Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3330,2,Mod(1999,3330)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3330, 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("3330.1999");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3330.d (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: | \(26.5901838731\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 51x^{6} - 124x^{5} + 154x^{4} - 46x^{3} + x^{2} + 4x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1999.7 | ||
Root | \(-1.95884 + 1.95884i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3330.1999 |
Dual form | 3330.2.d.p.1999.2 |
$q$-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 \(\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.74265 | − | 1.40113i | −0.779337 | − | 0.626605i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.20984i | 1.21320i | 0.795006 | + | 0.606602i | \(0.207468\pi\) | ||||
−0.795006 | + | 0.606602i | \(0.792532\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.40113 | − | 1.74265i | 0.443076 | − | 0.551075i | ||||
\(11\) | −3.82327 | −1.15276 | −0.576380 | − | 0.817182i | \(-0.695535\pi\) | ||||
−0.576380 | + | 0.817182i | \(0.695535\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.147332i | 0.0408626i | 0.999791 | + | 0.0204313i | \(0.00650394\pi\) | ||||
−0.999791 | + | 0.0204313i | \(0.993496\pi\) | |||||||
\(14\) | −3.20984 | −0.857865 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.978989i | 0.237440i | 0.992928 | + | 0.118720i | \(0.0378790\pi\) | ||||
−0.992928 | + | 0.118720i | \(0.962121\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.67594 | −0.613903 | −0.306951 | − | 0.951725i | \(-0.599309\pi\) | ||||
−0.306951 | + | 0.951725i | \(0.599309\pi\) | |||||||
\(20\) | 1.74265 | + | 1.40113i | 0.389669 | + | 0.313302i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 3.82327i | − | 0.815124i | ||||||
\(23\) | 2.33616i | 0.487122i | 0.969886 | + | 0.243561i | \(0.0783157\pi\) | ||||
−0.969886 | + | 0.243561i | \(0.921684\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.07367 | + | 4.88336i | 0.214733 | + | 0.976673i | ||||
\(26\) | −0.147332 | −0.0288942 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 3.20984i | − | 0.606602i | ||||||
\(29\) | 6.30425 | 1.17067 | 0.585335 | − | 0.810792i | \(-0.300963\pi\) | ||||
0.585335 | + | 0.810792i | \(0.300963\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.62372 | −0.650839 | −0.325420 | − | 0.945570i | \(-0.605506\pi\) | ||||
−0.325420 | + | 0.945570i | \(0.605506\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.978989 | −0.167895 | ||||||||
\(35\) | 4.49740 | − | 5.59362i | 0.760199 | − | 0.945495i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.00000i | − | 0.164399i | ||||||
\(38\) | − | 2.67594i | − | 0.434095i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.40113 | + | 1.74265i | −0.221538 | + | 0.275537i | ||||
\(41\) | −11.8265 | −1.84698 | −0.923491 | − | 0.383620i | \(-0.874677\pi\) | ||||
−0.923491 | + | 0.383620i | \(0.874677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.53390i | − | 0.691413i | −0.938343 | − | 0.345706i | \(-0.887639\pi\) | ||
0.938343 | − | 0.345706i | \(-0.112361\pi\) | |||||||
\(44\) | 3.82327 | 0.576380 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.33616 | −0.344448 | ||||||||
\(47\) | 6.23085i | 0.908863i | 0.890782 | + | 0.454431i | \(0.150157\pi\) | ||||
−0.890782 | + | 0.454431i | \(0.849843\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.30305 | −0.471864 | ||||||||
\(50\) | −4.88336 | + | 1.07367i | −0.690612 | + | 0.151839i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 0.147332i | − | 0.0204313i | ||||||
\(53\) | − | 11.2978i | − | 1.55188i | −0.630807 | − | 0.775939i | \(-0.717276\pi\) | ||
0.630807 | − | 0.775939i | \(-0.282724\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.66263 | + | 5.35690i | 0.898389 | + | 0.722325i | ||||
\(56\) | 3.20984 | 0.428932 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.30425i | 0.827788i | ||||||||
\(59\) | 6.92858 | 0.902025 | 0.451012 | − | 0.892518i | \(-0.351063\pi\) | ||||
0.451012 | + | 0.892518i | \(0.351063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4885 | 1.34291 | 0.671457 | − | 0.741044i | \(-0.265669\pi\) | ||||
0.671457 | + | 0.741044i | \(0.265669\pi\) | |||||||
\(62\) | − | 3.62372i | − | 0.460213i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.206432 | − | 0.256749i | 0.0256047 | − | 0.0318458i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.80936i | − | 0.343218i | −0.985165 | − | 0.171609i | \(-0.945103\pi\) | ||
0.985165 | − | 0.171609i | \(-0.0548966\pi\) | |||||||
\(68\) | − | 0.978989i | − | 0.118720i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.59362 | + | 4.49740i | 0.668566 | + | 0.537542i | ||||
\(71\) | 12.3189 | 1.46198 | 0.730990 | − | 0.682388i | \(-0.239059\pi\) | ||||
0.730990 | + | 0.682388i | \(0.239059\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.9966i | − | 1.63818i | −0.573665 | − | 0.819090i | \(-0.694479\pi\) | ||
0.573665 | − | 0.819090i | \(-0.305521\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.67594 | 0.306951 | ||||||||
\(77\) | − | 12.2721i | − | 1.39853i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.6057 | −1.75578 | −0.877890 | − | 0.478861i | \(-0.841050\pi\) | ||||
−0.877890 | + | 0.478861i | \(0.841050\pi\) | |||||||
\(80\) | −1.74265 | − | 1.40113i | −0.194834 | − | 0.156651i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 11.8265i | − | 1.30601i | ||||||
\(83\) | − | 13.5371i | − | 1.48589i | −0.669354 | − | 0.742944i | \(-0.733429\pi\) | ||
0.669354 | − | 0.742944i | \(-0.266571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.37169 | − | 1.70604i | 0.148781 | − | 0.185046i | ||||
\(86\) | 4.53390 | 0.488903 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.82327i | 0.407562i | ||||||||
\(89\) | −6.46929 | −0.685743 | −0.342872 | − | 0.939382i | \(-0.611400\pi\) | ||||
−0.342872 | + | 0.939382i | \(0.611400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.472913 | −0.0495747 | ||||||||
\(92\) | − | 2.33616i | − | 0.243561i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.23085 | −0.642663 | ||||||||
\(95\) | 4.66323 | + | 3.74934i | 0.478437 | + | 0.384674i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.07063i | 0.311775i | 0.987775 | + | 0.155887i | \(0.0498237\pi\) | ||||
−0.987775 | + | 0.155887i | \(0.950176\pi\) | |||||||
\(98\) | − | 3.30305i | − | 0.333658i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.07367 | − | 4.88336i | −0.107367 | − | 0.488336i | ||||
\(101\) | 6.57513 | 0.654250 | 0.327125 | − | 0.944981i | \(-0.393920\pi\) | ||||
0.327125 | + | 0.944981i | \(0.393920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.52180i | − | 0.248480i | −0.992252 | − | 0.124240i | \(-0.960351\pi\) | ||
0.992252 | − | 0.124240i | \(-0.0396493\pi\) | |||||||
\(104\) | 0.147332 | 0.0144471 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2978 | 1.09734 | ||||||||
\(107\) | 5.70291i | 0.551321i | 0.961255 | + | 0.275661i | \(0.0888966\pi\) | ||||
−0.961255 | + | 0.275661i | \(0.911103\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.9318 | −1.14286 | −0.571428 | − | 0.820652i | \(-0.693610\pi\) | ||||
−0.571428 | + | 0.820652i | \(0.693610\pi\) | |||||||
\(110\) | −5.35690 | + | 6.66263i | −0.510761 | + | 0.635257i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.20984i | 0.303301i | ||||||||
\(113\) | 2.18044i | 0.205119i | 0.994727 | + | 0.102559i | \(0.0327031\pi\) | ||||
−0.994727 | + | 0.102559i | \(0.967297\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.27326 | − | 4.07111i | 0.305233 | − | 0.379633i | ||||
\(116\) | −6.30425 | −0.585335 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.92858i | 0.637828i | ||||||||
\(119\) | −3.14239 | −0.288063 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.61741 | 0.328856 | ||||||||
\(122\) | 10.4885i | 0.949583i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.62372 | 0.325420 | ||||||||
\(125\) | 4.97120 | − | 10.0143i | 0.444638 | − | 0.895710i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.39390i | 0.478631i | 0.970942 | + | 0.239316i | \(0.0769231\pi\) | ||||
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.256749 | + | 0.206432i | 0.0225184 | + | 0.0181053i | ||||
\(131\) | 8.97060 | 0.783765 | 0.391883 | − | 0.920015i | \(-0.371824\pi\) | ||||
0.391883 | + | 0.920015i | \(0.371824\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 8.58933i | − | 0.744789i | ||||||
\(134\) | 2.80936 | 0.242692 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.978989 | 0.0839476 | ||||||||
\(137\) | − | 2.70352i | − | 0.230978i | −0.993309 | − | 0.115489i | \(-0.963157\pi\) | ||
0.993309 | − | 0.115489i | \(-0.0368434\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.30358 | −0.365025 | −0.182512 | − | 0.983204i | \(-0.558423\pi\) | ||||
−0.182512 | + | 0.983204i | \(0.558423\pi\) | |||||||
\(140\) | −4.49740 | + | 5.59362i | −0.380100 | + | 0.472748i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.3189i | 1.03378i | ||||||||
\(143\) | − | 0.563292i | − | 0.0471048i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.9861 | − | 8.83308i | −0.912346 | − | 0.733547i | ||||
\(146\) | 13.9966 | 1.15837 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.00000i | 0.0821995i | ||||||||
\(149\) | 21.6949 | 1.77732 | 0.888659 | − | 0.458568i | \(-0.151638\pi\) | ||||
0.888659 | + | 0.458568i | \(0.151638\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.06744 | 0.168246 | 0.0841230 | − | 0.996455i | \(-0.473191\pi\) | ||||
0.0841230 | + | 0.996455i | \(0.473191\pi\) | |||||||
\(152\) | 2.67594i | 0.217047i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.2721 | 0.988912 | ||||||||
\(155\) | 6.31488 | + | 5.07731i | 0.507223 | + | 0.407819i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 18.5439i | − | 1.47996i | −0.672627 | − | 0.739982i | \(-0.734834\pi\) | ||
0.672627 | − | 0.739982i | \(-0.265166\pi\) | |||||||
\(158\) | − | 15.6057i | − | 1.24152i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.40113 | − | 1.74265i | 0.110769 | − | 0.137769i | ||||
\(161\) | −7.49868 | −0.590979 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 21.6240i | − | 1.69372i | −0.531817 | − | 0.846860i | \(-0.678490\pi\) | ||
0.531817 | − | 0.846860i | \(-0.321510\pi\) | |||||||
\(164\) | 11.8265 | 0.923491 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.5371 | 1.05068 | ||||||||
\(167\) | − | 11.7729i | − | 0.911012i | −0.890233 | − | 0.455506i | \(-0.849458\pi\) | ||
0.890233 | − | 0.455506i | \(-0.150542\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9783 | 0.998330 | ||||||||
\(170\) | 1.70604 | + | 1.37169i | 0.130847 | + | 0.105204i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.53390i | 0.345706i | ||||||||
\(173\) | − | 14.0158i | − | 1.06560i | −0.846240 | − | 0.532801i | \(-0.821139\pi\) | ||
0.846240 | − | 0.532801i | \(-0.178861\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.6748 | + | 3.44629i | −1.18490 | + | 0.260515i | ||||
\(176\) | −3.82327 | −0.288190 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 6.46929i | − | 0.484894i | ||||||
\(179\) | −12.4160 | −0.928019 | −0.464009 | − | 0.885830i | \(-0.653590\pi\) | ||||
−0.464009 | + | 0.885830i | \(0.653590\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.19748 | 0.609314 | 0.304657 | − | 0.952462i | \(-0.401458\pi\) | ||||
0.304657 | + | 0.952462i | \(0.401458\pi\) | |||||||
\(182\) | − | 0.472913i | − | 0.0350546i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.33616 | 0.172224 | ||||||||
\(185\) | −1.40113 | + | 1.74265i | −0.103013 | + | 0.128122i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.74294i | − | 0.273711i | ||||||
\(188\) | − | 6.23085i | − | 0.454431i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.74934 | + | 4.66323i | −0.272006 | + | 0.338306i | ||||
\(191\) | −8.00137 | −0.578959 | −0.289479 | − | 0.957184i | \(-0.593482\pi\) | ||||
−0.289479 | + | 0.957184i | \(0.593482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 14.0420i | − | 1.01077i | −0.862895 | − | 0.505383i | \(-0.831351\pi\) | ||
0.862895 | − | 0.505383i | \(-0.168649\pi\) | |||||||
\(194\) | −3.07063 | −0.220458 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.30305 | 0.235932 | ||||||||
\(197\) | 3.36608i | 0.239823i | 0.992785 | + | 0.119912i | \(0.0382612\pi\) | ||||
−0.992785 | + | 0.119912i | \(0.961739\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8890 | 1.05545 | 0.527725 | − | 0.849415i | \(-0.323045\pi\) | ||||
0.527725 | + | 0.849415i | \(0.323045\pi\) | |||||||
\(200\) | 4.88336 | − | 1.07367i | 0.345306 | − | 0.0759197i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.57513i | 0.462624i | ||||||||
\(203\) | 20.2356i | 1.42026i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.6094 | + | 16.5704i | 1.43942 | + | 1.15733i | ||||
\(206\) | 2.52180 | 0.175702 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.147332i | 0.0102157i | ||||||||
\(209\) | 10.2308 | 0.707683 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.80544 | −0.675035 | −0.337517 | − | 0.941319i | \(-0.609587\pi\) | ||||
−0.337517 | + | 0.941319i | \(0.609587\pi\) | |||||||
\(212\) | 11.2978i | 0.775939i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.70291 | −0.389843 | ||||||||
\(215\) | −6.35258 | + | 7.90100i | −0.433242 | + | 0.538844i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 11.6316i | − | 0.789601i | ||||||
\(218\) | − | 11.9318i | − | 0.808121i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.66263 | − | 5.35690i | −0.449194 | − | 0.361162i | ||||
\(221\) | −0.144237 | −0.00970241 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.4447i | − | 1.03425i | −0.855910 | − | 0.517125i | \(-0.827002\pi\) | ||
0.855910 | − | 0.517125i | \(-0.172998\pi\) | |||||||
\(224\) | −3.20984 | −0.214466 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.18044 | −0.145041 | ||||||||
\(227\) | 6.46090i | 0.428825i | 0.976743 | + | 0.214413i | \(0.0687837\pi\) | ||||
−0.976743 | + | 0.214413i | \(0.931216\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.97458 | −0.526975 | −0.263488 | − | 0.964663i | \(-0.584873\pi\) | ||||
−0.263488 | + | 0.964663i | \(0.584873\pi\) | |||||||
\(230\) | 4.07111 | + | 3.27326i | 0.268441 | + | 0.215832i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.30425i | − | 0.413894i | ||||||
\(233\) | − | 25.2907i | − | 1.65685i | −0.560103 | − | 0.828423i | \(-0.689238\pi\) | ||
0.560103 | − | 0.828423i | \(-0.310762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.73023 | − | 10.8582i | 0.569497 | − | 0.708310i | ||||
\(236\) | −6.92858 | −0.451012 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 3.14239i | − | 0.203691i | ||||||
\(239\) | 5.11481 | 0.330850 | 0.165425 | − | 0.986222i | \(-0.447100\pi\) | ||||
0.165425 | + | 0.986222i | \(0.447100\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.4415 | 1.05909 | 0.529544 | − | 0.848282i | \(-0.322363\pi\) | ||||
0.529544 | + | 0.848282i | \(0.322363\pi\) | |||||||
\(242\) | 3.61741i | 0.232536i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.4885 | −0.671457 | ||||||||
\(245\) | 5.75606 | + | 4.62800i | 0.367741 | + | 0.295672i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.394252i | − | 0.0250857i | ||||||
\(248\) | 3.62372i | 0.230107i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.0143 | + | 4.97120i | 0.633363 | + | 0.314407i | ||||
\(251\) | −6.35586 | −0.401178 | −0.200589 | − | 0.979675i | \(-0.564286\pi\) | ||||
−0.200589 | + | 0.979675i | \(0.564286\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.93177i | − | 0.561535i | ||||||
\(254\) | −5.39390 | −0.338444 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 5.45772i | − | 0.340443i | −0.985406 | − | 0.170222i | \(-0.945552\pi\) | ||
0.985406 | − | 0.170222i | \(-0.0544484\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.20984 | 0.199450 | ||||||||
\(260\) | −0.206432 | + | 0.256749i | −0.0128024 | + | 0.0159229i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.97060i | 0.554206i | ||||||||
\(263\) | 14.8882i | 0.918044i | 0.888425 | + | 0.459022i | \(0.151800\pi\) | ||||
−0.888425 | + | 0.459022i | \(0.848200\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.8298 | + | 19.6882i | −0.972414 | + | 1.20944i | ||||
\(266\) | 8.58933 | 0.526646 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.80936i | 0.171609i | ||||||||
\(269\) | 15.5573 | 0.948546 | 0.474273 | − | 0.880378i | \(-0.342711\pi\) | ||||
0.474273 | + | 0.880378i | \(0.342711\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.462920 | 0.0281204 | 0.0140602 | − | 0.999901i | \(-0.495524\pi\) | ||||
0.0140602 | + | 0.999901i | \(0.495524\pi\) | |||||||
\(272\) | 0.978989i | 0.0593599i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.70352 | 0.163326 | ||||||||
\(275\) | −4.10492 | − | 18.6704i | −0.247536 | − | 1.12587i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.12112i | − | 0.548035i | −0.961725 | − | 0.274018i | \(-0.911647\pi\) | ||
0.961725 | − | 0.274018i | \(-0.0883526\pi\) | |||||||
\(278\) | − | 4.30358i | − | 0.258111i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.59362 | − | 4.49740i | −0.334283 | − | 0.268771i | ||||
\(281\) | 24.8734 | 1.48382 | 0.741912 | − | 0.670497i | \(-0.233919\pi\) | ||||
0.741912 | + | 0.670497i | \(0.233919\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.7259i | 1.17258i | 0.810100 | + | 0.586292i | \(0.199413\pi\) | ||||
−0.810100 | + | 0.586292i | \(0.800587\pi\) | |||||||
\(284\) | −12.3189 | −0.730990 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.563292 | 0.0333081 | ||||||||
\(287\) | − | 37.9610i | − | 2.24077i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0416 | 0.943622 | ||||||||
\(290\) | 8.83308 | − | 10.9861i | 0.518696 | − | 0.645126i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.9966i | 0.819090i | ||||||||
\(293\) | 2.65528i | 0.155123i | 0.996988 | + | 0.0775615i | \(0.0247134\pi\) | ||||
−0.996988 | + | 0.0775615i | \(0.975287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.0741 | − | 9.70785i | −0.702981 | − | 0.565213i | ||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.6949i | 1.25675i | ||||||||
\(299\) | −0.344191 | −0.0199051 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.5531 | 0.838825 | ||||||||
\(302\) | 2.06744i | 0.118968i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.67594 | −0.153476 | ||||||||
\(305\) | −18.2778 | − | 14.6957i | −1.04658 | − | 0.841476i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.3545i | 1.44706i | 0.690295 | + | 0.723528i | \(0.257481\pi\) | ||||
−0.690295 | + | 0.723528i | \(0.742519\pi\) | |||||||
\(308\) | 12.2721i | 0.699267i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.07731 | + | 6.31488i | −0.288372 | + | 0.358661i | ||||
\(311\) | −11.1234 | −0.630748 | −0.315374 | − | 0.948967i | \(-0.602130\pi\) | ||||
−0.315374 | + | 0.948967i | \(0.602130\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.49109i | 0.197328i | 0.995121 | + | 0.0986640i | \(0.0314569\pi\) | ||||
−0.995121 | + | 0.0986640i | \(0.968543\pi\) | |||||||
\(314\) | 18.5439 | 1.04649 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.6057 | 0.877890 | ||||||||
\(317\) | 18.3656i | 1.03152i | 0.856734 | + | 0.515759i | \(0.172490\pi\) | ||||
−0.856734 | + | 0.515759i | \(0.827510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.1029 | −1.34950 | ||||||||
\(320\) | 1.74265 | + | 1.40113i | 0.0974172 | + | 0.0783256i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 7.49868i | − | 0.417885i | ||||||
\(323\) | − | 2.61972i | − | 0.145765i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.719477 | + | 0.158186i | −0.0399094 | + | 0.00877457i | ||||
\(326\) | 21.6240 | 1.19764 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.8265i | 0.653007i | ||||||||
\(329\) | −20.0000 | −1.10264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21.9365 | −1.20574 | −0.602870 | − | 0.797839i | \(-0.705976\pi\) | ||||
−0.602870 | + | 0.797839i | \(0.705976\pi\) | |||||||
\(332\) | 13.5371i | 0.742944i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.7729 | 0.644183 | ||||||||
\(335\) | −3.93628 | + | 4.89574i | −0.215062 | + | 0.267483i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.65472i | 0.471453i | 0.971819 | + | 0.235726i | \(0.0757469\pi\) | ||||
−0.971819 | + | 0.235726i | \(0.924253\pi\) | |||||||
\(338\) | 12.9783i | 0.705926i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.37169 | + | 1.70604i | −0.0743904 | + | 0.0925228i | ||||
\(341\) | 13.8545 | 0.750262 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.8666i | 0.640737i | ||||||||
\(344\) | −4.53390 | −0.244451 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0158 | 0.753495 | ||||||||
\(347\) | − | 21.3265i | − | 1.14486i | −0.819952 | − | 0.572432i | \(-0.806000\pi\) | ||
0.819952 | − | 0.572432i | \(-0.194000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.16305 | 0.0622569 | 0.0311285 | − | 0.999515i | \(-0.490090\pi\) | ||||
0.0311285 | + | 0.999515i | \(0.490090\pi\) | |||||||
\(350\) | −3.44629 | − | 15.6748i | −0.184212 | − | 0.837853i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 3.82327i | − | 0.203781i | ||||||
\(353\) | 0.470079i | 0.0250198i | 0.999922 | + | 0.0125099i | \(0.00398213\pi\) | ||||
−0.999922 | + | 0.0125099i | \(0.996018\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.4675 | − | 17.2603i | −1.13938 | − | 0.916083i | ||||
\(356\) | 6.46929 | 0.342872 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 12.4160i | − | 0.656208i | ||||||
\(359\) | −33.3086 | −1.75796 | −0.878981 | − | 0.476856i | \(-0.841776\pi\) | ||||
−0.878981 | + | 0.476856i | \(0.841776\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.8393 | −0.623123 | ||||||||
\(362\) | 8.19748i | 0.430850i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.472913 | 0.0247874 | ||||||||
\(365\) | −19.6111 | + | 24.3912i | −1.02649 | + | 1.27669i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1884i | 0.584029i | 0.956414 | + | 0.292014i | \(0.0943255\pi\) | ||||
−0.956414 | + | 0.292014i | \(0.905674\pi\) | |||||||
\(368\) | 2.33616i | 0.121781i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.74265 | − | 1.40113i | −0.0905961 | − | 0.0728413i | ||||
\(371\) | 36.2642 | 1.88275 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.1634i | 1.19936i | 0.800242 | + | 0.599678i | \(0.204705\pi\) | ||||
−0.800242 | + | 0.599678i | \(0.795295\pi\) | |||||||
\(374\) | 3.74294 | 0.193543 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.23085 | 0.321331 | ||||||||
\(377\) | 0.928820i | 0.0478366i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.7721 | 1.37519 | 0.687595 | − | 0.726095i | \(-0.258667\pi\) | ||||
0.687595 | + | 0.726095i | \(0.258667\pi\) | |||||||
\(380\) | −4.66323 | − | 3.74934i | −0.239219 | − | 0.192337i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 8.00137i | − | 0.409386i | ||||||
\(383\) | − | 22.3189i | − | 1.14044i | −0.821492 | − | 0.570220i | \(-0.806858\pi\) | ||
0.821492 | − | 0.570220i | \(-0.193142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.1948 | + | 21.3860i | −0.876327 | + | 1.08993i | ||||
\(386\) | 14.0420 | 0.714720 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 3.07063i | − | 0.155887i | ||||||
\(389\) | −24.3011 | −1.23211 | −0.616057 | − | 0.787701i | \(-0.711271\pi\) | ||||
−0.616057 | + | 0.787701i | \(0.711271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.28707 | −0.115662 | ||||||||
\(392\) | 3.30305i | 0.166829i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.36608 | −0.169581 | ||||||||
\(395\) | 27.1953 | + | 21.8657i | 1.36835 | + | 1.10018i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 28.1888i | − | 1.41476i | −0.706835 | − | 0.707378i | \(-0.749878\pi\) | ||
0.706835 | − | 0.707378i | \(-0.250122\pi\) | |||||||
\(398\) | 14.8890i | 0.746316i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.07367 | + | 4.88336i | 0.0536833 | + | 0.244168i | ||||
\(401\) | 15.9528 | 0.796644 | 0.398322 | − | 0.917246i | \(-0.369593\pi\) | ||||
0.398322 | + | 0.917246i | \(0.369593\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 0.533891i | − | 0.0265950i | ||||||
\(404\) | −6.57513 | −0.327125 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.2356 | −1.00428 | ||||||||
\(407\) | 3.82327i | 0.189513i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.6014 | −1.56259 | −0.781294 | − | 0.624164i | \(-0.785440\pi\) | ||||
−0.781294 | + | 0.624164i | \(0.785440\pi\) | |||||||
\(410\) | −16.5704 | + | 20.6094i | −0.818354 | + | 1.01783i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.52180i | 0.124240i | ||||||||
\(413\) | 22.2396i | 1.09434i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.9672 | + | 23.5904i | −0.931064 | + | 1.15801i | ||||
\(416\) | −0.147332 | −0.00722356 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.2308i | 0.500407i | ||||||||
\(419\) | −18.4266 | −0.900197 | −0.450098 | − | 0.892979i | \(-0.648611\pi\) | ||||
−0.450098 | + | 0.892979i | \(0.648611\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.1570 | −0.933655 | −0.466828 | − | 0.884348i | \(-0.654603\pi\) | ||||
−0.466828 | + | 0.884348i | \(0.654603\pi\) | |||||||
\(422\) | − | 9.80544i | − | 0.477322i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.2978 | −0.548672 | ||||||||
\(425\) | −4.78076 | + | 1.05111i | −0.231901 | + | 0.0509862i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.6663i | 1.62923i | ||||||||
\(428\) | − | 5.70291i | − | 0.275661i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.90100 | − | 6.35258i | −0.381020 | − | 0.306349i | ||||
\(431\) | 10.3947 | 0.500694 | 0.250347 | − | 0.968156i | \(-0.419455\pi\) | ||||
0.250347 | + | 0.968156i | \(0.419455\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.36622i | 0.161770i | 0.996723 | + | 0.0808852i | \(0.0257747\pi\) | ||||
−0.996723 | + | 0.0808852i | \(0.974225\pi\) | |||||||
\(434\) | 11.6316 | 0.558332 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.9318 | 0.571428 | ||||||||
\(437\) | − | 6.25142i | − | 0.299046i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.5045 | 1.55135 | 0.775677 | − | 0.631130i | \(-0.217409\pi\) | ||||
0.775677 | + | 0.631130i | \(0.217409\pi\) | |||||||
\(440\) | 5.35690 | − | 6.66263i | 0.255380 | − | 0.317628i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 0.144237i | − | 0.00686064i | ||||||
\(443\) | 23.5479i | 1.11879i | 0.828900 | + | 0.559397i | \(0.188967\pi\) | ||||
−0.828900 | + | 0.559397i | \(0.811033\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.2737 | + | 9.06432i | 0.534425 | + | 0.429690i | ||||
\(446\) | 15.4447 | 0.731325 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3.20984i | − | 0.151651i | ||||||
\(449\) | 12.5629 | 0.592878 | 0.296439 | − | 0.955052i | \(-0.404201\pi\) | ||||
0.296439 | + | 0.955052i | \(0.404201\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 45.2158 | 2.12913 | ||||||||
\(452\) | − | 2.18044i | − | 0.102559i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.46090 | −0.303225 | ||||||||
\(455\) | 0.824122 | + | 0.662612i | 0.0386354 | + | 0.0310637i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.53390i | − | 0.305643i | −0.988254 | − | 0.152821i | \(-0.951164\pi\) | ||
0.988254 | − | 0.152821i | \(-0.0488359\pi\) | |||||||
\(458\) | − | 7.97458i | − | 0.372628i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.27326 | + | 4.07111i | −0.152617 | + | 0.189816i | ||||
\(461\) | −24.7616 | −1.15326 | −0.576631 | − | 0.817005i | \(-0.695633\pi\) | ||||
−0.576631 | + | 0.817005i | \(0.695633\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.9239i | 1.20479i | 0.798200 | + | 0.602393i | \(0.205786\pi\) | ||||
−0.798200 | + | 0.602393i | \(0.794214\pi\) | |||||||
\(464\) | 6.30425 | 0.292667 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.2907 | 1.17157 | ||||||||
\(467\) | 28.8182i | 1.33355i | 0.745261 | + | 0.666773i | \(0.232325\pi\) | ||||
−0.745261 | + | 0.666773i | \(0.767675\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.01759 | 0.416394 | ||||||||
\(470\) | 10.8582 | + | 8.73023i | 0.500851 | + | 0.402696i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 6.92858i | − | 0.318914i | ||||||
\(473\) | 17.3343i | 0.797033i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.87307 | − | 13.0676i | −0.131825 | − | 0.599582i | ||||
\(476\) | 3.14239 | 0.144031 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.11481i | 0.233946i | ||||||||
\(479\) | −41.7873 | −1.90931 | −0.954655 | − | 0.297714i | \(-0.903776\pi\) | ||||
−0.954655 | + | 0.297714i | \(0.903776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.147332 | 0.00671778 | ||||||||
\(482\) | 16.4415i | 0.748888i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.61741 | −0.164428 | ||||||||
\(485\) | 4.30235 | − | 5.35103i | 0.195360 | − | 0.242978i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.34463i | − | 0.423446i | −0.977330 | − | 0.211723i | \(-0.932093\pi\) | ||
0.977330 | − | 0.211723i | \(-0.0679074\pi\) | |||||||
\(488\) | − | 10.4885i | − | 0.474791i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.62800 | + | 5.75606i | −0.209072 | + | 0.260032i | ||||
\(491\) | 10.7558 | 0.485404 | 0.242702 | − | 0.970101i | \(-0.421966\pi\) | ||||
0.242702 | + | 0.970101i | \(0.421966\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.17179i | 0.277963i | ||||||||
\(494\) | 0.394252 | 0.0177383 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.62372 | −0.162710 | ||||||||
\(497\) | 39.5415i | 1.77368i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.0702 | −1.30136 | −0.650680 | − | 0.759352i | \(-0.725516\pi\) | ||||
−0.650680 | + | 0.759352i | \(0.725516\pi\) | |||||||
\(500\) | −4.97120 | + | 10.0143i | −0.222319 | + | 0.447855i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 6.35586i | − | 0.283676i | ||||||
\(503\) | − | 36.2683i | − | 1.61712i | −0.588412 | − | 0.808561i | \(-0.700247\pi\) | ||
0.588412 | − | 0.808561i | \(-0.299753\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.4582 | − | 9.21261i | −0.509881 | − | 0.409956i | ||||
\(506\) | 8.93177 | 0.397065 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 5.39390i | − | 0.239316i | ||||||
\(509\) | −22.2170 | −0.984751 | −0.492375 | − | 0.870383i | \(-0.663871\pi\) | ||||
−0.492375 | + | 0.870383i | \(0.663871\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.9268 | 1.98745 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.45772 | 0.240730 | ||||||||
\(515\) | −3.53337 | + | 4.39462i | −0.155699 | + | 0.193650i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 23.8222i | − | 1.04770i | ||||||
\(518\) | 3.20984i | 0.141032i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.256749 | − | 0.206432i | −0.0112592 | − | 0.00905263i | ||||
\(521\) | −41.2732 | −1.80821 | −0.904107 | − | 0.427306i | \(-0.859463\pi\) | ||||
−0.904107 | + | 0.427306i | \(0.859463\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0354i | 0.482545i | 0.970457 | + | 0.241273i | \(0.0775648\pi\) | ||||
−0.970457 | + | 0.241273i | \(0.922435\pi\) | |||||||
\(524\) | −8.97060 | −0.391883 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.8882 | −0.649155 | ||||||||
\(527\) | − | 3.54758i | − | 0.154535i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.5424 | 0.762712 | ||||||||
\(530\) | −19.6882 | − | 15.8298i | −0.855201 | − | 0.687601i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.58933i | 0.372395i | ||||||||
\(533\) | − | 1.74242i | − | 0.0754726i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.99052 | − | 9.93818i | 0.345460 | − | 0.429665i | ||||
\(536\) | −2.80936 | −0.121346 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.5573i | 0.670723i | ||||||||
\(539\) | 12.6285 | 0.543946 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.2338 | −1.38584 | −0.692920 | − | 0.721014i | \(-0.743676\pi\) | ||||
−0.692920 | + | 0.721014i | \(0.743676\pi\) | |||||||
\(542\) | 0.462920i | 0.0198841i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.978989 | −0.0419738 | ||||||||
\(545\) | 20.7929 | + | 16.7180i | 0.890670 | + | 0.716119i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 15.0234i | − | 0.642355i | −0.947019 | − | 0.321177i | \(-0.895921\pi\) | ||
0.947019 | − | 0.321177i | \(-0.104079\pi\) | |||||||
\(548\) | 2.70352i | 0.115489i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 18.6704 | − | 4.10492i | 0.796110 | − | 0.175034i | ||||
\(551\) | −16.8698 | −0.718677 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 50.0918i | − | 2.13012i | ||||||
\(554\) | 9.12112 | 0.387519 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.30358 | 0.182512 | ||||||||
\(557\) | 39.1275i | 1.65788i | 0.559334 | + | 0.828942i | \(0.311057\pi\) | ||||
−0.559334 | + | 0.828942i | \(0.688943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.667989 | 0.0282529 | ||||||||
\(560\) | 4.49740 | − | 5.59362i | 0.190050 | − | 0.236374i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.8734i | 1.04922i | ||||||||
\(563\) | 27.1970i | 1.14622i | 0.819479 | + | 0.573109i | \(0.194263\pi\) | ||||
−0.819479 | + | 0.573109i | \(0.805737\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.05508 | − | 3.79975i | 0.128528 | − | 0.159857i | ||||
\(566\) | −19.7259 | −0.829142 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 12.3189i | − | 0.516888i | ||||||
\(569\) | −33.4499 | −1.40229 | −0.701146 | − | 0.713018i | \(-0.747328\pi\) | ||||
−0.701146 | + | 0.713018i | \(0.747328\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.9145 | 1.21003 | 0.605017 | − | 0.796213i | \(-0.293166\pi\) | ||||
0.605017 | + | 0.796213i | \(0.293166\pi\) | |||||||
\(572\) | 0.563292i | 0.0235524i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 37.9610 | 1.58446 | ||||||||
\(575\) | −11.4083 | + | 2.50825i | −0.475759 | + | 0.104601i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 33.5613i | − | 1.39717i | −0.715525 | − | 0.698587i | \(-0.753812\pi\) | ||
0.715525 | − | 0.698587i | \(-0.246188\pi\) | |||||||
\(578\) | 16.0416i | 0.667242i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.9861 | + | 8.83308i | 0.456173 | + | 0.366774i | ||||
\(581\) | 43.4518 | 1.80268 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.1948i | 1.78894i | ||||||||
\(584\) | −13.9966 | −0.579184 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.65528 | −0.109689 | ||||||||
\(587\) | − | 4.83581i | − | 0.199595i | −0.995008 | − | 0.0997976i | \(-0.968180\pi\) | ||
0.995008 | − | 0.0997976i | \(-0.0318195\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.69686 | 0.399552 | ||||||||
\(590\) | 9.70785 | − | 12.0741i | 0.399666 | − | 0.497083i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.00000i | − | 0.0410997i | ||||||
\(593\) | − | 43.1680i | − | 1.77270i | −0.463020 | − | 0.886348i | \(-0.653234\pi\) | ||
0.463020 | − | 0.886348i | \(-0.346766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.47610 | + | 4.40290i | 0.224498 | + | 0.180501i | ||||
\(596\) | −21.6949 | −0.888659 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 0.344191i | − | 0.0140750i | ||||||
\(599\) | −38.7714 | −1.58416 | −0.792078 | − | 0.610420i | \(-0.791001\pi\) | ||||
−0.792078 | + | 0.610420i | \(0.791001\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.56064 | 0.0636597 | 0.0318299 | − | 0.999493i | \(-0.489867\pi\) | ||||
0.0318299 | + | 0.999493i | \(0.489867\pi\) | |||||||
\(602\) | 14.5531i | 0.593139i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.06744 | −0.0841230 | ||||||||
\(605\) | −6.30389 | − | 5.06847i | −0.256289 | − | 0.206062i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.0494i | − | 0.854370i | −0.904164 | − | 0.427185i | \(-0.859505\pi\) | ||
0.904164 | − | 0.427185i | \(-0.140495\pi\) | |||||||
\(608\) | − | 2.67594i | − | 0.108524i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.6957 | − | 18.2778i | 0.595013 | − | 0.740045i | ||||
\(611\) | −0.918005 | −0.0371385 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.28786i | − | 0.213574i | −0.994282 | − | 0.106787i | \(-0.965944\pi\) | ||
0.994282 | − | 0.106787i | \(-0.0340564\pi\) | |||||||
\(614\) | −25.3545 | −1.02322 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.2721 | −0.494456 | ||||||||
\(617\) | − | 34.8545i | − | 1.40319i | −0.712576 | − | 0.701595i | \(-0.752472\pi\) | ||
0.712576 | − | 0.701595i | \(-0.247528\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.30122 | 0.293461 | 0.146730 | − | 0.989177i | \(-0.453125\pi\) | ||||
0.146730 | + | 0.989177i | \(0.453125\pi\) | |||||||
\(620\) | −6.31488 | − | 5.07731i | −0.253612 | − | 0.203910i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 11.1234i | − | 0.446006i | ||||||
\(623\) | − | 20.7654i | − | 0.831946i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.6945 | + | 10.4862i | −0.907779 | + | 0.419448i | ||||
\(626\) | −3.49109 | −0.139532 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.5439i | 0.739982i | ||||||||
\(629\) | 0.978989 | 0.0390348 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.2752 | 0.966381 | 0.483190 | − | 0.875515i | \(-0.339478\pi\) | ||||
0.483190 | + | 0.875515i | \(0.339478\pi\) | |||||||
\(632\) | 15.6057i | 0.620762i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.3656 | −0.729393 | ||||||||
\(635\) | 7.55756 | − | 9.39969i | 0.299913 | − | 0.373015i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 0.486646i | − | 0.0192816i | ||||||
\(638\) | − | 24.1029i | − | 0.954241i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.40113 | + | 1.74265i | −0.0553845 | + | 0.0688843i | ||||
\(641\) | 8.22087 | 0.324705 | 0.162353 | − | 0.986733i | \(-0.448092\pi\) | ||||
0.162353 | + | 0.986733i | \(0.448092\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.7758i | 1.17424i | 0.809499 | + | 0.587121i | \(0.199739\pi\) | ||||
−0.809499 | + | 0.587121i | \(0.800261\pi\) | |||||||
\(644\) | 7.49868 | 0.295489 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.61972 | 0.103071 | ||||||||
\(647\) | − | 35.6356i | − | 1.40098i | −0.713662 | − | 0.700490i | \(-0.752965\pi\) | ||
0.713662 | − | 0.700490i | \(-0.247035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.4899 | −1.03982 | ||||||||
\(650\) | −0.158186 | − | 0.719477i | −0.00620455 | − | 0.0282202i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.6240i | 0.846860i | ||||||||
\(653\) | − | 37.6128i | − | 1.47190i | −0.677035 | − | 0.735951i | \(-0.736736\pi\) | ||
0.677035 | − | 0.735951i | \(-0.263264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.6326 | − | 12.5690i | −0.610818 | − | 0.491111i | ||||
\(656\) | −11.8265 | −0.461746 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 20.0000i | − | 0.779681i | ||||||
\(659\) | 45.0553 | 1.75510 | 0.877552 | − | 0.479481i | \(-0.159175\pi\) | ||||
0.877552 | + | 0.479481i | \(0.159175\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.32365 | 0.284857 | 0.142429 | − | 0.989805i | \(-0.454509\pi\) | ||||
0.142429 | + | 0.989805i | \(0.454509\pi\) | |||||||
\(662\) | − | 21.9365i | − | 0.852587i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.5371 | −0.525341 | ||||||||
\(665\) | −12.0348 | + | 14.9682i | −0.466688 | + | 0.580442i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.7277i | 0.570260i | ||||||||
\(668\) | 11.7729i | 0.455506i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.89574 | − | 3.93628i | −0.189139 | − | 0.152072i | ||||
\(671\) | −40.1003 | −1.54806 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 8.58807i | − | 0.331046i | −0.986206 | − | 0.165523i | \(-0.947069\pi\) | ||
0.986206 | − | 0.165523i | \(-0.0529312\pi\) | |||||||
\(674\) | −8.65472 | −0.333368 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9783 | −0.499165 | ||||||||
\(677\) | − | 9.13523i | − | 0.351096i | −0.984471 | − | 0.175548i | \(-0.943830\pi\) | ||
0.984471 | − | 0.175548i | \(-0.0561697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.85621 | −0.378247 | ||||||||
\(680\) | −1.70604 | − | 1.37169i | −0.0654235 | − | 0.0526020i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.8545i | 0.530515i | ||||||||
\(683\) | 40.7414i | 1.55893i | 0.626449 | + | 0.779463i | \(0.284508\pi\) | ||||
−0.626449 | + | 0.779463i | \(0.715492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.78799 | + | 4.71130i | −0.144732 | + | 0.180009i | ||||
\(686\) | −11.8666 | −0.453069 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 4.53390i | − | 0.172853i | ||||||
\(689\) | 1.66454 | 0.0634139 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.7543 | −1.09387 | −0.546933 | − | 0.837176i | \(-0.684205\pi\) | ||||
−0.546933 | + | 0.837176i | \(0.684205\pi\) | |||||||
\(692\) | 14.0158i | 0.532801i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.3265 | 0.809541 | ||||||||
\(695\) | 7.49964 | + | 6.02988i | 0.284477 | + | 0.228726i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 11.5780i | − | 0.438547i | ||||||
\(698\) | 1.16305i | 0.0440223i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15.6748 | − | 3.44629i | 0.592452 | − | 0.130258i | ||||
\(701\) | 7.87020 | 0.297253 | 0.148627 | − | 0.988893i | \(-0.452515\pi\) | ||||
0.148627 | + | 0.988893i | \(0.452515\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.67594i | 0.100925i | ||||||||
\(704\) | 3.82327 | 0.144095 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.470079 | −0.0176917 | ||||||||
\(707\) | 21.1051i | 0.793738i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.0458 | −1.24106 | −0.620530 | − | 0.784182i | \(-0.713083\pi\) | ||||
−0.620530 | + | 0.784182i | \(0.713083\pi\) | |||||||
\(710\) | 17.2603 | − | 21.4675i | 0.647769 | − | 0.805660i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.46929i | 0.242447i | ||||||||
\(713\) | − | 8.46558i | − | 0.317039i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.789245 | + | 0.981621i | −0.0295161 | + | 0.0367105i | ||||
\(716\) | 12.4160 | 0.464009 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 33.3086i | − | 1.24307i | ||||||
\(719\) | 4.94138 | 0.184282 | 0.0921412 | − | 0.995746i | \(-0.470629\pi\) | ||||
0.0921412 | + | 0.995746i | \(0.470629\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.09456 | 0.301457 | ||||||||
\(722\) | − | 11.8393i | − | 0.440615i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.19748 | −0.304657 | ||||||||
\(725\) | 6.76866 | + | 30.7859i | 0.251382 | + | 1.14336i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 42.5178i | − | 1.57690i | −0.615101 | − | 0.788448i | \(-0.710885\pi\) | ||
0.615101 | − | 0.788448i | \(-0.289115\pi\) | |||||||
\(728\) | 0.472913i | 0.0175273i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24.3912 | − | 19.6111i | −0.902759 | − | 0.725839i | ||||
\(731\) | 4.43863 | 0.164169 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.2114i | 0.377167i | 0.982057 | + | 0.188584i | \(0.0603896\pi\) | ||||
−0.982057 | + | 0.188584i | \(0.939610\pi\) | |||||||
\(734\) | −11.1884 | −0.412971 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.33616 | −0.0861119 | ||||||||
\(737\) | 10.7410i | 0.395648i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.5528 | −0.939975 | −0.469988 | − | 0.882673i | \(-0.655742\pi\) | ||||
−0.469988 | + | 0.882673i | \(0.655742\pi\) | |||||||
\(740\) | 1.40113 | − | 1.74265i | 0.0515066 | − | 0.0640611i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 36.2642i | 1.33130i | ||||||||
\(743\) | − | 44.2852i | − | 1.62467i | −0.583193 | − | 0.812334i | \(-0.698197\pi\) | ||
0.583193 | − | 0.812334i | \(-0.301803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −37.8067 | − | 30.3974i | −1.38513 | − | 1.11368i | ||||
\(746\) | −23.1634 | −0.848072 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.74294i | 0.136855i | ||||||||
\(749\) | −18.3054 | −0.668865 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.2897 | 1.50668 | 0.753342 | − | 0.657629i | \(-0.228440\pi\) | ||||
0.753342 | + | 0.657629i | \(0.228440\pi\) | |||||||
\(752\) | 6.23085i | 0.227216i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.928820 | −0.0338256 | ||||||||
\(755\) | −3.60283 | − | 2.89676i | −0.131120 | − | 0.105424i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 6.57802i | − | 0.239082i | −0.992829 | − | 0.119541i | \(-0.961858\pi\) | ||
0.992829 | − | 0.119541i | \(-0.0381423\pi\) | |||||||
\(758\) | 26.7721i | 0.972406i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.74934 | − | 4.66323i | 0.136003 | − | 0.169153i | ||||
\(761\) | −20.3166 | −0.736475 | −0.368237 | − | 0.929732i | \(-0.620039\pi\) | ||||
−0.368237 | + | 0.929732i | \(0.620039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 38.2990i | − | 1.38652i | ||||||
\(764\) | 8.00137 | 0.289479 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.3189 | 0.806413 | ||||||||
\(767\) | 1.02080i | 0.0368591i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.2435 | −0.910303 | −0.455151 | − | 0.890414i | \(-0.650415\pi\) | ||||
−0.455151 | + | 0.890414i | \(0.650415\pi\) | |||||||
\(770\) | −21.3860 | − | 17.1948i | −0.770696 | − | 0.619657i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.0420i | 0.505383i | ||||||||
\(773\) | 48.9781i | 1.76162i | 0.473470 | + | 0.880810i | \(0.343001\pi\) | ||||
−0.473470 | + | 0.880810i | \(0.656999\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.89067 | − | 17.6959i | −0.139757 | − | 0.635657i | ||||
\(776\) | 3.07063 | 0.110229 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 24.3011i | − | 0.871237i | ||||||
\(779\) | 31.6469 | 1.13387 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.0984 | −1.68531 | ||||||||
\(782\) | − | 2.28707i | − | 0.0817855i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.30305 | −0.117966 | ||||||||
\(785\) | −25.9824 | + | 32.3155i | −0.927352 | + | 1.15339i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.78073i | 0.134768i | 0.997727 | + | 0.0673842i | \(0.0214653\pi\) | ||||
−0.997727 | + | 0.0673842i | \(0.978535\pi\) | |||||||
\(788\) | − | 3.36608i | − | 0.119912i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.8657 | + | 27.1953i | −0.777945 | + | 0.967566i | ||||
\(791\) | −6.99886 | −0.248851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.54529i | 0.0548750i | ||||||||
\(794\) | 28.1888 | 1.00038 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.8890 | −0.527725 | ||||||||
\(797\) | − | 29.5487i | − | 1.04667i | −0.852128 | − | 0.523334i | \(-0.824688\pi\) | ||
0.852128 | − | 0.523334i | \(-0.175312\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.09993 | −0.215800 | ||||||||
\(800\) | −4.88336 | + | 1.07367i | −0.172653 | + | 0.0379598i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 15.9528i | 0.563312i | ||||||||
\(803\) | 53.5129i | 1.88843i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.0676 | + | 10.5066i | 0.460572 | + | 0.370310i | ||||
\(806\) | 0.533891 | 0.0188055 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 6.57513i | − | 0.231312i | ||||||
\(809\) | 47.4231 | 1.66731 | 0.833654 | − | 0.552287i | \(-0.186245\pi\) | ||||
0.833654 | + | 0.552287i | \(0.186245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.6962 | 0.902317 | 0.451159 | − | 0.892444i | \(-0.351011\pi\) | ||||
0.451159 | + | 0.892444i | \(0.351011\pi\) | |||||||
\(812\) | − | 20.2356i | − | 0.710131i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.82327 | −0.134006 | ||||||||
\(815\) | −30.2980 | + | 37.6830i | −1.06129 | + | 1.31998i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.1324i | 0.424460i | ||||||||
\(818\) | − | 31.6014i | − | 1.10492i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.6094 | − | 16.5704i | −0.719711 | − | 0.578664i | ||||
\(821\) | −0.286013 | −0.00998192 | −0.00499096 | − | 0.999988i | \(-0.501589\pi\) | ||||
−0.00499096 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.6093i | 1.55498i | 0.628893 | + | 0.777491i | \(0.283508\pi\) | ||||
−0.628893 | + | 0.777491i | \(0.716492\pi\) | |||||||
\(824\) | −2.52180 | −0.0878510 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22.2396 | −0.773815 | ||||||||
\(827\) | − | 55.1277i | − | 1.91698i | −0.285131 | − | 0.958488i | \(-0.592037\pi\) | ||
0.285131 | − | 0.958488i | \(-0.407963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2029 | 0.597482 | 0.298741 | − | 0.954334i | \(-0.403433\pi\) | ||||
0.298741 | + | 0.954334i | \(0.403433\pi\) | |||||||
\(830\) | −23.5904 | − | 18.9672i | −0.818835 | − | 0.658362i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.147332i | − | 0.00510783i | ||||||
\(833\) | − | 3.23365i | − | 0.112039i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.4953 | + | 20.5160i | −0.570844 | + | 0.709985i | ||||
\(836\) | −10.2308 | −0.353841 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 18.4266i | − | 0.636535i | ||||||
\(839\) | 27.3527 | 0.944320 | 0.472160 | − | 0.881513i | \(-0.343474\pi\) | ||||
0.472160 | + | 0.881513i | \(0.343474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7436 | 0.370467 | ||||||||
\(842\) | − | 19.1570i | − | 0.660194i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.80544 | 0.337517 | ||||||||
\(845\) | −22.6166 | − | 18.1843i | −0.778036 | − | 0.625558i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.6113i | 0.398969i | ||||||||
\(848\) | − | 11.2978i | − | 0.387970i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.05111 | − | 4.78076i | −0.0360527 | − | 0.163979i | ||||
\(851\) | 2.33616 | 0.0800824 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 51.8565i | − | 1.77553i | −0.460294 | − | 0.887766i | \(-0.652256\pi\) | ||
0.460294 | − | 0.887766i | \(-0.347744\pi\) | |||||||
\(854\) | −33.6663 | −1.15204 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.70291 | 0.194921 | ||||||||
\(857\) | − | 4.63553i | − | 0.158347i | −0.996861 | − | 0.0791733i | \(-0.974772\pi\) | ||
0.996861 | − | 0.0791733i | \(-0.0252280\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.1006 | −1.47057 | −0.735287 | − | 0.677755i | \(-0.762953\pi\) | ||||
−0.735287 | + | 0.677755i | \(0.762953\pi\) | |||||||
\(860\) | 6.35258 | − | 7.90100i | 0.216621 | − | 0.269422i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.3947i | 0.354044i | ||||||||
\(863\) | − | 11.2463i | − | 0.382829i | −0.981509 | − | 0.191414i | \(-0.938693\pi\) | ||
0.981509 | − | 0.191414i | \(-0.0613074\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.6380 | + | 24.4247i | −0.667711 | + | 0.830464i | ||||
\(866\) | −3.36622 | −0.114389 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.6316i | 0.394801i | ||||||||
\(869\) | 59.6649 | 2.02399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.413910 | 0.0140248 | ||||||||
\(872\) | 11.9318i | 0.404061i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.25142 | 0.211457 | ||||||||
\(875\) | 32.1444 | + | 15.9568i | 1.08668 | + | 0.539437i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.9444i | 0.605939i | 0.953000 | + | 0.302969i | \(0.0979780\pi\) | ||||
−0.953000 | + | 0.302969i | \(0.902022\pi\) | |||||||
\(878\) | 32.5045i | 1.09697i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.66263 | + | 5.35690i | 0.224597 | + | 0.180581i | ||||
\(881\) | 16.6495 | 0.560935 | 0.280468 | − | 0.959864i | \(-0.409511\pi\) | ||||
0.280468 | + | 0.959864i | \(0.409511\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.7758i | 0.968383i | 0.874962 | + | 0.484191i | \(0.160886\pi\) | ||||
−0.874962 | + | 0.484191i | \(0.839114\pi\) | |||||||
\(884\) | 0.144237 | 0.00485121 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.5479 | −0.791107 | ||||||||
\(887\) | − | 23.6957i | − | 0.795625i | −0.917467 | − | 0.397812i | \(-0.869770\pi\) | ||
0.917467 | − | 0.397812i | \(-0.130230\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.3135 | −0.580678 | ||||||||
\(890\) | −9.06432 | + | 11.2737i | −0.303837 | + | 0.377896i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.4447i | 0.517125i | ||||||||
\(893\) | − | 16.6734i | − | 0.557953i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.6368 | + | 17.3965i | 0.723240 | + | 0.581501i | ||||
\(896\) | 3.20984 | 0.107233 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.5629i | 0.419228i | ||||||||
\(899\) | −22.8448 | −0.761918 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.0605 | 0.368478 | ||||||||
\(902\) | 45.2158i | 1.50552i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.18044 | 0.0725204 | ||||||||
\(905\) | −14.2853 | − | 11.4857i | −0.474861 | − | 0.381799i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.56548i | 0.184799i | 0.995722 | + | 0.0923994i | \(0.0294537\pi\) | ||||
−0.995722 | + | 0.0923994i | \(0.970546\pi\) | |||||||
\(908\) | − | 6.46090i | − | 0.214413i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.662612 | + | 0.824122i | −0.0219654 | + | 0.0273194i | ||||
\(911\) | 17.2514 | 0.571565 | 0.285782 | − | 0.958295i | \(-0.407747\pi\) | ||||
0.285782 | + | 0.958295i | \(0.407747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.7559i | 1.71287i | ||||||||
\(914\) | 6.53390 | 0.216122 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.97458 | 0.263488 | ||||||||
\(917\) | 28.7942i | 0.950867i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.34007 | 0.275114 | 0.137557 | − | 0.990494i | \(-0.456075\pi\) | ||||
0.137557 | + | 0.990494i | \(0.456075\pi\) | |||||||
\(920\) | −4.07111 | − | 3.27326i | −0.134220 | − | 0.107916i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 24.7616i | − | 0.815480i | ||||||
\(923\) | 1.81497i | 0.0597403i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.88336 | − | 1.07367i | 0.160564 | − | 0.0353019i | ||||
\(926\) | −25.9239 | −0.851913 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.30425i | 0.206947i | ||||||||
\(929\) | −48.2529 | −1.58313 | −0.791564 | − | 0.611087i | \(-0.790733\pi\) | ||||
−0.791564 | + | 0.611087i | \(0.790733\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.83876 | 0.289679 | ||||||||
\(932\) | 25.2907i | 0.828423i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.8182 | −0.942959 | ||||||||
\(935\) | −5.24435 | + | 6.52264i | −0.171509 | + | 0.213313i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.2000i | 0.986592i | 0.869862 | + | 0.493296i | \(0.164208\pi\) | ||||
−0.869862 | + | 0.493296i | \(0.835792\pi\) | |||||||
\(938\) | 9.01759i | 0.294435i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.73023 | + | 10.8582i | −0.284749 | + | 0.354155i | ||||
\(941\) | −14.9206 | −0.486399 | −0.243199 | − | 0.969976i | \(-0.578197\pi\) | ||||
−0.243199 | + | 0.969976i | \(0.578197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 27.6285i | − | 0.899707i | ||||||
\(944\) | 6.92858 | 0.225506 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.3343 | −0.563587 | ||||||||
\(947\) | − | 48.1091i | − | 1.56334i | −0.623694 | − | 0.781668i | \(-0.714369\pi\) | ||
0.623694 | − | 0.781668i | \(-0.285631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.06215 | 0.0669403 | ||||||||
\(950\) | 13.0676 | − | 2.87307i | 0.423969 | − | 0.0932146i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.14239i | 0.101846i | ||||||||
\(953\) | 8.67149i | 0.280897i | 0.990088 | + | 0.140449i | \(0.0448545\pi\) | ||||
−0.990088 | + | 0.140449i | \(0.955146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.9436 | + | 11.2110i | 0.451204 | + | 0.362778i | ||||
\(956\) | −5.11481 | −0.165425 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 41.7873i | − | 1.35009i | ||||||
\(959\) | 8.67787 | 0.280223 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.8686 | −0.576408 | ||||||||
\(962\) | 0.147332i | 0.00475018i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16.4415 | −0.529544 | ||||||||
\(965\) | −19.6747 | + | 24.4703i | −0.633351 | + | 0.787728i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.5944i | 0.597955i | 0.954260 | + | 0.298978i | \(0.0966456\pi\) | ||||
−0.954260 | + | 0.298978i | \(0.903354\pi\) | |||||||
\(968\) | − | 3.61741i | − | 0.116268i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.35103 | + | 4.30235i | 0.171811 | + | 0.138140i | ||||
\(971\) | 32.6679 | 1.04836 | 0.524182 | − | 0.851606i | \(-0.324371\pi\) | ||||
0.524182 | + | 0.851606i | \(0.324371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 13.8138i | − | 0.442850i | ||||||
\(974\) | 9.34463 | 0.299421 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.4885 | 0.335728 | ||||||||
\(977\) | 28.1856i | 0.901737i | 0.892590 | + | 0.450868i | \(0.148886\pi\) | ||||
−0.892590 | + | 0.450868i | \(0.851114\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.7338 | 0.790497 | ||||||||
\(980\) | −5.75606 | − | 4.62800i | −0.183871 | − | 0.147836i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.7558i | 0.343232i | ||||||||
\(983\) | 25.3845i | 0.809639i | 0.914397 | + | 0.404819i | \(0.132666\pi\) | ||||
−0.914397 | + | 0.404819i | \(0.867334\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.71632 | − | 5.86591i | 0.150274 | − | 0.186903i | ||||
\(986\) | −6.17179 | −0.196550 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.394252i | 0.0125428i | ||||||||
\(989\) | 10.5919 | 0.336803 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.1083 | −0.670527 | −0.335264 | − | 0.942124i | \(-0.608825\pi\) | ||||
−0.335264 | + | 0.942124i | \(0.608825\pi\) | |||||||
\(992\) | − | 3.62372i | − | 0.115053i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −39.5415 | −1.25418 | ||||||||
\(995\) | −25.9463 | − | 20.8614i | −0.822552 | − | 0.661350i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 39.0978i | − | 1.23824i | −0.785296 | − | 0.619120i | \(-0.787489\pi\) | ||
0.785296 | − | 0.619120i | \(-0.212511\pi\) | |||||||
\(998\) | − | 29.0702i | − | 0.920201i | ||||||
\(999\) | 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 | 3330.2.d.p.1999.7 | 10 | ||
3.2 | odd | 2 | 370.2.b.d.149.2 | ✓ | 10 | ||
5.4 | even | 2 | inner | 3330.2.d.p.1999.2 | 10 | ||
15.2 | even | 4 | 1850.2.a.be.1.2 | 5 | |||
15.8 | even | 4 | 1850.2.a.bd.1.4 | 5 | |||
15.14 | odd | 2 | 370.2.b.d.149.9 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.b.d.149.2 | ✓ | 10 | 3.2 | odd | 2 | ||
370.2.b.d.149.9 | yes | 10 | 15.14 | odd | 2 | ||
1850.2.a.bd.1.4 | 5 | 15.8 | even | 4 | |||
1850.2.a.be.1.2 | 5 | 15.2 | even | 4 | |||
3330.2.d.p.1999.2 | 10 | 5.4 | even | 2 | inner | ||
3330.2.d.p.1999.7 | 10 | 1.1 | even | 1 | trivial |