Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
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.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.4 | ||
Root | \(-1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.w.1351.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 1.75302i | 0.662579i | 0.943529 | + | 0.331290i | \(0.107484\pi\) | ||||
−0.943529 | + | 0.331290i | \(0.892516\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.19806i | 0.361229i | 0.983554 | + | 0.180615i | \(0.0578087\pi\) | ||||
−0.983554 | + | 0.180615i | \(0.942191\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.75302 | −0.468514 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.76271 | 1.64020 | 0.820099 | − | 0.572222i | \(-0.193918\pi\) | ||||
0.820099 | + | 0.572222i | \(0.193918\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | − 8.63102i | − 1.98009i | −0.140743 | − | 0.990046i | \(-0.544949\pi\) | ||||
0.140743 | − | 0.990046i | \(-0.455051\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | 1.75302i | 0.382540i | ||||||||
\(22\) | −1.19806 | −0.255428 | ||||||||
\(23\) | 6.04892 | 1.26129 | 0.630643 | − | 0.776073i | \(-0.282791\pi\) | ||||
0.630643 | + | 0.776073i | \(0.282791\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 1.75302i | − 0.331290i | ||||||||
\(29\) | 4.07069 | 0.755908 | 0.377954 | − | 0.925824i | \(-0.376628\pi\) | ||||
0.377954 | + | 0.925824i | \(0.376628\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − 6.80194i | − 1.22166i | −0.791760 | − | 0.610832i | \(-0.790835\pi\) | ||||
0.791760 | − | 0.610832i | \(-0.209165\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.19806i | 0.208556i | ||||||||
\(34\) | 6.76271i | 1.15980i | ||||||||
\(35\) | −1.75302 | −0.296315 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 4.34481i | − 0.714283i | −0.934050 | − | 0.357142i | \(-0.883751\pi\) | ||||
0.934050 | − | 0.357142i | \(-0.116249\pi\) | |||||||
\(38\) | 8.63102 | 1.40014 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | − 6.63102i | − 1.03559i | −0.855504 | − | 0.517796i | \(-0.826753\pi\) | ||||
0.855504 | − | 0.517796i | \(-0.173247\pi\) | |||||||
\(42\) | −1.75302 | −0.270497 | ||||||||
\(43\) | −4.07606 | −0.621594 | −0.310797 | − | 0.950476i | \(-0.600596\pi\) | ||||
−0.310797 | + | 0.950476i | \(0.600596\pi\) | |||||||
\(44\) | − 1.19806i | − 0.180615i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 6.04892i | 0.891864i | ||||||||
\(47\) | − 11.1957i | − 1.63306i | −0.577306 | − | 0.816528i | \(-0.695896\pi\) | ||||
0.577306 | − | 0.816528i | \(-0.304104\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 3.92692 | 0.560988 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 6.76271 | 0.946969 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.14914 | −0.157847 | −0.0789236 | − | 0.996881i | \(-0.525148\pi\) | ||||
−0.0789236 | + | 0.996881i | \(0.525148\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −1.19806 | −0.161547 | ||||||||
\(56\) | 1.75302 | 0.234257 | ||||||||
\(57\) | − 8.63102i | − 1.14321i | ||||||||
\(58\) | 4.07069i | 0.534507i | ||||||||
\(59\) | 13.7235i | 1.78664i | 0.449416 | + | 0.893322i | \(0.351632\pi\) | ||||
−0.449416 | + | 0.893322i | \(0.648368\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | −1.18598 | −0.151849 | −0.0759246 | − | 0.997114i | \(-0.524191\pi\) | ||||
−0.0759246 | + | 0.997114i | \(0.524191\pi\) | |||||||
\(62\) | 6.80194 | 0.863847 | ||||||||
\(63\) | 1.75302i | 0.220860i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.19806 | −0.147471 | ||||||||
\(67\) | − 14.1468i | − 1.72830i | −0.503234 | − | 0.864150i | \(-0.667856\pi\) | ||||
0.503234 | − | 0.864150i | \(-0.332144\pi\) | |||||||
\(68\) | −6.76271 | −0.820099 | ||||||||
\(69\) | 6.04892 | 0.728204 | ||||||||
\(70\) | − 1.75302i | − 0.209526i | ||||||||
\(71\) | 2.32304i | 0.275695i | 0.990453 | + | 0.137847i | \(0.0440183\pi\) | ||||
−0.990453 | + | 0.137847i | \(0.955982\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 1.59850i | 0.187090i | 0.995615 | + | 0.0935451i | \(0.0298199\pi\) | ||||
−0.995615 | + | 0.0935451i | \(0.970180\pi\) | |||||||
\(74\) | 4.34481 | 0.505074 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 8.63102i | 0.990046i | ||||||||
\(77\) | −2.10023 | −0.239343 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.74094 | 0.420888 | 0.210444 | − | 0.977606i | \(-0.432509\pi\) | ||||
0.210444 | + | 0.977606i | \(0.432509\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.63102 | 0.732274 | ||||||||
\(83\) | − 8.40581i | − 0.922658i | −0.887229 | − | 0.461329i | \(-0.847373\pi\) | ||||
0.887229 | − | 0.461329i | \(-0.152627\pi\) | |||||||
\(84\) | − 1.75302i | − 0.191270i | ||||||||
\(85\) | 6.76271i | 0.733519i | ||||||||
\(86\) | − 4.07606i | − 0.439533i | ||||||||
\(87\) | 4.07069 | 0.436424 | ||||||||
\(88\) | 1.19806 | 0.127714 | ||||||||
\(89\) | 4.49934i | 0.476929i | 0.971151 | + | 0.238464i | \(0.0766440\pi\) | ||||
−0.971151 | + | 0.238464i | \(0.923356\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.04892 | −0.630643 | ||||||||
\(93\) | − 6.80194i | − 0.705328i | ||||||||
\(94\) | 11.1957 | 1.15475 | ||||||||
\(95\) | 8.63102 | 0.885524 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 10.7952i | 1.09609i | 0.836449 | + | 0.548045i | \(0.184628\pi\) | ||||
−0.836449 | + | 0.548045i | \(0.815372\pi\) | |||||||
\(98\) | 3.92692i | 0.396679i | ||||||||
\(99\) | 1.19806i | 0.120410i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −16.7875 | −1.67042 | −0.835208 | − | 0.549935i | \(-0.814653\pi\) | ||||
−0.835208 | + | 0.549935i | \(0.814653\pi\) | |||||||
\(102\) | 6.76271i | 0.669608i | ||||||||
\(103\) | 4.16421 | 0.410312 | 0.205156 | − | 0.978729i | \(-0.434230\pi\) | ||||
0.205156 | + | 0.978729i | \(0.434230\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.75302 | −0.171077 | ||||||||
\(106\) | − 1.14914i | − 0.111615i | ||||||||
\(107\) | 12.9661 | 1.25348 | 0.626742 | − | 0.779226i | \(-0.284388\pi\) | ||||
0.626742 | + | 0.779226i | \(0.284388\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 19.4644i | 1.86435i | 0.362004 | + | 0.932177i | \(0.382093\pi\) | ||||
−0.362004 | + | 0.932177i | \(0.617907\pi\) | |||||||
\(110\) | − 1.19806i | − 0.114231i | ||||||||
\(111\) | − 4.34481i | − 0.412392i | ||||||||
\(112\) | 1.75302i | 0.165645i | ||||||||
\(113\) | 0.515729 | 0.0485157 | 0.0242579 | − | 0.999706i | \(-0.492278\pi\) | ||||
0.0242579 | + | 0.999706i | \(0.492278\pi\) | |||||||
\(114\) | 8.63102 | 0.808369 | ||||||||
\(115\) | 6.04892i | 0.564064i | ||||||||
\(116\) | −4.07069 | −0.377954 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.7235 | −1.26335 | ||||||||
\(119\) | 11.8552i | 1.08676i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 9.56465 | 0.869513 | ||||||||
\(122\) | − 1.18598i | − 0.107374i | ||||||||
\(123\) | − 6.63102i | − 0.597899i | ||||||||
\(124\) | 6.80194i | 0.610832i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | −1.75302 | −0.156171 | ||||||||
\(127\) | −7.96077 | −0.706404 | −0.353202 | − | 0.935547i | \(-0.614907\pi\) | ||||
−0.353202 | + | 0.935547i | \(0.614907\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −4.07606 | −0.358877 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.08815 | −0.444553 | −0.222277 | − | 0.974984i | \(-0.571349\pi\) | ||||
−0.222277 | + | 0.974984i | \(0.571349\pi\) | |||||||
\(132\) | − 1.19806i | − 0.104278i | ||||||||
\(133\) | 15.1304 | 1.31197 | ||||||||
\(134\) | 14.1468 | 1.22209 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | − 6.76271i | − 0.579898i | ||||||||
\(137\) | 0.674563i | 0.0576318i | 0.999585 | + | 0.0288159i | \(0.00917366\pi\) | ||||
−0.999585 | + | 0.0288159i | \(0.990826\pi\) | |||||||
\(138\) | 6.04892i | 0.514918i | ||||||||
\(139\) | 8.26205 | 0.700778 | 0.350389 | − | 0.936604i | \(-0.386049\pi\) | ||||
0.350389 | + | 0.936604i | \(0.386049\pi\) | |||||||
\(140\) | 1.75302 | 0.148157 | ||||||||
\(141\) | − 11.1957i | − 0.942845i | ||||||||
\(142\) | −2.32304 | −0.194946 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.07069i | 0.338052i | ||||||||
\(146\) | −1.59850 | −0.132293 | ||||||||
\(147\) | 3.92692 | 0.323887 | ||||||||
\(148\) | 4.34481i | 0.357142i | ||||||||
\(149\) | 8.19136i | 0.671062i | 0.942029 | + | 0.335531i | \(0.108916\pi\) | ||||
−0.942029 | + | 0.335531i | \(0.891084\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | − 5.72348i | − 0.465770i | −0.972504 | − | 0.232885i | \(-0.925183\pi\) | ||||
0.972504 | − | 0.232885i | \(-0.0748166\pi\) | |||||||
\(152\) | −8.63102 | −0.700068 | ||||||||
\(153\) | 6.76271 | 0.546733 | ||||||||
\(154\) | − 2.10023i | − 0.169241i | ||||||||
\(155\) | 6.80194 | 0.546345 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.09246 | 0.246805 | 0.123403 | − | 0.992357i | \(-0.460619\pi\) | ||||
0.123403 | + | 0.992357i | \(0.460619\pi\) | |||||||
\(158\) | 3.74094i | 0.297613i | ||||||||
\(159\) | −1.14914 | −0.0911331 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 10.6039i | 0.835702i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 23.9541i | 1.87623i | 0.346328 | + | 0.938114i | \(0.387429\pi\) | ||||
−0.346328 | + | 0.938114i | \(0.612571\pi\) | |||||||
\(164\) | 6.63102i | 0.517796i | ||||||||
\(165\) | −1.19806 | −0.0932690 | ||||||||
\(166\) | 8.40581 | 0.652418 | ||||||||
\(167\) | − 1.19806i | − 0.0927088i | −0.998925 | − | 0.0463544i | \(-0.985240\pi\) | ||||
0.998925 | − | 0.0463544i | \(-0.0147604\pi\) | |||||||
\(168\) | 1.75302 | 0.135248 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −6.76271 | −0.518676 | ||||||||
\(171\) | − 8.63102i | − 0.660031i | ||||||||
\(172\) | 4.07606 | 0.310797 | ||||||||
\(173\) | 6.63773 | 0.504657 | 0.252329 | − | 0.967642i | \(-0.418804\pi\) | ||||
0.252329 | + | 0.967642i | \(0.418804\pi\) | |||||||
\(174\) | 4.07069i | 0.308598i | ||||||||
\(175\) | − 1.75302i | − 0.132516i | ||||||||
\(176\) | 1.19806i | 0.0903073i | ||||||||
\(177\) | 13.7235i | 1.03152i | ||||||||
\(178\) | −4.49934 | −0.337239 | ||||||||
\(179\) | −19.6353 | −1.46761 | −0.733807 | − | 0.679358i | \(-0.762258\pi\) | ||||
−0.733807 | + | 0.679358i | \(0.762258\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | −5.25906 | −0.390903 | −0.195451 | − | 0.980713i | \(-0.562617\pi\) | ||||
−0.195451 | + | 0.980713i | \(0.562617\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.18598 | −0.0876702 | ||||||||
\(184\) | − 6.04892i | − 0.445932i | ||||||||
\(185\) | 4.34481 | 0.319437 | ||||||||
\(186\) | 6.80194 | 0.498742 | ||||||||
\(187\) | 8.10215i | 0.592488i | ||||||||
\(188\) | 11.1957i | 0.816528i | ||||||||
\(189\) | 1.75302i | 0.127513i | ||||||||
\(190\) | 8.63102i | 0.626160i | ||||||||
\(191\) | 4.45473 | 0.322333 | 0.161166 | − | 0.986927i | \(-0.448474\pi\) | ||||
0.161166 | + | 0.986927i | \(0.448474\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − 0.818331i | − 0.0589048i | −0.999566 | − | 0.0294524i | \(-0.990624\pi\) | ||||
0.999566 | − | 0.0294524i | \(-0.00937634\pi\) | |||||||
\(194\) | −10.7952 | −0.775053 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.92692 | −0.280494 | ||||||||
\(197\) | − 12.7385i | − 0.907584i | −0.891108 | − | 0.453792i | \(-0.850071\pi\) | ||||
0.891108 | − | 0.453792i | \(-0.149929\pi\) | |||||||
\(198\) | −1.19806 | −0.0851426 | ||||||||
\(199\) | 4.02475 | 0.285307 | 0.142654 | − | 0.989773i | \(-0.454437\pi\) | ||||
0.142654 | + | 0.989773i | \(0.454437\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | − 14.1468i | − 0.997835i | ||||||||
\(202\) | − 16.7875i | − 1.18116i | ||||||||
\(203\) | 7.13600i | 0.500849i | ||||||||
\(204\) | −6.76271 | −0.473484 | ||||||||
\(205\) | 6.63102 | 0.463131 | ||||||||
\(206\) | 4.16421i | 0.290134i | ||||||||
\(207\) | 6.04892 | 0.420429 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.3405 | 0.715268 | ||||||||
\(210\) | − 1.75302i | − 0.120970i | ||||||||
\(211\) | 3.10992 | 0.214095 | 0.107048 | − | 0.994254i | \(-0.465860\pi\) | ||||
0.107048 | + | 0.994254i | \(0.465860\pi\) | |||||||
\(212\) | 1.14914 | 0.0789236 | ||||||||
\(213\) | 2.32304i | 0.159172i | ||||||||
\(214\) | 12.9661i | 0.886348i | ||||||||
\(215\) | − 4.07606i | − 0.277985i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | 11.9239 | 0.809449 | ||||||||
\(218\) | −19.4644 | −1.31830 | ||||||||
\(219\) | 1.59850i | 0.108017i | ||||||||
\(220\) | 1.19806 | 0.0807733 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.34481 | 0.291605 | ||||||||
\(223\) | − 14.3787i | − 0.962867i | −0.876483 | − | 0.481433i | \(-0.840116\pi\) | ||||
0.876483 | − | 0.481433i | \(-0.159884\pi\) | |||||||
\(224\) | −1.75302 | −0.117129 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 0.515729i | 0.0343058i | ||||||||
\(227\) | 5.97716i | 0.396718i | 0.980129 | + | 0.198359i | \(0.0635612\pi\) | ||||
−0.980129 | + | 0.198359i | \(0.936439\pi\) | |||||||
\(228\) | 8.63102i | 0.571603i | ||||||||
\(229\) | − 15.9172i | − 1.05184i | −0.850534 | − | 0.525920i | \(-0.823721\pi\) | ||||
0.850534 | − | 0.525920i | \(-0.176279\pi\) | |||||||
\(230\) | −6.04892 | −0.398854 | ||||||||
\(231\) | −2.10023 | −0.138185 | ||||||||
\(232\) | − 4.07069i | − 0.267254i | ||||||||
\(233\) | 6.92154 | 0.453445 | 0.226723 | − | 0.973959i | \(-0.427199\pi\) | ||||
0.226723 | + | 0.973959i | \(0.427199\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.1957 | 0.730325 | ||||||||
\(236\) | − 13.7235i | − 0.893322i | ||||||||
\(237\) | 3.74094 | 0.243000 | ||||||||
\(238\) | −11.8552 | −0.768456 | ||||||||
\(239\) | − 30.1075i | − 1.94749i | −0.227633 | − | 0.973747i | \(-0.573099\pi\) | ||||
0.227633 | − | 0.973747i | \(-0.426901\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | 12.0562i | 0.776609i | 0.921531 | + | 0.388304i | \(0.126939\pi\) | ||||
−0.921531 | + | 0.388304i | \(0.873061\pi\) | |||||||
\(242\) | 9.56465i | 0.614839i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.18598 | 0.0759246 | ||||||||
\(245\) | 3.92692i | 0.250882i | ||||||||
\(246\) | 6.63102 | 0.422779 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.80194 | −0.431923 | ||||||||
\(249\) | − 8.40581i | − 0.532697i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 14.8170 | 0.935241 | 0.467620 | − | 0.883929i | \(-0.345111\pi\) | ||||
0.467620 | + | 0.883929i | \(0.345111\pi\) | |||||||
\(252\) | − 1.75302i | − 0.110430i | ||||||||
\(253\) | 7.24698i | 0.455614i | ||||||||
\(254\) | − 7.96077i | − 0.499503i | ||||||||
\(255\) | 6.76271i | 0.423497i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.5743 | 0.659609 | 0.329804 | − | 0.944049i | \(-0.393017\pi\) | ||||
0.329804 | + | 0.944049i | \(0.393017\pi\) | |||||||
\(258\) | − 4.07606i | − 0.253765i | ||||||||
\(259\) | 7.61655 | 0.473269 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.07069 | 0.251969 | ||||||||
\(262\) | − 5.08815i | − 0.314347i | ||||||||
\(263\) | 11.9922 | 0.739473 | 0.369736 | − | 0.929137i | \(-0.379448\pi\) | ||||
0.369736 | + | 0.929137i | \(0.379448\pi\) | |||||||
\(264\) | 1.19806 | 0.0737356 | ||||||||
\(265\) | − 1.14914i | − 0.0705914i | ||||||||
\(266\) | 15.1304i | 0.927702i | ||||||||
\(267\) | 4.49934i | 0.275355i | ||||||||
\(268\) | 14.1468i | 0.864150i | ||||||||
\(269\) | −25.4359 | −1.55086 | −0.775428 | − | 0.631435i | \(-0.782466\pi\) | ||||
−0.775428 | + | 0.631435i | \(0.782466\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 20.3666i | 1.23718i | 0.785713 | + | 0.618591i | \(0.212296\pi\) | ||||
−0.785713 | + | 0.618591i | \(0.787704\pi\) | |||||||
\(272\) | 6.76271 | 0.410049 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.674563 | −0.0407518 | ||||||||
\(275\) | − 1.19806i | − 0.0722459i | ||||||||
\(276\) | −6.04892 | −0.364102 | ||||||||
\(277\) | −20.1323 | −1.20963 | −0.604816 | − | 0.796366i | \(-0.706753\pi\) | ||||
−0.604816 | + | 0.796366i | \(0.706753\pi\) | |||||||
\(278\) | 8.26205i | 0.495525i | ||||||||
\(279\) | − 6.80194i | − 0.407221i | ||||||||
\(280\) | 1.75302i | 0.104763i | ||||||||
\(281\) | − 29.7265i | − 1.77333i | −0.462410 | − | 0.886666i | \(-0.653015\pi\) | ||||
0.462410 | − | 0.886666i | \(-0.346985\pi\) | |||||||
\(282\) | 11.1957 | 0.666692 | ||||||||
\(283\) | −8.84117 | −0.525553 | −0.262776 | − | 0.964857i | \(-0.584638\pi\) | ||||
−0.262776 | + | 0.964857i | \(0.584638\pi\) | |||||||
\(284\) | − 2.32304i | − 0.137847i | ||||||||
\(285\) | 8.63102 | 0.511258 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6243 | 0.686162 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 28.7342 | 1.69025 | ||||||||
\(290\) | −4.07069 | −0.239039 | ||||||||
\(291\) | 10.7952i | 0.632828i | ||||||||
\(292\) | − 1.59850i | − 0.0935451i | ||||||||
\(293\) | 20.5918i | 1.20299i | 0.798878 | + | 0.601493i | \(0.205427\pi\) | ||||
−0.798878 | + | 0.601493i | \(0.794573\pi\) | |||||||
\(294\) | 3.92692i | 0.229023i | ||||||||
\(295\) | −13.7235 | −0.799012 | ||||||||
\(296\) | −4.34481 | −0.252537 | ||||||||
\(297\) | 1.19806i | 0.0695186i | ||||||||
\(298\) | −8.19136 | −0.474513 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | − 7.14542i | − 0.411855i | ||||||||
\(302\) | 5.72348 | 0.329349 | ||||||||
\(303\) | −16.7875 | −0.964415 | ||||||||
\(304\) | − 8.63102i | − 0.495023i | ||||||||
\(305\) | − 1.18598i | − 0.0679091i | ||||||||
\(306\) | 6.76271i | 0.386598i | ||||||||
\(307\) | 28.7265i | 1.63951i | 0.572717 | + | 0.819753i | \(0.305889\pi\) | ||||
−0.572717 | + | 0.819753i | \(0.694111\pi\) | |||||||
\(308\) | 2.10023 | 0.119672 | ||||||||
\(309\) | 4.16421 | 0.236894 | ||||||||
\(310\) | 6.80194i | 0.386324i | ||||||||
\(311\) | 18.6329 | 1.05658 | 0.528289 | − | 0.849065i | \(-0.322834\pi\) | ||||
0.528289 | + | 0.849065i | \(0.322834\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.3696 | −1.66007 | −0.830033 | − | 0.557714i | \(-0.811679\pi\) | ||||
−0.830033 | + | 0.557714i | \(0.811679\pi\) | |||||||
\(314\) | 3.09246i | 0.174517i | ||||||||
\(315\) | −1.75302 | −0.0987715 | ||||||||
\(316\) | −3.74094 | −0.210444 | ||||||||
\(317\) | − 20.8092i | − 1.16876i | −0.811479 | − | 0.584381i | \(-0.801337\pi\) | ||||
0.811479 | − | 0.584381i | \(-0.198663\pi\) | |||||||
\(318\) | − 1.14914i | − 0.0644408i | ||||||||
\(319\) | 4.87694i | 0.273056i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | 12.9661 | 0.723700 | ||||||||
\(322\) | −10.6039 | −0.590931 | ||||||||
\(323\) | − 58.3691i | − 3.24774i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.9541 | −1.32669 | ||||||||
\(327\) | 19.4644i | 1.07638i | ||||||||
\(328\) | −6.63102 | −0.366137 | ||||||||
\(329\) | 19.6262 | 1.08203 | ||||||||
\(330\) | − 1.19806i | − 0.0659512i | ||||||||
\(331\) | 11.7603i | 0.646405i | 0.946330 | + | 0.323203i | \(0.104760\pi\) | ||||
−0.946330 | + | 0.323203i | \(0.895240\pi\) | |||||||
\(332\) | 8.40581i | 0.461329i | ||||||||
\(333\) | − 4.34481i | − 0.238094i | ||||||||
\(334\) | 1.19806 | 0.0655551 | ||||||||
\(335\) | 14.1468 | 0.772920 | ||||||||
\(336\) | 1.75302i | 0.0956351i | ||||||||
\(337\) | 26.8732 | 1.46388 | 0.731939 | − | 0.681371i | \(-0.238616\pi\) | ||||
0.731939 | + | 0.681371i | \(0.238616\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.515729 | 0.0280106 | ||||||||
\(340\) | − 6.76271i | − 0.366759i | ||||||||
\(341\) | 8.14914 | 0.441301 | ||||||||
\(342\) | 8.63102 | 0.466712 | ||||||||
\(343\) | 19.1551i | 1.03428i | ||||||||
\(344\) | 4.07606i | 0.219767i | ||||||||
\(345\) | 6.04892i | 0.325663i | ||||||||
\(346\) | 6.63773i | 0.356846i | ||||||||
\(347\) | 29.5080 | 1.58407 | 0.792035 | − | 0.610476i | \(-0.209022\pi\) | ||||
0.792035 | + | 0.610476i | \(0.209022\pi\) | |||||||
\(348\) | −4.07069 | −0.218212 | ||||||||
\(349\) | 17.0519i | 0.912767i | 0.889783 | + | 0.456384i | \(0.150856\pi\) | ||||
−0.889783 | + | 0.456384i | \(0.849144\pi\) | |||||||
\(350\) | 1.75302 | 0.0937029 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.19806 | −0.0638569 | ||||||||
\(353\) | 21.8629i | 1.16365i | 0.813315 | + | 0.581823i | \(0.197660\pi\) | ||||
−0.813315 | + | 0.581823i | \(0.802340\pi\) | |||||||
\(354\) | −13.7235 | −0.729395 | ||||||||
\(355\) | −2.32304 | −0.123294 | ||||||||
\(356\) | − 4.49934i | − 0.238464i | ||||||||
\(357\) | 11.8552i | 0.627442i | ||||||||
\(358\) | − 19.6353i | − 1.03776i | ||||||||
\(359\) | 14.3026i | 0.754862i | 0.926038 | + | 0.377431i | \(0.123193\pi\) | ||||
−0.926038 | + | 0.377431i | \(0.876807\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −55.4946 | −2.92077 | ||||||||
\(362\) | − 5.25906i | − 0.276410i | ||||||||
\(363\) | 9.56465 | 0.502014 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.59850 | −0.0836692 | ||||||||
\(366\) | − 1.18598i | − 0.0619922i | ||||||||
\(367\) | −11.2416 | −0.586807 | −0.293403 | − | 0.955989i | \(-0.594788\pi\) | ||||
−0.293403 | + | 0.955989i | \(0.594788\pi\) | |||||||
\(368\) | 6.04892 | 0.315322 | ||||||||
\(369\) | − 6.63102i | − 0.345197i | ||||||||
\(370\) | 4.34481i | 0.225876i | ||||||||
\(371\) | − 2.01447i | − 0.104586i | ||||||||
\(372\) | 6.80194i | 0.352664i | ||||||||
\(373\) | −9.70171 | −0.502336 | −0.251168 | − | 0.967944i | \(-0.580815\pi\) | ||||
−0.251168 | + | 0.967944i | \(0.580815\pi\) | |||||||
\(374\) | −8.10215 | −0.418952 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | −11.1957 | −0.577373 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.75302 | −0.0901656 | ||||||||
\(379\) | 2.82802i | 0.145266i | 0.997359 | + | 0.0726328i | \(0.0231401\pi\) | ||||
−0.997359 | + | 0.0726328i | \(0.976860\pi\) | |||||||
\(380\) | −8.63102 | −0.442762 | ||||||||
\(381\) | −7.96077 | −0.407843 | ||||||||
\(382\) | 4.45473i | 0.227924i | ||||||||
\(383\) | − 11.6558i | − 0.595582i | −0.954631 | − | 0.297791i | \(-0.903750\pi\) | ||||
0.954631 | − | 0.297791i | \(-0.0962499\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | − 2.10023i | − 0.107038i | ||||||||
\(386\) | 0.818331 | 0.0416520 | ||||||||
\(387\) | −4.07606 | −0.207198 | ||||||||
\(388\) | − 10.7952i | − 0.548045i | ||||||||
\(389\) | −12.5157 | −0.634573 | −0.317286 | − | 0.948330i | \(-0.602772\pi\) | ||||
−0.317286 | + | 0.948330i | \(0.602772\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.9071 | 2.06876 | ||||||||
\(392\) | − 3.92692i | − 0.198339i | ||||||||
\(393\) | −5.08815 | −0.256663 | ||||||||
\(394\) | 12.7385 | 0.641759 | ||||||||
\(395\) | 3.74094i | 0.188227i | ||||||||
\(396\) | − 1.19806i | − 0.0602049i | ||||||||
\(397\) | 21.6136i | 1.08475i | 0.840135 | + | 0.542377i | \(0.182475\pi\) | ||||
−0.840135 | + | 0.542377i | \(0.817525\pi\) | |||||||
\(398\) | 4.02475i | 0.201743i | ||||||||
\(399\) | 15.1304 | 0.757465 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 11.5157i | − 0.575068i | −0.957770 | − | 0.287534i | \(-0.907165\pi\) | ||||
0.957770 | − | 0.287534i | \(-0.0928354\pi\) | |||||||
\(402\) | 14.1468 | 0.705576 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 16.7875 | 0.835208 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | −7.13600 | −0.354154 | ||||||||
\(407\) | 5.20536 | 0.258020 | ||||||||
\(408\) | − 6.76271i | − 0.334804i | ||||||||
\(409\) | 0.0991626i | 0.00490328i | 0.999997 | + | 0.00245164i | \(0.000780382\pi\) | ||||
−0.999997 | + | 0.00245164i | \(0.999220\pi\) | |||||||
\(410\) | 6.63102i | 0.327483i | ||||||||
\(411\) | 0.674563i | 0.0332737i | ||||||||
\(412\) | −4.16421 | −0.205156 | ||||||||
\(413\) | −24.0575 | −1.18379 | ||||||||
\(414\) | 6.04892i | 0.297288i | ||||||||
\(415\) | 8.40581 | 0.412625 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.26205 | 0.404594 | ||||||||
\(418\) | 10.3405i | 0.505771i | ||||||||
\(419\) | 31.2784 | 1.52805 | 0.764026 | − | 0.645186i | \(-0.223220\pi\) | ||||
0.764026 | + | 0.645186i | \(0.223220\pi\) | |||||||
\(420\) | 1.75302 | 0.0855386 | ||||||||
\(421\) | 38.0452i | 1.85421i | 0.374802 | + | 0.927105i | \(0.377711\pi\) | ||||
−0.374802 | + | 0.927105i | \(0.622289\pi\) | |||||||
\(422\) | 3.10992i | 0.151388i | ||||||||
\(423\) | − 11.1957i | − 0.544352i | ||||||||
\(424\) | 1.14914i | 0.0558074i | ||||||||
\(425\) | −6.76271 | −0.328040 | ||||||||
\(426\) | −2.32304 | −0.112552 | ||||||||
\(427\) | − 2.07905i | − 0.100612i | ||||||||
\(428\) | −12.9661 | −0.626742 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.07606 | 0.196565 | ||||||||
\(431\) | 14.4614i | 0.696583i | 0.937386 | + | 0.348291i | \(0.113238\pi\) | ||||
−0.937386 | + | 0.348291i | \(0.886762\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −21.6209 | −1.03903 | −0.519516 | − | 0.854461i | \(-0.673888\pi\) | ||||
−0.519516 | + | 0.854461i | \(0.673888\pi\) | |||||||
\(434\) | 11.9239i | 0.572367i | ||||||||
\(435\) | 4.07069i | 0.195175i | ||||||||
\(436\) | − 19.4644i | − 0.932177i | ||||||||
\(437\) | − 52.2083i | − 2.49746i | ||||||||
\(438\) | −1.59850 | −0.0763792 | ||||||||
\(439\) | 3.23623 | 0.154457 | 0.0772283 | − | 0.997013i | \(-0.475393\pi\) | ||||
0.0772283 | + | 0.997013i | \(0.475393\pi\) | |||||||
\(440\) | 1.19806i | 0.0571154i | ||||||||
\(441\) | 3.92692 | 0.186996 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.6649 | −0.696749 | −0.348375 | − | 0.937355i | \(-0.613266\pi\) | ||||
−0.348375 | + | 0.937355i | \(0.613266\pi\) | |||||||
\(444\) | 4.34481i | 0.206196i | ||||||||
\(445\) | −4.49934 | −0.213289 | ||||||||
\(446\) | 14.3787 | 0.680850 | ||||||||
\(447\) | 8.19136i | 0.387438i | ||||||||
\(448\) | − 1.75302i | − 0.0828224i | ||||||||
\(449\) | 4.08516i | 0.192791i | 0.995343 | + | 0.0963954i | \(0.0307313\pi\) | ||||
−0.995343 | + | 0.0963954i | \(0.969269\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | 7.94438 | 0.374086 | ||||||||
\(452\) | −0.515729 | −0.0242579 | ||||||||
\(453\) | − 5.72348i | − 0.268913i | ||||||||
\(454\) | −5.97716 | −0.280522 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.63102 | −0.404185 | ||||||||
\(457\) | − 41.8678i | − 1.95849i | −0.202668 | − | 0.979247i | \(-0.564961\pi\) | ||||
0.202668 | − | 0.979247i | \(-0.435039\pi\) | |||||||
\(458\) | 15.9172 | 0.743763 | ||||||||
\(459\) | 6.76271 | 0.315656 | ||||||||
\(460\) | − 6.04892i | − 0.282032i | ||||||||
\(461\) | 0.215521i | 0.0100378i | 0.999987 | + | 0.00501890i | \(0.00159757\pi\) | ||||
−0.999987 | + | 0.00501890i | \(0.998402\pi\) | |||||||
\(462\) | − 2.10023i | − 0.0977114i | ||||||||
\(463\) | 23.4795i | 1.09118i | 0.838051 | + | 0.545592i | \(0.183695\pi\) | ||||
−0.838051 | + | 0.545592i | \(0.816305\pi\) | |||||||
\(464\) | 4.07069 | 0.188977 | ||||||||
\(465\) | 6.80194 | 0.315432 | ||||||||
\(466\) | 6.92154i | 0.320634i | ||||||||
\(467\) | −10.1153 | −0.468080 | −0.234040 | − | 0.972227i | \(-0.575195\pi\) | ||||
−0.234040 | + | 0.972227i | \(0.575195\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.7995 | 1.14514 | ||||||||
\(470\) | 11.1957i | 0.516418i | ||||||||
\(471\) | 3.09246 | 0.142493 | ||||||||
\(472\) | 13.7235 | 0.631674 | ||||||||
\(473\) | − 4.88338i | − 0.224538i | ||||||||
\(474\) | 3.74094i | 0.171827i | ||||||||
\(475\) | 8.63102i | 0.396018i | ||||||||
\(476\) | − 11.8552i | − 0.543381i | ||||||||
\(477\) | −1.14914 | −0.0526157 | ||||||||
\(478\) | 30.1075 | 1.37709 | ||||||||
\(479\) | 0.980623i | 0.0448058i | 0.999749 | + | 0.0224029i | \(0.00713166\pi\) | ||||
−0.999749 | + | 0.0224029i | \(0.992868\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −12.0562 | −0.549145 | ||||||||
\(483\) | 10.6039i | 0.482493i | ||||||||
\(484\) | −9.56465 | −0.434757 | ||||||||
\(485\) | −10.7952 | −0.490186 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | − 7.18300i | − 0.325493i | −0.986668 | − | 0.162746i | \(-0.947965\pi\) | ||||
0.986668 | − | 0.162746i | \(-0.0520352\pi\) | |||||||
\(488\) | 1.18598i | 0.0536868i | ||||||||
\(489\) | 23.9541i | 1.08324i | ||||||||
\(490\) | −3.92692 | −0.177400 | ||||||||
\(491\) | −24.5918 | −1.10981 | −0.554906 | − | 0.831913i | \(-0.687246\pi\) | ||||
−0.554906 | + | 0.831913i | \(0.687246\pi\) | |||||||
\(492\) | 6.63102i | 0.298950i | ||||||||
\(493\) | 27.5289 | 1.23984 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.19806 | −0.0538489 | ||||||||
\(496\) | − 6.80194i | − 0.305416i | ||||||||
\(497\) | −4.07234 | −0.182670 | ||||||||
\(498\) | 8.40581 | 0.376673 | ||||||||
\(499\) | − 30.1608i | − 1.35018i | −0.737735 | − | 0.675090i | \(-0.764105\pi\) | ||||
0.737735 | − | 0.675090i | \(-0.235895\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | − 1.19806i | − 0.0535255i | ||||||||
\(502\) | 14.8170i | 0.661315i | ||||||||
\(503\) | −33.8883 | −1.51100 | −0.755502 | − | 0.655146i | \(-0.772607\pi\) | ||||
−0.755502 | + | 0.655146i | \(0.772607\pi\) | |||||||
\(504\) | 1.75302 | 0.0780857 | ||||||||
\(505\) | − 16.7875i | − 0.747032i | ||||||||
\(506\) | −7.24698 | −0.322168 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.96077 | 0.353202 | ||||||||
\(509\) | − 14.1089i | − 0.625364i | −0.949858 | − | 0.312682i | \(-0.898773\pi\) | ||||
0.949858 | − | 0.312682i | \(-0.101227\pi\) | |||||||
\(510\) | −6.76271 | −0.299458 | ||||||||
\(511\) | −2.80220 | −0.123962 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 8.63102i | − 0.381069i | ||||||||
\(514\) | 10.5743i | 0.466414i | ||||||||
\(515\) | 4.16421i | 0.183497i | ||||||||
\(516\) | 4.07606 | 0.179439 | ||||||||
\(517\) | 13.4131 | 0.589908 | ||||||||
\(518\) | 7.61655i | 0.334652i | ||||||||
\(519\) | 6.63773 | 0.291364 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3937 | 0.762033 | 0.381017 | − | 0.924568i | \(-0.375574\pi\) | ||||
0.381017 | + | 0.924568i | \(0.375574\pi\) | |||||||
\(522\) | 4.07069i | 0.178169i | ||||||||
\(523\) | −34.9879 | −1.52991 | −0.764957 | − | 0.644081i | \(-0.777240\pi\) | ||||
−0.764957 | + | 0.644081i | \(0.777240\pi\) | |||||||
\(524\) | 5.08815 | 0.222277 | ||||||||
\(525\) | − 1.75302i | − 0.0765081i | ||||||||
\(526\) | 11.9922i | 0.522886i | ||||||||
\(527\) | − 45.9995i | − 2.00377i | ||||||||
\(528\) | 1.19806i | 0.0521390i | ||||||||
\(529\) | 13.5894 | 0.590844 | ||||||||
\(530\) | 1.14914 | 0.0499157 | ||||||||
\(531\) | 13.7235i | 0.595548i | ||||||||
\(532\) | −15.1304 | −0.655984 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −4.49934 | −0.194705 | ||||||||
\(535\) | 12.9661i | 0.560575i | ||||||||
\(536\) | −14.1468 | −0.611047 | ||||||||
\(537\) | −19.6353 | −0.847327 | ||||||||
\(538\) | − 25.4359i | − 1.09662i | ||||||||
\(539\) | 4.70469i | 0.202646i | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | 20.8689i | 0.897224i | 0.893727 | + | 0.448612i | \(0.148082\pi\) | ||||
−0.893727 | + | 0.448612i | \(0.851918\pi\) | |||||||
\(542\) | −20.3666 | −0.874820 | ||||||||
\(543\) | −5.25906 | −0.225688 | ||||||||
\(544\) | 6.76271i | 0.289949i | ||||||||
\(545\) | −19.4644 | −0.833764 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.67456 | 0.242627 | 0.121313 | − | 0.992614i | \(-0.461289\pi\) | ||||
0.121313 | + | 0.992614i | \(0.461289\pi\) | |||||||
\(548\) | − 0.674563i | − 0.0288159i | ||||||||
\(549\) | −1.18598 | −0.0506164 | ||||||||
\(550\) | 1.19806 | 0.0510855 | ||||||||
\(551\) | − 35.1342i | − 1.49677i | ||||||||
\(552\) | − 6.04892i | − 0.257459i | ||||||||
\(553\) | 6.55794i | 0.278872i | ||||||||
\(554\) | − 20.1323i | − 0.855339i | ||||||||
\(555\) | 4.34481 | 0.184427 | ||||||||
\(556\) | −8.26205 | −0.350389 | ||||||||
\(557\) | − 14.7724i | − 0.625927i | −0.949765 | − | 0.312963i | \(-0.898678\pi\) | ||||
0.949765 | − | 0.312963i | \(-0.101322\pi\) | |||||||
\(558\) | 6.80194 | 0.287949 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.75302 | −0.0740786 | ||||||||
\(561\) | 8.10215i | 0.342073i | ||||||||
\(562\) | 29.7265 | 1.25394 | ||||||||
\(563\) | −18.0398 | −0.760288 | −0.380144 | − | 0.924927i | \(-0.624126\pi\) | ||||
−0.380144 | + | 0.924927i | \(0.624126\pi\) | |||||||
\(564\) | 11.1957i | 0.471423i | ||||||||
\(565\) | 0.515729i | 0.0216969i | ||||||||
\(566\) | − 8.84117i | − 0.371622i | ||||||||
\(567\) | 1.75302i | 0.0736199i | ||||||||
\(568\) | 2.32304 | 0.0974728 | ||||||||
\(569\) | 11.4886 | 0.481626 | 0.240813 | − | 0.970571i | \(-0.422586\pi\) | ||||
0.240813 | + | 0.970571i | \(0.422586\pi\) | |||||||
\(570\) | 8.63102i | 0.361514i | ||||||||
\(571\) | 44.3062 | 1.85416 | 0.927078 | − | 0.374869i | \(-0.122312\pi\) | ||||
0.927078 | + | 0.374869i | \(0.122312\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.45473 | 0.186099 | ||||||||
\(574\) | 11.6243i | 0.485190i | ||||||||
\(575\) | −6.04892 | −0.252257 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 28.0000i | − 1.16566i | −0.812596 | − | 0.582828i | \(-0.801946\pi\) | ||||
0.812596 | − | 0.582828i | \(-0.198054\pi\) | |||||||
\(578\) | 28.7342i | 1.19519i | ||||||||
\(579\) | − 0.818331i | − 0.0340087i | ||||||||
\(580\) | − 4.07069i | − 0.169026i | ||||||||
\(581\) | 14.7356 | 0.611334 | ||||||||
\(582\) | −10.7952 | −0.447477 | ||||||||
\(583\) | − 1.37675i | − 0.0570190i | ||||||||
\(584\) | 1.59850 | 0.0661463 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.5918 | −0.850639 | ||||||||
\(587\) | 35.4316i | 1.46242i | 0.682152 | + | 0.731210i | \(0.261044\pi\) | ||||
−0.682152 | + | 0.731210i | \(0.738956\pi\) | |||||||
\(588\) | −3.92692 | −0.161943 | ||||||||
\(589\) | −58.7077 | −2.41901 | ||||||||
\(590\) | − 13.7235i | − 0.564987i | ||||||||
\(591\) | − 12.7385i | − 0.523994i | ||||||||
\(592\) | − 4.34481i | − 0.178571i | ||||||||
\(593\) | 2.19567i | 0.0901653i | 0.998983 | + | 0.0450827i | \(0.0143551\pi\) | ||||
−0.998983 | + | 0.0450827i | \(0.985645\pi\) | |||||||
\(594\) | −1.19806 | −0.0491571 | ||||||||
\(595\) | −11.8552 | −0.486014 | ||||||||
\(596\) | − 8.19136i | − 0.335531i | ||||||||
\(597\) | 4.02475 | 0.164722 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.1855 | −1.27421 | −0.637103 | − | 0.770779i | \(-0.719867\pi\) | ||||
−0.637103 | + | 0.770779i | \(0.719867\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −24.2435 | −0.988914 | −0.494457 | − | 0.869202i | \(-0.664633\pi\) | ||||
−0.494457 | + | 0.869202i | \(0.664633\pi\) | |||||||
\(602\) | 7.14542 | 0.291226 | ||||||||
\(603\) | − 14.1468i | − 0.576100i | ||||||||
\(604\) | 5.72348i | 0.232885i | ||||||||
\(605\) | 9.56465i | 0.388858i | ||||||||
\(606\) | − 16.7875i | − 0.681944i | ||||||||
\(607\) | −17.7235 | −0.719374 | −0.359687 | − | 0.933073i | \(-0.617117\pi\) | ||||
−0.359687 | + | 0.933073i | \(0.617117\pi\) | |||||||
\(608\) | 8.63102 | 0.350034 | ||||||||
\(609\) | 7.13600i | 0.289165i | ||||||||
\(610\) | 1.18598 | 0.0480190 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.76271 | −0.273366 | ||||||||
\(613\) | 1.71140i | 0.0691227i | 0.999403 | + | 0.0345614i | \(0.0110034\pi\) | ||||
−0.999403 | + | 0.0345614i | \(0.988997\pi\) | |||||||
\(614\) | −28.7265 | −1.15931 | ||||||||
\(615\) | 6.63102 | 0.267389 | ||||||||
\(616\) | 2.10023i | 0.0846206i | ||||||||
\(617\) | 0.569433i | 0.0229245i | 0.999934 | + | 0.0114622i | \(0.00364863\pi\) | ||||
−0.999934 | + | 0.0114622i | \(0.996351\pi\) | |||||||
\(618\) | 4.16421i | 0.167509i | ||||||||
\(619\) | − 26.4282i | − 1.06224i | −0.847297 | − | 0.531119i | \(-0.821772\pi\) | ||||
0.847297 | − | 0.531119i | \(-0.178228\pi\) | |||||||
\(620\) | −6.80194 | −0.273172 | ||||||||
\(621\) | 6.04892 | 0.242735 | ||||||||
\(622\) | 18.6329i | 0.747113i | ||||||||
\(623\) | −7.88743 | −0.316003 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 29.3696i | − 1.17384i | ||||||||
\(627\) | 10.3405 | 0.412960 | ||||||||
\(628\) | −3.09246 | −0.123403 | ||||||||
\(629\) | − 29.3827i | − 1.17157i | ||||||||
\(630\) | − 1.75302i | − 0.0698420i | ||||||||
\(631\) | − 38.0006i | − 1.51278i | −0.654121 | − | 0.756390i | \(-0.726961\pi\) | ||||
0.654121 | − | 0.756390i | \(-0.273039\pi\) | |||||||
\(632\) | − 3.74094i | − 0.148807i | ||||||||
\(633\) | 3.10992 | 0.123608 | ||||||||
\(634\) | 20.8092 | 0.826440 | ||||||||
\(635\) | − 7.96077i | − 0.315914i | ||||||||
\(636\) | 1.14914 | 0.0455666 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.87694 | −0.193080 | ||||||||
\(639\) | 2.32304i | 0.0918982i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 25.9168 | 1.02365 | 0.511825 | − | 0.859090i | \(-0.328970\pi\) | ||||
0.511825 | + | 0.859090i | \(0.328970\pi\) | |||||||
\(642\) | 12.9661i | 0.511733i | ||||||||
\(643\) | 8.52243i | 0.336092i | 0.985779 | + | 0.168046i | \(0.0537457\pi\) | ||||
−0.985779 | + | 0.168046i | \(0.946254\pi\) | |||||||
\(644\) | − 10.6039i | − 0.417851i | ||||||||
\(645\) | − 4.07606i | − 0.160495i | ||||||||
\(646\) | 58.3691 | 2.29650 | ||||||||
\(647\) | −37.9318 | −1.49125 | −0.745627 | − | 0.666364i | \(-0.767850\pi\) | ||||
−0.745627 | + | 0.666364i | \(0.767850\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | −16.4416 | −0.645389 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.9239 | 0.467336 | ||||||||
\(652\) | − 23.9541i | − 0.938114i | ||||||||
\(653\) | −6.07846 | −0.237868 | −0.118934 | − | 0.992902i | \(-0.537948\pi\) | ||||
−0.118934 | + | 0.992902i | \(0.537948\pi\) | |||||||
\(654\) | −19.4644 | −0.761119 | ||||||||
\(655\) | − 5.08815i | − 0.198810i | ||||||||
\(656\) | − 6.63102i | − 0.258898i | ||||||||
\(657\) | 1.59850i | 0.0623634i | ||||||||
\(658\) | 19.6262i | 0.765110i | ||||||||
\(659\) | 38.9162 | 1.51596 | 0.757979 | − | 0.652279i | \(-0.226187\pi\) | ||||
0.757979 | + | 0.652279i | \(0.226187\pi\) | |||||||
\(660\) | 1.19806 | 0.0466345 | ||||||||
\(661\) | 25.9191i | 1.00814i | 0.863663 | + | 0.504069i | \(0.168164\pi\) | ||||
−0.863663 | + | 0.504069i | \(0.831836\pi\) | |||||||
\(662\) | −11.7603 | −0.457078 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.40581 | −0.326209 | ||||||||
\(665\) | 15.1304i | 0.586730i | ||||||||
\(666\) | 4.34481 | 0.168358 | ||||||||
\(667\) | 24.6233 | 0.953416 | ||||||||
\(668\) | 1.19806i | 0.0463544i | ||||||||
\(669\) | − 14.3787i | − 0.555911i | ||||||||
\(670\) | 14.1468i | 0.546537i | ||||||||
\(671\) | − 1.42088i | − 0.0548524i | ||||||||
\(672\) | −1.75302 | −0.0676242 | ||||||||
\(673\) | 25.5724 | 0.985744 | 0.492872 | − | 0.870102i | \(-0.335947\pi\) | ||||
0.492872 | + | 0.870102i | \(0.335947\pi\) | |||||||
\(674\) | 26.8732i | 1.03512i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7453 | 0.951037 | 0.475519 | − | 0.879706i | \(-0.342260\pi\) | ||||
0.475519 | + | 0.879706i | \(0.342260\pi\) | |||||||
\(678\) | 0.515729i | 0.0198065i | ||||||||
\(679\) | −18.9243 | −0.726247 | ||||||||
\(680\) | 6.76271 | 0.259338 | ||||||||
\(681\) | 5.97716i | 0.229045i | ||||||||
\(682\) | 8.14914i | 0.312047i | ||||||||
\(683\) | 22.4045i | 0.857284i | 0.903474 | + | 0.428642i | \(0.141008\pi\) | ||||
−0.903474 | + | 0.428642i | \(0.858992\pi\) | |||||||
\(684\) | 8.63102i | 0.330015i | ||||||||
\(685\) | −0.674563 | −0.0257737 | ||||||||
\(686\) | −19.1551 | −0.731346 | ||||||||
\(687\) | − 15.9172i | − 0.607280i | ||||||||
\(688\) | −4.07606 | −0.155398 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.04892 | −0.230278 | ||||||||
\(691\) | 16.0030i | 0.608782i | 0.952547 | + | 0.304391i | \(0.0984530\pi\) | ||||
−0.952547 | + | 0.304391i | \(0.901547\pi\) | |||||||
\(692\) | −6.63773 | −0.252329 | ||||||||
\(693\) | −2.10023 | −0.0797810 | ||||||||
\(694\) | 29.5080i | 1.12011i | ||||||||
\(695\) | 8.26205i | 0.313397i | ||||||||
\(696\) | − 4.07069i | − 0.154299i | ||||||||
\(697\) | − 44.8437i | − 1.69858i | ||||||||
\(698\) | −17.0519 | −0.645424 | ||||||||
\(699\) | 6.92154 | 0.261797 | ||||||||
\(700\) | 1.75302i | 0.0662579i | ||||||||
\(701\) | −32.7222 | −1.23590 | −0.617949 | − | 0.786218i | \(-0.712036\pi\) | ||||
−0.617949 | + | 0.786218i | \(0.712036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.5002 | −1.41435 | ||||||||
\(704\) | − 1.19806i | − 0.0451537i | ||||||||
\(705\) | 11.1957 | 0.421653 | ||||||||
\(706\) | −21.8629 | −0.822822 | ||||||||
\(707\) | − 29.4288i | − 1.10678i | ||||||||
\(708\) | − 13.7235i | − 0.515760i | ||||||||
\(709\) | 14.0597i | 0.528022i | 0.964520 | + | 0.264011i | \(0.0850455\pi\) | ||||
−0.964520 | + | 0.264011i | \(0.914954\pi\) | |||||||
\(710\) | − 2.32304i | − 0.0871823i | ||||||||
\(711\) | 3.74094 | 0.140296 | ||||||||
\(712\) | 4.49934 | 0.168620 | ||||||||
\(713\) | − 41.1444i | − 1.54087i | ||||||||
\(714\) | −11.8552 | −0.443668 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.6353 | 0.733807 | ||||||||
\(717\) | − 30.1075i | − 1.12439i | ||||||||
\(718\) | −14.3026 | −0.533768 | ||||||||
\(719\) | 7.15585 | 0.266868 | 0.133434 | − | 0.991058i | \(-0.457400\pi\) | ||||
0.133434 | + | 0.991058i | \(0.457400\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | 7.29995i | 0.271864i | ||||||||
\(722\) | − 55.4946i | − 2.06529i | ||||||||
\(723\) | 12.0562i | 0.448375i | ||||||||
\(724\) | 5.25906 | 0.195451 | ||||||||
\(725\) | −4.07069 | −0.151182 | ||||||||
\(726\) | 9.56465i | 0.354977i | ||||||||
\(727\) | −36.4704 | −1.35261 | −0.676306 | − | 0.736621i | \(-0.736420\pi\) | ||||
−0.676306 | + | 0.736621i | \(0.736420\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 1.59850i | − 0.0591631i | ||||||||
\(731\) | −27.5652 | −1.01954 | ||||||||
\(732\) | 1.18598 | 0.0438351 | ||||||||
\(733\) | 38.0646i | 1.40595i | 0.711216 | + | 0.702974i | \(0.248145\pi\) | ||||
−0.711216 | + | 0.702974i | \(0.751855\pi\) | |||||||
\(734\) | − 11.2416i | − 0.414935i | ||||||||
\(735\) | 3.92692i | 0.144847i | ||||||||
\(736\) | 6.04892i | 0.222966i | ||||||||
\(737\) | 16.9487 | 0.624313 | ||||||||
\(738\) | 6.63102 | 0.244091 | ||||||||
\(739\) | 35.5114i | 1.30631i | 0.757225 | + | 0.653154i | \(0.226555\pi\) | ||||
−0.757225 | + | 0.653154i | \(0.773445\pi\) | |||||||
\(740\) | −4.34481 | −0.159719 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.01447 | 0.0739537 | ||||||||
\(743\) | − 20.3696i | − 0.747287i | −0.927572 | − | 0.373643i | \(-0.878108\pi\) | ||||
0.927572 | − | 0.373643i | \(-0.121892\pi\) | |||||||
\(744\) | −6.80194 | −0.249371 | ||||||||
\(745\) | −8.19136 | −0.300108 | ||||||||
\(746\) | − 9.70171i | − 0.355205i | ||||||||
\(747\) | − 8.40581i | − 0.307553i | ||||||||
\(748\) | − 8.10215i | − 0.296244i | ||||||||
\(749\) | 22.7299i | 0.830533i | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 5.58104 | 0.203655 | 0.101828 | − | 0.994802i | \(-0.467531\pi\) | ||||
0.101828 | + | 0.994802i | \(0.467531\pi\) | |||||||
\(752\) | − 11.1957i | − 0.408264i | ||||||||
\(753\) | 14.8170 | 0.539962 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.72348 | 0.208299 | ||||||||
\(756\) | − 1.75302i | − 0.0637567i | ||||||||
\(757\) | 12.8267 | 0.466194 | 0.233097 | − | 0.972453i | \(-0.425114\pi\) | ||||
0.233097 | + | 0.972453i | \(0.425114\pi\) | |||||||
\(758\) | −2.82802 | −0.102718 | ||||||||
\(759\) | 7.24698i | 0.263049i | ||||||||
\(760\) | − 8.63102i | − 0.313080i | ||||||||
\(761\) | − 14.0084i | − 0.507803i | −0.967230 | − | 0.253901i | \(-0.918286\pi\) | ||||
0.967230 | − | 0.253901i | \(-0.0817139\pi\) | |||||||
\(762\) | − 7.96077i | − 0.288388i | ||||||||
\(763\) | −34.1215 | −1.23528 | ||||||||
\(764\) | −4.45473 | −0.161166 | ||||||||
\(765\) | 6.76271i | 0.244506i | ||||||||
\(766\) | 11.6558 | 0.421140 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 50.4051i | 1.81765i | 0.417174 | + | 0.908827i | \(0.363021\pi\) | ||||
−0.417174 | + | 0.908827i | \(0.636979\pi\) | |||||||
\(770\) | 2.10023 | 0.0756869 | ||||||||
\(771\) | 10.5743 | 0.380825 | ||||||||
\(772\) | 0.818331i | 0.0294524i | ||||||||
\(773\) | 42.5532i | 1.53053i | 0.643715 | + | 0.765265i | \(0.277392\pi\) | ||||
−0.643715 | + | 0.765265i | \(0.722608\pi\) | |||||||
\(774\) | − 4.07606i | − 0.146511i | ||||||||
\(775\) | 6.80194i | 0.244333i | ||||||||
\(776\) | 10.7952 | 0.387526 | ||||||||
\(777\) | 7.61655 | 0.273242 | ||||||||
\(778\) | − 12.5157i | − 0.448711i | ||||||||
\(779\) | −57.2325 | −2.05057 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.78315 | −0.0995890 | ||||||||
\(782\) | 40.9071i | 1.46283i | ||||||||
\(783\) | 4.07069 | 0.145475 | ||||||||
\(784\) | 3.92692 | 0.140247 | ||||||||
\(785\) | 3.09246i | 0.110375i | ||||||||
\(786\) | − 5.08815i | − 0.181488i | ||||||||
\(787\) | 12.1927i | 0.434622i | 0.976102 | + | 0.217311i | \(0.0697286\pi\) | ||||
−0.976102 | + | 0.217311i | \(0.930271\pi\) | |||||||
\(788\) | 12.7385i | 0.453792i | ||||||||
\(789\) | 11.9922 | 0.426935 | ||||||||
\(790\) | −3.74094 | −0.133097 | ||||||||
\(791\) | 0.904084i | 0.0321455i | ||||||||
\(792\) | 1.19806 | 0.0425713 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −21.6136 | −0.767037 | ||||||||
\(795\) | − 1.14914i | − 0.0407560i | ||||||||
\(796\) | −4.02475 | −0.142654 | ||||||||
\(797\) | −36.4534 | −1.29125 | −0.645623 | − | 0.763656i | \(-0.723402\pi\) | ||||
−0.645623 | + | 0.763656i | \(0.723402\pi\) | |||||||
\(798\) | 15.1304i | 0.535609i | ||||||||
\(799\) | − 75.7131i | − 2.67854i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 4.49934i | 0.158976i | ||||||||
\(802\) | 11.5157 | 0.406635 | ||||||||
\(803\) | −1.91510 | −0.0675824 | ||||||||
\(804\) | 14.1468i | 0.498917i | ||||||||
\(805\) | −10.6039 | −0.373738 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.4359 | −0.895388 | ||||||||
\(808\) | 16.7875i | 0.590581i | ||||||||
\(809\) | 9.70278 | 0.341131 | 0.170566 | − | 0.985346i | \(-0.445440\pi\) | ||||
0.170566 | + | 0.985346i | \(0.445440\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 26.6547i | 0.935974i | 0.883735 | + | 0.467987i | \(0.155021\pi\) | ||||
−0.883735 | + | 0.467987i | \(0.844979\pi\) | |||||||
\(812\) | − 7.13600i | − 0.250424i | ||||||||
\(813\) | 20.3666i | 0.714287i | ||||||||
\(814\) | 5.20536i | 0.182448i | ||||||||
\(815\) | −23.9541 | −0.839074 | ||||||||
\(816\) | 6.76271 | 0.236742 | ||||||||
\(817\) | 35.1806i | 1.23081i | ||||||||
\(818\) | −0.0991626 | −0.00346714 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.63102 | −0.231565 | ||||||||
\(821\) | 2.58343i | 0.0901624i | 0.998983 | + | 0.0450812i | \(0.0143547\pi\) | ||||
−0.998983 | + | 0.0450812i | \(0.985645\pi\) | |||||||
\(822\) | −0.674563 | −0.0235281 | ||||||||
\(823\) | −19.9855 | −0.696652 | −0.348326 | − | 0.937374i | \(-0.613250\pi\) | ||||
−0.348326 | + | 0.937374i | \(0.613250\pi\) | |||||||
\(824\) | − 4.16421i | − 0.145067i | ||||||||
\(825\) | − 1.19806i | − 0.0417112i | ||||||||
\(826\) | − 24.0575i | − 0.837069i | ||||||||
\(827\) | − 1.39506i | − 0.0485110i | −0.999706 | − | 0.0242555i | \(-0.992278\pi\) | ||||
0.999706 | − | 0.0242555i | \(-0.00772152\pi\) | |||||||
\(828\) | −6.04892 | −0.210214 | ||||||||
\(829\) | 27.6179 | 0.959208 | 0.479604 | − | 0.877485i | \(-0.340780\pi\) | ||||
0.479604 | + | 0.877485i | \(0.340780\pi\) | |||||||
\(830\) | 8.40581i | 0.291770i | ||||||||
\(831\) | −20.1323 | −0.698381 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.5566 | 0.920132 | ||||||||
\(834\) | 8.26205i | 0.286091i | ||||||||
\(835\) | 1.19806 | 0.0414607 | ||||||||
\(836\) | −10.3405 | −0.357634 | ||||||||
\(837\) | − 6.80194i | − 0.235109i | ||||||||
\(838\) | 31.2784i | 1.08050i | ||||||||
\(839\) | 54.3357i | 1.87588i | 0.346801 | + | 0.937939i | \(0.387268\pi\) | ||||
−0.346801 | + | 0.937939i | \(0.612732\pi\) | |||||||
\(840\) | 1.75302i | 0.0604850i | ||||||||
\(841\) | −12.4295 | −0.428604 | ||||||||
\(842\) | −38.0452 | −1.31112 | ||||||||
\(843\) | − 29.7265i | − 1.02383i | ||||||||
\(844\) | −3.10992 | −0.107048 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.1957 | 0.384915 | ||||||||
\(847\) | 16.7670i | 0.576122i | ||||||||
\(848\) | −1.14914 | −0.0394618 | ||||||||
\(849\) | −8.84117 | −0.303428 | ||||||||
\(850\) | − 6.76271i | − 0.231959i | ||||||||
\(851\) | − 26.2814i | − 0.900916i | ||||||||
\(852\) | − 2.32304i | − 0.0795862i | ||||||||
\(853\) | 13.4553i | 0.460701i | 0.973108 | + | 0.230351i | \(0.0739873\pi\) | ||||
−0.973108 | + | 0.230351i | \(0.926013\pi\) | |||||||
\(854\) | 2.07905 | 0.0711436 | ||||||||
\(855\) | 8.63102 | 0.295175 | ||||||||
\(856\) | − 12.9661i | − 0.443174i | ||||||||
\(857\) | −42.7200 | −1.45929 | −0.729644 | − | 0.683827i | \(-0.760314\pi\) | ||||
−0.729644 | + | 0.683827i | \(0.760314\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.3038 | 1.51163 | 0.755813 | − | 0.654788i | \(-0.227242\pi\) | ||||
0.755813 | + | 0.654788i | \(0.227242\pi\) | |||||||
\(860\) | 4.07606i | 0.138993i | ||||||||
\(861\) | 11.6243 | 0.396156 | ||||||||
\(862\) | −14.4614 | −0.492558 | ||||||||
\(863\) | − 5.47783i | − 0.186467i | −0.995644 | − | 0.0932337i | \(-0.970280\pi\) | ||||
0.995644 | − | 0.0932337i | \(-0.0297204\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | 6.63773i | 0.225689i | ||||||||
\(866\) | − 21.6209i | − 0.734707i | ||||||||
\(867\) | 28.7342 | 0.975866 | ||||||||
\(868\) | −11.9239 | −0.404725 | ||||||||
\(869\) | 4.48188i | 0.152037i | ||||||||
\(870\) | −4.07069 | −0.138009 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19.4644 | 0.659148 | ||||||||
\(873\) | 10.7952i | 0.365363i | ||||||||
\(874\) | 52.2083 | 1.76597 | ||||||||
\(875\) | 1.75302 | 0.0592629 | ||||||||
\(876\) | − 1.59850i | − 0.0540083i | ||||||||
\(877\) | − 41.3726i | − 1.39705i | −0.715585 | − | 0.698526i | \(-0.753840\pi\) | ||||
0.715585 | − | 0.698526i | \(-0.246160\pi\) | |||||||
\(878\) | 3.23623i | 0.109217i | ||||||||
\(879\) | 20.5918i | 0.694544i | ||||||||
\(880\) | −1.19806 | −0.0403867 | ||||||||
\(881\) | 42.3919 | 1.42822 | 0.714110 | − | 0.700033i | \(-0.246832\pi\) | ||||
0.714110 | + | 0.700033i | \(0.246832\pi\) | |||||||
\(882\) | 3.92692i | 0.132226i | ||||||||
\(883\) | 40.8412 | 1.37441 | 0.687207 | − | 0.726461i | \(-0.258836\pi\) | ||||
0.687207 | + | 0.726461i | \(0.258836\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.7235 | −0.461310 | ||||||||
\(886\) | − 14.6649i | − 0.492676i | ||||||||
\(887\) | −35.0810 | −1.17790 | −0.588952 | − | 0.808168i | \(-0.700459\pi\) | ||||
−0.588952 | + | 0.808168i | \(0.700459\pi\) | |||||||
\(888\) | −4.34481 | −0.145802 | ||||||||
\(889\) | − 13.9554i | − 0.468049i | ||||||||
\(890\) | − 4.49934i | − 0.150818i | ||||||||
\(891\) | 1.19806i | 0.0401366i | ||||||||
\(892\) | 14.3787i | 0.481433i | ||||||||
\(893\) | −96.6301 | −3.23360 | ||||||||
\(894\) | −8.19136 | −0.273960 | ||||||||
\(895\) | − 19.6353i | − 0.656337i | ||||||||
\(896\) | 1.75302 | 0.0585643 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.08516 | −0.136324 | ||||||||
\(899\) | − 27.6886i | − 0.923465i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −7.77133 | −0.258901 | ||||||||
\(902\) | 7.94438i | 0.264519i | ||||||||
\(903\) | − 7.14542i | − 0.237785i | ||||||||
\(904\) | − 0.515729i | − 0.0171529i | ||||||||
\(905\) | − 5.25906i | − 0.174817i | ||||||||
\(906\) | 5.72348 | 0.190150 | ||||||||
\(907\) | 45.4916 | 1.51052 | 0.755261 | − | 0.655424i | \(-0.227510\pi\) | ||||
0.755261 | + | 0.655424i | \(0.227510\pi\) | |||||||
\(908\) | − 5.97716i | − 0.198359i | ||||||||
\(909\) | −16.7875 | −0.556805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.4349 | 1.57159 | 0.785794 | − | 0.618489i | \(-0.212255\pi\) | ||||
0.785794 | + | 0.618489i | \(0.212255\pi\) | |||||||
\(912\) | − 8.63102i | − 0.285802i | ||||||||
\(913\) | 10.0707 | 0.333291 | ||||||||
\(914\) | 41.8678 | 1.38487 | ||||||||
\(915\) | − 1.18598i | − 0.0392073i | ||||||||
\(916\) | 15.9172i | 0.525920i | ||||||||
\(917\) | − 8.91962i | − 0.294552i | ||||||||
\(918\) | 6.76271i | 0.223203i | ||||||||
\(919\) | −20.3907 | −0.672629 | −0.336314 | − | 0.941750i | \(-0.609180\pi\) | ||||
−0.336314 | + | 0.941750i | \(0.609180\pi\) | |||||||
\(920\) | 6.04892 | 0.199427 | ||||||||
\(921\) | 28.7265i | 0.946569i | ||||||||
\(922\) | −0.215521 | −0.00709779 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.10023 | 0.0690924 | ||||||||
\(925\) | 4.34481i | 0.142857i | ||||||||
\(926\) | −23.4795 | −0.771584 | ||||||||
\(927\) | 4.16421 | 0.136771 | ||||||||
\(928\) | 4.07069i | 0.133627i | ||||||||
\(929\) | 1.26636i | 0.0415478i | 0.999784 | + | 0.0207739i | \(0.00661302\pi\) | ||||
−0.999784 | + | 0.0207739i | \(0.993387\pi\) | |||||||
\(930\) | 6.80194i | 0.223044i | ||||||||
\(931\) | − 33.8933i | − 1.11081i | ||||||||
\(932\) | −6.92154 | −0.226723 | ||||||||
\(933\) | 18.6329 | 0.610015 | ||||||||
\(934\) | − 10.1153i | − 0.330983i | ||||||||
\(935\) | −8.10215 | −0.264969 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.3558 | 0.893676 | 0.446838 | − | 0.894615i | \(-0.352550\pi\) | ||||
0.446838 | + | 0.894615i | \(0.352550\pi\) | |||||||
\(938\) | 24.7995i | 0.809734i | ||||||||
\(939\) | −29.3696 | −0.958440 | ||||||||
\(940\) | −11.1957 | −0.365162 | ||||||||
\(941\) | 60.6620i | 1.97752i | 0.149495 | + | 0.988762i | \(0.452235\pi\) | ||||
−0.149495 | + | 0.988762i | \(0.547765\pi\) | |||||||
\(942\) | 3.09246i | 0.100758i | ||||||||
\(943\) | − 40.1105i | − 1.30618i | ||||||||
\(944\) | 13.7235i | 0.446661i | ||||||||
\(945\) | −1.75302 | −0.0570258 | ||||||||
\(946\) | 4.88338 | 0.158772 | ||||||||
\(947\) | − 12.3797i | − 0.402287i | −0.979562 | − | 0.201144i | \(-0.935534\pi\) | ||||
0.979562 | − | 0.201144i | \(-0.0644658\pi\) | |||||||
\(948\) | −3.74094 | −0.121500 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.63102 | −0.280027 | ||||||||
\(951\) | − 20.8092i | − 0.674786i | ||||||||
\(952\) | 11.8552 | 0.384228 | ||||||||
\(953\) | −28.7784 | −0.932223 | −0.466111 | − | 0.884726i | \(-0.654345\pi\) | ||||
−0.466111 | + | 0.884726i | \(0.654345\pi\) | |||||||
\(954\) | − 1.14914i | − 0.0372049i | ||||||||
\(955\) | 4.45473i | 0.144152i | ||||||||
\(956\) | 30.1075i | 0.973747i | ||||||||
\(957\) | 4.87694i | 0.157649i | ||||||||
\(958\) | −0.980623 | −0.0316825 | ||||||||
\(959\) | −1.18252 | −0.0381857 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | −15.2664 | −0.492463 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.9661 | 0.417828 | ||||||||
\(964\) | − 12.0562i | − 0.388304i | ||||||||
\(965\) | 0.818331 | 0.0263430 | ||||||||
\(966\) | −10.6039 | −0.341174 | ||||||||
\(967\) | 23.1545i | 0.744599i | 0.928113 | + | 0.372300i | \(0.121431\pi\) | ||||
−0.928113 | + | 0.372300i | \(0.878569\pi\) | |||||||
\(968\) | − 9.56465i | − 0.307419i | ||||||||
\(969\) | − 58.3691i | − 1.87509i | ||||||||
\(970\) | − 10.7952i | − 0.346614i | ||||||||
\(971\) | −2.89572 | −0.0929282 | −0.0464641 | − | 0.998920i | \(-0.514795\pi\) | ||||
−0.0464641 | + | 0.998920i | \(0.514795\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 14.4835i | 0.464321i | ||||||||
\(974\) | 7.18300 | 0.230158 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.18598 | −0.0379623 | ||||||||
\(977\) | 4.86294i | 0.155579i | 0.996970 | + | 0.0777896i | \(0.0247862\pi\) | ||||
−0.996970 | + | 0.0777896i | \(0.975214\pi\) | |||||||
\(978\) | −23.9541 | −0.765967 | ||||||||
\(979\) | −5.39048 | −0.172281 | ||||||||
\(980\) | − 3.92692i | − 0.125441i | ||||||||
\(981\) | 19.4644i | 0.621451i | ||||||||
\(982\) | − 24.5918i | − 0.784756i | ||||||||
\(983\) | − 52.7506i | − 1.68248i | −0.540659 | − | 0.841242i | \(-0.681825\pi\) | ||||
0.540659 | − | 0.841242i | \(-0.318175\pi\) | |||||||
\(984\) | −6.63102 | −0.211389 | ||||||||
\(985\) | 12.7385 | 0.405884 | ||||||||
\(986\) | 27.5289i | 0.876698i | ||||||||
\(987\) | 19.6262 | 0.624710 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.6558 | −0.784008 | ||||||||
\(990\) | − 1.19806i | − 0.0380769i | ||||||||
\(991\) | 7.15538 | 0.227298 | 0.113649 | − | 0.993521i | \(-0.463746\pi\) | ||||
0.113649 | + | 0.993521i | \(0.463746\pi\) | |||||||
\(992\) | 6.80194 | 0.215962 | ||||||||
\(993\) | 11.7603i | 0.373202i | ||||||||
\(994\) | − 4.07234i | − 0.129167i | ||||||||
\(995\) | 4.02475i | 0.127593i | ||||||||
\(996\) | 8.40581i | 0.266348i | ||||||||
\(997\) | 39.3870 | 1.24740 | 0.623700 | − | 0.781664i | \(-0.285629\pi\) | ||||
0.623700 | + | 0.781664i | \(0.285629\pi\) | |||||||
\(998\) | 30.1608 | 0.954722 | ||||||||
\(999\) | − 4.34481i | − 0.137464i |
(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.b.w.1351.4 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bx.1.3 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bo.1.1 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.w.1351.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bo.1.1 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.bx.1.3 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.w.1351.3 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.w.1351.4 | 6 | 1.1 | even | 1 | trivial |