Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4284,2,Mod(3277,4284)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4284, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4284.3277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4284 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4284.z (of order \(4\), degree \(2\), 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: | \(34.2079122259\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 18x^{14} + 127x^{12} + 444x^{10} + 801x^{8} + 708x^{6} + 263x^{4} + 30x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 476) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 4033.4 | ||
Root | \(2.05350i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4284.4033 |
Dual form | 4284.2.z.b.3277.4 |
$q$-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 \(\left(\mathbb{Z}/4284\mathbb{Z}\right)^\times\).
\(n\) | \(1261\) | \(1837\) | \(2143\) | \(3809\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.25265 | + | 1.25265i | −0.560204 | + | 0.560204i | −0.929365 | − | 0.369161i | \(-0.879645\pi\) |
0.369161 | + | 0.929365i | \(0.379645\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.12117 | + | 2.12117i | 0.639558 | + | 0.639558i | 0.950446 | − | 0.310888i | \(-0.100626\pi\) |
−0.310888 | + | 0.950446i | \(0.600626\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.59917 | −0.720879 | −0.360440 | − | 0.932783i | \(-0.617373\pi\) | ||||
−0.360440 | + | 0.932783i | \(0.617373\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.08609 | − | 3.97749i | −0.263417 | − | 0.964682i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.57015i | 1.04846i | 0.851575 | + | 0.524232i | \(0.175648\pi\) | ||||
−0.851575 | + | 0.524232i | \(0.824352\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.09262 | − | 3.09262i | −0.644856 | − | 0.644856i | 0.306889 | − | 0.951745i | \(-0.400712\pi\) |
−0.951745 | + | 0.306889i | \(0.900712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.86172i | 0.372343i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.70313 | + | 1.70313i | −0.316264 | + | 0.316264i | −0.847330 | − | 0.531066i | \(-0.821792\pi\) |
0.531066 | + | 0.847330i | \(0.321792\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.86978 | − | 1.86978i | 0.335823 | − | 0.335823i | −0.518970 | − | 0.854793i | \(-0.673684\pi\) |
0.854793 | + | 0.518970i | \(0.173684\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.77152 | −0.299442 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.372597 | − | 0.372597i | 0.0612546 | − | 0.0612546i | −0.675816 | − | 0.737070i | \(-0.736209\pi\) |
0.737070 | + | 0.675816i | \(0.236209\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.52683 | + | 8.52683i | 1.33167 | + | 1.33167i | 0.903879 | + | 0.427789i | \(0.140707\pi\) |
0.427789 | + | 0.903879i | \(0.359293\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.63796i | 0.402285i | 0.979562 | + | 0.201143i | \(0.0644655\pi\) | ||||
−0.979562 | + | 0.201143i | \(0.935535\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.67463 | −1.41119 | −0.705595 | − | 0.708616i | \(-0.749320\pi\) | ||||
−0.705595 | + | 0.708616i | \(0.749320\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.88549i | − | 0.533713i | −0.963736 | − | 0.266857i | \(-0.914015\pi\) | ||
0.963736 | − | 0.266857i | \(-0.0859850\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.31420 | −0.716566 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2.63190i | − | 0.342645i | −0.985215 | − | 0.171322i | \(-0.945196\pi\) | ||
0.985215 | − | 0.171322i | \(-0.0548040\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.61920 | − | 6.61920i | −0.847501 | − | 0.847501i | 0.142319 | − | 0.989821i | \(-0.454544\pi\) |
−0.989821 | + | 0.142319i | \(0.954544\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.25586 | − | 3.25586i | 0.403839 | − | 0.403839i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.9050 | −1.82093 | −0.910467 | − | 0.413581i | \(-0.864278\pi\) | ||||
−0.910467 | + | 0.413581i | \(0.864278\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1101 | + | 10.1101i | −1.19985 | + | 1.19985i | −0.225638 | + | 0.974211i | \(0.572447\pi\) |
−0.974211 | + | 0.225638i | \(0.927553\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.22856 | − | 2.22856i | 0.260834 | − | 0.260834i | −0.564559 | − | 0.825393i | \(-0.690954\pi\) |
0.825393 | + | 0.564559i | \(0.190954\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.99979i | 0.341858i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.2409 | + | 12.2409i | 1.37721 | + | 1.37721i | 0.849309 | + | 0.527896i | \(0.177019\pi\) |
0.527896 | + | 0.849309i | \(0.322981\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.6749i | − | 1.39125i | −0.718406 | − | 0.695624i | \(-0.755128\pi\) | ||
0.718406 | − | 0.695624i | \(-0.244872\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.34291 | + | 3.62191i | 0.687986 | + | 0.392852i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.05547 | −0.217879 | −0.108940 | − | 0.994048i | \(-0.534746\pi\) | ||||
−0.108940 | + | 0.994048i | \(0.534746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.83789 | − | 1.83789i | −0.192663 | − | 0.192663i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.72482 | − | 5.72482i | −0.587354 | − | 0.587354i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.08951 | − | 5.08951i | 0.516761 | − | 0.516761i | −0.399829 | − | 0.916590i | \(-0.630930\pi\) |
0.916590 | + | 0.399829i | \(0.130930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.15980 | 0.115404 | 0.0577021 | − | 0.998334i | \(-0.481623\pi\) | ||||
0.0577021 | + | 0.998334i | \(0.481623\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.73357 | −0.860545 | −0.430272 | − | 0.902699i | \(-0.641582\pi\) | ||||
−0.430272 | + | 0.902699i | \(0.641582\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.34809 | − | 9.34809i | 0.903714 | − | 0.903714i | −0.0920415 | − | 0.995755i | \(-0.529339\pi\) |
0.995755 | + | 0.0920415i | \(0.0293392\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.28189 | − | 3.28189i | −0.314348 | − | 0.314348i | 0.532244 | − | 0.846591i | \(-0.321349\pi\) |
−0.846591 | + | 0.532244i | \(0.821349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.283749 | − | 0.283749i | −0.0266928 | − | 0.0266928i | 0.693634 | − | 0.720327i | \(-0.256008\pi\) |
−0.720327 | + | 0.693634i | \(0.756008\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.74797 | 0.722502 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.04452 | − | 3.58049i | 0.187421 | − | 0.328223i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.00124i | − | 0.181931i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.59536 | − | 8.59536i | −0.768792 | − | 0.768792i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 0.350103i | − | 0.0310666i | −0.999879 | − | 0.0155333i | \(-0.995055\pi\) | ||
0.999879 | − | 0.0155333i | \(-0.00494461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.57703 | − | 5.57703i | 0.487267 | − | 0.487267i | −0.420176 | − | 0.907443i | \(-0.638031\pi\) |
0.907443 | + | 0.420176i | \(0.138031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.23159 | + | 3.23159i | −0.280214 | + | 0.280214i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.64144 | −0.823724 | −0.411862 | − | 0.911246i | \(-0.635121\pi\) | ||||
−0.411862 | + | 0.911246i | \(0.635121\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.12776 | + | 9.12776i | −0.774206 | + | 0.774206i | −0.978839 | − | 0.204633i | \(-0.934400\pi\) |
0.204633 | + | 0.978839i | \(0.434400\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.51329 | − | 5.51329i | −0.461044 | − | 0.461044i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 4.26688i | − | 0.354345i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.94430 | 0.323129 | 0.161565 | − | 0.986862i | \(-0.448346\pi\) | ||||
0.161565 | + | 0.986862i | \(0.448346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.8865i | 1.94385i | 0.235281 | + | 0.971927i | \(0.424399\pi\) | ||||
−0.235281 | + | 0.971927i | \(0.575601\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.68438i | 0.376258i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.4697 | −1.47404 | −0.737020 | − | 0.675871i | \(-0.763768\pi\) | ||||
−0.737020 | + | 0.675871i | \(0.763768\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.37363i | − | 0.344690i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.0105 | − | 13.0105i | −1.01906 | − | 1.01906i | −0.999815 | − | 0.0192472i | \(-0.993873\pi\) |
−0.0192472 | − | 0.999815i | \(-0.506127\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.8488 | + | 16.8488i | −1.30380 | + | 1.30380i | −0.377988 | + | 0.925810i | \(0.623384\pi\) |
−0.925810 | + | 0.377988i | \(0.876616\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.24433 | −0.480333 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.43253 | + | 4.43253i | −0.336999 | + | 0.336999i | −0.855237 | − | 0.518238i | \(-0.826588\pi\) |
0.518238 | + | 0.855237i | \(0.326588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.31643 | + | 1.31643i | −0.0995129 | + | 0.0995129i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.8732i | − | 0.962190i | −0.876668 | − | 0.481095i | \(-0.840239\pi\) | ||
0.876668 | − | 0.481095i | \(-0.159761\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.1228 | − | 15.1228i | −1.12407 | − | 1.12407i | −0.991123 | − | 0.132948i | \(-0.957556\pi\) |
−0.132948 | − | 0.991123i | \(-0.542444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.933470i | 0.0686301i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.13315 | − | 10.7407i | 0.448500 | − | 0.785441i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.5198 | 1.26769 | 0.633846 | − | 0.773460i | \(-0.281475\pi\) | ||||
0.633846 | + | 0.773460i | \(0.281475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.64600 | + | 3.64600i | 0.262444 | + | 0.262444i | 0.826046 | − | 0.563602i | \(-0.190585\pi\) |
−0.563602 | + | 0.826046i | \(0.690585\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.48158 | + | 6.48158i | 0.461794 | + | 0.461794i | 0.899243 | − | 0.437449i | \(-0.144118\pi\) |
−0.437449 | + | 0.899243i | \(0.644118\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.23149 | − | 8.23149i | 0.583515 | − | 0.583515i | −0.352353 | − | 0.935867i | \(-0.614618\pi\) |
0.935867 | + | 0.352353i | \(0.114618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.40860 | −0.169050 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.3623 | −1.49201 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.69409 | + | 9.69409i | −0.670554 | + | 0.670554i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.52188 | + | 2.52188i | 0.173613 | + | 0.173613i | 0.788565 | − | 0.614952i | \(-0.210824\pi\) |
−0.614952 | + | 0.788565i | \(0.710824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.30445 | − | 3.30445i | −0.225362 | − | 0.225362i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.64427 | 0.179505 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.82294 | + | 10.3381i | 0.189892 | + | 0.695419i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 21.4094i | − | 1.43368i | −0.697238 | − | 0.716840i | \(-0.745588\pi\) | ||
0.697238 | − | 0.716840i | \(-0.254412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.9150 | − | 14.9150i | −0.989946 | − | 0.989946i | 0.0100041 | − | 0.999950i | \(-0.496816\pi\) |
−0.999950 | + | 0.0100041i | \(0.996816\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.2882i | − | 0.679866i | −0.940450 | − | 0.339933i | \(-0.889596\pi\) | ||
0.940450 | − | 0.339933i | \(-0.110404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.07234 | + | 8.07234i | −0.528837 | + | 0.528837i | −0.920225 | − | 0.391389i | \(-0.871995\pi\) |
0.391389 | + | 0.920225i | \(0.371995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1190 | − | 12.1190i | 0.790554 | − | 0.790554i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.00572125 | 0.000370077 | 0.000185039 | − | 1.00000i | \(-0.499941\pi\) | ||||
0.000185039 | 1.00000i | \(0.499941\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.1682 | + | 18.1682i | −1.17031 | + | 1.17031i | −0.188180 | + | 0.982135i | \(0.560259\pi\) |
−0.982135 | + | 0.188180i | \(0.939741\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.25265 | − | 1.25265i | −0.0800291 | − | 0.0800291i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 11.8786i | − | 0.755816i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.56127 | −0.540383 | −0.270191 | − | 0.962807i | \(-0.587087\pi\) | ||||
−0.270191 | + | 0.962807i | \(0.587087\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.1200i | − | 0.824846i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.3786i | 0.959291i | 0.877462 | + | 0.479646i | \(0.159235\pi\) | ||||
−0.877462 | + | 0.479646i | \(0.840765\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.526932 | 0.0327419 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.18787i | 0.0732471i | 0.999329 | + | 0.0366236i | \(0.0116603\pi\) | ||||
−0.999329 | + | 0.0366236i | \(0.988340\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.86717 | + | 4.86717i | 0.298988 | + | 0.298988i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.16855 | − | 3.16855i | 0.193190 | − | 0.193190i | −0.603883 | − | 0.797073i | \(-0.706381\pi\) |
0.797073 | + | 0.603883i | \(0.206381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5763 | −0.946192 | −0.473096 | − | 0.881011i | \(-0.656864\pi\) | ||||
−0.473096 | + | 0.881011i | \(0.656864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.94903 | + | 3.94903i | −0.238135 | + | 0.238135i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.8334 | + | 12.8334i | −0.771082 | + | 0.771082i | −0.978296 | − | 0.207214i | \(-0.933560\pi\) |
0.207214 | + | 0.978296i | \(0.433560\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0114i | 1.61137i | 0.592347 | + | 0.805683i | \(0.298202\pi\) | ||||
−0.592347 | + | 0.805683i | \(0.701798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.54071 | − | 4.54071i | −0.269917 | − | 0.269917i | 0.559150 | − | 0.829067i | \(-0.311128\pi\) |
−0.829067 | + | 0.559150i | \(0.811128\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0588i | 0.711806i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.6408 | + | 8.63985i | −0.861223 | + | 0.508227i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.4808 | −0.729134 | −0.364567 | − | 0.931177i | \(-0.618783\pi\) | ||||
−0.364567 | + | 0.931177i | \(0.618783\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.29686 | + | 3.29686i | 0.191951 | + | 0.191951i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.03824 | + | 8.03824i | 0.464863 | + | 0.464863i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.86532 | + | 1.86532i | −0.107515 | + | 0.107515i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.5831 | 0.949547 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.3966 | 1.67775 | 0.838877 | − | 0.544321i | \(-0.183213\pi\) | ||||
0.838877 | + | 0.544321i | \(0.183213\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.2210 | + | 11.2210i | −0.636286 | + | 0.636286i | −0.949637 | − | 0.313352i | \(-0.898548\pi\) |
0.313352 | + | 0.949637i | \(0.398548\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.2386 | − | 23.2386i | −1.31352 | − | 1.31352i | −0.918800 | − | 0.394722i | \(-0.870841\pi\) |
−0.394722 | − | 0.918800i | \(-0.629159\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.7827 | − | 18.7827i | −1.05494 | − | 1.05494i | −0.998400 | − | 0.0565423i | \(-0.981992\pi\) |
−0.0565423 | − | 0.998400i | \(-0.518008\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.22529 | −0.404539 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.1777 | − | 4.96362i | 1.01144 | − | 0.276183i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 4.83891i | − | 0.268414i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.84099 | − | 6.84099i | −0.377156 | − | 0.377156i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.9872i | 0.988666i | 0.869273 | + | 0.494333i | \(0.164588\pi\) | ||||
−0.869273 | + | 0.494333i | \(0.835412\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.6708 | − | 18.6708i | 1.02009 | − | 1.02009i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.8367 | + | 19.8367i | −1.08058 | + | 1.08058i | −0.0841196 | + | 0.996456i | \(0.526808\pi\) |
−0.996456 | + | 0.0841196i | \(0.973192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.93227 | 0.429556 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.5196 | + | 13.5196i | 0.725773 | + | 0.725773i | 0.969775 | − | 0.244002i | \(-0.0784604\pi\) |
−0.244002 | + | 0.969775i | \(0.578460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.4741i | − | 0.667725i | −0.942622 | − | 0.333863i | \(-0.891648\pi\) | ||
0.942622 | − | 0.333863i | \(-0.108352\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.0136 | 1.70391 | 0.851956 | − | 0.523613i | \(-0.175416\pi\) | ||||
0.851956 | + | 0.523613i | \(0.175416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 25.3289i | − | 1.34432i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 11.5673i | − | 0.610501i | −0.952272 | − | 0.305251i | \(-0.901260\pi\) | ||
0.952272 | − | 0.305251i | \(-0.0987402\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.88628 | −0.0992781 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.58324i | 0.292240i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.99418 | − | 3.99418i | −0.208495 | − | 0.208495i | 0.595133 | − | 0.803627i | \(-0.297099\pi\) |
−0.803627 | + | 0.595133i | \(0.797099\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.74746 | − | 2.74746i | 0.142641 | − | 0.142641i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0723 | −0.935750 | −0.467875 | − | 0.883795i | \(-0.654980\pi\) | ||||
−0.467875 | + | 0.883795i | \(0.654980\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.42673 | − | 4.42673i | 0.227988 | − | 0.227988i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.02455 | + | 3.02455i | −0.155361 | + | 0.155361i | −0.780507 | − | 0.625147i | \(-0.785039\pi\) |
0.625147 | + | 0.780507i | \(0.285039\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.28017i | 0.116511i | 0.998302 | + | 0.0582557i | \(0.0185539\pi\) | ||||
−0.998302 | + | 0.0582557i | \(0.981446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.75770 | − | 3.75770i | −0.191510 | − | 0.191510i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.16537i | − | 0.160491i | −0.996775 | − | 0.0802453i | \(-0.974430\pi\) | ||
0.996775 | − | 0.0802453i | \(-0.0255704\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.94198 | + | 15.6597i | −0.452215 | + | 0.791947i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.6671 | −1.54303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.03989 | − | 1.03989i | −0.0521904 | − | 0.0521904i | 0.680530 | − | 0.732720i | \(-0.261750\pi\) |
−0.732720 | + | 0.680530i | \(0.761750\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.2831 | − | 23.2831i | −1.16270 | − | 1.16270i | −0.983882 | − | 0.178821i | \(-0.942772\pi\) |
−0.178821 | − | 0.983882i | \(-0.557228\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.85987 | + | 4.85987i | −0.242088 | + | 0.242088i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.58069 | 0.0783517 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6136 | 0.574255 | 0.287128 | − | 0.957892i | \(-0.407300\pi\) | ||||
0.287128 | + | 0.957892i | \(0.407300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.86104 | − | 1.86104i | 0.0915756 | − | 0.0915756i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.8772 | + | 15.8772i | 0.779382 | + | 0.779382i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.0737 | + | 24.0737i | 1.17608 | + | 1.17608i | 0.980735 | + | 0.195342i | \(0.0625818\pi\) |
0.195342 | + | 0.980735i | \(0.437418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4720 | 0.802797 | 0.401399 | − | 0.915903i | \(-0.368524\pi\) | ||||
0.401399 | + | 0.915903i | \(0.368524\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.40495 | − | 2.02200i | 0.359193 | − | 0.0980814i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9.36096i | − | 0.453009i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.52263 | + | 2.52263i | 0.121511 | + | 0.121511i | 0.765247 | − | 0.643736i | \(-0.222617\pi\) |
−0.643736 | + | 0.765247i | \(0.722617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.7012i | 0.658436i | 0.944254 | + | 0.329218i | \(0.106785\pi\) | ||||
−0.944254 | + | 0.329218i | \(0.893215\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14.1338 | − | 14.1338i | 0.676109 | − | 0.676109i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.5344 | − | 25.5344i | 1.21869 | − | 1.21869i | 0.250601 | − | 0.968090i | \(-0.419372\pi\) |
0.968090 | − | 0.250601i | \(-0.0806283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.17342 | −0.293308 | −0.146654 | − | 0.989188i | \(-0.546850\pi\) | ||||
−0.146654 | + | 0.989188i | \(0.546850\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.57479 | − | 2.57479i | 0.122057 | − | 0.122057i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.2385 | + | 14.2385i | 0.671957 | + | 0.671957i | 0.958167 | − | 0.286210i | \(-0.0923955\pi\) |
−0.286210 | + | 0.958167i | \(0.592396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.1738i | 1.70336i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.60448 | 0.215861 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 13.0583i | − | 0.610842i | −0.952217 | − | 0.305421i | \(-0.901203\pi\) | ||
0.952217 | − | 0.305421i | \(-0.0987973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0878i | 0.702710i | 0.936242 | + | 0.351355i | \(0.114279\pi\) | ||||
−0.936242 | + | 0.351355i | \(0.885721\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.0923 | 1.39851 | 0.699255 | − | 0.714873i | \(-0.253515\pi\) | ||||
0.699255 | + | 0.714873i | \(0.253515\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.0220i | 0.602587i | 0.953531 | + | 0.301294i | \(0.0974185\pi\) | ||||
−0.953531 | + | 0.301294i | \(0.902582\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.5394 | − | 10.5394i | −0.486665 | − | 0.486665i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.59558 | + | 5.59558i | −0.257285 | + | 0.257285i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.50833 | −0.390389 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.5488 | − | 26.5488i | 1.21304 | − | 1.21304i | 0.243024 | − | 0.970020i | \(-0.421861\pi\) |
0.970020 | − | 0.243024i | \(-0.0781395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.968442 | + | 0.968442i | −0.0441571 | + | 0.0441571i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.7508i | 0.578983i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.7940 | + | 25.7940i | 1.16884 | + | 1.16884i | 0.982483 | + | 0.186354i | \(0.0596670\pi\) |
0.186354 | + | 0.982483i | \(0.440333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.2512i | 0.959053i | 0.877527 | + | 0.479526i | \(0.159192\pi\) | ||||
−0.877527 | + | 0.479526i | \(0.840808\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.62396 | + | 4.92443i | 0.388404 | + | 0.221785i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.2979 | −0.641347 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.3182 | − | 16.3182i | −0.730503 | − | 0.730503i | 0.240216 | − | 0.970719i | \(-0.422782\pi\) |
−0.970719 | + | 0.240216i | \(0.922782\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.460191 | + | 0.460191i | 0.0205189 | + | 0.0205189i | 0.717292 | − | 0.696773i | \(-0.245381\pi\) |
−0.696773 | + | 0.717292i | \(0.745381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.45282 | + | 1.45282i | −0.0646498 | + | 0.0646498i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.6793 | −1.13822 | −0.569108 | − | 0.822263i | \(-0.692711\pi\) | ||||
−0.569108 | + | 0.822263i | \(0.692711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.15166 | 0.139421 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.9401 | − | 10.9401i | 0.482080 | − | 0.482080i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.5216 | − | 20.5216i | −0.902538 | − | 0.902538i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.03446 | + | 6.03446i | 0.264374 | + | 0.264374i | 0.826829 | − | 0.562454i | \(-0.190143\pi\) |
−0.562454 | + | 0.826829i | \(0.690143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.7723 | 0.820856 | 0.410428 | − | 0.911893i | \(-0.365379\pi\) | ||||
0.410428 | + | 0.911893i | \(0.365379\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.46779 | − | 5.40627i | −0.412424 | − | 0.235501i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 3.87138i | − | 0.168321i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.1627 | − | 22.1627i | −0.959971 | − | 0.959971i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.4198i | 1.01253i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.12117 | + | 2.12117i | −0.0913655 | + | 0.0913655i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.76691 | − | 9.76691i | 0.419912 | − | 0.419912i | −0.465261 | − | 0.885173i | \(-0.654040\pi\) |
0.885173 | + | 0.465261i | \(0.154040\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.22213 | 0.352197 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.12577 | + | 7.12577i | −0.304676 | + | 0.304676i | −0.842840 | − | 0.538164i | \(-0.819118\pi\) |
0.538164 | + | 0.842840i | \(0.319118\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.78358 | − | 7.78358i | −0.331592 | − | 0.331592i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.3112i | 0.736147i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.0805 | −1.52878 | −0.764389 | − | 0.644756i | \(-0.776959\pi\) | ||||
−0.764389 | + | 0.644756i | \(0.776959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.85650i | − | 0.289999i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.6232i | 0.911309i | 0.890157 | + | 0.455655i | \(0.150595\pi\) | ||||
−0.890157 | + | 0.455655i | \(0.849405\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.710878 | 0.0299069 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.92834i | 0.374296i | 0.982332 | + | 0.187148i | \(0.0599243\pi\) | ||||
−0.982332 | + | 0.187148i | \(0.940076\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7616 | + | 26.7616i | 1.11994 | + | 1.11994i | 0.991750 | + | 0.128188i | \(0.0409160\pi\) |
0.128188 | + | 0.991750i | \(0.459084\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.75758 | − | 5.75758i | 0.240108 | − | 0.240108i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.3336 | 1.34607 | 0.673033 | − | 0.739612i | \(-0.264991\pi\) | ||||
0.673033 | + | 0.739612i | \(0.264991\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.96249 | − | 8.96249i | 0.371827 | − | 0.371827i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.24180 | − | 8.24180i | 0.341341 | − | 0.341341i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0489i | 0.744957i | 0.928041 | + | 0.372478i | \(0.121492\pi\) | ||||
−0.928041 | + | 0.372478i | \(0.878508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.54519 | + | 8.54519i | 0.352098 | + | 0.352098i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.95732i | 0.367833i | 0.982942 | + | 0.183917i | \(0.0588776\pi\) | ||||
−0.982942 | + | 0.183917i | \(0.941122\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.92404 | + | 7.04620i | 0.0788779 | + | 0.288866i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.29732 | 0.0530070 | 0.0265035 | − | 0.999649i | \(-0.491563\pi\) | ||||
0.0265035 | + | 0.999649i | \(0.491563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2262 | − | 22.2262i | −0.906626 | − | 0.906626i | 0.0893720 | − | 0.995998i | \(-0.471514\pi\) |
−0.995998 | + | 0.0893720i | \(0.971514\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.50686 | + | 2.50686i | 0.101918 | + | 0.101918i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.747075 | − | 0.747075i | 0.0303228 | − | 0.0303228i | −0.691783 | − | 0.722106i | \(-0.743174\pi\) |
0.722106 | + | 0.691783i | \(0.243174\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.1460 | 1.01730 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.7088 | −1.03837 | −0.519183 | − | 0.854663i | \(-0.673764\pi\) | ||||
−0.519183 | + | 0.854663i | \(0.673764\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.37161 | − | 5.37161i | 0.216253 | − | 0.216253i | −0.590664 | − | 0.806917i | \(-0.701134\pi\) |
0.806917 | + | 0.590664i | \(0.201134\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.4781 | − | 12.4781i | −0.501538 | − | 0.501538i | 0.410377 | − | 0.911916i | \(-0.365397\pi\) |
−0.911916 | + | 0.410377i | \(0.865397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.45344 | − | 1.45344i | −0.0582307 | − | 0.0582307i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.2254 | 0.489017 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.88668 | − | 1.07732i | −0.0752267 | − | 0.0429557i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20.2378i | − | 0.805653i | −0.915276 | − | 0.402827i | \(-0.868028\pi\) | ||
0.915276 | − | 0.402827i | \(-0.131972\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.438558 | + | 0.438558i | 0.0174036 | + | 0.0174036i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.59917i | − | 0.102983i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.3727 | − | 26.3727i | 1.04166 | − | 1.04166i | 0.0425664 | − | 0.999094i | \(-0.486447\pi\) |
0.999094 | − | 0.0425664i | \(-0.0135534\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.7438 | + | 16.7438i | −0.660310 | + | 0.660310i | −0.955453 | − | 0.295143i | \(-0.904633\pi\) |
0.295143 | + | 0.955453i | \(0.404633\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.2713 | 1.11146 | 0.555730 | − | 0.831363i | \(-0.312439\pi\) | ||||
0.555730 | + | 0.831363i | \(0.312439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.58273 | − | 5.58273i | 0.219141 | − | 0.219141i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.67767 | − | 9.67767i | −0.378716 | − | 0.378716i | 0.491923 | − | 0.870639i | \(-0.336294\pi\) |
−0.870639 | + | 0.491923i | \(0.836294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.9722i | 0.545938i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.7157 | 0.884878 | 0.442439 | − | 0.896799i | \(-0.354113\pi\) | ||||
0.442439 | + | 0.896799i | \(0.354113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.6821i | 1.85462i | 0.374294 | + | 0.927310i | \(0.377885\pi\) | ||||
−0.374294 | + | 0.927310i | \(0.622115\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 8.09612i | − | 0.313954i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.5343 | 0.407890 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 28.0809i | − | 1.08405i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.7768 | + | 33.7768i | 1.30200 | + | 1.30200i | 0.927041 | + | 0.374961i | \(0.122344\pi\) |
0.374961 | + | 0.927041i | \(0.377656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.8811 | + | 16.8811i | −0.648793 | + | 0.648793i | −0.952701 | − | 0.303908i | \(-0.901708\pi\) |
0.303908 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.19765 | 0.276220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.7364 | + | 14.7364i | −0.563871 | + | 0.563871i | −0.930405 | − | 0.366534i | \(-0.880544\pi\) |
0.366534 | + | 0.930405i | \(0.380544\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0774 | − | 12.0774i | 0.461453 | − | 0.461453i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.0990i | 0.384743i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.85086 | + | 7.85086i | 0.298661 | + | 0.298661i | 0.840489 | − | 0.541828i | \(-0.182268\pi\) |
−0.541828 | + | 0.840489i | \(0.682268\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 22.8678i | − | 0.867427i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.6544 | − | 43.1763i | 0.933852 | − | 1.63542i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.3141 | −0.729482 | −0.364741 | − | 0.931109i | \(-0.618842\pi\) | ||||
−0.364741 | + | 0.931109i | \(0.618842\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.70282 | + | 1.70282i | 0.0642233 | + | 0.0642233i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.820100 | + | 0.820100i | 0.0308431 | + | 0.0308431i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.84764 | − | 4.84764i | 0.182057 | − | 0.182057i | −0.610195 | − | 0.792252i | \(-0.708909\pi\) |
0.792252 | + | 0.610195i | \(0.208909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −11.5651 | −0.433115 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.8125 | 0.516557 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.4094 | + | 11.4094i | −0.425499 | + | 0.425499i | −0.887092 | − | 0.461593i | \(-0.847278\pi\) |
0.461593 | + | 0.887092i | \(0.347278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.17557 | − | 6.17557i | −0.229990 | − | 0.229990i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.17075 | − | 3.17075i | −0.117759 | − | 0.117759i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.8301 | −0.401665 | −0.200832 | − | 0.979626i | \(-0.564365\pi\) | ||||
−0.200832 | + | 0.979626i | \(0.564365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.4925 | − | 2.86508i | 0.388077 | − | 0.105969i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 27.4997i | − | 1.01573i | −0.861438 | − | 0.507863i | \(-0.830436\pi\) | ||
0.861438 | − | 0.507863i | \(-0.169564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.6161 | − | 31.6161i | −1.16459 | − | 1.16459i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.42719i | 0.236428i | 0.992988 | + | 0.118214i | \(0.0377169\pi\) | ||||
−0.992988 | + | 0.118214i | \(0.962283\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.6633 | + | 19.6633i | −0.721377 | + | 0.721377i | −0.968886 | − | 0.247509i | \(-0.920388\pi\) |
0.247509 | + | 0.968886i | \(0.420388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.94084 | + | 4.94084i | −0.181018 | + | 0.181018i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.2202 | 0.483055 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6745 | + | 12.6745i | −0.462498 | + | 0.462498i | −0.899473 | − | 0.436975i | \(-0.856050\pi\) |
0.436975 | + | 0.899473i | \(0.356050\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −29.9215 | − | 29.9215i | −1.08895 | − | 1.08895i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.96117i | 0.362045i | 0.983479 | + | 0.181023i | \(0.0579407\pi\) | ||||
−0.983479 | + | 0.181023i | \(0.942059\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.279750 | 0.0101409 | 0.00507046 | − | 0.999987i | \(-0.498386\pi\) | ||||
0.00507046 | + | 0.999987i | \(0.498386\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 4.64129i | − | 0.168026i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.84076i | 0.247005i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.8011 | 0.677986 | 0.338993 | − | 0.940789i | \(-0.389914\pi\) | ||||
0.338993 | + | 0.940789i | \(0.389914\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 14.9445i | − | 0.537518i | −0.963207 | − | 0.268759i | \(-0.913387\pi\) | ||
0.963207 | − | 0.268759i | \(-0.0866135\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.48100 | + | 3.48100i | 0.125041 | + | 0.125041i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −38.9689 | + | 38.9689i | −1.39621 | + | 1.39621i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.8906 | −1.53475 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.1361 | − | 23.1361i | 0.825763 | − | 0.825763i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.3686 | − | 37.3686i | 1.33205 | − | 1.33205i | 0.428511 | − | 0.903536i | \(-0.359038\pi\) |
0.903536 | − | 0.428511i | \(-0.140962\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 0.401281i | − | 0.0142679i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.2044 | + | 17.2044i | 0.610946 | + | 0.610946i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.3791i | 0.757286i | 0.925543 | + | 0.378643i | \(0.123609\pi\) | ||||
−0.925543 | + | 0.378643i | \(0.876391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.5076 | + | 38.4807i | 0.371731 | + | 1.36135i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.45434 | 0.333636 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.47864 | + | 5.47864i | 0.193097 | + | 0.193097i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.85381 | − | 4.85381i | −0.170651 | − | 0.170651i | 0.616614 | − | 0.787265i | \(-0.288504\pi\) |
−0.787265 | + | 0.616614i | \(0.788504\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1746 | − | 22.1746i | 0.778655 | − | 0.778655i | −0.200947 | − | 0.979602i | \(-0.564402\pi\) |
0.979602 | + | 0.200947i | \(0.0644020\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.5953 | 1.14176 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0559 | −0.421782 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.3362 | − | 18.3362i | 0.639936 | − | 0.639936i | −0.310603 | − | 0.950540i | \(-0.600531\pi\) |
0.950540 | + | 0.310603i | \(0.100531\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.9188 | + | 26.9188i | 0.938330 | + | 0.938330i | 0.998206 | − | 0.0598760i | \(-0.0190705\pi\) |
−0.0598760 | + | 0.998206i | \(0.519071\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.6471 | + | 18.6471i | 0.648424 | + | 0.648424i | 0.952612 | − | 0.304188i | \(-0.0983850\pi\) |
−0.304188 | + | 0.952612i | \(0.598385\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.7846 | −0.409298 | −0.204649 | − | 0.978835i | \(-0.565605\pi\) | ||||
−0.204649 | + | 0.978835i | \(0.565605\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.97749 | − | 1.08609i | 0.137812 | − | 0.0376310i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 42.2114i | − | 1.46079i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.1798 | − | 30.1798i | −1.04192 | − | 1.04192i | −0.999082 | − | 0.0428405i | \(-0.986359\pi\) |
−0.0428405 | − | 0.999082i | \(-0.513641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.1987i | 0.799954i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.82199 | − | 7.82199i | 0.269085 | − | 0.269085i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.41509 | − | 1.41509i | 0.0486230 | − | 0.0486230i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.30460 | −0.0790008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.02358 | + | 7.02358i | −0.240483 | + | 0.240483i | −0.817050 | − | 0.576567i | \(-0.804392\pi\) |
0.576567 | + | 0.817050i | \(0.304392\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.6172 | − | 20.6172i | −0.704271 | − | 0.704271i | 0.261053 | − | 0.965324i | \(-0.415930\pi\) |
−0.965324 | + | 0.261053i | \(0.915930\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.5644i | − | 0.872246i | −0.899887 | − | 0.436123i | \(-0.856351\pi\) | ||
0.899887 | − | 0.436123i | \(-0.143649\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.40501 | 0.149948 | 0.0749741 | − | 0.997185i | \(-0.476113\pi\) | ||||
0.0749741 | + | 0.997185i | \(0.476113\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 11.1048i | − | 0.377576i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 51.9300i | 1.76161i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.7406 | 1.31267 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 12.1557i | − | 0.410937i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.0662 | + | 18.0662i | 0.610052 | + | 0.610052i | 0.942959 | − | 0.332908i | \(-0.108030\pi\) |
−0.332908 | + | 0.942959i | \(0.608030\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.7536 | − | 27.7536i | 0.935041 | − | 0.935041i | −0.0629740 | − | 0.998015i | \(-0.520059\pi\) |
0.998015 | + | 0.0629740i | \(0.0200585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.1225 | 1.11466 | 0.557330 | − | 0.830291i | \(-0.311826\pi\) | ||||
0.557330 | + | 0.830291i | \(0.311826\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.1858 | − | 19.1858i | 0.644195 | − | 0.644195i | −0.307389 | − | 0.951584i | \(-0.599455\pi\) |
0.951584 | + | 0.307389i | \(0.0994552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.247560 | − | 0.247560i | 0.00830291 | − | 0.00830291i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 44.2145i | − | 1.47958i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.1257 | + | 16.1257i | 0.539023 | + | 0.539023i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.36898i | 0.212417i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.4545 | + | 4.22001i | −0.514864 | + | 0.140589i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.8873 | 1.25942 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.7896 | + | 39.7896i | 1.32119 | + | 1.32119i | 0.912812 | + | 0.408380i | \(0.133906\pi\) |
0.408380 | + | 0.912812i | \(0.366094\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.0658 | − | 32.0658i | −1.06239 | − | 1.06239i | −0.997920 | − | 0.0644668i | \(-0.979465\pi\) |
−0.0644668 | − | 0.997920i | \(-0.520535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.8856 | − | 26.8856i | 0.889784 | − | 0.889784i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.88711 | 0.260455 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.5827 | −1.00883 | −0.504415 | − | 0.863461i | \(-0.668292\pi\) | ||||
−0.504415 | + | 0.863461i | \(0.668292\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 26.2779 | − | 26.2779i | 0.864946 | − | 0.864946i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.693670 | + | 0.693670i | 0.0228077 | + | 0.0228077i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.4123 | − | 19.4123i | −0.636896 | − | 0.636896i | 0.312892 | − | 0.949789i | \(-0.398702\pi\) |
−0.949789 | + | 0.312892i | \(0.898702\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.57015 | −0.149781 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.77172 | + | 21.1371i | 0.188755 | + | 0.691258i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.3154i | 0.598337i | 0.954200 | + | 0.299169i | \(0.0967093\pi\) | ||||
−0.954200 | + | 0.299169i | \(0.903291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.8095 | + | 21.8095i | 0.710969 | + | 0.710969i | 0.966738 | − | 0.255769i | \(-0.0823287\pi\) |
−0.255769 | + | 0.966738i | \(0.582329\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 52.7405i | − | 1.71747i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.1276 | − | 11.1276i | 0.361599 | − | 0.361599i | −0.502802 | − | 0.864402i | \(-0.667698\pi\) |
0.864402 | + | 0.502802i | \(0.167698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.79241 | + | 5.79241i | −0.188029 | + | 0.188029i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51.5074 | 1.66849 | 0.834244 | − | 0.551395i | \(-0.185904\pi\) | ||||
0.834244 | + | 0.551395i | \(0.185904\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.9463 | + | 21.9463i | −0.710165 | + | 0.710165i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.81753 | − | 6.81753i | −0.220149 | − | 0.220149i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.0078i | 0.774446i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.13434 | −0.294045 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.6915i | 0.697552i | 0.937206 | + | 0.348776i | \(0.113403\pi\) | ||||
−0.937206 | + | 0.348776i | \(0.886597\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 14.7980i | − | 0.474889i | −0.971401 | − | 0.237444i | \(-0.923690\pi\) | ||
0.971401 | − | 0.237444i | \(-0.0763098\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.9086 | −0.413831 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.5724i | 0.754147i | 0.926183 | + | 0.377074i | \(0.123070\pi\) | ||||
−0.926183 | + | 0.377074i | \(0.876930\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.36001 | − | 4.36001i | −0.139347 | − | 0.139347i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −14.1621 | + | 14.1621i | −0.451702 | + | 0.451702i | −0.895919 | − | 0.444217i | \(-0.853482\pi\) |
0.444217 | + | 0.895919i | \(0.353482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.2384 | −0.517397 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.15822 | − | 8.15822i | 0.259416 | − | 0.259416i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.9668 | − | 10.9668i | 0.348372 | − | 0.348372i | −0.511131 | − | 0.859503i | \(-0.670773\pi\) |
0.859503 | + | 0.511131i | \(0.170773\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.6224i | 0.653774i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.4332 | + | 19.4332i | 0.615457 | + | 0.615457i | 0.944363 | − | 0.328906i | \(-0.106680\pi\) |
−0.328906 | + | 0.944363i | \(0.606680\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 4284.2.z.b.4033.4 | 16 | ||
3.2 | odd | 2 | 476.2.l.a.225.8 | ✓ | 16 | ||
17.13 | even | 4 | inner | 4284.2.z.b.3277.4 | 16 | ||
51.8 | odd | 8 | 8092.2.a.s.1.1 | 8 | |||
51.26 | odd | 8 | 8092.2.a.t.1.8 | 8 | |||
51.47 | odd | 4 | 476.2.l.a.421.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
476.2.l.a.225.8 | ✓ | 16 | 3.2 | odd | 2 | ||
476.2.l.a.421.8 | yes | 16 | 51.47 | odd | 4 | ||
4284.2.z.b.3277.4 | 16 | 17.13 | even | 4 | inner | ||
4284.2.z.b.4033.4 | 16 | 1.1 | even | 1 | trivial | ||
8092.2.a.s.1.1 | 8 | 51.8 | odd | 8 | |||
8092.2.a.t.1.8 | 8 | 51.26 | odd | 8 |