Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,22,Mod(47,48)]
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([1, 0, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.47");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.c (of order \(2\), degree \(1\), 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: | \(134.149125258\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.16 | ||
Character | \(\chi\) | \(=\) | 48.47 |
Dual form | 48.22.c.c.47.15 |
$q$-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 | ||||||||
\(3\) | 554.307 | + | 102274.i | 0.00541973 | + | 0.999985i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.49802e7i | 1.60191i | 0.598726 | + | 0.800954i | \(0.295674\pi\) | ||||
−0.598726 | + | 0.800954i | \(0.704326\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.47725e8i | − | 1.00049i | −0.865884 | − | 0.500245i | \(-0.833243\pi\) | ||
0.865884 | − | 0.500245i | \(-0.166757\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.04597e10 | + | 1.13383e8i | −0.999941 | + | 0.0108393i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00580e11 | 1.16920 | 0.584598 | − | 0.811323i | \(-0.301252\pi\) | ||||
0.584598 | + | 0.811323i | \(0.301252\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.55401e11 | 0.513828 | 0.256914 | − | 0.966434i | \(-0.417294\pi\) | ||||
0.256914 | + | 0.966434i | \(0.417294\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.57758e12 | + | 1.93898e10i | −1.60188 | + | 0.00868190i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.80713e12i | 0.818937i | 0.912324 | + | 0.409469i | \(0.134286\pi\) | ||||
−0.912324 | + | 0.409469i | \(0.865714\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.43464e13i | − | 1.65938i | −0.558226 | − | 0.829689i | \(-0.688518\pi\) | ||
0.558226 | − | 0.829689i | \(-0.311482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.64731e13 | − | 4.14469e11i | 1.00047 | − | 0.00542238i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.67379e14 | 1.34582 | 0.672908 | − | 0.739726i | \(-0.265045\pi\) | ||||
0.672908 | + | 0.739726i | \(0.265045\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.46779e14 | −1.56611 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.73941e13 | − | 1.06970e15i | −0.0162585 | − | 0.999868i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.19900e15i | 1.85339i | 0.375816 | + | 0.926694i | \(0.377362\pi\) | ||||
−0.375816 | + | 0.926694i | \(0.622638\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.81995e15i | 1.05620i | 0.849183 | + | 0.528098i | \(0.177095\pi\) | ||||
−0.849183 | + | 0.528098i | \(0.822905\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.57521e13 | + | 1.02867e16i | 0.00633673 | + | 1.16918i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.61556e16 | 1.60269 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.54159e16 | 1.21082 | 0.605411 | − | 0.795913i | \(-0.293009\pi\) | ||||
0.605411 | + | 0.795913i | \(0.293009\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.41571e14 | + | 2.61210e16i | 0.00278481 | + | 0.513820i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.43819e17i | 1.67335i | 0.547702 | + | 0.836674i | \(0.315503\pi\) | ||||
−0.547702 | + | 0.836674i | \(0.684497\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.16710e17i | 0.823546i | 0.911287 | + | 0.411773i | \(0.135090\pi\) | ||||
−0.911287 | + | 0.411773i | \(0.864910\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.96616e15 | − | 3.65884e17i | −0.0173636 | − | 1.60181i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.48520e17 | −0.411867 | −0.205934 | − | 0.978566i | \(-0.566023\pi\) | ||||
−0.205934 | + | 0.978566i | \(0.566023\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.46721e14 | −0.000978829 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.96195e17 | + | 3.77324e15i | −0.818925 | + | 0.00443842i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.61865e18i | − | 1.27132i | −0.771968 | − | 0.635661i | \(-0.780728\pi\) | ||
0.771968 | − | 0.635661i | \(-0.219272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.51830e18i | 1.87295i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.53550e18 | − | 2.45815e16i | 1.65935 | − | 0.00899338i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.11479e18 | 0.283953 | 0.141976 | − | 0.989870i | \(-0.454654\pi\) | ||||
0.141976 | + | 0.989870i | \(0.454654\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.49449e18 | 0.268244 | 0.134122 | − | 0.990965i | \(-0.457179\pi\) | ||||
0.134122 | + | 0.990965i | \(0.457179\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.47792e16 | + | 7.82101e18i | 0.0108446 | + | 1.00043i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.93398e18i | 0.823104i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.07807e19i | 0.722539i | 0.932461 | + | 0.361270i | \(0.117657\pi\) | ||||
−0.932461 | + | 0.361270i | \(0.882343\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.48210e17 | + | 2.73461e19i | 0.00729396 | + | 1.34580i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.20121e19 | 0.802508 | 0.401254 | − | 0.915967i | \(-0.368574\pi\) | ||||
0.401254 | + | 0.915967i | \(0.368574\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.19922e19 | −0.871271 | −0.435636 | − | 0.900123i | \(-0.643476\pi\) | ||||
−0.435636 | + | 0.900123i | \(0.643476\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.13945e17 | − | 7.63763e19i | −0.00848788 | − | 1.56609i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 7.52060e19i | − | 1.16977i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.21919e19i | − | 0.263700i | −0.991270 | − | 0.131850i | \(-0.957908\pi\) | ||
0.991270 | − | 0.131850i | \(-0.0420918\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.09393e20 | − | 2.37191e18i | 0.999765 | − | 0.0216773i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.26654e19 | −0.160341 | −0.0801704 | − | 0.996781i | \(-0.525546\pi\) | ||||
−0.0801704 | + | 0.996781i | \(0.525546\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.38115e20 | −1.31186 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.29450e20 | + | 2.32753e18i | −1.85336 | + | 0.0100449i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.74977e20i | − | 0.934762i | −0.884056 | − | 0.467381i | \(-0.845198\pi\) | ||
0.884056 | − | 0.467381i | \(-0.154802\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1.90970e20i | − | 0.514079i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.92957e20 | + | 2.67173e18i | −1.05618 | + | 0.00572430i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.55125e21 | 2.65817 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.33348e20 | 0.458981 | 0.229490 | − | 0.973311i | \(-0.426294\pi\) | ||||
0.229490 | + | 0.973311i | \(0.426294\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.05204e21 | + | 1.14040e19i | −1.16913 | + | 0.0126733i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.41944e20i | 0.848498i | 0.905546 | + | 0.424249i | \(0.139462\pi\) | ||||
−0.905546 | + | 0.424249i | \(0.860538\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.76930e20i | − | 0.422992i | −0.977379 | − | 0.211496i | \(-0.932166\pi\) | ||
0.977379 | − | 0.211496i | \(-0.0678335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.44982e19 | + | 2.67505e21i | 0.00868615 | + | 1.60267i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.97194e20 | 0.146053 | 0.0730264 | − | 0.997330i | \(-0.476734\pi\) | ||||
0.0730264 | + | 0.997330i | \(0.476734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.05933e20 | 0.0428601 | 0.0214300 | − | 0.999770i | \(-0.493178\pi\) | ||||
0.0214300 | + | 0.999770i | \(0.493178\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.96313e19 | + | 3.62214e21i | 0.00656233 | + | 1.21080i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.87340e21i | − | 1.62767i | −0.581097 | − | 0.813834i | \(-0.697377\pi\) | ||
0.581097 | − | 0.813834i | \(-0.302623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.35299e21i | 2.15587i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.67143e21 | + | 2.89581e19i | −0.513797 | + | 0.00556953i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.08986e21 | 0.819338 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.71605e21 | 0.367021 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.47090e22 | + | 7.97200e19i | −1.67332 | + | 0.00906909i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 9.44261e21i | − | 0.906853i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.86885e21i | − | 0.395811i | −0.980221 | − | 0.197905i | \(-0.936586\pi\) | ||
0.980221 | − | 0.197905i | \(-0.0634139\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.19364e22 | + | 6.46930e19i | −0.823534 | + | 0.00446339i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.36566e22 | −0.801667 | −0.400833 | − | 0.916151i | \(-0.631279\pi\) | ||||
−0.400833 | + | 0.916151i | \(0.631279\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.31589e22 | −1.66019 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.74184e22 | − | 6.08448e20i | 1.60170 | − | 0.0260447i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.35073e22i | 1.59586i | 0.602747 | + | 0.797932i | \(0.294073\pi\) | ||||
−0.602747 | + | 0.797932i | \(0.705927\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.00355e22i | − | 0.316144i | −0.987428 | − | 0.158072i | \(-0.949472\pi\) | ||
0.987428 | − | 0.158072i | \(-0.0505278\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.23257e19 | − | 1.51898e22i | −0.00223221 | − | 0.411861i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.56882e22 | 0.600766 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.46882e23 | −2.96896 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.03051e17 | − | 5.59155e19i | −5.30499e−6 | − | 0.000978815i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.87189e22i | 1.19570i | 0.801607 | + | 0.597852i | \(0.203979\pi\) | ||||
−0.801607 | + | 0.597852i | \(0.796021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.43792e23i | 1.89879i | 0.314088 | + | 0.949394i | \(0.398301\pi\) | ||||
−0.314088 | + | 0.949394i | \(0.601699\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.71812e20 | − | 7.12008e22i | −0.00887670 | − | 0.818889i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.68603e23 | −1.69193 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.87441e22 | −0.602961 | −0.301480 | − | 0.953472i | \(-0.597481\pi\) | ||||
−0.301480 | + | 0.953472i | \(0.597481\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.65546e23 | − | 8.97228e20i | 1.27130 | − | 0.00689022i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.99926e23i | − | 1.34647i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.84150e22i | 0.404745i | 0.979309 | + | 0.202373i | \(0.0648652\pi\) | ||||
−0.979309 | + | 0.202373i | \(0.935135\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.59832e23 | + | 1.95022e21i | −1.87292 | + | 0.0101509i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.56288e23 | −1.17545 | −0.587727 | − | 0.809059i | \(-0.699977\pi\) | ||||
−0.587727 | + | 0.809059i | \(0.699977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.81835e23 | −0.735981 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.02812e21 | + | 4.63852e23i | 0.0179865 | + | 1.65928i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.26369e22i | − | 0.293292i | −0.989189 | − | 0.146646i | \(-0.953152\pi\) | ||
0.989189 | − | 0.146646i | \(-0.0468478\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.58385e23i | 1.56687i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.17935e20 | + | 1.14014e23i | 0.00153895 | + | 0.283949i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.65105e23 | 1.25075 | 0.625377 | − | 0.780322i | \(-0.284945\pi\) | ||||
0.625377 | + | 0.780322i | \(0.284945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.77402e23 | −1.72812 | −0.864059 | − | 0.503390i | \(-0.832086\pi\) | ||||
−0.864059 | + | 0.503390i | \(0.832086\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.28409e20 | + | 1.52848e23i | 0.00145381 | + | 0.268240i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.23886e24i | 1.93963i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.84660e23i | 0.957499i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.99842e23 | + | 1.30060e22i | −1.00036 | + | 0.0162665i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.30255e21 | 0.00817757 | 0.00408879 | − | 0.999992i | \(-0.498698\pi\) | ||||
0.00408879 | + | 0.999992i | \(0.498698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.77036e23 | 0.478850 | 0.239425 | − | 0.970915i | \(-0.423041\pi\) | ||||
0.239425 | + | 0.970915i | \(0.423041\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.13718e23 | + | 4.95217e21i | −0.823092 | + | 0.00446100i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.14719e24i | − | 0.928407i | −0.885728 | − | 0.464204i | \(-0.846341\pi\) | ||
0.885728 | − | 0.464204i | \(-0.153659\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.98955e24i | − | 1.44810i | −0.689749 | − | 0.724048i | \(-0.742279\pi\) | ||
0.689749 | − | 0.724048i | \(-0.257721\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.10259e24 | + | 5.97582e21i | −0.722529 | + | 0.00391597i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.13969e24 | 1.85430 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.03082e24 | −2.68055 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.79672e24 | + | 3.03163e22i | −1.34574 | + | 0.0145877i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.46035e24i | − | 1.94014i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 5.41707e22i | − | 0.0213205i | −0.999943 | − | 0.0106603i | \(-0.996607\pi\) | ||
0.999943 | − | 0.0106603i | \(-0.00339333\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.22015e22 | + | 2.25128e24i | 0.00434938 | + | 0.802496i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.08253e24 | −1.31924 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.60400e24 | 1.05671 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.77335e22 | − | 3.27198e24i | −0.00472205 | − | 0.871259i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.73855e24i | 0.420793i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.60220e24i | 1.67393i | 0.547254 | + | 0.836967i | \(0.315673\pi\) | ||||
−0.547254 | + | 0.836967i | \(0.684327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.81111e24 | − | 8.46719e22i | 1.56602 | − | 0.0169755i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.20457e24 | 0.950854 | 0.475427 | − | 0.879755i | \(-0.342294\pi\) | ||||
0.475427 | + | 0.879755i | \(0.342294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.96569e24 | 0.494143 | 0.247071 | − | 0.968997i | \(-0.420532\pi\) | ||||
0.247071 | + | 0.968997i | \(0.420532\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.69165e24 | − | 4.16873e22i | 1.16975 | − | 0.00633983i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.55617e24i | 1.18862i | 0.804237 | + | 0.594309i | \(0.202574\pi\) | ||||
−0.804237 | + | 0.594309i | \(0.797426\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5.19526e24i | − | 0.659774i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.26967e24 | − | 1.23012e22i | 0.263696 | − | 0.00142918i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.38152e24 | −0.146953 | −0.0734767 | − | 0.997297i | \(-0.523409\pi\) | ||||
−0.0734767 | + | 0.997297i | \(0.523409\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.04275e25 | 1.01625 | 0.508125 | − | 0.861283i | \(-0.330339\pi\) | ||||
0.508125 | + | 0.861283i | \(0.330339\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.03223e23 | + | 1.11868e25i | 0.0270955 | + | 0.999633i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.91244e22i | − | 0.00156799i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.13261e25i | − | 0.852634i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.25636e22 | − | 2.31809e24i | −0.000869004 | − | 0.160338i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.75170e25 | −1.74995 | −0.874977 | − | 0.484165i | \(-0.839124\pi\) | ||||
−0.874977 | + | 0.484165i | \(0.839124\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.68930e25 | 1.57352 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.31989e23 | − | 2.43531e25i | −0.00710993 | − | 1.31184i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.13227e24i | − | 0.105814i | −0.998599 | − | 0.0529072i | \(-0.983151\pi\) | ||
0.998599 | − | 0.0529072i | \(-0.0168487\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.64814e25i | − | 1.21141i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.76094e23 | − | 4.39204e25i | −0.0200894 | − | 1.85328i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.14616e25 | 0.835848 | 0.417924 | − | 0.908482i | \(-0.362758\pi\) | ||||
0.417924 | + | 0.908482i | \(0.362758\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.66206e25 | 2.03654 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.81231e25 | − | 1.52422e23i | 0.934748 | − | 0.00506616i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.04389e25i | 0.320815i | 0.987051 | + | 0.160408i | \(0.0512808\pi\) | ||||
−0.987051 | + | 0.160408i | \(0.948719\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.61617e23i | − | 0.0216550i | −0.999941 | − | 0.0108275i | \(-0.996553\pi\) | ||
0.999941 | − | 0.0108275i | \(-0.00344657\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.95313e25 | − | 1.05856e23i | 0.514071 | − | 0.00278617i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.51109e25 | −1.83109 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.61108e25 | −1.04175 | −0.520877 | − | 0.853632i | \(-0.674395\pi\) | ||||
−0.520877 | + | 0.853632i | \(0.674395\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.46500e23 | − | 5.04154e25i | −0.0114484 | − | 1.05613i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.94908e25i | 0.378802i | 0.981900 | + | 0.189401i | \(0.0606547\pi\) | ||||
−0.981900 | + | 0.189401i | \(0.939345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7.01090e25i | − | 1.26478i | −0.774649 | − | 0.632391i | \(-0.782073\pi\) | ||
0.774649 | − | 0.632391i | \(-0.217927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.59867e23 | + | 1.58653e26i | 0.0144066 | + | 2.65813i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.07537e26 | 1.67417 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.27549e25 | 0.329342 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.84777e23 | + | 3.40929e25i | 0.00248755 | + | 0.458974i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.11825e25i | − | 0.891791i | −0.895085 | − | 0.445896i | \(-0.852885\pi\) | ||
0.895085 | − | 0.445896i | \(-0.147115\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.89955e25i | 0.454866i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.74949e24 | − | 1.07590e26i | −0.0190094 | − | 1.16904i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.82890e25 | 0.691518 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.72667e25 | 0.823949 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.63367e25 | + | 5.22126e23i | −0.848485 | + | 0.00459863i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.22777e25i | 0.429703i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.88150e26i | 1.44394i | 0.691922 | + | 0.721972i | \(0.256764\pi\) | ||||
−0.691922 | + | 0.721972i | \(0.743236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.90051e25 | − | 3.19796e23i | 0.422986 | − | 0.00229250i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.45675e25 | −0.365553 | −0.182776 | − | 0.983155i | \(-0.558508\pi\) | ||||
−0.182776 | + | 0.983155i | \(0.558508\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.02731e26 | −1.26971 | −0.634855 | − | 0.772632i | \(-0.718940\pi\) | ||||
−0.634855 | + | 0.772632i | \(0.718940\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.73581e26 | + | 2.96560e24i | −1.60260 | + | 0.0173721i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.87563e26i | − | 1.57620i | −0.615547 | − | 0.788100i | \(-0.711065\pi\) | ||
0.615547 | − | 0.788100i | \(-0.288935\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.22334e26i | 2.16698i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.64737e23 | + | 3.03953e25i | 0.000791566 | + | 0.146051i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.01872e26 | 1.35893 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.90728e26 | −0.804710 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.87194e22 | + | 1.08342e25i | 0.000232290 | + | 0.0428595i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.11052e26i | 0.412069i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.39437e26i | − | 0.485494i | −0.970090 | − | 0.242747i | \(-0.921952\pi\) | ||
0.970090 | − | 0.242747i | \(-0.0780485\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.70441e26 | + | 4.01556e24i | −1.21075 | + | 0.0131245i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.77111e26 | −1.15744 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.61456e26 | −1.61883 | −0.809416 | − | 0.587235i | \(-0.800216\pi\) | ||||
−0.809416 | + | 0.587235i | \(0.800216\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00698e26 | − | 3.25567e24i | 1.62764 | − | 0.00882152i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.84790e26i | 1.23490i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4.17230e26i | − | 0.999510i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.56571e26 | + | 5.18443e24i | −2.15584 | + | 0.0116842i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.40237e26 | 0.509542 | 0.254771 | − | 0.967001i | \(-0.418000\pi\) | ||||
0.254771 | + | 0.967001i | \(0.418000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.99552e26 | 1.59654 | 0.798269 | − | 0.602301i | \(-0.205749\pi\) | ||||
0.798269 | + | 0.602301i | \(0.205749\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.44246e24 | − | 2.73203e26i | −0.00835409 | − | 0.513760i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.64161e26i | 0.290827i | 0.989371 | + | 0.145414i | \(0.0464513\pi\) | ||||
−0.989371 | + | 0.145414i | \(0.953549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.69989e26i | 1.28554i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.82135e24 | + | 5.20563e26i | 0.00444059 | + | 0.819326i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.77626e26 | −0.708919 | −0.354459 | − | 0.935071i | \(-0.615335\pi\) | ||||
−0.354459 | + | 0.935071i | \(0.615335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.25239e27 | −1.75354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.50553e24 | + | 2.77782e26i | 0.00198916 | + | 0.367016i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.11909e27i | − | 1.39570i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.60572e26i | 0.777905i | 0.921258 | + | 0.388953i | \(0.127163\pi\) | ||||
−0.921258 | + | 0.388953i | \(0.872837\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.63066e25 | − | 1.50431e27i | −0.0181379 | − | 1.67325i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.21030e27 | −1.27194 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.29265e26 | −0.525691 | −0.262846 | − | 0.964838i | \(-0.584661\pi\) | ||||
−0.262846 | + | 0.964838i | \(0.584661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.65737e26 | − | 5.23411e24i | 0.906840 | − | 0.00491490i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.07243e27i | 0.952322i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.06272e26i | 0.341276i | 0.985334 | + | 0.170638i | \(0.0545828\pi\) | ||||
−0.985334 | + | 0.170638i | \(0.945417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.97959e26 | − | 2.69884e24i | 0.395805 | − | 0.00214519i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.98177e26 | −0.299564 | −0.149782 | − | 0.988719i | \(-0.547857\pi\) | ||||
−0.149782 | + | 0.988719i | \(0.547857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.63072e27 | 1.87386 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.32329e25 | − | 1.22075e27i | −0.00892666 | − | 0.823497i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 7.30481e26i | − | 0.466808i | −0.972380 | − | 0.233404i | \(-0.925014\pi\) | ||
0.972380 | − | 0.233404i | \(-0.0749865\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.82009e27i | 1.10214i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.56995e24 | − | 1.39672e27i | −0.00434482 | − | 0.801655i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.76279e26 | 0.422424 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.73510e26 | 0.502389 | 0.251194 | − | 0.967937i | \(-0.419177\pi\) | ||||
0.251194 | + | 0.967937i | \(0.419177\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.83802e25 | − | 3.39131e27i | −0.00899778 | − | 1.66017i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.45875e27i | 1.60658i | 0.595585 | + | 0.803292i | \(0.296920\pi\) | ||||
−0.595585 | + | 0.803292i | \(0.703080\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.23102e27i | 0.542703i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.29700e25 | + | 3.82660e27i | 0.0347251 | + | 1.60153i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.56213e27 | 1.41569 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.10563e27 | 1.54983 | 0.774917 | − | 0.632062i | \(-0.217791\pi\) | ||||
0.774917 | + | 0.632062i | \(0.217791\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.44968e27 | + | 2.41164e25i | −1.59584 | + | 0.00864915i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 8.33555e26i | − | 0.284092i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 7.92842e26i | − | 0.256851i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.02638e27 | − | 5.56277e24i | 0.316139 | − | 0.00171341i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.73761e27 | 0.508986 | 0.254493 | − | 0.967075i | \(-0.418091\pi\) | ||||
0.254493 | + | 0.967075i | \(0.418091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.45539e25 | −0.0124144 | −0.00620718 | − | 0.999981i | \(-0.501976\pi\) | ||||
−0.00620718 | + | 0.999981i | \(0.501976\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.55348e27 | − | 1.68396e25i | 0.411843 | − | 0.00446435i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5.08342e27i | − | 1.28254i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.11747e27i | − | 0.268376i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.42392e25 | + | 2.62724e27i | 0.00325599 | + | 0.600757i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.73857e26 | 0.212072 | 0.106036 | − | 0.994362i | \(-0.466184\pi\) | ||||
0.106036 | + | 0.994362i | \(0.466184\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.97484e27 | 1.23938 | 0.619689 | − | 0.784848i | \(-0.287259\pi\) | ||||
0.619689 | + | 0.784848i | \(0.287259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.14177e25 | − | 1.50222e28i | −0.0160909 | − | 2.96891i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.18573e28i | − | 2.23322i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.01308e28i | − | 1.81873i | −0.416004 | − | 0.909363i | \(-0.636570\pi\) | ||
0.416004 | − | 0.909363i | \(-0.363430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.71856e24 | − | 6.19888e22i | 0.000978771 | − | 1.06098e-5i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.02381e28 | −1.67101 | −0.835506 | − | 0.549481i | \(-0.814825\pi\) | ||||
−0.835506 | + | 0.549481i | \(0.814825\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.61875e27 | 1.49740 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.05093e27 | + | 4.36345e25i | −1.19569 | + | 0.00648039i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.14766e28i | 1.62640i | 0.581983 | + | 0.813201i | \(0.302277\pi\) | ||||
−0.581983 | + | 0.813201i | \(0.697723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.44653e28i | 1.95647i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.47062e28 | + | 7.97049e25i | −1.89876 | + | 0.0102909i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.68016e27 | 0.823507 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.13327e27 | 0.604330 | 0.302165 | − | 0.953256i | \(-0.402291\pi\) | ||||
0.302165 | + | 0.953256i | \(0.402291\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.28159e27 | − | 1.18404e26i | 0.818829 | − | 0.0133147i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.40154e27i | 0.472873i | 0.971647 | + | 0.236437i | \(0.0759795\pi\) | ||||
−0.971647 | + | 0.236437i | \(0.924020\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.61110e26i | 0.0986672i | 0.998782 | + | 0.0493336i | \(0.0157097\pi\) | ||||
−0.998782 | + | 0.0493336i | \(0.984290\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.34578e25 | − | 1.72437e28i | −0.00916979 | − | 1.69190i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.78197e28 | 1.67138 | 0.835688 | − | 0.549205i | \(-0.185069\pi\) | ||||
0.835688 | + | 0.549205i | \(0.185069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.06100e27 | 0.722893 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.81054e25 | − | 7.03076e27i | −0.00326788 | − | 0.602952i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.17386e28i | 0.962887i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.31169e28i | 2.59877i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.83527e26 | + | 1.69306e28i | 0.0137802 | + | 1.27125i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.22352e28 | −1.59778 | −0.798892 | − | 0.601475i | \(-0.794580\pi\) | ||||
−0.798892 | + | 0.601475i | \(0.794580\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.04526e27 | 0.622154 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.04473e28 | − | 1.10821e26i | 1.34646 | − | 0.00729753i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.16606e28i | 0.735244i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.75178e28i | 1.66173i | 0.556477 | + | 0.830863i | \(0.312153\pi\) | ||||
−0.556477 | + | 0.830863i | \(0.687847\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.99711e27 | + | 3.79230e25i | −0.404739 | + | 0.00219361i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.32096e28 | −1.28621 | −0.643106 | − | 0.765777i | \(-0.722354\pi\) | ||||
−0.643106 | + | 0.765777i | \(0.722354\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.85831e28 | −1.51781 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.98915e26 | − | 3.68005e28i | −0.0203014 | − | 1.87284i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.64590e28i | − | 0.802901i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.14869e28i | 0.537213i | 0.963250 | + | 0.268607i | \(0.0865632\pi\) | ||||
−0.963250 | + | 0.268607i | \(0.913437\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.42062e26 | − | 2.62117e28i | −0.00637064 | − | 1.17544i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.47081e27 | −0.278288 | −0.139144 | − | 0.990272i | \(-0.544435\pi\) | ||||
−0.139144 | + | 0.990272i | \(0.544435\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.29494e28 | −1.35921 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.00792e26 | − | 1.85970e28i | −0.00398882 | − | 0.735970i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3.07298e28i | − | 1.16687i | −0.812159 | − | 0.583437i | \(-0.801708\pi\) | ||
0.812159 | − | 0.583437i | \(-0.198292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.39213e28i | 0.871698i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.74373e28 | + | 7.71364e26i | −1.65916 | + | 0.0269791i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.01811e28 | 0.677594 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.49381e28 | −0.481554 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.47438e27 | − | 5.13493e25i | 0.293287 | − | 0.00158956i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.85510e27i | 0.0848838i | 0.999099 | + | 0.0424419i | \(0.0135137\pi\) | ||||
−0.999099 | + | 0.0424419i | \(0.986486\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.26243e28i | 0.646111i | 0.946380 | + | 0.323055i | \(0.104710\pi\) | ||||
−0.946380 | + | 0.323055i | \(0.895290\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.71085e28 | + | 3.09517e26i | −1.56685 | + | 0.00849203i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.28100e28 | −0.864958 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.20202e28 | 0.811222 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.16604e28 | + | 1.26398e26i | −0.283936 | + | 0.00307785i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.67316e28i | 0.859812i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.03959e28i | 0.233963i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.13242e26 | + | 5.77957e28i | 0.00677875 | + | 1.25074i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.49891e25 | −0.00114444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.78493e27 | −0.0557498 | −0.0278749 | − | 0.999611i | \(-0.508874\pi\) | ||||
−0.0278749 | + | 0.999611i | \(0.508874\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.86350e26 | − | 8.97357e28i | −0.00936593 | − | 1.72809i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.70556e27i | 0.0686579i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.91470e28i | 1.58942i | 0.606986 | + | 0.794712i | \(0.292378\pi\) | ||||
−0.606986 | + | 0.794712i | \(0.707622\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.56320e28 | + | 1.69450e26i | −0.268229 | + | 0.00290758i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.86210e29 | 3.07547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.65935e28 | −0.263829 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.26703e29 | + | 6.86707e26i | −1.93960 | + | 0.0105122i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 2.71342e27i | − | 0.0399979i | −0.999800 | − | 0.0199990i | \(-0.993634\pi\) | ||
0.999800 | − | 0.0199990i | \(-0.00636629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.98077e28i | 0.423160i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.00232e28 | + | 3.79512e26i | −0.957485 | + | 0.00518938i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.45195e28 | 1.11332 | 0.556658 | − | 0.830742i | \(-0.312083\pi\) | ||||
0.556658 | + | 0.830742i | \(0.312083\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.05453e29 | 2.60737 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.77354e27 | − | 8.17961e28i | −0.0216879 | − | 1.00025i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.37085e28i | − | 0.750790i | −0.926865 | − | 0.375395i | \(-0.877507\pi\) | ||
0.926865 | − | 0.375395i | \(-0.122493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.18041e29i | 1.34077i | 0.742013 | + | 0.670385i | \(0.233871\pi\) | ||||
−0.742013 | + | 0.670385i | \(0.766129\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.04786e24 | + | 7.46864e26i | 4.43202e−5 | + | 0.00817745i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.99673e29 | −2.10769 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.53533e28 | −0.461597 | −0.230798 | − | 0.973002i | \(-0.574134\pi\) | ||||
−0.230798 | + | 0.973002i | \(0.574134\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.64425e26 | + | 4.87886e28i | 0.00259524 | + | 0.478843i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.69475e28i | 0.160419i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.62803e29i | − | 1.48643i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.01296e27 | − | 9.34471e28i | −0.00892187 | − | 0.823056i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.79896e29 | −1.52870 | −0.764349 | − | 0.644803i | \(-0.776939\pi\) | ||||
−0.764349 | + | 0.644803i | \(0.776939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.13747e29 | 1.75263 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.17328e29 | − | 6.35894e26i | 0.928394 | − | 0.00503172i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.70822e29i | − | 1.30458i | −0.757971 | − | 0.652288i | \(-0.773809\pi\) | ||
0.757971 | − | 0.652288i | \(-0.226191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.78045e29i | 1.31250i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.03480e29 | − | 1.10282e27i | 1.44808 | − | 0.00784829i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.10298e29 | 1.44495 | 0.722476 | − | 0.691396i | \(-0.243004\pi\) | ||||
0.722476 | + | 0.691396i | \(0.243004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.42210e29 | 1.60698 | 0.803490 | − | 0.595318i | \(-0.202974\pi\) | ||||
0.803490 | + | 0.595318i | \(0.202974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.22235e27 | − | 1.12763e29i | −0.00783182 | − | 0.722497i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.50081e28i | 0.587935i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.05757e29i | − | 0.632161i | −0.948732 | − | 0.316080i | \(-0.897633\pi\) | ||
0.948732 | − | 0.316080i | \(-0.102367\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.74036e27 | + | 3.21110e29i | 0.0100498 | + | 1.85427i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.79322e28 | −0.211629 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.60853e29 | −0.867151 | −0.433576 | − | 0.901117i | \(-0.642748\pi\) | ||||
−0.433576 | + | 0.901117i | \(0.642748\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.78862e27 | − | 5.14524e29i | −0.0145278 | − | 2.68051i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.47123e29i | 0.740774i | 0.928878 | + | 0.370387i | \(0.120775\pi\) | ||||
−0.928878 | + | 0.370387i | \(0.879225\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.25054e29i | − | 0.608618i | −0.952573 | − | 0.304309i | \(-0.901574\pi\) | ||
0.952573 | − | 0.304309i | \(-0.0984255\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.65082e27 | − | 2.86016e29i | −0.0218810 | − | 1.34564i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.05607e29 | −0.935219 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.57871e28 | −0.113413 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.56180e29 | − | 2.47241e27i | 1.94011 | − | 0.0105150i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.41081e29i | 0.991587i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.46578e28i | − | 0.0583125i | −0.999575 | − | 0.0291562i | \(-0.990718\pi\) | ||
0.999575 | − | 0.0291562i | \(-0.00928203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.54027e27 | − | 3.00272e25i | 0.0213202 | − | 0.000115552i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.70314e29 | 0.634052 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.39633e26 | −0.000502949 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.30241e29 | + | 2.49580e27i | −0.802461 | + | 0.00869862i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.38597e29i | 0.804740i | 0.915477 | + | 0.402370i | \(0.131813\pi\) | ||||
−0.915477 | + | 0.402370i | \(0.868187\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.53371e29i | − | 0.500642i | −0.968163 | − | 0.250321i | \(-0.919464\pi\) | ||
0.968163 | − | 0.250321i | \(-0.0805361\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.26297e27 | − | 4.17538e29i | −0.00714994 | − | 1.31922i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.14797e29 | −0.962799 | −0.481399 | − | 0.876501i | \(-0.659871\pi\) | ||||
−0.481399 | + | 0.876501i | \(0.659871\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.12125e29 | 0.331997 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.99772e27 | + | 3.68596e29i | 0.00572710 | + | 1.05670i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.66658e28i | 0.212820i | 0.994322 | + | 0.106410i | \(0.0339357\pi\) | ||||
−0.994322 | + | 0.106410i | \(0.966064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.77711e29i | − | 1.28420i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.34630e29 | − | 3.62736e27i | 0.871220 | − | 0.00944397i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.20379e29 | −0.303567 | −0.151783 | − | 0.988414i | \(-0.548502\pi\) | ||||
−0.151783 | + | 0.988414i | \(0.548502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.11592e29 | 1.00543 | 0.502715 | − | 0.864452i | \(-0.332335\pi\) | ||||
0.502715 | + | 0.864452i | \(0.332335\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.77809e29 | + | 9.63690e26i | −0.420786 | + | 0.00228058i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.15991e30i | − | 2.65947i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.12273e30i | 2.49432i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.77510e29 | + | 4.21396e27i | −1.67391 | + | 0.00907226i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.50316e29 | 0.313630 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.22042e29 | 1.05572 | 0.527858 | − | 0.849332i | \(-0.322995\pi\) | ||||
0.527858 | + | 0.849332i | \(0.322995\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.29895e28 | + | 7.98829e29i | 0.0254626 | + | 1.56590i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.40097e29i | 0.456252i | 0.973632 | + | 0.228126i | \(0.0732599\pi\) | ||||
−0.973632 | + | 0.228126i | \(0.926740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.49252e29i | − | 0.459205i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.88493e27 | + | 5.32295e29i | 0.00515337 | + | 0.950840i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.33314e29 | 0.577345 | 0.288673 | − | 0.957428i | \(-0.406786\pi\) | ||||
0.288673 | + | 0.957428i | \(0.406786\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.52189e30 | −2.55643 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.64390e27 | + | 3.03314e29i | 0.00267812 | + | 0.494136i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 4.13404e29i | − | 0.653240i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.70770e29i | 1.02814i | 0.857747 | + | 0.514072i | \(0.171864\pi\) | ||||
−0.857747 | + | 0.514072i | \(0.828136\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.52708e27 | + | 7.86636e29i | 0.0126795 | + | 1.16970i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.51045e29 | 0.506433 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.78996e29 | −1.37037 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.75077e29 | + | 4.74275e27i | −1.18860 | + | 0.00644199i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.56695e29i | 0.997428i | 0.866766 | + | 0.498714i | \(0.166194\pi\) | ||||
−0.866766 | + | 0.498714i | \(0.833806\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.57057e30i | − | 2.00921i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.31342e29 | − | 2.87977e27i | 0.659764 | − | 0.00357579i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.04315e29 | 0.848913 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.09551e30 | −1.28183 | −0.640913 | − | 0.767613i | \(-0.721444\pi\) | ||||
−0.640913 | + | 0.767613i | \(0.721444\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.51619e27 | + | 2.32122e29i | 0.00285833 | + | 0.263685i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.28876e30i | 1.42145i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.98579e29i | 0.962371i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.65788e26 | − | 1.41294e29i | −0.000796448 | − | 0.146951i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.65035e29 | 0.671724 | 0.335862 | − | 0.941911i | \(-0.390972\pi\) | ||||
0.335862 | + | 0.941911i | \(0.390972\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.31385e29 | −0.423199 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.78003e27 | + | 1.06646e30i | 0.00550780 | + | 1.01624i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 3.13572e30i | − | 2.90261i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.20051e30i | − | 1.07958i | −0.841799 | − | 0.539791i | \(-0.818503\pi\) | ||
0.841799 | − | 0.539791i | \(-0.181497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.14396e30 | + | 3.72129e28i | −0.999471 | + | 0.0325128i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.94458e29 | −0.674432 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.89370e28 | −0.0568670 | −0.0284335 | − | 0.999596i | \(-0.509052\pi\) | ||||
−0.0284335 | + | 0.999596i | \(0.509052\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.95594e27 | − | 1.06008e25i | 0.00156797 | − | 8.49810e-6i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.08432e30i | 0.844791i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.29786e29i | 0.325451i | 0.986671 | + | 0.162725i | \(0.0520284\pi\) | ||||
−0.986671 | + | 0.162725i | \(0.947972\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.15837e30 | − | 6.27815e27i | 0.852622 | − | 0.00462105i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.13498e29 | 0.510517 | 0.255259 | − | 0.966873i | \(-0.417839\pi\) | ||||
0.255259 | + | 0.966873i | \(0.417839\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.75361e30 | −1.91541 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.37075e29 | − | 2.56987e27i | 0.160331 | − | 0.00173798i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.22219e29i | − | 0.146124i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.98079e30i | − | 1.26654i | −0.773932 | − | 0.633269i | \(-0.781713\pi\) | ||
0.773932 | − | 0.633269i | \(-0.218287\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.52529e28 | − | 2.81428e30i | −0.00948427 | − | 1.74993i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.02987e30 | −3.04168 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.86845e30 | −1.09894 | −0.549470 | − | 0.835513i | \(-0.685170\pi\) | ||||
−0.549470 | + | 0.835513i | \(0.685170\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.49070e28 | + | 2.75046e30i | 0.00852808 | + | 1.57350i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.84584e29i | 0.325318i | 0.986682 | + | 0.162659i | \(0.0520070\pi\) | ||||
−0.986682 | + | 0.162659i | \(0.947993\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 7.92087e28i | − | 0.0428811i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.49062e30 | − | 2.69982e28i | 1.31178 | − | 0.0142197i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.84718e29 | 0.145903 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.70264e30 | 0.848978 | 0.424489 | − | 0.905433i | \(-0.360454\pi\) | ||||
0.424489 | + | 0.905433i | \(0.360454\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.18077e29 | − | 1.18193e27i | 0.105813 | − | 0.000573485i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.89141e30i | 1.83748i | 0.394864 | + | 0.918740i | \(0.370792\pi\) | ||||
−0.394864 | + | 0.918740i | \(0.629208\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.59943e30i | − | 1.65412i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.70836e30 | − | 1.46788e28i | 1.21140 | − | 0.00656554i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.37786e30 | 2.77672 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.21398e30 | 0.938290 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.49167e30 | − | 7.30376e28i | 1.85314 | − | 0.0301334i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.40468e30i | − | 0.965887i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 5.77737e29i | − | 0.225941i | −0.993598 | − | 0.112971i | \(-0.963963\pi\) | ||
0.993598 | − | 0.112971i | \(-0.0360366\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.18963e28 | + | 2.19497e30i | 0.00453007 | + | 0.835835i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.39169e30 | −1.62846 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.81695e29 | 0.137831 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.13852e28 | + | 5.79084e30i | 0.0110375 | + | 2.03651i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 8.69220e29i | − | 0.297726i | −0.988858 | − | 0.148863i | \(-0.952439\pi\) | ||
0.988858 | − | 0.148863i | \(-0.0475614\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.01100e30i | − | 0.337294i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.11777e28 | + | 2.87619e30i | 0.0101322 | + | 0.934707i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.21776e30 | −1.01869 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.99347e30 | 2.15693 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.06763e30 | + | 5.78634e27i | −0.320810 | + | 0.00173873i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.64754e30i | 1.36070i | 0.732886 | + | 0.680352i | \(0.238173\pi\) | ||||
−0.732886 | + | 0.680352i | \(0.761827\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.41993e29i | − | 0.0405087i | −0.999795 | − | 0.0202543i | \(-0.993552\pi\) | ||
0.999795 | − | 0.0202543i | \(-0.00644759\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.78939e28 | − | 4.22170e26i | 0.0216547 | − | 0.000117364i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.39317e30 | −0.648365 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.17565e30 | 1.36657 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.16527e28 | + | 1.99749e30i | 0.00557226 | + | 0.514049i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 5.05400e30i | − | 1.26775i | −0.773437 | − | 0.633873i | \(-0.781464\pi\) | ||
0.773437 | − | 0.633873i | \(-0.218536\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 5.61530e30i | − | 1.37301i | −0.727124 | − | 0.686506i | \(-0.759143\pi\) | ||
0.727124 | − | 0.686506i | \(-0.240857\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.16345e28 | − | 7.68192e30i | −0.00992401 | − | 1.83106i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.24661e30 | 1.21919 | 0.609594 | − | 0.792713i | \(-0.291332\pi\) | ||||
0.609594 | + | 0.792713i | \(0.291332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.89648e30 | −0.656218 | −0.328109 | − | 0.944640i | \(-0.606411\pi\) | ||||
−0.328109 | + | 0.944640i | \(0.606411\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.55595e28 | − | 4.71595e30i | −0.00564602 | − | 1.04174i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.72160e27i | − | 0.000801599i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 8.96502e30i | − | 1.88297i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.15590e30 | − | 8.38385e28i | 1.05606 | − | 0.0171722i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.42250e30 | −0.284152 | −0.142076 | − | 0.989856i | \(-0.545378\pi\) | ||||
−0.142076 | + | 0.989856i | \(0.545378\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.24987e31 | −2.43505 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.99341e30 | + | 1.08039e28i | −0.378797 | + | 0.00205301i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 6.36062e30i | − | 1.17897i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.03086e30i | − | 0.367201i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.17035e30 | − | 3.88619e28i | 1.26476 | − | 0.00685478i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.46949e30 | 1.62954 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.82137e30 | 0.641584 | 0.320792 | − | 0.947150i | \(-0.396051\pi\) | ||||
0.320792 | + | 0.947150i | \(0.396051\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.62256e31 | + | 1.75885e29i | −2.65801 | + | 0.0288127i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.34205e30i | 0.534212i | 0.963667 | + | 0.267106i | \(0.0860674\pi\) | ||||
−0.963667 | + | 0.267106i | \(0.913933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 6.89441e30i | − | 1.07540i | −0.843137 | − | 0.537699i | \(-0.819294\pi\) | ||
0.843137 | − | 0.537699i | \(-0.180706\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.96086e28 | + | 1.09983e31i | 0.00907353 | + | 1.67414i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.61828e30 | 0.834623 | 0.417311 | − | 0.908764i | \(-0.362972\pi\) | ||||
0.417311 | + | 0.908764i | \(0.362972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.24046e30 | 0.469826 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.26132e28 | + | 2.32724e30i | 0.00178494 | + | 0.329337i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.23206e30i | − | 0.308318i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.75340e30i | 0.371261i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.48673e30 | + | 3.77959e28i | −0.458954 | + | 0.00497503i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.06048e30 | −0.907297 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.20149e31 | −1.50738 | −0.753692 | − | 0.657228i | \(-0.771729\pi\) | ||||
−0.753692 | + | 0.657228i | \(0.771729\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.28015e30 | − | 3.94570e28i | 0.891778 | − | 0.00483327i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.08367e31i | 1.29614i | 0.761582 | + | 0.648068i | \(0.224423\pi\) | ||||
−0.761582 | + | 0.648068i | \(0.775577\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.45236e31i | 1.69624i | 0.529804 | + | 0.848120i | \(0.322266\pi\) | ||||
−0.529804 | + | 0.848120i | \(0.677734\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.98824e30 | + | 2.16155e28i | −0.454860 | + | 0.00246525i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.62800e31 | 1.81324 | 0.906621 | − | 0.421946i | \(-0.138653\pi\) | ||||
0.906621 | + | 0.421946i | \(0.138653\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.64056e30 | −0.396004 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.10028e31 | − | 2.38566e29i | 1.16892 | − | 0.0253451i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.58632e30i | 0.683444i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.97675e31i | 2.00359i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.78531e28 | + | 6.98421e30i | 0.00374784 | + | 0.691507i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.02389e31 | −1.95754 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.10183e31 | 1.04113 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.83726e28 | + | 8.92514e30i | 0.00446558 | + | 0.823937i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 3.06917e31i | − | 2.76829i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.81303e30i | − | 0.159782i | −0.996804 | − | 0.0798911i | \(-0.974543\pi\) | ||
0.996804 | − | 0.0798911i | \(-0.0254573\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.06800e29 | − | 9.85249e30i | −0.00919712 | − | 0.848448i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.11199e30 | −0.346026 | −0.173013 | − | 0.984920i | \(-0.555350\pi\) | ||||
−0.173013 | + | 0.984920i | \(0.555350\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.27969e30 | −0.187470 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.34667e30 | + | 2.89779e28i | −0.429696 | + | 0.00232887i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.02114e31i | 0.802059i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4.28325e30i | − | 0.328822i | −0.986392 | − | 0.164411i | \(-0.947428\pi\) | ||
0.986392 | − | 0.164411i | \(-0.0525723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.92429e31 | + | 1.04293e29i | −1.44392 | + | 0.00782578i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.62192e30 | 0.412351 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.64478e31 | −1.89628 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.54140e28 | + | 6.03454e30i | 0.00458494 | + | 0.422967i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.09229e31i | 0.748465i | 0.927335 | + | 0.374233i | \(0.122094\pi\) | ||||
−0.927335 | + | 0.374233i | \(0.877906\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.42451e28i | 0.00162425i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.02472e28 | − | 5.58085e30i | −0.00198120 | − | 0.365547i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.39496e31 | −1.53382 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.24009e31 | 0.776582 | 0.388291 | − | 0.921537i | \(-0.373066\pi\) | ||||
0.388291 | + | 0.921537i | \(0.373066\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.12375e29 | − | 2.07342e31i | −0.00688148 | − | 1.26969i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.62316e31i | − | 0.972009i | −0.873956 | − | 0.486005i | \(-0.838454\pi\) | ||
0.873956 | − | 0.486005i | \(-0.161546\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.84543e31i | 2.25202i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.54952e29 | − | 2.79786e31i | −0.0260574 | − | 1.60248i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.64041e31 | −0.918920 | −0.459460 | − | 0.888199i | \(-0.651957\pi\) | ||||
−0.459460 | + | 0.888199i | \(0.651957\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.17083e30 | −0.447683 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.94104e31 | − | 1.59399e29i | 1.57618 | − | 0.00854258i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.29653e31i | 1.20392i | 0.798527 | + | 0.601959i | \(0.205613\pi\) | ||||
−0.798527 | + | 0.601959i | \(0.794387\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.55445e29i | 0.0130997i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.31940e31 | + | 2.34103e29i | −2.16694 | + | 0.0117444i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.25315e31 | 1.59665 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.40640e30 | −0.115550 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.10857e30 | + | 3.36967e28i | −0.146044 | + | 0.00158311i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.66868e31i | 0.767074i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.07315e31i | 0.482708i | 0.970437 | + | 0.241354i | \(0.0775915\pi\) | ||||
−0.970437 | + | 0.241354i | \(0.922409\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.67330e29 | + | 3.08737e31i | 0.00736501 | + | 1.35891i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.35451e31 | −0.583419 | −0.291709 | − | 0.956507i | \(-0.594224\pi\) | ||||
−0.291709 | + | 0.956507i | \(0.594224\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.50381e30 | −0.316298 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.05722e29 | − | 1.95066e31i | −0.00436131 | − | 0.804698i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.05742e30i | − | 0.163816i | −0.996640 | − | 0.0819082i | \(-0.973899\pi\) | ||
0.996640 | − | 0.0819082i | \(-0.0261014\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.76571e31i | − | 1.09292i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.10803e30 | + | 1.20110e28i | −0.0428576 | + | 0.000464573i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.95860e29 | 0.0339178 | 0.0169589 | − | 0.999856i | \(-0.494602\pi\) | ||||
0.0169589 | + | 0.999856i | \(0.494602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.01288e31 | 1.48722 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.13578e31 | + | 6.15570e28i | −0.412063 | + | 0.00223330i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.12057e31i | 1.10834i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.88992e31i | − | 0.657157i | −0.944477 | − | 0.328579i | \(-0.893430\pi\) | ||
0.944477 | − | 0.328579i | \(-0.106570\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.42608e31 | − | 7.72909e28i | 0.485487 | − | 0.00263124i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.95949e31 | 2.31972 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.83412e30 | 0.255677 | 0.127838 | − | 0.991795i | \(-0.459196\pi\) | ||||
0.127838 | + | 0.991795i | \(0.459196\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.16027e29 | − | 3.78844e31i | −0.0196862 | − | 1.21066i |
(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 | 48.22.c.c.47.16 | yes | 28 | |
3.2 | odd | 2 | inner | 48.22.c.c.47.14 | yes | 28 | |
4.3 | odd | 2 | inner | 48.22.c.c.47.13 | ✓ | 28 | |
12.11 | even | 2 | inner | 48.22.c.c.47.15 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.22.c.c.47.13 | ✓ | 28 | 4.3 | odd | 2 | inner | |
48.22.c.c.47.14 | yes | 28 | 3.2 | odd | 2 | inner | |
48.22.c.c.47.15 | yes | 28 | 12.11 | even | 2 | inner | |
48.22.c.c.47.16 | yes | 28 | 1.1 | even | 1 | trivial |