Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 | ||||||||
\(3\) | −1.95612 | −1.12937 | −0.564684 | − | 0.825307i | \(-0.691002\pi\) | ||||
−0.564684 | + | 0.825307i | \(0.691002\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.359780 | 0.160899 | 0.0804493 | − | 0.996759i | \(-0.474364\pi\) | ||||
0.0804493 | + | 0.996759i | \(0.474364\pi\) | |||||||
\(6\) | 1.95612 | 0.798583 | ||||||||
\(7\) | −1.34656 | −0.508950 | −0.254475 | − | 0.967079i | \(-0.581903\pi\) | ||||
−0.254475 | + | 0.967079i | \(0.581903\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.826410 | 0.275470 | ||||||||
\(10\) | −0.359780 | −0.113772 | ||||||||
\(11\) | −1.45863 | −0.439794 | −0.219897 | − | 0.975523i | \(-0.570572\pi\) | ||||
−0.219897 | + | 0.975523i | \(0.570572\pi\) | |||||||
\(12\) | −1.95612 | −0.564684 | ||||||||
\(13\) | −1.46403 | −0.406049 | −0.203025 | − | 0.979174i | \(-0.565077\pi\) | ||||
−0.203025 | + | 0.979174i | \(0.565077\pi\) | |||||||
\(14\) | 1.34656 | 0.359882 | ||||||||
\(15\) | −0.703774 | −0.181714 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.18699 | 0.530424 | 0.265212 | − | 0.964190i | \(-0.414558\pi\) | ||||
0.265212 | + | 0.964190i | \(0.414558\pi\) | |||||||
\(18\) | −0.826410 | −0.194787 | ||||||||
\(19\) | −0.0167571 | −0.00384434 | −0.00192217 | − | 0.999998i | \(-0.500612\pi\) | ||||
−0.00192217 | + | 0.999998i | \(0.500612\pi\) | |||||||
\(20\) | 0.359780 | 0.0804493 | ||||||||
\(21\) | 2.63403 | 0.574792 | ||||||||
\(22\) | 1.45863 | 0.310982 | ||||||||
\(23\) | 2.73171 | 0.569600 | 0.284800 | − | 0.958587i | \(-0.408073\pi\) | ||||
0.284800 | + | 0.958587i | \(0.408073\pi\) | |||||||
\(24\) | 1.95612 | 0.399292 | ||||||||
\(25\) | −4.87056 | −0.974112 | ||||||||
\(26\) | 1.46403 | 0.287120 | ||||||||
\(27\) | 4.25180 | 0.818260 | ||||||||
\(28\) | −1.34656 | −0.254475 | ||||||||
\(29\) | 8.45751 | 1.57052 | 0.785260 | − | 0.619166i | \(-0.212529\pi\) | ||||
0.785260 | + | 0.619166i | \(0.212529\pi\) | |||||||
\(30\) | 0.703774 | 0.128491 | ||||||||
\(31\) | 1.90088 | 0.341408 | 0.170704 | − | 0.985322i | \(-0.445396\pi\) | ||||
0.170704 | + | 0.985322i | \(0.445396\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.85326 | 0.496689 | ||||||||
\(34\) | −2.18699 | −0.375066 | ||||||||
\(35\) | −0.484464 | −0.0818894 | ||||||||
\(36\) | 0.826410 | 0.137735 | ||||||||
\(37\) | −4.97197 | −0.817387 | −0.408693 | − | 0.912672i | \(-0.634015\pi\) | ||||
−0.408693 | + | 0.912672i | \(0.634015\pi\) | |||||||
\(38\) | 0.0167571 | 0.00271836 | ||||||||
\(39\) | 2.86382 | 0.458579 | ||||||||
\(40\) | −0.359780 | −0.0568862 | ||||||||
\(41\) | 0.347278 | 0.0542356 | 0.0271178 | − | 0.999632i | \(-0.491367\pi\) | ||||
0.0271178 | + | 0.999632i | \(0.491367\pi\) | |||||||
\(42\) | −2.63403 | −0.406439 | ||||||||
\(43\) | −6.02157 | −0.918281 | −0.459140 | − | 0.888364i | \(-0.651843\pi\) | ||||
−0.459140 | + | 0.888364i | \(0.651843\pi\) | |||||||
\(44\) | −1.45863 | −0.219897 | ||||||||
\(45\) | 0.297326 | 0.0443228 | ||||||||
\(46\) | −2.73171 | −0.402768 | ||||||||
\(47\) | 11.8533 | 1.72898 | 0.864490 | − | 0.502650i | \(-0.167642\pi\) | ||||
0.864490 | + | 0.502650i | \(0.167642\pi\) | |||||||
\(48\) | −1.95612 | −0.282342 | ||||||||
\(49\) | −5.18679 | −0.740970 | ||||||||
\(50\) | 4.87056 | 0.688801 | ||||||||
\(51\) | −4.27803 | −0.599043 | ||||||||
\(52\) | −1.46403 | −0.203025 | ||||||||
\(53\) | −8.10403 | −1.11317 | −0.556587 | − | 0.830789i | \(-0.687889\pi\) | ||||
−0.556587 | + | 0.830789i | \(0.687889\pi\) | |||||||
\(54\) | −4.25180 | −0.578597 | ||||||||
\(55\) | −0.524787 | −0.0707623 | ||||||||
\(56\) | 1.34656 | 0.179941 | ||||||||
\(57\) | 0.0327789 | 0.00434167 | ||||||||
\(58\) | −8.45751 | −1.11053 | ||||||||
\(59\) | 0.940926 | 0.122498 | 0.0612491 | − | 0.998123i | \(-0.480492\pi\) | ||||
0.0612491 | + | 0.998123i | \(0.480492\pi\) | |||||||
\(60\) | −0.703774 | −0.0908568 | ||||||||
\(61\) | −0.574197 | −0.0735184 | −0.0367592 | − | 0.999324i | \(-0.511703\pi\) | ||||
−0.0367592 | + | 0.999324i | \(0.511703\pi\) | |||||||
\(62\) | −1.90088 | −0.241412 | ||||||||
\(63\) | −1.11281 | −0.140201 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.526729 | −0.0653327 | ||||||||
\(66\) | −2.85326 | −0.351212 | ||||||||
\(67\) | −9.88107 | −1.20716 | −0.603582 | − | 0.797301i | \(-0.706261\pi\) | ||||
−0.603582 | + | 0.797301i | \(0.706261\pi\) | |||||||
\(68\) | 2.18699 | 0.265212 | ||||||||
\(69\) | −5.34355 | −0.643288 | ||||||||
\(70\) | 0.484464 | 0.0579045 | ||||||||
\(71\) | −13.0279 | −1.54613 | −0.773065 | − | 0.634326i | \(-0.781278\pi\) | ||||
−0.773065 | + | 0.634326i | \(0.781278\pi\) | |||||||
\(72\) | −0.826410 | −0.0973934 | ||||||||
\(73\) | −6.35541 | −0.743845 | −0.371922 | − | 0.928264i | \(-0.621301\pi\) | ||||
−0.371922 | + | 0.928264i | \(0.621301\pi\) | |||||||
\(74\) | 4.97197 | 0.577980 | ||||||||
\(75\) | 9.52740 | 1.10013 | ||||||||
\(76\) | −0.0167571 | −0.00192217 | ||||||||
\(77\) | 1.96413 | 0.223834 | ||||||||
\(78\) | −2.86382 | −0.324264 | ||||||||
\(79\) | −8.79048 | −0.989006 | −0.494503 | − | 0.869176i | \(-0.664650\pi\) | ||||
−0.494503 | + | 0.869176i | \(0.664650\pi\) | |||||||
\(80\) | 0.359780 | 0.0402247 | ||||||||
\(81\) | −10.7963 | −1.19959 | ||||||||
\(82\) | −0.347278 | −0.0383504 | ||||||||
\(83\) | 10.2256 | 1.12241 | 0.561204 | − | 0.827678i | \(-0.310338\pi\) | ||||
0.561204 | + | 0.827678i | \(0.310338\pi\) | |||||||
\(84\) | 2.63403 | 0.287396 | ||||||||
\(85\) | 0.786837 | 0.0853445 | ||||||||
\(86\) | 6.02157 | 0.649323 | ||||||||
\(87\) | −16.5439 | −1.77369 | ||||||||
\(88\) | 1.45863 | 0.155491 | ||||||||
\(89\) | 7.08705 | 0.751225 | 0.375613 | − | 0.926777i | \(-0.377432\pi\) | ||||
0.375613 | + | 0.926777i | \(0.377432\pi\) | |||||||
\(90\) | −0.297326 | −0.0313409 | ||||||||
\(91\) | 1.97140 | 0.206659 | ||||||||
\(92\) | 2.73171 | 0.284800 | ||||||||
\(93\) | −3.71835 | −0.385575 | ||||||||
\(94\) | −11.8533 | −1.22257 | ||||||||
\(95\) | −0.00602887 | −0.000618549 0 | ||||||||
\(96\) | 1.95612 | 0.199646 | ||||||||
\(97\) | 18.5745 | 1.88595 | 0.942977 | − | 0.332857i | \(-0.108013\pi\) | ||||
0.942977 | + | 0.332857i | \(0.108013\pi\) | |||||||
\(98\) | 5.18679 | 0.523945 | ||||||||
\(99\) | −1.20543 | −0.121150 | ||||||||
\(100\) | −4.87056 | −0.487056 | ||||||||
\(101\) | −15.6453 | −1.55677 | −0.778384 | − | 0.627789i | \(-0.783960\pi\) | ||||
−0.778384 | + | 0.627789i | \(0.783960\pi\) | |||||||
\(102\) | 4.27803 | 0.423588 | ||||||||
\(103\) | 4.00189 | 0.394318 | 0.197159 | − | 0.980372i | \(-0.436828\pi\) | ||||
0.197159 | + | 0.980372i | \(0.436828\pi\) | |||||||
\(104\) | 1.46403 | 0.143560 | ||||||||
\(105\) | 0.947671 | 0.0924832 | ||||||||
\(106\) | 8.10403 | 0.787133 | ||||||||
\(107\) | −4.20779 | −0.406782 | −0.203391 | − | 0.979098i | \(-0.565196\pi\) | ||||
−0.203391 | + | 0.979098i | \(0.565196\pi\) | |||||||
\(108\) | 4.25180 | 0.409130 | ||||||||
\(109\) | 3.42355 | 0.327917 | 0.163958 | − | 0.986467i | \(-0.447574\pi\) | ||||
0.163958 | + | 0.986467i | \(0.447574\pi\) | |||||||
\(110\) | 0.524787 | 0.0500365 | ||||||||
\(111\) | 9.72577 | 0.923130 | ||||||||
\(112\) | −1.34656 | −0.127238 | ||||||||
\(113\) | 13.9681 | 1.31401 | 0.657004 | − | 0.753887i | \(-0.271823\pi\) | ||||
0.657004 | + | 0.753887i | \(0.271823\pi\) | |||||||
\(114\) | −0.0327789 | −0.00307002 | ||||||||
\(115\) | 0.982814 | 0.0916479 | ||||||||
\(116\) | 8.45751 | 0.785260 | ||||||||
\(117\) | −1.20989 | −0.111854 | ||||||||
\(118\) | −0.940926 | −0.0866193 | ||||||||
\(119\) | −2.94491 | −0.269959 | ||||||||
\(120\) | 0.703774 | 0.0642455 | ||||||||
\(121\) | −8.87239 | −0.806581 | ||||||||
\(122\) | 0.574197 | 0.0519853 | ||||||||
\(123\) | −0.679317 | −0.0612520 | ||||||||
\(124\) | 1.90088 | 0.170704 | ||||||||
\(125\) | −3.55123 | −0.317632 | ||||||||
\(126\) | 1.11281 | 0.0991368 | ||||||||
\(127\) | −4.15073 | −0.368318 | −0.184159 | − | 0.982896i | \(-0.558956\pi\) | ||||
−0.184159 | + | 0.982896i | \(0.558956\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.7789 | 1.03708 | ||||||||
\(130\) | 0.526729 | 0.0461972 | ||||||||
\(131\) | 4.50989 | 0.394031 | 0.197016 | − | 0.980400i | \(-0.436875\pi\) | ||||
0.197016 | + | 0.980400i | \(0.436875\pi\) | |||||||
\(132\) | 2.85326 | 0.248345 | ||||||||
\(133\) | 0.0225643 | 0.00195658 | ||||||||
\(134\) | 9.88107 | 0.853594 | ||||||||
\(135\) | 1.52972 | 0.131657 | ||||||||
\(136\) | −2.18699 | −0.187533 | ||||||||
\(137\) | −3.36358 | −0.287370 | −0.143685 | − | 0.989623i | \(-0.545895\pi\) | ||||
−0.143685 | + | 0.989623i | \(0.545895\pi\) | |||||||
\(138\) | 5.34355 | 0.454873 | ||||||||
\(139\) | 21.6408 | 1.83555 | 0.917773 | − | 0.397104i | \(-0.129985\pi\) | ||||
0.917773 | + | 0.397104i | \(0.129985\pi\) | |||||||
\(140\) | −0.484464 | −0.0409447 | ||||||||
\(141\) | −23.1865 | −1.95265 | ||||||||
\(142\) | 13.0279 | 1.09328 | ||||||||
\(143\) | 2.13548 | 0.178578 | ||||||||
\(144\) | 0.826410 | 0.0688675 | ||||||||
\(145\) | 3.04285 | 0.252695 | ||||||||
\(146\) | 6.35541 | 0.525978 | ||||||||
\(147\) | 10.1460 | 0.836827 | ||||||||
\(148\) | −4.97197 | −0.408693 | ||||||||
\(149\) | −22.9120 | −1.87703 | −0.938514 | − | 0.345242i | \(-0.887797\pi\) | ||||
−0.938514 | + | 0.345242i | \(0.887797\pi\) | |||||||
\(150\) | −9.52740 | −0.777909 | ||||||||
\(151\) | −24.2613 | −1.97436 | −0.987180 | − | 0.159610i | \(-0.948976\pi\) | ||||
−0.987180 | + | 0.159610i | \(0.948976\pi\) | |||||||
\(152\) | 0.0167571 | 0.00135918 | ||||||||
\(153\) | 1.80735 | 0.146116 | ||||||||
\(154\) | −1.96413 | −0.158274 | ||||||||
\(155\) | 0.683899 | 0.0549321 | ||||||||
\(156\) | 2.86382 | 0.229289 | ||||||||
\(157\) | 1.11609 | 0.0890734 | 0.0445367 | − | 0.999008i | \(-0.485819\pi\) | ||||
0.0445367 | + | 0.999008i | \(0.485819\pi\) | |||||||
\(158\) | 8.79048 | 0.699333 | ||||||||
\(159\) | 15.8525 | 1.25718 | ||||||||
\(160\) | −0.359780 | −0.0284431 | ||||||||
\(161\) | −3.67840 | −0.289898 | ||||||||
\(162\) | 10.7963 | 0.848236 | ||||||||
\(163\) | 20.8506 | 1.63315 | 0.816574 | − | 0.577241i | \(-0.195871\pi\) | ||||
0.816574 | + | 0.577241i | \(0.195871\pi\) | |||||||
\(164\) | 0.347278 | 0.0271178 | ||||||||
\(165\) | 1.02655 | 0.0799166 | ||||||||
\(166\) | −10.2256 | −0.793662 | ||||||||
\(167\) | −6.69157 | −0.517809 | −0.258904 | − | 0.965903i | \(-0.583361\pi\) | ||||
−0.258904 | + | 0.965903i | \(0.583361\pi\) | |||||||
\(168\) | −2.63403 | −0.203220 | ||||||||
\(169\) | −10.8566 | −0.835124 | ||||||||
\(170\) | −0.786837 | −0.0603477 | ||||||||
\(171\) | −0.0138482 | −0.00105900 | ||||||||
\(172\) | −6.02157 | −0.459140 | ||||||||
\(173\) | 0.619997 | 0.0471375 | 0.0235687 | − | 0.999722i | \(-0.492497\pi\) | ||||
0.0235687 | + | 0.999722i | \(0.492497\pi\) | |||||||
\(174\) | 16.5439 | 1.25419 | ||||||||
\(175\) | 6.55848 | 0.495774 | ||||||||
\(176\) | −1.45863 | −0.109949 | ||||||||
\(177\) | −1.84057 | −0.138345 | ||||||||
\(178\) | −7.08705 | −0.531197 | ||||||||
\(179\) | 7.23870 | 0.541046 | 0.270523 | − | 0.962714i | \(-0.412803\pi\) | ||||
0.270523 | + | 0.962714i | \(0.412803\pi\) | |||||||
\(180\) | 0.297326 | 0.0221614 | ||||||||
\(181\) | 14.1704 | 1.05328 | 0.526639 | − | 0.850089i | \(-0.323452\pi\) | ||||
0.526639 | + | 0.850089i | \(0.323452\pi\) | |||||||
\(182\) | −1.97140 | −0.146130 | ||||||||
\(183\) | 1.12320 | 0.0830292 | ||||||||
\(184\) | −2.73171 | −0.201384 | ||||||||
\(185\) | −1.78882 | −0.131516 | ||||||||
\(186\) | 3.71835 | 0.272643 | ||||||||
\(187\) | −3.19002 | −0.233277 | ||||||||
\(188\) | 11.8533 | 0.864490 | ||||||||
\(189\) | −5.72529 | −0.416454 | ||||||||
\(190\) | 0.00602887 | 0.000437380 0 | ||||||||
\(191\) | −19.3279 | −1.39852 | −0.699258 | − | 0.714869i | \(-0.746486\pi\) | ||||
−0.699258 | + | 0.714869i | \(0.746486\pi\) | |||||||
\(192\) | −1.95612 | −0.141171 | ||||||||
\(193\) | −2.91199 | −0.209610 | −0.104805 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104805 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(194\) | −18.5745 | −1.33357 | ||||||||
\(195\) | 1.03035 | 0.0737847 | ||||||||
\(196\) | −5.18679 | −0.370485 | ||||||||
\(197\) | 15.0270 | 1.07063 | 0.535315 | − | 0.844653i | \(-0.320193\pi\) | ||||
0.535315 | + | 0.844653i | \(0.320193\pi\) | |||||||
\(198\) | 1.20543 | 0.0856662 | ||||||||
\(199\) | −5.23835 | −0.371337 | −0.185668 | − | 0.982612i | \(-0.559445\pi\) | ||||
−0.185668 | + | 0.982612i | \(0.559445\pi\) | |||||||
\(200\) | 4.87056 | 0.344400 | ||||||||
\(201\) | 19.3286 | 1.36333 | ||||||||
\(202\) | 15.6453 | 1.10080 | ||||||||
\(203\) | −11.3885 | −0.799317 | ||||||||
\(204\) | −4.27803 | −0.299522 | ||||||||
\(205\) | 0.124944 | 0.00872644 | ||||||||
\(206\) | −4.00189 | −0.278825 | ||||||||
\(207\) | 2.25751 | 0.156908 | ||||||||
\(208\) | −1.46403 | −0.101512 | ||||||||
\(209\) | 0.0244424 | 0.00169072 | ||||||||
\(210\) | −0.947671 | −0.0653955 | ||||||||
\(211\) | 12.3093 | 0.847410 | 0.423705 | − | 0.905800i | \(-0.360729\pi\) | ||||
0.423705 | + | 0.905800i | \(0.360729\pi\) | |||||||
\(212\) | −8.10403 | −0.556587 | ||||||||
\(213\) | 25.4842 | 1.74615 | ||||||||
\(214\) | 4.20779 | 0.287639 | ||||||||
\(215\) | −2.16644 | −0.147750 | ||||||||
\(216\) | −4.25180 | −0.289299 | ||||||||
\(217\) | −2.55964 | −0.173760 | ||||||||
\(218\) | −3.42355 | −0.231872 | ||||||||
\(219\) | 12.4320 | 0.840074 | ||||||||
\(220\) | −0.524787 | −0.0353812 | ||||||||
\(221\) | −3.20183 | −0.215378 | ||||||||
\(222\) | −9.72577 | −0.652751 | ||||||||
\(223\) | 21.2435 | 1.42257 | 0.711284 | − | 0.702905i | \(-0.248114\pi\) | ||||
0.711284 | + | 0.702905i | \(0.248114\pi\) | |||||||
\(224\) | 1.34656 | 0.0899705 | ||||||||
\(225\) | −4.02508 | −0.268339 | ||||||||
\(226\) | −13.9681 | −0.929144 | ||||||||
\(227\) | −19.4120 | −1.28842 | −0.644211 | − | 0.764848i | \(-0.722814\pi\) | ||||
−0.644211 | + | 0.764848i | \(0.722814\pi\) | |||||||
\(228\) | 0.0327789 | 0.00217083 | ||||||||
\(229\) | −7.72343 | −0.510378 | −0.255189 | − | 0.966891i | \(-0.582138\pi\) | ||||
−0.255189 | + | 0.966891i | \(0.582138\pi\) | |||||||
\(230\) | −0.982814 | −0.0648048 | ||||||||
\(231\) | −3.84208 | −0.252790 | ||||||||
\(232\) | −8.45751 | −0.555263 | ||||||||
\(233\) | −9.42994 | −0.617776 | −0.308888 | − | 0.951098i | \(-0.599957\pi\) | ||||
−0.308888 | + | 0.951098i | \(0.599957\pi\) | |||||||
\(234\) | 1.20989 | 0.0790930 | ||||||||
\(235\) | 4.26458 | 0.278190 | ||||||||
\(236\) | 0.940926 | 0.0612491 | ||||||||
\(237\) | 17.1952 | 1.11695 | ||||||||
\(238\) | 2.94491 | 0.190890 | ||||||||
\(239\) | 7.35695 | 0.475882 | 0.237941 | − | 0.971280i | \(-0.423528\pi\) | ||||
0.237941 | + | 0.971280i | \(0.423528\pi\) | |||||||
\(240\) | −0.703774 | −0.0454284 | ||||||||
\(241\) | 12.0103 | 0.773654 | 0.386827 | − | 0.922152i | \(-0.373571\pi\) | ||||
0.386827 | + | 0.922152i | \(0.373571\pi\) | |||||||
\(242\) | 8.87239 | 0.570339 | ||||||||
\(243\) | 8.36341 | 0.536513 | ||||||||
\(244\) | −0.574197 | −0.0367592 | ||||||||
\(245\) | −1.86610 | −0.119221 | ||||||||
\(246\) | 0.679317 | 0.0433117 | ||||||||
\(247\) | 0.0245329 | 0.00156099 | ||||||||
\(248\) | −1.90088 | −0.120706 | ||||||||
\(249\) | −20.0026 | −1.26761 | ||||||||
\(250\) | 3.55123 | 0.224600 | ||||||||
\(251\) | 8.28533 | 0.522966 | 0.261483 | − | 0.965208i | \(-0.415789\pi\) | ||||
0.261483 | + | 0.965208i | \(0.415789\pi\) | |||||||
\(252\) | −1.11281 | −0.0701003 | ||||||||
\(253\) | −3.98456 | −0.250507 | ||||||||
\(254\) | 4.15073 | 0.260440 | ||||||||
\(255\) | −1.53915 | −0.0963852 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.6325 | −1.28702 | −0.643511 | − | 0.765437i | \(-0.722523\pi\) | ||||
−0.643511 | + | 0.765437i | \(0.722523\pi\) | |||||||
\(258\) | −11.7789 | −0.733324 | ||||||||
\(259\) | 6.69503 | 0.416009 | ||||||||
\(260\) | −0.526729 | −0.0326664 | ||||||||
\(261\) | 6.98938 | 0.432632 | ||||||||
\(262\) | −4.50989 | −0.278622 | ||||||||
\(263\) | 3.96611 | 0.244561 | 0.122280 | − | 0.992496i | \(-0.460979\pi\) | ||||
0.122280 | + | 0.992496i | \(0.460979\pi\) | |||||||
\(264\) | −2.85326 | −0.175606 | ||||||||
\(265\) | −2.91567 | −0.179108 | ||||||||
\(266\) | −0.0225643 | −0.00138351 | ||||||||
\(267\) | −13.8631 | −0.848409 | ||||||||
\(268\) | −9.88107 | −0.603582 | ||||||||
\(269\) | −11.8496 | −0.722485 | −0.361243 | − | 0.932472i | \(-0.617647\pi\) | ||||
−0.361243 | + | 0.932472i | \(0.617647\pi\) | |||||||
\(270\) | −1.52972 | −0.0930955 | ||||||||
\(271\) | −4.66837 | −0.283583 | −0.141792 | − | 0.989897i | \(-0.545286\pi\) | ||||
−0.141792 | + | 0.989897i | \(0.545286\pi\) | |||||||
\(272\) | 2.18699 | 0.132606 | ||||||||
\(273\) | −3.85630 | −0.233394 | ||||||||
\(274\) | 3.36358 | 0.203202 | ||||||||
\(275\) | 7.10436 | 0.428409 | ||||||||
\(276\) | −5.34355 | −0.321644 | ||||||||
\(277\) | 19.0624 | 1.14535 | 0.572675 | − | 0.819782i | \(-0.305906\pi\) | ||||
0.572675 | + | 0.819782i | \(0.305906\pi\) | |||||||
\(278\) | −21.6408 | −1.29793 | ||||||||
\(279\) | 1.57091 | 0.0940478 | ||||||||
\(280\) | 0.484464 | 0.0289523 | ||||||||
\(281\) | 1.48411 | 0.0885344 | 0.0442672 | − | 0.999020i | \(-0.485905\pi\) | ||||
0.0442672 | + | 0.999020i | \(0.485905\pi\) | |||||||
\(282\) | 23.1865 | 1.38073 | ||||||||
\(283\) | 25.8606 | 1.53725 | 0.768625 | − | 0.639699i | \(-0.220941\pi\) | ||||
0.768625 | + | 0.639699i | \(0.220941\pi\) | |||||||
\(284\) | −13.0279 | −0.773065 | ||||||||
\(285\) | 0.0117932 | 0.000698569 0 | ||||||||
\(286\) | −2.13548 | −0.126274 | ||||||||
\(287\) | −0.467629 | −0.0276032 | ||||||||
\(288\) | −0.826410 | −0.0486967 | ||||||||
\(289\) | −12.2171 | −0.718650 | ||||||||
\(290\) | −3.04285 | −0.178682 | ||||||||
\(291\) | −36.3340 | −2.12993 | ||||||||
\(292\) | −6.35541 | −0.371922 | ||||||||
\(293\) | 16.7854 | 0.980616 | 0.490308 | − | 0.871549i | \(-0.336884\pi\) | ||||
0.490308 | + | 0.871549i | \(0.336884\pi\) | |||||||
\(294\) | −10.1460 | −0.591726 | ||||||||
\(295\) | 0.338527 | 0.0197098 | ||||||||
\(296\) | 4.97197 | 0.288990 | ||||||||
\(297\) | −6.20182 | −0.359866 | ||||||||
\(298\) | 22.9120 | 1.32726 | ||||||||
\(299\) | −3.99930 | −0.231286 | ||||||||
\(300\) | 9.52740 | 0.550065 | ||||||||
\(301\) | 8.10838 | 0.467359 | ||||||||
\(302\) | 24.2613 | 1.39608 | ||||||||
\(303\) | 30.6041 | 1.75816 | ||||||||
\(304\) | −0.0167571 | −0.000961085 0 | ||||||||
\(305\) | −0.206585 | −0.0118290 | ||||||||
\(306\) | −1.80735 | −0.103320 | ||||||||
\(307\) | −6.29542 | −0.359299 | −0.179649 | − | 0.983731i | \(-0.557496\pi\) | ||||
−0.179649 | + | 0.983731i | \(0.557496\pi\) | |||||||
\(308\) | 1.96413 | 0.111917 | ||||||||
\(309\) | −7.82819 | −0.445330 | ||||||||
\(310\) | −0.683899 | −0.0388429 | ||||||||
\(311\) | 10.7360 | 0.608785 | 0.304392 | − | 0.952547i | \(-0.401547\pi\) | ||||
0.304392 | + | 0.952547i | \(0.401547\pi\) | |||||||
\(312\) | −2.86382 | −0.162132 | ||||||||
\(313\) | 3.22213 | 0.182126 | 0.0910628 | − | 0.995845i | \(-0.470974\pi\) | ||||
0.0910628 | + | 0.995845i | \(0.470974\pi\) | |||||||
\(314\) | −1.11609 | −0.0629844 | ||||||||
\(315\) | −0.400366 | −0.0225581 | ||||||||
\(316\) | −8.79048 | −0.494503 | ||||||||
\(317\) | −24.9930 | −1.40375 | −0.701874 | − | 0.712301i | \(-0.747653\pi\) | ||||
−0.701874 | + | 0.712301i | \(0.747653\pi\) | |||||||
\(318\) | −15.8525 | −0.888962 | ||||||||
\(319\) | −12.3364 | −0.690706 | ||||||||
\(320\) | 0.359780 | 0.0201123 | ||||||||
\(321\) | 8.23094 | 0.459407 | ||||||||
\(322\) | 3.67840 | 0.204989 | ||||||||
\(323\) | −0.0366476 | −0.00203913 | ||||||||
\(324\) | −10.7963 | −0.599793 | ||||||||
\(325\) | 7.13065 | 0.395537 | ||||||||
\(326\) | −20.8506 | −1.15481 | ||||||||
\(327\) | −6.69688 | −0.370339 | ||||||||
\(328\) | −0.347278 | −0.0191752 | ||||||||
\(329\) | −15.9611 | −0.879965 | ||||||||
\(330\) | −1.02655 | −0.0565096 | ||||||||
\(331\) | 13.6179 | 0.748508 | 0.374254 | − | 0.927326i | \(-0.377899\pi\) | ||||
0.374254 | + | 0.927326i | \(0.377899\pi\) | |||||||
\(332\) | 10.2256 | 0.561204 | ||||||||
\(333\) | −4.10889 | −0.225166 | ||||||||
\(334\) | 6.69157 | 0.366146 | ||||||||
\(335\) | −3.55501 | −0.194231 | ||||||||
\(336\) | 2.63403 | 0.143698 | ||||||||
\(337\) | −15.8385 | −0.862779 | −0.431390 | − | 0.902166i | \(-0.641977\pi\) | ||||
−0.431390 | + | 0.902166i | \(0.641977\pi\) | |||||||
\(338\) | 10.8566 | 0.590522 | ||||||||
\(339\) | −27.3233 | −1.48400 | ||||||||
\(340\) | 0.786837 | 0.0426722 | ||||||||
\(341\) | −2.77269 | −0.150149 | ||||||||
\(342\) | 0.0138482 | 0.000748826 0 | ||||||||
\(343\) | 16.4102 | 0.886067 | ||||||||
\(344\) | 6.02157 | 0.324661 | ||||||||
\(345\) | −1.92250 | −0.103504 | ||||||||
\(346\) | −0.619997 | −0.0333312 | ||||||||
\(347\) | 22.0889 | 1.18580 | 0.592898 | − | 0.805278i | \(-0.297984\pi\) | ||||
0.592898 | + | 0.805278i | \(0.297984\pi\) | |||||||
\(348\) | −16.5439 | −0.886847 | ||||||||
\(349\) | 3.46238 | 0.185337 | 0.0926685 | − | 0.995697i | \(-0.470460\pi\) | ||||
0.0926685 | + | 0.995697i | \(0.470460\pi\) | |||||||
\(350\) | −6.55848 | −0.350565 | ||||||||
\(351\) | −6.22477 | −0.332254 | ||||||||
\(352\) | 1.45863 | 0.0777454 | ||||||||
\(353\) | −31.3704 | −1.66968 | −0.834839 | − | 0.550495i | \(-0.814439\pi\) | ||||
−0.834839 | + | 0.550495i | \(0.814439\pi\) | |||||||
\(354\) | 1.84057 | 0.0978250 | ||||||||
\(355\) | −4.68719 | −0.248770 | ||||||||
\(356\) | 7.08705 | 0.375613 | ||||||||
\(357\) | 5.76060 | 0.304883 | ||||||||
\(358\) | −7.23870 | −0.382577 | ||||||||
\(359\) | 18.2289 | 0.962085 | 0.481042 | − | 0.876697i | \(-0.340258\pi\) | ||||
0.481042 | + | 0.876697i | \(0.340258\pi\) | |||||||
\(360\) | −0.297326 | −0.0156705 | ||||||||
\(361\) | −18.9997 | −0.999985 | ||||||||
\(362\) | −14.1704 | −0.744779 | ||||||||
\(363\) | 17.3555 | 0.910926 | ||||||||
\(364\) | 1.97140 | 0.103329 | ||||||||
\(365\) | −2.28655 | −0.119684 | ||||||||
\(366\) | −1.12320 | −0.0587105 | ||||||||
\(367\) | 29.8011 | 1.55560 | 0.777801 | − | 0.628510i | \(-0.216335\pi\) | ||||
0.777801 | + | 0.628510i | \(0.216335\pi\) | |||||||
\(368\) | 2.73171 | 0.142400 | ||||||||
\(369\) | 0.286994 | 0.0149403 | ||||||||
\(370\) | 1.78882 | 0.0929961 | ||||||||
\(371\) | 10.9125 | 0.566550 | ||||||||
\(372\) | −3.71835 | −0.192788 | ||||||||
\(373\) | −0.215926 | −0.0111802 | −0.00559011 | − | 0.999984i | \(-0.501779\pi\) | ||||
−0.00559011 | + | 0.999984i | \(0.501779\pi\) | |||||||
\(374\) | 3.19002 | 0.164952 | ||||||||
\(375\) | 6.94664 | 0.358723 | ||||||||
\(376\) | −11.8533 | −0.611287 | ||||||||
\(377\) | −12.3821 | −0.637709 | ||||||||
\(378\) | 5.72529 | 0.294477 | ||||||||
\(379\) | −4.94510 | −0.254013 | −0.127006 | − | 0.991902i | \(-0.540537\pi\) | ||||
−0.127006 | + | 0.991902i | \(0.540537\pi\) | |||||||
\(380\) | −0.00602887 | −0.000309274 0 | ||||||||
\(381\) | 8.11933 | 0.415966 | ||||||||
\(382\) | 19.3279 | 0.988900 | ||||||||
\(383\) | 38.5669 | 1.97068 | 0.985338 | − | 0.170614i | \(-0.0545751\pi\) | ||||
0.985338 | + | 0.170614i | \(0.0545751\pi\) | |||||||
\(384\) | 1.95612 | 0.0998229 | ||||||||
\(385\) | 0.706656 | 0.0360145 | ||||||||
\(386\) | 2.91199 | 0.148216 | ||||||||
\(387\) | −4.97629 | −0.252959 | ||||||||
\(388\) | 18.5745 | 0.942977 | ||||||||
\(389\) | 27.1464 | 1.37638 | 0.688190 | − | 0.725531i | \(-0.258406\pi\) | ||||
0.688190 | + | 0.725531i | \(0.258406\pi\) | |||||||
\(390\) | −1.03035 | −0.0521736 | ||||||||
\(391\) | 5.97423 | 0.302130 | ||||||||
\(392\) | 5.18679 | 0.261972 | ||||||||
\(393\) | −8.82190 | −0.445006 | ||||||||
\(394\) | −15.0270 | −0.757049 | ||||||||
\(395\) | −3.16264 | −0.159130 | ||||||||
\(396\) | −1.20543 | −0.0605751 | ||||||||
\(397\) | 1.22440 | 0.0614508 | 0.0307254 | − | 0.999528i | \(-0.490218\pi\) | ||||
0.0307254 | + | 0.999528i | \(0.490218\pi\) | |||||||
\(398\) | 5.23835 | 0.262575 | ||||||||
\(399\) | −0.0441386 | −0.00220969 | ||||||||
\(400\) | −4.87056 | −0.243528 | ||||||||
\(401\) | 3.20701 | 0.160151 | 0.0800753 | − | 0.996789i | \(-0.474484\pi\) | ||||
0.0800753 | + | 0.996789i | \(0.474484\pi\) | |||||||
\(402\) | −19.3286 | −0.964021 | ||||||||
\(403\) | −2.78295 | −0.138629 | ||||||||
\(404\) | −15.6453 | −0.778384 | ||||||||
\(405\) | −3.88429 | −0.193012 | ||||||||
\(406\) | 11.3885 | 0.565203 | ||||||||
\(407\) | 7.25228 | 0.359482 | ||||||||
\(408\) | 4.27803 | 0.211794 | ||||||||
\(409\) | 16.2981 | 0.805890 | 0.402945 | − | 0.915224i | \(-0.367987\pi\) | ||||
0.402945 | + | 0.915224i | \(0.367987\pi\) | |||||||
\(410\) | −0.124944 | −0.00617052 | ||||||||
\(411\) | 6.57958 | 0.324547 | ||||||||
\(412\) | 4.00189 | 0.197159 | ||||||||
\(413\) | −1.26701 | −0.0623455 | ||||||||
\(414\) | −2.25751 | −0.110951 | ||||||||
\(415\) | 3.67898 | 0.180594 | ||||||||
\(416\) | 1.46403 | 0.0717800 | ||||||||
\(417\) | −42.3320 | −2.07301 | ||||||||
\(418\) | −0.0244424 | −0.00119552 | ||||||||
\(419\) | −37.3045 | −1.82244 | −0.911221 | − | 0.411917i | \(-0.864859\pi\) | ||||
−0.911221 | + | 0.411917i | \(0.864859\pi\) | |||||||
\(420\) | 0.947671 | 0.0462416 | ||||||||
\(421\) | 0.961923 | 0.0468813 | 0.0234406 | − | 0.999725i | \(-0.492538\pi\) | ||||
0.0234406 | + | 0.999725i | \(0.492538\pi\) | |||||||
\(422\) | −12.3093 | −0.599210 | ||||||||
\(423\) | 9.79568 | 0.476282 | ||||||||
\(424\) | 8.10403 | 0.393567 | ||||||||
\(425\) | −10.6519 | −0.516692 | ||||||||
\(426\) | −25.4842 | −1.23471 | ||||||||
\(427\) | 0.773188 | 0.0374172 | ||||||||
\(428\) | −4.20779 | −0.203391 | ||||||||
\(429\) | −4.17727 | −0.201680 | ||||||||
\(430\) | 2.16644 | 0.104475 | ||||||||
\(431\) | 1.54267 | 0.0743077 | 0.0371538 | − | 0.999310i | \(-0.488171\pi\) | ||||
0.0371538 | + | 0.999310i | \(0.488171\pi\) | |||||||
\(432\) | 4.25180 | 0.204565 | ||||||||
\(433\) | −6.74748 | −0.324263 | −0.162131 | − | 0.986769i | \(-0.551837\pi\) | ||||
−0.162131 | + | 0.986769i | \(0.551837\pi\) | |||||||
\(434\) | 2.55964 | 0.122867 | ||||||||
\(435\) | −5.95218 | −0.285385 | ||||||||
\(436\) | 3.42355 | 0.163958 | ||||||||
\(437\) | −0.0457754 | −0.00218974 | ||||||||
\(438\) | −12.4320 | −0.594022 | ||||||||
\(439\) | 28.3413 | 1.35266 | 0.676328 | − | 0.736601i | \(-0.263570\pi\) | ||||
0.676328 | + | 0.736601i | \(0.263570\pi\) | |||||||
\(440\) | 0.524787 | 0.0250183 | ||||||||
\(441\) | −4.28642 | −0.204115 | ||||||||
\(442\) | 3.20183 | 0.152295 | ||||||||
\(443\) | −29.1627 | −1.38556 | −0.692780 | − | 0.721149i | \(-0.743614\pi\) | ||||
−0.692780 | + | 0.721149i | \(0.743614\pi\) | |||||||
\(444\) | 9.72577 | 0.461565 | ||||||||
\(445\) | 2.54978 | 0.120871 | ||||||||
\(446\) | −21.2435 | −1.00591 | ||||||||
\(447\) | 44.8187 | 2.11985 | ||||||||
\(448\) | −1.34656 | −0.0636188 | ||||||||
\(449\) | −26.6477 | −1.25758 | −0.628791 | − | 0.777575i | \(-0.716450\pi\) | ||||
−0.628791 | + | 0.777575i | \(0.716450\pi\) | |||||||
\(450\) | 4.02508 | 0.189744 | ||||||||
\(451\) | −0.506551 | −0.0238525 | ||||||||
\(452\) | 13.9681 | 0.657004 | ||||||||
\(453\) | 47.4581 | 2.22978 | ||||||||
\(454\) | 19.4120 | 0.911052 | ||||||||
\(455\) | 0.709271 | 0.0332511 | ||||||||
\(456\) | −0.0327789 | −0.00153501 | ||||||||
\(457\) | 19.1923 | 0.897779 | 0.448890 | − | 0.893587i | \(-0.351820\pi\) | ||||
0.448890 | + | 0.893587i | \(0.351820\pi\) | |||||||
\(458\) | 7.72343 | 0.360892 | ||||||||
\(459\) | 9.29867 | 0.434025 | ||||||||
\(460\) | 0.982814 | 0.0458239 | ||||||||
\(461\) | 13.5409 | 0.630662 | 0.315331 | − | 0.948982i | \(-0.397884\pi\) | ||||
0.315331 | + | 0.948982i | \(0.397884\pi\) | |||||||
\(462\) | 3.84208 | 0.178750 | ||||||||
\(463\) | 15.1001 | 0.701759 | 0.350880 | − | 0.936421i | \(-0.385883\pi\) | ||||
0.350880 | + | 0.936421i | \(0.385883\pi\) | |||||||
\(464\) | 8.45751 | 0.392630 | ||||||||
\(465\) | −1.33779 | −0.0620385 | ||||||||
\(466\) | 9.42994 | 0.436833 | ||||||||
\(467\) | −0.676254 | −0.0312933 | −0.0156467 | − | 0.999878i | \(-0.504981\pi\) | ||||
−0.0156467 | + | 0.999878i | \(0.504981\pi\) | |||||||
\(468\) | −1.20989 | −0.0559272 | ||||||||
\(469\) | 13.3054 | 0.614387 | ||||||||
\(470\) | −4.26458 | −0.196710 | ||||||||
\(471\) | −2.18320 | −0.100597 | ||||||||
\(472\) | −0.940926 | −0.0433096 | ||||||||
\(473\) | 8.78326 | 0.403855 | ||||||||
\(474\) | −17.1952 | −0.789804 | ||||||||
\(475\) | 0.0816163 | 0.00374481 | ||||||||
\(476\) | −2.94491 | −0.134980 | ||||||||
\(477\) | −6.69726 | −0.306646 | ||||||||
\(478\) | −7.35695 | −0.336499 | ||||||||
\(479\) | 29.0847 | 1.32891 | 0.664456 | − | 0.747327i | \(-0.268663\pi\) | ||||
0.664456 | + | 0.747327i | \(0.268663\pi\) | |||||||
\(480\) | 0.703774 | 0.0321227 | ||||||||
\(481\) | 7.27912 | 0.331899 | ||||||||
\(482\) | −12.0103 | −0.547056 | ||||||||
\(483\) | 7.19539 | 0.327401 | ||||||||
\(484\) | −8.87239 | −0.403290 | ||||||||
\(485\) | 6.68274 | 0.303447 | ||||||||
\(486\) | −8.36341 | −0.379372 | ||||||||
\(487\) | 25.0742 | 1.13622 | 0.568111 | − | 0.822952i | \(-0.307674\pi\) | ||||
0.568111 | + | 0.822952i | \(0.307674\pi\) | |||||||
\(488\) | 0.574197 | 0.0259927 | ||||||||
\(489\) | −40.7864 | −1.84442 | ||||||||
\(490\) | 1.86610 | 0.0843020 | ||||||||
\(491\) | 7.09457 | 0.320174 | 0.160087 | − | 0.987103i | \(-0.448823\pi\) | ||||
0.160087 | + | 0.987103i | \(0.448823\pi\) | |||||||
\(492\) | −0.679317 | −0.0306260 | ||||||||
\(493\) | 18.4965 | 0.833042 | ||||||||
\(494\) | −0.0245329 | −0.00110379 | ||||||||
\(495\) | −0.433690 | −0.0194929 | ||||||||
\(496\) | 1.90088 | 0.0853521 | ||||||||
\(497\) | 17.5428 | 0.786904 | ||||||||
\(498\) | 20.0026 | 0.896336 | ||||||||
\(499\) | 22.1068 | 0.989638 | 0.494819 | − | 0.868996i | \(-0.335234\pi\) | ||||
0.494819 | + | 0.868996i | \(0.335234\pi\) | |||||||
\(500\) | −3.55123 | −0.158816 | ||||||||
\(501\) | 13.0895 | 0.584796 | ||||||||
\(502\) | −8.28533 | −0.369793 | ||||||||
\(503\) | −10.5907 | −0.472216 | −0.236108 | − | 0.971727i | \(-0.575872\pi\) | ||||
−0.236108 | + | 0.971727i | \(0.575872\pi\) | |||||||
\(504\) | 1.11281 | 0.0495684 | ||||||||
\(505\) | −5.62887 | −0.250482 | ||||||||
\(506\) | 3.98456 | 0.177135 | ||||||||
\(507\) | 21.2369 | 0.943162 | ||||||||
\(508\) | −4.15073 | −0.184159 | ||||||||
\(509\) | −27.2672 | −1.20860 | −0.604300 | − | 0.796757i | \(-0.706547\pi\) | ||||
−0.604300 | + | 0.796757i | \(0.706547\pi\) | |||||||
\(510\) | 1.53915 | 0.0681547 | ||||||||
\(511\) | 8.55792 | 0.378580 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.0712478 | −0.00314567 | ||||||||
\(514\) | 20.6325 | 0.910062 | ||||||||
\(515\) | 1.43980 | 0.0634452 | ||||||||
\(516\) | 11.7789 | 0.518538 | ||||||||
\(517\) | −17.2896 | −0.760396 | ||||||||
\(518\) | −6.69503 | −0.294163 | ||||||||
\(519\) | −1.21279 | −0.0532355 | ||||||||
\(520\) | 0.526729 | 0.0230986 | ||||||||
\(521\) | 8.83870 | 0.387231 | 0.193615 | − | 0.981078i | \(-0.437979\pi\) | ||||
0.193615 | + | 0.981078i | \(0.437979\pi\) | |||||||
\(522\) | −6.98938 | −0.305917 | ||||||||
\(523\) | −32.6487 | −1.42763 | −0.713813 | − | 0.700336i | \(-0.753033\pi\) | ||||
−0.713813 | + | 0.700336i | \(0.753033\pi\) | |||||||
\(524\) | 4.50989 | 0.197016 | ||||||||
\(525\) | −12.8292 | −0.559911 | ||||||||
\(526\) | −3.96611 | −0.172931 | ||||||||
\(527\) | 4.15722 | 0.181091 | ||||||||
\(528\) | 2.85326 | 0.124172 | ||||||||
\(529\) | −15.5378 | −0.675556 | ||||||||
\(530\) | 2.91567 | 0.126649 | ||||||||
\(531\) | 0.777591 | 0.0337446 | ||||||||
\(532\) | 0.0225643 | 0.000978289 0 | ||||||||
\(533\) | −0.508425 | −0.0220223 | ||||||||
\(534\) | 13.8631 | 0.599916 | ||||||||
\(535\) | −1.51388 | −0.0654507 | ||||||||
\(536\) | 9.88107 | 0.426797 | ||||||||
\(537\) | −14.1598 | −0.611040 | ||||||||
\(538\) | 11.8496 | 0.510874 | ||||||||
\(539\) | 7.56562 | 0.325874 | ||||||||
\(540\) | 1.52972 | 0.0658285 | ||||||||
\(541\) | −27.6624 | −1.18930 | −0.594650 | − | 0.803985i | \(-0.702709\pi\) | ||||
−0.594650 | + | 0.803985i | \(0.702709\pi\) | |||||||
\(542\) | 4.66837 | 0.200524 | ||||||||
\(543\) | −27.7190 | −1.18954 | ||||||||
\(544\) | −2.18699 | −0.0937666 | ||||||||
\(545\) | 1.23173 | 0.0527614 | ||||||||
\(546\) | 3.85630 | 0.165034 | ||||||||
\(547\) | 18.6646 | 0.798042 | 0.399021 | − | 0.916942i | \(-0.369350\pi\) | ||||
0.399021 | + | 0.916942i | \(0.369350\pi\) | |||||||
\(548\) | −3.36358 | −0.143685 | ||||||||
\(549\) | −0.474522 | −0.0202521 | ||||||||
\(550\) | −7.10436 | −0.302931 | ||||||||
\(551\) | −0.141723 | −0.00603761 | ||||||||
\(552\) | 5.34355 | 0.227437 | ||||||||
\(553\) | 11.8369 | 0.503355 | ||||||||
\(554\) | −19.0624 | −0.809885 | ||||||||
\(555\) | 3.49914 | 0.148530 | ||||||||
\(556\) | 21.6408 | 0.917773 | ||||||||
\(557\) | 16.4010 | 0.694931 | 0.347465 | − | 0.937693i | \(-0.387042\pi\) | ||||
0.347465 | + | 0.937693i | \(0.387042\pi\) | |||||||
\(558\) | −1.57091 | −0.0665018 | ||||||||
\(559\) | 8.81577 | 0.372867 | ||||||||
\(560\) | −0.484464 | −0.0204723 | ||||||||
\(561\) | 6.24007 | 0.263456 | ||||||||
\(562\) | −1.48411 | −0.0626033 | ||||||||
\(563\) | 29.1156 | 1.22708 | 0.613538 | − | 0.789665i | \(-0.289746\pi\) | ||||
0.613538 | + | 0.789665i | \(0.289746\pi\) | |||||||
\(564\) | −23.1865 | −0.976326 | ||||||||
\(565\) | 5.02545 | 0.211422 | ||||||||
\(566\) | −25.8606 | −1.08700 | ||||||||
\(567\) | 14.5378 | 0.610530 | ||||||||
\(568\) | 13.0279 | 0.546640 | ||||||||
\(569\) | 14.1712 | 0.594088 | 0.297044 | − | 0.954864i | \(-0.403999\pi\) | ||||
0.297044 | + | 0.954864i | \(0.403999\pi\) | |||||||
\(570\) | −0.0117932 | −0.000493963 0 | ||||||||
\(571\) | 24.9937 | 1.04595 | 0.522976 | − | 0.852347i | \(-0.324822\pi\) | ||||
0.522976 | + | 0.852347i | \(0.324822\pi\) | |||||||
\(572\) | 2.13548 | 0.0892891 | ||||||||
\(573\) | 37.8077 | 1.57944 | ||||||||
\(574\) | 0.467629 | 0.0195184 | ||||||||
\(575\) | −13.3049 | −0.554854 | ||||||||
\(576\) | 0.826410 | 0.0344338 | ||||||||
\(577\) | −15.9444 | −0.663774 | −0.331887 | − | 0.943319i | \(-0.607685\pi\) | ||||
−0.331887 | + | 0.943319i | \(0.607685\pi\) | |||||||
\(578\) | 12.2171 | 0.508163 | ||||||||
\(579\) | 5.69620 | 0.236726 | ||||||||
\(580\) | 3.04285 | 0.126347 | ||||||||
\(581\) | −13.7694 | −0.571250 | ||||||||
\(582\) | 36.3340 | 1.50609 | ||||||||
\(583\) | 11.8208 | 0.489568 | ||||||||
\(584\) | 6.35541 | 0.262989 | ||||||||
\(585\) | −0.435295 | −0.0179972 | ||||||||
\(586\) | −16.7854 | −0.693400 | ||||||||
\(587\) | 0.134590 | 0.00555514 | 0.00277757 | − | 0.999996i | \(-0.499116\pi\) | ||||
0.00277757 | + | 0.999996i | \(0.499116\pi\) | |||||||
\(588\) | 10.1460 | 0.418413 | ||||||||
\(589\) | −0.0318532 | −0.00131249 | ||||||||
\(590\) | −0.338527 | −0.0139369 | ||||||||
\(591\) | −29.3946 | −1.20913 | ||||||||
\(592\) | −4.97197 | −0.204347 | ||||||||
\(593\) | 19.4114 | 0.797130 | 0.398565 | − | 0.917140i | \(-0.369508\pi\) | ||||
0.398565 | + | 0.917140i | \(0.369508\pi\) | |||||||
\(594\) | 6.20182 | 0.254464 | ||||||||
\(595\) | −1.05952 | −0.0434361 | ||||||||
\(596\) | −22.9120 | −0.938514 | ||||||||
\(597\) | 10.2469 | 0.419376 | ||||||||
\(598\) | 3.99930 | 0.163544 | ||||||||
\(599\) | 9.22942 | 0.377104 | 0.188552 | − | 0.982063i | \(-0.439621\pi\) | ||||
0.188552 | + | 0.982063i | \(0.439621\pi\) | |||||||
\(600\) | −9.52740 | −0.388955 | ||||||||
\(601\) | 21.6048 | 0.881276 | 0.440638 | − | 0.897685i | \(-0.354752\pi\) | ||||
0.440638 | + | 0.897685i | \(0.354752\pi\) | |||||||
\(602\) | −8.10838 | −0.330473 | ||||||||
\(603\) | −8.16582 | −0.332538 | ||||||||
\(604\) | −24.2613 | −0.987180 | ||||||||
\(605\) | −3.19211 | −0.129778 | ||||||||
\(606\) | −30.6041 | −1.24321 | ||||||||
\(607\) | −6.66214 | −0.270408 | −0.135204 | − | 0.990818i | \(-0.543169\pi\) | ||||
−0.135204 | + | 0.990818i | \(0.543169\pi\) | |||||||
\(608\) | 0.0167571 | 0.000679589 0 | ||||||||
\(609\) | 22.2773 | 0.902722 | ||||||||
\(610\) | 0.206585 | 0.00836437 | ||||||||
\(611\) | −17.3536 | −0.702051 | ||||||||
\(612\) | 1.80735 | 0.0730580 | ||||||||
\(613\) | −0.983677 | −0.0397303 | −0.0198652 | − | 0.999803i | \(-0.506324\pi\) | ||||
−0.0198652 | + | 0.999803i | \(0.506324\pi\) | |||||||
\(614\) | 6.29542 | 0.254063 | ||||||||
\(615\) | −0.244405 | −0.00985535 | ||||||||
\(616\) | −1.96413 | −0.0791371 | ||||||||
\(617\) | 27.4150 | 1.10369 | 0.551843 | − | 0.833948i | \(-0.313925\pi\) | ||||
0.551843 | + | 0.833948i | \(0.313925\pi\) | |||||||
\(618\) | 7.82819 | 0.314896 | ||||||||
\(619\) | 34.1310 | 1.37184 | 0.685921 | − | 0.727676i | \(-0.259399\pi\) | ||||
0.685921 | + | 0.727676i | \(0.259399\pi\) | |||||||
\(620\) | 0.683899 | 0.0274661 | ||||||||
\(621\) | 11.6147 | 0.466081 | ||||||||
\(622\) | −10.7360 | −0.430476 | ||||||||
\(623\) | −9.54310 | −0.382336 | ||||||||
\(624\) | 2.86382 | 0.114645 | ||||||||
\(625\) | 23.0751 | 0.923005 | ||||||||
\(626\) | −3.22213 | −0.128782 | ||||||||
\(627\) | −0.0478124 | −0.00190944 | ||||||||
\(628\) | 1.11609 | 0.0445367 | ||||||||
\(629\) | −10.8737 | −0.433561 | ||||||||
\(630\) | 0.400366 | 0.0159510 | ||||||||
\(631\) | −39.5158 | −1.57310 | −0.786550 | − | 0.617526i | \(-0.788135\pi\) | ||||
−0.786550 | + | 0.617526i | \(0.788135\pi\) | |||||||
\(632\) | 8.79048 | 0.349666 | ||||||||
\(633\) | −24.0786 | −0.957037 | ||||||||
\(634\) | 24.9930 | 0.992599 | ||||||||
\(635\) | −1.49335 | −0.0592618 | ||||||||
\(636\) | 15.8525 | 0.628591 | ||||||||
\(637\) | 7.59362 | 0.300870 | ||||||||
\(638\) | 12.3364 | 0.488403 | ||||||||
\(639\) | −10.7664 | −0.425913 | ||||||||
\(640\) | −0.359780 | −0.0142216 | ||||||||
\(641\) | 39.7321 | 1.56932 | 0.784662 | − | 0.619924i | \(-0.212837\pi\) | ||||
0.784662 | + | 0.619924i | \(0.212837\pi\) | |||||||
\(642\) | −8.23094 | −0.324849 | ||||||||
\(643\) | −16.3885 | −0.646297 | −0.323149 | − | 0.946348i | \(-0.604741\pi\) | ||||
−0.323149 | + | 0.946348i | \(0.604741\pi\) | |||||||
\(644\) | −3.67840 | −0.144949 | ||||||||
\(645\) | 4.23782 | 0.166864 | ||||||||
\(646\) | 0.0366476 | 0.00144188 | ||||||||
\(647\) | −3.59219 | −0.141224 | −0.0706118 | − | 0.997504i | \(-0.522495\pi\) | ||||
−0.0706118 | + | 0.997504i | \(0.522495\pi\) | |||||||
\(648\) | 10.7963 | 0.424118 | ||||||||
\(649\) | −1.37247 | −0.0538740 | ||||||||
\(650\) | −7.13065 | −0.279687 | ||||||||
\(651\) | 5.00697 | 0.196239 | ||||||||
\(652\) | 20.8506 | 0.816574 | ||||||||
\(653\) | −9.64575 | −0.377467 | −0.188734 | − | 0.982028i | \(-0.560438\pi\) | ||||
−0.188734 | + | 0.982028i | \(0.560438\pi\) | |||||||
\(654\) | 6.69688 | 0.261869 | ||||||||
\(655\) | 1.62257 | 0.0633991 | ||||||||
\(656\) | 0.347278 | 0.0135589 | ||||||||
\(657\) | −5.25218 | −0.204907 | ||||||||
\(658\) | 15.9611 | 0.622229 | ||||||||
\(659\) | −12.2049 | −0.475435 | −0.237717 | − | 0.971334i | \(-0.576399\pi\) | ||||
−0.237717 | + | 0.971334i | \(0.576399\pi\) | |||||||
\(660\) | 1.02655 | 0.0399583 | ||||||||
\(661\) | −2.55135 | −0.0992362 | −0.0496181 | − | 0.998768i | \(-0.515800\pi\) | ||||
−0.0496181 | + | 0.998768i | \(0.515800\pi\) | |||||||
\(662\) | −13.6179 | −0.529275 | ||||||||
\(663\) | 6.26316 | 0.243241 | ||||||||
\(664\) | −10.2256 | −0.396831 | ||||||||
\(665\) | 0.00811821 | 0.000314811 0 | ||||||||
\(666\) | 4.10889 | 0.159216 | ||||||||
\(667\) | 23.1034 | 0.894569 | ||||||||
\(668\) | −6.69157 | −0.258904 | ||||||||
\(669\) | −41.5548 | −1.60660 | ||||||||
\(670\) | 3.55501 | 0.137342 | ||||||||
\(671\) | 0.837542 | 0.0323330 | ||||||||
\(672\) | −2.63403 | −0.101610 | ||||||||
\(673\) | 21.9227 | 0.845058 | 0.422529 | − | 0.906349i | \(-0.361143\pi\) | ||||
0.422529 | + | 0.906349i | \(0.361143\pi\) | |||||||
\(674\) | 15.8385 | 0.610077 | ||||||||
\(675\) | −20.7087 | −0.797077 | ||||||||
\(676\) | −10.8566 | −0.417562 | ||||||||
\(677\) | 10.6471 | 0.409201 | 0.204601 | − | 0.978846i | \(-0.434410\pi\) | ||||
0.204601 | + | 0.978846i | \(0.434410\pi\) | |||||||
\(678\) | 27.3233 | 1.04934 | ||||||||
\(679\) | −25.0116 | −0.959857 | ||||||||
\(680\) | −0.786837 | −0.0301738 | ||||||||
\(681\) | 37.9723 | 1.45510 | ||||||||
\(682\) | 2.77269 | 0.106172 | ||||||||
\(683\) | 8.22433 | 0.314695 | 0.157348 | − | 0.987543i | \(-0.449706\pi\) | ||||
0.157348 | + | 0.987543i | \(0.449706\pi\) | |||||||
\(684\) | −0.0138482 | −0.000529500 0 | ||||||||
\(685\) | −1.21015 | −0.0462375 | ||||||||
\(686\) | −16.4102 | −0.626544 | ||||||||
\(687\) | 15.1080 | 0.576405 | ||||||||
\(688\) | −6.02157 | −0.229570 | ||||||||
\(689\) | 11.8646 | 0.452004 | ||||||||
\(690\) | 1.92250 | 0.0731885 | ||||||||
\(691\) | 6.55510 | 0.249368 | 0.124684 | − | 0.992197i | \(-0.460208\pi\) | ||||
0.124684 | + | 0.992197i | \(0.460208\pi\) | |||||||
\(692\) | 0.619997 | 0.0235687 | ||||||||
\(693\) | 1.62318 | 0.0616595 | ||||||||
\(694\) | −22.0889 | −0.838484 | ||||||||
\(695\) | 7.78592 | 0.295337 | ||||||||
\(696\) | 16.5439 | 0.627096 | ||||||||
\(697\) | 0.759494 | 0.0287679 | ||||||||
\(698\) | −3.46238 | −0.131053 | ||||||||
\(699\) | 18.4461 | 0.697696 | ||||||||
\(700\) | 6.55848 | 0.247887 | ||||||||
\(701\) | 3.06398 | 0.115725 | 0.0578625 | − | 0.998325i | \(-0.481571\pi\) | ||||
0.0578625 | + | 0.998325i | \(0.481571\pi\) | |||||||
\(702\) | 6.22477 | 0.234939 | ||||||||
\(703\) | 0.0833157 | 0.00314231 | ||||||||
\(704\) | −1.45863 | −0.0549743 | ||||||||
\(705\) | −8.34203 | −0.314179 | ||||||||
\(706\) | 31.3704 | 1.18064 | ||||||||
\(707\) | 21.0673 | 0.792317 | ||||||||
\(708\) | −1.84057 | −0.0691727 | ||||||||
\(709\) | 42.4237 | 1.59326 | 0.796628 | − | 0.604470i | \(-0.206615\pi\) | ||||
0.796628 | + | 0.604470i | \(0.206615\pi\) | |||||||
\(710\) | 4.68719 | 0.175907 | ||||||||
\(711\) | −7.26454 | −0.272442 | ||||||||
\(712\) | −7.08705 | −0.265598 | ||||||||
\(713\) | 5.19265 | 0.194466 | ||||||||
\(714\) | −5.76060 | −0.215585 | ||||||||
\(715\) | 0.768305 | 0.0287330 | ||||||||
\(716\) | 7.23870 | 0.270523 | ||||||||
\(717\) | −14.3911 | −0.537445 | ||||||||
\(718\) | −18.2289 | −0.680297 | ||||||||
\(719\) | 29.3888 | 1.09602 | 0.548008 | − | 0.836473i | \(-0.315386\pi\) | ||||
0.548008 | + | 0.836473i | \(0.315386\pi\) | |||||||
\(720\) | 0.297326 | 0.0110807 | ||||||||
\(721\) | −5.38877 | −0.200688 | ||||||||
\(722\) | 18.9997 | 0.707096 | ||||||||
\(723\) | −23.4937 | −0.873739 | ||||||||
\(724\) | 14.1704 | 0.526639 | ||||||||
\(725\) | −41.1928 | −1.52986 | ||||||||
\(726\) | −17.3555 | −0.644122 | ||||||||
\(727\) | 39.4000 | 1.46126 | 0.730632 | − | 0.682772i | \(-0.239226\pi\) | ||||
0.730632 | + | 0.682772i | \(0.239226\pi\) | |||||||
\(728\) | −1.97140 | −0.0730649 | ||||||||
\(729\) | 16.0290 | 0.593666 | ||||||||
\(730\) | 2.28655 | 0.0846290 | ||||||||
\(731\) | −13.1691 | −0.487078 | ||||||||
\(732\) | 1.12320 | 0.0415146 | ||||||||
\(733\) | −24.9413 | −0.921227 | −0.460614 | − | 0.887601i | \(-0.652371\pi\) | ||||
−0.460614 | + | 0.887601i | \(0.652371\pi\) | |||||||
\(734\) | −29.8011 | −1.09998 | ||||||||
\(735\) | 3.65032 | 0.134644 | ||||||||
\(736\) | −2.73171 | −0.100692 | ||||||||
\(737\) | 14.4129 | 0.530904 | ||||||||
\(738\) | −0.286994 | −0.0105644 | ||||||||
\(739\) | 8.61742 | 0.316997 | 0.158499 | − | 0.987359i | \(-0.449335\pi\) | ||||
0.158499 | + | 0.987359i | \(0.449335\pi\) | |||||||
\(740\) | −1.78882 | −0.0657582 | ||||||||
\(741\) | −0.0479893 | −0.00176293 | ||||||||
\(742\) | −10.9125 | −0.400612 | ||||||||
\(743\) | 35.2099 | 1.29173 | 0.645863 | − | 0.763453i | \(-0.276498\pi\) | ||||
0.645863 | + | 0.763453i | \(0.276498\pi\) | |||||||
\(744\) | 3.71835 | 0.136321 | ||||||||
\(745\) | −8.24330 | −0.302011 | ||||||||
\(746\) | 0.215926 | 0.00790561 | ||||||||
\(747\) | 8.45056 | 0.309190 | ||||||||
\(748\) | −3.19002 | −0.116639 | ||||||||
\(749\) | 5.66602 | 0.207032 | ||||||||
\(750\) | −6.94664 | −0.253655 | ||||||||
\(751\) | 36.7287 | 1.34025 | 0.670124 | − | 0.742249i | \(-0.266241\pi\) | ||||
0.670124 | + | 0.742249i | \(0.266241\pi\) | |||||||
\(752\) | 11.8533 | 0.432245 | ||||||||
\(753\) | −16.2071 | −0.590620 | ||||||||
\(754\) | 12.3821 | 0.450928 | ||||||||
\(755\) | −8.72875 | −0.317672 | ||||||||
\(756\) | −5.72529 | −0.208227 | ||||||||
\(757\) | 34.1062 | 1.23961 | 0.619806 | − | 0.784755i | \(-0.287211\pi\) | ||||
0.619806 | + | 0.784755i | \(0.287211\pi\) | |||||||
\(758\) | 4.94510 | 0.179614 | ||||||||
\(759\) | 7.79428 | 0.282914 | ||||||||
\(760\) | 0.00602887 | 0.000218690 0 | ||||||||
\(761\) | −1.00936 | −0.0365894 | −0.0182947 | − | 0.999833i | \(-0.505824\pi\) | ||||
−0.0182947 | + | 0.999833i | \(0.505824\pi\) | |||||||
\(762\) | −8.11933 | −0.294132 | ||||||||
\(763\) | −4.61001 | −0.166893 | ||||||||
\(764\) | −19.3279 | −0.699258 | ||||||||
\(765\) | 0.650250 | 0.0235099 | ||||||||
\(766\) | −38.5669 | −1.39348 | ||||||||
\(767\) | −1.37755 | −0.0497403 | ||||||||
\(768\) | −1.95612 | −0.0705854 | ||||||||
\(769\) | −15.2602 | −0.550297 | −0.275148 | − | 0.961402i | \(-0.588727\pi\) | ||||
−0.275148 | + | 0.961402i | \(0.588727\pi\) | |||||||
\(770\) | −0.706656 | −0.0254661 | ||||||||
\(771\) | 40.3598 | 1.45352 | ||||||||
\(772\) | −2.91199 | −0.104805 | ||||||||
\(773\) | 38.7251 | 1.39285 | 0.696423 | − | 0.717632i | \(-0.254774\pi\) | ||||
0.696423 | + | 0.717632i | \(0.254774\pi\) | |||||||
\(774\) | 4.97629 | 0.178869 | ||||||||
\(775\) | −9.25835 | −0.332570 | ||||||||
\(776\) | −18.5745 | −0.666786 | ||||||||
\(777\) | −13.0963 | −0.469827 | ||||||||
\(778\) | −27.1464 | −0.973247 | ||||||||
\(779\) | −0.00581936 | −0.000208500 0 | ||||||||
\(780\) | 1.03035 | 0.0368923 | ||||||||
\(781\) | 19.0030 | 0.679980 | ||||||||
\(782\) | −5.97423 | −0.213638 | ||||||||
\(783\) | 35.9597 | 1.28509 | ||||||||
\(784\) | −5.18679 | −0.185242 | ||||||||
\(785\) | 0.401546 | 0.0143318 | ||||||||
\(786\) | 8.82190 | 0.314667 | ||||||||
\(787\) | 52.5478 | 1.87313 | 0.936563 | − | 0.350500i | \(-0.113988\pi\) | ||||
0.936563 | + | 0.350500i | \(0.113988\pi\) | |||||||
\(788\) | 15.0270 | 0.535315 | ||||||||
\(789\) | −7.75819 | −0.276199 | ||||||||
\(790\) | 3.16264 | 0.112522 | ||||||||
\(791\) | −18.8088 | −0.668765 | ||||||||
\(792\) | 1.20543 | 0.0428331 | ||||||||
\(793\) | 0.840642 | 0.0298521 | ||||||||
\(794\) | −1.22440 | −0.0434522 | ||||||||
\(795\) | 5.70340 | 0.202279 | ||||||||
\(796\) | −5.23835 | −0.185668 | ||||||||
\(797\) | −22.9338 | −0.812355 | −0.406178 | − | 0.913794i | \(-0.633139\pi\) | ||||
−0.406178 | + | 0.913794i | \(0.633139\pi\) | |||||||
\(798\) | 0.0441386 | 0.00156249 | ||||||||
\(799\) | 25.9231 | 0.917092 | ||||||||
\(800\) | 4.87056 | 0.172200 | ||||||||
\(801\) | 5.85681 | 0.206940 | ||||||||
\(802\) | −3.20701 | −0.113244 | ||||||||
\(803\) | 9.27021 | 0.327139 | ||||||||
\(804\) | 19.3286 | 0.681666 | ||||||||
\(805\) | −1.32341 | −0.0466442 | ||||||||
\(806\) | 2.78295 | 0.0980252 | ||||||||
\(807\) | 23.1793 | 0.815951 | ||||||||
\(808\) | 15.6453 | 0.550400 | ||||||||
\(809\) | 44.4295 | 1.56206 | 0.781029 | − | 0.624495i | \(-0.214695\pi\) | ||||
0.781029 | + | 0.624495i | \(0.214695\pi\) | |||||||
\(810\) | 3.88429 | 0.136480 | ||||||||
\(811\) | −52.1653 | −1.83177 | −0.915885 | − | 0.401440i | \(-0.868510\pi\) | ||||
−0.915885 | + | 0.401440i | \(0.868510\pi\) | |||||||
\(812\) | −11.3885 | −0.399659 | ||||||||
\(813\) | 9.13190 | 0.320270 | ||||||||
\(814\) | −7.25228 | −0.254192 | ||||||||
\(815\) | 7.50165 | 0.262771 | ||||||||
\(816\) | −4.27803 | −0.149761 | ||||||||
\(817\) | 0.100904 | 0.00353018 | ||||||||
\(818\) | −16.2981 | −0.569850 | ||||||||
\(819\) | 1.62919 | 0.0569283 | ||||||||
\(820\) | 0.124944 | 0.00436322 | ||||||||
\(821\) | 20.0147 | 0.698517 | 0.349259 | − | 0.937026i | \(-0.386433\pi\) | ||||
0.349259 | + | 0.937026i | \(0.386433\pi\) | |||||||
\(822\) | −6.57958 | −0.229489 | ||||||||
\(823\) | −34.4856 | −1.20209 | −0.601046 | − | 0.799214i | \(-0.705249\pi\) | ||||
−0.601046 | + | 0.799214i | \(0.705249\pi\) | |||||||
\(824\) | −4.00189 | −0.139413 | ||||||||
\(825\) | −13.8970 | −0.483831 | ||||||||
\(826\) | 1.26701 | 0.0440849 | ||||||||
\(827\) | −3.07908 | −0.107070 | −0.0535351 | − | 0.998566i | \(-0.517049\pi\) | ||||
−0.0535351 | + | 0.998566i | \(0.517049\pi\) | |||||||
\(828\) | 2.25751 | 0.0784539 | ||||||||
\(829\) | 30.8419 | 1.07118 | 0.535592 | − | 0.844477i | \(-0.320089\pi\) | ||||
0.535592 | + | 0.844477i | \(0.320089\pi\) | |||||||
\(830\) | −3.67898 | −0.127699 | ||||||||
\(831\) | −37.2884 | −1.29352 | ||||||||
\(832\) | −1.46403 | −0.0507561 | ||||||||
\(833\) | −11.3435 | −0.393028 | ||||||||
\(834\) | 42.3320 | 1.46584 | ||||||||
\(835\) | −2.40749 | −0.0833147 | ||||||||
\(836\) | 0.0244424 | 0.000845359 0 | ||||||||
\(837\) | 8.08218 | 0.279361 | ||||||||
\(838\) | 37.3045 | 1.28866 | ||||||||
\(839\) | −46.1171 | −1.59214 | −0.796069 | − | 0.605206i | \(-0.793091\pi\) | ||||
−0.796069 | + | 0.605206i | \(0.793091\pi\) | |||||||
\(840\) | −0.947671 | −0.0326977 | ||||||||
\(841\) | 42.5295 | 1.46654 | ||||||||
\(842\) | −0.961923 | −0.0331501 | ||||||||
\(843\) | −2.90309 | −0.0999878 | ||||||||
\(844\) | 12.3093 | 0.423705 | ||||||||
\(845\) | −3.90599 | −0.134370 | ||||||||
\(846\) | −9.79568 | −0.336782 | ||||||||
\(847\) | 11.9472 | 0.410510 | ||||||||
\(848\) | −8.10403 | −0.278294 | ||||||||
\(849\) | −50.5864 | −1.73612 | ||||||||
\(850\) | 10.6519 | 0.365356 | ||||||||
\(851\) | −13.5820 | −0.465584 | ||||||||
\(852\) | 25.4842 | 0.873075 | ||||||||
\(853\) | 47.4535 | 1.62478 | 0.812389 | − | 0.583116i | \(-0.198167\pi\) | ||||
0.812389 | + | 0.583116i | \(0.198167\pi\) | |||||||
\(854\) | −0.773188 | −0.0264579 | ||||||||
\(855\) | −0.00498232 | −0.000170392 0 | ||||||||
\(856\) | 4.20779 | 0.143819 | ||||||||
\(857\) | −47.9501 | −1.63794 | −0.818971 | − | 0.573834i | \(-0.805455\pi\) | ||||
−0.818971 | + | 0.573834i | \(0.805455\pi\) | |||||||
\(858\) | 4.17727 | 0.142610 | ||||||||
\(859\) | 33.2022 | 1.13284 | 0.566422 | − | 0.824116i | \(-0.308327\pi\) | ||||
0.566422 | + | 0.824116i | \(0.308327\pi\) | |||||||
\(860\) | −2.16644 | −0.0738751 | ||||||||
\(861\) | 0.914738 | 0.0311742 | ||||||||
\(862\) | −1.54267 | −0.0525434 | ||||||||
\(863\) | 42.5475 | 1.44833 | 0.724166 | − | 0.689626i | \(-0.242225\pi\) | ||||
0.724166 | + | 0.689626i | \(0.242225\pi\) | |||||||
\(864\) | −4.25180 | −0.144649 | ||||||||
\(865\) | 0.223063 | 0.00758436 | ||||||||
\(866\) | 6.74748 | 0.229289 | ||||||||
\(867\) | 23.8980 | 0.811620 | ||||||||
\(868\) | −2.55964 | −0.0868799 | ||||||||
\(869\) | 12.8221 | 0.434959 | ||||||||
\(870\) | 5.95218 | 0.201798 | ||||||||
\(871\) | 14.4662 | 0.490168 | ||||||||
\(872\) | −3.42355 | −0.115936 | ||||||||
\(873\) | 15.3502 | 0.519524 | ||||||||
\(874\) | 0.0457754 | 0.00154838 | ||||||||
\(875\) | 4.78193 | 0.161659 | ||||||||
\(876\) | 12.4320 | 0.420037 | ||||||||
\(877\) | −34.2051 | −1.15502 | −0.577512 | − | 0.816383i | \(-0.695976\pi\) | ||||
−0.577512 | + | 0.816383i | \(0.695976\pi\) | |||||||
\(878\) | −28.3413 | −0.956472 | ||||||||
\(879\) | −32.8344 | −1.10748 | ||||||||
\(880\) | −0.524787 | −0.0176906 | ||||||||
\(881\) | −2.30736 | −0.0777368 | −0.0388684 | − | 0.999244i | \(-0.512375\pi\) | ||||
−0.0388684 | + | 0.999244i | \(0.512375\pi\) | |||||||
\(882\) | 4.28642 | 0.144331 | ||||||||
\(883\) | −8.85286 | −0.297922 | −0.148961 | − | 0.988843i | \(-0.547593\pi\) | ||||
−0.148961 | + | 0.988843i | \(0.547593\pi\) | |||||||
\(884\) | −3.20183 | −0.107689 | ||||||||
\(885\) | −0.662199 | −0.0222596 | ||||||||
\(886\) | 29.1627 | 0.979739 | ||||||||
\(887\) | 29.3076 | 0.984052 | 0.492026 | − | 0.870581i | \(-0.336257\pi\) | ||||
0.492026 | + | 0.870581i | \(0.336257\pi\) | |||||||
\(888\) | −9.72577 | −0.326376 | ||||||||
\(889\) | 5.58919 | 0.187455 | ||||||||
\(890\) | −2.54978 | −0.0854688 | ||||||||
\(891\) | 15.7478 | 0.527571 | ||||||||
\(892\) | 21.2435 | 0.711284 | ||||||||
\(893\) | −0.198627 | −0.00664678 | ||||||||
\(894\) | −44.8187 | −1.49896 | ||||||||
\(895\) | 2.60434 | 0.0870536 | ||||||||
\(896\) | 1.34656 | 0.0449853 | ||||||||
\(897\) | 7.82312 | 0.261206 | ||||||||
\(898\) | 26.6477 | 0.889244 | ||||||||
\(899\) | 16.0767 | 0.536189 | ||||||||
\(900\) | −4.02508 | −0.134169 | ||||||||
\(901\) | −17.7235 | −0.590454 | ||||||||
\(902\) | 0.506551 | 0.0168663 | ||||||||
\(903\) | −15.8610 | −0.527820 | ||||||||
\(904\) | −13.9681 | −0.464572 | ||||||||
\(905\) | 5.09823 | 0.169471 | ||||||||
\(906\) | −47.4581 | −1.57669 | ||||||||
\(907\) | 2.74117 | 0.0910190 | 0.0455095 | − | 0.998964i | \(-0.485509\pi\) | ||||
0.0455095 | + | 0.998964i | \(0.485509\pi\) | |||||||
\(908\) | −19.4120 | −0.644211 | ||||||||
\(909\) | −12.9295 | −0.428843 | ||||||||
\(910\) | −0.709271 | −0.0235121 | ||||||||
\(911\) | 40.3473 | 1.33676 | 0.668382 | − | 0.743818i | \(-0.266987\pi\) | ||||
0.668382 | + | 0.743818i | \(0.266987\pi\) | |||||||
\(912\) | 0.0327789 | 0.00108542 | ||||||||
\(913\) | −14.9154 | −0.493629 | ||||||||
\(914\) | −19.1923 | −0.634826 | ||||||||
\(915\) | 0.404105 | 0.0133593 | ||||||||
\(916\) | −7.72343 | −0.255189 | ||||||||
\(917\) | −6.07282 | −0.200542 | ||||||||
\(918\) | −9.29867 | −0.306902 | ||||||||
\(919\) | 6.08753 | 0.200809 | 0.100405 | − | 0.994947i | \(-0.467986\pi\) | ||||
0.100405 | + | 0.994947i | \(0.467986\pi\) | |||||||
\(920\) | −0.982814 | −0.0324024 | ||||||||
\(921\) | 12.3146 | 0.405780 | ||||||||
\(922\) | −13.5409 | −0.445945 | ||||||||
\(923\) | 19.0733 | 0.627805 | ||||||||
\(924\) | −3.84208 | −0.126395 | ||||||||
\(925\) | 24.2163 | 0.796226 | ||||||||
\(926\) | −15.1001 | −0.496219 | ||||||||
\(927\) | 3.30721 | 0.108623 | ||||||||
\(928\) | −8.45751 | −0.277631 | ||||||||
\(929\) | −3.40082 | −0.111577 | −0.0557887 | − | 0.998443i | \(-0.517767\pi\) | ||||
−0.0557887 | + | 0.998443i | \(0.517767\pi\) | |||||||
\(930\) | 1.33779 | 0.0438679 | ||||||||
\(931\) | 0.0869154 | 0.00284854 | ||||||||
\(932\) | −9.42994 | −0.308888 | ||||||||
\(933\) | −21.0010 | −0.687542 | ||||||||
\(934\) | 0.676254 | 0.0221277 | ||||||||
\(935\) | −1.14771 | −0.0375340 | ||||||||
\(936\) | 1.20989 | 0.0395465 | ||||||||
\(937\) | 22.3095 | 0.728819 | 0.364409 | − | 0.931239i | \(-0.381271\pi\) | ||||
0.364409 | + | 0.931239i | \(0.381271\pi\) | |||||||
\(938\) | −13.3054 | −0.434437 | ||||||||
\(939\) | −6.30288 | −0.205687 | ||||||||
\(940\) | 4.26458 | 0.139095 | ||||||||
\(941\) | −18.7550 | −0.611394 | −0.305697 | − | 0.952129i | \(-0.598889\pi\) | ||||
−0.305697 | + | 0.952129i | \(0.598889\pi\) | |||||||
\(942\) | 2.18320 | 0.0711325 | ||||||||
\(943\) | 0.948661 | 0.0308926 | ||||||||
\(944\) | 0.940926 | 0.0306245 | ||||||||
\(945\) | −2.05985 | −0.0670068 | ||||||||
\(946\) | −8.78326 | −0.285569 | ||||||||
\(947\) | −12.2526 | −0.398156 | −0.199078 | − | 0.979984i | \(-0.563795\pi\) | ||||
−0.199078 | + | 0.979984i | \(0.563795\pi\) | |||||||
\(948\) | 17.1952 | 0.558476 | ||||||||
\(949\) | 9.30452 | 0.302037 | ||||||||
\(950\) | −0.0816163 | −0.00264798 | ||||||||
\(951\) | 48.8894 | 1.58535 | ||||||||
\(952\) | 2.94491 | 0.0954451 | ||||||||
\(953\) | −9.37517 | −0.303691 | −0.151846 | − | 0.988404i | \(-0.548522\pi\) | ||||
−0.151846 | + | 0.988404i | \(0.548522\pi\) | |||||||
\(954\) | 6.69726 | 0.216832 | ||||||||
\(955\) | −6.95379 | −0.225019 | ||||||||
\(956\) | 7.35695 | 0.237941 | ||||||||
\(957\) | 24.1315 | 0.780061 | ||||||||
\(958\) | −29.0847 | −0.939683 | ||||||||
\(959\) | 4.52925 | 0.146257 | ||||||||
\(960\) | −0.703774 | −0.0227142 | ||||||||
\(961\) | −27.3867 | −0.883440 | ||||||||
\(962\) | −7.27912 | −0.234688 | ||||||||
\(963\) | −3.47736 | −0.112056 | ||||||||
\(964\) | 12.0103 | 0.386827 | ||||||||
\(965\) | −1.04768 | −0.0337259 | ||||||||
\(966\) | −7.19539 | −0.231508 | ||||||||
\(967\) | −12.1157 | −0.389615 | −0.194808 | − | 0.980841i | \(-0.562408\pi\) | ||||
−0.194808 | + | 0.980841i | \(0.562408\pi\) | |||||||
\(968\) | 8.87239 | 0.285169 | ||||||||
\(969\) | 0.0716872 | 0.00230293 | ||||||||
\(970\) | −6.68274 | −0.214570 | ||||||||
\(971\) | 37.7444 | 1.21127 | 0.605637 | − | 0.795741i | \(-0.292918\pi\) | ||||
0.605637 | + | 0.795741i | \(0.292918\pi\) | |||||||
\(972\) | 8.36341 | 0.268257 | ||||||||
\(973\) | −29.1405 | −0.934202 | ||||||||
\(974\) | −25.0742 | −0.803431 | ||||||||
\(975\) | −13.9484 | −0.446707 | ||||||||
\(976\) | −0.574197 | −0.0183796 | ||||||||
\(977\) | −28.4122 | −0.908987 | −0.454493 | − | 0.890750i | \(-0.650180\pi\) | ||||
−0.454493 | + | 0.890750i | \(0.650180\pi\) | |||||||
\(978\) | 40.7864 | 1.30420 | ||||||||
\(979\) | −10.3374 | −0.330385 | ||||||||
\(980\) | −1.86610 | −0.0596105 | ||||||||
\(981\) | 2.82926 | 0.0903313 | ||||||||
\(982\) | −7.09457 | −0.226397 | ||||||||
\(983\) | −0.148500 | −0.00473642 | −0.00236821 | − | 0.999997i | \(-0.500754\pi\) | ||||
−0.00236821 | + | 0.999997i | \(0.500754\pi\) | |||||||
\(984\) | 0.679317 | 0.0216558 | ||||||||
\(985\) | 5.40642 | 0.172263 | ||||||||
\(986\) | −18.4965 | −0.589050 | ||||||||
\(987\) | 31.2219 | 0.993803 | ||||||||
\(988\) | 0.0245329 | 0.000780495 0 | ||||||||
\(989\) | −16.4492 | −0.523053 | ||||||||
\(990\) | 0.433690 | 0.0137836 | ||||||||
\(991\) | −46.4227 | −1.47467 | −0.737333 | − | 0.675530i | \(-0.763915\pi\) | ||||
−0.737333 | + | 0.675530i | \(0.763915\pi\) | |||||||
\(992\) | −1.90088 | −0.0603530 | ||||||||
\(993\) | −26.6383 | −0.845341 | ||||||||
\(994\) | −17.5428 | −0.556425 | ||||||||
\(995\) | −1.88466 | −0.0597476 | ||||||||
\(996\) | −20.0026 | −0.633805 | ||||||||
\(997\) | 3.56426 | 0.112881 | 0.0564406 | − | 0.998406i | \(-0.482025\pi\) | ||||
0.0564406 | + | 0.998406i | \(0.482025\pi\) | |||||||
\(998\) | −22.1068 | −0.699780 | ||||||||
\(999\) | −21.1398 | −0.668835 |
(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 | 8042.2.a.c.1.19 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.c.1.19 | ✓ | 86 | 1.1 | even | 1 | trivial |