Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(557,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.s (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: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 557.2 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.557 |
Dual form | 882.3.s.a.863.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | −3.67423 | + | 2.12132i | −0.734847 | + | 0.424264i | −0.820193 | − | 0.572087i | \(-0.806134\pi\) |
0.0853458 | + | 0.996351i | \(0.472801\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.00000 | + | 5.19615i | −0.300000 | + | 0.519615i | ||||
\(11\) | 11.0227 | + | 6.36396i | 1.00206 | + | 0.578542i | 0.908858 | − | 0.417105i | \(-0.136955\pi\) |
0.0932057 | + | 0.995647i | \(0.470289\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.0769231 | 0.0384615 | − | 0.999260i | \(-0.487754\pi\) | ||||
0.0384615 | + | 0.999260i | \(0.487754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | −14.6969 | − | 8.48528i | −0.864526 | − | 0.499134i | 0.000999453 | − | 1.00000i | \(-0.499682\pi\) |
−0.865525 | + | 0.500865i | \(0.833015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.5000 | + | 19.9186i | 0.605263 | + | 1.04835i | 0.992010 | + | 0.126161i | \(0.0402654\pi\) |
−0.386747 | + | 0.922186i | \(0.626401\pi\) | |||||||
\(20\) | 8.48528i | 0.424264i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.0000 | 0.818182 | ||||||||
\(23\) | −14.6969 | + | 8.48528i | −0.638997 | + | 0.368925i | −0.784228 | − | 0.620473i | \(-0.786941\pi\) |
0.145231 | + | 0.989398i | \(0.453608\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.50000 | + | 6.06218i | −0.140000 | + | 0.242487i | ||||
\(26\) | 1.22474 | − | 0.707107i | 0.0471056 | − | 0.0271964i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 33.9411i | 1.17038i | 0.810895 | + | 0.585192i | \(0.198981\pi\) | ||||
−0.810895 | + | 0.585192i | \(0.801019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 23.5000 | − | 40.7032i | 0.758065 | − | 1.31301i | −0.185772 | − | 0.982593i | \(-0.559479\pi\) |
0.943836 | − | 0.330413i | \(-0.107188\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −24.0000 | −0.705882 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 27.5000 | + | 47.6314i | 0.743243 | + | 1.28734i | 0.951011 | + | 0.309157i | \(0.100047\pi\) |
−0.207768 | + | 0.978178i | \(0.566620\pi\) | |||||||
\(38\) | 28.1691 | + | 16.2635i | 0.741293 | + | 0.427986i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.00000 | + | 10.3923i | 0.150000 | + | 0.259808i | ||||
\(41\) | 46.6690i | 1.13827i | 0.822244 | + | 0.569135i | \(0.192722\pi\) | ||||
−0.822244 | + | 0.569135i | \(0.807278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 23.0000 | 0.534884 | 0.267442 | − | 0.963574i | \(-0.413822\pi\) | ||||
0.267442 | + | 0.963574i | \(0.413822\pi\) | |||||||
\(44\) | 22.0454 | − | 12.7279i | 0.501032 | − | 0.289271i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0000 | + | 20.7846i | −0.260870 | + | 0.451839i | ||||
\(47\) | 3.67423 | − | 2.12132i | 0.0781752 | − | 0.0451345i | −0.460403 | − | 0.887710i | \(-0.652295\pi\) |
0.538578 | + | 0.842576i | \(0.318962\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9.89949i | 0.197990i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | − | 1.73205i | 0.0192308 | − | 0.0333087i | ||||
\(53\) | 44.0908 | + | 25.4558i | 0.831902 | + | 0.480299i | 0.854504 | − | 0.519446i | \(-0.173862\pi\) |
−0.0226013 | + | 0.999745i | \(0.507195\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −54.0000 | −0.981818 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24.0000 | + | 41.5692i | 0.413793 | + | 0.716711i | ||||
\(59\) | 73.4847 | + | 42.4264i | 1.24550 | + | 0.719092i | 0.970209 | − | 0.242268i | \(-0.0778915\pi\) |
0.275294 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 52.0000 | + | 90.0666i | 0.852459 | + | 1.47650i | 0.878982 | + | 0.476854i | \(0.158223\pi\) |
−0.0265234 | + | 0.999648i | \(0.508444\pi\) | |||||||
\(62\) | − | 66.4680i | − | 1.07207i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −3.67423 | + | 2.12132i | −0.0565267 | + | 0.0326357i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 48.5000 | − | 84.0045i | 0.723881 | − | 1.25380i | −0.235553 | − | 0.971862i | \(-0.575690\pi\) |
0.959433 | − | 0.281936i | \(-0.0909767\pi\) | |||||||
\(68\) | −29.3939 | + | 16.9706i | −0.432263 | + | 0.249567i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 97.5807i | 1.37438i | 0.726479 | + | 0.687188i | \(0.241155\pi\) | ||||
−0.726479 | + | 0.687188i | \(0.758845\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 32.5000 | − | 56.2917i | 0.445205 | − | 0.771119i | −0.552861 | − | 0.833273i | \(-0.686464\pi\) |
0.998067 | + | 0.0621550i | \(0.0197973\pi\) | |||||||
\(74\) | 67.3610 | + | 38.8909i | 0.910283 | + | 0.525552i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 46.0000 | 0.605263 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −56.5000 | − | 97.8609i | −0.715190 | − | 1.23875i | −0.962886 | − | 0.269907i | \(-0.913007\pi\) |
0.247696 | − | 0.968838i | \(-0.420326\pi\) | |||||||
\(80\) | 14.6969 | + | 8.48528i | 0.183712 | + | 0.106066i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 33.0000 | + | 57.1577i | 0.402439 | + | 0.697045i | ||||
\(83\) | 29.6985i | 0.357813i | 0.983866 | + | 0.178907i | \(0.0572560\pi\) | ||||
−0.983866 | + | 0.178907i | \(0.942744\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 72.0000 | 0.847059 | ||||||||
\(86\) | 28.1691 | − | 16.2635i | 0.327548 | − | 0.189110i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 18.0000 | − | 31.1769i | 0.204545 | − | 0.354283i | ||||
\(89\) | −117.576 | + | 67.8823i | −1.32107 | + | 0.762722i | −0.983900 | − | 0.178721i | \(-0.942804\pi\) |
−0.337173 | + | 0.941443i | \(0.609471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 33.9411i | 0.368925i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.00000 | − | 5.19615i | 0.0319149 | − | 0.0552782i | ||||
\(95\) | −84.5074 | − | 48.7904i | −0.889552 | − | 0.513583i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −104.000 | −1.07216 | −0.536082 | − | 0.844166i | \(-0.680096\pi\) | ||||
−0.536082 | + | 0.844166i | \(0.680096\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.00000 | + | 12.1244i | 0.0700000 | + | 0.121244i | ||||
\(101\) | −128.598 | − | 74.2462i | −1.27325 | − | 0.735111i | −0.297651 | − | 0.954675i | \(-0.596203\pi\) |
−0.975598 | + | 0.219564i | \(0.929537\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 59.5000 | + | 103.057i | 0.577670 | + | 1.00055i | 0.995746 | + | 0.0921416i | \(0.0293712\pi\) |
−0.418076 | + | 0.908412i | \(0.637295\pi\) | |||||||
\(104\) | − | 2.82843i | − | 0.0271964i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 72.0000 | 0.679245 | ||||||||
\(107\) | −102.879 | + | 59.3970i | −0.961482 | + | 0.555112i | −0.896629 | − | 0.442783i | \(-0.853991\pi\) |
−0.0648531 | + | 0.997895i | \(0.520658\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 24.5000 | − | 42.4352i | 0.224771 | − | 0.389314i | −0.731480 | − | 0.681863i | \(-0.761170\pi\) |
0.956251 | + | 0.292549i | \(0.0945034\pi\) | |||||||
\(110\) | −66.1362 | + | 38.1838i | −0.601238 | + | 0.347125i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 97.5807i | − | 0.863546i | −0.901982 | − | 0.431773i | \(-0.857888\pi\) | ||
0.901982 | − | 0.431773i | \(-0.142112\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 36.0000 | − | 62.3538i | 0.313043 | − | 0.542207i | ||||
\(116\) | 58.7878 | + | 33.9411i | 0.506791 | + | 0.292596i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 120.000 | 1.01695 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.5000 | + | 35.5070i | 0.169421 | + | 0.293447i | ||||
\(122\) | 127.373 | + | 73.5391i | 1.04404 | + | 0.602780i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −47.0000 | − | 81.4064i | −0.379032 | − | 0.656503i | ||||
\(125\) | − | 135.765i | − | 1.08612i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 113.000 | 0.889764 | 0.444882 | − | 0.895589i | \(-0.353246\pi\) | ||||
0.444882 | + | 0.895589i | \(0.353246\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | + | 5.19615i | −0.0230769 | + | 0.0399704i | ||||
\(131\) | −18.3712 | + | 10.6066i | −0.140238 | + | 0.0809664i | −0.568477 | − | 0.822699i | \(-0.692467\pi\) |
0.428239 | + | 0.903665i | \(0.359134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 137.179i | − | 1.02372i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24.0000 | + | 41.5692i | −0.176471 | + | 0.305656i | ||||
\(137\) | −58.7878 | − | 33.9411i | −0.429108 | − | 0.247745i | 0.269859 | − | 0.962900i | \(-0.413023\pi\) |
−0.698966 | + | 0.715154i | \(0.746356\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 103.000 | 0.741007 | 0.370504 | − | 0.928831i | \(-0.379185\pi\) | ||||
0.370504 | + | 0.928831i | \(0.379185\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 69.0000 | + | 119.512i | 0.485915 | + | 0.841630i | ||||
\(143\) | 11.0227 | + | 6.36396i | 0.0770818 | + | 0.0445032i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −72.0000 | − | 124.708i | −0.496552 | − | 0.860053i | ||||
\(146\) | − | 91.9239i | − | 0.629616i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 110.000 | 0.743243 | ||||||||
\(149\) | −146.969 | + | 84.8528i | −0.986372 | + | 0.569482i | −0.904188 | − | 0.427135i | \(-0.859523\pi\) |
−0.0821839 | + | 0.996617i | \(0.526189\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −52.0000 | + | 90.0666i | −0.344371 | + | 0.596468i | −0.985239 | − | 0.171183i | \(-0.945241\pi\) |
0.640868 | + | 0.767651i | \(0.278574\pi\) | |||||||
\(152\) | 56.3383 | − | 32.5269i | 0.370646 | − | 0.213993i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 199.404i | 1.28648i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 76.0000 | − | 131.636i | 0.484076 | − | 0.838445i | −0.515756 | − | 0.856735i | \(-0.672489\pi\) |
0.999833 | + | 0.0182904i | \(0.00582233\pi\) | |||||||
\(158\) | −138.396 | − | 79.9031i | −0.875925 | − | 0.505716i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 24.0000 | 0.150000 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −28.0000 | − | 48.4974i | −0.171779 | − | 0.297530i | 0.767263 | − | 0.641333i | \(-0.221618\pi\) |
−0.939042 | + | 0.343803i | \(0.888285\pi\) | |||||||
\(164\) | 80.8332 | + | 46.6690i | 0.492885 | + | 0.284567i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.0000 | + | 36.3731i | 0.126506 | + | 0.219115i | ||||
\(167\) | 4.24264i | 0.0254050i | 0.999919 | + | 0.0127025i | \(0.00404345\pi\) | ||||
−0.999919 | + | 0.0127025i | \(0.995957\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.000 | −0.994083 | ||||||||
\(170\) | 88.1816 | − | 50.9117i | 0.518715 | − | 0.299481i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 23.0000 | − | 39.8372i | 0.133721 | − | 0.231611i | ||||
\(173\) | 132.272 | − | 76.3675i | 0.764581 | − | 0.441431i | −0.0663573 | − | 0.997796i | \(-0.521138\pi\) |
0.830938 | + | 0.556365i | \(0.187804\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 50.9117i | − | 0.289271i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −96.0000 | + | 166.277i | −0.539326 | + | 0.934140i | ||||
\(179\) | −3.67423 | − | 2.12132i | −0.0205265 | − | 0.0118510i | 0.489702 | − | 0.871890i | \(-0.337106\pi\) |
−0.510228 | + | 0.860039i | \(0.670439\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 55.0000 | 0.303867 | 0.151934 | − | 0.988391i | \(-0.451450\pi\) | ||||
0.151934 | + | 0.988391i | \(0.451450\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24.0000 | + | 41.5692i | 0.130435 | + | 0.225920i | ||||
\(185\) | −202.083 | − | 116.673i | −1.09234 | − | 0.630663i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −108.000 | − | 187.061i | −0.577540 | − | 1.00033i | ||||
\(188\) | − | 8.48528i | − | 0.0451345i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −138.000 | −0.726316 | ||||||||
\(191\) | −55.1135 | + | 31.8198i | −0.288552 | + | 0.166596i | −0.637289 | − | 0.770625i | \(-0.719944\pi\) |
0.348736 | + | 0.937221i | \(0.386611\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 75.5000 | − | 130.770i | 0.391192 | − | 0.677564i | −0.601415 | − | 0.798937i | \(-0.705396\pi\) |
0.992607 | + | 0.121373i | \(0.0387296\pi\) | |||||||
\(194\) | −127.373 | + | 73.5391i | −0.656564 | + | 0.379068i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.9706i | 0.0861450i | 0.999072 | + | 0.0430725i | \(0.0137146\pi\) | ||||
−0.999072 | + | 0.0430725i | \(0.986285\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −80.0000 | + | 138.564i | −0.402010 | + | 0.696302i | −0.993968 | − | 0.109667i | \(-0.965022\pi\) |
0.591958 | + | 0.805969i | \(0.298355\pi\) | |||||||
\(200\) | 17.1464 | + | 9.89949i | 0.0857321 | + | 0.0494975i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −210.000 | −1.03960 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −99.0000 | − | 171.473i | −0.482927 | − | 0.836454i | ||||
\(206\) | 145.745 | + | 84.1457i | 0.707498 | + | 0.408474i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.00000 | − | 3.46410i | −0.00961538 | − | 0.0166543i | ||||
\(209\) | 292.742i | 1.40068i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −208.000 | −0.985782 | −0.492891 | − | 0.870091i | \(-0.664060\pi\) | ||||
−0.492891 | + | 0.870091i | \(0.664060\pi\) | |||||||
\(212\) | 88.1816 | − | 50.9117i | 0.415951 | − | 0.240149i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −84.0000 | + | 145.492i | −0.392523 | + | 0.679870i | ||||
\(215\) | −84.5074 | + | 48.7904i | −0.393058 | + | 0.226932i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 69.2965i | − | 0.317874i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −54.0000 | + | 93.5307i | −0.245455 | + | 0.425140i | ||||
\(221\) | −14.6969 | − | 8.48528i | −0.0665020 | − | 0.0383949i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 40.0000 | 0.179372 | 0.0896861 | − | 0.995970i | \(-0.471414\pi\) | ||||
0.0896861 | + | 0.995970i | \(0.471414\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −69.0000 | − | 119.512i | −0.305310 | − | 0.528812i | ||||
\(227\) | −194.734 | − | 112.430i | −0.857861 | − | 0.495286i | 0.00543445 | − | 0.999985i | \(-0.498270\pi\) |
−0.863295 | + | 0.504699i | \(0.831603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 188.500 | + | 326.492i | 0.823144 | + | 1.42573i | 0.903329 | + | 0.428947i | \(0.141115\pi\) |
−0.0801853 | + | 0.996780i | \(0.525551\pi\) | |||||||
\(230\) | − | 101.823i | − | 0.442710i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 96.0000 | 0.413793 | ||||||||
\(233\) | 297.613 | − | 171.827i | 1.27731 | − | 0.737455i | 0.300956 | − | 0.953638i | \(-0.402694\pi\) |
0.976353 | + | 0.216183i | \(0.0693609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | + | 15.5885i | −0.0382979 | + | 0.0663339i | ||||
\(236\) | 146.969 | − | 84.8528i | 0.622752 | − | 0.359546i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 12.7279i | − | 0.0532549i | −0.999645 | − | 0.0266275i | \(-0.991523\pi\) | ||
0.999645 | − | 0.0266275i | \(-0.00847678\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −65.0000 | + | 112.583i | −0.269710 | + | 0.467151i | −0.968787 | − | 0.247896i | \(-0.920261\pi\) |
0.699077 | + | 0.715046i | \(0.253594\pi\) | |||||||
\(242\) | 50.2145 | + | 28.9914i | 0.207498 | + | 0.119799i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 208.000 | 0.852459 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.5000 | + | 19.9186i | 0.0465587 | + | 0.0806420i | ||||
\(248\) | −115.126 | − | 66.4680i | −0.464218 | − | 0.268016i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −96.0000 | − | 166.277i | −0.384000 | − | 0.665108i | ||||
\(251\) | 50.9117i | 0.202835i | 0.994844 | + | 0.101418i | \(0.0323379\pi\) | ||||
−0.994844 | + | 0.101418i | \(0.967662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −216.000 | −0.853755 | ||||||||
\(254\) | 138.396 | − | 79.9031i | 0.544867 | − | 0.314579i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 407.840 | − | 235.467i | 1.58693 | − | 0.916212i | 0.593117 | − | 0.805117i | \(-0.297897\pi\) |
0.993810 | − | 0.111096i | \(-0.0354360\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.48528i | 0.0326357i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.0000 | + | 25.9808i | −0.0572519 | + | 0.0991632i | ||||
\(263\) | 88.1816 | + | 50.9117i | 0.335291 | + | 0.193581i | 0.658188 | − | 0.752854i | \(-0.271323\pi\) |
−0.322897 | + | 0.946434i | \(0.604657\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −216.000 | −0.815094 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −97.0000 | − | 168.009i | −0.361940 | − | 0.626899i | ||||
\(269\) | 246.174 | + | 142.128i | 0.915144 | + | 0.528359i | 0.882083 | − | 0.471095i | \(-0.156141\pi\) |
0.0330613 | + | 0.999453i | \(0.489474\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −260.000 | − | 450.333i | −0.959410 | − | 1.66175i | −0.723938 | − | 0.689865i | \(-0.757670\pi\) |
−0.235471 | − | 0.971881i | \(-0.575663\pi\) | |||||||
\(272\) | 67.8823i | 0.249567i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −96.0000 | −0.350365 | ||||||||
\(275\) | −77.1589 | + | 44.5477i | −0.280578 | + | 0.161992i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −56.5000 | + | 97.8609i | −0.203971 | + | 0.353288i | −0.949804 | − | 0.312844i | \(-0.898718\pi\) |
0.745833 | + | 0.666133i | \(0.232052\pi\) | |||||||
\(278\) | 126.149 | − | 72.8320i | 0.453772 | − | 0.261986i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 458.205i | − | 1.63062i | −0.579022 | − | 0.815312i | \(-0.696566\pi\) | ||
0.579022 | − | 0.815312i | \(-0.303434\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 44.5000 | − | 77.0763i | 0.157244 | − | 0.272354i | −0.776630 | − | 0.629957i | \(-0.783072\pi\) |
0.933874 | + | 0.357603i | \(0.116406\pi\) | |||||||
\(284\) | 169.015 | + | 97.5807i | 0.595123 | + | 0.343594i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.0000 | 0.0629371 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.500000 | − | 0.866025i | −0.00173010 | − | 0.00299663i | ||||
\(290\) | −176.363 | − | 101.823i | −0.608149 | − | 0.351115i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −65.0000 | − | 112.583i | −0.222603 | − | 0.385559i | ||||
\(293\) | 67.8823i | 0.231680i | 0.993268 | + | 0.115840i | \(0.0369560\pi\) | ||||
−0.993268 | + | 0.115840i | \(0.963044\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −360.000 | −1.22034 | ||||||||
\(296\) | 134.722 | − | 77.7817i | 0.455142 | − | 0.262776i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −120.000 | + | 207.846i | −0.402685 | + | 0.697470i | ||||
\(299\) | −14.6969 | + | 8.48528i | −0.0491536 | + | 0.0283789i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 147.078i | 0.487014i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 46.0000 | − | 79.6743i | 0.151316 | − | 0.262087i | ||||
\(305\) | −382.120 | − | 220.617i | −1.25285 | − | 0.723335i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −233.000 | −0.758958 | −0.379479 | − | 0.925200i | \(-0.623897\pi\) | ||||
−0.379479 | + | 0.925200i | \(0.623897\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 141.000 | + | 244.219i | 0.454839 | + | 0.787804i | ||||
\(311\) | −216.780 | − | 125.158i | −0.697041 | − | 0.402437i | 0.109203 | − | 0.994019i | \(-0.465170\pi\) |
−0.806244 | + | 0.591582i | \(0.798503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −75.5000 | − | 130.770i | −0.241214 | − | 0.417795i | 0.719846 | − | 0.694133i | \(-0.244212\pi\) |
−0.961060 | + | 0.276338i | \(0.910879\pi\) | |||||||
\(314\) | − | 214.960i | − | 0.684587i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −226.000 | −0.715190 | ||||||||
\(317\) | −352.727 | + | 203.647i | −1.11270 | + | 0.642419i | −0.939528 | − | 0.342472i | \(-0.888736\pi\) |
−0.173174 | + | 0.984891i | \(0.555402\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −216.000 | + | 374.123i | −0.677116 | + | 1.17280i | ||||
\(320\) | 29.3939 | − | 16.9706i | 0.0918559 | − | 0.0530330i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 390.323i | − | 1.20843i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.50000 | + | 6.06218i | −0.0107692 | + | 0.0186529i | ||||
\(326\) | −68.5857 | − | 39.5980i | −0.210386 | − | 0.121466i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 132.000 | 0.402439 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 36.5000 | + | 63.2199i | 0.110272 | + | 0.190997i | 0.915880 | − | 0.401452i | \(-0.131495\pi\) |
−0.805608 | + | 0.592449i | \(0.798161\pi\) | |||||||
\(332\) | 51.4393 | + | 29.6985i | 0.154938 | + | 0.0894533i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.00000 | + | 5.19615i | 0.00898204 | + | 0.0155573i | ||||
\(335\) | 411.536i | 1.22847i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 527.000 | 1.56380 | 0.781899 | − | 0.623405i | \(-0.214251\pi\) | ||||
0.781899 | + | 0.623405i | \(0.214251\pi\) | |||||||
\(338\) | −205.757 | + | 118.794i | −0.608749 | + | 0.351461i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 72.0000 | − | 124.708i | 0.211765 | − | 0.366787i | ||||
\(341\) | 518.067 | − | 299.106i | 1.51926 | − | 0.877144i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 65.0538i | − | 0.189110i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 108.000 | − | 187.061i | 0.312139 | − | 0.540640i | ||||
\(347\) | 367.423 | + | 212.132i | 1.05886 | + | 0.611332i | 0.925116 | − | 0.379685i | \(-0.123968\pi\) |
0.133741 | + | 0.991016i | \(0.457301\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 112.000 | 0.320917 | 0.160458 | − | 0.987043i | \(-0.448703\pi\) | ||||
0.160458 | + | 0.987043i | \(0.448703\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −36.0000 | − | 62.3538i | −0.102273 | − | 0.177142i | ||||
\(353\) | −268.219 | − | 154.856i | −0.759828 | − | 0.438687i | 0.0694063 | − | 0.997588i | \(-0.477890\pi\) |
−0.829234 | + | 0.558902i | \(0.811223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −207.000 | − | 358.535i | −0.583099 | − | 1.00996i | ||||
\(356\) | 271.529i | 0.762722i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | −0.0167598 | ||||||||
\(359\) | 440.908 | − | 254.558i | 1.22816 | − | 0.709076i | 0.261512 | − | 0.965200i | \(-0.415779\pi\) |
0.966644 | + | 0.256124i | \(0.0824454\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −84.0000 | + | 145.492i | −0.232687 | + | 0.403026i | ||||
\(362\) | 67.3610 | − | 38.8909i | 0.186080 | − | 0.107433i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 275.772i | 0.755539i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −159.500 | + | 276.262i | −0.434605 | + | 0.752758i | −0.997263 | − | 0.0739317i | \(-0.976445\pi\) |
0.562658 | + | 0.826689i | \(0.309779\pi\) | |||||||
\(368\) | 58.7878 | + | 33.9411i | 0.159749 | + | 0.0922313i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −330.000 | −0.891892 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −104.500 | − | 180.999i | −0.280161 | − | 0.485253i | 0.691263 | − | 0.722603i | \(-0.257054\pi\) |
−0.971424 | + | 0.237350i | \(0.923721\pi\) | |||||||
\(374\) | −264.545 | − | 152.735i | −0.707339 | − | 0.408383i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | − | 10.3923i | −0.0159574 | − | 0.0276391i | ||||
\(377\) | 33.9411i | 0.0900295i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −433.000 | −1.14248 | −0.571240 | − | 0.820783i | \(-0.693537\pi\) | ||||
−0.571240 | + | 0.820783i | \(0.693537\pi\) | |||||||
\(380\) | −169.015 | + | 97.5807i | −0.444776 | + | 0.256791i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −45.0000 | + | 77.9423i | −0.117801 | + | 0.204037i | ||||
\(383\) | −338.030 | + | 195.161i | −0.882584 | + | 0.509560i | −0.871509 | − | 0.490379i | \(-0.836858\pi\) |
−0.0110743 | + | 0.999939i | \(0.503525\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 213.546i | − | 0.553229i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −104.000 | + | 180.133i | −0.268041 | + | 0.464261i | ||||
\(389\) | −319.658 | − | 184.555i | −0.821744 | − | 0.474434i | 0.0292735 | − | 0.999571i | \(-0.490681\pi\) |
−0.851018 | + | 0.525137i | \(0.824014\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 288.000 | 0.736573 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000 | + | 20.7846i | 0.0304569 | + | 0.0527528i | ||||
\(395\) | 415.189 | + | 239.709i | 1.05111 | + | 0.606859i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 56.5000 | + | 97.8609i | 0.142317 | + | 0.246501i | 0.928369 | − | 0.371660i | \(-0.121211\pi\) |
−0.786052 | + | 0.618161i | \(0.787878\pi\) | |||||||
\(398\) | 226.274i | 0.568528i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 28.0000 | 0.0700000 | ||||||||
\(401\) | 308.636 | − | 178.191i | 0.769665 | − | 0.444366i | −0.0630900 | − | 0.998008i | \(-0.520096\pi\) |
0.832755 | + | 0.553641i | \(0.186762\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.5000 | − | 40.7032i | 0.0583127 | − | 0.101000i | ||||
\(404\) | −257.196 | + | 148.492i | −0.636625 | + | 0.367556i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 700.036i | 1.71999i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −159.500 | + | 276.262i | −0.389976 | + | 0.675457i | −0.992446 | − | 0.122684i | \(-0.960850\pi\) |
0.602470 | + | 0.798141i | \(0.294183\pi\) | |||||||
\(410\) | −242.499 | − | 140.007i | −0.591462 | − | 0.341481i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 238.000 | 0.577670 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −63.0000 | − | 109.119i | −0.151807 | − | 0.262938i | ||||
\(416\) | −4.89898 | − | 2.82843i | −0.0117764 | − | 0.00679910i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 207.000 | + | 358.535i | 0.495215 | + | 0.857738i | ||||
\(419\) | − | 767.918i | − | 1.83274i | −0.400333 | − | 0.916370i | \(-0.631105\pi\) | ||
0.400333 | − | 0.916370i | \(-0.368895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 65.0000 | 0.154394 | 0.0771971 | − | 0.997016i | \(-0.475403\pi\) | ||||
0.0771971 | + | 0.997016i | \(0.475403\pi\) | |||||||
\(422\) | −254.747 | + | 147.078i | −0.603666 | + | 0.348527i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 72.0000 | − | 124.708i | 0.169811 | − | 0.294122i | ||||
\(425\) | 102.879 | − | 59.3970i | 0.242067 | − | 0.139758i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 237.588i | 0.555112i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −69.0000 | + | 119.512i | −0.160465 | + | 0.277934i | ||||
\(431\) | 415.189 | + | 239.709i | 0.963314 | + | 0.556170i | 0.897192 | − | 0.441642i | \(-0.145604\pi\) |
0.0661229 | + | 0.997811i | \(0.478937\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 367.000 | 0.847575 | 0.423788 | − | 0.905762i | \(-0.360700\pi\) | ||||
0.423788 | + | 0.905762i | \(0.360700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −49.0000 | − | 84.8705i | −0.112385 | − | 0.194657i | ||||
\(437\) | −338.030 | − | 195.161i | −0.773523 | − | 0.446594i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 268.000 | + | 464.190i | 0.610478 | + | 1.05738i | 0.991160 | + | 0.132673i | \(0.0423561\pi\) |
−0.380681 | + | 0.924706i | \(0.624311\pi\) | |||||||
\(440\) | 152.735i | 0.347125i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0000 | −0.0542986 | ||||||||
\(443\) | 73.4847 | − | 42.4264i | 0.165880 | − | 0.0957707i | −0.414762 | − | 0.909930i | \(-0.636135\pi\) |
0.580642 | + | 0.814159i | \(0.302802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 288.000 | − | 498.831i | 0.647191 | − | 1.12097i | ||||
\(446\) | 48.9898 | − | 28.2843i | 0.109843 | − | 0.0634176i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 615.183i | − | 1.37012i | −0.728488 | − | 0.685059i | \(-0.759776\pi\) | ||
0.728488 | − | 0.685059i | \(-0.240224\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −297.000 | + | 514.419i | −0.658537 | + | 1.14062i | ||||
\(452\) | −169.015 | − | 97.5807i | −0.373927 | − | 0.215887i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −318.000 | −0.700441 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 231.500 | + | 400.970i | 0.506565 | + | 0.877396i | 0.999971 | + | 0.00759675i | \(0.00241814\pi\) |
−0.493407 | + | 0.869799i | \(0.664249\pi\) | |||||||
\(458\) | 461.729 | + | 266.579i | 1.00814 | + | 0.582051i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −72.0000 | − | 124.708i | −0.156522 | − | 0.271104i | ||||
\(461\) | − | 271.529i | − | 0.589000i | −0.955651 | − | 0.294500i | \(-0.904847\pi\) | ||
0.955651 | − | 0.294500i | \(-0.0951531\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 47.0000 | 0.101512 | 0.0507559 | − | 0.998711i | \(-0.483837\pi\) | ||||
0.0507559 | + | 0.998711i | \(0.483837\pi\) | |||||||
\(464\) | 117.576 | − | 67.8823i | 0.253395 | − | 0.146298i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 243.000 | − | 420.888i | 0.521459 | − | 0.903194i | ||||
\(467\) | −642.991 | + | 371.231i | −1.37685 | + | 0.794927i | −0.991780 | − | 0.127958i | \(-0.959158\pi\) |
−0.385075 | + | 0.922885i | \(0.625824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 25.4558i | 0.0541614i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 120.000 | − | 207.846i | 0.254237 | − | 0.440352i | ||||
\(473\) | 253.522 | + | 146.371i | 0.535988 | + | 0.309453i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −161.000 | −0.338947 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.00000 | − | 15.5885i | −0.0188285 | − | 0.0326118i | ||||
\(479\) | 367.423 | + | 212.132i | 0.767064 | + | 0.442864i | 0.831826 | − | 0.555036i | \(-0.187296\pi\) |
−0.0647625 | + | 0.997901i | \(0.520629\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.5000 | + | 47.6314i | 0.0571726 | + | 0.0990258i | ||||
\(482\) | 183.848i | 0.381427i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 82.0000 | 0.169421 | ||||||||
\(485\) | 382.120 | − | 220.617i | 0.787877 | − | 0.454881i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −119.500 | + | 206.980i | −0.245380 | + | 0.425010i | −0.962238 | − | 0.272208i | \(-0.912246\pi\) |
0.716858 | + | 0.697219i | \(0.245579\pi\) | |||||||
\(488\) | 254.747 | − | 147.078i | 0.522022 | − | 0.301390i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 203.647i | 0.414759i | 0.978261 | + | 0.207380i | \(0.0664935\pi\) | ||||
−0.978261 | + | 0.207380i | \(0.933506\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 288.000 | − | 498.831i | 0.584178 | − | 1.01183i | ||||
\(494\) | 28.1691 | + | 16.2635i | 0.0570225 | + | 0.0329220i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −188.000 | −0.379032 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.5000 | + | 42.4352i | 0.0490982 | + | 0.0850406i | 0.889530 | − | 0.456877i | \(-0.151032\pi\) |
−0.840432 | + | 0.541917i | \(0.817699\pi\) | |||||||
\(500\) | −235.151 | − | 135.765i | −0.470302 | − | 0.271529i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 36.0000 | + | 62.3538i | 0.0717131 | + | 0.124211i | ||||
\(503\) | − | 589.727i | − | 1.17242i | −0.810159 | − | 0.586210i | \(-0.800619\pi\) | ||
0.810159 | − | 0.586210i | \(-0.199381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 630.000 | 1.24752 | ||||||||
\(506\) | −264.545 | + | 152.735i | −0.522816 | + | 0.301848i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 113.000 | − | 195.722i | 0.222441 | − | 0.385279i | ||||
\(509\) | 209.431 | − | 120.915i | 0.411457 | − | 0.237555i | −0.279959 | − | 0.960012i | \(-0.590321\pi\) |
0.691415 | + | 0.722457i | \(0.256987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 333.000 | − | 576.773i | 0.647860 | − | 1.12213i | ||||
\(515\) | −437.234 | − | 252.437i | −0.848998 | − | 0.490169i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 54.0000 | 0.104449 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.00000 | + | 10.3923i | 0.0115385 | + | 0.0199852i | ||||
\(521\) | 734.847 | + | 424.264i | 1.41045 | + | 0.814326i | 0.995431 | − | 0.0954841i | \(-0.0304399\pi\) |
0.415024 | + | 0.909811i | \(0.363773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −195.500 | − | 338.616i | −0.373805 | − | 0.647449i | 0.616342 | − | 0.787478i | \(-0.288614\pi\) |
−0.990147 | + | 0.140029i | \(0.955280\pi\) | |||||||
\(524\) | 42.4264i | 0.0809664i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 144.000 | 0.273764 | ||||||||
\(527\) | −690.756 | + | 398.808i | −1.31073 | + | 0.756752i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −120.500 | + | 208.712i | −0.227788 | + | 0.394541i | ||||
\(530\) | −264.545 | + | 152.735i | −0.499141 | + | 0.288179i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 46.6690i | 0.0875592i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 252.000 | − | 436.477i | 0.471028 | − | 0.815844i | ||||
\(536\) | −237.601 | − | 137.179i | −0.443285 | − | 0.255930i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 402.000 | 0.747212 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.5000 | + | 63.2199i | 0.0674677 | + | 0.116857i | 0.897786 | − | 0.440432i | \(-0.145175\pi\) |
−0.830318 | + | 0.557289i | \(0.811841\pi\) | |||||||
\(542\) | −636.867 | − | 367.696i | −1.17503 | − | 0.678405i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 48.0000 | + | 83.1384i | 0.0882353 | + | 0.152828i | ||||
\(545\) | 207.889i | 0.381448i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0000 | 0.0585009 | 0.0292505 | − | 0.999572i | \(-0.490688\pi\) | ||||
0.0292505 | + | 0.999572i | \(0.490688\pi\) | |||||||
\(548\) | −117.576 | + | 67.8823i | −0.214554 | + | 0.123873i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −63.0000 | + | 109.119i | −0.114545 | + | 0.198399i | ||||
\(551\) | −676.059 | + | 390.323i | −1.22697 | + | 0.708390i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 159.806i | 0.288459i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 103.000 | − | 178.401i | 0.185252 | − | 0.320866i | ||||
\(557\) | 40.4166 | + | 23.3345i | 0.0725612 | + | 0.0418932i | 0.535842 | − | 0.844319i | \(-0.319994\pi\) |
−0.463280 | + | 0.886212i | \(0.653328\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.0000 | 0.0411449 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −324.000 | − | 561.184i | −0.576512 | − | 0.998549i | ||||
\(563\) | 767.915 | + | 443.356i | 1.36397 | + | 0.787488i | 0.990150 | − | 0.140013i | \(-0.0447144\pi\) |
0.373820 | + | 0.927501i | \(0.378048\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 207.000 | + | 358.535i | 0.366372 | + | 0.634574i | ||||
\(566\) | − | 125.865i | − | 0.222376i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 276.000 | 0.485915 | ||||||||
\(569\) | −275.568 | + | 159.099i | −0.484302 | + | 0.279612i | −0.722207 | − | 0.691677i | \(-0.756872\pi\) |
0.237906 | + | 0.971288i | \(0.423539\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 267.500 | − | 463.324i | 0.468476 | − | 0.811425i | −0.530875 | − | 0.847450i | \(-0.678136\pi\) |
0.999351 | + | 0.0360256i | \(0.0114698\pi\) | |||||||
\(572\) | 22.0454 | − | 12.7279i | 0.0385409 | − | 0.0222516i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 118.794i | − | 0.206598i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 452.500 | − | 783.753i | 0.784229 | − | 1.35832i | −0.145230 | − | 0.989398i | \(-0.546392\pi\) |
0.929459 | − | 0.368926i | \(-0.120274\pi\) | |||||||
\(578\) | −1.22474 | − | 0.707107i | −0.00211894 | − | 0.00122337i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −288.000 | −0.496552 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 324.000 | + | 561.184i | 0.555746 | + | 0.962581i | ||||
\(584\) | −159.217 | − | 91.9239i | −0.272632 | − | 0.157404i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 48.0000 | + | 83.1384i | 0.0819113 | + | 0.141874i | ||||
\(587\) | − | 576.999i | − | 0.982963i | −0.870888 | − | 0.491481i | \(-0.836456\pi\) | ||
0.870888 | − | 0.491481i | \(-0.163544\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1081.00 | 1.83531 | ||||||||
\(590\) | −440.908 | + | 254.558i | −0.747302 | + | 0.431455i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 110.000 | − | 190.526i | 0.185811 | − | 0.321834i | ||||
\(593\) | −481.325 | + | 277.893i | −0.811677 | + | 0.468622i | −0.847538 | − | 0.530735i | \(-0.821916\pi\) |
0.0358606 | + | 0.999357i | \(0.488583\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 339.411i | 0.569482i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.0000 | + | 20.7846i | −0.0200669 | + | 0.0347569i | ||||
\(599\) | −176.363 | − | 101.823i | −0.294429 | − | 0.169989i | 0.345508 | − | 0.938416i | \(-0.387707\pi\) |
−0.639938 | + | 0.768427i | \(0.721040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −143.000 | −0.237937 | −0.118968 | − | 0.992898i | \(-0.537959\pi\) | ||||
−0.118968 | + | 0.992898i | \(0.537959\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 104.000 | + | 180.133i | 0.172185 | + | 0.298234i | ||||
\(605\) | −150.644 | − | 86.9741i | −0.248998 | − | 0.143759i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 299.500 | + | 518.749i | 0.493410 | + | 0.854612i | 0.999971 | − | 0.00759259i | \(-0.00241682\pi\) |
−0.506561 | + | 0.862204i | \(0.669083\pi\) | |||||||
\(608\) | − | 130.108i | − | 0.213993i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −624.000 | −1.02295 | ||||||||
\(611\) | 3.67423 | − | 2.12132i | 0.00601348 | − | 0.00347188i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 152.000 | − | 263.272i | 0.247961 | − | 0.429481i | −0.714999 | − | 0.699125i | \(-0.753573\pi\) |
0.962960 | + | 0.269645i | \(0.0869062\pi\) | |||||||
\(614\) | −285.366 | + | 164.756i | −0.464765 | + | 0.268332i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 292.742i | − | 0.474461i | −0.971453 | − | 0.237230i | \(-0.923760\pi\) | ||
0.971453 | − | 0.237230i | \(-0.0762396\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −171.500 | + | 297.047i | −0.277060 | + | 0.479882i | −0.970653 | − | 0.240486i | \(-0.922693\pi\) |
0.693593 | + | 0.720367i | \(0.256027\pi\) | |||||||
\(620\) | 345.378 | + | 199.404i | 0.557061 | + | 0.321620i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −354.000 | −0.569132 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 200.500 | + | 347.276i | 0.320800 | + | 0.555642i | ||||
\(626\) | −184.936 | − | 106.773i | −0.295426 | − | 0.170564i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −152.000 | − | 263.272i | −0.242038 | − | 0.419222i | ||||
\(629\) | − | 933.381i | − | 1.48391i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 272.000 | 0.431062 | 0.215531 | − | 0.976497i | \(-0.430852\pi\) | ||||
0.215531 | + | 0.976497i | \(0.430852\pi\) | |||||||
\(632\) | −276.792 | + | 159.806i | −0.437963 | + | 0.252858i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −288.000 | + | 498.831i | −0.454259 | + | 0.786799i | ||||
\(635\) | −415.189 | + | 239.709i | −0.653840 | + | 0.377495i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 610.940i | 0.957587i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 24.0000 | − | 41.5692i | 0.0375000 | − | 0.0649519i | ||||
\(641\) | 367.423 | + | 212.132i | 0.573204 | + | 0.330939i | 0.758428 | − | 0.651757i | \(-0.225968\pi\) |
−0.185224 | + | 0.982696i | \(0.559301\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 679.000 | 1.05599 | 0.527994 | − | 0.849248i | \(-0.322944\pi\) | ||||
0.527994 | + | 0.849248i | \(0.322944\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −276.000 | − | 478.046i | −0.427245 | − | 0.740009i | ||||
\(647\) | 834.051 | + | 481.540i | 1.28911 | + | 0.744265i | 0.978495 | − | 0.206272i | \(-0.0661331\pi\) |
0.310611 | + | 0.950537i | \(0.399466\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 540.000 | + | 935.307i | 0.832049 | + | 1.44115i | ||||
\(650\) | 9.89949i | 0.0152300i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −112.000 | −0.171779 | ||||||||
\(653\) | 775.264 | − | 447.599i | 1.18723 | − | 0.685450i | 0.229557 | − | 0.973295i | \(-0.426272\pi\) |
0.957677 | + | 0.287846i | \(0.0929390\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 45.0000 | − | 77.9423i | 0.0687023 | − | 0.118996i | ||||
\(656\) | 161.666 | − | 93.3381i | 0.246443 | − | 0.142284i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9706i | 0.0257520i | 0.999917 | + | 0.0128760i | \(0.00409867\pi\) | ||||
−0.999917 | + | 0.0128760i | \(0.995901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −216.500 | + | 374.989i | −0.327534 | + | 0.567306i | −0.982022 | − | 0.188767i | \(-0.939551\pi\) |
0.654488 | + | 0.756072i | \(0.272884\pi\) | |||||||
\(662\) | 89.4064 | + | 51.6188i | 0.135055 | + | 0.0779740i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 84.0000 | 0.126506 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −288.000 | − | 498.831i | −0.431784 | − | 0.747872i | ||||
\(668\) | 7.34847 | + | 4.24264i | 0.0110007 | + | 0.00635126i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 291.000 | + | 504.027i | 0.434328 | + | 0.752279i | ||||
\(671\) | 1323.70i | 1.97273i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 737.000 | 1.09510 | 0.547548 | − | 0.836774i | \(-0.315561\pi\) | ||||
0.547548 | + | 0.836774i | \(0.315561\pi\) | |||||||
\(674\) | 645.441 | − | 372.645i | 0.957627 | − | 0.552886i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −168.000 | + | 290.985i | −0.248521 | + | 0.430450i | ||||
\(677\) | −117.576 | + | 67.8823i | −0.173671 | + | 0.100269i | −0.584316 | − | 0.811526i | \(-0.698637\pi\) |
0.410644 | + | 0.911796i | \(0.365304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 203.647i | − | 0.299481i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 423.000 | − | 732.657i | 0.620235 | − | 1.07428i | ||||
\(683\) | 1102.27 | + | 636.396i | 1.61387 | + | 0.931766i | 0.988463 | + | 0.151464i | \(0.0483988\pi\) |
0.625403 | + | 0.780302i | \(0.284935\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 288.000 | 0.420438 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −46.0000 | − | 79.6743i | −0.0668605 | − | 0.115806i | ||||
\(689\) | 44.0908 | + | 25.4558i | 0.0639925 | + | 0.0369461i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −123.500 | − | 213.908i | −0.178726 | − | 0.309563i | 0.762718 | − | 0.646731i | \(-0.223864\pi\) |
−0.941445 | + | 0.337168i | \(0.890531\pi\) | |||||||
\(692\) | − | 305.470i | − | 0.441431i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 600.000 | 0.864553 | ||||||||
\(695\) | −378.446 | + | 218.496i | −0.544527 | + | 0.314383i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 396.000 | − | 685.892i | 0.568149 | − | 0.984063i | ||||
\(698\) | 137.171 | − | 79.1960i | 0.196521 | − | 0.113461i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 322.441i | − | 0.459972i | −0.973194 | − | 0.229986i | \(-0.926132\pi\) | ||
0.973194 | − | 0.229986i | \(-0.0738681\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −632.500 | + | 1095.52i | −0.899716 | + | 1.55835i | ||||
\(704\) | −88.1816 | − | 50.9117i | −0.125258 | − | 0.0723177i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −438.000 | −0.620397 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 524.000 | + | 907.595i | 0.739069 | + | 1.28011i | 0.952915 | + | 0.303238i | \(0.0980677\pi\) |
−0.213846 | + | 0.976867i | \(0.568599\pi\) | |||||||
\(710\) | −507.044 | − | 292.742i | −0.714147 | − | 0.412313i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 192.000 | + | 332.554i | 0.269663 | + | 0.467070i | ||||
\(713\) | 797.616i | 1.11868i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −54.0000 | −0.0755245 | ||||||||
\(716\) | −7.34847 | + | 4.24264i | −0.0102632 | + | 0.00592548i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 360.000 | − | 623.538i | 0.501393 | − | 0.868438i | ||||
\(719\) | 216.780 | − | 125.158i | 0.301502 | − | 0.174072i | −0.341616 | − | 0.939840i | \(-0.610974\pi\) |
0.643117 | + | 0.765768i | \(0.277641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 237.588i | 0.329069i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 55.0000 | − | 95.2628i | 0.0759669 | − | 0.131578i | ||||
\(725\) | −205.757 | − | 118.794i | −0.283803 | − | 0.163854i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −641.000 | −0.881706 | −0.440853 | − | 0.897579i | \(-0.645324\pi\) | ||||
−0.440853 | + | 0.897579i | \(0.645324\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 195.000 | + | 337.750i | 0.267123 | + | 0.462671i | ||||
\(731\) | −338.030 | − | 195.161i | −0.462421 | − | 0.266979i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5000 | − | 21.6506i | −0.0170532 | − | 0.0295370i | 0.857373 | − | 0.514696i | \(-0.172095\pi\) |
−0.874426 | + | 0.485159i | \(0.838762\pi\) | |||||||
\(734\) | 451.134i | 0.614624i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 96.0000 | 0.130435 | ||||||||
\(737\) | 1069.20 | − | 617.304i | 1.45075 | − | 0.837591i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 267.500 | − | 463.324i | 0.361976 | − | 0.626960i | −0.626310 | − | 0.779574i | \(-0.715436\pi\) |
0.988286 | + | 0.152614i | \(0.0487690\pi\) | |||||||
\(740\) | −404.166 | + | 233.345i | −0.546170 | + | 0.315331i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 937.624i | 1.26194i | 0.775806 | + | 0.630971i | \(0.217344\pi\) | ||||
−0.775806 | + | 0.630971i | \(0.782656\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 360.000 | − | 623.538i | 0.483221 | − | 0.836964i | ||||
\(746\) | −255.972 | − | 147.785i | −0.343126 | − | 0.198104i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −432.000 | −0.577540 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5000 | − | 35.5070i | −0.0272969 | − | 0.0472797i | 0.852054 | − | 0.523454i | \(-0.175357\pi\) |
−0.879351 | + | 0.476174i | \(0.842023\pi\) | |||||||
\(752\) | −14.6969 | − | 8.48528i | −0.0195438 | − | 0.0112836i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 24.0000 | + | 41.5692i | 0.0318302 | + | 0.0551316i | ||||
\(755\) | − | 441.235i | − | 0.584417i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1114.00 | −1.47160 | −0.735799 | − | 0.677200i | \(-0.763193\pi\) | ||||
−0.735799 | + | 0.677200i | \(0.763193\pi\) | |||||||
\(758\) | −530.315 | + | 306.177i | −0.699623 | + | 0.403928i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −138.000 | + | 239.023i | −0.181579 | + | 0.314504i | ||||
\(761\) | 249.848 | − | 144.250i | 0.328315 | − | 0.189553i | −0.326778 | − | 0.945101i | \(-0.605963\pi\) |
0.655093 | + | 0.755548i | \(0.272629\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 127.279i | 0.166596i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −276.000 | + | 478.046i | −0.360313 | + | 0.624081i | ||||
\(767\) | 73.4847 | + | 42.4264i | 0.0958079 | + | 0.0553147i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1127.00 | −1.46554 | −0.732770 | − | 0.680477i | \(-0.761773\pi\) | ||||
−0.732770 | + | 0.680477i | \(0.761773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −151.000 | − | 261.540i | −0.195596 | − | 0.338782i | ||||
\(773\) | −187.386 | − | 108.187i | −0.242414 | − | 0.139958i | 0.373872 | − | 0.927480i | \(-0.378030\pi\) |
−0.616286 | + | 0.787523i | \(0.711363\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 164.500 | + | 284.922i | 0.212258 | + | 0.367642i | ||||
\(776\) | 294.156i | 0.379068i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −522.000 | −0.670951 | ||||||||
\(779\) | −929.581 | + | 536.694i | −1.19330 | + | 0.688953i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −621.000 | + | 1075.60i | −0.795134 | + | 1.37721i | ||||
\(782\) | 352.727 | − | 203.647i | 0.451057 | − | 0.260418i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 644.881i | 0.821505i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 85.0000 | − | 147.224i | 0.108005 | − | 0.187070i | −0.806957 | − | 0.590610i | \(-0.798887\pi\) |
0.914962 | + | 0.403540i | \(0.132220\pi\) | |||||||
\(788\) | 29.3939 | + | 16.9706i | 0.0373019 | + | 0.0215362i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 678.000 | 0.858228 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 52.0000 | + | 90.0666i | 0.0655738 | + | 0.113577i | ||||
\(794\) | 138.396 | + | 79.9031i | 0.174302 | + | 0.100634i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 160.000 | + | 277.128i | 0.201005 | + | 0.348151i | ||||
\(797\) | 1170.97i | 1.46922i | 0.678489 | + | 0.734610i | \(0.262635\pi\) | ||||
−0.678489 | + | 0.734610i | \(0.737365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −72.0000 | −0.0901126 | ||||||||
\(800\) | 34.2929 | − | 19.7990i | 0.0428661 | − | 0.0247487i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 252.000 | − | 436.477i | 0.314214 | − | 0.544235i | ||||
\(803\) | 716.476 | − | 413.657i | 0.892249 | − | 0.515140i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 66.4680i | − | 0.0824665i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −210.000 | + | 363.731i | −0.259901 | + | 0.450162i | ||||
\(809\) | 290.265 | + | 167.584i | 0.358794 | + | 0.207150i | 0.668552 | − | 0.743666i | \(-0.266915\pi\) |
−0.309757 | + | 0.950816i | \(0.600248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1114.00 | 1.37361 | 0.686806 | − | 0.726840i | \(-0.259012\pi\) | ||||
0.686806 | + | 0.726840i | \(0.259012\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 495.000 | + | 857.365i | 0.608108 | + | 1.05327i | ||||
\(815\) | 205.757 | + | 118.794i | 0.252463 | + | 0.145759i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 264.500 | + | 458.127i | 0.323745 | + | 0.560743i | ||||
\(818\) | 451.134i | 0.551509i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −396.000 | −0.482927 | ||||||||
\(821\) | −84.5074 | + | 48.7904i | −0.102932 | + | 0.0594280i | −0.550582 | − | 0.834781i | \(-0.685594\pi\) |
0.447650 | + | 0.894209i | \(0.352261\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −796.000 | + | 1378.71i | −0.967193 | + | 1.67523i | −0.263590 | + | 0.964635i | \(0.584907\pi\) |
−0.703603 | + | 0.710593i | \(0.748427\pi\) | |||||||
\(824\) | 291.489 | − | 168.291i | 0.353749 | − | 0.204237i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1022.48i | 1.23637i | 0.786033 | + | 0.618184i | \(0.212131\pi\) | ||||
−0.786033 | + | 0.618184i | \(0.787869\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 191.500 | − | 331.688i | 0.231001 | − | 0.400106i | −0.727102 | − | 0.686530i | \(-0.759133\pi\) |
0.958103 | + | 0.286424i | \(0.0924665\pi\) | |||||||
\(830\) | −154.318 | − | 89.0955i | −0.185925 | − | 0.107344i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.00000 | −0.00961538 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.00000 | − | 15.5885i | −0.0107784 | − | 0.0186688i | ||||
\(836\) | 507.044 | + | 292.742i | 0.606512 | + | 0.350170i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −543.000 | − | 940.504i | −0.647971 | − | 1.12232i | ||||
\(839\) | − | 576.999i | − | 0.687722i | −0.939020 | − | 0.343861i | \(-0.888265\pi\) | ||
0.939020 | − | 0.343861i | \(-0.111735\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −311.000 | −0.369798 | ||||||||
\(842\) | 79.6084 | − | 45.9619i | 0.0945468 | − | 0.0545866i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −208.000 | + | 360.267i | −0.246445 | + | 0.426856i | ||||
\(845\) | 617.271 | − | 356.382i | 0.730499 | − | 0.421754i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 203.647i | − | 0.240149i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 84.0000 | − | 145.492i | 0.0988235 | − | 0.171167i | ||||
\(851\) | −808.332 | − | 466.690i | −0.949861 | − | 0.548402i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −527.000 | −0.617819 | −0.308910 | − | 0.951091i | \(-0.599964\pi\) | ||||
−0.308910 | + | 0.951091i | \(0.599964\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 168.000 | + | 290.985i | 0.196262 | + | 0.339935i | ||||
\(857\) | −1146.36 | − | 661.852i | −1.33764 | − | 0.772289i | −0.351187 | − | 0.936305i | \(-0.614222\pi\) |
−0.986458 | + | 0.164016i | \(0.947555\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −707.000 | − | 1224.56i | −0.823050 | − | 1.42556i | −0.903400 | − | 0.428798i | \(-0.858937\pi\) |
0.0803504 | − | 0.996767i | \(-0.474396\pi\) | |||||||
\(860\) | 195.161i | 0.226932i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 678.000 | 0.786543 | ||||||||
\(863\) | 1186.78 | − | 685.186i | 1.37518 | − | 0.793959i | 0.383603 | − | 0.923498i | \(-0.374683\pi\) |
0.991574 | + | 0.129539i | \(0.0413499\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −324.000 | + | 561.184i | −0.374566 | + | 0.648768i | ||||
\(866\) | 449.481 | − | 259.508i | 0.519032 | − | 0.299663i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1438.26i | − | 1.65507i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.5000 | − | 84.0045i | 0.0556831 | − | 0.0964460i | ||||
\(872\) | −120.025 | − | 69.2965i | −0.137643 | − | 0.0794684i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −552.000 | −0.631579 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −112.000 | − | 193.990i | −0.127708 | − | 0.221197i | 0.795080 | − | 0.606504i | \(-0.207429\pi\) |
−0.922788 | + | 0.385307i | \(0.874095\pi\) | |||||||
\(878\) | 656.463 | + | 379.009i | 0.747680 | + | 0.431673i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 108.000 | + | 187.061i | 0.122727 | + | 0.212570i | ||||
\(881\) | − | 1612.20i | − | 1.82997i | −0.403488 | − | 0.914985i | \(-0.632202\pi\) | ||
0.403488 | − | 0.914985i | \(-0.367798\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 329.000 | 0.372593 | 0.186297 | − | 0.982494i | \(-0.440351\pi\) | ||||
0.186297 | + | 0.982494i | \(0.440351\pi\) | |||||||
\(884\) | −29.3939 | + | 16.9706i | −0.0332510 | + | 0.0191975i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 60.0000 | − | 103.923i | 0.0677201 | − | 0.117295i | ||||
\(887\) | −47.7650 | + | 27.5772i | −0.0538501 | + | 0.0310904i | −0.526683 | − | 0.850062i | \(-0.676565\pi\) |
0.472833 | + | 0.881152i | \(0.343231\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 814.587i | − | 0.915266i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 40.0000 | − | 69.2820i | 0.0448430 | − | 0.0776704i | ||||
\(893\) | 84.5074 | + | 48.7904i | 0.0946331 | + | 0.0546365i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | 0.0201117 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −435.000 | − | 753.442i | −0.484410 | − | 0.839022i | ||||
\(899\) | 1381.51 | + | 797.616i | 1.53672 | + | 0.887226i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −432.000 | − | 748.246i | −0.479467 | − | 0.830462i | ||||
\(902\) | 840.043i | 0.931311i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −276.000 | −0.305310 | ||||||||
\(905\) | −202.083 | + | 116.673i | −0.223296 | + | 0.128920i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −155.500 | + | 269.334i | −0.171444 | + | 0.296950i | −0.938925 | − | 0.344122i | \(-0.888177\pi\) |
0.767481 | + | 0.641072i | \(0.221510\pi\) | |||||||
\(908\) | −389.469 | + | 224.860i | −0.428930 | + | 0.247643i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 356.382i | 0.391198i | 0.980684 | + | 0.195599i | \(0.0626652\pi\) | ||||
−0.980684 | + | 0.195599i | \(0.937335\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −189.000 | + | 327.358i | −0.207010 | + | 0.358552i | ||||
\(914\) | 567.057 | + | 327.390i | 0.620412 | + | 0.358195i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 754.000 | 0.823144 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 72.5000 | + | 125.574i | 0.0788901 | + | 0.136642i | 0.902771 | − | 0.430121i | \(-0.141529\pi\) |
−0.823881 | + | 0.566762i | \(0.808196\pi\) | |||||||
\(920\) | −176.363 | − | 101.823i | −0.191699 | − | 0.110678i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −192.000 | − | 332.554i | −0.208243 | − | 0.360687i | ||||
\(923\) | 97.5807i | 0.105721i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −385.000 | −0.416216 | ||||||||
\(926\) | 57.5630 | − | 33.2340i | 0.0621631 | − | 0.0358899i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 96.0000 | − | 166.277i | 0.103448 | − | 0.179178i | ||||
\(929\) | 268.219 | − | 154.856i | 0.288718 | − | 0.166691i | −0.348645 | − | 0.937255i | \(-0.613358\pi\) |
0.637364 | + | 0.770563i | \(0.280025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 687.308i | − | 0.737455i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −525.000 | + | 909.327i | −0.562099 | + | 0.973583i | ||||
\(935\) | 793.635 | + | 458.205i | 0.848807 | + | 0.490059i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 487.000 | 0.519744 | 0.259872 | − | 0.965643i | \(-0.416320\pi\) | ||||
0.259872 | + | 0.965643i | \(0.416320\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.0000 | + | 31.1769i | 0.0191489 | + | 0.0331669i | ||||
\(941\) | −1190.45 | − | 687.308i | −1.26509 | − | 0.730401i | −0.291037 | − | 0.956712i | \(-0.594000\pi\) |
−0.974055 | + | 0.226310i | \(0.927334\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −396.000 | − | 685.892i | −0.419936 | − | 0.727351i | ||||
\(944\) | − | 339.411i | − | 0.359546i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 414.000 | 0.437632 | ||||||||
\(947\) | −165.341 | + | 95.4594i | −0.174594 | + | 0.100802i | −0.584750 | − | 0.811213i | \(-0.698808\pi\) |
0.410156 | + | 0.912015i | \(0.365474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.5000 | − | 56.2917i | 0.0342466 | − | 0.0593168i | ||||
\(950\) | −197.184 | + | 113.844i | −0.207562 | + | 0.119836i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1035.20i | − | 1.08626i | −0.839649 | − | 0.543129i | \(-0.817239\pi\) | ||
0.839649 | − | 0.543129i | \(-0.182761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 135.000 | − | 233.827i | 0.141361 | − | 0.244845i | ||||
\(956\) | −22.0454 | − | 12.7279i | −0.0230600 | − | 0.0133137i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 600.000 | 0.626305 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −624.000 | − | 1080.80i | −0.649324 | − | 1.12466i | ||||
\(962\) | 67.3610 | + | 38.8909i | 0.0700218 | + | 0.0404271i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 130.000 | + | 225.167i | 0.134855 | + | 0.233575i | ||||
\(965\) | 640.639i | 0.663874i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1681.00 | −1.73837 | −0.869183 | − | 0.494490i | \(-0.835355\pi\) | ||||
−0.869183 | + | 0.494490i | \(0.835355\pi\) | |||||||
\(968\) | 100.429 | − | 57.9828i | 0.103749 | − | 0.0598995i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 312.000 | − | 540.400i | 0.321649 | − | 0.557113i | ||||
\(971\) | −1043.48 | + | 602.455i | −1.07465 | + | 0.620448i | −0.929448 | − | 0.368954i | \(-0.879716\pi\) |
−0.145200 | + | 0.989402i | \(0.546383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 337.997i | 0.347020i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 208.000 | − | 360.267i | 0.213115 | − | 0.369126i | ||||
\(977\) | −1017.76 | − | 587.606i | −1.04172 | − | 0.601439i | −0.121402 | − | 0.992603i | \(-0.538739\pi\) |
−0.920321 | + | 0.391165i | \(0.872072\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1728.00 | −1.76507 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 144.000 | + | 249.415i | 0.146640 | + | 0.253987i | ||||
\(983\) | −1660.75 | − | 958.837i | −1.68948 | − | 0.975419i | −0.954917 | − | 0.296873i | \(-0.904056\pi\) |
−0.734558 | − | 0.678546i | \(-0.762611\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | − | 62.3538i | −0.0365482 | − | 0.0633034i | ||||
\(986\) | − | 814.587i | − | 0.826153i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 46.0000 | 0.0465587 | ||||||||
\(989\) | −338.030 | + | 195.161i | −0.341789 | + | 0.197332i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 312.500 | − | 541.266i | 0.315338 | − | 0.546182i | −0.664171 | − | 0.747580i | \(-0.731215\pi\) |
0.979509 | + | 0.201399i | \(0.0645488\pi\) | |||||||
\(992\) | −230.252 | + | 132.936i | −0.232109 | + | 0.134008i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 678.823i | − | 0.682234i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −471.500 | + | 816.662i | −0.472919 | + | 0.819119i | −0.999520 | − | 0.0309934i | \(-0.990133\pi\) |
0.526601 | + | 0.850113i | \(0.323466\pi\) | |||||||
\(998\) | 60.0125 | + | 34.6482i | 0.0601328 | + | 0.0347177i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.3.s.a.557.2 | 4 | ||
3.2 | odd | 2 | inner | 882.3.s.a.557.1 | 4 | ||
7.2 | even | 3 | inner | 882.3.s.a.863.1 | 4 | ||
7.3 | odd | 6 | 882.3.b.b.197.2 | 2 | |||
7.4 | even | 3 | 882.3.b.e.197.2 | 2 | |||
7.5 | odd | 6 | 126.3.s.a.107.1 | yes | 4 | ||
7.6 | odd | 2 | 126.3.s.a.53.2 | yes | 4 | ||
21.2 | odd | 6 | inner | 882.3.s.a.863.2 | 4 | ||
21.5 | even | 6 | 126.3.s.a.107.2 | yes | 4 | ||
21.11 | odd | 6 | 882.3.b.e.197.1 | 2 | |||
21.17 | even | 6 | 882.3.b.b.197.1 | 2 | |||
21.20 | even | 2 | 126.3.s.a.53.1 | ✓ | 4 | ||
28.19 | even | 6 | 1008.3.dc.b.737.1 | 4 | |||
28.27 | even | 2 | 1008.3.dc.b.305.2 | 4 | |||
84.47 | odd | 6 | 1008.3.dc.b.737.2 | 4 | |||
84.83 | odd | 2 | 1008.3.dc.b.305.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.s.a.53.1 | ✓ | 4 | 21.20 | even | 2 | ||
126.3.s.a.53.2 | yes | 4 | 7.6 | odd | 2 | ||
126.3.s.a.107.1 | yes | 4 | 7.5 | odd | 6 | ||
126.3.s.a.107.2 | yes | 4 | 21.5 | even | 6 | ||
882.3.b.b.197.1 | 2 | 21.17 | even | 6 | |||
882.3.b.b.197.2 | 2 | 7.3 | odd | 6 | |||
882.3.b.e.197.1 | 2 | 21.11 | odd | 6 | |||
882.3.b.e.197.2 | 2 | 7.4 | even | 3 | |||
882.3.s.a.557.1 | 4 | 3.2 | odd | 2 | inner | ||
882.3.s.a.557.2 | 4 | 1.1 | even | 1 | trivial | ||
882.3.s.a.863.1 | 4 | 7.2 | even | 3 | inner | ||
882.3.s.a.863.2 | 4 | 21.2 | odd | 6 | inner | ||
1008.3.dc.b.305.1 | 4 | 84.83 | odd | 2 | |||
1008.3.dc.b.305.2 | 4 | 28.27 | even | 2 | |||
1008.3.dc.b.737.1 | 4 | 28.19 | even | 6 | |||
1008.3.dc.b.737.2 | 4 | 84.47 | odd | 6 |