Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | 0.846820 | 0.488912 | 0.244456 | − | 0.969660i | \(-0.421391\pi\) | ||||
0.244456 | + | 0.969660i | \(0.421391\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.51574 | 1.12507 | 0.562537 | − | 0.826772i | \(-0.309825\pi\) | ||||
0.562537 | + | 0.826772i | \(0.309825\pi\) | |||||||
\(6\) | 0.846820 | 0.345713 | ||||||||
\(7\) | −3.73115 | −1.41024 | −0.705122 | − | 0.709086i | \(-0.749108\pi\) | ||||
−0.705122 | + | 0.709086i | \(0.749108\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.28290 | −0.760965 | ||||||||
\(10\) | 2.51574 | 0.795547 | ||||||||
\(11\) | −0.0753521 | −0.0227195 | −0.0113598 | − | 0.999935i | \(-0.503616\pi\) | ||||
−0.0113598 | + | 0.999935i | \(0.503616\pi\) | |||||||
\(12\) | 0.846820 | 0.244456 | ||||||||
\(13\) | −5.73702 | −1.59116 | −0.795582 | − | 0.605846i | \(-0.792835\pi\) | ||||
−0.795582 | + | 0.605846i | \(0.792835\pi\) | |||||||
\(14\) | −3.73115 | −0.997193 | ||||||||
\(15\) | 2.13038 | 0.550062 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.44373 | 0.835228 | 0.417614 | − | 0.908625i | \(-0.362866\pi\) | ||||
0.417614 | + | 0.908625i | \(0.362866\pi\) | |||||||
\(18\) | −2.28290 | −0.538084 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.51574 | 0.562537 | ||||||||
\(21\) | −3.15962 | −0.689485 | ||||||||
\(22\) | −0.0753521 | −0.0160651 | ||||||||
\(23\) | 6.79036 | 1.41589 | 0.707944 | − | 0.706269i | \(-0.249623\pi\) | ||||
0.707944 | + | 0.706269i | \(0.249623\pi\) | |||||||
\(24\) | 0.846820 | 0.172856 | ||||||||
\(25\) | 1.32895 | 0.265791 | ||||||||
\(26\) | −5.73702 | −1.12512 | ||||||||
\(27\) | −4.47366 | −0.860957 | ||||||||
\(28\) | −3.73115 | −0.705122 | ||||||||
\(29\) | 1.05848 | 0.196555 | 0.0982777 | − | 0.995159i | \(-0.468667\pi\) | ||||
0.0982777 | + | 0.995159i | \(0.468667\pi\) | |||||||
\(30\) | 2.13038 | 0.388952 | ||||||||
\(31\) | −3.37751 | −0.606619 | −0.303310 | − | 0.952892i | \(-0.598092\pi\) | ||||
−0.303310 | + | 0.952892i | \(0.598092\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.0638097 | −0.0111078 | ||||||||
\(34\) | 3.44373 | 0.590595 | ||||||||
\(35\) | −9.38662 | −1.58663 | ||||||||
\(36\) | −2.28290 | −0.380483 | ||||||||
\(37\) | 0.0136820 | 0.00224930 | 0.00112465 | − | 0.999999i | \(-0.499642\pi\) | ||||
0.00112465 | + | 0.999999i | \(0.499642\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −4.85823 | −0.777939 | ||||||||
\(40\) | 2.51574 | 0.397774 | ||||||||
\(41\) | −5.23820 | −0.818069 | −0.409034 | − | 0.912519i | \(-0.634134\pi\) | ||||
−0.409034 | + | 0.912519i | \(0.634134\pi\) | |||||||
\(42\) | −3.15962 | −0.487539 | ||||||||
\(43\) | −8.50526 | −1.29704 | −0.648520 | − | 0.761198i | \(-0.724612\pi\) | ||||
−0.648520 | + | 0.761198i | \(0.724612\pi\) | |||||||
\(44\) | −0.0753521 | −0.0113598 | ||||||||
\(45\) | −5.74317 | −0.856142 | ||||||||
\(46\) | 6.79036 | 1.00118 | ||||||||
\(47\) | −6.20848 | −0.905600 | −0.452800 | − | 0.891612i | \(-0.649575\pi\) | ||||
−0.452800 | + | 0.891612i | \(0.649575\pi\) | |||||||
\(48\) | 0.846820 | 0.122228 | ||||||||
\(49\) | 6.92151 | 0.988788 | ||||||||
\(50\) | 1.32895 | 0.187943 | ||||||||
\(51\) | 2.91622 | 0.408353 | ||||||||
\(52\) | −5.73702 | −0.795582 | ||||||||
\(53\) | 3.31645 | 0.455550 | 0.227775 | − | 0.973714i | \(-0.426855\pi\) | ||||
0.227775 | + | 0.973714i | \(0.426855\pi\) | |||||||
\(54\) | −4.47366 | −0.608788 | ||||||||
\(55\) | −0.189566 | −0.0255611 | ||||||||
\(56\) | −3.73115 | −0.498596 | ||||||||
\(57\) | 0.846820 | 0.112164 | ||||||||
\(58\) | 1.05848 | 0.138986 | ||||||||
\(59\) | 8.85589 | 1.15294 | 0.576469 | − | 0.817119i | \(-0.304430\pi\) | ||||
0.576469 | + | 0.817119i | \(0.304430\pi\) | |||||||
\(60\) | 2.13038 | 0.275031 | ||||||||
\(61\) | −1.05386 | −0.134933 | −0.0674665 | − | 0.997722i | \(-0.521492\pi\) | ||||
−0.0674665 | + | 0.997722i | \(0.521492\pi\) | |||||||
\(62\) | −3.37751 | −0.428944 | ||||||||
\(63\) | 8.51784 | 1.07315 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −14.4329 | −1.79018 | ||||||||
\(66\) | −0.0638097 | −0.00785443 | ||||||||
\(67\) | −14.4792 | −1.76891 | −0.884455 | − | 0.466625i | \(-0.845470\pi\) | ||||
−0.884455 | + | 0.466625i | \(0.845470\pi\) | |||||||
\(68\) | 3.44373 | 0.417614 | ||||||||
\(69\) | 5.75021 | 0.692244 | ||||||||
\(70\) | −9.38662 | −1.12192 | ||||||||
\(71\) | −10.5764 | −1.25518 | −0.627592 | − | 0.778542i | \(-0.715960\pi\) | ||||
−0.627592 | + | 0.778542i | \(0.715960\pi\) | |||||||
\(72\) | −2.28290 | −0.269042 | ||||||||
\(73\) | −10.5869 | −1.23910 | −0.619550 | − | 0.784957i | \(-0.712685\pi\) | ||||
−0.619550 | + | 0.784957i | \(0.712685\pi\) | |||||||
\(74\) | 0.0136820 | 0.00159050 | ||||||||
\(75\) | 1.12539 | 0.129948 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0.281150 | 0.0320400 | ||||||||
\(78\) | −4.85823 | −0.550086 | ||||||||
\(79\) | 9.08302 | 1.02192 | 0.510960 | − | 0.859604i | \(-0.329290\pi\) | ||||
0.510960 | + | 0.859604i | \(0.329290\pi\) | |||||||
\(80\) | 2.51574 | 0.281268 | ||||||||
\(81\) | 3.06030 | 0.340033 | ||||||||
\(82\) | −5.23820 | −0.578462 | ||||||||
\(83\) | 0.661023 | 0.0725567 | 0.0362784 | − | 0.999342i | \(-0.488450\pi\) | ||||
0.0362784 | + | 0.999342i | \(0.488450\pi\) | |||||||
\(84\) | −3.15962 | −0.344742 | ||||||||
\(85\) | 8.66354 | 0.939693 | ||||||||
\(86\) | −8.50526 | −0.917145 | ||||||||
\(87\) | 0.896345 | 0.0960983 | ||||||||
\(88\) | −0.0753521 | −0.00803256 | ||||||||
\(89\) | −4.15153 | −0.440061 | −0.220030 | − | 0.975493i | \(-0.570616\pi\) | ||||
−0.220030 | + | 0.975493i | \(0.570616\pi\) | |||||||
\(90\) | −5.74317 | −0.605384 | ||||||||
\(91\) | 21.4057 | 2.24393 | ||||||||
\(92\) | 6.79036 | 0.707944 | ||||||||
\(93\) | −2.86015 | −0.296583 | ||||||||
\(94\) | −6.20848 | −0.640356 | ||||||||
\(95\) | 2.51574 | 0.258110 | ||||||||
\(96\) | 0.846820 | 0.0864282 | ||||||||
\(97\) | −0.682779 | −0.0693257 | −0.0346628 | − | 0.999399i | \(-0.511036\pi\) | ||||
−0.0346628 | + | 0.999399i | \(0.511036\pi\) | |||||||
\(98\) | 6.92151 | 0.699178 | ||||||||
\(99\) | 0.172021 | 0.0172888 | ||||||||
\(100\) | 1.32895 | 0.132895 | ||||||||
\(101\) | −6.09314 | −0.606290 | −0.303145 | − | 0.952944i | \(-0.598037\pi\) | ||||
−0.303145 | + | 0.952944i | \(0.598037\pi\) | |||||||
\(102\) | 2.91622 | 0.288749 | ||||||||
\(103\) | −16.5270 | −1.62846 | −0.814228 | − | 0.580545i | \(-0.802840\pi\) | ||||
−0.814228 | + | 0.580545i | \(0.802840\pi\) | |||||||
\(104\) | −5.73702 | −0.562561 | ||||||||
\(105\) | −7.94878 | −0.775721 | ||||||||
\(106\) | 3.31645 | 0.322122 | ||||||||
\(107\) | 9.14029 | 0.883625 | 0.441813 | − | 0.897107i | \(-0.354336\pi\) | ||||
0.441813 | + | 0.897107i | \(0.354336\pi\) | |||||||
\(108\) | −4.47366 | −0.430478 | ||||||||
\(109\) | 4.48298 | 0.429392 | 0.214696 | − | 0.976681i | \(-0.431124\pi\) | ||||
0.214696 | + | 0.976681i | \(0.431124\pi\) | |||||||
\(110\) | −0.189566 | −0.0180744 | ||||||||
\(111\) | 0.0115862 | 0.00109971 | ||||||||
\(112\) | −3.73115 | −0.352561 | ||||||||
\(113\) | −19.2161 | −1.80770 | −0.903850 | − | 0.427849i | \(-0.859271\pi\) | ||||
−0.903850 | + | 0.427849i | \(0.859271\pi\) | |||||||
\(114\) | 0.846820 | 0.0793120 | ||||||||
\(115\) | 17.0828 | 1.59298 | ||||||||
\(116\) | 1.05848 | 0.0982777 | ||||||||
\(117\) | 13.0970 | 1.21082 | ||||||||
\(118\) | 8.85589 | 0.815250 | ||||||||
\(119\) | −12.8491 | −1.17787 | ||||||||
\(120\) | 2.13038 | 0.194476 | ||||||||
\(121\) | −10.9943 | −0.999484 | ||||||||
\(122\) | −1.05386 | −0.0954121 | ||||||||
\(123\) | −4.43581 | −0.399964 | ||||||||
\(124\) | −3.37751 | −0.303310 | ||||||||
\(125\) | −9.23540 | −0.826039 | ||||||||
\(126\) | 8.51784 | 0.758829 | ||||||||
\(127\) | −13.1175 | −1.16399 | −0.581995 | − | 0.813192i | \(-0.697728\pi\) | ||||
−0.581995 | + | 0.813192i | \(0.697728\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.20242 | −0.634138 | ||||||||
\(130\) | −14.4329 | −1.26585 | ||||||||
\(131\) | 13.7876 | 1.20463 | 0.602316 | − | 0.798258i | \(-0.294245\pi\) | ||||
0.602316 | + | 0.798258i | \(0.294245\pi\) | |||||||
\(132\) | −0.0638097 | −0.00555392 | ||||||||
\(133\) | −3.73115 | −0.323532 | ||||||||
\(134\) | −14.4792 | −1.25081 | ||||||||
\(135\) | −11.2546 | −0.968640 | ||||||||
\(136\) | 3.44373 | 0.295298 | ||||||||
\(137\) | −3.46483 | −0.296020 | −0.148010 | − | 0.988986i | \(-0.547287\pi\) | ||||
−0.148010 | + | 0.988986i | \(0.547287\pi\) | |||||||
\(138\) | 5.75021 | 0.489491 | ||||||||
\(139\) | −4.06379 | −0.344686 | −0.172343 | − | 0.985037i | \(-0.555134\pi\) | ||||
−0.172343 | + | 0.985037i | \(0.555134\pi\) | |||||||
\(140\) | −9.38662 | −0.793314 | ||||||||
\(141\) | −5.25747 | −0.442759 | ||||||||
\(142\) | −10.5764 | −0.887550 | ||||||||
\(143\) | 0.432297 | 0.0361505 | ||||||||
\(144\) | −2.28290 | −0.190241 | ||||||||
\(145\) | 2.66287 | 0.221139 | ||||||||
\(146\) | −10.5869 | −0.876176 | ||||||||
\(147\) | 5.86128 | 0.483430 | ||||||||
\(148\) | 0.0136820 | 0.00112465 | ||||||||
\(149\) | 3.68372 | 0.301782 | 0.150891 | − | 0.988550i | \(-0.451786\pi\) | ||||
0.150891 | + | 0.988550i | \(0.451786\pi\) | |||||||
\(150\) | 1.12539 | 0.0918873 | ||||||||
\(151\) | 7.08380 | 0.576472 | 0.288236 | − | 0.957559i | \(-0.406931\pi\) | ||||
0.288236 | + | 0.957559i | \(0.406931\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −7.86168 | −0.635579 | ||||||||
\(154\) | 0.281150 | 0.0226557 | ||||||||
\(155\) | −8.49695 | −0.682491 | ||||||||
\(156\) | −4.85823 | −0.388969 | ||||||||
\(157\) | −1.84050 | −0.146888 | −0.0734439 | − | 0.997299i | \(-0.523399\pi\) | ||||
−0.0734439 | + | 0.997299i | \(0.523399\pi\) | |||||||
\(158\) | 9.08302 | 0.722607 | ||||||||
\(159\) | 2.80844 | 0.222724 | ||||||||
\(160\) | 2.51574 | 0.198887 | ||||||||
\(161\) | −25.3359 | −1.99675 | ||||||||
\(162\) | 3.06030 | 0.240440 | ||||||||
\(163\) | −9.61863 | −0.753390 | −0.376695 | − | 0.926337i | \(-0.622939\pi\) | ||||
−0.376695 | + | 0.926337i | \(0.622939\pi\) | |||||||
\(164\) | −5.23820 | −0.409034 | ||||||||
\(165\) | −0.160529 | −0.0124971 | ||||||||
\(166\) | 0.661023 | 0.0513053 | ||||||||
\(167\) | 10.5078 | 0.813120 | 0.406560 | − | 0.913624i | \(-0.366728\pi\) | ||||
0.406560 | + | 0.913624i | \(0.366728\pi\) | |||||||
\(168\) | −3.15962 | −0.243770 | ||||||||
\(169\) | 19.9134 | 1.53180 | ||||||||
\(170\) | 8.66354 | 0.664463 | ||||||||
\(171\) | −2.28290 | −0.174577 | ||||||||
\(172\) | −8.50526 | −0.648520 | ||||||||
\(173\) | −10.9446 | −0.832099 | −0.416049 | − | 0.909342i | \(-0.636586\pi\) | ||||
−0.416049 | + | 0.909342i | \(0.636586\pi\) | |||||||
\(174\) | 0.896345 | 0.0679517 | ||||||||
\(175\) | −4.95853 | −0.374830 | ||||||||
\(176\) | −0.0753521 | −0.00567988 | ||||||||
\(177\) | 7.49934 | 0.563685 | ||||||||
\(178\) | −4.15153 | −0.311170 | ||||||||
\(179\) | 6.23538 | 0.466054 | 0.233027 | − | 0.972470i | \(-0.425137\pi\) | ||||
0.233027 | + | 0.972470i | \(0.425137\pi\) | |||||||
\(180\) | −5.74317 | −0.428071 | ||||||||
\(181\) | 9.18136 | 0.682445 | 0.341223 | − | 0.939982i | \(-0.389159\pi\) | ||||
0.341223 | + | 0.939982i | \(0.389159\pi\) | |||||||
\(182\) | 21.4057 | 1.58670 | ||||||||
\(183\) | −0.892431 | −0.0659704 | ||||||||
\(184\) | 6.79036 | 0.500592 | ||||||||
\(185\) | 0.0344203 | 0.00253063 | ||||||||
\(186\) | −2.86015 | −0.209716 | ||||||||
\(187\) | −0.259492 | −0.0189760 | ||||||||
\(188\) | −6.20848 | −0.452800 | ||||||||
\(189\) | 16.6919 | 1.21416 | ||||||||
\(190\) | 2.51574 | 0.182511 | ||||||||
\(191\) | −4.66074 | −0.337239 | −0.168619 | − | 0.985681i | \(-0.553931\pi\) | ||||
−0.168619 | + | 0.985681i | \(0.553931\pi\) | |||||||
\(192\) | 0.846820 | 0.0611140 | ||||||||
\(193\) | 2.69972 | 0.194330 | 0.0971650 | − | 0.995268i | \(-0.469023\pi\) | ||||
0.0971650 | + | 0.995268i | \(0.469023\pi\) | |||||||
\(194\) | −0.682779 | −0.0490207 | ||||||||
\(195\) | −12.2220 | −0.875238 | ||||||||
\(196\) | 6.92151 | 0.494394 | ||||||||
\(197\) | −17.6195 | −1.25534 | −0.627668 | − | 0.778481i | \(-0.715990\pi\) | ||||
−0.627668 | + | 0.778481i | \(0.715990\pi\) | |||||||
\(198\) | 0.172021 | 0.0122250 | ||||||||
\(199\) | 11.3966 | 0.807887 | 0.403943 | − | 0.914784i | \(-0.367639\pi\) | ||||
0.403943 | + | 0.914784i | \(0.367639\pi\) | |||||||
\(200\) | 1.32895 | 0.0939713 | ||||||||
\(201\) | −12.2612 | −0.864841 | ||||||||
\(202\) | −6.09314 | −0.428712 | ||||||||
\(203\) | −3.94936 | −0.277191 | ||||||||
\(204\) | 2.91622 | 0.204176 | ||||||||
\(205\) | −13.1779 | −0.920388 | ||||||||
\(206\) | −16.5270 | −1.15149 | ||||||||
\(207\) | −15.5017 | −1.07744 | ||||||||
\(208\) | −5.73702 | −0.397791 | ||||||||
\(209\) | −0.0753521 | −0.00521221 | ||||||||
\(210\) | −7.94878 | −0.548518 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 3.31645 | 0.227775 | ||||||||
\(213\) | −8.95629 | −0.613675 | ||||||||
\(214\) | 9.14029 | 0.624817 | ||||||||
\(215\) | −21.3970 | −1.45927 | ||||||||
\(216\) | −4.47366 | −0.304394 | ||||||||
\(217\) | 12.6020 | 0.855481 | ||||||||
\(218\) | 4.48298 | 0.303626 | ||||||||
\(219\) | −8.96518 | −0.605811 | ||||||||
\(220\) | −0.189566 | −0.0127806 | ||||||||
\(221\) | −19.7568 | −1.32898 | ||||||||
\(222\) | 0.0115862 | 0.000777614 0 | ||||||||
\(223\) | −22.9125 | −1.53434 | −0.767169 | − | 0.641446i | \(-0.778335\pi\) | ||||
−0.767169 | + | 0.641446i | \(0.778335\pi\) | |||||||
\(224\) | −3.73115 | −0.249298 | ||||||||
\(225\) | −3.03386 | −0.202258 | ||||||||
\(226\) | −19.2161 | −1.27824 | ||||||||
\(227\) | −14.4216 | −0.957196 | −0.478598 | − | 0.878034i | \(-0.658855\pi\) | ||||
−0.478598 | + | 0.878034i | \(0.658855\pi\) | |||||||
\(228\) | 0.846820 | 0.0560820 | ||||||||
\(229\) | −23.6041 | −1.55980 | −0.779902 | − | 0.625901i | \(-0.784731\pi\) | ||||
−0.779902 | + | 0.625901i | \(0.784731\pi\) | |||||||
\(230\) | 17.0828 | 1.12641 | ||||||||
\(231\) | 0.238084 | 0.0156648 | ||||||||
\(232\) | 1.05848 | 0.0694928 | ||||||||
\(233\) | −25.4543 | −1.66757 | −0.833784 | − | 0.552090i | \(-0.813830\pi\) | ||||
−0.833784 | + | 0.552090i | \(0.813830\pi\) | |||||||
\(234\) | 13.0970 | 0.856179 | ||||||||
\(235\) | −15.6189 | −1.01887 | ||||||||
\(236\) | 8.85589 | 0.576469 | ||||||||
\(237\) | 7.69169 | 0.499629 | ||||||||
\(238\) | −12.8491 | −0.832883 | ||||||||
\(239\) | −8.55439 | −0.553338 | −0.276669 | − | 0.960965i | \(-0.589230\pi\) | ||||
−0.276669 | + | 0.960965i | \(0.589230\pi\) | |||||||
\(240\) | 2.13038 | 0.137515 | ||||||||
\(241\) | 25.2877 | 1.62893 | 0.814463 | − | 0.580215i | \(-0.197031\pi\) | ||||
0.814463 | + | 0.580215i | \(0.197031\pi\) | |||||||
\(242\) | −10.9943 | −0.706742 | ||||||||
\(243\) | 16.0125 | 1.02720 | ||||||||
\(244\) | −1.05386 | −0.0674665 | ||||||||
\(245\) | 17.4127 | 1.11246 | ||||||||
\(246\) | −4.43581 | −0.282817 | ||||||||
\(247\) | −5.73702 | −0.365038 | ||||||||
\(248\) | −3.37751 | −0.214472 | ||||||||
\(249\) | 0.559768 | 0.0354738 | ||||||||
\(250\) | −9.23540 | −0.584098 | ||||||||
\(251\) | 13.8372 | 0.873394 | 0.436697 | − | 0.899609i | \(-0.356148\pi\) | ||||
0.436697 | + | 0.899609i | \(0.356148\pi\) | |||||||
\(252\) | 8.51784 | 0.536573 | ||||||||
\(253\) | −0.511668 | −0.0321683 | ||||||||
\(254\) | −13.1175 | −0.823066 | ||||||||
\(255\) | 7.33646 | 0.459427 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.16464 | 0.0726482 | 0.0363241 | − | 0.999340i | \(-0.488435\pi\) | ||||
0.0363241 | + | 0.999340i | \(0.488435\pi\) | |||||||
\(258\) | −7.20242 | −0.448403 | ||||||||
\(259\) | −0.0510496 | −0.00317207 | ||||||||
\(260\) | −14.4329 | −0.895088 | ||||||||
\(261\) | −2.41641 | −0.149572 | ||||||||
\(262\) | 13.7876 | 0.851804 | ||||||||
\(263\) | 17.2266 | 1.06224 | 0.531120 | − | 0.847297i | \(-0.321771\pi\) | ||||
0.531120 | + | 0.847297i | \(0.321771\pi\) | |||||||
\(264\) | −0.0638097 | −0.00392721 | ||||||||
\(265\) | 8.34333 | 0.512527 | ||||||||
\(266\) | −3.73115 | −0.228772 | ||||||||
\(267\) | −3.51560 | −0.215151 | ||||||||
\(268\) | −14.4792 | −0.884455 | ||||||||
\(269\) | −5.59641 | −0.341219 | −0.170610 | − | 0.985339i | \(-0.554574\pi\) | ||||
−0.170610 | + | 0.985339i | \(0.554574\pi\) | |||||||
\(270\) | −11.2546 | −0.684932 | ||||||||
\(271\) | −6.36372 | −0.386568 | −0.193284 | − | 0.981143i | \(-0.561914\pi\) | ||||
−0.193284 | + | 0.981143i | \(0.561914\pi\) | |||||||
\(272\) | 3.44373 | 0.208807 | ||||||||
\(273\) | 18.1268 | 1.09708 | ||||||||
\(274\) | −3.46483 | −0.209318 | ||||||||
\(275\) | −0.100139 | −0.00603864 | ||||||||
\(276\) | 5.75021 | 0.346122 | ||||||||
\(277\) | 23.2939 | 1.39959 | 0.699797 | − | 0.714342i | \(-0.253274\pi\) | ||||
0.699797 | + | 0.714342i | \(0.253274\pi\) | |||||||
\(278\) | −4.06379 | −0.243730 | ||||||||
\(279\) | 7.71051 | 0.461616 | ||||||||
\(280\) | −9.38662 | −0.560958 | ||||||||
\(281\) | 30.9071 | 1.84376 | 0.921880 | − | 0.387475i | \(-0.126653\pi\) | ||||
0.921880 | + | 0.387475i | \(0.126653\pi\) | |||||||
\(282\) | −5.25747 | −0.313078 | ||||||||
\(283\) | 7.88482 | 0.468704 | 0.234352 | − | 0.972152i | \(-0.424703\pi\) | ||||
0.234352 | + | 0.972152i | \(0.424703\pi\) | |||||||
\(284\) | −10.5764 | −0.627592 | ||||||||
\(285\) | 2.13038 | 0.126193 | ||||||||
\(286\) | 0.432297 | 0.0255622 | ||||||||
\(287\) | 19.5445 | 1.15368 | ||||||||
\(288\) | −2.28290 | −0.134521 | ||||||||
\(289\) | −5.14071 | −0.302394 | ||||||||
\(290\) | 2.66287 | 0.156369 | ||||||||
\(291\) | −0.578191 | −0.0338942 | ||||||||
\(292\) | −10.5869 | −0.619550 | ||||||||
\(293\) | −26.7684 | −1.56382 | −0.781912 | − | 0.623389i | \(-0.785755\pi\) | ||||
−0.781912 | + | 0.623389i | \(0.785755\pi\) | |||||||
\(294\) | 5.86128 | 0.341837 | ||||||||
\(295\) | 22.2791 | 1.29714 | ||||||||
\(296\) | 0.0136820 | 0.000795249 0 | ||||||||
\(297\) | 0.337100 | 0.0195605 | ||||||||
\(298\) | 3.68372 | 0.213392 | ||||||||
\(299\) | −38.9564 | −2.25291 | ||||||||
\(300\) | 1.12539 | 0.0649741 | ||||||||
\(301\) | 31.7344 | 1.82914 | ||||||||
\(302\) | 7.08380 | 0.407627 | ||||||||
\(303\) | −5.15979 | −0.296422 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −2.65124 | −0.151810 | ||||||||
\(306\) | −7.86168 | −0.449422 | ||||||||
\(307\) | 21.6088 | 1.23328 | 0.616638 | − | 0.787247i | \(-0.288494\pi\) | ||||
0.616638 | + | 0.787247i | \(0.288494\pi\) | |||||||
\(308\) | 0.281150 | 0.0160200 | ||||||||
\(309\) | −13.9954 | −0.796172 | ||||||||
\(310\) | −8.49695 | −0.482594 | ||||||||
\(311\) | 4.23255 | 0.240006 | 0.120003 | − | 0.992774i | \(-0.461710\pi\) | ||||
0.120003 | + | 0.992774i | \(0.461710\pi\) | |||||||
\(312\) | −4.85823 | −0.275043 | ||||||||
\(313\) | 21.2458 | 1.20088 | 0.600442 | − | 0.799668i | \(-0.294991\pi\) | ||||
0.600442 | + | 0.799668i | \(0.294991\pi\) | |||||||
\(314\) | −1.84050 | −0.103865 | ||||||||
\(315\) | 21.4287 | 1.20737 | ||||||||
\(316\) | 9.08302 | 0.510960 | ||||||||
\(317\) | 24.3234 | 1.36614 | 0.683070 | − | 0.730353i | \(-0.260644\pi\) | ||||
0.683070 | + | 0.730353i | \(0.260644\pi\) | |||||||
\(318\) | 2.80844 | 0.157489 | ||||||||
\(319\) | −0.0797589 | −0.00446564 | ||||||||
\(320\) | 2.51574 | 0.140634 | ||||||||
\(321\) | 7.74018 | 0.432015 | ||||||||
\(322\) | −25.3359 | −1.41191 | ||||||||
\(323\) | 3.44373 | 0.191614 | ||||||||
\(324\) | 3.06030 | 0.170017 | ||||||||
\(325\) | −7.62424 | −0.422917 | ||||||||
\(326\) | −9.61863 | −0.532727 | ||||||||
\(327\) | 3.79628 | 0.209935 | ||||||||
\(328\) | −5.23820 | −0.289231 | ||||||||
\(329\) | 23.1648 | 1.27712 | ||||||||
\(330\) | −0.160529 | −0.00883681 | ||||||||
\(331\) | 9.82654 | 0.540115 | 0.270058 | − | 0.962844i | \(-0.412957\pi\) | ||||
0.270058 | + | 0.962844i | \(0.412957\pi\) | |||||||
\(332\) | 0.661023 | 0.0362784 | ||||||||
\(333\) | −0.0312345 | −0.00171164 | ||||||||
\(334\) | 10.5078 | 0.574962 | ||||||||
\(335\) | −36.4258 | −1.99015 | ||||||||
\(336\) | −3.15962 | −0.172371 | ||||||||
\(337\) | 16.0274 | 0.873070 | 0.436535 | − | 0.899687i | \(-0.356206\pi\) | ||||
0.436535 | + | 0.899687i | \(0.356206\pi\) | |||||||
\(338\) | 19.9134 | 1.08315 | ||||||||
\(339\) | −16.2726 | −0.883806 | ||||||||
\(340\) | 8.66354 | 0.469846 | ||||||||
\(341\) | 0.254503 | 0.0137821 | ||||||||
\(342\) | −2.28290 | −0.123445 | ||||||||
\(343\) | 0.292848 | 0.0158123 | ||||||||
\(344\) | −8.50526 | −0.458573 | ||||||||
\(345\) | 14.4661 | 0.778826 | ||||||||
\(346\) | −10.9446 | −0.588383 | ||||||||
\(347\) | 3.93856 | 0.211433 | 0.105717 | − | 0.994396i | \(-0.466286\pi\) | ||||
0.105717 | + | 0.994396i | \(0.466286\pi\) | |||||||
\(348\) | 0.896345 | 0.0480491 | ||||||||
\(349\) | 1.23767 | 0.0662512 | 0.0331256 | − | 0.999451i | \(-0.489454\pi\) | ||||
0.0331256 | + | 0.999451i | \(0.489454\pi\) | |||||||
\(350\) | −4.95853 | −0.265045 | ||||||||
\(351\) | 25.6655 | 1.36992 | ||||||||
\(352\) | −0.0753521 | −0.00401628 | ||||||||
\(353\) | 5.65440 | 0.300953 | 0.150477 | − | 0.988614i | \(-0.451919\pi\) | ||||
0.150477 | + | 0.988614i | \(0.451919\pi\) | |||||||
\(354\) | 7.49934 | 0.398586 | ||||||||
\(355\) | −26.6074 | −1.41218 | ||||||||
\(356\) | −4.15153 | −0.220030 | ||||||||
\(357\) | −10.8809 | −0.575877 | ||||||||
\(358\) | 6.23538 | 0.329550 | ||||||||
\(359\) | 9.74840 | 0.514501 | 0.257250 | − | 0.966345i | \(-0.417184\pi\) | ||||
0.257250 | + | 0.966345i | \(0.417184\pi\) | |||||||
\(360\) | −5.74317 | −0.302692 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 9.18136 | 0.482562 | ||||||||
\(363\) | −9.31021 | −0.488660 | ||||||||
\(364\) | 21.4057 | 1.12196 | ||||||||
\(365\) | −26.6339 | −1.39408 | ||||||||
\(366\) | −0.892431 | −0.0466481 | ||||||||
\(367\) | −8.60189 | −0.449015 | −0.224507 | − | 0.974472i | \(-0.572077\pi\) | ||||
−0.224507 | + | 0.974472i | \(0.572077\pi\) | |||||||
\(368\) | 6.79036 | 0.353972 | ||||||||
\(369\) | 11.9583 | 0.622522 | ||||||||
\(370\) | 0.0344203 | 0.00178943 | ||||||||
\(371\) | −12.3742 | −0.642436 | ||||||||
\(372\) | −2.86015 | −0.148292 | ||||||||
\(373\) | 6.05625 | 0.313581 | 0.156790 | − | 0.987632i | \(-0.449885\pi\) | ||||
0.156790 | + | 0.987632i | \(0.449885\pi\) | |||||||
\(374\) | −0.259492 | −0.0134180 | ||||||||
\(375\) | −7.82072 | −0.403860 | ||||||||
\(376\) | −6.20848 | −0.320178 | ||||||||
\(377\) | −6.07254 | −0.312752 | ||||||||
\(378\) | 16.6919 | 0.858540 | ||||||||
\(379\) | 20.3044 | 1.04296 | 0.521482 | − | 0.853262i | \(-0.325379\pi\) | ||||
0.521482 | + | 0.853262i | \(0.325379\pi\) | |||||||
\(380\) | 2.51574 | 0.129055 | ||||||||
\(381\) | −11.1082 | −0.569089 | ||||||||
\(382\) | −4.66074 | −0.238464 | ||||||||
\(383\) | 31.1049 | 1.58939 | 0.794694 | − | 0.607011i | \(-0.207632\pi\) | ||||
0.794694 | + | 0.607011i | \(0.207632\pi\) | |||||||
\(384\) | 0.846820 | 0.0432141 | ||||||||
\(385\) | 0.707301 | 0.0360474 | ||||||||
\(386\) | 2.69972 | 0.137412 | ||||||||
\(387\) | 19.4166 | 0.987002 | ||||||||
\(388\) | −0.682779 | −0.0346628 | ||||||||
\(389\) | −7.23787 | −0.366974 | −0.183487 | − | 0.983022i | \(-0.558739\pi\) | ||||
−0.183487 | + | 0.983022i | \(0.558739\pi\) | |||||||
\(390\) | −12.2220 | −0.618887 | ||||||||
\(391\) | 23.3842 | 1.18259 | ||||||||
\(392\) | 6.92151 | 0.349589 | ||||||||
\(393\) | 11.6757 | 0.588959 | ||||||||
\(394\) | −17.6195 | −0.887657 | ||||||||
\(395\) | 22.8505 | 1.14974 | ||||||||
\(396\) | 0.172021 | 0.00864438 | ||||||||
\(397\) | 22.1359 | 1.11097 | 0.555483 | − | 0.831528i | \(-0.312533\pi\) | ||||
0.555483 | + | 0.831528i | \(0.312533\pi\) | |||||||
\(398\) | 11.3966 | 0.571262 | ||||||||
\(399\) | −3.15962 | −0.158179 | ||||||||
\(400\) | 1.32895 | 0.0664477 | ||||||||
\(401\) | 13.9938 | 0.698816 | 0.349408 | − | 0.936971i | \(-0.386383\pi\) | ||||
0.349408 | + | 0.936971i | \(0.386383\pi\) | |||||||
\(402\) | −12.2612 | −0.611535 | ||||||||
\(403\) | 19.3769 | 0.965230 | ||||||||
\(404\) | −6.09314 | −0.303145 | ||||||||
\(405\) | 7.69892 | 0.382562 | ||||||||
\(406\) | −3.94936 | −0.196004 | ||||||||
\(407\) | −0.00103097 | −5.11031e−5 0 | ||||||||
\(408\) | 2.91622 | 0.144375 | ||||||||
\(409\) | 25.7319 | 1.27236 | 0.636180 | − | 0.771540i | \(-0.280513\pi\) | ||||
0.636180 | + | 0.771540i | \(0.280513\pi\) | |||||||
\(410\) | −13.1779 | −0.650812 | ||||||||
\(411\) | −2.93408 | −0.144728 | ||||||||
\(412\) | −16.5270 | −0.814228 | ||||||||
\(413\) | −33.0427 | −1.62592 | ||||||||
\(414\) | −15.5017 | −0.761866 | ||||||||
\(415\) | 1.66296 | 0.0816316 | ||||||||
\(416\) | −5.73702 | −0.281281 | ||||||||
\(417\) | −3.44130 | −0.168521 | ||||||||
\(418\) | −0.0753521 | −0.00368559 | ||||||||
\(419\) | 1.36340 | 0.0666064 | 0.0333032 | − | 0.999445i | \(-0.489397\pi\) | ||||
0.0333032 | + | 0.999445i | \(0.489397\pi\) | |||||||
\(420\) | −7.94878 | −0.387861 | ||||||||
\(421\) | −2.18984 | −0.106726 | −0.0533632 | − | 0.998575i | \(-0.516994\pi\) | ||||
−0.0533632 | + | 0.998575i | \(0.516994\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 14.1733 | 0.689130 | ||||||||
\(424\) | 3.31645 | 0.161061 | ||||||||
\(425\) | 4.57656 | 0.221996 | ||||||||
\(426\) | −8.95629 | −0.433934 | ||||||||
\(427\) | 3.93212 | 0.190288 | ||||||||
\(428\) | 9.14029 | 0.441813 | ||||||||
\(429\) | 0.366077 | 0.0176744 | ||||||||
\(430\) | −21.3970 | −1.03186 | ||||||||
\(431\) | 8.48009 | 0.408471 | 0.204236 | − | 0.978922i | \(-0.434529\pi\) | ||||
0.204236 | + | 0.978922i | \(0.434529\pi\) | |||||||
\(432\) | −4.47366 | −0.215239 | ||||||||
\(433\) | −10.4229 | −0.500893 | −0.250446 | − | 0.968130i | \(-0.580577\pi\) | ||||
−0.250446 | + | 0.968130i | \(0.580577\pi\) | |||||||
\(434\) | 12.6020 | 0.604916 | ||||||||
\(435\) | 2.25497 | 0.108118 | ||||||||
\(436\) | 4.48298 | 0.214696 | ||||||||
\(437\) | 6.79036 | 0.324827 | ||||||||
\(438\) | −8.96518 | −0.428373 | ||||||||
\(439\) | −12.6496 | −0.603733 | −0.301866 | − | 0.953350i | \(-0.597610\pi\) | ||||
−0.301866 | + | 0.953350i | \(0.597610\pi\) | |||||||
\(440\) | −0.189566 | −0.00903722 | ||||||||
\(441\) | −15.8011 | −0.752433 | ||||||||
\(442\) | −19.7568 | −0.939734 | ||||||||
\(443\) | −35.3294 | −1.67855 | −0.839276 | − | 0.543705i | \(-0.817021\pi\) | ||||
−0.839276 | + | 0.543705i | \(0.817021\pi\) | |||||||
\(444\) | 0.0115862 | 0.000549856 0 | ||||||||
\(445\) | −10.4442 | −0.495101 | ||||||||
\(446\) | −22.9125 | −1.08494 | ||||||||
\(447\) | 3.11945 | 0.147545 | ||||||||
\(448\) | −3.73115 | −0.176280 | ||||||||
\(449\) | −9.46560 | −0.446710 | −0.223355 | − | 0.974737i | \(-0.571701\pi\) | ||||
−0.223355 | + | 0.974737i | \(0.571701\pi\) | |||||||
\(450\) | −3.03386 | −0.143018 | ||||||||
\(451\) | 0.394709 | 0.0185861 | ||||||||
\(452\) | −19.2161 | −0.903850 | ||||||||
\(453\) | 5.99871 | 0.281844 | ||||||||
\(454\) | −14.4216 | −0.676840 | ||||||||
\(455\) | 53.8512 | 2.52459 | ||||||||
\(456\) | 0.846820 | 0.0396560 | ||||||||
\(457\) | −32.0612 | −1.49976 | −0.749879 | − | 0.661575i | \(-0.769889\pi\) | ||||
−0.749879 | + | 0.661575i | \(0.769889\pi\) | |||||||
\(458\) | −23.6041 | −1.10295 | ||||||||
\(459\) | −15.4061 | −0.719095 | ||||||||
\(460\) | 17.0828 | 0.796489 | ||||||||
\(461\) | 27.2979 | 1.27139 | 0.635696 | − | 0.771940i | \(-0.280713\pi\) | ||||
0.635696 | + | 0.771940i | \(0.280713\pi\) | |||||||
\(462\) | 0.238084 | 0.0110767 | ||||||||
\(463\) | 32.4611 | 1.50859 | 0.754297 | − | 0.656533i | \(-0.227978\pi\) | ||||
0.754297 | + | 0.656533i | \(0.227978\pi\) | |||||||
\(464\) | 1.05848 | 0.0491388 | ||||||||
\(465\) | −7.19539 | −0.333678 | ||||||||
\(466\) | −25.4543 | −1.17915 | ||||||||
\(467\) | −31.2049 | −1.44399 | −0.721996 | − | 0.691897i | \(-0.756775\pi\) | ||||
−0.721996 | + | 0.691897i | \(0.756775\pi\) | |||||||
\(468\) | 13.0970 | 0.605410 | ||||||||
\(469\) | 54.0240 | 2.49459 | ||||||||
\(470\) | −15.6189 | −0.720448 | ||||||||
\(471\) | −1.55857 | −0.0718152 | ||||||||
\(472\) | 8.85589 | 0.407625 | ||||||||
\(473\) | 0.640889 | 0.0294681 | ||||||||
\(474\) | 7.69169 | 0.353291 | ||||||||
\(475\) | 1.32895 | 0.0609766 | ||||||||
\(476\) | −12.8491 | −0.588937 | ||||||||
\(477\) | −7.57111 | −0.346657 | ||||||||
\(478\) | −8.55439 | −0.391269 | ||||||||
\(479\) | −22.2905 | −1.01848 | −0.509240 | − | 0.860625i | \(-0.670073\pi\) | ||||
−0.509240 | + | 0.860625i | \(0.670073\pi\) | |||||||
\(480\) | 2.13038 | 0.0972381 | ||||||||
\(481\) | −0.0784939 | −0.00357901 | ||||||||
\(482\) | 25.2877 | 1.15183 | ||||||||
\(483\) | −21.4549 | −0.976233 | ||||||||
\(484\) | −10.9943 | −0.499742 | ||||||||
\(485\) | −1.71770 | −0.0779965 | ||||||||
\(486\) | 16.0125 | 0.726342 | ||||||||
\(487\) | 4.50007 | 0.203918 | 0.101959 | − | 0.994789i | \(-0.467489\pi\) | ||||
0.101959 | + | 0.994789i | \(0.467489\pi\) | |||||||
\(488\) | −1.05386 | −0.0477060 | ||||||||
\(489\) | −8.14525 | −0.368341 | ||||||||
\(490\) | 17.4127 | 0.786627 | ||||||||
\(491\) | −39.6320 | −1.78857 | −0.894284 | − | 0.447499i | \(-0.852315\pi\) | ||||
−0.894284 | + | 0.447499i | \(0.852315\pi\) | |||||||
\(492\) | −4.43581 | −0.199982 | ||||||||
\(493\) | 3.64513 | 0.164169 | ||||||||
\(494\) | −5.73702 | −0.258121 | ||||||||
\(495\) | 0.432760 | 0.0194511 | ||||||||
\(496\) | −3.37751 | −0.151655 | ||||||||
\(497\) | 39.4621 | 1.77012 | ||||||||
\(498\) | 0.559768 | 0.0250838 | ||||||||
\(499\) | 17.7075 | 0.792696 | 0.396348 | − | 0.918100i | \(-0.370277\pi\) | ||||
0.396348 | + | 0.918100i | \(0.370277\pi\) | |||||||
\(500\) | −9.23540 | −0.413020 | ||||||||
\(501\) | 8.89823 | 0.397544 | ||||||||
\(502\) | 13.8372 | 0.617583 | ||||||||
\(503\) | 40.0337 | 1.78501 | 0.892507 | − | 0.451034i | \(-0.148945\pi\) | ||||
0.892507 | + | 0.451034i | \(0.148945\pi\) | |||||||
\(504\) | 8.51784 | 0.379415 | ||||||||
\(505\) | −15.3288 | −0.682121 | ||||||||
\(506\) | −0.511668 | −0.0227464 | ||||||||
\(507\) | 16.8631 | 0.748916 | ||||||||
\(508\) | −13.1175 | −0.581995 | ||||||||
\(509\) | 9.74155 | 0.431786 | 0.215893 | − | 0.976417i | \(-0.430734\pi\) | ||||
0.215893 | + | 0.976417i | \(0.430734\pi\) | |||||||
\(510\) | 7.33646 | 0.324864 | ||||||||
\(511\) | 39.5013 | 1.74743 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.47366 | −0.197517 | ||||||||
\(514\) | 1.16464 | 0.0513700 | ||||||||
\(515\) | −41.5777 | −1.83213 | ||||||||
\(516\) | −7.20242 | −0.317069 | ||||||||
\(517\) | 0.467822 | 0.0205748 | ||||||||
\(518\) | −0.0510496 | −0.00224299 | ||||||||
\(519\) | −9.26807 | −0.406823 | ||||||||
\(520\) | −14.4329 | −0.632923 | ||||||||
\(521\) | −16.2677 | −0.712700 | −0.356350 | − | 0.934353i | \(-0.615979\pi\) | ||||
−0.356350 | + | 0.934353i | \(0.615979\pi\) | |||||||
\(522\) | −2.41641 | −0.105763 | ||||||||
\(523\) | 34.1150 | 1.49174 | 0.745872 | − | 0.666090i | \(-0.232033\pi\) | ||||
0.745872 | + | 0.666090i | \(0.232033\pi\) | |||||||
\(524\) | 13.7876 | 0.602316 | ||||||||
\(525\) | −4.19899 | −0.183259 | ||||||||
\(526\) | 17.2266 | 0.751117 | ||||||||
\(527\) | −11.6312 | −0.506665 | ||||||||
\(528\) | −0.0638097 | −0.00277696 | ||||||||
\(529\) | 23.1090 | 1.00474 | ||||||||
\(530\) | 8.34333 | 0.362411 | ||||||||
\(531\) | −20.2171 | −0.877346 | ||||||||
\(532\) | −3.73115 | −0.161766 | ||||||||
\(533\) | 30.0516 | 1.30168 | ||||||||
\(534\) | −3.51560 | −0.152135 | ||||||||
\(535\) | 22.9946 | 0.994143 | ||||||||
\(536\) | −14.4792 | −0.625404 | ||||||||
\(537\) | 5.28024 | 0.227859 | ||||||||
\(538\) | −5.59641 | −0.241278 | ||||||||
\(539\) | −0.521550 | −0.0224648 | ||||||||
\(540\) | −11.2546 | −0.484320 | ||||||||
\(541\) | −14.8874 | −0.640059 | −0.320029 | − | 0.947408i | \(-0.603693\pi\) | ||||
−0.320029 | + | 0.947408i | \(0.603693\pi\) | |||||||
\(542\) | −6.36372 | −0.273345 | ||||||||
\(543\) | 7.77496 | 0.333656 | ||||||||
\(544\) | 3.44373 | 0.147649 | ||||||||
\(545\) | 11.2780 | 0.483097 | ||||||||
\(546\) | 18.1268 | 0.775755 | ||||||||
\(547\) | −33.1241 | −1.41628 | −0.708142 | − | 0.706070i | \(-0.750467\pi\) | ||||
−0.708142 | + | 0.706070i | \(0.750467\pi\) | |||||||
\(548\) | −3.46483 | −0.148010 | ||||||||
\(549\) | 2.40585 | 0.102679 | ||||||||
\(550\) | −0.100139 | −0.00426996 | ||||||||
\(551\) | 1.05848 | 0.0450929 | ||||||||
\(552\) | 5.75021 | 0.244745 | ||||||||
\(553\) | −33.8902 | −1.44116 | ||||||||
\(554\) | 23.2939 | 0.989662 | ||||||||
\(555\) | 0.0291478 | 0.00123726 | ||||||||
\(556\) | −4.06379 | −0.172343 | ||||||||
\(557\) | −19.4433 | −0.823839 | −0.411920 | − | 0.911220i | \(-0.635142\pi\) | ||||
−0.411920 | + | 0.911220i | \(0.635142\pi\) | |||||||
\(558\) | 7.71051 | 0.326412 | ||||||||
\(559\) | 48.7948 | 2.06380 | ||||||||
\(560\) | −9.38662 | −0.396657 | ||||||||
\(561\) | −0.219743 | −0.00927758 | ||||||||
\(562\) | 30.9071 | 1.30374 | ||||||||
\(563\) | 27.6601 | 1.16573 | 0.582867 | − | 0.812568i | \(-0.301931\pi\) | ||||
0.582867 | + | 0.812568i | \(0.301931\pi\) | |||||||
\(564\) | −5.25747 | −0.221379 | ||||||||
\(565\) | −48.3428 | −2.03380 | ||||||||
\(566\) | 7.88482 | 0.331424 | ||||||||
\(567\) | −11.4184 | −0.479530 | ||||||||
\(568\) | −10.5764 | −0.443775 | ||||||||
\(569\) | −25.2610 | −1.05900 | −0.529499 | − | 0.848311i | \(-0.677620\pi\) | ||||
−0.529499 | + | 0.848311i | \(0.677620\pi\) | |||||||
\(570\) | 2.13038 | 0.0892318 | ||||||||
\(571\) | −2.57697 | −0.107843 | −0.0539213 | − | 0.998545i | \(-0.517172\pi\) | ||||
−0.0539213 | + | 0.998545i | \(0.517172\pi\) | |||||||
\(572\) | 0.432297 | 0.0180752 | ||||||||
\(573\) | −3.94681 | −0.164880 | ||||||||
\(574\) | 19.5445 | 0.815772 | ||||||||
\(575\) | 9.02408 | 0.376330 | ||||||||
\(576\) | −2.28290 | −0.0951206 | ||||||||
\(577\) | 12.0125 | 0.500087 | 0.250043 | − | 0.968235i | \(-0.419555\pi\) | ||||
0.250043 | + | 0.968235i | \(0.419555\pi\) | |||||||
\(578\) | −5.14071 | −0.213825 | ||||||||
\(579\) | 2.28618 | 0.0950102 | ||||||||
\(580\) | 2.66287 | 0.110570 | ||||||||
\(581\) | −2.46638 | −0.102323 | ||||||||
\(582\) | −0.578191 | −0.0239668 | ||||||||
\(583\) | −0.249902 | −0.0103499 | ||||||||
\(584\) | −10.5869 | −0.438088 | ||||||||
\(585\) | 32.9487 | 1.36226 | ||||||||
\(586\) | −26.7684 | −1.10579 | ||||||||
\(587\) | −20.3688 | −0.840710 | −0.420355 | − | 0.907360i | \(-0.638095\pi\) | ||||
−0.420355 | + | 0.907360i | \(0.638095\pi\) | |||||||
\(588\) | 5.86128 | 0.241715 | ||||||||
\(589\) | −3.37751 | −0.139168 | ||||||||
\(590\) | 22.2791 | 0.917217 | ||||||||
\(591\) | −14.9205 | −0.613749 | ||||||||
\(592\) | 0.0136820 | 0.000562326 0 | ||||||||
\(593\) | 17.1310 | 0.703486 | 0.351743 | − | 0.936097i | \(-0.385589\pi\) | ||||
0.351743 | + | 0.936097i | \(0.385589\pi\) | |||||||
\(594\) | 0.337100 | 0.0138314 | ||||||||
\(595\) | −32.3250 | −1.32520 | ||||||||
\(596\) | 3.68372 | 0.150891 | ||||||||
\(597\) | 9.65091 | 0.394985 | ||||||||
\(598\) | −38.9564 | −1.59305 | ||||||||
\(599\) | 5.99149 | 0.244806 | 0.122403 | − | 0.992481i | \(-0.460940\pi\) | ||||
0.122403 | + | 0.992481i | \(0.460940\pi\) | |||||||
\(600\) | 1.12539 | 0.0459437 | ||||||||
\(601\) | 28.3842 | 1.15782 | 0.578908 | − | 0.815393i | \(-0.303479\pi\) | ||||
0.578908 | + | 0.815393i | \(0.303479\pi\) | |||||||
\(602\) | 31.7344 | 1.29340 | ||||||||
\(603\) | 33.0544 | 1.34608 | ||||||||
\(604\) | 7.08380 | 0.288236 | ||||||||
\(605\) | −27.6589 | −1.12449 | ||||||||
\(606\) | −5.15979 | −0.209602 | ||||||||
\(607\) | 36.1322 | 1.46656 | 0.733281 | − | 0.679926i | \(-0.237988\pi\) | ||||
0.733281 | + | 0.679926i | \(0.237988\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −3.34440 | −0.135522 | ||||||||
\(610\) | −2.65124 | −0.107346 | ||||||||
\(611\) | 35.6182 | 1.44096 | ||||||||
\(612\) | −7.86168 | −0.317790 | ||||||||
\(613\) | −19.6460 | −0.793496 | −0.396748 | − | 0.917928i | \(-0.629861\pi\) | ||||
−0.396748 | + | 0.917928i | \(0.629861\pi\) | |||||||
\(614\) | 21.6088 | 0.872058 | ||||||||
\(615\) | −11.1594 | −0.449988 | ||||||||
\(616\) | 0.281150 | 0.0113279 | ||||||||
\(617\) | −25.6886 | −1.03419 | −0.517093 | − | 0.855929i | \(-0.672986\pi\) | ||||
−0.517093 | + | 0.855929i | \(0.672986\pi\) | |||||||
\(618\) | −13.9954 | −0.562978 | ||||||||
\(619\) | 40.6099 | 1.63225 | 0.816124 | − | 0.577876i | \(-0.196118\pi\) | ||||
0.816124 | + | 0.577876i | \(0.196118\pi\) | |||||||
\(620\) | −8.49695 | −0.341246 | ||||||||
\(621\) | −30.3778 | −1.21902 | ||||||||
\(622\) | 4.23255 | 0.169710 | ||||||||
\(623\) | 15.4900 | 0.620593 | ||||||||
\(624\) | −4.85823 | −0.194485 | ||||||||
\(625\) | −29.8787 | −1.19515 | ||||||||
\(626\) | 21.2458 | 0.849153 | ||||||||
\(627\) | −0.0638097 | −0.00254831 | ||||||||
\(628\) | −1.84050 | −0.0734439 | ||||||||
\(629\) | 0.0471171 | 0.00187868 | ||||||||
\(630\) | 21.4287 | 0.853739 | ||||||||
\(631\) | −30.5871 | −1.21766 | −0.608828 | − | 0.793303i | \(-0.708360\pi\) | ||||
−0.608828 | + | 0.793303i | \(0.708360\pi\) | |||||||
\(632\) | 9.08302 | 0.361303 | ||||||||
\(633\) | −0.846820 | −0.0336581 | ||||||||
\(634\) | 24.3234 | 0.966007 | ||||||||
\(635\) | −33.0003 | −1.30958 | ||||||||
\(636\) | 2.80844 | 0.111362 | ||||||||
\(637\) | −39.7089 | −1.57332 | ||||||||
\(638\) | −0.0797589 | −0.00315769 | ||||||||
\(639\) | 24.1448 | 0.955152 | ||||||||
\(640\) | 2.51574 | 0.0994434 | ||||||||
\(641\) | −16.0251 | −0.632954 | −0.316477 | − | 0.948600i | \(-0.602500\pi\) | ||||
−0.316477 | + | 0.948600i | \(0.602500\pi\) | |||||||
\(642\) | 7.74018 | 0.305481 | ||||||||
\(643\) | 4.93100 | 0.194460 | 0.0972299 | − | 0.995262i | \(-0.469002\pi\) | ||||
0.0972299 | + | 0.995262i | \(0.469002\pi\) | |||||||
\(644\) | −25.3359 | −0.998374 | ||||||||
\(645\) | −18.1194 | −0.713452 | ||||||||
\(646\) | 3.44373 | 0.135492 | ||||||||
\(647\) | 25.6515 | 1.00847 | 0.504233 | − | 0.863568i | \(-0.331775\pi\) | ||||
0.504233 | + | 0.863568i | \(0.331775\pi\) | |||||||
\(648\) | 3.06030 | 0.120220 | ||||||||
\(649\) | −0.667309 | −0.0261942 | ||||||||
\(650\) | −7.62424 | −0.299047 | ||||||||
\(651\) | 10.6716 | 0.418255 | ||||||||
\(652\) | −9.61863 | −0.376695 | ||||||||
\(653\) | −27.2836 | −1.06769 | −0.533844 | − | 0.845583i | \(-0.679253\pi\) | ||||
−0.533844 | + | 0.845583i | \(0.679253\pi\) | |||||||
\(654\) | 3.79628 | 0.148446 | ||||||||
\(655\) | 34.6862 | 1.35530 | ||||||||
\(656\) | −5.23820 | −0.204517 | ||||||||
\(657\) | 24.1687 | 0.942912 | ||||||||
\(658\) | 23.1648 | 0.903058 | ||||||||
\(659\) | −41.1158 | −1.60164 | −0.800821 | − | 0.598904i | \(-0.795603\pi\) | ||||
−0.800821 | + | 0.598904i | \(0.795603\pi\) | |||||||
\(660\) | −0.160529 | −0.00624857 | ||||||||
\(661\) | 18.2616 | 0.710294 | 0.355147 | − | 0.934811i | \(-0.384431\pi\) | ||||
0.355147 | + | 0.934811i | \(0.384431\pi\) | |||||||
\(662\) | 9.82654 | 0.381919 | ||||||||
\(663\) | −16.7304 | −0.649756 | ||||||||
\(664\) | 0.661023 | 0.0256527 | ||||||||
\(665\) | −9.38662 | −0.363997 | ||||||||
\(666\) | −0.0312345 | −0.00121031 | ||||||||
\(667\) | 7.18748 | 0.278300 | ||||||||
\(668\) | 10.5078 | 0.406560 | ||||||||
\(669\) | −19.4028 | −0.750156 | ||||||||
\(670\) | −36.4258 | −1.40725 | ||||||||
\(671\) | 0.0794106 | 0.00306561 | ||||||||
\(672\) | −3.15962 | −0.121885 | ||||||||
\(673\) | −5.97396 | −0.230279 | −0.115140 | − | 0.993349i | \(-0.536732\pi\) | ||||
−0.115140 | + | 0.993349i | \(0.536732\pi\) | |||||||
\(674\) | 16.0274 | 0.617353 | ||||||||
\(675\) | −5.94529 | −0.228834 | ||||||||
\(676\) | 19.9134 | 0.765901 | ||||||||
\(677\) | 9.51990 | 0.365880 | 0.182940 | − | 0.983124i | \(-0.441439\pi\) | ||||
0.182940 | + | 0.983124i | \(0.441439\pi\) | |||||||
\(678\) | −16.2726 | −0.624945 | ||||||||
\(679\) | 2.54755 | 0.0977661 | ||||||||
\(680\) | 8.66354 | 0.332232 | ||||||||
\(681\) | −12.2125 | −0.467984 | ||||||||
\(682\) | 0.254503 | 0.00974541 | ||||||||
\(683\) | 32.9274 | 1.25993 | 0.629966 | − | 0.776623i | \(-0.283069\pi\) | ||||
0.629966 | + | 0.776623i | \(0.283069\pi\) | |||||||
\(684\) | −2.28290 | −0.0872887 | ||||||||
\(685\) | −8.71660 | −0.333044 | ||||||||
\(686\) | 0.292848 | 0.0111810 | ||||||||
\(687\) | −19.9885 | −0.762607 | ||||||||
\(688\) | −8.50526 | −0.324260 | ||||||||
\(689\) | −19.0266 | −0.724854 | ||||||||
\(690\) | 14.4661 | 0.550713 | ||||||||
\(691\) | −34.0226 | −1.29428 | −0.647140 | − | 0.762371i | \(-0.724035\pi\) | ||||
−0.647140 | + | 0.762371i | \(0.724035\pi\) | |||||||
\(692\) | −10.9446 | −0.416049 | ||||||||
\(693\) | −0.641837 | −0.0243814 | ||||||||
\(694\) | 3.93856 | 0.149506 | ||||||||
\(695\) | −10.2234 | −0.387797 | ||||||||
\(696\) | 0.896345 | 0.0339759 | ||||||||
\(697\) | −18.0389 | −0.683274 | ||||||||
\(698\) | 1.23767 | 0.0468467 | ||||||||
\(699\) | −21.5552 | −0.815294 | ||||||||
\(700\) | −4.95853 | −0.187415 | ||||||||
\(701\) | −25.5674 | −0.965668 | −0.482834 | − | 0.875712i | \(-0.660392\pi\) | ||||
−0.482834 | + | 0.875712i | \(0.660392\pi\) | |||||||
\(702\) | 25.6655 | 0.968682 | ||||||||
\(703\) | 0.0136820 | 0.000516026 0 | ||||||||
\(704\) | −0.0753521 | −0.00283994 | ||||||||
\(705\) | −13.2264 | −0.498136 | ||||||||
\(706\) | 5.65440 | 0.212806 | ||||||||
\(707\) | 22.7344 | 0.855016 | ||||||||
\(708\) | 7.49934 | 0.281843 | ||||||||
\(709\) | 10.2425 | 0.384663 | 0.192332 | − | 0.981330i | \(-0.438395\pi\) | ||||
0.192332 | + | 0.981330i | \(0.438395\pi\) | |||||||
\(710\) | −26.6074 | −0.998559 | ||||||||
\(711\) | −20.7356 | −0.777646 | ||||||||
\(712\) | −4.15153 | −0.155585 | ||||||||
\(713\) | −22.9345 | −0.858905 | ||||||||
\(714\) | −10.8809 | −0.407207 | ||||||||
\(715\) | 1.08755 | 0.0406719 | ||||||||
\(716\) | 6.23538 | 0.233027 | ||||||||
\(717\) | −7.24403 | −0.270533 | ||||||||
\(718\) | 9.74840 | 0.363807 | ||||||||
\(719\) | −18.3629 | −0.684820 | −0.342410 | − | 0.939551i | \(-0.611243\pi\) | ||||
−0.342410 | + | 0.939551i | \(0.611243\pi\) | |||||||
\(720\) | −5.74317 | −0.214035 | ||||||||
\(721\) | 61.6649 | 2.29652 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 21.4142 | 0.796402 | ||||||||
\(724\) | 9.18136 | 0.341223 | ||||||||
\(725\) | 1.40668 | 0.0522426 | ||||||||
\(726\) | −9.31021 | −0.345534 | ||||||||
\(727\) | 13.9659 | 0.517967 | 0.258983 | − | 0.965882i | \(-0.416613\pi\) | ||||
0.258983 | + | 0.965882i | \(0.416613\pi\) | |||||||
\(728\) | 21.4057 | 0.793349 | ||||||||
\(729\) | 4.37882 | 0.162179 | ||||||||
\(730\) | −26.6339 | −0.985763 | ||||||||
\(731\) | −29.2898 | −1.08332 | ||||||||
\(732\) | −0.892431 | −0.0329852 | ||||||||
\(733\) | −11.4936 | −0.424526 | −0.212263 | − | 0.977213i | \(-0.568083\pi\) | ||||
−0.212263 | + | 0.977213i | \(0.568083\pi\) | |||||||
\(734\) | −8.60189 | −0.317502 | ||||||||
\(735\) | 14.7455 | 0.543894 | ||||||||
\(736\) | 6.79036 | 0.250296 | ||||||||
\(737\) | 1.09103 | 0.0401888 | ||||||||
\(738\) | 11.9583 | 0.440189 | ||||||||
\(739\) | −8.84645 | −0.325422 | −0.162711 | − | 0.986674i | \(-0.552024\pi\) | ||||
−0.162711 | + | 0.986674i | \(0.552024\pi\) | |||||||
\(740\) | 0.0344203 | 0.00126532 | ||||||||
\(741\) | −4.85823 | −0.178471 | ||||||||
\(742\) | −12.3742 | −0.454271 | ||||||||
\(743\) | 19.4815 | 0.714708 | 0.357354 | − | 0.933969i | \(-0.383679\pi\) | ||||
0.357354 | + | 0.933969i | \(0.383679\pi\) | |||||||
\(744\) | −2.86015 | −0.104858 | ||||||||
\(745\) | 9.26729 | 0.339527 | ||||||||
\(746\) | 6.05625 | 0.221735 | ||||||||
\(747\) | −1.50905 | −0.0552131 | ||||||||
\(748\) | −0.259492 | −0.00948798 | ||||||||
\(749\) | −34.1038 | −1.24613 | ||||||||
\(750\) | −7.82072 | −0.285572 | ||||||||
\(751\) | −37.7993 | −1.37932 | −0.689658 | − | 0.724135i | \(-0.742239\pi\) | ||||
−0.689658 | + | 0.724135i | \(0.742239\pi\) | |||||||
\(752\) | −6.20848 | −0.226400 | ||||||||
\(753\) | 11.7176 | 0.427013 | ||||||||
\(754\) | −6.07254 | −0.221149 | ||||||||
\(755\) | 17.8210 | 0.648573 | ||||||||
\(756\) | 16.6919 | 0.607079 | ||||||||
\(757\) | −21.6737 | −0.787745 | −0.393873 | − | 0.919165i | \(-0.628865\pi\) | ||||
−0.393873 | + | 0.919165i | \(0.628865\pi\) | |||||||
\(758\) | 20.3044 | 0.737487 | ||||||||
\(759\) | −0.433291 | −0.0157275 | ||||||||
\(760\) | 2.51574 | 0.0912555 | ||||||||
\(761\) | 3.87589 | 0.140501 | 0.0702505 | − | 0.997529i | \(-0.477620\pi\) | ||||
0.0702505 | + | 0.997529i | \(0.477620\pi\) | |||||||
\(762\) | −11.1082 | −0.402407 | ||||||||
\(763\) | −16.7267 | −0.605547 | ||||||||
\(764\) | −4.66074 | −0.168619 | ||||||||
\(765\) | −19.7780 | −0.715074 | ||||||||
\(766\) | 31.1049 | 1.12387 | ||||||||
\(767\) | −50.8064 | −1.83451 | ||||||||
\(768\) | 0.846820 | 0.0305570 | ||||||||
\(769\) | −49.1946 | −1.77400 | −0.887002 | − | 0.461766i | \(-0.847216\pi\) | ||||
−0.887002 | + | 0.461766i | \(0.847216\pi\) | |||||||
\(770\) | 0.707301 | 0.0254894 | ||||||||
\(771\) | 0.986240 | 0.0355186 | ||||||||
\(772\) | 2.69972 | 0.0971650 | ||||||||
\(773\) | 30.8200 | 1.10852 | 0.554260 | − | 0.832344i | \(-0.313001\pi\) | ||||
0.554260 | + | 0.832344i | \(0.313001\pi\) | |||||||
\(774\) | 19.4166 | 0.697916 | ||||||||
\(775\) | −4.48856 | −0.161234 | ||||||||
\(776\) | −0.682779 | −0.0245103 | ||||||||
\(777\) | −0.0432298 | −0.00155086 | ||||||||
\(778\) | −7.23787 | −0.259490 | ||||||||
\(779\) | −5.23820 | −0.187678 | ||||||||
\(780\) | −12.2220 | −0.437619 | ||||||||
\(781\) | 0.796952 | 0.0285172 | ||||||||
\(782\) | 23.3842 | 0.836217 | ||||||||
\(783\) | −4.73530 | −0.169226 | ||||||||
\(784\) | 6.92151 | 0.247197 | ||||||||
\(785\) | −4.63022 | −0.165260 | ||||||||
\(786\) | 11.6757 | 0.416457 | ||||||||
\(787\) | −20.2589 | −0.722153 | −0.361077 | − | 0.932536i | \(-0.617591\pi\) | ||||
−0.361077 | + | 0.932536i | \(0.617591\pi\) | |||||||
\(788\) | −17.6195 | −0.627668 | ||||||||
\(789\) | 14.5879 | 0.519342 | ||||||||
\(790\) | 22.8505 | 0.812986 | ||||||||
\(791\) | 71.6983 | 2.54930 | ||||||||
\(792\) | 0.172021 | 0.00611250 | ||||||||
\(793\) | 6.04602 | 0.214701 | ||||||||
\(794\) | 22.1359 | 0.785572 | ||||||||
\(795\) | 7.06530 | 0.250580 | ||||||||
\(796\) | 11.3966 | 0.403943 | ||||||||
\(797\) | 42.7498 | 1.51428 | 0.757139 | − | 0.653254i | \(-0.226597\pi\) | ||||
0.757139 | + | 0.653254i | \(0.226597\pi\) | |||||||
\(798\) | −3.15962 | −0.111849 | ||||||||
\(799\) | −21.3803 | −0.756382 | ||||||||
\(800\) | 1.32895 | 0.0469856 | ||||||||
\(801\) | 9.47750 | 0.334871 | ||||||||
\(802\) | 13.9938 | 0.494138 | ||||||||
\(803\) | 0.797744 | 0.0281518 | ||||||||
\(804\) | −12.2612 | −0.432421 | ||||||||
\(805\) | −63.7385 | −2.24649 | ||||||||
\(806\) | 19.3769 | 0.682521 | ||||||||
\(807\) | −4.73915 | −0.166826 | ||||||||
\(808\) | −6.09314 | −0.214356 | ||||||||
\(809\) | −21.8005 | −0.766465 | −0.383232 | − | 0.923652i | \(-0.625189\pi\) | ||||
−0.383232 | + | 0.923652i | \(0.625189\pi\) | |||||||
\(810\) | 7.69892 | 0.270512 | ||||||||
\(811\) | 39.8101 | 1.39792 | 0.698962 | − | 0.715159i | \(-0.253646\pi\) | ||||
0.698962 | + | 0.715159i | \(0.253646\pi\) | |||||||
\(812\) | −3.94936 | −0.138595 | ||||||||
\(813\) | −5.38892 | −0.188998 | ||||||||
\(814\) | −0.00103097 | −3.61354e−5 0 | ||||||||
\(815\) | −24.1980 | −0.847619 | ||||||||
\(816\) | 2.91622 | 0.102088 | ||||||||
\(817\) | −8.50526 | −0.297561 | ||||||||
\(818\) | 25.7319 | 0.899695 | ||||||||
\(819\) | −48.8670 | −1.70755 | ||||||||
\(820\) | −13.1779 | −0.460194 | ||||||||
\(821\) | 34.0338 | 1.18779 | 0.593895 | − | 0.804543i | \(-0.297590\pi\) | ||||
0.593895 | + | 0.804543i | \(0.297590\pi\) | |||||||
\(822\) | −2.93408 | −0.102338 | ||||||||
\(823\) | 36.5418 | 1.27377 | 0.636883 | − | 0.770960i | \(-0.280223\pi\) | ||||
0.636883 | + | 0.770960i | \(0.280223\pi\) | |||||||
\(824\) | −16.5270 | −0.575746 | ||||||||
\(825\) | −0.0848001 | −0.00295236 | ||||||||
\(826\) | −33.0427 | −1.14970 | ||||||||
\(827\) | 50.5007 | 1.75608 | 0.878041 | − | 0.478585i | \(-0.158850\pi\) | ||||
0.878041 | + | 0.478585i | \(0.158850\pi\) | |||||||
\(828\) | −15.5017 | −0.538721 | ||||||||
\(829\) | −5.06039 | −0.175755 | −0.0878773 | − | 0.996131i | \(-0.528008\pi\) | ||||
−0.0878773 | + | 0.996131i | \(0.528008\pi\) | |||||||
\(830\) | 1.66296 | 0.0577223 | ||||||||
\(831\) | 19.7257 | 0.684278 | ||||||||
\(832\) | −5.73702 | −0.198895 | ||||||||
\(833\) | 23.8358 | 0.825863 | ||||||||
\(834\) | −3.44130 | −0.119162 | ||||||||
\(835\) | 26.4350 | 0.914819 | ||||||||
\(836\) | −0.0753521 | −0.00260611 | ||||||||
\(837\) | 15.1099 | 0.522273 | ||||||||
\(838\) | 1.36340 | 0.0470978 | ||||||||
\(839\) | −12.8972 | −0.445261 | −0.222630 | − | 0.974903i | \(-0.571464\pi\) | ||||
−0.222630 | + | 0.974903i | \(0.571464\pi\) | |||||||
\(840\) | −7.94878 | −0.274259 | ||||||||
\(841\) | −27.8796 | −0.961366 | ||||||||
\(842\) | −2.18984 | −0.0754670 | ||||||||
\(843\) | 26.1727 | 0.901437 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 50.0970 | 1.72339 | ||||||||
\(846\) | 14.1733 | 0.487288 | ||||||||
\(847\) | 41.0215 | 1.40952 | ||||||||
\(848\) | 3.31645 | 0.113887 | ||||||||
\(849\) | 6.67703 | 0.229155 | ||||||||
\(850\) | 4.57656 | 0.156975 | ||||||||
\(851\) | 0.0929056 | 0.00318476 | ||||||||
\(852\) | −8.95629 | −0.306837 | ||||||||
\(853\) | 13.0874 | 0.448103 | 0.224052 | − | 0.974577i | \(-0.428072\pi\) | ||||
0.224052 | + | 0.974577i | \(0.428072\pi\) | |||||||
\(854\) | 3.93212 | 0.134554 | ||||||||
\(855\) | −5.74317 | −0.196412 | ||||||||
\(856\) | 9.14029 | 0.312409 | ||||||||
\(857\) | −3.57872 | −0.122247 | −0.0611234 | − | 0.998130i | \(-0.519468\pi\) | ||||
−0.0611234 | + | 0.998130i | \(0.519468\pi\) | |||||||
\(858\) | 0.366077 | 0.0124977 | ||||||||
\(859\) | 35.9009 | 1.22492 | 0.612461 | − | 0.790501i | \(-0.290180\pi\) | ||||
0.612461 | + | 0.790501i | \(0.290180\pi\) | |||||||
\(860\) | −21.3970 | −0.729633 | ||||||||
\(861\) | 16.5507 | 0.564046 | ||||||||
\(862\) | 8.48009 | 0.288833 | ||||||||
\(863\) | 51.2372 | 1.74414 | 0.872068 | − | 0.489385i | \(-0.162779\pi\) | ||||
0.872068 | + | 0.489385i | \(0.162779\pi\) | |||||||
\(864\) | −4.47366 | −0.152197 | ||||||||
\(865\) | −27.5337 | −0.936172 | ||||||||
\(866\) | −10.4229 | −0.354185 | ||||||||
\(867\) | −4.35325 | −0.147844 | ||||||||
\(868\) | 12.6020 | 0.427740 | ||||||||
\(869\) | −0.684425 | −0.0232175 | ||||||||
\(870\) | 2.25497 | 0.0764507 | ||||||||
\(871\) | 83.0672 | 2.81463 | ||||||||
\(872\) | 4.48298 | 0.151813 | ||||||||
\(873\) | 1.55871 | 0.0527544 | ||||||||
\(874\) | 6.79036 | 0.229687 | ||||||||
\(875\) | 34.4587 | 1.16492 | ||||||||
\(876\) | −8.96518 | −0.302906 | ||||||||
\(877\) | 2.74250 | 0.0926076 | 0.0463038 | − | 0.998927i | \(-0.485256\pi\) | ||||
0.0463038 | + | 0.998927i | \(0.485256\pi\) | |||||||
\(878\) | −12.6496 | −0.426904 | ||||||||
\(879\) | −22.6680 | −0.764572 | ||||||||
\(880\) | −0.189566 | −0.00639028 | ||||||||
\(881\) | −28.3894 | −0.956462 | −0.478231 | − | 0.878234i | \(-0.658722\pi\) | ||||
−0.478231 | + | 0.878234i | \(0.658722\pi\) | |||||||
\(882\) | −15.8011 | −0.532050 | ||||||||
\(883\) | 43.2360 | 1.45501 | 0.727504 | − | 0.686103i | \(-0.240680\pi\) | ||||
0.727504 | + | 0.686103i | \(0.240680\pi\) | |||||||
\(884\) | −19.7568 | −0.664492 | ||||||||
\(885\) | 18.8664 | 0.634187 | ||||||||
\(886\) | −35.3294 | −1.18692 | ||||||||
\(887\) | −51.4742 | −1.72834 | −0.864168 | − | 0.503204i | \(-0.832154\pi\) | ||||
−0.864168 | + | 0.503204i | \(0.832154\pi\) | |||||||
\(888\) | 0.0115862 | 0.000388807 0 | ||||||||
\(889\) | 48.9434 | 1.64151 | ||||||||
\(890\) | −10.4442 | −0.350089 | ||||||||
\(891\) | −0.230600 | −0.00772539 | ||||||||
\(892\) | −22.9125 | −0.767169 | ||||||||
\(893\) | −6.20848 | −0.207759 | ||||||||
\(894\) | 3.11945 | 0.104330 | ||||||||
\(895\) | 15.6866 | 0.524345 | ||||||||
\(896\) | −3.73115 | −0.124649 | ||||||||
\(897\) | −32.9891 | −1.10147 | ||||||||
\(898\) | −9.46560 | −0.315871 | ||||||||
\(899\) | −3.57504 | −0.119234 | ||||||||
\(900\) | −3.03386 | −0.101129 | ||||||||
\(901\) | 11.4210 | 0.380488 | ||||||||
\(902\) | 0.394709 | 0.0131424 | ||||||||
\(903\) | 26.8734 | 0.894289 | ||||||||
\(904\) | −19.2161 | −0.639118 | ||||||||
\(905\) | 23.0979 | 0.767801 | ||||||||
\(906\) | 5.99871 | 0.199294 | ||||||||
\(907\) | 2.28392 | 0.0758365 | 0.0379182 | − | 0.999281i | \(-0.487927\pi\) | ||||
0.0379182 | + | 0.999281i | \(0.487927\pi\) | |||||||
\(908\) | −14.4216 | −0.478598 | ||||||||
\(909\) | 13.9100 | 0.461365 | ||||||||
\(910\) | 53.8512 | 1.78515 | ||||||||
\(911\) | −45.5629 | −1.50956 | −0.754782 | − | 0.655975i | \(-0.772258\pi\) | ||||
−0.754782 | + | 0.655975i | \(0.772258\pi\) | |||||||
\(912\) | 0.846820 | 0.0280410 | ||||||||
\(913\) | −0.0498095 | −0.00164845 | ||||||||
\(914\) | −32.0612 | −1.06049 | ||||||||
\(915\) | −2.24512 | −0.0742215 | ||||||||
\(916\) | −23.6041 | −0.779902 | ||||||||
\(917\) | −51.4438 | −1.69883 | ||||||||
\(918\) | −15.4061 | −0.508477 | ||||||||
\(919\) | −48.0167 | −1.58392 | −0.791962 | − | 0.610571i | \(-0.790940\pi\) | ||||
−0.791962 | + | 0.610571i | \(0.790940\pi\) | |||||||
\(920\) | 17.0828 | 0.563203 | ||||||||
\(921\) | 18.2987 | 0.602964 | ||||||||
\(922\) | 27.2979 | 0.899009 | ||||||||
\(923\) | 60.6769 | 1.99720 | ||||||||
\(924\) | 0.238084 | 0.00783238 | ||||||||
\(925\) | 0.0181827 | 0.000597845 0 | ||||||||
\(926\) | 32.4611 | 1.06674 | ||||||||
\(927\) | 37.7295 | 1.23920 | ||||||||
\(928\) | 1.05848 | 0.0347464 | ||||||||
\(929\) | −42.4245 | −1.39190 | −0.695951 | − | 0.718089i | \(-0.745017\pi\) | ||||
−0.695951 | + | 0.718089i | \(0.745017\pi\) | |||||||
\(930\) | −7.19539 | −0.235946 | ||||||||
\(931\) | 6.92151 | 0.226843 | ||||||||
\(932\) | −25.4543 | −0.833784 | ||||||||
\(933\) | 3.58421 | 0.117342 | ||||||||
\(934\) | −31.2049 | −1.02106 | ||||||||
\(935\) | −0.652816 | −0.0213494 | ||||||||
\(936\) | 13.0970 | 0.428090 | ||||||||
\(937\) | −49.6572 | −1.62223 | −0.811115 | − | 0.584886i | \(-0.801139\pi\) | ||||
−0.811115 | + | 0.584886i | \(0.801139\pi\) | |||||||
\(938\) | 54.0240 | 1.76394 | ||||||||
\(939\) | 17.9914 | 0.587126 | ||||||||
\(940\) | −15.6189 | −0.509433 | ||||||||
\(941\) | −45.4562 | −1.48183 | −0.740915 | − | 0.671599i | \(-0.765608\pi\) | ||||
−0.740915 | + | 0.671599i | \(0.765608\pi\) | |||||||
\(942\) | −1.55857 | −0.0507810 | ||||||||
\(943\) | −35.5692 | −1.15829 | ||||||||
\(944\) | 8.85589 | 0.288235 | ||||||||
\(945\) | 41.9926 | 1.36602 | ||||||||
\(946\) | 0.640889 | 0.0208371 | ||||||||
\(947\) | −16.2142 | −0.526892 | −0.263446 | − | 0.964674i | \(-0.584859\pi\) | ||||
−0.263446 | + | 0.964674i | \(0.584859\pi\) | |||||||
\(948\) | 7.69169 | 0.249814 | ||||||||
\(949\) | 60.7372 | 1.97161 | ||||||||
\(950\) | 1.32895 | 0.0431170 | ||||||||
\(951\) | 20.5976 | 0.667922 | ||||||||
\(952\) | −12.8491 | −0.416442 | ||||||||
\(953\) | −32.2726 | −1.04541 | −0.522706 | − | 0.852513i | \(-0.675078\pi\) | ||||
−0.522706 | + | 0.852513i | \(0.675078\pi\) | |||||||
\(954\) | −7.57111 | −0.245124 | ||||||||
\(955\) | −11.7252 | −0.379419 | ||||||||
\(956\) | −8.55439 | −0.276669 | ||||||||
\(957\) | −0.0675415 | −0.00218331 | ||||||||
\(958\) | −22.2905 | −0.720174 | ||||||||
\(959\) | 12.9278 | 0.417460 | ||||||||
\(960\) | 2.13038 | 0.0687577 | ||||||||
\(961\) | −19.5924 | −0.632013 | ||||||||
\(962\) | −0.0784939 | −0.00253074 | ||||||||
\(963\) | −20.8663 | −0.672408 | ||||||||
\(964\) | 25.2877 | 0.814463 | ||||||||
\(965\) | 6.79179 | 0.218636 | ||||||||
\(966\) | −21.4549 | −0.690301 | ||||||||
\(967\) | 17.3653 | 0.558431 | 0.279216 | − | 0.960228i | \(-0.409926\pi\) | ||||
0.279216 | + | 0.960228i | \(0.409926\pi\) | |||||||
\(968\) | −10.9943 | −0.353371 | ||||||||
\(969\) | 2.91622 | 0.0936826 | ||||||||
\(970\) | −1.71770 | −0.0551519 | ||||||||
\(971\) | −3.71071 | −0.119082 | −0.0595412 | − | 0.998226i | \(-0.518964\pi\) | ||||
−0.0595412 | + | 0.998226i | \(0.518964\pi\) | |||||||
\(972\) | 16.0125 | 0.513602 | ||||||||
\(973\) | 15.1626 | 0.486091 | ||||||||
\(974\) | 4.50007 | 0.144192 | ||||||||
\(975\) | −6.45636 | −0.206769 | ||||||||
\(976\) | −1.05386 | −0.0337333 | ||||||||
\(977\) | −30.3366 | −0.970554 | −0.485277 | − | 0.874360i | \(-0.661281\pi\) | ||||
−0.485277 | + | 0.874360i | \(0.661281\pi\) | |||||||
\(978\) | −8.14525 | −0.260456 | ||||||||
\(979\) | 0.312826 | 0.00999797 | ||||||||
\(980\) | 17.4127 | 0.556229 | ||||||||
\(981\) | −10.2342 | −0.326752 | ||||||||
\(982\) | −39.6320 | −1.26471 | ||||||||
\(983\) | 0.696013 | 0.0221994 | 0.0110997 | − | 0.999938i | \(-0.496467\pi\) | ||||
0.0110997 | + | 0.999938i | \(0.496467\pi\) | |||||||
\(984\) | −4.43581 | −0.141408 | ||||||||
\(985\) | −44.3261 | −1.41235 | ||||||||
\(986\) | 3.64513 | 0.116085 | ||||||||
\(987\) | 19.6164 | 0.624397 | ||||||||
\(988\) | −5.73702 | −0.182519 | ||||||||
\(989\) | −57.7538 | −1.83646 | ||||||||
\(990\) | 0.432760 | 0.0137540 | ||||||||
\(991\) | 8.15308 | 0.258991 | 0.129496 | − | 0.991580i | \(-0.458664\pi\) | ||||
0.129496 | + | 0.991580i | \(0.458664\pi\) | |||||||
\(992\) | −3.37751 | −0.107236 | ||||||||
\(993\) | 8.32131 | 0.264069 | ||||||||
\(994\) | 39.4621 | 1.25166 | ||||||||
\(995\) | 28.6710 | 0.908932 | ||||||||
\(996\) | 0.559768 | 0.0177369 | ||||||||
\(997\) | −22.6110 | −0.716098 | −0.358049 | − | 0.933703i | \(-0.616558\pi\) | ||||
−0.358049 | + | 0.933703i | \(0.616558\pi\) | |||||||
\(998\) | 17.7075 | 0.560521 | ||||||||
\(999\) | −0.0612086 | −0.00193655 |
(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 | 8018.2.a.d.1.20 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.20 | ✓ | 30 | 1.1 | even | 1 | trivial |