Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.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: | \(40.3563931816\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 24 x^{10} + 68 x^{9} + 213 x^{8} - 555 x^{7} - 814 x^{6} + 1911 x^{5} + 1005 x^{4} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 266) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.77114\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-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 | ||||||||
\(3\) | −2.77114 | −1.59992 | −0.799958 | − | 0.600056i | \(-0.795145\pi\) | ||||
−0.799958 | + | 0.600056i | \(0.795145\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.35329 | 0.605211 | 0.302605 | − | 0.953116i | \(-0.402144\pi\) | ||||
0.302605 | + | 0.953116i | \(0.402144\pi\) | |||||||
\(6\) | −2.77114 | −1.13131 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.67919 | 1.55973 | ||||||||
\(10\) | 1.35329 | 0.427948 | ||||||||
\(11\) | 0.777571 | 0.234447 | 0.117223 | − | 0.993106i | \(-0.462601\pi\) | ||||
0.117223 | + | 0.993106i | \(0.462601\pi\) | |||||||
\(12\) | −2.77114 | −0.799958 | ||||||||
\(13\) | −4.89563 | −1.35780 | −0.678901 | − | 0.734229i | \(-0.737544\pi\) | ||||
−0.678901 | + | 0.734229i | \(0.737544\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −3.75015 | −0.968286 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.66043 | 0.645248 | 0.322624 | − | 0.946527i | \(-0.395435\pi\) | ||||
0.322624 | + | 0.946527i | \(0.395435\pi\) | |||||||
\(18\) | 4.67919 | 1.10290 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.35329 | 0.302605 | ||||||||
\(21\) | −2.77114 | −0.604711 | ||||||||
\(22\) | 0.777571 | 0.165779 | ||||||||
\(23\) | 4.50585 | 0.939534 | 0.469767 | − | 0.882791i | \(-0.344338\pi\) | ||||
0.469767 | + | 0.882791i | \(0.344338\pi\) | |||||||
\(24\) | −2.77114 | −0.565656 | ||||||||
\(25\) | −3.16860 | −0.633720 | ||||||||
\(26\) | −4.89563 | −0.960112 | ||||||||
\(27\) | −4.65327 | −0.895522 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 0.997230 | 0.185181 | 0.0925904 | − | 0.995704i | \(-0.470485\pi\) | ||||
0.0925904 | + | 0.995704i | \(0.470485\pi\) | |||||||
\(30\) | −3.75015 | −0.684681 | ||||||||
\(31\) | −7.02486 | −1.26170 | −0.630851 | − | 0.775904i | \(-0.717294\pi\) | ||||
−0.630851 | + | 0.775904i | \(0.717294\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.15476 | −0.375095 | ||||||||
\(34\) | 2.66043 | 0.456259 | ||||||||
\(35\) | 1.35329 | 0.228748 | ||||||||
\(36\) | 4.67919 | 0.779865 | ||||||||
\(37\) | 5.59129 | 0.919203 | 0.459601 | − | 0.888125i | \(-0.347992\pi\) | ||||
0.459601 | + | 0.888125i | \(0.347992\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.5664 | 2.17237 | ||||||||
\(40\) | 1.35329 | 0.213974 | ||||||||
\(41\) | 10.7721 | 1.68232 | 0.841160 | − | 0.540786i | \(-0.181873\pi\) | ||||
0.841160 | + | 0.540786i | \(0.181873\pi\) | |||||||
\(42\) | −2.77114 | −0.427595 | ||||||||
\(43\) | 11.0411 | 1.68375 | 0.841875 | − | 0.539673i | \(-0.181452\pi\) | ||||
0.841875 | + | 0.539673i | \(0.181452\pi\) | |||||||
\(44\) | 0.777571 | 0.117223 | ||||||||
\(45\) | 6.33231 | 0.943965 | ||||||||
\(46\) | 4.50585 | 0.664351 | ||||||||
\(47\) | −3.93075 | −0.573358 | −0.286679 | − | 0.958027i | \(-0.592551\pi\) | ||||
−0.286679 | + | 0.958027i | \(0.592551\pi\) | |||||||
\(48\) | −2.77114 | −0.399979 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.16860 | −0.448108 | ||||||||
\(51\) | −7.37240 | −1.03234 | ||||||||
\(52\) | −4.89563 | −0.678901 | ||||||||
\(53\) | −7.53218 | −1.03462 | −0.517312 | − | 0.855797i | \(-0.673067\pi\) | ||||
−0.517312 | + | 0.855797i | \(0.673067\pi\) | |||||||
\(54\) | −4.65327 | −0.633229 | ||||||||
\(55\) | 1.05228 | 0.141890 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.997230 | 0.130943 | ||||||||
\(59\) | 3.36961 | 0.438686 | 0.219343 | − | 0.975648i | \(-0.429609\pi\) | ||||
0.219343 | + | 0.975648i | \(0.429609\pi\) | |||||||
\(60\) | −3.75015 | −0.484143 | ||||||||
\(61\) | −3.75523 | −0.480807 | −0.240404 | − | 0.970673i | \(-0.577280\pi\) | ||||
−0.240404 | + | 0.970673i | \(0.577280\pi\) | |||||||
\(62\) | −7.02486 | −0.892159 | ||||||||
\(63\) | 4.67919 | 0.589523 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.62521 | −0.821757 | ||||||||
\(66\) | −2.15476 | −0.265232 | ||||||||
\(67\) | −1.09883 | −0.134244 | −0.0671218 | − | 0.997745i | \(-0.521382\pi\) | ||||
−0.0671218 | + | 0.997745i | \(0.521382\pi\) | |||||||
\(68\) | 2.66043 | 0.322624 | ||||||||
\(69\) | −12.4863 | −1.50317 | ||||||||
\(70\) | 1.35329 | 0.161749 | ||||||||
\(71\) | 8.04901 | 0.955241 | 0.477621 | − | 0.878566i | \(-0.341499\pi\) | ||||
0.477621 | + | 0.878566i | \(0.341499\pi\) | |||||||
\(72\) | 4.67919 | 0.551448 | ||||||||
\(73\) | −14.4128 | −1.68689 | −0.843444 | − | 0.537217i | \(-0.819476\pi\) | ||||
−0.843444 | + | 0.537217i | \(0.819476\pi\) | |||||||
\(74\) | 5.59129 | 0.649974 | ||||||||
\(75\) | 8.78062 | 1.01390 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.777571 | 0.0886125 | ||||||||
\(78\) | 13.5664 | 1.53610 | ||||||||
\(79\) | 2.44722 | 0.275333 | 0.137667 | − | 0.990479i | \(-0.456040\pi\) | ||||
0.137667 | + | 0.990479i | \(0.456040\pi\) | |||||||
\(80\) | 1.35329 | 0.151303 | ||||||||
\(81\) | −1.14274 | −0.126971 | ||||||||
\(82\) | 10.7721 | 1.18958 | ||||||||
\(83\) | 13.9733 | 1.53376 | 0.766882 | − | 0.641788i | \(-0.221807\pi\) | ||||
0.766882 | + | 0.641788i | \(0.221807\pi\) | |||||||
\(84\) | −2.77114 | −0.302356 | ||||||||
\(85\) | 3.60033 | 0.390511 | ||||||||
\(86\) | 11.0411 | 1.19059 | ||||||||
\(87\) | −2.76346 | −0.296274 | ||||||||
\(88\) | 0.777571 | 0.0828894 | ||||||||
\(89\) | 14.7170 | 1.56000 | 0.780000 | − | 0.625780i | \(-0.215219\pi\) | ||||
0.780000 | + | 0.625780i | \(0.215219\pi\) | |||||||
\(90\) | 6.33231 | 0.667484 | ||||||||
\(91\) | −4.89563 | −0.513201 | ||||||||
\(92\) | 4.50585 | 0.469767 | ||||||||
\(93\) | 19.4668 | 2.01862 | ||||||||
\(94\) | −3.93075 | −0.405426 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.77114 | −0.282828 | ||||||||
\(97\) | −2.32027 | −0.235587 | −0.117794 | − | 0.993038i | \(-0.537582\pi\) | ||||
−0.117794 | + | 0.993038i | \(0.537582\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 3.63841 | 0.365674 | ||||||||
\(100\) | −3.16860 | −0.316860 | ||||||||
\(101\) | −5.26224 | −0.523612 | −0.261806 | − | 0.965120i | \(-0.584318\pi\) | ||||
−0.261806 | + | 0.965120i | \(0.584318\pi\) | |||||||
\(102\) | −7.37240 | −0.729976 | ||||||||
\(103\) | −10.9843 | −1.08232 | −0.541158 | − | 0.840921i | \(-0.682014\pi\) | ||||
−0.541158 | + | 0.840921i | \(0.682014\pi\) | |||||||
\(104\) | −4.89563 | −0.480056 | ||||||||
\(105\) | −3.75015 | −0.365978 | ||||||||
\(106\) | −7.53218 | −0.731590 | ||||||||
\(107\) | −4.44978 | −0.430176 | −0.215088 | − | 0.976595i | \(-0.569004\pi\) | ||||
−0.215088 | + | 0.976595i | \(0.569004\pi\) | |||||||
\(108\) | −4.65327 | −0.447761 | ||||||||
\(109\) | 10.4374 | 0.999720 | 0.499860 | − | 0.866106i | \(-0.333385\pi\) | ||||
0.499860 | + | 0.866106i | \(0.333385\pi\) | |||||||
\(110\) | 1.05228 | 0.100331 | ||||||||
\(111\) | −15.4942 | −1.47065 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −1.79945 | −0.169278 | −0.0846392 | − | 0.996412i | \(-0.526974\pi\) | ||||
−0.0846392 | + | 0.996412i | \(0.526974\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.09772 | 0.568616 | ||||||||
\(116\) | 0.997230 | 0.0925904 | ||||||||
\(117\) | −22.9076 | −2.11781 | ||||||||
\(118\) | 3.36961 | 0.310198 | ||||||||
\(119\) | 2.66043 | 0.243881 | ||||||||
\(120\) | −3.75015 | −0.342341 | ||||||||
\(121\) | −10.3954 | −0.945035 | ||||||||
\(122\) | −3.75523 | −0.339982 | ||||||||
\(123\) | −29.8510 | −2.69157 | ||||||||
\(124\) | −7.02486 | −0.630851 | ||||||||
\(125\) | −11.0545 | −0.988745 | ||||||||
\(126\) | 4.67919 | 0.416856 | ||||||||
\(127\) | 9.53273 | 0.845893 | 0.422947 | − | 0.906155i | \(-0.360996\pi\) | ||||
0.422947 | + | 0.906155i | \(0.360996\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −30.5963 | −2.69386 | ||||||||
\(130\) | −6.62521 | −0.581070 | ||||||||
\(131\) | 9.06565 | 0.792070 | 0.396035 | − | 0.918235i | \(-0.370386\pi\) | ||||
0.396035 | + | 0.918235i | \(0.370386\pi\) | |||||||
\(132\) | −2.15476 | −0.187547 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.09883 | −0.0949245 | ||||||||
\(135\) | −6.29723 | −0.541979 | ||||||||
\(136\) | 2.66043 | 0.228130 | ||||||||
\(137\) | −14.3031 | −1.22200 | −0.611000 | − | 0.791630i | \(-0.709233\pi\) | ||||
−0.611000 | + | 0.791630i | \(0.709233\pi\) | |||||||
\(138\) | −12.4863 | −1.06291 | ||||||||
\(139\) | 3.65688 | 0.310172 | 0.155086 | − | 0.987901i | \(-0.450434\pi\) | ||||
0.155086 | + | 0.987901i | \(0.450434\pi\) | |||||||
\(140\) | 1.35329 | 0.114374 | ||||||||
\(141\) | 10.8926 | 0.917325 | ||||||||
\(142\) | 8.04901 | 0.675458 | ||||||||
\(143\) | −3.80670 | −0.318332 | ||||||||
\(144\) | 4.67919 | 0.389933 | ||||||||
\(145\) | 1.34954 | 0.112073 | ||||||||
\(146\) | −14.4128 | −1.19281 | ||||||||
\(147\) | −2.77114 | −0.228559 | ||||||||
\(148\) | 5.59129 | 0.459601 | ||||||||
\(149\) | 18.9562 | 1.55295 | 0.776477 | − | 0.630145i | \(-0.217005\pi\) | ||||
0.776477 | + | 0.630145i | \(0.217005\pi\) | |||||||
\(150\) | 8.78062 | 0.716935 | ||||||||
\(151\) | 2.55886 | 0.208237 | 0.104119 | − | 0.994565i | \(-0.466798\pi\) | ||||
0.104119 | + | 0.994565i | \(0.466798\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.4486 | 1.00641 | ||||||||
\(154\) | 0.777571 | 0.0626585 | ||||||||
\(155\) | −9.50669 | −0.763596 | ||||||||
\(156\) | 13.5664 | 1.08619 | ||||||||
\(157\) | 15.4626 | 1.23405 | 0.617027 | − | 0.786942i | \(-0.288337\pi\) | ||||
0.617027 | + | 0.786942i | \(0.288337\pi\) | |||||||
\(158\) | 2.44722 | 0.194690 | ||||||||
\(159\) | 20.8727 | 1.65531 | ||||||||
\(160\) | 1.35329 | 0.106987 | ||||||||
\(161\) | 4.50585 | 0.355110 | ||||||||
\(162\) | −1.14274 | −0.0897823 | ||||||||
\(163\) | 21.1462 | 1.65630 | 0.828149 | − | 0.560508i | \(-0.189394\pi\) | ||||
0.828149 | + | 0.560508i | \(0.189394\pi\) | |||||||
\(164\) | 10.7721 | 0.841160 | ||||||||
\(165\) | −2.91601 | −0.227011 | ||||||||
\(166\) | 13.9733 | 1.08453 | ||||||||
\(167\) | 19.0996 | 1.47797 | 0.738986 | − | 0.673720i | \(-0.235305\pi\) | ||||
0.738986 | + | 0.673720i | \(0.235305\pi\) | |||||||
\(168\) | −2.77114 | −0.213798 | ||||||||
\(169\) | 10.9672 | 0.843629 | ||||||||
\(170\) | 3.60033 | 0.276133 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0411 | 0.841875 | ||||||||
\(173\) | −1.53344 | −0.116585 | −0.0582927 | − | 0.998300i | \(-0.518566\pi\) | ||||
−0.0582927 | + | 0.998300i | \(0.518566\pi\) | |||||||
\(174\) | −2.76346 | −0.209497 | ||||||||
\(175\) | −3.16860 | −0.239524 | ||||||||
\(176\) | 0.777571 | 0.0586117 | ||||||||
\(177\) | −9.33765 | −0.701861 | ||||||||
\(178\) | 14.7170 | 1.10309 | ||||||||
\(179\) | 25.2144 | 1.88461 | 0.942307 | − | 0.334749i | \(-0.108651\pi\) | ||||
0.942307 | + | 0.334749i | \(0.108651\pi\) | |||||||
\(180\) | 6.33231 | 0.471983 | ||||||||
\(181\) | −21.6479 | −1.60907 | −0.804537 | − | 0.593902i | \(-0.797587\pi\) | ||||
−0.804537 | + | 0.593902i | \(0.797587\pi\) | |||||||
\(182\) | −4.89563 | −0.362888 | ||||||||
\(183\) | 10.4062 | 0.769251 | ||||||||
\(184\) | 4.50585 | 0.332175 | ||||||||
\(185\) | 7.56665 | 0.556311 | ||||||||
\(186\) | 19.4668 | 1.42738 | ||||||||
\(187\) | 2.06867 | 0.151276 | ||||||||
\(188\) | −3.93075 | −0.286679 | ||||||||
\(189\) | −4.65327 | −0.338475 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.26341 | 0.453204 | 0.226602 | − | 0.973987i | \(-0.427238\pi\) | ||||
0.226602 | + | 0.973987i | \(0.427238\pi\) | |||||||
\(192\) | −2.77114 | −0.199989 | ||||||||
\(193\) | −13.9007 | −1.00060 | −0.500298 | − | 0.865854i | \(-0.666776\pi\) | ||||
−0.500298 | + | 0.865854i | \(0.666776\pi\) | |||||||
\(194\) | −2.32027 | −0.166585 | ||||||||
\(195\) | 18.3594 | 1.31474 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 4.38830 | 0.312653 | 0.156327 | − | 0.987705i | \(-0.450035\pi\) | ||||
0.156327 | + | 0.987705i | \(0.450035\pi\) | |||||||
\(198\) | 3.63841 | 0.258570 | ||||||||
\(199\) | −21.1608 | −1.50005 | −0.750025 | − | 0.661409i | \(-0.769959\pi\) | ||||
−0.750025 | + | 0.661409i | \(0.769959\pi\) | |||||||
\(200\) | −3.16860 | −0.224054 | ||||||||
\(201\) | 3.04501 | 0.214778 | ||||||||
\(202\) | −5.26224 | −0.370250 | ||||||||
\(203\) | 0.997230 | 0.0699918 | ||||||||
\(204\) | −7.37240 | −0.516171 | ||||||||
\(205\) | 14.5778 | 1.01816 | ||||||||
\(206\) | −10.9843 | −0.765313 | ||||||||
\(207\) | 21.0837 | 1.46542 | ||||||||
\(208\) | −4.89563 | −0.339451 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.75015 | −0.258785 | ||||||||
\(211\) | 5.11585 | 0.352190 | 0.176095 | − | 0.984373i | \(-0.443653\pi\) | ||||
0.176095 | + | 0.984373i | \(0.443653\pi\) | |||||||
\(212\) | −7.53218 | −0.517312 | ||||||||
\(213\) | −22.3049 | −1.52831 | ||||||||
\(214\) | −4.44978 | −0.304180 | ||||||||
\(215\) | 14.9418 | 1.01902 | ||||||||
\(216\) | −4.65327 | −0.316615 | ||||||||
\(217\) | −7.02486 | −0.476879 | ||||||||
\(218\) | 10.4374 | 0.706909 | ||||||||
\(219\) | 39.9398 | 2.69888 | ||||||||
\(220\) | 1.05228 | 0.0709448 | ||||||||
\(221\) | −13.0245 | −0.876120 | ||||||||
\(222\) | −15.4942 | −1.03990 | ||||||||
\(223\) | 9.49819 | 0.636046 | 0.318023 | − | 0.948083i | \(-0.396981\pi\) | ||||
0.318023 | + | 0.948083i | \(0.396981\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −14.8265 | −0.988433 | ||||||||
\(226\) | −1.79945 | −0.119698 | ||||||||
\(227\) | −0.0136096 | −0.000903303 0 | −0.000451651 | − | 1.00000i | \(-0.500144\pi\) | ||||
−0.000451651 | 1.00000i | \(0.500144\pi\) | ||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0961 | 1.39407 | 0.697033 | − | 0.717039i | \(-0.254503\pi\) | ||||
0.697033 | + | 0.717039i | \(0.254503\pi\) | |||||||
\(230\) | 6.09772 | 0.402072 | ||||||||
\(231\) | −2.15476 | −0.141773 | ||||||||
\(232\) | 0.997230 | 0.0654713 | ||||||||
\(233\) | 25.7459 | 1.68667 | 0.843334 | − | 0.537390i | \(-0.180590\pi\) | ||||
0.843334 | + | 0.537390i | \(0.180590\pi\) | |||||||
\(234\) | −22.9076 | −1.49752 | ||||||||
\(235\) | −5.31945 | −0.347003 | ||||||||
\(236\) | 3.36961 | 0.219343 | ||||||||
\(237\) | −6.78157 | −0.440510 | ||||||||
\(238\) | 2.66043 | 0.172450 | ||||||||
\(239\) | −1.70859 | −0.110519 | −0.0552597 | − | 0.998472i | \(-0.517599\pi\) | ||||
−0.0552597 | + | 0.998472i | \(0.517599\pi\) | |||||||
\(240\) | −3.75015 | −0.242071 | ||||||||
\(241\) | −6.93003 | −0.446402 | −0.223201 | − | 0.974772i | \(-0.571651\pi\) | ||||
−0.223201 | + | 0.974772i | \(0.571651\pi\) | |||||||
\(242\) | −10.3954 | −0.668241 | ||||||||
\(243\) | 17.1265 | 1.09867 | ||||||||
\(244\) | −3.75523 | −0.240404 | ||||||||
\(245\) | 1.35329 | 0.0864586 | ||||||||
\(246\) | −29.8510 | −1.90323 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.02486 | −0.446079 | ||||||||
\(249\) | −38.7218 | −2.45389 | ||||||||
\(250\) | −11.0545 | −0.699148 | ||||||||
\(251\) | 25.9231 | 1.63625 | 0.818126 | − | 0.575040i | \(-0.195013\pi\) | ||||
0.818126 | + | 0.575040i | \(0.195013\pi\) | |||||||
\(252\) | 4.67919 | 0.294761 | ||||||||
\(253\) | 3.50362 | 0.220270 | ||||||||
\(254\) | 9.53273 | 0.598137 | ||||||||
\(255\) | −9.97701 | −0.624785 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.1704 | 1.63246 | 0.816231 | − | 0.577725i | \(-0.196060\pi\) | ||||
0.816231 | + | 0.577725i | \(0.196060\pi\) | |||||||
\(258\) | −30.5963 | −1.90484 | ||||||||
\(259\) | 5.59129 | 0.347426 | ||||||||
\(260\) | −6.62521 | −0.410878 | ||||||||
\(261\) | 4.66623 | 0.288832 | ||||||||
\(262\) | 9.06565 | 0.560078 | ||||||||
\(263\) | 16.4992 | 1.01738 | 0.508692 | − | 0.860949i | \(-0.330129\pi\) | ||||
0.508692 | + | 0.860949i | \(0.330129\pi\) | |||||||
\(264\) | −2.15476 | −0.132616 | ||||||||
\(265\) | −10.1932 | −0.626165 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −40.7828 | −2.49587 | ||||||||
\(268\) | −1.09883 | −0.0671218 | ||||||||
\(269\) | 15.9629 | 0.973275 | 0.486637 | − | 0.873604i | \(-0.338223\pi\) | ||||
0.486637 | + | 0.873604i | \(0.338223\pi\) | |||||||
\(270\) | −6.29723 | −0.383237 | ||||||||
\(271\) | −17.8296 | −1.08307 | −0.541536 | − | 0.840678i | \(-0.682157\pi\) | ||||
−0.541536 | + | 0.840678i | \(0.682157\pi\) | |||||||
\(272\) | 2.66043 | 0.161312 | ||||||||
\(273\) | 13.5664 | 0.821079 | ||||||||
\(274\) | −14.3031 | −0.864085 | ||||||||
\(275\) | −2.46381 | −0.148574 | ||||||||
\(276\) | −12.4863 | −0.751587 | ||||||||
\(277\) | 24.8573 | 1.49353 | 0.746766 | − | 0.665087i | \(-0.231605\pi\) | ||||
0.746766 | + | 0.665087i | \(0.231605\pi\) | |||||||
\(278\) | 3.65688 | 0.219325 | ||||||||
\(279\) | −32.8707 | −1.96792 | ||||||||
\(280\) | 1.35329 | 0.0808747 | ||||||||
\(281\) | 12.0488 | 0.718772 | 0.359386 | − | 0.933189i | \(-0.382986\pi\) | ||||
0.359386 | + | 0.933189i | \(0.382986\pi\) | |||||||
\(282\) | 10.8926 | 0.648647 | ||||||||
\(283\) | −25.9628 | −1.54333 | −0.771663 | − | 0.636031i | \(-0.780575\pi\) | ||||
−0.771663 | + | 0.636031i | \(0.780575\pi\) | |||||||
\(284\) | 8.04901 | 0.477621 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.80670 | −0.225095 | ||||||||
\(287\) | 10.7721 | 0.635857 | ||||||||
\(288\) | 4.67919 | 0.275724 | ||||||||
\(289\) | −9.92214 | −0.583655 | ||||||||
\(290\) | 1.34954 | 0.0792479 | ||||||||
\(291\) | 6.42977 | 0.376920 | ||||||||
\(292\) | −14.4128 | −0.843444 | ||||||||
\(293\) | 6.69334 | 0.391029 | 0.195515 | − | 0.980701i | \(-0.437362\pi\) | ||||
0.195515 | + | 0.980701i | \(0.437362\pi\) | |||||||
\(294\) | −2.77114 | −0.161616 | ||||||||
\(295\) | 4.56007 | 0.265497 | ||||||||
\(296\) | 5.59129 | 0.324987 | ||||||||
\(297\) | −3.61825 | −0.209952 | ||||||||
\(298\) | 18.9562 | 1.09810 | ||||||||
\(299\) | −22.0589 | −1.27570 | ||||||||
\(300\) | 8.78062 | 0.506950 | ||||||||
\(301\) | 11.0411 | 0.636397 | ||||||||
\(302\) | 2.55886 | 0.147246 | ||||||||
\(303\) | 14.5824 | 0.837736 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.08192 | −0.290990 | ||||||||
\(306\) | 12.4486 | 0.711641 | ||||||||
\(307\) | −3.94665 | −0.225247 | −0.112624 | − | 0.993638i | \(-0.535925\pi\) | ||||
−0.112624 | + | 0.993638i | \(0.535925\pi\) | |||||||
\(308\) | 0.777571 | 0.0443062 | ||||||||
\(309\) | 30.4390 | 1.73162 | ||||||||
\(310\) | −9.50669 | −0.539944 | ||||||||
\(311\) | 14.8167 | 0.840177 | 0.420089 | − | 0.907483i | \(-0.361999\pi\) | ||||
0.420089 | + | 0.907483i | \(0.361999\pi\) | |||||||
\(312\) | 13.5664 | 0.768049 | ||||||||
\(313\) | −17.7509 | −1.00334 | −0.501670 | − | 0.865059i | \(-0.667281\pi\) | ||||
−0.501670 | + | 0.865059i | \(0.667281\pi\) | |||||||
\(314\) | 15.4626 | 0.872608 | ||||||||
\(315\) | 6.33231 | 0.356785 | ||||||||
\(316\) | 2.44722 | 0.137667 | ||||||||
\(317\) | −2.83911 | −0.159460 | −0.0797301 | − | 0.996816i | \(-0.525406\pi\) | ||||
−0.0797301 | + | 0.996816i | \(0.525406\pi\) | |||||||
\(318\) | 20.8727 | 1.17048 | ||||||||
\(319\) | 0.775417 | 0.0434150 | ||||||||
\(320\) | 1.35329 | 0.0756513 | ||||||||
\(321\) | 12.3309 | 0.688246 | ||||||||
\(322\) | 4.50585 | 0.251101 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.14274 | −0.0634857 | ||||||||
\(325\) | 15.5123 | 0.860467 | ||||||||
\(326\) | 21.1462 | 1.17118 | ||||||||
\(327\) | −28.9234 | −1.59947 | ||||||||
\(328\) | 10.7721 | 0.594790 | ||||||||
\(329\) | −3.93075 | −0.216709 | ||||||||
\(330\) | −2.91601 | −0.160521 | ||||||||
\(331\) | 2.76023 | 0.151716 | 0.0758581 | − | 0.997119i | \(-0.475830\pi\) | ||||
0.0758581 | + | 0.997119i | \(0.475830\pi\) | |||||||
\(332\) | 13.9733 | 0.766882 | ||||||||
\(333\) | 26.1627 | 1.43371 | ||||||||
\(334\) | 19.0996 | 1.04508 | ||||||||
\(335\) | −1.48704 | −0.0812456 | ||||||||
\(336\) | −2.77114 | −0.151178 | ||||||||
\(337\) | −24.6577 | −1.34319 | −0.671595 | − | 0.740918i | \(-0.734391\pi\) | ||||
−0.671595 | + | 0.740918i | \(0.734391\pi\) | |||||||
\(338\) | 10.9672 | 0.596536 | ||||||||
\(339\) | 4.98653 | 0.270831 | ||||||||
\(340\) | 3.60033 | 0.195255 | ||||||||
\(341\) | −5.46233 | −0.295802 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.0411 | 0.595295 | ||||||||
\(345\) | −16.8976 | −0.909737 | ||||||||
\(346\) | −1.53344 | −0.0824384 | ||||||||
\(347\) | −28.8696 | −1.54980 | −0.774901 | − | 0.632082i | \(-0.782200\pi\) | ||||
−0.774901 | + | 0.632082i | \(0.782200\pi\) | |||||||
\(348\) | −2.76346 | −0.148137 | ||||||||
\(349\) | 36.6608 | 1.96241 | 0.981204 | − | 0.192972i | \(-0.0618125\pi\) | ||||
0.981204 | + | 0.192972i | \(0.0618125\pi\) | |||||||
\(350\) | −3.16860 | −0.169369 | ||||||||
\(351\) | 22.7807 | 1.21594 | ||||||||
\(352\) | 0.777571 | 0.0414447 | ||||||||
\(353\) | 12.3935 | 0.659639 | 0.329820 | − | 0.944044i | \(-0.393012\pi\) | ||||
0.329820 | + | 0.944044i | \(0.393012\pi\) | |||||||
\(354\) | −9.33765 | −0.496290 | ||||||||
\(355\) | 10.8927 | 0.578122 | ||||||||
\(356\) | 14.7170 | 0.780000 | ||||||||
\(357\) | −7.37240 | −0.390189 | ||||||||
\(358\) | 25.2144 | 1.33262 | ||||||||
\(359\) | −17.9682 | −0.948326 | −0.474163 | − | 0.880437i | \(-0.657249\pi\) | ||||
−0.474163 | + | 0.880437i | \(0.657249\pi\) | |||||||
\(360\) | 6.33231 | 0.333742 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −21.6479 | −1.13779 | ||||||||
\(363\) | 28.8070 | 1.51198 | ||||||||
\(364\) | −4.89563 | −0.256601 | ||||||||
\(365\) | −19.5047 | −1.02092 | ||||||||
\(366\) | 10.4062 | 0.543943 | ||||||||
\(367\) | 20.7229 | 1.08173 | 0.540864 | − | 0.841110i | \(-0.318097\pi\) | ||||
0.540864 | + | 0.841110i | \(0.318097\pi\) | |||||||
\(368\) | 4.50585 | 0.234883 | ||||||||
\(369\) | 50.4047 | 2.62397 | ||||||||
\(370\) | 7.56665 | 0.393371 | ||||||||
\(371\) | −7.53218 | −0.391051 | ||||||||
\(372\) | 19.4668 | 1.00931 | ||||||||
\(373\) | 0.769222 | 0.0398288 | 0.0199144 | − | 0.999802i | \(-0.493661\pi\) | ||||
0.0199144 | + | 0.999802i | \(0.493661\pi\) | |||||||
\(374\) | 2.06867 | 0.106968 | ||||||||
\(375\) | 30.6335 | 1.58191 | ||||||||
\(376\) | −3.93075 | −0.202713 | ||||||||
\(377\) | −4.88207 | −0.251439 | ||||||||
\(378\) | −4.65327 | −0.239338 | ||||||||
\(379\) | 25.0167 | 1.28502 | 0.642512 | − | 0.766276i | \(-0.277892\pi\) | ||||
0.642512 | + | 0.766276i | \(0.277892\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −26.4165 | −1.35336 | ||||||||
\(382\) | 6.26341 | 0.320464 | ||||||||
\(383\) | −21.8893 | −1.11849 | −0.559246 | − | 0.829002i | \(-0.688909\pi\) | ||||
−0.559246 | + | 0.829002i | \(0.688909\pi\) | |||||||
\(384\) | −2.77114 | −0.141414 | ||||||||
\(385\) | 1.05228 | 0.0536292 | ||||||||
\(386\) | −13.9007 | −0.707528 | ||||||||
\(387\) | 51.6633 | 2.62620 | ||||||||
\(388\) | −2.32027 | −0.117794 | ||||||||
\(389\) | −36.1139 | −1.83105 | −0.915525 | − | 0.402262i | \(-0.868224\pi\) | ||||
−0.915525 | + | 0.402262i | \(0.868224\pi\) | |||||||
\(390\) | 18.3594 | 0.929663 | ||||||||
\(391\) | 11.9875 | 0.606232 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −25.1222 | −1.26725 | ||||||||
\(394\) | 4.38830 | 0.221079 | ||||||||
\(395\) | 3.31180 | 0.166635 | ||||||||
\(396\) | 3.63841 | 0.182837 | ||||||||
\(397\) | −13.6226 | −0.683698 | −0.341849 | − | 0.939755i | \(-0.611053\pi\) | ||||
−0.341849 | + | 0.939755i | \(0.611053\pi\) | |||||||
\(398\) | −21.1608 | −1.06070 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.16860 | −0.158430 | ||||||||
\(401\) | 28.4546 | 1.42096 | 0.710478 | − | 0.703719i | \(-0.248479\pi\) | ||||
0.710478 | + | 0.703719i | \(0.248479\pi\) | |||||||
\(402\) | 3.04501 | 0.151871 | ||||||||
\(403\) | 34.3911 | 1.71314 | ||||||||
\(404\) | −5.26224 | −0.261806 | ||||||||
\(405\) | −1.54646 | −0.0768444 | ||||||||
\(406\) | 0.997230 | 0.0494917 | ||||||||
\(407\) | 4.34763 | 0.215504 | ||||||||
\(408\) | −7.37240 | −0.364988 | ||||||||
\(409\) | −6.17138 | −0.305155 | −0.152578 | − | 0.988291i | \(-0.548757\pi\) | ||||
−0.152578 | + | 0.988291i | \(0.548757\pi\) | |||||||
\(410\) | 14.5778 | 0.719946 | ||||||||
\(411\) | 39.6360 | 1.95510 | ||||||||
\(412\) | −10.9843 | −0.541158 | ||||||||
\(413\) | 3.36961 | 0.165808 | ||||||||
\(414\) | 21.0837 | 1.03621 | ||||||||
\(415\) | 18.9099 | 0.928250 | ||||||||
\(416\) | −4.89563 | −0.240028 | ||||||||
\(417\) | −10.1337 | −0.496250 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.97201 | 0.194045 | 0.0970227 | − | 0.995282i | \(-0.469068\pi\) | ||||
0.0970227 | + | 0.995282i | \(0.469068\pi\) | |||||||
\(420\) | −3.75015 | −0.182989 | ||||||||
\(421\) | −2.21450 | −0.107928 | −0.0539640 | − | 0.998543i | \(-0.517186\pi\) | ||||
−0.0539640 | + | 0.998543i | \(0.517186\pi\) | |||||||
\(422\) | 5.11585 | 0.249036 | ||||||||
\(423\) | −18.3927 | −0.894285 | ||||||||
\(424\) | −7.53218 | −0.365795 | ||||||||
\(425\) | −8.42983 | −0.408907 | ||||||||
\(426\) | −22.3049 | −1.08068 | ||||||||
\(427\) | −3.75523 | −0.181728 | ||||||||
\(428\) | −4.44978 | −0.215088 | ||||||||
\(429\) | 10.5489 | 0.509305 | ||||||||
\(430\) | 14.9418 | 0.720558 | ||||||||
\(431\) | 35.0260 | 1.68714 | 0.843572 | − | 0.537016i | \(-0.180448\pi\) | ||||
0.843572 | + | 0.537016i | \(0.180448\pi\) | |||||||
\(432\) | −4.65327 | −0.223880 | ||||||||
\(433\) | −25.2504 | −1.21346 | −0.606728 | − | 0.794909i | \(-0.707518\pi\) | ||||
−0.606728 | + | 0.794909i | \(0.707518\pi\) | |||||||
\(434\) | −7.02486 | −0.337204 | ||||||||
\(435\) | −3.73977 | −0.179308 | ||||||||
\(436\) | 10.4374 | 0.499860 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 39.9398 | 1.90840 | ||||||||
\(439\) | 32.0708 | 1.53066 | 0.765329 | − | 0.643639i | \(-0.222576\pi\) | ||||
0.765329 | + | 0.643639i | \(0.222576\pi\) | |||||||
\(440\) | 1.05228 | 0.0501655 | ||||||||
\(441\) | 4.67919 | 0.222819 | ||||||||
\(442\) | −13.0245 | −0.619510 | ||||||||
\(443\) | 20.5097 | 0.974444 | 0.487222 | − | 0.873278i | \(-0.338010\pi\) | ||||
0.487222 | + | 0.873278i | \(0.338010\pi\) | |||||||
\(444\) | −15.4942 | −0.735323 | ||||||||
\(445\) | 19.9164 | 0.944128 | ||||||||
\(446\) | 9.49819 | 0.449752 | ||||||||
\(447\) | −52.5303 | −2.48460 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −14.1242 | −0.666563 | −0.333282 | − | 0.942827i | \(-0.608156\pi\) | ||||
−0.333282 | + | 0.942827i | \(0.608156\pi\) | |||||||
\(450\) | −14.8265 | −0.698928 | ||||||||
\(451\) | 8.37608 | 0.394414 | ||||||||
\(452\) | −1.79945 | −0.0846392 | ||||||||
\(453\) | −7.09095 | −0.333162 | ||||||||
\(454\) | −0.0136096 | −0.000638732 0 | ||||||||
\(455\) | −6.62521 | −0.310595 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.6803 | −1.10772 | −0.553859 | − | 0.832610i | \(-0.686845\pi\) | ||||
−0.553859 | + | 0.832610i | \(0.686845\pi\) | |||||||
\(458\) | 21.0961 | 0.985754 | ||||||||
\(459\) | −12.3797 | −0.577834 | ||||||||
\(460\) | 6.09772 | 0.284308 | ||||||||
\(461\) | 16.3005 | 0.759188 | 0.379594 | − | 0.925153i | \(-0.376064\pi\) | ||||
0.379594 | + | 0.925153i | \(0.376064\pi\) | |||||||
\(462\) | −2.15476 | −0.100248 | ||||||||
\(463\) | 25.4188 | 1.18131 | 0.590655 | − | 0.806924i | \(-0.298869\pi\) | ||||
0.590655 | + | 0.806924i | \(0.298869\pi\) | |||||||
\(464\) | 0.997230 | 0.0462952 | ||||||||
\(465\) | 26.3443 | 1.22169 | ||||||||
\(466\) | 25.7459 | 1.19265 | ||||||||
\(467\) | −25.3370 | −1.17246 | −0.586229 | − | 0.810146i | \(-0.699388\pi\) | ||||
−0.586229 | + | 0.810146i | \(0.699388\pi\) | |||||||
\(468\) | −22.9076 | −1.05890 | ||||||||
\(469\) | −1.09883 | −0.0507393 | ||||||||
\(470\) | −5.31945 | −0.245368 | ||||||||
\(471\) | −42.8491 | −1.97438 | ||||||||
\(472\) | 3.36961 | 0.155099 | ||||||||
\(473\) | 8.58523 | 0.394749 | ||||||||
\(474\) | −6.78157 | −0.311488 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.66043 | 0.121940 | ||||||||
\(477\) | −35.2445 | −1.61374 | ||||||||
\(478\) | −1.70859 | −0.0781491 | ||||||||
\(479\) | −28.2100 | −1.28895 | −0.644474 | − | 0.764626i | \(-0.722924\pi\) | ||||
−0.644474 | + | 0.764626i | \(0.722924\pi\) | |||||||
\(480\) | −3.75015 | −0.171170 | ||||||||
\(481\) | −27.3729 | −1.24810 | ||||||||
\(482\) | −6.93003 | −0.315654 | ||||||||
\(483\) | −12.4863 | −0.568147 | ||||||||
\(484\) | −10.3954 | −0.472517 | ||||||||
\(485\) | −3.14000 | −0.142580 | ||||||||
\(486\) | 17.1265 | 0.776873 | ||||||||
\(487\) | 28.1520 | 1.27569 | 0.637845 | − | 0.770164i | \(-0.279826\pi\) | ||||
0.637845 | + | 0.770164i | \(0.279826\pi\) | |||||||
\(488\) | −3.75523 | −0.169991 | ||||||||
\(489\) | −58.5990 | −2.64994 | ||||||||
\(490\) | 1.35329 | 0.0611355 | ||||||||
\(491\) | −19.1536 | −0.864392 | −0.432196 | − | 0.901780i | \(-0.642261\pi\) | ||||
−0.432196 | + | 0.901780i | \(0.642261\pi\) | |||||||
\(492\) | −29.8510 | −1.34579 | ||||||||
\(493\) | 2.65306 | 0.119488 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.92382 | 0.221309 | ||||||||
\(496\) | −7.02486 | −0.315426 | ||||||||
\(497\) | 8.04901 | 0.361047 | ||||||||
\(498\) | −38.7218 | −1.73516 | ||||||||
\(499\) | 7.01992 | 0.314255 | 0.157127 | − | 0.987578i | \(-0.449777\pi\) | ||||
0.157127 | + | 0.987578i | \(0.449777\pi\) | |||||||
\(500\) | −11.0545 | −0.494372 | ||||||||
\(501\) | −52.9276 | −2.36463 | ||||||||
\(502\) | 25.9231 | 1.15700 | ||||||||
\(503\) | 8.77808 | 0.391395 | 0.195698 | − | 0.980664i | \(-0.437303\pi\) | ||||
0.195698 | + | 0.980664i | \(0.437303\pi\) | |||||||
\(504\) | 4.67919 | 0.208428 | ||||||||
\(505\) | −7.12134 | −0.316896 | ||||||||
\(506\) | 3.50362 | 0.155755 | ||||||||
\(507\) | −30.3915 | −1.34974 | ||||||||
\(508\) | 9.53273 | 0.422947 | ||||||||
\(509\) | 31.3906 | 1.39137 | 0.695683 | − | 0.718349i | \(-0.255102\pi\) | ||||
0.695683 | + | 0.718349i | \(0.255102\pi\) | |||||||
\(510\) | −9.97701 | −0.441789 | ||||||||
\(511\) | −14.4128 | −0.637584 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.1704 | 1.15433 | ||||||||
\(515\) | −14.8650 | −0.655029 | ||||||||
\(516\) | −30.5963 | −1.34693 | ||||||||
\(517\) | −3.05644 | −0.134422 | ||||||||
\(518\) | 5.59129 | 0.245667 | ||||||||
\(519\) | 4.24938 | 0.186527 | ||||||||
\(520\) | −6.62521 | −0.290535 | ||||||||
\(521\) | −26.7461 | −1.17177 | −0.585884 | − | 0.810395i | \(-0.699253\pi\) | ||||
−0.585884 | + | 0.810395i | \(0.699253\pi\) | |||||||
\(522\) | 4.66623 | 0.204235 | ||||||||
\(523\) | −10.4679 | −0.457729 | −0.228865 | − | 0.973458i | \(-0.573501\pi\) | ||||
−0.228865 | + | 0.973458i | \(0.573501\pi\) | |||||||
\(524\) | 9.06565 | 0.396035 | ||||||||
\(525\) | 8.78062 | 0.383218 | ||||||||
\(526\) | 16.4992 | 0.719399 | ||||||||
\(527\) | −18.6891 | −0.814111 | ||||||||
\(528\) | −2.15476 | −0.0937737 | ||||||||
\(529\) | −2.69736 | −0.117277 | ||||||||
\(530\) | −10.1932 | −0.442766 | ||||||||
\(531\) | 15.7671 | 0.684232 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −52.7362 | −2.28426 | ||||||||
\(534\) | −40.7828 | −1.76484 | ||||||||
\(535\) | −6.02185 | −0.260347 | ||||||||
\(536\) | −1.09883 | −0.0474622 | ||||||||
\(537\) | −69.8726 | −3.01523 | ||||||||
\(538\) | 15.9629 | 0.688209 | ||||||||
\(539\) | 0.777571 | 0.0334924 | ||||||||
\(540\) | −6.29723 | −0.270990 | ||||||||
\(541\) | 1.22831 | 0.0528094 | 0.0264047 | − | 0.999651i | \(-0.491594\pi\) | ||||
0.0264047 | + | 0.999651i | \(0.491594\pi\) | |||||||
\(542\) | −17.8296 | −0.765848 | ||||||||
\(543\) | 59.9892 | 2.57438 | ||||||||
\(544\) | 2.66043 | 0.114065 | ||||||||
\(545\) | 14.1248 | 0.605041 | ||||||||
\(546\) | 13.5664 | 0.580590 | ||||||||
\(547\) | −8.42041 | −0.360031 | −0.180015 | − | 0.983664i | \(-0.557615\pi\) | ||||
−0.180015 | + | 0.983664i | \(0.557615\pi\) | |||||||
\(548\) | −14.3031 | −0.611000 | ||||||||
\(549\) | −17.5714 | −0.749930 | ||||||||
\(550\) | −2.46381 | −0.105057 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −12.4863 | −0.531453 | ||||||||
\(553\) | 2.44722 | 0.104066 | ||||||||
\(554\) | 24.8573 | 1.05609 | ||||||||
\(555\) | −20.9682 | −0.890051 | ||||||||
\(556\) | 3.65688 | 0.155086 | ||||||||
\(557\) | 31.3157 | 1.32689 | 0.663445 | − | 0.748225i | \(-0.269094\pi\) | ||||
0.663445 | + | 0.748225i | \(0.269094\pi\) | |||||||
\(558\) | −32.8707 | −1.39153 | ||||||||
\(559\) | −54.0530 | −2.28620 | ||||||||
\(560\) | 1.35329 | 0.0571870 | ||||||||
\(561\) | −5.73257 | −0.242029 | ||||||||
\(562\) | 12.0488 | 0.508248 | ||||||||
\(563\) | −32.7400 | −1.37983 | −0.689913 | − | 0.723892i | \(-0.742351\pi\) | ||||
−0.689913 | + | 0.723892i | \(0.742351\pi\) | |||||||
\(564\) | 10.8926 | 0.458663 | ||||||||
\(565\) | −2.43519 | −0.102449 | ||||||||
\(566\) | −25.9628 | −1.09130 | ||||||||
\(567\) | −1.14274 | −0.0479907 | ||||||||
\(568\) | 8.04901 | 0.337729 | ||||||||
\(569\) | −24.5608 | −1.02964 | −0.514821 | − | 0.857297i | \(-0.672142\pi\) | ||||
−0.514821 | + | 0.857297i | \(0.672142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.8657 | 1.08244 | 0.541222 | − | 0.840880i | \(-0.317962\pi\) | ||||
0.541222 | + | 0.840880i | \(0.317962\pi\) | |||||||
\(572\) | −3.80670 | −0.159166 | ||||||||
\(573\) | −17.3568 | −0.725089 | ||||||||
\(574\) | 10.7721 | 0.449619 | ||||||||
\(575\) | −14.2772 | −0.595401 | ||||||||
\(576\) | 4.67919 | 0.194966 | ||||||||
\(577\) | 20.2526 | 0.843128 | 0.421564 | − | 0.906799i | \(-0.361481\pi\) | ||||
0.421564 | + | 0.906799i | \(0.361481\pi\) | |||||||
\(578\) | −9.92214 | −0.412706 | ||||||||
\(579\) | 38.5208 | 1.60087 | ||||||||
\(580\) | 1.34954 | 0.0560367 | ||||||||
\(581\) | 13.9733 | 0.579708 | ||||||||
\(582\) | 6.42977 | 0.266523 | ||||||||
\(583\) | −5.85681 | −0.242564 | ||||||||
\(584\) | −14.4128 | −0.596405 | ||||||||
\(585\) | −31.0006 | −1.28172 | ||||||||
\(586\) | 6.69334 | 0.276499 | ||||||||
\(587\) | 16.2617 | 0.671194 | 0.335597 | − | 0.942006i | \(-0.391062\pi\) | ||||
0.335597 | + | 0.942006i | \(0.391062\pi\) | |||||||
\(588\) | −2.77114 | −0.114280 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 4.56007 | 0.187735 | ||||||||
\(591\) | −12.1606 | −0.500219 | ||||||||
\(592\) | 5.59129 | 0.229801 | ||||||||
\(593\) | −16.6460 | −0.683571 | −0.341786 | − | 0.939778i | \(-0.611032\pi\) | ||||
−0.341786 | + | 0.939778i | \(0.611032\pi\) | |||||||
\(594\) | −3.61825 | −0.148458 | ||||||||
\(595\) | 3.60033 | 0.147599 | ||||||||
\(596\) | 18.9562 | 0.776477 | ||||||||
\(597\) | 58.6395 | 2.39995 | ||||||||
\(598\) | −22.0589 | −0.902057 | ||||||||
\(599\) | 23.8542 | 0.974656 | 0.487328 | − | 0.873219i | \(-0.337972\pi\) | ||||
0.487328 | + | 0.873219i | \(0.337972\pi\) | |||||||
\(600\) | 8.78062 | 0.358467 | ||||||||
\(601\) | −13.4655 | −0.549271 | −0.274635 | − | 0.961548i | \(-0.588557\pi\) | ||||
−0.274635 | + | 0.961548i | \(0.588557\pi\) | |||||||
\(602\) | 11.0411 | 0.450001 | ||||||||
\(603\) | −5.14164 | −0.209384 | ||||||||
\(604\) | 2.55886 | 0.104119 | ||||||||
\(605\) | −14.0680 | −0.571945 | ||||||||
\(606\) | 14.5824 | 0.592368 | ||||||||
\(607\) | 4.04138 | 0.164035 | 0.0820173 | − | 0.996631i | \(-0.473864\pi\) | ||||
0.0820173 | + | 0.996631i | \(0.473864\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.76346 | −0.111981 | ||||||||
\(610\) | −5.08192 | −0.205761 | ||||||||
\(611\) | 19.2435 | 0.778508 | ||||||||
\(612\) | 12.4486 | 0.503206 | ||||||||
\(613\) | 17.0804 | 0.689870 | 0.344935 | − | 0.938626i | \(-0.387901\pi\) | ||||
0.344935 | + | 0.938626i | \(0.387901\pi\) | |||||||
\(614\) | −3.94665 | −0.159274 | ||||||||
\(615\) | −40.3971 | −1.62897 | ||||||||
\(616\) | 0.777571 | 0.0313292 | ||||||||
\(617\) | −28.9761 | −1.16653 | −0.583266 | − | 0.812281i | \(-0.698226\pi\) | ||||
−0.583266 | + | 0.812281i | \(0.698226\pi\) | |||||||
\(618\) | 30.4390 | 1.22444 | ||||||||
\(619\) | −22.6036 | −0.908515 | −0.454258 | − | 0.890870i | \(-0.650095\pi\) | ||||
−0.454258 | + | 0.890870i | \(0.650095\pi\) | |||||||
\(620\) | −9.50669 | −0.381798 | ||||||||
\(621\) | −20.9669 | −0.841373 | ||||||||
\(622\) | 14.8167 | 0.594095 | ||||||||
\(623\) | 14.7170 | 0.589624 | ||||||||
\(624\) | 13.5664 | 0.543093 | ||||||||
\(625\) | 0.883040 | 0.0353216 | ||||||||
\(626\) | −17.7509 | −0.709468 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.4626 | 0.617027 | ||||||||
\(629\) | 14.8752 | 0.593114 | ||||||||
\(630\) | 6.33231 | 0.252285 | ||||||||
\(631\) | 19.1450 | 0.762150 | 0.381075 | − | 0.924544i | \(-0.375554\pi\) | ||||
0.381075 | + | 0.924544i | \(0.375554\pi\) | |||||||
\(632\) | 2.44722 | 0.0973451 | ||||||||
\(633\) | −14.1767 | −0.563474 | ||||||||
\(634\) | −2.83911 | −0.112755 | ||||||||
\(635\) | 12.9006 | 0.511943 | ||||||||
\(636\) | 20.8727 | 0.827656 | ||||||||
\(637\) | −4.89563 | −0.193972 | ||||||||
\(638\) | 0.775417 | 0.0306991 | ||||||||
\(639\) | 37.6628 | 1.48992 | ||||||||
\(640\) | 1.35329 | 0.0534936 | ||||||||
\(641\) | −4.21500 | −0.166483 | −0.0832413 | − | 0.996529i | \(-0.526527\pi\) | ||||
−0.0832413 | + | 0.996529i | \(0.526527\pi\) | |||||||
\(642\) | 12.3309 | 0.486663 | ||||||||
\(643\) | 37.5432 | 1.48056 | 0.740280 | − | 0.672299i | \(-0.234693\pi\) | ||||
0.740280 | + | 0.672299i | \(0.234693\pi\) | |||||||
\(644\) | 4.50585 | 0.177555 | ||||||||
\(645\) | −41.4058 | −1.63035 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.8823 | −0.978225 | −0.489112 | − | 0.872221i | \(-0.662679\pi\) | ||||
−0.489112 | + | 0.872221i | \(0.662679\pi\) | |||||||
\(648\) | −1.14274 | −0.0448911 | ||||||||
\(649\) | 2.62011 | 0.102848 | ||||||||
\(650\) | 15.5123 | 0.608442 | ||||||||
\(651\) | 19.4668 | 0.762966 | ||||||||
\(652\) | 21.1462 | 0.828149 | ||||||||
\(653\) | −18.7262 | −0.732815 | −0.366407 | − | 0.930455i | \(-0.619412\pi\) | ||||
−0.366407 | + | 0.930455i | \(0.619412\pi\) | |||||||
\(654\) | −28.9234 | −1.13099 | ||||||||
\(655\) | 12.2685 | 0.479369 | ||||||||
\(656\) | 10.7721 | 0.420580 | ||||||||
\(657\) | −67.4402 | −2.63109 | ||||||||
\(658\) | −3.93075 | −0.153237 | ||||||||
\(659\) | −29.3137 | −1.14190 | −0.570949 | − | 0.820985i | \(-0.693425\pi\) | ||||
−0.570949 | + | 0.820985i | \(0.693425\pi\) | |||||||
\(660\) | −2.91601 | −0.113506 | ||||||||
\(661\) | −16.1369 | −0.627654 | −0.313827 | − | 0.949480i | \(-0.601611\pi\) | ||||
−0.313827 | + | 0.949480i | \(0.601611\pi\) | |||||||
\(662\) | 2.76023 | 0.107280 | ||||||||
\(663\) | 36.0925 | 1.40172 | ||||||||
\(664\) | 13.9733 | 0.542267 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 26.1627 | 1.01378 | ||||||||
\(667\) | 4.49336 | 0.173984 | ||||||||
\(668\) | 19.0996 | 0.738986 | ||||||||
\(669\) | −26.3208 | −1.01762 | ||||||||
\(670\) | −1.48704 | −0.0574493 | ||||||||
\(671\) | −2.91996 | −0.112724 | ||||||||
\(672\) | −2.77114 | −0.106899 | ||||||||
\(673\) | −19.0332 | −0.733677 | −0.366838 | − | 0.930285i | \(-0.619560\pi\) | ||||
−0.366838 | + | 0.930285i | \(0.619560\pi\) | |||||||
\(674\) | −24.6577 | −0.949779 | ||||||||
\(675\) | 14.7443 | 0.567510 | ||||||||
\(676\) | 10.9672 | 0.421814 | ||||||||
\(677\) | −25.2624 | −0.970914 | −0.485457 | − | 0.874260i | \(-0.661347\pi\) | ||||
−0.485457 | + | 0.874260i | \(0.661347\pi\) | |||||||
\(678\) | 4.98653 | 0.191507 | ||||||||
\(679\) | −2.32027 | −0.0890437 | ||||||||
\(680\) | 3.60033 | 0.138066 | ||||||||
\(681\) | 0.0377141 | 0.00144521 | ||||||||
\(682\) | −5.46233 | −0.209164 | ||||||||
\(683\) | 9.66935 | 0.369987 | 0.184994 | − | 0.982740i | \(-0.440774\pi\) | ||||
0.184994 | + | 0.982740i | \(0.440774\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.3563 | −0.739568 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −58.4600 | −2.23039 | ||||||||
\(688\) | 11.0411 | 0.420937 | ||||||||
\(689\) | 36.8747 | 1.40482 | ||||||||
\(690\) | −16.8976 | −0.643281 | ||||||||
\(691\) | −19.4773 | −0.740950 | −0.370475 | − | 0.928843i | \(-0.620805\pi\) | ||||
−0.370475 | + | 0.928843i | \(0.620805\pi\) | |||||||
\(692\) | −1.53344 | −0.0582927 | ||||||||
\(693\) | 3.63841 | 0.138212 | ||||||||
\(694\) | −28.8696 | −1.09588 | ||||||||
\(695\) | 4.94882 | 0.187720 | ||||||||
\(696\) | −2.76346 | −0.104749 | ||||||||
\(697\) | 28.6584 | 1.08551 | ||||||||
\(698\) | 36.6608 | 1.38763 | ||||||||
\(699\) | −71.3453 | −2.69853 | ||||||||
\(700\) | −3.16860 | −0.119762 | ||||||||
\(701\) | −30.7390 | −1.16100 | −0.580498 | − | 0.814262i | \(-0.697142\pi\) | ||||
−0.580498 | + | 0.814262i | \(0.697142\pi\) | |||||||
\(702\) | 22.7807 | 0.859801 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.777571 | 0.0293058 | ||||||||
\(705\) | 14.7409 | 0.555175 | ||||||||
\(706\) | 12.3935 | 0.466436 | ||||||||
\(707\) | −5.26224 | −0.197907 | ||||||||
\(708\) | −9.33765 | −0.350930 | ||||||||
\(709\) | −1.80008 | −0.0676036 | −0.0338018 | − | 0.999429i | \(-0.510761\pi\) | ||||
−0.0338018 | + | 0.999429i | \(0.510761\pi\) | |||||||
\(710\) | 10.8927 | 0.408794 | ||||||||
\(711\) | 11.4510 | 0.429446 | ||||||||
\(712\) | 14.7170 | 0.551543 | ||||||||
\(713\) | −31.6529 | −1.18541 | ||||||||
\(714\) | −7.37240 | −0.275905 | ||||||||
\(715\) | −5.15158 | −0.192658 | ||||||||
\(716\) | 25.2144 | 0.942307 | ||||||||
\(717\) | 4.73473 | 0.176822 | ||||||||
\(718\) | −17.9682 | −0.670568 | ||||||||
\(719\) | −7.65913 | −0.285637 | −0.142819 | − | 0.989749i | \(-0.545617\pi\) | ||||
−0.142819 | + | 0.989749i | \(0.545617\pi\) | |||||||
\(720\) | 6.33231 | 0.235991 | ||||||||
\(721\) | −10.9843 | −0.409077 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.2040 | 0.714206 | ||||||||
\(724\) | −21.6479 | −0.804537 | ||||||||
\(725\) | −3.15982 | −0.117353 | ||||||||
\(726\) | 28.8070 | 1.06913 | ||||||||
\(727\) | −29.7957 | −1.10506 | −0.552531 | − | 0.833492i | \(-0.686338\pi\) | ||||
−0.552531 | + | 0.833492i | \(0.686338\pi\) | |||||||
\(728\) | −4.89563 | −0.181444 | ||||||||
\(729\) | −44.0316 | −1.63080 | ||||||||
\(730\) | −19.5047 | −0.721901 | ||||||||
\(731\) | 29.3740 | 1.08644 | ||||||||
\(732\) | 10.4062 | 0.384626 | ||||||||
\(733\) | −26.0986 | −0.963975 | −0.481988 | − | 0.876178i | \(-0.660085\pi\) | ||||
−0.481988 | + | 0.876178i | \(0.660085\pi\) | |||||||
\(734\) | 20.7229 | 0.764898 | ||||||||
\(735\) | −3.75015 | −0.138327 | ||||||||
\(736\) | 4.50585 | 0.166088 | ||||||||
\(737\) | −0.854419 | −0.0314729 | ||||||||
\(738\) | 50.4047 | 1.85542 | ||||||||
\(739\) | 13.9798 | 0.514255 | 0.257128 | − | 0.966377i | \(-0.417224\pi\) | ||||
0.257128 | + | 0.966377i | \(0.417224\pi\) | |||||||
\(740\) | 7.56665 | 0.278156 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.53218 | −0.276515 | ||||||||
\(743\) | 13.7329 | 0.503810 | 0.251905 | − | 0.967752i | \(-0.418943\pi\) | ||||
0.251905 | + | 0.967752i | \(0.418943\pi\) | |||||||
\(744\) | 19.4668 | 0.713689 | ||||||||
\(745\) | 25.6533 | 0.939864 | ||||||||
\(746\) | 0.769222 | 0.0281632 | ||||||||
\(747\) | 65.3835 | 2.39226 | ||||||||
\(748\) | 2.06867 | 0.0756381 | ||||||||
\(749\) | −4.44978 | −0.162591 | ||||||||
\(750\) | 30.6335 | 1.11858 | ||||||||
\(751\) | −34.4342 | −1.25652 | −0.628260 | − | 0.778003i | \(-0.716233\pi\) | ||||
−0.628260 | + | 0.778003i | \(0.716233\pi\) | |||||||
\(752\) | −3.93075 | −0.143340 | ||||||||
\(753\) | −71.8364 | −2.61786 | ||||||||
\(754\) | −4.88207 | −0.177794 | ||||||||
\(755\) | 3.46289 | 0.126027 | ||||||||
\(756\) | −4.65327 | −0.169238 | ||||||||
\(757\) | −38.1734 | −1.38743 | −0.693717 | − | 0.720247i | \(-0.744028\pi\) | ||||
−0.693717 | + | 0.720247i | \(0.744028\pi\) | |||||||
\(758\) | 25.0167 | 0.908649 | ||||||||
\(759\) | −9.70900 | −0.352414 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.76087 | −0.281331 | −0.140666 | − | 0.990057i | \(-0.544924\pi\) | ||||
−0.140666 | + | 0.990057i | \(0.544924\pi\) | |||||||
\(762\) | −26.4165 | −0.956968 | ||||||||
\(763\) | 10.4374 | 0.377859 | ||||||||
\(764\) | 6.26341 | 0.226602 | ||||||||
\(765\) | 16.8466 | 0.609092 | ||||||||
\(766\) | −21.8893 | −0.790893 | ||||||||
\(767\) | −16.4964 | −0.595649 | ||||||||
\(768\) | −2.77114 | −0.0999947 | ||||||||
\(769\) | 24.4338 | 0.881106 | 0.440553 | − | 0.897727i | \(-0.354782\pi\) | ||||
0.440553 | + | 0.897727i | \(0.354782\pi\) | |||||||
\(770\) | 1.05228 | 0.0379216 | ||||||||
\(771\) | −72.5216 | −2.61180 | ||||||||
\(772\) | −13.9007 | −0.500298 | ||||||||
\(773\) | 13.5422 | 0.487078 | 0.243539 | − | 0.969891i | \(-0.421692\pi\) | ||||
0.243539 | + | 0.969891i | \(0.421692\pi\) | |||||||
\(774\) | 51.6633 | 1.85700 | ||||||||
\(775\) | 22.2590 | 0.799567 | ||||||||
\(776\) | −2.32027 | −0.0832927 | ||||||||
\(777\) | −15.4942 | −0.555852 | ||||||||
\(778\) | −36.1139 | −1.29475 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 18.3594 | 0.657371 | ||||||||
\(781\) | 6.25868 | 0.223953 | ||||||||
\(782\) | 11.9875 | 0.428671 | ||||||||
\(783\) | −4.64038 | −0.165833 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 20.9255 | 0.746862 | ||||||||
\(786\) | −25.1222 | −0.896078 | ||||||||
\(787\) | −40.9894 | −1.46112 | −0.730558 | − | 0.682851i | \(-0.760740\pi\) | ||||
−0.730558 | + | 0.682851i | \(0.760740\pi\) | |||||||
\(788\) | 4.38830 | 0.156327 | ||||||||
\(789\) | −45.7215 | −1.62773 | ||||||||
\(790\) | 3.31180 | 0.117829 | ||||||||
\(791\) | −1.79945 | −0.0639812 | ||||||||
\(792\) | 3.63841 | 0.129285 | ||||||||
\(793\) | 18.3842 | 0.652842 | ||||||||
\(794\) | −13.6226 | −0.483448 | ||||||||
\(795\) | 28.2468 | 1.00181 | ||||||||
\(796\) | −21.1608 | −0.750025 | ||||||||
\(797\) | −11.7912 | −0.417665 | −0.208833 | − | 0.977951i | \(-0.566966\pi\) | ||||
−0.208833 | + | 0.977951i | \(0.566966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.4575 | −0.369958 | ||||||||
\(800\) | −3.16860 | −0.112027 | ||||||||
\(801\) | 68.8637 | 2.43318 | ||||||||
\(802\) | 28.4546 | 1.00477 | ||||||||
\(803\) | −11.2070 | −0.395485 | ||||||||
\(804\) | 3.04501 | 0.107389 | ||||||||
\(805\) | 6.09772 | 0.214917 | ||||||||
\(806\) | 34.3911 | 1.21138 | ||||||||
\(807\) | −44.2353 | −1.55716 | ||||||||
\(808\) | −5.26224 | −0.185125 | ||||||||
\(809\) | −22.7546 | −0.800008 | −0.400004 | − | 0.916513i | \(-0.630991\pi\) | ||||
−0.400004 | + | 0.916513i | \(0.630991\pi\) | |||||||
\(810\) | −1.54646 | −0.0543372 | ||||||||
\(811\) | −27.6974 | −0.972586 | −0.486293 | − | 0.873796i | \(-0.661651\pi\) | ||||
−0.486293 | + | 0.873796i | \(0.661651\pi\) | |||||||
\(812\) | 0.997230 | 0.0349959 | ||||||||
\(813\) | 49.4083 | 1.73282 | ||||||||
\(814\) | 4.34763 | 0.152384 | ||||||||
\(815\) | 28.6170 | 1.00241 | ||||||||
\(816\) | −7.37240 | −0.258086 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6.17138 | −0.215777 | ||||||||
\(819\) | −22.9076 | −0.800456 | ||||||||
\(820\) | 14.5778 | 0.509079 | ||||||||
\(821\) | 17.8867 | 0.624249 | 0.312125 | − | 0.950041i | \(-0.398959\pi\) | ||||
0.312125 | + | 0.950041i | \(0.398959\pi\) | |||||||
\(822\) | 39.6360 | 1.38246 | ||||||||
\(823\) | 23.7619 | 0.828286 | 0.414143 | − | 0.910212i | \(-0.364081\pi\) | ||||
0.414143 | + | 0.910212i | \(0.364081\pi\) | |||||||
\(824\) | −10.9843 | −0.382657 | ||||||||
\(825\) | 6.82756 | 0.237705 | ||||||||
\(826\) | 3.36961 | 0.117244 | ||||||||
\(827\) | −4.73016 | −0.164484 | −0.0822419 | − | 0.996612i | \(-0.526208\pi\) | ||||
−0.0822419 | + | 0.996612i | \(0.526208\pi\) | |||||||
\(828\) | 21.0837 | 0.732710 | ||||||||
\(829\) | −26.5287 | −0.921378 | −0.460689 | − | 0.887562i | \(-0.652398\pi\) | ||||
−0.460689 | + | 0.887562i | \(0.652398\pi\) | |||||||
\(830\) | 18.9099 | 0.656372 | ||||||||
\(831\) | −68.8830 | −2.38953 | ||||||||
\(832\) | −4.89563 | −0.169725 | ||||||||
\(833\) | 2.66043 | 0.0921783 | ||||||||
\(834\) | −10.1337 | −0.350901 | ||||||||
\(835\) | 25.8474 | 0.894485 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.6886 | 1.12988 | ||||||||
\(838\) | 3.97201 | 0.137211 | ||||||||
\(839\) | 26.6397 | 0.919706 | 0.459853 | − | 0.887995i | \(-0.347902\pi\) | ||||
0.459853 | + | 0.887995i | \(0.347902\pi\) | |||||||
\(840\) | −3.75015 | −0.129393 | ||||||||
\(841\) | −28.0055 | −0.965708 | ||||||||
\(842\) | −2.21450 | −0.0763166 | ||||||||
\(843\) | −33.3889 | −1.14997 | ||||||||
\(844\) | 5.11585 | 0.176095 | ||||||||
\(845\) | 14.8418 | 0.510573 | ||||||||
\(846\) | −18.3927 | −0.632355 | ||||||||
\(847\) | −10.3954 | −0.357190 | ||||||||
\(848\) | −7.53218 | −0.258656 | ||||||||
\(849\) | 71.9464 | 2.46919 | ||||||||
\(850\) | −8.42983 | −0.289141 | ||||||||
\(851\) | 25.1935 | 0.863622 | ||||||||
\(852\) | −22.3049 | −0.764153 | ||||||||
\(853\) | 22.1664 | 0.758964 | 0.379482 | − | 0.925199i | \(-0.376102\pi\) | ||||
0.379482 | + | 0.925199i | \(0.376102\pi\) | |||||||
\(854\) | −3.75523 | −0.128501 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.44978 | −0.152090 | ||||||||
\(857\) | −21.2045 | −0.724332 | −0.362166 | − | 0.932114i | \(-0.617963\pi\) | ||||
−0.362166 | + | 0.932114i | \(0.617963\pi\) | |||||||
\(858\) | 10.5489 | 0.360133 | ||||||||
\(859\) | 39.3164 | 1.34146 | 0.670730 | − | 0.741702i | \(-0.265981\pi\) | ||||
0.670730 | + | 0.741702i | \(0.265981\pi\) | |||||||
\(860\) | 14.9418 | 0.509511 | ||||||||
\(861\) | −29.8510 | −1.01732 | ||||||||
\(862\) | 35.0260 | 1.19299 | ||||||||
\(863\) | 14.6679 | 0.499301 | 0.249651 | − | 0.968336i | \(-0.419684\pi\) | ||||
0.249651 | + | 0.968336i | \(0.419684\pi\) | |||||||
\(864\) | −4.65327 | −0.158307 | ||||||||
\(865\) | −2.07519 | −0.0705587 | ||||||||
\(866\) | −25.2504 | −0.858043 | ||||||||
\(867\) | 27.4956 | 0.933799 | ||||||||
\(868\) | −7.02486 | −0.238439 | ||||||||
\(869\) | 1.90289 | 0.0645510 | ||||||||
\(870\) | −3.73977 | −0.126790 | ||||||||
\(871\) | 5.37947 | 0.182276 | ||||||||
\(872\) | 10.4374 | 0.353454 | ||||||||
\(873\) | −10.8570 | −0.367453 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0545 | −0.373710 | ||||||||
\(876\) | 39.9398 | 1.34944 | ||||||||
\(877\) | −6.23078 | −0.210398 | −0.105199 | − | 0.994451i | \(-0.533548\pi\) | ||||
−0.105199 | + | 0.994451i | \(0.533548\pi\) | |||||||
\(878\) | 32.0708 | 1.08234 | ||||||||
\(879\) | −18.5482 | −0.625614 | ||||||||
\(880\) | 1.05228 | 0.0354724 | ||||||||
\(881\) | −18.1699 | −0.612159 | −0.306079 | − | 0.952006i | \(-0.599017\pi\) | ||||
−0.306079 | + | 0.952006i | \(0.599017\pi\) | |||||||
\(882\) | 4.67919 | 0.157557 | ||||||||
\(883\) | −53.5155 | −1.80094 | −0.900471 | − | 0.434917i | \(-0.856778\pi\) | ||||
−0.900471 | + | 0.434917i | \(0.856778\pi\) | |||||||
\(884\) | −13.0245 | −0.438060 | ||||||||
\(885\) | −12.6366 | −0.424773 | ||||||||
\(886\) | 20.5097 | 0.689036 | ||||||||
\(887\) | −7.45643 | −0.250362 | −0.125181 | − | 0.992134i | \(-0.539951\pi\) | ||||
−0.125181 | + | 0.992134i | \(0.539951\pi\) | |||||||
\(888\) | −15.4942 | −0.519952 | ||||||||
\(889\) | 9.53273 | 0.319718 | ||||||||
\(890\) | 19.9164 | 0.667599 | ||||||||
\(891\) | −0.888563 | −0.0297680 | ||||||||
\(892\) | 9.49819 | 0.318023 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −52.5303 | −1.75687 | ||||||||
\(895\) | 34.1225 | 1.14059 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 61.1283 | 2.04102 | ||||||||
\(898\) | −14.1242 | −0.471331 | ||||||||
\(899\) | −7.00540 | −0.233643 | ||||||||
\(900\) | −14.8265 | −0.494216 | ||||||||
\(901\) | −20.0388 | −0.667589 | ||||||||
\(902\) | 8.37608 | 0.278893 | ||||||||
\(903\) | −30.5963 | −1.01818 | ||||||||
\(904\) | −1.79945 | −0.0598489 | ||||||||
\(905\) | −29.2959 | −0.973829 | ||||||||
\(906\) | −7.09095 | −0.235581 | ||||||||
\(907\) | 4.81173 | 0.159771 | 0.0798854 | − | 0.996804i | \(-0.474545\pi\) | ||||
0.0798854 | + | 0.996804i | \(0.474545\pi\) | |||||||
\(908\) | −0.0136096 | −0.000451651 0 | ||||||||
\(909\) | −24.6230 | −0.816694 | ||||||||
\(910\) | −6.62521 | −0.219624 | ||||||||
\(911\) | 22.6397 | 0.750086 | 0.375043 | − | 0.927007i | \(-0.377628\pi\) | ||||
0.375043 | + | 0.927007i | \(0.377628\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.8652 | 0.359586 | ||||||||
\(914\) | −23.6803 | −0.783275 | ||||||||
\(915\) | 14.0827 | 0.465559 | ||||||||
\(916\) | 21.0961 | 0.697033 | ||||||||
\(917\) | 9.06565 | 0.299374 | ||||||||
\(918\) | −12.3797 | −0.408590 | ||||||||
\(919\) | 21.5407 | 0.710562 | 0.355281 | − | 0.934760i | \(-0.384385\pi\) | ||||
0.355281 | + | 0.934760i | \(0.384385\pi\) | |||||||
\(920\) | 6.09772 | 0.201036 | ||||||||
\(921\) | 10.9367 | 0.360376 | ||||||||
\(922\) | 16.3005 | 0.536827 | ||||||||
\(923\) | −39.4049 | −1.29703 | ||||||||
\(924\) | −2.15476 | −0.0708863 | ||||||||
\(925\) | −17.7166 | −0.582517 | ||||||||
\(926\) | 25.4188 | 0.835312 | ||||||||
\(927\) | −51.3977 | −1.68812 | ||||||||
\(928\) | 0.997230 | 0.0327357 | ||||||||
\(929\) | 9.88080 | 0.324179 | 0.162089 | − | 0.986776i | \(-0.448177\pi\) | ||||
0.162089 | + | 0.986776i | \(0.448177\pi\) | |||||||
\(930\) | 26.3443 | 0.863864 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25.7459 | 0.843334 | ||||||||
\(933\) | −41.0591 | −1.34421 | ||||||||
\(934\) | −25.3370 | −0.829052 | ||||||||
\(935\) | 2.79952 | 0.0915539 | ||||||||
\(936\) | −22.9076 | −0.748758 | ||||||||
\(937\) | 40.4795 | 1.32241 | 0.661204 | − | 0.750206i | \(-0.270046\pi\) | ||||
0.661204 | + | 0.750206i | \(0.270046\pi\) | |||||||
\(938\) | −1.09883 | −0.0358781 | ||||||||
\(939\) | 49.1901 | 1.60526 | ||||||||
\(940\) | −5.31945 | −0.173501 | ||||||||
\(941\) | 39.2993 | 1.28112 | 0.640560 | − | 0.767908i | \(-0.278702\pi\) | ||||
0.640560 | + | 0.767908i | \(0.278702\pi\) | |||||||
\(942\) | −42.8491 | −1.39610 | ||||||||
\(943\) | 48.5374 | 1.58060 | ||||||||
\(944\) | 3.36961 | 0.109671 | ||||||||
\(945\) | −6.29723 | −0.204849 | ||||||||
\(946\) | 8.58523 | 0.279130 | ||||||||
\(947\) | −29.5011 | −0.958657 | −0.479329 | − | 0.877635i | \(-0.659120\pi\) | ||||
−0.479329 | + | 0.877635i | \(0.659120\pi\) | |||||||
\(948\) | −6.78157 | −0.220255 | ||||||||
\(949\) | 70.5596 | 2.29046 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.86755 | 0.255123 | ||||||||
\(952\) | 2.66043 | 0.0862249 | ||||||||
\(953\) | −17.1798 | −0.556509 | −0.278254 | − | 0.960507i | \(-0.589756\pi\) | ||||
−0.278254 | + | 0.960507i | \(0.589756\pi\) | |||||||
\(954\) | −35.2445 | −1.14108 | ||||||||
\(955\) | 8.47622 | 0.274284 | ||||||||
\(956\) | −1.70859 | −0.0552597 | ||||||||
\(957\) | −2.14879 | −0.0694604 | ||||||||
\(958\) | −28.2100 | −0.911424 | ||||||||
\(959\) | −14.3031 | −0.461873 | ||||||||
\(960\) | −3.75015 | −0.121036 | ||||||||
\(961\) | 18.3487 | 0.591894 | ||||||||
\(962\) | −27.3729 | −0.882537 | ||||||||
\(963\) | −20.8214 | −0.670959 | ||||||||
\(964\) | −6.93003 | −0.223201 | ||||||||
\(965\) | −18.8117 | −0.605571 | ||||||||
\(966\) | −12.4863 | −0.401740 | ||||||||
\(967\) | −38.1823 | −1.22786 | −0.613929 | − | 0.789361i | \(-0.710412\pi\) | ||||
−0.613929 | + | 0.789361i | \(0.710412\pi\) | |||||||
\(968\) | −10.3954 | −0.334120 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.14000 | −0.100819 | ||||||||
\(971\) | −2.36181 | −0.0757940 | −0.0378970 | − | 0.999282i | \(-0.512066\pi\) | ||||
−0.0378970 | + | 0.999282i | \(0.512066\pi\) | |||||||
\(972\) | 17.1265 | 0.549333 | ||||||||
\(973\) | 3.65688 | 0.117234 | ||||||||
\(974\) | 28.1520 | 0.902050 | ||||||||
\(975\) | −42.9867 | −1.37668 | ||||||||
\(976\) | −3.75523 | −0.120202 | ||||||||
\(977\) | −35.2488 | −1.12771 | −0.563854 | − | 0.825874i | \(-0.690682\pi\) | ||||
−0.563854 | + | 0.825874i | \(0.690682\pi\) | |||||||
\(978\) | −58.5990 | −1.87379 | ||||||||
\(979\) | 11.4435 | 0.365737 | ||||||||
\(980\) | 1.35329 | 0.0432293 | ||||||||
\(981\) | 48.8385 | 1.55929 | ||||||||
\(982\) | −19.1536 | −0.611217 | ||||||||
\(983\) | 23.1990 | 0.739934 | 0.369967 | − | 0.929045i | \(-0.379369\pi\) | ||||
0.369967 | + | 0.929045i | \(0.379369\pi\) | |||||||
\(984\) | −29.8510 | −0.951614 | ||||||||
\(985\) | 5.93864 | 0.189221 | ||||||||
\(986\) | 2.65306 | 0.0844905 | ||||||||
\(987\) | 10.8926 | 0.346716 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 49.7494 | 1.58194 | ||||||||
\(990\) | 4.92382 | 0.156489 | ||||||||
\(991\) | 23.9624 | 0.761190 | 0.380595 | − | 0.924742i | \(-0.375719\pi\) | ||||
0.380595 | + | 0.924742i | \(0.375719\pi\) | |||||||
\(992\) | −7.02486 | −0.223040 | ||||||||
\(993\) | −7.64898 | −0.242733 | ||||||||
\(994\) | 8.04901 | 0.255299 | ||||||||
\(995\) | −28.6368 | −0.907846 | ||||||||
\(996\) | −38.7218 | −1.22695 | ||||||||
\(997\) | −9.40995 | −0.298016 | −0.149008 | − | 0.988836i | \(-0.547608\pi\) | ||||
−0.149008 | + | 0.988836i | \(0.547608\pi\) | |||||||
\(998\) | 7.01992 | 0.222212 | ||||||||
\(999\) | −26.0178 | −0.823166 |
(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 | 5054.2.a.bm.1.1 | 12 | ||
19.2 | odd | 18 | 266.2.u.d.99.4 | yes | 24 | ||
19.10 | odd | 18 | 266.2.u.d.43.4 | ✓ | 24 | ||
19.18 | odd | 2 | 5054.2.a.bl.1.12 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
266.2.u.d.43.4 | ✓ | 24 | 19.10 | odd | 18 | ||
266.2.u.d.99.4 | yes | 24 | 19.2 | odd | 18 | ||
5054.2.a.bl.1.12 | 12 | 19.18 | odd | 2 | |||
5054.2.a.bm.1.1 | 12 | 1.1 | even | 1 | trivial |