Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.223362 | −0.157941 | −0.0789704 | − | 0.996877i | \(-0.525163\pi\) | ||||
−0.0789704 | + | 0.996877i | \(0.525163\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.95011 | −0.975055 | ||||||||
\(5\) | 1.64565 | 0.735957 | 0.367979 | − | 0.929834i | \(-0.380050\pi\) | ||||
0.367979 | + | 0.929834i | \(0.380050\pi\) | |||||||
\(6\) | −0.223362 | −0.0911871 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.882304 | 0.311942 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.367576 | −0.116238 | ||||||||
\(11\) | 4.86719 | 1.46751 | 0.733756 | − | 0.679413i | \(-0.237765\pi\) | ||||
0.733756 | + | 0.679413i | \(0.237765\pi\) | |||||||
\(12\) | −1.95011 | −0.562948 | ||||||||
\(13\) | 4.77509 | 1.32437 | 0.662186 | − | 0.749340i | \(-0.269629\pi\) | ||||
0.662186 | + | 0.749340i | \(0.269629\pi\) | |||||||
\(14\) | 0.223362 | 0.0596960 | ||||||||
\(15\) | 1.64565 | 0.424905 | ||||||||
\(16\) | 3.70315 | 0.925786 | ||||||||
\(17\) | 2.25251 | 0.546315 | 0.273157 | − | 0.961969i | \(-0.411932\pi\) | ||||
0.273157 | + | 0.961969i | \(0.411932\pi\) | |||||||
\(18\) | −0.223362 | −0.0526469 | ||||||||
\(19\) | −1.51705 | −0.348035 | −0.174018 | − | 0.984743i | \(-0.555675\pi\) | ||||
−0.174018 | + | 0.984743i | \(0.555675\pi\) | |||||||
\(20\) | −3.20920 | −0.717598 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −1.08714 | −0.231780 | ||||||||
\(23\) | −1.56513 | −0.326352 | −0.163176 | − | 0.986597i | \(-0.552174\pi\) | ||||
−0.163176 | + | 0.986597i | \(0.552174\pi\) | |||||||
\(24\) | 0.882304 | 0.180100 | ||||||||
\(25\) | −2.29184 | −0.458367 | ||||||||
\(26\) | −1.06657 | −0.209172 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.95011 | 0.368536 | ||||||||
\(29\) | 5.30592 | 0.985285 | 0.492642 | − | 0.870232i | \(-0.336031\pi\) | ||||
0.492642 | + | 0.870232i | \(0.336031\pi\) | |||||||
\(30\) | −0.367576 | −0.0671098 | ||||||||
\(31\) | −5.90322 | −1.06025 | −0.530125 | − | 0.847919i | \(-0.677855\pi\) | ||||
−0.530125 | + | 0.847919i | \(0.677855\pi\) | |||||||
\(32\) | −2.59175 | −0.458161 | ||||||||
\(33\) | 4.86719 | 0.847269 | ||||||||
\(34\) | −0.503126 | −0.0862853 | ||||||||
\(35\) | −1.64565 | −0.278166 | ||||||||
\(36\) | −1.95011 | −0.325018 | ||||||||
\(37\) | 9.20145 | 1.51271 | 0.756354 | − | 0.654162i | \(-0.226979\pi\) | ||||
0.756354 | + | 0.654162i | \(0.226979\pi\) | |||||||
\(38\) | 0.338851 | 0.0549689 | ||||||||
\(39\) | 4.77509 | 0.764626 | ||||||||
\(40\) | 1.45196 | 0.229576 | ||||||||
\(41\) | −6.69771 | −1.04601 | −0.523004 | − | 0.852330i | \(-0.675189\pi\) | ||||
−0.523004 | + | 0.852330i | \(0.675189\pi\) | |||||||
\(42\) | 0.223362 | 0.0344655 | ||||||||
\(43\) | 9.36637 | 1.42836 | 0.714179 | − | 0.699963i | \(-0.246800\pi\) | ||||
0.714179 | + | 0.699963i | \(0.246800\pi\) | |||||||
\(44\) | −9.49155 | −1.43091 | ||||||||
\(45\) | 1.64565 | 0.245319 | ||||||||
\(46\) | 0.349590 | 0.0515442 | ||||||||
\(47\) | −2.53680 | −0.370030 | −0.185015 | − | 0.982736i | \(-0.559233\pi\) | ||||
−0.185015 | + | 0.982736i | \(0.559233\pi\) | |||||||
\(48\) | 3.70315 | 0.534503 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.511909 | 0.0723949 | ||||||||
\(51\) | 2.25251 | 0.315415 | ||||||||
\(52\) | −9.31195 | −1.29133 | ||||||||
\(53\) | 6.61461 | 0.908587 | 0.454294 | − | 0.890852i | \(-0.349892\pi\) | ||||
0.454294 | + | 0.890852i | \(0.349892\pi\) | |||||||
\(54\) | −0.223362 | −0.0303957 | ||||||||
\(55\) | 8.00969 | 1.08003 | ||||||||
\(56\) | −0.882304 | −0.117903 | ||||||||
\(57\) | −1.51705 | −0.200938 | ||||||||
\(58\) | −1.18514 | −0.155617 | ||||||||
\(59\) | −6.16906 | −0.803143 | −0.401571 | − | 0.915828i | \(-0.631536\pi\) | ||||
−0.401571 | + | 0.915828i | \(0.631536\pi\) | |||||||
\(60\) | −3.20920 | −0.414306 | ||||||||
\(61\) | 7.37451 | 0.944209 | 0.472105 | − | 0.881543i | \(-0.343494\pi\) | ||||
0.472105 | + | 0.881543i | \(0.343494\pi\) | |||||||
\(62\) | 1.31856 | 0.167457 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −6.82739 | −0.853424 | ||||||||
\(65\) | 7.85812 | 0.974680 | ||||||||
\(66\) | −1.08714 | −0.133818 | ||||||||
\(67\) | −0.551822 | −0.0674158 | −0.0337079 | − | 0.999432i | \(-0.510732\pi\) | ||||
−0.0337079 | + | 0.999432i | \(0.510732\pi\) | |||||||
\(68\) | −4.39265 | −0.532687 | ||||||||
\(69\) | −1.56513 | −0.188419 | ||||||||
\(70\) | 0.367576 | 0.0439337 | ||||||||
\(71\) | −10.5578 | −1.25298 | −0.626492 | − | 0.779428i | \(-0.715510\pi\) | ||||
−0.626492 | + | 0.779428i | \(0.715510\pi\) | |||||||
\(72\) | 0.882304 | 0.103981 | ||||||||
\(73\) | 3.39844 | 0.397758 | 0.198879 | − | 0.980024i | \(-0.436270\pi\) | ||||
0.198879 | + | 0.980024i | \(0.436270\pi\) | |||||||
\(74\) | −2.05525 | −0.238918 | ||||||||
\(75\) | −2.29184 | −0.264638 | ||||||||
\(76\) | 2.95841 | 0.339353 | ||||||||
\(77\) | −4.86719 | −0.554668 | ||||||||
\(78\) | −1.06657 | −0.120766 | ||||||||
\(79\) | −11.4131 | −1.28408 | −0.642038 | − | 0.766673i | \(-0.721911\pi\) | ||||
−0.642038 | + | 0.766673i | \(0.721911\pi\) | |||||||
\(80\) | 6.09408 | 0.681339 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.49601 | 0.165207 | ||||||||
\(83\) | −8.33903 | −0.915327 | −0.457664 | − | 0.889125i | \(-0.651314\pi\) | ||||
−0.457664 | + | 0.889125i | \(0.651314\pi\) | |||||||
\(84\) | 1.95011 | 0.212774 | ||||||||
\(85\) | 3.70685 | 0.402064 | ||||||||
\(86\) | −2.09209 | −0.225596 | ||||||||
\(87\) | 5.30592 | 0.568854 | ||||||||
\(88\) | 4.29434 | 0.457778 | ||||||||
\(89\) | −11.6275 | −1.23251 | −0.616254 | − | 0.787547i | \(-0.711351\pi\) | ||||
−0.616254 | + | 0.787547i | \(0.711351\pi\) | |||||||
\(90\) | −0.367576 | −0.0387459 | ||||||||
\(91\) | −4.77509 | −0.500565 | ||||||||
\(92\) | 3.05217 | 0.318211 | ||||||||
\(93\) | −5.90322 | −0.612136 | ||||||||
\(94\) | 0.566624 | 0.0584428 | ||||||||
\(95\) | −2.49653 | −0.256139 | ||||||||
\(96\) | −2.59175 | −0.264519 | ||||||||
\(97\) | 5.63135 | 0.571777 | 0.285889 | − | 0.958263i | \(-0.407711\pi\) | ||||
0.285889 | + | 0.958263i | \(0.407711\pi\) | |||||||
\(98\) | −0.223362 | −0.0225630 | ||||||||
\(99\) | 4.86719 | 0.489171 | ||||||||
\(100\) | 4.46933 | 0.446933 | ||||||||
\(101\) | 9.56571 | 0.951824 | 0.475912 | − | 0.879493i | \(-0.342118\pi\) | ||||
0.475912 | + | 0.879493i | \(0.342118\pi\) | |||||||
\(102\) | −0.503126 | −0.0498168 | ||||||||
\(103\) | −9.20767 | −0.907259 | −0.453629 | − | 0.891190i | \(-0.649871\pi\) | ||||
−0.453629 | + | 0.891190i | \(0.649871\pi\) | |||||||
\(104\) | 4.21308 | 0.413127 | ||||||||
\(105\) | −1.64565 | −0.160599 | ||||||||
\(106\) | −1.47745 | −0.143503 | ||||||||
\(107\) | 18.5977 | 1.79791 | 0.898955 | − | 0.438040i | \(-0.144327\pi\) | ||||
0.898955 | + | 0.438040i | \(0.144327\pi\) | |||||||
\(108\) | −1.95011 | −0.187649 | ||||||||
\(109\) | −10.0096 | −0.958750 | −0.479375 | − | 0.877610i | \(-0.659137\pi\) | ||||
−0.479375 | + | 0.877610i | \(0.659137\pi\) | |||||||
\(110\) | −1.78906 | −0.170580 | ||||||||
\(111\) | 9.20145 | 0.873363 | ||||||||
\(112\) | −3.70315 | −0.349914 | ||||||||
\(113\) | 12.1724 | 1.14509 | 0.572543 | − | 0.819875i | \(-0.305957\pi\) | ||||
0.572543 | + | 0.819875i | \(0.305957\pi\) | |||||||
\(114\) | 0.338851 | 0.0317363 | ||||||||
\(115\) | −2.57565 | −0.240181 | ||||||||
\(116\) | −10.3471 | −0.960706 | ||||||||
\(117\) | 4.77509 | 0.441457 | ||||||||
\(118\) | 1.37793 | 0.126849 | ||||||||
\(119\) | −2.25251 | −0.206487 | ||||||||
\(120\) | 1.45196 | 0.132546 | ||||||||
\(121\) | 12.6895 | 1.15359 | ||||||||
\(122\) | −1.64718 | −0.149129 | ||||||||
\(123\) | −6.69771 | −0.603913 | ||||||||
\(124\) | 11.5119 | 1.03380 | ||||||||
\(125\) | −11.9998 | −1.07330 | ||||||||
\(126\) | 0.223362 | 0.0198987 | ||||||||
\(127\) | 21.4700 | 1.90515 | 0.952577 | − | 0.304298i | \(-0.0984220\pi\) | ||||
0.952577 | + | 0.304298i | \(0.0984220\pi\) | |||||||
\(128\) | 6.70848 | 0.592951 | ||||||||
\(129\) | 9.36637 | 0.824663 | ||||||||
\(130\) | −1.75521 | −0.153942 | ||||||||
\(131\) | −0.303802 | −0.0265433 | −0.0132717 | − | 0.999912i | \(-0.504225\pi\) | ||||
−0.0132717 | + | 0.999912i | \(0.504225\pi\) | |||||||
\(132\) | −9.49155 | −0.826134 | ||||||||
\(133\) | 1.51705 | 0.131545 | ||||||||
\(134\) | 0.123256 | 0.0106477 | ||||||||
\(135\) | 1.64565 | 0.141635 | ||||||||
\(136\) | 1.98740 | 0.170418 | ||||||||
\(137\) | −0.770104 | −0.0657944 | −0.0328972 | − | 0.999459i | \(-0.510473\pi\) | ||||
−0.0328972 | + | 0.999459i | \(0.510473\pi\) | |||||||
\(138\) | 0.349590 | 0.0297591 | ||||||||
\(139\) | −7.08197 | −0.600685 | −0.300343 | − | 0.953831i | \(-0.597101\pi\) | ||||
−0.300343 | + | 0.953831i | \(0.597101\pi\) | |||||||
\(140\) | 3.20920 | 0.271227 | ||||||||
\(141\) | −2.53680 | −0.213637 | ||||||||
\(142\) | 2.35822 | 0.197897 | ||||||||
\(143\) | 23.2413 | 1.94353 | ||||||||
\(144\) | 3.70315 | 0.308595 | ||||||||
\(145\) | 8.73169 | 0.725127 | ||||||||
\(146\) | −0.759083 | −0.0628222 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −17.9438 | −1.47497 | ||||||||
\(149\) | 11.3047 | 0.926120 | 0.463060 | − | 0.886327i | \(-0.346751\pi\) | ||||
0.463060 | + | 0.886327i | \(0.346751\pi\) | |||||||
\(150\) | 0.511909 | 0.0417972 | ||||||||
\(151\) | 8.18096 | 0.665757 | 0.332879 | − | 0.942970i | \(-0.391980\pi\) | ||||
0.332879 | + | 0.942970i | \(0.391980\pi\) | |||||||
\(152\) | −1.33850 | −0.108567 | ||||||||
\(153\) | 2.25251 | 0.182105 | ||||||||
\(154\) | 1.08714 | 0.0876046 | ||||||||
\(155\) | −9.71464 | −0.780298 | ||||||||
\(156\) | −9.31195 | −0.745552 | ||||||||
\(157\) | −8.21090 | −0.655301 | −0.327651 | − | 0.944799i | \(-0.606257\pi\) | ||||
−0.327651 | + | 0.944799i | \(0.606257\pi\) | |||||||
\(158\) | 2.54926 | 0.202808 | ||||||||
\(159\) | 6.61461 | 0.524573 | ||||||||
\(160\) | −4.26511 | −0.337187 | ||||||||
\(161\) | 1.56513 | 0.123349 | ||||||||
\(162\) | −0.223362 | −0.0175490 | ||||||||
\(163\) | 13.7864 | 1.07984 | 0.539918 | − | 0.841718i | \(-0.318455\pi\) | ||||
0.539918 | + | 0.841718i | \(0.318455\pi\) | |||||||
\(164\) | 13.0613 | 1.01991 | ||||||||
\(165\) | 8.00969 | 0.623553 | ||||||||
\(166\) | 1.86262 | 0.144567 | ||||||||
\(167\) | 9.64070 | 0.746020 | 0.373010 | − | 0.927827i | \(-0.378326\pi\) | ||||
0.373010 | + | 0.927827i | \(0.378326\pi\) | |||||||
\(168\) | −0.882304 | −0.0680712 | ||||||||
\(169\) | 9.80148 | 0.753960 | ||||||||
\(170\) | −0.827968 | −0.0635023 | ||||||||
\(171\) | −1.51705 | −0.116012 | ||||||||
\(172\) | −18.2655 | −1.39273 | ||||||||
\(173\) | 6.30279 | 0.479192 | 0.239596 | − | 0.970873i | \(-0.422985\pi\) | ||||
0.239596 | + | 0.970873i | \(0.422985\pi\) | |||||||
\(174\) | −1.18514 | −0.0898453 | ||||||||
\(175\) | 2.29184 | 0.173247 | ||||||||
\(176\) | 18.0239 | 1.35860 | ||||||||
\(177\) | −6.16906 | −0.463695 | ||||||||
\(178\) | 2.59713 | 0.194663 | ||||||||
\(179\) | −7.80163 | −0.583121 | −0.291561 | − | 0.956552i | \(-0.594175\pi\) | ||||
−0.291561 | + | 0.956552i | \(0.594175\pi\) | |||||||
\(180\) | −3.20920 | −0.239199 | ||||||||
\(181\) | 25.2714 | 1.87841 | 0.939204 | − | 0.343360i | \(-0.111565\pi\) | ||||
0.939204 | + | 0.343360i | \(0.111565\pi\) | |||||||
\(182\) | 1.06657 | 0.0790597 | ||||||||
\(183\) | 7.37451 | 0.545139 | ||||||||
\(184\) | −1.38092 | −0.101803 | ||||||||
\(185\) | 15.1424 | 1.11329 | ||||||||
\(186\) | 1.31856 | 0.0966812 | ||||||||
\(187\) | 10.9634 | 0.801724 | ||||||||
\(188\) | 4.94704 | 0.360800 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0.557631 | 0.0404548 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | −6.82739 | −0.492725 | ||||||||
\(193\) | 23.5978 | 1.69861 | 0.849303 | − | 0.527906i | \(-0.177023\pi\) | ||||
0.849303 | + | 0.527906i | \(0.177023\pi\) | |||||||
\(194\) | −1.25783 | −0.0903069 | ||||||||
\(195\) | 7.85812 | 0.562732 | ||||||||
\(196\) | −1.95011 | −0.139294 | ||||||||
\(197\) | −14.6505 | −1.04381 | −0.521904 | − | 0.853004i | \(-0.674778\pi\) | ||||
−0.521904 | + | 0.853004i | \(0.674778\pi\) | |||||||
\(198\) | −1.08714 | −0.0772600 | ||||||||
\(199\) | −21.1058 | −1.49615 | −0.748076 | − | 0.663614i | \(-0.769022\pi\) | ||||
−0.748076 | + | 0.663614i | \(0.769022\pi\) | |||||||
\(200\) | −2.02210 | −0.142984 | ||||||||
\(201\) | −0.551822 | −0.0389225 | ||||||||
\(202\) | −2.13662 | −0.150332 | ||||||||
\(203\) | −5.30592 | −0.372403 | ||||||||
\(204\) | −4.39265 | −0.307547 | ||||||||
\(205\) | −11.0221 | −0.769816 | ||||||||
\(206\) | 2.05664 | 0.143293 | ||||||||
\(207\) | −1.56513 | −0.108784 | ||||||||
\(208\) | 17.6829 | 1.22609 | ||||||||
\(209\) | −7.38377 | −0.510746 | ||||||||
\(210\) | 0.367576 | 0.0253651 | ||||||||
\(211\) | −5.58343 | −0.384379 | −0.192190 | − | 0.981358i | \(-0.561559\pi\) | ||||
−0.192190 | + | 0.981358i | \(0.561559\pi\) | |||||||
\(212\) | −12.8992 | −0.885922 | ||||||||
\(213\) | −10.5578 | −0.723411 | ||||||||
\(214\) | −4.15403 | −0.283963 | ||||||||
\(215\) | 15.4138 | 1.05121 | ||||||||
\(216\) | 0.882304 | 0.0600332 | ||||||||
\(217\) | 5.90322 | 0.400737 | ||||||||
\(218\) | 2.23577 | 0.151426 | ||||||||
\(219\) | 3.39844 | 0.229646 | ||||||||
\(220\) | −15.6198 | −1.05308 | ||||||||
\(221\) | 10.7559 | 0.723523 | ||||||||
\(222\) | −2.05525 | −0.137940 | ||||||||
\(223\) | 23.8421 | 1.59658 | 0.798292 | − | 0.602271i | \(-0.205737\pi\) | ||||
0.798292 | + | 0.602271i | \(0.205737\pi\) | |||||||
\(224\) | 2.59175 | 0.173169 | ||||||||
\(225\) | −2.29184 | −0.152789 | ||||||||
\(226\) | −2.71886 | −0.180856 | ||||||||
\(227\) | 13.9517 | 0.926005 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(228\) | 2.95841 | 0.195926 | ||||||||
\(229\) | −0.970158 | −0.0641099 | −0.0320549 | − | 0.999486i | \(-0.510205\pi\) | ||||
−0.0320549 | + | 0.999486i | \(0.510205\pi\) | |||||||
\(230\) | 0.575303 | 0.0379343 | ||||||||
\(231\) | −4.86719 | −0.320238 | ||||||||
\(232\) | 4.68143 | 0.307351 | ||||||||
\(233\) | 12.6698 | 0.830027 | 0.415013 | − | 0.909815i | \(-0.363777\pi\) | ||||
0.415013 | + | 0.909815i | \(0.363777\pi\) | |||||||
\(234\) | −1.06657 | −0.0697241 | ||||||||
\(235\) | −4.17468 | −0.272326 | ||||||||
\(236\) | 12.0303 | 0.783108 | ||||||||
\(237\) | −11.4131 | −0.741362 | ||||||||
\(238\) | 0.503126 | 0.0326128 | ||||||||
\(239\) | −6.15618 | −0.398210 | −0.199105 | − | 0.979978i | \(-0.563804\pi\) | ||||
−0.199105 | + | 0.979978i | \(0.563804\pi\) | |||||||
\(240\) | 6.09408 | 0.393371 | ||||||||
\(241\) | 10.2118 | 0.657798 | 0.328899 | − | 0.944365i | \(-0.393322\pi\) | ||||
0.328899 | + | 0.944365i | \(0.393322\pi\) | |||||||
\(242\) | −2.83436 | −0.182199 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −14.3811 | −0.920656 | ||||||||
\(245\) | 1.64565 | 0.105137 | ||||||||
\(246\) | 1.49601 | 0.0953824 | ||||||||
\(247\) | −7.24405 | −0.460928 | ||||||||
\(248\) | −5.20844 | −0.330736 | ||||||||
\(249\) | −8.33903 | −0.528464 | ||||||||
\(250\) | 2.68030 | 0.169517 | ||||||||
\(251\) | 7.90110 | 0.498713 | 0.249356 | − | 0.968412i | \(-0.419781\pi\) | ||||
0.249356 | + | 0.968412i | \(0.419781\pi\) | |||||||
\(252\) | 1.95011 | 0.122845 | ||||||||
\(253\) | −7.61777 | −0.478925 | ||||||||
\(254\) | −4.79558 | −0.300901 | ||||||||
\(255\) | 3.70685 | 0.232132 | ||||||||
\(256\) | 12.1564 | 0.759773 | ||||||||
\(257\) | −28.0298 | −1.74845 | −0.874227 | − | 0.485518i | \(-0.838631\pi\) | ||||
−0.874227 | + | 0.485518i | \(0.838631\pi\) | |||||||
\(258\) | −2.09209 | −0.130248 | ||||||||
\(259\) | −9.20145 | −0.571750 | ||||||||
\(260\) | −15.3242 | −0.950367 | ||||||||
\(261\) | 5.30592 | 0.328428 | ||||||||
\(262\) | 0.0678578 | 0.00419227 | ||||||||
\(263\) | −15.3246 | −0.944954 | −0.472477 | − | 0.881343i | \(-0.656640\pi\) | ||||
−0.472477 | + | 0.881343i | \(0.656640\pi\) | |||||||
\(264\) | 4.29434 | 0.264298 | ||||||||
\(265\) | 10.8853 | 0.668681 | ||||||||
\(266\) | −0.338851 | −0.0207763 | ||||||||
\(267\) | −11.6275 | −0.711589 | ||||||||
\(268\) | 1.07611 | 0.0657341 | ||||||||
\(269\) | 2.50287 | 0.152603 | 0.0763014 | − | 0.997085i | \(-0.475689\pi\) | ||||
0.0763014 | + | 0.997085i | \(0.475689\pi\) | |||||||
\(270\) | −0.367576 | −0.0223699 | ||||||||
\(271\) | −6.89447 | −0.418809 | −0.209405 | − | 0.977829i | \(-0.567153\pi\) | ||||
−0.209405 | + | 0.977829i | \(0.567153\pi\) | |||||||
\(272\) | 8.34138 | 0.505771 | ||||||||
\(273\) | −4.77509 | −0.289002 | ||||||||
\(274\) | 0.172012 | 0.0103916 | ||||||||
\(275\) | −11.1548 | −0.672660 | ||||||||
\(276\) | 3.05217 | 0.183719 | ||||||||
\(277\) | −24.9943 | −1.50176 | −0.750882 | − | 0.660436i | \(-0.770371\pi\) | ||||
−0.750882 | + | 0.660436i | \(0.770371\pi\) | |||||||
\(278\) | 1.58184 | 0.0948726 | ||||||||
\(279\) | −5.90322 | −0.353417 | ||||||||
\(280\) | −1.45196 | −0.0867714 | ||||||||
\(281\) | 21.3653 | 1.27455 | 0.637273 | − | 0.770638i | \(-0.280062\pi\) | ||||
0.637273 | + | 0.770638i | \(0.280062\pi\) | |||||||
\(282\) | 0.566624 | 0.0337420 | ||||||||
\(283\) | −9.44217 | −0.561279 | −0.280639 | − | 0.959813i | \(-0.590547\pi\) | ||||
−0.280639 | + | 0.959813i | \(0.590547\pi\) | |||||||
\(284\) | 20.5889 | 1.22173 | ||||||||
\(285\) | −2.49653 | −0.147882 | ||||||||
\(286\) | −5.19121 | −0.306963 | ||||||||
\(287\) | 6.69771 | 0.395354 | ||||||||
\(288\) | −2.59175 | −0.152720 | ||||||||
\(289\) | −11.9262 | −0.701540 | ||||||||
\(290\) | −1.95033 | −0.114527 | ||||||||
\(291\) | 5.63135 | 0.330116 | ||||||||
\(292\) | −6.62734 | −0.387836 | ||||||||
\(293\) | −3.95148 | −0.230848 | −0.115424 | − | 0.993316i | \(-0.536823\pi\) | ||||
−0.115424 | + | 0.993316i | \(0.536823\pi\) | |||||||
\(294\) | −0.223362 | −0.0130267 | ||||||||
\(295\) | −10.1521 | −0.591079 | ||||||||
\(296\) | 8.11847 | 0.471877 | ||||||||
\(297\) | 4.86719 | 0.282423 | ||||||||
\(298\) | −2.52505 | −0.146272 | ||||||||
\(299\) | −7.47362 | −0.432211 | ||||||||
\(300\) | 4.46933 | 0.258037 | ||||||||
\(301\) | −9.36637 | −0.539869 | ||||||||
\(302\) | −1.82732 | −0.105150 | ||||||||
\(303\) | 9.56571 | 0.549536 | ||||||||
\(304\) | −5.61786 | −0.322206 | ||||||||
\(305\) | 12.1359 | 0.694897 | ||||||||
\(306\) | −0.503126 | −0.0287618 | ||||||||
\(307\) | 23.8890 | 1.36342 | 0.681708 | − | 0.731624i | \(-0.261237\pi\) | ||||
0.681708 | + | 0.731624i | \(0.261237\pi\) | |||||||
\(308\) | 9.49155 | 0.540831 | ||||||||
\(309\) | −9.20767 | −0.523806 | ||||||||
\(310\) | 2.16988 | 0.123241 | ||||||||
\(311\) | −7.71261 | −0.437342 | −0.218671 | − | 0.975799i | \(-0.570172\pi\) | ||||
−0.218671 | + | 0.975799i | \(0.570172\pi\) | |||||||
\(312\) | 4.21308 | 0.238519 | ||||||||
\(313\) | −12.5329 | −0.708402 | −0.354201 | − | 0.935169i | \(-0.615247\pi\) | ||||
−0.354201 | + | 0.935169i | \(0.615247\pi\) | |||||||
\(314\) | 1.83400 | 0.103499 | ||||||||
\(315\) | −1.64565 | −0.0927219 | ||||||||
\(316\) | 22.2568 | 1.25204 | ||||||||
\(317\) | 0.316613 | 0.0177828 | 0.00889138 | − | 0.999960i | \(-0.497170\pi\) | ||||
0.00889138 | + | 0.999960i | \(0.497170\pi\) | |||||||
\(318\) | −1.47745 | −0.0828514 | ||||||||
\(319\) | 25.8249 | 1.44592 | ||||||||
\(320\) | −11.2355 | −0.628083 | ||||||||
\(321\) | 18.5977 | 1.03802 | ||||||||
\(322\) | −0.349590 | −0.0194819 | ||||||||
\(323\) | −3.41718 | −0.190137 | ||||||||
\(324\) | −1.95011 | −0.108339 | ||||||||
\(325\) | −10.9437 | −0.607049 | ||||||||
\(326\) | −3.07936 | −0.170550 | ||||||||
\(327\) | −10.0096 | −0.553535 | ||||||||
\(328\) | −5.90942 | −0.326293 | ||||||||
\(329\) | 2.53680 | 0.139858 | ||||||||
\(330\) | −1.78906 | −0.0984845 | ||||||||
\(331\) | 1.81798 | 0.0999254 | 0.0499627 | − | 0.998751i | \(-0.484090\pi\) | ||||
0.0499627 | + | 0.998751i | \(0.484090\pi\) | |||||||
\(332\) | 16.2620 | 0.892494 | ||||||||
\(333\) | 9.20145 | 0.504236 | ||||||||
\(334\) | −2.15337 | −0.117827 | ||||||||
\(335\) | −0.908106 | −0.0496151 | ||||||||
\(336\) | −3.70315 | −0.202023 | ||||||||
\(337\) | −3.17086 | −0.172728 | −0.0863638 | − | 0.996264i | \(-0.527525\pi\) | ||||
−0.0863638 | + | 0.996264i | \(0.527525\pi\) | |||||||
\(338\) | −2.18928 | −0.119081 | ||||||||
\(339\) | 12.1724 | 0.661116 | ||||||||
\(340\) | −7.22876 | −0.392034 | ||||||||
\(341\) | −28.7321 | −1.55593 | ||||||||
\(342\) | 0.338851 | 0.0183230 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 8.26399 | 0.445564 | ||||||||
\(345\) | −2.57565 | −0.138668 | ||||||||
\(346\) | −1.40780 | −0.0756840 | ||||||||
\(347\) | −25.3635 | −1.36158 | −0.680791 | − | 0.732478i | \(-0.738364\pi\) | ||||
−0.680791 | + | 0.732478i | \(0.738364\pi\) | |||||||
\(348\) | −10.3471 | −0.554664 | ||||||||
\(349\) | −1.31709 | −0.0705023 | −0.0352511 | − | 0.999378i | \(-0.511223\pi\) | ||||
−0.0352511 | + | 0.999378i | \(0.511223\pi\) | |||||||
\(350\) | −0.511909 | −0.0273627 | ||||||||
\(351\) | 4.77509 | 0.254875 | ||||||||
\(352\) | −12.6145 | −0.672357 | ||||||||
\(353\) | 16.2871 | 0.866877 | 0.433438 | − | 0.901183i | \(-0.357300\pi\) | ||||
0.433438 | + | 0.901183i | \(0.357300\pi\) | |||||||
\(354\) | 1.37793 | 0.0732363 | ||||||||
\(355\) | −17.3745 | −0.922143 | ||||||||
\(356\) | 22.6748 | 1.20176 | ||||||||
\(357\) | −2.25251 | −0.119216 | ||||||||
\(358\) | 1.74259 | 0.0920986 | ||||||||
\(359\) | 15.9051 | 0.839437 | 0.419719 | − | 0.907654i | \(-0.362129\pi\) | ||||
0.419719 | + | 0.907654i | \(0.362129\pi\) | |||||||
\(360\) | 1.45196 | 0.0765252 | ||||||||
\(361\) | −16.6986 | −0.878871 | ||||||||
\(362\) | −5.64467 | −0.296677 | ||||||||
\(363\) | 12.6895 | 0.666028 | ||||||||
\(364\) | 9.31195 | 0.488079 | ||||||||
\(365\) | 5.59265 | 0.292733 | ||||||||
\(366\) | −1.64718 | −0.0860997 | ||||||||
\(367\) | −8.20766 | −0.428436 | −0.214218 | − | 0.976786i | \(-0.568720\pi\) | ||||
−0.214218 | + | 0.976786i | \(0.568720\pi\) | |||||||
\(368\) | −5.79590 | −0.302132 | ||||||||
\(369\) | −6.69771 | −0.348669 | ||||||||
\(370\) | −3.38223 | −0.175834 | ||||||||
\(371\) | −6.61461 | −0.343414 | ||||||||
\(372\) | 11.5119 | 0.596866 | ||||||||
\(373\) | 17.8290 | 0.923150 | 0.461575 | − | 0.887101i | \(-0.347285\pi\) | ||||
0.461575 | + | 0.887101i | \(0.347285\pi\) | |||||||
\(374\) | −2.44881 | −0.126625 | ||||||||
\(375\) | −11.9998 | −0.619668 | ||||||||
\(376\) | −2.23823 | −0.115428 | ||||||||
\(377\) | 25.3362 | 1.30488 | ||||||||
\(378\) | 0.223362 | 0.0114885 | ||||||||
\(379\) | −6.32961 | −0.325130 | −0.162565 | − | 0.986698i | \(-0.551977\pi\) | ||||
−0.162565 | + | 0.986698i | \(0.551977\pi\) | |||||||
\(380\) | 4.86851 | 0.249750 | ||||||||
\(381\) | 21.4700 | 1.09994 | ||||||||
\(382\) | 0.223362 | 0.0114282 | ||||||||
\(383\) | 29.0791 | 1.48587 | 0.742936 | − | 0.669363i | \(-0.233433\pi\) | ||||
0.742936 | + | 0.669363i | \(0.233433\pi\) | |||||||
\(384\) | 6.70848 | 0.342341 | ||||||||
\(385\) | −8.00969 | −0.408212 | ||||||||
\(386\) | −5.27084 | −0.268279 | ||||||||
\(387\) | 9.36637 | 0.476119 | ||||||||
\(388\) | −10.9818 | −0.557514 | ||||||||
\(389\) | 0.0476793 | 0.00241744 | 0.00120872 | − | 0.999999i | \(-0.499615\pi\) | ||||
0.00120872 | + | 0.999999i | \(0.499615\pi\) | |||||||
\(390\) | −1.75521 | −0.0888783 | ||||||||
\(391\) | −3.52547 | −0.178291 | ||||||||
\(392\) | 0.882304 | 0.0445631 | ||||||||
\(393\) | −0.303802 | −0.0153248 | ||||||||
\(394\) | 3.27237 | 0.164860 | ||||||||
\(395\) | −18.7820 | −0.945025 | ||||||||
\(396\) | −9.49155 | −0.476968 | ||||||||
\(397\) | 1.71013 | 0.0858287 | 0.0429144 | − | 0.999079i | \(-0.486336\pi\) | ||||
0.0429144 | + | 0.999079i | \(0.486336\pi\) | |||||||
\(398\) | 4.71423 | 0.236303 | ||||||||
\(399\) | 1.51705 | 0.0759475 | ||||||||
\(400\) | −8.48700 | −0.424350 | ||||||||
\(401\) | 25.3818 | 1.26751 | 0.633753 | − | 0.773535i | \(-0.281513\pi\) | ||||
0.633753 | + | 0.773535i | \(0.281513\pi\) | |||||||
\(402\) | 0.123256 | 0.00614745 | ||||||||
\(403\) | −28.1884 | −1.40416 | ||||||||
\(404\) | −18.6542 | −0.928080 | ||||||||
\(405\) | 1.64565 | 0.0817730 | ||||||||
\(406\) | 1.18514 | 0.0588175 | ||||||||
\(407\) | 44.7852 | 2.21992 | ||||||||
\(408\) | 1.98740 | 0.0983910 | ||||||||
\(409\) | 22.7962 | 1.12720 | 0.563600 | − | 0.826048i | \(-0.309416\pi\) | ||||
0.563600 | + | 0.826048i | \(0.309416\pi\) | |||||||
\(410\) | 2.46192 | 0.121585 | ||||||||
\(411\) | −0.770104 | −0.0379864 | ||||||||
\(412\) | 17.9560 | 0.884627 | ||||||||
\(413\) | 6.16906 | 0.303559 | ||||||||
\(414\) | 0.349590 | 0.0171814 | ||||||||
\(415\) | −13.7231 | −0.673642 | ||||||||
\(416\) | −12.3758 | −0.606775 | ||||||||
\(417\) | −7.08197 | −0.346806 | ||||||||
\(418\) | 1.64925 | 0.0806676 | ||||||||
\(419\) | 32.0283 | 1.56469 | 0.782343 | − | 0.622848i | \(-0.214025\pi\) | ||||
0.782343 | + | 0.622848i | \(0.214025\pi\) | |||||||
\(420\) | 3.20920 | 0.156593 | ||||||||
\(421\) | −30.1308 | −1.46849 | −0.734243 | − | 0.678887i | \(-0.762463\pi\) | ||||
−0.734243 | + | 0.678887i | \(0.762463\pi\) | |||||||
\(422\) | 1.24713 | 0.0607092 | ||||||||
\(423\) | −2.53680 | −0.123343 | ||||||||
\(424\) | 5.83610 | 0.283426 | ||||||||
\(425\) | −5.16239 | −0.250413 | ||||||||
\(426\) | 2.35822 | 0.114256 | ||||||||
\(427\) | −7.37451 | −0.356878 | ||||||||
\(428\) | −36.2676 | −1.75306 | ||||||||
\(429\) | 23.2413 | 1.12210 | ||||||||
\(430\) | −3.44285 | −0.166029 | ||||||||
\(431\) | 24.2478 | 1.16798 | 0.583988 | − | 0.811762i | \(-0.301492\pi\) | ||||
0.583988 | + | 0.811762i | \(0.301492\pi\) | |||||||
\(432\) | 3.70315 | 0.178168 | ||||||||
\(433\) | −27.5399 | −1.32348 | −0.661741 | − | 0.749733i | \(-0.730182\pi\) | ||||
−0.661741 | + | 0.749733i | \(0.730182\pi\) | |||||||
\(434\) | −1.31856 | −0.0632927 | ||||||||
\(435\) | 8.73169 | 0.418652 | ||||||||
\(436\) | 19.5199 | 0.934834 | ||||||||
\(437\) | 2.37438 | 0.113582 | ||||||||
\(438\) | −0.759083 | −0.0362704 | ||||||||
\(439\) | −20.3765 | −0.972519 | −0.486260 | − | 0.873814i | \(-0.661639\pi\) | ||||
−0.486260 | + | 0.873814i | \(0.661639\pi\) | |||||||
\(440\) | 7.06698 | 0.336905 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −2.40247 | −0.114274 | ||||||||
\(443\) | 15.4318 | 0.733189 | 0.366594 | − | 0.930381i | \(-0.380524\pi\) | ||||
0.366594 | + | 0.930381i | \(0.380524\pi\) | |||||||
\(444\) | −17.9438 | −0.851576 | ||||||||
\(445\) | −19.1347 | −0.907073 | ||||||||
\(446\) | −5.32541 | −0.252166 | ||||||||
\(447\) | 11.3047 | 0.534696 | ||||||||
\(448\) | 6.82739 | 0.322564 | ||||||||
\(449\) | 38.3342 | 1.80910 | 0.904551 | − | 0.426366i | \(-0.140207\pi\) | ||||
0.904551 | + | 0.426366i | \(0.140207\pi\) | |||||||
\(450\) | 0.511909 | 0.0241316 | ||||||||
\(451\) | −32.5990 | −1.53503 | ||||||||
\(452\) | −23.7376 | −1.11652 | ||||||||
\(453\) | 8.18096 | 0.384375 | ||||||||
\(454\) | −3.11627 | −0.146254 | ||||||||
\(455\) | −7.85812 | −0.368395 | ||||||||
\(456\) | −1.33850 | −0.0626810 | ||||||||
\(457\) | −29.0968 | −1.36109 | −0.680545 | − | 0.732707i | \(-0.738257\pi\) | ||||
−0.680545 | + | 0.732707i | \(0.738257\pi\) | |||||||
\(458\) | 0.216696 | 0.0101256 | ||||||||
\(459\) | 2.25251 | 0.105138 | ||||||||
\(460\) | 5.02280 | 0.234189 | ||||||||
\(461\) | 0.713652 | 0.0332381 | 0.0166190 | − | 0.999862i | \(-0.494710\pi\) | ||||
0.0166190 | + | 0.999862i | \(0.494710\pi\) | |||||||
\(462\) | 1.08714 | 0.0505785 | ||||||||
\(463\) | −29.8664 | −1.38801 | −0.694005 | − | 0.719970i | \(-0.744155\pi\) | ||||
−0.694005 | + | 0.719970i | \(0.744155\pi\) | |||||||
\(464\) | 19.6486 | 0.912163 | ||||||||
\(465\) | −9.71464 | −0.450506 | ||||||||
\(466\) | −2.82995 | −0.131095 | ||||||||
\(467\) | −14.8655 | −0.687895 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(468\) | −9.31195 | −0.430445 | ||||||||
\(469\) | 0.551822 | 0.0254808 | ||||||||
\(470\) | 0.932465 | 0.0430114 | ||||||||
\(471\) | −8.21090 | −0.378338 | ||||||||
\(472\) | −5.44298 | −0.250534 | ||||||||
\(473\) | 45.5879 | 2.09613 | ||||||||
\(474\) | 2.54926 | 0.117091 | ||||||||
\(475\) | 3.47683 | 0.159528 | ||||||||
\(476\) | 4.39265 | 0.201337 | ||||||||
\(477\) | 6.61461 | 0.302862 | ||||||||
\(478\) | 1.37506 | 0.0628936 | ||||||||
\(479\) | 31.6472 | 1.44600 | 0.722998 | − | 0.690850i | \(-0.242764\pi\) | ||||
0.722998 | + | 0.690850i | \(0.242764\pi\) | |||||||
\(480\) | −4.26511 | −0.194675 | ||||||||
\(481\) | 43.9377 | 2.00339 | ||||||||
\(482\) | −2.28092 | −0.103893 | ||||||||
\(483\) | 1.56513 | 0.0712158 | ||||||||
\(484\) | −24.7460 | −1.12482 | ||||||||
\(485\) | 9.26724 | 0.420804 | ||||||||
\(486\) | −0.223362 | −0.0101319 | ||||||||
\(487\) | −21.2101 | −0.961120 | −0.480560 | − | 0.876962i | \(-0.659567\pi\) | ||||
−0.480560 | + | 0.876962i | \(0.659567\pi\) | |||||||
\(488\) | 6.50656 | 0.294538 | ||||||||
\(489\) | 13.7864 | 0.623444 | ||||||||
\(490\) | −0.367576 | −0.0166054 | ||||||||
\(491\) | −12.4276 | −0.560848 | −0.280424 | − | 0.959876i | \(-0.590475\pi\) | ||||
−0.280424 | + | 0.959876i | \(0.590475\pi\) | |||||||
\(492\) | 13.0613 | 0.588848 | ||||||||
\(493\) | 11.9517 | 0.538275 | ||||||||
\(494\) | 1.61805 | 0.0727993 | ||||||||
\(495\) | 8.00969 | 0.360009 | ||||||||
\(496\) | −21.8605 | −0.981565 | ||||||||
\(497\) | 10.5578 | 0.473584 | ||||||||
\(498\) | 1.86262 | 0.0834661 | ||||||||
\(499\) | −12.9368 | −0.579131 | −0.289566 | − | 0.957158i | \(-0.593511\pi\) | ||||
−0.289566 | + | 0.957158i | \(0.593511\pi\) | |||||||
\(500\) | 23.4009 | 1.04652 | ||||||||
\(501\) | 9.64070 | 0.430715 | ||||||||
\(502\) | −1.76480 | −0.0787671 | ||||||||
\(503\) | 30.0964 | 1.34193 | 0.670967 | − | 0.741487i | \(-0.265879\pi\) | ||||
0.670967 | + | 0.741487i | \(0.265879\pi\) | |||||||
\(504\) | −0.882304 | −0.0393009 | ||||||||
\(505\) | 15.7418 | 0.700501 | ||||||||
\(506\) | 1.70152 | 0.0756418 | ||||||||
\(507\) | 9.80148 | 0.435299 | ||||||||
\(508\) | −41.8688 | −1.85763 | ||||||||
\(509\) | −19.1384 | −0.848296 | −0.424148 | − | 0.905593i | \(-0.639426\pi\) | ||||
−0.424148 | + | 0.905593i | \(0.639426\pi\) | |||||||
\(510\) | −0.827968 | −0.0366631 | ||||||||
\(511\) | −3.39844 | −0.150338 | ||||||||
\(512\) | −16.1322 | −0.712951 | ||||||||
\(513\) | −1.51705 | −0.0669794 | ||||||||
\(514\) | 6.26080 | 0.276152 | ||||||||
\(515\) | −15.1526 | −0.667703 | ||||||||
\(516\) | −18.2655 | −0.804092 | ||||||||
\(517\) | −12.3471 | −0.543024 | ||||||||
\(518\) | 2.05525 | 0.0903026 | ||||||||
\(519\) | 6.30279 | 0.276662 | ||||||||
\(520\) | 6.93326 | 0.304043 | ||||||||
\(521\) | −16.2645 | −0.712560 | −0.356280 | − | 0.934379i | \(-0.615955\pi\) | ||||
−0.356280 | + | 0.934379i | \(0.615955\pi\) | |||||||
\(522\) | −1.18514 | −0.0518722 | ||||||||
\(523\) | −21.4200 | −0.936629 | −0.468315 | − | 0.883562i | \(-0.655139\pi\) | ||||
−0.468315 | + | 0.883562i | \(0.655139\pi\) | |||||||
\(524\) | 0.592447 | 0.0258812 | ||||||||
\(525\) | 2.29184 | 0.100024 | ||||||||
\(526\) | 3.42293 | 0.149247 | ||||||||
\(527\) | −13.2971 | −0.579230 | ||||||||
\(528\) | 18.0239 | 0.784390 | ||||||||
\(529\) | −20.5504 | −0.893495 | ||||||||
\(530\) | −2.43137 | −0.105612 | ||||||||
\(531\) | −6.16906 | −0.267714 | ||||||||
\(532\) | −2.95841 | −0.128264 | ||||||||
\(533\) | −31.9822 | −1.38530 | ||||||||
\(534\) | 2.59713 | 0.112389 | ||||||||
\(535\) | 30.6054 | 1.32319 | ||||||||
\(536\) | −0.486875 | −0.0210298 | ||||||||
\(537\) | −7.80163 | −0.336665 | ||||||||
\(538\) | −0.559047 | −0.0241022 | ||||||||
\(539\) | 4.86719 | 0.209645 | ||||||||
\(540\) | −3.20920 | −0.138102 | ||||||||
\(541\) | 4.31352 | 0.185453 | 0.0927264 | − | 0.995692i | \(-0.470442\pi\) | ||||
0.0927264 | + | 0.995692i | \(0.470442\pi\) | |||||||
\(542\) | 1.53996 | 0.0661470 | ||||||||
\(543\) | 25.2714 | 1.08450 | ||||||||
\(544\) | −5.83795 | −0.250300 | ||||||||
\(545\) | −16.4724 | −0.705599 | ||||||||
\(546\) | 1.06657 | 0.0456451 | ||||||||
\(547\) | −26.3839 | −1.12809 | −0.564047 | − | 0.825743i | \(-0.690756\pi\) | ||||
−0.564047 | + | 0.825743i | \(0.690756\pi\) | |||||||
\(548\) | 1.50179 | 0.0641532 | ||||||||
\(549\) | 7.37451 | 0.314736 | ||||||||
\(550\) | 2.49156 | 0.106240 | ||||||||
\(551\) | −8.04935 | −0.342914 | ||||||||
\(552\) | −1.38092 | −0.0587758 | ||||||||
\(553\) | 11.4131 | 0.485335 | ||||||||
\(554\) | 5.58278 | 0.237190 | ||||||||
\(555\) | 15.1424 | 0.642757 | ||||||||
\(556\) | 13.8106 | 0.585701 | ||||||||
\(557\) | −46.9422 | −1.98901 | −0.994503 | − | 0.104707i | \(-0.966610\pi\) | ||||
−0.994503 | + | 0.104707i | \(0.966610\pi\) | |||||||
\(558\) | 1.31856 | 0.0558189 | ||||||||
\(559\) | 44.7253 | 1.89168 | ||||||||
\(560\) | −6.09408 | −0.257522 | ||||||||
\(561\) | 10.9634 | 0.462875 | ||||||||
\(562\) | −4.77219 | −0.201303 | ||||||||
\(563\) | −3.83498 | −0.161625 | −0.0808126 | − | 0.996729i | \(-0.525752\pi\) | ||||
−0.0808126 | + | 0.996729i | \(0.525752\pi\) | |||||||
\(564\) | 4.94704 | 0.208308 | ||||||||
\(565\) | 20.0316 | 0.842734 | ||||||||
\(566\) | 2.10902 | 0.0886488 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −9.31522 | −0.390858 | ||||||||
\(569\) | −13.3813 | −0.560972 | −0.280486 | − | 0.959858i | \(-0.590496\pi\) | ||||
−0.280486 | + | 0.959858i | \(0.590496\pi\) | |||||||
\(570\) | 0.557631 | 0.0233566 | ||||||||
\(571\) | −43.0700 | −1.80242 | −0.901211 | − | 0.433381i | \(-0.857320\pi\) | ||||
−0.901211 | + | 0.433381i | \(0.857320\pi\) | |||||||
\(572\) | −45.3230 | −1.89505 | ||||||||
\(573\) | −1.00000 | −0.0417756 | ||||||||
\(574\) | −1.49601 | −0.0624424 | ||||||||
\(575\) | 3.58702 | 0.149589 | ||||||||
\(576\) | −6.82739 | −0.284475 | ||||||||
\(577\) | 44.5747 | 1.85567 | 0.927834 | − | 0.372993i | \(-0.121669\pi\) | ||||
0.927834 | + | 0.372993i | \(0.121669\pi\) | |||||||
\(578\) | 2.66386 | 0.110802 | ||||||||
\(579\) | 23.5978 | 0.980690 | ||||||||
\(580\) | −17.0277 | −0.707039 | ||||||||
\(581\) | 8.33903 | 0.345961 | ||||||||
\(582\) | −1.25783 | −0.0521387 | ||||||||
\(583\) | 32.1946 | 1.33336 | ||||||||
\(584\) | 2.99846 | 0.124077 | ||||||||
\(585\) | 7.85812 | 0.324893 | ||||||||
\(586\) | 0.882609 | 0.0364602 | ||||||||
\(587\) | −13.2505 | −0.546906 | −0.273453 | − | 0.961885i | \(-0.588166\pi\) | ||||
−0.273453 | + | 0.961885i | \(0.588166\pi\) | |||||||
\(588\) | −1.95011 | −0.0804212 | ||||||||
\(589\) | 8.95549 | 0.369004 | ||||||||
\(590\) | 2.26759 | 0.0933554 | ||||||||
\(591\) | −14.6505 | −0.602643 | ||||||||
\(592\) | 34.0743 | 1.40045 | ||||||||
\(593\) | −40.2704 | −1.65371 | −0.826853 | − | 0.562418i | \(-0.809871\pi\) | ||||
−0.826853 | + | 0.562418i | \(0.809871\pi\) | |||||||
\(594\) | −1.08714 | −0.0446061 | ||||||||
\(595\) | −3.70685 | −0.151966 | ||||||||
\(596\) | −22.0455 | −0.903018 | ||||||||
\(597\) | −21.1058 | −0.863803 | ||||||||
\(598\) | 1.66932 | 0.0682637 | ||||||||
\(599\) | −21.3921 | −0.874055 | −0.437028 | − | 0.899448i | \(-0.643969\pi\) | ||||
−0.437028 | + | 0.899448i | \(0.643969\pi\) | |||||||
\(600\) | −2.02210 | −0.0825517 | ||||||||
\(601\) | −21.7809 | −0.888463 | −0.444231 | − | 0.895912i | \(-0.646523\pi\) | ||||
−0.444231 | + | 0.895912i | \(0.646523\pi\) | |||||||
\(602\) | 2.09209 | 0.0852673 | ||||||||
\(603\) | −0.551822 | −0.0224719 | ||||||||
\(604\) | −15.9538 | −0.649150 | ||||||||
\(605\) | 20.8825 | 0.848995 | ||||||||
\(606\) | −2.13662 | −0.0867941 | ||||||||
\(607\) | −11.5745 | −0.469794 | −0.234897 | − | 0.972020i | \(-0.575475\pi\) | ||||
−0.234897 | + | 0.972020i | \(0.575475\pi\) | |||||||
\(608\) | 3.93182 | 0.159456 | ||||||||
\(609\) | −5.30592 | −0.215007 | ||||||||
\(610\) | −2.71069 | −0.109753 | ||||||||
\(611\) | −12.1134 | −0.490057 | ||||||||
\(612\) | −4.39265 | −0.177562 | ||||||||
\(613\) | 12.9157 | 0.521660 | 0.260830 | − | 0.965385i | \(-0.416004\pi\) | ||||
0.260830 | + | 0.965385i | \(0.416004\pi\) | |||||||
\(614\) | −5.33589 | −0.215339 | ||||||||
\(615\) | −11.0221 | −0.444454 | ||||||||
\(616\) | −4.29434 | −0.173024 | ||||||||
\(617\) | −34.5405 | −1.39055 | −0.695274 | − | 0.718745i | \(-0.744717\pi\) | ||||
−0.695274 | + | 0.718745i | \(0.744717\pi\) | |||||||
\(618\) | 2.05664 | 0.0827303 | ||||||||
\(619\) | −10.4591 | −0.420386 | −0.210193 | − | 0.977660i | \(-0.567409\pi\) | ||||
−0.210193 | + | 0.977660i | \(0.567409\pi\) | |||||||
\(620\) | 18.9446 | 0.760834 | ||||||||
\(621\) | −1.56513 | −0.0628064 | ||||||||
\(622\) | 1.72270 | 0.0690741 | ||||||||
\(623\) | 11.6275 | 0.465844 | ||||||||
\(624\) | 17.6829 | 0.707881 | ||||||||
\(625\) | −8.28830 | −0.331532 | ||||||||
\(626\) | 2.79938 | 0.111886 | ||||||||
\(627\) | −7.38377 | −0.294879 | ||||||||
\(628\) | 16.0122 | 0.638955 | ||||||||
\(629\) | 20.7264 | 0.826415 | ||||||||
\(630\) | 0.367576 | 0.0146446 | ||||||||
\(631\) | −42.9499 | −1.70981 | −0.854904 | − | 0.518786i | \(-0.826384\pi\) | ||||
−0.854904 | + | 0.518786i | \(0.826384\pi\) | |||||||
\(632\) | −10.0698 | −0.400557 | ||||||||
\(633\) | −5.58343 | −0.221922 | ||||||||
\(634\) | −0.0707193 | −0.00280862 | ||||||||
\(635\) | 35.3321 | 1.40211 | ||||||||
\(636\) | −12.8992 | −0.511487 | ||||||||
\(637\) | 4.77509 | 0.189196 | ||||||||
\(638\) | −5.76830 | −0.228369 | ||||||||
\(639\) | −10.5578 | −0.417662 | ||||||||
\(640\) | 11.0398 | 0.436387 | ||||||||
\(641\) | 5.36544 | 0.211922 | 0.105961 | − | 0.994370i | \(-0.466208\pi\) | ||||
0.105961 | + | 0.994370i | \(0.466208\pi\) | |||||||
\(642\) | −4.15403 | −0.163946 | ||||||||
\(643\) | 13.3645 | 0.527045 | 0.263522 | − | 0.964653i | \(-0.415116\pi\) | ||||
0.263522 | + | 0.964653i | \(0.415116\pi\) | |||||||
\(644\) | −3.05217 | −0.120272 | ||||||||
\(645\) | 15.4138 | 0.606917 | ||||||||
\(646\) | 0.763267 | 0.0300303 | ||||||||
\(647\) | −44.0694 | −1.73255 | −0.866274 | − | 0.499569i | \(-0.833492\pi\) | ||||
−0.866274 | + | 0.499569i | \(0.833492\pi\) | |||||||
\(648\) | 0.882304 | 0.0346602 | ||||||||
\(649\) | −30.0260 | −1.17862 | ||||||||
\(650\) | 2.44441 | 0.0958777 | ||||||||
\(651\) | 5.90322 | 0.231366 | ||||||||
\(652\) | −26.8850 | −1.05290 | ||||||||
\(653\) | 5.13038 | 0.200767 | 0.100384 | − | 0.994949i | \(-0.467993\pi\) | ||||
0.100384 | + | 0.994949i | \(0.467993\pi\) | |||||||
\(654\) | 2.23577 | 0.0874257 | ||||||||
\(655\) | −0.499952 | −0.0195347 | ||||||||
\(656\) | −24.8026 | −0.968379 | ||||||||
\(657\) | 3.39844 | 0.132586 | ||||||||
\(658\) | −0.566624 | −0.0220893 | ||||||||
\(659\) | 21.5484 | 0.839408 | 0.419704 | − | 0.907661i | \(-0.362134\pi\) | ||||
0.419704 | + | 0.907661i | \(0.362134\pi\) | |||||||
\(660\) | −15.6198 | −0.607999 | ||||||||
\(661\) | −25.6285 | −0.996833 | −0.498416 | − | 0.866938i | \(-0.666085\pi\) | ||||
−0.498416 | + | 0.866938i | \(0.666085\pi\) | |||||||
\(662\) | −0.406068 | −0.0157823 | ||||||||
\(663\) | 10.7559 | 0.417726 | ||||||||
\(664\) | −7.35756 | −0.285529 | ||||||||
\(665\) | 2.49653 | 0.0968114 | ||||||||
\(666\) | −2.05525 | −0.0796394 | ||||||||
\(667\) | −8.30444 | −0.321549 | ||||||||
\(668\) | −18.8004 | −0.727410 | ||||||||
\(669\) | 23.8421 | 0.921788 | ||||||||
\(670\) | 0.202836 | 0.00783625 | ||||||||
\(671\) | 35.8931 | 1.38564 | ||||||||
\(672\) | 2.59175 | 0.0999789 | ||||||||
\(673\) | 36.1879 | 1.39494 | 0.697470 | − | 0.716614i | \(-0.254309\pi\) | ||||
0.697470 | + | 0.716614i | \(0.254309\pi\) | |||||||
\(674\) | 0.708248 | 0.0272807 | ||||||||
\(675\) | −2.29184 | −0.0882128 | ||||||||
\(676\) | −19.1139 | −0.735152 | ||||||||
\(677\) | −24.8477 | −0.954976 | −0.477488 | − | 0.878638i | \(-0.658453\pi\) | ||||
−0.477488 | + | 0.878638i | \(0.658453\pi\) | |||||||
\(678\) | −2.71886 | −0.104417 | ||||||||
\(679\) | −5.63135 | −0.216112 | ||||||||
\(680\) | 3.27057 | 0.125420 | ||||||||
\(681\) | 13.9517 | 0.534629 | ||||||||
\(682\) | 6.41766 | 0.245745 | ||||||||
\(683\) | 22.5038 | 0.861085 | 0.430542 | − | 0.902570i | \(-0.358322\pi\) | ||||
0.430542 | + | 0.902570i | \(0.358322\pi\) | |||||||
\(684\) | 2.95841 | 0.113118 | ||||||||
\(685\) | −1.26732 | −0.0484219 | ||||||||
\(686\) | 0.223362 | 0.00852800 | ||||||||
\(687\) | −0.970158 | −0.0370138 | ||||||||
\(688\) | 34.6850 | 1.32235 | ||||||||
\(689\) | 31.5854 | 1.20331 | ||||||||
\(690\) | 0.575303 | 0.0219014 | ||||||||
\(691\) | −17.4227 | −0.662792 | −0.331396 | − | 0.943492i | \(-0.607520\pi\) | ||||
−0.331396 | + | 0.943492i | \(0.607520\pi\) | |||||||
\(692\) | −12.2911 | −0.467239 | ||||||||
\(693\) | −4.86719 | −0.184889 | ||||||||
\(694\) | 5.66523 | 0.215049 | ||||||||
\(695\) | −11.6544 | −0.442078 | ||||||||
\(696\) | 4.68143 | 0.177449 | ||||||||
\(697\) | −15.0867 | −0.571449 | ||||||||
\(698\) | 0.294188 | 0.0111352 | ||||||||
\(699\) | 12.6698 | 0.479216 | ||||||||
\(700\) | −4.46933 | −0.168925 | ||||||||
\(701\) | 37.3696 | 1.41143 | 0.705715 | − | 0.708496i | \(-0.250626\pi\) | ||||
0.705715 | + | 0.708496i | \(0.250626\pi\) | |||||||
\(702\) | −1.06657 | −0.0402552 | ||||||||
\(703\) | −13.9591 | −0.526476 | ||||||||
\(704\) | −33.2302 | −1.25241 | ||||||||
\(705\) | −4.17468 | −0.157228 | ||||||||
\(706\) | −3.63793 | −0.136915 | ||||||||
\(707\) | −9.56571 | −0.359756 | ||||||||
\(708\) | 12.0303 | 0.452128 | ||||||||
\(709\) | −41.8739 | −1.57261 | −0.786303 | − | 0.617840i | \(-0.788008\pi\) | ||||
−0.786303 | + | 0.617840i | \(0.788008\pi\) | |||||||
\(710\) | 3.88080 | 0.145644 | ||||||||
\(711\) | −11.4131 | −0.428025 | ||||||||
\(712\) | −10.2590 | −0.384471 | ||||||||
\(713\) | 9.23930 | 0.346014 | ||||||||
\(714\) | 0.503126 | 0.0188290 | ||||||||
\(715\) | 38.2470 | 1.43036 | ||||||||
\(716\) | 15.2140 | 0.568575 | ||||||||
\(717\) | −6.15618 | −0.229907 | ||||||||
\(718\) | −3.55259 | −0.132581 | ||||||||
\(719\) | 41.4719 | 1.54664 | 0.773320 | − | 0.634015i | \(-0.218594\pi\) | ||||
0.773320 | + | 0.634015i | \(0.218594\pi\) | |||||||
\(720\) | 6.09408 | 0.227113 | ||||||||
\(721\) | 9.20767 | 0.342912 | ||||||||
\(722\) | 3.72982 | 0.138810 | ||||||||
\(723\) | 10.2118 | 0.379780 | ||||||||
\(724\) | −49.2820 | −1.83155 | ||||||||
\(725\) | −12.1603 | −0.451622 | ||||||||
\(726\) | −2.83436 | −0.105193 | ||||||||
\(727\) | 21.9046 | 0.812396 | 0.406198 | − | 0.913785i | \(-0.366854\pi\) | ||||
0.406198 | + | 0.913785i | \(0.366854\pi\) | |||||||
\(728\) | −4.21308 | −0.156147 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.24918 | −0.0462344 | ||||||||
\(731\) | 21.0979 | 0.780333 | ||||||||
\(732\) | −14.3811 | −0.531541 | ||||||||
\(733\) | 31.6650 | 1.16957 | 0.584787 | − | 0.811187i | \(-0.301178\pi\) | ||||
0.584787 | + | 0.811187i | \(0.301178\pi\) | |||||||
\(734\) | 1.83328 | 0.0676676 | ||||||||
\(735\) | 1.64565 | 0.0607007 | ||||||||
\(736\) | 4.05642 | 0.149522 | ||||||||
\(737\) | −2.68582 | −0.0989336 | ||||||||
\(738\) | 1.49601 | 0.0550691 | ||||||||
\(739\) | −24.3883 | −0.897139 | −0.448569 | − | 0.893748i | \(-0.648066\pi\) | ||||
−0.448569 | + | 0.893748i | \(0.648066\pi\) | |||||||
\(740\) | −29.5293 | −1.08552 | ||||||||
\(741\) | −7.24405 | −0.266117 | ||||||||
\(742\) | 1.47745 | 0.0542390 | ||||||||
\(743\) | −13.2264 | −0.485230 | −0.242615 | − | 0.970123i | \(-0.578005\pi\) | ||||
−0.242615 | + | 0.970123i | \(0.578005\pi\) | |||||||
\(744\) | −5.20844 | −0.190951 | ||||||||
\(745\) | 18.6036 | 0.681585 | ||||||||
\(746\) | −3.98232 | −0.145803 | ||||||||
\(747\) | −8.33903 | −0.305109 | ||||||||
\(748\) | −21.3798 | −0.781724 | ||||||||
\(749\) | −18.5977 | −0.679546 | ||||||||
\(750\) | 2.68030 | 0.0978707 | ||||||||
\(751\) | 51.3872 | 1.87515 | 0.937573 | − | 0.347789i | \(-0.113068\pi\) | ||||
0.937573 | + | 0.347789i | \(0.113068\pi\) | |||||||
\(752\) | −9.39414 | −0.342569 | ||||||||
\(753\) | 7.90110 | 0.287932 | ||||||||
\(754\) | −5.65915 | −0.206094 | ||||||||
\(755\) | 13.4630 | 0.489969 | ||||||||
\(756\) | 1.95011 | 0.0709248 | ||||||||
\(757\) | 54.2128 | 1.97040 | 0.985199 | − | 0.171412i | \(-0.0548330\pi\) | ||||
0.985199 | + | 0.171412i | \(0.0548330\pi\) | |||||||
\(758\) | 1.41379 | 0.0513513 | ||||||||
\(759\) | −7.61777 | −0.276508 | ||||||||
\(760\) | −2.20270 | −0.0799004 | ||||||||
\(761\) | 16.0740 | 0.582684 | 0.291342 | − | 0.956619i | \(-0.405898\pi\) | ||||
0.291342 | + | 0.956619i | \(0.405898\pi\) | |||||||
\(762\) | −4.79558 | −0.173725 | ||||||||
\(763\) | 10.0096 | 0.362374 | ||||||||
\(764\) | 1.95011 | 0.0705525 | ||||||||
\(765\) | 3.70685 | 0.134021 | ||||||||
\(766\) | −6.49516 | −0.234680 | ||||||||
\(767\) | −29.4578 | −1.06366 | ||||||||
\(768\) | 12.1564 | 0.438655 | ||||||||
\(769\) | 9.19946 | 0.331741 | 0.165871 | − | 0.986148i | \(-0.446957\pi\) | ||||
0.165871 | + | 0.986148i | \(0.446957\pi\) | |||||||
\(770\) | 1.78906 | 0.0644732 | ||||||||
\(771\) | −28.0298 | −1.00947 | ||||||||
\(772\) | −46.0182 | −1.65623 | ||||||||
\(773\) | −29.0805 | −1.04595 | −0.522976 | − | 0.852348i | \(-0.675178\pi\) | ||||
−0.522976 | + | 0.852348i | \(0.675178\pi\) | |||||||
\(774\) | −2.09209 | −0.0751987 | ||||||||
\(775\) | 13.5292 | 0.485984 | ||||||||
\(776\) | 4.96857 | 0.178361 | ||||||||
\(777\) | −9.20145 | −0.330100 | ||||||||
\(778\) | −0.0106497 | −0.000381811 0 | ||||||||
\(779\) | 10.1608 | 0.364047 | ||||||||
\(780\) | −15.3242 | −0.548694 | ||||||||
\(781\) | −51.3870 | −1.83877 | ||||||||
\(782\) | 0.787456 | 0.0281594 | ||||||||
\(783\) | 5.30592 | 0.189618 | ||||||||
\(784\) | 3.70315 | 0.132255 | ||||||||
\(785\) | −13.5123 | −0.482274 | ||||||||
\(786\) | 0.0678578 | 0.00242041 | ||||||||
\(787\) | −0.755113 | −0.0269169 | −0.0134584 | − | 0.999909i | \(-0.504284\pi\) | ||||
−0.0134584 | + | 0.999909i | \(0.504284\pi\) | |||||||
\(788\) | 28.5702 | 1.01777 | ||||||||
\(789\) | −15.3246 | −0.545570 | ||||||||
\(790\) | 4.19518 | 0.149258 | ||||||||
\(791\) | −12.1724 | −0.432802 | ||||||||
\(792\) | 4.29434 | 0.152593 | ||||||||
\(793\) | 35.2139 | 1.25048 | ||||||||
\(794\) | −0.381977 | −0.0135559 | ||||||||
\(795\) | 10.8853 | 0.386063 | ||||||||
\(796\) | 41.1586 | 1.45883 | ||||||||
\(797\) | 24.2393 | 0.858601 | 0.429301 | − | 0.903162i | \(-0.358760\pi\) | ||||
0.429301 | + | 0.903162i | \(0.358760\pi\) | |||||||
\(798\) | −0.338851 | −0.0119952 | ||||||||
\(799\) | −5.71417 | −0.202153 | ||||||||
\(800\) | 5.93987 | 0.210006 | ||||||||
\(801\) | −11.6275 | −0.410836 | ||||||||
\(802\) | −5.66933 | −0.200191 | ||||||||
\(803\) | 16.5409 | 0.583715 | ||||||||
\(804\) | 1.07611 | 0.0379516 | ||||||||
\(805\) | 2.57565 | 0.0907798 | ||||||||
\(806\) | 6.29622 | 0.221775 | ||||||||
\(807\) | 2.50287 | 0.0881053 | ||||||||
\(808\) | 8.43986 | 0.296913 | ||||||||
\(809\) | −4.06154 | −0.142796 | −0.0713981 | − | 0.997448i | \(-0.522746\pi\) | ||||
−0.0713981 | + | 0.997448i | \(0.522746\pi\) | |||||||
\(810\) | −0.367576 | −0.0129153 | ||||||||
\(811\) | −15.8676 | −0.557185 | −0.278593 | − | 0.960409i | \(-0.589868\pi\) | ||||
−0.278593 | + | 0.960409i | \(0.589868\pi\) | |||||||
\(812\) | 10.3471 | 0.363113 | ||||||||
\(813\) | −6.89447 | −0.241800 | ||||||||
\(814\) | −10.0033 | −0.350616 | ||||||||
\(815\) | 22.6876 | 0.794713 | ||||||||
\(816\) | 8.34138 | 0.292007 | ||||||||
\(817\) | −14.2093 | −0.497119 | ||||||||
\(818\) | −5.09180 | −0.178031 | ||||||||
\(819\) | −4.77509 | −0.166855 | ||||||||
\(820\) | 21.4943 | 0.750613 | ||||||||
\(821\) | 7.32970 | 0.255808 | 0.127904 | − | 0.991787i | \(-0.459175\pi\) | ||||
0.127904 | + | 0.991787i | \(0.459175\pi\) | |||||||
\(822\) | 0.172012 | 0.00599960 | ||||||||
\(823\) | −48.1052 | −1.67684 | −0.838421 | − | 0.545023i | \(-0.816521\pi\) | ||||
−0.838421 | + | 0.545023i | \(0.816521\pi\) | |||||||
\(824\) | −8.12397 | −0.283012 | ||||||||
\(825\) | −11.1548 | −0.388360 | ||||||||
\(826\) | −1.37793 | −0.0479444 | ||||||||
\(827\) | 6.84983 | 0.238192 | 0.119096 | − | 0.992883i | \(-0.462000\pi\) | ||||
0.119096 | + | 0.992883i | \(0.462000\pi\) | |||||||
\(828\) | 3.05217 | 0.106070 | ||||||||
\(829\) | −27.3764 | −0.950821 | −0.475410 | − | 0.879764i | \(-0.657700\pi\) | ||||
−0.475410 | + | 0.879764i | \(0.657700\pi\) | |||||||
\(830\) | 3.06522 | 0.106395 | ||||||||
\(831\) | −24.9943 | −0.867044 | ||||||||
\(832\) | −32.6014 | −1.13025 | ||||||||
\(833\) | 2.25251 | 0.0780449 | ||||||||
\(834\) | 1.58184 | 0.0547747 | ||||||||
\(835\) | 15.8652 | 0.549038 | ||||||||
\(836\) | 14.3992 | 0.498005 | ||||||||
\(837\) | −5.90322 | −0.204045 | ||||||||
\(838\) | −7.15390 | −0.247128 | ||||||||
\(839\) | 14.8460 | 0.512541 | 0.256271 | − | 0.966605i | \(-0.417506\pi\) | ||||
0.256271 | + | 0.966605i | \(0.417506\pi\) | |||||||
\(840\) | −1.45196 | −0.0500975 | ||||||||
\(841\) | −0.847214 | −0.0292143 | ||||||||
\(842\) | 6.73007 | 0.231934 | ||||||||
\(843\) | 21.3653 | 0.735860 | ||||||||
\(844\) | 10.8883 | 0.374791 | ||||||||
\(845\) | 16.1298 | 0.554882 | ||||||||
\(846\) | 0.566624 | 0.0194809 | ||||||||
\(847\) | −12.6895 | −0.436017 | ||||||||
\(848\) | 24.4949 | 0.841158 | ||||||||
\(849\) | −9.44217 | −0.324055 | ||||||||
\(850\) | 1.15308 | 0.0395504 | ||||||||
\(851\) | −14.4014 | −0.493675 | ||||||||
\(852\) | 20.5889 | 0.705365 | ||||||||
\(853\) | −21.5697 | −0.738532 | −0.369266 | − | 0.929324i | \(-0.620391\pi\) | ||||
−0.369266 | + | 0.929324i | \(0.620391\pi\) | |||||||
\(854\) | 1.64718 | 0.0563655 | ||||||||
\(855\) | −2.49653 | −0.0853797 | ||||||||
\(856\) | 16.4089 | 0.560843 | ||||||||
\(857\) | −13.5451 | −0.462692 | −0.231346 | − | 0.972871i | \(-0.574313\pi\) | ||||
−0.231346 | + | 0.972871i | \(0.574313\pi\) | |||||||
\(858\) | −5.19121 | −0.177225 | ||||||||
\(859\) | 1.46474 | 0.0499762 | 0.0249881 | − | 0.999688i | \(-0.492045\pi\) | ||||
0.0249881 | + | 0.999688i | \(0.492045\pi\) | |||||||
\(860\) | −30.0585 | −1.02499 | ||||||||
\(861\) | 6.69771 | 0.228258 | ||||||||
\(862\) | −5.41604 | −0.184471 | ||||||||
\(863\) | 46.0152 | 1.56638 | 0.783188 | − | 0.621785i | \(-0.213592\pi\) | ||||
0.783188 | + | 0.621785i | \(0.213592\pi\) | |||||||
\(864\) | −2.59175 | −0.0881731 | ||||||||
\(865\) | 10.3722 | 0.352665 | ||||||||
\(866\) | 6.15136 | 0.209032 | ||||||||
\(867\) | −11.9262 | −0.405035 | ||||||||
\(868\) | −11.5119 | −0.390740 | ||||||||
\(869\) | −55.5498 | −1.88440 | ||||||||
\(870\) | −1.95033 | −0.0661223 | ||||||||
\(871\) | −2.63500 | −0.0892836 | ||||||||
\(872\) | −8.83155 | −0.299074 | ||||||||
\(873\) | 5.63135 | 0.190592 | ||||||||
\(874\) | −0.530346 | −0.0179392 | ||||||||
\(875\) | 11.9998 | 0.405668 | ||||||||
\(876\) | −6.62734 | −0.223917 | ||||||||
\(877\) | 42.6501 | 1.44019 | 0.720096 | − | 0.693875i | \(-0.244098\pi\) | ||||
0.720096 | + | 0.693875i | \(0.244098\pi\) | |||||||
\(878\) | 4.55134 | 0.153600 | ||||||||
\(879\) | −3.95148 | −0.133280 | ||||||||
\(880\) | 29.6610 | 0.999874 | ||||||||
\(881\) | −36.3417 | −1.22438 | −0.612191 | − | 0.790710i | \(-0.709712\pi\) | ||||
−0.612191 | + | 0.790710i | \(0.709712\pi\) | |||||||
\(882\) | −0.223362 | −0.00752099 | ||||||||
\(883\) | 33.8777 | 1.14008 | 0.570038 | − | 0.821619i | \(-0.306929\pi\) | ||||
0.570038 | + | 0.821619i | \(0.306929\pi\) | |||||||
\(884\) | −20.9753 | −0.705475 | ||||||||
\(885\) | −10.1521 | −0.341259 | ||||||||
\(886\) | −3.44689 | −0.115800 | ||||||||
\(887\) | −27.3629 | −0.918755 | −0.459378 | − | 0.888241i | \(-0.651928\pi\) | ||||
−0.459378 | + | 0.888241i | \(0.651928\pi\) | |||||||
\(888\) | 8.11847 | 0.272438 | ||||||||
\(889\) | −21.4700 | −0.720080 | ||||||||
\(890\) | 4.27397 | 0.143264 | ||||||||
\(891\) | 4.86719 | 0.163057 | ||||||||
\(892\) | −46.4947 | −1.55676 | ||||||||
\(893\) | 3.84845 | 0.128784 | ||||||||
\(894\) | −2.52505 | −0.0844502 | ||||||||
\(895\) | −12.8388 | −0.429152 | ||||||||
\(896\) | −6.70848 | −0.224115 | ||||||||
\(897\) | −7.47362 | −0.249537 | ||||||||
\(898\) | −8.56239 | −0.285731 | ||||||||
\(899\) | −31.3220 | −1.04465 | ||||||||
\(900\) | 4.46933 | 0.148978 | ||||||||
\(901\) | 14.8995 | 0.496374 | ||||||||
\(902\) | 7.28138 | 0.242444 | ||||||||
\(903\) | −9.36637 | −0.311693 | ||||||||
\(904\) | 10.7398 | 0.357200 | ||||||||
\(905\) | 41.5879 | 1.38243 | ||||||||
\(906\) | −1.82732 | −0.0607085 | ||||||||
\(907\) | −13.8138 | −0.458681 | −0.229340 | − | 0.973346i | \(-0.573657\pi\) | ||||
−0.229340 | + | 0.973346i | \(0.573657\pi\) | |||||||
\(908\) | −27.2073 | −0.902905 | ||||||||
\(909\) | 9.56571 | 0.317275 | ||||||||
\(910\) | 1.75521 | 0.0581845 | ||||||||
\(911\) | 0.348944 | 0.0115610 | 0.00578051 | − | 0.999983i | \(-0.498160\pi\) | ||||
0.00578051 | + | 0.999983i | \(0.498160\pi\) | |||||||
\(912\) | −5.61786 | −0.186026 | ||||||||
\(913\) | −40.5876 | −1.34325 | ||||||||
\(914\) | 6.49911 | 0.214971 | ||||||||
\(915\) | 12.1359 | 0.401199 | ||||||||
\(916\) | 1.89191 | 0.0625106 | ||||||||
\(917\) | 0.303802 | 0.0100324 | ||||||||
\(918\) | −0.503126 | −0.0166056 | ||||||||
\(919\) | −12.2068 | −0.402665 | −0.201333 | − | 0.979523i | \(-0.564527\pi\) | ||||
−0.201333 | + | 0.979523i | \(0.564527\pi\) | |||||||
\(920\) | −2.27251 | −0.0749224 | ||||||||
\(921\) | 23.8890 | 0.787169 | ||||||||
\(922\) | −0.159403 | −0.00524965 | ||||||||
\(923\) | −50.4146 | −1.65942 | ||||||||
\(924\) | 9.49155 | 0.312249 | ||||||||
\(925\) | −21.0882 | −0.693376 | ||||||||
\(926\) | 6.67102 | 0.219223 | ||||||||
\(927\) | −9.20767 | −0.302420 | ||||||||
\(928\) | −13.7516 | −0.451419 | ||||||||
\(929\) | 16.4967 | 0.541238 | 0.270619 | − | 0.962686i | \(-0.412772\pi\) | ||||
0.270619 | + | 0.962686i | \(0.412772\pi\) | |||||||
\(930\) | 2.16988 | 0.0711532 | ||||||||
\(931\) | −1.51705 | −0.0497193 | ||||||||
\(932\) | −24.7075 | −0.809322 | ||||||||
\(933\) | −7.71261 | −0.252500 | ||||||||
\(934\) | 3.32039 | 0.108647 | ||||||||
\(935\) | 18.0419 | 0.590034 | ||||||||
\(936\) | 4.21308 | 0.137709 | ||||||||
\(937\) | −54.8587 | −1.79216 | −0.896078 | − | 0.443898i | \(-0.853595\pi\) | ||||
−0.896078 | + | 0.443898i | \(0.853595\pi\) | |||||||
\(938\) | −0.123256 | −0.00402445 | ||||||||
\(939\) | −12.5329 | −0.408996 | ||||||||
\(940\) | 8.14109 | 0.265533 | ||||||||
\(941\) | 19.7793 | 0.644788 | 0.322394 | − | 0.946606i | \(-0.395512\pi\) | ||||
0.322394 | + | 0.946606i | \(0.395512\pi\) | |||||||
\(942\) | 1.83400 | 0.0597551 | ||||||||
\(943\) | 10.4828 | 0.341366 | ||||||||
\(944\) | −22.8449 | −0.743539 | ||||||||
\(945\) | −1.64565 | −0.0535330 | ||||||||
\(946\) | −10.1826 | −0.331065 | ||||||||
\(947\) | 51.3059 | 1.66722 | 0.833609 | − | 0.552355i | \(-0.186271\pi\) | ||||
0.833609 | + | 0.552355i | \(0.186271\pi\) | |||||||
\(948\) | 22.2568 | 0.722868 | ||||||||
\(949\) | 16.2279 | 0.526779 | ||||||||
\(950\) | −0.776592 | −0.0251960 | ||||||||
\(951\) | 0.316613 | 0.0102669 | ||||||||
\(952\) | −1.98740 | −0.0644120 | ||||||||
\(953\) | −24.3952 | −0.790239 | −0.395120 | − | 0.918630i | \(-0.629297\pi\) | ||||
−0.395120 | + | 0.918630i | \(0.629297\pi\) | |||||||
\(954\) | −1.47745 | −0.0478343 | ||||||||
\(955\) | −1.64565 | −0.0532520 | ||||||||
\(956\) | 12.0052 | 0.388277 | ||||||||
\(957\) | 25.8249 | 0.834801 | ||||||||
\(958\) | −7.06877 | −0.228382 | ||||||||
\(959\) | 0.770104 | 0.0248680 | ||||||||
\(960\) | −11.2355 | −0.362624 | ||||||||
\(961\) | 3.84804 | 0.124130 | ||||||||
\(962\) | −9.81401 | −0.316417 | ||||||||
\(963\) | 18.5977 | 0.599304 | ||||||||
\(964\) | −19.9141 | −0.641389 | ||||||||
\(965\) | 38.8337 | 1.25010 | ||||||||
\(966\) | −0.349590 | −0.0112479 | ||||||||
\(967\) | −34.8517 | −1.12075 | −0.560377 | − | 0.828238i | \(-0.689344\pi\) | ||||
−0.560377 | + | 0.828238i | \(0.689344\pi\) | |||||||
\(968\) | 11.1960 | 0.359854 | ||||||||
\(969\) | −3.41718 | −0.109775 | ||||||||
\(970\) | −2.06995 | −0.0664620 | ||||||||
\(971\) | −11.6094 | −0.372564 | −0.186282 | − | 0.982496i | \(-0.559644\pi\) | ||||
−0.186282 | + | 0.982496i | \(0.559644\pi\) | |||||||
\(972\) | −1.95011 | −0.0625498 | ||||||||
\(973\) | 7.08197 | 0.227038 | ||||||||
\(974\) | 4.73752 | 0.151800 | ||||||||
\(975\) | −10.9437 | −0.350480 | ||||||||
\(976\) | 27.3089 | 0.874136 | ||||||||
\(977\) | −48.7283 | −1.55896 | −0.779478 | − | 0.626430i | \(-0.784515\pi\) | ||||
−0.779478 | + | 0.626430i | \(0.784515\pi\) | |||||||
\(978\) | −3.07936 | −0.0984672 | ||||||||
\(979\) | −56.5930 | −1.80872 | ||||||||
\(980\) | −3.20920 | −0.102514 | ||||||||
\(981\) | −10.0096 | −0.319583 | ||||||||
\(982\) | 2.77584 | 0.0885808 | ||||||||
\(983\) | −46.4993 | −1.48310 | −0.741548 | − | 0.670900i | \(-0.765908\pi\) | ||||
−0.741548 | + | 0.670900i | \(0.765908\pi\) | |||||||
\(984\) | −5.90942 | −0.188385 | ||||||||
\(985\) | −24.1097 | −0.768198 | ||||||||
\(986\) | −2.66954 | −0.0850156 | ||||||||
\(987\) | 2.53680 | 0.0807472 | ||||||||
\(988\) | 14.1267 | 0.449430 | ||||||||
\(989\) | −14.6596 | −0.466147 | ||||||||
\(990\) | −1.78906 | −0.0568600 | ||||||||
\(991\) | 42.8927 | 1.36253 | 0.681266 | − | 0.732036i | \(-0.261430\pi\) | ||||
0.681266 | + | 0.732036i | \(0.261430\pi\) | |||||||
\(992\) | 15.2997 | 0.485765 | ||||||||
\(993\) | 1.81798 | 0.0576919 | ||||||||
\(994\) | −2.35822 | −0.0747981 | ||||||||
\(995\) | −34.7328 | −1.10110 | ||||||||
\(996\) | 16.2620 | 0.515282 | ||||||||
\(997\) | −39.6127 | −1.25455 | −0.627273 | − | 0.778799i | \(-0.715829\pi\) | ||||
−0.627273 | + | 0.778799i | \(0.715829\pi\) | |||||||
\(998\) | 2.88959 | 0.0914684 | ||||||||
\(999\) | 9.20145 | 0.291121 |
(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 | 4011.2.a.m.1.13 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.m.1.13 | ✓ | 29 | 1.1 | even | 1 | trivial |