Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(-1.63746 - 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.361 |
Dual form | 441.4.e.p.226.2 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13746 | + | 1.97014i | 0.402152 | + | 0.696548i | 0.993985 | − | 0.109512i | \(-0.0349289\pi\) |
−0.591833 | + | 0.806061i | \(0.701596\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.41238 | − | 2.44631i | 0.176547 | − | 0.305788i | ||||
\(5\) | 2.27492 | + | 3.94027i | 0.203475 | + | 0.352429i | 0.949646 | − | 0.313326i | \(-0.101443\pi\) |
−0.746171 | + | 0.665754i | \(0.768110\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.6254 | 1.08830 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.17525 | + | 8.96379i | −0.163656 | + | 0.283460i | ||||
\(11\) | −20.3746 | + | 35.2898i | −0.558470 | + | 0.967298i | 0.439155 | + | 0.898412i | \(0.355278\pi\) |
−0.997624 | + | 0.0688867i | \(0.978055\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −53.2990 | −1.13711 | −0.568557 | − | 0.822644i | \(-0.692498\pi\) | ||||
−0.568557 | + | 0.822644i | \(0.692498\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.7114 | + | 28.9450i | 0.261115 | + | 0.452265i | ||||
\(17\) | −2.27492 | + | 3.94027i | −0.0324558 | + | 0.0562151i | −0.881797 | − | 0.471629i | \(-0.843666\pi\) |
0.849341 | + | 0.527844i | \(0.176999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 61.2990 | + | 106.173i | 0.740156 | + | 1.28199i | 0.952424 | + | 0.304776i | \(0.0985815\pi\) |
−0.212269 | + | 0.977211i | \(0.568085\pi\) | |||||||
\(20\) | 12.8522 | 0.143691 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −92.7010 | −0.898360 | ||||||||
\(23\) | 65.6736 | + | 113.750i | 0.595387 | + | 1.03124i | 0.993492 | + | 0.113900i | \(0.0363344\pi\) |
−0.398106 | + | 0.917340i | \(0.630332\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 52.1495 | − | 90.3256i | 0.417196 | − | 0.722605i | ||||
\(26\) | −60.6254 | − | 105.006i | −0.457293 | − | 0.792055i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 216.598 | 1.38694 | 0.693470 | − | 0.720486i | \(-0.256081\pi\) | ||||
0.693470 | + | 0.720486i | \(0.256081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −125.897 | + | 218.060i | −0.729412 | + | 1.26338i | 0.227720 | + | 0.973727i | \(0.426873\pi\) |
−0.957132 | + | 0.289652i | \(0.906460\pi\) | |||||||
\(32\) | 60.4846 | − | 104.762i | 0.334134 | − | 0.578736i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.3505 | −0.0522087 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.94851 | − | 10.3031i | −0.0264305 | − | 0.0457790i | 0.852508 | − | 0.522715i | \(-0.175081\pi\) |
−0.878938 | + | 0.476936i | \(0.841747\pi\) | |||||||
\(38\) | −139.450 | + | 241.535i | −0.595311 | + | 1.03111i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 56.0208 | + | 97.0308i | 0.221442 | + | 0.383548i | ||||
\(41\) | −111.752 | −0.425678 | −0.212839 | − | 0.977087i | \(-0.568271\pi\) | ||||
−0.212839 | + | 0.977087i | \(0.568271\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 369.196 | 1.30935 | 0.654673 | − | 0.755912i | \(-0.272806\pi\) | ||||
0.654673 | + | 0.755912i | \(0.272806\pi\) | |||||||
\(44\) | 57.5531 | + | 99.6850i | 0.197192 | + | 0.341547i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −149.402 | + | 258.772i | −0.478872 | + | 0.829431i | ||||
\(47\) | 131.347 | + | 227.500i | 0.407637 | + | 0.706049i | 0.994624 | − | 0.103548i | \(-0.0330194\pi\) |
−0.586987 | + | 0.809596i | \(0.699686\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 237.272 | 0.671105 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −75.2782 | + | 130.386i | −0.200754 | + | 0.347716i | ||||
\(53\) | −283.550 | + | 491.123i | −0.734879 | + | 1.27285i | 0.219898 | + | 0.975523i | \(0.429428\pi\) |
−0.954777 | + | 0.297324i | \(0.903906\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −185.402 | −0.454538 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 246.371 | + | 426.728i | 0.557761 | + | 0.966070i | ||||
\(59\) | −419.945 | + | 727.366i | −0.926648 | + | 1.60500i | −0.137758 | + | 0.990466i | \(0.543990\pi\) |
−0.788890 | + | 0.614535i | \(0.789344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −242.897 | − | 420.710i | −0.509832 | − | 0.883056i | −0.999935 | − | 0.0113909i | \(-0.996374\pi\) |
0.490103 | − | 0.871665i | \(-0.336959\pi\) | |||||||
\(62\) | −572.811 | −1.17334 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 542.577 | 1.05972 | ||||||||
\(65\) | −121.251 | − | 210.013i | −0.231374 | − | 0.400752i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 166.846 | − | 288.985i | 0.304230 | − | 0.526942i | −0.672859 | − | 0.739770i | \(-0.734934\pi\) |
0.977090 | + | 0.212828i | \(0.0682675\pi\) | |||||||
\(68\) | 6.42608 | + | 11.1303i | 0.0114599 | + | 0.0198492i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −590.248 | −0.986613 | −0.493306 | − | 0.869856i | \(-0.664212\pi\) | ||||
−0.493306 | + | 0.869856i | \(0.664212\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 245.350 | − | 424.960i | 0.393371 | − | 0.681339i | −0.599521 | − | 0.800359i | \(-0.704642\pi\) |
0.992892 | + | 0.119020i | \(0.0379754\pi\) | |||||||
\(74\) | 13.5324 | − | 23.4387i | 0.0212582 | − | 0.0368203i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 346.309 | 0.522689 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −60.8455 | − | 105.388i | −0.0866539 | − | 0.150089i | 0.819441 | − | 0.573164i | \(-0.194284\pi\) |
−0.906095 | + | 0.423075i | \(0.860951\pi\) | |||||||
\(80\) | −76.0340 | + | 131.695i | −0.106261 | + | 0.184049i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −127.114 | − | 220.168i | −0.171187 | − | 0.296505i | ||||
\(83\) | 609.608 | 0.806183 | 0.403091 | − | 0.915160i | \(-0.367936\pi\) | ||||
0.403091 | + | 0.915160i | \(0.367936\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.7010 | −0.0264157 | ||||||||
\(86\) | 419.945 | + | 727.366i | 0.526556 | + | 0.912023i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −501.733 | + | 869.026i | −0.607783 | + | 1.05271i | ||||
\(89\) | −359.519 | − | 622.705i | −0.428190 | − | 0.741648i | 0.568522 | − | 0.822668i | \(-0.307515\pi\) |
−0.996712 | + | 0.0810204i | \(0.974182\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 371.023 | 0.420455 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −298.804 | + | 517.544i | −0.327865 | + | 0.567878i | ||||
\(95\) | −278.900 | + | 483.070i | −0.301206 | + | 0.521704i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 637.877 | 0.667697 | 0.333849 | − | 0.942627i | \(-0.391653\pi\) | ||||
0.333849 | + | 0.942627i | \(0.391653\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −147.309 | − | 255.147i | −0.147309 | − | 0.255147i | ||||
\(101\) | −335.574 | + | 581.231i | −0.330603 | + | 0.572620i | −0.982630 | − | 0.185575i | \(-0.940585\pi\) |
0.652028 | + | 0.758195i | \(0.273919\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −456.206 | − | 790.172i | −0.436420 | − | 0.755902i | 0.560990 | − | 0.827823i | \(-0.310421\pi\) |
−0.997410 | + | 0.0719202i | \(0.977087\pi\) | |||||||
\(104\) | −1312.51 | −1.23752 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1290.10 | −1.18213 | ||||||||
\(107\) | −58.3680 | − | 101.096i | −0.0527350 | − | 0.0913397i | 0.838453 | − | 0.544974i | \(-0.183461\pi\) |
−0.891188 | + | 0.453634i | \(0.850127\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −418.588 | + | 725.016i | −0.367830 | + | 0.637100i | −0.989226 | − | 0.146396i | \(-0.953232\pi\) |
0.621396 | + | 0.783497i | \(0.286566\pi\) | |||||||
\(110\) | −210.887 | − | 365.267i | −0.182794 | − | 0.316608i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1086.58 | 0.904572 | 0.452286 | − | 0.891873i | \(-0.350609\pi\) | ||||
0.452286 | + | 0.891873i | \(0.350609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −298.804 | + | 517.544i | −0.242292 | + | 0.419663i | ||||
\(116\) | 305.918 | − | 529.865i | 0.244860 | − | 0.424110i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1910.68 | −1.49061 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −164.748 | − | 285.351i | −0.123777 | − | 0.214388i | ||||
\(122\) | 552.571 | − | 957.080i | 0.410061 | − | 0.710246i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 355.628 | + | 615.965i | 0.257551 | + | 0.446091i | ||||
\(125\) | 1043.27 | 0.746505 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −537.113 | −0.375284 | −0.187642 | − | 0.982237i | \(-0.560084\pi\) | ||||
−0.187642 | + | 0.982237i | \(0.560084\pi\) | |||||||
\(128\) | 133.282 | + | 230.851i | 0.0920357 | + | 0.159411i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 275.836 | − | 477.761i | 0.186095 | − | 0.322326i | ||||
\(131\) | −748.694 | − | 1296.78i | −0.499341 | − | 0.864885i | 0.500658 | − | 0.865645i | \(-0.333091\pi\) |
−1.00000 | 0.000760253i | \(0.999758\pi\) | ||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 759.120 | 0.489388 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −56.0208 | + | 97.0308i | −0.0353216 | + | 0.0611789i | ||||
\(137\) | −690.045 | + | 1195.19i | −0.430325 | + | 0.745345i | −0.996901 | − | 0.0786647i | \(-0.974934\pi\) |
0.566576 | + | 0.824009i | \(0.308268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 141.980 | 0.0866374 | 0.0433187 | − | 0.999061i | \(-0.486207\pi\) | ||||
0.0433187 | + | 0.999061i | \(0.486207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −671.382 | − | 1162.87i | −0.396769 | − | 0.687223i | ||||
\(143\) | 1085.95 | − | 1880.91i | 0.635044 | − | 1.09993i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 492.743 | + | 853.455i | 0.282207 | + | 0.488797i | ||||
\(146\) | 1116.30 | 0.632781 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −33.6061 | −0.0186649 | ||||||||
\(149\) | −971.935 | − | 1683.44i | −0.534390 | − | 0.925590i | −0.999193 | − | 0.0401757i | \(-0.987208\pi\) |
0.464803 | − | 0.885414i | \(-0.346125\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1327.38 | − | 2299.09i | 0.715370 | − | 1.23906i | −0.247447 | − | 0.968901i | \(-0.579592\pi\) |
0.962817 | − | 0.270155i | \(-0.0870750\pi\) | |||||||
\(152\) | 1509.51 | + | 2614.55i | 0.805511 | + | 1.39519i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1145.62 | −0.593668 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 832.608 | − | 1442.12i | 0.423244 | − | 0.733081i | −0.573010 | − | 0.819548i | \(-0.694225\pi\) |
0.996255 | + | 0.0864675i | \(0.0275579\pi\) | |||||||
\(158\) | 138.419 | − | 239.748i | 0.0696961 | − | 0.120717i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 550.390 | 0.271951 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.5366 | + | 28.6422i | 0.00794629 | + | 0.0137634i | 0.869971 | − | 0.493103i | \(-0.164137\pi\) |
−0.862025 | + | 0.506866i | \(0.830804\pi\) | |||||||
\(164\) | −157.837 | + | 273.381i | −0.0751522 | + | 0.130167i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 693.404 | + | 1201.01i | 0.324208 | + | 0.561545i | ||||
\(167\) | 1654.48 | 0.766630 | 0.383315 | − | 0.923618i | \(-0.374782\pi\) | ||||
0.383315 | + | 0.923618i | \(0.374782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 643.784 | 0.293029 | ||||||||
\(170\) | −23.5465 | − | 40.7838i | −0.0106232 | − | 0.0183998i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 521.444 | − | 903.167i | 0.231161 | − | 0.400383i | ||||
\(173\) | −32.0954 | − | 55.5909i | −0.0141050 | − | 0.0244306i | 0.858887 | − | 0.512166i | \(-0.171157\pi\) |
−0.872992 | + | 0.487735i | \(0.837823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1361.95 | −0.583300 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 817.876 | − | 1416.60i | 0.344396 | − | 0.596511i | ||||
\(179\) | 1957.34 | − | 3390.21i | 0.817309 | − | 1.41562i | −0.0903489 | − | 0.995910i | \(-0.528798\pi\) |
0.907658 | − | 0.419711i | \(-0.137868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2058.04 | 0.845156 | 0.422578 | − | 0.906327i | \(-0.361125\pi\) | ||||
0.422578 | + | 0.906327i | \(0.361125\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1617.24 | + | 2801.14i | 0.647959 | + | 1.12230i | ||||
\(185\) | 27.0647 | − | 46.8775i | 0.0107559 | − | 0.0186297i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −92.7010 | − | 160.563i | −0.0362512 | − | 0.0627889i | ||||
\(188\) | 742.046 | 0.287869 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1268.95 | −0.484523 | ||||||||
\(191\) | 214.024 | + | 370.701i | 0.0810798 | + | 0.140434i | 0.903714 | − | 0.428137i | \(-0.140830\pi\) |
−0.822634 | + | 0.568571i | \(0.807496\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −802.463 | + | 1389.91i | −0.299288 | + | 0.518382i | −0.975973 | − | 0.217890i | \(-0.930082\pi\) |
0.676685 | + | 0.736272i | \(0.263416\pi\) | |||||||
\(194\) | 725.559 | + | 1256.70i | 0.268516 | + | 0.465083i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3738.83 | −1.35218 | −0.676092 | − | 0.736817i | \(-0.736328\pi\) | ||||
−0.676092 | + | 0.736817i | \(0.736328\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −174.515 | + | 302.269i | −0.0621660 | + | 0.107675i | −0.895433 | − | 0.445196i | \(-0.853134\pi\) |
0.833267 | + | 0.552870i | \(0.186467\pi\) | |||||||
\(200\) | 1284.20 | − | 2224.31i | 0.454034 | − | 0.786411i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1526.81 | −0.531810 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −254.228 | − | 440.335i | −0.0866148 | − | 0.150021i | ||||
\(206\) | 1037.83 | − | 1797.58i | 0.351015 | − | 0.607976i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −890.700 | − | 1542.74i | −0.296918 | − | 0.514277i | ||||
\(209\) | −4995.77 | −1.65342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2588.58 | 0.844574 | 0.422287 | − | 0.906462i | \(-0.361227\pi\) | ||||
0.422287 | + | 0.906462i | \(0.361227\pi\) | |||||||
\(212\) | 800.958 | + | 1387.30i | 0.259481 | + | 0.449435i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 132.782 | − | 229.986i | 0.0424150 | − | 0.0734649i | ||||
\(215\) | 839.890 | + | 1454.73i | 0.266419 | + | 0.461451i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1904.51 | −0.591695 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −261.857 | + | 453.550i | −0.0802473 | + | 0.138992i | ||||
\(221\) | 121.251 | − | 210.013i | 0.0369059 | − | 0.0639230i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3236.21 | 0.971804 | 0.485902 | − | 0.874013i | \(-0.338491\pi\) | ||||
0.485902 | + | 0.874013i | \(0.338491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1235.94 | + | 2140.71i | 0.363776 | + | 0.630078i | ||||
\(227\) | 2815.81 | − | 4877.12i | 0.823312 | − | 1.42602i | −0.0798906 | − | 0.996804i | \(-0.525457\pi\) |
0.903203 | − | 0.429215i | \(-0.141210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1885.12 | + | 3265.13i | 0.543985 | + | 0.942210i | 0.998670 | + | 0.0515573i | \(0.0164185\pi\) |
−0.454685 | + | 0.890652i | \(0.650248\pi\) | |||||||
\(230\) | −1359.51 | −0.389754 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5333.82 | 1.50941 | ||||||||
\(233\) | −3280.45 | − | 5681.91i | −0.922358 | − | 1.59757i | −0.795756 | − | 0.605618i | \(-0.792926\pi\) |
−0.126602 | − | 0.991954i | \(-0.540407\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −597.608 | + | 1035.09i | −0.165888 | + | 0.287326i | ||||
\(236\) | 1186.24 | + | 2054.63i | 0.327194 | + | 0.566716i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 771.444 | 0.208789 | 0.104394 | − | 0.994536i | \(-0.466710\pi\) | ||||
0.104394 | + | 0.994536i | \(0.466710\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 626.051 | − | 1084.35i | 0.167334 | − | 0.289831i | −0.770148 | − | 0.637866i | \(-0.779817\pi\) |
0.937482 | + | 0.348035i | \(0.113151\pi\) | |||||||
\(242\) | 374.787 | − | 649.150i | 0.0995546 | − | 0.172434i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1372.25 | −0.360037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3267.18 | − | 5658.92i | −0.841641 | − | 1.45777i | ||||
\(248\) | −3100.27 | + | 5369.82i | −0.793819 | + | 1.37493i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1186.68 | + | 2055.39i | 0.300209 | + | 0.519977i | ||||
\(251\) | 5166.27 | 1.29917 | 0.649586 | − | 0.760288i | \(-0.274942\pi\) | ||||
0.649586 | + | 0.760288i | \(0.274942\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5352.29 | −1.33002 | ||||||||
\(254\) | −610.944 | − | 1058.19i | −0.150921 | − | 0.261403i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1867.10 | − | 3233.92i | 0.455836 | − | 0.789531i | ||||
\(257\) | −1383.73 | − | 2396.68i | −0.335854 | − | 0.581716i | 0.647795 | − | 0.761815i | \(-0.275691\pi\) |
−0.983648 | + | 0.180099i | \(0.942358\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −685.007 | −0.163394 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1703.22 | − | 2950.06i | 0.401623 | − | 0.695631i | ||||
\(263\) | −2050.89 | + | 3552.25i | −0.480849 | + | 0.832855i | −0.999759 | − | 0.0219739i | \(-0.993005\pi\) |
0.518909 | + | 0.854829i | \(0.326338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2580.21 | −0.598117 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −471.297 | − | 816.311i | −0.107422 | − | 0.186060i | ||||
\(269\) | 3475.42 | − | 6019.60i | 0.787732 | − | 1.36439i | −0.139621 | − | 0.990205i | \(-0.544588\pi\) |
0.927353 | − | 0.374187i | \(-0.122078\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3570.15 | − | 6183.67i | −0.800262 | − | 1.38609i | −0.919444 | − | 0.393222i | \(-0.871361\pi\) |
0.119182 | − | 0.992872i | \(-0.461973\pi\) | |||||||
\(272\) | −152.068 | −0.0338988 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3139.59 | −0.692225 | ||||||||
\(275\) | 2125.05 | + | 3680.69i | 0.465983 | + | 0.807106i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −660.257 | + | 1143.60i | −0.143217 | + | 0.248059i | −0.928706 | − | 0.370816i | \(-0.879078\pi\) |
0.785490 | + | 0.618875i | \(0.212411\pi\) | |||||||
\(278\) | 161.497 | + | 279.720i | 0.0348414 | + | 0.0603471i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 204.309 | 0.0433738 | 0.0216869 | − | 0.999765i | \(-0.493096\pi\) | ||||
0.0216869 | + | 0.999765i | \(0.493096\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 487.897 | − | 845.062i | 0.102482 | − | 0.177504i | −0.810225 | − | 0.586120i | \(-0.800655\pi\) |
0.912707 | + | 0.408615i | \(0.133988\pi\) | |||||||
\(284\) | −833.651 | + | 1443.93i | −0.174183 | + | 0.301695i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4940.87 | 1.02154 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2446.15 | + | 4236.86i | 0.497893 | + | 0.862376i | ||||
\(290\) | −1120.95 | + | 1941.54i | −0.226981 | + | 0.393142i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −693.054 | − | 1200.41i | −0.138897 | − | 0.240577i | ||||
\(293\) | 607.919 | 0.121212 | 0.0606058 | − | 0.998162i | \(-0.480697\pi\) | ||||
0.0606058 | + | 0.998162i | \(0.480697\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3821.36 | −0.754198 | ||||||||
\(296\) | −146.485 | − | 253.719i | −0.0287643 | − | 0.0498213i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2211.07 | − | 3829.69i | 0.429812 | − | 0.744456i | ||||
\(299\) | −3500.34 | − | 6062.76i | −0.677023 | − | 1.17264i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6039.37 | 1.15075 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2048.78 | + | 3548.60i | −0.386532 | + | 0.669493i | ||||
\(305\) | 1105.14 | − | 1914.16i | 0.207476 | − | 0.359359i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8037.08 | −1.49414 | −0.747069 | − | 0.664747i | \(-0.768539\pi\) | ||||
−0.747069 | + | 0.664747i | \(0.768539\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1303.10 | − | 2257.03i | −0.238745 | − | 0.413518i | ||||
\(311\) | −2655.80 | + | 4599.98i | −0.484234 | + | 0.838718i | −0.999836 | − | 0.0181104i | \(-0.994235\pi\) |
0.515602 | + | 0.856828i | \(0.327568\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −765.804 | − | 1326.41i | −0.138293 | − | 0.239531i | 0.788557 | − | 0.614961i | \(-0.210828\pi\) |
−0.926851 | + | 0.375430i | \(0.877495\pi\) | |||||||
\(314\) | 3788.23 | 0.680835 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −343.747 | −0.0611939 | ||||||||
\(317\) | 2109.59 | + | 3653.92i | 0.373775 | + | 0.647397i | 0.990143 | − | 0.140061i | \(-0.0447300\pi\) |
−0.616368 | + | 0.787458i | \(0.711397\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4413.09 | + | 7643.70i | −0.774564 | + | 1.34158i | ||||
\(320\) | 1234.32 | + | 2137.90i | 0.215627 | + | 0.373476i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −557.801 | −0.0960893 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2779.52 | + | 4814.26i | −0.474400 | + | 0.821684i | ||||
\(326\) | −37.6194 | + | 65.1587i | −0.00639124 | + | 0.0110700i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2751.95 | −0.463265 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4149.09 | − | 7186.44i | −0.688987 | − | 1.19336i | −0.972166 | − | 0.234294i | \(-0.924722\pi\) |
0.283179 | − | 0.959067i | \(-0.408611\pi\) | |||||||
\(332\) | 860.996 | − | 1491.29i | 0.142329 | − | 0.246521i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1881.90 | + | 3259.54i | 0.308302 | + | 0.533994i | ||||
\(335\) | 1518.24 | 0.247613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4348.44 | −0.702892 | −0.351446 | − | 0.936208i | \(-0.614310\pi\) | ||||
−0.351446 | + | 0.936208i | \(0.614310\pi\) | |||||||
\(338\) | 732.278 | + | 1268.34i | 0.117842 | + | 0.204109i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −29.2376 | + | 50.6410i | −0.00466362 | + | 0.00807763i | ||||
\(341\) | −5130.20 | − | 8885.77i | −0.814709 | − | 1.41112i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9091.60 | 1.42496 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 73.0145 | − | 126.465i | 0.0113447 | − | 0.0196497i | ||||
\(347\) | −4172.77 | + | 7227.45i | −0.645550 | + | 1.11813i | 0.338624 | + | 0.940922i | \(0.390039\pi\) |
−0.984174 | + | 0.177204i | \(0.943295\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9982.54 | 1.53110 | 0.765549 | − | 0.643378i | \(-0.222468\pi\) | ||||
0.765549 | + | 0.643378i | \(0.222468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2464.70 | + | 4268.98i | 0.373207 | + | 0.646414i | ||||
\(353\) | −4400.79 | + | 7622.40i | −0.663543 | + | 1.14929i | 0.316135 | + | 0.948714i | \(0.397615\pi\) |
−0.979678 | + | 0.200576i | \(0.935719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1342.76 | − | 2325.74i | −0.200751 | − | 0.347711i | ||||
\(356\) | −2031.10 | −0.302383 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8905.56 | 1.31473 | ||||||||
\(359\) | −262.019 | − | 453.831i | −0.0385205 | − | 0.0667194i | 0.846122 | − | 0.532989i | \(-0.178931\pi\) |
−0.884643 | + | 0.466269i | \(0.845598\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4085.64 | + | 7076.53i | −0.595661 | + | 1.03171i | ||||
\(362\) | 2340.94 | + | 4054.63i | 0.339881 | + | 0.588692i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2232.61 | 0.320165 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3181.36 | + | 5510.28i | −0.452495 | + | 0.783745i | −0.998540 | − | 0.0540110i | \(-0.982799\pi\) |
0.546045 | + | 0.837756i | \(0.316133\pi\) | |||||||
\(368\) | −2194.99 | + | 3801.84i | −0.310929 | + | 0.538545i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 123.140 | 0.0173020 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5632.92 | + | 9756.50i | 0.781935 | + | 1.35435i | 0.930813 | + | 0.365495i | \(0.119100\pi\) |
−0.148879 | + | 0.988855i | \(0.547566\pi\) | |||||||
\(374\) | 210.887 | − | 365.267i | 0.0291570 | − | 0.0505014i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3234.48 | + | 5602.28i | 0.443632 | + | 0.768393i | ||||
\(377\) | −11544.5 | −1.57711 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1151.71 | −0.156094 | −0.0780470 | − | 0.996950i | \(-0.524868\pi\) | ||||
−0.0780470 | + | 0.996950i | \(0.524868\pi\) | |||||||
\(380\) | 787.824 | + | 1364.55i | 0.106354 | + | 0.184211i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −486.887 | + | 843.313i | −0.0652129 | + | 0.112952i | ||||
\(383\) | 75.7772 | + | 131.250i | 0.0101097 | + | 0.0175106i | 0.871036 | − | 0.491219i | \(-0.163449\pi\) |
−0.860926 | + | 0.508730i | \(0.830115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3651.08 | −0.481437 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 900.922 | − | 1560.44i | 0.117880 | − | 0.204174i | ||||
\(389\) | 2397.09 | − | 4151.88i | 0.312435 | − | 0.541154i | −0.666454 | − | 0.745546i | \(-0.732189\pi\) |
0.978889 | + | 0.204393i | \(0.0655220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −597.608 | −0.0772950 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4252.76 | − | 7366.00i | −0.543784 | − | 0.941862i | ||||
\(395\) | 276.837 | − | 479.496i | 0.0352638 | − | 0.0610786i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2311.97 | − | 4004.45i | −0.292278 | − | 0.506241i | 0.682070 | − | 0.731287i | \(-0.261080\pi\) |
−0.974348 | + | 0.225046i | \(0.927747\pi\) | |||||||
\(398\) | −794.014 | −0.100001 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3485.96 | 0.435745 | ||||||||
\(401\) | −1805.32 | − | 3126.90i | −0.224821 | − | 0.389402i | 0.731445 | − | 0.681901i | \(-0.238846\pi\) |
−0.956266 | + | 0.292499i | \(0.905513\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6710.19 | − | 11622.4i | 0.829425 | − | 1.43661i | ||||
\(404\) | 947.913 | + | 1641.83i | 0.116734 | + | 0.202189i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 484.794 | 0.0590426 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4479.79 | − | 7759.22i | 0.541592 | − | 0.938065i | −0.457221 | − | 0.889353i | \(-0.651155\pi\) |
0.998813 | − | 0.0487118i | \(-0.0155116\pi\) | |||||||
\(410\) | 578.347 | − | 1001.73i | 0.0696647 | − | 0.120663i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2577.34 | −0.308195 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1386.81 | + | 2402.02i | 0.164038 | + | 0.284122i | ||||
\(416\) | −3223.77 | + | 5583.74i | −0.379948 | + | 0.658089i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5682.48 | − | 9842.34i | −0.664926 | − | 1.15169i | ||||
\(419\) | −7078.28 | −0.825290 | −0.412645 | − | 0.910892i | \(-0.635395\pi\) | ||||
−0.412645 | + | 0.910892i | \(0.635395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11551.5 | 1.33725 | 0.668626 | − | 0.743599i | \(-0.266883\pi\) | ||||
0.668626 | + | 0.743599i | \(0.266883\pi\) | |||||||
\(422\) | 2944.40 | + | 5099.85i | 0.339647 | + | 0.588286i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6982.53 | + | 12094.1i | −0.799768 | + | 1.38524i | ||||
\(425\) | 237.272 | + | 410.966i | 0.0270809 | + | 0.0469054i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −329.750 | −0.0372408 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1910.68 | + | 3309.40i | −0.214282 | + | 0.371147i | ||||
\(431\) | −2032.19 | + | 3519.85i | −0.227116 | + | 0.393377i | −0.956952 | − | 0.290245i | \(-0.906263\pi\) |
0.729836 | + | 0.683622i | \(0.239596\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17456.3 | −1.93740 | −0.968701 | − | 0.248229i | \(-0.920151\pi\) | ||||
−0.968701 | + | 0.248229i | \(0.920151\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1182.41 | + | 2047.99i | 0.129879 | + | 0.224956i | ||||
\(437\) | −8051.45 | + | 13945.5i | −0.881357 | + | 1.52656i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2297.69 | + | 3979.72i | 0.249802 | + | 0.432669i | 0.963471 | − | 0.267814i | \(-0.0863012\pi\) |
−0.713669 | + | 0.700483i | \(0.752968\pi\) | |||||||
\(440\) | −4565.60 | −0.494674 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 551.671 | 0.0593672 | ||||||||
\(443\) | −153.107 | − | 265.189i | −0.0164206 | − | 0.0284413i | 0.857698 | − | 0.514153i | \(-0.171894\pi\) |
−0.874119 | + | 0.485712i | \(0.838560\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1635.75 | − | 2833.21i | 0.174252 | − | 0.301813i | ||||
\(446\) | 3681.05 | + | 6375.77i | 0.390813 | + | 0.676909i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9229.22 | −0.970053 | −0.485026 | − | 0.874500i | \(-0.661190\pi\) | ||||
−0.485026 | + | 0.874500i | \(0.661190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2276.91 | − | 3943.72i | 0.237728 | − | 0.411758i | ||||
\(452\) | 1534.66 | − | 2658.10i | 0.159700 | − | 0.276608i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12811.5 | 1.32439 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5496.12 | + | 9519.55i | 0.562577 | + | 0.974411i | 0.997271 | + | 0.0738330i | \(0.0235232\pi\) |
−0.434694 | + | 0.900578i | \(0.643143\pi\) | |||||||
\(458\) | −4288.50 | + | 7427.90i | −0.437530 | + | 0.757824i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 844.047 | + | 1461.93i | 0.0855519 | + | 0.148180i | ||||
\(461\) | 7387.88 | 0.746394 | 0.373197 | − | 0.927752i | \(-0.378261\pi\) | ||||
0.373197 | + | 0.927752i | \(0.378261\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10163.8 | 1.02020 | 0.510101 | − | 0.860114i | \(-0.329608\pi\) | ||||
0.510101 | + | 0.860114i | \(0.329608\pi\) | |||||||
\(464\) | 3619.65 | + | 6269.42i | 0.362151 | + | 0.627264i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7462.75 | − | 12925.9i | 0.741857 | − | 1.28493i | ||||
\(467\) | 7907.29 | + | 13695.8i | 0.783524 | + | 1.35710i | 0.929877 | + | 0.367871i | \(0.119913\pi\) |
−0.146353 | + | 0.989232i | \(0.546754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2719.02 | −0.266849 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10341.3 | + | 17911.7i | −1.00847 | + | 1.74672i | ||||
\(473\) | −7522.22 | + | 13028.9i | −0.731230 | + | 1.26653i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12786.9 | 1.23516 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 877.485 | + | 1519.85i | 0.0839649 | + | 0.145432i | ||||
\(479\) | 722.427 | − | 1251.28i | 0.0689113 | − | 0.119358i | −0.829511 | − | 0.558490i | \(-0.811381\pi\) |
0.898422 | + | 0.439132i | \(0.144714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 317.050 | + | 549.146i | 0.0300545 | + | 0.0520559i | ||||
\(482\) | 2848.43 | 0.269175 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −930.742 | −0.0874100 | ||||||||
\(485\) | 1451.12 | + | 2513.41i | 0.135860 | + | 0.235316i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 244.701 | − | 423.835i | 0.0227689 | − | 0.0394369i | −0.854416 | − | 0.519589i | \(-0.826085\pi\) |
0.877185 | + | 0.480152i | \(0.159418\pi\) | |||||||
\(488\) | −5981.44 | − | 10360.2i | −0.554851 | − | 0.961029i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3941.30 | 0.362257 | 0.181129 | − | 0.983459i | \(-0.442025\pi\) | ||||
0.181129 | + | 0.983459i | \(0.442025\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −492.743 | + | 853.455i | −0.0450142 | + | 0.0779669i | ||||
\(494\) | 7432.56 | − | 12873.6i | 0.676936 | − | 1.17249i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8415.65 | −0.761843 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.54470 | − | 9.60371i | −0.000497425 | − | 0.000861565i | 0.865777 | − | 0.500431i | \(-0.166825\pi\) |
−0.866274 | + | 0.499569i | \(0.833492\pi\) | |||||||
\(500\) | 1473.49 | − | 2552.16i | 0.131793 | − | 0.228273i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5876.42 | + | 10178.3i | 0.522465 | + | 0.904936i | ||||
\(503\) | 7088.41 | 0.628343 | 0.314172 | − | 0.949366i | \(-0.398273\pi\) | ||||
0.314172 | + | 0.949366i | \(0.398273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3053.61 | −0.269077 | ||||||||
\(506\) | −6088.01 | − | 10544.7i | −0.534871 | − | 0.926424i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −758.605 | + | 1313.94i | −0.0662553 | + | 0.114757i | ||||
\(509\) | −8794.22 | − | 15232.0i | −0.765810 | − | 1.32642i | −0.939817 | − | 0.341677i | \(-0.889005\pi\) |
0.174008 | − | 0.984744i | \(-0.444328\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10627.5 | 0.917333 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3147.86 | − | 5452.25i | 0.270129 | − | 0.467877i | ||||
\(515\) | 2075.66 | − | 3595.15i | 0.177601 | − | 0.307614i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10704.6 | −0.910613 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2985.85 | − | 5171.65i | −0.251804 | − | 0.436138i | ||||
\(521\) | 5823.30 | − | 10086.2i | 0.489680 | − | 0.848151i | −0.510249 | − | 0.860026i | \(-0.670447\pi\) |
0.999929 | + | 0.0118758i | \(0.00378028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4482.91 | + | 7764.63i | 0.374807 | + | 0.649185i | 0.990298 | − | 0.138959i | \(-0.0443757\pi\) |
−0.615491 | + | 0.788144i | \(0.711042\pi\) | |||||||
\(524\) | −4229.75 | −0.352629 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9331.22 | −0.773499 | ||||||||
\(527\) | −572.811 | − | 992.137i | −0.0473473 | − | 0.0820079i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2542.54 | + | 4403.81i | −0.208970 | + | 0.361947i | ||||
\(530\) | −2934.88 | − | 5083.36i | −0.240534 | − | 0.416617i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5956.30 | 0.484045 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 265.565 | − | 459.971i | 0.0214605 | − | 0.0371706i | ||||
\(536\) | 4108.64 | − | 7116.37i | 0.331094 | − | 0.573471i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15812.6 | 1.26715 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 97.6359 | + | 169.110i | 0.00775914 | + | 0.0134392i | 0.869879 | − | 0.493265i | \(-0.164197\pi\) |
−0.862120 | + | 0.506705i | \(0.830863\pi\) | |||||||
\(542\) | 8121.79 | − | 14067.3i | 0.643654 | − | 1.11484i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 275.195 | + | 476.652i | 0.0216891 | + | 0.0375667i | ||||
\(545\) | −3809.01 | −0.299376 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1399.26 | −0.109375 | −0.0546874 | − | 0.998504i | \(-0.517416\pi\) | ||||
−0.0546874 | + | 0.998504i | \(0.517416\pi\) | |||||||
\(548\) | 1949.21 | + | 3376.12i | 0.151945 | + | 0.263177i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4834.31 | + | 8373.27i | −0.374792 | + | 0.649159i | ||||
\(551\) | 13277.2 | + | 22996.9i | 1.02655 | + | 1.77804i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3004.06 | −0.230380 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 200.529 | − | 347.327i | 0.0152956 | − | 0.0264927i | ||||
\(557\) | 21.5233 | − | 37.2795i | 0.00163730 | − | 0.00283588i | −0.865206 | − | 0.501417i | \(-0.832812\pi\) |
0.866843 | + | 0.498581i | \(0.166145\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19677.8 | −1.48888 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 232.393 | + | 402.516i | 0.0174429 | + | 0.0302120i | ||||
\(563\) | 9616.43 | − | 16656.1i | 0.719865 | − | 1.24684i | −0.241187 | − | 0.970479i | \(-0.577537\pi\) |
0.961053 | − | 0.276365i | \(-0.0891298\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2471.88 | + | 4281.41i | 0.184058 | + | 0.318797i | ||||
\(566\) | 2219.85 | 0.164854 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14535.1 | −1.07373 | ||||||||
\(569\) | 2581.99 | + | 4472.14i | 0.190233 | + | 0.329493i | 0.945327 | − | 0.326123i | \(-0.105742\pi\) |
−0.755094 | + | 0.655616i | \(0.772409\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5115.96 | − | 8861.10i | 0.374950 | − | 0.649432i | −0.615370 | − | 0.788238i | \(-0.710993\pi\) |
0.990319 | + | 0.138807i | \(0.0443267\pi\) | |||||||
\(572\) | −3067.53 | − | 5313.11i | −0.224230 | − | 0.388378i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13699.4 | 0.993572 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8281.87 | − | 14344.6i | 0.597537 | − | 1.03496i | −0.395647 | − | 0.918403i | \(-0.629480\pi\) |
0.993184 | − | 0.116561i | \(-0.0371871\pi\) | |||||||
\(578\) | −5564.79 | + | 9638.49i | −0.400458 | + | 0.693613i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2783.75 | 0.199291 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11554.4 | − | 20012.8i | −0.820815 | − | 1.42169i | ||||
\(584\) | 6041.86 | − | 10464.8i | 0.428106 | − | 0.741501i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 691.482 | + | 1197.68i | 0.0487455 | + | 0.0844297i | ||||
\(587\) | 16020.6 | 1.12648 | 0.563239 | − | 0.826294i | \(-0.309555\pi\) | ||||
0.563239 | + | 0.826294i | \(0.309555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30869.4 | −2.15951 | ||||||||
\(590\) | −4346.64 | − | 7528.60i | −0.303302 | − | 0.525335i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 198.816 | − | 344.359i | 0.0138028 | − | 0.0239072i | ||||
\(593\) | 3385.57 | + | 5863.98i | 0.234450 | + | 0.406079i | 0.959113 | − | 0.283025i | \(-0.0913378\pi\) |
−0.724663 | + | 0.689104i | \(0.758004\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5490.95 | −0.377379 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7962.98 | − | 13792.3i | 0.544532 | − | 0.943158i | ||||
\(599\) | 5535.11 | − | 9587.09i | 0.377560 | − | 0.653953i | −0.613147 | − | 0.789969i | \(-0.710097\pi\) |
0.990707 | + | 0.136016i | \(0.0434299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24187.7 | 1.64166 | 0.820830 | − | 0.571173i | \(-0.193511\pi\) | ||||
0.820830 | + | 0.571173i | \(0.193511\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3749.52 | − | 6494.37i | −0.252593 | − | 0.437503i | ||||
\(605\) | 749.574 | − | 1298.30i | 0.0503711 | − | 0.0872453i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5037.04 | − | 8724.40i | −0.336816 | − | 0.583382i | 0.647016 | − | 0.762476i | \(-0.276017\pi\) |
−0.983832 | + | 0.179095i | \(0.942683\pi\) | |||||||
\(608\) | 14830.6 | 0.989243 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5028.21 | 0.333748 | ||||||||
\(611\) | −7000.67 | − | 12125.5i | −0.463530 | − | 0.802858i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5557.29 | − | 9625.51i | 0.366161 | − | 0.634210i | −0.622800 | − | 0.782381i | \(-0.714005\pi\) |
0.988962 | + | 0.148171i | \(0.0473385\pi\) | |||||||
\(614\) | −9141.84 | − | 15834.1i | −0.600871 | − | 1.04074i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20496.4 | −1.33737 | −0.668683 | − | 0.743548i | \(-0.733142\pi\) | ||||
−0.668683 | + | 0.743548i | \(0.733142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8357.22 | + | 14475.1i | −0.542658 | + | 0.939910i | 0.456093 | + | 0.889932i | \(0.349249\pi\) |
−0.998750 | + | 0.0499782i | \(0.984085\pi\) | |||||||
\(620\) | −1618.05 | + | 2802.54i | −0.104810 | + | 0.181537i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12083.5 | −0.778943 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4145.33 | − | 7179.92i | −0.265301 | − | 0.459515i | ||||
\(626\) | 1742.14 | − | 3017.48i | 0.111230 | − | 0.192656i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2351.91 | − | 4073.63i | −0.149445 | − | 0.258846i | ||||
\(629\) | 54.1295 | 0.00343129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9168.53 | 0.578437 | 0.289218 | − | 0.957263i | \(-0.406605\pi\) | ||||
0.289218 | + | 0.957263i | \(0.406605\pi\) | |||||||
\(632\) | −1498.35 | − | 2595.21i | −0.0943054 | − | 0.163342i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4799.15 | + | 8312.37i | −0.300629 | + | 0.520704i | ||||
\(635\) | −1221.89 | − | 2116.37i | −0.0763608 | − | 0.132261i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −20078.9 | −1.24597 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −606.411 | + | 1050.33i | −0.0374539 | + | 0.0648721i | ||||
\(641\) | −2136.68 | + | 3700.84i | −0.131660 | + | 0.228041i | −0.924316 | − | 0.381627i | \(-0.875364\pi\) |
0.792657 | + | 0.609668i | \(0.208697\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2955.75 | −0.181281 | −0.0906404 | − | 0.995884i | \(-0.528891\pi\) | ||||
−0.0906404 | + | 0.995884i | \(0.528891\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −634.475 | − | 1098.94i | −0.0386426 | − | 0.0669309i | ||||
\(647\) | −11350.6 | + | 19659.8i | −0.689704 | + | 1.19460i | 0.282229 | + | 0.959347i | \(0.408926\pi\) |
−0.971934 | + | 0.235256i | \(0.924407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17112.4 | − | 29639.6i | −1.03501 | − | 1.79269i | ||||
\(650\) | −12646.3 | −0.763124 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 93.4235 | 0.00561158 | ||||||||
\(653\) | 768.907 | + | 1331.79i | 0.0460791 | + | 0.0798113i | 0.888145 | − | 0.459563i | \(-0.151994\pi\) |
−0.842066 | + | 0.539375i | \(0.818661\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3406.44 | − | 5900.12i | 0.203207 | − | 0.351964i | ||||
\(656\) | −1867.54 | − | 3234.67i | −0.111151 | − | 0.192519i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12338.1 | −0.729323 | −0.364661 | − | 0.931140i | \(-0.618815\pi\) | ||||
−0.364661 | + | 0.931140i | \(0.618815\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 922.548 | − | 1597.90i | 0.0542859 | − | 0.0940259i | −0.837605 | − | 0.546276i | \(-0.816045\pi\) |
0.891891 | + | 0.452250i | \(0.149378\pi\) | |||||||
\(662\) | 9438.84 | − | 16348.6i | 0.554156 | − | 0.959826i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15011.8 | 0.877369 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14224.8 | + | 24638.0i | 0.825765 | + | 1.43027i | ||||
\(668\) | 2336.74 | − | 4047.35i | 0.135346 | − | 0.234426i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1726.93 | + | 2991.14i | 0.0995780 | + | 0.172474i | ||||
\(671\) | 19795.7 | 1.13890 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23955.4 | 1.37208 | 0.686041 | − | 0.727563i | \(-0.259347\pi\) | ||||
0.686041 | + | 0.727563i | \(0.259347\pi\) | |||||||
\(674\) | −4946.17 | − | 8567.02i | −0.282670 | − | 0.489598i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 909.265 | − | 1574.89i | 0.0517333 | − | 0.0896048i | ||||
\(677\) | 1839.13 | + | 3185.46i | 0.104407 | + | 0.180838i | 0.913496 | − | 0.406848i | \(-0.133372\pi\) |
−0.809089 | + | 0.587686i | \(0.800039\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −509.771 | −0.0287482 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 11670.8 | − | 20214.4i | 0.655275 | − | 1.13497i | ||||
\(683\) | 2195.43 | − | 3802.60i | 0.122996 | − | 0.213034i | −0.797952 | − | 0.602721i | \(-0.794083\pi\) |
0.920948 | + | 0.389686i | \(0.127417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6279.18 | −0.350241 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6169.78 | + | 10686.4i | 0.341890 | + | 0.592171i | ||||
\(689\) | 15112.9 | − | 26176.4i | 0.835641 | − | 1.44737i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5185.84 | + | 8982.13i | 0.285497 | + | 0.494496i | 0.972730 | − | 0.231942i | \(-0.0745079\pi\) |
−0.687232 | + | 0.726438i | \(0.741175\pi\) | |||||||
\(692\) | −181.323 | −0.00996081 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18985.4 | −1.03844 | ||||||||
\(695\) | 322.993 | + | 559.440i | 0.0176285 | + | 0.0305335i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 254.228 | − | 440.335i | 0.0138157 | − | 0.0239295i | ||||
\(698\) | 11354.7 | + | 19667.0i | 0.615734 | + | 1.06648i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −109.675 | −0.00590922 | −0.00295461 | − | 0.999996i | \(-0.500940\pi\) | ||||
−0.00295461 | + | 0.999996i | \(0.500940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 729.275 | − | 1263.14i | 0.0391254 | − | 0.0677672i | ||||
\(704\) | −11054.8 | + | 19147.5i | −0.591822 | + | 1.02507i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20022.9 | −1.06738 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13459.4 | − | 23312.3i | −0.712944 | − | 1.23486i | −0.963747 | − | 0.266818i | \(-0.914028\pi\) |
0.250803 | − | 0.968038i | \(-0.419306\pi\) | |||||||
\(710\) | 3054.68 | − | 5290.86i | 0.161465 | − | 0.279665i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8853.31 | − | 15334.4i | −0.466000 | − | 0.807135i | ||||
\(713\) | −33072.4 | −1.73713 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9881.74 | 0.516862 | ||||||||
\(716\) | −5528.99 | − | 9576.50i | −0.288587 | − | 0.499847i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 596.072 | − | 1032.43i | 0.0309822 | − | 0.0536627i | ||||
\(719\) | −7585.38 | − | 13138.3i | −0.393445 | − | 0.681466i | 0.599457 | − | 0.800407i | \(-0.295383\pi\) |
−0.992901 | + | 0.118941i | \(0.962050\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18589.0 | −0.958185 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2906.73 | − | 5034.61i | 0.149210 | − | 0.258439i | ||||
\(725\) | 11295.5 | − | 19564.3i | 0.578626 | − | 1.00221i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33286.9 | 1.69813 | 0.849066 | − | 0.528288i | \(-0.177166\pi\) | ||||
0.849066 | + | 0.528288i | \(0.177166\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2539.50 | + | 4398.54i | 0.128755 | + | 0.223010i | ||||
\(731\) | −839.890 | + | 1454.73i | −0.0424959 | + | 0.0736050i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10272.0 | + | 17791.7i | 0.517607 | + | 0.896521i | 0.999791 | + | 0.0204512i | \(0.00651026\pi\) |
−0.482184 | + | 0.876070i | \(0.660156\pi\) | |||||||
\(734\) | −14474.7 | −0.727888 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15889.0 | 0.795755 | ||||||||
\(737\) | 6798.82 | + | 11775.9i | 0.339807 | + | 0.588563i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17178.6 | + | 29754.2i | −0.855109 | + | 1.48109i | 0.0214356 | + | 0.999770i | \(0.493176\pi\) |
−0.876544 | + | 0.481321i | \(0.840157\pi\) | |||||||
\(740\) | −76.4512 | − | 132.417i | −0.00379784 | − | 0.00657805i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8166.99 | −0.403254 | −0.201627 | − | 0.979462i | \(-0.564623\pi\) | ||||
−0.201627 | + | 0.979462i | \(0.564623\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4422.14 | − | 7659.38i | 0.217470 | − | 0.376668i | ||||
\(746\) | −12814.4 | + | 22195.2i | −0.628914 | + | 1.08931i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −523.715 | −0.0256001 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8540.05 | − | 14791.8i | −0.414954 | − | 0.718722i | 0.580469 | − | 0.814282i | \(-0.302869\pi\) |
−0.995424 | + | 0.0955601i | \(0.969536\pi\) | |||||||
\(752\) | −4389.99 | + | 7603.68i | −0.212881 | + | 0.368720i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13131.3 | − | 22744.2i | −0.634238 | − | 1.09853i | ||||
\(755\) | 12078.7 | 0.582239 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16324.0 | −0.783758 | −0.391879 | − | 0.920017i | \(-0.628175\pi\) | ||||
−0.391879 | + | 0.920017i | \(0.628175\pi\) | |||||||
\(758\) | −1310.03 | − | 2269.03i | −0.0627735 | − | 0.108727i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6868.04 | + | 11895.8i | −0.327802 | + | 0.567770i | ||||
\(761\) | 16183.1 | + | 28029.9i | 0.770875 | + | 1.33520i | 0.937084 | + | 0.349105i | \(0.113514\pi\) |
−0.166208 | + | 0.986091i | \(0.553152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1209.13 | 0.0572576 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −172.387 | + | 298.583i | −0.00813131 | + | 0.0140838i | ||||
\(767\) | 22382.7 | − | 38767.9i | 1.05370 | − | 1.82507i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7948.44 | 0.372728 | 0.186364 | − | 0.982481i | \(-0.440330\pi\) | ||||
0.186364 | + | 0.982481i | \(0.440330\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2266.76 | + | 3926.14i | 0.105677 | + | 0.183038i | ||||
\(773\) | −8909.64 | + | 15432.0i | −0.414564 | + | 0.718045i | −0.995383 | − | 0.0959876i | \(-0.969399\pi\) |
0.580819 | + | 0.814033i | \(0.302732\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13130.9 | + | 22743.4i | 0.608616 | + | 1.05415i | ||||
\(776\) | 15708.0 | 0.726655 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10906.4 | 0.502586 | ||||||||
\(779\) | −6850.32 | − | 11865.1i | −0.315068 | − | 0.545714i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12026.0 | − | 20829.7i | 0.550993 | − | 0.954349i | ||||
\(782\) | −679.754 | − | 1177.37i | −0.0310844 | − | 0.0538397i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7576.46 | 0.344478 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1456.19 | − | 2522.19i | 0.0659562 | − | 0.114240i | −0.831162 | − | 0.556031i | \(-0.812324\pi\) |
0.897118 | + | 0.441791i | \(0.145657\pi\) | |||||||
\(788\) | −5280.63 | + | 9146.32i | −0.238724 | + | 0.413482i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1259.56 | 0.0567256 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12946.2 | + | 22423.4i | 0.579738 | + | 1.00414i | ||||
\(794\) | 5259.54 | − | 9109.79i | 0.235081 | − | 0.407172i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 492.961 | + | 853.834i | 0.0219504 | + | 0.0380193i | ||||
\(797\) | −33789.1 | −1.50172 | −0.750861 | − | 0.660460i | \(-0.770361\pi\) | ||||
−0.750861 | + | 0.660460i | \(0.770361\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1195.22 | −0.0529208 | ||||||||
\(800\) | −6308.49 | − | 10926.6i | −0.278798 | − | 0.482893i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4106.95 | − | 7113.44i | 0.180825 | − | 0.313197i | ||||
\(803\) | 9997.83 | + | 17316.7i | 0.439372 | + | 0.761015i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30530.2 | 1.33422 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8263.65 | + | 14313.1i | −0.359795 | + | 0.623183i | ||||
\(809\) | 626.064 | − | 1084.37i | 0.0272079 | − | 0.0471255i | −0.852101 | − | 0.523378i | \(-0.824672\pi\) |
0.879309 | + | 0.476252i | \(0.158005\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31913.1 | 1.38178 | 0.690889 | − | 0.722961i | \(-0.257219\pi\) | ||||
0.690889 | + | 0.722961i | \(0.257219\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 551.433 | + | 955.110i | 0.0237441 | + | 0.0411260i | ||||
\(815\) | −75.2387 | + | 130.317i | −0.00323374 | + | 0.00560100i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22631.3 | + | 39198.6i | 0.969120 | + | 1.67856i | ||||
\(818\) | 20382.3 | 0.871210 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1436.26 | −0.0611663 | ||||||||
\(821\) | 15371.2 | + | 26623.7i | 0.653421 | + | 1.13176i | 0.982287 | + | 0.187382i | \(0.0600001\pi\) |
−0.328866 | + | 0.944376i | \(0.606667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6911.28 | − | 11970.7i | 0.292724 | − | 0.507014i | −0.681729 | − | 0.731605i | \(-0.738771\pi\) |
0.974453 | + | 0.224592i | \(0.0721048\pi\) | |||||||
\(824\) | −11234.3 | − | 19458.3i | −0.474956 | − | 0.822648i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42107.1 | 1.77051 | 0.885253 | − | 0.465110i | \(-0.153985\pi\) | ||||
0.885253 | + | 0.465110i | \(0.153985\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19381.9 | + | 33570.4i | −0.812015 | + | 1.40645i | 0.0994360 | + | 0.995044i | \(0.468296\pi\) |
−0.911451 | + | 0.411408i | \(0.865037\pi\) | |||||||
\(830\) | −3154.87 | + | 5464.40i | −0.131936 | + | 0.228521i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −28918.8 | −1.20502 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3763.79 | + | 6519.08i | 0.155990 | + | 0.270182i | ||||
\(836\) | −7055.90 | + | 12221.2i | −0.291906 | + | 0.505596i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8051.25 | − | 13945.2i | −0.331892 | − | 0.574854i | ||||
\(839\) | 16896.3 | 0.695262 | 0.347631 | − | 0.937631i | \(-0.386986\pi\) | ||||
0.347631 | + | 0.937631i | \(0.386986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22525.7 | 0.923601 | ||||||||
\(842\) | 13139.3 | + | 22757.9i | 0.537779 | + | 0.931461i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3656.05 | − | 6332.46i | 0.149107 | − | 0.258261i | ||||
\(845\) | 1464.56 | + | 2536.68i | 0.0596240 | + | 0.103272i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −18954.0 | −0.767552 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −539.773 | + | 934.915i | −0.0217813 | + | 0.0377262i | ||||
\(851\) | 781.320 | − | 1353.29i | 0.0314727 | − | 0.0545124i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46429.3 | −1.86367 | −0.931833 | − | 0.362887i | \(-0.881791\pi\) | ||||
−0.931833 | + | 0.362887i | \(0.881791\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1437.34 | − | 2489.54i | −0.0573915 | − | 0.0994050i | ||||
\(857\) | −10603.2 | + | 18365.3i | −0.422636 | + | 0.732027i | −0.996196 | − | 0.0871364i | \(-0.972228\pi\) |
0.573561 | + | 0.819163i | \(0.305562\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6938.09 | + | 12017.1i | 0.275581 | + | 0.477321i | 0.970282 | − | 0.241978i | \(-0.0777963\pi\) |
−0.694700 | + | 0.719299i | \(0.744463\pi\) | |||||||
\(860\) | 4744.96 | 0.188142 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9246.12 | −0.365341 | ||||||||
\(863\) | 7168.53 | + | 12416.3i | 0.282757 | + | 0.489750i | 0.972063 | − | 0.234721i | \(-0.0754176\pi\) |
−0.689306 | + | 0.724471i | \(0.742084\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 146.029 | − | 252.930i | 0.00574004 | − | 0.00994204i | ||||
\(866\) | −19855.8 | − | 34391.2i | −0.779131 | − | 1.34949i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4958.81 | 0.193574 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8892.70 | + | 15402.6i | −0.345945 | + | 0.599193i | ||||
\(872\) | −10307.9 | + | 17853.8i | −0.400309 | + | 0.693356i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −36632.8 | −1.41776 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12184.6 | + | 21104.4i | 0.469152 | + | 0.812595i | 0.999378 | − | 0.0352614i | \(-0.0112264\pi\) |
−0.530226 | + | 0.847856i | \(0.677893\pi\) | |||||||
\(878\) | −5227.07 | + | 9053.54i | −0.200917 | + | 0.347998i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3098.32 | − | 5366.45i | −0.118687 | − | 0.205572i | ||||
\(881\) | −26127.0 | −0.999140 | −0.499570 | − | 0.866273i | \(-0.666509\pi\) | ||||
−0.499570 | + | 0.866273i | \(0.666509\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15713.1 | −0.598855 | −0.299428 | − | 0.954119i | \(-0.596796\pi\) | ||||
−0.299428 | + | 0.954119i | \(0.596796\pi\) | |||||||
\(884\) | −342.503 | − | 593.233i | −0.0130313 | − | 0.0225708i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 348.305 | − | 603.283i | 0.0132072 | − | 0.0228755i | ||||
\(887\) | −6569.74 | − | 11379.1i | −0.248692 | − | 0.430748i | 0.714471 | − | 0.699665i | \(-0.246667\pi\) |
−0.963163 | + | 0.268917i | \(0.913334\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7442.40 | 0.280303 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4570.74 | − | 7916.75i | 0.171569 | − | 0.297166i | ||||
\(893\) | −16102.9 | + | 27891.0i | −0.603430 | + | 1.04517i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17811.1 | 0.665207 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10497.9 | − | 18182.8i | −0.390109 | − | 0.675689i | ||||
\(899\) | −27269.0 | + | 47231.4i | −1.01165 | + | 1.75223i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1290.10 | − | 2234.53i | −0.0477021 | − | 0.0826225i | ||||
\(902\) | 10359.6 | 0.382412 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26757.4 | 0.984446 | ||||||||
\(905\) | 4681.88 | + | 8109.25i | 0.171968 | + | 0.297857i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1899.85 | − | 3290.64i | 0.0695519 | − | 0.120467i | −0.829152 | − | 0.559023i | \(-0.811176\pi\) |
0.898704 | + | 0.438555i | \(0.144510\pi\) | |||||||
\(908\) | −7953.96 | − | 13776.7i | −0.290706 | − | 0.503518i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51528.4 | 1.87400 | 0.936998 | − | 0.349334i | \(-0.113592\pi\) | ||||
0.936998 | + | 0.349334i | \(0.113592\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12420.5 | + | 21513.0i | −0.450229 | + | 0.779819i | ||||
\(914\) | −12503.2 | + | 21656.2i | −0.452483 | + | 0.783723i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10650.0 | 0.384156 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8492.37 | + | 14709.2i | 0.304828 | + | 0.527978i | 0.977223 | − | 0.212214i | \(-0.0680675\pi\) |
−0.672395 | + | 0.740193i | \(0.734734\pi\) | |||||||
\(920\) | −7358.17 | + | 12744.7i | −0.263687 | + | 0.456719i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8403.41 | + | 14555.1i | 0.300164 | + | 0.519900i | ||||
\(923\) | 31459.6 | 1.12189 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1240.85 | −0.0441068 | ||||||||
\(926\) | 11560.9 | + | 20024.1i | 0.410277 | + | 0.710620i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13100.9 | − | 22691.3i | 0.463423 | − | 0.802672i | ||||
\(929\) | 2725.93 | + | 4721.44i | 0.0962699 | + | 0.166744i | 0.910138 | − | 0.414305i | \(-0.135975\pi\) |
−0.813868 | + | 0.581050i | \(0.802642\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18532.9 | −0.651358 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17988.4 | + | 31156.9i | −0.630192 | + | 1.09152i | ||||
\(935\) | 421.774 | − | 730.534i | 0.0147524 | − | 0.0255519i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42429.4 | −1.47930 | −0.739652 | − | 0.672989i | \(-0.765010\pi\) | ||||
−0.739652 | + | 0.672989i | \(0.765010\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1688.09 | + | 2923.86i | 0.0585740 | + | 0.101453i | ||||
\(941\) | 16488.9 | − | 28559.7i | 0.571226 | − | 0.989393i | −0.425214 | − | 0.905093i | \(-0.639801\pi\) |
0.996440 | − | 0.0843003i | \(-0.0268655\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7339.19 | − | 12711.8i | −0.253443 | − | 0.438976i | ||||
\(944\) | −28071.5 | −0.967848 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34224.8 | −1.17626 | ||||||||
\(947\) | −11876.7 | − | 20571.1i | −0.407541 | − | 0.705882i | 0.587073 | − | 0.809534i | \(-0.300280\pi\) |
−0.994614 | + | 0.103653i | \(0.966947\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13076.9 | + | 22649.9i | −0.447308 | + | 0.774760i | ||||
\(950\) | 14544.5 | + | 25191.8i | 0.496722 | + | 0.860349i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28074.3 | 0.954267 | 0.477134 | − | 0.878831i | \(-0.341676\pi\) | ||||
0.477134 | + | 0.878831i | \(0.341676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −973.774 | + | 1686.63i | −0.0329954 | + | 0.0571497i | ||||
\(956\) | 1089.57 | − | 1887.19i | 0.0368610 | − | 0.0638452i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3286.92 | 0.110851 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16804.6 | − | 29106.5i | −0.564084 | − | 0.977022i | ||||
\(962\) | −721.262 | + | 1249.26i | −0.0241730 | + | 0.0418688i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1768.44 | − | 3063.03i | −0.0590847 | − | 0.102338i | ||||
\(965\) | −7302.15 | −0.243590 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11150.3 | −0.370806 | −0.185403 | − | 0.982663i | \(-0.559359\pi\) | ||||
−0.185403 | + | 0.982663i | \(0.559359\pi\) | |||||||
\(968\) | −4056.98 | − | 7026.89i | −0.134707 | − | 0.233319i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3301.17 | + | 5717.80i | −0.109272 | + | 0.189265i | ||||
\(971\) | −3029.52 | − | 5247.29i | −0.100126 | − | 0.173423i | 0.811611 | − | 0.584199i | \(-0.198591\pi\) |
−0.911736 | + | 0.410776i | \(0.865258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1113.35 | 0.0366263 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8118.29 | − | 14061.3i | 0.266250 | − | 0.461159i | ||||
\(977\) | 2850.24 | − | 4936.77i | 0.0933341 | − | 0.161659i | −0.815578 | − | 0.578647i | \(-0.803581\pi\) |
0.908912 | + | 0.416988i | \(0.136914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29300.2 | 0.956526 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4483.06 | + | 7764.89i | 0.145683 | + | 0.252330i | ||||
\(983\) | −98.7401 | + | 171.023i | −0.00320378 | + | 0.00554912i | −0.867623 | − | 0.497223i | \(-0.834353\pi\) |
0.864419 | + | 0.502772i | \(0.167686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8505.52 | − | 14732.0i | −0.275136 | − | 0.476549i | ||||
\(986\) | −2241.90 | −0.0724103 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18457.9 | −0.594357 | ||||||||
\(989\) | 24246.4 | + | 41996.0i | 0.779567 | + | 1.35025i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10310.4 | + | 17858.1i | −0.330495 | + | 0.572434i | −0.982609 | − | 0.185687i | \(-0.940549\pi\) |
0.652114 | + | 0.758121i | \(0.273882\pi\) | |||||||
\(992\) | 15229.7 | + | 26378.6i | 0.487442 | + | 0.844275i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1588.03 | −0.0505969 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9663.41 | − | 16737.5i | 0.306964 | − | 0.531678i | −0.670733 | − | 0.741699i | \(-0.734020\pi\) |
0.977697 | + | 0.210022i | \(0.0673535\pi\) | |||||||
\(998\) | 12.6137 | − | 21.8476i | 0.000400081 | − | 0.000692961i | ||||
\(999\) | 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 | 441.4.e.p.361.2 | 4 | ||
3.2 | odd | 2 | 147.4.e.m.67.1 | 4 | |||
7.2 | even | 3 | inner | 441.4.e.p.226.2 | 4 | ||
7.3 | odd | 6 | 63.4.a.e.1.1 | 2 | |||
7.4 | even | 3 | 441.4.a.r.1.1 | 2 | |||
7.5 | odd | 6 | 441.4.e.q.226.2 | 4 | |||
7.6 | odd | 2 | 441.4.e.q.361.2 | 4 | |||
21.2 | odd | 6 | 147.4.e.m.79.1 | 4 | |||
21.5 | even | 6 | 147.4.e.l.79.1 | 4 | |||
21.11 | odd | 6 | 147.4.a.i.1.2 | 2 | |||
21.17 | even | 6 | 21.4.a.c.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 147.4.e.l.67.1 | 4 | |||
28.3 | even | 6 | 1008.4.a.ba.1.2 | 2 | |||
35.24 | odd | 6 | 1575.4.a.p.1.2 | 2 | |||
84.11 | even | 6 | 2352.4.a.bz.1.2 | 2 | |||
84.59 | odd | 6 | 336.4.a.m.1.1 | 2 | |||
105.17 | odd | 12 | 525.4.d.g.274.3 | 4 | |||
105.38 | odd | 12 | 525.4.d.g.274.2 | 4 | |||
105.59 | even | 6 | 525.4.a.n.1.1 | 2 | |||
168.59 | odd | 6 | 1344.4.a.bo.1.2 | 2 | |||
168.101 | even | 6 | 1344.4.a.bg.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.c.1.2 | ✓ | 2 | 21.17 | even | 6 | ||
63.4.a.e.1.1 | 2 | 7.3 | odd | 6 | |||
147.4.a.i.1.2 | 2 | 21.11 | odd | 6 | |||
147.4.e.l.67.1 | 4 | 21.20 | even | 2 | |||
147.4.e.l.79.1 | 4 | 21.5 | even | 6 | |||
147.4.e.m.67.1 | 4 | 3.2 | odd | 2 | |||
147.4.e.m.79.1 | 4 | 21.2 | odd | 6 | |||
336.4.a.m.1.1 | 2 | 84.59 | odd | 6 | |||
441.4.a.r.1.1 | 2 | 7.4 | even | 3 | |||
441.4.e.p.226.2 | 4 | 7.2 | even | 3 | inner | ||
441.4.e.p.361.2 | 4 | 1.1 | even | 1 | trivial | ||
441.4.e.q.226.2 | 4 | 7.5 | odd | 6 | |||
441.4.e.q.361.2 | 4 | 7.6 | odd | 2 | |||
525.4.a.n.1.1 | 2 | 105.59 | even | 6 | |||
525.4.d.g.274.2 | 4 | 105.38 | odd | 12 | |||
525.4.d.g.274.3 | 4 | 105.17 | odd | 12 | |||
1008.4.a.ba.1.2 | 2 | 28.3 | even | 6 | |||
1344.4.a.bg.1.2 | 2 | 168.101 | even | 6 | |||
1344.4.a.bo.1.2 | 2 | 168.59 | odd | 6 | |||
1575.4.a.p.1.2 | 2 | 35.24 | odd | 6 | |||
2352.4.a.bz.1.2 | 2 | 84.11 | even | 6 |