Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (of order \(6\), 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: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{11} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.8 | ||
Root | \(-2.81518 - 1.03671i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.17 |
Dual form | 336.4.bc.e.257.8 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.87603 | + | 1.79564i | 0.938393 | + | 0.345571i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.90442 | − | 17.1550i | −0.885879 | − | 1.53439i | −0.844703 | − | 0.535235i | \(-0.820223\pi\) |
−0.0411754 | − | 0.999152i | \(-0.513110\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.4277 | − | 1.84901i | −0.995004 | − | 0.0998373i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 20.5514 | + | 17.5112i | 0.761161 | + | 0.648563i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.28742 | + | 2.47535i | 0.117519 | + | 0.0678495i | 0.557607 | − | 0.830105i | \(-0.311720\pi\) |
−0.440088 | + | 0.897954i | \(0.645053\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.7414i | 0.378505i | 0.981928 | + | 0.189253i | \(0.0606065\pi\) | ||||
−0.981928 | + | 0.189253i | \(0.939394\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −17.4901 | − | 101.433i | −0.301062 | − | 1.74599i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.947671 | + | 1.64141i | −0.0135202 | + | 0.0234177i | −0.872706 | − | 0.488245i | \(-0.837637\pi\) |
0.859186 | + | 0.511663i | \(0.170970\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −83.9968 | + | 48.4956i | −1.01422 | + | 0.585561i | −0.912425 | − | 0.409245i | \(-0.865792\pi\) |
−0.101796 | + | 0.994805i | \(0.532459\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −86.5340 | − | 42.1054i | −0.899203 | − | 0.437531i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −135.935 | + | 78.4822i | −1.23237 | + | 0.711508i | −0.967523 | − | 0.252783i | \(-0.918654\pi\) |
−0.264845 | + | 0.964291i | \(0.585321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −133.695 | + | 231.567i | −1.06956 | + | 1.85254i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 68.7652 | + | 122.288i | 0.490143 | + | 0.871642i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 92.0138i | 0.589191i | 0.955622 | + | 0.294595i | \(0.0951849\pi\) | ||||
−0.955622 | + | 0.294595i | \(0.904815\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −67.3521 | − | 38.8857i | −0.390219 | − | 0.225293i | 0.292036 | − | 0.956407i | \(-0.405667\pi\) |
−0.682255 | + | 0.731114i | \(0.739001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.4608 | + | 19.7685i | 0.0868319 | + | 0.104281i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 150.796 | + | 334.440i | 0.728264 | + | 1.61516i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −124.469 | − | 215.587i | −0.553044 | − | 0.957901i | −0.998053 | − | 0.0623743i | \(-0.980133\pi\) |
0.445009 | − | 0.895526i | \(-0.353201\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −31.8571 | + | 86.5074i | −0.130800 | + | 0.355186i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −343.701 | −1.30920 | −0.654598 | − | 0.755977i | \(-0.727162\pi\) | ||||
−0.654598 | + | 0.755977i | \(0.727162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.5859 | 0.0871934 | 0.0435967 | − | 0.999049i | \(-0.486118\pi\) | ||||
0.0435967 | + | 0.999049i | \(0.486118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 96.8547 | − | 525.996i | 0.320850 | − | 1.74246i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −235.248 | − | 407.461i | −0.730093 | − | 1.26456i | −0.956843 | − | 0.290606i | \(-0.906143\pi\) |
0.226750 | − | 0.973953i | \(-0.427190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 336.162 | + | 68.1462i | 0.980065 | + | 0.198677i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.56826 | + | 6.30191i | −0.0207798 | + | 0.0173028i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 344.910 | + | 199.134i | 0.893907 | + | 0.516097i | 0.875218 | − | 0.483728i | \(-0.160718\pi\) |
0.0186885 | + | 0.999825i | \(0.494051\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 98.0675i | − | 0.240426i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −496.652 | + | 85.6379i | −1.15409 | + | 0.199000i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 335.568 | − | 581.220i | 0.740461 | − | 1.28252i | −0.211825 | − | 0.977308i | \(-0.567941\pi\) |
0.952286 | − | 0.305208i | \(-0.0987261\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −273.703 | + | 158.023i | −0.574494 | + | 0.331684i | −0.758942 | − | 0.651158i | \(-0.774284\pi\) |
0.184448 | + | 0.982842i | \(0.440950\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −346.336 | − | 360.691i | −0.692607 | − | 0.721315i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 304.352 | − | 175.718i | 0.580773 | − | 0.335310i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −116.895 | + | 202.469i | −0.213150 | + | 0.369186i | −0.952699 | − | 0.303917i | \(-0.901706\pi\) |
0.739549 | + | 0.673103i | \(0.235039\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −803.750 | + | 138.591i | −1.40232 | + | 0.241803i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 152.225i | − | 0.254447i | −0.991874 | − | 0.127224i | \(-0.959393\pi\) | ||
0.991874 | − | 0.127224i | \(-0.0406066\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 539.897 | + | 311.709i | 0.865618 | + | 0.499765i | 0.865890 | − | 0.500235i | \(-0.166753\pi\) |
−0.000271580 | 1.00000i | \(0.500086\pi\) | ||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1067.71 | + | 889.059i | −1.64385 | + | 1.36880i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −74.4305 | − | 53.5425i | −0.110158 | − | 0.0792433i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 151.191 | + | 261.870i | 0.215320 | + | 0.372945i | 0.953371 | − | 0.301799i | \(-0.0975873\pi\) |
−0.738052 | + | 0.674744i | \(0.764254\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 115.716 | + | 719.757i | 0.158733 | + | 0.987322i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −856.438 | −1.13261 | −0.566303 | − | 0.824197i | \(-0.691627\pi\) | ||||
−0.566303 | + | 0.824197i | \(0.691627\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 37.5446 | 0.0479092 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −165.224 | + | 448.662i | −0.203607 | + | 0.552892i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −453.577 | − | 785.618i | −0.540214 | − | 0.935678i | −0.998891 | − | 0.0470750i | \(-0.985010\pi\) |
0.458678 | − | 0.888603i | \(-0.348323\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 32.8040 | − | 326.933i | 0.0377889 | − | 0.376614i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −258.586 | − | 310.548i | −0.288324 | − | 0.346262i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1663.88 | + | 960.642i | 1.79695 | + | 1.03747i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 70.3731i | − | 0.0736629i | −0.999321 | − | 0.0368315i | \(-0.988274\pi\) | ||
0.999321 | − | 0.0368315i | \(-0.0117265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 44.7661 | + | 125.950i | 0.0454461 | + | 0.127863i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −119.274 | + | 206.588i | −0.117507 | + | 0.203527i | −0.918779 | − | 0.394772i | \(-0.870823\pi\) |
0.801272 | + | 0.598300i | \(0.204157\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9592 | − | 9.79138i | 0.0162237 | − | 0.00936674i | −0.491866 | − | 0.870671i | \(-0.663685\pi\) |
0.508090 | + | 0.861304i | \(0.330352\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 134.753 | + | 1901.52i | 0.125243 | + | 1.76733i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −419.010 | + | 241.915i | −0.378572 | + | 0.218569i | −0.677197 | − | 0.735802i | \(-0.736805\pi\) |
0.298625 | + | 0.954371i | \(0.403472\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21.4023 | + | 37.0698i | −0.0188070 | + | 0.0325747i | −0.875276 | − | 0.483624i | \(-0.839320\pi\) |
0.856469 | + | 0.516199i | \(0.172653\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −219.799 | − | 1274.71i | −0.187950 | − | 1.09000i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 378.359i | − | 0.314983i | −0.987520 | − | 0.157491i | \(-0.949659\pi\) | ||
0.987520 | − | 0.157491i | \(-0.0503406\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2692.72 | + | 1554.64i | 2.18346 | + | 1.26062i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −310.672 | + | 364.609i | −0.245484 | + | 0.288103i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.4984 | − | 28.4953i | 0.0157906 | − | 0.0219509i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −653.245 | − | 1131.45i | −0.490793 | − | 0.850078i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1675.90 | − | 617.163i | −1.22854 | − | 0.452421i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2820.59 | 2.01825 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −112.805 | −0.0788177 | −0.0394088 | − | 0.999223i | \(-0.512547\pi\) | ||||
−0.0394088 | + | 0.999223i | \(0.512547\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 119.882 | + | 44.1474i | 0.0818216 | + | 0.0301315i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −790.927 | − | 1369.93i | −0.527508 | − | 0.913671i | −0.999486 | − | 0.0320608i | \(-0.989793\pi\) |
0.471977 | − | 0.881611i | \(-0.343540\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1637.54 | − | 738.353i | 1.06761 | − | 0.481378i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1416.77 | − | 2390.86i | 0.903228 | − | 1.52424i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1597.31 | − | 922.210i | −0.996115 | − | 0.575107i | −0.0890187 | − | 0.996030i | \(-0.528373\pi\) |
−0.907097 | + | 0.420923i | \(0.861706\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 55.8671i | 0.0340905i | 0.999855 | + | 0.0170453i | \(0.00542594\pi\) | ||||
−0.999855 | + | 0.0170453i | \(0.994574\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −415.421 | − | 2409.21i | −0.248119 | − | 1.43895i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −43.9160 | + | 76.0647i | −0.0256814 | + | 0.0444815i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1578.49 | − | 911.344i | 0.904046 | − | 0.521951i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1516.77 | + | 935.910i | 0.851029 | + | 0.525119i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2951.20 | + | 1703.87i | −1.62263 | + | 0.936824i | −0.636414 | + | 0.771348i | \(0.719583\pi\) |
−0.986214 | + | 0.165477i | \(0.947084\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1627.89 | − | 2819.59i | 0.877324 | − | 1.51957i | 0.0230569 | − | 0.999734i | \(-0.492660\pi\) |
0.854267 | − | 0.519835i | \(-0.174007\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −48.2191 | + | 17.1384i | −0.0254790 | + | 0.00905595i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1540.56i | 0.798329i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2199.76 | + | 1270.03i | 1.11822 | + | 0.645602i | 0.940945 | − | 0.338560i | \(-0.109940\pi\) |
0.177271 | + | 0.984162i | \(0.443273\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1324.22 | + | 1590.32i | 0.660487 | + | 0.793210i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2650.09 | − | 1194.90i | 1.29725 | − | 0.584917i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 862.851 | + | 1494.50i | 0.414624 | + | 0.718150i | 0.995389 | − | 0.0959216i | \(-0.0305798\pi\) |
−0.580765 | + | 0.814071i | \(0.697246\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 176.094 | − | 478.180i | 0.0830842 | − | 0.225614i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 485.621 | 0.225021 | 0.112510 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112510 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1882.24 | 0.856734 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2575.46 | − | 474.235i | −1.15176 | − | 0.212080i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 726.552 | + | 1258.43i | 0.319299 | + | 0.553042i | 0.980342 | − | 0.197306i | \(-0.0632192\pi\) |
−0.661043 | + | 0.750348i | \(0.729886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2891.87 | − | 4020.05i | 1.24917 | − | 1.73650i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2679.90 | − | 2231.49i | 1.13804 | − | 0.947622i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1099.44 | + | 634.760i | 0.459082 | + | 0.265051i | 0.711658 | − | 0.702526i | \(-0.247944\pi\) |
−0.252576 | + | 0.967577i | \(0.581278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3289.26i | − | 1.35076i | −0.737468 | − | 0.675382i | \(-0.763979\pi\) | ||
0.737468 | − | 0.675382i | \(-0.236021\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1618.34 | + | 279.051i | −0.653721 | + | 0.112721i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2465.59 | + | 4270.53i | −0.979860 | + | 1.69717i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.12614 | + | 4.69163i | −0.00317776 | + | 0.00183468i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1041.07 | − | 2380.64i | −0.400672 | − | 0.916222i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1713.46 | + | 989.265i | −0.649117 | + | 0.374768i | −0.788118 | − | 0.615524i | \(-0.788944\pi\) |
0.139001 | + | 0.990292i | \(0.455611\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 459.923 | − | 796.611i | 0.171534 | − | 0.297105i | −0.767423 | − | 0.641142i | \(-0.778461\pi\) |
0.938956 | + | 0.344037i | \(0.111794\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1799.56 | − | 310.299i | 0.660867 | − | 0.113954i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3061.98i | 1.10740i | 0.832717 | + | 0.553699i | \(0.186784\pi\) | ||||
−0.832717 | + | 0.553699i | \(0.813216\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 451.592 | + | 260.727i | 0.160867 | + | 0.0928766i | 0.578272 | − | 0.815844i | \(-0.303727\pi\) |
−0.417405 | + | 0.908720i | \(0.637060\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −933.546 | + | 777.342i | −0.327598 | + | 0.272783i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 170.135 | − | 1695.60i | 0.0588232 | − | 0.586247i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3404.16 | + | 5896.18i | 1.15979 | + | 2.00881i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4167.97 | − | 767.472i | −1.39949 | − | 0.257696i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −480.173 | −0.158920 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −99.6288 | −0.0325058 | −0.0162529 | − | 0.999868i | \(-0.505174\pi\) | ||||
−0.0162529 | + | 0.999868i | \(0.505174\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 273.341 | − | 742.253i | 0.0879297 | − | 0.238772i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −243.509 | − | 421.770i | −0.0772427 | − | 0.133788i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1169.25 | + | 841.111i | 0.365777 | + | 0.263126i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2072.83 | + | 2489.36i | 0.639585 | + | 0.768108i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.1209 | − | 16.8130i | −0.00886373 | − | 0.00511748i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1782.29i | − | 0.535206i | −0.963529 | − | 0.267603i | \(-0.913768\pi\) | ||
0.963529 | − | 0.267603i | \(-0.0862316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6802.63 | + | 2417.85i | −2.01559 | + | 0.716400i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1721.58 | + | 2981.86i | −0.503370 | + | 0.871863i | 0.496622 | + | 0.867967i | \(0.334573\pi\) |
−0.999992 | + | 0.00389579i | \(0.998760\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4706.78 | + | 2717.46i | −1.35822 | + | 0.784169i | −0.989384 | − | 0.145325i | \(-0.953577\pi\) |
−0.368837 | + | 0.929494i | \(0.620244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −266.782 | − | 394.725i | −0.0759870 | − | 0.112429i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3815.33 | − | 2202.78i | 1.07275 | − | 0.619351i | 0.143817 | − | 0.989604i | \(-0.454062\pi\) |
0.928931 | + | 0.370253i | \(0.120729\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4659.98 | + | 8071.33i | −1.29355 | + | 2.24049i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 266.986 | + | 1548.37i | 0.0731755 | + | 0.424377i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 2020.29i | − | 0.546786i | −0.961902 | − | 0.273393i | \(-0.911854\pi\) | ||
0.961902 | − | 0.273393i | \(-0.0881459\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1966.82 | − | 1135.54i | −0.525700 | − | 0.303513i | 0.213563 | − | 0.976929i | \(-0.431493\pi\) |
−0.739264 | + | 0.673416i | \(0.764826\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −728.191 | + | 3717.34i | −0.192236 | + | 0.981349i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2160.45 | − | 6441.80i | −0.563371 | − | 1.67980i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −860.378 | − | 1490.22i | −0.221638 | − | 0.383888i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4176.02 | − | 1537.85i | −1.06283 | − | 0.391396i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4513.50 | 1.13502 | 0.567510 | − | 0.823367i | \(-0.307907\pi\) | ||||
0.567510 | + | 0.823367i | \(0.307907\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −777.082 | −0.193102 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 183.068 | + | 67.4165i | 0.0449576 | + | 0.0165560i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2969.31 | − | 5142.99i | −0.720701 | − | 1.24829i | −0.960719 | − | 0.277523i | \(-0.910487\pi\) |
0.240018 | − | 0.970769i | \(-0.422847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1895.06 | + | 4202.93i | 0.454647 | + | 1.00833i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1611.27 | + | 1891.01i | −0.382127 | + | 0.448469i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4727.20 | − | 2729.25i | −1.10833 | − | 0.639897i | −0.169936 | − | 0.985455i | \(-0.554356\pi\) |
−0.938397 | + | 0.345558i | \(0.887690\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7889.23i | − | 1.82880i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −800.967 | − | 4645.16i | −0.183589 | − | 1.06472i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2642.46 | − | 4576.87i | 0.598935 | − | 1.03739i | −0.394043 | − | 0.919092i | \(-0.628924\pi\) |
0.992979 | − | 0.118294i | \(-0.0377427\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5436.74 | − | 3138.90i | 1.21866 | − | 0.703596i | 0.254033 | − | 0.967196i | \(-0.418243\pi\) |
0.964632 | + | 0.263599i | \(0.0849096\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 747.007 | − | 1535.23i | 0.165608 | − | 0.340353i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1146.42 | + | 661.884i | −0.251387 | + | 0.145139i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3748.17 | + | 6492.02i | −0.813017 | + | 1.40819i | 0.0977256 | + | 0.995213i | \(0.468843\pi\) |
−0.910743 | + | 0.412974i | \(0.864490\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −703.240 | − | 1978.57i | −0.150903 | − | 0.424566i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 745.889i | 0.158349i | 0.996861 | + | 0.0791744i | \(0.0252284\pi\) | ||||
−0.996861 | + | 0.0791744i | \(0.974772\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2280.55 | − | 1316.68i | −0.479027 | − | 0.276566i | 0.240984 | − | 0.970529i | \(-0.422530\pi\) |
−0.720011 | + | 0.693963i | \(0.755863\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6388.17 | + | 7671.85i | 1.32773 | + | 1.59453i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6333.63 | + | 635.507i | 1.30266 | + | 0.130707i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2454.70 | + | 4251.67i | 0.499634 | + | 0.865392i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 126.365 | − | 343.141i | 0.0254558 | − | 0.0691247i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 889.363 | 0.177328 | 0.0886640 | − | 0.996062i | \(-0.471740\pi\) | ||||
0.0886640 | + | 0.996062i | \(0.471740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13294.4 | −2.62383 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.87936 | + | 694.518i | −0.00153942 | + | 0.135690i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1392.38 | − | 2411.68i | −0.269309 | − | 0.466457i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −453.062 | − | 45.4596i | −0.0867577 | − | 0.00870515i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −952.539 | + | 793.156i | −0.180600 | + | 0.150382i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5421.75 | + | 3130.25i | 1.01786 | + | 0.587664i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3995.12i | − | 0.742715i | −0.928490 | − | 0.371357i | \(-0.878893\pi\) | ||
0.928490 | − | 0.371357i | \(-0.121107\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 100.275 | − | 17.2905i | 0.0184610 | − | 0.00318325i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 256.008 | − | 443.420i | 0.0466782 | − | 0.0808489i | −0.841742 | − | 0.539879i | \(-0.818470\pi\) |
0.888420 | + | 0.459031i | \(0.151803\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1271.68 | + | 734.205i | −0.229647 | + | 0.132587i | −0.610409 | − | 0.792086i | \(-0.708995\pi\) |
0.380762 | + | 0.924673i | \(0.375662\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2757.38 | + | 9513.83i | −0.493210 | + | 1.70173i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6545.26 | + | 3778.91i | −1.15968 | + | 0.669542i | −0.951227 | − | 0.308491i | \(-0.900176\pi\) |
−0.208453 | + | 0.978032i | \(0.566843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −227.766 | + | 394.502i | −0.0399763 | + | 0.0692410i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2477.50 | + | 427.196i | −0.430780 | + | 0.0742796i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 183.832i | − | 0.0316677i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4108.31 | − | 2371.93i | −0.701194 | − | 0.404835i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −170.922 | + | 142.323i | −0.0289053 | + | 0.0240687i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3581.68 | + | 7943.55i | 0.600196 | + | 1.33113i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2932.76 | + | 5079.69i | 0.487007 | + | 0.843520i | 0.999888 | − | 0.0149389i | \(-0.00475537\pi\) |
−0.512882 | + | 0.858459i | \(0.671422\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1217.18 | − | 6610.22i | 0.200303 | − | 1.08780i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4631.12 | 0.755300 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8489.10 | −1.37220 | −0.686099 | − | 0.727508i | \(-0.740678\pi\) | ||||
−0.686099 | + | 0.727508i | \(0.740678\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 679.397 | − | 1844.89i | 0.108849 | − | 0.295577i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −192.511 | − | 333.439i | −0.0305720 | − | 0.0529523i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6068.70 | − | 1877.35i | −0.955333 | − | 0.295531i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10338.2 | + | 12415.6i | 1.61331 | + | 1.93749i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 968.873 | + | 559.379i | 0.149890 | + | 0.0865390i | 0.573069 | − | 0.819507i | \(-0.305753\pi\) |
−0.423179 | + | 0.906046i | \(0.639086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2364.44i | − | 0.362652i | −0.983423 | − | 0.181326i | \(-0.941961\pi\) | ||
0.983423 | − | 0.181326i | \(-0.0580389\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2169.55 | + | 1219.99i | −0.329921 | + | 0.185522i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1411.12 | + | 2444.13i | −0.212766 | + | 0.368522i | −0.952579 | − | 0.304291i | \(-0.901581\pi\) |
0.739813 | + | 0.672812i | \(0.234914\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2611.41 | + | 1507.70i | −0.390421 | + | 0.225410i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 151.118 | − | 102.136i | 0.0224034 | − | 0.0151418i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4504.97 | + | 2600.95i | −0.662293 | + | 0.382375i | −0.793150 | − | 0.609026i | \(-0.791560\pi\) |
0.130857 | + | 0.991401i | \(0.458227\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1274.15 | − | 2206.89i | 0.185763 | − | 0.321751i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1153.56 | − | 6690.00i | −0.166794 | − | 0.967311i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 12349.2i | − | 1.77092i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4876.42 | + | 2815.40i | 0.693589 | + | 0.400444i | 0.804955 | − | 0.593336i | \(-0.202189\pi\) |
−0.111366 | + | 0.993779i | \(0.535523\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7063.52 | − | 6018.61i | −0.996510 | − | 0.849096i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5987.71 | − | 4307.33i | −0.837915 | − | 0.602764i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3422.23 | − | 5927.47i | −0.475057 | − | 0.822822i | 0.524535 | − | 0.851389i | \(-0.324239\pi\) |
−0.999592 | + | 0.0285664i | \(0.990906\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13753.3 | + | 5064.77i | 1.89391 | + | 0.697449i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1632.45 | −0.223012 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5690.62 | −0.771260 | −0.385630 | − | 0.922654i | \(-0.626016\pi\) | ||||
−0.385630 | + | 0.922654i | \(0.626016\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −550.042 | − | 202.558i | −0.0739619 | − | 0.0272371i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2151.66 | + | 3726.78i | 0.287062 | + | 0.497206i | 0.973107 | − | 0.230353i | \(-0.0739881\pi\) |
−0.686045 | + | 0.727559i | \(0.740655\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −181.328 | + | 1807.16i | −0.0240035 | + | 0.239225i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 505.273 | + | 430.528i | 0.0663682 | + | 0.0565504i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6143.61 | + | 3547.01i | 0.800754 | + | 0.462315i | 0.843735 | − | 0.536760i | \(-0.180352\pi\) |
−0.0429809 | + | 0.999076i | \(0.513685\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 297.501i | − | 0.0384790i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1396.69 | − | 8100.02i | −0.179271 | − | 1.03967i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2994.91 | − | 5187.34i | 0.381494 | − | 0.660768i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3898.27 | − | 2250.67i | 0.492817 | − | 0.284528i | −0.232925 | − | 0.972495i | \(-0.574830\pi\) |
0.725742 | + | 0.687967i | \(0.241496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9310.51 | − | 659.797i | 1.16819 | − | 0.0827848i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6038.64 | + | 3486.41i | −0.752008 | + | 0.434172i | −0.826419 | − | 0.563055i | \(-0.809626\pi\) |
0.0744107 | + | 0.997228i | \(0.476292\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 689.886 | − | 1194.92i | 0.0852746 | − | 0.147700i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11201.3 | − | 9113.89i | 1.37432 | − | 1.11820i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1232.42i | − | 0.150095i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12431.9 | + | 7177.56i | 1.50298 | + | 0.867745i | 0.999994 | + | 0.00344923i | \(0.00109793\pi\) |
0.502984 | + | 0.864296i | \(0.332235\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6132.60 | − | 7364.93i | −0.736007 | − | 0.883905i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7258.43 | + | 10090.1i | −0.864804 | + | 1.20218i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8482.52 | + | 14692.2i | 1.00335 | + | 1.73785i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −100.317 | + | 272.410i | −0.0117807 | + | 0.0319903i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14839.8 | −1.73024 | −0.865122 | − | 0.501562i | \(-0.832759\pi\) | ||||
−0.865122 | + | 0.501562i | \(0.832759\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11073.0 | −1.28187 | −0.640935 | − | 0.767595i | \(-0.721453\pi\) | ||||
−0.640935 | + | 0.767595i | \(0.721453\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2300.47 | − | 12493.3i | 0.264427 | − | 1.43604i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −253.398 | − | 438.899i | −0.0289215 | − | 0.0500934i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5335.92 | − | 2405.92i | 0.604738 | − | 0.272671i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −350.721 | + | 292.037i | −0.0394707 | + | 0.0328663i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5552.06 | + | 3205.49i | 0.620495 | + | 0.358243i | 0.777062 | − | 0.629424i | \(-0.216709\pi\) |
−0.156566 | + | 0.987667i | \(0.550043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12881.0i | − | 1.42961i | −0.699322 | − | 0.714807i | \(-0.746514\pi\) | ||
0.699322 | − | 0.714807i | \(-0.253486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9333.23 | − | 1609.33i | 1.02872 | − | 0.177383i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7612.09 | − | 13184.5i | 0.833262 | − | 1.44325i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8024.85 | − | 4633.15i | 0.872449 | − | 0.503709i | 0.00428790 | − | 0.999991i | \(-0.498635\pi\) |
0.868161 | + | 0.496282i | \(0.165302\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5715.27 | + | 7287.10i | 0.617133 | + | 0.786859i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7691.54 | − | 4440.71i | 0.824912 | − | 0.476263i | −0.0271952 | − | 0.999630i | \(-0.508658\pi\) |
0.852108 | + | 0.523367i | \(0.175324\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8984.83 | + | 15562.2i | −0.957128 | + | 1.65779i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17449.7 | + | 3008.86i | −1.84640 | + | 0.318376i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6080.93i | 0.639147i | 0.947562 | + | 0.319573i | \(0.103540\pi\) | ||||
−0.947562 | + | 0.319573i | \(0.896460\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1473.59 | − | 850.778i | −0.153855 | − | 0.0888283i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13000.6 | − | 10825.3i | 1.34839 | − | 1.12277i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5933.43 | + | 2675.33i | −0.611348 | + | 0.275652i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −278.827 | − | 482.943i | −0.0285404 | − | 0.0494335i | 0.851402 | − | 0.524513i | \(-0.175753\pi\) |
−0.879943 | + | 0.475080i | \(0.842419\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −265.892 | − | 3.01657i | −0.0270387 | − | 0.000306757i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7422.24 | −0.749866 | −0.374933 | − | 0.927052i | \(-0.622334\pi\) | ||||
−0.374933 | + | 0.927052i | \(0.622334\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10478.8 | −1.05182 | −0.525908 | − | 0.850541i | \(-0.676274\pi\) | ||||
−0.525908 | + | 0.850541i | \(0.676274\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2766.30 | + | 7511.83i | −0.275880 | + | 0.749146i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4708.74 | + | 8155.78i | 0.466584 | + | 0.808147i | 0.999271 | − | 0.0381650i | \(-0.0121512\pi\) |
−0.532688 | + | 0.846312i | \(0.678818\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2528.48 | − | 3514.90i | 0.248943 | − | 0.346062i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8445.57 | + | 10142.7i | 0.826224 | + | 0.992251i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 105.410 | + | 60.8586i | 0.0102469 | + | 0.00591603i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 25934.5i | − | 2.50517i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3601.30 | + | 10132.3i | 0.345686 | + | 0.972588i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5303.15 | + | 9185.32i | −0.505860 | + | 0.876176i | 0.494117 | + | 0.869396i | \(0.335492\pi\) |
−0.999977 | + | 0.00678003i | \(0.997842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3824.81 | − | 2208.25i | 0.362570 | − | 0.209330i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15067.5 | − | 1067.77i | 1.41946 | − | 0.100591i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1207.25 | + | 697.005i | −0.113027 | + | 0.0652564i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6387.19 | + | 11062.9i | −0.594314 | + | 1.02938i | 0.399329 | + | 0.916808i | \(0.369243\pi\) |
−0.993643 | + | 0.112575i | \(0.964090\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1523.70 | + | 8836.61i | 0.140908 | + | 0.817188i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18689.8i | 1.71784i | 0.512110 | + | 0.858920i | \(0.328864\pi\) | ||||
−0.512110 | + | 0.858920i | \(0.671136\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −151.033 | − | 87.1988i | −0.0137975 | − | 0.00796600i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1717.28 | − | 2015.42i | 0.155931 | − | 0.183003i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −281.466 | + | 2805.16i | −0.0254033 | + | 0.253176i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6862.74 | − | 11886.6i | −0.615668 | − | 1.06637i | −0.990267 | − | 0.139182i | \(-0.955553\pi\) |
0.374599 | − | 0.927187i | \(-0.377780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2367.90 | + | 872.001i | 0.211158 | + | 0.0777608i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5480.28 | 0.485793 | 0.242896 | − | 0.970052i | \(-0.421902\pi\) | ||||
0.242896 | + | 0.970052i | \(0.421902\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4725.34 | 0.416386 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9177.88 | + | 3379.83i | 0.803953 | + | 0.296063i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5331.28 | + | 9234.05i | 0.464253 | + | 0.804111i | 0.999168 | − | 0.0407959i | \(-0.0129893\pi\) |
−0.534914 | + | 0.844906i | \(0.679656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9372.71 | − | 6742.37i | −0.811398 | − | 0.583689i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11706.5 | − | 6936.99i | −1.00751 | − | 0.597029i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −335.942 | − | 193.956i | −0.0287444 | − | 0.0165956i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2329.28i | − | 0.198146i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1283.01 | + | 7440.75i | 0.108512 | + | 0.629311i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5750.00 | − | 9959.29i | 0.483517 | − | 0.837475i | −0.516304 | − | 0.856405i | \(-0.672693\pi\) |
0.999821 | + | 0.0189300i | \(0.00602596\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8319.57 | + | 4803.31i | −0.695582 | + | 0.401594i | −0.805700 | − | 0.592324i | \(-0.798211\pi\) |
0.110118 | + | 0.993919i | \(0.464877\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21319.4 | − | 14409.1i | 1.77230 | − | 1.19784i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 127.655 | − | 73.7018i | 0.0105517 | − | 0.00609203i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6235.42 | − | 10800.1i | 0.512486 | − | 0.887653i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17074.2 | − | 6068.67i | 1.39540 | − | 0.495966i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6097.72i | − | 0.495538i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8300.10 | + | 4792.07i | 0.670738 | + | 0.387251i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4221.08 | + | 5069.30i | 0.339205 | + | 0.407368i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1272.58 | + | 1124.29i | 0.101696 | + | 0.0898452i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8782.28 | + | 15211.3i | 0.697929 | + | 1.20885i | 0.969183 | + | 0.246341i | \(0.0792282\pi\) |
−0.271254 | + | 0.962508i | \(0.587438\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5906.32 | − | 16038.5i | 0.466785 | − | 1.26755i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 847.909 | 0.0666430 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14541.1 | 1.13662 | 0.568311 | − | 0.822814i | \(-0.307597\pi\) | ||||
0.568311 | + | 0.822814i | \(0.307597\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8392.14 | − | 1545.29i | −0.652400 | − | 0.120130i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4462.26 | − | 7728.87i | −0.345007 | − | 0.597570i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2301.90 | − | 5105.22i | −0.177010 | − | 0.392578i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19690.7 | + | 16395.9i | −1.50599 | + | 1.25400i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11945.8 | − | 6896.92i | −0.908726 | − | 0.524653i | −0.0287052 | − | 0.999588i | \(-0.509138\pi\) |
−0.880021 | + | 0.474935i | \(0.842472\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 436.187i | 0.0330031i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −48.0478 | + | 8.28490i | −0.00361600 | + | 0.000623509i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4598.06 | − | 7964.08i | 0.344201 | − | 0.596174i | −0.641007 | − | 0.767535i | \(-0.721483\pi\) |
0.985208 | + | 0.171361i | \(0.0548165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6490.74 | + | 3747.43i | −0.483305 | + | 0.279036i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −801.543 | − | 13477.5i | −0.0593680 | − | 0.998236i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15644.0 | − | 9032.06i | 1.15260 | − | 0.665455i | 0.203082 | − | 0.979162i | \(-0.434904\pi\) |
0.949520 | + | 0.313707i | \(0.101571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7626.26 | − | 13209.1i | 0.558930 | − | 0.968095i | −0.438656 | − | 0.898655i | \(-0.644545\pi\) |
0.997586 | − | 0.0694402i | \(-0.0221213\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10131.2 | + | 1746.93i | −0.738636 | + | 0.127363i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 41970.8i | − | 3.04401i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4709.42 | − | 2718.99i | −0.339785 | − | 0.196175i | 0.320392 | − | 0.947285i | \(-0.396185\pi\) |
−0.660177 | + | 0.751110i | \(0.729519\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3673.03 | − | 3058.44i | 0.263637 | − | 0.219524i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15782.2 | + | 1583.56i | 1.12695 | + | 0.113076i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 985.851 | + | 1707.54i | 0.0700339 | + | 0.121302i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 9331.88 | + | 1718.33i | 0.659531 | + | 0.121443i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23972.1 | 1.68558 | 0.842791 | − | 0.538241i | \(-0.180911\pi\) | ||||
0.842791 | + | 0.538241i | \(0.180911\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7543.15 | 0.527691 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5498.22 | + | 14930.3i | −0.382685 | + | 1.03917i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −697.071 | − | 1207.36i | −0.0482720 | − | 0.0836095i | 0.840880 | − | 0.541222i | \(-0.182038\pi\) |
−0.889152 | + | 0.457612i | \(0.848705\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −691.861 | − | 69.4203i | −0.0476698 | − | 0.00478312i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1733.81 | + | 2082.21i | 0.118861 | + | 0.142746i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20811.2 | − | 12015.4i | −1.41957 | − | 0.819591i | −0.423312 | − | 0.905984i | \(-0.639133\pi\) |
−0.996261 | + | 0.0863929i | \(0.972466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10741.9i | − | 0.729073i | −0.931189 | − | 0.364536i | \(-0.881227\pi\) | ||
0.931189 | − | 0.364536i | \(-0.118773\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5947.83 | + | 2114.03i | −0.401682 | + | 0.142769i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12940.0 | + | 22412.8i | −0.869566 | + | 1.50613i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23506.4 | + | 13571.4i | −1.57182 | + | 0.907492i | −0.575876 | + | 0.817537i | \(0.695339\pi\) |
−0.995946 | + | 0.0899549i | \(0.971328\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3874.28 | − | 7962.32i | 0.257789 | − | 0.529802i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7228.91 | − | 4173.61i | 0.478642 | − | 0.276344i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14388.2 | + | 24921.1i | −0.948015 | + | 1.64201i | −0.198415 | + | 0.980118i | \(0.563579\pi\) |
−0.749600 | + | 0.661891i | \(0.769754\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6011.37 | + | 34862.6i | 0.394149 | + | 2.28585i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2160.03i | 0.140939i | 0.997514 | + | 0.0704697i | \(0.0224498\pi\) | ||||
−0.997514 | + | 0.0704697i | \(0.977550\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2505.32 | − | 1446.45i | −0.162677 | − | 0.0939218i | 0.416451 | − | 0.909158i | \(-0.363274\pi\) |
−0.579128 | + | 0.815236i | \(0.696607\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18945.0 | − | 11226.4i | −1.22422 | − | 0.725442i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6905.77 | + | 15315.8i | 0.444099 | + | 0.984936i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11224.4 | − | 19441.3i | −0.718364 | − | 1.24424i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2341.34 | − | 862.219i | −0.149129 | − | 0.0549182i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 471.824 | 0.0299092 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13779.4 | 0.869335 | 0.434667 | − | 0.900591i | \(-0.356866\pi\) | ||||
0.434667 | + | 0.900591i | \(0.356866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −485.793 | − | 178.898i | −0.0305032 | − | 0.0112331i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1117.27 | + | 1935.17i | 0.0698229 | + | 0.120937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1209.01 | + | 5963.98i | −0.0752002 | + | 0.370960i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2665.64 | − | 3128.43i | 0.165025 | − | 0.193676i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12252.1 | − | 7073.73i | −0.754957 | − | 0.435875i | 0.0725251 | − | 0.997367i | \(-0.476894\pi\) |
−0.827482 | + | 0.561492i | \(0.810228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4248.35i | − | 0.260557i | −0.991477 | − | 0.130279i | \(-0.958413\pi\) | ||
0.991477 | − | 0.130279i | \(-0.0415872\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −430.010 | − | 2493.82i | −0.0262506 | − | 0.152239i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8314.83 | + | 14401.7i | −0.505239 | + | 0.875100i | 0.494742 | + | 0.869040i | \(0.335262\pi\) |
−0.999982 | + | 0.00606041i | \(0.998071\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2877.44 | − | 1661.29i | 0.174036 | − | 0.100480i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4190.94 | + | 6200.83i | 0.252313 | + | 0.373317i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26164.5 | − | 15106.1i | 1.56798 | − | 0.905276i | 0.571581 | − | 0.820546i | \(-0.306330\pi\) |
0.996404 | − | 0.0847307i | \(-0.0270030\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15667.4 | + | 27136.7i | −0.934617 | + | 1.61880i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5637.20 | + | 15860.3i | 0.334746 | + | 0.941809i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 533.821i | 0.0315549i | 0.999876 | + | 0.0157775i | \(0.00502233\pi\) | ||||
−0.999876 | + | 0.0157775i | \(0.994978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6638.24 | − | 3832.59i | −0.390617 | − | 0.225523i | 0.291811 | − | 0.956476i | \(-0.405742\pi\) |
−0.682427 | + | 0.730954i | \(0.739076\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −111.804 | − | 134.271i | −0.00654921 | − | 0.00786526i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28885.3 | − | 20779.0i | −1.68440 | − | 1.21169i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7221.45 | − | 12507.9i | −0.419214 | − | 0.726099i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3200.35 | − | 8690.50i | 0.184952 | − | 0.502234i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1564.64 | −0.0900184 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28054.4 | −1.60686 | −0.803430 | − | 0.595400i | \(-0.796994\pi\) | ||||
−0.803430 | + | 0.595400i | \(0.796994\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −37511.4 | − | 425.570i | −2.13899 | − | 0.0242670i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5256.30 | + | 9104.19i | 0.298399 | + | 0.516842i | 0.975770 | − | 0.218799i | \(-0.0702140\pi\) |
−0.677371 | + | 0.735642i | \(0.736881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −130.121 | + | 1296.82i | −0.00735431 | + | 0.0732949i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13748.8 | + | 11448.3i | −0.773649 | + | 0.644199i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15679.7 | − | 9052.66i | −0.878427 | − | 0.507160i | −0.00828788 | − | 0.999966i | \(-0.502638\pi\) |
−0.870140 | + | 0.492805i | \(0.835971\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36535.8i | 2.03790i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27830.0 | + | 4798.73i | −1.54553 | + | 0.266496i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3532.91 | + | 6119.18i | −0.195346 | + | 0.338348i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7660.53 | + | 4422.81i | −0.421737 | + | 0.243490i | −0.695820 | − | 0.718216i | \(-0.744959\pi\) |
0.274083 | + | 0.961706i | \(0.411626\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −592.055 | − | 2403.74i | −0.0324535 | − | 0.131761i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 958.398 | − | 553.331i | 0.0523080 | − | 0.0302001i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 325.715 | − | 564.156i | 0.0177006 | − | 0.0306584i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22559.0 | − | 3889.87i | 1.22069 | − | 0.210484i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32985.2i | 1.77723i | 0.458658 | + | 0.888613i | \(0.348330\pi\) | ||||
−0.458658 | + | 0.888613i | \(0.651670\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20910.1 | + | 12072.4i | 1.12182 | + | 0.647682i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −37215.4 | + | 30988.4i | −1.98811 | + | 1.65545i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2579.92 | − | 3586.41i | 0.137239 | − | 0.190779i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7996.91 | − | 13851.1i | −0.423597 | − | 0.733692i | 0.572691 | − | 0.819771i | \(-0.305899\pi\) |
−0.996288 | + | 0.0860795i | \(0.972566\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1478.48 | + | 8029.30i | −0.0779851 | + | 0.423520i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12207.4 | 0.641191 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1739.85 | 0.0910024 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3627.72 | − | 9851.01i | 0.188953 | − | 0.513100i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10462.3 | + | 18121.2i | 0.542668 | + | 0.939928i | 0.998750 | + | 0.0499905i | \(0.0159191\pi\) |
−0.456082 | + | 0.889938i | \(0.650748\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −330.623 | + | 149.075i | −0.0170778 | + | 0.00770021i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7551.23 | − | 9068.63i | −0.388428 | − | 0.466481i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21307.4 | − | 12301.8i | −1.09150 | − | 0.630176i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21598.1i | 1.10183i | 0.834562 | + | 0.550915i | \(0.185721\pi\) | ||||
−0.834562 | + | 0.550915i | \(0.814279\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10225.7 | + | 16818.3i | −0.519519 | + | 0.854459i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.2993 | + | 40.3557i | −0.00117887 | + | 0.00204187i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8894.03 | − | 5134.97i | 0.448170 | − | 0.258751i | −0.258887 | − | 0.965908i | \(-0.583356\pi\) |
0.707057 | + | 0.707157i | \(0.250022\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1032.75 | − | 35289.8i | 0.0518278 | − | 1.77100i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1002.36 | + | 578.713i | −0.0500982 | + | 0.0289242i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9022.60 | + | 15627.6i | −0.449123 | + | 0.777903i | −0.998329 | − | 0.0577833i | \(-0.981597\pi\) |
0.549206 | + | 0.835687i | \(0.314930\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1519.33 | − | 8811.28i | −0.0753226 | − | 0.436829i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29700.6i | 1.46650i | 0.679960 | + | 0.733249i | \(0.261997\pi\) | ||||
−0.679960 | + | 0.733249i | \(0.738003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 58459.8 | + | 33751.8i | 2.87490 | + | 1.65983i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17600.9 | − | 14997.2i | −0.862095 | − | 0.734566i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8168.70 | − | 3683.20i | 0.398502 | − | 0.179681i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9431.09 | − | 16335.1i | −0.458249 | − | 0.793711i | 0.540619 | − | 0.841267i | \(-0.318190\pi\) |
−0.998869 | + | 0.0475563i | \(0.984857\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22008.0 | + | 8104.63i | 1.06509 | + | 0.392230i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −64493.3 | −3.10881 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12141.1 | 0.582929 | 0.291464 | − | 0.956582i | \(-0.405858\pi\) | ||||
0.291464 | + | 0.956582i | \(0.405858\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3789.08 | − | 1395.36i | −0.181205 | − | 0.0667304i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12563.5 | + | 21760.6i | 0.598457 | + | 1.03656i | 0.993049 | + | 0.117702i | \(0.0375526\pi\) |
−0.394592 | + | 0.918856i | \(0.629114\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 462.938 | − | 643.540i | 0.0219652 | − | 0.0305343i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 771.591 | + | 657.450i | 0.0364666 | + | 0.0310721i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10311.6 | + | 5953.43i | 0.485439 | + | 0.280268i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 23475.2i | − | 1.10083i | −0.834892 | − | 0.550413i | \(-0.814470\pi\) | ||
0.834892 | − | 0.550413i | \(-0.185530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5243.47 | − | 30409.2i | −0.244927 | − | 1.42044i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15695.6 | + | 27185.6i | −0.730313 | + | 1.26494i | 0.226436 | + | 0.974026i | \(0.427292\pi\) |
−0.956749 | + | 0.290913i | \(0.906041\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18009.3 | − | 10397.7i | 0.834727 | − | 0.481930i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1693.44 | + | 23896.5i | 0.0781877 | + | 1.10332i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28869.8 | − | 16668.0i | 1.32781 | − | 0.766614i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 376.809 | − | 652.653i | 0.0172641 | − | 0.0299024i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11252.2 | + | 6327.35i | −0.513563 | + | 0.288788i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 50315.7i | − | 2.28770i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4012.16 | + | 2316.42i | 0.181726 | + | 0.104919i | 0.588103 | − | 0.808786i | \(-0.299875\pi\) |
−0.406378 | + | 0.913705i | \(0.633208\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18149.2 | − | 21796.3i | −0.818922 | − | 0.983482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −699.591 | + | 6972.30i | −0.0314470 | + | 0.313409i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2803.54 | − | 4855.87i | −0.125544 | − | 0.217449i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14166.2 | − | 38468.1i | 0.631980 | − | 1.71613i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 121.248 | 0.00538874 | 0.00269437 | − | 0.999996i | \(-0.499142\pi\) | ||||
0.00269437 | + | 0.999996i | \(0.499142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 891.749 | 0.0394841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4435.49 | − | 24088.2i | 0.195656 | − | 1.06256i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1543.18 | + | 2672.86i | 0.0678176 | + | 0.117464i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −46746.2 | − | 33627.4i | −2.04669 | − | 1.47231i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21103.1 | − | 17572.1i | 0.920527 | − | 0.766501i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −11357.9 | − | 6557.47i | −0.493599 | − | 0.284979i | 0.232467 | − | 0.972604i | \(-0.425320\pi\) |
−0.726066 | + | 0.687625i | \(0.758653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2601.55i | 0.112642i | 0.998413 | + | 0.0563211i | \(0.0179371\pi\) | ||||
−0.998413 | + | 0.0563211i | \(0.982063\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32146.0 | − | 5542.95i | 1.38673 | − | 0.239114i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17092.1 | − | 29604.4i | 0.734613 | − | 1.27239i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2065.14 | + | 1192.31i | −0.0884333 | + | 0.0510570i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6399.15 | − | 6144.48i | 0.273021 | − | 0.262155i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13977.1 | − | 8069.68i | 0.594158 | − | 0.343038i | −0.172582 | − | 0.984995i | \(-0.555211\pi\) |
0.766740 | + | 0.641958i | \(0.221878\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9786.73 | − | 16951.1i | 0.414513 | − | 0.717957i | −0.580864 | − | 0.814000i | \(-0.697285\pi\) |
0.995377 | + | 0.0960431i | \(0.0306187\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6778.47 | + | 1168.81i | −0.286056 | + | 0.0493247i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19041.3i | 0.800641i | 0.916375 | + | 0.400320i | \(0.131101\pi\) | ||||
−0.916375 | + | 0.400320i | \(0.868899\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4754.65 | − | 2745.10i | −0.199199 | − | 0.115007i | 0.397083 | − | 0.917783i | \(-0.370023\pi\) |
−0.596282 | + | 0.802775i | \(0.703356\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29933.5 | + | 24924.9i | −1.24956 | + | 1.04048i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −430.427 | + | 487.202i | −0.0179033 | + | 0.0202647i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4809.80 | − | 8330.82i | −0.199341 | − | 0.345269i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 123.779 | − | 10910.3i | 0.00511161 | − | 0.450557i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25774.7 | 1.06060 | 0.530299 | − | 0.847811i | \(-0.322080\pi\) | ||||
0.530299 | + | 0.847811i | \(0.322080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15922.5 | 0.652854 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1339.35 | + | 3636.98i | −0.0547208 | + | 0.148593i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18642.5 | − | 32289.8i | −0.758962 | − | 1.31456i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9945.75 | + | 22058.0i | 0.403471 | + | 0.894830i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8755.76 | − | 10515.2i | −0.353942 | − | 0.425066i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33839.5 | + | 19537.3i | 1.36311 | + | 0.786990i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15407.3i | 0.618447i | 0.950989 | + | 0.309224i | \(0.100069\pi\) | ||||
−0.950989 | + | 0.309224i | \(0.899931\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 17373.0 | + | 48879.0i | 0.694906 | + | 1.95512i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5708.14 | + | 9886.78i | −0.227522 | + | 0.394079i | −0.957073 | − | 0.289847i | \(-0.906396\pi\) |
0.729551 | + | 0.683926i | \(0.239729\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32407.3 | − | 18710.4i | 1.28722 | − | 0.743178i | 0.309064 | − | 0.951041i | \(-0.399984\pi\) |
0.978158 | + | 0.207863i | \(0.0666510\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29741.8 | + | 14471.7i | 1.17723 | + | 0.572814i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30175.4 | + | 17421.8i | −1.19025 | + | 0.687189i | −0.958362 | − | 0.285554i | \(-0.907822\pi\) |
−0.231884 | + | 0.972743i | \(0.574489\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14392.2 | − | 24928.0i | 0.565720 | − | 0.979856i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4334.74 | + | 25139.0i | 0.169799 | + | 0.984737i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1496.99i | 0.0584374i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3592.07 | − | 2073.88i | −0.139739 | − | 0.0806783i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1232.32 | − | 1446.26i | 0.0477750 | − | 0.0560694i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −51977.1 | − | 5215.31i | −2.00817 | − | 0.201497i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14281.1 | + | 24735.6i | 0.549874 | + | 0.952409i | 0.998283 | + | 0.0585807i | \(0.0186575\pi\) |
−0.448409 | + | 0.893828i | \(0.648009\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4336.56 | + | 1596.98i | 0.166403 | + | 0.0612795i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25098.4 | 0.959804 | 0.479902 | − | 0.877322i | \(-0.340672\pi\) | ||||
0.479902 | + | 0.877322i | \(0.340672\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32704.3 | 1.24642 | 0.623208 | − | 0.782056i | \(-0.285829\pi\) | ||||
0.623208 | + | 0.782056i | \(0.285829\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −64824.0 | − | 23872.0i | −2.46219 | − | 0.906721i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11659.7 | − | 20195.2i | −0.441368 | − | 0.764472i | 0.556423 | − | 0.830899i | \(-0.312173\pi\) |
−0.997791 | + | 0.0664269i | \(0.978840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2078.74 | + | 208.578i | 0.0784239 | + | 0.00786894i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1285.52 | + | 3372.34i | −0.0483352 | + | 0.126799i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39520.1 | + | 22816.9i | 1.48095 | + | 0.855028i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 25147.7i | − | 0.939213i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2458.79 | − | 14259.6i | −0.0915236 | − | 0.530786i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3578.02 | − | 6197.32i | 0.132741 | − | 0.229913i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −653.723 | + | 377.427i | −0.0241717 | + | 0.0139555i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2127.52 | − | 1035.20i | −0.0784045 | − | 0.0381498i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −56427.1 | + | 32578.2i | −2.07260 | + | 1.19661i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18663.6 | + | 32326.3i | −0.683258 | + | 1.18344i | 0.290723 | + | 0.956807i | \(0.406104\pi\) |
−0.973981 | + | 0.226631i | \(0.927229\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6068.83 | + | 2157.04i | −0.221442 | + | 0.0787067i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 33130.2i | − | 1.20489i | −0.798161 | − | 0.602444i | \(-0.794194\pi\) | ||
0.798161 | − | 0.602444i | \(-0.205806\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3671.91 | − | 2119.98i | −0.133102 | − | 0.0768467i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20815.8 | + | 24998.7i | 0.752076 | + | 0.903204i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12042.0 | + | 26707.1i | 0.433654 | + | 0.961772i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11879.4 | − | 20575.7i | −0.426404 | − | 0.738553i | 0.570146 | − | 0.821543i | \(-0.306886\pi\) |
−0.996550 | + | 0.0829898i | \(0.973553\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7173.79 | − | 19480.3i | 0.256661 | − | 0.696958i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2700.68 | 0.0963097 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 66563.8 | 2.36606 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 519.993 | + | 95.7493i | 0.0184237 | + | 0.00339247i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17720.4 | + | 30692.6i | 0.625819 | + | 1.08395i | 0.988382 | + | 0.151991i | \(0.0485685\pi\) |
−0.362563 | + | 0.931959i | \(0.618098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31541.4 | + | 10578.3i | −1.11034 | + | 0.372385i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2044.53 | − | 1702.43i | 0.0717415 | − | 0.0597374i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 160.969 | + | 92.9357i | 0.00563023 | + | 0.00325061i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42936.0i | 1.49697i | 0.663154 | + | 0.748483i | \(0.269218\pi\) | ||||
−0.663154 | + | 0.748483i | \(0.730782\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7519.12 | + | 1296.53i | −0.261318 | + | 0.0450591i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16115.3 | − | 27912.5i | 0.558282 | − | 0.966972i | −0.439359 | − | 0.898312i | \(-0.644794\pi\) |
0.997640 | − | 0.0686602i | \(-0.0218724\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46721.1 | − | 26974.4i | 1.61341 | − | 0.931503i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −30528.5 | + | 41438.4i | −1.05089 | + | 1.42645i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9522.57 | − | 5497.86i | 0.326760 | − | 0.188655i | −0.327642 | − | 0.944802i | \(-0.606254\pi\) |
0.654402 | + | 0.756147i | \(0.272921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5530.15 | + | 9578.50i | −0.189164 | + | 0.327641i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38700.5 | + | 6673.14i | −1.31961 | + | 0.227541i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10083.0i | 0.342728i | 0.985208 | + | 0.171364i | \(0.0548174\pi\) | ||||
−0.985208 | + | 0.171364i | \(0.945183\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33941.6 | + | 19596.2i | 1.15008 | + | 0.663998i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1818.98 | + | 1514.62i | −0.0614412 | + | 0.0511606i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 27729.7 | + | 19947.7i | 0.933721 | + | 0.671684i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11871.3 | − | 20561.7i | −0.398486 | − | 0.690198i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12847.4 | − | 2365.67i | −0.429910 | − | 0.0791618i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18221.1 | −0.607832 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24809.9 | 0.825061 | 0.412530 | − | 0.910944i | \(-0.364645\pi\) | ||||
0.412530 | + | 0.910944i | \(0.364645\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 330.095 | − | 896.368i | 0.0109434 | − | 0.0297167i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3033.74 | − | 5254.60i | −0.100265 | − | 0.173664i | 0.811529 | − | 0.584313i | \(-0.198636\pi\) |
−0.911794 | + | 0.410648i | \(0.865302\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 103.299 | − | 1029.50i | 0.00340351 | − | 0.0339202i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15773.1 | − | 18942.7i | −0.518096 | − | 0.622206i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11370.3 | + | 6564.62i | 0.372331 | + | 0.214965i | 0.674476 | − | 0.738297i | \(-0.264370\pi\) |
−0.302146 | + | 0.953262i | \(0.597703\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4491.03i | − | 0.146613i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1088.98 | + | 387.056i | −0.0354420 | + | 0.0125971i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13427.3 | − | 23256.8i | 0.435671 | − | 0.754605i | −0.561679 | − | 0.827355i | \(-0.689844\pi\) |
0.997350 | + | 0.0727505i | \(0.0231777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52528.2 | − | 30327.2i | 1.69918 | − | 0.981019i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3200.61 | + | 45164.4i | 0.103218 | + | 1.45653i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3342.09 | + | 1929.56i | −0.107454 | + | 0.0620387i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13495.1 | − | 23374.1i | 0.432578 | − | 0.749247i | −0.564516 | − | 0.825422i | \(-0.690937\pi\) |
0.997094 | + | 0.0761745i | \(0.0242706\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5178.94 | + | 30034.9i | 0.165507 | + | 0.959849i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 10329.4i | − | 0.329109i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12247.7 | + | 7071.22i | 0.389056 | + | 0.224622i | 0.681751 | − | 0.731584i | \(-0.261219\pi\) |
−0.292695 | + | 0.956206i | \(0.594552\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17804.6 | − | 30046.0i | 0.563875 | − | 0.951565i |
(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 | 336.4.bc.e.17.8 | 16 | ||
3.2 | odd | 2 | inner | 336.4.bc.e.17.6 | 16 | ||
4.3 | odd | 2 | 42.4.f.a.17.5 | yes | 16 | ||
7.5 | odd | 6 | inner | 336.4.bc.e.257.6 | 16 | ||
12.11 | even | 2 | 42.4.f.a.17.2 | yes | 16 | ||
21.5 | even | 6 | inner | 336.4.bc.e.257.8 | 16 | ||
28.3 | even | 6 | 294.4.d.a.293.12 | 16 | |||
28.11 | odd | 6 | 294.4.d.a.293.13 | 16 | |||
28.19 | even | 6 | 42.4.f.a.5.2 | ✓ | 16 | ||
28.23 | odd | 6 | 294.4.f.a.215.3 | 16 | |||
28.27 | even | 2 | 294.4.f.a.227.8 | 16 | |||
84.11 | even | 6 | 294.4.d.a.293.4 | 16 | |||
84.23 | even | 6 | 294.4.f.a.215.8 | 16 | |||
84.47 | odd | 6 | 42.4.f.a.5.5 | yes | 16 | ||
84.59 | odd | 6 | 294.4.d.a.293.5 | 16 | |||
84.83 | odd | 2 | 294.4.f.a.227.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.f.a.5.2 | ✓ | 16 | 28.19 | even | 6 | ||
42.4.f.a.5.5 | yes | 16 | 84.47 | odd | 6 | ||
42.4.f.a.17.2 | yes | 16 | 12.11 | even | 2 | ||
42.4.f.a.17.5 | yes | 16 | 4.3 | odd | 2 | ||
294.4.d.a.293.4 | 16 | 84.11 | even | 6 | |||
294.4.d.a.293.5 | 16 | 84.59 | odd | 6 | |||
294.4.d.a.293.12 | 16 | 28.3 | even | 6 | |||
294.4.d.a.293.13 | 16 | 28.11 | odd | 6 | |||
294.4.f.a.215.3 | 16 | 28.23 | odd | 6 | |||
294.4.f.a.215.8 | 16 | 84.23 | even | 6 | |||
294.4.f.a.227.3 | 16 | 84.83 | odd | 2 | |||
294.4.f.a.227.8 | 16 | 28.27 | even | 2 | |||
336.4.bc.e.17.6 | 16 | 3.2 | odd | 2 | inner | ||
336.4.bc.e.17.8 | 16 | 1.1 | even | 1 | trivial | ||
336.4.bc.e.257.6 | 16 | 7.5 | odd | 6 | inner | ||
336.4.bc.e.257.8 | 16 | 21.5 | even | 6 | inner |