Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, 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("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.75302 | 0.662579 | 0.331290 | − | 0.943529i | \(-0.392516\pi\) | ||||
0.331290 | + | 0.943529i | \(0.392516\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.19806 | 0.361229 | 0.180615 | − | 0.983554i | \(-0.442191\pi\) | ||||
0.180615 | + | 0.983554i | \(0.442191\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.75302 | −0.468514 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.76271 | −1.64020 | −0.820099 | − | 0.572222i | \(-0.806082\pi\) | ||||
−0.820099 | + | 0.572222i | \(0.806082\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 8.63102 | 1.98009 | 0.990046 | − | 0.140743i | \(-0.0449491\pi\) | ||||
0.990046 | + | 0.140743i | \(0.0449491\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.75302 | 0.382540 | ||||||||
\(22\) | −1.19806 | −0.255428 | ||||||||
\(23\) | −6.04892 | −1.26129 | −0.630643 | − | 0.776073i | \(-0.717209\pi\) | ||||
−0.630643 | + | 0.776073i | \(0.717209\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.75302 | 0.331290 | ||||||||
\(29\) | 4.07069 | 0.755908 | 0.377954 | − | 0.925824i | \(-0.376628\pi\) | ||||
0.377954 | + | 0.925824i | \(0.376628\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 6.80194 | 1.22166 | 0.610832 | − | 0.791760i | \(-0.290835\pi\) | ||||
0.610832 | + | 0.791760i | \(0.290835\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.19806 | 0.208556 | ||||||||
\(34\) | 6.76271 | 1.15980 | ||||||||
\(35\) | −1.75302 | −0.296315 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.34481 | −0.714283 | −0.357142 | − | 0.934050i | \(-0.616249\pi\) | ||||
−0.357142 | + | 0.934050i | \(0.616249\pi\) | |||||||
\(38\) | −8.63102 | −1.40014 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 6.63102 | 1.03559 | 0.517796 | − | 0.855504i | \(-0.326753\pi\) | ||||
0.517796 | + | 0.855504i | \(0.326753\pi\) | |||||||
\(42\) | −1.75302 | −0.270497 | ||||||||
\(43\) | 4.07606 | 0.621594 | 0.310797 | − | 0.950476i | \(-0.399404\pi\) | ||||
0.310797 | + | 0.950476i | \(0.399404\pi\) | |||||||
\(44\) | 1.19806 | 0.180615 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 6.04892 | 0.891864 | ||||||||
\(47\) | −11.1957 | −1.63306 | −0.816528 | − | 0.577306i | \(-0.804104\pi\) | ||||
−0.816528 | + | 0.577306i | \(0.804104\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −3.92692 | −0.560988 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −6.76271 | −0.946969 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.14914 | −0.157847 | −0.0789236 | − | 0.996881i | \(-0.525148\pi\) | ||||
−0.0789236 | + | 0.996881i | \(0.525148\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.19806 | −0.161547 | ||||||||
\(56\) | −1.75302 | −0.234257 | ||||||||
\(57\) | 8.63102 | 1.14321 | ||||||||
\(58\) | −4.07069 | −0.534507 | ||||||||
\(59\) | 13.7235 | 1.78664 | 0.893322 | − | 0.449416i | \(-0.148368\pi\) | ||||
0.893322 | + | 0.449416i | \(0.148368\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −1.18598 | −0.151849 | −0.0759246 | − | 0.997114i | \(-0.524191\pi\) | ||||
−0.0759246 | + | 0.997114i | \(0.524191\pi\) | |||||||
\(62\) | −6.80194 | −0.863847 | ||||||||
\(63\) | 1.75302 | 0.220860 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.19806 | −0.147471 | ||||||||
\(67\) | 14.1468 | 1.72830 | 0.864150 | − | 0.503234i | \(-0.167856\pi\) | ||||
0.864150 | + | 0.503234i | \(0.167856\pi\) | |||||||
\(68\) | −6.76271 | −0.820099 | ||||||||
\(69\) | −6.04892 | −0.728204 | ||||||||
\(70\) | 1.75302 | 0.209526 | ||||||||
\(71\) | −2.32304 | −0.275695 | −0.137847 | − | 0.990453i | \(-0.544018\pi\) | ||||
−0.137847 | + | 0.990453i | \(0.544018\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 1.59850 | 0.187090 | 0.0935451 | − | 0.995615i | \(-0.470180\pi\) | ||||
0.0935451 | + | 0.995615i | \(0.470180\pi\) | |||||||
\(74\) | 4.34481 | 0.505074 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 8.63102 | 0.990046 | ||||||||
\(77\) | 2.10023 | 0.239343 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.74094 | 0.420888 | 0.210444 | − | 0.977606i | \(-0.432509\pi\) | ||||
0.210444 | + | 0.977606i | \(0.432509\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.63102 | −0.732274 | ||||||||
\(83\) | 8.40581 | 0.922658 | 0.461329 | − | 0.887229i | \(-0.347373\pi\) | ||||
0.461329 | + | 0.887229i | \(0.347373\pi\) | |||||||
\(84\) | 1.75302 | 0.191270 | ||||||||
\(85\) | 6.76271 | 0.733519 | ||||||||
\(86\) | −4.07606 | −0.439533 | ||||||||
\(87\) | 4.07069 | 0.436424 | ||||||||
\(88\) | −1.19806 | −0.127714 | ||||||||
\(89\) | 4.49934 | 0.476929 | 0.238464 | − | 0.971151i | \(-0.423356\pi\) | ||||
0.238464 | + | 0.971151i | \(0.423356\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.04892 | −0.630643 | ||||||||
\(93\) | 6.80194 | 0.705328 | ||||||||
\(94\) | 11.1957 | 1.15475 | ||||||||
\(95\) | −8.63102 | −0.885524 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −10.7952 | −1.09609 | −0.548045 | − | 0.836449i | \(-0.684628\pi\) | ||||
−0.548045 | + | 0.836449i | \(0.684628\pi\) | |||||||
\(98\) | 3.92692 | 0.396679 | ||||||||
\(99\) | 1.19806 | 0.120410 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 16.7875 | 1.67042 | 0.835208 | − | 0.549935i | \(-0.185347\pi\) | ||||
0.835208 | + | 0.549935i | \(0.185347\pi\) | |||||||
\(102\) | 6.76271 | 0.669608 | ||||||||
\(103\) | −4.16421 | −0.410312 | −0.205156 | − | 0.978729i | \(-0.565770\pi\) | ||||
−0.205156 | + | 0.978729i | \(0.565770\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.75302 | −0.171077 | ||||||||
\(106\) | 1.14914 | 0.111615 | ||||||||
\(107\) | 12.9661 | 1.25348 | 0.626742 | − | 0.779226i | \(-0.284388\pi\) | ||||
0.626742 | + | 0.779226i | \(0.284388\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −19.4644 | −1.86435 | −0.932177 | − | 0.362004i | \(-0.882093\pi\) | ||||
−0.932177 | + | 0.362004i | \(0.882093\pi\) | |||||||
\(110\) | 1.19806 | 0.114231 | ||||||||
\(111\) | −4.34481 | −0.412392 | ||||||||
\(112\) | 1.75302 | 0.165645 | ||||||||
\(113\) | 0.515729 | 0.0485157 | 0.0242579 | − | 0.999706i | \(-0.492278\pi\) | ||||
0.0242579 | + | 0.999706i | \(0.492278\pi\) | |||||||
\(114\) | −8.63102 | −0.808369 | ||||||||
\(115\) | 6.04892 | 0.564064 | ||||||||
\(116\) | 4.07069 | 0.377954 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.7235 | −1.26335 | ||||||||
\(119\) | −11.8552 | −1.08676 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −9.56465 | −0.869513 | ||||||||
\(122\) | 1.18598 | 0.107374 | ||||||||
\(123\) | 6.63102 | 0.597899 | ||||||||
\(124\) | 6.80194 | 0.610832 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.75302 | −0.156171 | ||||||||
\(127\) | 7.96077 | 0.706404 | 0.353202 | − | 0.935547i | \(-0.385093\pi\) | ||||
0.353202 | + | 0.935547i | \(0.385093\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.07606 | 0.358877 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.08815 | −0.444553 | −0.222277 | − | 0.974984i | \(-0.571349\pi\) | ||||
−0.222277 | + | 0.974984i | \(0.571349\pi\) | |||||||
\(132\) | 1.19806 | 0.104278 | ||||||||
\(133\) | 15.1304 | 1.31197 | ||||||||
\(134\) | −14.1468 | −1.22209 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 6.76271 | 0.579898 | ||||||||
\(137\) | 0.674563 | 0.0576318 | 0.0288159 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288159 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(138\) | 6.04892 | 0.514918 | ||||||||
\(139\) | 8.26205 | 0.700778 | 0.350389 | − | 0.936604i | \(-0.386049\pi\) | ||||
0.350389 | + | 0.936604i | \(0.386049\pi\) | |||||||
\(140\) | −1.75302 | −0.148157 | ||||||||
\(141\) | −11.1957 | −0.942845 | ||||||||
\(142\) | 2.32304 | 0.194946 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.07069 | −0.338052 | ||||||||
\(146\) | −1.59850 | −0.132293 | ||||||||
\(147\) | −3.92692 | −0.323887 | ||||||||
\(148\) | −4.34481 | −0.357142 | ||||||||
\(149\) | −8.19136 | −0.671062 | −0.335531 | − | 0.942029i | \(-0.608916\pi\) | ||||
−0.335531 | + | 0.942029i | \(0.608916\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −5.72348 | −0.465770 | −0.232885 | − | 0.972504i | \(-0.574817\pi\) | ||||
−0.232885 | + | 0.972504i | \(0.574817\pi\) | |||||||
\(152\) | −8.63102 | −0.700068 | ||||||||
\(153\) | −6.76271 | −0.546733 | ||||||||
\(154\) | −2.10023 | −0.169241 | ||||||||
\(155\) | −6.80194 | −0.546345 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.09246 | 0.246805 | 0.123403 | − | 0.992357i | \(-0.460619\pi\) | ||||
0.123403 | + | 0.992357i | \(0.460619\pi\) | |||||||
\(158\) | −3.74094 | −0.297613 | ||||||||
\(159\) | −1.14914 | −0.0911331 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −10.6039 | −0.835702 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 23.9541 | 1.87623 | 0.938114 | − | 0.346328i | \(-0.112571\pi\) | ||||
0.938114 | + | 0.346328i | \(0.112571\pi\) | |||||||
\(164\) | 6.63102 | 0.517796 | ||||||||
\(165\) | −1.19806 | −0.0932690 | ||||||||
\(166\) | −8.40581 | −0.652418 | ||||||||
\(167\) | −1.19806 | −0.0927088 | −0.0463544 | − | 0.998925i | \(-0.514760\pi\) | ||||
−0.0463544 | + | 0.998925i | \(0.514760\pi\) | |||||||
\(168\) | −1.75302 | −0.135248 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.76271 | −0.518676 | ||||||||
\(171\) | 8.63102 | 0.660031 | ||||||||
\(172\) | 4.07606 | 0.310797 | ||||||||
\(173\) | −6.63773 | −0.504657 | −0.252329 | − | 0.967642i | \(-0.581196\pi\) | ||||
−0.252329 | + | 0.967642i | \(0.581196\pi\) | |||||||
\(174\) | −4.07069 | −0.308598 | ||||||||
\(175\) | 1.75302 | 0.132516 | ||||||||
\(176\) | 1.19806 | 0.0903073 | ||||||||
\(177\) | 13.7235 | 1.03152 | ||||||||
\(178\) | −4.49934 | −0.337239 | ||||||||
\(179\) | 19.6353 | 1.46761 | 0.733807 | − | 0.679358i | \(-0.237742\pi\) | ||||
0.733807 | + | 0.679358i | \(0.237742\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 5.25906 | 0.390903 | 0.195451 | − | 0.980713i | \(-0.437383\pi\) | ||||
0.195451 | + | 0.980713i | \(0.437383\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.18598 | −0.0876702 | ||||||||
\(184\) | 6.04892 | 0.445932 | ||||||||
\(185\) | 4.34481 | 0.319437 | ||||||||
\(186\) | −6.80194 | −0.498742 | ||||||||
\(187\) | −8.10215 | −0.592488 | ||||||||
\(188\) | −11.1957 | −0.816528 | ||||||||
\(189\) | 1.75302 | 0.127513 | ||||||||
\(190\) | 8.63102 | 0.626160 | ||||||||
\(191\) | 4.45473 | 0.322333 | 0.161166 | − | 0.986927i | \(-0.448474\pi\) | ||||
0.161166 | + | 0.986927i | \(0.448474\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −0.818331 | −0.0589048 | −0.0294524 | − | 0.999566i | \(-0.509376\pi\) | ||||
−0.0294524 | + | 0.999566i | \(0.509376\pi\) | |||||||
\(194\) | 10.7952 | 0.775053 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.92692 | −0.280494 | ||||||||
\(197\) | 12.7385 | 0.907584 | 0.453792 | − | 0.891108i | \(-0.350071\pi\) | ||||
0.453792 | + | 0.891108i | \(0.350071\pi\) | |||||||
\(198\) | −1.19806 | −0.0851426 | ||||||||
\(199\) | −4.02475 | −0.285307 | −0.142654 | − | 0.989773i | \(-0.545563\pi\) | ||||
−0.142654 | + | 0.989773i | \(0.545563\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 14.1468 | 0.997835 | ||||||||
\(202\) | −16.7875 | −1.18116 | ||||||||
\(203\) | 7.13600 | 0.500849 | ||||||||
\(204\) | −6.76271 | −0.473484 | ||||||||
\(205\) | −6.63102 | −0.463131 | ||||||||
\(206\) | 4.16421 | 0.290134 | ||||||||
\(207\) | −6.04892 | −0.420429 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3405 | 0.715268 | ||||||||
\(210\) | 1.75302 | 0.120970 | ||||||||
\(211\) | 3.10992 | 0.214095 | 0.107048 | − | 0.994254i | \(-0.465860\pi\) | ||||
0.107048 | + | 0.994254i | \(0.465860\pi\) | |||||||
\(212\) | −1.14914 | −0.0789236 | ||||||||
\(213\) | −2.32304 | −0.159172 | ||||||||
\(214\) | −12.9661 | −0.886348 | ||||||||
\(215\) | −4.07606 | −0.277985 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 11.9239 | 0.809449 | ||||||||
\(218\) | 19.4644 | 1.31830 | ||||||||
\(219\) | 1.59850 | 0.108017 | ||||||||
\(220\) | −1.19806 | −0.0807733 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.34481 | 0.291605 | ||||||||
\(223\) | 14.3787 | 0.962867 | 0.481433 | − | 0.876483i | \(-0.340116\pi\) | ||||
0.481433 | + | 0.876483i | \(0.340116\pi\) | |||||||
\(224\) | −1.75302 | −0.117129 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −0.515729 | −0.0343058 | ||||||||
\(227\) | −5.97716 | −0.396718 | −0.198359 | − | 0.980129i | \(-0.563561\pi\) | ||||
−0.198359 | + | 0.980129i | \(0.563561\pi\) | |||||||
\(228\) | 8.63102 | 0.571603 | ||||||||
\(229\) | −15.9172 | −1.05184 | −0.525920 | − | 0.850534i | \(-0.676279\pi\) | ||||
−0.525920 | + | 0.850534i | \(0.676279\pi\) | |||||||
\(230\) | −6.04892 | −0.398854 | ||||||||
\(231\) | 2.10023 | 0.138185 | ||||||||
\(232\) | −4.07069 | −0.267254 | ||||||||
\(233\) | −6.92154 | −0.453445 | −0.226723 | − | 0.973959i | \(-0.572801\pi\) | ||||
−0.226723 | + | 0.973959i | \(0.572801\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.1957 | 0.730325 | ||||||||
\(236\) | 13.7235 | 0.893322 | ||||||||
\(237\) | 3.74094 | 0.243000 | ||||||||
\(238\) | 11.8552 | 0.768456 | ||||||||
\(239\) | 30.1075 | 1.94749 | 0.973747 | − | 0.227633i | \(-0.0730988\pi\) | ||||
0.973747 | + | 0.227633i | \(0.0730988\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 12.0562 | 0.776609 | 0.388304 | − | 0.921531i | \(-0.373061\pi\) | ||||
0.388304 | + | 0.921531i | \(0.373061\pi\) | |||||||
\(242\) | 9.56465 | 0.614839 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.18598 | −0.0759246 | ||||||||
\(245\) | 3.92692 | 0.250882 | ||||||||
\(246\) | −6.63102 | −0.422779 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.80194 | −0.431923 | ||||||||
\(249\) | 8.40581 | 0.532697 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −14.8170 | −0.935241 | −0.467620 | − | 0.883929i | \(-0.654889\pi\) | ||||
−0.467620 | + | 0.883929i | \(0.654889\pi\) | |||||||
\(252\) | 1.75302 | 0.110430 | ||||||||
\(253\) | −7.24698 | −0.455614 | ||||||||
\(254\) | −7.96077 | −0.499503 | ||||||||
\(255\) | 6.76271 | 0.423497 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.5743 | −0.659609 | −0.329804 | − | 0.944049i | \(-0.606983\pi\) | ||||
−0.329804 | + | 0.944049i | \(0.606983\pi\) | |||||||
\(258\) | −4.07606 | −0.253765 | ||||||||
\(259\) | −7.61655 | −0.473269 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.07069 | 0.251969 | ||||||||
\(262\) | 5.08815 | 0.314347 | ||||||||
\(263\) | 11.9922 | 0.739473 | 0.369736 | − | 0.929137i | \(-0.379448\pi\) | ||||
0.369736 | + | 0.929137i | \(0.379448\pi\) | |||||||
\(264\) | −1.19806 | −0.0737356 | ||||||||
\(265\) | 1.14914 | 0.0705914 | ||||||||
\(266\) | −15.1304 | −0.927702 | ||||||||
\(267\) | 4.49934 | 0.275355 | ||||||||
\(268\) | 14.1468 | 0.864150 | ||||||||
\(269\) | −25.4359 | −1.55086 | −0.775428 | − | 0.631435i | \(-0.782466\pi\) | ||||
−0.775428 | + | 0.631435i | \(0.782466\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | 20.3666 | 1.23718 | 0.618591 | − | 0.785713i | \(-0.287704\pi\) | ||||
0.618591 | + | 0.785713i | \(0.287704\pi\) | |||||||
\(272\) | −6.76271 | −0.410049 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.674563 | −0.0407518 | ||||||||
\(275\) | 1.19806 | 0.0722459 | ||||||||
\(276\) | −6.04892 | −0.364102 | ||||||||
\(277\) | 20.1323 | 1.20963 | 0.604816 | − | 0.796366i | \(-0.293247\pi\) | ||||
0.604816 | + | 0.796366i | \(0.293247\pi\) | |||||||
\(278\) | −8.26205 | −0.495525 | ||||||||
\(279\) | 6.80194 | 0.407221 | ||||||||
\(280\) | 1.75302 | 0.104763 | ||||||||
\(281\) | −29.7265 | −1.77333 | −0.886666 | − | 0.462410i | \(-0.846985\pi\) | ||||
−0.886666 | + | 0.462410i | \(0.846985\pi\) | |||||||
\(282\) | 11.1957 | 0.666692 | ||||||||
\(283\) | 8.84117 | 0.525553 | 0.262776 | − | 0.964857i | \(-0.415362\pi\) | ||||
0.262776 | + | 0.964857i | \(0.415362\pi\) | |||||||
\(284\) | −2.32304 | −0.137847 | ||||||||
\(285\) | −8.63102 | −0.511258 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6243 | 0.686162 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 28.7342 | 1.69025 | ||||||||
\(290\) | 4.07069 | 0.239039 | ||||||||
\(291\) | −10.7952 | −0.632828 | ||||||||
\(292\) | 1.59850 | 0.0935451 | ||||||||
\(293\) | 20.5918 | 1.20299 | 0.601493 | − | 0.798878i | \(-0.294573\pi\) | ||||
0.601493 | + | 0.798878i | \(0.294573\pi\) | |||||||
\(294\) | 3.92692 | 0.229023 | ||||||||
\(295\) | −13.7235 | −0.799012 | ||||||||
\(296\) | 4.34481 | 0.252537 | ||||||||
\(297\) | 1.19806 | 0.0695186 | ||||||||
\(298\) | 8.19136 | 0.474513 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 7.14542 | 0.411855 | ||||||||
\(302\) | 5.72348 | 0.329349 | ||||||||
\(303\) | 16.7875 | 0.964415 | ||||||||
\(304\) | 8.63102 | 0.495023 | ||||||||
\(305\) | 1.18598 | 0.0679091 | ||||||||
\(306\) | 6.76271 | 0.386598 | ||||||||
\(307\) | 28.7265 | 1.63951 | 0.819753 | − | 0.572717i | \(-0.194111\pi\) | ||||
0.819753 | + | 0.572717i | \(0.194111\pi\) | |||||||
\(308\) | 2.10023 | 0.119672 | ||||||||
\(309\) | −4.16421 | −0.236894 | ||||||||
\(310\) | 6.80194 | 0.386324 | ||||||||
\(311\) | −18.6329 | −1.05658 | −0.528289 | − | 0.849065i | \(-0.677166\pi\) | ||||
−0.528289 | + | 0.849065i | \(0.677166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.3696 | −1.66007 | −0.830033 | − | 0.557714i | \(-0.811679\pi\) | ||||
−0.830033 | + | 0.557714i | \(0.811679\pi\) | |||||||
\(314\) | −3.09246 | −0.174517 | ||||||||
\(315\) | −1.75302 | −0.0987715 | ||||||||
\(316\) | 3.74094 | 0.210444 | ||||||||
\(317\) | 20.8092 | 1.16876 | 0.584381 | − | 0.811479i | \(-0.301337\pi\) | ||||
0.584381 | + | 0.811479i | \(0.301337\pi\) | |||||||
\(318\) | 1.14914 | 0.0644408 | ||||||||
\(319\) | 4.87694 | 0.273056 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 12.9661 | 0.723700 | ||||||||
\(322\) | 10.6039 | 0.590931 | ||||||||
\(323\) | −58.3691 | −3.24774 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.9541 | −1.32669 | ||||||||
\(327\) | −19.4644 | −1.07638 | ||||||||
\(328\) | −6.63102 | −0.366137 | ||||||||
\(329\) | −19.6262 | −1.08203 | ||||||||
\(330\) | 1.19806 | 0.0659512 | ||||||||
\(331\) | −11.7603 | −0.646405 | −0.323203 | − | 0.946330i | \(-0.604760\pi\) | ||||
−0.323203 | + | 0.946330i | \(0.604760\pi\) | |||||||
\(332\) | 8.40581 | 0.461329 | ||||||||
\(333\) | −4.34481 | −0.238094 | ||||||||
\(334\) | 1.19806 | 0.0655551 | ||||||||
\(335\) | −14.1468 | −0.772920 | ||||||||
\(336\) | 1.75302 | 0.0956351 | ||||||||
\(337\) | −26.8732 | −1.46388 | −0.731939 | − | 0.681371i | \(-0.761384\pi\) | ||||
−0.731939 | + | 0.681371i | \(0.761384\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.515729 | 0.0280106 | ||||||||
\(340\) | 6.76271 | 0.366759 | ||||||||
\(341\) | 8.14914 | 0.441301 | ||||||||
\(342\) | −8.63102 | −0.466712 | ||||||||
\(343\) | −19.1551 | −1.03428 | ||||||||
\(344\) | −4.07606 | −0.219767 | ||||||||
\(345\) | 6.04892 | 0.325663 | ||||||||
\(346\) | 6.63773 | 0.356846 | ||||||||
\(347\) | 29.5080 | 1.58407 | 0.792035 | − | 0.610476i | \(-0.209022\pi\) | ||||
0.792035 | + | 0.610476i | \(0.209022\pi\) | |||||||
\(348\) | 4.07069 | 0.218212 | ||||||||
\(349\) | 17.0519 | 0.912767 | 0.456384 | − | 0.889783i | \(-0.349144\pi\) | ||||
0.456384 | + | 0.889783i | \(0.349144\pi\) | |||||||
\(350\) | −1.75302 | −0.0937029 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.19806 | −0.0638569 | ||||||||
\(353\) | −21.8629 | −1.16365 | −0.581823 | − | 0.813315i | \(-0.697660\pi\) | ||||
−0.581823 | + | 0.813315i | \(0.697660\pi\) | |||||||
\(354\) | −13.7235 | −0.729395 | ||||||||
\(355\) | 2.32304 | 0.123294 | ||||||||
\(356\) | 4.49934 | 0.238464 | ||||||||
\(357\) | −11.8552 | −0.627442 | ||||||||
\(358\) | −19.6353 | −1.03776 | ||||||||
\(359\) | 14.3026 | 0.754862 | 0.377431 | − | 0.926038i | \(-0.376807\pi\) | ||||
0.377431 | + | 0.926038i | \(0.376807\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 55.4946 | 2.92077 | ||||||||
\(362\) | −5.25906 | −0.276410 | ||||||||
\(363\) | −9.56465 | −0.502014 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.59850 | −0.0836692 | ||||||||
\(366\) | 1.18598 | 0.0619922 | ||||||||
\(367\) | −11.2416 | −0.586807 | −0.293403 | − | 0.955989i | \(-0.594788\pi\) | ||||
−0.293403 | + | 0.955989i | \(0.594788\pi\) | |||||||
\(368\) | −6.04892 | −0.315322 | ||||||||
\(369\) | 6.63102 | 0.345197 | ||||||||
\(370\) | −4.34481 | −0.225876 | ||||||||
\(371\) | −2.01447 | −0.104586 | ||||||||
\(372\) | 6.80194 | 0.352664 | ||||||||
\(373\) | −9.70171 | −0.502336 | −0.251168 | − | 0.967944i | \(-0.580815\pi\) | ||||
−0.251168 | + | 0.967944i | \(0.580815\pi\) | |||||||
\(374\) | 8.10215 | 0.418952 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 11.1957 | 0.577373 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.75302 | −0.0901656 | ||||||||
\(379\) | −2.82802 | −0.145266 | −0.0726328 | − | 0.997359i | \(-0.523140\pi\) | ||||
−0.0726328 | + | 0.997359i | \(0.523140\pi\) | |||||||
\(380\) | −8.63102 | −0.442762 | ||||||||
\(381\) | 7.96077 | 0.407843 | ||||||||
\(382\) | −4.45473 | −0.227924 | ||||||||
\(383\) | 11.6558 | 0.595582 | 0.297791 | − | 0.954631i | \(-0.403750\pi\) | ||||
0.297791 | + | 0.954631i | \(0.403750\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.10023 | −0.107038 | ||||||||
\(386\) | 0.818331 | 0.0416520 | ||||||||
\(387\) | 4.07606 | 0.207198 | ||||||||
\(388\) | −10.7952 | −0.548045 | ||||||||
\(389\) | 12.5157 | 0.634573 | 0.317286 | − | 0.948330i | \(-0.397228\pi\) | ||||
0.317286 | + | 0.948330i | \(0.397228\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.9071 | 2.06876 | ||||||||
\(392\) | 3.92692 | 0.198339 | ||||||||
\(393\) | −5.08815 | −0.256663 | ||||||||
\(394\) | −12.7385 | −0.641759 | ||||||||
\(395\) | −3.74094 | −0.188227 | ||||||||
\(396\) | 1.19806 | 0.0602049 | ||||||||
\(397\) | 21.6136 | 1.08475 | 0.542377 | − | 0.840135i | \(-0.317525\pi\) | ||||
0.542377 | + | 0.840135i | \(0.317525\pi\) | |||||||
\(398\) | 4.02475 | 0.201743 | ||||||||
\(399\) | 15.1304 | 0.757465 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −11.5157 | −0.575068 | −0.287534 | − | 0.957770i | \(-0.592835\pi\) | ||||
−0.287534 | + | 0.957770i | \(0.592835\pi\) | |||||||
\(402\) | −14.1468 | −0.705576 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 16.7875 | 0.835208 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −7.13600 | −0.354154 | ||||||||
\(407\) | −5.20536 | −0.258020 | ||||||||
\(408\) | 6.76271 | 0.334804 | ||||||||
\(409\) | −0.0991626 | −0.00490328 | −0.00245164 | − | 0.999997i | \(-0.500780\pi\) | ||||
−0.00245164 | + | 0.999997i | \(0.500780\pi\) | |||||||
\(410\) | 6.63102 | 0.327483 | ||||||||
\(411\) | 0.674563 | 0.0332737 | ||||||||
\(412\) | −4.16421 | −0.205156 | ||||||||
\(413\) | 24.0575 | 1.18379 | ||||||||
\(414\) | 6.04892 | 0.297288 | ||||||||
\(415\) | −8.40581 | −0.412625 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.26205 | 0.404594 | ||||||||
\(418\) | −10.3405 | −0.505771 | ||||||||
\(419\) | 31.2784 | 1.52805 | 0.764026 | − | 0.645186i | \(-0.223220\pi\) | ||||
0.764026 | + | 0.645186i | \(0.223220\pi\) | |||||||
\(420\) | −1.75302 | −0.0855386 | ||||||||
\(421\) | −38.0452 | −1.85421 | −0.927105 | − | 0.374802i | \(-0.877711\pi\) | ||||
−0.927105 | + | 0.374802i | \(0.877711\pi\) | |||||||
\(422\) | −3.10992 | −0.151388 | ||||||||
\(423\) | −11.1957 | −0.544352 | ||||||||
\(424\) | 1.14914 | 0.0558074 | ||||||||
\(425\) | −6.76271 | −0.328040 | ||||||||
\(426\) | 2.32304 | 0.112552 | ||||||||
\(427\) | −2.07905 | −0.100612 | ||||||||
\(428\) | 12.9661 | 0.626742 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.07606 | 0.196565 | ||||||||
\(431\) | −14.4614 | −0.696583 | −0.348291 | − | 0.937386i | \(-0.613238\pi\) | ||||
−0.348291 | + | 0.937386i | \(0.613238\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 21.6209 | 1.03903 | 0.519516 | − | 0.854461i | \(-0.326112\pi\) | ||||
0.519516 | + | 0.854461i | \(0.326112\pi\) | |||||||
\(434\) | −11.9239 | −0.572367 | ||||||||
\(435\) | −4.07069 | −0.195175 | ||||||||
\(436\) | −19.4644 | −0.932177 | ||||||||
\(437\) | −52.2083 | −2.49746 | ||||||||
\(438\) | −1.59850 | −0.0763792 | ||||||||
\(439\) | −3.23623 | −0.154457 | −0.0772283 | − | 0.997013i | \(-0.524607\pi\) | ||||
−0.0772283 | + | 0.997013i | \(0.524607\pi\) | |||||||
\(440\) | 1.19806 | 0.0571154 | ||||||||
\(441\) | −3.92692 | −0.186996 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.6649 | −0.696749 | −0.348375 | − | 0.937355i | \(-0.613266\pi\) | ||||
−0.348375 | + | 0.937355i | \(0.613266\pi\) | |||||||
\(444\) | −4.34481 | −0.206196 | ||||||||
\(445\) | −4.49934 | −0.213289 | ||||||||
\(446\) | −14.3787 | −0.680850 | ||||||||
\(447\) | −8.19136 | −0.387438 | ||||||||
\(448\) | 1.75302 | 0.0828224 | ||||||||
\(449\) | 4.08516 | 0.192791 | 0.0963954 | − | 0.995343i | \(-0.469269\pi\) | ||||
0.0963954 | + | 0.995343i | \(0.469269\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 7.94438 | 0.374086 | ||||||||
\(452\) | 0.515729 | 0.0242579 | ||||||||
\(453\) | −5.72348 | −0.268913 | ||||||||
\(454\) | 5.97716 | 0.280522 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.63102 | −0.404185 | ||||||||
\(457\) | 41.8678 | 1.95849 | 0.979247 | − | 0.202668i | \(-0.0649613\pi\) | ||||
0.979247 | + | 0.202668i | \(0.0649613\pi\) | |||||||
\(458\) | 15.9172 | 0.743763 | ||||||||
\(459\) | −6.76271 | −0.315656 | ||||||||
\(460\) | 6.04892 | 0.282032 | ||||||||
\(461\) | −0.215521 | −0.0100378 | −0.00501890 | − | 0.999987i | \(-0.501598\pi\) | ||||
−0.00501890 | + | 0.999987i | \(0.501598\pi\) | |||||||
\(462\) | −2.10023 | −0.0977114 | ||||||||
\(463\) | 23.4795 | 1.09118 | 0.545592 | − | 0.838051i | \(-0.316305\pi\) | ||||
0.545592 | + | 0.838051i | \(0.316305\pi\) | |||||||
\(464\) | 4.07069 | 0.188977 | ||||||||
\(465\) | −6.80194 | −0.315432 | ||||||||
\(466\) | 6.92154 | 0.320634 | ||||||||
\(467\) | 10.1153 | 0.468080 | 0.234040 | − | 0.972227i | \(-0.424805\pi\) | ||||
0.234040 | + | 0.972227i | \(0.424805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.7995 | 1.14514 | ||||||||
\(470\) | −11.1957 | −0.516418 | ||||||||
\(471\) | 3.09246 | 0.142493 | ||||||||
\(472\) | −13.7235 | −0.631674 | ||||||||
\(473\) | 4.88338 | 0.224538 | ||||||||
\(474\) | −3.74094 | −0.171827 | ||||||||
\(475\) | 8.63102 | 0.396018 | ||||||||
\(476\) | −11.8552 | −0.543381 | ||||||||
\(477\) | −1.14914 | −0.0526157 | ||||||||
\(478\) | −30.1075 | −1.37709 | ||||||||
\(479\) | 0.980623 | 0.0448058 | 0.0224029 | − | 0.999749i | \(-0.492868\pi\) | ||||
0.0224029 | + | 0.999749i | \(0.492868\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12.0562 | −0.549145 | ||||||||
\(483\) | −10.6039 | −0.482493 | ||||||||
\(484\) | −9.56465 | −0.434757 | ||||||||
\(485\) | 10.7952 | 0.490186 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 7.18300 | 0.325493 | 0.162746 | − | 0.986668i | \(-0.447965\pi\) | ||||
0.162746 | + | 0.986668i | \(0.447965\pi\) | |||||||
\(488\) | 1.18598 | 0.0536868 | ||||||||
\(489\) | 23.9541 | 1.08324 | ||||||||
\(490\) | −3.92692 | −0.177400 | ||||||||
\(491\) | 24.5918 | 1.10981 | 0.554906 | − | 0.831913i | \(-0.312754\pi\) | ||||
0.554906 | + | 0.831913i | \(0.312754\pi\) | |||||||
\(492\) | 6.63102 | 0.298950 | ||||||||
\(493\) | −27.5289 | −1.23984 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.19806 | −0.0538489 | ||||||||
\(496\) | 6.80194 | 0.305416 | ||||||||
\(497\) | −4.07234 | −0.182670 | ||||||||
\(498\) | −8.40581 | −0.376673 | ||||||||
\(499\) | 30.1608 | 1.35018 | 0.675090 | − | 0.737735i | \(-0.264105\pi\) | ||||
0.675090 | + | 0.737735i | \(0.264105\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −1.19806 | −0.0535255 | ||||||||
\(502\) | 14.8170 | 0.661315 | ||||||||
\(503\) | −33.8883 | −1.51100 | −0.755502 | − | 0.655146i | \(-0.772607\pi\) | ||||
−0.755502 | + | 0.655146i | \(0.772607\pi\) | |||||||
\(504\) | −1.75302 | −0.0780857 | ||||||||
\(505\) | −16.7875 | −0.747032 | ||||||||
\(506\) | 7.24698 | 0.322168 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.96077 | 0.353202 | ||||||||
\(509\) | 14.1089 | 0.625364 | 0.312682 | − | 0.949858i | \(-0.398773\pi\) | ||||
0.312682 | + | 0.949858i | \(0.398773\pi\) | |||||||
\(510\) | −6.76271 | −0.299458 | ||||||||
\(511\) | 2.80220 | 0.123962 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 8.63102 | 0.381069 | ||||||||
\(514\) | 10.5743 | 0.466414 | ||||||||
\(515\) | 4.16421 | 0.183497 | ||||||||
\(516\) | 4.07606 | 0.179439 | ||||||||
\(517\) | −13.4131 | −0.589908 | ||||||||
\(518\) | 7.61655 | 0.334652 | ||||||||
\(519\) | −6.63773 | −0.291364 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3937 | 0.762033 | 0.381017 | − | 0.924568i | \(-0.375574\pi\) | ||||
0.381017 | + | 0.924568i | \(0.375574\pi\) | |||||||
\(522\) | −4.07069 | −0.178169 | ||||||||
\(523\) | −34.9879 | −1.52991 | −0.764957 | − | 0.644081i | \(-0.777240\pi\) | ||||
−0.764957 | + | 0.644081i | \(0.777240\pi\) | |||||||
\(524\) | −5.08815 | −0.222277 | ||||||||
\(525\) | 1.75302 | 0.0765081 | ||||||||
\(526\) | −11.9922 | −0.522886 | ||||||||
\(527\) | −45.9995 | −2.00377 | ||||||||
\(528\) | 1.19806 | 0.0521390 | ||||||||
\(529\) | 13.5894 | 0.590844 | ||||||||
\(530\) | −1.14914 | −0.0499157 | ||||||||
\(531\) | 13.7235 | 0.595548 | ||||||||
\(532\) | 15.1304 | 0.655984 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −4.49934 | −0.194705 | ||||||||
\(535\) | −12.9661 | −0.560575 | ||||||||
\(536\) | −14.1468 | −0.611047 | ||||||||
\(537\) | 19.6353 | 0.847327 | ||||||||
\(538\) | 25.4359 | 1.09662 | ||||||||
\(539\) | −4.70469 | −0.202646 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 20.8689 | 0.897224 | 0.448612 | − | 0.893727i | \(-0.351918\pi\) | ||||
0.448612 | + | 0.893727i | \(0.351918\pi\) | |||||||
\(542\) | −20.3666 | −0.874820 | ||||||||
\(543\) | 5.25906 | 0.225688 | ||||||||
\(544\) | 6.76271 | 0.289949 | ||||||||
\(545\) | 19.4644 | 0.833764 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.67456 | 0.242627 | 0.121313 | − | 0.992614i | \(-0.461289\pi\) | ||||
0.121313 | + | 0.992614i | \(0.461289\pi\) | |||||||
\(548\) | 0.674563 | 0.0288159 | ||||||||
\(549\) | −1.18598 | −0.0506164 | ||||||||
\(550\) | −1.19806 | −0.0510855 | ||||||||
\(551\) | 35.1342 | 1.49677 | ||||||||
\(552\) | 6.04892 | 0.257459 | ||||||||
\(553\) | 6.55794 | 0.278872 | ||||||||
\(554\) | −20.1323 | −0.855339 | ||||||||
\(555\) | 4.34481 | 0.184427 | ||||||||
\(556\) | 8.26205 | 0.350389 | ||||||||
\(557\) | −14.7724 | −0.625927 | −0.312963 | − | 0.949765i | \(-0.601322\pi\) | ||||
−0.312963 | + | 0.949765i | \(0.601322\pi\) | |||||||
\(558\) | −6.80194 | −0.287949 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.75302 | −0.0740786 | ||||||||
\(561\) | −8.10215 | −0.342073 | ||||||||
\(562\) | 29.7265 | 1.25394 | ||||||||
\(563\) | 18.0398 | 0.760288 | 0.380144 | − | 0.924927i | \(-0.375874\pi\) | ||||
0.380144 | + | 0.924927i | \(0.375874\pi\) | |||||||
\(564\) | −11.1957 | −0.471423 | ||||||||
\(565\) | −0.515729 | −0.0216969 | ||||||||
\(566\) | −8.84117 | −0.371622 | ||||||||
\(567\) | 1.75302 | 0.0736199 | ||||||||
\(568\) | 2.32304 | 0.0974728 | ||||||||
\(569\) | −11.4886 | −0.481626 | −0.240813 | − | 0.970571i | \(-0.577414\pi\) | ||||
−0.240813 | + | 0.970571i | \(0.577414\pi\) | |||||||
\(570\) | 8.63102 | 0.361514 | ||||||||
\(571\) | −44.3062 | −1.85416 | −0.927078 | − | 0.374869i | \(-0.877688\pi\) | ||||
−0.927078 | + | 0.374869i | \(0.877688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.45473 | 0.186099 | ||||||||
\(574\) | −11.6243 | −0.485190 | ||||||||
\(575\) | −6.04892 | −0.252257 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 28.0000 | 1.16566 | 0.582828 | − | 0.812596i | \(-0.301946\pi\) | ||||
0.582828 | + | 0.812596i | \(0.301946\pi\) | |||||||
\(578\) | −28.7342 | −1.19519 | ||||||||
\(579\) | −0.818331 | −0.0340087 | ||||||||
\(580\) | −4.07069 | −0.169026 | ||||||||
\(581\) | 14.7356 | 0.611334 | ||||||||
\(582\) | 10.7952 | 0.447477 | ||||||||
\(583\) | −1.37675 | −0.0570190 | ||||||||
\(584\) | −1.59850 | −0.0661463 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.5918 | −0.850639 | ||||||||
\(587\) | −35.4316 | −1.46242 | −0.731210 | − | 0.682152i | \(-0.761044\pi\) | ||||
−0.731210 | + | 0.682152i | \(0.761044\pi\) | |||||||
\(588\) | −3.92692 | −0.161943 | ||||||||
\(589\) | 58.7077 | 2.41901 | ||||||||
\(590\) | 13.7235 | 0.564987 | ||||||||
\(591\) | 12.7385 | 0.523994 | ||||||||
\(592\) | −4.34481 | −0.178571 | ||||||||
\(593\) | 2.19567 | 0.0901653 | 0.0450827 | − | 0.998983i | \(-0.485645\pi\) | ||||
0.0450827 | + | 0.998983i | \(0.485645\pi\) | |||||||
\(594\) | −1.19806 | −0.0491571 | ||||||||
\(595\) | 11.8552 | 0.486014 | ||||||||
\(596\) | −8.19136 | −0.335531 | ||||||||
\(597\) | −4.02475 | −0.164722 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.1855 | −1.27421 | −0.637103 | − | 0.770779i | \(-0.719867\pi\) | ||||
−0.637103 | + | 0.770779i | \(0.719867\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | −24.2435 | −0.988914 | −0.494457 | − | 0.869202i | \(-0.664633\pi\) | ||||
−0.494457 | + | 0.869202i | \(0.664633\pi\) | |||||||
\(602\) | −7.14542 | −0.291226 | ||||||||
\(603\) | 14.1468 | 0.576100 | ||||||||
\(604\) | −5.72348 | −0.232885 | ||||||||
\(605\) | 9.56465 | 0.388858 | ||||||||
\(606\) | −16.7875 | −0.681944 | ||||||||
\(607\) | −17.7235 | −0.719374 | −0.359687 | − | 0.933073i | \(-0.617117\pi\) | ||||
−0.359687 | + | 0.933073i | \(0.617117\pi\) | |||||||
\(608\) | −8.63102 | −0.350034 | ||||||||
\(609\) | 7.13600 | 0.289165 | ||||||||
\(610\) | −1.18598 | −0.0480190 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.76271 | −0.273366 | ||||||||
\(613\) | −1.71140 | −0.0691227 | −0.0345614 | − | 0.999403i | \(-0.511003\pi\) | ||||
−0.0345614 | + | 0.999403i | \(0.511003\pi\) | |||||||
\(614\) | −28.7265 | −1.15931 | ||||||||
\(615\) | −6.63102 | −0.267389 | ||||||||
\(616\) | −2.10023 | −0.0846206 | ||||||||
\(617\) | −0.569433 | −0.0229245 | −0.0114622 | − | 0.999934i | \(-0.503649\pi\) | ||||
−0.0114622 | + | 0.999934i | \(0.503649\pi\) | |||||||
\(618\) | 4.16421 | 0.167509 | ||||||||
\(619\) | −26.4282 | −1.06224 | −0.531119 | − | 0.847297i | \(-0.678228\pi\) | ||||
−0.531119 | + | 0.847297i | \(0.678228\pi\) | |||||||
\(620\) | −6.80194 | −0.273172 | ||||||||
\(621\) | −6.04892 | −0.242735 | ||||||||
\(622\) | 18.6329 | 0.747113 | ||||||||
\(623\) | 7.88743 | 0.316003 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 29.3696 | 1.17384 | ||||||||
\(627\) | 10.3405 | 0.412960 | ||||||||
\(628\) | 3.09246 | 0.123403 | ||||||||
\(629\) | 29.3827 | 1.17157 | ||||||||
\(630\) | 1.75302 | 0.0698420 | ||||||||
\(631\) | −38.0006 | −1.51278 | −0.756390 | − | 0.654121i | \(-0.773039\pi\) | ||||
−0.756390 | + | 0.654121i | \(0.773039\pi\) | |||||||
\(632\) | −3.74094 | −0.148807 | ||||||||
\(633\) | 3.10992 | 0.123608 | ||||||||
\(634\) | −20.8092 | −0.826440 | ||||||||
\(635\) | −7.96077 | −0.315914 | ||||||||
\(636\) | −1.14914 | −0.0455666 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.87694 | −0.193080 | ||||||||
\(639\) | −2.32304 | −0.0918982 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −25.9168 | −1.02365 | −0.511825 | − | 0.859090i | \(-0.671030\pi\) | ||||
−0.511825 | + | 0.859090i | \(0.671030\pi\) | |||||||
\(642\) | −12.9661 | −0.511733 | ||||||||
\(643\) | −8.52243 | −0.336092 | −0.168046 | − | 0.985779i | \(-0.553746\pi\) | ||||
−0.168046 | + | 0.985779i | \(0.553746\pi\) | |||||||
\(644\) | −10.6039 | −0.417851 | ||||||||
\(645\) | −4.07606 | −0.160495 | ||||||||
\(646\) | 58.3691 | 2.29650 | ||||||||
\(647\) | 37.9318 | 1.49125 | 0.745627 | − | 0.666364i | \(-0.232150\pi\) | ||||
0.745627 | + | 0.666364i | \(0.232150\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 16.4416 | 0.645389 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.9239 | 0.467336 | ||||||||
\(652\) | 23.9541 | 0.938114 | ||||||||
\(653\) | −6.07846 | −0.237868 | −0.118934 | − | 0.992902i | \(-0.537948\pi\) | ||||
−0.118934 | + | 0.992902i | \(0.537948\pi\) | |||||||
\(654\) | 19.4644 | 0.761119 | ||||||||
\(655\) | 5.08815 | 0.198810 | ||||||||
\(656\) | 6.63102 | 0.258898 | ||||||||
\(657\) | 1.59850 | 0.0623634 | ||||||||
\(658\) | 19.6262 | 0.765110 | ||||||||
\(659\) | 38.9162 | 1.51596 | 0.757979 | − | 0.652279i | \(-0.226187\pi\) | ||||
0.757979 | + | 0.652279i | \(0.226187\pi\) | |||||||
\(660\) | −1.19806 | −0.0466345 | ||||||||
\(661\) | 25.9191 | 1.00814 | 0.504069 | − | 0.863663i | \(-0.331836\pi\) | ||||
0.504069 | + | 0.863663i | \(0.331836\pi\) | |||||||
\(662\) | 11.7603 | 0.457078 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.40581 | −0.326209 | ||||||||
\(665\) | −15.1304 | −0.586730 | ||||||||
\(666\) | 4.34481 | 0.168358 | ||||||||
\(667\) | −24.6233 | −0.953416 | ||||||||
\(668\) | −1.19806 | −0.0463544 | ||||||||
\(669\) | 14.3787 | 0.555911 | ||||||||
\(670\) | 14.1468 | 0.546537 | ||||||||
\(671\) | −1.42088 | −0.0548524 | ||||||||
\(672\) | −1.75302 | −0.0676242 | ||||||||
\(673\) | −25.5724 | −0.985744 | −0.492872 | − | 0.870102i | \(-0.664053\pi\) | ||||
−0.492872 | + | 0.870102i | \(0.664053\pi\) | |||||||
\(674\) | 26.8732 | 1.03512 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7453 | 0.951037 | 0.475519 | − | 0.879706i | \(-0.342260\pi\) | ||||
0.475519 | + | 0.879706i | \(0.342260\pi\) | |||||||
\(678\) | −0.515729 | −0.0198065 | ||||||||
\(679\) | −18.9243 | −0.726247 | ||||||||
\(680\) | −6.76271 | −0.259338 | ||||||||
\(681\) | −5.97716 | −0.229045 | ||||||||
\(682\) | −8.14914 | −0.312047 | ||||||||
\(683\) | 22.4045 | 0.857284 | 0.428642 | − | 0.903474i | \(-0.358992\pi\) | ||||
0.428642 | + | 0.903474i | \(0.358992\pi\) | |||||||
\(684\) | 8.63102 | 0.330015 | ||||||||
\(685\) | −0.674563 | −0.0257737 | ||||||||
\(686\) | 19.1551 | 0.731346 | ||||||||
\(687\) | −15.9172 | −0.607280 | ||||||||
\(688\) | 4.07606 | 0.155398 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.04892 | −0.230278 | ||||||||
\(691\) | −16.0030 | −0.608782 | −0.304391 | − | 0.952547i | \(-0.598453\pi\) | ||||
−0.304391 | + | 0.952547i | \(0.598453\pi\) | |||||||
\(692\) | −6.63773 | −0.252329 | ||||||||
\(693\) | 2.10023 | 0.0797810 | ||||||||
\(694\) | −29.5080 | −1.12011 | ||||||||
\(695\) | −8.26205 | −0.313397 | ||||||||
\(696\) | −4.07069 | −0.154299 | ||||||||
\(697\) | −44.8437 | −1.69858 | ||||||||
\(698\) | −17.0519 | −0.645424 | ||||||||
\(699\) | −6.92154 | −0.261797 | ||||||||
\(700\) | 1.75302 | 0.0662579 | ||||||||
\(701\) | 32.7222 | 1.23590 | 0.617949 | − | 0.786218i | \(-0.287964\pi\) | ||||
0.617949 | + | 0.786218i | \(0.287964\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.5002 | −1.41435 | ||||||||
\(704\) | 1.19806 | 0.0451537 | ||||||||
\(705\) | 11.1957 | 0.421653 | ||||||||
\(706\) | 21.8629 | 0.822822 | ||||||||
\(707\) | 29.4288 | 1.10678 | ||||||||
\(708\) | 13.7235 | 0.515760 | ||||||||
\(709\) | 14.0597 | 0.528022 | 0.264011 | − | 0.964520i | \(-0.414954\pi\) | ||||
0.264011 | + | 0.964520i | \(0.414954\pi\) | |||||||
\(710\) | −2.32304 | −0.0871823 | ||||||||
\(711\) | 3.74094 | 0.140296 | ||||||||
\(712\) | −4.49934 | −0.168620 | ||||||||
\(713\) | −41.1444 | −1.54087 | ||||||||
\(714\) | 11.8552 | 0.443668 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.6353 | 0.733807 | ||||||||
\(717\) | 30.1075 | 1.12439 | ||||||||
\(718\) | −14.3026 | −0.533768 | ||||||||
\(719\) | −7.15585 | −0.266868 | −0.133434 | − | 0.991058i | \(-0.542600\pi\) | ||||
−0.133434 | + | 0.991058i | \(0.542600\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −7.29995 | −0.271864 | ||||||||
\(722\) | −55.4946 | −2.06529 | ||||||||
\(723\) | 12.0562 | 0.448375 | ||||||||
\(724\) | 5.25906 | 0.195451 | ||||||||
\(725\) | 4.07069 | 0.151182 | ||||||||
\(726\) | 9.56465 | 0.354977 | ||||||||
\(727\) | 36.4704 | 1.35261 | 0.676306 | − | 0.736621i | \(-0.263580\pi\) | ||||
0.676306 | + | 0.736621i | \(0.263580\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.59850 | 0.0591631 | ||||||||
\(731\) | −27.5652 | −1.01954 | ||||||||
\(732\) | −1.18598 | −0.0438351 | ||||||||
\(733\) | −38.0646 | −1.40595 | −0.702974 | − | 0.711216i | \(-0.748145\pi\) | ||||
−0.702974 | + | 0.711216i | \(0.748145\pi\) | |||||||
\(734\) | 11.2416 | 0.414935 | ||||||||
\(735\) | 3.92692 | 0.144847 | ||||||||
\(736\) | 6.04892 | 0.222966 | ||||||||
\(737\) | 16.9487 | 0.624313 | ||||||||
\(738\) | −6.63102 | −0.244091 | ||||||||
\(739\) | 35.5114 | 1.30631 | 0.653154 | − | 0.757225i | \(-0.273445\pi\) | ||||
0.653154 | + | 0.757225i | \(0.273445\pi\) | |||||||
\(740\) | 4.34481 | 0.159719 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.01447 | 0.0739537 | ||||||||
\(743\) | 20.3696 | 0.747287 | 0.373643 | − | 0.927572i | \(-0.378108\pi\) | ||||
0.373643 | + | 0.927572i | \(0.378108\pi\) | |||||||
\(744\) | −6.80194 | −0.249371 | ||||||||
\(745\) | 8.19136 | 0.300108 | ||||||||
\(746\) | 9.70171 | 0.355205 | ||||||||
\(747\) | 8.40581 | 0.307553 | ||||||||
\(748\) | −8.10215 | −0.296244 | ||||||||
\(749\) | 22.7299 | 0.830533 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −5.58104 | −0.203655 | −0.101828 | − | 0.994802i | \(-0.532469\pi\) | ||||
−0.101828 | + | 0.994802i | \(0.532469\pi\) | |||||||
\(752\) | −11.1957 | −0.408264 | ||||||||
\(753\) | −14.8170 | −0.539962 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.72348 | 0.208299 | ||||||||
\(756\) | 1.75302 | 0.0637567 | ||||||||
\(757\) | 12.8267 | 0.466194 | 0.233097 | − | 0.972453i | \(-0.425114\pi\) | ||||
0.233097 | + | 0.972453i | \(0.425114\pi\) | |||||||
\(758\) | 2.82802 | 0.102718 | ||||||||
\(759\) | −7.24698 | −0.263049 | ||||||||
\(760\) | 8.63102 | 0.313080 | ||||||||
\(761\) | −14.0084 | −0.507803 | −0.253901 | − | 0.967230i | \(-0.581714\pi\) | ||||
−0.253901 | + | 0.967230i | \(0.581714\pi\) | |||||||
\(762\) | −7.96077 | −0.288388 | ||||||||
\(763\) | −34.1215 | −1.23528 | ||||||||
\(764\) | 4.45473 | 0.161166 | ||||||||
\(765\) | 6.76271 | 0.244506 | ||||||||
\(766\) | −11.6558 | −0.421140 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −50.4051 | −1.81765 | −0.908827 | − | 0.417174i | \(-0.863021\pi\) | ||||
−0.908827 | + | 0.417174i | \(0.863021\pi\) | |||||||
\(770\) | 2.10023 | 0.0756869 | ||||||||
\(771\) | −10.5743 | −0.380825 | ||||||||
\(772\) | −0.818331 | −0.0294524 | ||||||||
\(773\) | −42.5532 | −1.53053 | −0.765265 | − | 0.643715i | \(-0.777392\pi\) | ||||
−0.765265 | + | 0.643715i | \(0.777392\pi\) | |||||||
\(774\) | −4.07606 | −0.146511 | ||||||||
\(775\) | 6.80194 | 0.244333 | ||||||||
\(776\) | 10.7952 | 0.387526 | ||||||||
\(777\) | −7.61655 | −0.273242 | ||||||||
\(778\) | −12.5157 | −0.448711 | ||||||||
\(779\) | 57.2325 | 2.05057 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.78315 | −0.0995890 | ||||||||
\(782\) | −40.9071 | −1.46283 | ||||||||
\(783\) | 4.07069 | 0.145475 | ||||||||
\(784\) | −3.92692 | −0.140247 | ||||||||
\(785\) | −3.09246 | −0.110375 | ||||||||
\(786\) | 5.08815 | 0.181488 | ||||||||
\(787\) | 12.1927 | 0.434622 | 0.217311 | − | 0.976102i | \(-0.430271\pi\) | ||||
0.217311 | + | 0.976102i | \(0.430271\pi\) | |||||||
\(788\) | 12.7385 | 0.453792 | ||||||||
\(789\) | 11.9922 | 0.426935 | ||||||||
\(790\) | 3.74094 | 0.133097 | ||||||||
\(791\) | 0.904084 | 0.0321455 | ||||||||
\(792\) | −1.19806 | −0.0425713 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21.6136 | −0.767037 | ||||||||
\(795\) | 1.14914 | 0.0407560 | ||||||||
\(796\) | −4.02475 | −0.142654 | ||||||||
\(797\) | 36.4534 | 1.29125 | 0.645623 | − | 0.763656i | \(-0.276598\pi\) | ||||
0.645623 | + | 0.763656i | \(0.276598\pi\) | |||||||
\(798\) | −15.1304 | −0.535609 | ||||||||
\(799\) | 75.7131 | 2.67854 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 4.49934 | 0.158976 | ||||||||
\(802\) | 11.5157 | 0.406635 | ||||||||
\(803\) | 1.91510 | 0.0675824 | ||||||||
\(804\) | 14.1468 | 0.498917 | ||||||||
\(805\) | 10.6039 | 0.373738 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.4359 | −0.895388 | ||||||||
\(808\) | −16.7875 | −0.590581 | ||||||||
\(809\) | 9.70278 | 0.341131 | 0.170566 | − | 0.985346i | \(-0.445440\pi\) | ||||
0.170566 | + | 0.985346i | \(0.445440\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −26.6547 | −0.935974 | −0.467987 | − | 0.883735i | \(-0.655021\pi\) | ||||
−0.467987 | + | 0.883735i | \(0.655021\pi\) | |||||||
\(812\) | 7.13600 | 0.250424 | ||||||||
\(813\) | 20.3666 | 0.714287 | ||||||||
\(814\) | 5.20536 | 0.182448 | ||||||||
\(815\) | −23.9541 | −0.839074 | ||||||||
\(816\) | −6.76271 | −0.236742 | ||||||||
\(817\) | 35.1806 | 1.23081 | ||||||||
\(818\) | 0.0991626 | 0.00346714 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.63102 | −0.231565 | ||||||||
\(821\) | −2.58343 | −0.0901624 | −0.0450812 | − | 0.998983i | \(-0.514355\pi\) | ||||
−0.0450812 | + | 0.998983i | \(0.514355\pi\) | |||||||
\(822\) | −0.674563 | −0.0235281 | ||||||||
\(823\) | 19.9855 | 0.696652 | 0.348326 | − | 0.937374i | \(-0.386750\pi\) | ||||
0.348326 | + | 0.937374i | \(0.386750\pi\) | |||||||
\(824\) | 4.16421 | 0.145067 | ||||||||
\(825\) | 1.19806 | 0.0417112 | ||||||||
\(826\) | −24.0575 | −0.837069 | ||||||||
\(827\) | −1.39506 | −0.0485110 | −0.0242555 | − | 0.999706i | \(-0.507722\pi\) | ||||
−0.0242555 | + | 0.999706i | \(0.507722\pi\) | |||||||
\(828\) | −6.04892 | −0.210214 | ||||||||
\(829\) | −27.6179 | −0.959208 | −0.479604 | − | 0.877485i | \(-0.659220\pi\) | ||||
−0.479604 | + | 0.877485i | \(0.659220\pi\) | |||||||
\(830\) | 8.40581 | 0.291770 | ||||||||
\(831\) | 20.1323 | 0.698381 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.5566 | 0.920132 | ||||||||
\(834\) | −8.26205 | −0.286091 | ||||||||
\(835\) | 1.19806 | 0.0414607 | ||||||||
\(836\) | 10.3405 | 0.357634 | ||||||||
\(837\) | 6.80194 | 0.235109 | ||||||||
\(838\) | −31.2784 | −1.08050 | ||||||||
\(839\) | 54.3357 | 1.87588 | 0.937939 | − | 0.346801i | \(-0.112732\pi\) | ||||
0.937939 | + | 0.346801i | \(0.112732\pi\) | |||||||
\(840\) | 1.75302 | 0.0604850 | ||||||||
\(841\) | −12.4295 | −0.428604 | ||||||||
\(842\) | 38.0452 | 1.31112 | ||||||||
\(843\) | −29.7265 | −1.02383 | ||||||||
\(844\) | 3.10992 | 0.107048 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.1957 | 0.384915 | ||||||||
\(847\) | −16.7670 | −0.576122 | ||||||||
\(848\) | −1.14914 | −0.0394618 | ||||||||
\(849\) | 8.84117 | 0.303428 | ||||||||
\(850\) | 6.76271 | 0.231959 | ||||||||
\(851\) | 26.2814 | 0.900916 | ||||||||
\(852\) | −2.32304 | −0.0795862 | ||||||||
\(853\) | 13.4553 | 0.460701 | 0.230351 | − | 0.973108i | \(-0.426013\pi\) | ||||
0.230351 | + | 0.973108i | \(0.426013\pi\) | |||||||
\(854\) | 2.07905 | 0.0711436 | ||||||||
\(855\) | −8.63102 | −0.295175 | ||||||||
\(856\) | −12.9661 | −0.443174 | ||||||||
\(857\) | 42.7200 | 1.45929 | 0.729644 | − | 0.683827i | \(-0.239686\pi\) | ||||
0.729644 | + | 0.683827i | \(0.239686\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.3038 | 1.51163 | 0.755813 | − | 0.654788i | \(-0.227242\pi\) | ||||
0.755813 | + | 0.654788i | \(0.227242\pi\) | |||||||
\(860\) | −4.07606 | −0.138993 | ||||||||
\(861\) | 11.6243 | 0.396156 | ||||||||
\(862\) | 14.4614 | 0.492558 | ||||||||
\(863\) | 5.47783 | 0.186467 | 0.0932337 | − | 0.995644i | \(-0.470280\pi\) | ||||
0.0932337 | + | 0.995644i | \(0.470280\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 6.63773 | 0.225689 | ||||||||
\(866\) | −21.6209 | −0.734707 | ||||||||
\(867\) | 28.7342 | 0.975866 | ||||||||
\(868\) | 11.9239 | 0.404725 | ||||||||
\(869\) | 4.48188 | 0.152037 | ||||||||
\(870\) | 4.07069 | 0.138009 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19.4644 | 0.659148 | ||||||||
\(873\) | −10.7952 | −0.365363 | ||||||||
\(874\) | 52.2083 | 1.76597 | ||||||||
\(875\) | −1.75302 | −0.0592629 | ||||||||
\(876\) | 1.59850 | 0.0540083 | ||||||||
\(877\) | 41.3726 | 1.39705 | 0.698526 | − | 0.715585i | \(-0.253840\pi\) | ||||
0.698526 | + | 0.715585i | \(0.253840\pi\) | |||||||
\(878\) | 3.23623 | 0.109217 | ||||||||
\(879\) | 20.5918 | 0.694544 | ||||||||
\(880\) | −1.19806 | −0.0403867 | ||||||||
\(881\) | −42.3919 | −1.42822 | −0.714110 | − | 0.700033i | \(-0.753168\pi\) | ||||
−0.714110 | + | 0.700033i | \(0.753168\pi\) | |||||||
\(882\) | 3.92692 | 0.132226 | ||||||||
\(883\) | −40.8412 | −1.37441 | −0.687207 | − | 0.726461i | \(-0.741164\pi\) | ||||
−0.687207 | + | 0.726461i | \(0.741164\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.7235 | −0.461310 | ||||||||
\(886\) | 14.6649 | 0.492676 | ||||||||
\(887\) | −35.0810 | −1.17790 | −0.588952 | − | 0.808168i | \(-0.700459\pi\) | ||||
−0.588952 | + | 0.808168i | \(0.700459\pi\) | |||||||
\(888\) | 4.34481 | 0.145802 | ||||||||
\(889\) | 13.9554 | 0.468049 | ||||||||
\(890\) | 4.49934 | 0.150818 | ||||||||
\(891\) | 1.19806 | 0.0401366 | ||||||||
\(892\) | 14.3787 | 0.481433 | ||||||||
\(893\) | −96.6301 | −3.23360 | ||||||||
\(894\) | 8.19136 | 0.273960 | ||||||||
\(895\) | −19.6353 | −0.656337 | ||||||||
\(896\) | −1.75302 | −0.0585643 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.08516 | −0.136324 | ||||||||
\(899\) | 27.6886 | 0.923465 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 7.77133 | 0.258901 | ||||||||
\(902\) | −7.94438 | −0.264519 | ||||||||
\(903\) | 7.14542 | 0.237785 | ||||||||
\(904\) | −0.515729 | −0.0171529 | ||||||||
\(905\) | −5.25906 | −0.174817 | ||||||||
\(906\) | 5.72348 | 0.190150 | ||||||||
\(907\) | −45.4916 | −1.51052 | −0.755261 | − | 0.655424i | \(-0.772490\pi\) | ||||
−0.755261 | + | 0.655424i | \(0.772490\pi\) | |||||||
\(908\) | −5.97716 | −0.198359 | ||||||||
\(909\) | 16.7875 | 0.556805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.4349 | 1.57159 | 0.785794 | − | 0.618489i | \(-0.212255\pi\) | ||||
0.785794 | + | 0.618489i | \(0.212255\pi\) | |||||||
\(912\) | 8.63102 | 0.285802 | ||||||||
\(913\) | 10.0707 | 0.333291 | ||||||||
\(914\) | −41.8678 | −1.38487 | ||||||||
\(915\) | 1.18598 | 0.0392073 | ||||||||
\(916\) | −15.9172 | −0.525920 | ||||||||
\(917\) | −8.91962 | −0.294552 | ||||||||
\(918\) | 6.76271 | 0.223203 | ||||||||
\(919\) | −20.3907 | −0.672629 | −0.336314 | − | 0.941750i | \(-0.609180\pi\) | ||||
−0.336314 | + | 0.941750i | \(0.609180\pi\) | |||||||
\(920\) | −6.04892 | −0.199427 | ||||||||
\(921\) | 28.7265 | 0.946569 | ||||||||
\(922\) | 0.215521 | 0.00709779 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.10023 | 0.0690924 | ||||||||
\(925\) | −4.34481 | −0.142857 | ||||||||
\(926\) | −23.4795 | −0.771584 | ||||||||
\(927\) | −4.16421 | −0.136771 | ||||||||
\(928\) | −4.07069 | −0.133627 | ||||||||
\(929\) | −1.26636 | −0.0415478 | −0.0207739 | − | 0.999784i | \(-0.506613\pi\) | ||||
−0.0207739 | + | 0.999784i | \(0.506613\pi\) | |||||||
\(930\) | 6.80194 | 0.223044 | ||||||||
\(931\) | −33.8933 | −1.11081 | ||||||||
\(932\) | −6.92154 | −0.226723 | ||||||||
\(933\) | −18.6329 | −0.610015 | ||||||||
\(934\) | −10.1153 | −0.330983 | ||||||||
\(935\) | 8.10215 | 0.264969 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.3558 | 0.893676 | 0.446838 | − | 0.894615i | \(-0.352550\pi\) | ||||
0.446838 | + | 0.894615i | \(0.352550\pi\) | |||||||
\(938\) | −24.7995 | −0.809734 | ||||||||
\(939\) | −29.3696 | −0.958440 | ||||||||
\(940\) | 11.1957 | 0.365162 | ||||||||
\(941\) | −60.6620 | −1.97752 | −0.988762 | − | 0.149495i | \(-0.952235\pi\) | ||||
−0.988762 | + | 0.149495i | \(0.952235\pi\) | |||||||
\(942\) | −3.09246 | −0.100758 | ||||||||
\(943\) | −40.1105 | −1.30618 | ||||||||
\(944\) | 13.7235 | 0.446661 | ||||||||
\(945\) | −1.75302 | −0.0570258 | ||||||||
\(946\) | −4.88338 | −0.158772 | ||||||||
\(947\) | −12.3797 | −0.402287 | −0.201144 | − | 0.979562i | \(-0.564466\pi\) | ||||
−0.201144 | + | 0.979562i | \(0.564466\pi\) | |||||||
\(948\) | 3.74094 | 0.121500 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.63102 | −0.280027 | ||||||||
\(951\) | 20.8092 | 0.674786 | ||||||||
\(952\) | 11.8552 | 0.384228 | ||||||||
\(953\) | 28.7784 | 0.932223 | 0.466111 | − | 0.884726i | \(-0.345655\pi\) | ||||
0.466111 | + | 0.884726i | \(0.345655\pi\) | |||||||
\(954\) | 1.14914 | 0.0372049 | ||||||||
\(955\) | −4.45473 | −0.144152 | ||||||||
\(956\) | 30.1075 | 0.973747 | ||||||||
\(957\) | 4.87694 | 0.157649 | ||||||||
\(958\) | −0.980623 | −0.0316825 | ||||||||
\(959\) | 1.18252 | 0.0381857 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 15.2664 | 0.492463 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.9661 | 0.417828 | ||||||||
\(964\) | 12.0562 | 0.388304 | ||||||||
\(965\) | 0.818331 | 0.0263430 | ||||||||
\(966\) | 10.6039 | 0.341174 | ||||||||
\(967\) | −23.1545 | −0.744599 | −0.372300 | − | 0.928113i | \(-0.621431\pi\) | ||||
−0.372300 | + | 0.928113i | \(0.621431\pi\) | |||||||
\(968\) | 9.56465 | 0.307419 | ||||||||
\(969\) | −58.3691 | −1.87509 | ||||||||
\(970\) | −10.7952 | −0.346614 | ||||||||
\(971\) | −2.89572 | −0.0929282 | −0.0464641 | − | 0.998920i | \(-0.514795\pi\) | ||||
−0.0464641 | + | 0.998920i | \(0.514795\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 14.4835 | 0.464321 | ||||||||
\(974\) | −7.18300 | −0.230158 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.18598 | −0.0379623 | ||||||||
\(977\) | −4.86294 | −0.155579 | −0.0777896 | − | 0.996970i | \(-0.524786\pi\) | ||||
−0.0777896 | + | 0.996970i | \(0.524786\pi\) | |||||||
\(978\) | −23.9541 | −0.765967 | ||||||||
\(979\) | 5.39048 | 0.172281 | ||||||||
\(980\) | 3.92692 | 0.125441 | ||||||||
\(981\) | −19.4644 | −0.621451 | ||||||||
\(982\) | −24.5918 | −0.784756 | ||||||||
\(983\) | −52.7506 | −1.68248 | −0.841242 | − | 0.540659i | \(-0.818175\pi\) | ||||
−0.841242 | + | 0.540659i | \(0.818175\pi\) | |||||||
\(984\) | −6.63102 | −0.211389 | ||||||||
\(985\) | −12.7385 | −0.405884 | ||||||||
\(986\) | 27.5289 | 0.876698 | ||||||||
\(987\) | −19.6262 | −0.624710 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.6558 | −0.784008 | ||||||||
\(990\) | 1.19806 | 0.0380769 | ||||||||
\(991\) | 7.15538 | 0.227298 | 0.113649 | − | 0.993521i | \(-0.463746\pi\) | ||||
0.113649 | + | 0.993521i | \(0.463746\pi\) | |||||||
\(992\) | −6.80194 | −0.215962 | ||||||||
\(993\) | −11.7603 | −0.373202 | ||||||||
\(994\) | 4.07234 | 0.129167 | ||||||||
\(995\) | 4.02475 | 0.127593 | ||||||||
\(996\) | 8.40581 | 0.266348 | ||||||||
\(997\) | 39.3870 | 1.24740 | 0.623700 | − | 0.781664i | \(-0.285629\pi\) | ||||
0.623700 | + | 0.781664i | \(0.285629\pi\) | |||||||
\(998\) | −30.1608 | −0.954722 | ||||||||
\(999\) | −4.34481 | −0.137464 |
(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 | 5070.2.a.bo.1.1 | ✓ | 3 | |
13.5 | odd | 4 | 5070.2.b.w.1351.4 | 6 | |||
13.8 | odd | 4 | 5070.2.b.w.1351.3 | 6 | |||
13.12 | even | 2 | 5070.2.a.bx.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bo.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5070.2.a.bx.1.3 | yes | 3 | 13.12 | even | 2 | ||
5070.2.b.w.1351.3 | 6 | 13.8 | odd | 4 | |||
5070.2.b.w.1351.4 | 6 | 13.5 | odd | 4 |