Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,11,Mod(17,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.17");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.e (of order \(2\), degree \(1\), 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: | \(30.4971481283\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{85})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 37x^{2} + 38x + 531 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 6) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Root | \(-4.10977 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.17 |
Dual form | 48.11.e.d.17.3 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 200.269 | + | 137.627i | 0.824153 | + | 0.566368i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3630.47i | − | 1.16175i | −0.813992 | − | 0.580876i | \(-0.802710\pi\) | ||
0.813992 | − | 0.580876i | \(-0.197290\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23226.5 | 1.38196 | 0.690978 | − | 0.722876i | \(-0.257180\pi\) | ||||
0.690978 | + | 0.722876i | \(0.257180\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 21166.4 | + | 55125.0i | 0.358455 | + | 0.933547i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 62442.7i | − | 0.387720i | −0.981029 | − | 0.193860i | \(-0.937899\pi\) | ||
0.981029 | − | 0.193860i | \(-0.0621007\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −170161. | −0.458292 | −0.229146 | − | 0.973392i | \(-0.573593\pi\) | ||||
−0.229146 | + | 0.973392i | \(0.573593\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 499653. | − | 727072.i | 0.657979 | − | 0.957460i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.66626e6i | − | 1.87784i | −0.344139 | − | 0.938919i | \(-0.611829\pi\) | ||
0.344139 | − | 0.938919i | \(-0.388171\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −766825. | −0.309691 | −0.154845 | − | 0.987939i | \(-0.549488\pi\) | ||||
−0.154845 | + | 0.987939i | \(0.549488\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.65156e6 | + | 3.19661e6i | 1.13894 | + | 0.782695i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.40327e6i | − | 0.218022i | −0.994041 | − | 0.109011i | \(-0.965232\pi\) | ||
0.994041 | − | 0.109011i | \(-0.0347684\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.41471e6 | −0.349667 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.34774e6 | + | 1.39529e7i | −0.233310 | + | 0.972402i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.83245e6i | 0.235601i | 0.993037 | + | 0.117801i | \(0.0375844\pi\) | ||||
−0.993037 | + | 0.117801i | \(0.962416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.18297e7 | 1.46109 | 0.730544 | − | 0.682865i | \(-0.239266\pi\) | ||||
0.730544 | + | 0.682865i | \(0.239266\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.59382e6 | − | 1.25053e7i | 0.219592 | − | 0.319540i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 8.43233e7i | − | 1.60549i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.01619e7 | 0.723378 | 0.361689 | − | 0.932299i | \(-0.382200\pi\) | ||||
0.361689 | + | 0.932299i | \(0.382200\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.40779e7 | − | 2.34188e7i | −0.377702 | − | 0.259562i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.49239e8i | − | 1.28814i | −0.764967 | − | 0.644069i | \(-0.777245\pi\) | ||
0.764967 | − | 0.644069i | \(-0.222755\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.98719e8 | 1.35175 | 0.675876 | − | 0.737015i | \(-0.263765\pi\) | ||||
0.675876 | + | 0.737015i | \(0.263765\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00130e8 | − | 7.68440e7i | 1.08455 | − | 0.416435i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.55059e8i | 0.676093i | 0.941129 | + | 0.338047i | \(0.109766\pi\) | ||||
−0.941129 | + | 0.338047i | \(0.890234\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.56996e8 | 0.909802 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.66951e8 | − | 5.33970e8i | 1.06355 | − | 1.54762i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.21541e7i | 0.100800i | 0.998729 | + | 0.0503999i | \(0.0160496\pi\) | ||||
−0.998729 | + | 0.0503999i | \(0.983950\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.26696e8 | −0.450434 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.53571e8 | − | 1.05536e8i | −0.255233 | − | 0.175399i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2.92026e8i | − | 0.408471i | −0.978922 | − | 0.204236i | \(-0.934529\pi\) | ||
0.978922 | − | 0.204236i | \(-0.0654708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.30727e8 | −0.628379 | −0.314190 | − | 0.949360i | \(-0.601733\pi\) | ||||
−0.314190 | + | 0.949360i | \(0.601733\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.91622e8 | + | 1.28036e9i | 0.495369 | + | 1.29012i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.17764e8i | 0.532421i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.22093e8 | −0.386700 | −0.193350 | − | 0.981130i | \(-0.561935\pi\) | ||||
−0.193350 | + | 0.981130i | \(0.561935\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.93128e8 | − | 2.81031e8i | 0.123481 | − | 0.179684i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.71364e8i | − | 0.316681i | −0.987385 | − | 0.158340i | \(-0.949386\pi\) | ||
0.987385 | − | 0.158340i | \(-0.0506143\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.18588e9 | 1.05441 | 0.527207 | − | 0.849737i | \(-0.323239\pi\) | ||||
0.527207 | + | 0.849737i | \(0.323239\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.83861e8 | − | 4.69958e8i | −0.288179 | − | 0.198040i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.45033e9i | − | 0.535812i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.96592e9 | −0.638897 | −0.319449 | − | 0.947604i | \(-0.603498\pi\) | ||||
−0.319449 | + | 0.947604i | \(0.603498\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.59075e9 | + | 2.33360e9i | −0.743020 | + | 0.669269i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.18558e9i | 0.554850i | 0.960747 | + | 0.277425i | \(0.0894810\pi\) | ||||
−0.960747 | + | 0.277425i | \(0.910519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.67979e9 | −2.18158 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.65078e8 | + | 9.67791e8i | −0.133437 | + | 0.194171i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.38742e8i | − | 0.0427542i | −0.999771 | − | 0.0213771i | \(-0.993195\pi\) | ||
0.999771 | − | 0.0213771i | \(-0.00680506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.95224e9 | −0.633339 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.37720e9 | + | 5.75692e9i | 1.20416 | + | 0.827514i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.78394e9i | 0.359784i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.84112e9 | −1.02955 | −0.514776 | − | 0.857324i | \(-0.672125\pi\) | ||||
−0.514776 | + | 0.857324i | \(0.672125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.44215e9 | − | 1.32169e9i | 0.361955 | − | 0.138980i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.67928e10i | 1.59778i | 0.601477 | + | 0.798890i | \(0.294579\pi\) | ||||
−0.601477 | + | 0.798890i | \(0.705421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.36865e9 | −0.721887 | −0.360944 | − | 0.932588i | \(-0.617545\pi\) | ||||
−0.360944 | + | 0.932588i | \(0.617545\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.16052e10 | − | 1.68873e10i | 0.909297 | − | 1.32317i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.43555e10i | 1.02353i | 0.859126 | + | 0.511764i | \(0.171008\pi\) | ||||
−0.859126 | + | 0.511764i | \(0.828992\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.72564e9 | −0.307134 | −0.153567 | − | 0.988138i | \(-0.549076\pi\) | ||||
−0.153567 | + | 0.988138i | \(0.549076\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.00459e10 | + | 6.90365e9i | 0.596174 | + | 0.409698i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.32158e10i | − | 0.717303i | −0.933472 | − | 0.358651i | \(-0.883237\pi\) | ||
0.933472 | − | 0.358651i | \(-0.116763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.09452e9 | −0.253288 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.60169e9 | − | 9.38011e9i | −0.164277 | − | 0.427837i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 6.19280e10i | − | 2.59509i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.20383e10 | 0.849673 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.05393e10 | − | 2.98879e10i | 0.729560 | − | 1.06162i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.30568e10i | − | 0.755526i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.17814e10 | 0.961953 | 0.480976 | − | 0.876733i | \(-0.340282\pi\) | ||||
0.480976 | + | 0.876733i | \(0.340282\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.97973e10 | + | 2.73492e10i | 1.11405 | + | 0.765589i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.01094e10i | 1.29886i | 0.760421 | + | 0.649430i | \(0.224993\pi\) | ||||
−0.760421 | + | 0.649430i | \(0.775007\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.78107e10 | −0.427979 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.06557e10 | + | 1.21539e10i | 1.12969 | + | 0.271048i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.74744e10i | − | 0.569279i | −0.958635 | − | 0.284639i | \(-0.908126\pi\) | ||
0.958635 | − | 0.284639i | \(-0.0918738\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.32488e10 | −1.21893 | −0.609464 | − | 0.792814i | \(-0.708615\pi\) | ||||
−0.609464 | + | 0.792814i | \(0.708615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.13403e10 | + | 3.10534e10i | −0.382917 | + | 0.557204i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.06253e10i | 0.177689i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.75441e10 | 0.273710 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.14684e10 | + | 3.53697e10i | 0.749815 | + | 0.515282i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.38479e10i | 0.460893i | 0.973085 | + | 0.230446i | \(0.0740186\pi\) | ||||
−0.973085 | + | 0.230446i | \(0.925981\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.22386e11 | −1.55901 | −0.779503 | − | 0.626399i | \(-0.784528\pi\) | ||||
−0.779503 | + | 0.626399i | \(0.784528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.46978e11 | − | 5.64351e10i | 1.75305 | − | 0.673120i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1.51862e11i | − | 1.69742i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.58971e11 | −1.66656 | −0.833279 | − | 0.552853i | \(-0.813539\pi\) | ||||
−0.833279 | + | 0.552853i | \(0.813539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.80155e9 | + | 8.44215e9i | −0.0570898 | + | 0.0830745i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.25930e10i | − | 0.301297i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.20831e10 | 0.800280 | 0.400140 | − | 0.916454i | \(-0.368962\pi\) | ||||
0.400140 | + | 0.916454i | \(0.368962\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.54003e10 | − | 3.11996e10i | −0.371226 | − | 0.255111i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.12416e11i | 1.63533i | 0.575697 | + | 0.817663i | \(0.304731\pi\) | ||||
−0.575697 | + | 0.817663i | \(0.695269\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.08904e11 | −0.789968 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.62309e10 | − | 4.22713e10i | −0.111010 | − | 0.289111i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.04132e11i | 1.96260i | 0.192482 | + | 0.981300i | \(0.438346\pi\) | ||||
−0.192482 | + | 0.981300i | \(0.561654\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.93119e10 | −0.483224 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.01908e10 | − | 5.84837e10i | 0.231345 | − | 0.336642i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 7.07114e9i | − | 0.0384791i | −0.999815 | − | 0.0192395i | \(-0.993875\pi\) | ||
0.999815 | − | 0.0192395i | \(-0.00612451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.27309e11 | −0.655337 | −0.327669 | − | 0.944793i | \(-0.606263\pi\) | ||||
−0.327669 | + | 0.944793i | \(0.606263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.06288e11 | − | 7.30425e10i | −0.517880 | − | 0.355894i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.82111e11i | − | 0.840386i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.66488e11 | −0.728075 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.77563e10 | + | 3.24078e11i | −0.322424 | + | 1.34382i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.06460e11i | 0.812209i | 0.913827 | + | 0.406105i | \(0.133113\pi\) | ||||
−0.913827 | + | 0.406105i | \(0.866887\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.11606e11 | 1.16364 | 0.581821 | − | 0.813317i | \(-0.302340\pi\) | ||||
0.581821 | + | 0.813317i | \(0.302340\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.50212e10 | + | 1.23719e11i | −0.301546 | + | 0.438796i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.51694e11i | − | 0.511255i | −0.966775 | − | 0.255628i | \(-0.917718\pi\) | ||
0.966775 | − | 0.255628i | \(-0.0822821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.11692e11 | 0.357895 | 0.178947 | − | 0.983859i | \(-0.442731\pi\) | ||||
0.178947 | + | 0.983859i | \(0.442731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.04559e11 | − | 7.18543e10i | −0.318700 | − | 0.219014i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.12241e11i | 0.325591i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.41807e11 | −1.49650 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.73551e10 | − | 2.97021e10i | 0.203534 | − | 0.0781512i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.78826e10i | 0.120073i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.53066e11 | −0.365987 | −0.182994 | − | 0.983114i | \(-0.558579\pi\) | ||||
−0.182994 | + | 0.983114i | \(0.558579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.86354e10 | − | 1.14427e11i | 0.179358 | − | 0.260993i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 7.21444e11i | − | 1.57040i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.71560e11 | 2.01916 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.37763e11 | + | 3.00836e11i | 0.868998 | + | 0.597186i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.53693e11i | 0.860598i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.05759e11 | 1.09844 | 0.549219 | − | 0.835678i | \(-0.314925\pi\) | ||||
0.549219 | + | 0.835678i | \(0.314925\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.22772e10 | − | 1.88236e11i | −0.125340 | − | 0.326430i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.70588e11i | − | 1.11257i | −0.830992 | − | 0.556284i | \(-0.812227\pi\) | ||
0.830992 | − | 0.556284i | \(-0.187773\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.53356e11 | 0.561094 | 0.280547 | − | 0.959840i | \(-0.409484\pi\) | ||||
0.280547 | + | 0.959840i | \(0.409484\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.99605e11 | − | 2.90456e11i | 0.303467 | − | 0.441591i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.12390e12i | − | 1.63662i | −0.574779 | − | 0.818309i | \(-0.694912\pi\) | ||
0.574779 | − | 0.818309i | \(-0.305088\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.62936e11 | 0.785452 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.93714e11 | − | 2.70565e11i | −0.526549 | − | 0.361851i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.64603e11i | 0.339317i | 0.985503 | + | 0.169658i | \(0.0542665\pi\) | ||||
−0.985503 | + | 0.169658i | \(0.945734\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.86768e11 | 1.09075 | 0.545375 | − | 0.838192i | \(-0.316387\pi\) | ||||
0.545375 | + | 0.838192i | \(0.316387\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.40014e11 | + | 1.10789e11i | −0.991414 | + | 0.130757i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 9.33019e11i | − | 1.05696i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.30483e11 | 0.141929 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.00795e11 | + | 4.37704e11i | −0.314249 | + | 0.457281i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.59494e11i | 0.862729i | 0.902178 | + | 0.431364i | \(0.141968\pi\) | ||||
−0.902178 | + | 0.431364i | \(0.858032\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.76237e10 | −0.0845316 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.93856e12 | − | 1.33220e12i | −1.79796 | − | 1.23558i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.17900e12i | 1.94353i | 0.235954 | + | 0.971764i | \(0.424179\pi\) | ||||
−0.235954 | + | 0.971764i | \(0.575821\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.16509e12 | 0.999677 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.66389e11 | + | 1.02286e11i | −0.219945 | + | 0.0844524i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.37942e12i | 1.09627i | 0.836391 | + | 0.548134i | \(0.184661\pi\) | ||||
−0.836391 | + | 0.548134i | \(0.815339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.53039e11 | 0.117104 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.28574e10 | − | 4.78126e10i | 0.0242146 | − | 0.0352360i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.18129e12i | 0.838680i | 0.907829 | + | 0.419340i | \(0.137738\pi\) | ||||
−0.907829 | + | 0.419340i | \(0.862262\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.42251e12 | 0.973213 | 0.486606 | − | 0.873621i | \(-0.338235\pi\) | ||||
0.486606 | + | 0.873621i | \(0.338235\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.91511e11 | − | 5.43937e11i | −0.521968 | − | 0.358703i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.13224e11i | 0.135573i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.29960e11 | 0.324971 | 0.162485 | − | 0.986711i | \(-0.448049\pi\) | ||||
0.162485 | + | 0.986711i | \(0.448049\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.85385e11 | + | 2.30587e12i | 0.523734 | + | 1.36400i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.28441e12i | − | 1.30389i | −0.758265 | − | 0.651946i | \(-0.773953\pi\) | ||
0.758265 | − | 0.651946i | \(-0.226047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.31274e12 | −1.27408 | −0.637038 | − | 0.770833i | \(-0.719840\pi\) | ||||
−0.637038 | + | 0.770833i | \(0.719840\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.83146e11 | + | 5.57537e11i | −0.203770 | + | 0.296517i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 3.46630e12i | − | 1.78015i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.09295e12 | −2.52627 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.77060e12 | − | 1.21678e12i | −0.848509 | − | 0.583106i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.05989e12i | 0.490822i | 0.969419 | + | 0.245411i | \(0.0789229\pi\) | ||||
−0.969419 | + | 0.245411i | \(0.921077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.06019e12 | −0.474542 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.71257e11 | + | 2.09042e11i | 0.377020 | + | 0.0904588i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.38781e11i | 0.0999179i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.61555e12 | 1.86806 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.31115e12 | + | 3.36308e12i | −0.904931 | + | 1.31681i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.92679e12i | 0.730020i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.89209e11 | −0.252731 | −0.126366 | − | 0.991984i | \(-0.540331\pi\) | ||||
−0.126366 | + | 0.991984i | \(0.540331\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.67598e12 | − | 1.15176e12i | −0.594945 | − | 0.408854i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.95674e12i | 0.672559i | 0.941762 | + | 0.336280i | \(0.109169\pi\) | ||||
−0.941762 | + | 0.336280i | \(0.890831\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.48821e11 | −0.0828256 | −0.0414128 | − | 0.999142i | \(-0.513186\pi\) | ||||
−0.0414128 | + | 0.999142i | \(0.513186\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.64832e12 | − | 1.78482e12i | 1.49880 | − | 0.575495i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.63675e12i | − | 1.44850i | −0.689539 | − | 0.724249i | \(-0.742187\pi\) | ||
0.689539 | − | 0.724249i | \(-0.257813\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.01751e11 | 0.0913473 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.97571e12 | + | 2.87497e12i | −0.579694 | + | 0.843544i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.04456e12i | 0.581549i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.81050e11 | 0.160249 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.46400e11 | − | 6.50378e11i | −0.253125 | − | 0.173951i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.60147e12i | 0.934331i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.41443e12 | 0.355994 | 0.177997 | − | 0.984031i | \(-0.443038\pi\) | ||||
0.177997 | + | 0.984031i | \(0.443038\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.06175e12 | + | 2.76518e12i | 0.259298 | + | 0.675308i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.89545e12i | 0.449249i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.67755e11 | 0.199640 | 0.0998201 | − | 0.995006i | \(-0.468173\pi\) | ||||
0.0998201 | + | 0.995006i | \(0.468173\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.81886e12 | − | 2.64672e12i | 0.406257 | − | 0.591167i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.61196e12i | − | 0.566493i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.91785e11 | −0.124650 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.02028e12 | − | 7.01146e11i | −0.208748 | − | 0.143454i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 5.20712e12i | − | 1.03502i | −0.855676 | − | 0.517512i | \(-0.826858\pi\) | ||
0.855676 | − | 0.517512i | \(-0.173142\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.11953e12 | 0.216226 | 0.108113 | − | 0.994139i | \(-0.465519\pi\) | ||||
0.108113 | + | 0.994139i | \(0.465519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.69653e11 | − | 2.37424e12i | 0.106924 | − | 0.445644i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.73952e12i | 0.682248i | 0.940018 | + | 0.341124i | \(0.110808\pi\) | ||||
−0.940018 | + | 0.341124i | \(0.889192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.07432e12 | −0.367904 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.52299e12 | − | 1.24023e13i | 1.46977 | − | 2.13875i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 3.54489e12i | − | 0.594471i | −0.954804 | − | 0.297235i | \(-0.903935\pi\) | ||
0.954804 | − | 0.297235i | \(-0.0960646\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.54305e12 | −0.904092 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.41360e12 | + | 3.03308e12i | 0.700260 | + | 0.481228i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 7.93577e12i | − | 1.22497i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.01161e13 | 1.51944 | 0.759722 | − | 0.650248i | \(-0.225335\pi\) | ||||
0.759722 | + | 0.650248i | \(0.225335\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.22679e12 | − | 3.15885e12i | 1.20254 | − | 0.461739i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.79093e11i | 0.139301i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.81055e12 | 0.527769 | 0.263885 | − | 0.964554i | \(-0.414996\pi\) | ||||
0.263885 | + | 0.964554i | \(0.414996\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.17325e12 | − | 4.61757e12i | 0.427906 | − | 0.622669i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.22293e11i | − | 0.107974i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.11052e13 | −1.42014 | −0.710069 | − | 0.704132i | \(-0.751336\pi\) | ||||
−0.710069 | + | 0.704132i | \(0.751336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.36482e12 | + | 4.37399e12i | 0.792796 | + | 0.544819i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4.29169e12i | − | 0.520756i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) | ||
0.965507 | − | 0.260378i | \(-0.0838472\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.26537e12 | −0.622480 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.20617e12 | + | 1.09544e13i | 0.484542 | + | 1.26192i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.50554e13i | 1.69023i | 0.534588 | + | 0.845113i | \(0.320467\pi\) | ||||
−0.534588 | + | 0.845113i | \(0.679533\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.74148e12 | −0.409411 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.89642e12 | + | 1.00354e13i | −0.735633 | + | 1.07046i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.13723e12i | 0.742240i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.11669e13 | −1.13235 | −0.566174 | − | 0.824286i | \(-0.691577\pi\) | ||||
−0.566174 | + | 0.824286i | \(0.691577\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.56693e12 | − | 2.45124e12i | −0.352720 | − | 0.242394i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.15685e13i | − | 1.11572i | −0.829935 | − | 0.557861i | \(-0.811622\pi\) | ||
0.829935 | − | 0.557861i | \(-0.188378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.11777e12 | −0.669605 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.47206e12 | + | 9.40565e12i | 0.777524 | + | 0.863205i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.13224e12i | − | 0.280468i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.07411e13 | −0.938498 | −0.469249 | − | 0.883066i | \(-0.655475\pi\) | ||||
−0.469249 | + | 0.883066i | \(0.655475\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.78123e12 | − | 5.50227e12i | 0.322421 | − | 0.469172i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.78275e12i | − | 0.564489i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.93468e12 | 0.644598 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.26668e13 | − | 8.70477e12i | −1.00458 | − | 0.690362i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.81717e12i | 0.682746i | 0.939928 | + | 0.341373i | \(0.110892\pi\) | ||||
−0.939928 | + | 0.341373i | \(0.889108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.69741e12 | −0.430792 | −0.215396 | − | 0.976527i | \(-0.569104\pi\) | ||||
−0.215396 | + | 0.976527i | \(0.569104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.54761e12 | + | 3.28203e12i | −0.631165 | + | 0.242349i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.10451e12i | 0.656617i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.23269e13 | −0.868392 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.46233e12 | + | 2.12792e12i | −0.100637 | + | 0.146443i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.80323e13i | 1.21245i | 0.795293 | + | 0.606226i | \(0.207317\pi\) | ||||
−0.795293 | + | 0.606226i | \(0.792683\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.06339e13 | 1.35563 | 0.677816 | − | 0.735232i | \(-0.262927\pi\) | ||||
0.677816 | + | 0.735232i | \(0.262927\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.51354e12 | + | 2.41455e12i | 0.225579 | + | 0.155021i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.07606e12i | 0.0675195i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.95313e13 | −1.19787 | −0.598935 | − | 0.800798i | \(-0.704409\pi\) | ||||
−0.598935 | + | 0.800798i | \(0.704409\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.43969e12 | + | 1.41669e13i | 0.326123 | + | 0.849343i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2.97469e13i | − | 1.74351i | −0.489946 | − | 0.871753i | \(-0.662984\pi\) | ||
0.489946 | − | 0.871753i | \(-0.337016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.66747e11 | −0.0496698 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.65839e12 | + | 6.77868e12i | −0.261035 | + | 0.379846i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.37505e13i | 0.753509i | 0.926313 | + | 0.376754i | \(0.122960\pi\) | ||||
−0.926313 | + | 0.376754i | \(0.877040\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.31887e12 | −0.499437 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.45102e13 | − | 1.68437e13i | −1.28486 | − | 0.882971i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.43485e13i | 0.735783i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.10224e11 | 0.0205798 | 0.0102899 | − | 0.999947i | \(-0.496725\pi\) | ||||
0.0102899 | + | 0.999947i | \(0.496725\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.72021e13 | + | 8.92594e12i | 1.82601 | + | 0.438118i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.10914e11i | 0.0101298i | 0.999987 | + | 0.00506490i | \(0.00161221\pi\) | ||||
−0.999987 | + | 0.00506490i | \(0.998388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.96738e13 | 0.924660 | 0.462330 | − | 0.886708i | \(-0.347013\pi\) | ||||
0.462330 | + | 0.886708i | \(0.347013\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.09003e13 | − | 3.04132e13i | 0.961365 | − | 1.39893i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.21902e13i | − | 0.548815i | −0.961614 | − | 0.274407i | \(-0.911518\pi\) | ||
0.961614 | − | 0.274407i | \(-0.0884817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.21264e13 | −0.534402 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.18370e13 | − | 2.18788e13i | −1.37350 | − | 0.943885i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.24085e13i | − | 0.524101i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.61849e12 | 0.108289 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.32374e12 | + | 8.92250e11i | −0.0941014 | + | 0.0361322i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.00886e12i | 0.198637i | 0.995056 | + | 0.0993187i | \(0.0316663\pi\) | ||||
−0.995056 | + | 0.0993187i | \(0.968334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.53558e12 | −0.331518 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.48569e12 | − | 6.52737e12i | 0.170645 | − | 0.248315i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.20975e13i | 1.19608i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.17000e13 | 1.52227 | 0.761134 | − | 0.648595i | \(-0.224643\pi\) | ||||
0.761134 | + | 0.648595i | \(0.224643\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.84414e13 | + | 1.26732e13i | 0.659553 | + | 0.453253i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.10340e12i | − | 0.0737081i | −0.999321 | − | 0.0368540i | \(-0.988266\pi\) | ||
0.999321 | − | 0.0368540i | \(-0.0117337\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.28846e13 | 0.442421 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.79835e12 | − | 1.24966e13i | −0.161460 | − | 0.420501i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.32708e13i | − | 0.437639i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.74482e13 | −0.887179 | −0.443589 | − | 0.896230i | \(-0.646295\pi\) | ||||
−0.443589 | + | 0.896230i | \(0.646295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.92342e13 | + | 4.25403e13i | −0.926197 | + | 1.34776i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.26985e13i | 0.704949i | 0.935822 | + | 0.352474i | \(0.114660\pi\) | ||||
−0.935822 | + | 0.352474i | \(0.885340\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.09659e13 | 1.85622 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.18101e13 | − | 1.49882e13i | −0.651055 | − | 0.447413i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 4.21460e13i | − | 1.23358i | −0.787127 | − | 0.616791i | \(-0.788433\pi\) | ||
0.787127 | − | 0.616791i | \(-0.211567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.07703e13 | 1.45715 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.56713e12 | − | 1.06994e13i | 0.0722539 | − | 0.301144i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.03822e13i | 0.838653i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.68227e12 | 0.262135 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.18569e13 | + | 6.09083e13i | −1.11155 | + | 1.61748i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 6.54420e13i | − | 1.70478i | −0.522907 | − | 0.852390i | \(-0.675152\pi\) | ||
0.522907 | − | 0.852390i | \(-0.324848\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.14531e13 | 1.57049 | 0.785245 | − | 0.619185i | \(-0.212537\pi\) | ||||
0.785245 | + | 0.619185i | \(0.212537\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.58837e13 | − | 1.09155e13i | −0.398250 | − | 0.273682i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.11529e14i | − | 2.74369i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.94574e13 | 0.952466 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.60979e13 | − | 6.18114e12i | 0.381327 | − | 0.146418i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.53946e13i | 0.590343i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.21173e13 | 1.18909 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.73183e11 | − | 1.41613e12i | 0.0217933 | − | 0.0317126i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.60475e13i | − | 0.352748i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.50207e13 | 0.324118 | 0.162059 | − | 0.986781i | \(-0.448187\pi\) | ||||
0.162059 | + | 0.986781i | \(0.448187\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.54960e13 | − | 1.75211e13i | −0.540098 | − | 0.371162i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.71563e13i | 0.356814i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.15097e13 | −1.46025 | −0.730127 | − | 0.683312i | \(-0.760539\pi\) | ||||
−0.730127 | + | 0.683312i | \(0.760539\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.12336e13 | − | 2.92563e13i | −0.225245 | − | 0.586621i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.70565e12i | − | 0.0729636i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.56616e13 | −0.882928 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.50635e13 | − | 3.64713e13i | 0.475967 | − | 0.692606i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.34107e13i | 1.36925i | 0.728895 | + | 0.684626i | \(0.240034\pi\) | ||||
−0.728895 | + | 0.684626i | \(0.759966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.38141e13 | −0.619497 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.33425e13 | − | 2.29134e13i | −0.600045 | − | 0.412358i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.77347e13i | 0.843902i | 0.906619 | + | 0.421951i | \(0.138655\pi\) | ||||
−0.906619 | + | 0.421951i | \(0.861345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.79797e13 | −0.833327 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.01742e13 | + | 5.42013e13i | −1.02682 | + | 0.924900i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.90951e13i | − | 0.320156i | −0.987104 | − | 0.160078i | \(-0.948825\pi\) | ||
0.987104 | − | 0.160078i | \(-0.0511745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.09448e13 | 0.345060 | 0.172530 | − | 0.985004i | \(-0.444806\pi\) | ||||
0.172530 | + | 0.985004i | \(0.444806\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.84145e13 | + | 4.13475e13i | −0.460009 | + | 0.669385i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.79175e12i | 0.0762351i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.56688e13 | 0.557711 | 0.278855 | − | 0.960333i | \(-0.410045\pi\) | ||||
0.278855 | + | 0.960333i | \(0.410045\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.24051e13 | + | 4.28856e13i | 0.959019 | + | 0.659050i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.07634e13i | 0.766778i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.63221e12 | 0.0390821 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.40542e13 | + | 1.30758e13i | −0.497040 | + | 0.190849i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.29418e14i | 1.85697i | 0.371375 | + | 0.928483i | \(0.378886\pi\) | ||||
−0.371375 | + | 0.928483i | \(0.621114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.20761e13 | −0.452486 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.08773e13 | − | 3.03797e13i | 0.289559 | − | 0.421352i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.96596e13i | 0.540848i | 0.962741 | + | 0.270424i | \(0.0871639\pi\) | ||||
−0.962741 | + | 0.270424i | \(0.912836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.24828e14 | −3.01485 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.23684e13 | + | 1.53718e13i | 0.294960 | + | 0.202700i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.57555e13i | 0.593347i | 0.954979 | + | 0.296674i | \(0.0958774\pi\) | ||||
−0.954979 | + | 0.296674i | \(0.904123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.06033e14 | 1.35229 | 0.676143 | − | 0.736770i | \(-0.263650\pi\) | ||||
0.676143 | + | 0.736770i | \(0.263650\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.10508e13 | − | 2.87804e13i | −0.138614 | − | 0.361003i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 8.00096e13i | − | 0.987109i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.55067e13 | 1.15902 | 0.579509 | − | 0.814966i | \(-0.303244\pi\) | ||||
0.579509 | + | 0.814966i | \(0.303244\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.54475e13 | + | 2.24784e13i | −0.184404 | + | 0.268336i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2.63849e13i | − | 0.309848i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.18411e13 | −0.598924 | −0.299462 | − | 0.954108i | \(-0.596807\pi\) | ||||
−0.299462 | + | 0.954108i | \(0.596807\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.08507e14 | − | 7.45675e13i | −1.23334 | − | 0.847567i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.05443e13i | 0.900760i | 0.892837 | + | 0.450380i | \(0.148711\pi\) | ||||
−0.892837 | + | 0.450380i | \(0.851289\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.14946e13 | 0.566642 | 0.283321 | − | 0.959025i | \(-0.408564\pi\) | ||||
0.283321 | + | 0.959025i | \(0.408564\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.95797e13 | + | 4.69777e12i | 0.212005 | + | 0.0508667i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 5.54515e12i | − | 0.0590844i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.17054e14 | −1.22740 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.58996e12 | + | 9.58941e12i | −0.0680057 | + | 0.0989587i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.33745e14i | − | 1.35839i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.02922e13 | 0.102887 | 0.0514435 | − | 0.998676i | \(-0.483618\pi\) | ||||
0.0514435 | + | 0.998676i | \(0.483618\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.06543e13 | − | 2.10660e13i | −0.301629 | − | 0.207283i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 1.15381e14i | − | 1.11755i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.37307e13 | −0.416955 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.14965e13 | − | 1.20937e13i | 0.295636 | − | 0.113516i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.62451e13i | − | 0.427342i | −0.976906 | − | 0.213671i | \(-0.931458\pi\) | ||
0.976906 | − | 0.213671i | \(-0.0685420\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.73102e13 | −0.248468 | −0.124234 | − | 0.992253i | \(-0.539647\pi\) | ||||
−0.124234 | + | 0.992253i | \(0.539647\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.92905e13 | − | 1.44483e14i | 0.889424 | − | 1.29425i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.34984e13i | − | 0.119059i | −0.998227 | − | 0.0595293i | \(-0.981040\pi\) | ||
0.998227 | − | 0.0595293i | \(-0.0189600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.82349e13 | −0.158372 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.94573e14 | + | 1.33713e14i | 1.66410 | + | 1.14359i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.41840e13i | 0.709029i | 0.935051 | + | 0.354514i | \(0.115354\pi\) | ||||
−0.935051 | + | 0.354514i | \(0.884646\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.81921e14 | 1.50895 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.62671e13 | + | 1.20496e14i | 0.377960 | + | 0.984345i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.65464e14i | − | 1.33130i | −0.746264 | − | 0.665650i | \(-0.768154\pi\) | ||
0.746264 | − | 0.665650i | \(-0.231846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.01681e14 | 1.59830 | 0.799148 | − | 0.601135i | \(-0.205284\pi\) | ||||
0.799148 | + | 0.601135i | \(0.205284\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.24405e13 | + | 9.08606e13i | −0.487415 | + | 0.709264i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.46612e13i | 0.497205i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.78122e12 | 0.0513664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.21315e14 | + | 8.33691e13i | 0.905281 | + | 0.622120i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.31400e13i | 0.243635i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.04368e12 | 0.0437750 | 0.0218875 | − | 0.999760i | \(-0.493032\pi\) | ||||
0.0218875 | + | 0.999760i | \(0.493032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.14316e13 | − | 4.76452e13i | 0.0815806 | − | 0.340017i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1.21474e14i | − | 0.854164i | −0.904213 | − | 0.427082i | \(-0.859542\pi\) | ||
0.904213 | − | 0.427082i | \(-0.140458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.05349e14 | −1.42280 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.22913e13 | − | 1.34298e14i | 0.630123 | − | 0.916926i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1.51629e14i | − | 1.02019i | −0.860119 | − | 0.510094i | \(-0.829611\pi\) | ||
0.860119 | − | 0.510094i | \(-0.170389\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.97450e13 | −0.661360 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.07663e13 | + | 4.86315e13i | 0.462427 | + | 0.317785i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 7.17296e12i | − | 0.0461958i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.62249e13 | −0.420369 | −0.210185 | − | 0.977662i | \(-0.567407\pi\) | ||||
−0.210185 | + | 0.977662i | \(0.567407\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.99493e13 | − | 3.06982e13i | 0.500205 | − | 0.192064i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.29623e14i | 1.41609i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.97909e14 | −2.41891 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.54679e14 | − | 2.25082e14i | 0.926928 | − | 1.34882i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.78990e13i | − | 0.342043i | −0.985267 | − | 0.171022i | \(-0.945293\pi\) | ||
0.985267 | − | 0.171022i | \(-0.0547068\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.84654e13 | −0.224024 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.12739e14 | + | 7.74754e13i | 0.647332 | + | 0.444855i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.90039e14i | 2.20806i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.70077e14 | 1.50750 | 0.753750 | − | 0.657162i | \(-0.228243\pi\) | ||||
0.753750 | + | 0.657162i | \(0.228243\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.16115e13 | − | 1.08372e14i | −0.229016 | − | 0.596441i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.86983e13i | − | 0.318550i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.85748e13 | 0.206430 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.64166e13 | + | 5.29918e13i | −0.192178 | + | 0.279649i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.48102e14i | − | 0.770755i | −0.922759 | − | 0.385377i | \(-0.874071\pi\) | ||
0.922759 | − | 0.385377i | \(-0.125929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.94375e14 | −0.997616 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.77592e14 | + | 1.22044e14i | 0.898944 | + | 0.617765i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 1.65014e13i | − | 0.0823819i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.21602e13 | −0.256842 | −0.128421 | − | 0.991720i | \(-0.540991\pi\) | ||||
−0.128421 | + | 0.991720i | \(0.540991\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.83476e14 | − | 9.34214e13i | −0.891133 | − | 0.453742i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 5.29837e14i | − | 2.53837i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.21782e14 | 1.52069 | 0.760346 | − | 0.649518i | \(-0.225029\pi\) | ||||
0.760346 | + | 0.649518i | \(0.225029\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.28409e14 | − | 1.86855e14i | 0.598630 | − | 0.871099i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.26009e13i | 0.149931i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.66542e14 | −0.755617 | −0.377809 | − | 0.925884i | \(-0.623322\pi\) | ||||
−0.377809 | + | 0.925884i | \(0.623322\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.61318e13 | + | 1.79581e13i | 0.116971 | + | 0.0803839i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.13631e14i | 0.501825i | 0.968010 | + | 0.250912i | \(0.0807306\pi\) | ||||
−0.968010 | + | 0.250912i | \(0.919269\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.22884e14 | 0.535443 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.20480e14 | + | 4.62608e13i | −0.517979 | + | 0.198889i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.33429e14i | 1.41447i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.64956e14 | 0.690508 | 0.345254 | − | 0.938509i | \(-0.387793\pi\) | ||||
0.345254 | + | 0.938509i | \(0.387793\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.18290e14 | + | 1.72130e14i | −0.488622 | + | 0.711020i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.44320e14i | 1.81118i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.67990e14 | −1.07805 | −0.539026 | − | 0.842289i | \(-0.681207\pi\) | ||||
−0.539026 | + | 0.842289i | \(0.681207\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.75483e13 | − | 1.20594e13i | −0.0696669 | − | 0.0478760i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.29795e14i | 0.508550i | 0.967132 | + | 0.254275i | \(0.0818368\pi\) | ||||
−0.967132 | + | 0.254275i | \(0.918163\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.09760e14 | −0.424446 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.04886e14 | − | 5.33599e14i | −0.781998 | − | 2.03661i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.96913e13i | 0.187199i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.19185e14 | −0.815041 | −0.407521 | − | 0.913196i | \(-0.633607\pi\) | ||||
−0.407521 | + | 0.913196i | \(0.633607\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.99890e14 | + | 4.36386e14i | −1.10075 | + | 1.60176i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 4.05042e14i | − | 1.46758i | −0.679374 | − | 0.733792i | \(-0.737749\pi\) | ||
0.679374 | − | 0.733792i | \(-0.262251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.42837e14 | −0.510894 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.33331e14 | + | 1.60348e14i | 0.823886 | + | 0.566185i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.14440e14i | 0.398925i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.56775e13 | −0.122783 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.74268e13 | − | 1.61778e13i | −0.229099 | − | 0.0549681i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.77141e14i | 1.93613i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.98729e14 | −1.65193 | −0.825963 | − | 0.563724i | \(-0.809368\pi\) | ||||
−0.825963 | + | 0.563724i | \(0.809368\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.89845e14 | + | 2.76254e14i | −0.620890 | + | 0.903491i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.06958e14i | − | 0.991280i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.03088e13 | 0.287981 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.06490e13 | + | 2.10624e13i | 0.0965119 | + | 0.0663242i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.48672e14i | − | 0.462314i | −0.972917 | − | 0.231157i | \(-0.925749\pi\) | ||
0.972917 | − | 0.231157i | \(-0.0742510\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.13427e14 | 1.26959 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.31607e13 | − | 5.05331e12i | 0.0399131 | − | 0.0153255i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.36492e14i | − | 0.408817i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.18328e14 | −0.350033 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.62578e14 | + | 2.36576e14i | −0.475001 | + | 0.691200i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.32296e14i | − | 0.381772i | −0.981612 | − | 0.190886i | \(-0.938864\pi\) | ||
0.981612 | − | 0.190886i | \(-0.0611361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.75449e14 | 1.07016 | 0.535078 | − | 0.844803i | \(-0.320282\pi\) | ||||
0.535078 | + | 0.844803i | \(0.320282\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.84884e14 | + | 1.95776e14i | 0.802076 | + | 0.551197i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 3.34305e14i | − | 0.929726i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.52383e14 | −0.418625 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.36547e13 | − | 2.17867e14i | −0.227023 | − | 0.591252i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 4.64480e12i | − | 0.0124524i | −0.999981 | − | 0.00622618i | \(-0.998018\pi\) | ||
0.999981 | − | 0.00622618i | \(-0.00198187\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.38146e14 | −1.69013 | −0.845067 | − | 0.534661i | \(-0.820439\pi\) | ||||
−0.845067 | + | 0.534661i | \(0.820439\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.93454e13 | + | 4.27021e13i | −0.0767840 | + | 0.111733i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.33624e14i | 1.37946i | 0.724068 | + | 0.689728i | \(0.242270\pi\) | ||||
−0.724068 | + | 0.689728i | \(0.757730\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.63626e13 | −0.220573 | −0.110287 | − | 0.993900i | \(-0.535177\pi\) | ||||
−0.110287 | + | 0.993900i | \(0.535177\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.06135e14 | + | 7.29370e13i | 0.267825 | + | 0.184053i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.85220e14i | − | 1.70846i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.71170e14 | 1.89984 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.40035e14 | + | 5.83647e14i | −0.340886 | + | 1.42077i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.28770e14i | 1.03137i | 0.856778 | + | 0.515685i | \(0.172462\pi\) | ||||
−0.856778 | + | 0.515685i | \(0.827538\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.97355e14 | 0.944492 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.14397e14 | − | 4.57496e14i | 0.738483 | − | 1.07461i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.95373e14i | 0.917747i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.11874e14 | 1.17421 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.63171e14 | − | 3.18297e14i | −1.05003 | − | 0.721595i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 7.03905e13i | − | 0.157713i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.99493e10 | −0.000199183 | −9.95916e−5 | − | 1.00000i | \(-0.500032\pi\) | ||||
−9.95916e−5 | 1.00000i | \(0.500032\pi\) | ||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.53465e14 | + | 5.89260e13i | −0.335875 | + | 0.128966i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.45265e14i | − | 0.314238i | −0.987580 | − | 0.157119i | \(-0.949779\pi\) | ||
0.987580 | − | 0.157119i | \(-0.0502205\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.53555e14 | 0.755947 | 0.377974 | − | 0.925816i | \(-0.376621\pi\) | ||||
0.377974 | + | 0.925816i | \(0.376621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.77058e14 | − | 6.94192e14i | 1.00822 | − | 1.46711i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 5.16372e14i | − | 1.07872i | −0.842075 | − | 0.539360i | \(-0.818666\pi\) | ||
0.842075 | − | 0.539360i | \(-0.181334\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.10414e15 | 2.28005 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.01996e15 | − | 7.00930e14i | −2.08204 | − | 1.43080i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.22757e14i | 0.247713i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.88397e13 | 0.177221 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.87135e14 | − | 4.87367e14i | −0.369048 | − | 0.961136i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 5.35530e14i | − | 1.04410i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.23487e13 | 0.0623532 | 0.0311766 | − | 0.999514i | \(-0.490075\pi\) | ||||
0.0311766 | + | 0.999514i | \(0.490075\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.45870e14 | + | 2.12264e14i | −0.277986 | + | 0.404512i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.45484e14i | − | 0.650950i | −0.945551 | − | 0.325475i | \(-0.894476\pi\) | ||
0.945551 | − | 0.325475i | \(-0.105524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.94069e14 | 0.361537 | 0.180769 | − | 0.983526i | \(-0.442141\pi\) | ||||
0.180769 | + | 0.983526i | \(0.442141\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.12324e14 | − | 1.45911e14i | −0.391095 | − | 0.268765i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.06383e14i | − | 0.375885i | −0.982180 | − | 0.187943i | \(-0.939818\pi\) | ||
0.982180 | − | 0.187943i | \(-0.0601819\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.38171e14 | 1.32938 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.45716e14 | + | 1.61773e14i | 0.259489 | + | 0.288084i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.18903e14i | − | 0.209380i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.56716e13 | −0.0447031 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.28628e13 | + | 4.78204e13i | −0.0565903 | + | 0.0823476i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.02140e14i | 0.344234i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.12394e14 | 0.189286 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.24353e14 | + | 6.35227e14i | 1.53957 | + | 1.05801i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.62190e14i | 0.761339i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.53646e14 | 0.576145 | 0.288073 | − | 0.957609i | \(-0.406986\pi\) | ||||
0.288073 | + | 0.957609i | \(0.406986\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.25705e14 | + | 3.55444e14i | −1.49160 | + | 0.572732i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.57044e14i | 0.728394i | 0.931322 | + | 0.364197i | \(0.118656\pi\) | ||||
−0.931322 | + | 0.364197i | \(0.881344\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.36473e14 | 0.215126 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.65179e14 | + | 3.85876e14i | −0.413460 | + | 0.601648i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.16387e15i | 1.79497i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.85254e14 | −0.740273 | −0.370136 | − | 0.928977i | \(-0.620689\pi\) | ||||
−0.370136 | + | 0.928977i | \(0.620689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.38027e14 | − | 9.48541e13i | −0.208289 | − | 0.143139i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.72237e13i | 0.145132i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.71288e14 | −0.252941 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.77134e14 | − | 4.61322e14i | −0.258764 | − | 0.673916i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.16207e14i | − | 1.17957i | −0.807562 | − | 0.589783i | \(-0.799213\pi\) | ||
0.807562 | − | 0.589783i | \(-0.200787\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.97071e14 | −0.281757 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.69301e14 | + | 3.91874e14i | −0.380916 | + | 0.554292i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.04432e14i | 0.845842i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.90133e14 | −0.955510 | −0.477755 | − | 0.878493i | \(-0.658549\pi\) | ||||
−0.477755 | + | 0.878493i | \(0.658549\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.98311e13 | − | 3.42445e13i | −0.0682609 | − | 0.0469098i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.26481e14i | − | 0.171426i | −0.996320 | − | 0.0857129i | \(-0.972683\pi\) | ||
0.996320 | − | 0.0857129i | \(-0.0273168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.09422e14 | −0.280843 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.17656e15 | + | 2.82292e14i | 1.56118 | + | 0.374576i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3.05743e14i | − | 0.401427i | −0.979650 | − | 0.200713i | \(-0.935674\pi\) | ||
0.979650 | − | 0.200713i | \(-0.0643260\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.71950e14 | −0.483230 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.38144e14 | − | 9.28598e14i | 0.820382 | − | 1.19378i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.71039e14i | 0.980870i | 0.871478 | + | 0.490435i | \(0.163162\pi\) | ||||
−0.871478 | + | 0.490435i | \(0.836838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.49546e14 | 0.943586 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.04315e13 | + | 4.15292e13i | 0.0752841 | + | 0.0517362i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 6.38134e14i | − | 0.786718i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.30098e14 | 1.13478 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.91348e14 | + | 3.03855e14i | −0.955512 | + | 0.366889i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.13128e15i | − | 1.35186i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.27364e15 | −1.50631 | −0.753154 | − | 0.657845i | \(-0.771468\pi\) | ||||
−0.753154 | + | 0.657845i | \(0.771468\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.81387e14 | + | 4.09461e14i | −0.329371 | + | 0.479285i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.71364e14i | − | 0.546085i | −0.962002 | − | 0.273043i | \(-0.911970\pi\) | ||
0.962002 | − | 0.273043i | \(-0.0880300\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.46905e15 | −1.68451 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.16366e14 | + | 7.99683e13i | 0.132070 | + | 0.0907601i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.09733e15i | − | 1.23272i | −0.787465 | − | 0.616360i | \(-0.788607\pi\) | ||
0.787465 | − | 0.616360i | \(-0.211393\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.49077e13 | −0.0165767 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.00025e14 | − | 2.60501e14i | −0.110094 | − | 0.286724i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.52240e15i | 1.65867i | 0.558751 | + | 0.829336i | \(0.311281\pi\) | ||||
−0.558751 | + | 0.829336i | \(0.688719\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.50722e14 | −0.593952 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.95661e14 | + | 7.21264e14i | −0.529175 | + | 0.770031i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.78856e14i | − | 0.294712i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.79461e14 | −0.397008 | −0.198504 | − | 0.980100i | \(-0.563608\pi\) | ||||
−0.198504 | + | 0.980100i | \(0.563608\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.83267e14 | + | 1.94665e14i | 0.293393 | + | 0.201623i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 4.05493e14i | − | 0.415785i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.25337e13 | 0.0330262 | 0.0165131 | − | 0.999864i | \(-0.494743\pi\) | ||||
0.0165131 | + | 0.999864i | \(0.494743\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.67929e14 | + | 6.99905e14i | −0.168771 | + | 0.703415i |
(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 | 48.11.e.d.17.4 | 4 | ||
3.2 | odd | 2 | inner | 48.11.e.d.17.3 | 4 | ||
4.3 | odd | 2 | 6.11.b.a.5.3 | yes | 4 | ||
8.3 | odd | 2 | 192.11.e.g.65.4 | 4 | |||
8.5 | even | 2 | 192.11.e.h.65.1 | 4 | |||
12.11 | even | 2 | 6.11.b.a.5.1 | ✓ | 4 | ||
20.3 | even | 4 | 150.11.b.a.149.7 | 8 | |||
20.7 | even | 4 | 150.11.b.a.149.2 | 8 | |||
20.19 | odd | 2 | 150.11.d.a.101.2 | 4 | |||
24.5 | odd | 2 | 192.11.e.h.65.2 | 4 | |||
24.11 | even | 2 | 192.11.e.g.65.3 | 4 | |||
36.7 | odd | 6 | 162.11.d.d.53.4 | 8 | |||
36.11 | even | 6 | 162.11.d.d.53.1 | 8 | |||
36.23 | even | 6 | 162.11.d.d.107.4 | 8 | |||
36.31 | odd | 6 | 162.11.d.d.107.1 | 8 | |||
60.23 | odd | 4 | 150.11.b.a.149.1 | 8 | |||
60.47 | odd | 4 | 150.11.b.a.149.8 | 8 | |||
60.59 | even | 2 | 150.11.d.a.101.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.11.b.a.5.1 | ✓ | 4 | 12.11 | even | 2 | ||
6.11.b.a.5.3 | yes | 4 | 4.3 | odd | 2 | ||
48.11.e.d.17.3 | 4 | 3.2 | odd | 2 | inner | ||
48.11.e.d.17.4 | 4 | 1.1 | even | 1 | trivial | ||
150.11.b.a.149.1 | 8 | 60.23 | odd | 4 | |||
150.11.b.a.149.2 | 8 | 20.7 | even | 4 | |||
150.11.b.a.149.7 | 8 | 20.3 | even | 4 | |||
150.11.b.a.149.8 | 8 | 60.47 | odd | 4 | |||
150.11.d.a.101.2 | 4 | 20.19 | odd | 2 | |||
150.11.d.a.101.4 | 4 | 60.59 | even | 2 | |||
162.11.d.d.53.1 | 8 | 36.11 | even | 6 | |||
162.11.d.d.53.4 | 8 | 36.7 | odd | 6 | |||
162.11.d.d.107.1 | 8 | 36.31 | odd | 6 | |||
162.11.d.d.107.4 | 8 | 36.23 | even | 6 | |||
192.11.e.g.65.3 | 4 | 24.11 | even | 2 | |||
192.11.e.g.65.4 | 4 | 8.3 | odd | 2 | |||
192.11.e.h.65.1 | 4 | 8.5 | even | 2 | |||
192.11.e.h.65.2 | 4 | 24.5 | odd | 2 |