Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58291 | −1.82640 | −0.913198 | − | 0.407516i | \(-0.866395\pi\) | ||||
−0.913198 | + | 0.407516i | \(0.866395\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.67145 | 2.33572 | ||||||||
\(5\) | 2.37262 | 1.06107 | 0.530535 | − | 0.847663i | \(-0.321991\pi\) | ||||
0.530535 | + | 0.847663i | \(0.321991\pi\) | |||||||
\(6\) | −2.58291 | −1.05447 | ||||||||
\(7\) | −1.51271 | −0.571750 | −0.285875 | − | 0.958267i | \(-0.592284\pi\) | ||||
−0.285875 | + | 0.958267i | \(0.592284\pi\) | |||||||
\(8\) | −6.90012 | −2.43956 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.12828 | −1.93793 | ||||||||
\(11\) | 0.0286762 | 0.00864620 | 0.00432310 | − | 0.999991i | \(-0.498624\pi\) | ||||
0.00432310 | + | 0.999991i | \(0.498624\pi\) | |||||||
\(12\) | 4.67145 | 1.34853 | ||||||||
\(13\) | −2.28200 | −0.632913 | −0.316457 | − | 0.948607i | \(-0.602493\pi\) | ||||
−0.316457 | + | 0.948607i | \(0.602493\pi\) | |||||||
\(14\) | 3.90720 | 1.04424 | ||||||||
\(15\) | 2.37262 | 0.612609 | ||||||||
\(16\) | 8.47952 | 2.11988 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.58291 | −0.608799 | ||||||||
\(19\) | 3.73826 | 0.857616 | 0.428808 | − | 0.903396i | \(-0.358934\pi\) | ||||
0.428808 | + | 0.903396i | \(0.358934\pi\) | |||||||
\(20\) | 11.0836 | 2.47837 | ||||||||
\(21\) | −1.51271 | −0.330100 | ||||||||
\(22\) | −0.0740682 | −0.0157914 | ||||||||
\(23\) | 0.0338407 | 0.00705627 | 0.00352814 | − | 0.999994i | \(-0.498877\pi\) | ||||
0.00352814 | + | 0.999994i | \(0.498877\pi\) | |||||||
\(24\) | −6.90012 | −1.40848 | ||||||||
\(25\) | 0.629343 | 0.125869 | ||||||||
\(26\) | 5.89421 | 1.15595 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −7.06654 | −1.33545 | ||||||||
\(29\) | −5.28971 | −0.982275 | −0.491138 | − | 0.871082i | \(-0.663419\pi\) | ||||
−0.491138 | + | 0.871082i | \(0.663419\pi\) | |||||||
\(30\) | −6.12828 | −1.11887 | ||||||||
\(31\) | 5.40462 | 0.970699 | 0.485350 | − | 0.874320i | \(-0.338692\pi\) | ||||
0.485350 | + | 0.874320i | \(0.338692\pi\) | |||||||
\(32\) | −8.10165 | −1.43218 | ||||||||
\(33\) | 0.0286762 | 0.00499189 | ||||||||
\(34\) | 2.58291 | 0.442966 | ||||||||
\(35\) | −3.58909 | −0.606667 | ||||||||
\(36\) | 4.67145 | 0.778575 | ||||||||
\(37\) | −4.32358 | −0.710791 | −0.355396 | − | 0.934716i | \(-0.615654\pi\) | ||||
−0.355396 | + | 0.934716i | \(0.615654\pi\) | |||||||
\(38\) | −9.65561 | −1.56635 | ||||||||
\(39\) | −2.28200 | −0.365413 | ||||||||
\(40\) | −16.3714 | −2.58854 | ||||||||
\(41\) | 9.63055 | 1.50404 | 0.752020 | − | 0.659140i | \(-0.229080\pi\) | ||||
0.752020 | + | 0.659140i | \(0.229080\pi\) | |||||||
\(42\) | 3.90720 | 0.602894 | ||||||||
\(43\) | −6.66478 | −1.01637 | −0.508184 | − | 0.861248i | \(-0.669683\pi\) | ||||
−0.508184 | + | 0.861248i | \(0.669683\pi\) | |||||||
\(44\) | 0.133959 | 0.0201951 | ||||||||
\(45\) | 2.37262 | 0.353690 | ||||||||
\(46\) | −0.0874076 | −0.0128876 | ||||||||
\(47\) | −7.80572 | −1.13858 | −0.569291 | − | 0.822136i | \(-0.692782\pi\) | ||||
−0.569291 | + | 0.822136i | \(0.692782\pi\) | |||||||
\(48\) | 8.47952 | 1.22391 | ||||||||
\(49\) | −4.71171 | −0.673102 | ||||||||
\(50\) | −1.62554 | −0.229886 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −10.6602 | −1.47831 | ||||||||
\(53\) | −4.66126 | −0.640273 | −0.320137 | − | 0.947371i | \(-0.603729\pi\) | ||||
−0.320137 | + | 0.947371i | \(0.603729\pi\) | |||||||
\(54\) | −2.58291 | −0.351490 | ||||||||
\(55\) | 0.0680378 | 0.00917422 | ||||||||
\(56\) | 10.4379 | 1.39482 | ||||||||
\(57\) | 3.73826 | 0.495145 | ||||||||
\(58\) | 13.6629 | 1.79402 | ||||||||
\(59\) | −6.95607 | −0.905603 | −0.452802 | − | 0.891611i | \(-0.649575\pi\) | ||||
−0.452802 | + | 0.891611i | \(0.649575\pi\) | |||||||
\(60\) | 11.0836 | 1.43088 | ||||||||
\(61\) | 12.0288 | 1.54013 | 0.770066 | − | 0.637964i | \(-0.220223\pi\) | ||||
0.770066 | + | 0.637964i | \(0.220223\pi\) | |||||||
\(62\) | −13.9597 | −1.77288 | ||||||||
\(63\) | −1.51271 | −0.190583 | ||||||||
\(64\) | 3.96681 | 0.495851 | ||||||||
\(65\) | −5.41433 | −0.671565 | ||||||||
\(66\) | −0.0740682 | −0.00911716 | ||||||||
\(67\) | −10.8834 | −1.32962 | −0.664811 | − | 0.747012i | \(-0.731488\pi\) | ||||
−0.664811 | + | 0.747012i | \(0.731488\pi\) | |||||||
\(68\) | −4.67145 | −0.566496 | ||||||||
\(69\) | 0.0338407 | 0.00407394 | ||||||||
\(70\) | 9.27031 | 1.10801 | ||||||||
\(71\) | −14.3426 | −1.70215 | −0.851076 | − | 0.525043i | \(-0.824049\pi\) | ||||
−0.851076 | + | 0.525043i | \(0.824049\pi\) | |||||||
\(72\) | −6.90012 | −0.813187 | ||||||||
\(73\) | 6.50034 | 0.760807 | 0.380404 | − | 0.924821i | \(-0.375785\pi\) | ||||
0.380404 | + | 0.924821i | \(0.375785\pi\) | |||||||
\(74\) | 11.1674 | 1.29819 | ||||||||
\(75\) | 0.629343 | 0.0726702 | ||||||||
\(76\) | 17.4631 | 2.00315 | ||||||||
\(77\) | −0.0433788 | −0.00494347 | ||||||||
\(78\) | 5.89421 | 0.667388 | ||||||||
\(79\) | 7.88568 | 0.887209 | 0.443604 | − | 0.896223i | \(-0.353700\pi\) | ||||
0.443604 | + | 0.896223i | \(0.353700\pi\) | |||||||
\(80\) | 20.1187 | 2.24934 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −24.8749 | −2.74697 | ||||||||
\(83\) | −6.05338 | −0.664445 | −0.332222 | − | 0.943201i | \(-0.607798\pi\) | ||||
−0.332222 | + | 0.943201i | \(0.607798\pi\) | |||||||
\(84\) | −7.06654 | −0.771023 | ||||||||
\(85\) | −2.37262 | −0.257347 | ||||||||
\(86\) | 17.2145 | 1.85629 | ||||||||
\(87\) | −5.28971 | −0.567117 | ||||||||
\(88\) | −0.197869 | −0.0210929 | ||||||||
\(89\) | 14.4772 | 1.53458 | 0.767291 | − | 0.641299i | \(-0.221604\pi\) | ||||
0.767291 | + | 0.641299i | \(0.221604\pi\) | |||||||
\(90\) | −6.12828 | −0.645978 | ||||||||
\(91\) | 3.45200 | 0.361868 | ||||||||
\(92\) | 0.158085 | 0.0164815 | ||||||||
\(93\) | 5.40462 | 0.560433 | ||||||||
\(94\) | 20.1615 | 2.07950 | ||||||||
\(95\) | 8.86949 | 0.909990 | ||||||||
\(96\) | −8.10165 | −0.826871 | ||||||||
\(97\) | −17.9042 | −1.81790 | −0.908951 | − | 0.416904i | \(-0.863115\pi\) | ||||
−0.908951 | + | 0.416904i | \(0.863115\pi\) | |||||||
\(98\) | 12.1699 | 1.22935 | ||||||||
\(99\) | 0.0286762 | 0.00288207 | ||||||||
\(100\) | 2.93994 | 0.293994 | ||||||||
\(101\) | 3.95845 | 0.393881 | 0.196940 | − | 0.980415i | \(-0.436899\pi\) | ||||
0.196940 | + | 0.980415i | \(0.436899\pi\) | |||||||
\(102\) | 2.58291 | 0.255747 | ||||||||
\(103\) | 7.76336 | 0.764947 | 0.382473 | − | 0.923967i | \(-0.375072\pi\) | ||||
0.382473 | + | 0.923967i | \(0.375072\pi\) | |||||||
\(104\) | 15.7461 | 1.54403 | ||||||||
\(105\) | −3.58909 | −0.350259 | ||||||||
\(106\) | 12.0396 | 1.16939 | ||||||||
\(107\) | 1.85870 | 0.179687 | 0.0898436 | − | 0.995956i | \(-0.471363\pi\) | ||||
0.0898436 | + | 0.995956i | \(0.471363\pi\) | |||||||
\(108\) | 4.67145 | 0.449510 | ||||||||
\(109\) | 9.08366 | 0.870057 | 0.435028 | − | 0.900417i | \(-0.356738\pi\) | ||||
0.435028 | + | 0.900417i | \(0.356738\pi\) | |||||||
\(110\) | −0.175736 | −0.0167558 | ||||||||
\(111\) | −4.32358 | −0.410376 | ||||||||
\(112\) | −12.8271 | −1.21204 | ||||||||
\(113\) | −14.5043 | −1.36445 | −0.682224 | − | 0.731143i | \(-0.738987\pi\) | ||||
−0.682224 | + | 0.731143i | \(0.738987\pi\) | |||||||
\(114\) | −9.65561 | −0.904331 | ||||||||
\(115\) | 0.0802912 | 0.00748720 | ||||||||
\(116\) | −24.7106 | −2.29432 | ||||||||
\(117\) | −2.28200 | −0.210971 | ||||||||
\(118\) | 17.9669 | 1.65399 | ||||||||
\(119\) | 1.51271 | 0.138670 | ||||||||
\(120\) | −16.3714 | −1.49450 | ||||||||
\(121\) | −10.9992 | −0.999925 | ||||||||
\(122\) | −31.0694 | −2.81289 | ||||||||
\(123\) | 9.63055 | 0.868358 | ||||||||
\(124\) | 25.2474 | 2.26728 | ||||||||
\(125\) | −10.3699 | −0.927514 | ||||||||
\(126\) | 3.90720 | 0.348081 | ||||||||
\(127\) | 8.52240 | 0.756241 | 0.378120 | − | 0.925756i | \(-0.376571\pi\) | ||||
0.378120 | + | 0.925756i | \(0.376571\pi\) | |||||||
\(128\) | 5.95736 | 0.526561 | ||||||||
\(129\) | −6.66478 | −0.586801 | ||||||||
\(130\) | 13.9848 | 1.22654 | ||||||||
\(131\) | 3.65276 | 0.319143 | 0.159572 | − | 0.987186i | \(-0.448989\pi\) | ||||
0.159572 | + | 0.987186i | \(0.448989\pi\) | |||||||
\(132\) | 0.133959 | 0.0116597 | ||||||||
\(133\) | −5.65490 | −0.490342 | ||||||||
\(134\) | 28.1110 | 2.42842 | ||||||||
\(135\) | 2.37262 | 0.204203 | ||||||||
\(136\) | 6.90012 | 0.591680 | ||||||||
\(137\) | 4.43424 | 0.378842 | 0.189421 | − | 0.981896i | \(-0.439339\pi\) | ||||
0.189421 | + | 0.981896i | \(0.439339\pi\) | |||||||
\(138\) | −0.0874076 | −0.00744063 | ||||||||
\(139\) | 15.4863 | 1.31353 | 0.656766 | − | 0.754094i | \(-0.271924\pi\) | ||||
0.656766 | + | 0.754094i | \(0.271924\pi\) | |||||||
\(140\) | −16.7662 | −1.41701 | ||||||||
\(141\) | −7.80572 | −0.657360 | ||||||||
\(142\) | 37.0457 | 3.10880 | ||||||||
\(143\) | −0.0654391 | −0.00547230 | ||||||||
\(144\) | 8.47952 | 0.706627 | ||||||||
\(145\) | −12.5505 | −1.04226 | ||||||||
\(146\) | −16.7898 | −1.38954 | ||||||||
\(147\) | −4.71171 | −0.388615 | ||||||||
\(148\) | −20.1974 | −1.66021 | ||||||||
\(149\) | −24.1740 | −1.98041 | −0.990207 | − | 0.139605i | \(-0.955417\pi\) | ||||
−0.990207 | + | 0.139605i | \(0.955417\pi\) | |||||||
\(150\) | −1.62554 | −0.132725 | ||||||||
\(151\) | −8.74504 | −0.711662 | −0.355831 | − | 0.934550i | \(-0.615802\pi\) | ||||
−0.355831 | + | 0.934550i | \(0.615802\pi\) | |||||||
\(152\) | −25.7944 | −2.09221 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0.112044 | 0.00902873 | ||||||||
\(155\) | 12.8231 | 1.02998 | ||||||||
\(156\) | −10.6602 | −0.853503 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | −20.3680 | −1.62039 | ||||||||
\(159\) | −4.66126 | −0.369662 | ||||||||
\(160\) | −19.2222 | −1.51964 | ||||||||
\(161\) | −0.0511911 | −0.00403443 | ||||||||
\(162\) | −2.58291 | −0.202933 | ||||||||
\(163\) | 8.83357 | 0.691898 | 0.345949 | − | 0.938253i | \(-0.387557\pi\) | ||||
0.345949 | + | 0.938253i | \(0.387557\pi\) | |||||||
\(164\) | 44.9886 | 3.51302 | ||||||||
\(165\) | 0.0680378 | 0.00529674 | ||||||||
\(166\) | 15.6354 | 1.21354 | ||||||||
\(167\) | 0.442060 | 0.0342077 | 0.0171038 | − | 0.999854i | \(-0.494555\pi\) | ||||
0.0171038 | + | 0.999854i | \(0.494555\pi\) | |||||||
\(168\) | 10.4379 | 0.805299 | ||||||||
\(169\) | −7.79247 | −0.599421 | ||||||||
\(170\) | 6.12828 | 0.470018 | ||||||||
\(171\) | 3.73826 | 0.285872 | ||||||||
\(172\) | −31.1341 | −2.37396 | ||||||||
\(173\) | −20.4052 | −1.55138 | −0.775688 | − | 0.631117i | \(-0.782597\pi\) | ||||
−0.775688 | + | 0.631117i | \(0.782597\pi\) | |||||||
\(174\) | 13.6629 | 1.03578 | ||||||||
\(175\) | −0.952012 | −0.0719654 | ||||||||
\(176\) | 0.243161 | 0.0183289 | ||||||||
\(177\) | −6.95607 | −0.522850 | ||||||||
\(178\) | −37.3934 | −2.80275 | ||||||||
\(179\) | −7.46180 | −0.557721 | −0.278860 | − | 0.960332i | \(-0.589957\pi\) | ||||
−0.278860 | + | 0.960332i | \(0.589957\pi\) | |||||||
\(180\) | 11.0836 | 0.826122 | ||||||||
\(181\) | 12.9590 | 0.963237 | 0.481619 | − | 0.876381i | \(-0.340049\pi\) | ||||
0.481619 | + | 0.876381i | \(0.340049\pi\) | |||||||
\(182\) | −8.91623 | −0.660915 | ||||||||
\(183\) | 12.0288 | 0.889196 | ||||||||
\(184\) | −0.233505 | −0.0172142 | ||||||||
\(185\) | −10.2582 | −0.754199 | ||||||||
\(186\) | −13.9597 | −1.02357 | ||||||||
\(187\) | −0.0286762 | −0.00209701 | ||||||||
\(188\) | −36.4640 | −2.65941 | ||||||||
\(189\) | −1.51271 | −0.110033 | ||||||||
\(190\) | −22.9091 | −1.66200 | ||||||||
\(191\) | 11.3965 | 0.824624 | 0.412312 | − | 0.911043i | \(-0.364721\pi\) | ||||
0.412312 | + | 0.911043i | \(0.364721\pi\) | |||||||
\(192\) | 3.96681 | 0.286280 | ||||||||
\(193\) | 20.0172 | 1.44087 | 0.720435 | − | 0.693523i | \(-0.243942\pi\) | ||||
0.720435 | + | 0.693523i | \(0.243942\pi\) | |||||||
\(194\) | 46.2451 | 3.32021 | ||||||||
\(195\) | −5.41433 | −0.387728 | ||||||||
\(196\) | −22.0105 | −1.57218 | ||||||||
\(197\) | −22.2550 | −1.58560 | −0.792801 | − | 0.609480i | \(-0.791378\pi\) | ||||
−0.792801 | + | 0.609480i | \(0.791378\pi\) | |||||||
\(198\) | −0.0740682 | −0.00526380 | ||||||||
\(199\) | 0.846276 | 0.0599909 | 0.0299955 | − | 0.999550i | \(-0.490451\pi\) | ||||
0.0299955 | + | 0.999550i | \(0.490451\pi\) | |||||||
\(200\) | −4.34254 | −0.307064 | ||||||||
\(201\) | −10.8834 | −0.767658 | ||||||||
\(202\) | −10.2243 | −0.719382 | ||||||||
\(203\) | 8.00180 | 0.561616 | ||||||||
\(204\) | −4.67145 | −0.327067 | ||||||||
\(205\) | 22.8497 | 1.59589 | ||||||||
\(206\) | −20.0521 | −1.39710 | ||||||||
\(207\) | 0.0338407 | 0.00235209 | ||||||||
\(208\) | −19.3503 | −1.34170 | ||||||||
\(209\) | 0.107199 | 0.00741512 | ||||||||
\(210\) | 9.27031 | 0.639712 | ||||||||
\(211\) | −25.3900 | −1.74792 | −0.873961 | − | 0.485996i | \(-0.838457\pi\) | ||||
−0.873961 | + | 0.485996i | \(0.838457\pi\) | |||||||
\(212\) | −21.7748 | −1.49550 | ||||||||
\(213\) | −14.3426 | −0.982738 | ||||||||
\(214\) | −4.80086 | −0.328180 | ||||||||
\(215\) | −15.8130 | −1.07844 | ||||||||
\(216\) | −6.90012 | −0.469494 | ||||||||
\(217\) | −8.17562 | −0.554998 | ||||||||
\(218\) | −23.4623 | −1.58907 | ||||||||
\(219\) | 6.50034 | 0.439252 | ||||||||
\(220\) | 0.317835 | 0.0214284 | ||||||||
\(221\) | 2.28200 | 0.153504 | ||||||||
\(222\) | 11.1674 | 0.749508 | ||||||||
\(223\) | 2.62729 | 0.175936 | 0.0879682 | − | 0.996123i | \(-0.471963\pi\) | ||||
0.0879682 | + | 0.996123i | \(0.471963\pi\) | |||||||
\(224\) | 12.2554 | 0.818850 | ||||||||
\(225\) | 0.629343 | 0.0419562 | ||||||||
\(226\) | 37.4633 | 2.49202 | ||||||||
\(227\) | 14.8856 | 0.987990 | 0.493995 | − | 0.869465i | \(-0.335536\pi\) | ||||
0.493995 | + | 0.869465i | \(0.335536\pi\) | |||||||
\(228\) | 17.4631 | 1.15652 | ||||||||
\(229\) | −13.0204 | −0.860413 | −0.430206 | − | 0.902731i | \(-0.641559\pi\) | ||||
−0.430206 | + | 0.902731i | \(0.641559\pi\) | |||||||
\(230\) | −0.207385 | −0.0136746 | ||||||||
\(231\) | −0.0433788 | −0.00285411 | ||||||||
\(232\) | 36.4997 | 2.39632 | ||||||||
\(233\) | −21.9985 | −1.44117 | −0.720583 | − | 0.693368i | \(-0.756126\pi\) | ||||
−0.720583 | + | 0.693368i | \(0.756126\pi\) | |||||||
\(234\) | 5.89421 | 0.385317 | ||||||||
\(235\) | −18.5200 | −1.20811 | ||||||||
\(236\) | −32.4949 | −2.11524 | ||||||||
\(237\) | 7.88568 | 0.512230 | ||||||||
\(238\) | −3.90720 | −0.253266 | ||||||||
\(239\) | −11.3861 | −0.736505 | −0.368253 | − | 0.929726i | \(-0.620044\pi\) | ||||
−0.368253 | + | 0.929726i | \(0.620044\pi\) | |||||||
\(240\) | 20.1187 | 1.29866 | ||||||||
\(241\) | 4.02368 | 0.259188 | 0.129594 | − | 0.991567i | \(-0.458633\pi\) | ||||
0.129594 | + | 0.991567i | \(0.458633\pi\) | |||||||
\(242\) | 28.4099 | 1.82626 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 56.1920 | 3.59732 | ||||||||
\(245\) | −11.1791 | −0.714208 | ||||||||
\(246\) | −24.8749 | −1.58597 | ||||||||
\(247\) | −8.53072 | −0.542797 | ||||||||
\(248\) | −37.2926 | −2.36808 | ||||||||
\(249\) | −6.05338 | −0.383617 | ||||||||
\(250\) | 26.7846 | 1.69401 | ||||||||
\(251\) | −19.8345 | −1.25194 | −0.625971 | − | 0.779847i | \(-0.715297\pi\) | ||||
−0.625971 | + | 0.779847i | \(0.715297\pi\) | |||||||
\(252\) | −7.06654 | −0.445150 | ||||||||
\(253\) | 0.000970423 0 | 6.10100e−5 0 | ||||||||
\(254\) | −22.0126 | −1.38120 | ||||||||
\(255\) | −2.37262 | −0.148579 | ||||||||
\(256\) | −23.3210 | −1.45756 | ||||||||
\(257\) | −22.4275 | −1.39899 | −0.699495 | − | 0.714637i | \(-0.746592\pi\) | ||||
−0.699495 | + | 0.714637i | \(0.746592\pi\) | |||||||
\(258\) | 17.2145 | 1.07173 | ||||||||
\(259\) | 6.54031 | 0.406395 | ||||||||
\(260\) | −25.2928 | −1.56859 | ||||||||
\(261\) | −5.28971 | −0.327425 | ||||||||
\(262\) | −9.43478 | −0.582882 | ||||||||
\(263\) | −16.1298 | −0.994607 | −0.497304 | − | 0.867577i | \(-0.665677\pi\) | ||||
−0.497304 | + | 0.867577i | \(0.665677\pi\) | |||||||
\(264\) | −0.197869 | −0.0121780 | ||||||||
\(265\) | −11.0594 | −0.679374 | ||||||||
\(266\) | 14.6061 | 0.895559 | ||||||||
\(267\) | 14.4772 | 0.885991 | ||||||||
\(268\) | −50.8413 | −3.10563 | ||||||||
\(269\) | −16.2546 | −0.991062 | −0.495531 | − | 0.868590i | \(-0.665026\pi\) | ||||
−0.495531 | + | 0.868590i | \(0.665026\pi\) | |||||||
\(270\) | −6.12828 | −0.372955 | ||||||||
\(271\) | −21.3796 | −1.29872 | −0.649360 | − | 0.760481i | \(-0.724963\pi\) | ||||
−0.649360 | + | 0.760481i | \(0.724963\pi\) | |||||||
\(272\) | −8.47952 | −0.514147 | ||||||||
\(273\) | 3.45200 | 0.208925 | ||||||||
\(274\) | −11.4533 | −0.691917 | ||||||||
\(275\) | 0.0180472 | 0.00108828 | ||||||||
\(276\) | 0.158085 | 0.00951560 | ||||||||
\(277\) | 21.3761 | 1.28436 | 0.642182 | − | 0.766552i | \(-0.278029\pi\) | ||||
0.642182 | + | 0.766552i | \(0.278029\pi\) | |||||||
\(278\) | −39.9999 | −2.39903 | ||||||||
\(279\) | 5.40462 | 0.323566 | ||||||||
\(280\) | 24.7651 | 1.48000 | ||||||||
\(281\) | −11.0237 | −0.657620 | −0.328810 | − | 0.944396i | \(-0.606648\pi\) | ||||
−0.328810 | + | 0.944396i | \(0.606648\pi\) | |||||||
\(282\) | 20.1615 | 1.20060 | ||||||||
\(283\) | 11.1859 | 0.664931 | 0.332466 | − | 0.943115i | \(-0.392119\pi\) | ||||
0.332466 | + | 0.943115i | \(0.392119\pi\) | |||||||
\(284\) | −67.0006 | −3.97576 | ||||||||
\(285\) | 8.86949 | 0.525383 | ||||||||
\(286\) | 0.169024 | 0.00999458 | ||||||||
\(287\) | −14.5682 | −0.859935 | ||||||||
\(288\) | −8.10165 | −0.477394 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 32.4169 | 1.90358 | ||||||||
\(291\) | −17.9042 | −1.04957 | ||||||||
\(292\) | 30.3660 | 1.77704 | ||||||||
\(293\) | −14.6330 | −0.854870 | −0.427435 | − | 0.904046i | \(-0.640583\pi\) | ||||
−0.427435 | + | 0.904046i | \(0.640583\pi\) | |||||||
\(294\) | 12.1699 | 0.709766 | ||||||||
\(295\) | −16.5041 | −0.960908 | ||||||||
\(296\) | 29.8332 | 1.73402 | ||||||||
\(297\) | 0.0286762 | 0.00166396 | ||||||||
\(298\) | 62.4395 | 3.61702 | ||||||||
\(299\) | −0.0772245 | −0.00446601 | ||||||||
\(300\) | 2.93994 | 0.169738 | ||||||||
\(301\) | 10.0819 | 0.581109 | ||||||||
\(302\) | 22.5877 | 1.29978 | ||||||||
\(303\) | 3.95845 | 0.227407 | ||||||||
\(304\) | 31.6987 | 1.81804 | ||||||||
\(305\) | 28.5399 | 1.63419 | ||||||||
\(306\) | 2.58291 | 0.147655 | ||||||||
\(307\) | −17.6730 | −1.00865 | −0.504327 | − | 0.863513i | \(-0.668259\pi\) | ||||
−0.504327 | + | 0.863513i | \(0.668259\pi\) | |||||||
\(308\) | −0.202642 | −0.0115466 | ||||||||
\(309\) | 7.76336 | 0.441642 | ||||||||
\(310\) | −33.1211 | −1.88115 | ||||||||
\(311\) | 11.9994 | 0.680421 | 0.340210 | − | 0.940349i | \(-0.389502\pi\) | ||||
0.340210 | + | 0.940349i | \(0.389502\pi\) | |||||||
\(312\) | 15.7461 | 0.891446 | ||||||||
\(313\) | 23.4022 | 1.32277 | 0.661384 | − | 0.750047i | \(-0.269969\pi\) | ||||
0.661384 | + | 0.750047i | \(0.269969\pi\) | |||||||
\(314\) | −2.58291 | −0.145762 | ||||||||
\(315\) | −3.58909 | −0.202222 | ||||||||
\(316\) | 36.8376 | 2.07227 | ||||||||
\(317\) | 30.6745 | 1.72285 | 0.861427 | − | 0.507882i | \(-0.169571\pi\) | ||||
0.861427 | + | 0.507882i | \(0.169571\pi\) | |||||||
\(318\) | 12.0396 | 0.675149 | ||||||||
\(319\) | −0.151689 | −0.00849295 | ||||||||
\(320\) | 9.41175 | 0.526133 | ||||||||
\(321\) | 1.85870 | 0.103742 | ||||||||
\(322\) | 0.132222 | 0.00736846 | ||||||||
\(323\) | −3.73826 | −0.208002 | ||||||||
\(324\) | 4.67145 | 0.259525 | ||||||||
\(325\) | −1.43616 | −0.0796639 | ||||||||
\(326\) | −22.8163 | −1.26368 | ||||||||
\(327\) | 9.08366 | 0.502328 | ||||||||
\(328\) | −66.4520 | −3.66920 | ||||||||
\(329\) | 11.8078 | 0.650984 | ||||||||
\(330\) | −0.175736 | −0.00967394 | ||||||||
\(331\) | −5.21080 | −0.286412 | −0.143206 | − | 0.989693i | \(-0.545741\pi\) | ||||
−0.143206 | + | 0.989693i | \(0.545741\pi\) | |||||||
\(332\) | −28.2780 | −1.55196 | ||||||||
\(333\) | −4.32358 | −0.236930 | ||||||||
\(334\) | −1.14180 | −0.0624768 | ||||||||
\(335\) | −25.8223 | −1.41082 | ||||||||
\(336\) | −12.8271 | −0.699773 | ||||||||
\(337\) | 30.7138 | 1.67309 | 0.836544 | − | 0.547900i | \(-0.184573\pi\) | ||||
0.836544 | + | 0.547900i | \(0.184573\pi\) | |||||||
\(338\) | 20.1273 | 1.09478 | ||||||||
\(339\) | −14.5043 | −0.787765 | ||||||||
\(340\) | −11.0836 | −0.601092 | ||||||||
\(341\) | 0.154984 | 0.00839286 | ||||||||
\(342\) | −9.65561 | −0.522115 | ||||||||
\(343\) | 17.7164 | 0.956596 | ||||||||
\(344\) | 45.9877 | 2.47949 | ||||||||
\(345\) | 0.0802912 | 0.00432274 | ||||||||
\(346\) | 52.7048 | 2.83343 | ||||||||
\(347\) | 22.9647 | 1.23281 | 0.616406 | − | 0.787429i | \(-0.288588\pi\) | ||||
0.616406 | + | 0.787429i | \(0.288588\pi\) | |||||||
\(348\) | −24.7106 | −1.32463 | ||||||||
\(349\) | −17.6342 | −0.943935 | −0.471968 | − | 0.881616i | \(-0.656456\pi\) | ||||
−0.471968 | + | 0.881616i | \(0.656456\pi\) | |||||||
\(350\) | 2.45897 | 0.131437 | ||||||||
\(351\) | −2.28200 | −0.121804 | ||||||||
\(352\) | −0.232324 | −0.0123829 | ||||||||
\(353\) | −18.5631 | −0.988012 | −0.494006 | − | 0.869459i | \(-0.664468\pi\) | ||||
−0.494006 | + | 0.869459i | \(0.664468\pi\) | |||||||
\(354\) | 17.9669 | 0.954932 | ||||||||
\(355\) | −34.0296 | −1.80610 | ||||||||
\(356\) | 67.6295 | 3.58436 | ||||||||
\(357\) | 1.51271 | 0.0800610 | ||||||||
\(358\) | 19.2732 | 1.01862 | ||||||||
\(359\) | −22.1744 | −1.17032 | −0.585160 | − | 0.810918i | \(-0.698968\pi\) | ||||
−0.585160 | + | 0.810918i | \(0.698968\pi\) | |||||||
\(360\) | −16.3714 | −0.862848 | ||||||||
\(361\) | −5.02541 | −0.264495 | ||||||||
\(362\) | −33.4721 | −1.75925 | ||||||||
\(363\) | −10.9992 | −0.577307 | ||||||||
\(364\) | 16.1259 | 0.845224 | ||||||||
\(365\) | 15.4229 | 0.807270 | ||||||||
\(366\) | −31.0694 | −1.62402 | ||||||||
\(367\) | 36.6906 | 1.91524 | 0.957618 | − | 0.288043i | \(-0.0930045\pi\) | ||||
0.957618 | + | 0.288043i | \(0.0930045\pi\) | |||||||
\(368\) | 0.286953 | 0.0149585 | ||||||||
\(369\) | 9.63055 | 0.501347 | ||||||||
\(370\) | 26.4961 | 1.37747 | ||||||||
\(371\) | 7.05113 | 0.366076 | ||||||||
\(372\) | 25.2474 | 1.30902 | ||||||||
\(373\) | −18.7946 | −0.973148 | −0.486574 | − | 0.873639i | \(-0.661754\pi\) | ||||
−0.486574 | + | 0.873639i | \(0.661754\pi\) | |||||||
\(374\) | 0.0740682 | 0.00382997 | ||||||||
\(375\) | −10.3699 | −0.535501 | ||||||||
\(376\) | 53.8604 | 2.77764 | ||||||||
\(377\) | 12.0711 | 0.621695 | ||||||||
\(378\) | 3.90720 | 0.200965 | ||||||||
\(379\) | −19.8808 | −1.02121 | −0.510605 | − | 0.859816i | \(-0.670578\pi\) | ||||
−0.510605 | + | 0.859816i | \(0.670578\pi\) | |||||||
\(380\) | 41.4333 | 2.12549 | ||||||||
\(381\) | 8.52240 | 0.436616 | ||||||||
\(382\) | −29.4363 | −1.50609 | ||||||||
\(383\) | 20.6523 | 1.05528 | 0.527642 | − | 0.849467i | \(-0.323076\pi\) | ||||
0.527642 | + | 0.849467i | \(0.323076\pi\) | |||||||
\(384\) | 5.95736 | 0.304010 | ||||||||
\(385\) | −0.102921 | −0.00524536 | ||||||||
\(386\) | −51.7027 | −2.63160 | ||||||||
\(387\) | −6.66478 | −0.338790 | ||||||||
\(388\) | −83.6388 | −4.24611 | ||||||||
\(389\) | 18.9814 | 0.962397 | 0.481199 | − | 0.876612i | \(-0.340202\pi\) | ||||
0.481199 | + | 0.876612i | \(0.340202\pi\) | |||||||
\(390\) | 13.9848 | 0.708145 | ||||||||
\(391\) | −0.0338407 | −0.00171140 | ||||||||
\(392\) | 32.5114 | 1.64207 | ||||||||
\(393\) | 3.65276 | 0.184258 | ||||||||
\(394\) | 57.4828 | 2.89594 | ||||||||
\(395\) | 18.7098 | 0.941390 | ||||||||
\(396\) | 0.133959 | 0.00673171 | ||||||||
\(397\) | −9.79340 | −0.491517 | −0.245758 | − | 0.969331i | \(-0.579037\pi\) | ||||
−0.245758 | + | 0.969331i | \(0.579037\pi\) | |||||||
\(398\) | −2.18586 | −0.109567 | ||||||||
\(399\) | −5.65490 | −0.283099 | ||||||||
\(400\) | 5.33653 | 0.266826 | ||||||||
\(401\) | −0.655997 | −0.0327589 | −0.0163795 | − | 0.999866i | \(-0.505214\pi\) | ||||
−0.0163795 | + | 0.999866i | \(0.505214\pi\) | |||||||
\(402\) | 28.1110 | 1.40205 | ||||||||
\(403\) | −12.3334 | −0.614368 | ||||||||
\(404\) | 18.4917 | 0.919997 | ||||||||
\(405\) | 2.37262 | 0.117897 | ||||||||
\(406\) | −20.6680 | −1.02573 | ||||||||
\(407\) | −0.123984 | −0.00614565 | ||||||||
\(408\) | 6.90012 | 0.341607 | ||||||||
\(409\) | 35.9707 | 1.77864 | 0.889319 | − | 0.457287i | \(-0.151179\pi\) | ||||
0.889319 | + | 0.457287i | \(0.151179\pi\) | |||||||
\(410\) | −59.0188 | −2.91473 | ||||||||
\(411\) | 4.43424 | 0.218725 | ||||||||
\(412\) | 36.2661 | 1.78670 | ||||||||
\(413\) | 10.5225 | 0.517779 | ||||||||
\(414\) | −0.0874076 | −0.00429585 | ||||||||
\(415\) | −14.3624 | −0.705022 | ||||||||
\(416\) | 18.4880 | 0.906447 | ||||||||
\(417\) | 15.4863 | 0.758369 | ||||||||
\(418\) | −0.276886 | −0.0135429 | ||||||||
\(419\) | 6.54048 | 0.319523 | 0.159762 | − | 0.987156i | \(-0.448927\pi\) | ||||
0.159762 | + | 0.987156i | \(0.448927\pi\) | |||||||
\(420\) | −16.7662 | −0.818109 | ||||||||
\(421\) | 1.25924 | 0.0613718 | 0.0306859 | − | 0.999529i | \(-0.490231\pi\) | ||||
0.0306859 | + | 0.999529i | \(0.490231\pi\) | |||||||
\(422\) | 65.5803 | 3.19240 | ||||||||
\(423\) | −7.80572 | −0.379527 | ||||||||
\(424\) | 32.1632 | 1.56199 | ||||||||
\(425\) | −0.629343 | −0.0305276 | ||||||||
\(426\) | 37.0457 | 1.79487 | ||||||||
\(427\) | −18.1961 | −0.880571 | ||||||||
\(428\) | 8.68281 | 0.419700 | ||||||||
\(429\) | −0.0654391 | −0.00315943 | ||||||||
\(430\) | 40.8436 | 1.96965 | ||||||||
\(431\) | 35.8060 | 1.72471 | 0.862357 | − | 0.506301i | \(-0.168988\pi\) | ||||
0.862357 | + | 0.506301i | \(0.168988\pi\) | |||||||
\(432\) | 8.47952 | 0.407971 | ||||||||
\(433\) | −20.8729 | −1.00309 | −0.501545 | − | 0.865132i | \(-0.667235\pi\) | ||||
−0.501545 | + | 0.865132i | \(0.667235\pi\) | |||||||
\(434\) | 21.1169 | 1.01365 | ||||||||
\(435\) | −12.5505 | −0.601750 | ||||||||
\(436\) | 42.4338 | 2.03221 | ||||||||
\(437\) | 0.126505 | 0.00605157 | ||||||||
\(438\) | −16.7898 | −0.802249 | ||||||||
\(439\) | −36.6084 | −1.74722 | −0.873612 | − | 0.486622i | \(-0.838229\pi\) | ||||
−0.873612 | + | 0.486622i | \(0.838229\pi\) | |||||||
\(440\) | −0.469469 | −0.0223811 | ||||||||
\(441\) | −4.71171 | −0.224367 | ||||||||
\(442\) | −5.89421 | −0.280359 | ||||||||
\(443\) | 12.2761 | 0.583257 | 0.291629 | − | 0.956532i | \(-0.405803\pi\) | ||||
0.291629 | + | 0.956532i | \(0.405803\pi\) | |||||||
\(444\) | −20.1974 | −0.958524 | ||||||||
\(445\) | 34.3490 | 1.62830 | ||||||||
\(446\) | −6.78607 | −0.321330 | ||||||||
\(447\) | −24.1740 | −1.14339 | ||||||||
\(448\) | −6.00063 | −0.283503 | ||||||||
\(449\) | −41.6897 | −1.96746 | −0.983730 | − | 0.179651i | \(-0.942503\pi\) | ||||
−0.983730 | + | 0.179651i | \(0.942503\pi\) | |||||||
\(450\) | −1.62554 | −0.0766286 | ||||||||
\(451\) | 0.276168 | 0.0130042 | ||||||||
\(452\) | −67.7560 | −3.18698 | ||||||||
\(453\) | −8.74504 | −0.410878 | ||||||||
\(454\) | −38.4482 | −1.80446 | ||||||||
\(455\) | 8.19031 | 0.383967 | ||||||||
\(456\) | −25.7944 | −1.20794 | ||||||||
\(457\) | 25.6731 | 1.20094 | 0.600468 | − | 0.799649i | \(-0.294981\pi\) | ||||
0.600468 | + | 0.799649i | \(0.294981\pi\) | |||||||
\(458\) | 33.6306 | 1.57145 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0.375076 | 0.0174880 | ||||||||
\(461\) | 27.7166 | 1.29089 | 0.645446 | − | 0.763806i | \(-0.276671\pi\) | ||||
0.645446 | + | 0.763806i | \(0.276671\pi\) | |||||||
\(462\) | 0.112044 | 0.00521274 | ||||||||
\(463\) | −0.997341 | −0.0463504 | −0.0231752 | − | 0.999731i | \(-0.507378\pi\) | ||||
−0.0231752 | + | 0.999731i | \(0.507378\pi\) | |||||||
\(464\) | −44.8543 | −2.08231 | ||||||||
\(465\) | 12.8231 | 0.594659 | ||||||||
\(466\) | 56.8201 | 2.63214 | ||||||||
\(467\) | −41.6728 | −1.92839 | −0.964194 | − | 0.265199i | \(-0.914562\pi\) | ||||
−0.964194 | + | 0.265199i | \(0.914562\pi\) | |||||||
\(468\) | −10.6602 | −0.492770 | ||||||||
\(469\) | 16.4635 | 0.760212 | ||||||||
\(470\) | 47.8357 | 2.20649 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 47.9977 | 2.20927 | ||||||||
\(473\) | −0.191120 | −0.00878773 | ||||||||
\(474\) | −20.3680 | −0.935535 | ||||||||
\(475\) | 2.35265 | 0.107947 | ||||||||
\(476\) | 7.06654 | 0.323894 | ||||||||
\(477\) | −4.66126 | −0.213424 | ||||||||
\(478\) | 29.4093 | 1.34515 | ||||||||
\(479\) | 4.86314 | 0.222202 | 0.111101 | − | 0.993809i | \(-0.464562\pi\) | ||||
0.111101 | + | 0.993809i | \(0.464562\pi\) | |||||||
\(480\) | −19.2222 | −0.877367 | ||||||||
\(481\) | 9.86641 | 0.449869 | ||||||||
\(482\) | −10.3928 | −0.473380 | ||||||||
\(483\) | −0.0511911 | −0.00232928 | ||||||||
\(484\) | −51.3821 | −2.33555 | ||||||||
\(485\) | −42.4800 | −1.92892 | ||||||||
\(486\) | −2.58291 | −0.117163 | ||||||||
\(487\) | −20.0544 | −0.908753 | −0.454376 | − | 0.890810i | \(-0.650138\pi\) | ||||
−0.454376 | + | 0.890810i | \(0.650138\pi\) | |||||||
\(488\) | −83.0003 | −3.75725 | ||||||||
\(489\) | 8.83357 | 0.399468 | ||||||||
\(490\) | 28.8747 | 1.30443 | ||||||||
\(491\) | −7.57996 | −0.342079 | −0.171039 | − | 0.985264i | \(-0.554713\pi\) | ||||
−0.171039 | + | 0.985264i | \(0.554713\pi\) | |||||||
\(492\) | 44.9886 | 2.02824 | ||||||||
\(493\) | 5.28971 | 0.238237 | ||||||||
\(494\) | 22.0341 | 0.991362 | ||||||||
\(495\) | 0.0680378 | 0.00305807 | ||||||||
\(496\) | 45.8286 | 2.05777 | ||||||||
\(497\) | 21.6962 | 0.973206 | ||||||||
\(498\) | 15.6354 | 0.700637 | ||||||||
\(499\) | −21.0943 | −0.944311 | −0.472155 | − | 0.881515i | \(-0.656524\pi\) | ||||
−0.472155 | + | 0.881515i | \(0.656524\pi\) | |||||||
\(500\) | −48.4426 | −2.16642 | ||||||||
\(501\) | 0.442060 | 0.0197498 | ||||||||
\(502\) | 51.2308 | 2.28654 | ||||||||
\(503\) | −20.9533 | −0.934260 | −0.467130 | − | 0.884189i | \(-0.654712\pi\) | ||||
−0.467130 | + | 0.884189i | \(0.654712\pi\) | |||||||
\(504\) | 10.4379 | 0.464940 | ||||||||
\(505\) | 9.39192 | 0.417935 | ||||||||
\(506\) | −0.00250652 | −0.000111428 0 | ||||||||
\(507\) | −7.79247 | −0.346076 | ||||||||
\(508\) | 39.8119 | 1.76637 | ||||||||
\(509\) | 28.6678 | 1.27068 | 0.635339 | − | 0.772233i | \(-0.280860\pi\) | ||||
0.635339 | + | 0.772233i | \(0.280860\pi\) | |||||||
\(510\) | 6.12828 | 0.271365 | ||||||||
\(511\) | −9.83312 | −0.434992 | ||||||||
\(512\) | 48.3214 | 2.13552 | ||||||||
\(513\) | 3.73826 | 0.165048 | ||||||||
\(514\) | 57.9284 | 2.55511 | ||||||||
\(515\) | 18.4195 | 0.811662 | ||||||||
\(516\) | −31.1341 | −1.37060 | ||||||||
\(517\) | −0.223838 | −0.00984440 | ||||||||
\(518\) | −16.8931 | −0.742239 | ||||||||
\(519\) | −20.4052 | −0.895687 | ||||||||
\(520\) | 37.3595 | 1.63832 | ||||||||
\(521\) | −27.3387 | −1.19773 | −0.598864 | − | 0.800851i | \(-0.704381\pi\) | ||||
−0.598864 | + | 0.800851i | \(0.704381\pi\) | |||||||
\(522\) | 13.6629 | 0.598008 | ||||||||
\(523\) | 41.8747 | 1.83105 | 0.915526 | − | 0.402260i | \(-0.131775\pi\) | ||||
0.915526 | + | 0.402260i | \(0.131775\pi\) | |||||||
\(524\) | 17.0637 | 0.745431 | ||||||||
\(525\) | −0.952012 | −0.0415492 | ||||||||
\(526\) | 41.6619 | 1.81655 | ||||||||
\(527\) | −5.40462 | −0.235429 | ||||||||
\(528\) | 0.243161 | 0.0105822 | ||||||||
\(529\) | −22.9989 | −0.999950 | ||||||||
\(530\) | 28.5655 | 1.24081 | ||||||||
\(531\) | −6.95607 | −0.301868 | ||||||||
\(532\) | −26.4166 | −1.14530 | ||||||||
\(533\) | −21.9769 | −0.951927 | ||||||||
\(534\) | −37.3934 | −1.61817 | ||||||||
\(535\) | 4.40999 | 0.190661 | ||||||||
\(536\) | 75.0969 | 3.24369 | ||||||||
\(537\) | −7.46180 | −0.322000 | ||||||||
\(538\) | 41.9843 | 1.81007 | ||||||||
\(539\) | −0.135114 | −0.00581977 | ||||||||
\(540\) | 11.0836 | 0.476962 | ||||||||
\(541\) | 24.8749 | 1.06945 | 0.534727 | − | 0.845025i | \(-0.320414\pi\) | ||||
0.534727 | + | 0.845025i | \(0.320414\pi\) | |||||||
\(542\) | 55.2218 | 2.37198 | ||||||||
\(543\) | 12.9590 | 0.556125 | ||||||||
\(544\) | 8.10165 | 0.347355 | ||||||||
\(545\) | 21.5521 | 0.923191 | ||||||||
\(546\) | −8.91623 | −0.381579 | ||||||||
\(547\) | −3.06881 | −0.131213 | −0.0656063 | − | 0.997846i | \(-0.520898\pi\) | ||||
−0.0656063 | + | 0.997846i | \(0.520898\pi\) | |||||||
\(548\) | 20.7143 | 0.884871 | ||||||||
\(549\) | 12.0288 | 0.513377 | ||||||||
\(550\) | −0.0466143 | −0.00198764 | ||||||||
\(551\) | −19.7743 | −0.842415 | ||||||||
\(552\) | −0.233505 | −0.00993863 | ||||||||
\(553\) | −11.9287 | −0.507262 | ||||||||
\(554\) | −55.2126 | −2.34576 | ||||||||
\(555\) | −10.2582 | −0.435437 | ||||||||
\(556\) | 72.3435 | 3.06805 | ||||||||
\(557\) | −4.80336 | −0.203525 | −0.101762 | − | 0.994809i | \(-0.532448\pi\) | ||||
−0.101762 | + | 0.994809i | \(0.532448\pi\) | |||||||
\(558\) | −13.9597 | −0.590960 | ||||||||
\(559\) | 15.2090 | 0.643273 | ||||||||
\(560\) | −30.4338 | −1.28606 | ||||||||
\(561\) | −0.0286762 | −0.00121071 | ||||||||
\(562\) | 28.4733 | 1.20107 | ||||||||
\(563\) | −16.8888 | −0.711776 | −0.355888 | − | 0.934529i | \(-0.615822\pi\) | ||||
−0.355888 | + | 0.934529i | \(0.615822\pi\) | |||||||
\(564\) | −36.4640 | −1.53541 | ||||||||
\(565\) | −34.4132 | −1.44777 | ||||||||
\(566\) | −28.8922 | −1.21443 | ||||||||
\(567\) | −1.51271 | −0.0635278 | ||||||||
\(568\) | 98.9656 | 4.15250 | ||||||||
\(569\) | 19.9842 | 0.837780 | 0.418890 | − | 0.908037i | \(-0.362419\pi\) | ||||
0.418890 | + | 0.908037i | \(0.362419\pi\) | |||||||
\(570\) | −22.9091 | −0.959558 | ||||||||
\(571\) | 8.52893 | 0.356925 | 0.178462 | − | 0.983947i | \(-0.442888\pi\) | ||||
0.178462 | + | 0.983947i | \(0.442888\pi\) | |||||||
\(572\) | −0.305695 | −0.0127818 | ||||||||
\(573\) | 11.3965 | 0.476097 | ||||||||
\(574\) | 37.6285 | 1.57058 | ||||||||
\(575\) | 0.0212974 | 0.000888163 0 | ||||||||
\(576\) | 3.96681 | 0.165284 | ||||||||
\(577\) | −18.7931 | −0.782366 | −0.391183 | − | 0.920313i | \(-0.627934\pi\) | ||||
−0.391183 | + | 0.920313i | \(0.627934\pi\) | |||||||
\(578\) | −2.58291 | −0.107435 | ||||||||
\(579\) | 20.0172 | 0.831886 | ||||||||
\(580\) | −58.6290 | −2.43444 | ||||||||
\(581\) | 9.15700 | 0.379896 | ||||||||
\(582\) | 46.2451 | 1.91692 | ||||||||
\(583\) | −0.133667 | −0.00553593 | ||||||||
\(584\) | −44.8531 | −1.85604 | ||||||||
\(585\) | −5.41433 | −0.223855 | ||||||||
\(586\) | 37.7958 | 1.56133 | ||||||||
\(587\) | 5.70930 | 0.235648 | 0.117824 | − | 0.993034i | \(-0.462408\pi\) | ||||
0.117824 | + | 0.993034i | \(0.462408\pi\) | |||||||
\(588\) | −22.0105 | −0.907698 | ||||||||
\(589\) | 20.2039 | 0.832487 | ||||||||
\(590\) | 42.6288 | 1.75500 | ||||||||
\(591\) | −22.2550 | −0.915448 | ||||||||
\(592\) | −36.6619 | −1.50679 | ||||||||
\(593\) | −31.6183 | −1.29841 | −0.649204 | − | 0.760614i | \(-0.724898\pi\) | ||||
−0.649204 | + | 0.760614i | \(0.724898\pi\) | |||||||
\(594\) | −0.0740682 | −0.00303905 | ||||||||
\(595\) | 3.58909 | 0.147138 | ||||||||
\(596\) | −112.928 | −4.62570 | ||||||||
\(597\) | 0.846276 | 0.0346358 | ||||||||
\(598\) | 0.199464 | 0.00815670 | ||||||||
\(599\) | −27.0048 | −1.10339 | −0.551693 | − | 0.834048i | \(-0.686018\pi\) | ||||
−0.551693 | + | 0.834048i | \(0.686018\pi\) | |||||||
\(600\) | −4.34254 | −0.177283 | ||||||||
\(601\) | −4.78688 | −0.195261 | −0.0976304 | − | 0.995223i | \(-0.531126\pi\) | ||||
−0.0976304 | + | 0.995223i | \(0.531126\pi\) | |||||||
\(602\) | −26.0406 | −1.06134 | ||||||||
\(603\) | −10.8834 | −0.443207 | ||||||||
\(604\) | −40.8520 | −1.66224 | ||||||||
\(605\) | −26.0969 | −1.06099 | ||||||||
\(606\) | −10.2243 | −0.415336 | ||||||||
\(607\) | −28.2056 | −1.14483 | −0.572415 | − | 0.819964i | \(-0.693993\pi\) | ||||
−0.572415 | + | 0.819964i | \(0.693993\pi\) | |||||||
\(608\) | −30.2861 | −1.22826 | ||||||||
\(609\) | 8.00180 | 0.324249 | ||||||||
\(610\) | −73.7160 | −2.98467 | ||||||||
\(611\) | 17.8127 | 0.720623 | ||||||||
\(612\) | −4.67145 | −0.188832 | ||||||||
\(613\) | 4.49092 | 0.181387 | 0.0906933 | − | 0.995879i | \(-0.471092\pi\) | ||||
0.0906933 | + | 0.995879i | \(0.471092\pi\) | |||||||
\(614\) | 45.6479 | 1.84220 | ||||||||
\(615\) | 22.8497 | 0.921388 | ||||||||
\(616\) | 0.299319 | 0.0120599 | ||||||||
\(617\) | −15.9359 | −0.641557 | −0.320778 | − | 0.947154i | \(-0.603945\pi\) | ||||
−0.320778 | + | 0.947154i | \(0.603945\pi\) | |||||||
\(618\) | −20.0521 | −0.806614 | ||||||||
\(619\) | 47.2496 | 1.89912 | 0.949560 | − | 0.313585i | \(-0.101530\pi\) | ||||
0.949560 | + | 0.313585i | \(0.101530\pi\) | |||||||
\(620\) | 59.9026 | 2.40575 | ||||||||
\(621\) | 0.0338407 | 0.00135798 | ||||||||
\(622\) | −30.9933 | −1.24272 | ||||||||
\(623\) | −21.8998 | −0.877397 | ||||||||
\(624\) | −19.3503 | −0.774631 | ||||||||
\(625\) | −27.7506 | −1.11003 | ||||||||
\(626\) | −60.4458 | −2.41590 | ||||||||
\(627\) | 0.107199 | 0.00428112 | ||||||||
\(628\) | 4.67145 | 0.186411 | ||||||||
\(629\) | 4.32358 | 0.172392 | ||||||||
\(630\) | 9.27031 | 0.369338 | ||||||||
\(631\) | 43.4005 | 1.72775 | 0.863874 | − | 0.503709i | \(-0.168032\pi\) | ||||
0.863874 | + | 0.503709i | \(0.168032\pi\) | |||||||
\(632\) | −54.4122 | −2.16440 | ||||||||
\(633\) | −25.3900 | −1.00916 | ||||||||
\(634\) | −79.2297 | −3.14661 | ||||||||
\(635\) | 20.2205 | 0.802424 | ||||||||
\(636\) | −21.7748 | −0.863428 | ||||||||
\(637\) | 10.7521 | 0.426015 | ||||||||
\(638\) | 0.391799 | 0.0155115 | ||||||||
\(639\) | −14.3426 | −0.567384 | ||||||||
\(640\) | 14.1346 | 0.558718 | ||||||||
\(641\) | 43.2254 | 1.70730 | 0.853650 | − | 0.520847i | \(-0.174384\pi\) | ||||
0.853650 | + | 0.520847i | \(0.174384\pi\) | |||||||
\(642\) | −4.80086 | −0.189475 | ||||||||
\(643\) | −31.2128 | −1.23091 | −0.615457 | − | 0.788170i | \(-0.711029\pi\) | ||||
−0.615457 | + | 0.788170i | \(0.711029\pi\) | |||||||
\(644\) | −0.239137 | −0.00942330 | ||||||||
\(645\) | −15.8130 | −0.622636 | ||||||||
\(646\) | 9.65561 | 0.379895 | ||||||||
\(647\) | −29.6126 | −1.16419 | −0.582096 | − | 0.813120i | \(-0.697767\pi\) | ||||
−0.582096 | + | 0.813120i | \(0.697767\pi\) | |||||||
\(648\) | −6.90012 | −0.271062 | ||||||||
\(649\) | −0.199474 | −0.00783003 | ||||||||
\(650\) | 3.70948 | 0.145498 | ||||||||
\(651\) | −8.17562 | −0.320428 | ||||||||
\(652\) | 41.2655 | 1.61608 | ||||||||
\(653\) | 19.9254 | 0.779743 | 0.389871 | − | 0.920869i | \(-0.372519\pi\) | ||||
0.389871 | + | 0.920869i | \(0.372519\pi\) | |||||||
\(654\) | −23.4623 | −0.917449 | ||||||||
\(655\) | 8.66663 | 0.338633 | ||||||||
\(656\) | 81.6625 | 3.18839 | ||||||||
\(657\) | 6.50034 | 0.253602 | ||||||||
\(658\) | −30.4985 | −1.18895 | ||||||||
\(659\) | 22.6520 | 0.882395 | 0.441197 | − | 0.897410i | \(-0.354554\pi\) | ||||
0.441197 | + | 0.897410i | \(0.354554\pi\) | |||||||
\(660\) | 0.317835 | 0.0123717 | ||||||||
\(661\) | 9.50529 | 0.369713 | 0.184857 | − | 0.982766i | \(-0.440818\pi\) | ||||
0.184857 | + | 0.982766i | \(0.440818\pi\) | |||||||
\(662\) | 13.4591 | 0.523101 | ||||||||
\(663\) | 2.28200 | 0.0886256 | ||||||||
\(664\) | 41.7690 | 1.62095 | ||||||||
\(665\) | −13.4170 | −0.520287 | ||||||||
\(666\) | 11.1674 | 0.432729 | ||||||||
\(667\) | −0.179008 | −0.00693120 | ||||||||
\(668\) | 2.06506 | 0.0798997 | ||||||||
\(669\) | 2.62729 | 0.101577 | ||||||||
\(670\) | 66.6967 | 2.57672 | ||||||||
\(671\) | 0.344941 | 0.0133163 | ||||||||
\(672\) | 12.2554 | 0.472764 | ||||||||
\(673\) | −39.6317 | −1.52769 | −0.763846 | − | 0.645399i | \(-0.776691\pi\) | ||||
−0.763846 | + | 0.645399i | \(0.776691\pi\) | |||||||
\(674\) | −79.3311 | −3.05572 | ||||||||
\(675\) | 0.629343 | 0.0242234 | ||||||||
\(676\) | −36.4021 | −1.40008 | ||||||||
\(677\) | 14.6513 | 0.563096 | 0.281548 | − | 0.959547i | \(-0.409152\pi\) | ||||
0.281548 | + | 0.959547i | \(0.409152\pi\) | |||||||
\(678\) | 37.4633 | 1.43877 | ||||||||
\(679\) | 27.0839 | 1.03939 | ||||||||
\(680\) | 16.3714 | 0.627814 | ||||||||
\(681\) | 14.8856 | 0.570417 | ||||||||
\(682\) | −0.400311 | −0.0153287 | ||||||||
\(683\) | 23.4988 | 0.899157 | 0.449579 | − | 0.893241i | \(-0.351574\pi\) | ||||
0.449579 | + | 0.893241i | \(0.351574\pi\) | |||||||
\(684\) | 17.4631 | 0.667718 | ||||||||
\(685\) | 10.5208 | 0.401978 | ||||||||
\(686\) | −45.7600 | −1.74712 | ||||||||
\(687\) | −13.0204 | −0.496760 | ||||||||
\(688\) | −56.5141 | −2.15458 | ||||||||
\(689\) | 10.6370 | 0.405237 | ||||||||
\(690\) | −0.207385 | −0.00789503 | ||||||||
\(691\) | 15.5103 | 0.590041 | 0.295020 | − | 0.955491i | \(-0.404674\pi\) | ||||
0.295020 | + | 0.955491i | \(0.404674\pi\) | |||||||
\(692\) | −95.3216 | −3.62358 | ||||||||
\(693\) | −0.0433788 | −0.00164782 | ||||||||
\(694\) | −59.3159 | −2.25160 | ||||||||
\(695\) | 36.7432 | 1.39375 | ||||||||
\(696\) | 36.4997 | 1.38352 | ||||||||
\(697\) | −9.63055 | −0.364783 | ||||||||
\(698\) | 45.5475 | 1.72400 | ||||||||
\(699\) | −21.9985 | −0.832058 | ||||||||
\(700\) | −4.44728 | −0.168091 | ||||||||
\(701\) | 0.516175 | 0.0194957 | 0.00974783 | − | 0.999952i | \(-0.496897\pi\) | ||||
0.00974783 | + | 0.999952i | \(0.496897\pi\) | |||||||
\(702\) | 5.89421 | 0.222463 | ||||||||
\(703\) | −16.1627 | −0.609586 | ||||||||
\(704\) | 0.113753 | 0.00428723 | ||||||||
\(705\) | −18.5200 | −0.697505 | ||||||||
\(706\) | 47.9468 | 1.80450 | ||||||||
\(707\) | −5.98799 | −0.225201 | ||||||||
\(708\) | −32.4949 | −1.22123 | ||||||||
\(709\) | 40.0680 | 1.50478 | 0.752392 | − | 0.658715i | \(-0.228900\pi\) | ||||
0.752392 | + | 0.658715i | \(0.228900\pi\) | |||||||
\(710\) | 87.8954 | 3.29866 | ||||||||
\(711\) | 7.88568 | 0.295736 | ||||||||
\(712\) | −99.8945 | −3.74370 | ||||||||
\(713\) | 0.182896 | 0.00684952 | ||||||||
\(714\) | −3.90720 | −0.146223 | ||||||||
\(715\) | −0.155262 | −0.00580649 | ||||||||
\(716\) | −34.8574 | −1.30268 | ||||||||
\(717\) | −11.3861 | −0.425222 | ||||||||
\(718\) | 57.2745 | 2.13747 | ||||||||
\(719\) | −36.8765 | −1.37526 | −0.687631 | − | 0.726060i | \(-0.741349\pi\) | ||||
−0.687631 | + | 0.726060i | \(0.741349\pi\) | |||||||
\(720\) | 20.1187 | 0.749780 | ||||||||
\(721\) | −11.7437 | −0.437358 | ||||||||
\(722\) | 12.9802 | 0.483073 | ||||||||
\(723\) | 4.02368 | 0.149642 | ||||||||
\(724\) | 60.5374 | 2.24986 | ||||||||
\(725\) | −3.32904 | −0.123638 | ||||||||
\(726\) | 28.4099 | 1.05439 | ||||||||
\(727\) | −30.7527 | −1.14056 | −0.570278 | − | 0.821452i | \(-0.693164\pi\) | ||||
−0.570278 | + | 0.821452i | \(0.693164\pi\) | |||||||
\(728\) | −23.8192 | −0.882800 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −39.8359 | −1.47439 | ||||||||
\(731\) | 6.66478 | 0.246506 | ||||||||
\(732\) | 56.1920 | 2.07692 | ||||||||
\(733\) | −24.1240 | −0.891042 | −0.445521 | − | 0.895271i | \(-0.646982\pi\) | ||||
−0.445521 | + | 0.895271i | \(0.646982\pi\) | |||||||
\(734\) | −94.7688 | −3.49798 | ||||||||
\(735\) | −11.1791 | −0.412348 | ||||||||
\(736\) | −0.274165 | −0.0101059 | ||||||||
\(737\) | −0.312095 | −0.0114962 | ||||||||
\(738\) | −24.8749 | −0.915658 | ||||||||
\(739\) | −30.5703 | −1.12455 | −0.562273 | − | 0.826951i | \(-0.690073\pi\) | ||||
−0.562273 | + | 0.826951i | \(0.690073\pi\) | |||||||
\(740\) | −47.9207 | −1.76160 | ||||||||
\(741\) | −8.53072 | −0.313384 | ||||||||
\(742\) | −18.2125 | −0.668601 | ||||||||
\(743\) | 21.5567 | 0.790840 | 0.395420 | − | 0.918500i | \(-0.370599\pi\) | ||||
0.395420 | + | 0.918500i | \(0.370599\pi\) | |||||||
\(744\) | −37.2926 | −1.36721 | ||||||||
\(745\) | −57.3559 | −2.10136 | ||||||||
\(746\) | 48.5449 | 1.77735 | ||||||||
\(747\) | −6.05338 | −0.221482 | ||||||||
\(748\) | −0.133959 | −0.00489804 | ||||||||
\(749\) | −2.81167 | −0.102736 | ||||||||
\(750\) | 26.7846 | 0.978036 | ||||||||
\(751\) | 34.4229 | 1.25611 | 0.628054 | − | 0.778170i | \(-0.283852\pi\) | ||||
0.628054 | + | 0.778170i | \(0.283852\pi\) | |||||||
\(752\) | −66.1888 | −2.41366 | ||||||||
\(753\) | −19.8345 | −0.722809 | ||||||||
\(754\) | −31.1787 | −1.13546 | ||||||||
\(755\) | −20.7487 | −0.755122 | ||||||||
\(756\) | −7.06654 | −0.257008 | ||||||||
\(757\) | −33.0431 | −1.20097 | −0.600486 | − | 0.799635i | \(-0.705026\pi\) | ||||
−0.600486 | + | 0.799635i | \(0.705026\pi\) | |||||||
\(758\) | 51.3505 | 1.86513 | ||||||||
\(759\) | 0.000970423 0 | 3.52241e−5 0 | ||||||||
\(760\) | −61.2005 | −2.21998 | ||||||||
\(761\) | −13.5002 | −0.489382 | −0.244691 | − | 0.969601i | \(-0.578687\pi\) | ||||
−0.244691 | + | 0.969601i | \(0.578687\pi\) | |||||||
\(762\) | −22.0126 | −0.797434 | ||||||||
\(763\) | −13.7409 | −0.497455 | ||||||||
\(764\) | 53.2383 | 1.92609 | ||||||||
\(765\) | −2.37262 | −0.0857824 | ||||||||
\(766\) | −53.3432 | −1.92737 | ||||||||
\(767\) | 15.8738 | 0.573168 | ||||||||
\(768\) | −23.3210 | −0.841523 | ||||||||
\(769\) | 38.0526 | 1.37221 | 0.686106 | − | 0.727502i | \(-0.259319\pi\) | ||||
0.686106 | + | 0.727502i | \(0.259319\pi\) | |||||||
\(770\) | 0.265837 | 0.00958011 | ||||||||
\(771\) | −22.4275 | −0.807708 | ||||||||
\(772\) | 93.5093 | 3.36547 | ||||||||
\(773\) | −5.98815 | −0.215379 | −0.107689 | − | 0.994185i | \(-0.534345\pi\) | ||||
−0.107689 | + | 0.994185i | \(0.534345\pi\) | |||||||
\(774\) | 17.2145 | 0.618764 | ||||||||
\(775\) | 3.40136 | 0.122180 | ||||||||
\(776\) | 123.541 | 4.43488 | ||||||||
\(777\) | 6.54031 | 0.234632 | ||||||||
\(778\) | −49.0274 | −1.75772 | ||||||||
\(779\) | 36.0015 | 1.28989 | ||||||||
\(780\) | −25.2928 | −0.905626 | ||||||||
\(781\) | −0.411291 | −0.0147171 | ||||||||
\(782\) | 0.0874076 | 0.00312569 | ||||||||
\(783\) | −5.28971 | −0.189039 | ||||||||
\(784\) | −39.9531 | −1.42690 | ||||||||
\(785\) | 2.37262 | 0.0846826 | ||||||||
\(786\) | −9.43478 | −0.336527 | ||||||||
\(787\) | 32.4237 | 1.15578 | 0.577890 | − | 0.816115i | \(-0.303876\pi\) | ||||
0.577890 | + | 0.816115i | \(0.303876\pi\) | |||||||
\(788\) | −103.963 | −3.70353 | ||||||||
\(789\) | −16.1298 | −0.574237 | ||||||||
\(790\) | −48.3257 | −1.71935 | ||||||||
\(791\) | 21.9408 | 0.780124 | ||||||||
\(792\) | −0.197869 | −0.00703098 | ||||||||
\(793\) | −27.4498 | −0.974770 | ||||||||
\(794\) | 25.2955 | 0.897705 | ||||||||
\(795\) | −11.0594 | −0.392237 | ||||||||
\(796\) | 3.95333 | 0.140122 | ||||||||
\(797\) | 9.29495 | 0.329244 | 0.164622 | − | 0.986357i | \(-0.447360\pi\) | ||||
0.164622 | + | 0.986357i | \(0.447360\pi\) | |||||||
\(798\) | 14.6061 | 0.517051 | ||||||||
\(799\) | 7.80572 | 0.276146 | ||||||||
\(800\) | −5.09871 | −0.180267 | ||||||||
\(801\) | 14.4772 | 0.511527 | ||||||||
\(802\) | 1.69438 | 0.0598308 | ||||||||
\(803\) | 0.186405 | 0.00657809 | ||||||||
\(804\) | −50.8413 | −1.79304 | ||||||||
\(805\) | −0.121457 | −0.00428081 | ||||||||
\(806\) | 31.8560 | 1.12208 | ||||||||
\(807\) | −16.2546 | −0.572190 | ||||||||
\(808\) | −27.3138 | −0.960896 | ||||||||
\(809\) | −47.0654 | −1.65473 | −0.827366 | − | 0.561663i | \(-0.810162\pi\) | ||||
−0.827366 | + | 0.561663i | \(0.810162\pi\) | |||||||
\(810\) | −6.12828 | −0.215326 | ||||||||
\(811\) | −49.1822 | −1.72702 | −0.863510 | − | 0.504331i | \(-0.831739\pi\) | ||||
−0.863510 | + | 0.504331i | \(0.831739\pi\) | |||||||
\(812\) | 37.3800 | 1.31178 | ||||||||
\(813\) | −21.3796 | −0.749817 | ||||||||
\(814\) | 0.320239 | 0.0112244 | ||||||||
\(815\) | 20.9587 | 0.734152 | ||||||||
\(816\) | −8.47952 | −0.296843 | ||||||||
\(817\) | −24.9147 | −0.871654 | ||||||||
\(818\) | −92.9093 | −3.24850 | ||||||||
\(819\) | 3.45200 | 0.120623 | ||||||||
\(820\) | 106.741 | 3.72756 | ||||||||
\(821\) | 8.57676 | 0.299331 | 0.149666 | − | 0.988737i | \(-0.452180\pi\) | ||||
0.149666 | + | 0.988737i | \(0.452180\pi\) | |||||||
\(822\) | −11.4533 | −0.399478 | ||||||||
\(823\) | 1.25206 | 0.0436442 | 0.0218221 | − | 0.999762i | \(-0.493053\pi\) | ||||
0.0218221 | + | 0.999762i | \(0.493053\pi\) | |||||||
\(824\) | −53.5681 | −1.86613 | ||||||||
\(825\) | 0.0180472 | 0.000628321 0 | ||||||||
\(826\) | −27.1787 | −0.945669 | ||||||||
\(827\) | 38.9584 | 1.35472 | 0.677358 | − | 0.735654i | \(-0.263125\pi\) | ||||
0.677358 | + | 0.735654i | \(0.263125\pi\) | |||||||
\(828\) | 0.158085 | 0.00549383 | ||||||||
\(829\) | 10.3655 | 0.360008 | 0.180004 | − | 0.983666i | \(-0.442389\pi\) | ||||
0.180004 | + | 0.983666i | \(0.442389\pi\) | |||||||
\(830\) | 37.0968 | 1.28765 | ||||||||
\(831\) | 21.3761 | 0.741528 | ||||||||
\(832\) | −9.05226 | −0.313831 | ||||||||
\(833\) | 4.71171 | 0.163251 | ||||||||
\(834\) | −39.9999 | −1.38508 | ||||||||
\(835\) | 1.04884 | 0.0362967 | ||||||||
\(836\) | 0.500775 | 0.0173197 | ||||||||
\(837\) | 5.40462 | 0.186811 | ||||||||
\(838\) | −16.8935 | −0.583576 | ||||||||
\(839\) | −16.4567 | −0.568147 | −0.284073 | − | 0.958803i | \(-0.591686\pi\) | ||||
−0.284073 | + | 0.958803i | \(0.591686\pi\) | |||||||
\(840\) | 24.7651 | 0.854479 | ||||||||
\(841\) | −1.01893 | −0.0351355 | ||||||||
\(842\) | −3.25252 | −0.112089 | ||||||||
\(843\) | −11.0237 | −0.379677 | ||||||||
\(844\) | −118.608 | −4.08266 | ||||||||
\(845\) | −18.4886 | −0.636027 | ||||||||
\(846\) | 20.1615 | 0.693167 | ||||||||
\(847\) | 16.6386 | 0.571708 | ||||||||
\(848\) | −39.5253 | −1.35730 | ||||||||
\(849\) | 11.1859 | 0.383898 | ||||||||
\(850\) | 1.62554 | 0.0557555 | ||||||||
\(851\) | −0.146313 | −0.00501554 | ||||||||
\(852\) | −67.0006 | −2.29540 | ||||||||
\(853\) | −14.1523 | −0.484566 | −0.242283 | − | 0.970206i | \(-0.577896\pi\) | ||||
−0.242283 | + | 0.970206i | \(0.577896\pi\) | |||||||
\(854\) | 46.9990 | 1.60827 | ||||||||
\(855\) | 8.86949 | 0.303330 | ||||||||
\(856\) | −12.8252 | −0.438358 | ||||||||
\(857\) | −35.3956 | −1.20909 | −0.604545 | − | 0.796571i | \(-0.706645\pi\) | ||||
−0.604545 | + | 0.796571i | \(0.706645\pi\) | |||||||
\(858\) | 0.169024 | 0.00577037 | ||||||||
\(859\) | −7.80266 | −0.266223 | −0.133112 | − | 0.991101i | \(-0.542497\pi\) | ||||
−0.133112 | + | 0.991101i | \(0.542497\pi\) | |||||||
\(860\) | −73.8696 | −2.51893 | ||||||||
\(861\) | −14.5682 | −0.496484 | ||||||||
\(862\) | −92.4838 | −3.15001 | ||||||||
\(863\) | −43.0230 | −1.46452 | −0.732260 | − | 0.681026i | \(-0.761534\pi\) | ||||
−0.732260 | + | 0.681026i | \(0.761534\pi\) | |||||||
\(864\) | −8.10165 | −0.275624 | ||||||||
\(865\) | −48.4138 | −1.64612 | ||||||||
\(866\) | 53.9130 | 1.83204 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −38.1920 | −1.29632 | ||||||||
\(869\) | 0.226131 | 0.00767098 | ||||||||
\(870\) | 32.4169 | 1.09903 | ||||||||
\(871\) | 24.8360 | 0.841536 | ||||||||
\(872\) | −62.6783 | −2.12256 | ||||||||
\(873\) | −17.9042 | −0.605967 | ||||||||
\(874\) | −0.326753 | −0.0110526 | ||||||||
\(875\) | 15.6867 | 0.530307 | ||||||||
\(876\) | 30.3660 | 1.02597 | ||||||||
\(877\) | −11.9359 | −0.403048 | −0.201524 | − | 0.979484i | \(-0.564589\pi\) | ||||
−0.201524 | + | 0.979484i | \(0.564589\pi\) | |||||||
\(878\) | 94.5564 | 3.19113 | ||||||||
\(879\) | −14.6330 | −0.493559 | ||||||||
\(880\) | 0.576928 | 0.0194483 | ||||||||
\(881\) | −57.4822 | −1.93662 | −0.968312 | − | 0.249742i | \(-0.919654\pi\) | ||||
−0.968312 | + | 0.249742i | \(0.919654\pi\) | |||||||
\(882\) | 12.1699 | 0.409783 | ||||||||
\(883\) | 3.38181 | 0.113807 | 0.0569035 | − | 0.998380i | \(-0.481877\pi\) | ||||
0.0569035 | + | 0.998380i | \(0.481877\pi\) | |||||||
\(884\) | 10.6602 | 0.358543 | ||||||||
\(885\) | −16.5041 | −0.554780 | ||||||||
\(886\) | −31.7082 | −1.06526 | ||||||||
\(887\) | −21.2891 | −0.714818 | −0.357409 | − | 0.933948i | \(-0.616340\pi\) | ||||
−0.357409 | + | 0.933948i | \(0.616340\pi\) | |||||||
\(888\) | 29.8332 | 1.00114 | ||||||||
\(889\) | −12.8919 | −0.432381 | ||||||||
\(890\) | −88.7205 | −2.97392 | ||||||||
\(891\) | 0.0286762 | 0.000960689 0 | ||||||||
\(892\) | 12.2733 | 0.410939 | ||||||||
\(893\) | −29.1798 | −0.976465 | ||||||||
\(894\) | 62.4395 | 2.08829 | ||||||||
\(895\) | −17.7040 | −0.591781 | ||||||||
\(896\) | −9.01175 | −0.301062 | ||||||||
\(897\) | −0.0772245 | −0.00257845 | ||||||||
\(898\) | 107.681 | 3.59336 | ||||||||
\(899\) | −28.5889 | −0.953494 | ||||||||
\(900\) | 2.93994 | 0.0979980 | ||||||||
\(901\) | 4.66126 | 0.155289 | ||||||||
\(902\) | −0.713318 | −0.0237509 | ||||||||
\(903\) | 10.0819 | 0.335503 | ||||||||
\(904\) | 100.081 | 3.32866 | ||||||||
\(905\) | 30.7469 | 1.02206 | ||||||||
\(906\) | 22.5877 | 0.750426 | ||||||||
\(907\) | −5.16508 | −0.171504 | −0.0857518 | − | 0.996317i | \(-0.527329\pi\) | ||||
−0.0857518 | + | 0.996317i | \(0.527329\pi\) | |||||||
\(908\) | 69.5372 | 2.30767 | ||||||||
\(909\) | 3.95845 | 0.131294 | ||||||||
\(910\) | −21.1549 | −0.701277 | ||||||||
\(911\) | 26.6273 | 0.882203 | 0.441101 | − | 0.897457i | \(-0.354588\pi\) | ||||
0.441101 | + | 0.897457i | \(0.354588\pi\) | |||||||
\(912\) | 31.6987 | 1.04965 | ||||||||
\(913\) | −0.173588 | −0.00574492 | ||||||||
\(914\) | −66.3113 | −2.19338 | ||||||||
\(915\) | 28.5399 | 0.943499 | ||||||||
\(916\) | −60.8241 | −2.00969 | ||||||||
\(917\) | −5.52557 | −0.182470 | ||||||||
\(918\) | 2.58291 | 0.0852489 | ||||||||
\(919\) | 16.5329 | 0.545372 | 0.272686 | − | 0.962103i | \(-0.412088\pi\) | ||||
0.272686 | + | 0.962103i | \(0.412088\pi\) | |||||||
\(920\) | −0.554019 | −0.0182655 | ||||||||
\(921\) | −17.6730 | −0.582346 | ||||||||
\(922\) | −71.5897 | −2.35768 | ||||||||
\(923\) | 32.7298 | 1.07731 | ||||||||
\(924\) | −0.202642 | −0.00666642 | ||||||||
\(925\) | −2.72101 | −0.0894663 | ||||||||
\(926\) | 2.57605 | 0.0846542 | ||||||||
\(927\) | 7.76336 | 0.254982 | ||||||||
\(928\) | 42.8554 | 1.40680 | ||||||||
\(929\) | −27.5828 | −0.904963 | −0.452481 | − | 0.891774i | \(-0.649461\pi\) | ||||
−0.452481 | + | 0.891774i | \(0.649461\pi\) | |||||||
\(930\) | −33.1211 | −1.08608 | ||||||||
\(931\) | −17.6136 | −0.577263 | ||||||||
\(932\) | −102.765 | −3.36617 | ||||||||
\(933\) | 11.9994 | 0.392841 | ||||||||
\(934\) | 107.637 | 3.52200 | ||||||||
\(935\) | −0.0680378 | −0.00222508 | ||||||||
\(936\) | 15.7461 | 0.514677 | ||||||||
\(937\) | 16.6308 | 0.543304 | 0.271652 | − | 0.962396i | \(-0.412430\pi\) | ||||
0.271652 | + | 0.962396i | \(0.412430\pi\) | |||||||
\(938\) | −42.5237 | −1.38845 | ||||||||
\(939\) | 23.4022 | 0.763701 | ||||||||
\(940\) | −86.5153 | −2.82182 | ||||||||
\(941\) | −36.7704 | −1.19868 | −0.599341 | − | 0.800494i | \(-0.704571\pi\) | ||||
−0.599341 | + | 0.800494i | \(0.704571\pi\) | |||||||
\(942\) | −2.58291 | −0.0841559 | ||||||||
\(943\) | 0.325905 | 0.0106129 | ||||||||
\(944\) | −58.9842 | −1.91977 | ||||||||
\(945\) | −3.58909 | −0.116753 | ||||||||
\(946\) | 0.493648 | 0.0160499 | ||||||||
\(947\) | 48.1935 | 1.56608 | 0.783039 | − | 0.621972i | \(-0.213668\pi\) | ||||
0.783039 | + | 0.621972i | \(0.213668\pi\) | |||||||
\(948\) | 36.8376 | 1.19643 | ||||||||
\(949\) | −14.8338 | −0.481525 | ||||||||
\(950\) | −6.07669 | −0.197154 | ||||||||
\(951\) | 30.6745 | 0.994690 | ||||||||
\(952\) | −10.4379 | −0.338293 | ||||||||
\(953\) | 21.7547 | 0.704704 | 0.352352 | − | 0.935868i | \(-0.385382\pi\) | ||||
0.352352 | + | 0.935868i | \(0.385382\pi\) | |||||||
\(954\) | 12.0396 | 0.389798 | ||||||||
\(955\) | 27.0397 | 0.874983 | ||||||||
\(956\) | −53.1896 | −1.72027 | ||||||||
\(957\) | −0.151689 | −0.00490341 | ||||||||
\(958\) | −12.5611 | −0.405830 | ||||||||
\(959\) | −6.70771 | −0.216603 | ||||||||
\(960\) | 9.41175 | 0.303763 | ||||||||
\(961\) | −1.79004 | −0.0577431 | ||||||||
\(962\) | −25.4841 | −0.821640 | ||||||||
\(963\) | 1.85870 | 0.0598957 | ||||||||
\(964\) | 18.7964 | 0.605392 | ||||||||
\(965\) | 47.4933 | 1.52886 | ||||||||
\(966\) | 0.132222 | 0.00425418 | ||||||||
\(967\) | −17.3147 | −0.556805 | −0.278402 | − | 0.960465i | \(-0.589805\pi\) | ||||
−0.278402 | + | 0.960465i | \(0.589805\pi\) | |||||||
\(968\) | 75.8956 | 2.43938 | ||||||||
\(969\) | −3.73826 | −0.120090 | ||||||||
\(970\) | 109.722 | 3.52297 | ||||||||
\(971\) | 9.92492 | 0.318506 | 0.159253 | − | 0.987238i | \(-0.449091\pi\) | ||||
0.159253 | + | 0.987238i | \(0.449091\pi\) | |||||||
\(972\) | 4.67145 | 0.149837 | ||||||||
\(973\) | −23.4263 | −0.751013 | ||||||||
\(974\) | 51.7989 | 1.65974 | ||||||||
\(975\) | −1.43616 | −0.0459940 | ||||||||
\(976\) | 101.999 | 3.26490 | ||||||||
\(977\) | 13.8017 | 0.441556 | 0.220778 | − | 0.975324i | \(-0.429140\pi\) | ||||
0.220778 | + | 0.975324i | \(0.429140\pi\) | |||||||
\(978\) | −22.8163 | −0.729586 | ||||||||
\(979\) | 0.415152 | 0.0132683 | ||||||||
\(980\) | −52.2227 | −1.66819 | ||||||||
\(981\) | 9.08366 | 0.290019 | ||||||||
\(982\) | 19.5784 | 0.624772 | ||||||||
\(983\) | 28.3122 | 0.903018 | 0.451509 | − | 0.892267i | \(-0.350886\pi\) | ||||
0.451509 | + | 0.892267i | \(0.350886\pi\) | |||||||
\(984\) | −66.4520 | −2.11841 | ||||||||
\(985\) | −52.8027 | −1.68243 | ||||||||
\(986\) | −13.6629 | −0.435115 | ||||||||
\(987\) | 11.8078 | 0.375846 | ||||||||
\(988\) | −39.8508 | −1.26782 | ||||||||
\(989\) | −0.225541 | −0.00717178 | ||||||||
\(990\) | −0.175736 | −0.00558525 | ||||||||
\(991\) | 20.1767 | 0.640933 | 0.320467 | − | 0.947260i | \(-0.396160\pi\) | ||||
0.320467 | + | 0.947260i | \(0.396160\pi\) | |||||||
\(992\) | −43.7863 | −1.39022 | ||||||||
\(993\) | −5.21080 | −0.165360 | ||||||||
\(994\) | −56.0393 | −1.77746 | ||||||||
\(995\) | 2.00789 | 0.0636545 | ||||||||
\(996\) | −28.2780 | −0.896024 | ||||||||
\(997\) | −33.4910 | −1.06067 | −0.530335 | − | 0.847788i | \(-0.677934\pi\) | ||||
−0.530335 | + | 0.847788i | \(0.677934\pi\) | |||||||
\(998\) | 54.4848 | 1.72469 | ||||||||
\(999\) | −4.32358 | −0.136792 |
(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 | 8007.2.a.e.1.4 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.e.1.4 | ✓ | 46 | 1.1 | even | 1 | trivial |