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 | 257.6 | ||
Root | \(2.30541 - 1.91966i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.257 |
Dual form | 336.4.bc.e.17.6 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 3.99309 | − | 3.32495i | 0.768470 | − | 0.639886i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.90442 | − | 17.1550i | 0.885879 | − | 1.53439i | 0.0411754 | − | 0.999152i | \(-0.486890\pi\) |
0.844703 | − | 0.535235i | \(-0.179777\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.4277 | + | 1.84901i | −0.995004 | + | 0.0998373i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.88947 | − | 26.5536i | 0.181091 | − | 0.983466i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.28742 | + | 2.47535i | −0.117519 | + | 0.0678495i | −0.557607 | − | 0.830105i | \(-0.688280\pi\) |
0.440088 | + | 0.897954i | \(0.354947\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 17.7414i | − | 0.378505i | −0.981928 | − | 0.189253i | \(-0.939394\pi\) | ||
0.981928 | − | 0.189253i | \(-0.0606065\pi\) | |||||||
\(14\) | 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 | \(-0.162363\pi\) |
−0.859186 | + | 0.511663i | \(0.829030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −83.9968 | − | 48.4956i | −1.01422 | − | 0.585561i | −0.101796 | − | 0.994805i | \(-0.532459\pi\) |
−0.912425 | + | 0.409245i | \(0.865792\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −67.4356 | + | 68.6545i | −0.700746 | + | 0.713411i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 135.935 | + | 78.4822i | 1.23237 | + | 0.711508i | 0.967523 | − | 0.252783i | \(-0.0813460\pi\) |
0.264845 | + | 0.964291i | \(0.414679\pi\) | |||||||
\(24\) | 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 | −0.682255 | − | 0.731114i | \(-0.739001\pi\) |
0.292036 | + | 0.956407i | \(0.405667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.88966 | + | 24.1397i | −0.0468937 | + | 0.127339i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −150.796 | + | 334.440i | −0.728264 | + | 1.61516i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −124.469 | + | 215.587i | −0.553044 | + | 0.957901i | 0.445009 | + | 0.895526i | \(0.353201\pi\) |
−0.998053 | + | 0.0623743i | \(0.980133\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −58.9891 | − | 70.8428i | −0.242200 | − | 0.290870i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 343.701 | 1.30920 | 0.654598 | − | 0.755977i | \(-0.272838\pi\) | ||||
0.654598 | + | 0.755977i | \(0.272838\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 24.5859 | 0.0871934 | 0.0435967 | − | 0.999049i | \(-0.486118\pi\) | ||||
0.0435967 | + | 0.999049i | \(0.486118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −407.099 | − | 346.877i | −1.34859 | − | 1.14910i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 235.248 | − | 407.461i | 0.730093 | − | 1.26456i | −0.226750 | − | 0.973953i | \(-0.572810\pi\) |
0.956843 | − | 0.290606i | \(-0.0938568\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 336.162 | − | 68.1462i | 0.980065 | − | 0.198677i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.24175 | + | 3.40335i | 0.0253746 | + | 0.00934441i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −344.910 | + | 199.134i | −0.893907 | + | 0.516097i | −0.875218 | − | 0.483728i | \(-0.839282\pi\) |
−0.0186885 | + | 0.999825i | \(0.505949\pi\) | |||||||
\(54\) | 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 | −0.952286 | − | 0.305208i | \(-0.901274\pi\) |
0.211825 | − | 0.977308i | \(-0.432059\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −273.703 | − | 158.023i | −0.574494 | − | 0.331684i | 0.184448 | − | 0.982842i | \(-0.440950\pi\) |
−0.758942 | + | 0.651158i | \(0.774284\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −41.0038 | + | 498.363i | −0.0819999 | + | 0.996632i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −304.352 | − | 175.718i | −0.580773 | − | 0.335310i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −116.895 | − | 202.469i | −0.213150 | − | 0.369186i | 0.739549 | − | 0.673103i | \(-0.235039\pi\) |
−0.952699 | + | 0.303917i | \(0.901706\pi\) | |||||||
\(68\) | 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 | −0.000271580 | − | 1.00000i | \(-0.500086\pi\) |
0.865890 | + | 0.500235i | \(0.166753\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1303.80 | − | 480.137i | −2.00734 | − | 0.739220i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 74.4305 | − | 53.5425i | 0.110158 | − | 0.0792433i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 151.191 | − | 261.870i | 0.215320 | − | 0.372945i | −0.738052 | − | 0.674744i | \(-0.764254\pi\) |
0.953371 | + | 0.301799i | \(0.0975873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −681.186 | − | 259.666i | −0.934412 | − | 0.356194i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 856.438 | 1.13261 | 0.566303 | − | 0.824197i | \(-0.308373\pi\) | ||||
0.566303 | + | 0.824197i | \(0.308373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 37.5446 | 0.0479092 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 305.941 | + | 367.419i | 0.377015 | + | 0.452775i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 453.577 | − | 785.618i | 0.540214 | − | 0.935678i | −0.458678 | − | 0.888603i | \(-0.651677\pi\) |
0.998891 | − | 0.0470750i | \(-0.0149900\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 32.8040 | + | 326.933i | 0.0377889 | + | 0.376614i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −139.650 | + | 379.216i | −0.155710 | + | 0.422827i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1663.88 | + | 960.642i | −1.79695 | + | 1.03747i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 70.3731i | 0.0736629i | 0.999321 | + | 0.0368315i | \(0.0117265\pi\) | ||||
−0.999321 | + | 0.0368315i | \(0.988274\pi\) | |||||||
\(98\) | 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 | \(-0.129177\pi\) |
−0.801272 | + | 0.598300i | \(0.795843\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9592 | + | 9.79138i | 0.0162237 | + | 0.00936674i | 0.508090 | − | 0.861304i | \(-0.330352\pi\) |
−0.491866 | + | 0.870671i | \(0.663685\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 509.854 | + | 1836.84i | 0.473873 | + | 1.70721i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 419.010 | + | 241.915i | 0.378572 | + | 0.218569i | 0.677197 | − | 0.735802i | \(-0.263195\pi\) |
−0.298625 | + | 0.954371i | \(0.596528\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21.4023 | − | 37.0698i | −0.0188070 | − | 0.0325747i | 0.856469 | − | 0.516199i | \(-0.172653\pi\) |
−0.875276 | + | 0.483624i | \(0.839320\pi\) | |||||||
\(110\) | 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 | ||||||||
\(117\) | −471.097 | − | 86.7457i | −0.372247 | − | 0.0685440i | ||||
\(118\) | 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 | ||||||||
\(123\) | 1372.43 | − | 1142.79i | 1.00608 | − | 0.837737i | ||||
\(124\) | 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 | ||||||||
\(129\) | 98.1736 | − | 81.7468i | 0.0670054 | − | 0.0557938i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 790.927 | − | 1369.93i | 0.527508 | − | 0.913671i | −0.471977 | − | 0.881611i | \(-0.656460\pi\) |
0.999486 | − | 0.0320608i | \(-0.0102070\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1637.54 | + | 738.353i | 1.06761 | + | 0.481378i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2778.93 | − | 31.5271i | −1.77164 | − | 0.0200994i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1597.31 | − | 922.210i | 0.996115 | − | 0.575107i | 0.0890187 | − | 0.996030i | \(-0.471627\pi\) |
0.907097 | + | 0.420923i | \(0.138294\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 55.8671i | − | 0.0340905i | −0.999855 | − | 0.0170453i | \(-0.994574\pi\) | ||
0.999855 | − | 0.0170453i | \(-0.00542594\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 1115.74 | − | 1389.84i | 0.626020 | − | 0.779807i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2951.20 | + | 1703.87i | 1.62263 | + | 0.936824i | 0.986214 | + | 0.165477i | \(0.0529163\pi\) |
0.636414 | + | 0.771348i | \(0.280417\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1627.89 | + | 2819.59i | 0.877324 | + | 1.51957i | 0.854267 | + | 0.519835i | \(0.174007\pi\) |
0.0230569 | + | 0.999734i | \(0.492660\pi\) | |||||||
\(152\) | 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 | 0.177271 | − | 0.984162i | \(-0.443273\pi\) |
0.940945 | + | 0.338560i | \(0.109940\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −715.146 | + | 1941.97i | −0.356697 | + | 0.968604i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2650.09 | − | 1194.90i | −1.29725 | − | 0.584917i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 862.851 | − | 1494.50i | 0.414624 | − | 0.718150i | −0.580765 | − | 0.814071i | \(-0.697246\pi\) |
0.995389 | + | 0.0959216i | \(0.0305798\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 326.069 | + | 391.592i | 0.153845 | + | 0.184760i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −485.621 | −0.225021 | −0.112510 | − | 0.993651i | \(-0.535889\pi\) | ||||
−0.112510 | + | 0.993651i | \(0.535889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1882.24 | 0.856734 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1698.43 | + | 1993.30i | −0.759546 | + | 0.891412i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −726.552 | + | 1258.43i | −0.319299 | + | 0.553042i | −0.980342 | − | 0.197306i | \(-0.936781\pi\) |
0.661043 | + | 0.750348i | \(0.270114\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2891.87 | + | 4020.05i | 1.24917 | + | 1.73650i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3272.48 | − | 1205.12i | −1.38969 | − | 0.511764i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1099.44 | + | 634.760i | −0.459082 | + | 0.265051i | −0.711658 | − | 0.702526i | \(-0.752056\pi\) |
0.252576 | + | 0.967577i | \(0.418722\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3289.26i | 1.35076i | 0.737468 | + | 0.675382i | \(0.236021\pi\) | ||||
−0.737468 | + | 0.675382i | \(0.763979\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | 1493.30 | + | 2126.34i | 0.574717 | + | 0.818352i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1713.46 | + | 989.265i | 0.649117 | + | 0.374768i | 0.788118 | − | 0.615524i | \(-0.211056\pi\) |
−0.139001 | + | 0.990292i | \(0.544389\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 459.923 | + | 796.611i | 0.171534 | + | 0.297105i | 0.938956 | − | 0.344037i | \(-0.111794\pi\) |
−0.767423 | + | 0.641142i | \(0.778461\pi\) | |||||||
\(194\) | 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 | −0.417405 | − | 0.908720i | \(-0.637060\pi\) |
0.578272 | + | 0.815844i | \(0.303727\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1139.97 | − | 419.804i | −0.400036 | − | 0.147317i | ||||
\(202\) | 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 | ||||||||
\(207\) | 2748.64 | − | 3225.83i | 0.922915 | − | 1.08314i | ||||
\(208\) | 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 | ||||||||
\(213\) | −506.140 | − | 607.847i | −0.162817 | − | 0.195535i | ||||
\(214\) | 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 | ||||||||
\(219\) | 1119.44 | − | 3039.81i | 0.345409 | − | 0.937951i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 29.1209 | − | 16.8130i | 0.00886373 | − | 0.00511748i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1782.29i | 0.535206i | 0.963529 | + | 0.267603i | \(0.0862316\pi\) | ||||
−0.963529 | + | 0.267603i | \(0.913768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6802.63 | + | 2417.85i | −2.01559 | + | 0.716400i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1721.58 | + | 2981.86i | 0.503370 | + | 0.871863i | 0.999992 | + | 0.00389579i | \(0.00124007\pi\) |
−0.496622 | + | 0.867967i | \(0.665427\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4706.78 | − | 2717.46i | −1.35822 | − | 0.784169i | −0.368837 | − | 0.929494i | \(-0.620244\pi\) |
−0.989384 | + | 0.145325i | \(0.953577\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 119.182 | − | 461.277i | 0.0339462 | − | 0.131384i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3815.33 | − | 2202.78i | −1.07275 | − | 0.619351i | −0.143817 | − | 0.989604i | \(-0.545938\pi\) |
−0.928931 | + | 0.370253i | \(0.879271\pi\) | |||||||
\(234\) | 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 | −0.739264 | − | 0.673416i | \(-0.764826\pi\) |
0.213563 | + | 0.976929i | \(0.431493\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3583.41 | + | 1228.04i | −0.945991 | + | 0.324193i | ||||
\(244\) | 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 | ||||||||
\(249\) | 3419.83 | − | 2847.61i | 0.870373 | − | 0.724738i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4513.50 | −1.13502 | −0.567510 | − | 0.823367i | \(-0.692093\pi\) | ||||
−0.567510 | + | 0.823367i | \(0.692093\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −777.082 | −0.193102 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 149.919 | − | 124.834i | 0.0368167 | − | 0.0306564i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2969.31 | − | 5142.99i | 0.720701 | − | 1.24829i | −0.240018 | − | 0.970769i | \(-0.577153\pi\) |
0.960719 | − | 0.277523i | \(-0.0895134\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1895.06 | − | 4202.93i | 0.454647 | − | 1.00833i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2443.30 | + | 449.898i | 0.579449 | + | 0.106697i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4727.20 | − | 2729.25i | 1.10833 | − | 0.639897i | 0.169936 | − | 0.985455i | \(-0.445644\pi\) |
0.938397 | + | 0.345558i | \(0.112310\pi\) | |||||||
\(264\) | 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 | −0.992979 | − | 0.118294i | \(-0.962257\pi\) |
0.394043 | − | 0.919092i | \(-0.371076\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5436.74 | + | 3138.90i | 1.21866 | + | 0.703596i | 0.964632 | − | 0.263599i | \(-0.0849096\pi\) |
0.254033 | + | 0.967196i | \(0.418243\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1218.02 | + | 1196.40i | 0.270030 | + | 0.265236i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1146.42 | + | 661.884i | 0.251387 | + | 0.145139i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3748.17 | − | 6492.02i | −0.813017 | − | 1.40819i | −0.910743 | − | 0.412974i | \(-0.864490\pi\) |
0.0977256 | − | 0.995213i | \(-0.468843\pi\) | |||||||
\(278\) | 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 | −0.720011 | − | 0.693963i | \(-0.755863\pi\) |
0.240984 | + | 0.970529i | \(0.422530\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3449.94 | + | 9368.24i | −0.717040 | + | 1.94711i | ||||
\(286\) | 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 | ||||||||
\(291\) | 233.987 | + | 281.006i | 0.0471359 | + | 0.0566077i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −889.363 | −0.177328 | −0.0886640 | − | 0.996062i | \(-0.528260\pi\) | ||||
−0.0886640 | + | 0.996062i | \(0.528260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13294.4 | −2.62383 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 597.530 | + | 354.083i | 0.116742 | + | 0.0691783i | ||||
\(298\) | 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 | ||||||||
\(303\) | 1163.16 | + | 428.345i | 0.220534 | + | 0.0812137i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5421.75 | + | 3130.25i | −1.01786 | + | 0.587664i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3995.12i | 0.742715i | 0.928490 | + | 0.371357i | \(0.121107\pi\) | ||||
−0.928490 | + | 0.371357i | \(0.878893\pi\) | |||||||
\(308\) | 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 | \(-0.181530\pi\) |
−0.888420 | + | 0.459031i | \(0.848197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1271.68 | − | 734.205i | −0.229647 | − | 0.132587i | 0.380762 | − | 0.924673i | \(-0.375662\pi\) |
−0.610409 | + | 0.792086i | \(0.708995\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8143.28 | + | 5639.42i | 1.45658 | + | 1.00871i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6545.26 | + | 3778.91i | 1.15968 | + | 0.669542i | 0.951227 | − | 0.308491i | \(-0.0998239\pi\) |
0.208453 | + | 0.978032i | \(0.433157\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | −208.716 | − | 76.8616i | −0.0352968 | − | 0.0129983i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3581.68 | + | 7943.55i | −0.600196 | + | 1.33113i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2932.76 | − | 5079.69i | 0.487007 | − | 0.843520i | −0.512882 | − | 0.858459i | \(-0.671422\pi\) |
0.999888 | + | 0.0149389i | \(0.00475537\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5116.03 | + | 4359.21i | 0.841911 | + | 0.717368i | ||||
\(334\) | 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 | ||||||||
\(339\) | −1258.02 | − | 1510.82i | −0.201553 | − | 0.242055i | ||||
\(340\) | 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 | ||||||||
\(345\) | 5583.16 | − | 15161.0i | 0.871267 | − | 2.36591i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −968.873 | + | 559.379i | −0.149890 | + | 0.0865390i | −0.573069 | − | 0.819507i | \(-0.694247\pi\) |
0.423179 | + | 0.906046i | \(0.360914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2364.44i | 0.362652i | 0.983423 | + | 0.181326i | \(0.0580389\pi\) | ||||
−0.983423 | + | 0.181326i | \(0.941961\pi\) | |||||||
\(350\) | 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 | \(-0.0984194\pi\) |
−0.739813 | + | 0.672812i | \(0.765086\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2611.41 | − | 1507.70i | −0.390421 | − | 0.225410i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −176.597 | − | 45.6280i | −0.0261807 | − | 0.00676439i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4504.97 | + | 2600.95i | 0.662293 | + | 0.382375i | 0.793150 | − | 0.609026i | \(-0.208440\pi\) |
−0.130857 | + | 0.991401i | \(0.541773\pi\) | |||||||
\(360\) | 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 | −0.111366 | − | 0.993779i | \(-0.535523\pi\) |
0.804955 | + | 0.593336i | \(0.202189\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1680.51 | − | 9126.49i | 0.237084 | − | 1.28755i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5987.71 | − | 4307.33i | 0.837915 | − | 0.602764i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3422.23 | + | 5927.47i | −0.475057 | + | 0.822822i | −0.999592 | − | 0.0285664i | \(-0.990906\pi\) |
0.524535 | + | 0.851389i | \(0.324239\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11262.9 | + | 9378.32i | −1.55096 | + | 1.29145i | ||||
\(376\) | 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 | ||||||||
\(381\) | −450.441 | + | 375.071i | −0.0605690 | + | 0.0504343i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2151.66 | + | 3726.78i | −0.287062 | + | 0.497206i | −0.973107 | − | 0.230353i | \(-0.926012\pi\) |
0.686045 | + | 0.727559i | \(0.259345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −181.328 | − | 1807.16i | −0.0240035 | − | 0.239225i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 120.212 | − | 652.844i | 0.0157900 | − | 0.0857517i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6143.61 | + | 3547.01i | −0.800754 | + | 0.462315i | −0.843735 | − | 0.536760i | \(-0.819648\pi\) |
0.0429809 | + | 0.999076i | \(0.486315\pi\) | |||||||
\(390\) | 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 | 0.725742 | − | 0.687967i | \(-0.241496\pi\) |
−0.232925 | + | 0.972495i | \(0.574830\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8993.82 | − | 2496.43i | 1.12846 | − | 0.313227i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6038.64 | + | 3486.41i | 0.752008 | + | 0.434172i | 0.826419 | − | 0.563055i | \(-0.190374\pi\) |
−0.0744107 | + | 0.997228i | \(0.523708\pi\) | |||||||
\(402\) | 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 | 0.502984 | − | 0.864296i | \(-0.332235\pi\) |
0.999994 | − | 0.00344923i | \(-0.00109793\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3311.92 | − | 8993.45i | 0.397481 | − | 1.07935i | ||||
\(412\) | 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 | ||||||||
\(417\) | −185.755 | − | 223.082i | −0.0218141 | − | 0.0261975i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14839.8 | 1.73024 | 0.865122 | − | 0.501562i | \(-0.167241\pi\) | ||||
0.865122 | + | 0.501562i | \(0.167241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11073.0 | −1.28187 | −0.640935 | − | 0.767595i | \(-0.721453\pi\) | ||||
−0.640935 | + | 0.767595i | \(0.721453\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9669.31 | − | 8238.93i | −1.11144 | − | 0.947023i | ||||
\(424\) | 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 | ||||||||
\(429\) | 428.271 | + | 157.715i | 0.0481984 | + | 0.0177495i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5552.06 | + | 3205.49i | −0.620495 | + | 0.358243i | −0.777062 | − | 0.629424i | \(-0.783291\pi\) |
0.156566 | + | 0.987667i | \(0.449957\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12881.0i | 1.42961i | 0.699322 | + | 0.714807i | \(0.253486\pi\) | ||||
−0.699322 | + | 0.714807i | \(0.746514\pi\) | |||||||
\(434\) | 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 | 0.868161 | − | 0.496282i | \(-0.165302\pi\) |
0.00428790 | + | 0.999991i | \(0.498635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −165.872 | − | 9259.51i | −0.0179108 | − | 0.999840i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7691.54 | − | 4440.71i | −0.824912 | − | 0.476263i | 0.0271952 | − | 0.999630i | \(-0.491342\pi\) |
−0.852108 | + | 0.523367i | \(0.824676\pi\) | |||||||
\(444\) | 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 | ||||||||
\(453\) | 15875.3 | + | 5846.21i | 1.64655 | + | 0.606356i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5933.43 | + | 2675.33i | 0.611348 | + | 0.275652i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −278.827 | + | 482.943i | −0.0285404 | + | 0.0494335i | −0.879943 | − | 0.475080i | \(-0.842419\pi\) |
0.851402 | + | 0.524513i | \(0.175753\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 135.558 | − | 228.761i | 0.0137850 | − | 0.0232629i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7422.24 | 0.749866 | 0.374933 | − | 0.927052i | \(-0.377666\pi\) | ||||
0.374933 | + | 0.927052i | \(0.377666\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10478.8 | −1.05182 | −0.525908 | − | 0.850541i | \(-0.676274\pi\) | ||||
−0.525908 | + | 0.850541i | \(0.676274\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5122.29 | + | 6151.60i | 0.510840 | + | 0.613492i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4708.74 | + | 8155.78i | −0.466584 | + | 0.808147i | −0.999271 | − | 0.0381650i | \(-0.987849\pi\) |
0.532688 | + | 0.846312i | \(0.321182\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2528.48 | + | 3514.90i | 0.248943 | + | 0.346062i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4561.04 | − | 12385.4i | 0.446203 | − | 1.21166i | ||||
\(472\) | 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 | 0.999977 | + | 0.00678003i | \(0.00215817\pi\) |
−0.494117 | + | 0.869396i | \(0.664508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3824.81 | + | 2208.25i | 0.362570 | + | 0.209330i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14555.0 | + | 4040.06i | −1.37117 | + | 0.380599i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1207.25 | + | 697.005i | 0.113027 | + | 0.0652564i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6387.19 | − | 11062.9i | −0.594314 | − | 1.02938i | −0.993643 | − | 0.112575i | \(-0.964090\pi\) |
0.399329 | − | 0.916808i | \(-0.369243\pi\) | |||||||
\(488\) | 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 | ||||||||
\(495\) | 2604.04 | + | 479.497i | 0.236451 | + | 0.0435390i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 281.466 | + | 2805.16i | 0.0254033 | + | 0.253176i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6862.74 | + | 11886.6i | −0.615668 | + | 1.06637i | 0.374599 | + | 0.927187i | \(0.377780\pi\) |
−0.990267 | + | 0.139182i | \(0.955553\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1939.13 | + | 1614.66i | −0.172922 | + | 0.143988i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5480.28 | −0.485793 | −0.242896 | − | 0.970052i | \(-0.578098\pi\) | ||||
−0.242896 | + | 0.970052i | \(0.578098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4725.34 | 0.416386 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7515.96 | − | 6258.36i | 0.658374 | − | 0.548212i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5331.28 | + | 9234.05i | −0.464253 | + | 0.804111i | −0.999168 | − | 0.0407959i | \(-0.987011\pi\) |
0.534914 | + | 0.844906i | \(0.320344\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9372.71 | + | 6742.37i | −0.811398 | + | 0.583689i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −154.368 | + | 13606.6i | −0.0132856 | + | 1.17105i | ||||
\(514\) | 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 | \(-0.327307\pi\) |
−0.999821 | + | 0.0189300i | \(0.993974\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8319.57 | − | 4803.31i | −0.695582 | − | 0.401594i | 0.110118 | − | 0.993919i | \(-0.464877\pi\) |
−0.805700 | + | 0.592324i | \(0.798211\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24913.9 | + | 6437.09i | 2.07111 | + | 0.535119i | ||||
\(526\) | 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 | ||||||||
\(537\) | −2279.60 | + | 6190.22i | −0.183188 | + | 0.497444i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1272.58 | + | 1124.29i | −0.101696 | + | 0.0898452i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8782.28 | − | 15211.3i | 0.697929 | − | 1.20885i | −0.271254 | − | 0.962508i | \(-0.587438\pi\) |
0.969183 | − | 0.246341i | \(-0.0792282\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10936.6 | + | 13134.3i | 0.864336 | + | 1.03802i | ||||
\(544\) | 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 | ||||||||
\(549\) | −5534.33 | + | 6495.16i | −0.430236 | + | 0.504930i | ||||
\(550\) | 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 | ||||||||
\(555\) | 24044.6 | + | 8854.64i | 1.83899 | + | 0.677223i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11945.8 | − | 6896.92i | 0.908726 | − | 0.524653i | 0.0287052 | − | 0.999588i | \(-0.490862\pi\) |
0.880021 | + | 0.474935i | \(0.157528\pi\) | |||||||
\(558\) | 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 | \(-0.278517\pi\) |
−0.985208 | + | 0.171361i | \(0.945184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6490.74 | − | 3747.43i | −0.483305 | − | 0.279036i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13032.8 | + | 3525.53i | 0.965305 | + | 0.261126i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15644.0 | − | 9032.06i | −1.15260 | − | 0.665455i | −0.203082 | − | 0.979162i | \(-0.565096\pi\) |
−0.949520 | + | 0.313707i | \(0.898429\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7626.26 | + | 13209.1i | 0.558930 | + | 0.968095i | 0.997586 | + | 0.0694402i | \(0.0221213\pi\) |
−0.438656 | + | 0.898655i | \(0.644545\pi\) | |||||||
\(572\) | 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 | −0.660177 | − | 0.751110i | \(-0.729519\pi\) |
0.320392 | + | 0.947285i | \(0.396185\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4485.20 | + | 1651.71i | 0.321932 | + | 0.118554i | ||||
\(580\) | 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 | ||||||||
\(585\) | −6154.06 | + | 7222.48i | −0.434939 | + | 0.510449i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23972.1 | −1.68558 | −0.842791 | − | 0.538241i | \(-0.819089\pi\) | ||||
−0.842791 | + | 0.538241i | \(0.819089\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7543.15 | 0.527691 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10180.9 | + | 12226.8i | 0.708608 | + | 0.851001i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 697.071 | − | 1207.36i | 0.0482720 | − | 0.0836095i | −0.840880 | − | 0.541222i | \(-0.817962\pi\) |
0.889152 | + | 0.457612i | \(0.151295\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −691.861 | + | 69.4203i | −0.0476698 | + | 0.00478312i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 936.343 | − | 2542.62i | 0.0641909 | − | 0.174309i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20811.2 | − | 12015.4i | 1.41957 | − | 0.819591i | 0.423312 | − | 0.905984i | \(-0.360867\pi\) |
0.996261 | + | 0.0863929i | \(0.0275340\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10741.9i | 0.729073i | 0.931189 | + | 0.364536i | \(0.118773\pi\) | ||||
−0.931189 | + | 0.364536i | \(0.881227\pi\) | |||||||
\(602\) | 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 | −0.995946 | − | 0.0899549i | \(-0.971328\pi\) |
−0.575876 | − | 0.817537i | \(-0.695339\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6317.16 | − | 6205.01i | −0.420335 | − | 0.412873i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7228.91 | − | 4173.61i | −0.478642 | − | 0.276344i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14388.2 | − | 24921.1i | −0.948015 | − | 1.64201i | −0.749600 | − | 0.661891i | \(-0.769754\pi\) |
−0.198415 | − | 0.980118i | \(-0.563579\pi\) | |||||||
\(614\) | 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 | −0.579128 | − | 0.815236i | \(-0.696607\pi\) |
0.416451 | + | 0.909158i | \(0.363274\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 249.820 | − | 22020.1i | 0.0161432 | − | 1.42292i | ||||
\(622\) | 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 | ||||||||
\(627\) | 1917.37 | − | 1596.55i | 0.122125 | − | 0.101691i | ||||
\(628\) | 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 | ||||||||
\(633\) | −397.826 | + | 331.260i | −0.0249797 | + | 0.0208000i | ||||
\(634\) | 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 | ||||||||
\(639\) | −4042.12 | − | 744.298i | −0.250241 | − | 0.0460782i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12252.1 | − | 7073.73i | 0.754957 | − | 0.435875i | −0.0725251 | − | 0.997367i | \(-0.523106\pi\) |
0.827482 | + | 0.561492i | \(0.189772\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4248.35i | 0.260557i | 0.991477 | + | 0.130279i | \(0.0415872\pi\) | ||||
−0.991477 | + | 0.130279i | \(0.958413\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −430.010 | − | 2493.82i | −0.0262506 | − | 0.152239i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8314.83 | + | 14401.7i | 0.505239 | + | 0.875100i | 0.999982 | + | 0.00606041i | \(0.00192910\pi\) |
−0.494742 | + | 0.869040i | \(0.664738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2877.44 | + | 1661.29i | 0.174036 | + | 0.100480i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1872.25 | − | 7246.30i | 0.112718 | − | 0.436260i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26164.5 | − | 15106.1i | −1.56798 | − | 0.905276i | −0.996404 | − | 0.0847307i | \(-0.972997\pi\) |
−0.571581 | − | 0.820546i | \(-0.693670\pi\) | |||||||
\(654\) | 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 | −0.682427 | − | 0.730954i | \(-0.739076\pi\) |
0.291811 | + | 0.956476i | \(0.405742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 60.3801 | − | 163.961i | 0.00353691 | − | 0.00960441i | ||||
\(664\) | 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 | ||||||||
\(669\) | 5926.02 | + | 7116.84i | 0.342471 | + | 0.411290i | ||||
\(670\) | 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 | ||||||||
\(675\) | −19124.3 | + | 32273.1i | −1.09051 | + | 1.84028i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5256.30 | + | 9104.19i | −0.298399 | + | 0.516842i | −0.975770 | − | 0.218799i | \(-0.929786\pi\) |
0.677371 | + | 0.735642i | \(0.263119\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −130.121 | − | 1296.82i | −0.00735431 | − | 0.0732949i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16788.9 | + | 6182.66i | 0.944717 | + | 0.347900i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15679.7 | − | 9052.66i | 0.878427 | − | 0.507160i | 0.00828788 | − | 0.999966i | \(-0.497362\pi\) |
0.870140 | + | 0.492805i | \(0.164029\pi\) | |||||||
\(684\) | 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 | 0.274083 | − | 0.961706i | \(-0.411626\pi\) |
−0.695820 | + | 0.718216i | \(0.744959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1057.82 | − | 2238.19i | −0.0579845 | − | 0.122687i | ||||
\(694\) | 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 | ||||||||
\(705\) | −45444.4 | − | 16735.3i | −2.42771 | − | 0.894026i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2579.92 | − | 3586.41i | −0.137239 | − | 0.190779i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7996.91 | + | 13851.1i | −0.423597 | + | 0.733692i | −0.996288 | − | 0.0860795i | \(-0.972566\pi\) |
0.572691 | + | 0.819771i | \(0.305899\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6214.34 | − | 5295.05i | −0.327786 | − | 0.279297i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12207.4 | −0.641191 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1739.85 | 0.0910024 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6717.36 | − | 8067.20i | −0.349881 | − | 0.420188i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10462.3 | + | 18121.2i | −0.542668 | + | 0.939928i | 0.456082 | + | 0.889938i | \(0.349252\pi\) |
−0.998750 | + | 0.0499905i | \(0.984081\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −330.623 | − | 149.075i | −0.0170778 | − | 0.00770021i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4078.05 | + | 11073.9i | −0.209771 | + | 0.569629i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21307.4 | − | 12301.8i | 1.09150 | − | 0.630176i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21598.1i | − | 1.10183i | −0.834562 | − | 0.550915i | \(-0.814279\pi\) | ||
0.834562 | − | 0.550915i | \(-0.185721\pi\) | |||||||
\(728\) | 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 | 0.707057 | − | 0.707157i | \(-0.250022\pi\) |
−0.258887 | + | 0.965908i | \(0.583356\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12791.8 | − | 32906.0i | −0.641949 | − | 1.65137i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1002.36 | + | 578.713i | 0.0500982 | + | 0.0289242i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9022.60 | − | 15627.6i | −0.449123 | − | 0.777903i | 0.549206 | − | 0.835687i | \(-0.314930\pi\) |
−0.998329 | + | 0.0577833i | \(0.981597\pi\) | |||||||
\(740\) | 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 | ||||||||
\(747\) | 4187.52 | − | 22741.5i | 0.205105 | − | 1.11388i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8168.70 | − | 3683.20i | −0.398502 | − | 0.179681i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9431.09 | + | 16335.1i | −0.458249 | + | 0.793711i | −0.998869 | − | 0.0475563i | \(-0.984857\pi\) |
0.540619 | + | 0.841267i | \(0.318190\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18022.8 | + | 15007.2i | −0.872228 | + | 0.726283i | ||||
\(754\) | 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 | ||||||||
\(759\) | −3102.96 | + | 2583.76i | −0.148393 | + | 0.123563i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12563.5 | + | 21760.6i | −0.598457 | + | 1.03656i | 0.394592 | + | 0.918856i | \(0.370886\pi\) |
−0.993049 | + | 0.117702i | \(0.962447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 462.938 | + | 643.540i | 0.0219652 | + | 0.0305343i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 183.573 | − | 996.943i | 0.00867593 | − | 0.0471170i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10311.6 | + | 5953.43i | −0.485439 | + | 0.280268i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23475.2i | 1.10083i | 0.834892 | + | 0.550413i | \(0.185530\pi\) | ||||
−0.834892 | + | 0.550413i | \(0.814470\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5243.47 | − | 30409.2i | −0.244927 | − | 1.42044i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15695.6 | + | 27185.6i | 0.730313 | + | 1.26494i | 0.956749 | + | 0.290913i | \(0.0939592\pi\) |
−0.226436 | + | 0.974026i | \(0.572708\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18009.3 | + | 10397.7i | 0.834727 | + | 0.481930i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6407.36 | − | 23083.6i | −0.295834 | − | 1.06579i | ||||
\(778\) | 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 | −0.406378 | − | 0.913705i | \(-0.633208\pi\) |
0.588103 | + | 0.808786i | \(0.299875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9801.51 | − | 26615.8i | 0.442260 | − | 1.20095i | ||||
\(790\) | 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 | ||||||||
\(795\) | 26231.3 | + | 31502.4i | 1.17022 | + | 1.40538i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −121.248 | −0.00538874 | −0.00269437 | − | 0.999996i | \(-0.500858\pi\) | ||||
−0.00269437 | + | 0.999996i | \(0.500858\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 891.749 | 0.0394841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18643.2 | − | 15885.3i | −0.822379 | − | 0.700725i | ||||
\(802\) | 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 | ||||||||
\(807\) | −25769.4 | − | 9489.81i | −1.12407 | − | 0.413949i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11357.9 | − | 6557.47i | 0.493599 | − | 0.284979i | −0.232467 | − | 0.972604i | \(-0.574680\pi\) |
0.726066 | + | 0.687625i | \(0.241347\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2601.55i | − | 0.112642i | −0.998413 | − | 0.0563211i | \(-0.982063\pi\) | ||
0.998413 | − | 0.0563211i | \(-0.0179371\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | 8841.64 | + | 727.463i | 0.377230 | + | 0.0310374i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13977.1 | − | 8069.68i | −0.594158 | − | 0.343038i | 0.172582 | − | 0.984995i | \(-0.444789\pi\) |
−0.766740 | + | 0.641958i | \(0.778122\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9786.73 | + | 16951.1i | 0.414513 | + | 0.717957i | 0.995377 | − | 0.0960431i | \(-0.0306187\pi\) |
−0.580864 | + | 0.814000i | \(0.697285\pi\) | |||||||
\(824\) | 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 | −0.596282 | − | 0.802775i | \(-0.703356\pi\) |
0.397083 | + | 0.917783i | \(0.370023\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36552.4 | − | 13460.7i | −1.52586 | − | 0.561911i | ||||
\(832\) | 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 | ||||||||
\(837\) | 9386.74 | + | 5562.36i | 0.387638 | + | 0.229705i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25774.7 | −1.06060 | −0.530299 | − | 0.847811i | \(-0.677920\pi\) | ||||
−0.530299 | + | 0.847811i | \(0.677920\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15922.5 | 0.652854 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2480.04 | + | 2978.40i | 0.101325 | + | 0.121686i | ||||
\(844\) | 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 | ||||||||
\(849\) | −4728.56 | + | 12840.3i | −0.191147 | + | 0.519056i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33839.5 | + | 19537.3i | −1.36311 | + | 0.786990i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 15407.3i | − | 0.618447i | −0.950989 | − | 0.309224i | \(-0.899931\pi\) | ||
0.950989 | − | 0.309224i | \(-0.100069\pi\) | |||||||
\(854\) | 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 | \(-0.0936043\pi\) |
−0.729551 | + | 0.683926i | \(0.760271\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32407.3 | + | 18710.4i | 1.28722 | + | 0.743178i | 0.978158 | − | 0.207863i | \(-0.0666510\pi\) |
0.309064 | + | 0.951041i | \(0.399984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23177.7 | + | 23596.6i | −0.917414 | + | 0.933995i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30175.4 | + | 17421.8i | 1.19025 | + | 0.687189i | 0.958362 | − | 0.285554i | \(-0.0921777\pi\) |
0.231884 | + | 0.972743i | \(0.425511\pi\) | |||||||
\(864\) | 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 | ||||||||
\(873\) | 1868.66 | + | 344.087i | 0.0724450 | + | 0.0133397i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 51977.1 | − | 5215.31i | 2.00817 | − | 0.201497i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14281.1 | − | 24735.6i | 0.549874 | − | 0.952409i | −0.448409 | − | 0.893828i | \(-0.648009\pi\) |
0.998283 | − | 0.0585807i | \(-0.0186575\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3551.30 | + | 2957.08i | −0.136271 | + | 0.113470i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25098.4 | −0.959804 | −0.479902 | − | 0.877322i | \(-0.659328\pi\) | ||||
−0.479902 | + | 0.877322i | \(0.659328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32704.3 | 1.24642 | 0.623208 | − | 0.782056i | \(-0.285829\pi\) | ||||
0.623208 | + | 0.782056i | \(0.285829\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −53085.8 | + | 44203.2i | −2.01634 | + | 1.67896i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11659.7 | − | 20195.2i | 0.441368 | − | 0.764472i | −0.556423 | − | 0.830899i | \(-0.687827\pi\) |
0.997791 | + | 0.0664269i | \(0.0211599\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2078.74 | − | 208.578i | 0.0784239 | − | 0.00786894i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3563.30 | − | 572.874i | 0.133979 | − | 0.0215399i | ||||
\(892\) | 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 | ||||||||
\(903\) | −1657.97 | + | 1687.93i | −0.0611004 | + | 0.0622047i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 56427.1 | + | 32578.2i | 2.07260 | + | 1.19661i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18663.6 | − | 32326.3i | −0.683258 | − | 1.18344i | −0.973981 | − | 0.226631i | \(-0.927229\pi\) |
0.290723 | − | 0.956807i | \(-0.406104\pi\) | |||||||
\(908\) | 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 | ||||||||
\(915\) | −11241.6 | + | 30526.4i | −0.406159 | + | 1.10292i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12042.0 | + | 26707.1i | −0.433654 | + | 0.961772i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11879.4 | + | 20575.7i | −0.426404 | + | 0.738553i | −0.996550 | − | 0.0829898i | \(-0.973553\pi\) |
0.570146 | + | 0.821543i | \(0.306886\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13283.5 | + | 15952.8i | 0.475253 | + | 0.570754i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2700.68 | −0.0963097 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 66563.8 | 2.36606 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 342.918 | − | 402.452i | 0.0121498 | − | 0.0142592i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17720.4 | + | 30692.6i | −0.625819 | + | 1.08395i | 0.362563 | + | 0.931959i | \(0.381902\pi\) |
−0.988382 | + | 0.151991i | \(0.951431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31541.4 | − | 10578.3i | −1.11034 | − | 0.372385i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2496.61 | − | 919.398i | −0.0876049 | − | 0.0322612i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −160.969 | + | 92.9357i | −0.00563023 | + | 0.00325061i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 42936.0i | − | 1.49697i | −0.663154 | − | 0.748483i | \(-0.730782\pi\) | ||
0.663154 | − | 0.748483i | \(-0.269218\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7519.12 | + | 1296.53i | −0.261318 | + | 0.0450591i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16115.3 | − | 27912.5i | −0.558282 | − | 0.966972i | −0.997640 | − | 0.0686602i | \(-0.978128\pi\) |
0.439359 | − | 0.898312i | \(-0.355206\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46721.1 | + | 26974.4i | 1.61341 | + | 0.931503i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 51267.6 | − | 4557.29i | 1.76480 | − | 0.156877i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9522.57 | − | 5497.86i | −0.326760 | − | 0.188655i | 0.327642 | − | 0.944802i | \(-0.393746\pi\) |
−0.654402 | + | 0.756147i | \(0.727079\pi\) | |||||||
\(948\) | 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 | ||||||||
\(957\) | −2221.19 | − | 817.971i | −0.0750269 | − | 0.0276293i | ||||
\(958\) | 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 | ||||||||
\(963\) | 8472.46 | − | 9943.38i | 0.283511 | − | 0.332732i | ||||
\(964\) | 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 | ||||||||
\(969\) | −611.230 | − | 734.055i | −0.0202637 | − | 0.0243357i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3033.74 | − | 5254.60i | 0.100265 | − | 0.173664i | −0.811529 | − | 0.584313i | \(-0.801364\pi\) |
0.911794 | + | 0.410648i | \(0.134698\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 103.299 | + | 1029.50i | 0.00340351 | + | 0.0339202i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8518.28 | + | 23131.3i | −0.279798 | + | 0.759788i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11370.3 | + | 6564.62i | −0.372331 | + | 0.214965i | −0.674476 | − | 0.738297i | \(-0.735630\pi\) |
0.302146 | + | 0.953262i | \(0.402297\pi\) | |||||||
\(978\) | 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 | \(-0.310156\pi\) |
−0.997350 | + | 0.0727505i | \(0.976822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52528.2 | + | 30327.2i | 1.69918 | + | 0.981019i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12109.9 | + | 43628.2i | 0.390540 | + | 1.40699i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3342.09 | + | 1929.56i | 0.107454 | + | 0.0620387i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13495.1 | + | 23374.1i | 0.432578 | + | 0.749247i | 0.997094 | − | 0.0761745i | \(-0.0242706\pi\) |
−0.564516 | + | 0.825422i | \(0.690937\pi\) | |||||||
\(992\) | 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 | −0.292695 | − | 0.956206i | \(-0.594552\pi\) |
0.681751 | + | 0.731584i | \(0.261219\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34922.9 | + | 396.203i | 1.10602 | + | 0.0125479i |
(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.257.6 | 16 | ||
3.2 | odd | 2 | inner | 336.4.bc.e.257.8 | 16 | ||
4.3 | odd | 2 | 42.4.f.a.5.2 | ✓ | 16 | ||
7.3 | odd | 6 | inner | 336.4.bc.e.17.8 | 16 | ||
12.11 | even | 2 | 42.4.f.a.5.5 | yes | 16 | ||
21.17 | even | 6 | inner | 336.4.bc.e.17.6 | 16 | ||
28.3 | even | 6 | 42.4.f.a.17.5 | yes | 16 | ||
28.11 | odd | 6 | 294.4.f.a.227.8 | 16 | |||
28.19 | even | 6 | 294.4.d.a.293.13 | 16 | |||
28.23 | odd | 6 | 294.4.d.a.293.12 | 16 | |||
28.27 | even | 2 | 294.4.f.a.215.3 | 16 | |||
84.11 | even | 6 | 294.4.f.a.227.3 | 16 | |||
84.23 | even | 6 | 294.4.d.a.293.5 | 16 | |||
84.47 | odd | 6 | 294.4.d.a.293.4 | 16 | |||
84.59 | odd | 6 | 42.4.f.a.17.2 | yes | 16 | ||
84.83 | odd | 2 | 294.4.f.a.215.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.f.a.5.2 | ✓ | 16 | 4.3 | odd | 2 | ||
42.4.f.a.5.5 | yes | 16 | 12.11 | even | 2 | ||
42.4.f.a.17.2 | yes | 16 | 84.59 | odd | 6 | ||
42.4.f.a.17.5 | yes | 16 | 28.3 | even | 6 | ||
294.4.d.a.293.4 | 16 | 84.47 | odd | 6 | |||
294.4.d.a.293.5 | 16 | 84.23 | even | 6 | |||
294.4.d.a.293.12 | 16 | 28.23 | odd | 6 | |||
294.4.d.a.293.13 | 16 | 28.19 | even | 6 | |||
294.4.f.a.215.3 | 16 | 28.27 | even | 2 | |||
294.4.f.a.215.8 | 16 | 84.83 | odd | 2 | |||
294.4.f.a.227.3 | 16 | 84.11 | even | 6 | |||
294.4.f.a.227.8 | 16 | 28.11 | odd | 6 | |||
336.4.bc.e.17.6 | 16 | 21.17 | even | 6 | inner | ||
336.4.bc.e.17.8 | 16 | 7.3 | odd | 6 | inner | ||
336.4.bc.e.257.6 | 16 | 1.1 | even | 1 | trivial | ||
336.4.bc.e.257.8 | 16 | 3.2 | odd | 2 | inner |