Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5054,2,Mod(1,5054)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5054, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5054.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5054 = 2 \cdot 7 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5054.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(40.3563931816\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.19520000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 12x^{6} + 16x^{5} + 50x^{4} - 24x^{3} - 72x^{2} - 32x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.236286\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5054.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.04815 | −1.75985 | −0.879924 | − | 0.475115i | \(-0.842407\pi\) | ||||
−0.879924 | + | 0.475115i | \(0.842407\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.90247 | 1.74524 | 0.872618 | − | 0.488404i | \(-0.162421\pi\) | ||||
0.872618 | + | 0.488404i | \(0.162421\pi\) | |||||||
\(6\) | −3.04815 | −1.24440 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 6.29119 | 2.09706 | ||||||||
\(10\) | 3.90247 | 1.23407 | ||||||||
\(11\) | −5.43763 | −1.63951 | −0.819754 | − | 0.572716i | \(-0.805890\pi\) | ||||
−0.819754 | + | 0.572716i | \(0.805890\pi\) | |||||||
\(12\) | −3.04815 | −0.879924 | ||||||||
\(13\) | −2.24823 | −0.623548 | −0.311774 | − | 0.950156i | \(-0.600923\pi\) | ||||
−0.311774 | + | 0.950156i | \(0.600923\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −11.8953 | −3.07135 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.977224 | 0.237012 | 0.118506 | − | 0.992953i | \(-0.462190\pi\) | ||||
0.118506 | + | 0.992953i | \(0.462190\pi\) | |||||||
\(18\) | 6.29119 | 1.48285 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 3.90247 | 0.872618 | ||||||||
\(21\) | −3.04815 | −0.665160 | ||||||||
\(22\) | −5.43763 | −1.15931 | ||||||||
\(23\) | 0.640603 | 0.133575 | 0.0667875 | − | 0.997767i | \(-0.478725\pi\) | ||||
0.0667875 | + | 0.997767i | \(0.478725\pi\) | |||||||
\(24\) | −3.04815 | −0.622200 | ||||||||
\(25\) | 10.2292 | 2.04585 | ||||||||
\(26\) | −2.24823 | −0.440915 | ||||||||
\(27\) | −10.0320 | −1.93067 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −6.85823 | −1.27354 | −0.636771 | − | 0.771053i | \(-0.719730\pi\) | ||||
−0.636771 | + | 0.771053i | \(0.719730\pi\) | |||||||
\(30\) | −11.8953 | −2.17177 | ||||||||
\(31\) | −3.00774 | −0.540205 | −0.270103 | − | 0.962832i | \(-0.587058\pi\) | ||||
−0.270103 | + | 0.962832i | \(0.587058\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 16.5747 | 2.88528 | ||||||||
\(34\) | 0.977224 | 0.167592 | ||||||||
\(35\) | 3.90247 | 0.659637 | ||||||||
\(36\) | 6.29119 | 1.04853 | ||||||||
\(37\) | −0.824327 | −0.135518 | −0.0677592 | − | 0.997702i | \(-0.521585\pi\) | ||||
−0.0677592 | + | 0.997702i | \(0.521585\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.85294 | 1.09735 | ||||||||
\(40\) | 3.90247 | 0.617034 | ||||||||
\(41\) | −11.3245 | −1.76859 | −0.884295 | − | 0.466928i | \(-0.845361\pi\) | ||||
−0.884295 | + | 0.466928i | \(0.845361\pi\) | |||||||
\(42\) | −3.04815 | −0.470339 | ||||||||
\(43\) | −12.2093 | −1.86190 | −0.930952 | − | 0.365142i | \(-0.881020\pi\) | ||||
−0.930952 | + | 0.365142i | \(0.881020\pi\) | |||||||
\(44\) | −5.43763 | −0.819754 | ||||||||
\(45\) | 24.5512 | 3.65987 | ||||||||
\(46\) | 0.640603 | 0.0944517 | ||||||||
\(47\) | −12.6901 | −1.85104 | −0.925518 | − | 0.378704i | \(-0.876370\pi\) | ||||
−0.925518 | + | 0.378704i | \(0.876370\pi\) | |||||||
\(48\) | −3.04815 | −0.439962 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 10.2292 | 1.44663 | ||||||||
\(51\) | −2.97872 | −0.417104 | ||||||||
\(52\) | −2.24823 | −0.311774 | ||||||||
\(53\) | 2.05679 | 0.282521 | 0.141261 | − | 0.989972i | \(-0.454884\pi\) | ||||
0.141261 | + | 0.989972i | \(0.454884\pi\) | |||||||
\(54\) | −10.0320 | −1.36519 | ||||||||
\(55\) | −21.2202 | −2.86133 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.85823 | −0.900530 | ||||||||
\(59\) | 3.71241 | 0.483315 | 0.241658 | − | 0.970362i | \(-0.422309\pi\) | ||||
0.241658 | + | 0.970362i | \(0.422309\pi\) | |||||||
\(60\) | −11.8953 | −1.53567 | ||||||||
\(61\) | 3.56439 | 0.456374 | 0.228187 | − | 0.973617i | \(-0.426720\pi\) | ||||
0.228187 | + | 0.973617i | \(0.426720\pi\) | |||||||
\(62\) | −3.00774 | −0.381983 | ||||||||
\(63\) | 6.29119 | 0.792616 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.77365 | −1.08824 | ||||||||
\(66\) | 16.5747 | 2.04020 | ||||||||
\(67\) | −1.14843 | −0.140303 | −0.0701516 | − | 0.997536i | \(-0.522348\pi\) | ||||
−0.0701516 | + | 0.997536i | \(0.522348\pi\) | |||||||
\(68\) | 0.977224 | 0.118506 | ||||||||
\(69\) | −1.95265 | −0.235072 | ||||||||
\(70\) | 3.90247 | 0.466434 | ||||||||
\(71\) | 4.58975 | 0.544703 | 0.272352 | − | 0.962198i | \(-0.412199\pi\) | ||||
0.272352 | + | 0.962198i | \(0.412199\pi\) | |||||||
\(72\) | 6.29119 | 0.741424 | ||||||||
\(73\) | −6.31633 | −0.739271 | −0.369635 | − | 0.929177i | \(-0.620517\pi\) | ||||
−0.369635 | + | 0.929177i | \(0.620517\pi\) | |||||||
\(74\) | −0.824327 | −0.0958260 | ||||||||
\(75\) | −31.1802 | −3.60038 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.43763 | −0.619675 | ||||||||
\(78\) | 6.85294 | 0.775943 | ||||||||
\(79\) | −12.3096 | −1.38494 | −0.692471 | − | 0.721446i | \(-0.743478\pi\) | ||||
−0.692471 | + | 0.721446i | \(0.743478\pi\) | |||||||
\(80\) | 3.90247 | 0.436309 | ||||||||
\(81\) | 11.7055 | 1.30061 | ||||||||
\(82\) | −11.3245 | −1.25058 | ||||||||
\(83\) | −9.84224 | −1.08033 | −0.540163 | − | 0.841561i | \(-0.681637\pi\) | ||||
−0.540163 | + | 0.841561i | \(0.681637\pi\) | |||||||
\(84\) | −3.04815 | −0.332580 | ||||||||
\(85\) | 3.81358 | 0.413641 | ||||||||
\(86\) | −12.2093 | −1.31656 | ||||||||
\(87\) | 20.9049 | 2.24124 | ||||||||
\(88\) | −5.43763 | −0.579653 | ||||||||
\(89\) | 11.8845 | 1.25976 | 0.629879 | − | 0.776693i | \(-0.283104\pi\) | ||||
0.629879 | + | 0.776693i | \(0.283104\pi\) | |||||||
\(90\) | 24.5512 | 2.58792 | ||||||||
\(91\) | −2.24823 | −0.235679 | ||||||||
\(92\) | 0.640603 | 0.0667875 | ||||||||
\(93\) | 9.16802 | 0.950679 | ||||||||
\(94\) | −12.6901 | −1.30888 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.04815 | −0.311100 | ||||||||
\(97\) | 7.94295 | 0.806485 | 0.403242 | − | 0.915093i | \(-0.367883\pi\) | ||||
0.403242 | + | 0.915093i | \(0.367883\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −34.2092 | −3.43815 | ||||||||
\(100\) | 10.2292 | 1.02292 | ||||||||
\(101\) | 12.5382 | 1.24760 | 0.623799 | − | 0.781585i | \(-0.285588\pi\) | ||||
0.623799 | + | 0.781585i | \(0.285588\pi\) | |||||||
\(102\) | −2.97872 | −0.294937 | ||||||||
\(103\) | 13.4463 | 1.32490 | 0.662450 | − | 0.749106i | \(-0.269517\pi\) | ||||
0.662450 | + | 0.749106i | \(0.269517\pi\) | |||||||
\(104\) | −2.24823 | −0.220457 | ||||||||
\(105\) | −11.8953 | −1.16086 | ||||||||
\(106\) | 2.05679 | 0.199773 | ||||||||
\(107\) | 11.5515 | 1.11673 | 0.558363 | − | 0.829597i | \(-0.311430\pi\) | ||||
0.558363 | + | 0.829597i | \(0.311430\pi\) | |||||||
\(108\) | −10.0320 | −0.965333 | ||||||||
\(109\) | −18.8662 | −1.80706 | −0.903528 | − | 0.428528i | \(-0.859032\pi\) | ||||
−0.903528 | + | 0.428528i | \(0.859032\pi\) | |||||||
\(110\) | −21.2202 | −2.02326 | ||||||||
\(111\) | 2.51267 | 0.238492 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 2.61917 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.49993 | 0.233120 | ||||||||
\(116\) | −6.85823 | −0.636771 | ||||||||
\(117\) | −14.1441 | −1.30762 | ||||||||
\(118\) | 3.71241 | 0.341755 | ||||||||
\(119\) | 0.977224 | 0.0895819 | ||||||||
\(120\) | −11.8953 | −1.08589 | ||||||||
\(121\) | 18.5678 | 1.68798 | ||||||||
\(122\) | 3.56439 | 0.322705 | ||||||||
\(123\) | 34.5188 | 3.11245 | ||||||||
\(124\) | −3.00774 | −0.270103 | ||||||||
\(125\) | 20.4069 | 1.82525 | ||||||||
\(126\) | 6.29119 | 0.560464 | ||||||||
\(127\) | −2.91792 | −0.258924 | −0.129462 | − | 0.991584i | \(-0.541325\pi\) | ||||
−0.129462 | + | 0.991584i | \(0.541325\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 37.2158 | 3.27667 | ||||||||
\(130\) | −8.77365 | −0.769500 | ||||||||
\(131\) | 0.814699 | 0.0711805 | 0.0355903 | − | 0.999366i | \(-0.488669\pi\) | ||||
0.0355903 | + | 0.999366i | \(0.488669\pi\) | |||||||
\(132\) | 16.5747 | 1.44264 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.14843 | −0.0992094 | ||||||||
\(135\) | −39.1497 | −3.36947 | ||||||||
\(136\) | 0.977224 | 0.0837962 | ||||||||
\(137\) | −7.30748 | −0.624320 | −0.312160 | − | 0.950029i | \(-0.601053\pi\) | ||||
−0.312160 | + | 0.950029i | \(0.601053\pi\) | |||||||
\(138\) | −1.95265 | −0.166221 | ||||||||
\(139\) | 15.1627 | 1.28608 | 0.643040 | − | 0.765833i | \(-0.277673\pi\) | ||||
0.643040 | + | 0.765833i | \(0.277673\pi\) | |||||||
\(140\) | 3.90247 | 0.329819 | ||||||||
\(141\) | 38.6812 | 3.25754 | ||||||||
\(142\) | 4.58975 | 0.385164 | ||||||||
\(143\) | 12.2251 | 1.02231 | ||||||||
\(144\) | 6.29119 | 0.524266 | ||||||||
\(145\) | −26.7640 | −2.22263 | ||||||||
\(146\) | −6.31633 | −0.522743 | ||||||||
\(147\) | −3.04815 | −0.251407 | ||||||||
\(148\) | −0.824327 | −0.0677592 | ||||||||
\(149\) | −5.81139 | −0.476088 | −0.238044 | − | 0.971254i | \(-0.576506\pi\) | ||||
−0.238044 | + | 0.971254i | \(0.576506\pi\) | |||||||
\(150\) | −31.1802 | −2.54585 | ||||||||
\(151\) | 0.480998 | 0.0391430 | 0.0195715 | − | 0.999808i | \(-0.493770\pi\) | ||||
0.0195715 | + | 0.999808i | \(0.493770\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.14790 | 0.497028 | ||||||||
\(154\) | −5.43763 | −0.438177 | ||||||||
\(155\) | −11.7376 | −0.942786 | ||||||||
\(156\) | 6.85294 | 0.548675 | ||||||||
\(157\) | −5.53300 | −0.441581 | −0.220791 | − | 0.975321i | \(-0.570864\pi\) | ||||
−0.220791 | + | 0.975321i | \(0.570864\pi\) | |||||||
\(158\) | −12.3096 | −0.979302 | ||||||||
\(159\) | −6.26939 | −0.497195 | ||||||||
\(160\) | 3.90247 | 0.308517 | ||||||||
\(161\) | 0.640603 | 0.0504866 | ||||||||
\(162\) | 11.7055 | 0.919673 | ||||||||
\(163\) | −2.43842 | −0.190992 | −0.0954958 | − | 0.995430i | \(-0.530444\pi\) | ||||
−0.0954958 | + | 0.995430i | \(0.530444\pi\) | |||||||
\(164\) | −11.3245 | −0.884295 | ||||||||
\(165\) | 64.6822 | 5.03550 | ||||||||
\(166\) | −9.84224 | −0.763906 | ||||||||
\(167\) | −3.74745 | −0.289986 | −0.144993 | − | 0.989433i | \(-0.546316\pi\) | ||||
−0.144993 | + | 0.989433i | \(0.546316\pi\) | |||||||
\(168\) | −3.04815 | −0.235170 | ||||||||
\(169\) | −7.94545 | −0.611188 | ||||||||
\(170\) | 3.81358 | 0.292488 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.2093 | −0.930952 | ||||||||
\(173\) | −6.84994 | −0.520792 | −0.260396 | − | 0.965502i | \(-0.583853\pi\) | ||||
−0.260396 | + | 0.965502i | \(0.583853\pi\) | |||||||
\(174\) | 20.9049 | 1.58480 | ||||||||
\(175\) | 10.2292 | 0.773258 | ||||||||
\(176\) | −5.43763 | −0.409877 | ||||||||
\(177\) | −11.3160 | −0.850561 | ||||||||
\(178\) | 11.8845 | 0.890784 | ||||||||
\(179\) | −13.2215 | −0.988222 | −0.494111 | − | 0.869399i | \(-0.664506\pi\) | ||||
−0.494111 | + | 0.869399i | \(0.664506\pi\) | |||||||
\(180\) | 24.5512 | 1.82994 | ||||||||
\(181\) | −5.11234 | −0.379997 | −0.189998 | − | 0.981784i | \(-0.560848\pi\) | ||||
−0.189998 | + | 0.981784i | \(0.560848\pi\) | |||||||
\(182\) | −2.24823 | −0.166650 | ||||||||
\(183\) | −10.8648 | −0.803149 | ||||||||
\(184\) | 0.640603 | 0.0472259 | ||||||||
\(185\) | −3.21691 | −0.236512 | ||||||||
\(186\) | 9.16802 | 0.672232 | ||||||||
\(187\) | −5.31378 | −0.388582 | ||||||||
\(188\) | −12.6901 | −0.925518 | ||||||||
\(189\) | −10.0320 | −0.729723 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.4002 | 1.91025 | 0.955124 | − | 0.296206i | \(-0.0957216\pi\) | ||||
0.955124 | + | 0.296206i | \(0.0957216\pi\) | |||||||
\(192\) | −3.04815 | −0.219981 | ||||||||
\(193\) | −15.7941 | −1.13688 | −0.568442 | − | 0.822723i | \(-0.692454\pi\) | ||||
−0.568442 | + | 0.822723i | \(0.692454\pi\) | |||||||
\(194\) | 7.94295 | 0.570271 | ||||||||
\(195\) | 26.7434 | 1.91513 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −3.73311 | −0.265973 | −0.132987 | − | 0.991118i | \(-0.542457\pi\) | ||||
−0.132987 | + | 0.991118i | \(0.542457\pi\) | |||||||
\(198\) | −34.2092 | −2.43114 | ||||||||
\(199\) | −16.1988 | −1.14830 | −0.574151 | − | 0.818749i | \(-0.694668\pi\) | ||||
−0.574151 | + | 0.818749i | \(0.694668\pi\) | |||||||
\(200\) | 10.2292 | 0.723317 | ||||||||
\(201\) | 3.50059 | 0.246912 | ||||||||
\(202\) | 12.5382 | 0.882185 | ||||||||
\(203\) | −6.85823 | −0.481353 | ||||||||
\(204\) | −2.97872 | −0.208552 | ||||||||
\(205\) | −44.1935 | −3.08661 | ||||||||
\(206\) | 13.4463 | 0.936845 | ||||||||
\(207\) | 4.03016 | 0.280115 | ||||||||
\(208\) | −2.24823 | −0.155887 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −11.8953 | −0.820853 | ||||||||
\(211\) | −13.9798 | −0.962412 | −0.481206 | − | 0.876607i | \(-0.659801\pi\) | ||||
−0.481206 | + | 0.876607i | \(0.659801\pi\) | |||||||
\(212\) | 2.05679 | 0.141261 | ||||||||
\(213\) | −13.9902 | −0.958595 | ||||||||
\(214\) | 11.5515 | 0.789644 | ||||||||
\(215\) | −47.6464 | −3.24946 | ||||||||
\(216\) | −10.0320 | −0.682594 | ||||||||
\(217\) | −3.00774 | −0.204178 | ||||||||
\(218\) | −18.8662 | −1.27778 | ||||||||
\(219\) | 19.2531 | 1.30100 | ||||||||
\(220\) | −21.2202 | −1.43066 | ||||||||
\(221\) | −2.19703 | −0.147788 | ||||||||
\(222\) | 2.51267 | 0.168639 | ||||||||
\(223\) | 11.9087 | 0.797466 | 0.398733 | − | 0.917067i | \(-0.369450\pi\) | ||||
0.398733 | + | 0.917067i | \(0.369450\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 64.3541 | 4.29028 | ||||||||
\(226\) | 2.61917 | 0.174224 | ||||||||
\(227\) | 13.4459 | 0.892438 | 0.446219 | − | 0.894924i | \(-0.352770\pi\) | ||||
0.446219 | + | 0.894924i | \(0.352770\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.02164 | −0.331839 | −0.165920 | − | 0.986139i | \(-0.553059\pi\) | ||||
−0.165920 | + | 0.986139i | \(0.553059\pi\) | |||||||
\(230\) | 2.49993 | 0.164841 | ||||||||
\(231\) | 16.5747 | 1.09053 | ||||||||
\(232\) | −6.85823 | −0.450265 | ||||||||
\(233\) | 3.80785 | 0.249460 | 0.124730 | − | 0.992191i | \(-0.460193\pi\) | ||||
0.124730 | + | 0.992191i | \(0.460193\pi\) | |||||||
\(234\) | −14.1441 | −0.924627 | ||||||||
\(235\) | −49.5225 | −3.23049 | ||||||||
\(236\) | 3.71241 | 0.241658 | ||||||||
\(237\) | 37.5216 | 2.43729 | ||||||||
\(238\) | 0.977224 | 0.0633440 | ||||||||
\(239\) | −2.48796 | −0.160933 | −0.0804663 | − | 0.996757i | \(-0.525641\pi\) | ||||
−0.0804663 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(240\) | −11.8953 | −0.767837 | ||||||||
\(241\) | 5.53763 | 0.356710 | 0.178355 | − | 0.983966i | \(-0.442922\pi\) | ||||
0.178355 | + | 0.983966i | \(0.442922\pi\) | |||||||
\(242\) | 18.5678 | 1.19358 | ||||||||
\(243\) | −5.58406 | −0.358218 | ||||||||
\(244\) | 3.56439 | 0.228187 | ||||||||
\(245\) | 3.90247 | 0.249319 | ||||||||
\(246\) | 34.5188 | 2.20084 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.00774 | −0.190991 | ||||||||
\(249\) | 30.0006 | 1.90121 | ||||||||
\(250\) | 20.4069 | 1.29065 | ||||||||
\(251\) | −5.55332 | −0.350523 | −0.175261 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175261 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(252\) | 6.29119 | 0.396308 | ||||||||
\(253\) | −3.48336 | −0.218997 | ||||||||
\(254\) | −2.91792 | −0.183087 | ||||||||
\(255\) | −11.6244 | −0.727945 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.9978 | 1.37219 | 0.686093 | − | 0.727514i | \(-0.259324\pi\) | ||||
0.686093 | + | 0.727514i | \(0.259324\pi\) | |||||||
\(258\) | 37.2158 | 2.31695 | ||||||||
\(259\) | −0.824327 | −0.0512212 | ||||||||
\(260\) | −8.77365 | −0.544119 | ||||||||
\(261\) | −43.1464 | −2.67070 | ||||||||
\(262\) | 0.814699 | 0.0503322 | ||||||||
\(263\) | −22.9548 | −1.41546 | −0.707728 | − | 0.706485i | \(-0.750280\pi\) | ||||
−0.707728 | + | 0.706485i | \(0.750280\pi\) | |||||||
\(264\) | 16.5747 | 1.02010 | ||||||||
\(265\) | 8.02654 | 0.493066 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.2258 | −2.21698 | ||||||||
\(268\) | −1.14843 | −0.0701516 | ||||||||
\(269\) | −18.7189 | −1.14131 | −0.570656 | − | 0.821189i | \(-0.693311\pi\) | ||||
−0.570656 | + | 0.821189i | \(0.693311\pi\) | |||||||
\(270\) | −39.1497 | −2.38257 | ||||||||
\(271\) | 13.1366 | 0.797994 | 0.398997 | − | 0.916952i | \(-0.369358\pi\) | ||||
0.398997 | + | 0.916952i | \(0.369358\pi\) | |||||||
\(272\) | 0.977224 | 0.0592529 | ||||||||
\(273\) | 6.85294 | 0.414759 | ||||||||
\(274\) | −7.30748 | −0.441461 | ||||||||
\(275\) | −55.6228 | −3.35418 | ||||||||
\(276\) | −1.95265 | −0.117536 | ||||||||
\(277\) | 9.00748 | 0.541207 | 0.270604 | − | 0.962691i | \(-0.412777\pi\) | ||||
0.270604 | + | 0.962691i | \(0.412777\pi\) | |||||||
\(278\) | 15.1627 | 0.909396 | ||||||||
\(279\) | −18.9223 | −1.13285 | ||||||||
\(280\) | 3.90247 | 0.233217 | ||||||||
\(281\) | 13.8823 | 0.828149 | 0.414074 | − | 0.910243i | \(-0.364105\pi\) | ||||
0.414074 | + | 0.910243i | \(0.364105\pi\) | |||||||
\(282\) | 38.6812 | 2.30343 | ||||||||
\(283\) | 3.52545 | 0.209566 | 0.104783 | − | 0.994495i | \(-0.466585\pi\) | ||||
0.104783 | + | 0.994495i | \(0.466585\pi\) | |||||||
\(284\) | 4.58975 | 0.272352 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.2251 | 0.722883 | ||||||||
\(287\) | −11.3245 | −0.668465 | ||||||||
\(288\) | 6.29119 | 0.370712 | ||||||||
\(289\) | −16.0450 | −0.943826 | ||||||||
\(290\) | −26.7640 | −1.57164 | ||||||||
\(291\) | −24.2113 | −1.41929 | ||||||||
\(292\) | −6.31633 | −0.369635 | ||||||||
\(293\) | −30.6355 | −1.78975 | −0.894873 | − | 0.446321i | \(-0.852734\pi\) | ||||
−0.894873 | + | 0.446321i | \(0.852734\pi\) | |||||||
\(294\) | −3.04815 | −0.177771 | ||||||||
\(295\) | 14.4876 | 0.843499 | ||||||||
\(296\) | −0.824327 | −0.0479130 | ||||||||
\(297\) | 54.5505 | 3.16534 | ||||||||
\(298\) | −5.81139 | −0.336645 | ||||||||
\(299\) | −1.44022 | −0.0832903 | ||||||||
\(300\) | −31.1802 | −1.80019 | ||||||||
\(301\) | −12.2093 | −0.703733 | ||||||||
\(302\) | 0.480998 | 0.0276783 | ||||||||
\(303\) | −38.2183 | −2.19558 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.9099 | 0.796480 | ||||||||
\(306\) | 6.14790 | 0.351452 | ||||||||
\(307\) | 25.2223 | 1.43951 | 0.719756 | − | 0.694227i | \(-0.244254\pi\) | ||||
0.719756 | + | 0.694227i | \(0.244254\pi\) | |||||||
\(308\) | −5.43763 | −0.309838 | ||||||||
\(309\) | −40.9862 | −2.33162 | ||||||||
\(310\) | −11.7376 | −0.666650 | ||||||||
\(311\) | −5.26030 | −0.298285 | −0.149142 | − | 0.988816i | \(-0.547651\pi\) | ||||
−0.149142 | + | 0.988816i | \(0.547651\pi\) | |||||||
\(312\) | 6.85294 | 0.387971 | ||||||||
\(313\) | −3.76787 | −0.212972 | −0.106486 | − | 0.994314i | \(-0.533960\pi\) | ||||
−0.106486 | + | 0.994314i | \(0.533960\pi\) | |||||||
\(314\) | −5.53300 | −0.312245 | ||||||||
\(315\) | 24.5512 | 1.38330 | ||||||||
\(316\) | −12.3096 | −0.692471 | ||||||||
\(317\) | −16.6180 | −0.933359 | −0.466679 | − | 0.884427i | \(-0.654550\pi\) | ||||
−0.466679 | + | 0.884427i | \(0.654550\pi\) | |||||||
\(318\) | −6.26939 | −0.351570 | ||||||||
\(319\) | 37.2925 | 2.08798 | ||||||||
\(320\) | 3.90247 | 0.218154 | ||||||||
\(321\) | −35.2106 | −1.96527 | ||||||||
\(322\) | 0.640603 | 0.0356994 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 11.7055 | 0.650307 | ||||||||
\(325\) | −22.9977 | −1.27568 | ||||||||
\(326\) | −2.43842 | −0.135052 | ||||||||
\(327\) | 57.5070 | 3.18014 | ||||||||
\(328\) | −11.3245 | −0.625291 | ||||||||
\(329\) | −12.6901 | −0.699626 | ||||||||
\(330\) | 64.6822 | 3.56064 | ||||||||
\(331\) | −12.6506 | −0.695341 | −0.347671 | − | 0.937617i | \(-0.613027\pi\) | ||||
−0.347671 | + | 0.937617i | \(0.613027\pi\) | |||||||
\(332\) | −9.84224 | −0.540163 | ||||||||
\(333\) | −5.18600 | −0.284191 | ||||||||
\(334\) | −3.74745 | −0.205051 | ||||||||
\(335\) | −4.48172 | −0.244862 | ||||||||
\(336\) | −3.04815 | −0.166290 | ||||||||
\(337\) | 9.93403 | 0.541141 | 0.270570 | − | 0.962700i | \(-0.412788\pi\) | ||||
0.270570 | + | 0.962700i | \(0.412788\pi\) | |||||||
\(338\) | −7.94545 | −0.432175 | ||||||||
\(339\) | −7.98360 | −0.433610 | ||||||||
\(340\) | 3.81358 | 0.206821 | ||||||||
\(341\) | 16.3550 | 0.885671 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −12.2093 | −0.658282 | ||||||||
\(345\) | −7.62015 | −0.410255 | ||||||||
\(346\) | −6.84994 | −0.368255 | ||||||||
\(347\) | −13.2140 | −0.709366 | −0.354683 | − | 0.934987i | \(-0.615411\pi\) | ||||
−0.354683 | + | 0.934987i | \(0.615411\pi\) | |||||||
\(348\) | 20.9049 | 1.12062 | ||||||||
\(349\) | −2.44779 | −0.131027 | −0.0655137 | − | 0.997852i | \(-0.520869\pi\) | ||||
−0.0655137 | + | 0.997852i | \(0.520869\pi\) | |||||||
\(350\) | 10.2292 | 0.546776 | ||||||||
\(351\) | 22.5544 | 1.20386 | ||||||||
\(352\) | −5.43763 | −0.289827 | ||||||||
\(353\) | 35.5373 | 1.89146 | 0.945729 | − | 0.324957i | \(-0.105350\pi\) | ||||
0.945729 | + | 0.324957i | \(0.105350\pi\) | |||||||
\(354\) | −11.3160 | −0.601438 | ||||||||
\(355\) | 17.9114 | 0.950636 | ||||||||
\(356\) | 11.8845 | 0.629879 | ||||||||
\(357\) | −2.97872 | −0.157651 | ||||||||
\(358\) | −13.2215 | −0.698778 | ||||||||
\(359\) | −28.0462 | −1.48022 | −0.740112 | − | 0.672483i | \(-0.765228\pi\) | ||||
−0.740112 | + | 0.672483i | \(0.765228\pi\) | |||||||
\(360\) | 24.5512 | 1.29396 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −5.11234 | −0.268698 | ||||||||
\(363\) | −56.5974 | −2.97060 | ||||||||
\(364\) | −2.24823 | −0.117839 | ||||||||
\(365\) | −24.6493 | −1.29020 | ||||||||
\(366\) | −10.8648 | −0.567912 | ||||||||
\(367\) | 5.52498 | 0.288402 | 0.144201 | − | 0.989548i | \(-0.453939\pi\) | ||||
0.144201 | + | 0.989548i | \(0.453939\pi\) | |||||||
\(368\) | 0.640603 | 0.0333937 | ||||||||
\(369\) | −71.2447 | −3.70885 | ||||||||
\(370\) | −3.21691 | −0.167239 | ||||||||
\(371\) | 2.05679 | 0.106783 | ||||||||
\(372\) | 9.16802 | 0.475340 | ||||||||
\(373\) | 1.66659 | 0.0862927 | 0.0431464 | − | 0.999069i | \(-0.486262\pi\) | ||||
0.0431464 | + | 0.999069i | \(0.486262\pi\) | |||||||
\(374\) | −5.31378 | −0.274769 | ||||||||
\(375\) | −62.2033 | −3.21216 | ||||||||
\(376\) | −12.6901 | −0.654440 | ||||||||
\(377\) | 15.4189 | 0.794114 | ||||||||
\(378\) | −10.0320 | −0.515992 | ||||||||
\(379\) | −24.2234 | −1.24427 | −0.622137 | − | 0.782908i | \(-0.713735\pi\) | ||||
−0.622137 | + | 0.782908i | \(0.713735\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.89426 | 0.455667 | ||||||||
\(382\) | 26.4002 | 1.35075 | ||||||||
\(383\) | 5.06432 | 0.258774 | 0.129387 | − | 0.991594i | \(-0.458699\pi\) | ||||
0.129387 | + | 0.991594i | \(0.458699\pi\) | |||||||
\(384\) | −3.04815 | −0.155550 | ||||||||
\(385\) | −21.2202 | −1.08148 | ||||||||
\(386\) | −15.7941 | −0.803898 | ||||||||
\(387\) | −76.8112 | −3.90453 | ||||||||
\(388\) | 7.94295 | 0.403242 | ||||||||
\(389\) | −23.5536 | −1.19421 | −0.597107 | − | 0.802162i | \(-0.703683\pi\) | ||||
−0.597107 | + | 0.802162i | \(0.703683\pi\) | |||||||
\(390\) | 26.7434 | 1.35420 | ||||||||
\(391\) | 0.626012 | 0.0316588 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −2.48332 | −0.125267 | ||||||||
\(394\) | −3.73311 | −0.188072 | ||||||||
\(395\) | −48.0379 | −2.41705 | ||||||||
\(396\) | −34.2092 | −1.71908 | ||||||||
\(397\) | −16.9499 | −0.850691 | −0.425345 | − | 0.905031i | \(-0.639847\pi\) | ||||
−0.425345 | + | 0.905031i | \(0.639847\pi\) | |||||||
\(398\) | −16.1988 | −0.811972 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.2292 | 0.511462 | ||||||||
\(401\) | 22.6365 | 1.13041 | 0.565207 | − | 0.824949i | \(-0.308796\pi\) | ||||
0.565207 | + | 0.824949i | \(0.308796\pi\) | |||||||
\(402\) | 3.50059 | 0.174593 | ||||||||
\(403\) | 6.76209 | 0.336844 | ||||||||
\(404\) | 12.5382 | 0.623799 | ||||||||
\(405\) | 45.6804 | 2.26988 | ||||||||
\(406\) | −6.85823 | −0.340368 | ||||||||
\(407\) | 4.48238 | 0.222183 | ||||||||
\(408\) | −2.97872 | −0.147469 | ||||||||
\(409\) | 1.54005 | 0.0761503 | 0.0380752 | − | 0.999275i | \(-0.487877\pi\) | ||||
0.0380752 | + | 0.999275i | \(0.487877\pi\) | |||||||
\(410\) | −44.1935 | −2.18256 | ||||||||
\(411\) | 22.2743 | 1.09871 | ||||||||
\(412\) | 13.4463 | 0.662450 | ||||||||
\(413\) | 3.71241 | 0.182676 | ||||||||
\(414\) | 4.03016 | 0.198071 | ||||||||
\(415\) | −38.4090 | −1.88542 | ||||||||
\(416\) | −2.24823 | −0.110229 | ||||||||
\(417\) | −46.2180 | −2.26330 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.33850 | −0.114243 | −0.0571216 | − | 0.998367i | \(-0.518192\pi\) | ||||
−0.0571216 | + | 0.998367i | \(0.518192\pi\) | |||||||
\(420\) | −11.8953 | −0.580430 | ||||||||
\(421\) | 9.21012 | 0.448874 | 0.224437 | − | 0.974489i | \(-0.427946\pi\) | ||||
0.224437 | + | 0.974489i | \(0.427946\pi\) | |||||||
\(422\) | −13.9798 | −0.680528 | ||||||||
\(423\) | −79.8356 | −3.88174 | ||||||||
\(424\) | 2.05679 | 0.0998864 | ||||||||
\(425\) | 9.99625 | 0.484890 | ||||||||
\(426\) | −13.9902 | −0.677829 | ||||||||
\(427\) | 3.56439 | 0.172493 | ||||||||
\(428\) | 11.5515 | 0.558363 | ||||||||
\(429\) | −37.2638 | −1.79911 | ||||||||
\(430\) | −47.6464 | −2.29772 | ||||||||
\(431\) | −7.77763 | −0.374635 | −0.187318 | − | 0.982299i | \(-0.559979\pi\) | ||||
−0.187318 | + | 0.982299i | \(0.559979\pi\) | |||||||
\(432\) | −10.0320 | −0.482667 | ||||||||
\(433\) | 3.43962 | 0.165298 | 0.0826488 | − | 0.996579i | \(-0.473662\pi\) | ||||
0.0826488 | + | 0.996579i | \(0.473662\pi\) | |||||||
\(434\) | −3.00774 | −0.144376 | ||||||||
\(435\) | 81.5806 | 3.91149 | ||||||||
\(436\) | −18.8662 | −0.903528 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 19.2531 | 0.919949 | ||||||||
\(439\) | −27.4754 | −1.31133 | −0.655664 | − | 0.755053i | \(-0.727611\pi\) | ||||
−0.655664 | + | 0.755053i | \(0.727611\pi\) | |||||||
\(440\) | −21.2202 | −1.01163 | ||||||||
\(441\) | 6.29119 | 0.299581 | ||||||||
\(442\) | −2.19703 | −0.104502 | ||||||||
\(443\) | 29.7544 | 1.41367 | 0.706836 | − | 0.707377i | \(-0.250122\pi\) | ||||
0.706836 | + | 0.707377i | \(0.250122\pi\) | |||||||
\(444\) | 2.51267 | 0.119246 | ||||||||
\(445\) | 46.3790 | 2.19858 | ||||||||
\(446\) | 11.9087 | 0.563894 | ||||||||
\(447\) | 17.7140 | 0.837842 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 27.8042 | 1.31216 | 0.656081 | − | 0.754690i | \(-0.272213\pi\) | ||||
0.656081 | + | 0.754690i | \(0.272213\pi\) | |||||||
\(450\) | 64.3541 | 3.03368 | ||||||||
\(451\) | 61.5785 | 2.89962 | ||||||||
\(452\) | 2.61917 | 0.123195 | ||||||||
\(453\) | −1.46615 | −0.0688858 | ||||||||
\(454\) | 13.4459 | 0.631049 | ||||||||
\(455\) | −8.77365 | −0.411315 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.02276 | −0.328511 | −0.164255 | − | 0.986418i | \(-0.552522\pi\) | ||||
−0.164255 | + | 0.986418i | \(0.552522\pi\) | |||||||
\(458\) | −5.02164 | −0.234646 | ||||||||
\(459\) | −9.80354 | −0.457590 | ||||||||
\(460\) | 2.49993 | 0.116560 | ||||||||
\(461\) | −11.0511 | −0.514699 | −0.257350 | − | 0.966318i | \(-0.582849\pi\) | ||||
−0.257350 | + | 0.966318i | \(0.582849\pi\) | |||||||
\(462\) | 16.5747 | 0.771124 | ||||||||
\(463\) | −11.9667 | −0.556138 | −0.278069 | − | 0.960561i | \(-0.589694\pi\) | ||||
−0.278069 | + | 0.960561i | \(0.589694\pi\) | |||||||
\(464\) | −6.85823 | −0.318385 | ||||||||
\(465\) | 35.7779 | 1.65916 | ||||||||
\(466\) | 3.80785 | 0.176395 | ||||||||
\(467\) | −33.3755 | −1.54444 | −0.772218 | − | 0.635358i | \(-0.780853\pi\) | ||||
−0.772218 | + | 0.635358i | \(0.780853\pi\) | |||||||
\(468\) | −14.1441 | −0.653810 | ||||||||
\(469\) | −1.14843 | −0.0530297 | ||||||||
\(470\) | −49.5225 | −2.28430 | ||||||||
\(471\) | 16.8654 | 0.777116 | ||||||||
\(472\) | 3.71241 | 0.170878 | ||||||||
\(473\) | 66.3898 | 3.05260 | ||||||||
\(474\) | 37.5216 | 1.72342 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.977224 | 0.0447910 | ||||||||
\(477\) | 12.9396 | 0.592465 | ||||||||
\(478\) | −2.48796 | −0.113797 | ||||||||
\(479\) | 28.5407 | 1.30406 | 0.652029 | − | 0.758194i | \(-0.273918\pi\) | ||||
0.652029 | + | 0.758194i | \(0.273918\pi\) | |||||||
\(480\) | −11.8953 | −0.542943 | ||||||||
\(481\) | 1.85328 | 0.0845022 | ||||||||
\(482\) | 5.53763 | 0.252232 | ||||||||
\(483\) | −1.95265 | −0.0888487 | ||||||||
\(484\) | 18.5678 | 0.843992 | ||||||||
\(485\) | 30.9971 | 1.40751 | ||||||||
\(486\) | −5.58406 | −0.253298 | ||||||||
\(487\) | −27.5006 | −1.24617 | −0.623087 | − | 0.782153i | \(-0.714122\pi\) | ||||
−0.623087 | + | 0.782153i | \(0.714122\pi\) | |||||||
\(488\) | 3.56439 | 0.161353 | ||||||||
\(489\) | 7.43266 | 0.336116 | ||||||||
\(490\) | 3.90247 | 0.176295 | ||||||||
\(491\) | 16.7667 | 0.756671 | 0.378336 | − | 0.925669i | \(-0.376497\pi\) | ||||
0.378336 | + | 0.925669i | \(0.376497\pi\) | |||||||
\(492\) | 34.5188 | 1.55623 | ||||||||
\(493\) | −6.70202 | −0.301844 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −133.500 | −6.00039 | ||||||||
\(496\) | −3.00774 | −0.135051 | ||||||||
\(497\) | 4.58975 | 0.205879 | ||||||||
\(498\) | 30.0006 | 1.34436 | ||||||||
\(499\) | −39.8615 | −1.78444 | −0.892222 | − | 0.451597i | \(-0.850854\pi\) | ||||
−0.892222 | + | 0.451597i | \(0.850854\pi\) | |||||||
\(500\) | 20.4069 | 0.912626 | ||||||||
\(501\) | 11.4228 | 0.510331 | ||||||||
\(502\) | −5.55332 | −0.247857 | ||||||||
\(503\) | 16.5023 | 0.735800 | 0.367900 | − | 0.929865i | \(-0.380077\pi\) | ||||
0.367900 | + | 0.929865i | \(0.380077\pi\) | |||||||
\(504\) | 6.29119 | 0.280232 | ||||||||
\(505\) | 48.9299 | 2.17735 | ||||||||
\(506\) | −3.48336 | −0.154854 | ||||||||
\(507\) | 24.2189 | 1.07560 | ||||||||
\(508\) | −2.91792 | −0.129462 | ||||||||
\(509\) | 27.8470 | 1.23429 | 0.617147 | − | 0.786848i | \(-0.288288\pi\) | ||||
0.617147 | + | 0.786848i | \(0.288288\pi\) | |||||||
\(510\) | −11.6244 | −0.514735 | ||||||||
\(511\) | −6.31633 | −0.279418 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.9978 | 0.970282 | ||||||||
\(515\) | 52.4736 | 2.31226 | ||||||||
\(516\) | 37.2158 | 1.63833 | ||||||||
\(517\) | 69.0039 | 3.03479 | ||||||||
\(518\) | −0.824327 | −0.0362188 | ||||||||
\(519\) | 20.8796 | 0.916514 | ||||||||
\(520\) | −8.77365 | −0.384750 | ||||||||
\(521\) | 28.0944 | 1.23084 | 0.615418 | − | 0.788201i | \(-0.288987\pi\) | ||||
0.615418 | + | 0.788201i | \(0.288987\pi\) | |||||||
\(522\) | −43.1464 | −1.88847 | ||||||||
\(523\) | 14.6392 | 0.640129 | 0.320064 | − | 0.947396i | \(-0.396295\pi\) | ||||
0.320064 | + | 0.947396i | \(0.396295\pi\) | |||||||
\(524\) | 0.814699 | 0.0355903 | ||||||||
\(525\) | −31.1802 | −1.36082 | ||||||||
\(526\) | −22.9548 | −1.00088 | ||||||||
\(527\) | −2.93923 | −0.128035 | ||||||||
\(528\) | 16.5747 | 0.721321 | ||||||||
\(529\) | −22.5896 | −0.982158 | ||||||||
\(530\) | 8.02654 | 0.348651 | ||||||||
\(531\) | 23.3555 | 1.01354 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.4601 | 1.10280 | ||||||||
\(534\) | −36.2258 | −1.56764 | ||||||||
\(535\) | 45.0793 | 1.94895 | ||||||||
\(536\) | −1.14843 | −0.0496047 | ||||||||
\(537\) | 40.3011 | 1.73912 | ||||||||
\(538\) | −18.7189 | −0.807030 | ||||||||
\(539\) | −5.43763 | −0.234215 | ||||||||
\(540\) | −39.1497 | −1.68473 | ||||||||
\(541\) | −10.3054 | −0.443064 | −0.221532 | − | 0.975153i | \(-0.571106\pi\) | ||||
−0.221532 | + | 0.975153i | \(0.571106\pi\) | |||||||
\(542\) | 13.1366 | 0.564267 | ||||||||
\(543\) | 15.5831 | 0.668737 | ||||||||
\(544\) | 0.977224 | 0.0418981 | ||||||||
\(545\) | −73.6248 | −3.15374 | ||||||||
\(546\) | 6.85294 | 0.293279 | ||||||||
\(547\) | 24.8564 | 1.06278 | 0.531392 | − | 0.847126i | \(-0.321669\pi\) | ||||
0.531392 | + | 0.847126i | \(0.321669\pi\) | |||||||
\(548\) | −7.30748 | −0.312160 | ||||||||
\(549\) | 22.4243 | 0.957045 | ||||||||
\(550\) | −55.6228 | −2.37177 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.95265 | −0.0831103 | ||||||||
\(553\) | −12.3096 | −0.523459 | ||||||||
\(554\) | 9.00748 | 0.382691 | ||||||||
\(555\) | 9.80560 | 0.416225 | ||||||||
\(556\) | 15.1627 | 0.643040 | ||||||||
\(557\) | −36.8917 | −1.56315 | −0.781575 | − | 0.623812i | \(-0.785583\pi\) | ||||
−0.781575 | + | 0.623812i | \(0.785583\pi\) | |||||||
\(558\) | −18.9223 | −0.801043 | ||||||||
\(559\) | 27.4494 | 1.16099 | ||||||||
\(560\) | 3.90247 | 0.164909 | ||||||||
\(561\) | 16.1972 | 0.683845 | ||||||||
\(562\) | 13.8823 | 0.585589 | ||||||||
\(563\) | −7.28154 | −0.306880 | −0.153440 | − | 0.988158i | \(-0.549035\pi\) | ||||
−0.153440 | + | 0.988158i | \(0.549035\pi\) | |||||||
\(564\) | 38.6812 | 1.62877 | ||||||||
\(565\) | 10.2212 | 0.430009 | ||||||||
\(566\) | 3.52545 | 0.148186 | ||||||||
\(567\) | 11.7055 | 0.491586 | ||||||||
\(568\) | 4.58975 | 0.192582 | ||||||||
\(569\) | −11.4629 | −0.480551 | −0.240276 | − | 0.970705i | \(-0.577238\pi\) | ||||
−0.240276 | + | 0.970705i | \(0.577238\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.3517 | 0.851691 | 0.425846 | − | 0.904796i | \(-0.359977\pi\) | ||||
0.425846 | + | 0.904796i | \(0.359977\pi\) | |||||||
\(572\) | 12.2251 | 0.511156 | ||||||||
\(573\) | −80.4715 | −3.36175 | ||||||||
\(574\) | −11.3245 | −0.472676 | ||||||||
\(575\) | 6.55288 | 0.273274 | ||||||||
\(576\) | 6.29119 | 0.262133 | ||||||||
\(577\) | 37.2381 | 1.55024 | 0.775122 | − | 0.631811i | \(-0.217688\pi\) | ||||
0.775122 | + | 0.631811i | \(0.217688\pi\) | |||||||
\(578\) | −16.0450 | −0.667385 | ||||||||
\(579\) | 48.1427 | 2.00074 | ||||||||
\(580\) | −26.7640 | −1.11131 | ||||||||
\(581\) | −9.84224 | −0.408325 | ||||||||
\(582\) | −24.2113 | −1.00359 | ||||||||
\(583\) | −11.1840 | −0.463196 | ||||||||
\(584\) | −6.31633 | −0.261372 | ||||||||
\(585\) | −55.1968 | −2.28210 | ||||||||
\(586\) | −30.6355 | −1.26554 | ||||||||
\(587\) | 11.2034 | 0.462416 | 0.231208 | − | 0.972904i | \(-0.425732\pi\) | ||||
0.231208 | + | 0.972904i | \(0.425732\pi\) | |||||||
\(588\) | −3.04815 | −0.125703 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 14.4876 | 0.596444 | ||||||||
\(591\) | 11.3791 | 0.468073 | ||||||||
\(592\) | −0.824327 | −0.0338796 | ||||||||
\(593\) | −37.0804 | −1.52271 | −0.761354 | − | 0.648337i | \(-0.775465\pi\) | ||||
−0.761354 | + | 0.648337i | \(0.775465\pi\) | |||||||
\(594\) | 54.5505 | 2.23823 | ||||||||
\(595\) | 3.81358 | 0.156342 | ||||||||
\(596\) | −5.81139 | −0.238044 | ||||||||
\(597\) | 49.3763 | 2.02084 | ||||||||
\(598\) | −1.44022 | −0.0588952 | ||||||||
\(599\) | −31.7534 | −1.29741 | −0.648705 | − | 0.761040i | \(-0.724689\pi\) | ||||
−0.648705 | + | 0.761040i | \(0.724689\pi\) | |||||||
\(600\) | −31.1802 | −1.27293 | ||||||||
\(601\) | 19.7428 | 0.805324 | 0.402662 | − | 0.915349i | \(-0.368085\pi\) | ||||
0.402662 | + | 0.915349i | \(0.368085\pi\) | |||||||
\(602\) | −12.2093 | −0.497615 | ||||||||
\(603\) | −7.22501 | −0.294225 | ||||||||
\(604\) | 0.480998 | 0.0195715 | ||||||||
\(605\) | 72.4603 | 2.94593 | ||||||||
\(606\) | −38.2183 | −1.55251 | ||||||||
\(607\) | −21.2159 | −0.861128 | −0.430564 | − | 0.902560i | \(-0.641685\pi\) | ||||
−0.430564 | + | 0.902560i | \(0.641685\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.9049 | 0.847109 | ||||||||
\(610\) | 13.9099 | 0.563196 | ||||||||
\(611\) | 28.5302 | 1.15421 | ||||||||
\(612\) | 6.14790 | 0.248514 | ||||||||
\(613\) | 19.9161 | 0.804405 | 0.402203 | − | 0.915551i | \(-0.368245\pi\) | ||||
0.402203 | + | 0.915551i | \(0.368245\pi\) | |||||||
\(614\) | 25.2223 | 1.01789 | ||||||||
\(615\) | 134.708 | 5.43196 | ||||||||
\(616\) | −5.43763 | −0.219088 | ||||||||
\(617\) | 18.0683 | 0.727402 | 0.363701 | − | 0.931516i | \(-0.381513\pi\) | ||||
0.363701 | + | 0.931516i | \(0.381513\pi\) | |||||||
\(618\) | −40.9862 | −1.64871 | ||||||||
\(619\) | 31.5626 | 1.26861 | 0.634303 | − | 0.773084i | \(-0.281287\pi\) | ||||
0.634303 | + | 0.773084i | \(0.281287\pi\) | |||||||
\(620\) | −11.7376 | −0.471393 | ||||||||
\(621\) | −6.42655 | −0.257889 | ||||||||
\(622\) | −5.26030 | −0.210919 | ||||||||
\(623\) | 11.8845 | 0.476144 | ||||||||
\(624\) | 6.85294 | 0.274337 | ||||||||
\(625\) | 28.4912 | 1.13965 | ||||||||
\(626\) | −3.76787 | −0.150594 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.53300 | −0.220791 | ||||||||
\(629\) | −0.805551 | −0.0321194 | ||||||||
\(630\) | 24.5512 | 0.978142 | ||||||||
\(631\) | 25.1232 | 1.00014 | 0.500070 | − | 0.865985i | \(-0.333308\pi\) | ||||
0.500070 | + | 0.865985i | \(0.333308\pi\) | |||||||
\(632\) | −12.3096 | −0.489651 | ||||||||
\(633\) | 42.6126 | 1.69370 | ||||||||
\(634\) | −16.6180 | −0.659984 | ||||||||
\(635\) | −11.3871 | −0.451883 | ||||||||
\(636\) | −6.26939 | −0.248597 | ||||||||
\(637\) | −2.24823 | −0.0890782 | ||||||||
\(638\) | 37.2925 | 1.47642 | ||||||||
\(639\) | 28.8750 | 1.14228 | ||||||||
\(640\) | 3.90247 | 0.154259 | ||||||||
\(641\) | −3.23583 | −0.127808 | −0.0639039 | − | 0.997956i | \(-0.520355\pi\) | ||||
−0.0639039 | + | 0.997956i | \(0.520355\pi\) | |||||||
\(642\) | −35.2106 | −1.38965 | ||||||||
\(643\) | −19.3127 | −0.761619 | −0.380809 | − | 0.924654i | \(-0.624355\pi\) | ||||
−0.380809 | + | 0.924654i | \(0.624355\pi\) | |||||||
\(644\) | 0.640603 | 0.0252433 | ||||||||
\(645\) | 145.233 | 5.71856 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.5212 | −0.452943 | −0.226472 | − | 0.974018i | \(-0.572719\pi\) | ||||
−0.226472 | + | 0.974018i | \(0.572719\pi\) | |||||||
\(648\) | 11.7055 | 0.459837 | ||||||||
\(649\) | −20.1867 | −0.792399 | ||||||||
\(650\) | −22.9977 | −0.902045 | ||||||||
\(651\) | 9.16802 | 0.359323 | ||||||||
\(652\) | −2.43842 | −0.0954958 | ||||||||
\(653\) | −43.5279 | −1.70338 | −0.851689 | − | 0.524047i | \(-0.824421\pi\) | ||||
−0.851689 | + | 0.524047i | \(0.824421\pi\) | |||||||
\(654\) | 57.5070 | 2.24870 | ||||||||
\(655\) | 3.17933 | 0.124227 | ||||||||
\(656\) | −11.3245 | −0.442148 | ||||||||
\(657\) | −39.7373 | −1.55030 | ||||||||
\(658\) | −12.6901 | −0.494710 | ||||||||
\(659\) | 5.02462 | 0.195731 | 0.0978657 | − | 0.995200i | \(-0.468798\pi\) | ||||
0.0978657 | + | 0.995200i | \(0.468798\pi\) | |||||||
\(660\) | 64.6822 | 2.51775 | ||||||||
\(661\) | −16.0652 | −0.624864 | −0.312432 | − | 0.949940i | \(-0.601144\pi\) | ||||
−0.312432 | + | 0.949940i | \(0.601144\pi\) | |||||||
\(662\) | −12.6506 | −0.491680 | ||||||||
\(663\) | 6.69686 | 0.260084 | ||||||||
\(664\) | −9.84224 | −0.381953 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.18600 | −0.200953 | ||||||||
\(667\) | −4.39340 | −0.170113 | ||||||||
\(668\) | −3.74745 | −0.144993 | ||||||||
\(669\) | −36.2995 | −1.40342 | ||||||||
\(670\) | −4.48172 | −0.173144 | ||||||||
\(671\) | −19.3819 | −0.748228 | ||||||||
\(672\) | −3.04815 | −0.117585 | ||||||||
\(673\) | −1.32631 | −0.0511255 | −0.0255627 | − | 0.999673i | \(-0.508138\pi\) | ||||
−0.0255627 | + | 0.999673i | \(0.508138\pi\) | |||||||
\(674\) | 9.93403 | 0.382644 | ||||||||
\(675\) | −102.620 | −3.94985 | ||||||||
\(676\) | −7.94545 | −0.305594 | ||||||||
\(677\) | 17.6403 | 0.677971 | 0.338986 | − | 0.940792i | \(-0.389916\pi\) | ||||
0.338986 | + | 0.940792i | \(0.389916\pi\) | |||||||
\(678\) | −7.98360 | −0.306608 | ||||||||
\(679\) | 7.94295 | 0.304823 | ||||||||
\(680\) | 3.81358 | 0.146244 | ||||||||
\(681\) | −40.9852 | −1.57056 | ||||||||
\(682\) | 16.3550 | 0.626264 | ||||||||
\(683\) | −17.9010 | −0.684965 | −0.342482 | − | 0.939524i | \(-0.611268\pi\) | ||||
−0.342482 | + | 0.939524i | \(0.611268\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.5172 | −1.08959 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 15.3067 | 0.583986 | ||||||||
\(688\) | −12.2093 | −0.465476 | ||||||||
\(689\) | −4.62414 | −0.176166 | ||||||||
\(690\) | −7.62015 | −0.290094 | ||||||||
\(691\) | 10.4222 | 0.396480 | 0.198240 | − | 0.980153i | \(-0.436477\pi\) | ||||
0.198240 | + | 0.980153i | \(0.436477\pi\) | |||||||
\(692\) | −6.84994 | −0.260396 | ||||||||
\(693\) | −34.2092 | −1.29950 | ||||||||
\(694\) | −13.2140 | −0.501598 | ||||||||
\(695\) | 59.1718 | 2.24451 | ||||||||
\(696\) | 20.9049 | 0.792398 | ||||||||
\(697\) | −11.0666 | −0.419176 | ||||||||
\(698\) | −2.44779 | −0.0926503 | ||||||||
\(699\) | −11.6069 | −0.439012 | ||||||||
\(700\) | 10.2292 | 0.386629 | ||||||||
\(701\) | −45.9994 | −1.73737 | −0.868686 | − | 0.495362i | \(-0.835035\pi\) | ||||
−0.868686 | + | 0.495362i | \(0.835035\pi\) | |||||||
\(702\) | 22.5544 | 0.851259 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −5.43763 | −0.204938 | ||||||||
\(705\) | 150.952 | 5.68518 | ||||||||
\(706\) | 35.5373 | 1.33746 | ||||||||
\(707\) | 12.5382 | 0.471548 | ||||||||
\(708\) | −11.3160 | −0.425281 | ||||||||
\(709\) | 4.31058 | 0.161887 | 0.0809436 | − | 0.996719i | \(-0.474207\pi\) | ||||
0.0809436 | + | 0.996719i | \(0.474207\pi\) | |||||||
\(710\) | 17.9114 | 0.672201 | ||||||||
\(711\) | −77.4423 | −2.90431 | ||||||||
\(712\) | 11.8845 | 0.445392 | ||||||||
\(713\) | −1.92676 | −0.0721579 | ||||||||
\(714\) | −2.97872 | −0.111476 | ||||||||
\(715\) | 47.7079 | 1.78417 | ||||||||
\(716\) | −13.2215 | −0.494111 | ||||||||
\(717\) | 7.58366 | 0.283217 | ||||||||
\(718\) | −28.0462 | −1.04668 | ||||||||
\(719\) | 32.1996 | 1.20084 | 0.600421 | − | 0.799684i | \(-0.295000\pi\) | ||||
0.600421 | + | 0.799684i | \(0.295000\pi\) | |||||||
\(720\) | 24.5512 | 0.914968 | ||||||||
\(721\) | 13.4463 | 0.500765 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.8795 | −0.627755 | ||||||||
\(724\) | −5.11234 | −0.189998 | ||||||||
\(725\) | −70.1545 | −2.60547 | ||||||||
\(726\) | −56.5974 | −2.10053 | ||||||||
\(727\) | 15.3908 | 0.570814 | 0.285407 | − | 0.958406i | \(-0.407871\pi\) | ||||
0.285407 | + | 0.958406i | \(0.407871\pi\) | |||||||
\(728\) | −2.24823 | −0.0833251 | ||||||||
\(729\) | −18.0956 | −0.670206 | ||||||||
\(730\) | −24.6493 | −0.912310 | ||||||||
\(731\) | −11.9312 | −0.441293 | ||||||||
\(732\) | −10.8648 | −0.401574 | ||||||||
\(733\) | −1.87547 | −0.0692719 | −0.0346360 | − | 0.999400i | \(-0.511027\pi\) | ||||
−0.0346360 | + | 0.999400i | \(0.511027\pi\) | |||||||
\(734\) | 5.52498 | 0.203931 | ||||||||
\(735\) | −11.8953 | −0.438764 | ||||||||
\(736\) | 0.640603 | 0.0236129 | ||||||||
\(737\) | 6.24475 | 0.230028 | ||||||||
\(738\) | −71.2447 | −2.62255 | ||||||||
\(739\) | −23.4196 | −0.861502 | −0.430751 | − | 0.902471i | \(-0.641751\pi\) | ||||
−0.430751 | + | 0.902471i | \(0.641751\pi\) | |||||||
\(740\) | −3.21691 | −0.118256 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.05679 | 0.0755070 | ||||||||
\(743\) | 18.5235 | 0.679561 | 0.339780 | − | 0.940505i | \(-0.389647\pi\) | ||||
0.339780 | + | 0.940505i | \(0.389647\pi\) | |||||||
\(744\) | 9.16802 | 0.336116 | ||||||||
\(745\) | −22.6788 | −0.830886 | ||||||||
\(746\) | 1.66659 | 0.0610182 | ||||||||
\(747\) | −61.9194 | −2.26551 | ||||||||
\(748\) | −5.31378 | −0.194291 | ||||||||
\(749\) | 11.5515 | 0.422082 | ||||||||
\(750\) | −62.2033 | −2.27134 | ||||||||
\(751\) | 1.49895 | 0.0546974 | 0.0273487 | − | 0.999626i | \(-0.491294\pi\) | ||||
0.0273487 | + | 0.999626i | \(0.491294\pi\) | |||||||
\(752\) | −12.6901 | −0.462759 | ||||||||
\(753\) | 16.9273 | 0.616867 | ||||||||
\(754\) | 15.4189 | 0.561523 | ||||||||
\(755\) | 1.87708 | 0.0683138 | ||||||||
\(756\) | −10.0320 | −0.364862 | ||||||||
\(757\) | 28.5048 | 1.03603 | 0.518013 | − | 0.855373i | \(-0.326672\pi\) | ||||
0.518013 | + | 0.855373i | \(0.326672\pi\) | |||||||
\(758\) | −24.2234 | −0.879835 | ||||||||
\(759\) | 10.6178 | 0.385401 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.9783 | 1.37671 | 0.688356 | − | 0.725373i | \(-0.258333\pi\) | ||||
0.688356 | + | 0.725373i | \(0.258333\pi\) | |||||||
\(762\) | 8.89426 | 0.322205 | ||||||||
\(763\) | −18.8662 | −0.683003 | ||||||||
\(764\) | 26.4002 | 0.955124 | ||||||||
\(765\) | 23.9920 | 0.867432 | ||||||||
\(766\) | 5.06432 | 0.182981 | ||||||||
\(767\) | −8.34637 | −0.301370 | ||||||||
\(768\) | −3.04815 | −0.109990 | ||||||||
\(769\) | −32.6697 | −1.17810 | −0.589049 | − | 0.808097i | \(-0.700498\pi\) | ||||
−0.589049 | + | 0.808097i | \(0.700498\pi\) | |||||||
\(770\) | −21.2202 | −0.764722 | ||||||||
\(771\) | −67.0526 | −2.41484 | ||||||||
\(772\) | −15.7941 | −0.568442 | ||||||||
\(773\) | 19.9190 | 0.716436 | 0.358218 | − | 0.933638i | \(-0.383385\pi\) | ||||
0.358218 | + | 0.933638i | \(0.383385\pi\) | |||||||
\(774\) | −76.8112 | −2.76092 | ||||||||
\(775\) | −30.7669 | −1.10518 | ||||||||
\(776\) | 7.94295 | 0.285135 | ||||||||
\(777\) | 2.51267 | 0.0901414 | ||||||||
\(778\) | −23.5536 | −0.844437 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 26.7434 | 0.957566 | ||||||||
\(781\) | −24.9574 | −0.893045 | ||||||||
\(782\) | 0.626012 | 0.0223861 | ||||||||
\(783\) | 68.8020 | 2.45878 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −21.5923 | −0.770664 | ||||||||
\(786\) | −2.48332 | −0.0885771 | ||||||||
\(787\) | −6.83078 | −0.243491 | −0.121745 | − | 0.992561i | \(-0.538849\pi\) | ||||
−0.121745 | + | 0.992561i | \(0.538849\pi\) | |||||||
\(788\) | −3.73311 | −0.132987 | ||||||||
\(789\) | 69.9697 | 2.49099 | ||||||||
\(790\) | −48.0379 | −1.70911 | ||||||||
\(791\) | 2.61917 | 0.0931268 | ||||||||
\(792\) | −34.2092 | −1.21557 | ||||||||
\(793\) | −8.01359 | −0.284571 | ||||||||
\(794\) | −16.9499 | −0.601529 | ||||||||
\(795\) | −24.4661 | −0.867722 | ||||||||
\(796\) | −16.1988 | −0.574151 | ||||||||
\(797\) | −14.9421 | −0.529275 | −0.264638 | − | 0.964348i | \(-0.585252\pi\) | ||||
−0.264638 | + | 0.964348i | \(0.585252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.4010 | −0.438717 | ||||||||
\(800\) | 10.2292 | 0.361658 | ||||||||
\(801\) | 74.7679 | 2.64179 | ||||||||
\(802\) | 22.6365 | 0.799324 | ||||||||
\(803\) | 34.3459 | 1.21204 | ||||||||
\(804\) | 3.50059 | 0.123456 | ||||||||
\(805\) | 2.49993 | 0.0881110 | ||||||||
\(806\) | 6.76209 | 0.238185 | ||||||||
\(807\) | 57.0580 | 2.00854 | ||||||||
\(808\) | 12.5382 | 0.441092 | ||||||||
\(809\) | 14.6592 | 0.515390 | 0.257695 | − | 0.966226i | \(-0.417037\pi\) | ||||
0.257695 | + | 0.966226i | \(0.417037\pi\) | |||||||
\(810\) | 45.6804 | 1.60505 | ||||||||
\(811\) | −49.7049 | −1.74537 | −0.872687 | − | 0.488280i | \(-0.837625\pi\) | ||||
−0.872687 | + | 0.488280i | \(0.837625\pi\) | |||||||
\(812\) | −6.85823 | −0.240677 | ||||||||
\(813\) | −40.0424 | −1.40435 | ||||||||
\(814\) | 4.48238 | 0.157107 | ||||||||
\(815\) | −9.51585 | −0.333326 | ||||||||
\(816\) | −2.97872 | −0.104276 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.54005 | 0.0538464 | ||||||||
\(819\) | −14.1441 | −0.494234 | ||||||||
\(820\) | −44.1935 | −1.54330 | ||||||||
\(821\) | −26.7176 | −0.932449 | −0.466225 | − | 0.884666i | \(-0.654386\pi\) | ||||
−0.466225 | + | 0.884666i | \(0.654386\pi\) | |||||||
\(822\) | 22.2743 | 0.776905 | ||||||||
\(823\) | 3.16141 | 0.110200 | 0.0550999 | − | 0.998481i | \(-0.482452\pi\) | ||||
0.0550999 | + | 0.998481i | \(0.482452\pi\) | |||||||
\(824\) | 13.4463 | 0.468423 | ||||||||
\(825\) | 169.546 | 5.90285 | ||||||||
\(826\) | 3.71241 | 0.129171 | ||||||||
\(827\) | 24.2855 | 0.844488 | 0.422244 | − | 0.906482i | \(-0.361243\pi\) | ||||
0.422244 | + | 0.906482i | \(0.361243\pi\) | |||||||
\(828\) | 4.03016 | 0.140058 | ||||||||
\(829\) | −22.9819 | −0.798195 | −0.399098 | − | 0.916908i | \(-0.630677\pi\) | ||||
−0.399098 | + | 0.916908i | \(0.630677\pi\) | |||||||
\(830\) | −38.4090 | −1.33320 | ||||||||
\(831\) | −27.4561 | −0.952442 | ||||||||
\(832\) | −2.24823 | −0.0779435 | ||||||||
\(833\) | 0.977224 | 0.0338588 | ||||||||
\(834\) | −46.2180 | −1.60040 | ||||||||
\(835\) | −14.6243 | −0.506094 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.1737 | 1.04296 | ||||||||
\(838\) | −2.33850 | −0.0807821 | ||||||||
\(839\) | −7.80775 | −0.269553 | −0.134777 | − | 0.990876i | \(-0.543032\pi\) | ||||
−0.134777 | + | 0.990876i | \(0.543032\pi\) | |||||||
\(840\) | −11.8953 | −0.410426 | ||||||||
\(841\) | 18.0353 | 0.621907 | ||||||||
\(842\) | 9.21012 | 0.317402 | ||||||||
\(843\) | −42.3153 | −1.45742 | ||||||||
\(844\) | −13.9798 | −0.481206 | ||||||||
\(845\) | −31.0068 | −1.06667 | ||||||||
\(846\) | −79.8356 | −2.74481 | ||||||||
\(847\) | 18.5678 | 0.637998 | ||||||||
\(848\) | 2.05679 | 0.0706303 | ||||||||
\(849\) | −10.7461 | −0.368805 | ||||||||
\(850\) | 9.99625 | 0.342869 | ||||||||
\(851\) | −0.528066 | −0.0181019 | ||||||||
\(852\) | −13.9902 | −0.479298 | ||||||||
\(853\) | −0.148294 | −0.00507747 | −0.00253874 | − | 0.999997i | \(-0.500808\pi\) | ||||
−0.00253874 | + | 0.999997i | \(0.500808\pi\) | |||||||
\(854\) | 3.56439 | 0.121971 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.5515 | 0.394822 | ||||||||
\(857\) | 17.4431 | 0.595845 | 0.297923 | − | 0.954590i | \(-0.403706\pi\) | ||||
0.297923 | + | 0.954590i | \(0.403706\pi\) | |||||||
\(858\) | −37.2638 | −1.27216 | ||||||||
\(859\) | 44.9110 | 1.53234 | 0.766171 | − | 0.642636i | \(-0.222159\pi\) | ||||
0.766171 | + | 0.642636i | \(0.222159\pi\) | |||||||
\(860\) | −47.6464 | −1.62473 | ||||||||
\(861\) | 34.5188 | 1.17640 | ||||||||
\(862\) | −7.77763 | −0.264907 | ||||||||
\(863\) | 4.73021 | 0.161018 | 0.0805091 | − | 0.996754i | \(-0.474345\pi\) | ||||
0.0805091 | + | 0.996754i | \(0.474345\pi\) | |||||||
\(864\) | −10.0320 | −0.341297 | ||||||||
\(865\) | −26.7317 | −0.908904 | ||||||||
\(866\) | 3.43962 | 0.116883 | ||||||||
\(867\) | 48.9076 | 1.66099 | ||||||||
\(868\) | −3.00774 | −0.102089 | ||||||||
\(869\) | 66.9352 | 2.27062 | ||||||||
\(870\) | 81.5806 | 2.76584 | ||||||||
\(871\) | 2.58194 | 0.0874858 | ||||||||
\(872\) | −18.8662 | −0.638891 | ||||||||
\(873\) | 49.9707 | 1.69125 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.4069 | 0.689880 | ||||||||
\(876\) | 19.2531 | 0.650502 | ||||||||
\(877\) | 22.3767 | 0.755608 | 0.377804 | − | 0.925886i | \(-0.376679\pi\) | ||||
0.377804 | + | 0.925886i | \(0.376679\pi\) | |||||||
\(878\) | −27.4754 | −0.927249 | ||||||||
\(879\) | 93.3815 | 3.14968 | ||||||||
\(880\) | −21.2202 | −0.715332 | ||||||||
\(881\) | 17.3063 | 0.583064 | 0.291532 | − | 0.956561i | \(-0.405835\pi\) | ||||
0.291532 | + | 0.956561i | \(0.405835\pi\) | |||||||
\(882\) | 6.29119 | 0.211835 | ||||||||
\(883\) | 22.2407 | 0.748459 | 0.374230 | − | 0.927336i | \(-0.377907\pi\) | ||||
0.374230 | + | 0.927336i | \(0.377907\pi\) | |||||||
\(884\) | −2.19703 | −0.0738940 | ||||||||
\(885\) | −44.1602 | −1.48443 | ||||||||
\(886\) | 29.7544 | 0.999618 | ||||||||
\(887\) | −31.6781 | −1.06365 | −0.531823 | − | 0.846856i | \(-0.678493\pi\) | ||||
−0.531823 | + | 0.846856i | \(0.678493\pi\) | |||||||
\(888\) | 2.51267 | 0.0843196 | ||||||||
\(889\) | −2.91792 | −0.0978640 | ||||||||
\(890\) | 46.3790 | 1.55463 | ||||||||
\(891\) | −63.6504 | −2.13237 | ||||||||
\(892\) | 11.9087 | 0.398733 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 17.7140 | 0.592444 | ||||||||
\(895\) | −51.5965 | −1.72468 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 4.39001 | 0.146578 | ||||||||
\(898\) | 27.8042 | 0.927839 | ||||||||
\(899\) | 20.6277 | 0.687974 | ||||||||
\(900\) | 64.3541 | 2.14514 | ||||||||
\(901\) | 2.00994 | 0.0669608 | ||||||||
\(902\) | 61.5785 | 2.05034 | ||||||||
\(903\) | 37.2158 | 1.23846 | ||||||||
\(904\) | 2.61917 | 0.0871122 | ||||||||
\(905\) | −19.9507 | −0.663184 | ||||||||
\(906\) | −1.46615 | −0.0487096 | ||||||||
\(907\) | 35.7705 | 1.18774 | 0.593870 | − | 0.804561i | \(-0.297599\pi\) | ||||
0.593870 | + | 0.804561i | \(0.297599\pi\) | |||||||
\(908\) | 13.4459 | 0.446219 | ||||||||
\(909\) | 78.8803 | 2.61629 | ||||||||
\(910\) | −8.77365 | −0.290844 | ||||||||
\(911\) | −1.00147 | −0.0331803 | −0.0165902 | − | 0.999862i | \(-0.505281\pi\) | ||||
−0.0165902 | + | 0.999862i | \(0.505281\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 53.5184 | 1.77120 | ||||||||
\(914\) | −7.02276 | −0.232292 | ||||||||
\(915\) | −42.3995 | −1.40168 | ||||||||
\(916\) | −5.02164 | −0.165920 | ||||||||
\(917\) | 0.814699 | 0.0269037 | ||||||||
\(918\) | −9.80354 | −0.323565 | ||||||||
\(919\) | 27.1273 | 0.894847 | 0.447423 | − | 0.894322i | \(-0.352342\pi\) | ||||
0.447423 | + | 0.894322i | \(0.352342\pi\) | |||||||
\(920\) | 2.49993 | 0.0824203 | ||||||||
\(921\) | −76.8812 | −2.53332 | ||||||||
\(922\) | −11.0511 | −0.363947 | ||||||||
\(923\) | −10.3188 | −0.339649 | ||||||||
\(924\) | 16.5747 | 0.545267 | ||||||||
\(925\) | −8.43223 | −0.277250 | ||||||||
\(926\) | −11.9667 | −0.393249 | ||||||||
\(927\) | 84.5930 | 2.77840 | ||||||||
\(928\) | −6.85823 | −0.225132 | ||||||||
\(929\) | 2.19665 | 0.0720697 | 0.0360349 | − | 0.999351i | \(-0.488527\pi\) | ||||
0.0360349 | + | 0.999351i | \(0.488527\pi\) | |||||||
\(930\) | 35.7779 | 1.17320 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.80785 | 0.124730 | ||||||||
\(933\) | 16.0342 | 0.524935 | ||||||||
\(934\) | −33.3755 | −1.09208 | ||||||||
\(935\) | −20.7368 | −0.678167 | ||||||||
\(936\) | −14.1441 | −0.462313 | ||||||||
\(937\) | −16.3687 | −0.534742 | −0.267371 | − | 0.963594i | \(-0.586155\pi\) | ||||
−0.267371 | + | 0.963594i | \(0.586155\pi\) | |||||||
\(938\) | −1.14843 | −0.0374976 | ||||||||
\(939\) | 11.4850 | 0.374799 | ||||||||
\(940\) | −49.5225 | −1.61525 | ||||||||
\(941\) | −49.5617 | −1.61566 | −0.807832 | − | 0.589413i | \(-0.799359\pi\) | ||||
−0.807832 | + | 0.589413i | \(0.799359\pi\) | |||||||
\(942\) | 16.8654 | 0.549504 | ||||||||
\(943\) | −7.25451 | −0.236239 | ||||||||
\(944\) | 3.71241 | 0.120829 | ||||||||
\(945\) | −39.1497 | −1.27354 | ||||||||
\(946\) | 66.3898 | 2.15852 | ||||||||
\(947\) | 32.3241 | 1.05039 | 0.525196 | − | 0.850981i | \(-0.323992\pi\) | ||||
0.525196 | + | 0.850981i | \(0.323992\pi\) | |||||||
\(948\) | 37.5216 | 1.21864 | ||||||||
\(949\) | 14.2006 | 0.460971 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.6540 | 1.64257 | ||||||||
\(952\) | 0.977224 | 0.0316720 | ||||||||
\(953\) | 29.6712 | 0.961143 | 0.480572 | − | 0.876955i | \(-0.340429\pi\) | ||||
0.480572 | + | 0.876955i | \(0.340429\pi\) | |||||||
\(954\) | 12.9396 | 0.418936 | ||||||||
\(955\) | 103.026 | 3.33383 | ||||||||
\(956\) | −2.48796 | −0.0804663 | ||||||||
\(957\) | −113.673 | −3.67453 | ||||||||
\(958\) | 28.5407 | 0.922109 | ||||||||
\(959\) | −7.30748 | −0.235971 | ||||||||
\(960\) | −11.8953 | −0.383919 | ||||||||
\(961\) | −21.9535 | −0.708178 | ||||||||
\(962\) | 1.85328 | 0.0597521 | ||||||||
\(963\) | 72.6727 | 2.34184 | ||||||||
\(964\) | 5.53763 | 0.178355 | ||||||||
\(965\) | −61.6359 | −1.98413 | ||||||||
\(966\) | −1.95265 | −0.0628255 | ||||||||
\(967\) | 23.6909 | 0.761847 | 0.380923 | − | 0.924607i | \(-0.375606\pi\) | ||||
0.380923 | + | 0.924607i | \(0.375606\pi\) | |||||||
\(968\) | 18.5678 | 0.596792 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 30.9971 | 0.995257 | ||||||||
\(971\) | 29.8444 | 0.957753 | 0.478876 | − | 0.877882i | \(-0.341044\pi\) | ||||
0.478876 | + | 0.877882i | \(0.341044\pi\) | |||||||
\(972\) | −5.58406 | −0.179109 | ||||||||
\(973\) | 15.1627 | 0.486093 | ||||||||
\(974\) | −27.5006 | −0.881177 | ||||||||
\(975\) | 70.1004 | 2.24501 | ||||||||
\(976\) | 3.56439 | 0.114093 | ||||||||
\(977\) | 55.2708 | 1.76827 | 0.884135 | − | 0.467232i | \(-0.154749\pi\) | ||||
0.884135 | + | 0.467232i | \(0.154749\pi\) | |||||||
\(978\) | 7.43266 | 0.237670 | ||||||||
\(979\) | −64.6237 | −2.06538 | ||||||||
\(980\) | 3.90247 | 0.124660 | ||||||||
\(981\) | −118.691 | −3.78951 | ||||||||
\(982\) | 16.7667 | 0.535047 | ||||||||
\(983\) | 24.8474 | 0.792508 | 0.396254 | − | 0.918141i | \(-0.370310\pi\) | ||||
0.396254 | + | 0.918141i | \(0.370310\pi\) | |||||||
\(984\) | 34.5188 | 1.10042 | ||||||||
\(985\) | −14.5683 | −0.464186 | ||||||||
\(986\) | −6.70202 | −0.213436 | ||||||||
\(987\) | 38.6812 | 1.23123 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.82132 | −0.248704 | ||||||||
\(990\) | −133.500 | −4.24291 | ||||||||
\(991\) | 37.4253 | 1.18885 | 0.594427 | − | 0.804150i | \(-0.297379\pi\) | ||||
0.594427 | + | 0.804150i | \(0.297379\pi\) | |||||||
\(992\) | −3.00774 | −0.0954957 | ||||||||
\(993\) | 38.5609 | 1.22369 | ||||||||
\(994\) | 4.58975 | 0.145578 | ||||||||
\(995\) | −63.2152 | −2.00406 | ||||||||
\(996\) | 30.0006 | 0.950604 | ||||||||
\(997\) | 33.0295 | 1.04605 | 0.523027 | − | 0.852316i | \(-0.324803\pi\) | ||||
0.523027 | + | 0.852316i | \(0.324803\pi\) | |||||||
\(998\) | −39.8615 | −1.26179 | ||||||||
\(999\) | 8.26967 | 0.261641 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5054.2.a.bh.1.2 | yes | 8 | |
19.18 | odd | 2 | 5054.2.a.bg.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5054.2.a.bg.1.7 | ✓ | 8 | 19.18 | odd | 2 | ||
5054.2.a.bh.1.2 | yes | 8 | 1.1 | even | 1 | trivial |