Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,10,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.a (trivial) |
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: | yes |
Analytic conductor: | \(115.883063137\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −448.000 | −0.875000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4242.00 | −0.667774 | −0.333887 | − | 0.942613i | \(-0.608360\pi\) | ||||
−0.333887 | + | 0.942613i | \(0.608360\pi\) | |||||||
\(8\) | 7680.00 | 0.662913 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 46208.0 | 0.951590 | 0.475795 | − | 0.879556i | \(-0.342160\pi\) | ||||
0.475795 | + | 0.879556i | \(0.342160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 115934. | 1.12581 | 0.562906 | − | 0.826521i | \(-0.309683\pi\) | ||||
0.562906 | + | 0.826521i | \(0.309683\pi\) | |||||||
\(14\) | 33936.0 | 0.236094 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 167936. | 0.640625 | ||||||||
\(17\) | 494842. | 1.43697 | 0.718483 | − | 0.695545i | \(-0.244837\pi\) | ||||
0.718483 | + | 0.695545i | \(0.244837\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00874e6 | −1.77578 | −0.887888 | − | 0.460060i | \(-0.847828\pi\) | ||||
−0.887888 | + | 0.460060i | \(0.847828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −369664. | −0.336438 | ||||||||
\(23\) | −532554. | −0.396815 | −0.198408 | − | 0.980120i | \(-0.563577\pi\) | ||||
−0.198408 | + | 0.980120i | \(0.563577\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −927472. | −0.398035 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.90042e6 | 0.584302 | ||||||||
\(29\) | −4.19639e6 | −1.10175 | −0.550877 | − | 0.834586i | \(-0.685707\pi\) | ||||
−0.550877 | + | 0.834586i | \(0.685707\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.36503e6 | −0.654427 | −0.327213 | − | 0.944950i | \(-0.606110\pi\) | ||||
−0.327213 | + | 0.944950i | \(0.606110\pi\) | |||||||
\(32\) | −5.27565e6 | −0.889408 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.95874e6 | −0.508044 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.49314e7 | 1.30976 | 0.654880 | − | 0.755733i | \(-0.272719\pi\) | ||||
0.654880 | + | 0.755733i | \(0.272719\pi\) | |||||||
\(38\) | 8.06992e6 | 0.627831 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.10563e7 | −0.611056 | −0.305528 | − | 0.952183i | \(-0.598833\pi\) | ||||
−0.305528 | + | 0.952183i | \(0.598833\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.39679e6 | 0.285335 | 0.142667 | − | 0.989771i | \(-0.454432\pi\) | ||||
0.142667 | + | 0.989771i | \(0.454432\pi\) | |||||||
\(44\) | −2.07012e7 | −0.832642 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.26043e6 | 0.140295 | ||||||||
\(47\) | −3.55592e7 | −1.06295 | −0.531473 | − | 0.847075i | \(-0.678361\pi\) | ||||
−0.531473 | + | 0.847075i | \(0.678361\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.23590e7 | −0.554078 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.19384e7 | −0.985085 | ||||||||
\(53\) | 3.97386e7 | 0.691785 | 0.345892 | − | 0.938274i | \(-0.387576\pi\) | ||||
0.345892 | + | 0.938274i | \(0.387576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.25786e7 | −0.442676 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.35711e7 | 0.389529 | ||||||||
\(59\) | 8.51856e7 | 0.915234 | 0.457617 | − | 0.889149i | \(-0.348703\pi\) | ||||
0.457617 | + | 0.889149i | \(0.348703\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.57486e7 | 0.423052 | 0.211526 | − | 0.977372i | \(-0.432157\pi\) | ||||
0.211526 | + | 0.977372i | \(0.432157\pi\) | |||||||
\(62\) | 2.69202e7 | 0.231375 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.37780e7 | −0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.52862e7 | 0.274555 | 0.137277 | − | 0.990533i | \(-0.456165\pi\) | ||||
0.137277 | + | 0.990533i | \(0.456165\pi\) | |||||||
\(68\) | −2.21689e8 | −1.25735 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.89967e8 | 0.887190 | 0.443595 | − | 0.896227i | \(-0.353703\pi\) | ||||
0.443595 | + | 0.896227i | \(0.353703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.12171e8 | −1.69873 | −0.849365 | − | 0.527805i | \(-0.823015\pi\) | ||||
−0.849365 | + | 0.527805i | \(0.823015\pi\) | |||||||
\(74\) | −1.19451e8 | −0.463070 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.51916e8 | 1.55380 | ||||||||
\(77\) | −1.96014e8 | −0.635447 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.50408e7 | 0.274529 | 0.137265 | − | 0.990534i | \(-0.456169\pi\) | ||||
0.137265 | + | 0.990534i | \(0.456169\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.84501e7 | 0.216041 | ||||||||
\(83\) | 2.61706e8 | 0.605289 | 0.302645 | − | 0.953104i | \(-0.402131\pi\) | ||||
0.302645 | + | 0.953104i | \(0.402131\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.11744e7 | −0.100881 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.54877e8 | 0.630821 | ||||||||
\(89\) | 1.99386e7 | 0.0336853 | 0.0168426 | − | 0.999858i | \(-0.494639\pi\) | ||||
0.0168426 | + | 0.999858i | \(0.494639\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.91792e8 | −0.751788 | ||||||||
\(92\) | 2.38584e8 | 0.347213 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.84473e8 | 0.375808 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.95034e7 | 0.0223685 | 0.0111842 | − | 0.999937i | \(-0.496440\pi\) | ||||
0.0111842 | + | 0.999937i | \(0.496440\pi\) | |||||||
\(98\) | 1.78872e8 | 0.195896 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.16672e8 | 0.207184 | 0.103592 | − | 0.994620i | \(-0.466966\pi\) | ||||
0.103592 | + | 0.994620i | \(0.466966\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.48234e8 | 0.655043 | 0.327522 | − | 0.944844i | \(-0.393787\pi\) | ||||
0.327522 | + | 0.944844i | \(0.393787\pi\) | |||||||
\(104\) | 8.90373e8 | 0.746315 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.17909e8 | −0.244583 | ||||||||
\(107\) | 1.05711e9 | 0.779637 | 0.389819 | − | 0.920892i | \(-0.372538\pi\) | ||||
0.389819 | + | 0.920892i | \(0.372538\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.49659e9 | −1.69406 | −0.847029 | − | 0.531547i | \(-0.821611\pi\) | ||||
−0.847029 | + | 0.531547i | \(0.821611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.12385e8 | −0.427793 | ||||||||
\(113\) | 1.11566e9 | 0.643695 | 0.321848 | − | 0.946791i | \(-0.395696\pi\) | ||||
0.321848 | + | 0.946791i | \(0.395696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.87998e9 | 0.964035 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.81485e8 | −0.323584 | ||||||||
\(119\) | −2.09912e9 | −0.959568 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.22768e8 | −0.0944756 | ||||||||
\(122\) | −3.65989e8 | −0.149572 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.50753e9 | 0.572623 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.12054e8 | −0.106442 | −0.0532210 | − | 0.998583i | \(-0.516949\pi\) | ||||
−0.0532210 | + | 0.998583i | \(0.516949\pi\) | |||||||
\(128\) | 3.05136e9 | 1.00473 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.81701e9 | 0.835733 | 0.417867 | − | 0.908508i | \(-0.362778\pi\) | ||||
0.417867 | + | 0.908508i | \(0.362778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.27908e9 | 1.18582 | ||||||||
\(134\) | −3.62289e8 | −0.0970697 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.80039e9 | 0.952583 | ||||||||
\(137\) | −7.15311e9 | −1.73481 | −0.867406 | − | 0.497600i | \(-0.834215\pi\) | ||||
−0.867406 | + | 0.497600i | \(0.834215\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.52323e9 | 0.573310 | 0.286655 | − | 0.958034i | \(-0.407457\pi\) | ||||
0.286655 | + | 0.958034i | \(0.407457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.51974e9 | −0.313669 | ||||||||
\(143\) | 5.35708e9 | 1.07131 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.29737e9 | 0.600592 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.68925e9 | −1.14604 | ||||||||
\(149\) | −1.46531e9 | −0.243551 | −0.121775 | − | 0.992558i | \(-0.538859\pi\) | ||||
−0.121775 | + | 0.992558i | \(0.538859\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.65515e9 | 0.572149 | 0.286075 | − | 0.958207i | \(-0.407650\pi\) | ||||
0.286075 | + | 0.958207i | \(0.407650\pi\) | |||||||
\(152\) | −7.74712e9 | −1.17718 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.56811e9 | 0.224665 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.55191e9 | −0.729279 | −0.364639 | − | 0.931149i | \(-0.618808\pi\) | ||||
−0.364639 | + | 0.931149i | \(0.618808\pi\) | |||||||
\(158\) | −7.60327e8 | −0.0970607 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.25909e9 | 0.264983 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.67637e10 | 1.86006 | 0.930029 | − | 0.367485i | \(-0.119781\pi\) | ||||
0.930029 | + | 0.367485i | \(0.119781\pi\) | |||||||
\(164\) | 4.95321e9 | 0.534674 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.09365e9 | −0.214002 | ||||||||
\(167\) | 1.39549e10 | 1.38836 | 0.694182 | − | 0.719799i | \(-0.255766\pi\) | ||||
0.694182 | + | 0.719799i | \(0.255766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.83619e9 | 0.267452 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.86576e9 | −0.249668 | ||||||||
\(173\) | 1.57000e10 | 1.33258 | 0.666289 | − | 0.745694i | \(-0.267882\pi\) | ||||
0.666289 | + | 0.745694i | \(0.267882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.75999e9 | 0.609613 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.59509e8 | −0.0119095 | ||||||||
\(179\) | 2.51902e10 | 1.83397 | 0.916985 | − | 0.398921i | \(-0.130615\pi\) | ||||
0.916985 | + | 0.398921i | \(0.130615\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.04482e10 | 0.723579 | 0.361789 | − | 0.932260i | \(-0.382166\pi\) | ||||
0.361789 | + | 0.932260i | \(0.382166\pi\) | |||||||
\(182\) | 3.93434e9 | 0.265797 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.09001e9 | −0.263054 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.28657e10 | 1.36740 | ||||||||
\(188\) | 1.59305e10 | 0.930078 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.68625e9 | 0.526630 | 0.263315 | − | 0.964710i | \(-0.415184\pi\) | ||||
0.263315 | + | 0.964710i | \(0.415184\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.04431e10 | 1.06057 | 0.530285 | − | 0.847820i | \(-0.322085\pi\) | ||||
0.530285 | + | 0.847820i | \(0.322085\pi\) | |||||||
\(194\) | −1.56027e8 | −0.00790845 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00169e10 | 0.484818 | ||||||||
\(197\) | −2.52431e10 | −1.19411 | −0.597056 | − | 0.802200i | \(-0.703663\pi\) | ||||
−0.597056 | + | 0.802200i | \(0.703663\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.06736e9 | 0.364664 | 0.182332 | − | 0.983237i | \(-0.441635\pi\) | ||||
0.182332 | + | 0.983237i | \(0.441635\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.73338e9 | −0.0732506 | ||||||||
\(203\) | 1.78011e10 | 0.735723 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.98587e9 | −0.231593 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.94695e10 | 0.721223 | ||||||||
\(209\) | −4.66119e10 | −1.68981 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.04589e9 | −0.279449 | −0.139725 | − | 0.990190i | \(-0.544622\pi\) | ||||
−0.139725 | + | 0.990190i | \(0.544622\pi\) | |||||||
\(212\) | −1.78029e10 | −0.605312 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.45687e9 | −0.275643 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.42744e10 | 0.437009 | ||||||||
\(218\) | 1.99727e10 | 0.598940 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.73690e10 | 1.61775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.18618e10 | −0.862777 | −0.431388 | − | 0.902166i | \(-0.641976\pi\) | ||||
−0.431388 | + | 0.902166i | \(0.641976\pi\) | |||||||
\(224\) | 2.23793e10 | 0.593923 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.92531e9 | −0.227581 | ||||||||
\(227\) | 3.02621e10 | 0.756454 | 0.378227 | − | 0.925713i | \(-0.376534\pi\) | ||||
0.378227 | + | 0.925713i | \(0.376534\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.06101e10 | 0.495245 | 0.247623 | − | 0.968857i | \(-0.420351\pi\) | ||||
0.247623 | + | 0.968857i | \(0.420351\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.22283e10 | −0.730367 | ||||||||
\(233\) | 3.61735e9 | 0.0804061 | 0.0402031 | − | 0.999192i | \(-0.487200\pi\) | ||||
0.0402031 | + | 0.999192i | \(0.487200\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.81632e10 | −0.800830 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.67930e10 | 0.339259 | ||||||||
\(239\) | −2.21916e9 | −0.0439945 | −0.0219973 | − | 0.999758i | \(-0.507003\pi\) | ||||
−0.0219973 | + | 0.999758i | \(0.507003\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.57977e10 | 0.492611 | 0.246306 | − | 0.969192i | \(-0.420783\pi\) | ||||
0.246306 | + | 0.969192i | \(0.420783\pi\) | |||||||
\(242\) | 1.78215e9 | 0.0334022 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.04954e10 | −0.370171 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.16947e11 | −1.99919 | ||||||||
\(248\) | −2.58434e10 | −0.433828 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.91848e10 | 1.41827 | 0.709135 | − | 0.705072i | \(-0.249086\pi\) | ||||
0.709135 | + | 0.705072i | \(0.249086\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.46083e10 | −0.377606 | ||||||||
\(254\) | 2.49643e9 | 0.0376329 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.99649e9 | −0.0290527 | ||||||||
\(257\) | −1.10058e11 | −1.57371 | −0.786853 | − | 0.617141i | \(-0.788291\pi\) | ||||
−0.786853 | + | 0.617141i | \(0.788291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.33388e10 | −0.874623 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.25361e10 | −0.295476 | ||||||||
\(263\) | 2.06374e10 | 0.265983 | 0.132992 | − | 0.991117i | \(-0.457542\pi\) | ||||
0.132992 | + | 0.991117i | \(0.457542\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.42326e10 | −0.419249 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.02882e10 | −0.240235 | ||||||||
\(269\) | 2.64890e10 | 0.308446 | 0.154223 | − | 0.988036i | \(-0.450713\pi\) | ||||
0.154223 | + | 0.988036i | \(0.450713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.44004e10 | 0.387438 | 0.193719 | − | 0.981057i | \(-0.437945\pi\) | ||||
0.193719 | + | 0.981057i | \(0.437945\pi\) | |||||||
\(272\) | 8.31018e10 | 0.920556 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.72249e10 | 0.613349 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.06023e11 | 1.08203 | 0.541017 | − | 0.841012i | \(-0.318040\pi\) | ||||
0.541017 | + | 0.841012i | \(0.318040\pi\) | |||||||
\(278\) | −2.01858e10 | −0.202696 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00299e11 | −0.959662 | −0.479831 | − | 0.877361i | \(-0.659302\pi\) | ||||
−0.479831 | + | 0.877361i | \(0.659302\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.49296e9 | 0.0231035 | 0.0115517 | − | 0.999933i | \(-0.496323\pi\) | ||||
0.0115517 | + | 0.999933i | \(0.496323\pi\) | |||||||
\(284\) | −8.51054e10 | −0.776291 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.28566e10 | −0.378766 | ||||||||
\(287\) | 4.69007e10 | 0.408047 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.26281e11 | 1.06487 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.84653e11 | 1.48639 | ||||||||
\(293\) | −8.47068e10 | −0.671451 | −0.335725 | − | 0.941960i | \(-0.608981\pi\) | ||||
−0.335725 | + | 0.941960i | \(0.608981\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.14673e11 | 0.868256 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.17224e10 | 0.0861083 | ||||||||
\(299\) | −6.17411e10 | −0.446739 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.71352e10 | −0.190539 | ||||||||
\(302\) | −2.92412e10 | −0.202285 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.69404e11 | −1.13761 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.35507e9 | −0.0408317 | −0.0204159 | − | 0.999792i | \(-0.506499\pi\) | ||||
−0.0204159 | + | 0.999792i | \(0.506499\pi\) | |||||||
\(308\) | 8.78144e10 | 0.556016 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.71253e11 | −1.64419 | −0.822096 | − | 0.569350i | \(-0.807195\pi\) | ||||
−0.822096 | + | 0.569350i | \(0.807195\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.63499e11 | −0.962865 | −0.481432 | − | 0.876483i | \(-0.659883\pi\) | ||||
−0.481432 | + | 0.876483i | \(0.659883\pi\) | |||||||
\(314\) | 4.44153e10 | 0.257839 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.25783e10 | −0.240213 | ||||||||
\(317\) | 2.53606e11 | 1.41056 | 0.705282 | − | 0.708927i | \(-0.250820\pi\) | ||||
0.705282 | + | 0.708927i | \(0.250820\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.93907e11 | −1.04842 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.80728e10 | −0.0936856 | ||||||||
\(323\) | −4.99167e11 | −2.55173 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.34110e11 | −0.657630 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.49121e10 | −0.405077 | ||||||||
\(329\) | 1.50842e11 | 0.709808 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.40064e11 | −1.09926 | −0.549631 | − | 0.835408i | \(-0.685232\pi\) | ||||
−0.549631 | + | 0.835408i | \(0.685232\pi\) | |||||||
\(332\) | −1.17244e11 | −0.529628 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.11639e11 | −0.490861 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.13812e10 | 0.217005 | 0.108502 | − | 0.994096i | \(-0.465394\pi\) | ||||
0.108502 | + | 0.994096i | \(0.465394\pi\) | |||||||
\(338\) | −2.26895e10 | −0.0945585 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.55491e11 | −0.622746 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.66027e11 | 1.03777 | ||||||||
\(344\) | 4.91274e10 | 0.189152 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.25600e11 | −0.471137 | ||||||||
\(347\) | 2.76560e11 | 1.02401 | 0.512007 | − | 0.858981i | \(-0.328902\pi\) | ||||
0.512007 | + | 0.858981i | \(0.328902\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.66592e11 | 1.68354 | 0.841770 | − | 0.539837i | \(-0.181514\pi\) | ||||
0.841770 | + | 0.539837i | \(0.181514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.43777e11 | −0.846352 | ||||||||
\(353\) | −1.00998e11 | −0.346198 | −0.173099 | − | 0.984904i | \(-0.555378\pi\) | ||||
−0.173099 | + | 0.984904i | \(0.555378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.93251e9 | −0.0294746 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.01521e11 | −0.648406 | ||||||||
\(359\) | 1.66447e11 | 0.528874 | 0.264437 | − | 0.964403i | \(-0.414814\pi\) | ||||
0.264437 | + | 0.964403i | \(0.414814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.94869e11 | 2.15338 | ||||||||
\(362\) | −8.35852e10 | −0.255824 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.20323e11 | 0.657814 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.97381e11 | 0.855688 | 0.427844 | − | 0.903853i | \(-0.359273\pi\) | ||||
0.427844 | + | 0.903853i | \(0.359273\pi\) | |||||||
\(368\) | −8.94350e10 | −0.254210 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.68571e11 | −0.461956 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.95714e11 | −0.523517 | −0.261759 | − | 0.965133i | \(-0.584302\pi\) | ||||
−0.261759 | + | 0.965133i | \(0.584302\pi\) | |||||||
\(374\) | −1.82925e11 | −0.483450 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.73094e11 | −0.704640 | ||||||||
\(377\) | −4.86504e11 | −1.24037 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.67009e11 | −0.415781 | −0.207890 | − | 0.978152i | \(-0.566660\pi\) | ||||
−0.207890 | + | 0.978152i | \(0.566660\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.74900e10 | −0.186192 | ||||||||
\(383\) | 7.20782e10 | 0.171163 | 0.0855814 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855814 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.63545e11 | −0.374968 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.73750e9 | −0.0195724 | ||||||||
\(389\) | −7.92249e11 | −1.75424 | −0.877119 | − | 0.480272i | \(-0.840538\pi\) | ||||
−0.877119 | + | 0.480272i | \(0.840538\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.63530e11 | −0.570210 | ||||||||
\(392\) | −1.71717e11 | −0.367305 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.01945e11 | 0.422182 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.47288e11 | 0.297584 | 0.148792 | − | 0.988869i | \(-0.452462\pi\) | ||||
0.148792 | + | 0.988869i | \(0.452462\pi\) | |||||||
\(398\) | −6.45389e10 | −0.128928 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.22101e11 | 0.622075 | 0.311037 | − | 0.950398i | \(-0.399324\pi\) | ||||
0.311037 | + | 0.950398i | \(0.399324\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.90121e11 | −0.736761 | ||||||||
\(404\) | −9.70690e10 | −0.181286 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.42409e11 | −0.260117 | ||||||||
\(407\) | 6.89948e11 | 1.24635 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.96423e11 | −0.700493 | −0.350247 | − | 0.936658i | \(-0.613902\pi\) | ||||
−0.350247 | + | 0.936658i | \(0.613902\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.35209e11 | −0.573163 | ||||||||
\(413\) | −3.61357e11 | −0.611170 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.11627e11 | −1.00131 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.72895e11 | 0.597438 | ||||||||
\(419\) | 1.23162e12 | 1.95215 | 0.976074 | − | 0.217441i | \(-0.0697708\pi\) | ||||
0.976074 | + | 0.217441i | \(0.0697708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.17500e12 | −1.82293 | −0.911465 | − | 0.411379i | \(-0.865047\pi\) | ||||
−0.911465 | + | 0.411379i | \(0.865047\pi\) | |||||||
\(422\) | 6.43671e10 | 0.0988002 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.05192e11 | 0.458593 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.94066e11 | −0.282503 | ||||||||
\(428\) | −4.73585e11 | −0.682183 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.32327e11 | 0.324304 | 0.162152 | − | 0.986766i | \(-0.448157\pi\) | ||||
0.162152 | + | 0.986766i | \(0.448157\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.51554e11 | 0.207191 | 0.103596 | − | 0.994620i | \(-0.466965\pi\) | ||||
0.103596 | + | 0.994620i | \(0.466965\pi\) | |||||||
\(434\) | −1.14196e11 | −0.154506 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.11847e12 | 1.48230 | ||||||||
\(437\) | 5.37209e11 | 0.704655 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.21385e11 | −0.669990 | −0.334995 | − | 0.942220i | \(-0.608735\pi\) | ||||
−0.334995 | + | 0.942220i | \(0.608735\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.58952e11 | −0.571962 | ||||||||
\(443\) | 1.10169e12 | 1.35908 | 0.679539 | − | 0.733639i | \(-0.262180\pi\) | ||||
0.679539 | + | 0.733639i | \(0.262180\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.54894e11 | 0.305038 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.85706e11 | 0.217809 | ||||||||
\(449\) | −5.85672e11 | −0.680058 | −0.340029 | − | 0.940415i | \(-0.610437\pi\) | ||||
−0.340029 | + | 0.940415i | \(0.610437\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.10888e11 | −0.581475 | ||||||||
\(452\) | −4.99817e11 | −0.563233 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.42097e11 | −0.267447 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.70804e11 | 0.612159 | 0.306079 | − | 0.952006i | \(-0.400983\pi\) | ||||
0.306079 | + | 0.952006i | \(0.400983\pi\) | |||||||
\(458\) | −1.64881e11 | −0.175096 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.60279e11 | 0.784005 | 0.392002 | − | 0.919964i | \(-0.371782\pi\) | ||||
0.392002 | + | 0.919964i | \(0.371782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.14289e11 | 0.722370 | 0.361185 | − | 0.932494i | \(-0.382372\pi\) | ||||
0.361185 | + | 0.932494i | \(0.382372\pi\) | |||||||
\(464\) | −7.04725e11 | −0.705812 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.89388e10 | −0.0284279 | ||||||||
\(467\) | 7.82521e11 | 0.761325 | 0.380662 | − | 0.924714i | \(-0.375696\pi\) | ||||
0.380662 | + | 0.924714i | \(0.375696\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.92104e11 | −0.183340 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.54226e11 | 0.606720 | ||||||||
\(473\) | 2.95583e11 | 0.271522 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.40406e11 | 0.839622 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.77533e10 | 0.0155544 | ||||||||
\(479\) | 6.95738e11 | 0.603860 | 0.301930 | − | 0.953330i | \(-0.402369\pi\) | ||||
0.301930 | + | 0.953330i | \(0.402369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.73105e12 | 1.47454 | ||||||||
\(482\) | −2.06382e11 | −0.174164 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.98003e10 | 0.0826661 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.65196e12 | 1.33082 | 0.665408 | − | 0.746480i | \(-0.268258\pi\) | ||||
0.665408 | + | 0.746480i | \(0.268258\pi\) | |||||||
\(488\) | 3.51350e11 | 0.280447 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.19989e12 | −0.931694 | −0.465847 | − | 0.884865i | \(-0.654250\pi\) | ||||
−0.465847 | + | 0.884865i | \(0.654250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.07655e12 | −1.58318 | ||||||||
\(494\) | 9.35578e11 | 0.706820 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.65109e11 | −0.419242 | ||||||||
\(497\) | −8.05842e11 | −0.592442 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.43146e12 | 1.03354 | 0.516768 | − | 0.856125i | \(-0.327135\pi\) | ||||
0.516768 | + | 0.856125i | \(0.327135\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.13478e11 | −0.501434 | ||||||||
\(503\) | 1.41833e12 | 0.987919 | 0.493959 | − | 0.869485i | \(-0.335549\pi\) | ||||
0.493959 | + | 0.869485i | \(0.335549\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.96866e11 | 0.133504 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.39800e11 | 0.0931367 | ||||||||
\(509\) | 1.16463e12 | 0.769059 | 0.384529 | − | 0.923113i | \(-0.374364\pi\) | ||||
0.384529 | + | 0.923113i | \(0.374364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.74843e12 | 1.13437 | ||||||||
\(512\) | −1.54632e12 | −0.994455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.80466e11 | 0.556389 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.64312e12 | −1.01149 | ||||||||
\(518\) | 5.06711e11 | 0.309226 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.36946e11 | 0.497654 | 0.248827 | − | 0.968548i | \(-0.419955\pi\) | ||||
0.248827 | + | 0.968548i | \(0.419955\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.60288e12 | 1.52124 | 0.760618 | − | 0.649199i | \(-0.224896\pi\) | ||||
0.760618 | + | 0.649199i | \(0.224896\pi\) | |||||||
\(524\) | −1.26202e12 | −0.731267 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.65099e11 | −0.0940394 | ||||||||
\(527\) | −1.66516e12 | −0.940389 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.51754e12 | −0.842538 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.91703e12 | −1.03759 | ||||||||
\(533\) | −1.28180e12 | −0.687934 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.47798e11 | 0.182006 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.11912e11 | −0.109052 | ||||||||
\(539\) | −1.03317e12 | −0.527255 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.07406e12 | 1.54286 | 0.771428 | − | 0.636317i | \(-0.219543\pi\) | ||||
0.771428 | + | 0.636317i | \(0.219543\pi\) | |||||||
\(542\) | −2.75203e11 | −0.136980 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.61061e12 | −1.27805 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.32972e12 | −0.635062 | −0.317531 | − | 0.948248i | \(-0.602854\pi\) | ||||
−0.317531 | + | 0.948248i | \(0.602854\pi\) | |||||||
\(548\) | 3.20460e12 | 1.51796 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.23307e12 | 1.95647 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.03163e11 | −0.183323 | ||||||||
\(554\) | −8.48183e11 | −0.382557 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.13041e12 | −0.501647 | ||||||||
\(557\) | 2.49418e12 | 1.09794 | 0.548971 | − | 0.835841i | \(-0.315020\pi\) | ||||
0.548971 | + | 0.835841i | \(0.315020\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.41606e11 | 0.321233 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.02392e11 | 0.339292 | ||||||||
\(563\) | 1.06689e12 | 0.447541 | 0.223770 | − | 0.974642i | \(-0.428163\pi\) | ||||
0.223770 | + | 0.974642i | \(0.428163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.99437e10 | −0.00816831 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.45895e12 | 0.588129 | ||||||||
\(569\) | 4.57278e12 | 1.82884 | 0.914420 | − | 0.404768i | \(-0.132648\pi\) | ||||
0.914420 | + | 0.404768i | \(0.132648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.32305e12 | −0.914525 | −0.457263 | − | 0.889332i | \(-0.651170\pi\) | ||||
−0.457263 | + | 0.889332i | \(0.651170\pi\) | |||||||
\(572\) | −2.39997e12 | −0.937398 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.75205e11 | −0.144266 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.01144e12 | −0.379881 | −0.189940 | − | 0.981796i | \(-0.560829\pi\) | ||||
−0.189940 | + | 0.981796i | \(0.560829\pi\) | |||||||
\(578\) | −1.01025e12 | −0.376489 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.11016e12 | −0.404196 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.83624e12 | 0.658296 | ||||||||
\(584\) | −3.16547e12 | −1.12611 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.77654e11 | 0.237394 | ||||||||
\(587\) | −1.10143e12 | −0.382899 | −0.191449 | − | 0.981502i | \(-0.561319\pi\) | ||||
−0.191449 | + | 0.981502i | \(0.561319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.39444e12 | 1.16211 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.50751e12 | 0.839065 | ||||||||
\(593\) | 9.84366e11 | 0.326897 | 0.163448 | − | 0.986552i | \(-0.447738\pi\) | ||||
0.163448 | + | 0.986552i | \(0.447738\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.56457e11 | 0.213107 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.93929e11 | 0.157946 | ||||||||
\(599\) | −4.51397e12 | −1.43264 | −0.716321 | − | 0.697771i | \(-0.754175\pi\) | ||||
−0.716321 | + | 0.697771i | \(0.754175\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.44212e12 | −0.450885 | −0.225443 | − | 0.974256i | \(-0.572383\pi\) | ||||
−0.225443 | + | 0.974256i | \(0.572383\pi\) | |||||||
\(602\) | 2.17082e11 | 0.0673657 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.63751e12 | −0.500630 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.12105e12 | 1.23214 | 0.616069 | − | 0.787692i | \(-0.288724\pi\) | ||||
0.616069 | + | 0.787692i | \(0.288724\pi\) | |||||||
\(608\) | 5.32176e12 | 1.57939 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.12252e12 | −1.19668 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.38470e12 | −0.396080 | −0.198040 | − | 0.980194i | \(-0.563458\pi\) | ||||
−0.198040 | + | 0.980194i | \(0.563458\pi\) | |||||||
\(614\) | 5.08406e10 | 0.0144362 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.50539e12 | −0.421246 | ||||||||
\(617\) | 6.22714e11 | 0.172984 | 0.0864918 | − | 0.996253i | \(-0.472434\pi\) | ||||
0.0864918 | + | 0.996253i | \(0.472434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.89438e12 | 0.518631 | 0.259315 | − | 0.965793i | \(-0.416503\pi\) | ||||
0.259315 | + | 0.965793i | \(0.416503\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.17002e12 | 0.581309 | ||||||||
\(623\) | −8.45797e10 | −0.0224942 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.30799e12 | 0.340424 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.48725e12 | 0.638119 | ||||||||
\(629\) | 7.38866e12 | 1.88208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.10160e12 | −0.276624 | −0.138312 | − | 0.990389i | \(-0.544168\pi\) | ||||
−0.138312 | + | 0.990389i | \(0.544168\pi\) | |||||||
\(632\) | 7.29914e11 | 0.181989 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.02885e12 | −0.498710 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.59217e12 | −0.623787 | ||||||||
\(638\) | 1.55125e12 | 0.370672 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.85252e12 | 1.13529 | 0.567644 | − | 0.823274i | \(-0.307855\pi\) | ||||
0.567644 | + | 0.823274i | \(0.307855\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.57487e12 | −0.363325 | −0.181662 | − | 0.983361i | \(-0.558148\pi\) | ||||
−0.181662 | + | 0.983361i | \(0.558148\pi\) | |||||||
\(644\) | −1.01207e12 | −0.231860 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.99334e12 | 0.902172 | ||||||||
\(647\) | 6.93025e12 | 1.55482 | 0.777410 | − | 0.628995i | \(-0.216533\pi\) | ||||
0.777410 | + | 0.628995i | \(0.216533\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.93626e12 | 0.870928 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.51015e12 | −1.62755 | ||||||||
\(653\) | −8.15499e12 | −1.75515 | −0.877575 | − | 0.479440i | \(-0.840840\pi\) | ||||
−0.877575 | + | 0.479440i | \(0.840840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.85674e12 | −0.391458 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.20674e12 | −0.250955 | ||||||||
\(659\) | 2.92553e12 | 0.604255 | 0.302127 | − | 0.953268i | \(-0.402303\pi\) | ||||
0.302127 | + | 0.953268i | \(0.402303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.62921e12 | −0.331947 | −0.165974 | − | 0.986130i | \(-0.553077\pi\) | ||||
−0.165974 | + | 0.986130i | \(0.553077\pi\) | |||||||
\(662\) | 1.92051e12 | 0.388648 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.00990e12 | 0.401254 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.23480e12 | 0.437193 | ||||||||
\(668\) | −6.25181e12 | −1.21482 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.11395e12 | 0.402572 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.87521e12 | 0.540258 | 0.270129 | − | 0.962824i | \(-0.412934\pi\) | ||||
0.270129 | + | 0.962824i | \(0.412934\pi\) | |||||||
\(674\) | −4.11049e11 | −0.0767228 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.27061e12 | −0.234020 | ||||||||
\(677\) | 3.19620e12 | 0.584769 | 0.292385 | − | 0.956301i | \(-0.405551\pi\) | ||||
0.292385 | + | 0.956301i | \(0.405551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.27332e10 | −0.0149371 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.24393e12 | 0.220174 | ||||||||
\(683\) | −5.47901e11 | −0.0963406 | −0.0481703 | − | 0.998839i | \(-0.515339\pi\) | ||||
−0.0481703 | + | 0.998839i | \(0.515339\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.12822e12 | −0.366908 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.07425e12 | 0.182792 | ||||||||
\(689\) | 4.60705e12 | 0.778819 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.90996e11 | 0.0986128 | 0.0493064 | − | 0.998784i | \(-0.484299\pi\) | ||||
0.0493064 | + | 0.998784i | \(0.484299\pi\) | |||||||
\(692\) | −7.03361e12 | −1.16601 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.21248e12 | −0.362044 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.47110e12 | −0.878066 | ||||||||
\(698\) | −3.73274e12 | −0.595221 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.12738e12 | −1.11481 | −0.557403 | − | 0.830242i | \(-0.688202\pi\) | ||||
−0.557403 | + | 0.830242i | \(0.688202\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.50619e13 | −2.32584 | ||||||||
\(704\) | −2.02290e12 | −0.310382 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.07981e11 | 0.122400 | ||||||||
\(707\) | −9.19122e11 | −0.138352 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.09269e11 | 0.135140 | 0.0675701 | − | 0.997715i | \(-0.478475\pi\) | ||||
0.0675701 | + | 0.997715i | \(0.478475\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.53129e11 | 0.0223304 | ||||||||
\(713\) | 1.79206e12 | 0.259687 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.12852e13 | −1.60472 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.33158e12 | −0.186985 | ||||||||
\(719\) | −1.08017e13 | −1.50734 | −0.753669 | − | 0.657254i | \(-0.771718\pi\) | ||||
−0.753669 | + | 0.657254i | \(0.771718\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.17401e12 | −0.437421 | ||||||||
\(722\) | −5.55895e12 | −0.761334 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.68077e12 | −0.633132 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.77691e12 | 1.29807 | 0.649033 | − | 0.760760i | \(-0.275174\pi\) | ||||
0.649033 | + | 0.760760i | \(0.275174\pi\) | |||||||
\(728\) | −3.77696e12 | −0.498370 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.16540e12 | 0.410016 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.52295e11 | −0.0450753 | −0.0225377 | − | 0.999746i | \(-0.507175\pi\) | ||||
−0.0225377 | + | 0.999746i | \(0.507175\pi\) | |||||||
\(734\) | −2.37905e12 | −0.302531 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.80957e12 | 0.352931 | ||||||||
\(737\) | 2.09258e12 | 0.261264 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.72124e12 | −0.335635 | −0.167818 | − | 0.985818i | \(-0.553672\pi\) | ||||
−0.167818 | + | 0.985818i | \(0.553672\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.34857e12 | 0.163326 | ||||||||
\(743\) | −5.85311e12 | −0.704590 | −0.352295 | − | 0.935889i | \(-0.614599\pi\) | ||||
−0.352295 | + | 0.935889i | \(0.614599\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.56571e12 | 0.185091 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.02438e13 | −1.19648 | ||||||||
\(749\) | −4.48426e12 | −0.520622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.13723e12 | −0.589317 | −0.294659 | − | 0.955603i | \(-0.595206\pi\) | ||||
−0.294659 | + | 0.955603i | \(0.595206\pi\) | |||||||
\(752\) | −5.97166e12 | −0.680950 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.89203e12 | 0.438536 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.45713e13 | 1.61275 | 0.806373 | − | 0.591407i | \(-0.201427\pi\) | ||||
0.806373 | + | 0.591407i | \(0.201427\pi\) | |||||||
\(758\) | 1.33607e12 | 0.147001 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.03936e13 | −1.12340 | −0.561700 | − | 0.827341i | \(-0.689852\pi\) | ||||
−0.561700 | + | 0.827341i | \(0.689852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.05905e13 | 1.13125 | ||||||||
\(764\) | −4.33944e12 | −0.460801 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.76626e11 | −0.0605152 | ||||||||
\(767\) | 9.87591e12 | 1.03038 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.91664e12 | −0.403873 | −0.201936 | − | 0.979399i | \(-0.564723\pi\) | ||||
−0.201936 | + | 0.979399i | \(0.564723\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.15851e12 | −0.927998 | ||||||||
\(773\) | −6.36894e12 | −0.641592 | −0.320796 | − | 0.947148i | \(-0.603950\pi\) | ||||
−0.320796 | + | 0.947148i | \(0.603950\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.49786e11 | 0.0148284 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.33800e12 | 0.620217 | ||||||||
\(779\) | 1.11529e13 | 1.08510 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.77802e12 | 0.844242 | ||||||||
\(782\) | 2.10824e12 | 0.201600 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.75489e12 | −0.354956 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.55343e11 | −0.0608951 | −0.0304475 | − | 0.999536i | \(-0.509693\pi\) | ||||
−0.0304475 | + | 0.999536i | \(0.509693\pi\) | |||||||
\(788\) | 1.13089e13 | 1.04485 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.73265e12 | −0.429843 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.30382e12 | 0.476277 | ||||||||
\(794\) | −1.17830e12 | −0.105212 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.61418e12 | −0.319081 | ||||||||
\(797\) | 3.83799e12 | 0.336931 | 0.168466 | − | 0.985708i | \(-0.446119\pi\) | ||||
0.168466 | + | 0.985708i | \(0.446119\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.75962e13 | −1.52742 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.57681e12 | −0.219937 | ||||||||
\(803\) | −1.90456e13 | −1.61650 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.12097e12 | 0.260484 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.66404e12 | 0.137345 | ||||||||
\(809\) | −2.67581e12 | −0.219627 | −0.109814 | − | 0.993952i | \(-0.535025\pi\) | ||||
−0.109814 | + | 0.993952i | \(0.535025\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.32586e13 | −1.88795 | −0.943973 | − | 0.330023i | \(-0.892943\pi\) | ||||
−0.943973 | + | 0.330023i | \(0.892943\pi\) | |||||||
\(812\) | −7.97489e12 | −0.643758 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.51959e12 | −0.440653 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.45270e12 | −0.506690 | ||||||||
\(818\) | 3.17138e12 | 0.247662 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.65740e13 | −1.27316 | −0.636580 | − | 0.771211i | \(-0.719651\pi\) | ||||
−0.636580 | + | 0.771211i | \(0.719651\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.37332e13 | −1.04345 | −0.521726 | − | 0.853113i | \(-0.674712\pi\) | ||||
−0.521726 | + | 0.853113i | \(0.674712\pi\) | |||||||
\(824\) | 5.74644e12 | 0.434236 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.89086e12 | 0.216081 | ||||||||
\(827\) | 1.80036e13 | 1.33840 | 0.669198 | − | 0.743085i | \(-0.266638\pi\) | ||||
0.669198 | + | 0.743085i | \(0.266638\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.11116e13 | 1.55248 | 0.776240 | − | 0.630438i | \(-0.217125\pi\) | ||||
0.776240 | + | 0.630438i | \(0.217125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.07536e12 | −0.367208 | ||||||||
\(833\) | −1.10642e13 | −0.796191 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.08821e13 | 1.47858 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.85294e12 | −0.690188 | ||||||||
\(839\) | 3.47988e12 | 0.242458 | 0.121229 | − | 0.992625i | \(-0.461317\pi\) | ||||
0.121229 | + | 0.992625i | \(0.461317\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.10254e12 | 0.213863 | ||||||||
\(842\) | 9.40003e12 | 0.644503 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.60456e12 | 0.244518 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.44984e11 | 0.0630883 | ||||||||
\(848\) | 6.67354e12 | 0.443175 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.95175e12 | −0.519733 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.12686e13 | −0.728784 | −0.364392 | − | 0.931246i | \(-0.618723\pi\) | ||||
−0.364392 | + | 0.931246i | \(0.618723\pi\) | |||||||
\(854\) | 1.55253e12 | 0.0998800 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.11860e12 | 0.516832 | ||||||||
\(857\) | 3.75227e12 | 0.237618 | 0.118809 | − | 0.992917i | \(-0.462092\pi\) | ||||
0.118809 | + | 0.992917i | \(0.462092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.57014e13 | 0.983944 | 0.491972 | − | 0.870611i | \(-0.336276\pi\) | ||||
0.491972 | + | 0.870611i | \(0.336276\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.85862e12 | −0.114659 | ||||||||
\(863\) | −1.39316e13 | −0.854975 | −0.427487 | − | 0.904021i | \(-0.640601\pi\) | ||||
−0.427487 | + | 0.904021i | \(0.640601\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.21243e12 | −0.0732531 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.39495e12 | −0.382383 | ||||||||
\(869\) | 4.39165e12 | 0.261239 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.25021e12 | 0.309097 | ||||||||
\(872\) | −1.91738e13 | −1.12301 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.29767e12 | −0.249133 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.59832e13 | 0.912357 | 0.456179 | − | 0.889888i | \(-0.349218\pi\) | ||||
0.456179 | + | 0.889888i | \(0.349218\pi\) | |||||||
\(878\) | 4.17108e12 | 0.236877 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.16227e13 | 1.76851 | 0.884255 | − | 0.467005i | \(-0.154667\pi\) | ||||
0.884255 | + | 0.467005i | \(0.154667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.48526e13 | 0.822202 | 0.411101 | − | 0.911590i | \(-0.365144\pi\) | ||||
0.411101 | + | 0.911590i | \(0.365144\pi\) | |||||||
\(884\) | −2.57013e13 | −1.41553 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.81356e12 | −0.480507 | ||||||||
\(887\) | −9.39325e12 | −0.509518 | −0.254759 | − | 0.967005i | \(-0.581996\pi\) | ||||
−0.254759 | + | 0.967005i | \(0.581996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.32373e12 | 0.0710792 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.42741e13 | 0.754930 | ||||||||
\(893\) | 3.58699e13 | 1.88755 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.29439e13 | −0.670930 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.68538e12 | 0.240437 | ||||||||
\(899\) | 1.41210e13 | 0.721018 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.96643e13 | 0.994071 | ||||||||
\(902\) | 4.08710e12 | 0.205582 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.56830e12 | 0.426714 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.64429e13 | −1.29741 | −0.648704 | − | 0.761041i | \(-0.724689\pi\) | ||||
−0.648704 | + | 0.761041i | \(0.724689\pi\) | |||||||
\(908\) | −1.35574e13 | −0.661898 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.41645e13 | 1.64339 | 0.821697 | − | 0.569924i | \(-0.193028\pi\) | ||||
0.821697 | + | 0.569924i | \(0.193028\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.20929e13 | 0.575987 | ||||||||
\(914\) | −4.56643e12 | −0.216431 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.23333e12 | −0.433340 | ||||||||
\(917\) | −1.19498e13 | −0.558081 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.14366e13 | 1.45384 | 0.726920 | − | 0.686723i | \(-0.240951\pi\) | ||||
0.726920 | + | 0.686723i | \(0.240951\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.08223e12 | −0.277188 | ||||||||
\(923\) | 2.20237e13 | 0.998809 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.71431e12 | −0.255396 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.21387e13 | 0.979909 | ||||||||
\(929\) | 8.77007e12 | 0.386307 | 0.193153 | − | 0.981169i | \(-0.438128\pi\) | ||||
0.193153 | + | 0.981169i | \(0.438128\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.25545e13 | 0.983918 | ||||||||
\(932\) | −1.62057e12 | −0.0703553 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.26017e12 | −0.269169 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.66294e13 | 0.704770 | 0.352385 | − | 0.935855i | \(-0.385371\pi\) | ||||
0.352385 | + | 0.935855i | \(0.385371\pi\) | |||||||
\(938\) | 1.53683e12 | 0.0648206 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.56052e12 | 0.314339 | 0.157169 | − | 0.987572i | \(-0.449763\pi\) | ||||
0.157169 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.88806e12 | 0.242476 | ||||||||
\(944\) | 1.43057e13 | 0.586322 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.36466e12 | −0.0959974 | ||||||||
\(947\) | 3.40925e13 | 1.37747 | 0.688737 | − | 0.725011i | \(-0.258165\pi\) | ||||
0.688737 | + | 0.725011i | \(0.258165\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.77846e13 | −1.91245 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.61212e13 | −0.636110 | ||||||||
\(953\) | 3.45885e13 | 1.35836 | 0.679178 | − | 0.733973i | \(-0.262336\pi\) | ||||
0.679178 | + | 0.733973i | \(0.262336\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.94185e11 | 0.0384952 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.56591e12 | −0.213497 | ||||||||
\(959\) | 3.03435e13 | 1.15846 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.51162e13 | −0.571726 | ||||||||
\(962\) | −1.38484e13 | −0.521329 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.15574e13 | −0.431035 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.59891e13 | −1.69136 | −0.845680 | − | 0.533691i | \(-0.820805\pi\) | ||||
−0.845680 | + | 0.533691i | \(0.820805\pi\) | |||||||
\(968\) | −1.71086e12 | −0.0626290 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.72663e13 | −0.984327 | −0.492164 | − | 0.870503i | \(-0.663794\pi\) | ||||
−0.492164 | + | 0.870503i | \(0.663794\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.07035e13 | −0.382842 | ||||||||
\(974\) | −1.32156e13 | −0.470515 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.68284e12 | 0.271018 | ||||||||
\(977\) | −4.92228e13 | −1.72839 | −0.864193 | − | 0.503160i | \(-0.832171\pi\) | ||||
−0.864193 | + | 0.503160i | \(0.832171\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.21324e11 | 0.0320546 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.59909e12 | 0.329404 | ||||||||
\(983\) | 3.98337e13 | 1.36069 | 0.680346 | − | 0.732891i | \(-0.261830\pi\) | ||||
0.680346 | + | 0.732891i | \(0.261830\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.66124e13 | 0.559740 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.23924e13 | 1.74929 | ||||||||
\(989\) | −3.40664e12 | −0.113225 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.56388e13 | −0.844434 | −0.422217 | − | 0.906495i | \(-0.638748\pi\) | ||||
−0.422217 | + | 0.906495i | \(0.638748\pi\) | |||||||
\(992\) | 1.77527e13 | 0.582052 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.44674e12 | 0.209460 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.97241e13 | 1.59382 | 0.796909 | − | 0.604099i | \(-0.206467\pi\) | ||||
0.796909 | + | 0.604099i | \(0.206467\pi\) | |||||||
\(998\) | −1.14517e13 | −0.365410 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.10.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 25.10.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 225.10.b.d.199.1 | 2 | |||
5.3 | odd | 4 | 225.10.b.d.199.2 | 2 | |||
5.4 | even | 2 | 45.10.a.c.1.1 | 1 | |||
12.11 | even | 2 | 400.10.a.c.1.1 | 1 | |||
15.2 | even | 4 | 25.10.b.a.24.2 | 2 | |||
15.8 | even | 4 | 25.10.b.a.24.1 | 2 | |||
15.14 | odd | 2 | 5.10.a.a.1.1 | ✓ | 1 | ||
60.23 | odd | 4 | 400.10.c.e.49.1 | 2 | |||
60.47 | odd | 4 | 400.10.c.e.49.2 | 2 | |||
60.59 | even | 2 | 80.10.a.d.1.1 | 1 | |||
105.104 | even | 2 | 245.10.a.a.1.1 | 1 | |||
120.29 | odd | 2 | 320.10.a.h.1.1 | 1 | |||
120.59 | even | 2 | 320.10.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.10.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
25.10.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
25.10.b.a.24.1 | 2 | 15.8 | even | 4 | |||
25.10.b.a.24.2 | 2 | 15.2 | even | 4 | |||
45.10.a.c.1.1 | 1 | 5.4 | even | 2 | |||
80.10.a.d.1.1 | 1 | 60.59 | even | 2 | |||
225.10.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.10.b.d.199.1 | 2 | 5.2 | odd | 4 | |||
225.10.b.d.199.2 | 2 | 5.3 | odd | 4 | |||
245.10.a.a.1.1 | 1 | 105.104 | even | 2 | |||
320.10.a.c.1.1 | 1 | 120.59 | even | 2 | |||
320.10.a.h.1.1 | 1 | 120.29 | odd | 2 | |||
400.10.a.c.1.1 | 1 | 12.11 | even | 2 | |||
400.10.c.e.49.1 | 2 | 60.23 | odd | 4 | |||
400.10.c.e.49.2 | 2 | 60.47 | odd | 4 |