.763364 | ||||||||
\(496\) | 13.7170 | 0.615911 | ||||||||
\(497\) | 14.3450 | 0.643461 | ||||||||
\(498\) | −92.1052 | −4.12733 | ||||||||
\(499\) | 2.75083 | 0.123144 | 0.0615721 | − | 0.998103i | \(-0.480389\pi\) | ||||
0.0615721 | + | 0.998103i | \(0.480389\pi\) | |||||||
\(500\) | 59.7029 | 2.66999 | ||||||||
\(501\) | 14.8926 | 0.665354 | ||||||||
\(502\) | −60.9905 | −2.72214 | ||||||||
\(503\) | −14.3451 | −0.639618 | −0.319809 | − | 0.947482i | \(-0.603619\pi\) | ||||
−0.319809 | + | 0.947482i | \(0.603619\pi\) | |||||||
\(504\) | −13.8339 | −0.616212 | ||||||||
\(505\) | −33.5122 | −1.49127 | ||||||||
\(506\) | 86.8905 | 3.86276 | ||||||||
\(507\) | 33.5856 | 1.49159 | ||||||||
\(508\) | −33.4067 | −1.48218 | ||||||||
\(509\) | 25.9304 | 1.14935 | 0.574673 | − | 0.818383i | \(-0.305129\pi\) | ||||
0.574673 | + | 0.818383i | \(0.305129\pi\) | |||||||
\(510\) | 86.5253 | 3.83140 | ||||||||
\(511\) | 11.7703 | 0.520687 | ||||||||
\(512\) | −15.2871 | −0.675601 | ||||||||
\(513\) | 2.41005 | 0.106406 | ||||||||
\(514\) | 18.5679 | 0.818997 | ||||||||
\(515\) | 12.2827 | 0.541243 | ||||||||
\(516\) | −19.9184 | −0.876860 | ||||||||
\(517\) | −28.0202 | −1.23233 | ||||||||
\(518\) | −2.70672 | −0.118926 | ||||||||
\(519\) | 1.83078 | 0.0803623 | ||||||||
\(520\) | −107.702 | −4.72306 | ||||||||
\(521\) | 20.6937 | 0.906608 | 0.453304 | − | 0.891356i | \(-0.350245\pi\) | ||||
0.453304 | + | 0.891356i | \(0.350245\pi\) | |||||||
\(522\) | −21.5700 | −0.944093 | ||||||||
\(523\) | −28.8744 | −1.26259 | −0.631295 | − | 0.775543i | \(-0.717476\pi\) | ||||
−0.631295 | + | 0.775543i | \(0.717476\pi\) | |||||||
\(524\) | 19.3676 | 0.846077 | ||||||||
\(525\) | −0.0550277 | −0.00240161 | ||||||||
\(526\) | −0.166724 | −0.00726951 | ||||||||
\(527\) | 6.72943 | 0.293139 | ||||||||
\(528\) | 144.796 | 6.30142 | ||||||||
\(529\) | 18.9557 | 0.824159 | ||||||||
\(530\) | 9.40349 | 0.408462 | ||||||||
\(531\) | −1.76933 | −0.0767824 | ||||||||
\(532\) | −4.11819 | −0.178546 | ||||||||
\(533\) | 51.6872 | 2.23882 | ||||||||
\(534\) | −99.4988 | −4.30573 | ||||||||
\(535\) | 1.14509 | 0.0495068 | ||||||||
\(536\) | −61.6100 | −2.66115 | ||||||||
\(537\) | 14.9166 | 0.643699 | ||||||||
\(538\) | −30.1034 | −1.29785 | ||||||||
\(539\) | 4.95603 | 0.213472 | ||||||||
\(540\) | 37.0283 | 1.59344 | ||||||||
\(541\) | −35.1306 | −1.51038 | −0.755190 | − | 0.655506i | \(-0.772456\pi\) | ||||
−0.755190 | + | 0.655506i | \(0.772456\pi\) | |||||||
\(542\) | 71.4014 | 3.06695 | ||||||||
\(543\) | −38.5389 | −1.65386 | ||||||||
\(544\) | −128.675 | −5.51690 | ||||||||
\(545\) | 33.7439 | 1.44543 | ||||||||
\(546\) | 30.9217 | 1.32333 | ||||||||
\(547\) | 32.6671 | 1.39674 | 0.698371 | − | 0.715736i | \(-0.253909\pi\) | ||||
0.698371 | + | 0.715736i | \(0.253909\pi\) | |||||||
\(548\) | 66.4945 | 2.84050 | ||||||||
\(549\) | −9.03593 | −0.385644 | ||||||||
\(550\) | 0.346575 | 0.0147780 | ||||||||
\(551\) | −4.01003 | −0.170833 | ||||||||
\(552\) | 124.212 | 5.28681 | ||||||||
\(553\) | 12.1352 | 0.516043 | ||||||||
\(554\) | 14.3527 | 0.609787 | ||||||||
\(555\) | −4.75031 | −0.201639 | ||||||||
\(556\) | 48.2587 | 2.04662 | ||||||||
\(557\) | −21.3207 | −0.903386 | −0.451693 | − | 0.892173i | \(-0.649180\pi\) | ||||
−0.451693 | + | 0.892173i | \(0.649180\pi\) | |||||||
\(558\) | −4.15894 | −0.176062 | ||||||||
\(559\) | 9.41729 | 0.398309 | ||||||||
\(560\) | −30.5928 | −1.29278 | ||||||||
\(561\) | 71.0353 | 2.99911 | ||||||||
\(562\) | −83.7617 | −3.53327 | ||||||||
\(563\) | 42.6582 | 1.79783 | 0.898914 | − | 0.438125i | \(-0.144357\pi\) | ||||
0.898914 | + | 0.438125i | \(0.144357\pi\) | |||||||
\(564\) | −64.1395 | −2.70076 | ||||||||
\(565\) | 12.6711 | 0.533075 | ||||||||
\(566\) | −35.8181 | −1.50555 | ||||||||
\(567\) | −11.2487 | −0.472400 | ||||||||
\(568\) | −129.154 | −5.41916 | ||||||||
\(569\) | 7.60001 | 0.318609 | 0.159305 | − | 0.987229i | \(-0.449075\pi\) | ||||
0.159305 | + | 0.987229i | \(0.449075\pi\) | |||||||
\(570\) | −9.94132 | −0.416396 | ||||||||
\(571\) | 24.2485 | 1.01477 | 0.507385 | − | 0.861719i | \(-0.330612\pi\) | ||||
0.507385 | + | 0.861719i | \(0.330612\pi\) | |||||||
\(572\) | −141.586 | −5.92001 | ||||||||
\(573\) | 1.05419 | 0.0440393 | ||||||||
\(574\) | 26.0835 | 1.08871 | ||||||||
\(575\) | 0.167346 | 0.00697881 | ||||||||
\(576\) | 37.3711 | 1.55713 | ||||||||
\(577\) | 3.62156 | 0.150768 | 0.0753838 | − | 0.997155i | \(-0.475982\pi\) | ||||
0.0753838 | + | 0.997155i | \(0.475982\pi\) | |||||||
\(578\) | −76.5602 | −3.18448 | ||||||||
\(579\) | 37.7582 | 1.56918 | ||||||||
\(580\) | −61.6105 | −2.55824 | ||||||||
\(581\) | 15.9764 | 0.662814 | ||||||||
\(582\) | 30.5372 | 1.26581 | ||||||||
\(583\) | 7.72006 | 0.319732 | ||||||||
\(584\) | −105.972 | −4.38517 | ||||||||
\(585\) | 18.3806 | 0.759943 | ||||||||
\(586\) | 11.7189 | 0.484105 | ||||||||
\(587\) | −33.2563 | −1.37263 | −0.686317 | − | 0.727303i | \(-0.740774\pi\) | ||||
−0.686317 | + | 0.727303i | \(0.740774\pi\) | |||||||
\(588\) | 11.3446 | 0.467843 | ||||||||
\(589\) | −0.773178 | −0.0318583 | ||||||||
\(590\) | −6.95140 | −0.286185 | ||||||||
\(591\) | −24.4383 | −1.00526 | ||||||||
\(592\) | 13.7170 | 0.563765 | ||||||||
\(593\) | 23.2605 | 0.955193 | 0.477597 | − | 0.878579i | \(-0.341508\pi\) | ||||
0.477597 | + | 0.878579i | \(0.341508\pi\) | |||||||
\(594\) | 41.8142 | 1.71566 | ||||||||
\(595\) | −15.0085 | −0.615290 | ||||||||
\(596\) | 39.2290 | 1.60688 | ||||||||
\(597\) | −0.773840 | −0.0316712 | ||||||||
\(598\) | −94.0367 | −3.84544 | ||||||||
\(599\) | −38.2467 | −1.56272 | −0.781359 | − | 0.624082i | \(-0.785473\pi\) | ||||
−0.781359 | + | 0.624082i | \(0.785473\pi\) | |||||||
\(600\) | 0.495436 | 0.0202261 | ||||||||
\(601\) | −20.1839 | −0.823319 | −0.411659 | − | 0.911338i | \(-0.635051\pi\) | ||||
−0.411659 | + | 0.911338i | \(0.635051\pi\) | |||||||
\(602\) | 4.75236 | 0.193692 | ||||||||
\(603\) | 10.5144 | 0.428180 | ||||||||
\(604\) | −26.5685 | −1.08106 | ||||||||
\(605\) | −30.2477 | −1.22975 | ||||||||
\(606\) | −86.6258 | −3.51893 | ||||||||
\(607\) | −26.5553 | −1.07785 | −0.538924 | − | 0.842355i | \(-0.681169\pi\) | ||||
−0.538924 | + | 0.842355i | \(0.681169\pi\) | |||||||
\(608\) | 14.7841 | 0.599576 | ||||||||
\(609\) | 11.0466 | 0.447631 | ||||||||
\(610\) | −35.5006 | −1.43738 | ||||||||
\(611\) | 30.3247 | 1.22681 | ||||||||
\(612\) | 55.0738 | 2.22623 | ||||||||
\(613\) | −3.45638 | −0.139602 | −0.0698010 | − | 0.997561i | \(-0.522236\pi\) | ||||
−0.0698010 | + | 0.997561i | \(0.522236\pi\) | |||||||
\(614\) | −35.4774 | −1.43175 | ||||||||
\(615\) | 45.7768 | 1.84590 | ||||||||
\(616\) | −44.6211 | −1.79784 | ||||||||
\(617\) | −24.5763 | −0.989407 | −0.494703 | − | 0.869062i | \(-0.664723\pi\) | ||||
−0.494703 | + | 0.869062i | \(0.664723\pi\) | |||||||
\(618\) | 31.7497 | 1.27716 | ||||||||
\(619\) | −18.4586 | −0.741914 | −0.370957 | − | 0.928650i | \(-0.620970\pi\) | ||||
−0.370957 | + | 0.928650i | \(0.620970\pi\) | |||||||
\(620\) | −11.8792 | −0.477080 | ||||||||
\(621\) | 20.1903 | 0.810208 | ||||||||
\(622\) | −29.0265 | −1.16386 | ||||||||
\(623\) | 17.2589 | 0.691464 | ||||||||
\(624\) | −156.704 | −6.27318 | ||||||||
\(625\) | −24.8702 | −0.994806 | ||||||||
\(626\) | 50.7956 | 2.03020 | ||||||||
\(627\) | −8.16161 | −0.325943 | ||||||||
\(628\) | −14.9153 | −0.595184 | ||||||||
\(629\) | 6.72943 | 0.268320 | ||||||||
\(630\) | 9.27561 | 0.369549 | ||||||||
\(631\) | 31.9814 | 1.27316 | 0.636580 | − | 0.771211i | \(-0.280349\pi\) | ||||
0.636580 | + | 0.771211i | \(0.280349\pi\) | |||||||
\(632\) | −109.258 | −4.34606 | ||||||||
\(633\) | −29.0403 | −1.15425 | ||||||||
\(634\) | −43.4425 | −1.72532 | ||||||||
\(635\) | 13.9884 | 0.555112 | ||||||||
\(636\) | 17.6716 | 0.700723 | ||||||||
\(637\) | −5.36363 | −0.212515 | ||||||||
\(638\) | −69.5736 | −2.75445 | ||||||||
\(639\) | 22.0414 | 0.871946 | ||||||||
\(640\) | 61.5329 | 2.43230 | ||||||||
\(641\) | 10.2768 | 0.405911 | 0.202955 | − | 0.979188i | \(-0.434945\pi\) | ||||
0.202955 | + | 0.979188i | \(0.434945\pi\) | |||||||
\(642\) | 2.95996 | 0.116820 | ||||||||
\(643\) | −34.7751 | −1.37140 | −0.685699 | − | 0.727885i | \(-0.740503\pi\) | ||||
−0.685699 | + | 0.727885i | \(0.740503\pi\) | |||||||
\(644\) | −34.5002 | −1.35950 | ||||||||
\(645\) | 8.34043 | 0.328404 | ||||||||
\(646\) | 14.0832 | 0.554095 | ||||||||
\(647\) | 1.13797 | 0.0447384 | 0.0223692 | − | 0.999750i | \(-0.492879\pi\) | ||||
0.0223692 | + | 0.999750i | \(0.492879\pi\) | |||||||
\(648\) | 101.276 | 3.97850 | ||||||||
\(649\) | −5.70695 | −0.224017 | ||||||||
\(650\) | −0.375078 | −0.0147118 | ||||||||
\(651\) | 2.12991 | 0.0834778 | ||||||||
\(652\) | −119.229 | −4.66937 | ||||||||
\(653\) | 30.1586 | 1.18020 | 0.590099 | − | 0.807331i | \(-0.299089\pi\) | ||||
0.590099 | + | 0.807331i | \(0.299089\pi\) | |||||||
\(654\) | 87.2247 | 3.41076 | ||||||||
\(655\) | −8.10977 | −0.316875 | ||||||||
\(656\) | −132.185 | −5.16096 | ||||||||
\(657\) | 18.0853 | 0.705576 | ||||||||
\(658\) | 15.3031 | 0.596578 | ||||||||
\(659\) | −25.8396 | −1.00657 | −0.503284 | − | 0.864121i | \(-0.667875\pi\) | ||||
−0.503284 | + | 0.864121i | \(0.667875\pi\) | |||||||
\(660\) | −125.396 | −4.88102 | ||||||||
\(661\) | 41.3589 | 1.60868 | 0.804338 | − | 0.594173i | \(-0.202520\pi\) | ||||
0.804338 | + | 0.594173i | \(0.202520\pi\) | |||||||
\(662\) | −42.4723 | −1.65073 | ||||||||
\(663\) | −76.8775 | −2.98567 | ||||||||
\(664\) | −143.842 | −5.58215 | ||||||||
\(665\) | 1.72441 | 0.0668696 | ||||||||
\(666\) | −4.15894 | −0.161156 | ||||||||
\(667\) | −33.5941 | −1.30077 | ||||||||
\(668\) | 37.2423 | 1.44095 | ||||||||
\(669\) | 36.3667 | 1.40602 | ||||||||
\(670\) | 41.3093 | 1.59592 | ||||||||
\(671\) | −29.1452 | −1.12514 | ||||||||
\(672\) | −40.7266 | −1.57106 | ||||||||
\(673\) | 21.0157 | 0.810095 | 0.405047 | − | 0.914296i | \(-0.367255\pi\) | ||||
0.405047 | + | 0.914296i | \(0.367255\pi\) | |||||||
\(674\) | 24.8216 | 0.956094 | ||||||||
\(675\) | 0.0805317 | 0.00309967 | ||||||||
\(676\) | 83.9883 | 3.23032 | ||||||||
\(677\) | −10.7118 | −0.411689 | −0.205845 | − | 0.978585i | \(-0.565994\pi\) | ||||
−0.205845 | + | 0.978585i | \(0.565994\pi\) | |||||||
\(678\) | 32.7535 | 1.25789 | ||||||||
\(679\) | −5.29694 | −0.203278 | ||||||||
\(680\) | 135.128 | 5.18191 | ||||||||
\(681\) | 39.3095 | 1.50634 | ||||||||
\(682\) | −13.4146 | −0.513671 | ||||||||
\(683\) | 18.8890 | 0.722768 | 0.361384 | − | 0.932417i | \(-0.382304\pi\) | ||||
0.361384 | + | 0.932417i | \(0.382304\pi\) | |||||||
\(684\) | −6.32770 | −0.241946 | ||||||||
\(685\) | −27.8432 | −1.06383 | ||||||||
\(686\) | −2.70672 | −0.103343 | ||||||||
\(687\) | 21.1966 | 0.808700 | ||||||||
\(688\) | −24.0838 | −0.918188 | ||||||||
\(689\) | −8.35498 | −0.318299 | ||||||||
\(690\) | −83.2837 | −3.17055 | ||||||||
\(691\) | 30.7547 | 1.16997 | 0.584983 | − | 0.811046i | \(-0.301101\pi\) | ||||
0.584983 | + | 0.811046i | \(0.301101\pi\) | |||||||
\(692\) | 4.57827 | 0.174040 | ||||||||
\(693\) | 7.61507 | 0.289273 | ||||||||
\(694\) | −1.32477 | −0.0502877 | ||||||||
\(695\) | −20.2073 | −0.766507 | ||||||||
\(696\) | −99.4570 | −3.76991 | ||||||||
\(697\) | −64.8488 | −2.45632 | ||||||||
\(698\) | −18.2122 | −0.689340 | ||||||||
\(699\) | −54.5853 | −2.06460 | ||||||||
\(700\) | −0.137609 | −0.00520113 | ||||||||
\(701\) | 37.4913 | 1.41603 | 0.708014 | − | 0.706198i | \(-0.249591\pi\) | ||||
0.708014 | + | 0.706198i | \(0.249591\pi\) | |||||||
\(702\) | −45.2532 | −1.70797 | ||||||||
\(703\) | −0.773178 | −0.0291610 | ||||||||
\(704\) | 120.540 | 4.54301 | ||||||||
\(705\) | 26.8571 | 1.01150 | ||||||||
\(706\) | 56.3245 | 2.11980 | ||||||||
\(707\) | 15.0260 | 0.565110 | ||||||||
\(708\) | −13.0635 | −0.490955 | ||||||||
\(709\) | 11.2896 | 0.423988 | 0.211994 | − | 0.977271i | \(-0.432004\pi\) | ||||
0.211994 | + | 0.977271i | \(0.432004\pi\) | |||||||
\(710\) | 86.5970 | 3.24993 | ||||||||
\(711\) | 18.6461 | 0.699284 | ||||||||
\(712\) | −155.389 | −5.82344 | ||||||||
\(713\) | −6.47732 | −0.242578 | ||||||||
\(714\) | −38.7956 | −1.45189 | ||||||||
\(715\) | 59.2862 | 2.21718 | ||||||||
\(716\) | 37.3023 | 1.39405 | ||||||||
\(717\) | −8.77996 | −0.327894 | ||||||||
\(718\) | 50.9499 | 1.90143 | ||||||||
\(719\) | 31.7421 | 1.18378 | 0.591890 | − | 0.806019i | \(-0.298382\pi\) | ||||
0.591890 | + | 0.806019i | \(0.298382\pi\) | |||||||
\(720\) | −47.0066 | −1.75183 | ||||||||
\(721\) | −5.50726 | −0.205101 | ||||||||
\(722\) | 49.8095 | 1.85372 | ||||||||
\(723\) | 20.0397 | 0.745286 | ||||||||
\(724\) | −96.3750 | −3.58175 | ||||||||
\(725\) | −0.133995 | −0.00497644 | ||||||||
\(726\) | −78.1875 | −2.90181 | ||||||||
\(727\) | −43.7135 | −1.62124 | −0.810622 | − | 0.585570i | \(-0.800871\pi\) | ||||
−0.810622 | + | 0.585570i | \(0.800871\pi\) | |||||||
\(728\) | 48.2909 | 1.78978 | ||||||||
\(729\) | 2.63342 | 0.0975339 | ||||||||
\(730\) | 71.0542 | 2.62983 | ||||||||
\(731\) | −11.8153 | −0.437005 | ||||||||
\(732\) | −66.7147 | −2.46585 | ||||||||
\(733\) | 19.3095 | 0.713212 | 0.356606 | − | 0.934255i | \(-0.383934\pi\) | ||||
0.356606 | + | 0.934255i | \(0.383934\pi\) | |||||||
\(734\) | −98.3973 | −3.63191 | ||||||||
\(735\) | −4.75031 | −0.175218 | ||||||||
\(736\) | 123.854 | 4.56533 | ||||||||
\(737\) | 33.9141 | 1.24924 | ||||||||
\(738\) | 40.0780 | 1.47529 | ||||||||
\(739\) | −1.02619 | −0.0377490 | −0.0188745 | − | 0.999822i | \(-0.506008\pi\) | ||||
−0.0188745 | + | 0.999822i | \(0.506008\pi\) | |||||||
\(740\) | −11.8792 | −0.436688 | ||||||||
\(741\) | 8.83284 | 0.324482 | ||||||||
\(742\) | −4.21628 | −0.154784 | ||||||||
\(743\) | 11.9787 | 0.439455 | 0.219728 | − | 0.975561i | \(-0.429483\pi\) | ||||
0.219728 | + | 0.975561i | \(0.429483\pi\) | |||||||
\(744\) | −19.1764 | −0.703042 | ||||||||
\(745\) | −16.4263 | −0.601813 | ||||||||
\(746\) | 86.6777 | 3.17350 | ||||||||
\(747\) | 24.5482 | 0.898171 | ||||||||
\(748\) | 177.640 | 6.49514 | ||||||||
\(749\) | −0.513430 | −0.0187603 | ||||||||
\(750\) | −64.6209 | −2.35962 | ||||||||
\(751\) | −0.0981807 | −0.00358266 | −0.00179133 | − | 0.999998i | \(-0.500570\pi\) | ||||
−0.00179133 | + | 0.999998i | \(0.500570\pi\) | |||||||
\(752\) | −77.5526 | −2.82805 | ||||||||
\(753\) | 47.9933 | 1.74897 | ||||||||
\(754\) | 75.2956 | 2.74210 | ||||||||
\(755\) | 11.1250 | 0.404880 | ||||||||
\(756\) | −16.6025 | −0.603828 | ||||||||
\(757\) | −12.1189 | −0.440470 | −0.220235 | − | 0.975447i | \(-0.570682\pi\) | ||||
−0.220235 | + | 0.975447i | \(0.570682\pi\) | |||||||
\(758\) | −89.5513 | −3.25265 | ||||||||
\(759\) | −68.3740 | −2.48182 | ||||||||
\(760\) | −15.5255 | −0.563169 | ||||||||
\(761\) | −5.89734 | −0.213778 | −0.106889 | − | 0.994271i | \(-0.534089\pi\) | ||||
−0.106889 | + | 0.994271i | \(0.534089\pi\) | |||||||
\(762\) | 36.1586 | 1.30989 | ||||||||
\(763\) | −15.1299 | −0.547738 | ||||||||
\(764\) | 2.63622 | 0.0953753 | ||||||||
\(765\) | −23.0610 | −0.833772 | ||||||||
\(766\) | −83.4072 | −3.01362 | ||||||||
\(767\) | 6.17630 | 0.223013 | ||||||||
\(768\) | 55.4500 | 2.00088 | ||||||||
\(769\) | 48.9344 | 1.76462 | 0.882309 | − | 0.470671i | \(-0.155988\pi\) | ||||
0.882309 | + | 0.470671i | \(0.155988\pi\) | |||||||
\(770\) | 29.9183 | 1.07818 | ||||||||
\(771\) | −14.6111 | −0.526205 | ||||||||
\(772\) | 94.4227 | 3.39835 | ||||||||
\(773\) | 44.0262 | 1.58351 | 0.791756 | − | 0.610837i | \(-0.209167\pi\) | ||||
0.791756 | + | 0.610837i | \(0.209167\pi\) | |||||||
\(774\) | 7.30212 | 0.262469 | ||||||||
\(775\) | −0.0258357 | −0.000928045 0 | ||||||||
\(776\) | 47.6904 | 1.71199 | ||||||||
\(777\) | 2.12991 | 0.0764102 | ||||||||
\(778\) | 22.2655 | 0.798258 | ||||||||
\(779\) | 7.45081 | 0.266953 | ||||||||
\(780\) | 135.709 | 4.85915 | ||||||||
\(781\) | 71.0943 | 2.54395 | ||||||||
\(782\) | 117.982 | 4.21903 | ||||||||
\(783\) | −16.1664 | −0.577742 | ||||||||
\(784\) | 13.7170 | 0.489893 | ||||||||
\(785\) | 6.24546 | 0.222910 | ||||||||
\(786\) | −20.9630 | −0.747725 | ||||||||
\(787\) | 4.78562 | 0.170589 | 0.0852945 | − | 0.996356i | \(-0.472817\pi\) | ||||
0.0852945 | + | 0.996356i | \(0.472817\pi\) | |||||||
\(788\) | −61.1133 | −2.17707 | ||||||||
\(789\) | 0.131195 | 0.00467066 | ||||||||
\(790\) | 73.2574 | 2.60638 | ||||||||
\(791\) | −5.68137 | −0.202006 | ||||||||
\(792\) | −68.5615 | −2.43623 | ||||||||
\(793\) | 31.5422 | 1.12010 | ||||||||
\(794\) | −28.5808 | −1.01430 | ||||||||
\(795\) | −7.39960 | −0.262437 | ||||||||
\(796\) | −1.93516 | −0.0685898 | ||||||||
\(797\) | 52.2526 | 1.85088 | 0.925440 | − | 0.378893i | \(-0.123695\pi\) | ||||
0.925440 | + | 0.378893i | \(0.123695\pi\) | |||||||
\(798\) | 4.45743 | 0.157791 | ||||||||
\(799\) | −38.0466 | −1.34599 | ||||||||
\(800\) | 0.494011 | 0.0174659 | ||||||||
\(801\) | 26.5188 | 0.936994 | ||||||||
\(802\) | −72.8192 | −2.57133 | ||||||||
\(803\) | 58.3339 | 2.05856 | ||||||||
\(804\) | 77.6308 | 2.73783 | ||||||||
\(805\) | 14.4463 | 0.509164 | ||||||||
\(806\) | 14.5178 | 0.511369 | ||||||||
\(807\) | 23.6883 | 0.833868 | ||||||||
\(808\) | −135.285 | −4.75930 | ||||||||
\(809\) | 26.1186 | 0.918281 | 0.459140 | − | 0.888364i | \(-0.348157\pi\) | ||||
0.459140 | + | 0.888364i | \(0.348157\pi\) | |||||||
\(810\) | −67.9053 | −2.38595 | ||||||||
\(811\) | −43.4580 | −1.52602 | −0.763009 | − | 0.646388i | \(-0.776279\pi\) | ||||
−0.763009 | + | 0.646388i | \(0.776279\pi\) | |||||||
\(812\) | 27.6245 | 0.969430 | ||||||||
\(813\) | −56.1857 | −1.97052 | ||||||||
\(814\) | −13.4146 | −0.470181 | ||||||||
\(815\) | 49.9247 | 1.74879 | ||||||||
\(816\) | 196.607 | 6.88262 | ||||||||
\(817\) | 1.35752 | 0.0474936 | ||||||||
\(818\) | −45.9113 | −1.60525 | ||||||||
\(819\) | −8.24136 | −0.287976 | ||||||||
\(820\) | 114.475 | 3.99764 | ||||||||
\(821\) | −2.54141 | −0.0886958 | −0.0443479 | − | 0.999016i | \(-0.514121\pi\) | ||||
−0.0443479 | + | 0.999016i | \(0.514121\pi\) | |||||||
\(822\) | −71.9719 | −2.51031 | ||||||||
\(823\) | 47.5239 | 1.65658 | 0.828290 | − | 0.560299i | \(-0.189314\pi\) | ||||
0.828290 | + | 0.560299i | \(0.189314\pi\) | |||||||
\(824\) | 49.5840 | 1.72734 | ||||||||
\(825\) | −0.272719 | −0.00949487 | ||||||||
\(826\) | 3.11682 | 0.108448 | ||||||||
\(827\) | −35.2877 | −1.22707 | −0.613537 | − | 0.789666i | \(-0.710254\pi\) | ||||
−0.613537 | + | 0.789666i | \(0.710254\pi\) | |||||||
\(828\) | −53.0105 | −1.84224 | ||||||||
\(829\) | 0.510918 | 0.0177449 | 0.00887246 | − | 0.999961i | \(-0.497176\pi\) | ||||
0.00887246 | + | 0.999961i | \(0.497176\pi\) | |||||||
\(830\) | 96.4456 | 3.34768 | ||||||||
\(831\) | −11.2941 | −0.391788 | ||||||||
\(832\) | −130.453 | −4.52265 | ||||||||
\(833\) | 6.72943 | 0.233161 | ||||||||
\(834\) | −52.2340 | −1.80871 | ||||||||
\(835\) | −15.5945 | −0.539668 | ||||||||
\(836\) | −20.4099 | −0.705891 | ||||||||
\(837\) | −3.11707 | −0.107742 | ||||||||
\(838\) | −87.7205 | −3.03025 | ||||||||
\(839\) | 48.0248 | 1.65800 | 0.829001 | − | 0.559247i | \(-0.188910\pi\) | ||||
0.829001 | + | 0.559247i | \(0.188910\pi\) | |||||||
\(840\) | 42.7689 | 1.47567 | ||||||||
\(841\) | −2.10105 | −0.0724501 | ||||||||
\(842\) | −73.5602 | −2.53505 | ||||||||
\(843\) | 65.9119 | 2.27013 | ||||||||
\(844\) | −72.6218 | −2.49974 | ||||||||
\(845\) | −35.1684 | −1.20983 | ||||||||
\(846\) | 23.5136 | 0.808415 | ||||||||
\(847\) | 13.5623 | 0.466005 | ||||||||
\(848\) | 21.3671 | 0.733749 | ||||||||
\(849\) | 28.1852 | 0.967313 | ||||||||
\(850\) | 0.470588 | 0.0161411 | ||||||||
\(851\) | −6.47732 | −0.222040 | ||||||||
\(852\) | 162.738 | 5.57531 | ||||||||
\(853\) | −20.8181 | −0.712797 | −0.356398 | − | 0.934334i | \(-0.615995\pi\) | ||||
−0.356398 | + | 0.934334i | \(0.615995\pi\) | |||||||
\(854\) | 15.9175 | 0.544687 | ||||||||
\(855\) | 2.64959 | 0.0906142 | ||||||||
\(856\) | 4.62261 | 0.157998 | ||||||||
\(857\) | 37.0033 | 1.26401 | 0.632005 | − | 0.774964i | \(-0.282232\pi\) | ||||
0.632005 | + | 0.774964i | \(0.282232\pi\) | |||||||
\(858\) | 153.249 | 5.23184 | ||||||||
\(859\) | 10.4623 | 0.356967 | 0.178484 | − | 0.983943i | \(-0.442881\pi\) | ||||
0.178484 | + | 0.983943i | \(0.442881\pi\) | |||||||
\(860\) | 20.8571 | 0.711221 | ||||||||
\(861\) | −20.5251 | −0.699494 | ||||||||
\(862\) | 44.4090 | 1.51258 | ||||||||
\(863\) | 2.43568 | 0.0829115 | 0.0414557 | − | 0.999140i | \(-0.486800\pi\) | ||||
0.0414557 | + | 0.999140i | \(0.486800\pi\) | |||||||
\(864\) | 59.6023 | 2.02771 | ||||||||
\(865\) | −1.91705 | −0.0651818 | ||||||||
\(866\) | 16.6091 | 0.564402 | ||||||||
\(867\) | 60.2451 | 2.04603 | ||||||||
\(868\) | 5.32631 | 0.180787 | ||||||||
\(869\) | 60.1427 | 2.04020 | ||||||||
\(870\) | 66.6856 | 2.26085 | ||||||||
\(871\) | −36.7032 | −1.24364 | ||||||||
\(872\) | 136.220 | 4.61300 | ||||||||
\(873\) | −8.13888 | −0.275459 | ||||||||
\(874\) | −13.5556 | −0.458524 | ||||||||
\(875\) | 11.2090 | 0.378935 | ||||||||
\(876\) | 133.529 | 4.51152 | ||||||||
\(877\) | −32.9610 | −1.11301 | −0.556507 | − | 0.830843i | \(-0.687859\pi\) | ||||
−0.556507 | + | 0.830843i | \(0.687859\pi\) | |||||||
\(878\) | −93.8179 | −3.16620 | ||||||||
\(879\) | −9.22162 | −0.311037 | ||||||||
\(880\) | −151.619 | −5.11107 | ||||||||
\(881\) | 33.2002 | 1.11854 | 0.559272 | − | 0.828984i | \(-0.311081\pi\) | ||||
0.559272 | + | 0.828984i | \(0.311081\pi\) | |||||||
\(882\) | −4.15894 | −0.140039 | ||||||||
\(883\) | 34.8091 | 1.17142 | 0.585709 | − | 0.810521i | \(-0.300816\pi\) | ||||
0.585709 | + | 0.810521i | \(0.300816\pi\) | |||||||
\(884\) | −192.249 | −6.46604 | ||||||||
\(885\) | 5.47005 | 0.183874 | ||||||||
\(886\) | 9.42312 | 0.316576 | ||||||||
\(887\) | −3.57310 | −0.119973 | −0.0599864 | − | 0.998199i | \(-0.519106\pi\) | ||||
−0.0599864 | + | 0.998199i | \(0.519106\pi\) | |||||||
\(888\) | −19.1764 | −0.643519 | ||||||||
\(889\) | −6.27201 | −0.210357 | ||||||||
\(890\) | 104.188 | 3.49238 | ||||||||
\(891\) | −55.7488 | −1.86765 | ||||||||
\(892\) | 90.9429 | 3.04499 | ||||||||
\(893\) | 4.37136 | 0.146282 | ||||||||
\(894\) | −42.4604 | −1.42009 | ||||||||
\(895\) | −15.6195 | −0.522104 | ||||||||
\(896\) | −27.5897 | −0.921708 | ||||||||
\(897\) | 73.9973 | 2.47070 | ||||||||
\(898\) | 43.2697 | 1.44393 | ||||||||
\(899\) | 5.18642 | 0.172977 | ||||||||
\(900\) | −0.211440 | −0.00704799 | ||||||||
\(901\) | 10.4825 | 0.349223 | ||||||||
\(902\) | 129.271 | 4.30425 | ||||||||
\(903\) | −3.73963 | −0.124447 | ||||||||
\(904\) | 51.1516 | 1.70128 | ||||||||
\(905\) | 40.3550 | 1.34145 | ||||||||
\(906\) | 28.7571 | 0.955389 | ||||||||
\(907\) | −49.4292 | −1.64127 | −0.820635 | − | 0.571453i | \(-0.806380\pi\) | ||||
−0.820635 | + | 0.571453i | \(0.806380\pi\) | |||||||
\(908\) | 98.3021 | 3.26227 | ||||||||
\(909\) | 23.0878 | 0.765774 | ||||||||
\(910\) | −32.3789 | −1.07335 | ||||||||
\(911\) | −44.5730 | −1.47677 | −0.738385 | − | 0.674379i | \(-0.764411\pi\) | ||||
−0.738385 | + | 0.674379i | \(0.764411\pi\) | |||||||
\(912\) | −22.5892 | −0.748002 | ||||||||
\(913\) | 79.1797 | 2.62047 | ||||||||
\(914\) | −37.5781 | −1.24297 | ||||||||
\(915\) | 27.9354 | 0.923516 | ||||||||
\(916\) | 53.0067 | 1.75139 | ||||||||
\(917\) | 3.63621 | 0.120078 | ||||||||
\(918\) | 56.7764 | 1.87390 | ||||||||
\(919\) | −13.7219 | −0.452645 | −0.226322 | − | 0.974052i | \(-0.572670\pi\) | ||||
−0.226322 | + | 0.974052i | \(0.572670\pi\) | |||||||
\(920\) | −130.065 | −4.28813 | ||||||||
\(921\) | 27.9171 | 0.919900 | ||||||||
\(922\) | 29.0345 | 0.956202 | ||||||||
\(923\) | −76.9413 | −2.53255 | ||||||||
\(924\) | 56.2241 | 1.84964 | ||||||||
\(925\) | −0.0258357 | −0.000849472 0 | ||||||||
\(926\) | 1.57525 | 0.0517658 | ||||||||
\(927\) | −8.46204 | −0.277930 | ||||||||
\(928\) | −99.1708 | −3.25544 | ||||||||
\(929\) | −37.9634 | −1.24554 | −0.622770 | − | 0.782405i | \(-0.713993\pi\) | ||||
−0.622770 | + | 0.782405i | \(0.713993\pi\) | |||||||
\(930\) | 12.8577 | 0.421622 | ||||||||
\(931\) | −0.773178 | −0.0253399 | ||||||||
\(932\) | −136.502 | −4.47129 | ||||||||
\(933\) | 22.8409 | 0.747778 | ||||||||
\(934\) | 42.9116 | 1.40411 | ||||||||
\(935\) | −74.3828 | −2.43258 | ||||||||
\(936\) | 74.2002 | 2.42531 | ||||||||
\(937\) | 55.6687 | 1.81862 | 0.909309 | − | 0.416123i | \(-0.136611\pi\) | ||||
0.909309 | + | 0.416123i | \(0.136611\pi\) | |||||||
\(938\) | −18.5220 | −0.604765 | ||||||||
\(939\) | −39.9710 | −1.30440 | ||||||||
\(940\) | 67.1621 | 2.19059 | ||||||||
\(941\) | 9.46269 | 0.308475 | 0.154237 | − | 0.988034i | \(-0.450708\pi\) | ||||
0.154237 | + | 0.988034i | \(0.450708\pi\) | |||||||
\(942\) | 16.1439 | 0.525997 | ||||||||
\(943\) | 62.4193 | 2.03265 | ||||||||
\(944\) | −15.7953 | −0.514094 | ||||||||
\(945\) | 6.95196 | 0.226147 | ||||||||
\(946\) | 23.5529 | 0.765770 | ||||||||
\(947\) | −55.1487 | −1.79209 | −0.896047 | − | 0.443960i | \(-0.853573\pi\) | ||||
−0.896047 | + | 0.443960i | \(0.853573\pi\) | |||||||
\(948\) | 137.669 | 4.47129 | ||||||||
\(949\) | −63.1315 | −2.04933 | ||||||||
\(950\) | −0.0540683 | −0.00175421 | ||||||||
\(951\) | 34.1849 | 1.10852 | ||||||||
\(952\) | −60.5877 | −1.96366 | ||||||||
\(953\) | 1.73841 | 0.0563125 | 0.0281562 | − | 0.999604i | \(-0.491036\pi\) | ||||
0.0281562 | + | 0.999604i | \(0.491036\pi\) | |||||||
\(954\) | −6.47841 | −0.209746 | ||||||||
\(955\) | −1.10386 | −0.0357202 | ||||||||
\(956\) | −21.9562 | −0.710115 | ||||||||
\(957\) | 54.7474 | 1.76973 | ||||||||
\(958\) | 53.5297 | 1.72946 | ||||||||
\(959\) | 12.4841 | 0.403134 | ||||||||
\(960\) | −115.536 | −3.72891 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 14.5178 | 0.468074 | ||||||||
\(963\) | −0.788898 | −0.0254219 | ||||||||
\(964\) | 50.1138 | 1.61406 | ||||||||
\(965\) | −39.5375 | −1.27276 | ||||||||
\(966\) | 37.3422 | 1.20147 | ||||||||
\(967\) | −0.657920 | −0.0211573 | −0.0105786 | − | 0.999944i | \(-0.503367\pi\) | ||||
−0.0105786 | + | 0.999944i | \(0.503367\pi\) | |||||||
\(968\) | −122.107 | −3.92465 | ||||||||
\(969\) | −11.0820 | −0.356006 | ||||||||
\(970\) | −31.9763 | −1.02670 | ||||||||
\(971\) | 29.0373 | 0.931850 | 0.465925 | − | 0.884824i | \(-0.345722\pi\) | ||||
0.465925 | + | 0.884824i | \(0.345722\pi\) | |||||||
\(972\) | −77.8039 | −2.49556 | ||||||||
\(973\) | 9.06042 | 0.290464 | ||||||||
\(974\) | −57.8927 | −1.85500 | ||||||||
\(975\) | 0.295149 | 0.00945232 | ||||||||
\(976\) | −80.6663 | −2.58207 | ||||||||
\(977\) | 58.3705 | 1.86744 | 0.933718 | − | 0.358009i | \(-0.116544\pi\) | ||||
0.933718 | + | 0.358009i | \(0.116544\pi\) | |||||||
\(978\) | 129.051 | 4.12658 | ||||||||
\(979\) | 85.5358 | 2.73374 | ||||||||
\(980\) | −11.8792 | −0.379467 | ||||||||
\(981\) | −23.2474 | −0.742233 | ||||||||
\(982\) | 112.687 | 3.59599 | ||||||||
\(983\) | −21.3073 | −0.679598 | −0.339799 | − | 0.940498i | \(-0.610359\pi\) | ||||
−0.339799 | + | 0.940498i | \(0.610359\pi\) | |||||||
\(984\) | 184.796 | 5.89107 | ||||||||
\(985\) | 25.5899 | 0.815363 | ||||||||
\(986\) | −94.4689 | −3.00850 | ||||||||
\(987\) | −12.0420 | −0.383301 | ||||||||
\(988\) | 22.0885 | 0.702728 | ||||||||
\(989\) | 11.3727 | 0.361630 | ||||||||
\(990\) | 45.9702 | 1.46103 | ||||||||
\(991\) | −2.95350 | −0.0938209 | −0.0469104 | − | 0.998899i | \(-0.514938\pi\) | ||||
−0.0469104 | + | 0.998899i | \(0.514938\pi\) | |||||||
\(992\) | −19.1212 | −0.607100 | ||||||||
\(993\) | 33.4214 | 1.06060 | ||||||||
\(994\) | −38.8278 | −1.23154 | ||||||||
\(995\) | 0.810307 | 0.0256885 | ||||||||
\(996\) | 181.246 | 5.74300 | ||||||||
\(997\) | 37.0037 | 1.17192 | 0.585960 | − | 0.810340i | \(-0.300718\pi\) | ||||
0.585960 | + | 0.810340i | \(0.300718\pi\) | |||||||
\(998\) | −7.44573 | −0.235690 | ||||||||
\(999\) | −3.11707 | −0.0986198 |
(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 | 8029.2.a.g.1.2 | ✓ | 70 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8029.2.a.g.1.2 | ✓ | 70 | 1.1 | even | 1 | trivial |