Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,12,Mod(1,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.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: | \(9.22011816672\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 12.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9990.00 | 1.42965 | 0.714826 | − | 0.699302i | \(-0.246506\pi\) | ||||
0.714826 | + | 0.699302i | \(0.246506\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −86128.0 | −1.93689 | −0.968445 | − | 0.249226i | \(-0.919824\pi\) | ||||
−0.968445 | + | 0.249226i | \(0.919824\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −806004. | −1.50896 | −0.754479 | − | 0.656324i | \(-0.772111\pi\) | ||||
−0.754479 | + | 0.656324i | \(0.772111\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −960250. | −0.717292 | −0.358646 | − | 0.933474i | \(-0.616761\pi\) | ||||
−0.358646 | + | 0.933474i | \(0.616761\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.42757e6 | −0.825410 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.30688e6 | −0.735688 | −0.367844 | − | 0.929888i | \(-0.619904\pi\) | ||||
−0.367844 | + | 0.929888i | \(0.619904\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 401300. | 0.0371813 | 0.0185906 | − | 0.999827i | \(-0.494082\pi\) | ||||
0.0185906 | + | 0.999827i | \(0.494082\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.09291e7 | 1.11826 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.77515e7 | 0.575086 | 0.287543 | − | 0.957768i | \(-0.407162\pi\) | ||||
0.287543 | + | 0.957768i | \(0.407162\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.09720e7 | 1.04391 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.47050e7 | −0.766867 | −0.383433 | − | 0.923568i | \(-0.625258\pi\) | ||||
−0.383433 | + | 0.923568i | \(0.625258\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.40931e8 | 0.884129 | 0.442065 | − | 0.896983i | \(-0.354246\pi\) | ||||
0.442065 | + | 0.896983i | \(0.354246\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.95859e8 | 0.871198 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.60419e8 | −2.76908 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.13507e8 | −0.980331 | −0.490166 | − | 0.871629i | \(-0.663064\pi\) | ||||
−0.490166 | + | 0.871629i | \(0.663064\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.33341e8 | 0.414129 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50095e8 | 0.202327 | 0.101164 | − | 0.994870i | \(-0.467743\pi\) | ||||
0.101164 | + | 0.994870i | \(0.467743\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.06702e8 | 0.733094 | 0.366547 | − | 0.930399i | \(-0.380540\pi\) | ||||
0.366547 | + | 0.930399i | \(0.380540\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.89900e8 | 0.476551 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.47573e9 | −1.57458 | −0.787289 | − | 0.616584i | \(-0.788516\pi\) | ||||
−0.787289 | + | 0.616584i | \(0.788516\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.44071e9 | 2.75155 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.04657e9 | 0.424749 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.60012e9 | 0.525577 | 0.262789 | − | 0.964853i | \(-0.415358\pi\) | ||||
0.262789 | + | 0.964853i | \(0.415358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.05198e9 | −2.15729 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.75159e7 | −0.0214666 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.94549e9 | 0.718481 | 0.359240 | − | 0.933245i | \(-0.383036\pi\) | ||||
0.359240 | + | 0.933245i | \(0.383036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.85973e8 | −0.134309 | −0.0671547 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671547 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.08577e9 | −0.645630 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.59290e9 | −1.02548 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.88160e9 | −0.441724 | −0.220862 | − | 0.975305i | \(-0.570887\pi\) | ||||
−0.220862 | + | 0.975305i | \(0.570887\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.31362e9 | −0.332026 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.26315e10 | 0.830870 | 0.415435 | − | 0.909623i | \(-0.363629\pi\) | ||||
0.415435 | + | 0.909623i | \(0.363629\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.42334e9 | 0.0803584 | 0.0401792 | − | 0.999192i | \(-0.487207\pi\) | ||||
0.0401792 | + | 0.999192i | \(0.487207\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.23862e10 | −0.602699 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.94195e10 | 2.92269 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.67408e8 | 0.0244029 | 0.0122015 | − | 0.999926i | \(-0.496116\pi\) | ||||
0.0122015 | + | 0.999926i | \(0.496116\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.71607e9 | 0.159283 | 0.0796413 | − | 0.996824i | \(-0.474623\pi\) | ||||
0.0796413 | + | 0.996824i | \(0.474623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.30257e10 | −1.05178 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.05833e10 | 0.442751 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.57387e10 | −1.62754 | −0.813771 | − | 0.581186i | \(-0.802589\pi\) | ||||
−0.813771 | + | 0.581186i | \(0.802589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.27044e10 | 1.38932 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.42461e10 | −0.510452 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00899e9 | 0.0531563 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.23026e10 | −0.618414 | −0.309207 | − | 0.950995i | \(-0.600064\pi\) | ||||
−0.309207 | + | 0.950995i | \(0.600064\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.75937e10 | −0.502986 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.61154e11 | −1.52572 | −0.762859 | − | 0.646564i | \(-0.776205\pi\) | ||||
−0.762859 | + | 0.646564i | \(0.776205\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.77986e10 | −0.576257 | −0.288128 | − | 0.957592i | \(-0.593033\pi\) | ||||
−0.288128 | + | 0.957592i | \(0.593033\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.09082e11 | 1.59873 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.55967e10 | 0.589992 | 0.294996 | − | 0.955498i | \(-0.404682\pi\) | ||||
0.294996 | + | 0.955498i | \(0.404682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.82523e11 | 1.13624 | 0.568122 | − | 0.822945i | \(-0.307670\pi\) | ||||
0.568122 | + | 0.822945i | \(0.307670\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.00482e11 | 0.565995 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.44055e11 | −1.75669 | −0.878347 | − | 0.478024i | \(-0.841353\pi\) | ||||
−0.878347 | + | 0.478024i | \(0.841353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.77338e11 | 0.822173 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.67018e10 | −0.239097 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.70943e11 | 1.42495 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.64331e11 | 1.27696 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.64731e10 | −0.116814 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.14171e10 | 0.0627704 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.89240e11 | −1.85119 | −0.925593 | − | 0.378521i | \(-0.876433\pi\) | ||||
−0.925593 | + | 0.378521i | \(0.876433\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.71729e11 | −0.423252 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.30533e11 | −1.42796 | −0.713979 | − | 0.700167i | \(-0.753109\pi\) | ||||
−0.713979 | + | 0.700167i | \(0.753109\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.45632e10 | −0.0720161 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.43346e11 | −0.275137 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.98781e11 | 0.705946 | 0.352973 | − | 0.935634i | \(-0.385171\pi\) | ||||
0.352973 | + | 0.935634i | \(0.385171\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.20521e11 | −0.687395 | −0.343697 | − | 0.939080i | \(-0.611679\pi\) | ||||
−0.343697 | + | 0.939080i | \(0.611679\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.01601e11 | 0.909083 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.73965e11 | 1.08236 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.46203e11 | −1.09635 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.32209e12 | −1.58861 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.37126e11 | 1.04538 | 0.522689 | − | 0.852523i | \(-0.324929\pi\) | ||||
0.522689 | + | 0.852523i | \(0.324929\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.26258e11 | 0.338212 | 0.169106 | − | 0.985598i | \(-0.445912\pi\) | ||||
0.169106 | + | 0.985598i | \(0.445912\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.54317e11 | −0.245229 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.40790e12 | 1.26400 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.13610e12 | 1.78720 | 0.893601 | − | 0.448863i | \(-0.148171\pi\) | ||||
0.893601 | + | 0.448863i | \(0.148171\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.88830e11 | −0.303442 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.52890e12 | −1.11388 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.90837e10 | −0.0538338 | −0.0269169 | − | 0.999638i | \(-0.508569\pi\) | ||||
−0.0269169 | + | 0.999638i | \(0.508569\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.95663e12 | 1.24551 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.56078e12 | 0.929824 | 0.464912 | − | 0.885357i | \(-0.346086\pi\) | ||||
0.464912 | + | 0.885357i | \(0.346086\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.70080e11 | −0.485492 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.36964e10 | 0.0123938 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.15093e12 | −1.54591 | −0.772956 | − | 0.634460i | \(-0.781222\pi\) | ||||
−0.772956 | + | 0.634460i | \(0.781222\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.39011e12 | −2.02193 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.58755e11 | −0.414815 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.59872e11 | 0.187045 | 0.0935223 | − | 0.995617i | \(-0.470187\pi\) | ||||
0.0935223 | + | 0.995617i | \(0.470187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.50019e12 | 0.956623 | 0.478311 | − | 0.878190i | \(-0.341249\pi\) | ||||
0.478311 | + | 0.878190i | \(0.341249\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.15292e11 | 0.0775436 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.13093e12 | −1.40153 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.47136e12 | 1.11012 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.23584e12 | 0.372755 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.25760e12 | −1.21194 | −0.605970 | − | 0.795487i | \(-0.707215\pi\) | ||||
−0.605970 | + | 0.795487i | \(0.707215\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.32441e10 | −0.0250643 | −0.0125322 | − | 0.999921i | \(-0.503989\pi\) | ||||
−0.0125322 | + | 0.999921i | \(0.503989\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.33107e12 | 0.592060 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.24661e12 | −0.539466 | −0.269733 | − | 0.962935i | \(-0.586935\pi\) | ||||
−0.269733 | + | 0.962935i | \(0.586935\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.18786e12 | 1.40556 | 0.702779 | − | 0.711408i | \(-0.251942\pi\) | ||||
0.702779 | + | 0.711408i | \(0.251942\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.18623e12 | 0.255029 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.29547e12 | 1.48534 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.49945e12 | 0.289258 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.04821e12 | 0.191695 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.23449e11 | −0.0561050 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.04749e12 | −0.830849 | −0.415425 | − | 0.909628i | \(-0.636367\pi\) | ||||
−0.415425 | + | 0.909628i | \(0.636367\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.06945e12 | −0.479703 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.05995e12 | 1.04807 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.21381e13 | −1.71246 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.45870e11 | −0.0463950 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.13568e12 | 0.527703 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.12235e12 | 0.864862 | 0.432431 | − | 0.901667i | \(-0.357656\pi\) | ||||
0.432431 | + | 0.901667i | \(0.357656\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00984e12 | 0.347969 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.82409e12 | −0.971690 | −0.485845 | − | 0.874045i | \(-0.661488\pi\) | ||||
−0.485845 | + | 0.874045i | \(0.661488\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.22311e13 | 1.28343 | 0.641713 | − | 0.766945i | \(-0.278224\pi\) | ||||
0.641713 | + | 0.766945i | \(0.278224\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.68689e13 | −1.68742 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.26728e13 | −1.20897 | −0.604485 | − | 0.796616i | \(-0.706621\pi\) | ||||
−0.604485 | + | 0.796616i | \(0.706621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.47325e13 | −2.25110 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.62180e11 | −0.0140890 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.39071e11 | 0.0696002 | 0.0348001 | − | 0.999394i | \(-0.488921\pi\) | ||||
0.0348001 | + | 0.999394i | \(0.488921\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.50963e12 | −0.357312 | −0.178656 | − | 0.983912i | \(-0.557175\pi\) | ||||
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.43526e13 | 3.93375 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.85348e11 | −0.0266698 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.38901e12 | −0.0919618 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.93358e12 | 0.629362 | 0.314681 | − | 0.949197i | \(-0.398102\pi\) | ||||
0.314681 | + | 0.949197i | \(0.398102\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.43078e13 | −0.867781 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.04552e13 | 0.607244 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.23707e13 | −0.688277 | −0.344139 | − | 0.938919i | \(-0.611829\pi\) | ||||
−0.344139 | + | 0.938919i | \(0.611829\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.56145e13 | 1.89880 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00175e12 | −0.255622 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.12644e13 | −1.53212 | −0.766061 | − | 0.642768i | \(-0.777786\pi\) | ||||
−0.766061 | + | 0.642768i | \(0.777786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.59852e13 | 0.751393 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.08345e13 | 0.939661 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.65927e13 | 0.718256 | 0.359128 | − | 0.933288i | \(-0.383074\pi\) | ||||
0.359128 | + | 0.933288i | \(0.383074\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.74246e12 | −0.404890 | −0.202445 | − | 0.979294i | \(-0.564889\pi\) | ||||
−0.202445 | + | 0.979294i | \(0.564889\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00972e13 | −0.802122 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.10836e13 | −1.57521 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.96465e13 | 1.09228 | 0.546140 | − | 0.837694i | \(-0.316097\pi\) | ||||
0.546140 | + | 0.837694i | \(0.316097\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.32181e12 | 0.294710 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.49493e12 | 0.0509020 | 0.0254510 | − | 0.999676i | \(-0.491898\pi\) | ||||
0.0254510 | + | 0.999676i | \(0.491898\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.24492e13 | −1.39009 | −0.695047 | − | 0.718964i | \(-0.744617\pi\) | ||||
−0.695047 | + | 0.718964i | \(0.744617\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.74184e11 | −0.0306898 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.29274e13 | −0.391886 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.57227e13 | −0.458764 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.27095e13 | 0.357041 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.60424e13 | −1.51616 | −0.758080 | − | 0.652162i | \(-0.773862\pi\) | ||||
−0.758080 | + | 0.652162i | \(0.773862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.94155e13 | 1.02718 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.15653e13 | 0.290399 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.70459e13 | −0.412504 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.08668e13 | −1.41992 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.91605e13 | 0.880874 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.85088e12 | −0.192016 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.76774e13 | 1.20710 | 0.603552 | − | 0.797324i | \(-0.293752\pi\) | ||||
0.603552 | + | 0.797324i | \(0.293752\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.64751e13 | 0.332702 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.64879e13 | 1.10096 | 0.550482 | − | 0.834847i | \(-0.314444\pi\) | ||||
0.550482 | + | 0.834847i | \(0.314444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.86939e13 | 0.539878 | 0.269939 | − | 0.962877i | \(-0.412996\pi\) | ||||
0.269939 | + | 0.962877i | \(0.412996\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.08069e13 | −0.923027 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.24332e13 | 0.218151 | 0.109075 | − | 0.994033i | \(-0.465211\pi\) | ||||
0.109075 | + | 0.994033i | \(0.465211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.82726e13 | 1.15717 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.08000e13 | −0.340632 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.72835e12 | −0.0273538 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.89458e13 | −0.748785 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.43530e13 | −0.656010 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.13229e14 | 3.04979 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.38818e13 | 1.29876 | 0.649378 | − | 0.760466i | \(-0.275029\pi\) | ||||
0.649378 | + | 0.760466i | \(0.275029\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.44172e13 | −0.326777 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.87672e13 | −0.631511 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.47739e14 | −1.85153 | −0.925766 | − | 0.378096i | \(-0.876579\pi\) | ||||
−0.925766 | + | 0.378096i | \(0.876579\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.36053e13 | 1.01423 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.13591e14 | −1.33411 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.98294e14 | −3.39255 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.30931e13 | −0.474682 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.44519e12 | 0.0260916 | 0.0130458 | − | 0.999915i | \(-0.495847\pi\) | ||||
0.0130458 | + | 0.999915i | \(0.495847\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.08907e14 | 1.12594 | 0.562971 | − | 0.826477i | \(-0.309658\pi\) | ||||
0.562971 | + | 0.826477i | \(0.309658\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.37785e13 | 0.138043 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.05373e13 | 0.393635 | 0.196817 | − | 0.980440i | \(-0.436939\pi\) | ||||
0.196817 | + | 0.980440i | \(0.436939\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.26188e14 | 1.18785 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.01391e13 | −0.822693 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.67076e14 | 1.47875 | 0.739374 | − | 0.673295i | \(-0.235122\pi\) | ||||
0.739374 | + | 0.673295i | \(0.235122\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.16329e14 | −0.998618 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.85324e13 | −0.737252 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.42191e13 | 0.114885 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.13245e12 | −0.0637614 | −0.0318807 | − | 0.999492i | \(-0.510150\pi\) | ||||
−0.0318807 | + | 0.999492i | \(0.510150\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.86295e12 | 0.0674425 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.37815e14 | −1.01799 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.11946e13 | 0.510562 | 0.255281 | − | 0.966867i | \(-0.417832\pi\) | ||||
0.255281 | + | 0.966867i | \(0.417832\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.20435e12 | −0.0362405 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.13380e13 | 0.550067 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.32772e14 | −0.872148 | −0.436074 | − | 0.899911i | \(-0.643631\pi\) | ||||
−0.436074 | + | 0.899911i | \(0.643631\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.67485e14 | 1.06878 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.42537e13 | −0.522391 | −0.261196 | − | 0.965286i | \(-0.584117\pi\) | ||||
−0.261196 | + | 0.965286i | \(0.584117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.93501e14 | 4.17843 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.17300e13 | 0.244365 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.15986e13 | −0.179864 | −0.0899321 | − | 0.995948i | \(-0.528665\pi\) | ||||
−0.0899321 | + | 0.995948i | \(0.528665\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.64537e13 | −0.423084 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.53220e14 | 0.824432 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.66740e12 | 0.0348877 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.87957e14 | −1.46548 | −0.732739 | − | 0.680510i | \(-0.761758\pi\) | ||||
−0.732739 | + | 0.680510i | \(0.761758\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.39885e12 | 0.0415785 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.36601e14 | −1.62114 | −0.810571 | − | 0.585640i | \(-0.800843\pi\) | ||||
−0.810571 | + | 0.585640i | \(0.800843\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.35329e14 | −0.634179 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.48330e13 | 0.158850 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.33288e14 | 1.47928 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.67590e13 | 0.115609 | 0.0578046 | − | 0.998328i | \(-0.481590\pi\) | ||||
0.0578046 | + | 0.998328i | \(0.481590\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.69038e13 | −0.407578 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.39817e14 | −1.39162 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.71036e13 | 0.227719 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.02187e14 | 0.396867 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.04568e14 | −1.15214 | −0.576072 | − | 0.817399i | \(-0.695415\pi\) | ||||
−0.576072 | + | 0.817399i | \(0.695415\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.19907e13 | −0.0810377 | −0.0405188 | − | 0.999179i | \(-0.512901\pi\) | ||||
−0.0405188 | + | 0.999179i | \(0.512901\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.46189e14 | −0.524859 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.19530e14 | −0.767989 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.63071e13 | 0.260143 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.88074e14 | −0.624903 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.84103e14 | −0.596261 | −0.298130 | − | 0.954525i | \(-0.596363\pi\) | ||||
−0.298130 | + | 0.954525i | \(0.596363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.87650e14 | 0.592469 | 0.296234 | − | 0.955115i | \(-0.404269\pi\) | ||||
0.296234 | + | 0.955115i | \(0.404269\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.05627e14 | 0.632980 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.12369e12 | 0.0213824 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.22200e14 | 1.52856 | 0.764279 | − | 0.644885i | \(-0.223095\pi\) | ||||
0.764279 | + | 0.644885i | \(0.223095\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.21268e14 | 0.917182 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.02043e14 | 1.11957 | 0.559785 | − | 0.828638i | \(-0.310884\pi\) | ||||
0.559785 | + | 0.828638i | \(0.310884\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.56530e14 | −2.32682 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.27722e14 | −0.603550 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.62244e14 | 1.45402 | 0.727009 | − | 0.686628i | \(-0.240910\pi\) | ||||
0.727009 | + | 0.686628i | \(0.240910\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.20977e14 | −0.305304 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.92808e13 | −0.195267 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.26217e14 | 1.98624 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00143e13 | −0.164304 | −0.0821519 | − | 0.996620i | \(-0.526179\pi\) | ||||
−0.0821519 | + | 0.996620i | \(0.526179\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.17990e13 | 0.141583 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.63273e14 | 0.812603 | 0.406301 | − | 0.913739i | \(-0.366818\pi\) | ||||
0.406301 | + | 0.913739i | \(0.366818\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.81837e14 | −0.397179 | −0.198589 | − | 0.980083i | \(-0.563636\pi\) | ||||
−0.198589 | + | 0.980083i | \(0.563636\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.42119e14 | −0.729769 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.99364e14 | 0.415339 | 0.207670 | − | 0.978199i | \(-0.433412\pi\) | ||||
0.207670 | + | 0.978199i | \(0.433412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.20442e14 | 0.855570 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.19072e14 | −1.03184 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.69605e14 | −1.10621 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.04551e13 | 0.0388138 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.44857e13 | 0.175192 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.99891e13 | 0.144939 | 0.0724696 | − | 0.997371i | \(-0.476912\pi\) | ||||
0.0724696 | + | 0.997371i | \(0.476912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.97070e14 | 0.703184 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.71524e14 | 0.643098 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.22503e14 | −0.884117 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.53441e14 | −1.41177 | −0.705885 | − | 0.708326i | \(-0.749451\pi\) | ||||
−0.705885 | + | 0.708326i | \(0.749451\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.92173e13 | 0.0310810 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.39015e14 | 0.852418 | 0.426209 | − | 0.904625i | \(-0.359849\pi\) | ||||
0.426209 | + | 0.904625i | \(0.359849\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.64814e14 | 0.564175 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.75461e14 | −0.719096 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.08792e15 | −1.60930 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.46806e14 | −0.791189 | −0.395594 | − | 0.918425i | \(-0.629461\pi\) | ||||
−0.395594 | + | 0.918425i | \(0.629461\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.79269e14 | −0.536834 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.85282e14 | 0.810477 | 0.405239 | − | 0.914211i | \(-0.367188\pi\) | ||||
0.405239 | + | 0.914211i | \(0.367188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.60993e15 | −2.18125 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.11430e14 | 0.280299 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.30032e14 | 0.298429 | 0.149214 | − | 0.988805i | \(-0.452326\pi\) | ||||
0.149214 | + | 0.988805i | \(0.452326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.22589e14 | −0.155646 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.75822e12 | −0.00715554 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.77308e14 | −0.823847 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.99544e15 | 2.37597 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.65675e14 | 0.892532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.44985e15 | 1.65469 | 0.827345 | − | 0.561694i | \(-0.189850\pi\) | ||||
0.827345 | + | 0.561694i | \(0.189850\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.87051e14 | 0.991264 | 0.495632 | − | 0.868533i | \(-0.334936\pi\) | ||||
0.495632 | + | 0.868533i | \(0.334936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.06680e15 | 1.16736 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.06970e14 | −0.650443 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.37693e14 | −0.669276 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.32977e14 | 0.239494 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.44129e14 | −0.145128 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.55112e14 | 0.843484 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.11749e14 | −0.107990 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.38523e15 | −4.15197 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.21596e15 | 1.12807 | 0.564034 | − | 0.825752i | \(-0.309249\pi\) | ||||
0.564034 | + | 0.825752i | \(0.309249\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.07546e14 | −0.552306 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.82340e15 | 1.62443 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.77148e15 | 1.54670 | 0.773348 | − | 0.633982i | \(-0.218581\pi\) | ||||
0.773348 | + | 0.633982i | \(0.218581\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.23158e13 | −0.0447698 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.39921e13 | −0.0285131 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.74825e13 | −0.0472658 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.00382e15 | 0.809176 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.12842e15 | 0.891801 | 0.445900 | − | 0.895083i | \(-0.352884\pi\) | ||||
0.445900 | + | 0.895083i | \(0.352884\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.78611e14 | −0.525843 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.43541e14 | −0.640930 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.21047e14 | −0.462731 | −0.231365 | − | 0.972867i | \(-0.574319\pi\) | ||||
−0.231365 | + | 0.972867i | \(0.574319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.43711e15 | −2.51146 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.00310e14 | −0.215210 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.21509e15 | −0.854068 | −0.427034 | − | 0.904236i | \(-0.640441\pi\) | ||||
−0.427034 | + | 0.904236i | \(0.640441\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.36046e15 | −0.937964 | −0.468982 | − | 0.883208i | \(-0.655379\pi\) | ||||
−0.468982 | + | 0.883208i | \(0.655379\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.03460e15 | 0.699714 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.04830e14 | 0.600336 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.26592e14 | 0.538052 | 0.269026 | − | 0.963133i | \(-0.413298\pi\) | ||||
0.269026 | + | 0.963133i | \(0.413298\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.26583e13 | 0.0144709 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.92314e14 | −0.308513 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.28971e15 | −0.793074 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.66451e14 | −0.341826 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.88505e14 | 0.289307 | 0.144654 | − | 0.989482i | \(-0.453793\pi\) | ||||
0.144654 | + | 0.989482i | \(0.453793\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.65554e13 | 0.0328731 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.45927e14 | 0.311461 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.06917e15 | −0.598751 | −0.299376 | − | 0.954135i | \(-0.596778\pi\) | ||||
−0.299376 | + | 0.954135i | \(0.596778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.70572e15 | 2.03718 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.50365e15 | −0.811499 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.36019e14 | −0.336994 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.52046e14 | −0.391232 | −0.195616 | − | 0.980681i | \(-0.562671\pi\) | ||||
−0.195616 | + | 0.980681i | \(0.562671\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.88253e14 | −0.147241 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.63966e15 | 1.82560 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.11325e15 | −1.53347 | −0.766737 | − | 0.641962i | \(-0.778121\pi\) | ||||
−0.766737 | + | 0.641962i | \(0.778121\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.77280e15 | −0.857560 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.37732e15 | 1.12943 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.57054e15 | 1.66610 | 0.833051 | − | 0.553197i | \(-0.186592\pi\) | ||||
0.833051 | + | 0.553197i | \(0.186592\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.64366e14 | −0.167003 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.11912e15 | 0.503858 | 0.251929 | − | 0.967746i | \(-0.418935\pi\) | ||||
0.251929 | + | 0.967746i | \(0.418935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.16601e14 | −0.184256 | −0.0921280 | − | 0.995747i | \(-0.529367\pi\) | ||||
−0.0921280 | + | 0.995747i | \(0.529367\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.54715e14 | −0.110675 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.38451e15 | 3.15237 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.27491e15 | −0.954166 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.85982e13 | 0.0323923 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.78092e15 | 0.721218 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.55936e15 | 1.41648 | 0.708240 | − | 0.705972i | \(-0.249490\pi\) | ||||
0.708240 | + | 0.705972i | \(0.249490\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.22654e15 | 0.479691 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.88551e15 | −2.64655 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.22444e15 | −1.97366 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.45876e14 | 0.276957 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.00307e15 | −1.82607 | −0.913036 | − | 0.407880i | \(-0.866268\pi\) | ||||
−0.913036 | + | 0.407880i | \(0.866268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.51393e15 | 1.61955 | 0.809775 | − | 0.586740i | \(-0.199589\pi\) | ||||
0.809775 | + | 0.586740i | \(0.199589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.71557e15 | −0.605104 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.87451e15 | 0.996758 | 0.498379 | − | 0.866959i | \(-0.333929\pi\) | ||||
0.498379 | + | 0.866959i | \(0.333929\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.18008e15 | −1.08416 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.94955e15 | 0.988690 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.33676e14 | 0.307733 | 0.153866 | − | 0.988092i | \(-0.450827\pi\) | ||||
0.153866 | + | 0.988092i | \(0.450827\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.29902e15 | −2.04148 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.40465e13 | 0.0267861 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.86905e15 | −1.83949 | −0.919746 | − | 0.392515i | \(-0.871605\pi\) | ||||
−0.919746 | + | 0.392515i | \(0.871605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.97430e15 | 0.916804 | 0.458402 | − | 0.888745i | \(-0.348422\pi\) | ||||
0.458402 | + | 0.888745i | \(0.348422\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.00497e15 | −0.304669 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.45286e14 | −0.102958 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.50364e15 | −0.441014 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.73073e15 | −0.499328 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.14098e14 | 0.202667 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.98702e15 | 1.11318 | 0.556590 | − | 0.830787i | \(-0.312109\pi\) | ||||
0.556590 | + | 0.830787i | \(0.312109\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.31392e14 | −0.200900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.91335e15 | 0.787326 | 0.393663 | − | 0.919255i | \(-0.371208\pi\) | ||||
0.393663 | + | 0.919255i | \(0.371208\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.50472e15 | 1.19780 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.14425e15 | 0.561005 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.17859e15 | −1.84810 | −0.924049 | − | 0.382273i | \(-0.875141\pi\) | ||||
−0.924049 | + | 0.382273i | \(0.875141\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.98382e15 | 1.00926 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.97216e15 | −0.740987 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.53652e15 | −0.376992 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.13258e15 | −0.273488 | −0.136744 | − | 0.990606i | \(-0.543664\pi\) | ||||
−0.136744 | + | 0.990606i | \(0.543664\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.09915e15 | 0.974230 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.20100e15 | −0.982735 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.46440e14 | −0.148850 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.07949e15 | 0.697999 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.88948e15 | −1.53722 | −0.768612 | − | 0.639715i | \(-0.779052\pi\) | ||||
−0.768612 | + | 0.639715i | \(0.779052\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.65940e14 | −0.0364500 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.01000e15 | 1.29967 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.38799e16 | 2.95515 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.12864e15 | −0.655846 | −0.327923 | − | 0.944704i | \(-0.606349\pi\) | ||||
−0.327923 | + | 0.944704i | \(0.606349\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.94097e13 | 0.00813431 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.50173e15 | 0.508450 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.73191e15 | 1.54740 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.03894e14 | −0.0401837 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.24806e15 | 0.242228 | 0.121114 | − | 0.992639i | \(-0.461353\pi\) | ||||
0.121114 | + | 0.992639i | \(0.461353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.83936e15 | 1.11615 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.09584e15 | 0.206294 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.31758e15 | −0.800537 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.33188e15 | −1.15636 | −0.578181 | − | 0.815909i | \(-0.696237\pi\) | ||||
−0.578181 | + | 0.815909i | \(0.696237\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.04368e15 | −0.539328 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.73279e15 | −0.826124 | −0.413062 | − | 0.910703i | \(-0.635541\pi\) | ||||
−0.413062 | + | 0.910703i | \(0.635541\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.32077e16 | −2.27115 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.93459e15 | 0.666543 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.08206e15 | −1.01509 | −0.507547 | − | 0.861624i | \(-0.669448\pi\) | ||||
−0.507547 | + | 0.861624i | \(0.669448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.36396e13 | 0.0153978 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.07307e15 | 0.659909 | 0.329954 | − | 0.943997i | \(-0.392967\pi\) | ||||
0.329954 | + | 0.943997i | \(0.392967\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.36189e15 | 1.49453 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.37528e14 | 0.0530942 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.37228e15 | −1.14275 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.73635e15 | −1.33447 | −0.667237 | − | 0.744845i | \(-0.732523\pi\) | ||||
−0.667237 | + | 0.744845i | \(0.732523\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.41386e15 | −0.363362 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.25932e15 | 0.483525 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.84148e15 | 1.14649 | 0.573245 | − | 0.819384i | \(-0.305684\pi\) | ||||
0.573245 | + | 0.819384i | \(0.305684\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.47680e15 | 0.501014 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.57189e15 | 0.223258 | 0.111629 | − | 0.993750i | \(-0.464393\pi\) | ||||
0.111629 | + | 0.993750i | \(0.464393\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.57203e16 | −2.20078 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.54063e15 | −0.350593 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.78866e15 | −0.515360 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.76621e14 | −0.117548 | −0.0587742 | − | 0.998271i | \(-0.518719\pi\) | ||||
−0.0587742 | + | 0.998271i | \(0.518719\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.00609e15 | 0.397377 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.53836e15 | −0.721762 | −0.360881 | − | 0.932612i | \(-0.617524\pi\) | ||||
−0.360881 | + | 0.932612i | \(0.617524\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.18351e15 | 0.922948 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.65432e15 | −1.09627 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.02331e13 | 0.00752279 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.01810e16 | −1.25375 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.21542e15 | 0.147584 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.13396e16 | 2.55508 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.11368e15 | 0.131493 | 0.0657463 | − | 0.997836i | \(-0.479057\pi\) | ||||
0.0657463 | + | 0.997836i | \(0.479057\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.59724e15 | 0.884571 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.96327e16 | 3.40252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.50756e14 | 0.0963391 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.88441e15 | −0.433817 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.19780e15 | −0.131936 | −0.0659681 | − | 0.997822i | \(-0.521014\pi\) | ||||
−0.0659681 | + | 0.997822i | \(0.521014\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.06626e16 | 1.15840 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.06279e15 | −0.542514 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.14721e15 | −0.121258 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.52737e16 | −1.59246 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.03202e15 | −0.414685 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.08896e15 | −0.922141 | −0.461070 | − | 0.887364i | \(-0.652534\pi\) | ||||
−0.461070 | + | 0.887364i | \(0.652534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.75285e15 | 0.475707 | 0.237854 | − | 0.971301i | \(-0.423556\pi\) | ||||
0.237854 | + | 0.971301i | \(0.423556\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.36742e15 | 0.233764 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.90046e14 | −0.0769637 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.83600e14 | 0.0272574 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.88361e15 | 0.463105 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.46358e15 | −0.698328 | −0.349164 | − | 0.937062i | \(-0.613534\pi\) | ||||
−0.349164 | + | 0.937062i | \(0.613534\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.33712e16 | 1.23444 | 0.617222 | − | 0.786789i | \(-0.288258\pi\) | ||||
0.617222 | + | 0.786789i | \(0.288258\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.98332e15 | 0.909449 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.28236e15 | −0.744515 | −0.372258 | − | 0.928129i | \(-0.621416\pi\) | ||||
−0.372258 | + | 0.928129i | \(0.621416\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.81760e16 | 1.61231 | 0.806153 | − | 0.591707i | \(-0.201546\pi\) | ||||
0.806153 | + | 0.591707i | \(0.201546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.20409e15 | −0.630628 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.34325e16 | −2.02428 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.55922e16 | 1.32933 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.02220e15 | −0.170151 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.04343e15 | 0.584916 | 0.292458 | − | 0.956278i | \(-0.405527\pi\) | ||||
0.292458 | + | 0.956278i | \(0.405527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.02557e15 | −0.411915 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.63267e14 | −0.0293883 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.69210e15 | −0.694085 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.13791e16 | −2.47333 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.03152e16 | 0.802571 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.34037e15 | −0.563775 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.02559e16 | −0.777597 | −0.388798 | − | 0.921323i | \(-0.627110\pi\) | ||||
−0.388798 | + | 0.921323i | \(0.627110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.36727e14 | 0.0177188 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.30722e16 | 0.965952 | 0.482976 | − | 0.875634i | \(-0.339556\pi\) | ||||
0.482976 | + | 0.875634i | \(0.339556\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.07866e15 | 0.224594 | 0.112297 | − | 0.993675i | \(-0.464179\pi\) | ||||
0.112297 | + | 0.993675i | \(0.464179\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.14135e15 | 0.226256 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.90413e16 | −1.35406 | −0.677029 | − | 0.735956i | \(-0.736733\pi\) | ||||
−0.677029 | + | 0.735956i | \(0.736733\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.14777e16 | −2.21012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.82062e15 | 0.264867 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.37933e14 | −0.0368230 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.68755e15 | 0.316845 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.08842e15 | −0.206138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.84461e15 | −0.121579 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.88173e16 | 1.22479 | 0.612394 | − | 0.790553i | \(-0.290207\pi\) | ||||
0.612394 | + | 0.790553i | \(0.290207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.36183e16 | 0.875355 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.40222e15 | −0.152491 | −0.0762456 | − | 0.997089i | \(-0.524293\pi\) | ||||
−0.0762456 | + | 0.997089i | \(0.524293\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.31415e15 | 0.0823877 | 0.0411938 | − | 0.999151i | \(-0.486884\pi\) | ||||
0.0411938 | + | 0.999151i | \(0.486884\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.57796e15 | −0.593041 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.02583e15 | −0.246193 | −0.123096 | − | 0.992395i | \(-0.539282\pi\) | ||||
−0.123096 | + | 0.992395i | \(0.539282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.93629e16 | 3.58554 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.81036e15 | −0.167662 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.93509e14 | −0.0585448 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.59412e15 | 0.267409 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.14215e15 | 0.238159 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.19375e16 | −0.678009 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.89154e15 | −0.386661 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.47906e16 | 0.819793 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.49769e16 | 1.36764 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.01871e16 | 0.551076 | 0.275538 | − | 0.961290i | \(-0.411144\pi\) | ||||
0.275538 | + | 0.961290i | \(0.411144\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.51600e15 | −0.508573 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.10881e16 | −1.11349 | −0.556745 | − | 0.830683i | \(-0.687950\pi\) | ||||
−0.556745 | + | 0.830683i | \(0.687950\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.60718e15 | −0.240351 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.15076e15 | 0.110860 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.43065e16 | 2.76580 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.64106e16 | −0.825829 | −0.412914 | − | 0.910770i | \(-0.635489\pi\) | ||||
−0.412914 | + | 0.910770i | \(0.635489\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.40156e16 | −0.696922 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.21294e16 | −0.595976 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.10772e16 | −1.02337 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00344e15 | −0.192086 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.18346e15 | −0.293188 | −0.146594 | − | 0.989197i | \(-0.546831\pi\) | ||||
−0.146594 | + | 0.989197i | \(0.546831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.18336e15 | 0.102306 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.37266e16 | −0.635642 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.46789e16 | 1.58709 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.53085e16 | −1.14472 | −0.572358 | − | 0.820004i | \(-0.693971\pi\) | ||||
−0.572358 | + | 0.820004i | \(0.693971\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.97262e15 | −0.311699 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.95742e16 | 1.30668 | 0.653341 | − | 0.757064i | \(-0.273367\pi\) | ||||
0.653341 | + | 0.757064i | \(0.273367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.66441e15 | 0.116356 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.23461e16 | 0.532910 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.62003e16 | 0.691192 | 0.345596 | − | 0.938383i | \(-0.387677\pi\) | ||||
0.345596 | + | 0.938383i | \(0.387677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.36676e15 | −0.0576404 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.02126e15 | −0.125949 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.76004e16 | −1.13738 | −0.568688 | − | 0.822554i | \(-0.692549\pi\) | ||||
−0.568688 | + | 0.822554i | \(0.692549\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.25334e16 | −1.73265 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.65902e16 | −0.668093 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.43462e16 | −1.36734 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.54707e15 | −0.218316 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.05440e15 | 0.196664 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.31508e14 | −0.0358333 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.38626e16 | −1.66820 | −0.834102 | − | 0.551610i | \(-0.814014\pi\) | ||||
−0.834102 | + | 0.551610i | \(0.814014\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.19989e14 | 0.0157927 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.19932e16 | −1.18946 | −0.594732 | − | 0.803924i | \(-0.702742\pi\) | ||||
−0.594732 | + | 0.803924i | \(0.702742\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.62186e16 | 1.33141 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.18938e16 | 0.432311 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.96188e16 | 1.42391 | 0.711954 | − | 0.702226i | \(-0.247811\pi\) | ||||
0.711954 | + | 0.702226i | \(0.247811\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.91058e16 | 2.45589 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.07778e16 | 0.378748 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.01905e15 | 0.139662 | 0.0698312 | − | 0.997559i | \(-0.477754\pi\) | ||||
0.0698312 | + | 0.997559i | \(0.477754\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.24437e16 | −0.771249 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.18147e16 | −1.76079 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.25450e16 | 0.421592 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.49658e16 | 0.829737 | 0.414869 | − | 0.909881i | \(-0.363828\pi\) | ||||
0.414869 | + | 0.909881i | \(0.363828\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.28133e16 | −0.749837 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.18167e16 | 2.00946 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.79381e16 | −0.576704 | −0.288352 | − | 0.957525i | \(-0.593107\pi\) | ||||
−0.288352 | + | 0.957525i | \(0.593107\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.93337e15 | 0.188665 |
(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 | 12.12.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 36.12.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 48.12.a.i.1.1 | 1 | |||
8.3 | odd | 2 | 192.12.a.a.1.1 | 1 | |||
8.5 | even | 2 | 192.12.a.k.1.1 | 1 | |||
12.11 | even | 2 | 144.12.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.12.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
36.12.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
48.12.a.i.1.1 | 1 | 4.3 | odd | 2 | |||
144.12.a.a.1.1 | 1 | 12.11 | even | 2 | |||
192.12.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
192.12.a.k.1.1 | 1 | 8.5 | even | 2 |