Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 17x^{6} + 37x^{5} + 105x^{4} - 117x^{3} - 238x^{2} + 42x + 90 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.32287\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.86769 | 1.28247 | 0.641236 | − | 0.767344i | \(-0.278422\pi\) | ||||
0.641236 | + | 0.767344i | \(0.278422\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.636539 | 0.240589 | 0.120295 | − | 0.992738i | \(-0.461616\pi\) | ||||
0.120295 | + | 0.992738i | \(0.461616\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.86769 | −0.906844 | ||||||||
\(11\) | −3.08318 | −0.929613 | −0.464807 | − | 0.885412i | \(-0.653876\pi\) | ||||
−0.464807 | + | 0.885412i | \(0.653876\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.26426 | 0.350642 | 0.175321 | − | 0.984511i | \(-0.443904\pi\) | ||||
0.175321 | + | 0.984511i | \(0.443904\pi\) | |||||||
\(14\) | −0.636539 | −0.170122 | ||||||||
\(15\) | −2.86769 | −0.740435 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.75412 | 1.54950 | 0.774751 | − | 0.632266i | \(-0.217875\pi\) | ||||
0.774751 | + | 0.632266i | \(0.217875\pi\) | |||||||
\(20\) | 2.86769 | 0.641236 | ||||||||
\(21\) | −0.636539 | −0.138904 | ||||||||
\(22\) | 3.08318 | 0.657336 | ||||||||
\(23\) | −6.12526 | −1.27720 | −0.638602 | − | 0.769537i | \(-0.720487\pi\) | ||||
−0.638602 | + | 0.769537i | \(0.720487\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 3.22366 | 0.644732 | ||||||||
\(26\) | −1.26426 | −0.247941 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.636539 | 0.120295 | ||||||||
\(29\) | 2.06981 | 0.384354 | 0.192177 | − | 0.981360i | \(-0.438445\pi\) | ||||
0.192177 | + | 0.981360i | \(0.438445\pi\) | |||||||
\(30\) | 2.86769 | 0.523567 | ||||||||
\(31\) | 8.03376 | 1.44291 | 0.721453 | − | 0.692463i | \(-0.243475\pi\) | ||||
0.721453 | + | 0.692463i | \(0.243475\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.08318 | 0.536712 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 1.82540 | 0.308549 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.884221 | −0.145365 | −0.0726825 | − | 0.997355i | \(-0.523156\pi\) | ||||
−0.0726825 | + | 0.997355i | \(0.523156\pi\) | |||||||
\(38\) | −6.75412 | −1.09566 | ||||||||
\(39\) | −1.26426 | −0.202443 | ||||||||
\(40\) | −2.86769 | −0.453422 | ||||||||
\(41\) | −7.06013 | −1.10261 | −0.551303 | − | 0.834305i | \(-0.685869\pi\) | ||||
−0.551303 | + | 0.834305i | \(0.685869\pi\) | |||||||
\(42\) | 0.636539 | 0.0982201 | ||||||||
\(43\) | 6.55402 | 0.999479 | 0.499739 | − | 0.866176i | \(-0.333429\pi\) | ||||
0.499739 | + | 0.866176i | \(0.333429\pi\) | |||||||
\(44\) | −3.08318 | −0.464807 | ||||||||
\(45\) | 2.86769 | 0.427490 | ||||||||
\(46\) | 6.12526 | 0.903120 | ||||||||
\(47\) | −0.660560 | −0.0963526 | −0.0481763 | − | 0.998839i | \(-0.515341\pi\) | ||||
−0.0481763 | + | 0.998839i | \(0.515341\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.59482 | −0.942117 | ||||||||
\(50\) | −3.22366 | −0.455894 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 1.26426 | 0.175321 | ||||||||
\(53\) | 2.83430 | 0.389321 | 0.194661 | − | 0.980871i | \(-0.437639\pi\) | ||||
0.194661 | + | 0.980871i | \(0.437639\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −8.84161 | −1.19220 | ||||||||
\(56\) | −0.636539 | −0.0850611 | ||||||||
\(57\) | −6.75412 | −0.894605 | ||||||||
\(58\) | −2.06981 | −0.271779 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | −2.86769 | −0.370218 | ||||||||
\(61\) | −10.1283 | −1.29679 | −0.648396 | − | 0.761303i | \(-0.724560\pi\) | ||||
−0.648396 | + | 0.761303i | \(0.724560\pi\) | |||||||
\(62\) | −8.03376 | −1.02029 | ||||||||
\(63\) | 0.636539 | 0.0801964 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.62550 | 0.449688 | ||||||||
\(66\) | −3.08318 | −0.379513 | ||||||||
\(67\) | 0.0139862 | 0.00170868 | 0.000854342 | − | 1.00000i | \(-0.499728\pi\) | ||||
0.000854342 | 1.00000i | \(0.499728\pi\) | ||||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 6.12526 | 0.737395 | ||||||||
\(70\) | −1.82540 | −0.218177 | ||||||||
\(71\) | 5.73708 | 0.680867 | 0.340433 | − | 0.940269i | \(-0.389426\pi\) | ||||
0.340433 | + | 0.940269i | \(0.389426\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 6.30289 | 0.737697 | 0.368849 | − | 0.929489i | \(-0.379752\pi\) | ||||
0.368849 | + | 0.929489i | \(0.379752\pi\) | |||||||
\(74\) | 0.884221 | 0.102789 | ||||||||
\(75\) | −3.22366 | −0.372236 | ||||||||
\(76\) | 6.75412 | 0.774751 | ||||||||
\(77\) | −1.96256 | −0.223655 | ||||||||
\(78\) | 1.26426 | 0.143149 | ||||||||
\(79\) | 7.12879 | 0.802052 | 0.401026 | − | 0.916067i | \(-0.368654\pi\) | ||||
0.401026 | + | 0.916067i | \(0.368654\pi\) | |||||||
\(80\) | 2.86769 | 0.320618 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.06013 | 0.779661 | ||||||||
\(83\) | 14.6054 | 1.60315 | 0.801574 | − | 0.597895i | \(-0.203996\pi\) | ||||
0.801574 | + | 0.597895i | \(0.203996\pi\) | |||||||
\(84\) | −0.636539 | −0.0694521 | ||||||||
\(85\) | −2.86769 | −0.311045 | ||||||||
\(86\) | −6.55402 | −0.706738 | ||||||||
\(87\) | −2.06981 | −0.221907 | ||||||||
\(88\) | 3.08318 | 0.328668 | ||||||||
\(89\) | 1.32107 | 0.140033 | 0.0700164 | − | 0.997546i | \(-0.477695\pi\) | ||||
0.0700164 | + | 0.997546i | \(0.477695\pi\) | |||||||
\(90\) | −2.86769 | −0.302281 | ||||||||
\(91\) | 0.804748 | 0.0843605 | ||||||||
\(92\) | −6.12526 | −0.638602 | ||||||||
\(93\) | −8.03376 | −0.833062 | ||||||||
\(94\) | 0.660560 | 0.0681316 | ||||||||
\(95\) | 19.3687 | 1.98719 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 15.2562 | 1.54903 | 0.774517 | − | 0.632553i | \(-0.217993\pi\) | ||||
0.774517 | + | 0.632553i | \(0.217993\pi\) | |||||||
\(98\) | 6.59482 | 0.666177 | ||||||||
\(99\) | −3.08318 | −0.309871 | ||||||||
\(100\) | 3.22366 | 0.322366 | ||||||||
\(101\) | 4.52152 | 0.449908 | 0.224954 | − | 0.974369i | \(-0.427777\pi\) | ||||
0.224954 | + | 0.974369i | \(0.427777\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | 18.1452 | 1.78790 | 0.893948 | − | 0.448171i | \(-0.147924\pi\) | ||||
0.893948 | + | 0.448171i | \(0.147924\pi\) | |||||||
\(104\) | −1.26426 | −0.123971 | ||||||||
\(105\) | −1.82540 | −0.178141 | ||||||||
\(106\) | −2.83430 | −0.275292 | ||||||||
\(107\) | 6.90533 | 0.667564 | 0.333782 | − | 0.942650i | \(-0.391675\pi\) | ||||
0.333782 | + | 0.942650i | \(0.391675\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 2.23129 | 0.213719 | 0.106859 | − | 0.994274i | \(-0.465921\pi\) | ||||
0.106859 | + | 0.994274i | \(0.465921\pi\) | |||||||
\(110\) | 8.84161 | 0.843014 | ||||||||
\(111\) | 0.884221 | 0.0839265 | ||||||||
\(112\) | 0.636539 | 0.0601473 | ||||||||
\(113\) | 9.41503 | 0.885691 | 0.442846 | − | 0.896598i | \(-0.353969\pi\) | ||||
0.442846 | + | 0.896598i | \(0.353969\pi\) | |||||||
\(114\) | 6.75412 | 0.632582 | ||||||||
\(115\) | −17.5654 | −1.63798 | ||||||||
\(116\) | 2.06981 | 0.192177 | ||||||||
\(117\) | 1.26426 | 0.116881 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −0.636539 | −0.0583514 | ||||||||
\(120\) | 2.86769 | 0.261783 | ||||||||
\(121\) | −1.49402 | −0.135820 | ||||||||
\(122\) | 10.1283 | 0.916971 | ||||||||
\(123\) | 7.06013 | 0.636590 | ||||||||
\(124\) | 8.03376 | 0.721453 | ||||||||
\(125\) | −5.09400 | −0.455621 | ||||||||
\(126\) | −0.636539 | −0.0567074 | ||||||||
\(127\) | −9.67015 | −0.858087 | −0.429044 | − | 0.903284i | \(-0.641149\pi\) | ||||
−0.429044 | + | 0.903284i | \(0.641149\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.55402 | −0.577049 | ||||||||
\(130\) | −3.62550 | −0.317977 | ||||||||
\(131\) | 12.1575 | 1.06220 | 0.531101 | − | 0.847308i | \(-0.321778\pi\) | ||||
0.531101 | + | 0.847308i | \(0.321778\pi\) | |||||||
\(132\) | 3.08318 | 0.268356 | ||||||||
\(133\) | 4.29926 | 0.372793 | ||||||||
\(134\) | −0.0139862 | −0.00120822 | ||||||||
\(135\) | −2.86769 | −0.246812 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −16.0035 | −1.36727 | −0.683634 | − | 0.729825i | \(-0.739601\pi\) | ||||
−0.683634 | + | 0.729825i | \(0.739601\pi\) | |||||||
\(138\) | −6.12526 | −0.521417 | ||||||||
\(139\) | −20.1857 | −1.71213 | −0.856066 | − | 0.516866i | \(-0.827098\pi\) | ||||
−0.856066 | + | 0.516866i | \(0.827098\pi\) | |||||||
\(140\) | 1.82540 | 0.154274 | ||||||||
\(141\) | 0.660560 | 0.0556292 | ||||||||
\(142\) | −5.73708 | −0.481445 | ||||||||
\(143\) | −3.89793 | −0.325961 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 5.93557 | 0.492922 | ||||||||
\(146\) | −6.30289 | −0.521631 | ||||||||
\(147\) | 6.59482 | 0.543931 | ||||||||
\(148\) | −0.884221 | −0.0726825 | ||||||||
\(149\) | −16.2296 | −1.32958 | −0.664792 | − | 0.747029i | \(-0.731480\pi\) | ||||
−0.664792 | + | 0.747029i | \(0.731480\pi\) | |||||||
\(150\) | 3.22366 | 0.263211 | ||||||||
\(151\) | −4.37879 | −0.356341 | −0.178170 | − | 0.984000i | \(-0.557018\pi\) | ||||
−0.178170 | + | 0.984000i | \(0.557018\pi\) | |||||||
\(152\) | −6.75412 | −0.547832 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 1.96256 | 0.158148 | ||||||||
\(155\) | 23.0384 | 1.85049 | ||||||||
\(156\) | −1.26426 | −0.101221 | ||||||||
\(157\) | 10.5021 | 0.838155 | 0.419078 | − | 0.907950i | \(-0.362354\pi\) | ||||
0.419078 | + | 0.907950i | \(0.362354\pi\) | |||||||
\(158\) | −7.12879 | −0.567136 | ||||||||
\(159\) | −2.83430 | −0.224775 | ||||||||
\(160\) | −2.86769 | −0.226711 | ||||||||
\(161\) | −3.89897 | −0.307282 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 14.2087 | 1.11291 | 0.556454 | − | 0.830878i | \(-0.312162\pi\) | ||||
0.556454 | + | 0.830878i | \(0.312162\pi\) | |||||||
\(164\) | −7.06013 | −0.551303 | ||||||||
\(165\) | 8.84161 | 0.688318 | ||||||||
\(166\) | −14.6054 | −1.13360 | ||||||||
\(167\) | 9.29493 | 0.719264 | 0.359632 | − | 0.933094i | \(-0.382902\pi\) | ||||
0.359632 | + | 0.933094i | \(0.382902\pi\) | |||||||
\(168\) | 0.636539 | 0.0491100 | ||||||||
\(169\) | −11.4017 | −0.877051 | ||||||||
\(170\) | 2.86769 | 0.219942 | ||||||||
\(171\) | 6.75412 | 0.516501 | ||||||||
\(172\) | 6.55402 | 0.499739 | ||||||||
\(173\) | 13.4939 | 1.02592 | 0.512961 | − | 0.858412i | \(-0.328549\pi\) | ||||
0.512961 | + | 0.858412i | \(0.328549\pi\) | |||||||
\(174\) | 2.06981 | 0.156912 | ||||||||
\(175\) | 2.05199 | 0.155116 | ||||||||
\(176\) | −3.08318 | −0.232403 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | −1.32107 | −0.0990182 | ||||||||
\(179\) | −10.8405 | −0.810254 | −0.405127 | − | 0.914260i | \(-0.632773\pi\) | ||||
−0.405127 | + | 0.914260i | \(0.632773\pi\) | |||||||
\(180\) | 2.86769 | 0.213745 | ||||||||
\(181\) | −0.350673 | −0.0260653 | −0.0130327 | − | 0.999915i | \(-0.504149\pi\) | ||||
−0.0130327 | + | 0.999915i | \(0.504149\pi\) | |||||||
\(182\) | −0.804748 | −0.0596519 | ||||||||
\(183\) | 10.1283 | 0.748703 | ||||||||
\(184\) | 6.12526 | 0.451560 | ||||||||
\(185\) | −2.53567 | −0.186426 | ||||||||
\(186\) | 8.03376 | 0.589064 | ||||||||
\(187\) | 3.08318 | 0.225464 | ||||||||
\(188\) | −0.660560 | −0.0481763 | ||||||||
\(189\) | −0.636539 | −0.0463014 | ||||||||
\(190\) | −19.3687 | −1.40516 | ||||||||
\(191\) | −5.71664 | −0.413642 | −0.206821 | − | 0.978379i | \(-0.566312\pi\) | ||||
−0.206821 | + | 0.978379i | \(0.566312\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −18.2524 | −1.31384 | −0.656920 | − | 0.753960i | \(-0.728141\pi\) | ||||
−0.656920 | + | 0.753960i | \(0.728141\pi\) | |||||||
\(194\) | −15.2562 | −1.09533 | ||||||||
\(195\) | −3.62550 | −0.259627 | ||||||||
\(196\) | −6.59482 | −0.471058 | ||||||||
\(197\) | 16.0335 | 1.14234 | 0.571170 | − | 0.820832i | \(-0.306490\pi\) | ||||
0.571170 | + | 0.820832i | \(0.306490\pi\) | |||||||
\(198\) | 3.08318 | 0.219112 | ||||||||
\(199\) | 14.7301 | 1.04419 | 0.522094 | − | 0.852888i | \(-0.325151\pi\) | ||||
0.522094 | + | 0.852888i | \(0.325151\pi\) | |||||||
\(200\) | −3.22366 | −0.227947 | ||||||||
\(201\) | −0.0139862 | −0.000986509 0 | ||||||||
\(202\) | −4.52152 | −0.318133 | ||||||||
\(203\) | 1.31751 | 0.0924713 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −20.2463 | −1.41406 | ||||||||
\(206\) | −18.1452 | −1.26423 | ||||||||
\(207\) | −6.12526 | −0.425735 | ||||||||
\(208\) | 1.26426 | 0.0876604 | ||||||||
\(209\) | −20.8242 | −1.44044 | ||||||||
\(210\) | 1.82540 | 0.125964 | ||||||||
\(211\) | 18.1318 | 1.24825 | 0.624124 | − | 0.781325i | \(-0.285456\pi\) | ||||
0.624124 | + | 0.781325i | \(0.285456\pi\) | |||||||
\(212\) | 2.83430 | 0.194661 | ||||||||
\(213\) | −5.73708 | −0.393099 | ||||||||
\(214\) | −6.90533 | −0.472039 | ||||||||
\(215\) | 18.7949 | 1.28180 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 5.11380 | 0.347147 | ||||||||
\(218\) | −2.23129 | −0.151122 | ||||||||
\(219\) | −6.30289 | −0.425910 | ||||||||
\(220\) | −8.84161 | −0.596101 | ||||||||
\(221\) | −1.26426 | −0.0850431 | ||||||||
\(222\) | −0.884221 | −0.0593450 | ||||||||
\(223\) | 5.29242 | 0.354407 | 0.177203 | − | 0.984174i | \(-0.443295\pi\) | ||||
0.177203 | + | 0.984174i | \(0.443295\pi\) | |||||||
\(224\) | −0.636539 | −0.0425305 | ||||||||
\(225\) | 3.22366 | 0.214911 | ||||||||
\(226\) | −9.41503 | −0.626278 | ||||||||
\(227\) | 5.38961 | 0.357721 | 0.178860 | − | 0.983874i | \(-0.442759\pi\) | ||||
0.178860 | + | 0.983874i | \(0.442759\pi\) | |||||||
\(228\) | −6.75412 | −0.447303 | ||||||||
\(229\) | −7.41385 | −0.489921 | −0.244960 | − | 0.969533i | \(-0.578775\pi\) | ||||
−0.244960 | + | 0.969533i | \(0.578775\pi\) | |||||||
\(230\) | 17.5654 | 1.15823 | ||||||||
\(231\) | 1.96256 | 0.129127 | ||||||||
\(232\) | −2.06981 | −0.135890 | ||||||||
\(233\) | −23.6396 | −1.54868 | −0.774342 | − | 0.632768i | \(-0.781919\pi\) | ||||
−0.774342 | + | 0.632768i | \(0.781919\pi\) | |||||||
\(234\) | −1.26426 | −0.0826470 | ||||||||
\(235\) | −1.89428 | −0.123569 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | −7.12879 | −0.463065 | ||||||||
\(238\) | 0.636539 | 0.0412607 | ||||||||
\(239\) | 20.6309 | 1.33450 | 0.667252 | − | 0.744832i | \(-0.267471\pi\) | ||||
0.667252 | + | 0.744832i | \(0.267471\pi\) | |||||||
\(240\) | −2.86769 | −0.185109 | ||||||||
\(241\) | 19.8421 | 1.27814 | 0.639072 | − | 0.769147i | \(-0.279319\pi\) | ||||
0.639072 | + | 0.769147i | \(0.279319\pi\) | |||||||
\(242\) | 1.49402 | 0.0960389 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −10.1283 | −0.648396 | ||||||||
\(245\) | −18.9119 | −1.20824 | ||||||||
\(246\) | −7.06013 | −0.450137 | ||||||||
\(247\) | 8.53894 | 0.543320 | ||||||||
\(248\) | −8.03376 | −0.510144 | ||||||||
\(249\) | −14.6054 | −0.925578 | ||||||||
\(250\) | 5.09400 | 0.322173 | ||||||||
\(251\) | 15.3852 | 0.971104 | 0.485552 | − | 0.874208i | \(-0.338619\pi\) | ||||
0.485552 | + | 0.874208i | \(0.338619\pi\) | |||||||
\(252\) | 0.636539 | 0.0400982 | ||||||||
\(253\) | 18.8853 | 1.18731 | ||||||||
\(254\) | 9.67015 | 0.606759 | ||||||||
\(255\) | 2.86769 | 0.179582 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.7400 | −1.23135 | −0.615673 | − | 0.788002i | \(-0.711116\pi\) | ||||
−0.615673 | + | 0.788002i | \(0.711116\pi\) | |||||||
\(258\) | 6.55402 | 0.408035 | ||||||||
\(259\) | −0.562841 | −0.0349732 | ||||||||
\(260\) | 3.62550 | 0.224844 | ||||||||
\(261\) | 2.06981 | 0.128118 | ||||||||
\(262\) | −12.1575 | −0.751091 | ||||||||
\(263\) | −9.87594 | −0.608977 | −0.304488 | − | 0.952516i | \(-0.598485\pi\) | ||||
−0.304488 | + | 0.952516i | \(0.598485\pi\) | |||||||
\(264\) | −3.08318 | −0.189756 | ||||||||
\(265\) | 8.12791 | 0.499293 | ||||||||
\(266\) | −4.29926 | −0.263605 | ||||||||
\(267\) | −1.32107 | −0.0808480 | ||||||||
\(268\) | 0.0139862 | 0.000854342 0 | ||||||||
\(269\) | 14.3719 | 0.876268 | 0.438134 | − | 0.898910i | \(-0.355639\pi\) | ||||
0.438134 | + | 0.898910i | \(0.355639\pi\) | |||||||
\(270\) | 2.86769 | 0.174522 | ||||||||
\(271\) | −20.9059 | −1.26994 | −0.634971 | − | 0.772536i | \(-0.718988\pi\) | ||||
−0.634971 | + | 0.772536i | \(0.718988\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −0.804748 | −0.0487056 | ||||||||
\(274\) | 16.0035 | 0.966804 | ||||||||
\(275\) | −9.93912 | −0.599351 | ||||||||
\(276\) | 6.12526 | 0.368697 | ||||||||
\(277\) | 20.3650 | 1.22361 | 0.611807 | − | 0.791007i | \(-0.290443\pi\) | ||||
0.611807 | + | 0.791007i | \(0.290443\pi\) | |||||||
\(278\) | 20.1857 | 1.21066 | ||||||||
\(279\) | 8.03376 | 0.480969 | ||||||||
\(280\) | −1.82540 | −0.109088 | ||||||||
\(281\) | −6.13616 | −0.366053 | −0.183026 | − | 0.983108i | \(-0.558589\pi\) | ||||
−0.183026 | + | 0.983108i | \(0.558589\pi\) | |||||||
\(282\) | −0.660560 | −0.0393358 | ||||||||
\(283\) | −4.66780 | −0.277472 | −0.138736 | − | 0.990329i | \(-0.544304\pi\) | ||||
−0.138736 | + | 0.990329i | \(0.544304\pi\) | |||||||
\(284\) | 5.73708 | 0.340433 | ||||||||
\(285\) | −19.3687 | −1.14731 | ||||||||
\(286\) | 3.89793 | 0.230489 | ||||||||
\(287\) | −4.49405 | −0.265275 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −5.93557 | −0.348549 | ||||||||
\(291\) | −15.2562 | −0.894335 | ||||||||
\(292\) | 6.30289 | 0.368849 | ||||||||
\(293\) | −25.8627 | −1.51091 | −0.755457 | − | 0.655199i | \(-0.772585\pi\) | ||||
−0.755457 | + | 0.655199i | \(0.772585\pi\) | |||||||
\(294\) | −6.59482 | −0.384618 | ||||||||
\(295\) | 2.86769 | 0.166964 | ||||||||
\(296\) | 0.884221 | 0.0513943 | ||||||||
\(297\) | 3.08318 | 0.178904 | ||||||||
\(298\) | 16.2296 | 0.940158 | ||||||||
\(299\) | −7.74390 | −0.447841 | ||||||||
\(300\) | −3.22366 | −0.186118 | ||||||||
\(301\) | 4.17189 | 0.240464 | ||||||||
\(302\) | 4.37879 | 0.251971 | ||||||||
\(303\) | −4.52152 | −0.259754 | ||||||||
\(304\) | 6.75412 | 0.387376 | ||||||||
\(305\) | −29.0448 | −1.66310 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 2.39542 | 0.136714 | 0.0683568 | − | 0.997661i | \(-0.478224\pi\) | ||||
0.0683568 | + | 0.997661i | \(0.478224\pi\) | |||||||
\(308\) | −1.96256 | −0.111827 | ||||||||
\(309\) | −18.1452 | −1.03224 | ||||||||
\(310\) | −23.0384 | −1.30849 | ||||||||
\(311\) | −2.92768 | −0.166013 | −0.0830067 | − | 0.996549i | \(-0.526452\pi\) | ||||
−0.0830067 | + | 0.996549i | \(0.526452\pi\) | |||||||
\(312\) | 1.26426 | 0.0715744 | ||||||||
\(313\) | 9.91154 | 0.560233 | 0.280117 | − | 0.959966i | \(-0.409627\pi\) | ||||
0.280117 | + | 0.959966i | \(0.409627\pi\) | |||||||
\(314\) | −10.5021 | −0.592665 | ||||||||
\(315\) | 1.82540 | 0.102850 | ||||||||
\(316\) | 7.12879 | 0.401026 | ||||||||
\(317\) | 7.04898 | 0.395910 | 0.197955 | − | 0.980211i | \(-0.436570\pi\) | ||||
0.197955 | + | 0.980211i | \(0.436570\pi\) | |||||||
\(318\) | 2.83430 | 0.158940 | ||||||||
\(319\) | −6.38159 | −0.357300 | ||||||||
\(320\) | 2.86769 | 0.160309 | ||||||||
\(321\) | −6.90533 | −0.385418 | ||||||||
\(322\) | 3.89897 | 0.217281 | ||||||||
\(323\) | −6.75412 | −0.375809 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.07553 | 0.226070 | ||||||||
\(326\) | −14.2087 | −0.786945 | ||||||||
\(327\) | −2.23129 | −0.123391 | ||||||||
\(328\) | 7.06013 | 0.389830 | ||||||||
\(329\) | −0.420472 | −0.0231814 | ||||||||
\(330\) | −8.84161 | −0.486714 | ||||||||
\(331\) | 19.4349 | 1.06824 | 0.534120 | − | 0.845409i | \(-0.320643\pi\) | ||||
0.534120 | + | 0.845409i | \(0.320643\pi\) | |||||||
\(332\) | 14.6054 | 0.801574 | ||||||||
\(333\) | −0.884221 | −0.0484550 | ||||||||
\(334\) | −9.29493 | −0.508596 | ||||||||
\(335\) | 0.0401080 | 0.00219134 | ||||||||
\(336\) | −0.636539 | −0.0347260 | ||||||||
\(337\) | 8.43905 | 0.459704 | 0.229852 | − | 0.973226i | \(-0.426176\pi\) | ||||
0.229852 | + | 0.973226i | \(0.426176\pi\) | |||||||
\(338\) | 11.4017 | 0.620168 | ||||||||
\(339\) | −9.41503 | −0.511354 | ||||||||
\(340\) | −2.86769 | −0.155522 | ||||||||
\(341\) | −24.7695 | −1.34134 | ||||||||
\(342\) | −6.75412 | −0.365221 | ||||||||
\(343\) | −8.65363 | −0.467252 | ||||||||
\(344\) | −6.55402 | −0.353369 | ||||||||
\(345\) | 17.5654 | 0.945687 | ||||||||
\(346\) | −13.4939 | −0.725436 | ||||||||
\(347\) | 20.3612 | 1.09305 | 0.546524 | − | 0.837443i | \(-0.315951\pi\) | ||||
0.546524 | + | 0.837443i | \(0.315951\pi\) | |||||||
\(348\) | −2.06981 | −0.110953 | ||||||||
\(349\) | 23.9847 | 1.28387 | 0.641935 | − | 0.766759i | \(-0.278132\pi\) | ||||
0.641935 | + | 0.766759i | \(0.278132\pi\) | |||||||
\(350\) | −2.05199 | −0.109683 | ||||||||
\(351\) | −1.26426 | −0.0674810 | ||||||||
\(352\) | 3.08318 | 0.164334 | ||||||||
\(353\) | 1.45037 | 0.0771956 | 0.0385978 | − | 0.999255i | \(-0.487711\pi\) | ||||
0.0385978 | + | 0.999255i | \(0.487711\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | 16.4522 | 0.873192 | ||||||||
\(356\) | 1.32107 | 0.0700164 | ||||||||
\(357\) | 0.636539 | 0.0336892 | ||||||||
\(358\) | 10.8405 | 0.572936 | ||||||||
\(359\) | −28.2900 | −1.49309 | −0.746543 | − | 0.665337i | \(-0.768288\pi\) | ||||
−0.746543 | + | 0.665337i | \(0.768288\pi\) | |||||||
\(360\) | −2.86769 | −0.151141 | ||||||||
\(361\) | 26.6182 | 1.40096 | ||||||||
\(362\) | 0.350673 | 0.0184310 | ||||||||
\(363\) | 1.49402 | 0.0784155 | ||||||||
\(364\) | 0.804748 | 0.0421803 | ||||||||
\(365\) | 18.0748 | 0.946076 | ||||||||
\(366\) | −10.1283 | −0.529413 | ||||||||
\(367\) | 19.5178 | 1.01882 | 0.509411 | − | 0.860523i | \(-0.329863\pi\) | ||||
0.509411 | + | 0.860523i | \(0.329863\pi\) | |||||||
\(368\) | −6.12526 | −0.319301 | ||||||||
\(369\) | −7.06013 | −0.367536 | ||||||||
\(370\) | 2.53567 | 0.131823 | ||||||||
\(371\) | 1.80414 | 0.0936665 | ||||||||
\(372\) | −8.03376 | −0.416531 | ||||||||
\(373\) | −6.22265 | −0.322196 | −0.161098 | − | 0.986938i | \(-0.551504\pi\) | ||||
−0.161098 | + | 0.986938i | \(0.551504\pi\) | |||||||
\(374\) | −3.08318 | −0.159427 | ||||||||
\(375\) | 5.09400 | 0.263053 | ||||||||
\(376\) | 0.660560 | 0.0340658 | ||||||||
\(377\) | 2.61677 | 0.134770 | ||||||||
\(378\) | 0.636539 | 0.0327400 | ||||||||
\(379\) | −20.5389 | −1.05501 | −0.527507 | − | 0.849551i | \(-0.676873\pi\) | ||||
−0.527507 | + | 0.849551i | \(0.676873\pi\) | |||||||
\(380\) | 19.3687 | 0.993596 | ||||||||
\(381\) | 9.67015 | 0.495417 | ||||||||
\(382\) | 5.71664 | 0.292489 | ||||||||
\(383\) | 24.5322 | 1.25354 | 0.626769 | − | 0.779205i | \(-0.284377\pi\) | ||||
0.626769 | + | 0.779205i | \(0.284377\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −5.62803 | −0.286831 | ||||||||
\(386\) | 18.2524 | 0.929025 | ||||||||
\(387\) | 6.55402 | 0.333160 | ||||||||
\(388\) | 15.2562 | 0.774517 | ||||||||
\(389\) | −14.9943 | −0.760241 | −0.380120 | − | 0.924937i | \(-0.624117\pi\) | ||||
−0.380120 | + | 0.924937i | \(0.624117\pi\) | |||||||
\(390\) | 3.62550 | 0.183584 | ||||||||
\(391\) | 6.12526 | 0.309768 | ||||||||
\(392\) | 6.59482 | 0.333089 | ||||||||
\(393\) | −12.1575 | −0.613263 | ||||||||
\(394\) | −16.0335 | −0.807756 | ||||||||
\(395\) | 20.4432 | 1.02861 | ||||||||
\(396\) | −3.08318 | −0.154936 | ||||||||
\(397\) | 16.9911 | 0.852757 | 0.426378 | − | 0.904545i | \(-0.359789\pi\) | ||||
0.426378 | + | 0.904545i | \(0.359789\pi\) | |||||||
\(398\) | −14.7301 | −0.738352 | ||||||||
\(399\) | −4.29926 | −0.215232 | ||||||||
\(400\) | 3.22366 | 0.161183 | ||||||||
\(401\) | 9.16169 | 0.457513 | 0.228756 | − | 0.973484i | \(-0.426534\pi\) | ||||
0.228756 | + | 0.973484i | \(0.426534\pi\) | |||||||
\(402\) | 0.0139862 | 0.000697567 0 | ||||||||
\(403\) | 10.1567 | 0.505943 | ||||||||
\(404\) | 4.52152 | 0.224954 | ||||||||
\(405\) | 2.86769 | 0.142497 | ||||||||
\(406\) | −1.31751 | −0.0653871 | ||||||||
\(407\) | 2.72621 | 0.135133 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | 9.77838 | 0.483510 | 0.241755 | − | 0.970337i | \(-0.422277\pi\) | ||||
0.241755 | + | 0.970337i | \(0.422277\pi\) | |||||||
\(410\) | 20.2463 | 0.999892 | ||||||||
\(411\) | 16.0035 | 0.789392 | ||||||||
\(412\) | 18.1452 | 0.893948 | ||||||||
\(413\) | 0.636539 | 0.0313220 | ||||||||
\(414\) | 6.12526 | 0.301040 | ||||||||
\(415\) | 41.8837 | 2.05599 | ||||||||
\(416\) | −1.26426 | −0.0619853 | ||||||||
\(417\) | 20.1857 | 0.988500 | ||||||||
\(418\) | 20.8242 | 1.01854 | ||||||||
\(419\) | −12.0030 | −0.586385 | −0.293193 | − | 0.956053i | \(-0.594718\pi\) | ||||
−0.293193 | + | 0.956053i | \(0.594718\pi\) | |||||||
\(420\) | −1.82540 | −0.0890703 | ||||||||
\(421\) | −16.6688 | −0.812386 | −0.406193 | − | 0.913787i | \(-0.633144\pi\) | ||||
−0.406193 | + | 0.913787i | \(0.633144\pi\) | |||||||
\(422\) | −18.1318 | −0.882644 | ||||||||
\(423\) | −0.660560 | −0.0321175 | ||||||||
\(424\) | −2.83430 | −0.137646 | ||||||||
\(425\) | −3.22366 | −0.156371 | ||||||||
\(426\) | 5.73708 | 0.277963 | ||||||||
\(427\) | −6.44704 | −0.311994 | ||||||||
\(428\) | 6.90533 | 0.333782 | ||||||||
\(429\) | 3.89793 | 0.188194 | ||||||||
\(430\) | −18.7949 | −0.906371 | ||||||||
\(431\) | −8.75516 | −0.421721 | −0.210860 | − | 0.977516i | \(-0.567627\pi\) | ||||
−0.210860 | + | 0.977516i | \(0.567627\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −29.7186 | −1.42819 | −0.714093 | − | 0.700051i | \(-0.753161\pi\) | ||||
−0.714093 | + | 0.700051i | \(0.753161\pi\) | |||||||
\(434\) | −5.11380 | −0.245470 | ||||||||
\(435\) | −5.93557 | −0.284589 | ||||||||
\(436\) | 2.23129 | 0.106859 | ||||||||
\(437\) | −41.3708 | −1.97903 | ||||||||
\(438\) | 6.30289 | 0.301164 | ||||||||
\(439\) | −33.6068 | −1.60396 | −0.801982 | − | 0.597348i | \(-0.796221\pi\) | ||||
−0.801982 | + | 0.597348i | \(0.796221\pi\) | |||||||
\(440\) | 8.84161 | 0.421507 | ||||||||
\(441\) | −6.59482 | −0.314039 | ||||||||
\(442\) | 1.26426 | 0.0601345 | ||||||||
\(443\) | 21.8571 | 1.03846 | 0.519232 | − | 0.854634i | \(-0.326218\pi\) | ||||
0.519232 | + | 0.854634i | \(0.326218\pi\) | |||||||
\(444\) | 0.884221 | 0.0419633 | ||||||||
\(445\) | 3.78842 | 0.179588 | ||||||||
\(446\) | −5.29242 | −0.250604 | ||||||||
\(447\) | 16.2296 | 0.767635 | ||||||||
\(448\) | 0.636539 | 0.0300736 | ||||||||
\(449\) | 0.330027 | 0.0155750 | 0.00778748 | − | 0.999970i | \(-0.497521\pi\) | ||||
0.00778748 | + | 0.999970i | \(0.497521\pi\) | |||||||
\(450\) | −3.22366 | −0.151965 | ||||||||
\(451\) | 21.7676 | 1.02500 | ||||||||
\(452\) | 9.41503 | 0.442846 | ||||||||
\(453\) | 4.37879 | 0.205733 | ||||||||
\(454\) | −5.38961 | −0.252947 | ||||||||
\(455\) | 2.30777 | 0.108190 | ||||||||
\(456\) | 6.75412 | 0.316291 | ||||||||
\(457\) | 23.9610 | 1.12085 | 0.560423 | − | 0.828207i | \(-0.310639\pi\) | ||||
0.560423 | + | 0.828207i | \(0.310639\pi\) | |||||||
\(458\) | 7.41385 | 0.346426 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −17.5654 | −0.818989 | ||||||||
\(461\) | 15.4035 | 0.717411 | 0.358705 | − | 0.933451i | \(-0.383218\pi\) | ||||
0.358705 | + | 0.933451i | \(0.383218\pi\) | |||||||
\(462\) | −1.96256 | −0.0913067 | ||||||||
\(463\) | 9.07029 | 0.421532 | 0.210766 | − | 0.977537i | \(-0.432404\pi\) | ||||
0.210766 | + | 0.977537i | \(0.432404\pi\) | |||||||
\(464\) | 2.06981 | 0.0960884 | ||||||||
\(465\) | −23.0384 | −1.06838 | ||||||||
\(466\) | 23.6396 | 1.09508 | ||||||||
\(467\) | 9.37346 | 0.433752 | 0.216876 | − | 0.976199i | \(-0.430413\pi\) | ||||
0.216876 | + | 0.976199i | \(0.430413\pi\) | |||||||
\(468\) | 1.26426 | 0.0584403 | ||||||||
\(469\) | 0.00890274 | 0.000411091 0 | ||||||||
\(470\) | 1.89428 | 0.0873768 | ||||||||
\(471\) | −10.5021 | −0.483909 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −20.2072 | −0.929128 | ||||||||
\(474\) | 7.12879 | 0.327436 | ||||||||
\(475\) | 21.7730 | 0.999014 | ||||||||
\(476\) | −0.636539 | −0.0291757 | ||||||||
\(477\) | 2.83430 | 0.129774 | ||||||||
\(478\) | −20.6309 | −0.943636 | ||||||||
\(479\) | 19.9688 | 0.912399 | 0.456199 | − | 0.889878i | \(-0.349210\pi\) | ||||
0.456199 | + | 0.889878i | \(0.349210\pi\) | |||||||
\(480\) | 2.86769 | 0.130892 | ||||||||
\(481\) | −1.11788 | −0.0509710 | ||||||||
\(482\) | −19.8421 | −0.903784 | ||||||||
\(483\) | 3.89897 | 0.177409 | ||||||||
\(484\) | −1.49402 | −0.0679098 | ||||||||
\(485\) | 43.7501 | 1.98659 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 2.20781 | 0.100046 | 0.0500228 | − | 0.998748i | \(-0.484071\pi\) | ||||
0.0500228 | + | 0.998748i | \(0.484071\pi\) | |||||||
\(488\) | 10.1283 | 0.458485 | ||||||||
\(489\) | −14.2087 | −0.642538 | ||||||||
\(490\) | 18.9119 | 0.854353 | ||||||||
\(491\) | −7.72087 | −0.348438 | −0.174219 | − | 0.984707i | \(-0.555740\pi\) | ||||
−0.174219 | + | 0.984707i | \(0.555740\pi\) | |||||||
\(492\) | 7.06013 | 0.318295 | ||||||||
\(493\) | −2.06981 | −0.0932195 | ||||||||
\(494\) | −8.53894 | −0.384185 | ||||||||
\(495\) | −8.84161 | −0.397401 | ||||||||
\(496\) | 8.03376 | 0.360726 | ||||||||
\(497\) | 3.65188 | 0.163809 | ||||||||
\(498\) | 14.6054 | 0.654483 | ||||||||
\(499\) | 23.7571 | 1.06351 | 0.531757 | − | 0.846897i | \(-0.321532\pi\) | ||||
0.531757 | + | 0.846897i | \(0.321532\pi\) | |||||||
\(500\) | −5.09400 | −0.227810 | ||||||||
\(501\) | −9.29493 | −0.415267 | ||||||||
\(502\) | −15.3852 | −0.686674 | ||||||||
\(503\) | −16.5416 | −0.737555 | −0.368777 | − | 0.929518i | \(-0.620224\pi\) | ||||
−0.368777 | + | 0.929518i | \(0.620224\pi\) | |||||||
\(504\) | −0.636539 | −0.0283537 | ||||||||
\(505\) | 12.9663 | 0.576994 | ||||||||
\(506\) | −18.8853 | −0.839552 | ||||||||
\(507\) | 11.4017 | 0.506365 | ||||||||
\(508\) | −9.67015 | −0.429044 | ||||||||
\(509\) | 37.4627 | 1.66050 | 0.830252 | − | 0.557388i | \(-0.188196\pi\) | ||||
0.830252 | + | 0.557388i | \(0.188196\pi\) | |||||||
\(510\) | −2.86769 | −0.126984 | ||||||||
\(511\) | 4.01203 | 0.177482 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.75412 | −0.298202 | ||||||||
\(514\) | 19.7400 | 0.870693 | ||||||||
\(515\) | 52.0347 | 2.29292 | ||||||||
\(516\) | −6.55402 | −0.288525 | ||||||||
\(517\) | 2.03662 | 0.0895707 | ||||||||
\(518\) | 0.562841 | 0.0247298 | ||||||||
\(519\) | −13.4939 | −0.592316 | ||||||||
\(520\) | −3.62550 | −0.158989 | ||||||||
\(521\) | −29.0834 | −1.27417 | −0.637083 | − | 0.770795i | \(-0.719859\pi\) | ||||
−0.637083 | + | 0.770795i | \(0.719859\pi\) | |||||||
\(522\) | −2.06981 | −0.0905930 | ||||||||
\(523\) | −7.03125 | −0.307455 | −0.153728 | − | 0.988113i | \(-0.549128\pi\) | ||||
−0.153728 | + | 0.988113i | \(0.549128\pi\) | |||||||
\(524\) | 12.1575 | 0.531101 | ||||||||
\(525\) | −2.05199 | −0.0895560 | ||||||||
\(526\) | 9.87594 | 0.430612 | ||||||||
\(527\) | −8.03376 | −0.349956 | ||||||||
\(528\) | 3.08318 | 0.134178 | ||||||||
\(529\) | 14.5188 | 0.631252 | ||||||||
\(530\) | −8.12791 | −0.353054 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 4.29926 | 0.186397 | ||||||||
\(533\) | −8.92581 | −0.386620 | ||||||||
\(534\) | 1.32107 | 0.0571682 | ||||||||
\(535\) | 19.8024 | 0.856131 | ||||||||
\(536\) | −0.0139862 | −0.000604111 0 | ||||||||
\(537\) | 10.8405 | 0.467800 | ||||||||
\(538\) | −14.3719 | −0.619615 | ||||||||
\(539\) | 20.3330 | 0.875804 | ||||||||
\(540\) | −2.86769 | −0.123406 | ||||||||
\(541\) | 23.3056 | 1.00198 | 0.500992 | − | 0.865452i | \(-0.332969\pi\) | ||||
0.500992 | + | 0.865452i | \(0.332969\pi\) | |||||||
\(542\) | 20.9059 | 0.897984 | ||||||||
\(543\) | 0.350673 | 0.0150488 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 6.39865 | 0.274088 | ||||||||
\(546\) | 0.804748 | 0.0344400 | ||||||||
\(547\) | 16.2453 | 0.694599 | 0.347300 | − | 0.937754i | \(-0.387099\pi\) | ||||
0.347300 | + | 0.937754i | \(0.387099\pi\) | |||||||
\(548\) | −16.0035 | −0.683634 | ||||||||
\(549\) | −10.1283 | −0.432264 | ||||||||
\(550\) | 9.93912 | 0.423805 | ||||||||
\(551\) | 13.9797 | 0.595557 | ||||||||
\(552\) | −6.12526 | −0.260708 | ||||||||
\(553\) | 4.53775 | 0.192965 | ||||||||
\(554\) | −20.3650 | −0.865226 | ||||||||
\(555\) | 2.53567 | 0.107633 | ||||||||
\(556\) | −20.1857 | −0.856066 | ||||||||
\(557\) | −33.3654 | −1.41374 | −0.706868 | − | 0.707345i | \(-0.749893\pi\) | ||||
−0.706868 | + | 0.707345i | \(0.749893\pi\) | |||||||
\(558\) | −8.03376 | −0.340096 | ||||||||
\(559\) | 8.28596 | 0.350459 | ||||||||
\(560\) | 1.82540 | 0.0771371 | ||||||||
\(561\) | −3.08318 | −0.130172 | ||||||||
\(562\) | 6.13616 | 0.258838 | ||||||||
\(563\) | 0.176635 | 0.00744427 | 0.00372214 | − | 0.999993i | \(-0.498815\pi\) | ||||
0.00372214 | + | 0.999993i | \(0.498815\pi\) | |||||||
\(564\) | 0.660560 | 0.0278146 | ||||||||
\(565\) | 26.9994 | 1.13587 | ||||||||
\(566\) | 4.66780 | 0.196202 | ||||||||
\(567\) | 0.636539 | 0.0267321 | ||||||||
\(568\) | −5.73708 | −0.240723 | ||||||||
\(569\) | 21.3506 | 0.895062 | 0.447531 | − | 0.894268i | \(-0.352303\pi\) | ||||
0.447531 | + | 0.894268i | \(0.352303\pi\) | |||||||
\(570\) | 19.3687 | 0.811268 | ||||||||
\(571\) | 8.10989 | 0.339388 | 0.169694 | − | 0.985497i | \(-0.445722\pi\) | ||||
0.169694 | + | 0.985497i | \(0.445722\pi\) | |||||||
\(572\) | −3.89793 | −0.162980 | ||||||||
\(573\) | 5.71664 | 0.238816 | ||||||||
\(574\) | 4.49405 | 0.187578 | ||||||||
\(575\) | −19.7458 | −0.823455 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 21.7216 | 0.904284 | 0.452142 | − | 0.891946i | \(-0.350660\pi\) | ||||
0.452142 | + | 0.891946i | \(0.350660\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 18.2524 | 0.758546 | ||||||||
\(580\) | 5.93557 | 0.246461 | ||||||||
\(581\) | 9.29689 | 0.385700 | ||||||||
\(582\) | 15.2562 | 0.632390 | ||||||||
\(583\) | −8.73866 | −0.361918 | ||||||||
\(584\) | −6.30289 | −0.260815 | ||||||||
\(585\) | 3.62550 | 0.149896 | ||||||||
\(586\) | 25.8627 | 1.06838 | ||||||||
\(587\) | 3.88011 | 0.160149 | 0.0800746 | − | 0.996789i | \(-0.474484\pi\) | ||||
0.0800746 | + | 0.996789i | \(0.474484\pi\) | |||||||
\(588\) | 6.59482 | 0.271966 | ||||||||
\(589\) | 54.2610 | 2.23579 | ||||||||
\(590\) | −2.86769 | −0.118061 | ||||||||
\(591\) | −16.0335 | −0.659530 | ||||||||
\(592\) | −0.884221 | −0.0363413 | ||||||||
\(593\) | 32.1503 | 1.32025 | 0.660126 | − | 0.751155i | \(-0.270503\pi\) | ||||
0.660126 | + | 0.751155i | \(0.270503\pi\) | |||||||
\(594\) | −3.08318 | −0.126504 | ||||||||
\(595\) | −1.82540 | −0.0748340 | ||||||||
\(596\) | −16.2296 | −0.664792 | ||||||||
\(597\) | −14.7301 | −0.602862 | ||||||||
\(598\) | 7.74390 | 0.316671 | ||||||||
\(599\) | 32.2735 | 1.31866 | 0.659329 | − | 0.751854i | \(-0.270840\pi\) | ||||
0.659329 | + | 0.751854i | \(0.270840\pi\) | |||||||
\(600\) | 3.22366 | 0.131605 | ||||||||
\(601\) | 35.6452 | 1.45400 | 0.726999 | − | 0.686639i | \(-0.240915\pi\) | ||||
0.726999 | + | 0.686639i | \(0.240915\pi\) | |||||||
\(602\) | −4.17189 | −0.170033 | ||||||||
\(603\) | 0.0139862 | 0.000569561 0 | ||||||||
\(604\) | −4.37879 | −0.178170 | ||||||||
\(605\) | −4.28438 | −0.174185 | ||||||||
\(606\) | 4.52152 | 0.183674 | ||||||||
\(607\) | 32.5590 | 1.32153 | 0.660765 | − | 0.750593i | \(-0.270232\pi\) | ||||
0.660765 | + | 0.750593i | \(0.270232\pi\) | |||||||
\(608\) | −6.75412 | −0.273916 | ||||||||
\(609\) | −1.31751 | −0.0533883 | ||||||||
\(610\) | 29.0448 | 1.17599 | ||||||||
\(611\) | −0.835117 | −0.0337852 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −13.6814 | −0.552588 | −0.276294 | − | 0.961073i | \(-0.589106\pi\) | ||||
−0.276294 | + | 0.961073i | \(0.589106\pi\) | |||||||
\(614\) | −2.39542 | −0.0966711 | ||||||||
\(615\) | 20.2463 | 0.816409 | ||||||||
\(616\) | 1.96256 | 0.0790739 | ||||||||
\(617\) | −20.4629 | −0.823803 | −0.411902 | − | 0.911228i | \(-0.635135\pi\) | ||||
−0.411902 | + | 0.911228i | \(0.635135\pi\) | |||||||
\(618\) | 18.1452 | 0.729905 | ||||||||
\(619\) | 33.8274 | 1.35964 | 0.679819 | − | 0.733380i | \(-0.262058\pi\) | ||||
0.679819 | + | 0.733380i | \(0.262058\pi\) | |||||||
\(620\) | 23.0384 | 0.925243 | ||||||||
\(621\) | 6.12526 | 0.245798 | ||||||||
\(622\) | 2.92768 | 0.117389 | ||||||||
\(623\) | 0.840911 | 0.0336904 | ||||||||
\(624\) | −1.26426 | −0.0506107 | ||||||||
\(625\) | −30.7263 | −1.22905 | ||||||||
\(626\) | −9.91154 | −0.396145 | ||||||||
\(627\) | 20.8242 | 0.831637 | ||||||||
\(628\) | 10.5021 | 0.419078 | ||||||||
\(629\) | 0.884221 | 0.0352562 | ||||||||
\(630\) | −1.82540 | −0.0727256 | ||||||||
\(631\) | −35.3128 | −1.40578 | −0.702890 | − | 0.711298i | \(-0.748107\pi\) | ||||
−0.702890 | + | 0.711298i | \(0.748107\pi\) | |||||||
\(632\) | −7.12879 | −0.283568 | ||||||||
\(633\) | −18.1318 | −0.720676 | ||||||||
\(634\) | −7.04898 | −0.279951 | ||||||||
\(635\) | −27.7310 | −1.10047 | ||||||||
\(636\) | −2.83430 | −0.112387 | ||||||||
\(637\) | −8.33754 | −0.330345 | ||||||||
\(638\) | 6.38159 | 0.252649 | ||||||||
\(639\) | 5.73708 | 0.226956 | ||||||||
\(640\) | −2.86769 | −0.113356 | ||||||||
\(641\) | −10.1247 | −0.399902 | −0.199951 | − | 0.979806i | \(-0.564078\pi\) | ||||
−0.199951 | + | 0.979806i | \(0.564078\pi\) | |||||||
\(642\) | 6.90533 | 0.272532 | ||||||||
\(643\) | 17.8410 | 0.703579 | 0.351790 | − | 0.936079i | \(-0.385573\pi\) | ||||
0.351790 | + | 0.936079i | \(0.385573\pi\) | |||||||
\(644\) | −3.89897 | −0.153641 | ||||||||
\(645\) | −18.7949 | −0.740049 | ||||||||
\(646\) | 6.75412 | 0.265737 | ||||||||
\(647\) | −9.26085 | −0.364082 | −0.182041 | − | 0.983291i | \(-0.558270\pi\) | ||||
−0.182041 | + | 0.983291i | \(0.558270\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −3.08318 | −0.121025 | ||||||||
\(650\) | −4.07553 | −0.159856 | ||||||||
\(651\) | −5.11380 | −0.200426 | ||||||||
\(652\) | 14.2087 | 0.556454 | ||||||||
\(653\) | 48.0871 | 1.88179 | 0.940897 | − | 0.338694i | \(-0.109985\pi\) | ||||
0.940897 | + | 0.338694i | \(0.109985\pi\) | |||||||
\(654\) | 2.23129 | 0.0872503 | ||||||||
\(655\) | 34.8639 | 1.36224 | ||||||||
\(656\) | −7.06013 | −0.275652 | ||||||||
\(657\) | 6.30289 | 0.245899 | ||||||||
\(658\) | 0.420472 | 0.0163917 | ||||||||
\(659\) | −35.8621 | −1.39699 | −0.698495 | − | 0.715615i | \(-0.746146\pi\) | ||||
−0.698495 | + | 0.715615i | \(0.746146\pi\) | |||||||
\(660\) | 8.84161 | 0.344159 | ||||||||
\(661\) | 20.9952 | 0.816620 | 0.408310 | − | 0.912843i | \(-0.366118\pi\) | ||||
0.408310 | + | 0.912843i | \(0.366118\pi\) | |||||||
\(662\) | −19.4349 | −0.755359 | ||||||||
\(663\) | 1.26426 | 0.0490996 | ||||||||
\(664\) | −14.6054 | −0.566799 | ||||||||
\(665\) | 12.3290 | 0.478097 | ||||||||
\(666\) | 0.884221 | 0.0342629 | ||||||||
\(667\) | −12.6781 | −0.490898 | ||||||||
\(668\) | 9.29493 | 0.359632 | ||||||||
\(669\) | −5.29242 | −0.204617 | ||||||||
\(670\) | −0.0401080 | −0.00154951 | ||||||||
\(671\) | 31.2273 | 1.20552 | ||||||||
\(672\) | 0.636539 | 0.0245550 | ||||||||
\(673\) | 0.321940 | 0.0124099 | 0.00620494 | − | 0.999981i | \(-0.498025\pi\) | ||||
0.00620494 | + | 0.999981i | \(0.498025\pi\) | |||||||
\(674\) | −8.43905 | −0.325060 | ||||||||
\(675\) | −3.22366 | −0.124079 | ||||||||
\(676\) | −11.4017 | −0.438525 | ||||||||
\(677\) | 20.9026 | 0.803354 | 0.401677 | − | 0.915781i | \(-0.368427\pi\) | ||||
0.401677 | + | 0.915781i | \(0.368427\pi\) | |||||||
\(678\) | 9.41503 | 0.361582 | ||||||||
\(679\) | 9.71117 | 0.372681 | ||||||||
\(680\) | 2.86769 | 0.109971 | ||||||||
\(681\) | −5.38961 | −0.206530 | ||||||||
\(682\) | 24.7695 | 0.948474 | ||||||||
\(683\) | −14.4561 | −0.553146 | −0.276573 | − | 0.960993i | \(-0.589199\pi\) | ||||
−0.276573 | + | 0.960993i | \(0.589199\pi\) | |||||||
\(684\) | 6.75412 | 0.258250 | ||||||||
\(685\) | −45.8930 | −1.75348 | ||||||||
\(686\) | 8.65363 | 0.330397 | ||||||||
\(687\) | 7.41385 | 0.282856 | ||||||||
\(688\) | 6.55402 | 0.249870 | ||||||||
\(689\) | 3.58328 | 0.136512 | ||||||||
\(690\) | −17.5654 | −0.668702 | ||||||||
\(691\) | 9.18531 | 0.349426 | 0.174713 | − | 0.984619i | \(-0.444100\pi\) | ||||
0.174713 | + | 0.984619i | \(0.444100\pi\) | |||||||
\(692\) | 13.4939 | 0.512961 | ||||||||
\(693\) | −1.96256 | −0.0745516 | ||||||||
\(694\) | −20.3612 | −0.772902 | ||||||||
\(695\) | −57.8865 | −2.19576 | ||||||||
\(696\) | 2.06981 | 0.0784559 | ||||||||
\(697\) | 7.06013 | 0.267421 | ||||||||
\(698\) | −23.9847 | −0.907833 | ||||||||
\(699\) | 23.6396 | 0.894133 | ||||||||
\(700\) | 2.05199 | 0.0775578 | ||||||||
\(701\) | −16.3096 | −0.616004 | −0.308002 | − | 0.951386i | \(-0.599660\pi\) | ||||
−0.308002 | + | 0.951386i | \(0.599660\pi\) | |||||||
\(702\) | 1.26426 | 0.0477163 | ||||||||
\(703\) | −5.97214 | −0.225243 | ||||||||
\(704\) | −3.08318 | −0.116202 | ||||||||
\(705\) | 1.89428 | 0.0713429 | ||||||||
\(706\) | −1.45037 | −0.0545855 | ||||||||
\(707\) | 2.87812 | 0.108243 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | −15.7670 | −0.592142 | −0.296071 | − | 0.955166i | \(-0.595677\pi\) | ||||
−0.296071 | + | 0.955166i | \(0.595677\pi\) | |||||||
\(710\) | −16.4522 | −0.617440 | ||||||||
\(711\) | 7.12879 | 0.267351 | ||||||||
\(712\) | −1.32107 | −0.0495091 | ||||||||
\(713\) | −49.2089 | −1.84289 | ||||||||
\(714\) | −0.636539 | −0.0238219 | ||||||||
\(715\) | −11.1781 | −0.418036 | ||||||||
\(716\) | −10.8405 | −0.405127 | ||||||||
\(717\) | −20.6309 | −0.770476 | ||||||||
\(718\) | 28.2900 | 1.05577 | ||||||||
\(719\) | −19.5878 | −0.730500 | −0.365250 | − | 0.930909i | \(-0.619017\pi\) | ||||
−0.365250 | + | 0.930909i | \(0.619017\pi\) | |||||||
\(720\) | 2.86769 | 0.106873 | ||||||||
\(721\) | 11.5501 | 0.430148 | ||||||||
\(722\) | −26.6182 | −0.990626 | ||||||||
\(723\) | −19.8421 | −0.737937 | ||||||||
\(724\) | −0.350673 | −0.0130327 | ||||||||
\(725\) | 6.67236 | 0.247805 | ||||||||
\(726\) | −1.49402 | −0.0554481 | ||||||||
\(727\) | −38.1925 | −1.41648 | −0.708241 | − | 0.705970i | \(-0.750511\pi\) | ||||
−0.708241 | + | 0.705970i | \(0.750511\pi\) | |||||||
\(728\) | −0.804748 | −0.0298260 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −18.0748 | −0.668977 | ||||||||
\(731\) | −6.55402 | −0.242409 | ||||||||
\(732\) | 10.1283 | 0.374352 | ||||||||
\(733\) | 30.8428 | 1.13921 | 0.569603 | − | 0.821920i | \(-0.307097\pi\) | ||||
0.569603 | + | 0.821920i | \(0.307097\pi\) | |||||||
\(734\) | −19.5178 | −0.720416 | ||||||||
\(735\) | 18.9119 | 0.697576 | ||||||||
\(736\) | 6.12526 | 0.225780 | ||||||||
\(737\) | −0.0431219 | −0.00158841 | ||||||||
\(738\) | 7.06013 | 0.259887 | ||||||||
\(739\) | −33.1652 | −1.22000 | −0.610001 | − | 0.792400i | \(-0.708831\pi\) | ||||
−0.610001 | + | 0.792400i | \(0.708831\pi\) | |||||||
\(740\) | −2.53567 | −0.0932132 | ||||||||
\(741\) | −8.53894 | −0.313686 | ||||||||
\(742\) | −1.80414 | −0.0662322 | ||||||||
\(743\) | −6.83482 | −0.250745 | −0.125373 | − | 0.992110i | \(-0.540013\pi\) | ||||
−0.125373 | + | 0.992110i | \(0.540013\pi\) | |||||||
\(744\) | 8.03376 | 0.294532 | ||||||||
\(745\) | −46.5416 | −1.70515 | ||||||||
\(746\) | 6.22265 | 0.227827 | ||||||||
\(747\) | 14.6054 | 0.534383 | ||||||||
\(748\) | 3.08318 | 0.112732 | ||||||||
\(749\) | 4.39551 | 0.160609 | ||||||||
\(750\) | −5.09400 | −0.186006 | ||||||||
\(751\) | 24.7062 | 0.901543 | 0.450771 | − | 0.892639i | \(-0.351149\pi\) | ||||
0.450771 | + | 0.892639i | \(0.351149\pi\) | |||||||
\(752\) | −0.660560 | −0.0240882 | ||||||||
\(753\) | −15.3852 | −0.560667 | ||||||||
\(754\) | −2.61677 | −0.0952970 | ||||||||
\(755\) | −12.5570 | −0.456997 | ||||||||
\(756\) | −0.636539 | −0.0231507 | ||||||||
\(757\) | −31.9271 | −1.16041 | −0.580205 | − | 0.814471i | \(-0.697027\pi\) | ||||
−0.580205 | + | 0.814471i | \(0.697027\pi\) | |||||||
\(758\) | 20.5389 | 0.746007 | ||||||||
\(759\) | −18.8853 | −0.685492 | ||||||||
\(760\) | −19.3687 | −0.702578 | ||||||||
\(761\) | 46.0195 | 1.66820 | 0.834102 | − | 0.551610i | \(-0.185986\pi\) | ||||
0.834102 | + | 0.551610i | \(0.185986\pi\) | |||||||
\(762\) | −9.67015 | −0.350313 | ||||||||
\(763\) | 1.42030 | 0.0514184 | ||||||||
\(764\) | −5.71664 | −0.206821 | ||||||||
\(765\) | −2.86769 | −0.103682 | ||||||||
\(766\) | −24.5322 | −0.886385 | ||||||||
\(767\) | 1.26426 | 0.0456496 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −3.55901 | −0.128341 | −0.0641707 | − | 0.997939i | \(-0.520440\pi\) | ||||
−0.0641707 | + | 0.997939i | \(0.520440\pi\) | |||||||
\(770\) | 5.62803 | 0.202820 | ||||||||
\(771\) | 19.7400 | 0.710918 | ||||||||
\(772\) | −18.2524 | −0.656920 | ||||||||
\(773\) | 13.7187 | 0.493427 | 0.246714 | − | 0.969088i | \(-0.420649\pi\) | ||||
0.246714 | + | 0.969088i | \(0.420649\pi\) | |||||||
\(774\) | −6.55402 | −0.235579 | ||||||||
\(775\) | 25.8981 | 0.930288 | ||||||||
\(776\) | −15.2562 | −0.547666 | ||||||||
\(777\) | 0.562841 | 0.0201918 | ||||||||
\(778\) | 14.9943 | 0.537572 | ||||||||
\(779\) | −47.6850 | −1.70849 | ||||||||
\(780\) | −3.62550 | −0.129814 | ||||||||
\(781\) | −17.6885 | −0.632943 | ||||||||
\(782\) | −6.12526 | −0.219039 | ||||||||
\(783\) | −2.06981 | −0.0739689 | ||||||||
\(784\) | −6.59482 | −0.235529 | ||||||||
\(785\) | 30.1167 | 1.07491 | ||||||||
\(786\) | 12.1575 | 0.433642 | ||||||||
\(787\) | 19.6825 | 0.701606 | 0.350803 | − | 0.936449i | \(-0.385909\pi\) | ||||
0.350803 | + | 0.936449i | \(0.385909\pi\) | |||||||
\(788\) | 16.0335 | 0.571170 | ||||||||
\(789\) | 9.87594 | 0.351593 | ||||||||
\(790\) | −20.4432 | −0.727336 | ||||||||
\(791\) | 5.99303 | 0.213088 | ||||||||
\(792\) | 3.08318 | 0.109556 | ||||||||
\(793\) | −12.8047 | −0.454709 | ||||||||
\(794\) | −16.9911 | −0.602990 | ||||||||
\(795\) | −8.12791 | −0.288267 | ||||||||
\(796\) | 14.7301 | 0.522094 | ||||||||
\(797\) | −8.88139 | −0.314595 | −0.157297 | − | 0.987551i | \(-0.550278\pi\) | ||||
−0.157297 | + | 0.987551i | \(0.550278\pi\) | |||||||
\(798\) | 4.29926 | 0.152192 | ||||||||
\(799\) | 0.660560 | 0.0233689 | ||||||||
\(800\) | −3.22366 | −0.113974 | ||||||||
\(801\) | 1.32107 | 0.0466776 | ||||||||
\(802\) | −9.16169 | −0.323510 | ||||||||
\(803\) | −19.4329 | −0.685773 | ||||||||
\(804\) | −0.0139862 | −0.000493254 0 | ||||||||
\(805\) | −11.1810 | −0.394080 | ||||||||
\(806\) | −10.1567 | −0.357756 | ||||||||
\(807\) | −14.3719 | −0.505914 | ||||||||
\(808\) | −4.52152 | −0.159066 | ||||||||
\(809\) | −10.7058 | −0.376395 | −0.188198 | − | 0.982131i | \(-0.560265\pi\) | ||||
−0.188198 | + | 0.982131i | \(0.560265\pi\) | |||||||
\(810\) | −2.86769 | −0.100760 | ||||||||
\(811\) | 0.293301 | 0.0102992 | 0.00514960 | − | 0.999987i | \(-0.498361\pi\) | ||||
0.00514960 | + | 0.999987i | \(0.498361\pi\) | |||||||
\(812\) | 1.31751 | 0.0462356 | ||||||||
\(813\) | 20.9059 | 0.733201 | ||||||||
\(814\) | −2.72621 | −0.0955536 | ||||||||
\(815\) | 40.7461 | 1.42727 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | 44.2667 | 1.54869 | ||||||||
\(818\) | −9.77838 | −0.341893 | ||||||||
\(819\) | 0.804748 | 0.0281202 | ||||||||
\(820\) | −20.2463 | −0.707031 | ||||||||
\(821\) | 40.8843 | 1.42687 | 0.713436 | − | 0.700720i | \(-0.247138\pi\) | ||||
0.713436 | + | 0.700720i | \(0.247138\pi\) | |||||||
\(822\) | −16.0035 | −0.558185 | ||||||||
\(823\) | 17.2997 | 0.603029 | 0.301514 | − | 0.953462i | \(-0.402508\pi\) | ||||
0.301514 | + | 0.953462i | \(0.402508\pi\) | |||||||
\(824\) | −18.1452 | −0.632117 | ||||||||
\(825\) | 9.93912 | 0.346036 | ||||||||
\(826\) | −0.636539 | −0.0221480 | ||||||||
\(827\) | 2.63202 | 0.0915243 | 0.0457622 | − | 0.998952i | \(-0.485428\pi\) | ||||
0.0457622 | + | 0.998952i | \(0.485428\pi\) | |||||||
\(828\) | −6.12526 | −0.212867 | ||||||||
\(829\) | −57.2712 | −1.98911 | −0.994555 | − | 0.104213i | \(-0.966768\pi\) | ||||
−0.994555 | + | 0.104213i | \(0.966768\pi\) | |||||||
\(830\) | −41.8837 | −1.45381 | ||||||||
\(831\) | −20.3650 | −0.706454 | ||||||||
\(832\) | 1.26426 | 0.0438302 | ||||||||
\(833\) | 6.59482 | 0.228497 | ||||||||
\(834\) | −20.1857 | −0.698975 | ||||||||
\(835\) | 26.6550 | 0.922435 | ||||||||
\(836\) | −20.8242 | −0.720219 | ||||||||
\(837\) | −8.03376 | −0.277687 | ||||||||
\(838\) | 12.0030 | 0.414637 | ||||||||
\(839\) | −23.8197 | −0.822349 | −0.411174 | − | 0.911557i | \(-0.634881\pi\) | ||||
−0.411174 | + | 0.911557i | \(0.634881\pi\) | |||||||
\(840\) | 1.82540 | 0.0629822 | ||||||||
\(841\) | −24.7159 | −0.852272 | ||||||||
\(842\) | 16.6688 | 0.574443 | ||||||||
\(843\) | 6.13616 | 0.211341 | ||||||||
\(844\) | 18.1318 | 0.624124 | ||||||||
\(845\) | −32.6964 | −1.12479 | ||||||||
\(846\) | 0.660560 | 0.0227105 | ||||||||
\(847\) | −0.950999 | −0.0326767 | ||||||||
\(848\) | 2.83430 | 0.0973303 | ||||||||
\(849\) | 4.66780 | 0.160198 | ||||||||
\(850\) | 3.22366 | 0.110571 | ||||||||
\(851\) | 5.41608 | 0.185661 | ||||||||
\(852\) | −5.73708 | −0.196549 | ||||||||
\(853\) | 13.3256 | 0.456260 | 0.228130 | − | 0.973631i | \(-0.426739\pi\) | ||||
0.228130 | + | 0.973631i | \(0.426739\pi\) | |||||||
\(854\) | 6.44704 | 0.220613 | ||||||||
\(855\) | 19.3687 | 0.662397 | ||||||||
\(856\) | −6.90533 | −0.236019 | ||||||||
\(857\) | −12.1185 | −0.413961 | −0.206980 | − | 0.978345i | \(-0.566364\pi\) | ||||
−0.206980 | + | 0.978345i | \(0.566364\pi\) | |||||||
\(858\) | −3.89793 | −0.133073 | ||||||||
\(859\) | 28.5240 | 0.973226 | 0.486613 | − | 0.873618i | \(-0.338232\pi\) | ||||
0.486613 | + | 0.873618i | \(0.338232\pi\) | |||||||
\(860\) | 18.7949 | 0.640901 | ||||||||
\(861\) | 4.49405 | 0.153157 | ||||||||
\(862\) | 8.75516 | 0.298202 | ||||||||
\(863\) | 50.5592 | 1.72105 | 0.860527 | − | 0.509405i | \(-0.170135\pi\) | ||||
0.860527 | + | 0.509405i | \(0.170135\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 38.6963 | 1.31571 | ||||||||
\(866\) | 29.7186 | 1.00988 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 5.11380 | 0.173574 | ||||||||
\(869\) | −21.9793 | −0.745598 | ||||||||
\(870\) | 5.93557 | 0.201235 | ||||||||
\(871\) | 0.0176821 | 0.000599135 0 | ||||||||
\(872\) | −2.23129 | −0.0755610 | ||||||||
\(873\) | 15.2562 | 0.516345 | ||||||||
\(874\) | 41.3708 | 1.39939 | ||||||||
\(875\) | −3.24253 | −0.109617 | ||||||||
\(876\) | −6.30289 | −0.212955 | ||||||||
\(877\) | 9.00840 | 0.304192 | 0.152096 | − | 0.988366i | \(-0.451398\pi\) | ||||
0.152096 | + | 0.988366i | \(0.451398\pi\) | |||||||
\(878\) | 33.6068 | 1.13417 | ||||||||
\(879\) | 25.8627 | 0.872326 | ||||||||
\(880\) | −8.84161 | −0.298050 | ||||||||
\(881\) | 3.85028 | 0.129719 | 0.0648595 | − | 0.997894i | \(-0.479340\pi\) | ||||
0.0648595 | + | 0.997894i | \(0.479340\pi\) | |||||||
\(882\) | 6.59482 | 0.222059 | ||||||||
\(883\) | −12.8248 | −0.431589 | −0.215795 | − | 0.976439i | \(-0.569234\pi\) | ||||
−0.215795 | + | 0.976439i | \(0.569234\pi\) | |||||||
\(884\) | −1.26426 | −0.0425215 | ||||||||
\(885\) | −2.86769 | −0.0963964 | ||||||||
\(886\) | −21.8571 | −0.734304 | ||||||||
\(887\) | −6.34607 | −0.213080 | −0.106540 | − | 0.994308i | \(-0.533977\pi\) | ||||
−0.106540 | + | 0.994308i | \(0.533977\pi\) | |||||||
\(888\) | −0.884221 | −0.0296725 | ||||||||
\(889\) | −6.15543 | −0.206446 | ||||||||
\(890\) | −3.78842 | −0.126988 | ||||||||
\(891\) | −3.08318 | −0.103290 | ||||||||
\(892\) | 5.29242 | 0.177203 | ||||||||
\(893\) | −4.46151 | −0.149299 | ||||||||
\(894\) | −16.2296 | −0.542800 | ||||||||
\(895\) | −31.0871 | −1.03913 | ||||||||
\(896\) | −0.636539 | −0.0212653 | ||||||||
\(897\) | 7.74390 | 0.258561 | ||||||||
\(898\) | −0.330027 | −0.0110132 | ||||||||
\(899\) | 16.6283 | 0.554586 | ||||||||
\(900\) | 3.22366 | 0.107455 | ||||||||
\(901\) | −2.83430 | −0.0944243 | ||||||||
\(902\) | −21.7676 | −0.724783 | ||||||||
\(903\) | −4.17189 | −0.138832 | ||||||||
\(904\) | −9.41503 | −0.313139 | ||||||||
\(905\) | −1.00562 | −0.0334280 | ||||||||
\(906\) | −4.37879 | −0.145475 | ||||||||
\(907\) | −33.6554 | −1.11751 | −0.558754 | − | 0.829334i | \(-0.688720\pi\) | ||||
−0.558754 | + | 0.829334i | \(0.688720\pi\) | |||||||
\(908\) | 5.38961 | 0.178860 | ||||||||
\(909\) | 4.52152 | 0.149969 | ||||||||
\(910\) | −2.30777 | −0.0765018 | ||||||||
\(911\) | 5.90483 | 0.195636 | 0.0978179 | − | 0.995204i | \(-0.468814\pi\) | ||||
0.0978179 | + | 0.995204i | \(0.468814\pi\) | |||||||
\(912\) | −6.75412 | −0.223651 | ||||||||
\(913\) | −45.0310 | −1.49031 | ||||||||
\(914\) | −23.9610 | −0.792558 | ||||||||
\(915\) | 29.0448 | 0.960190 | ||||||||
\(916\) | −7.41385 | −0.244960 | ||||||||
\(917\) | 7.73870 | 0.255554 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 2.81640 | 0.0929045 | 0.0464522 | − | 0.998921i | \(-0.485208\pi\) | ||||
0.0464522 | + | 0.998921i | \(0.485208\pi\) | |||||||
\(920\) | 17.5654 | 0.579113 | ||||||||
\(921\) | −2.39542 | −0.0789317 | ||||||||
\(922\) | −15.4035 | −0.507286 | ||||||||
\(923\) | 7.25314 | 0.238740 | ||||||||
\(924\) | 1.96256 | 0.0645636 | ||||||||
\(925\) | −2.85043 | −0.0937215 | ||||||||
\(926\) | −9.07029 | −0.298068 | ||||||||
\(927\) | 18.1452 | 0.595965 | ||||||||
\(928\) | −2.06981 | −0.0679448 | ||||||||
\(929\) | −28.6049 | −0.938497 | −0.469249 | − | 0.883066i | \(-0.655475\pi\) | ||||
−0.469249 | + | 0.883066i | \(0.655475\pi\) | |||||||
\(930\) | 23.0384 | 0.755457 | ||||||||
\(931\) | −44.5422 | −1.45981 | ||||||||
\(932\) | −23.6396 | −0.774342 | ||||||||
\(933\) | 2.92768 | 0.0958478 | ||||||||
\(934\) | −9.37346 | −0.306709 | ||||||||
\(935\) | 8.84161 | 0.289151 | ||||||||
\(936\) | −1.26426 | −0.0413235 | ||||||||
\(937\) | 44.7778 | 1.46283 | 0.731414 | − | 0.681934i | \(-0.238861\pi\) | ||||
0.731414 | + | 0.681934i | \(0.238861\pi\) | |||||||
\(938\) | −0.00890274 | −0.000290685 0 | ||||||||
\(939\) | −9.91154 | −0.323451 | ||||||||
\(940\) | −1.89428 | −0.0617847 | ||||||||
\(941\) | −32.3694 | −1.05521 | −0.527606 | − | 0.849489i | \(-0.676910\pi\) | ||||
−0.527606 | + | 0.849489i | \(0.676910\pi\) | |||||||
\(942\) | 10.5021 | 0.342175 | ||||||||
\(943\) | 43.2451 | 1.40825 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | −1.82540 | −0.0593802 | ||||||||
\(946\) | 20.2072 | 0.656993 | ||||||||
\(947\) | 18.1673 | 0.590357 | 0.295179 | − | 0.955442i | \(-0.404621\pi\) | ||||
0.295179 | + | 0.955442i | \(0.404621\pi\) | |||||||
\(948\) | −7.12879 | −0.231532 | ||||||||
\(949\) | 7.96847 | 0.258667 | ||||||||
\(950\) | −21.7730 | −0.706409 | ||||||||
\(951\) | −7.04898 | −0.228579 | ||||||||
\(952\) | 0.636539 | 0.0206303 | ||||||||
\(953\) | 44.9009 | 1.45448 | 0.727242 | − | 0.686382i | \(-0.240802\pi\) | ||||
0.727242 | + | 0.686382i | \(0.240802\pi\) | |||||||
\(954\) | −2.83430 | −0.0917639 | ||||||||
\(955\) | −16.3936 | −0.530483 | ||||||||
\(956\) | 20.6309 | 0.667252 | ||||||||
\(957\) | 6.38159 | 0.206287 | ||||||||
\(958\) | −19.9688 | −0.645163 | ||||||||
\(959\) | −10.1868 | −0.328950 | ||||||||
\(960\) | −2.86769 | −0.0925544 | ||||||||
\(961\) | 33.5413 | 1.08198 | ||||||||
\(962\) | 1.11788 | 0.0360419 | ||||||||
\(963\) | 6.90533 | 0.222521 | ||||||||
\(964\) | 19.8421 | 0.639072 | ||||||||
\(965\) | −52.3424 | −1.68496 | ||||||||
\(966\) | −3.89897 | −0.125447 | ||||||||
\(967\) | 21.3686 | 0.687169 | 0.343585 | − | 0.939122i | \(-0.388359\pi\) | ||||
0.343585 | + | 0.939122i | \(0.388359\pi\) | |||||||
\(968\) | 1.49402 | 0.0480195 | ||||||||
\(969\) | 6.75412 | 0.216974 | ||||||||
\(970\) | −43.7501 | −1.40473 | ||||||||
\(971\) | −53.7462 | −1.72480 | −0.862400 | − | 0.506228i | \(-0.831039\pi\) | ||||
−0.862400 | + | 0.506228i | \(0.831039\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −12.8490 | −0.411920 | ||||||||
\(974\) | −2.20781 | −0.0707429 | ||||||||
\(975\) | −4.07553 | −0.130521 | ||||||||
\(976\) | −10.1283 | −0.324198 | ||||||||
\(977\) | −40.8608 | −1.30725 | −0.653626 | − | 0.756818i | \(-0.726753\pi\) | ||||
−0.653626 | + | 0.756818i | \(0.726753\pi\) | |||||||
\(978\) | 14.2087 | 0.454343 | ||||||||
\(979\) | −4.07309 | −0.130176 | ||||||||
\(980\) | −18.9119 | −0.604119 | ||||||||
\(981\) | 2.23129 | 0.0712396 | ||||||||
\(982\) | 7.72087 | 0.246383 | ||||||||
\(983\) | 39.2707 | 1.25254 | 0.626270 | − | 0.779606i | \(-0.284581\pi\) | ||||
0.626270 | + | 0.779606i | \(0.284581\pi\) | |||||||
\(984\) | −7.06013 | −0.225069 | ||||||||
\(985\) | 45.9791 | 1.46502 | ||||||||
\(986\) | 2.06981 | 0.0659161 | ||||||||
\(987\) | 0.420472 | 0.0133838 | ||||||||
\(988\) | 8.53894 | 0.271660 | ||||||||
\(989\) | −40.1451 | −1.27654 | ||||||||
\(990\) | 8.84161 | 0.281005 | ||||||||
\(991\) | −45.1682 | −1.43481 | −0.717407 | − | 0.696654i | \(-0.754671\pi\) | ||||
−0.717407 | + | 0.696654i | \(0.754671\pi\) | |||||||
\(992\) | −8.03376 | −0.255072 | ||||||||
\(993\) | −19.4349 | −0.616748 | ||||||||
\(994\) | −3.65188 | −0.115831 | ||||||||
\(995\) | 42.2413 | 1.33914 | ||||||||
\(996\) | −14.6054 | −0.462789 | ||||||||
\(997\) | −2.33896 | −0.0740755 | −0.0370377 | − | 0.999314i | \(-0.511792\pi\) | ||||
−0.0370377 | + | 0.999314i | \(0.511792\pi\) | |||||||
\(998\) | −23.7571 | −0.752019 | ||||||||
\(999\) | 0.884221 | 0.0279755 |
(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 | 6018.2.a.s.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.s.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial |