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 | 863.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.863 |
Dual form | 882.3.s.a.557.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 | \(-0.193866\pi\) |
−0.0853458 | + | 0.996351i | \(0.527199\pi\) | |||||||
\(6\) | 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 | \(-0.863045\pi\) |
−0.0932057 | + | 0.995647i | \(0.529711\pi\) | |||||||
\(12\) | 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 | \(-0.500318\pi\) |
0.865525 | + | 0.500865i | \(0.166985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.5000 | − | 19.9186i | 0.605263 | − | 1.04835i | −0.386747 | − | 0.922186i | \(-0.626401\pi\) |
0.992010 | − | 0.126161i | \(-0.0402654\pi\) | |||||||
\(20\) | 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 | \(-0.213059\pi\) |
−0.145231 | + | 0.989398i | \(0.546392\pi\) | |||||||
\(24\) | 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 | 0.943836 | + | 0.330413i | \(0.107188\pi\) |
−0.185772 | + | 0.982593i | \(0.559479\pi\) | |||||||
\(32\) | 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 | −0.207768 | − | 0.978178i | \(-0.566620\pi\) |
0.951011 | − | 0.309157i | \(-0.100047\pi\) | |||||||
\(38\) | −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 | \(-0.347705\pi\) |
−0.538578 | + | 0.842576i | \(0.681038\pi\) | |||||||
\(48\) | 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 | \(-0.826138\pi\) |
0.0226013 | + | 0.999745i | \(0.492805\pi\) | |||||||
\(54\) | 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 | \(-0.922109\pi\) |
−0.275294 | + | 0.961360i | \(0.588775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 52.0000 | − | 90.0666i | 0.852459 | − | 1.47650i | −0.0265234 | − | 0.999648i | \(-0.508444\pi\) |
0.878982 | − | 0.476854i | \(-0.158223\pi\) | |||||||
\(62\) | − | 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 | 0.959433 | + | 0.281936i | \(0.0909767\pi\) |
−0.235553 | + | 0.971862i | \(0.575690\pi\) | |||||||
\(68\) | 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 | 0.998067 | − | 0.0621550i | \(-0.0197973\pi\) |
−0.552861 | + | 0.833273i | \(0.686464\pi\) | |||||||
\(74\) | −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 | 0.247696 | + | 0.968838i | \(0.420326\pi\) |
−0.962886 | + | 0.269907i | \(0.913007\pi\) | |||||||
\(80\) | −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 | \(-0.0571958\pi\) |
0.337173 | + | 0.941443i | \(0.390529\pi\) | |||||||
\(90\) | 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 | \(-0.403797\pi\) |
0.975598 | + | 0.219564i | \(0.0704633\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 59.5000 | − | 103.057i | 0.577670 | − | 1.00055i | −0.418076 | − | 0.908412i | \(-0.637295\pi\) |
0.995746 | − | 0.0921416i | \(-0.0293712\pi\) | |||||||
\(104\) | − | 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 | \(-0.146009\pi\) |
0.0648531 | + | 0.997895i | \(0.479342\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 24.5000 | + | 42.4352i | 0.224771 | + | 0.389314i | 0.956251 | − | 0.292549i | \(-0.0945034\pi\) |
−0.731480 | + | 0.681863i | \(0.761170\pi\) | |||||||
\(110\) | 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 | \(-0.307533\pi\) |
−0.428239 | + | 0.903665i | \(0.640866\pi\) | |||||||
\(132\) | 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 | \(-0.586977\pi\) |
0.698966 | + | 0.715154i | \(0.253644\pi\) | |||||||
\(138\) | 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 | \(-0.140477\pi\) |
0.0821839 | + | 0.996617i | \(0.473811\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −52.0000 | − | 90.0666i | −0.344371 | − | 0.596468i | 0.640868 | − | 0.767651i | \(-0.278574\pi\) |
−0.985239 | + | 0.171183i | \(0.945241\pi\) | |||||||
\(152\) | −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 | 0.999833 | − | 0.0182904i | \(-0.00582233\pi\) |
−0.515756 | + | 0.856735i | \(0.672489\pi\) | |||||||
\(158\) | 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 | −0.939042 | − | 0.343803i | \(-0.888285\pi\) |
0.767263 | + | 0.641333i | \(0.221618\pi\) | |||||||
\(164\) | −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 | \(-0.478862\pi\) |
−0.830938 | + | 0.556365i | \(0.812196\pi\) | |||||||
\(174\) | 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 | \(-0.662894\pi\) |
0.510228 | + | 0.860039i | \(0.329561\pi\) | |||||||
\(180\) | 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 | \(-0.280056\pi\) |
−0.348736 | + | 0.937221i | \(0.613389\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 75.5000 | + | 130.770i | 0.391192 | + | 0.677564i | 0.992607 | − | 0.121373i | \(-0.0387296\pi\) |
−0.601415 | + | 0.798937i | \(0.705396\pi\) | |||||||
\(194\) | 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 | 0.591958 | − | 0.805969i | \(-0.298355\pi\) |
−0.993968 | + | 0.109667i | \(0.965022\pi\) | |||||||
\(200\) | −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 | \(-0.501730\pi\) |
0.863295 | + | 0.504699i | \(0.168397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 188.500 | − | 326.492i | 0.823144 | − | 1.42573i | −0.0801853 | − | 0.996780i | \(-0.525551\pi\) |
0.903329 | − | 0.428947i | \(-0.141115\pi\) | |||||||
\(230\) | − | 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 | \(-0.597306\pi\) |
−0.976353 | + | 0.216183i | \(0.930639\pi\) | |||||||
\(234\) | 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 | 0.699077 | − | 0.715046i | \(-0.253594\pi\) |
−0.968787 | + | 0.247896i | \(0.920261\pi\) | |||||||
\(242\) | −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 | −0.993810 | − | 0.111096i | \(-0.964564\pi\) |
−0.593117 | − | 0.805117i | \(-0.702103\pi\) | |||||||
\(258\) | 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 | \(-0.728677\pi\) |
0.322897 | + | 0.946434i | \(0.395343\pi\) | |||||||
\(264\) | 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 | \(-0.843859\pi\) |
−0.0330613 | + | 0.999453i | \(0.510526\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −260.000 | + | 450.333i | −0.959410 | + | 1.66175i | −0.235471 | + | 0.971881i | \(0.575663\pi\) |
−0.723938 | + | 0.689865i | \(0.757670\pi\) | |||||||
\(272\) | 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 | 0.745833 | − | 0.666133i | \(-0.232052\pi\) |
−0.949804 | + | 0.312844i | \(0.898718\pi\) | |||||||
\(278\) | −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 | 0.933874 | − | 0.357603i | \(-0.116406\pi\) |
−0.776630 | + | 0.629957i | \(0.783072\pi\) | |||||||
\(284\) | −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 | \(-0.534830\pi\) |
0.806244 | + | 0.591582i | \(0.201497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −75.5000 | + | 130.770i | −0.241214 | + | 0.417795i | −0.961060 | − | 0.276338i | \(-0.910879\pi\) |
0.719846 | + | 0.694133i | \(0.244212\pi\) | |||||||
\(314\) | − | 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 | \(-0.111264\pi\) |
0.173174 | + | 0.984891i | \(0.444598\pi\) | |||||||
\(318\) | 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 | −0.805608 | − | 0.592449i | \(-0.798161\pi\) |
0.915880 | + | 0.401452i | \(0.131495\pi\) | |||||||
\(332\) | −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 | \(-0.876032\pi\) |
−0.133741 | + | 0.991016i | \(0.542699\pi\) | |||||||
\(348\) | 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 | \(-0.522110\pi\) |
0.829234 | + | 0.558902i | \(0.188777\pi\) | |||||||
\(354\) | 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 | \(-0.584221\pi\) |
−0.966644 | + | 0.256124i | \(0.917555\pi\) | |||||||
\(360\) | 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 | 0.562658 | − | 0.826689i | \(-0.309779\pi\) |
−0.997263 | + | 0.0739317i | \(0.976445\pi\) | |||||||
\(368\) | −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 | −0.971424 | − | 0.237350i | \(-0.923721\pi\) |
0.691263 | + | 0.722603i | \(0.257054\pi\) | |||||||
\(374\) | 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 | \(-0.163142\pi\) |
0.0110743 | + | 0.999939i | \(0.496475\pi\) | |||||||
\(384\) | 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 | \(-0.509319\pi\) |
0.851018 | + | 0.525137i | \(0.175986\pi\) | |||||||
\(390\) | 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 | −0.786052 | − | 0.618161i | \(-0.787878\pi\) |
0.928369 | + | 0.371660i | \(0.121211\pi\) | |||||||
\(398\) | 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 | \(-0.479904\pi\) |
−0.832755 | + | 0.553641i | \(0.813238\pi\) | |||||||
\(402\) | 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 | 0.602470 | − | 0.798141i | \(-0.294183\pi\) |
−0.992446 | + | 0.122684i | \(0.960850\pi\) | |||||||
\(410\) | 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 | \(-0.854396\pi\) |
−0.0661229 | + | 0.997811i | \(0.521063\pi\) | |||||||
\(432\) | 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 | −0.380681 | − | 0.924706i | \(-0.624311\pi\) |
0.991160 | − | 0.132673i | \(-0.0423561\pi\) | |||||||
\(440\) | 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 | \(-0.363865\pi\) |
−0.580642 | + | 0.814159i | \(0.697198\pi\) | |||||||
\(444\) | 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 | −0.493407 | − | 0.869799i | \(-0.664249\pi\) |
0.999971 | − | 0.00759675i | \(-0.00241814\pi\) | |||||||
\(458\) | −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 | \(-0.0408423\pi\) |
0.385075 | + | 0.922885i | \(0.374176\pi\) | |||||||
\(468\) | 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 | \(-0.812704\pi\) |
0.0647625 | + | 0.997901i | \(0.479371\pi\) | |||||||
\(480\) | 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 | 0.716858 | − | 0.697219i | \(-0.245579\pi\) |
−0.962238 | + | 0.272208i | \(0.912246\pi\) | |||||||
\(488\) | −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 | −0.840432 | − | 0.541917i | \(-0.817699\pi\) |
0.889530 | + | 0.456877i | \(0.151032\pi\) | |||||||
\(500\) | 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 | \(-0.409679\pi\) |
−0.691415 | + | 0.722457i | \(0.743013\pi\) | |||||||
\(510\) | 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 | \(-0.969560\pi\) |
−0.415024 | + | 0.909811i | \(0.636227\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −195.500 | + | 338.616i | −0.373805 | + | 0.647449i | −0.990147 | − | 0.140029i | \(-0.955280\pi\) |
0.616342 | + | 0.787478i | \(0.288614\pi\) | |||||||
\(524\) | 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 | −0.830318 | − | 0.557289i | \(-0.811841\pi\) |
0.897786 | + | 0.440432i | \(0.145175\pi\) | |||||||
\(542\) | 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 | \(-0.680006\pi\) |
0.463280 | + | 0.886212i | \(0.346672\pi\) | |||||||
\(558\) | 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 | \(-0.955286\pi\) |
−0.373820 | + | 0.927501i | \(0.621952\pi\) | |||||||
\(564\) | 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 | \(-0.243128\pi\) |
−0.237906 | + | 0.971288i | \(0.576461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 267.500 | + | 463.324i | 0.468476 | + | 0.811425i | 0.999351 | − | 0.0360256i | \(-0.0114698\pi\) |
−0.530875 | + | 0.847450i | \(0.678136\pi\) | |||||||
\(572\) | −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 | 0.929459 | + | 0.368926i | \(0.120274\pi\) |
−0.145230 | + | 0.989398i | \(0.546392\pi\) | |||||||
\(578\) | 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 | \(-0.178084\pi\) |
−0.0358606 | + | 0.999357i | \(0.511417\pi\) | |||||||
\(594\) | 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 | \(-0.612293\pi\) |
0.639938 | + | 0.768427i | \(0.278960\pi\) | |||||||
\(600\) | 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 | −0.506561 | − | 0.862204i | \(-0.669083\pi\) |
0.999971 | + | 0.00759259i | \(0.00241682\pi\) | |||||||
\(608\) | − | 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 | 0.962960 | − | 0.269645i | \(-0.0869062\pi\) |
−0.714999 | + | 0.699125i | \(0.753573\pi\) | |||||||
\(614\) | 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 | 0.693593 | − | 0.720367i | \(-0.256027\pi\) |
−0.970653 | + | 0.240486i | \(0.922693\pi\) | |||||||
\(620\) | −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 | \(-0.774032\pi\) |
0.185224 | + | 0.982696i | \(0.440699\pi\) | |||||||
\(642\) | 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 | \(-0.933867\pi\) |
−0.310611 | + | 0.950537i | \(0.600534\pi\) | |||||||
\(648\) | 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 | \(-0.573728\pi\) |
−0.957677 | + | 0.287846i | \(0.907061\pi\) | |||||||
\(654\) | 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 | 0.654488 | − | 0.756072i | \(-0.272884\pi\) |
−0.982022 | + | 0.188767i | \(0.939551\pi\) | |||||||
\(662\) | −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 | \(-0.301363\pi\) |
−0.410644 | + | 0.911796i | \(0.634696\pi\) | |||||||
\(678\) | 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 | −0.625403 | + | 0.780302i | \(0.715065\pi\) |
−0.988463 | + | 0.151464i | \(0.951601\pi\) | |||||||
\(684\) | 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 | −0.941445 | − | 0.337168i | \(-0.890531\pi\) |
0.762718 | + | 0.646731i | \(0.223864\pi\) | |||||||
\(692\) | − | 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 | −0.213846 | − | 0.976867i | \(-0.568599\pi\) |
0.952915 | − | 0.303238i | \(-0.0980677\pi\) | |||||||
\(710\) | 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 | \(-0.389026\pi\) |
−0.643117 | + | 0.765768i | \(0.722359\pi\) | |||||||
\(720\) | 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 | −0.874426 | − | 0.485159i | \(-0.838762\pi\) |
0.857373 | + | 0.514696i | \(0.172095\pi\) | |||||||
\(734\) | 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 | 0.988286 | − | 0.152614i | \(-0.0487690\pi\) |
−0.626310 | + | 0.779574i | \(0.715436\pi\) | |||||||
\(740\) | 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 | −0.879351 | − | 0.476174i | \(-0.842023\pi\) |
0.852054 | + | 0.523454i | \(0.175357\pi\) | |||||||
\(752\) | 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 | \(-0.394037\pi\) |
−0.655093 | + | 0.755548i | \(0.727371\pi\) | |||||||
\(762\) | 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 | \(-0.621970\pi\) |
0.616286 | + | 0.787523i | \(0.288637\pi\) | |||||||
\(774\) | 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 | 0.914962 | − | 0.403540i | \(-0.132220\pi\) |
−0.806957 | + | 0.590610i | \(0.798887\pi\) | |||||||
\(788\) | −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 | \(-0.733085\pi\) |
0.309757 | + | 0.950816i | \(0.399752\pi\) | |||||||
\(810\) | 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 | \(-0.314406\pi\) |
−0.447650 | + | 0.894209i | \(0.647739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −796.000 | − | 1378.71i | −0.967193 | − | 1.67523i | −0.703603 | − | 0.710593i | \(-0.748427\pi\) |
−0.263590 | − | 0.964635i | \(-0.584907\pi\) | |||||||
\(824\) | −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 | 0.958103 | − | 0.286424i | \(-0.0924665\pi\) |
−0.727102 | + | 0.686530i | \(0.759133\pi\) | |||||||
\(830\) | 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 | \(-0.385778\pi\) |
0.986458 | + | 0.164016i | \(0.0524449\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −707.000 | + | 1224.56i | −0.823050 | + | 1.42556i | 0.0803504 | + | 0.996767i | \(0.474396\pi\) |
−0.903400 | + | 0.428798i | \(0.858937\pi\) | |||||||
\(860\) | 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 | \(-0.625317\pi\) |
−0.991574 | + | 0.129539i | \(0.958650\pi\) | |||||||
\(864\) | 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 | −0.922788 | − | 0.385307i | \(-0.874095\pi\) |
0.795080 | + | 0.606504i | \(0.207429\pi\) | |||||||
\(878\) | −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 | \(-0.323435\pi\) |
−0.472833 | + | 0.881152i | \(0.656769\pi\) | |||||||
\(888\) | 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 | 0.767481 | − | 0.641072i | \(-0.221510\pi\) |
−0.938925 | + | 0.344122i | \(0.888177\pi\) | |||||||
\(908\) | 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 | −0.823881 | − | 0.566762i | \(-0.808196\pi\) |
0.902771 | + | 0.430121i | \(0.141529\pi\) | |||||||
\(920\) | 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 | \(-0.386642\pi\) |
−0.637364 | + | 0.770563i | \(0.719975\pi\) | |||||||
\(930\) | 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 | \(-0.406000\pi\) |
0.974055 | + | 0.226310i | \(0.0726663\pi\) | |||||||
\(942\) | 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 | \(-0.301192\pi\) |
−0.410156 | + | 0.912015i | \(0.634526\pi\) | |||||||
\(948\) | 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 | \(-0.120284\pi\) |
0.145200 | + | 0.989402i | \(0.453617\pi\) | |||||||
\(972\) | 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 | \(-0.461261\pi\) |
0.920321 | + | 0.391165i | \(0.127928\pi\) | |||||||
\(978\) | 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 | 0.734558 | − | 0.678546i | \(-0.237389\pi\) |
0.954917 | − | 0.296873i | \(-0.0959439\pi\) | |||||||
\(984\) | 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 | 0.979509 | − | 0.201399i | \(-0.0645488\pi\) |
−0.664171 | + | 0.747580i | \(0.731215\pi\) | |||||||
\(992\) | 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 | 0.526601 | − | 0.850113i | \(-0.323466\pi\) |
−0.999520 | + | 0.0309934i | \(0.990133\pi\) | |||||||
\(998\) | −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.863.1 | 4 | ||
3.2 | odd | 2 | inner | 882.3.s.a.863.2 | 4 | ||
7.2 | even | 3 | 882.3.b.e.197.2 | 2 | |||
7.3 | odd | 6 | 126.3.s.a.53.2 | yes | 4 | ||
7.4 | even | 3 | inner | 882.3.s.a.557.2 | 4 | ||
7.5 | odd | 6 | 882.3.b.b.197.2 | 2 | |||
7.6 | odd | 2 | 126.3.s.a.107.1 | yes | 4 | ||
21.2 | odd | 6 | 882.3.b.e.197.1 | 2 | |||
21.5 | even | 6 | 882.3.b.b.197.1 | 2 | |||
21.11 | odd | 6 | inner | 882.3.s.a.557.1 | 4 | ||
21.17 | even | 6 | 126.3.s.a.53.1 | ✓ | 4 | ||
21.20 | even | 2 | 126.3.s.a.107.2 | yes | 4 | ||
28.3 | even | 6 | 1008.3.dc.b.305.2 | 4 | |||
28.27 | even | 2 | 1008.3.dc.b.737.1 | 4 | |||
84.59 | odd | 6 | 1008.3.dc.b.305.1 | 4 | |||
84.83 | odd | 2 | 1008.3.dc.b.737.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.s.a.53.1 | ✓ | 4 | 21.17 | even | 6 | ||
126.3.s.a.53.2 | yes | 4 | 7.3 | odd | 6 | ||
126.3.s.a.107.1 | yes | 4 | 7.6 | odd | 2 | ||
126.3.s.a.107.2 | yes | 4 | 21.20 | even | 2 | ||
882.3.b.b.197.1 | 2 | 21.5 | even | 6 | |||
882.3.b.b.197.2 | 2 | 7.5 | odd | 6 | |||
882.3.b.e.197.1 | 2 | 21.2 | odd | 6 | |||
882.3.b.e.197.2 | 2 | 7.2 | even | 3 | |||
882.3.s.a.557.1 | 4 | 21.11 | odd | 6 | inner | ||
882.3.s.a.557.2 | 4 | 7.4 | even | 3 | inner | ||
882.3.s.a.863.1 | 4 | 1.1 | even | 1 | trivial | ||
882.3.s.a.863.2 | 4 | 3.2 | odd | 2 | inner | ||
1008.3.dc.b.305.1 | 4 | 84.59 | odd | 6 | |||
1008.3.dc.b.305.2 | 4 | 28.3 | even | 6 | |||
1008.3.dc.b.737.1 | 4 | 28.27 | even | 2 | |||
1008.3.dc.b.737.2 | 4 | 84.83 | odd | 2 |