Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4802,2,Mod(1,4802)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4802, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4802.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4802 = 2 \cdot 7^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4802.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: | \(38.3441630506\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 21x^{7} + 27x^{6} + 142x^{5} - 221x^{4} - 293x^{3} + 567x^{2} - 61x - 113 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 98) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.07434\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4802.1 |
$q$-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 | ||||||||
\(3\) | −3.07434 | −1.77497 | −0.887485 | − | 0.460837i | \(-0.847549\pi\) | ||||
−0.887485 | + | 0.460837i | \(0.847549\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.02538 | −1.35299 | −0.676496 | − | 0.736447i | \(-0.736502\pi\) | ||||
−0.676496 | + | 0.736447i | \(0.736502\pi\) | |||||||
\(6\) | 3.07434 | 1.25509 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.45155 | 2.15052 | ||||||||
\(10\) | 3.02538 | 0.956709 | ||||||||
\(11\) | 3.02538 | 0.912187 | 0.456093 | − | 0.889932i | \(-0.349248\pi\) | ||||
0.456093 | + | 0.889932i | \(0.349248\pi\) | |||||||
\(12\) | −3.07434 | −0.887485 | ||||||||
\(13\) | −2.39132 | −0.663232 | −0.331616 | − | 0.943414i | \(-0.607594\pi\) | ||||
−0.331616 | + | 0.943414i | \(0.607594\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.30104 | 2.40152 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.643016 | −0.155954 | −0.0779772 | − | 0.996955i | \(-0.524846\pi\) | ||||
−0.0779772 | + | 0.996955i | \(0.524846\pi\) | |||||||
\(18\) | −6.45155 | −1.52064 | ||||||||
\(19\) | 0.629295 | 0.144370 | 0.0721851 | − | 0.997391i | \(-0.477003\pi\) | ||||
0.0721851 | + | 0.997391i | \(0.477003\pi\) | |||||||
\(20\) | −3.02538 | −0.676496 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.02538 | −0.645013 | ||||||||
\(23\) | −9.39694 | −1.95940 | −0.979698 | − | 0.200478i | \(-0.935751\pi\) | ||||
−0.979698 | + | 0.200478i | \(0.935751\pi\) | |||||||
\(24\) | 3.07434 | 0.627546 | ||||||||
\(25\) | 4.15293 | 0.830585 | ||||||||
\(26\) | 2.39132 | 0.468976 | ||||||||
\(27\) | −10.6112 | −2.04213 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.26461 | 0.791918 | 0.395959 | − | 0.918268i | \(-0.370412\pi\) | ||||
0.395959 | + | 0.918268i | \(0.370412\pi\) | |||||||
\(30\) | −9.30104 | −1.69813 | ||||||||
\(31\) | −2.51075 | −0.450944 | −0.225472 | − | 0.974250i | \(-0.572392\pi\) | ||||
−0.225472 | + | 0.974250i | \(0.572392\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −9.30104 | −1.61910 | ||||||||
\(34\) | 0.643016 | 0.110276 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.45155 | 1.07526 | ||||||||
\(37\) | −6.42392 | −1.05609 | −0.528043 | − | 0.849218i | \(-0.677074\pi\) | ||||
−0.528043 | + | 0.849218i | \(0.677074\pi\) | |||||||
\(38\) | −0.629295 | −0.102085 | ||||||||
\(39\) | 7.35171 | 1.17722 | ||||||||
\(40\) | 3.02538 | 0.478355 | ||||||||
\(41\) | 2.07039 | 0.323341 | 0.161670 | − | 0.986845i | \(-0.448312\pi\) | ||||
0.161670 | + | 0.986845i | \(0.448312\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.35656 | 0.206873 | 0.103436 | − | 0.994636i | \(-0.467016\pi\) | ||||
0.103436 | + | 0.994636i | \(0.467016\pi\) | |||||||
\(44\) | 3.02538 | 0.456093 | ||||||||
\(45\) | −19.5184 | −2.90963 | ||||||||
\(46\) | 9.39694 | 1.38550 | ||||||||
\(47\) | 1.06025 | 0.154654 | 0.0773268 | − | 0.997006i | \(-0.475362\pi\) | ||||
0.0773268 | + | 0.997006i | \(0.475362\pi\) | |||||||
\(48\) | −3.07434 | −0.443742 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.15293 | −0.587313 | ||||||||
\(51\) | 1.97685 | 0.276814 | ||||||||
\(52\) | −2.39132 | −0.331616 | ||||||||
\(53\) | 4.68623 | 0.643704 | 0.321852 | − | 0.946790i | \(-0.395695\pi\) | ||||
0.321852 | + | 0.946790i | \(0.395695\pi\) | |||||||
\(54\) | 10.6112 | 1.44400 | ||||||||
\(55\) | −9.15293 | −1.23418 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.93466 | −0.256253 | ||||||||
\(58\) | −4.26461 | −0.559971 | ||||||||
\(59\) | 3.14452 | 0.409381 | 0.204691 | − | 0.978827i | \(-0.434381\pi\) | ||||
0.204691 | + | 0.978827i | \(0.434381\pi\) | |||||||
\(60\) | 9.30104 | 1.20076 | ||||||||
\(61\) | −5.39679 | −0.690988 | −0.345494 | − | 0.938421i | \(-0.612289\pi\) | ||||
−0.345494 | + | 0.938421i | \(0.612289\pi\) | |||||||
\(62\) | 2.51075 | 0.318866 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.23464 | 0.897347 | ||||||||
\(66\) | 9.30104 | 1.14488 | ||||||||
\(67\) | 6.32287 | 0.772462 | 0.386231 | − | 0.922402i | \(-0.373777\pi\) | ||||
0.386231 | + | 0.922402i | \(0.373777\pi\) | |||||||
\(68\) | −0.643016 | −0.0779772 | ||||||||
\(69\) | 28.8893 | 3.47787 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.1609 | 1.68059 | 0.840296 | − | 0.542127i | \(-0.182381\pi\) | ||||
0.840296 | + | 0.542127i | \(0.182381\pi\) | |||||||
\(72\) | −6.45155 | −0.760322 | ||||||||
\(73\) | 4.15896 | 0.486769 | 0.243385 | − | 0.969930i | \(-0.421742\pi\) | ||||
0.243385 | + | 0.969930i | \(0.421742\pi\) | |||||||
\(74\) | 6.42392 | 0.746766 | ||||||||
\(75\) | −12.7675 | −1.47426 | ||||||||
\(76\) | 0.629295 | 0.0721851 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.35171 | −0.832418 | ||||||||
\(79\) | −11.2211 | −1.26247 | −0.631236 | − | 0.775590i | \(-0.717452\pi\) | ||||
−0.631236 | + | 0.775590i | \(0.717452\pi\) | |||||||
\(80\) | −3.02538 | −0.338248 | ||||||||
\(81\) | 13.2678 | 1.47420 | ||||||||
\(82\) | −2.07039 | −0.228636 | ||||||||
\(83\) | 7.62465 | 0.836914 | 0.418457 | − | 0.908237i | \(-0.362571\pi\) | ||||
0.418457 | + | 0.908237i | \(0.362571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.94537 | 0.211005 | ||||||||
\(86\) | −1.35656 | −0.146281 | ||||||||
\(87\) | −13.1108 | −1.40563 | ||||||||
\(88\) | −3.02538 | −0.322507 | ||||||||
\(89\) | 1.19130 | 0.126278 | 0.0631388 | − | 0.998005i | \(-0.479889\pi\) | ||||
0.0631388 | + | 0.998005i | \(0.479889\pi\) | |||||||
\(90\) | 19.5184 | 2.05742 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.39694 | −0.979698 | ||||||||
\(93\) | 7.71890 | 0.800412 | ||||||||
\(94\) | −1.06025 | −0.109357 | ||||||||
\(95\) | −1.90386 | −0.195332 | ||||||||
\(96\) | 3.07434 | 0.313773 | ||||||||
\(97\) | 16.3992 | 1.66509 | 0.832543 | − | 0.553961i | \(-0.186884\pi\) | ||||
0.832543 | + | 0.553961i | \(0.186884\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.5184 | 1.96167 | ||||||||
\(100\) | 4.15293 | 0.415293 | ||||||||
\(101\) | 14.3697 | 1.42984 | 0.714921 | − | 0.699205i | \(-0.246463\pi\) | ||||
0.714921 | + | 0.699205i | \(0.246463\pi\) | |||||||
\(102\) | −1.97685 | −0.195737 | ||||||||
\(103\) | −16.3323 | −1.60927 | −0.804633 | − | 0.593773i | \(-0.797638\pi\) | ||||
−0.804633 | + | 0.593773i | \(0.797638\pi\) | |||||||
\(104\) | 2.39132 | 0.234488 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.68623 | −0.455167 | ||||||||
\(107\) | 16.6838 | 1.61288 | 0.806441 | − | 0.591315i | \(-0.201391\pi\) | ||||
0.806441 | + | 0.591315i | \(0.201391\pi\) | |||||||
\(108\) | −10.6112 | −1.02106 | ||||||||
\(109\) | 1.66514 | 0.159492 | 0.0797458 | − | 0.996815i | \(-0.474589\pi\) | ||||
0.0797458 | + | 0.996815i | \(0.474589\pi\) | |||||||
\(110\) | 9.15293 | 0.872697 | ||||||||
\(111\) | 19.7493 | 1.87452 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.25578 | −0.870711 | −0.435355 | − | 0.900259i | \(-0.643377\pi\) | ||||
−0.435355 | + | 0.900259i | \(0.643377\pi\) | |||||||
\(114\) | 1.93466 | 0.181198 | ||||||||
\(115\) | 28.4293 | 2.65105 | ||||||||
\(116\) | 4.26461 | 0.395959 | ||||||||
\(117\) | −15.4277 | −1.42629 | ||||||||
\(118\) | −3.14452 | −0.289476 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −9.30104 | −0.849065 | ||||||||
\(121\) | −1.84707 | −0.167916 | ||||||||
\(122\) | 5.39679 | 0.488602 | ||||||||
\(123\) | −6.36508 | −0.573920 | ||||||||
\(124\) | −2.51075 | −0.225472 | ||||||||
\(125\) | 2.56272 | 0.229217 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.3955 | −1.18866 | −0.594328 | − | 0.804223i | \(-0.702582\pi\) | ||||
−0.594328 | + | 0.804223i | \(0.702582\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.17051 | −0.367193 | ||||||||
\(130\) | −7.23464 | −0.634520 | ||||||||
\(131\) | 19.4378 | 1.69829 | 0.849146 | − | 0.528158i | \(-0.177117\pi\) | ||||
0.849146 | + | 0.528158i | \(0.177117\pi\) | |||||||
\(132\) | −9.30104 | −0.809551 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.32287 | −0.546213 | ||||||||
\(135\) | 32.1030 | 2.76298 | ||||||||
\(136\) | 0.643016 | 0.0551382 | ||||||||
\(137\) | 7.88612 | 0.673757 | 0.336879 | − | 0.941548i | \(-0.390629\pi\) | ||||
0.336879 | + | 0.941548i | \(0.390629\pi\) | |||||||
\(138\) | −28.8893 | −2.45922 | ||||||||
\(139\) | −0.293193 | −0.0248683 | −0.0124342 | − | 0.999923i | \(-0.503958\pi\) | ||||
−0.0124342 | + | 0.999923i | \(0.503958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.25957 | −0.274505 | ||||||||
\(142\) | −14.1609 | −1.18836 | ||||||||
\(143\) | −7.23464 | −0.604991 | ||||||||
\(144\) | 6.45155 | 0.537629 | ||||||||
\(145\) | −12.9021 | −1.07146 | ||||||||
\(146\) | −4.15896 | −0.344198 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.42392 | −0.528043 | ||||||||
\(149\) | −7.09335 | −0.581110 | −0.290555 | − | 0.956858i | \(-0.593840\pi\) | ||||
−0.290555 | + | 0.956858i | \(0.593840\pi\) | |||||||
\(150\) | 12.7675 | 1.04246 | ||||||||
\(151\) | 11.7970 | 0.960025 | 0.480013 | − | 0.877262i | \(-0.340632\pi\) | ||||
0.480013 | + | 0.877262i | \(0.340632\pi\) | |||||||
\(152\) | −0.629295 | −0.0510426 | ||||||||
\(153\) | −4.14845 | −0.335382 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.59598 | 0.610124 | ||||||||
\(156\) | 7.35171 | 0.588608 | ||||||||
\(157\) | −13.1571 | −1.05005 | −0.525024 | − | 0.851087i | \(-0.675944\pi\) | ||||
−0.525024 | + | 0.851087i | \(0.675944\pi\) | |||||||
\(158\) | 11.2211 | 0.892703 | ||||||||
\(159\) | −14.4071 | −1.14255 | ||||||||
\(160\) | 3.02538 | 0.239177 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −13.2678 | −1.04242 | ||||||||
\(163\) | 13.4107 | 1.05041 | 0.525204 | − | 0.850977i | \(-0.323989\pi\) | ||||
0.525204 | + | 0.850977i | \(0.323989\pi\) | |||||||
\(164\) | 2.07039 | 0.161670 | ||||||||
\(165\) | 28.1392 | 2.19063 | ||||||||
\(166\) | −7.62465 | −0.591787 | ||||||||
\(167\) | −9.48237 | −0.733768 | −0.366884 | − | 0.930267i | \(-0.619575\pi\) | ||||
−0.366884 | + | 0.930267i | \(0.619575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.28160 | −0.560123 | ||||||||
\(170\) | −1.94537 | −0.149203 | ||||||||
\(171\) | 4.05993 | 0.310470 | ||||||||
\(172\) | 1.35656 | 0.103436 | ||||||||
\(173\) | −1.05249 | −0.0800192 | −0.0400096 | − | 0.999199i | \(-0.512739\pi\) | ||||
−0.0400096 | + | 0.999199i | \(0.512739\pi\) | |||||||
\(174\) | 13.1108 | 0.993930 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.02538 | 0.228047 | ||||||||
\(177\) | −9.66730 | −0.726639 | ||||||||
\(178\) | −1.19130 | −0.0892917 | ||||||||
\(179\) | −10.1920 | −0.761787 | −0.380894 | − | 0.924619i | \(-0.624384\pi\) | ||||
−0.380894 | + | 0.924619i | \(0.624384\pi\) | |||||||
\(180\) | −19.5184 | −1.45481 | ||||||||
\(181\) | 13.8789 | 1.03161 | 0.515806 | − | 0.856706i | \(-0.327493\pi\) | ||||
0.515806 | + | 0.856706i | \(0.327493\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.5915 | 1.22648 | ||||||||
\(184\) | 9.39694 | 0.692751 | ||||||||
\(185\) | 19.4348 | 1.42888 | ||||||||
\(186\) | −7.71890 | −0.565977 | ||||||||
\(187\) | −1.94537 | −0.142259 | ||||||||
\(188\) | 1.06025 | 0.0773268 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.90386 | 0.138120 | ||||||||
\(191\) | 6.72199 | 0.486386 | 0.243193 | − | 0.969978i | \(-0.421805\pi\) | ||||
0.243193 | + | 0.969978i | \(0.421805\pi\) | |||||||
\(192\) | −3.07434 | −0.221871 | ||||||||
\(193\) | −2.32059 | −0.167039 | −0.0835197 | − | 0.996506i | \(-0.526616\pi\) | ||||
−0.0835197 | + | 0.996506i | \(0.526616\pi\) | |||||||
\(194\) | −16.3992 | −1.17739 | ||||||||
\(195\) | −22.2417 | −1.59276 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.72306 | 0.621492 | 0.310746 | − | 0.950493i | \(-0.399421\pi\) | ||||
0.310746 | + | 0.950493i | \(0.399421\pi\) | |||||||
\(198\) | −19.5184 | −1.38711 | ||||||||
\(199\) | −10.6790 | −0.757017 | −0.378509 | − | 0.925598i | \(-0.623563\pi\) | ||||
−0.378509 | + | 0.925598i | \(0.623563\pi\) | |||||||
\(200\) | −4.15293 | −0.293656 | ||||||||
\(201\) | −19.4386 | −1.37110 | ||||||||
\(202\) | −14.3697 | −1.01105 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.97685 | 0.138407 | ||||||||
\(205\) | −6.26372 | −0.437477 | ||||||||
\(206\) | 16.3323 | 1.13792 | ||||||||
\(207\) | −60.6248 | −4.21371 | ||||||||
\(208\) | −2.39132 | −0.165808 | ||||||||
\(209\) | 1.90386 | 0.131693 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2225 | −0.979115 | −0.489557 | − | 0.871971i | \(-0.662842\pi\) | ||||
−0.489557 | + | 0.871971i | \(0.662842\pi\) | |||||||
\(212\) | 4.68623 | 0.321852 | ||||||||
\(213\) | −43.5355 | −2.98300 | ||||||||
\(214\) | −16.6838 | −1.14048 | ||||||||
\(215\) | −4.10410 | −0.279897 | ||||||||
\(216\) | 10.6112 | 0.722002 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.66514 | −0.112778 | ||||||||
\(219\) | −12.7860 | −0.864000 | ||||||||
\(220\) | −9.15293 | −0.617090 | ||||||||
\(221\) | 1.53766 | 0.103434 | ||||||||
\(222\) | −19.7493 | −1.32549 | ||||||||
\(223\) | −9.69578 | −0.649278 | −0.324639 | − | 0.945838i | \(-0.605243\pi\) | ||||
−0.324639 | + | 0.945838i | \(0.605243\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 26.7928 | 1.78619 | ||||||||
\(226\) | 9.25578 | 0.615686 | ||||||||
\(227\) | −6.19599 | −0.411242 | −0.205621 | − | 0.978632i | \(-0.565921\pi\) | ||||
−0.205621 | + | 0.978632i | \(0.565921\pi\) | |||||||
\(228\) | −1.93466 | −0.128126 | ||||||||
\(229\) | 0.547320 | 0.0361679 | 0.0180840 | − | 0.999836i | \(-0.494243\pi\) | ||||
0.0180840 | + | 0.999836i | \(0.494243\pi\) | |||||||
\(230\) | −28.4293 | −1.87457 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.26461 | −0.279985 | ||||||||
\(233\) | 6.77776 | 0.444026 | 0.222013 | − | 0.975044i | \(-0.428737\pi\) | ||||
0.222013 | + | 0.975044i | \(0.428737\pi\) | |||||||
\(234\) | 15.4277 | 1.00854 | ||||||||
\(235\) | −3.20767 | −0.209245 | ||||||||
\(236\) | 3.14452 | 0.204691 | ||||||||
\(237\) | 34.4975 | 2.24085 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.80155 | −0.439956 | −0.219978 | − | 0.975505i | \(-0.570599\pi\) | ||||
−0.219978 | + | 0.975505i | \(0.570599\pi\) | |||||||
\(240\) | 9.30104 | 0.600379 | ||||||||
\(241\) | 26.0644 | 1.67895 | 0.839477 | − | 0.543395i | \(-0.182861\pi\) | ||||
0.839477 | + | 0.543395i | \(0.182861\pi\) | |||||||
\(242\) | 1.84707 | 0.118734 | ||||||||
\(243\) | −8.95609 | −0.574533 | ||||||||
\(244\) | −5.39679 | −0.345494 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.36508 | 0.405822 | ||||||||
\(247\) | −1.50484 | −0.0957509 | ||||||||
\(248\) | 2.51075 | 0.159433 | ||||||||
\(249\) | −23.4407 | −1.48550 | ||||||||
\(250\) | −2.56272 | −0.162081 | ||||||||
\(251\) | −26.1920 | −1.65322 | −0.826611 | − | 0.562774i | \(-0.809734\pi\) | ||||
−0.826611 | + | 0.562774i | \(0.809734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −28.4293 | −1.78734 | ||||||||
\(254\) | 13.3955 | 0.840507 | ||||||||
\(255\) | −5.98072 | −0.374527 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.4073 | 0.836326 | 0.418163 | − | 0.908372i | \(-0.362674\pi\) | ||||
0.418163 | + | 0.908372i | \(0.362674\pi\) | |||||||
\(258\) | 4.17051 | 0.259644 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.23464 | 0.448674 | ||||||||
\(261\) | 27.5133 | 1.70303 | ||||||||
\(262\) | −19.4378 | −1.20087 | ||||||||
\(263\) | −10.5626 | −0.651320 | −0.325660 | − | 0.945487i | \(-0.605586\pi\) | ||||
−0.325660 | + | 0.945487i | \(0.605586\pi\) | |||||||
\(264\) | 9.30104 | 0.572439 | ||||||||
\(265\) | −14.1776 | −0.870925 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.66246 | −0.224139 | ||||||||
\(268\) | 6.32287 | 0.386231 | ||||||||
\(269\) | −11.9198 | −0.726761 | −0.363380 | − | 0.931641i | \(-0.618377\pi\) | ||||
−0.363380 | + | 0.931641i | \(0.618377\pi\) | |||||||
\(270\) | −32.1030 | −1.95372 | ||||||||
\(271\) | 24.8700 | 1.51075 | 0.755373 | − | 0.655295i | \(-0.227455\pi\) | ||||
0.755373 | + | 0.655295i | \(0.227455\pi\) | |||||||
\(272\) | −0.643016 | −0.0389886 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.88612 | −0.476418 | ||||||||
\(275\) | 12.5642 | 0.757649 | ||||||||
\(276\) | 28.8893 | 1.73893 | ||||||||
\(277\) | 27.7796 | 1.66911 | 0.834557 | − | 0.550921i | \(-0.185723\pi\) | ||||
0.834557 | + | 0.550921i | \(0.185723\pi\) | |||||||
\(278\) | 0.293193 | 0.0175846 | ||||||||
\(279\) | −16.1982 | −0.969763 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.1896 | −1.86061 | −0.930306 | − | 0.366783i | \(-0.880459\pi\) | ||||
−0.930306 | + | 0.366783i | \(0.880459\pi\) | |||||||
\(282\) | 3.25957 | 0.194105 | ||||||||
\(283\) | −18.9829 | −1.12841 | −0.564207 | − | 0.825634i | \(-0.690818\pi\) | ||||
−0.564207 | + | 0.825634i | \(0.690818\pi\) | |||||||
\(284\) | 14.1609 | 0.840296 | ||||||||
\(285\) | 5.85310 | 0.346708 | ||||||||
\(286\) | 7.23464 | 0.427793 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −6.45155 | −0.380161 | ||||||||
\(289\) | −16.5865 | −0.975678 | ||||||||
\(290\) | 12.9021 | 0.757635 | ||||||||
\(291\) | −50.4166 | −2.95548 | ||||||||
\(292\) | 4.15896 | 0.243385 | ||||||||
\(293\) | 19.6220 | 1.14633 | 0.573163 | − | 0.819441i | \(-0.305716\pi\) | ||||
0.573163 | + | 0.819441i | \(0.305716\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.51336 | −0.553889 | ||||||||
\(296\) | 6.42392 | 0.373383 | ||||||||
\(297\) | −32.1030 | −1.86280 | ||||||||
\(298\) | 7.09335 | 0.410907 | ||||||||
\(299\) | 22.4711 | 1.29953 | ||||||||
\(300\) | −12.7675 | −0.737132 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11.7970 | −0.678840 | ||||||||
\(303\) | −44.1774 | −2.53793 | ||||||||
\(304\) | 0.629295 | 0.0360925 | ||||||||
\(305\) | 16.3273 | 0.934901 | ||||||||
\(306\) | 4.14845 | 0.237151 | ||||||||
\(307\) | 21.0550 | 1.20167 | 0.600836 | − | 0.799372i | \(-0.294835\pi\) | ||||
0.600836 | + | 0.799372i | \(0.294835\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 50.2109 | 2.85640 | ||||||||
\(310\) | −7.59598 | −0.431423 | ||||||||
\(311\) | −11.7755 | −0.667728 | −0.333864 | − | 0.942621i | \(-0.608353\pi\) | ||||
−0.333864 | + | 0.942621i | \(0.608353\pi\) | |||||||
\(312\) | −7.35171 | −0.416209 | ||||||||
\(313\) | 21.4522 | 1.21255 | 0.606275 | − | 0.795255i | \(-0.292663\pi\) | ||||
0.606275 | + | 0.795255i | \(0.292663\pi\) | |||||||
\(314\) | 13.1571 | 0.742497 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.2211 | −0.631236 | ||||||||
\(317\) | 29.6833 | 1.66718 | 0.833591 | − | 0.552382i | \(-0.186281\pi\) | ||||
0.833591 | + | 0.552382i | \(0.186281\pi\) | |||||||
\(318\) | 14.4071 | 0.807908 | ||||||||
\(319\) | 12.9021 | 0.722377 | ||||||||
\(320\) | −3.02538 | −0.169124 | ||||||||
\(321\) | −51.2915 | −2.86281 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.404647 | −0.0225152 | ||||||||
\(324\) | 13.2678 | 0.737101 | ||||||||
\(325\) | −9.93096 | −0.550871 | ||||||||
\(326\) | −13.4107 | −0.742750 | ||||||||
\(327\) | −5.11920 | −0.283093 | ||||||||
\(328\) | −2.07039 | −0.114318 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −28.1392 | −1.54901 | ||||||||
\(331\) | −0.820937 | −0.0451228 | −0.0225614 | − | 0.999745i | \(-0.507182\pi\) | ||||
−0.0225614 | + | 0.999745i | \(0.507182\pi\) | |||||||
\(332\) | 7.62465 | 0.418457 | ||||||||
\(333\) | −41.4442 | −2.27113 | ||||||||
\(334\) | 9.48237 | 0.518852 | ||||||||
\(335\) | −19.1291 | −1.04513 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.60599 | 0.196431 | 0.0982154 | − | 0.995165i | \(-0.468687\pi\) | ||||
0.0982154 | + | 0.995165i | \(0.468687\pi\) | |||||||
\(338\) | 7.28160 | 0.396067 | ||||||||
\(339\) | 28.4554 | 1.54549 | ||||||||
\(340\) | 1.94537 | 0.105502 | ||||||||
\(341\) | −7.59598 | −0.411345 | ||||||||
\(342\) | −4.05993 | −0.219536 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.35656 | −0.0731406 | ||||||||
\(345\) | −87.4013 | −4.70553 | ||||||||
\(346\) | 1.05249 | 0.0565821 | ||||||||
\(347\) | −16.5428 | −0.888066 | −0.444033 | − | 0.896010i | \(-0.646453\pi\) | ||||
−0.444033 | + | 0.896010i | \(0.646453\pi\) | |||||||
\(348\) | −13.1108 | −0.702815 | ||||||||
\(349\) | 2.36067 | 0.126364 | 0.0631819 | − | 0.998002i | \(-0.479875\pi\) | ||||
0.0631819 | + | 0.998002i | \(0.479875\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.3748 | 1.35441 | ||||||||
\(352\) | −3.02538 | −0.161253 | ||||||||
\(353\) | −3.79697 | −0.202092 | −0.101046 | − | 0.994882i | \(-0.532219\pi\) | ||||
−0.101046 | + | 0.994882i | \(0.532219\pi\) | |||||||
\(354\) | 9.66730 | 0.513811 | ||||||||
\(355\) | −42.8422 | −2.27383 | ||||||||
\(356\) | 1.19130 | 0.0631388 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.1920 | 0.538665 | ||||||||
\(359\) | −27.9367 | −1.47444 | −0.737221 | − | 0.675652i | \(-0.763862\pi\) | ||||
−0.737221 | + | 0.675652i | \(0.763862\pi\) | |||||||
\(360\) | 19.5184 | 1.02871 | ||||||||
\(361\) | −18.6040 | −0.979157 | ||||||||
\(362\) | −13.8789 | −0.729459 | ||||||||
\(363\) | 5.67853 | 0.298045 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.5824 | −0.658594 | ||||||||
\(366\) | −16.5915 | −0.867254 | ||||||||
\(367\) | −31.1857 | −1.62788 | −0.813941 | − | 0.580948i | \(-0.802682\pi\) | ||||
−0.813941 | + | 0.580948i | \(0.802682\pi\) | |||||||
\(368\) | −9.39694 | −0.489849 | ||||||||
\(369\) | 13.3572 | 0.695349 | ||||||||
\(370\) | −19.4348 | −1.01037 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.71890 | 0.400206 | ||||||||
\(373\) | −16.2454 | −0.841155 | −0.420578 | − | 0.907257i | \(-0.638173\pi\) | ||||
−0.420578 | + | 0.907257i | \(0.638173\pi\) | |||||||
\(374\) | 1.94537 | 0.100593 | ||||||||
\(375\) | −7.87866 | −0.406852 | ||||||||
\(376\) | −1.06025 | −0.0546783 | ||||||||
\(377\) | −10.1980 | −0.525225 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.4790 | 1.51423 | 0.757117 | − | 0.653279i | \(-0.226607\pi\) | ||||
0.757117 | + | 0.653279i | \(0.226607\pi\) | |||||||
\(380\) | −1.90386 | −0.0976658 | ||||||||
\(381\) | 41.1822 | 2.10983 | ||||||||
\(382\) | −6.72199 | −0.343927 | ||||||||
\(383\) | −16.7973 | −0.858304 | −0.429152 | − | 0.903232i | \(-0.641187\pi\) | ||||
−0.429152 | + | 0.903232i | \(0.641187\pi\) | |||||||
\(384\) | 3.07434 | 0.156887 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.32059 | 0.118115 | ||||||||
\(387\) | 8.75188 | 0.444883 | ||||||||
\(388\) | 16.3992 | 0.832543 | ||||||||
\(389\) | −11.5943 | −0.587853 | −0.293927 | − | 0.955828i | \(-0.594962\pi\) | ||||
−0.293927 | + | 0.955828i | \(0.594962\pi\) | |||||||
\(390\) | 22.2417 | 1.12625 | ||||||||
\(391\) | 6.04238 | 0.305576 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −59.7585 | −3.01442 | ||||||||
\(394\) | −8.72306 | −0.439461 | ||||||||
\(395\) | 33.9481 | 1.70811 | ||||||||
\(396\) | 19.5184 | 0.980836 | ||||||||
\(397\) | 13.6535 | 0.685252 | 0.342626 | − | 0.939472i | \(-0.388684\pi\) | ||||
0.342626 | + | 0.939472i | \(0.388684\pi\) | |||||||
\(398\) | 10.6790 | 0.535292 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.15293 | 0.207646 | ||||||||
\(401\) | 12.0822 | 0.603355 | 0.301677 | − | 0.953410i | \(-0.402453\pi\) | ||||
0.301677 | + | 0.953410i | \(0.402453\pi\) | |||||||
\(402\) | 19.4386 | 0.969512 | ||||||||
\(403\) | 6.00400 | 0.299081 | ||||||||
\(404\) | 14.3697 | 0.714921 | ||||||||
\(405\) | −40.1402 | −1.99458 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19.4348 | −0.963348 | ||||||||
\(408\) | −1.97685 | −0.0978686 | ||||||||
\(409\) | −25.1668 | −1.24442 | −0.622209 | − | 0.782851i | \(-0.713765\pi\) | ||||
−0.622209 | + | 0.782851i | \(0.713765\pi\) | |||||||
\(410\) | 6.26372 | 0.309343 | ||||||||
\(411\) | −24.2446 | −1.19590 | ||||||||
\(412\) | −16.3323 | −0.804633 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 60.6248 | 2.97955 | ||||||||
\(415\) | −23.0675 | −1.13234 | ||||||||
\(416\) | 2.39132 | 0.117244 | ||||||||
\(417\) | 0.901375 | 0.0441405 | ||||||||
\(418\) | −1.90386 | −0.0931207 | ||||||||
\(419\) | 21.5314 | 1.05188 | 0.525940 | − | 0.850522i | \(-0.323714\pi\) | ||||
0.525940 | + | 0.850522i | \(0.323714\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.9955 | −1.36442 | −0.682208 | − | 0.731158i | \(-0.738980\pi\) | ||||
−0.682208 | + | 0.731158i | \(0.738980\pi\) | |||||||
\(422\) | 14.2225 | 0.692339 | ||||||||
\(423\) | 6.84026 | 0.332585 | ||||||||
\(424\) | −4.68623 | −0.227584 | ||||||||
\(425\) | −2.67040 | −0.129533 | ||||||||
\(426\) | 43.5355 | 2.10930 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.6838 | 0.806441 | ||||||||
\(429\) | 22.2417 | 1.07384 | ||||||||
\(430\) | 4.10410 | 0.197917 | ||||||||
\(431\) | −17.6794 | −0.851587 | −0.425794 | − | 0.904820i | \(-0.640005\pi\) | ||||
−0.425794 | + | 0.904820i | \(0.640005\pi\) | |||||||
\(432\) | −10.6112 | −0.510532 | ||||||||
\(433\) | −1.18020 | −0.0567168 | −0.0283584 | − | 0.999598i | \(-0.509028\pi\) | ||||
−0.0283584 | + | 0.999598i | \(0.509028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 39.6653 | 1.90181 | ||||||||
\(436\) | 1.66514 | 0.0797458 | ||||||||
\(437\) | −5.91344 | −0.282878 | ||||||||
\(438\) | 12.7860 | 0.610941 | ||||||||
\(439\) | −21.3498 | −1.01897 | −0.509486 | − | 0.860479i | \(-0.670164\pi\) | ||||
−0.509486 | + | 0.860479i | \(0.670164\pi\) | |||||||
\(440\) | 9.15293 | 0.436349 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.53766 | −0.0731388 | ||||||||
\(443\) | 8.62280 | 0.409682 | 0.204841 | − | 0.978795i | \(-0.434332\pi\) | ||||
0.204841 | + | 0.978795i | \(0.434332\pi\) | |||||||
\(444\) | 19.7493 | 0.937260 | ||||||||
\(445\) | −3.60414 | −0.170852 | ||||||||
\(446\) | 9.69578 | 0.459109 | ||||||||
\(447\) | 21.8074 | 1.03145 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.7479 | 0.790381 | 0.395190 | − | 0.918599i | \(-0.370679\pi\) | ||||
0.395190 | + | 0.918599i | \(0.370679\pi\) | |||||||
\(450\) | −26.7928 | −1.26302 | ||||||||
\(451\) | 6.26372 | 0.294947 | ||||||||
\(452\) | −9.25578 | −0.435355 | ||||||||
\(453\) | −36.2679 | −1.70402 | ||||||||
\(454\) | 6.19599 | 0.290792 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.93466 | 0.0905990 | ||||||||
\(457\) | 8.01576 | 0.374962 | 0.187481 | − | 0.982268i | \(-0.439968\pi\) | ||||
0.187481 | + | 0.982268i | \(0.439968\pi\) | |||||||
\(458\) | −0.547320 | −0.0255746 | ||||||||
\(459\) | 6.82319 | 0.318479 | ||||||||
\(460\) | 28.4293 | 1.32552 | ||||||||
\(461\) | 18.1143 | 0.843668 | 0.421834 | − | 0.906673i | \(-0.361387\pi\) | ||||
0.421834 | + | 0.906673i | \(0.361387\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.32065 | 0.247272 | 0.123636 | − | 0.992328i | \(-0.460545\pi\) | ||||
0.123636 | + | 0.992328i | \(0.460545\pi\) | |||||||
\(464\) | 4.26461 | 0.197979 | ||||||||
\(465\) | −23.3526 | −1.08295 | ||||||||
\(466\) | −6.77776 | −0.313974 | ||||||||
\(467\) | −33.5558 | −1.55278 | −0.776388 | − | 0.630256i | \(-0.782950\pi\) | ||||
−0.776388 | + | 0.630256i | \(0.782950\pi\) | |||||||
\(468\) | −15.4277 | −0.713145 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.20767 | 0.147959 | ||||||||
\(471\) | 40.4493 | 1.86380 | ||||||||
\(472\) | −3.14452 | −0.144738 | ||||||||
\(473\) | 4.10410 | 0.188707 | ||||||||
\(474\) | −34.4975 | −1.58452 | ||||||||
\(475\) | 2.61342 | 0.119912 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.2335 | 1.38429 | ||||||||
\(478\) | 6.80155 | 0.311096 | ||||||||
\(479\) | −16.7425 | −0.764983 | −0.382492 | − | 0.923959i | \(-0.624934\pi\) | ||||
−0.382492 | + | 0.923959i | \(0.624934\pi\) | |||||||
\(480\) | −9.30104 | −0.424532 | ||||||||
\(481\) | 15.3616 | 0.700430 | ||||||||
\(482\) | −26.0644 | −1.18720 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.84707 | −0.0839579 | ||||||||
\(485\) | −49.6138 | −2.25285 | ||||||||
\(486\) | 8.95609 | 0.406256 | ||||||||
\(487\) | 26.6484 | 1.20756 | 0.603778 | − | 0.797152i | \(-0.293661\pi\) | ||||
0.603778 | + | 0.797152i | \(0.293661\pi\) | |||||||
\(488\) | 5.39679 | 0.244301 | ||||||||
\(489\) | −41.2290 | −1.86444 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.56655 | 0.341474 | 0.170737 | − | 0.985317i | \(-0.445385\pi\) | ||||
0.170737 | + | 0.985317i | \(0.445385\pi\) | |||||||
\(492\) | −6.36508 | −0.286960 | ||||||||
\(493\) | −2.74221 | −0.123503 | ||||||||
\(494\) | 1.50484 | 0.0677061 | ||||||||
\(495\) | −59.0505 | −2.65412 | ||||||||
\(496\) | −2.51075 | −0.112736 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 23.4407 | 1.05040 | ||||||||
\(499\) | −10.4872 | −0.469473 | −0.234736 | − | 0.972059i | \(-0.575423\pi\) | ||||
−0.234736 | + | 0.972059i | \(0.575423\pi\) | |||||||
\(500\) | 2.56272 | 0.114608 | ||||||||
\(501\) | 29.1520 | 1.30242 | ||||||||
\(502\) | 26.1920 | 1.16900 | ||||||||
\(503\) | −0.490508 | −0.0218707 | −0.0109353 | − | 0.999940i | \(-0.503481\pi\) | ||||
−0.0109353 | + | 0.999940i | \(0.503481\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −43.4739 | −1.93456 | ||||||||
\(506\) | 28.4293 | 1.26384 | ||||||||
\(507\) | 22.3861 | 0.994202 | ||||||||
\(508\) | −13.3955 | −0.594328 | ||||||||
\(509\) | −15.9439 | −0.706703 | −0.353351 | − | 0.935491i | \(-0.614958\pi\) | ||||
−0.353351 | + | 0.935491i | \(0.614958\pi\) | |||||||
\(510\) | 5.98072 | 0.264831 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.67759 | −0.294823 | ||||||||
\(514\) | −13.4073 | −0.591372 | ||||||||
\(515\) | 49.4113 | 2.17732 | ||||||||
\(516\) | −4.17051 | −0.183596 | ||||||||
\(517\) | 3.20767 | 0.141073 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.23570 | 0.142032 | ||||||||
\(520\) | −7.23464 | −0.317260 | ||||||||
\(521\) | 31.8495 | 1.39535 | 0.697677 | − | 0.716413i | \(-0.254217\pi\) | ||||
0.697677 | + | 0.716413i | \(0.254217\pi\) | |||||||
\(522\) | −27.5133 | −1.20423 | ||||||||
\(523\) | −42.4318 | −1.85541 | −0.927706 | − | 0.373311i | \(-0.878222\pi\) | ||||
−0.927706 | + | 0.373311i | \(0.878222\pi\) | |||||||
\(524\) | 19.4378 | 0.849146 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.5626 | 0.460553 | ||||||||
\(527\) | 1.61445 | 0.0703267 | ||||||||
\(528\) | −9.30104 | −0.404776 | ||||||||
\(529\) | 65.3024 | 2.83923 | ||||||||
\(530\) | 14.1776 | 0.615837 | ||||||||
\(531\) | 20.2870 | 0.880381 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.95096 | −0.214450 | ||||||||
\(534\) | 3.66246 | 0.158490 | ||||||||
\(535\) | −50.4748 | −2.18221 | ||||||||
\(536\) | −6.32287 | −0.273107 | ||||||||
\(537\) | 31.3337 | 1.35215 | ||||||||
\(538\) | 11.9198 | 0.513898 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 32.1030 | 1.38149 | ||||||||
\(541\) | 6.54151 | 0.281241 | 0.140621 | − | 0.990064i | \(-0.455090\pi\) | ||||
0.140621 | + | 0.990064i | \(0.455090\pi\) | |||||||
\(542\) | −24.8700 | −1.06826 | ||||||||
\(543\) | −42.6684 | −1.83108 | ||||||||
\(544\) | 0.643016 | 0.0275691 | ||||||||
\(545\) | −5.03768 | −0.215791 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2734 | 0.781314 | 0.390657 | − | 0.920536i | \(-0.372248\pi\) | ||||
0.390657 | + | 0.920536i | \(0.372248\pi\) | |||||||
\(548\) | 7.88612 | 0.336879 | ||||||||
\(549\) | −34.8176 | −1.48598 | ||||||||
\(550\) | −12.5642 | −0.535739 | ||||||||
\(551\) | 2.68370 | 0.114329 | ||||||||
\(552\) | −28.8893 | −1.22961 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −27.7796 | −1.18024 | ||||||||
\(555\) | −59.7492 | −2.53621 | ||||||||
\(556\) | −0.293193 | −0.0124342 | ||||||||
\(557\) | −36.4469 | −1.54431 | −0.772153 | − | 0.635436i | \(-0.780820\pi\) | ||||
−0.772153 | + | 0.635436i | \(0.780820\pi\) | |||||||
\(558\) | 16.1982 | 0.685726 | ||||||||
\(559\) | −3.24395 | −0.137205 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.98072 | 0.252506 | ||||||||
\(562\) | 31.1896 | 1.31565 | ||||||||
\(563\) | 6.15519 | 0.259410 | 0.129705 | − | 0.991553i | \(-0.458597\pi\) | ||||
0.129705 | + | 0.991553i | \(0.458597\pi\) | |||||||
\(564\) | −3.25957 | −0.137253 | ||||||||
\(565\) | 28.0023 | 1.17806 | ||||||||
\(566\) | 18.9829 | 0.797909 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.1609 | −0.594179 | ||||||||
\(569\) | 8.41931 | 0.352956 | 0.176478 | − | 0.984305i | \(-0.443530\pi\) | ||||
0.176478 | + | 0.984305i | \(0.443530\pi\) | |||||||
\(570\) | −5.85310 | −0.245159 | ||||||||
\(571\) | −35.0354 | −1.46619 | −0.733094 | − | 0.680128i | \(-0.761924\pi\) | ||||
−0.733094 | + | 0.680128i | \(0.761924\pi\) | |||||||
\(572\) | −7.23464 | −0.302496 | ||||||||
\(573\) | −20.6657 | −0.863320 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.0248 | −1.62745 | ||||||||
\(576\) | 6.45155 | 0.268814 | ||||||||
\(577\) | −34.8056 | −1.44898 | −0.724488 | − | 0.689287i | \(-0.757924\pi\) | ||||
−0.724488 | + | 0.689287i | \(0.757924\pi\) | |||||||
\(578\) | 16.5865 | 0.689909 | ||||||||
\(579\) | 7.13426 | 0.296490 | ||||||||
\(580\) | −12.9021 | −0.535729 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 50.4166 | 2.08984 | ||||||||
\(583\) | 14.1776 | 0.587178 | ||||||||
\(584\) | −4.15896 | −0.172099 | ||||||||
\(585\) | 46.6746 | 1.92976 | ||||||||
\(586\) | −19.6220 | −0.810575 | ||||||||
\(587\) | 19.8051 | 0.817443 | 0.408722 | − | 0.912659i | \(-0.365975\pi\) | ||||
0.408722 | + | 0.912659i | \(0.365975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.58000 | −0.0651029 | ||||||||
\(590\) | 9.51336 | 0.391659 | ||||||||
\(591\) | −26.8176 | −1.10313 | ||||||||
\(592\) | −6.42392 | −0.264022 | ||||||||
\(593\) | 10.5375 | 0.432724 | 0.216362 | − | 0.976313i | \(-0.430581\pi\) | ||||
0.216362 | + | 0.976313i | \(0.430581\pi\) | |||||||
\(594\) | 32.1030 | 1.31720 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.09335 | −0.290555 | ||||||||
\(597\) | 32.8310 | 1.34368 | ||||||||
\(598\) | −22.4711 | −0.918910 | ||||||||
\(599\) | −3.72145 | −0.152054 | −0.0760271 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760271 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(600\) | 12.7675 | 0.521231 | ||||||||
\(601\) | 0.194282 | 0.00792491 | 0.00396246 | − | 0.999992i | \(-0.498739\pi\) | ||||
0.00396246 | + | 0.999992i | \(0.498739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.7923 | 1.66119 | ||||||||
\(604\) | 11.7970 | 0.480013 | ||||||||
\(605\) | 5.58810 | 0.227189 | ||||||||
\(606\) | 44.1774 | 1.79458 | ||||||||
\(607\) | −20.2928 | −0.823658 | −0.411829 | − | 0.911261i | \(-0.635110\pi\) | ||||
−0.411829 | + | 0.911261i | \(0.635110\pi\) | |||||||
\(608\) | −0.629295 | −0.0255213 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.3273 | −0.661075 | ||||||||
\(611\) | −2.53540 | −0.102571 | ||||||||
\(612\) | −4.14845 | −0.167691 | ||||||||
\(613\) | 14.6071 | 0.589977 | 0.294988 | − | 0.955501i | \(-0.404684\pi\) | ||||
0.294988 | + | 0.955501i | \(0.404684\pi\) | |||||||
\(614\) | −21.0550 | −0.849710 | ||||||||
\(615\) | 19.2568 | 0.776508 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.6953 | 0.470837 | 0.235418 | − | 0.971894i | \(-0.424354\pi\) | ||||
0.235418 | + | 0.971894i | \(0.424354\pi\) | |||||||
\(618\) | −50.2109 | −2.01978 | ||||||||
\(619\) | −37.4631 | −1.50577 | −0.752885 | − | 0.658152i | \(-0.771338\pi\) | ||||
−0.752885 | + | 0.658152i | \(0.771338\pi\) | |||||||
\(620\) | 7.59598 | 0.305062 | ||||||||
\(621\) | 99.7129 | 4.00134 | ||||||||
\(622\) | 11.7755 | 0.472155 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.35171 | 0.294304 | ||||||||
\(625\) | −28.5178 | −1.14071 | ||||||||
\(626\) | −21.4522 | −0.857402 | ||||||||
\(627\) | −5.85310 | −0.233750 | ||||||||
\(628\) | −13.1571 | −0.525024 | ||||||||
\(629\) | 4.13069 | 0.164701 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.1060 | −0.521740 | −0.260870 | − | 0.965374i | \(-0.584009\pi\) | ||||
−0.260870 | + | 0.965374i | \(0.584009\pi\) | |||||||
\(632\) | 11.2211 | 0.446352 | ||||||||
\(633\) | 43.7246 | 1.73790 | ||||||||
\(634\) | −29.6833 | −1.17888 | ||||||||
\(635\) | 40.5264 | 1.60824 | ||||||||
\(636\) | −14.4071 | −0.571277 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −12.9021 | −0.510798 | ||||||||
\(639\) | 91.3599 | 3.61414 | ||||||||
\(640\) | 3.02538 | 0.119589 | ||||||||
\(641\) | −11.5281 | −0.455331 | −0.227666 | − | 0.973739i | \(-0.573109\pi\) | ||||
−0.227666 | + | 0.973739i | \(0.573109\pi\) | |||||||
\(642\) | 51.2915 | 2.02432 | ||||||||
\(643\) | −22.9575 | −0.905357 | −0.452678 | − | 0.891674i | \(-0.649531\pi\) | ||||
−0.452678 | + | 0.891674i | \(0.649531\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.6174 | 0.496809 | ||||||||
\(646\) | 0.404647 | 0.0159206 | ||||||||
\(647\) | 2.60155 | 0.102277 | 0.0511387 | − | 0.998692i | \(-0.483715\pi\) | ||||
0.0511387 | + | 0.998692i | \(0.483715\pi\) | |||||||
\(648\) | −13.2678 | −0.521209 | ||||||||
\(649\) | 9.51336 | 0.373432 | ||||||||
\(650\) | 9.93096 | 0.389524 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.4107 | 0.525204 | ||||||||
\(653\) | 35.4045 | 1.38548 | 0.692742 | − | 0.721186i | \(-0.256403\pi\) | ||||
0.692742 | + | 0.721186i | \(0.256403\pi\) | |||||||
\(654\) | 5.11920 | 0.200177 | ||||||||
\(655\) | −58.8069 | −2.29777 | ||||||||
\(656\) | 2.07039 | 0.0808351 | ||||||||
\(657\) | 26.8317 | 1.04680 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.3486 | −1.06535 | −0.532675 | − | 0.846320i | \(-0.678813\pi\) | ||||
−0.532675 | + | 0.846320i | \(0.678813\pi\) | |||||||
\(660\) | 28.1392 | 1.09532 | ||||||||
\(661\) | 3.45634 | 0.134436 | 0.0672181 | − | 0.997738i | \(-0.478588\pi\) | ||||
0.0672181 | + | 0.997738i | \(0.478588\pi\) | |||||||
\(662\) | 0.820937 | 0.0319066 | ||||||||
\(663\) | −4.72727 | −0.183592 | ||||||||
\(664\) | −7.62465 | −0.295894 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 41.4442 | 1.60593 | ||||||||
\(667\) | −40.0743 | −1.55168 | ||||||||
\(668\) | −9.48237 | −0.366884 | ||||||||
\(669\) | 29.8081 | 1.15245 | ||||||||
\(670\) | 19.1291 | 0.739022 | ||||||||
\(671\) | −16.3273 | −0.630310 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.4177 | −0.825592 | −0.412796 | − | 0.910823i | \(-0.635448\pi\) | ||||
−0.412796 | + | 0.910823i | \(0.635448\pi\) | |||||||
\(674\) | −3.60599 | −0.138898 | ||||||||
\(675\) | −44.0676 | −1.69616 | ||||||||
\(676\) | −7.28160 | −0.280062 | ||||||||
\(677\) | −18.6228 | −0.715734 | −0.357867 | − | 0.933773i | \(-0.616496\pi\) | ||||
−0.357867 | + | 0.933773i | \(0.616496\pi\) | |||||||
\(678\) | −28.4554 | −1.09282 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.94537 | −0.0746015 | ||||||||
\(681\) | 19.0486 | 0.729942 | ||||||||
\(682\) | 7.59598 | 0.290865 | ||||||||
\(683\) | −6.22994 | −0.238382 | −0.119191 | − | 0.992871i | \(-0.538030\pi\) | ||||
−0.119191 | + | 0.992871i | \(0.538030\pi\) | |||||||
\(684\) | 4.05993 | 0.155235 | ||||||||
\(685\) | −23.8585 | −0.911587 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.68264 | −0.0641969 | ||||||||
\(688\) | 1.35656 | 0.0517182 | ||||||||
\(689\) | −11.2063 | −0.426925 | ||||||||
\(690\) | 87.4013 | 3.32731 | ||||||||
\(691\) | −22.4779 | −0.855100 | −0.427550 | − | 0.903992i | \(-0.640623\pi\) | ||||
−0.427550 | + | 0.903992i | \(0.640623\pi\) | |||||||
\(692\) | −1.05249 | −0.0400096 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.5428 | 0.627958 | ||||||||
\(695\) | 0.887021 | 0.0336466 | ||||||||
\(696\) | 13.1108 | 0.496965 | ||||||||
\(697\) | −1.33129 | −0.0504264 | ||||||||
\(698\) | −2.36067 | −0.0893526 | ||||||||
\(699\) | −20.8371 | −0.788132 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.5946 | −0.928924 | −0.464462 | − | 0.885593i | \(-0.653752\pi\) | ||||
−0.464462 | + | 0.885593i | \(0.653752\pi\) | |||||||
\(702\) | −25.3748 | −0.957710 | ||||||||
\(703\) | −4.04254 | −0.152467 | ||||||||
\(704\) | 3.02538 | 0.114023 | ||||||||
\(705\) | 9.86144 | 0.371403 | ||||||||
\(706\) | 3.79697 | 0.142901 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.66730 | −0.363319 | ||||||||
\(709\) | 4.20095 | 0.157770 | 0.0788850 | − | 0.996884i | \(-0.474864\pi\) | ||||
0.0788850 | + | 0.996884i | \(0.474864\pi\) | |||||||
\(710\) | 42.8422 | 1.60784 | ||||||||
\(711\) | −72.3935 | −2.71497 | ||||||||
\(712\) | −1.19130 | −0.0446459 | ||||||||
\(713\) | 23.5934 | 0.883579 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.8875 | 0.818548 | ||||||||
\(716\) | −10.1920 | −0.380894 | ||||||||
\(717\) | 20.9103 | 0.780908 | ||||||||
\(718\) | 27.9367 | 1.04259 | ||||||||
\(719\) | 46.2368 | 1.72434 | 0.862172 | − | 0.506616i | \(-0.169104\pi\) | ||||
0.862172 | + | 0.506616i | \(0.169104\pi\) | |||||||
\(720\) | −19.5184 | −0.727407 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.6040 | 0.692369 | ||||||||
\(723\) | −80.1307 | −2.98009 | ||||||||
\(724\) | 13.8789 | 0.515806 | ||||||||
\(725\) | 17.7106 | 0.657755 | ||||||||
\(726\) | −5.67853 | −0.210750 | ||||||||
\(727\) | 0.541534 | 0.0200844 | 0.0100422 | − | 0.999950i | \(-0.496803\pi\) | ||||
0.0100422 | + | 0.999950i | \(0.496803\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.2694 | −0.454423 | ||||||||
\(730\) | 12.5824 | 0.465697 | ||||||||
\(731\) | −0.872287 | −0.0322627 | ||||||||
\(732\) | 16.5915 | 0.613241 | ||||||||
\(733\) | 16.8334 | 0.621756 | 0.310878 | − | 0.950450i | \(-0.399377\pi\) | ||||
0.310878 | + | 0.950450i | \(0.399377\pi\) | |||||||
\(734\) | 31.1857 | 1.15109 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.39694 | 0.346376 | ||||||||
\(737\) | 19.1291 | 0.704630 | ||||||||
\(738\) | −13.3572 | −0.491686 | ||||||||
\(739\) | −13.3478 | −0.491007 | −0.245504 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245504 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(740\) | 19.4348 | 0.714438 | ||||||||
\(741\) | 4.62640 | 0.169955 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.5560 | −1.48786 | −0.743928 | − | 0.668260i | \(-0.767039\pi\) | ||||
−0.743928 | + | 0.668260i | \(0.767039\pi\) | |||||||
\(744\) | −7.71890 | −0.282988 | ||||||||
\(745\) | 21.4601 | 0.786237 | ||||||||
\(746\) | 16.2454 | 0.594787 | ||||||||
\(747\) | 49.1908 | 1.79980 | ||||||||
\(748\) | −1.94537 | −0.0711297 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 7.87866 | 0.287688 | ||||||||
\(751\) | −22.1713 | −0.809044 | −0.404522 | − | 0.914528i | \(-0.632562\pi\) | ||||
−0.404522 | + | 0.914528i | \(0.632562\pi\) | |||||||
\(752\) | 1.06025 | 0.0386634 | ||||||||
\(753\) | 80.5229 | 2.93442 | ||||||||
\(754\) | 10.1980 | 0.371390 | ||||||||
\(755\) | −35.6904 | −1.29891 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.3097 | 0.665479 | 0.332739 | − | 0.943019i | \(-0.392027\pi\) | ||||
0.332739 | + | 0.943019i | \(0.392027\pi\) | |||||||
\(758\) | −29.4790 | −1.07073 | ||||||||
\(759\) | 87.4013 | 3.17246 | ||||||||
\(760\) | 1.90386 | 0.0690601 | ||||||||
\(761\) | 26.4821 | 0.959975 | 0.479988 | − | 0.877275i | \(-0.340641\pi\) | ||||
0.479988 | + | 0.877275i | \(0.340641\pi\) | |||||||
\(762\) | −41.1822 | −1.49187 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.72199 | 0.243193 | ||||||||
\(765\) | 12.5506 | 0.453769 | ||||||||
\(766\) | 16.7973 | 0.606912 | ||||||||
\(767\) | −7.51953 | −0.271515 | ||||||||
\(768\) | −3.07434 | −0.110936 | ||||||||
\(769\) | −50.0568 | −1.80509 | −0.902547 | − | 0.430591i | \(-0.858305\pi\) | ||||
−0.902547 | + | 0.430591i | \(0.858305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.2187 | −1.48445 | ||||||||
\(772\) | −2.32059 | −0.0835197 | ||||||||
\(773\) | −9.47987 | −0.340967 | −0.170484 | − | 0.985361i | \(-0.554533\pi\) | ||||
−0.170484 | + | 0.985361i | \(0.554533\pi\) | |||||||
\(774\) | −8.75188 | −0.314580 | ||||||||
\(775\) | −10.4270 | −0.374548 | ||||||||
\(776\) | −16.3992 | −0.588697 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.5943 | 0.415675 | ||||||||
\(779\) | 1.30289 | 0.0466807 | ||||||||
\(780\) | −22.2417 | −0.796382 | ||||||||
\(781\) | 42.8422 | 1.53301 | ||||||||
\(782\) | −6.04238 | −0.216075 | ||||||||
\(783\) | −45.2527 | −1.61720 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.8052 | 1.42071 | ||||||||
\(786\) | 59.7585 | 2.13151 | ||||||||
\(787\) | −43.6250 | −1.55506 | −0.777531 | − | 0.628845i | \(-0.783528\pi\) | ||||
−0.777531 | + | 0.628845i | \(0.783528\pi\) | |||||||
\(788\) | 8.72306 | 0.310746 | ||||||||
\(789\) | 32.4731 | 1.15607 | ||||||||
\(790\) | −33.9481 | −1.20782 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −19.5184 | −0.693556 | ||||||||
\(793\) | 12.9054 | 0.458285 | ||||||||
\(794\) | −13.6535 | −0.484546 | ||||||||
\(795\) | 43.5868 | 1.54587 | ||||||||
\(796\) | −10.6790 | −0.378509 | ||||||||
\(797\) | −6.57856 | −0.233024 | −0.116512 | − | 0.993189i | \(-0.537171\pi\) | ||||
−0.116512 | + | 0.993189i | \(0.537171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.681759 | −0.0241189 | ||||||||
\(800\) | −4.15293 | −0.146828 | ||||||||
\(801\) | 7.68573 | 0.271562 | ||||||||
\(802\) | −12.0822 | −0.426636 | ||||||||
\(803\) | 12.5824 | 0.444024 | ||||||||
\(804\) | −19.4386 | −0.685548 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.00400 | −0.211482 | ||||||||
\(807\) | 36.6454 | 1.28998 | ||||||||
\(808\) | −14.3697 | −0.505526 | ||||||||
\(809\) | 35.8429 | 1.26017 | 0.630084 | − | 0.776527i | \(-0.283020\pi\) | ||||
0.630084 | + | 0.776527i | \(0.283020\pi\) | |||||||
\(810\) | 40.1402 | 1.41038 | ||||||||
\(811\) | 26.2868 | 0.923053 | 0.461526 | − | 0.887126i | \(-0.347302\pi\) | ||||
0.461526 | + | 0.887126i | \(0.347302\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −76.4589 | −2.68153 | ||||||||
\(814\) | 19.4348 | 0.681190 | ||||||||
\(815\) | −40.5725 | −1.42119 | ||||||||
\(816\) | 1.97685 | 0.0692035 | ||||||||
\(817\) | 0.853673 | 0.0298663 | ||||||||
\(818\) | 25.1668 | 0.879936 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.26372 | −0.218738 | ||||||||
\(821\) | 35.0033 | 1.22162 | 0.610812 | − | 0.791775i | \(-0.290843\pi\) | ||||
0.610812 | + | 0.791775i | \(0.290843\pi\) | |||||||
\(822\) | 24.2446 | 0.845628 | ||||||||
\(823\) | 27.0562 | 0.943120 | 0.471560 | − | 0.881834i | \(-0.343691\pi\) | ||||
0.471560 | + | 0.881834i | \(0.343691\pi\) | |||||||
\(824\) | 16.3323 | 0.568961 | ||||||||
\(825\) | −38.6265 | −1.34480 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.4179 | −1.09251 | −0.546254 | − | 0.837620i | \(-0.683947\pi\) | ||||
−0.546254 | + | 0.837620i | \(0.683947\pi\) | |||||||
\(828\) | −60.6248 | −2.10686 | ||||||||
\(829\) | −19.1143 | −0.663867 | −0.331934 | − | 0.943303i | \(-0.607701\pi\) | ||||
−0.331934 | + | 0.943303i | \(0.607701\pi\) | |||||||
\(830\) | 23.0675 | 0.800683 | ||||||||
\(831\) | −85.4039 | −2.96263 | ||||||||
\(832\) | −2.39132 | −0.0829040 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.901375 | −0.0312121 | ||||||||
\(835\) | 28.6878 | 0.992782 | ||||||||
\(836\) | 1.90386 | 0.0658463 | ||||||||
\(837\) | 26.6421 | 0.920887 | ||||||||
\(838\) | −21.5314 | −0.743791 | ||||||||
\(839\) | 10.9451 | 0.377868 | 0.188934 | − | 0.981990i | \(-0.439497\pi\) | ||||
0.188934 | + | 0.981990i | \(0.439497\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.8131 | −0.372866 | ||||||||
\(842\) | 27.9955 | 0.964788 | ||||||||
\(843\) | 95.8872 | 3.30253 | ||||||||
\(844\) | −14.2225 | −0.489557 | ||||||||
\(845\) | 22.0296 | 0.757842 | ||||||||
\(846\) | −6.84026 | −0.235173 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.68623 | 0.160926 | ||||||||
\(849\) | 58.3597 | 2.00290 | ||||||||
\(850\) | 2.67040 | 0.0915939 | ||||||||
\(851\) | 60.3652 | 2.06929 | ||||||||
\(852\) | −43.5355 | −1.49150 | ||||||||
\(853\) | −49.0131 | −1.67818 | −0.839088 | − | 0.543995i | \(-0.816911\pi\) | ||||
−0.839088 | + | 0.543995i | \(0.816911\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.2828 | −0.420064 | ||||||||
\(856\) | −16.6838 | −0.570240 | ||||||||
\(857\) | −11.0683 | −0.378084 | −0.189042 | − | 0.981969i | \(-0.560538\pi\) | ||||
−0.189042 | + | 0.981969i | \(0.560538\pi\) | |||||||
\(858\) | −22.2417 | −0.759320 | ||||||||
\(859\) | −14.7784 | −0.504233 | −0.252116 | − | 0.967697i | \(-0.581127\pi\) | ||||
−0.252116 | + | 0.967697i | \(0.581127\pi\) | |||||||
\(860\) | −4.10410 | −0.139948 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.6794 | 0.602163 | ||||||||
\(863\) | −7.06992 | −0.240663 | −0.120331 | − | 0.992734i | \(-0.538396\pi\) | ||||
−0.120331 | + | 0.992734i | \(0.538396\pi\) | |||||||
\(864\) | 10.6112 | 0.361001 | ||||||||
\(865\) | 3.18418 | 0.108265 | ||||||||
\(866\) | 1.18020 | 0.0401049 | ||||||||
\(867\) | 50.9926 | 1.73180 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.9481 | −1.15161 | ||||||||
\(870\) | −39.6653 | −1.34478 | ||||||||
\(871\) | −15.1200 | −0.512322 | ||||||||
\(872\) | −1.66514 | −0.0563888 | ||||||||
\(873\) | 105.800 | 3.58079 | ||||||||
\(874\) | 5.91344 | 0.200025 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.7860 | −0.432000 | ||||||||
\(877\) | 48.1941 | 1.62740 | 0.813699 | − | 0.581286i | \(-0.197450\pi\) | ||||
0.813699 | + | 0.581286i | \(0.197450\pi\) | |||||||
\(878\) | 21.3498 | 0.720522 | ||||||||
\(879\) | −60.3245 | −2.03469 | ||||||||
\(880\) | −9.15293 | −0.308545 | ||||||||
\(881\) | 5.91801 | 0.199383 | 0.0996915 | − | 0.995018i | \(-0.468214\pi\) | ||||
0.0996915 | + | 0.995018i | \(0.468214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.4616 | −0.991461 | −0.495730 | − | 0.868477i | \(-0.665100\pi\) | ||||
−0.495730 | + | 0.868477i | \(0.665100\pi\) | |||||||
\(884\) | 1.53766 | 0.0517170 | ||||||||
\(885\) | 29.2473 | 0.983136 | ||||||||
\(886\) | −8.62280 | −0.289689 | ||||||||
\(887\) | 23.2506 | 0.780679 | 0.390340 | − | 0.920671i | \(-0.372358\pi\) | ||||
0.390340 | + | 0.920671i | \(0.372358\pi\) | |||||||
\(888\) | −19.7493 | −0.662743 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.60414 | 0.120811 | ||||||||
\(891\) | 40.1402 | 1.34475 | ||||||||
\(892\) | −9.69578 | −0.324639 | ||||||||
\(893\) | 0.667211 | 0.0223274 | ||||||||
\(894\) | −21.8074 | −0.729347 | ||||||||
\(895\) | 30.8347 | 1.03069 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −69.0836 | −2.30663 | ||||||||
\(898\) | −16.7479 | −0.558884 | ||||||||
\(899\) | −10.7074 | −0.357111 | ||||||||
\(900\) | 26.7928 | 0.893093 | ||||||||
\(901\) | −3.01332 | −0.100388 | ||||||||
\(902\) | −6.26372 | −0.208559 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.25578 | 0.307843 | ||||||||
\(905\) | −41.9890 | −1.39576 | ||||||||
\(906\) | 36.2679 | 1.20492 | ||||||||
\(907\) | 16.8991 | 0.561126 | 0.280563 | − | 0.959836i | \(-0.409479\pi\) | ||||
0.280563 | + | 0.959836i | \(0.409479\pi\) | |||||||
\(908\) | −6.19599 | −0.205621 | ||||||||
\(909\) | 92.7070 | 3.07490 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.2207 | 1.59762 | 0.798812 | − | 0.601581i | \(-0.205462\pi\) | ||||
0.798812 | + | 0.601581i | \(0.205462\pi\) | |||||||
\(912\) | −1.93466 | −0.0640632 | ||||||||
\(913\) | 23.0675 | 0.763421 | ||||||||
\(914\) | −8.01576 | −0.265138 | ||||||||
\(915\) | −50.1958 | −1.65942 | ||||||||
\(916\) | 0.547320 | 0.0180840 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.82319 | −0.225199 | ||||||||
\(919\) | −10.5044 | −0.346507 | −0.173253 | − | 0.984877i | \(-0.555428\pi\) | ||||
−0.173253 | + | 0.984877i | \(0.555428\pi\) | |||||||
\(920\) | −28.4293 | −0.937286 | ||||||||
\(921\) | −64.7301 | −2.13293 | ||||||||
\(922\) | −18.1143 | −0.596563 | ||||||||
\(923\) | −33.8633 | −1.11462 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.6781 | −0.877170 | ||||||||
\(926\) | −5.32065 | −0.174848 | ||||||||
\(927\) | −105.368 | −3.46075 | ||||||||
\(928\) | −4.26461 | −0.139993 | ||||||||
\(929\) | 35.1667 | 1.15378 | 0.576891 | − | 0.816821i | \(-0.304266\pi\) | ||||
0.576891 | + | 0.816821i | \(0.304266\pi\) | |||||||
\(930\) | 23.3526 | 0.765762 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.77776 | 0.222013 | ||||||||
\(933\) | 36.2019 | 1.18520 | ||||||||
\(934\) | 33.5558 | 1.09798 | ||||||||
\(935\) | 5.88548 | 0.192476 | ||||||||
\(936\) | 15.4277 | 0.504270 | ||||||||
\(937\) | 25.7519 | 0.841276 | 0.420638 | − | 0.907228i | \(-0.361806\pi\) | ||||
0.420638 | + | 0.907228i | \(0.361806\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −65.9513 | −2.15224 | ||||||||
\(940\) | −3.20767 | −0.104622 | ||||||||
\(941\) | −1.03902 | −0.0338711 | −0.0169355 | − | 0.999857i | \(-0.505391\pi\) | ||||
−0.0169355 | + | 0.999857i | \(0.505391\pi\) | |||||||
\(942\) | −40.4493 | −1.31791 | ||||||||
\(943\) | −19.4553 | −0.633552 | ||||||||
\(944\) | 3.14452 | 0.102345 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.10410 | −0.133436 | ||||||||
\(947\) | −34.2003 | −1.11136 | −0.555680 | − | 0.831396i | \(-0.687542\pi\) | ||||
−0.555680 | + | 0.831396i | \(0.687542\pi\) | |||||||
\(948\) | 34.4975 | 1.12043 | ||||||||
\(949\) | −9.94539 | −0.322841 | ||||||||
\(950\) | −2.61342 | −0.0847904 | ||||||||
\(951\) | −91.2566 | −2.95920 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.6131 | −0.700116 | −0.350058 | − | 0.936728i | \(-0.613838\pi\) | ||||
−0.350058 | + | 0.936728i | \(0.613838\pi\) | |||||||
\(954\) | −30.2335 | −0.978844 | ||||||||
\(955\) | −20.3366 | −0.658076 | ||||||||
\(956\) | −6.80155 | −0.219978 | ||||||||
\(957\) | −39.6653 | −1.28220 | ||||||||
\(958\) | 16.7425 | 0.540925 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.30104 | 0.300190 | ||||||||
\(961\) | −24.6961 | −0.796649 | ||||||||
\(962\) | −15.3616 | −0.495279 | ||||||||
\(963\) | 107.636 | 3.46853 | ||||||||
\(964\) | 26.0644 | 0.839477 | ||||||||
\(965\) | 7.02065 | 0.226003 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.2390 | −1.00458 | −0.502289 | − | 0.864700i | \(-0.667509\pi\) | ||||
−0.502289 | + | 0.864700i | \(0.667509\pi\) | |||||||
\(968\) | 1.84707 | 0.0593672 | ||||||||
\(969\) | 1.24402 | 0.0399637 | ||||||||
\(970\) | 49.6138 | 1.59300 | ||||||||
\(971\) | 8.49816 | 0.272719 | 0.136359 | − | 0.990659i | \(-0.456460\pi\) | ||||
0.136359 | + | 0.990659i | \(0.456460\pi\) | |||||||
\(972\) | −8.95609 | −0.287267 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −26.6484 | −0.853871 | ||||||||
\(975\) | 30.5311 | 0.977779 | ||||||||
\(976\) | −5.39679 | −0.172747 | ||||||||
\(977\) | 2.17623 | 0.0696238 | 0.0348119 | − | 0.999394i | \(-0.488917\pi\) | ||||
0.0348119 | + | 0.999394i | \(0.488917\pi\) | |||||||
\(978\) | 41.2290 | 1.31836 | ||||||||
\(979\) | 3.60414 | 0.115189 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.7427 | 0.342989 | ||||||||
\(982\) | −7.56655 | −0.241458 | ||||||||
\(983\) | −27.4934 | −0.876904 | −0.438452 | − | 0.898755i | \(-0.644473\pi\) | ||||
−0.438452 | + | 0.898755i | \(0.644473\pi\) | |||||||
\(984\) | 6.36508 | 0.202911 | ||||||||
\(985\) | −26.3906 | −0.840873 | ||||||||
\(986\) | 2.74221 | 0.0873298 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.50484 | −0.0478755 | ||||||||
\(989\) | −12.7475 | −0.405346 | ||||||||
\(990\) | 59.0505 | 1.87675 | ||||||||
\(991\) | −0.631072 | −0.0200467 | −0.0100233 | − | 0.999950i | \(-0.503191\pi\) | ||||
−0.0100233 | + | 0.999950i | \(0.503191\pi\) | |||||||
\(992\) | 2.51075 | 0.0797164 | ||||||||
\(993\) | 2.52384 | 0.0800916 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.3082 | 1.02424 | ||||||||
\(996\) | −23.4407 | −0.742748 | ||||||||
\(997\) | 20.4945 | 0.649067 | 0.324534 | − | 0.945874i | \(-0.394793\pi\) | ||||
0.324534 | + | 0.945874i | \(0.394793\pi\) | |||||||
\(998\) | 10.4872 | 0.331967 | ||||||||
\(999\) | 68.1657 | 2.15667 |
(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 | 4802.2.a.d.1.1 | 9 | ||
7.6 | odd | 2 | 4802.2.a.c.1.9 | 9 | |||
49.3 | odd | 42 | 686.2.g.g.177.1 | 36 | |||
49.5 | odd | 42 | 686.2.g.g.67.3 | 36 | |||
49.6 | odd | 14 | 686.2.e.b.589.3 | 18 | |||
49.8 | even | 7 | 98.2.e.b.15.1 | ✓ | 18 | ||
49.10 | odd | 42 | 686.2.g.g.471.3 | 36 | |||
49.16 | even | 21 | 686.2.g.h.655.3 | 36 | |||
49.33 | odd | 42 | 686.2.g.g.655.1 | 36 | |||
49.39 | even | 21 | 686.2.g.h.471.1 | 36 | |||
49.41 | odd | 14 | 686.2.e.b.99.3 | 18 | |||
49.43 | even | 7 | 98.2.e.b.85.1 | yes | 18 | ||
49.44 | even | 21 | 686.2.g.h.67.1 | 36 | |||
49.46 | even | 21 | 686.2.g.h.177.3 | 36 | |||
147.8 | odd | 14 | 882.2.u.g.505.3 | 18 | |||
147.92 | odd | 14 | 882.2.u.g.379.3 | 18 | |||
196.43 | odd | 14 | 784.2.u.d.673.3 | 18 | |||
196.155 | odd | 14 | 784.2.u.d.113.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.2.e.b.15.1 | ✓ | 18 | 49.8 | even | 7 | ||
98.2.e.b.85.1 | yes | 18 | 49.43 | even | 7 | ||
686.2.e.b.99.3 | 18 | 49.41 | odd | 14 | |||
686.2.e.b.589.3 | 18 | 49.6 | odd | 14 | |||
686.2.g.g.67.3 | 36 | 49.5 | odd | 42 | |||
686.2.g.g.177.1 | 36 | 49.3 | odd | 42 | |||
686.2.g.g.471.3 | 36 | 49.10 | odd | 42 | |||
686.2.g.g.655.1 | 36 | 49.33 | odd | 42 | |||
686.2.g.h.67.1 | 36 | 49.44 | even | 21 | |||
686.2.g.h.177.3 | 36 | 49.46 | even | 21 | |||
686.2.g.h.471.1 | 36 | 49.39 | even | 21 | |||
686.2.g.h.655.3 | 36 | 49.16 | even | 21 | |||
784.2.u.d.113.3 | 18 | 196.155 | odd | 14 | |||
784.2.u.d.673.3 | 18 | 196.43 | odd | 14 | |||
882.2.u.g.379.3 | 18 | 147.92 | odd | 14 | |||
882.2.u.g.505.3 | 18 | 147.8 | odd | 14 | |||
4802.2.a.c.1.9 | 9 | 7.6 | odd | 2 | |||
4802.2.a.d.1.1 | 9 | 1.1 | even | 1 | trivial |