Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(369,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("460.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.c (of order \(2\), degree \(1\), 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: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 24x^{10} + 188x^{8} + 530x^{6} + 508x^{4} + 80x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.3 | ||
Root | \(-1.26443i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.369 |
Dual form | 460.2.c.a.369.10 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.40050i | − | 1.38593i | −0.720971 | − | 0.692965i | \(-0.756304\pi\) | ||
0.720971 | − | 0.692965i | \(-0.243696\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.817027 | − | 2.08146i | −0.365386 | − | 0.930856i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.41307i | − | 1.66798i | −0.551777 | − | 0.833992i | \(-0.686050\pi\) | ||
0.551777 | − | 0.833992i | \(-0.313950\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.76241 | −0.920804 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.29289 | 0.691332 | 0.345666 | − | 0.938358i | \(-0.387653\pi\) | ||||
0.345666 | + | 0.938358i | \(0.387653\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.92936i | 1.92186i | 0.276792 | + | 0.960930i | \(0.410729\pi\) | ||||
−0.276792 | + | 0.960930i | \(0.589271\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.99655 | + | 1.96128i | −1.29010 | + | 0.506399i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.51387i | − | 0.367168i | −0.983004 | − | 0.183584i | \(-0.941230\pi\) | ||
0.983004 | − | 0.183584i | \(-0.0587699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.89920 | −0.665121 | −0.332561 | − | 0.943082i | \(-0.607913\pi\) | ||||
−0.332561 | + | 0.943082i | \(0.607913\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.5936 | −2.31171 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.66493 | + | 3.40122i | −0.732987 | + | 0.680243i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 0.570328i | − | 0.109760i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.68764 | 1.42756 | 0.713779 | − | 0.700371i | \(-0.246982\pi\) | ||||
0.713779 | + | 0.700371i | \(0.246982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.85746 | 0.692821 | 0.346410 | − | 0.938083i | \(-0.387401\pi\) | ||||
0.346410 | + | 0.938083i | \(0.387401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5.50408i | − | 0.958138i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.18562 | + | 3.60560i | −1.55265 | + | 0.609457i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.62830i | − | 1.41848i | −0.704965 | − | 0.709242i | \(-0.749037\pi\) | ||
0.704965 | − | 0.709242i | \(-0.250963\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.6340 | 2.66356 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.44324 | −1.00626 | −0.503132 | − | 0.864209i | \(-0.667819\pi\) | ||||
−0.503132 | + | 0.864209i | \(0.667819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.48497i | − | 0.531453i | −0.964048 | − | 0.265727i | \(-0.914388\pi\) | ||
0.964048 | − | 0.265727i | \(-0.0856119\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.25697 | + | 5.74985i | 0.336449 | + | 0.857136i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.19747i | 0.903994i | 0.892019 | + | 0.451997i | \(0.149288\pi\) | ||||
−0.892019 | + | 0.451997i | \(0.850712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.4752 | −1.78217 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.63405 | −0.508869 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.17710i | 0.299047i | 0.988758 | + | 0.149524i | \(0.0477740\pi\) | ||||
−0.988758 | + | 0.149524i | \(0.952226\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.87335 | − | 4.77255i | −0.252603 | − | 0.643530i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.95953i | 0.921812i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7637 | 1.53150 | 0.765750 | − | 0.643138i | \(-0.222368\pi\) | ||||
0.765750 | + | 0.643138i | \(0.222368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.11443 | −0.654835 | −0.327418 | − | 0.944880i | \(-0.606178\pi\) | ||||
−0.327418 | + | 0.944880i | \(0.606178\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.1907i | 1.53589i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.4232 | − | 5.66148i | 1.78898 | − | 0.702220i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.94597i | − | 1.21509i | −0.794284 | − | 0.607547i | \(-0.792154\pi\) | ||
0.794284 | − | 0.607547i | \(-0.207846\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.40050 | 0.288987 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.41407 | 0.405175 | 0.202588 | − | 0.979264i | \(-0.435065\pi\) | ||||
0.202588 | + | 0.979264i | \(0.435065\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.95307i | − | 1.04788i | −0.851756 | − | 0.523939i | \(-0.824462\pi\) | ||
0.851756 | − | 0.523939i | \(-0.175538\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.16463 | + | 8.79768i | 0.942770 | + | 1.01587i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 10.1187i | − | 1.15313i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.92694 | 0.216798 | 0.108399 | − | 0.994107i | \(-0.465428\pi\) | ||||
0.108399 | + | 0.994107i | \(0.465428\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.65631 | −1.07292 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.04131i | 0.882648i | 0.897348 | + | 0.441324i | \(0.145491\pi\) | ||||
−0.897348 | + | 0.441324i | \(0.854509\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.15106 | + | 1.23687i | −0.341781 | + | 0.134158i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 18.4542i | − | 1.97850i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.09273 | 0.115829 | 0.0579147 | − | 0.998322i | \(-0.481555\pi\) | ||||
0.0579147 | + | 0.998322i | \(0.481555\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.5798 | 3.20563 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 9.25985i | − | 0.960201i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.36872 | + | 6.03456i | 0.243026 | + | 0.619132i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.9208i | 1.71805i | 0.511933 | + | 0.859026i | \(0.328930\pi\) | ||||
−0.511933 | + | 0.859026i | \(0.671070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.33390 | −0.636581 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9497 | 1.28855 | 0.644274 | − | 0.764795i | \(-0.277160\pi\) | ||||
0.644274 | + | 0.764795i | \(0.277160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9754i | 1.08144i | 0.841202 | + | 0.540721i | \(0.181848\pi\) | ||||
−0.841202 | + | 0.540721i | \(0.818152\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.65525 | + | 22.0501i | 0.844666 | + | 2.15187i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 19.8821i | − | 1.92208i | −0.276411 | − | 0.961040i | \(-0.589145\pi\) | ||
0.276411 | − | 0.961040i | \(-0.410855\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.427249 | −0.0409231 | −0.0204615 | − | 0.999791i | \(-0.506514\pi\) | ||||
−0.0204615 | + | 0.999791i | \(0.506514\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.7123 | −1.96592 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.38533i | − | 0.506609i | −0.967387 | − | 0.253304i | \(-0.918483\pi\) | ||
0.967387 | − | 0.253304i | \(-0.0815174\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.08146 | − | 0.817027i | 0.194097 | − | 0.0761882i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 19.1418i | − | 1.76966i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.68082 | −0.612430 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.74267 | −0.522061 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.4670i | 1.39461i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.0738 | + | 4.84952i | 0.901031 | + | 0.433754i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.16014i | − | 0.546624i | −0.961925 | − | 0.273312i | \(-0.911881\pi\) | ||
0.961925 | − | 0.273312i | \(-0.0881191\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.36569 | −0.736558 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.6325 | 1.27845 | 0.639225 | − | 0.769020i | \(-0.279255\pi\) | ||||
0.639225 | + | 0.769020i | \(0.279255\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.7944i | 1.10941i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.18711 | + | 0.465974i | −0.102171 | + | 0.0401046i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 0.972256i | − | 0.0830654i | −0.999137 | − | 0.0415327i | \(-0.986776\pi\) | ||
0.999137 | − | 0.0415327i | \(-0.0132241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.74312 | −0.656763 | −0.328382 | − | 0.944545i | \(-0.606503\pi\) | ||||
−0.328382 | + | 0.944545i | \(0.606503\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.8770 | 1.25287 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.8883i | 1.32864i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.28101 | − | 16.0015i | −0.521609 | − | 1.32885i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 29.9467i | 2.46996i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.6823 | 1.44859 | 0.724293 | − | 0.689492i | \(-0.242166\pi\) | ||||
0.724293 | + | 0.689492i | \(0.242166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.01286 | −0.163804 | −0.0819022 | − | 0.996640i | \(-0.526100\pi\) | ||||
−0.0819022 | + | 0.996640i | \(0.526100\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.18194i | 0.338090i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.15165 | − | 8.02914i | −0.253147 | − | 0.644916i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.82703i | 0.465048i | 0.972591 | + | 0.232524i | \(0.0746984\pi\) | ||||
−0.972591 | + | 0.232524i | \(0.925302\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.22612 | 0.414459 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.41307 | 0.347799 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.75147i | − | 0.528816i | −0.964411 | − | 0.264408i | \(-0.914823\pi\) | ||
0.964411 | − | 0.264408i | \(-0.0851765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.4565 | + | 4.49698i | −0.891889 | + | 0.350090i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.4541i | 1.81493i | 0.420125 | + | 0.907466i | \(0.361986\pi\) | ||||
−0.420125 | + | 0.907466i | \(0.638014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.0161 | −2.69355 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00878 | 0.612447 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 8.28850i | − | 0.630163i | −0.949065 | − | 0.315081i | \(-0.897968\pi\) | ||
0.949065 | − | 0.315081i | \(-0.102032\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.0098 | + | 16.1736i | 1.13463 | + | 1.22261i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 28.2387i | − | 2.12255i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.04002 | −0.0777345 | −0.0388673 | − | 0.999244i | \(-0.512375\pi\) | ||||
−0.0388673 | + | 0.999244i | \(0.512375\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.71850 | 0.202065 | 0.101032 | − | 0.994883i | \(-0.467785\pi\) | ||||
0.101032 | + | 0.994883i | \(0.467785\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.2772i | 0.907557i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.9594 | + | 7.04956i | −1.32040 | + | 0.518294i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.47114i | − | 0.253835i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.51690 | −0.183077 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.04858 | 0.582375 | 0.291187 | − | 0.956666i | \(-0.405950\pi\) | ||||
0.291187 | + | 0.956666i | \(0.405950\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 16.0276i | − | 1.15370i | −0.816852 | − | 0.576848i | \(-0.804283\pi\) | ||
0.816852 | − | 0.576848i | \(-0.195717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.5904 | − | 34.6229i | −0.973228 | − | 2.47940i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.06316i | − | 0.289488i | −0.989469 | − | 0.144744i | \(-0.953764\pi\) | ||
0.989469 | − | 0.144744i | \(-0.0462359\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.7042 | −1.32590 | −0.662952 | − | 0.748662i | \(-0.730697\pi\) | ||||
−0.662952 | + | 0.748662i | \(0.730697\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.8753 | −1.68404 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 33.9261i | − | 2.38114i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.26430 | + | 13.4113i | 0.367675 | + | 0.936688i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.76241i | − | 0.192001i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.64753 | −0.459819 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.87839 | 0.542371 | 0.271185 | − | 0.962527i | \(-0.412584\pi\) | ||||
0.271185 | + | 0.962527i | \(0.412584\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.19548i | − | 0.561545i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.25382 | + | 2.84732i | −0.494707 | + | 0.194185i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 17.0232i | − | 1.15561i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21.4919 | −1.45229 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.4902 | 0.705645 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.29263i | − | 0.153526i | −0.997049 | − | 0.0767628i | \(-0.975542\pi\) | ||
0.997049 | − | 0.0767628i | \(-0.0244584\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.1241 | − | 9.39556i | 0.674937 | − | 0.626371i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 12.8325i | − | 0.851725i | −0.904788 | − | 0.425862i | \(-0.859971\pi\) | ||
0.904788 | − | 0.425862i | \(-0.140029\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2528 | 1.07401 | 0.537007 | − | 0.843578i | \(-0.319555\pi\) | ||||
0.537007 | + | 0.843578i | \(0.319555\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.2899 | −1.59816 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.5410i | 1.41120i | 0.708613 | + | 0.705598i | \(0.249321\pi\) | ||||
−0.708613 | + | 0.705598i | \(0.750679\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8998 | − | 5.06350i | 0.841489 | − | 0.330307i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 4.62563i | − | 0.300467i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0622 | 0.715555 | 0.357778 | − | 0.933807i | \(-0.383535\pi\) | ||||
0.357778 | + | 0.933807i | \(0.383535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.2164 | 1.17342 | 0.586710 | − | 0.809797i | \(-0.300423\pi\) | ||||
0.586710 | + | 0.809797i | \(0.300423\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.4690i | 1.37724i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.1926 | + | 25.9666i | 0.651179 | + | 1.65894i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 20.0896i | − | 1.27827i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.3032 | 1.22329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.0182 | −0.632345 | −0.316172 | − | 0.948702i | \(-0.602398\pi\) | ||||
−0.316172 | + | 0.948702i | \(0.602398\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.29289i | 0.144153i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.96912 | + | 7.56413i | 0.185934 | + | 0.473684i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.3021i | 0.892141i | 0.894998 | + | 0.446070i | \(0.147177\pi\) | ||||
−0.894998 | + | 0.446070i | \(0.852823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −38.0773 | −2.36601 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.2364 | −1.31450 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 9.44361i | − | 0.582318i | −0.956675 | − | 0.291159i | \(-0.905959\pi\) | ||
0.956675 | − | 0.291159i | \(-0.0940409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.53153 | − | 1.77875i | 0.278370 | − | 0.109268i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.62311i | − | 0.160531i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.7630 | −1.44886 | −0.724428 | − | 0.689350i | \(-0.757896\pi\) | ||||
−0.724428 | + | 0.689350i | \(0.757896\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5939 | −1.06875 | −0.534375 | − | 0.845247i | \(-0.679453\pi\) | ||||
−0.534375 | + | 0.845247i | \(0.679453\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 73.4068i | − | 4.44278i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.40328 | + | 7.79860i | −0.506737 | + | 0.470273i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.6582i | 1.78199i | 0.454014 | + | 0.890995i | \(0.349992\pi\) | ||||
−0.454014 | + | 0.890995i | \(0.650008\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.6559 | −0.637952 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.25484 | −0.492442 | −0.246221 | − | 0.969214i | \(-0.579189\pi\) | ||||
−0.246221 | + | 0.969214i | \(0.579189\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.21317i | 0.547666i | 0.961777 | + | 0.273833i | \(0.0882916\pi\) | ||||
−0.961777 | + | 0.273833i | \(0.911708\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.4860 | − | 5.68613i | 0.858075 | − | 0.336817i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.4344i | 1.67843i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.7082 | 0.865188 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 40.6185 | 2.38110 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.1138i | 0.649277i | 0.945838 | + | 0.324639i | \(0.105243\pi\) | ||||
−0.945838 | + | 0.324639i | \(0.894757\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.61125 | − | 24.4856i | −0.559588 | − | 1.42561i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.30770i | − | 0.0758804i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.92936 | −0.400735 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.3794 | −0.886455 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 31.0859i | − | 1.78584i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.17863 | + | 10.6455i | 0.239267 | + | 0.609558i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.7800i | − | 1.07183i | −0.844272 | − | 0.535916i | \(-0.819967\pi\) | ||
0.844272 | − | 0.535916i | \(-0.180033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.3465 | 1.49880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.51258 | 0.142475 | 0.0712377 | − | 0.997459i | \(-0.477305\pi\) | ||||
0.0712377 | + | 0.997459i | \(0.477305\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.9278i | 1.12638i | 0.826326 | + | 0.563192i | \(0.190427\pi\) | ||||
−0.826326 | + | 0.563192i | \(0.809573\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 25.3745 | − | 9.96015i | 1.42969 | − | 0.561191i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.8849i | 1.56617i | 0.621912 | + | 0.783087i | \(0.286356\pi\) | ||||
−0.621912 | + | 0.783087i | \(0.713644\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.6269 | 0.986916 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −47.7271 | −2.66387 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.38901i | 0.244211i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.5683 | − | 25.3957i | −1.30733 | − | 1.40870i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.02561i | 0.0567165i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.3499 | 1.50785 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.5409 | −1.56875 | −0.784375 | − | 0.620287i | \(-0.787016\pi\) | ||||
−0.784375 | + | 0.620287i | \(0.787016\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.8349i | 1.30615i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.7021 | + | 8.12612i | −1.13108 | + | 0.443978i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.71371i | − | 0.202298i | −0.994871 | − | 0.101149i | \(-0.967748\pi\) | ||
0.994871 | − | 0.101149i | \(-0.0322520\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.9275 | −0.702125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.84472 | 0.478969 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 24.1624i | 1.30464i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.96128 | − | 4.99655i | −0.105592 | − | 0.269005i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 14.1459i | − | 0.759393i | −0.925111 | − | 0.379696i | \(-0.876028\pi\) | ||
0.925111 | − | 0.379696i | \(-0.123972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.2802 | 1.13910 | 0.569550 | − | 0.821957i | \(-0.307117\pi\) | ||||
0.569550 | + | 0.821957i | \(0.307117\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.95201 | 0.210943 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.4641i | 1.30209i | 0.759038 | + | 0.651046i | \(0.225669\pi\) | ||||
−0.759038 | + | 0.651046i | \(0.774331\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.78939 | − | 7.10624i | −0.148045 | − | 0.377160i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.0373i | 0.848786i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.0252 | 1.21522 | 0.607612 | − | 0.794234i | \(-0.292128\pi\) | ||||
0.607612 | + | 0.794234i | \(0.292128\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.5947 | −0.557613 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.7853i | 0.723540i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.6354 | + | 7.31490i | −0.975424 | + | 0.382880i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 0.478057i | − | 0.0249544i | −0.999922 | − | 0.0124772i | \(-0.996028\pi\) | ||
0.999922 | − | 0.0124772i | \(-0.00397171\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.7989 | 0.926573 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.60767 | 0.498806 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.3508i | 1.41617i | 0.706127 | + | 0.708085i | \(0.250441\pi\) | ||||
−0.706127 | + | 0.708085i | \(0.749559\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.6413 | − | 24.1823i | 0.601153 | − | 1.24877i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 53.2704i | 2.74357i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.35358 | 0.377728 | 0.188864 | − | 0.982003i | \(-0.439519\pi\) | ||||
0.188864 | + | 0.982003i | \(0.439519\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.7874 | −0.757583 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.34108i | − | 0.170721i | −0.996350 | − | 0.0853606i | \(-0.972796\pi\) | ||
0.996350 | − | 0.0853606i | \(-0.0272042\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.0616 | + | 8.26723i | −1.07340 | + | 0.421337i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.62693i | 0.489364i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.366568 | −0.0185858 | −0.00929288 | − | 0.999957i | \(-0.502958\pi\) | ||||
−0.00929288 | + | 0.999957i | \(0.502958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.51387 | 0.0765598 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 35.1254i | − | 1.77184i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.57436 | − | 4.01085i | −0.0792148 | − | 0.201808i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3222i | 0.568245i | 0.958788 | + | 0.284122i | \(0.0917022\pi\) | ||||
−0.958788 | + | 0.284122i | \(0.908298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 30.7129 | 1.53757 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.1673 | 1.85605 | 0.928024 | − | 0.372520i | \(-0.121506\pi\) | ||||
0.928024 | + | 0.372520i | \(0.121506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.7298i | 1.33150i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.88947 | + | 20.0992i | 0.392031 | + | 0.998738i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 19.7837i | − | 0.980643i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.7745 | 0.681107 | 0.340553 | − | 0.940225i | \(-0.389386\pi\) | ||||
0.340553 | + | 0.940225i | \(0.389386\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.33390 | −0.115123 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 51.9139i | − | 2.55452i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.7376 | − | 6.56997i | 0.821619 | − | 0.322507i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.5874i | 0.910228i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.50726 | −0.366753 | −0.183377 | − | 0.983043i | \(-0.558703\pi\) | ||||
−0.183377 | + | 0.983043i | \(0.558703\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.65685 | −0.373172 | −0.186586 | − | 0.982439i | \(-0.559742\pi\) | ||||
−0.186586 | + | 0.982439i | \(0.559742\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 17.1200i | − | 0.832402i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.14900 | + | 5.54824i | 0.249763 | + | 0.269129i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.5703i | 1.09225i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 38.1398 | 1.84141 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.22764 | 0.299975 | 0.149987 | − | 0.988688i | \(-0.452077\pi\) | ||||
0.149987 | + | 0.988688i | \(0.452077\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.704087i | 0.0338362i | 0.999857 | + | 0.0169181i | \(0.00538546\pi\) | ||||
−0.999857 | + | 0.0169181i | \(0.994615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −38.4116 | + | 15.0776i | −1.84170 | + | 0.722914i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.89920i | − | 0.138687i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.8570 | 1.66363 | 0.831816 | − | 0.555052i | \(-0.187301\pi\) | ||||
0.831816 | + | 0.555052i | \(0.187301\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 34.4616 | 1.64103 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 24.8165i | − | 1.17907i | −0.807745 | − | 0.589533i | \(-0.799312\pi\) | ||
0.807745 | − | 0.589533i | \(-0.200688\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.892792 | − | 2.27448i | −0.0423224 | − | 0.107820i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 42.4463i | − | 2.00764i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.77738 | −0.319844 | −0.159922 | − | 0.987130i | \(-0.551124\pi\) | ||||
−0.159922 | + | 0.987130i | \(0.551124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.7736 | −0.695662 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.83188i | 0.227021i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −24.9845 | − | 63.6505i | −1.17129 | − | 2.98398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.47169i | − | 0.0688429i | −0.999407 | − | 0.0344214i | \(-0.989041\pi\) | ||
0.999407 | − | 0.0344214i | \(-0.0109588\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.863404 | −0.0403003 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.8037 | 1.20180 | 0.600899 | − | 0.799325i | \(-0.294809\pi\) | ||||
0.600899 | + | 0.799325i | \(0.294809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.3469i | − | 0.713231i | −0.934251 | − | 0.356616i | \(-0.883931\pi\) | ||
0.934251 | − | 0.356616i | \(-0.116069\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.2740 | + | 7.56555i | −0.893809 | + | 0.350844i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.2933i | − | 0.476315i | −0.971227 | − | 0.238157i | \(-0.923457\pi\) | ||
0.971227 | − | 0.238157i | \(-0.0765434\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −43.8922 | −2.02676 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.9878 | 0.644524 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.99065i | − | 0.367410i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.6254 | − | 9.86079i | 0.487525 | − | 0.452444i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.01404i | − | 0.275364i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.50453 | −0.205817 | −0.102909 | − | 0.994691i | \(-0.532815\pi\) | ||||
−0.102909 | + | 0.994691i | \(0.532815\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 59.7886 | 2.72613 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 10.5936i | − | 0.482025i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 35.2200 | − | 13.8248i | 1.59926 | − | 0.627751i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.2669i | 1.23558i | 0.786343 | + | 0.617790i | \(0.211972\pi\) | ||||
−0.786343 | + | 0.617790i | \(0.788028\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.2069 | −0.732902 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.4866 | 1.10507 | 0.552533 | − | 0.833491i | \(-0.313661\pi\) | ||||
0.552533 | + | 0.833491i | \(0.313661\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 11.6381i | − | 0.524154i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.17497 | + | 13.1838i | 0.232598 | + | 0.592566i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 15.0665i | − | 0.675826i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.1892 | 1.08286 | 0.541429 | − | 0.840746i | \(-0.317883\pi\) | ||||
0.541429 | + | 0.840746i | \(0.317883\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 56.3016 | 2.51537 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.6230i | 1.36541i | 0.730693 | + | 0.682706i | \(0.239197\pi\) | ||||
−0.730693 | + | 0.682706i | \(0.760803\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5803 | − | 26.9543i | −0.470817 | − | 1.19945i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 84.0562i | 3.73307i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.56826 | 0.113836 | 0.0569181 | − | 0.998379i | \(-0.481873\pi\) | ||||
0.0569181 | + | 0.998379i | \(0.481873\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.5105 | −1.74784 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.65349i | 0.0730035i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.8449 | − | 8.96722i | 1.00667 | − | 0.395143i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.2101i | 0.624960i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.8966 | −0.873362 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −44.1355 | −1.93361 | −0.966807 | − | 0.255509i | \(-0.917757\pi\) | ||||
−0.966807 | + | 0.255509i | \(0.917757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.2884i | 1.84914i | 0.381008 | + | 0.924572i | \(0.375577\pi\) | ||||
−0.381008 | + | 0.924572i | \(0.624423\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 38.8248 | − | 36.0311i | 1.69445 | − | 1.57252i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 5.83970i | − | 0.254381i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −32.4961 | −1.41021 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 44.6475i | − | 1.93390i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.3838 | + | 16.2443i | −1.78918 | + | 0.702300i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.49656i | 0.107735i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −28.6042 | −1.23207 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.2776 | 0.441871 | 0.220935 | − | 0.975288i | \(-0.429089\pi\) | ||||
0.220935 | + | 0.975288i | \(0.429089\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 6.52577i | − | 0.280048i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.349074 | + | 0.889302i | 0.0149527 | + | 0.0380935i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.87305i | 0.165600i | 0.996566 | + | 0.0827998i | \(0.0263862\pi\) | ||||
−0.996566 | + | 0.0827998i | \(0.973614\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.1282 | 0.602975 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.2880 | −0.949500 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 8.50373i | − | 0.361615i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.9225 | + | 43.1117i | 0.718319 | + | 1.82999i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.62364i | 0.407767i | 0.978995 | + | 0.203883i | \(0.0653563\pi\) | ||||
−0.978995 | + | 0.203883i | \(0.934644\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.1486 | 1.02138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.33248 | −0.351797 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.35865i | 0.141550i | 0.997492 | + | 0.0707751i | \(0.0225473\pi\) | ||||
−0.997492 | + | 0.0707751i | \(0.977453\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.2093 | + | 4.39996i | −0.471580 | + | 0.185108i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 42.6140i | 1.78962i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.26939 | 0.178982 | 0.0894910 | − | 0.995988i | \(-0.471476\pi\) | ||||
0.0894910 | + | 0.995988i | \(0.471476\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4567 | 0.688689 | 0.344345 | − | 0.938843i | \(-0.388101\pi\) | ||||
0.344345 | + | 0.938843i | \(0.388101\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 19.3206i | − | 0.807131i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.40122 | − | 3.66493i | −0.141840 | − | 0.152838i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.98780i | − | 0.0827530i | −0.999144 | − | 0.0413765i | \(-0.986826\pi\) | ||
0.999144 | − | 0.0413765i | \(-0.0131743\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −38.4744 | −1.59894 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.4869 | 1.47224 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.99184i | 0.206741i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −39.8428 | + | 15.6393i | −1.64730 | + | 0.646607i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.9720i | 1.19580i | 0.801570 | + | 0.597900i | \(0.203998\pi\) | ||||
−0.801570 | + | 0.597900i | \(0.796002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.1835 | −0.460810 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.75363 | −0.401211 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 19.4799i | − | 0.799944i | −0.916527 | − | 0.399972i | \(-0.869020\pi\) | ||
0.916527 | − | 0.399972i | \(-0.130980\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.45841 | + | 13.9059i | 0.223773 | + | 0.570084i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 44.8994i | 1.83761i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.8442 | −1.54627 | −0.773136 | − | 0.634240i | \(-0.781313\pi\) | ||||
−0.773136 | + | 0.634240i | \(0.781313\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.2347 | −0.825389 | −0.412695 | − | 0.910869i | \(-0.635412\pi\) | ||||
−0.412695 | + | 0.910869i | \(0.635412\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.4749i | 1.11886i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.69191 | + | 11.9531i | 0.190753 | + | 0.485963i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.4075i | − | 0.990670i | −0.868702 | − | 0.495335i | \(-0.835045\pi\) | ||
0.868702 | − | 0.495335i | \(-0.164955\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −81.4396 | −3.30010 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −42.9445 | −1.73735 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6964i | 0.432025i | 0.976391 | + | 0.216012i | \(0.0693051\pi\) | ||||
−0.976391 | + | 0.216012i | \(0.930695\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.1939 | − | 12.6370i | 1.29818 | − | 0.509572i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.4738i | 1.10605i | 0.833164 | + | 0.553026i | \(0.186527\pi\) | ||||
−0.833164 | + | 0.553026i | \(0.813473\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.389330 | 0.0156485 | 0.00782425 | − | 0.999969i | \(-0.497509\pi\) | ||||
0.00782425 | + | 0.999969i | \(0.497509\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.570328 | 0.0228865 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 4.82230i | − | 0.193201i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.86347 | − | 24.9305i | 0.0745389 | − | 0.997218i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.9574i | 0.637278i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.0621 | −0.520822 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.9330 | −0.475047 | −0.237523 | − | 0.971382i | \(-0.576336\pi\) | ||||
−0.237523 | + | 0.971382i | \(0.576336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 18.9121i | − | 0.751689i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.8221 | + | 5.03300i | −0.508828 | + | 0.199729i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 86.4451i | − | 3.42508i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.43106 | −0.373087 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.8525 | 0.902621 | 0.451311 | − | 0.892367i | \(-0.350957\pi\) | ||||
0.451311 | + | 0.892367i | \(0.350957\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.9279i | 1.37742i | 0.725036 | + | 0.688711i | \(0.241823\pi\) | ||||
−0.725036 | + | 0.688711i | \(0.758177\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.83499 | + | 17.4128i | 0.269128 | + | 0.685629i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 26.3738i | − | 1.03686i | −0.855120 | − | 0.518430i | \(-0.826517\pi\) | ||
0.855120 | − | 0.518430i | \(-0.173483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 26.9728 | 1.05877 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.8643 | −1.60160 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.17022i | − | 0.0849274i | −0.999098 | − | 0.0424637i | \(-0.986479\pi\) | ||
0.999098 | − | 0.0424637i | \(-0.0135207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.9552 | − | 30.4570i | −0.467127 | − | 1.19005i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.7321i | 0.964891i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.7820 | −0.770596 | −0.385298 | − | 0.922792i | \(-0.625901\pi\) | ||||
−0.385298 | + | 0.922792i | \(0.625901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.7505 | 1.77949 | 0.889743 | − | 0.456461i | \(-0.150883\pi\) | ||||
0.889743 | + | 0.456461i | \(0.150883\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 25.1817i | − | 0.977976i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.6309 | − | 10.4533i | 1.03270 | − | 0.405363i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.68764i | 0.297666i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.50346 | −0.212776 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.7268 | −0.452708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.99940i | 0.269807i | 0.990859 | + | 0.134904i | \(0.0430725\pi\) | ||||
−0.990859 | + | 0.134904i | \(0.956928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.93981 | + | 2.09021i | 0.0746633 | + | 0.0804524i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 26.7178i | − | 1.02685i | −0.858134 | − | 0.513425i | \(-0.828376\pi\) | ||
0.858134 | − | 0.513425i | \(-0.171624\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 74.6728 | 2.86568 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.8045 | −1.18043 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19.8947i | − | 0.761248i | −0.924730 | − | 0.380624i | \(-0.875709\pi\) | ||
0.924730 | − | 0.380624i | \(-0.124291\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.02371 | + | 0.794359i | −0.0773219 | + | 0.0303509i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 39.0148i | − | 1.48851i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −15.0859 | −0.574727 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.24438 | 0.0473385 | 0.0236693 | − | 0.999720i | \(-0.492465\pi\) | ||||
0.0236693 | + | 0.999720i | \(0.492465\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 27.9520i | 1.06181i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.32634 | + | 16.1170i | 0.239972 | + | 0.611352i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.75424i | 0.369468i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 51.7091 | 1.95582 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.8454 | −1.12724 | −0.563622 | − | 0.826033i | \(-0.690592\pi\) | ||||
−0.563622 | + | 0.826033i | \(0.690592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.0151i | 0.943464i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.1550 | − | 30.9660i | −0.457782 | − | 1.16625i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 57.1481i | − | 2.14928i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.2255 | −0.947362 | −0.473681 | − | 0.880697i | \(-0.657075\pi\) | ||||
−0.473681 | + | 0.880697i | \(0.657075\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.32301 | −0.199628 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.85746i | 0.144463i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.0707 | − | 12.9811i | 1.23678 | − | 0.485467i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 26.5549i | − | 0.991710i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.7787 | 0.886797 | 0.443398 | − | 0.896325i | \(-0.353773\pi\) | ||||
0.443398 | + | 0.896325i | \(0.353773\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.4353 | 1.80383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 43.7285i | − | 1.62628i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.1747 | + | 26.1473i | −1.04638 | + | 0.971086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 36.5849i | − | 1.35686i | −0.734666 | − | 0.678429i | \(-0.762661\pi\) | ||
0.734666 | − | 0.678429i | \(-0.237339\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.5675 | 0.835833 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.27580 | −0.195133 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.7593i | − | 0.803698i | −0.915706 | − | 0.401849i | \(-0.868368\pi\) | ||
0.915706 | − | 0.401849i | \(-0.131632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 62.3328 | − | 24.4673i | 2.29918 | − | 0.902489i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 22.8050i | − | 0.840032i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.72303 | −0.100168 | −0.0500842 | − | 0.998745i | \(-0.515949\pi\) | ||||
−0.0500842 | + | 0.998745i | \(0.515949\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −48.2251 | −1.77159 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 32.0161i | − | 1.17456i | −0.809385 | − | 0.587278i | \(-0.800200\pi\) | ||
0.809385 | − | 0.587278i | \(-0.199800\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.4469 | − | 36.8049i | −0.529293 | − | 1.34843i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 22.2134i | − | 0.812746i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −87.7413 | −3.20600 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0949 | −1.31712 | −0.658561 | − | 0.752527i | \(-0.728835\pi\) | ||||
−0.658561 | + | 0.752527i | \(0.728835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.0488i | 0.876386i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.64456 | + | 4.18969i | 0.0598517 | + | 0.152478i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.8188i | 1.70166i | 0.525442 | + | 0.850830i | \(0.323900\pi\) | ||||
−0.525442 | + | 0.850830i | \(0.676100\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.50408 | 0.199786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.8182 | −1.04466 | −0.522330 | − | 0.852744i | \(-0.674937\pi\) | ||||
−0.522330 | + | 0.852744i | \(0.674937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.88548i | 0.0682590i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.70453 | − | 3.41676i | 0.314713 | − | 0.123533i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 81.5148i | 2.94333i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.6243 | −1.86162 | −0.930811 | − | 0.365501i | \(-0.880898\pi\) | ||||
−0.930811 | + | 0.365501i | \(0.880898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.3322 | 1.23645 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.9610i | 0.933753i | 0.884322 | + | 0.466877i | \(0.154621\pi\) | ||||
−0.884322 | + | 0.466877i | \(0.845379\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.1373 | + | 13.1201i | −0.507828 | + | 0.471286i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 91.4046i | 3.27912i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.6802 | 0.669288 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.82807 | 0.280110 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 4.38448i | − | 0.156688i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.1287 | − | 4.76084i | 0.432893 | − | 0.169922i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 53.2258i | − | 1.89730i | −0.316333 | − | 0.948648i | \(-0.602452\pi\) | ||
0.316333 | − | 0.948648i | \(-0.397548\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.6694 | −0.807053 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.7658 | −0.845015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 35.4397i | − | 1.25850i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.26988 | − | 10.8780i | −0.151437 | − | 0.385801i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 31.1874i | − | 1.10471i | −0.833608 | − | 0.552357i | \(-0.813729\pi\) | ||
0.833608 | − | 0.552357i | \(-0.186271\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.38218 | 0.331918 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.01858 | −0.106656 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 20.5284i | − | 0.724431i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.60560 | − | 9.18562i | −0.127081 | − | 0.323750i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 57.0432i | 2.00802i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.60251 | 0.0563414 | 0.0281707 | − | 0.999603i | \(-0.491032\pi\) | ||||
0.0281707 | + | 0.999603i | \(0.491032\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.9545 | −1.29765 | −0.648824 | − | 0.760938i | \(-0.724739\pi\) | ||||
−0.648824 | + | 0.760938i | \(0.724739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 42.2341i | 1.48121i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.0529 | + | 5.51613i | −0.492251 | + | 0.193222i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.1036i | 0.353481i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −84.4739 | −2.95176 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.5583 | −0.577890 | −0.288945 | − | 0.957346i | \(-0.593304\pi\) | ||||
−0.288945 | + | 0.957346i | \(0.593304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 7.63201i | − | 0.266035i | −0.991114 | − | 0.133018i | \(-0.957533\pi\) | ||
0.991114 | − | 0.133018i | \(-0.0424667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.7206 | + | 20.1721i | 0.651767 | + | 0.702302i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.1969i | 0.667543i | 0.942654 | + | 0.333772i | \(0.108321\pi\) | ||||
−0.942654 | + | 0.333772i | \(0.891679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.32413 | 0.219646 | 0.109823 | − | 0.993951i | \(-0.464972\pi\) | ||||
0.109823 | + | 0.993951i | \(0.464972\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 71.1946 | 2.46971 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.8858i | 0.654355i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.8187 | − | 19.1626i | 1.68944 | − | 0.663150i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 2.20002i | − | 0.0760438i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.1158 | −0.798046 | −0.399023 | − | 0.916941i | \(-0.630651\pi\) | ||||
−0.399023 | + | 0.916941i | \(0.630651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.0997 | 1.03792 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.8158i | 0.682491i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.6091 | + | 72.8845i | 0.984183 | + | 2.50730i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.3428i | 0.870789i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.1163 | 0.759028 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.62830 | 0.295774 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 37.7049i | − | 1.29099i | −0.763764 | − | 0.645496i | \(-0.776651\pi\) | ||
0.763764 | − | 0.645496i | \(-0.223349\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.54339 | − | 16.6699i | −0.223779 | − | 0.570100i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 19.7133i | − | 0.673395i | −0.941613 | − | 0.336697i | \(-0.890690\pi\) | ||
0.941613 | − | 0.336697i | \(-0.109310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.00609 | −0.0684471 | −0.0342235 | − | 0.999414i | \(-0.510896\pi\) | ||||
−0.0342235 | + | 0.999414i | \(0.510896\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 68.2570 | 2.32619 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.8127i | 0.572312i | 0.958183 | + | 0.286156i | \(0.0923775\pi\) | ||||
−0.958183 | + | 0.286156i | \(0.907623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.2522 | + | 6.77193i | −0.586591 | + | 0.230252i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 35.3071i | − | 1.19909i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.41826 | 0.149879 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 68.9192 | 2.33524 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 46.7424i | − | 1.58199i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.4013 | − | 44.4565i | 0.723495 | − | 1.50291i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 14.8922i | − | 0.502874i | −0.967874 | − | 0.251437i | \(-0.919097\pi\) | ||
0.967874 | − | 0.251437i | \(-0.0809031\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.6788 | 0.899853 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.5218 | −0.556632 | −0.278316 | − | 0.960490i | \(-0.589776\pi\) | ||||
−0.278316 | + | 0.960490i | \(0.589776\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.7254i | 1.30321i | 0.758557 | + | 0.651607i | \(0.225905\pi\) | ||||
−0.758557 | + | 0.651607i | \(0.774095\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −58.7778 | + | 23.0718i | −1.97579 | + | 0.775551i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.16364i | − | 0.0390711i | −0.999809 | − | 0.0195355i | \(-0.993781\pi\) | ||
0.999809 | − | 0.0195355i | \(-0.00621875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.1851 | −0.911760 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −22.1408 | −0.741746 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 17.9677i | − | 0.601266i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.849722 | + | 2.16475i | 0.0284031 | + | 0.0723597i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.6340i | 0.555392i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.6548 | 0.989042 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.29584 | 0.109800 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.9183i | 1.22857i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.22109 | − | 5.65845i | −0.0738316 | − | 0.188093i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 30.2796i | − | 1.00542i | −0.864456 | − | 0.502709i | \(-0.832337\pi\) | ||
0.864456 | − | 0.502709i | \(-0.167663\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35.7725 | −1.18650 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.2296 | −0.935290 | −0.467645 | − | 0.883916i | \(-0.654897\pi\) | ||||
−0.467645 | + | 0.883916i | \(0.654897\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.4378i | 0.610203i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25.5545 | − | 10.0308i | 0.844805 | − | 0.331608i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 64.5744i | − | 2.13243i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.28150 | −0.108247 | −0.0541233 | − | 0.998534i | \(-0.517236\pi\) | ||||
−0.0541233 | + | 0.998534i | \(0.517236\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −45.0814 | −1.48548 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 23.6573i | 0.778690i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.3467 | + | 31.6221i | 0.964914 | + | 1.03973i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 30.3187i | − | 0.995796i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.64745 | −0.250905 | −0.125452 | − | 0.992100i | \(-0.540038\pi\) | ||||
−0.125452 | + | 0.992100i | \(0.540038\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.1680 | 1.18536 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 6.03146i | − | 0.197461i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.22503 | + | 2.83601i | −0.236284 | + | 0.0927476i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.95226i | 0.161783i | 0.996723 | + | 0.0808917i | \(0.0257768\pi\) | ||||
−0.996723 | + | 0.0808917i | \(0.974223\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 47.8366 | 1.56109 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.62677 | −0.281225 | −0.140612 | − | 0.990065i | \(-0.544907\pi\) | ||||
−0.140612 | + | 0.990065i | \(0.544907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.44324i | − | 0.209821i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.05637 | + | 5.23882i | 0.0668939 | + | 0.170419i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.6807i | 1.51692i | 0.651720 | + | 0.758460i | \(0.274048\pi\) | ||||
−0.651720 | + | 0.758460i | \(0.725952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62.0391 | 2.01387 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 66.9378 | 2.17061 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.2343i | − | 0.396307i | −0.980171 | − | 0.198154i | \(-0.936505\pi\) | ||
0.980171 | − | 0.198154i | \(-0.0634945\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.57591 | − | 16.7528i | −0.212791 | − | 0.542107i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 42.3134i | − | 1.36780i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.29063 | −0.138552 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.1200 | −0.520000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 54.9227i | 1.76986i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.3609 | + | 13.0950i | −1.07392 | + | 0.421544i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.8318i | 1.76327i | 0.471932 | + | 0.881635i | \(0.343557\pi\) | ||||
−0.471932 | + | 0.881635i | \(0.656443\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.5358 | 0.338460 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.3804 | 1.29587 | 0.647935 | − | 0.761696i | \(-0.275633\pi\) | ||||
0.647935 | + | 0.761696i | \(0.275633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.1709i | 1.09547i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −60.9623 | + | 56.5757i | −1.95236 | + | 1.81187i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6700i | 0.341363i | 0.985326 | + | 0.170681i | \(0.0545968\pi\) | ||||
−0.985326 | + | 0.170681i | \(0.945403\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.50551 | 0.0800765 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.18024 | 0.0376821 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.27812i | 0.200241i | 0.994975 | + | 0.100120i | \(0.0319228\pi\) | ||||
−0.994975 | + | 0.100120i | \(0.968077\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.45730 | + | 3.31971i | −0.269472 | + | 0.105775i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 65.6535i | − | 2.08977i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.48497 | 0.110816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.2864 | 1.94683 | 0.973413 | − | 0.229057i | \(-0.0735643\pi\) | ||||
0.973413 | + | 0.229057i | \(0.0735643\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 68.5125i | 2.17418i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.2818 | + | 38.9320i | 0.484466 | + | 1.23423i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 39.9799i | − | 1.26618i | −0.774080 | − | 0.633088i | \(-0.781787\pi\) | ||
0.774080 | − | 0.633088i | \(-0.218213\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.92096 | −0.155692 |
(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 | 460.2.c.a.369.3 | ✓ | 12 | |
3.2 | odd | 2 | 4140.2.f.b.829.8 | 12 | |||
4.3 | odd | 2 | 1840.2.e.f.369.10 | 12 | |||
5.2 | odd | 4 | 2300.2.a.o.1.1 | 6 | |||
5.3 | odd | 4 | 2300.2.a.n.1.6 | 6 | |||
5.4 | even | 2 | inner | 460.2.c.a.369.10 | yes | 12 | |
15.14 | odd | 2 | 4140.2.f.b.829.7 | 12 | |||
20.3 | even | 4 | 9200.2.a.cy.1.1 | 6 | |||
20.7 | even | 4 | 9200.2.a.cx.1.6 | 6 | |||
20.19 | odd | 2 | 1840.2.e.f.369.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
460.2.c.a.369.10 | yes | 12 | 5.4 | even | 2 | inner | |
1840.2.e.f.369.3 | 12 | 20.19 | odd | 2 | |||
1840.2.e.f.369.10 | 12 | 4.3 | odd | 2 | |||
2300.2.a.n.1.6 | 6 | 5.3 | odd | 4 | |||
2300.2.a.o.1.1 | 6 | 5.2 | odd | 4 | |||
4140.2.f.b.829.7 | 12 | 15.14 | odd | 2 | |||
4140.2.f.b.829.8 | 12 | 3.2 | odd | 2 | |||
9200.2.a.cx.1.6 | 6 | 20.7 | even | 4 | |||
9200.2.a.cy.1.1 | 6 | 20.3 | even | 4 |