Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(3649,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3800.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.d (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: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 760) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.1 | ||
Root | \(1.32001 + 1.32001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.3649 |
Dual form | 3800.2.d.k.3649.6 |
$q$-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 \(\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(951\) | \(1901\) | \(1977\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.12489i | − 1.80415i | −0.431576 | − | 0.902077i | \(-0.642042\pi\) | ||||
0.431576 | − | 0.902077i | \(-0.357958\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.51514i | 0.572668i | 0.958130 | + | 0.286334i | \(0.0924368\pi\) | ||||
−0.958130 | + | 0.286334i | \(0.907563\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.76491 | −2.25497 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24977 | 1.28135 | 0.640677 | − | 0.767810i | \(-0.278654\pi\) | ||||
0.640677 | + | 0.767810i | \(0.278654\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.15516i | 1.15243i | 0.817297 | + | 0.576217i | \(0.195472\pi\) | ||||
−0.817297 | + | 0.576217i | \(0.804528\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.51514i | 0.852546i | 0.904595 | + | 0.426273i | \(0.140174\pi\) | ||||
−0.904595 | + | 0.426273i | \(0.859826\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.73463 | 1.03318 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 8.73463i | − 1.82130i | −0.413182 | − | 0.910648i | \(-0.635583\pi\) | ||||
0.413182 | − | 0.910648i | \(-0.364417\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.7649i | 2.26416i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.45459 | −0.270110 | −0.135055 | − | 0.990838i | \(-0.543121\pi\) | ||||
−0.135055 | + | 0.990838i | \(0.543121\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.96972 | −0.892589 | −0.446294 | − | 0.894886i | \(-0.647257\pi\) | ||||
−0.446294 | + | 0.894886i | \(0.647257\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 13.2800i | − 2.31176i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.60975i | − 1.25103i | −0.780210 | − | 0.625517i | \(-0.784888\pi\) | ||||
0.780210 | − | 0.625517i | \(-0.215112\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.9844 | 2.07917 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.21949 | −1.43984 | −0.719922 | − | 0.694055i | \(-0.755822\pi\) | ||||
−0.719922 | + | 0.694055i | \(0.755822\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.31032i | − 1.26731i | −0.773615 | − | 0.633656i | \(-0.781553\pi\) | ||||
0.773615 | − | 0.633656i | \(-0.218447\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 5.28005i | − 0.770174i | −0.922880 | − | 0.385087i | \(-0.874171\pi\) | ||||
0.922880 | − | 0.385087i | \(-0.125829\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.70436 | 0.672051 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.9844 | 1.53812 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.155162i | 0.0213131i | 0.999943 | + | 0.0106565i | \(0.00339215\pi\) | ||||
−0.999943 | + | 0.0106565i | \(0.996608\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 3.12489i | − 0.413901i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.48486 | 0.323501 | 0.161751 | − | 0.986832i | \(-0.448286\pi\) | ||||
0.161751 | + | 0.986832i | \(0.448286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.49954 | −0.576107 | −0.288054 | − | 0.957614i | \(-0.593008\pi\) | ||||
−0.288054 | + | 0.957614i | \(0.593008\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 10.2498i | − 1.29135i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 7.43521i | − 0.908355i | −0.890911 | − | 0.454178i | \(-0.849933\pi\) | ||||
0.890911 | − | 0.454178i | \(-0.150067\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −27.2947 | −3.28590 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.49954 | 1.00871 | 0.504355 | − | 0.863496i | \(-0.331730\pi\) | ||||
0.504355 | + | 0.863496i | \(0.331730\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 15.0450i | − 1.76088i | −0.474159 | − | 0.880439i | \(-0.657248\pi\) | ||||
0.474159 | − | 0.880439i | \(-0.342752\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.43899i | 0.733791i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.310323 | 0.0349141 | 0.0174570 | − | 0.999848i | \(-0.494443\pi\) | ||||
0.0174570 | + | 0.999848i | \(0.494443\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.4693 | 1.82992 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 8.96972i | − 0.984555i | −0.870438 | − | 0.492278i | \(-0.836165\pi\) | ||||
0.870438 | − | 0.492278i | \(-0.163835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.54541i | 0.487320i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.719953 | −0.0763149 | −0.0381574 | − | 0.999272i | \(-0.512149\pi\) | ||||
−0.0381574 | + | 0.999272i | \(0.512149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.29564 | −0.659963 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.5298i | 1.61037i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 17.3893i | − 1.76562i | −0.469731 | − | 0.882810i | \(-0.655649\pi\) | ||||
0.469731 | − | 0.882810i | \(-0.344351\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −28.7493 | −2.88941 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.4995 | −1.24375 | −0.621875 | − | 0.783116i | \(-0.713629\pi\) | ||||
−0.621875 | + | 0.783116i | \(0.713629\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 10.8898i | − 1.07300i | −0.843899 | − | 0.536502i | \(-0.819746\pi\) | ||||
0.843899 | − | 0.536502i | \(-0.180254\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.43521i | 0.718789i | 0.933186 | + | 0.359394i | \(0.117017\pi\) | ||||
−0.933186 | + | 0.359394i | \(0.882983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.3553 | 1.85390 | 0.926950 | − | 0.375186i | \(-0.122421\pi\) | ||||
0.926950 | + | 0.375186i | \(0.122421\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.7796 | −2.25706 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 17.8595i | − 1.68008i | −0.542523 | − | 0.840041i | \(-0.682531\pi\) | ||||
0.542523 | − | 0.840041i | \(-0.317469\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 28.1093i | − 2.59870i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.32592 | −0.488226 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.06055 | 0.641868 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.8099i | 2.59770i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.70058i | − 0.239637i | −0.992796 | − | 0.119819i | \(-0.961769\pi\) | ||||
0.992796 | − | 0.119819i | \(-0.0382313\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −25.9688 | −2.28643 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.51514i | 0.131379i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.51514i | 0.642062i | 0.947069 | + | 0.321031i | \(0.104029\pi\) | ||||
−0.947069 | + | 0.321031i | \(0.895971\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.7493 | −1.42066 | −0.710329 | − | 0.703870i | \(-0.751454\pi\) | ||||
−0.710329 | + | 0.703870i | \(0.751454\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.4995 | −1.38951 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.6585i | 1.47668i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 14.7006i | − 1.21248i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4995 | 1.02400 | 0.512001 | − | 0.858985i | \(-0.328904\pi\) | ||||
0.512001 | + | 0.858985i | \(0.328904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.2498 | 1.15963 | 0.579815 | − | 0.814748i | \(-0.303125\pi\) | ||||
0.579815 | + | 0.814748i | \(0.303125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 23.7796i | − 1.92247i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 4.71995i | − 0.376693i | −0.982103 | − | 0.188347i | \(-0.939687\pi\) | ||||
0.982103 | − | 0.188347i | \(-0.0603128\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.484862 | 0.0384521 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.2342 | 1.04300 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.7493i | 0.841951i | 0.907072 | + | 0.420976i | \(0.138312\pi\) | ||||
−0.907072 | + | 0.420976i | \(0.861688\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.7006i | 0.828035i | 0.910269 | + | 0.414018i | \(0.135875\pi\) | ||||
−0.910269 | + | 0.414018i | \(0.864125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.26537 | −0.328105 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.76491 | −0.517326 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 4.39025i | − 0.333785i | −0.985975 | − | 0.166892i | \(-0.946627\pi\) | ||||
0.985975 | − | 0.166892i | \(-0.0533732\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 7.76491i | − 0.583646i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.21949 | 0.240636 | 0.120318 | − | 0.992735i | \(-0.461609\pi\) | ||||
0.120318 | + | 0.992735i | \(0.461609\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.0606i | 1.03939i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.9385i | 1.09241i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.8255 | −1.29661 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.2342 | 0.957591 | 0.478796 | − | 0.877926i | \(-0.341073\pi\) | ||||
0.478796 | + | 0.877926i | \(0.341073\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3893i | 1.25171i | 0.779939 | + | 0.625856i | \(0.215250\pi\) | ||||
−0.779939 | + | 0.625856i | \(0.784750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000i | 0.142494i | 0.997459 | + | 0.0712470i | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3250 | 1.01547 | 0.507736 | − | 0.861513i | \(-0.330482\pi\) | ||||
0.507736 | + | 0.861513i | \(0.330482\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.2342 | −1.63881 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.20390i | − 0.154683i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 59.0890i | 4.10697i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.24977 | 0.293963 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.98440 | −0.480826 | −0.240413 | − | 0.970671i | \(-0.577283\pi\) | ||||
−0.240413 | + | 0.970671i | \(0.577283\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 26.5601i | − 1.81987i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 7.52982i | − 0.511157i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −47.0138 | −3.17690 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.6060 | −0.982504 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.4802i | 1.63931i | 0.572855 | + | 0.819657i | \(0.305836\pi\) | ||||
−0.572855 | + | 0.819657i | \(0.694164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.9045i | 1.65297i | 0.562960 | + | 0.826484i | \(0.309662\pi\) | ||||
−0.562960 | + | 0.826484i | \(0.690338\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.47018 | −0.295398 | −0.147699 | − | 0.989032i | \(-0.547187\pi\) | ||||
−0.147699 | + | 0.989032i | \(0.547187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.1211 | 1.32387 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3.93945i | − 0.258082i | −0.991639 | − | 0.129041i | \(-0.958810\pi\) | ||||
0.991639 | − | 0.129041i | \(-0.0411899\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 0.969724i | − 0.0629903i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.8255 | 1.15303 | 0.576517 | − | 0.817085i | \(-0.304412\pi\) | ||||
0.576517 | + | 0.817085i | \(0.304412\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.3094 | −1.75915 | −0.879577 | − | 0.475757i | \(-0.842174\pi\) | ||||
−0.879577 | + | 0.475757i | \(0.842174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 16.1698i | − 1.03730i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.15516i | 0.264387i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −28.0294 | −1.77629 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.4390 | −1.16386 | −0.581929 | − | 0.813239i | \(-0.697702\pi\) | ||||
−0.581929 | + | 0.813239i | \(0.697702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 37.1202i | − 2.33373i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.889794i | 0.0555038i | 0.999615 | + | 0.0277519i | \(0.00883485\pi\) | ||||
−0.999615 | + | 0.0277519i | \(0.991165\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.5298 | 0.716428 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.84014 | 0.609089 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 12.6206i | − 0.778222i | −0.921191 | − | 0.389111i | \(-0.872782\pi\) | ||||
0.921191 | − | 0.389111i | \(-0.127218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.24977i | 0.137684i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.4390 | 1.00230 | 0.501151 | − | 0.865360i | \(-0.332910\pi\) | ||||
0.501151 | + | 0.865360i | \(0.332910\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6050 | 1.55540 | 0.777698 | − | 0.628638i | \(-0.216387\pi\) | ||||
0.777698 | + | 0.628638i | \(0.216387\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.6732i | 1.19067i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 0.749313i | − 0.0450218i | −0.999747 | − | 0.0225109i | \(-0.992834\pi\) | ||||
0.999747 | − | 0.0225109i | \(-0.00716605\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.6197 | 2.01276 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.77959 | 0.225471 | 0.112736 | − | 0.993625i | \(-0.464039\pi\) | ||||
0.112736 | + | 0.993625i | \(0.464039\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 9.46927i | − 0.562889i | −0.959577 | − | 0.281445i | \(-0.909186\pi\) | ||||
0.959577 | − | 0.281445i | \(-0.0908136\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 13.9688i | − 0.824553i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.64380 | 0.273165 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −54.3397 | −3.18545 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.6841i | 1.44206i | 0.692905 | + | 0.721029i | \(0.256331\pi\) | ||||
−0.692905 | + | 0.721029i | \(0.743669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 49.9982i | 2.90119i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.2938 | 2.09893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.5913 | 0.725750 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 39.0596i | 2.24392i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 13.3288i | − 0.760714i | −0.924840 | − | 0.380357i | \(-0.875801\pi\) | ||||
0.924840 | − | 0.380357i | \(-0.124199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.0294 | −1.93586 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4546 | −0.762940 | −0.381470 | − | 0.924381i | \(-0.624582\pi\) | ||||
−0.381470 | + | 0.924381i | \(0.624582\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 21.7649i | − 1.23023i | −0.788439 | − | 0.615113i | \(-0.789111\pi\) | ||||
0.788439 | − | 0.615113i | \(-0.210889\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 23.5639i | − 1.32348i | −0.749734 | − | 0.661740i | \(-0.769818\pi\) | ||||
0.749734 | − | 0.661740i | \(-0.230182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.18166 | −0.346106 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.2342 | 1.29681 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.51514i | 0.195588i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 60.4830i | − 3.34472i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9541 | −0.657058 | −0.328529 | − | 0.944494i | \(-0.606553\pi\) | ||||
−0.328529 | + | 0.944494i | \(0.606553\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 51.4792i | 2.82105i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.8292i | 1.24359i | 0.783181 | + | 0.621794i | \(0.213596\pi\) | ||||
−0.783181 | + | 0.621794i | \(0.786404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −55.8089 | −3.03113 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.1202 | −1.14372 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7337i | 0.957531i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 29.4693i | − 1.58199i | −0.611821 | − | 0.790997i | \(-0.709563\pi\) | ||||
0.611821 | − | 0.790997i | \(-0.290437\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.56009 | −0.244096 | −0.122048 | − | 0.992524i | \(-0.538946\pi\) | ||||
−0.122048 | + | 0.992524i | \(0.538946\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −48.8851 | −2.60929 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 24.4849i | − 1.30320i | −0.758564 | − | 0.651599i | \(-0.774099\pi\) | ||||
0.758564 | − | 0.651599i | \(-0.225901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.6429i | 0.880835i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0147 | −0.634111 | −0.317055 | − | 0.948407i | \(-0.602694\pi\) | ||||
−0.317055 | + | 0.948407i | \(0.602694\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 22.0634i | − 1.15803i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.1589i | 1.31329i | 0.754201 | + | 0.656643i | \(0.228024\pi\) | ||||
−0.754201 | + | 0.656643i | \(0.771976\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 62.3690 | 3.24680 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.235091 | −0.0122053 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.62443i | 0.498334i | 0.968461 | + | 0.249167i | \(0.0801568\pi\) | ||||
−0.968461 | + | 0.249167i | \(0.919843\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 6.04404i | − 0.311284i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.7943 | −1.01676 | −0.508382 | − | 0.861132i | \(-0.669756\pi\) | ||||
−0.508382 | + | 0.861132i | \(0.669756\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.43899 | −0.432343 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.3288i | 1.70302i | 0.524337 | + | 0.851511i | \(0.324313\pi\) | ||||
−0.524337 | + | 0.851511i | \(0.675687\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 56.2186i | 2.85775i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.5904 | −0.587655 | −0.293828 | − | 0.955858i | \(-0.594929\pi\) | ||||
−0.293828 | + | 0.955858i | \(0.594929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.7034 | 1.55274 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.4995i | 0.630518i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.74931i | 0.439115i | 0.975600 | + | 0.219558i | \(0.0704614\pi\) | ||||
−0.975600 | + | 0.219558i | \(0.929539\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.73463 | 0.237028 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6206 | −0.929871 | −0.464935 | − | 0.885345i | \(-0.653922\pi\) | ||||
−0.464935 | + | 0.885345i | \(0.653922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 20.6500i | − 1.02865i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 32.3397i | − 1.60302i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.93945 | −0.392580 | −0.196290 | − | 0.980546i | \(-0.562889\pi\) | ||||
−0.196290 | + | 0.980546i | \(0.562889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.4839 | 1.15838 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.76491i | 0.185259i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 52.3397i | 2.56309i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.0908 | 0.639529 | 0.319764 | − | 0.947497i | \(-0.396396\pi\) | ||||
0.319764 | + | 0.947497i | \(0.396396\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.8936 | 0.969554 | 0.484777 | − | 0.874638i | \(-0.338901\pi\) | ||||
0.484777 | + | 0.874638i | \(0.338901\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 35.7190i | 1.73672i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.81743i | − 0.329918i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 55.1807 | 2.66415 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.7796 | −1.62711 | −0.813553 | − | 0.581491i | \(-0.802470\pi\) | ||||
−0.813553 | + | 0.581491i | \(0.802470\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.07901i | 0.436310i | 0.975914 | + | 0.218155i | \(0.0700038\pi\) | ||||
−0.975914 | + | 0.218155i | \(0.929996\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8.73463i | − 0.417834i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.3103 | 0.587540 | 0.293770 | − | 0.955876i | \(-0.405090\pi\) | ||||
0.293770 | + | 0.955876i | \(0.405090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −31.8245 | −1.51545 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.56009i | 0.121634i | 0.998149 | + | 0.0608169i | \(0.0193706\pi\) | ||||
−0.998149 | + | 0.0608169i | \(0.980629\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 39.0596i | − 1.84746i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.9991 | −1.08539 | −0.542697 | − | 0.839929i | \(-0.682597\pi\) | ||||
−0.542697 | + | 0.839929i | \(0.682597\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.1807 | −1.84495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 44.5289i | − 2.09215i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 20.6741i | − 0.967093i | −0.875319 | − | 0.483546i | \(-0.839348\pi\) | ||||
0.875319 | − | 0.483546i | \(-0.160652\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −41.3553 | −1.93030 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.87890 | −0.273807 | −0.136904 | − | 0.990584i | \(-0.543715\pi\) | ||||
−0.136904 | + | 0.990584i | \(0.543715\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.5592i | 1.65258i | 0.563249 | + | 0.826288i | \(0.309551\pi\) | ||||
−0.563249 | + | 0.826288i | \(0.690449\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 41.7408i | − 1.93154i | −0.259408 | − | 0.965768i | \(-0.583528\pi\) | ||||
0.259408 | − | 0.965768i | \(-0.416472\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2654 | 0.520186 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.7493 | −0.679612 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 35.3170i | − 1.62388i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1.04965i | − 0.0480603i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.8704 | −0.770829 | −0.385415 | − | 0.922744i | \(-0.625942\pi\) | ||||
−0.385415 | + | 0.922744i | \(0.625942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.6197 | 1.44174 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 41.3553i | − 1.88173i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 3.64094i | − 0.164987i | −0.996592 | − | 0.0824934i | \(-0.973712\pi\) | ||||
0.996592 | − | 0.0824934i | \(-0.0262883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33.5904 | 1.51901 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.96881 | −0.0888510 | −0.0444255 | − | 0.999013i | \(-0.514146\pi\) | ||||
−0.0444255 | + | 0.999013i | \(0.514146\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.11307i | − 0.230281i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.8780i | 0.577656i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.7787 | 1.64644 | 0.823220 | − | 0.567723i | \(-0.192175\pi\) | ||||
0.823220 | + | 0.567723i | \(0.192175\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.4381 | 1.49390 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.8860i | 0.708322i | 0.935184 | + | 0.354161i | \(0.115234\pi\) | ||||
−0.935184 | + | 0.354161i | \(0.884766\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.3288i | 0.591952i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.2791 | −0.898857 | −0.449428 | − | 0.893316i | \(-0.648372\pi\) | ||||
−0.449428 | + | 0.893316i | \(0.648372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.7952 | 1.00840 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.7649i | 0.519433i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 22.4390i | − 0.986866i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.7190 | −0.602199 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.4693 | −1.02821 | −0.514104 | − | 0.857728i | \(-0.671875\pi\) | ||||
−0.514104 | + | 0.857728i | \(0.671875\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 26.3737i | − 1.15324i | −0.817011 | − | 0.576622i | \(-0.804371\pi\) | ||||
0.817011 | − | 0.576622i | \(-0.195629\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 17.4693i | − 0.760973i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −53.2938 | −2.31712 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.8099 | −0.729486 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 38.3085i | − 1.65932i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 10.0606i | − 0.434145i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.9924 | 0.861135 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5601 | 0.969934 | 0.484967 | − | 0.874532i | \(-0.338832\pi\) | ||||
0.484967 | + | 0.874532i | \(0.338832\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 68.7475i | − 2.95024i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20.6694i | − 0.883759i | −0.897074 | − | 0.441879i | \(-0.854312\pi\) | ||||
0.897074 | − | 0.441879i | \(-0.145688\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.4390 | 1.29910 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.45459 | −0.0619674 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.470182i | 0.0199942i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.7484i | 1.59945i | 0.600366 | + | 0.799725i | \(0.295022\pi\) | ||||
−0.600366 | + | 0.799725i | \(0.704978\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.5307 | 1.46049 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 46.6812 | 1.97088 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 36.6694i | − 1.54543i | −0.634753 | − | 0.772715i | \(-0.718898\pi\) | ||||
0.634753 | − | 0.772715i | \(-0.281102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.9532i | 1.04794i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.84862 | −0.119420 | −0.0597102 | − | 0.998216i | \(-0.519018\pi\) | ||||
−0.0597102 | + | 0.998216i | \(0.519018\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.4002 | 1.18851 | 0.594256 | − | 0.804276i | \(-0.297446\pi\) | ||||
0.594256 | + | 0.804276i | \(0.297446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 41.3553i | − 1.72764i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.2947i | 1.21956i | 0.792572 | + | 0.609778i | \(0.208741\pi\) | ||||
−0.792572 | + | 0.609778i | \(0.791259\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 54.3397 | 2.25828 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.5904 | 0.563824 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.659401i | 0.0273096i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 22.4683i | − 0.927368i | −0.886001 | − | 0.463684i | \(-0.846527\pi\) | ||||
0.886001 | − | 0.463684i | \(-0.153473\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.96972 | −0.204774 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.24977 | 0.257081 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.0606i | 0.659528i | 0.944063 | + | 0.329764i | \(0.106969\pi\) | ||||
−0.944063 | + | 0.329764i | \(0.893031\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 44.7640i | − 1.83207i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.2489 | 0.949922 | 0.474961 | − | 0.880007i | \(-0.342462\pi\) | ||||
0.474961 | + | 0.880007i | \(0.342462\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.841057 | −0.0343074 | −0.0171537 | − | 0.999853i | \(-0.505460\pi\) | ||||
−0.0171537 | + | 0.999853i | \(0.505460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 50.2985i | 2.04831i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.4802i | 1.31833i | 0.751999 | + | 0.659165i | \(0.229090\pi\) | ||||
−0.751999 | + | 0.659165i | \(0.770910\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.88693 | −0.279072 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.9394 | 0.887575 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 19.4305i | − 0.784791i | −0.919797 | − | 0.392395i | \(-0.871646\pi\) | ||||
0.919797 | − | 0.392395i | \(-0.128354\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 20.7787i | − 0.836518i | −0.908328 | − | 0.418259i | \(-0.862640\pi\) | ||||
0.908328 | − | 0.418259i | \(-0.137360\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.9310 | −0.760900 | −0.380450 | − | 0.924802i | \(-0.624231\pi\) | ||||
−0.380450 | + | 0.924802i | \(0.624231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 102.762 | 4.12370 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 1.09083i | − 0.0437031i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 13.2800i | − 0.530354i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.7493 | 1.06656 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.370875 | −0.0147643 | −0.00738215 | − | 0.999973i | \(-0.502350\pi\) | ||||
−0.00738215 | + | 0.999973i | \(0.502350\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.8255i | 0.867484i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.5474i | 0.774495i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −57.4986 | −2.27461 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.8099 | 1.05893 | 0.529463 | − | 0.848333i | \(-0.322393\pi\) | ||||
0.529463 | + | 0.848333i | \(0.322393\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 0.969724i | − 0.0382422i | −0.999817 | − | 0.0191211i | \(-0.993913\pi\) | ||||
0.999817 | − | 0.0191211i | \(-0.00608680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1.20482i | − 0.0473662i | −0.999720 | − | 0.0236831i | \(-0.992461\pi\) | ||||
0.999720 | − | 0.0236831i | \(-0.00753926\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.5601 | 0.414520 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.5298 | −0.922206 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 22.9310i | − 0.897358i | −0.893693 | − | 0.448679i | \(-0.851895\pi\) | ||||
0.893693 | − | 0.448679i | \(-0.148105\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 101.778i | 3.97073i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.1055 | −0.588427 | −0.294214 | − | 0.955740i | \(-0.595058\pi\) | ||||
−0.294214 | + | 0.955740i | \(0.595058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.0450 | 0.740763 | 0.370381 | − | 0.928880i | \(-0.379227\pi\) | ||||
0.370381 | + | 0.928880i | \(0.379227\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 45.6420i | 1.77259i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.7053i | 0.491950i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 76.4977 | 2.95757 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.1220 | −0.738197 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.4205i | 0.594418i | 0.954812 | + | 0.297209i | \(0.0960558\pi\) | ||||
−0.954812 | + | 0.297209i | \(0.903944\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 8.62534i | − 0.331499i | −0.986168 | − | 0.165749i | \(-0.946996\pi\) | ||||
0.986168 | − | 0.165749i | \(-0.0530043\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.3472 | 1.01111 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 77.8236 | 2.98221 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.8898i | 1.48808i | 0.668137 | + | 0.744038i | \(0.267092\pi\) | ||||
−0.668137 | + | 0.744038i | \(0.732908\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.9688i | 0.532943i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.644721 | −0.0245619 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.5979 | −0.821624 | −0.410812 | − | 0.911720i | \(-0.634755\pi\) | ||||
−0.410812 | + | 0.911720i | \(0.634755\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 43.5592i | − 1.65468i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 32.4078i | − 1.22753i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.3103 | −0.465619 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.8183 | 0.672990 | 0.336495 | − | 0.941685i | \(-0.390759\pi\) | ||||
0.336495 | + | 0.941685i | \(0.390759\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 7.60975i | − 0.287007i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 18.9385i | − 0.712257i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.4986 | −1.78385 | −0.891924 | − | 0.452185i | \(-0.850645\pi\) | ||||
−0.891924 | + | 0.452185i | \(0.850645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.09931 | −0.0787302 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 43.4087i | 1.62567i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 55.7025i | − 2.08025i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.4546 | 0.949296 | 0.474648 | − | 0.880176i | \(-0.342575\pi\) | ||||
0.474648 | + | 0.880176i | \(0.342575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.4995 | 0.614475 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 85.3388i | 3.17378i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 21.5445i | − 0.799041i | −0.916724 | − | 0.399521i | \(-0.869177\pi\) | ||||
0.916724 | − | 0.399521i | \(-0.130823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.12110 | −0.0415224 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.2119 | 1.08044 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.2110i | 0.894254i | 0.894470 | + | 0.447127i | \(0.147553\pi\) | ||||
−0.894470 | + | 0.447127i | \(0.852447\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 31.5979i | − 1.16392i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.4693 | 1.37833 | 0.689165 | − | 0.724605i | \(-0.257978\pi\) | ||||
0.689165 | + | 0.724605i | \(0.257978\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.9844 | 0.476994 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 15.8595i | − 0.581829i | −0.956749 | − | 0.290915i | \(-0.906040\pi\) | ||||
0.956749 | − | 0.290915i | \(-0.0939596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 60.6794i | 2.22014i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.2654 | −0.411628 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.12958 | 0.187181 | 0.0935906 | − | 0.995611i | \(-0.470166\pi\) | ||||
0.0935906 | + | 0.995611i | \(0.470166\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 57.6197i | 2.09978i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 37.4381i | − 1.36071i | −0.732883 | − | 0.680355i | \(-0.761826\pi\) | ||||
0.732883 | − | 0.680355i | \(-0.238174\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −115.996 | −4.21040 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.5833 | 0.782392 | 0.391196 | − | 0.920307i | \(-0.372061\pi\) | ||||
0.391196 | + | 0.920307i | \(0.372061\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.3259i | 1.06167i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.3250i | 0.372814i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.7640 | 1.46999 | 0.734994 | − | 0.678074i | \(-0.237185\pi\) | ||||
0.734994 | + | 0.678074i | \(0.237185\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.78051 | 0.100137 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.1845i | 1.73308i | 0.499110 | + | 0.866538i | \(0.333660\pi\) | ||||
−0.499110 | + | 0.866538i | \(0.666340\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 36.0294i | − 1.29255i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.21949 | −0.330323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.1211 | 1.29251 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 17.1131i | − 0.611571i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 27.6925i | − 0.987132i | −0.869708 | − | 0.493566i | \(-0.835693\pi\) | ||||
0.869708 | − | 0.493566i | \(-0.164307\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −39.4381 | −1.40403 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.0596 | 0.962130 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 18.6963i | − 0.663926i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 10.3368i | − 0.366149i | −0.983099 | − | 0.183074i | \(-0.941395\pi\) | ||||
0.983099 | − | 0.183074i | \(-0.0586049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.5601 | 0.656609 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.87042 | 0.172088 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 63.9376i | − 2.25631i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 51.3700i | − 1.80831i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23.2342 | 0.816870 | 0.408435 | − | 0.912787i | \(-0.366075\pi\) | ||||
0.408435 | + | 0.912787i | \(0.366075\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.1433 | 1.12871 | 0.564353 | − | 0.825534i | \(-0.309126\pi\) | ||||
0.564353 | + | 0.825534i | \(0.309126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 80.0128i | − 2.80617i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 8.31032i | − 0.290741i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 42.5895 | 1.48820 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.0908 | −0.945476 | −0.472738 | − | 0.881203i | \(-0.656734\pi\) | ||||
−0.472738 | + | 0.881203i | \(0.656734\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 14.4849i | − 0.504911i | −0.967609 | − | 0.252455i | \(-0.918762\pi\) | ||||
0.967609 | − | 0.252455i | \(-0.0812381\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.0247i | 1.87862i | 0.343067 | + | 0.939311i | \(0.388534\pi\) | ||||
−0.343067 | + | 0.939311i | \(0.611466\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.7640 | −0.651700 | −0.325850 | − | 0.945421i | \(-0.605651\pi\) | ||||
−0.325850 | + | 0.945421i | \(0.605651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.34152 | −0.0812263 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.5365i | 0.572954i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 58.4683i | − 2.02096i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.84014 | 0.270672 | 0.135336 | − | 0.990800i | \(-0.456789\pi\) | ||||
0.135336 | + | 0.990800i | \(0.456789\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8842 | −0.927041 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 11.8108i | − 0.406785i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.6977i | 0.367578i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.5904 | −1.01554 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −66.4683 | −2.27851 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.8174i | 1.26060i | 0.776350 | + | 0.630302i | \(0.217069\pi\) | ||||
−0.776350 | + | 0.630302i | \(0.782931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.23887i | 0.178956i | 0.995989 | + | 0.0894782i | \(0.0285199\pi\) | ||||
−0.995989 | + | 0.0894782i | \(0.971480\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.6197 | 1.01061 | 0.505306 | − | 0.862940i | \(-0.331380\pi\) | ||||
0.505306 | + | 0.862940i | \(0.331380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −43.6509 | −1.48762 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 35.8889i | − 1.22167i | −0.791757 | − | 0.610836i | \(-0.790834\pi\) | ||||
0.791757 | − | 0.610836i | \(-0.209166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 14.5114i | − 0.492832i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.31880 | 0.0447373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.8945 | 1.04682 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 117.637i | 3.98142i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.8136i | 1.00674i | 0.864072 | + | 0.503368i | \(0.167906\pi\) | ||||
−0.864072 | + | 0.503368i | \(0.832094\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 77.1349 | 2.60169 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.9679 | −1.31286 | −0.656431 | − | 0.754386i | \(-0.727935\pi\) | ||||
−0.656431 | + | 0.754386i | \(0.727935\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 28.5677i | − 0.961378i | −0.876891 | − | 0.480689i | \(-0.840387\pi\) | ||||
0.876891 | − | 0.480689i | \(-0.159613\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 27.5104i | − 0.923710i | −0.886955 | − | 0.461855i | \(-0.847184\pi\) | ||||
0.886955 | − | 0.461855i | \(-0.152816\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.09174 | 0.137233 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 69.9906 | 2.34477 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 5.28005i | − 0.176690i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 113.414i | − 3.78678i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.22889 | 0.241097 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.545414 | −0.0181704 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 39.3463i | − 1.30936i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 55.4939i | 1.84265i | 0.388799 | + | 0.921323i | \(0.372890\pi\) | ||||
−0.388799 | + | 0.921323i | \(0.627110\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 84.5583 | 2.80462 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.84106 | 0.226654 | 0.113327 | − | 0.993558i | \(-0.463849\pi\) | ||||
0.113327 | + | 0.993558i | \(0.463849\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 38.1193i | − 1.26156i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6.06055i | − 0.200137i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.17454 | 0.203679 | 0.101840 | − | 0.994801i | \(-0.467527\pi\) | ||||
0.101840 | + | 0.994801i | \(0.467527\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41.6509 | −1.37244 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.3170i | 1.16247i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 73.6685i | 2.41959i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.7034 | −1.46667 | −0.733336 | − | 0.679866i | \(-0.762038\pi\) | ||||
−0.733336 | + | 0.679866i | \(0.762038\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.70436 | 0.154179 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 42.0440i | 1.37646i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.1064i | 0.395500i | 0.980253 | + | 0.197750i | \(0.0633634\pi\) | ||||
−0.980253 | + | 0.197750i | \(0.936637\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −68.0128 | −2.21952 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.2645 | −0.856197 | −0.428098 | − | 0.903732i | \(-0.640816\pi\) | ||||
−0.428098 | + | 0.903732i | \(0.640816\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 80.5289i | 2.62238i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 7.37935i | − 0.239797i | −0.992786 | − | 0.119898i | \(-0.961743\pi\) | ||||
0.992786 | − | 0.119898i | \(-0.0382569\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62.5142 | 2.02930 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −73.6344 | −2.38776 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 21.5398i | − 0.697743i | −0.937171 | − | 0.348871i | \(-0.886565\pi\) | ||||
0.937171 | − | 0.348871i | \(-0.113435\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.3170i | 0.624429i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.3865 | −0.367688 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.30184 | −0.203285 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 50.2985i | − 1.62085i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.8789i | 1.28242i | 0.767366 | + | 0.641209i | \(0.221567\pi\) | ||||
−0.767366 | + | 0.641209i | \(0.778433\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.9844 | 0.352870 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.7408 | −0.954429 | −0.477214 | − | 0.878787i | \(-0.658353\pi\) | ||||
−0.477214 | + | 0.878787i | \(0.658353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 25.3775i | − 0.813566i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 58.6694i | 1.87700i | 0.345279 | + | 0.938500i | \(0.387784\pi\) | ||||
−0.345279 | + | 0.938500i | \(0.612216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.05964 | −0.0977864 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −130.937 | −4.18049 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.7384i | 0.374397i | 0.982322 | + | 0.187199i | \(0.0599408\pi\) | ||||
−0.982322 | + | 0.187199i | \(0.940059\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 24.9991i | − 0.795730i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −72.5876 | −2.30815 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.7493 | −0.849720 | −0.424860 | − | 0.905259i | \(-0.639677\pi\) | ||||
−0.424860 | + | 0.905259i | \(0.639677\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 37.3553i | 1.18543i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 45.8401i | − 1.45177i | −0.687815 | − | 0.725886i | \(-0.741430\pi\) | ||||
0.687815 | − | 0.725886i | \(-0.258570\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 89.5280 | 2.83254 |
(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 | 3800.2.d.k.3649.1 | 6 | ||
5.2 | odd | 4 | 760.2.a.h.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 3800.2.a.y.1.3 | 3 | |||
5.4 | even | 2 | inner | 3800.2.d.k.3649.6 | 6 | ||
15.2 | even | 4 | 6840.2.a.bj.1.2 | 3 | |||
20.3 | even | 4 | 7600.2.a.bo.1.1 | 3 | |||
20.7 | even | 4 | 1520.2.a.r.1.3 | 3 | |||
40.27 | even | 4 | 6080.2.a.bs.1.1 | 3 | |||
40.37 | odd | 4 | 6080.2.a.bw.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.a.h.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
1520.2.a.r.1.3 | 3 | 20.7 | even | 4 | |||
3800.2.a.y.1.3 | 3 | 5.3 | odd | 4 | |||
3800.2.d.k.3649.1 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.d.k.3649.6 | 6 | 5.4 | even | 2 | inner | ||
6080.2.a.bs.1.1 | 3 | 40.27 | even | 4 | |||
6080.2.a.bw.1.3 | 3 | 40.37 | odd | 4 | |||
6840.2.a.bj.1.2 | 3 | 15.2 | even | 4 | |||
7600.2.a.bo.1.1 | 3 | 20.3 | even | 4 |