Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [153,10,Mod(1,153)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(153, 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("153.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 153 = 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 153.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: | \(78.8004829331\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-43.1213\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 153.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −43.1213 | −1.90571 | −0.952855 | − | 0.303426i | \(-0.901869\pi\) | ||||
−0.952855 | + | 0.303426i | \(0.901869\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1347.45 | 2.63173 | ||||||||
\(5\) | −1536.21 | −1.09923 | −0.549613 | − | 0.835420i | \(-0.685225\pi\) | ||||
−0.549613 | + | 0.835420i | \(0.685225\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3027.69 | 0.476617 | 0.238309 | − | 0.971189i | \(-0.423407\pi\) | ||||
0.238309 | + | 0.971189i | \(0.423407\pi\) | |||||||
\(8\) | −36025.5 | −3.10960 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 66243.5 | 2.09480 | ||||||||
\(11\) | −51964.2 | −1.07013 | −0.535066 | − | 0.844810i | \(-0.679713\pi\) | ||||
−0.535066 | + | 0.844810i | \(0.679713\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −166337. | −1.61527 | −0.807635 | − | 0.589683i | \(-0.799253\pi\) | ||||
−0.807635 | + | 0.589683i | \(0.799253\pi\) | |||||||
\(14\) | −130558. | −0.908294 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 863574. | 3.29427 | ||||||||
\(17\) | −83521.0 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.03482e6 | −1.82168 | −0.910840 | − | 0.412759i | \(-0.864565\pi\) | ||||
−0.910840 | + | 0.412759i | \(0.864565\pi\) | |||||||
\(20\) | −2.06997e6 | −2.89286 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.24076e6 | 2.03936 | ||||||||
\(23\) | 647595. | 0.482535 | 0.241267 | − | 0.970459i | \(-0.422437\pi\) | ||||
0.241267 | + | 0.970459i | \(0.422437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 406829. | 0.208297 | ||||||||
\(26\) | 7.17269e6 | 3.07824 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.07964e6 | 1.25433 | ||||||||
\(29\) | −101038. | −0.0265274 | −0.0132637 | − | 0.999912i | \(-0.504222\pi\) | ||||
−0.0132637 | + | 0.999912i | \(0.504222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.03448e6 | 0.201184 | 0.100592 | − | 0.994928i | \(-0.467926\pi\) | ||||
0.100592 | + | 0.994928i | \(0.467926\pi\) | |||||||
\(32\) | −1.87934e7 | −3.16833 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.60153e6 | 0.462203 | ||||||||
\(35\) | −4.65118e6 | −0.523910 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.58601e6 | −0.489998 | −0.244999 | − | 0.969523i | \(-0.578788\pi\) | ||||
−0.244999 | + | 0.969523i | \(0.578788\pi\) | |||||||
\(38\) | 4.46226e7 | 3.47159 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.53429e7 | 3.41816 | ||||||||
\(41\) | 4.18736e6 | 0.231426 | 0.115713 | − | 0.993283i | \(-0.463085\pi\) | ||||
0.115713 | + | 0.993283i | \(0.463085\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.60190e6 | −0.428301 | −0.214151 | − | 0.976801i | \(-0.568698\pi\) | ||||
−0.214151 | + | 0.976801i | \(0.568698\pi\) | |||||||
\(44\) | −7.00190e7 | −2.81630 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.79251e7 | −0.919571 | ||||||||
\(47\) | −3.98318e7 | −1.19067 | −0.595333 | − | 0.803479i | \(-0.702980\pi\) | ||||
−0.595333 | + | 0.803479i | \(0.702980\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.11867e7 | −0.772836 | ||||||||
\(50\) | −1.75430e7 | −0.396953 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.24131e8 | −4.25095 | ||||||||
\(53\) | −6.22183e7 | −1.08312 | −0.541560 | − | 0.840662i | \(-0.682166\pi\) | ||||
−0.541560 | + | 0.840662i | \(0.682166\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.98282e7 | 1.17632 | ||||||||
\(56\) | −1.09074e8 | −1.48209 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.35690e6 | 0.0505536 | ||||||||
\(59\) | −9.60858e7 | −1.03235 | −0.516173 | − | 0.856484i | \(-0.672644\pi\) | ||||
−0.516173 | + | 0.856484i | \(0.672644\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.86877e8 | −1.72811 | −0.864055 | − | 0.503398i | \(-0.832083\pi\) | ||||
−0.864055 | + | 0.503398i | \(0.832083\pi\) | |||||||
\(62\) | −4.46079e7 | −0.383398 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.68245e8 | 2.74364 | ||||||||
\(65\) | 2.55530e8 | 1.77555 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.73689e7 | 0.226555 | 0.113278 | − | 0.993563i | \(-0.463865\pi\) | ||||
0.113278 | + | 0.993563i | \(0.463865\pi\) | |||||||
\(68\) | −1.12540e8 | −0.638288 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.00565e8 | 0.998420 | ||||||||
\(71\) | −2.04593e8 | −0.955495 | −0.477748 | − | 0.878497i | \(-0.658547\pi\) | ||||
−0.477748 | + | 0.878497i | \(0.658547\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.95705e8 | −0.806581 | −0.403291 | − | 0.915072i | \(-0.632134\pi\) | ||||
−0.403291 | + | 0.915072i | \(0.632134\pi\) | |||||||
\(74\) | 2.40876e8 | 0.933793 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.39436e9 | −4.79417 | ||||||||
\(77\) | −1.57331e8 | −0.510043 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.72638e8 | 0.787524 | 0.393762 | − | 0.919212i | \(-0.371173\pi\) | ||||
0.393762 | + | 0.919212i | \(0.371173\pi\) | |||||||
\(80\) | −1.32663e9 | −3.62115 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.80564e8 | −0.441032 | ||||||||
\(83\) | 1.96272e8 | 0.453950 | 0.226975 | − | 0.973901i | \(-0.427116\pi\) | ||||
0.226975 | + | 0.973901i | \(0.427116\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.28306e8 | 0.266601 | ||||||||
\(86\) | 4.14046e8 | 0.816218 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.87204e9 | 3.32769 | ||||||||
\(89\) | 3.93217e8 | 0.664319 | 0.332160 | − | 0.943223i | \(-0.392223\pi\) | ||||
0.332160 | + | 0.943223i | \(0.392223\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.03618e8 | −0.769865 | ||||||||
\(92\) | 8.72600e8 | 1.26990 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.71760e9 | 2.26906 | ||||||||
\(95\) | 1.58970e9 | 2.00244 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.75485e8 | 1.00410 | 0.502049 | − | 0.864839i | \(-0.332580\pi\) | ||||
0.502049 | + | 0.864839i | \(0.332580\pi\) | |||||||
\(98\) | 1.34481e9 | 1.47280 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.48180e8 | 0.548180 | ||||||||
\(101\) | −2.76987e8 | −0.264858 | −0.132429 | − | 0.991192i | \(-0.542278\pi\) | ||||
−0.132429 | + | 0.991192i | \(0.542278\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.47928e7 | −0.0479685 | −0.0239842 | − | 0.999712i | \(-0.507635\pi\) | ||||
−0.0239842 | + | 0.999712i | \(0.507635\pi\) | |||||||
\(104\) | 5.99239e9 | 5.02285 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.68293e9 | 2.06411 | ||||||||
\(107\) | −1.33346e9 | −0.983449 | −0.491724 | − | 0.870751i | \(-0.663633\pi\) | ||||
−0.491724 | + | 0.870751i | \(0.663633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.04251e8 | −0.477868 | −0.238934 | − | 0.971036i | \(-0.576798\pi\) | ||||
−0.238934 | + | 0.971036i | \(0.576798\pi\) | |||||||
\(110\) | −3.44229e9 | −2.24172 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.61463e9 | 1.57011 | ||||||||
\(113\) | −1.40406e9 | −0.810091 | −0.405045 | − | 0.914297i | \(-0.632744\pi\) | ||||
−0.405045 | + | 0.914297i | \(0.632744\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.94845e8 | −0.530414 | ||||||||
\(116\) | −1.36144e8 | −0.0698130 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.14335e9 | 1.96735 | ||||||||
\(119\) | −2.52875e8 | −0.115597 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.42331e8 | 0.145182 | ||||||||
\(122\) | 8.05837e9 | 3.29328 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.39390e9 | 0.529461 | ||||||||
\(125\) | 2.37544e9 | 0.870261 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.64719e8 | 0.158516 | 0.0792581 | − | 0.996854i | \(-0.474745\pi\) | ||||
0.0792581 | + | 0.996854i | \(0.474745\pi\) | |||||||
\(128\) | −6.25697e9 | −2.06025 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.10188e10 | −3.38367 | ||||||||
\(131\) | −4.70705e9 | −1.39646 | −0.698229 | − | 0.715874i | \(-0.746028\pi\) | ||||
−0.698229 | + | 0.715874i | \(0.746028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.13310e9 | −0.868244 | ||||||||
\(134\) | −1.61140e9 | −0.431748 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00889e9 | 0.754190 | ||||||||
\(137\) | −4.09197e9 | −0.992407 | −0.496203 | − | 0.868206i | \(-0.665273\pi\) | ||||
−0.496203 | + | 0.868206i | \(0.665273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.61710e8 | −0.104907 | −0.0524533 | − | 0.998623i | \(-0.516704\pi\) | ||||
−0.0524533 | + | 0.998623i | \(0.516704\pi\) | |||||||
\(140\) | −6.26721e9 | −1.37879 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.82232e9 | 1.82090 | ||||||||
\(143\) | 8.64359e9 | 1.72855 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.55216e8 | 0.0291596 | ||||||||
\(146\) | 8.43904e9 | 1.53711 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.52685e9 | −1.28954 | ||||||||
\(149\) | −1.87018e9 | −0.310847 | −0.155423 | − | 0.987848i | \(-0.549674\pi\) | ||||
−0.155423 | + | 0.987848i | \(0.549674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.04895e9 | −0.946856 | −0.473428 | − | 0.880833i | \(-0.656984\pi\) | ||||
−0.473428 | + | 0.880833i | \(0.656984\pi\) | |||||||
\(152\) | 3.72798e10 | 5.66470 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.78433e9 | 0.971994 | ||||||||
\(155\) | −1.58918e9 | −0.221146 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.87552e9 | 0.771788 | 0.385894 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385894 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(158\) | −1.17565e10 | −1.50079 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.88706e10 | 3.48270 | ||||||||
\(161\) | 1.96072e9 | 0.229984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.19332e10 | 1.32408 | 0.662039 | − | 0.749470i | \(-0.269691\pi\) | ||||
0.662039 | + | 0.749470i | \(0.269691\pi\) | |||||||
\(164\) | 5.64224e9 | 0.609052 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.46352e9 | −0.865096 | ||||||||
\(167\) | −2.11741e9 | −0.210659 | −0.105330 | − | 0.994437i | \(-0.533590\pi\) | ||||
−0.105330 | + | 0.994437i | \(0.533590\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.70637e10 | 1.60910 | ||||||||
\(170\) | −5.53273e9 | −0.508065 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.29380e10 | −1.12717 | ||||||||
\(173\) | −4.37524e9 | −0.371359 | −0.185680 | − | 0.982610i | \(-0.559449\pi\) | ||||
−0.185680 | + | 0.982610i | \(0.559449\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.23175e9 | 0.0992777 | ||||||||
\(176\) | −4.48749e10 | −3.52531 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.69560e10 | −1.26600 | ||||||||
\(179\) | −2.12791e9 | −0.154922 | −0.0774612 | − | 0.996995i | \(-0.524681\pi\) | ||||
−0.0774612 | + | 0.996995i | \(0.524681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.80496e10 | 1.25001 | 0.625007 | − | 0.780619i | \(-0.285096\pi\) | ||||
0.625007 | + | 0.780619i | \(0.285096\pi\) | |||||||
\(182\) | 2.17166e10 | 1.46714 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.33299e10 | −1.50049 | ||||||||
\(185\) | 8.58131e9 | 0.538618 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.34010e9 | 0.259545 | ||||||||
\(188\) | −5.36713e10 | −3.13351 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.85499e10 | −3.81606 | ||||||||
\(191\) | 6.31774e8 | 0.0343488 | 0.0171744 | − | 0.999853i | \(-0.494533\pi\) | ||||
0.0171744 | + | 0.999853i | \(0.494533\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.51993e10 | 0.788524 | 0.394262 | − | 0.918998i | \(-0.371000\pi\) | ||||
0.394262 | + | 0.918998i | \(0.371000\pi\) | |||||||
\(194\) | −3.77520e10 | −1.91352 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.20224e10 | −2.03390 | ||||||||
\(197\) | 2.63264e10 | 1.24535 | 0.622677 | − | 0.782479i | \(-0.286045\pi\) | ||||
0.622677 | + | 0.782479i | \(0.286045\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.40221e10 | 1.53788 | 0.768940 | − | 0.639321i | \(-0.220784\pi\) | ||||
0.768940 | + | 0.639321i | \(0.220784\pi\) | |||||||
\(200\) | −1.46562e10 | −0.647720 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.19440e10 | 0.504743 | ||||||||
\(203\) | −3.05912e8 | −0.0126434 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.43268e9 | −0.254390 | ||||||||
\(206\) | 2.36273e9 | 0.0914140 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.43645e11 | −5.32114 | ||||||||
\(209\) | 5.37734e10 | 1.94944 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.29918e10 | −0.798550 | −0.399275 | − | 0.916831i | \(-0.630738\pi\) | ||||
−0.399275 | + | 0.916831i | \(0.630738\pi\) | |||||||
\(212\) | −8.38358e10 | −2.85048 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.75003e10 | 1.87417 | ||||||||
\(215\) | 1.47506e10 | 0.470800 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.13207e9 | 0.0958876 | ||||||||
\(218\) | 3.03682e10 | 0.910678 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.07564e11 | 3.09575 | ||||||||
\(221\) | 1.38927e10 | 0.391760 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.81614e10 | −1.57494 | −0.787468 | − | 0.616355i | \(-0.788609\pi\) | ||||
−0.787468 | + | 0.616355i | \(0.788609\pi\) | |||||||
\(224\) | −5.69004e10 | −1.51008 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.05450e10 | 1.54380 | ||||||||
\(227\) | 6.36497e9 | 0.159104 | 0.0795518 | − | 0.996831i | \(-0.474651\pi\) | ||||
0.0795518 | + | 0.996831i | \(0.474651\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.25334e10 | −1.74292 | −0.871461 | − | 0.490464i | \(-0.836827\pi\) | ||||
−0.871461 | + | 0.490464i | \(0.836827\pi\) | |||||||
\(230\) | 4.28990e10 | 1.01082 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.63996e9 | 0.0824898 | ||||||||
\(233\) | 8.13370e10 | 1.80795 | 0.903975 | − | 0.427585i | \(-0.140635\pi\) | ||||
0.903975 | + | 0.427585i | \(0.140635\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.11902e10 | 1.30881 | ||||||||
\(236\) | −1.29470e11 | −2.71686 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.09043e10 | 0.220294 | ||||||||
\(239\) | −7.48651e10 | −1.48419 | −0.742094 | − | 0.670296i | \(-0.766167\pi\) | ||||
−0.742094 | + | 0.670296i | \(0.766167\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.06255e10 | −0.202896 | −0.101448 | − | 0.994841i | \(-0.532348\pi\) | ||||
−0.101448 | + | 0.994841i | \(0.532348\pi\) | |||||||
\(242\) | −1.47618e10 | −0.276674 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.51806e11 | −4.54792 | ||||||||
\(245\) | 4.79095e10 | 0.849521 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.72129e11 | 2.94250 | ||||||||
\(248\) | −3.72675e10 | −0.625602 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.02432e11 | −1.65846 | ||||||||
\(251\) | 9.55285e10 | 1.51915 | 0.759576 | − | 0.650418i | \(-0.225406\pi\) | ||||
0.759576 | + | 0.650418i | \(0.225406\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.36518e10 | −0.516376 | ||||||||
\(254\) | −2.00393e10 | −0.302086 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.12676e10 | 1.18260 | ||||||||
\(257\) | −6.50855e10 | −0.930647 | −0.465324 | − | 0.885141i | \(-0.654062\pi\) | ||||
−0.465324 | + | 0.885141i | \(0.654062\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.69127e10 | −0.233541 | ||||||||
\(260\) | 3.44313e11 | 4.67276 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.02974e11 | 2.66124 | ||||||||
\(263\) | 6.33984e10 | 0.817104 | 0.408552 | − | 0.912735i | \(-0.366034\pi\) | ||||
0.408552 | + | 0.912735i | \(0.366034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.55806e10 | 1.19059 | ||||||||
\(266\) | 1.35103e11 | 1.65462 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.03526e10 | 0.596232 | ||||||||
\(269\) | 7.50317e10 | 0.873695 | 0.436847 | − | 0.899536i | \(-0.356095\pi\) | ||||
0.436847 | + | 0.899536i | \(0.356095\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.55753e10 | −1.07643 | −0.538213 | − | 0.842809i | \(-0.680900\pi\) | ||||
−0.538213 | + | 0.842809i | \(0.680900\pi\) | |||||||
\(272\) | −7.21266e10 | −0.798979 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.76451e11 | 1.89124 | ||||||||
\(275\) | −2.11406e10 | −0.222905 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.40532e10 | −0.143422 | −0.0717110 | − | 0.997425i | \(-0.522846\pi\) | ||||
−0.0717110 | + | 0.997425i | \(0.522846\pi\) | |||||||
\(278\) | 1.99095e10 | 0.199922 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.67561e11 | 1.62915 | ||||||||
\(281\) | −1.00661e11 | −0.963124 | −0.481562 | − | 0.876412i | \(-0.659930\pi\) | ||||
−0.481562 | + | 0.876412i | \(0.659930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.78714e10 | 0.721670 | 0.360835 | − | 0.932630i | \(-0.382492\pi\) | ||||
0.360835 | + | 0.932630i | \(0.382492\pi\) | |||||||
\(284\) | −2.75678e11 | −2.51461 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.72723e11 | −3.29412 | ||||||||
\(287\) | 1.26780e10 | 0.110302 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.97576e9 | 0.0588235 | ||||||||
\(290\) | −6.69314e9 | −0.0555698 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.63701e11 | −2.12270 | ||||||||
\(293\) | 8.86150e10 | 0.702429 | 0.351215 | − | 0.936295i | \(-0.385769\pi\) | ||||
0.351215 | + | 0.936295i | \(0.385769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.47608e11 | 1.13478 | ||||||||
\(296\) | 2.01239e11 | 1.52370 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.06447e10 | 0.592383 | ||||||||
\(299\) | −1.07719e11 | −0.779423 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.90716e10 | −0.204136 | ||||||||
\(302\) | 2.60839e11 | 1.80443 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.93641e11 | −6.00111 | ||||||||
\(305\) | 2.87083e11 | 1.89958 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.69929e11 | −1.09180 | −0.545902 | − | 0.837849i | \(-0.683813\pi\) | ||||
−0.545902 | + | 0.837849i | \(0.683813\pi\) | |||||||
\(308\) | −2.11995e11 | −1.34230 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.85274e10 | 0.421441 | ||||||||
\(311\) | −1.18662e11 | −0.719265 | −0.359633 | − | 0.933094i | \(-0.617098\pi\) | ||||
−0.359633 | + | 0.933094i | \(0.617098\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.52103e11 | 1.48467 | 0.742333 | − | 0.670032i | \(-0.233719\pi\) | ||||
0.742333 | + | 0.670032i | \(0.233719\pi\) | |||||||
\(314\) | −2.53360e11 | −1.47080 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.67365e11 | 2.07255 | ||||||||
\(317\) | −7.54487e10 | −0.419648 | −0.209824 | − | 0.977739i | \(-0.567289\pi\) | ||||
−0.209824 | + | 0.977739i | \(0.567289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.25038e9 | 0.0283878 | ||||||||
\(320\) | −5.65702e11 | −3.01587 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.45486e10 | −0.438283 | ||||||||
\(323\) | 8.64289e10 | 0.441822 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.76709e10 | −0.336455 | ||||||||
\(326\) | −5.14576e11 | −2.52331 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.50852e11 | −0.719645 | ||||||||
\(329\) | −1.20598e11 | −0.567492 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.39508e11 | −1.09672 | −0.548358 | − | 0.836244i | \(-0.684747\pi\) | ||||
−0.548358 | + | 0.836244i | \(0.684747\pi\) | |||||||
\(332\) | 2.64466e11 | 1.19467 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.13054e10 | 0.401455 | ||||||||
\(335\) | −5.74067e10 | −0.249035 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.05715e10 | 0.340288 | 0.170144 | − | 0.985419i | \(-0.445577\pi\) | ||||
0.170144 | + | 0.985419i | \(0.445577\pi\) | |||||||
\(338\) | −7.35807e11 | −3.06647 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.72886e11 | 0.701623 | ||||||||
\(341\) | −5.37557e10 | −0.215293 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.16602e11 | −0.844964 | ||||||||
\(344\) | 3.45913e11 | 1.33185 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.88666e11 | 0.707703 | ||||||||
\(347\) | 3.81897e11 | 1.41405 | 0.707024 | − | 0.707190i | \(-0.250037\pi\) | ||||
0.707024 | + | 0.707190i | \(0.250037\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.86306e11 | −1.03304 | −0.516518 | − | 0.856276i | \(-0.672772\pi\) | ||||
−0.516518 | + | 0.856276i | \(0.672772\pi\) | |||||||
\(350\) | −5.31147e10 | −0.189195 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.76583e11 | 3.39053 | ||||||||
\(353\) | −3.83234e10 | −0.131364 | −0.0656822 | − | 0.997841i | \(-0.520922\pi\) | ||||
−0.0656822 | + | 0.997841i | \(0.520922\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.14299e11 | 1.05030 | ||||||||
\(356\) | 5.29838e11 | 1.74831 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.17581e10 | 0.295237 | ||||||||
\(359\) | 8.46163e10 | 0.268862 | 0.134431 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134431 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.48157e11 | 2.31852 | ||||||||
\(362\) | −7.78323e11 | −2.38216 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.78598e11 | −2.02608 | ||||||||
\(365\) | 3.00644e11 | 0.886615 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.52825e11 | 1.87845 | 0.939225 | − | 0.343301i | \(-0.111545\pi\) | ||||
0.939225 | + | 0.343301i | \(0.111545\pi\) | |||||||
\(368\) | 5.59246e11 | 1.58960 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.70037e11 | −1.02645 | ||||||||
\(371\) | −1.88377e11 | −0.516234 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.69405e10 | −0.259308 | −0.129654 | − | 0.991559i | \(-0.541387\pi\) | ||||
−0.129654 | + | 0.991559i | \(0.541387\pi\) | |||||||
\(374\) | −1.87151e11 | −0.494618 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.43496e12 | 3.70250 | ||||||||
\(377\) | 1.68065e10 | 0.0428489 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.80659e11 | −1.69454 | −0.847272 | − | 0.531159i | \(-0.821757\pi\) | ||||
−0.847272 | + | 0.531159i | \(0.821757\pi\) | |||||||
\(380\) | 2.14203e12 | 5.26987 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.72429e10 | −0.0654589 | ||||||||
\(383\) | −1.56533e11 | −0.371717 | −0.185858 | − | 0.982577i | \(-0.559507\pi\) | ||||
−0.185858 | + | 0.982577i | \(0.559507\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.41695e11 | 0.560652 | ||||||||
\(386\) | −6.55412e11 | −1.50270 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.17967e12 | 2.64251 | ||||||||
\(389\) | 5.55777e11 | 1.23063 | 0.615315 | − | 0.788282i | \(-0.289029\pi\) | ||||
0.615315 | + | 0.788282i | \(0.289029\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.40878e10 | −0.117032 | ||||||||
\(392\) | 1.12352e12 | 2.40321 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.13523e12 | −2.37328 | ||||||||
\(395\) | −4.18830e11 | −0.865667 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.61410e11 | −0.528159 | −0.264079 | − | 0.964501i | \(-0.585068\pi\) | ||||
−0.264079 | + | 0.964501i | \(0.585068\pi\) | |||||||
\(398\) | −1.46708e12 | −2.93075 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.51327e11 | 0.686186 | ||||||||
\(401\) | −8.04746e10 | −0.155421 | −0.0777104 | − | 0.996976i | \(-0.524761\pi\) | ||||
−0.0777104 | + | 0.996976i | \(0.524761\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.72072e11 | −0.324966 | ||||||||
\(404\) | −3.73225e11 | −0.697035 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.31913e10 | 0.0240947 | ||||||||
\(407\) | 2.90273e11 | 0.524362 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.96676e11 | 0.877643 | 0.438822 | − | 0.898574i | \(-0.355396\pi\) | ||||
0.438822 | + | 0.898574i | \(0.355396\pi\) | |||||||
\(410\) | 2.77386e11 | 0.484793 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.38303e10 | −0.126240 | ||||||||
\(413\) | −2.90918e11 | −0.492034 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.01516e11 | −0.498993 | ||||||||
\(416\) | 3.12604e12 | 5.11770 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.31878e12 | −3.71506 | ||||||||
\(419\) | −5.00093e11 | −0.792661 | −0.396331 | − | 0.918108i | \(-0.629717\pi\) | ||||
−0.396331 | + | 0.918108i | \(0.629717\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.47398e11 | 1.46982 | 0.734908 | − | 0.678167i | \(-0.237225\pi\) | ||||
0.734908 | + | 0.678167i | \(0.237225\pi\) | |||||||
\(422\) | 9.91436e11 | 1.52180 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.24145e12 | 3.36808 | ||||||||
\(425\) | −3.39788e10 | −0.0505193 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.65805e11 | −0.823647 | ||||||||
\(428\) | −1.79676e12 | −2.58817 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.36064e11 | −0.897207 | ||||||||
\(431\) | 5.09374e11 | 0.711032 | 0.355516 | − | 0.934670i | \(-0.384305\pi\) | ||||
0.355516 | + | 0.934670i | \(0.384305\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.25104e12 | 1.71032 | 0.855160 | − | 0.518365i | \(-0.173459\pi\) | ||||
0.855160 | + | 0.518365i | \(0.173459\pi\) | |||||||
\(434\) | −1.35059e11 | −0.182734 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.48940e11 | −1.25762 | ||||||||
\(437\) | −6.70142e11 | −0.879024 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.15261e12 | −1.48112 | −0.740561 | − | 0.671989i | \(-0.765440\pi\) | ||||
−0.740561 | + | 0.671989i | \(0.765440\pi\) | |||||||
\(440\) | −2.87585e12 | −3.65788 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.99070e11 | −0.746582 | ||||||||
\(443\) | −1.57617e12 | −1.94440 | −0.972199 | − | 0.234155i | \(-0.924768\pi\) | ||||
−0.972199 | + | 0.234155i | \(0.924768\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.04065e11 | −0.730237 | ||||||||
\(446\) | 2.50800e12 | 3.00137 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.11493e12 | 1.30766 | ||||||||
\(449\) | 1.39885e12 | 1.62428 | 0.812141 | − | 0.583461i | \(-0.198302\pi\) | ||||
0.812141 | + | 0.583461i | \(0.198302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.17593e11 | −0.247657 | ||||||||
\(452\) | −1.89190e12 | −2.13194 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.74466e11 | −0.303205 | ||||||||
\(455\) | 7.73665e11 | 0.846255 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.76472e11 | 0.403747 | 0.201874 | − | 0.979412i | \(-0.435297\pi\) | ||||
0.201874 | + | 0.979412i | \(0.435297\pi\) | |||||||
\(458\) | 3.12773e12 | 3.32151 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.34050e12 | −1.39591 | ||||||||
\(461\) | −2.03996e11 | −0.210362 | −0.105181 | − | 0.994453i | \(-0.533542\pi\) | ||||
−0.105181 | + | 0.994453i | \(0.533542\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.19166e12 | −1.20514 | −0.602571 | − | 0.798065i | \(-0.705857\pi\) | ||||
−0.602571 | + | 0.798065i | \(0.705857\pi\) | |||||||
\(464\) | −8.72541e10 | −0.0873886 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.50736e12 | −3.44543 | ||||||||
\(467\) | 1.20046e12 | 1.16795 | 0.583973 | − | 0.811773i | \(-0.301497\pi\) | ||||
0.583973 | + | 0.811773i | \(0.301497\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.13141e11 | 0.107980 | ||||||||
\(470\) | −2.63860e12 | −2.49421 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.46154e12 | 3.21019 | ||||||||
\(473\) | 4.98955e11 | 0.458339 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.20994e11 | −0.379450 | ||||||||
\(476\) | −3.40736e11 | −0.304219 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.22828e12 | 2.82843 | ||||||||
\(479\) | 3.78765e10 | 0.0328746 | 0.0164373 | − | 0.999865i | \(-0.494768\pi\) | ||||
0.0164373 | + | 0.999865i | \(0.494768\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.29163e11 | 0.791478 | ||||||||
\(482\) | 4.58187e11 | 0.386662 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.61273e11 | 0.382079 | ||||||||
\(485\) | −1.34493e12 | −1.10373 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.88071e12 | 1.51510 | 0.757550 | − | 0.652778i | \(-0.226396\pi\) | ||||
0.757550 | + | 0.652778i | \(0.226396\pi\) | |||||||
\(488\) | 6.73233e12 | 5.37374 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.06592e12 | −1.61894 | ||||||||
\(491\) | 2.42874e11 | 0.188588 | 0.0942942 | − | 0.995544i | \(-0.469941\pi\) | ||||
0.0942942 | + | 0.995544i | \(0.469941\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.43882e9 | 0.00643384 | ||||||||
\(494\) | −7.42241e12 | −5.60756 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.93347e11 | 0.662754 | ||||||||
\(497\) | −6.19444e11 | −0.455405 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.88648e11 | 0.569417 | 0.284709 | − | 0.958614i | \(-0.408103\pi\) | ||||
0.284709 | + | 0.958614i | \(0.408103\pi\) | |||||||
\(500\) | 3.20078e12 | 2.29029 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.11931e12 | −2.89506 | ||||||||
\(503\) | −1.92372e12 | −1.33994 | −0.669972 | − | 0.742386i | \(-0.733694\pi\) | ||||
−0.669972 | + | 0.742386i | \(0.733694\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.25512e11 | 0.291139 | ||||||||
\(506\) | 1.45111e12 | 0.984062 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.26184e11 | 0.417172 | ||||||||
\(509\) | −2.87805e12 | −1.90050 | −0.950250 | − | 0.311487i | \(-0.899173\pi\) | ||||
−0.950250 | + | 0.311487i | \(0.899173\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.92532e11 | −0.384431 | ||||||||
\(512\) | −3.00794e11 | −0.193443 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.80657e12 | 1.77354 | ||||||||
\(515\) | 8.41734e10 | 0.0527281 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.06983e12 | 1.27417 | ||||||||
\(518\) | 7.29297e11 | 0.445062 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.20560e12 | −5.52124 | ||||||||
\(521\) | −2.41942e12 | −1.43861 | −0.719303 | − | 0.694697i | \(-0.755539\pi\) | ||||
−0.719303 | + | 0.694697i | \(0.755539\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.25636e12 | 1.31872 | 0.659358 | − | 0.751829i | \(-0.270828\pi\) | ||||
0.659358 | + | 0.751829i | \(0.270828\pi\) | |||||||
\(524\) | −6.34249e12 | −3.67510 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.73382e12 | −1.55716 | ||||||||
\(527\) | −8.64005e10 | −0.0487942 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.38177e12 | −0.767160 | ||||||||
\(530\) | −4.12156e12 | −2.26893 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.22168e12 | −2.28498 | ||||||||
\(533\) | −6.96515e11 | −0.373816 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.04847e12 | 1.08103 | ||||||||
\(536\) | −1.34623e12 | −0.704497 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.23547e12 | −1.66501 | ||||||||
\(539\) | 1.62059e12 | 0.827036 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.18649e12 | −1.09739 | −0.548694 | − | 0.836023i | \(-0.684875\pi\) | ||||
−0.548694 | + | 0.836023i | \(0.684875\pi\) | |||||||
\(542\) | 4.12133e12 | 2.05135 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.56964e12 | 0.768432 | ||||||||
\(545\) | 1.08188e12 | 0.525285 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.53862e11 | −0.360039 | −0.180019 | − | 0.983663i | \(-0.557616\pi\) | ||||
−0.180019 | + | 0.983663i | \(0.557616\pi\) | |||||||
\(548\) | −5.51371e12 | −2.61175 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.11608e11 | 0.424792 | ||||||||
\(551\) | 1.04556e11 | 0.0483245 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.25462e11 | 0.375348 | ||||||||
\(554\) | 6.05991e11 | 0.273321 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.22130e11 | −0.276086 | ||||||||
\(557\) | 2.08949e12 | 0.919797 | 0.459898 | − | 0.887972i | \(-0.347886\pi\) | ||||
0.459898 | + | 0.887972i | \(0.347886\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.59716e12 | 0.691822 | ||||||||
\(560\) | −4.01663e12 | −1.72590 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.34063e12 | 1.83544 | ||||||||
\(563\) | 6.61278e11 | 0.277393 | 0.138697 | − | 0.990335i | \(-0.455709\pi\) | ||||
0.138697 | + | 0.990335i | \(0.455709\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.15694e12 | 0.890472 | ||||||||
\(566\) | −3.35791e12 | −1.37529 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.37057e12 | 2.97121 | ||||||||
\(569\) | 1.47797e12 | 0.591100 | 0.295550 | − | 0.955327i | \(-0.404497\pi\) | ||||
0.295550 | + | 0.955327i | \(0.404497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.27003e12 | −0.893652 | −0.446826 | − | 0.894621i | \(-0.647446\pi\) | ||||
−0.446826 | + | 0.894621i | \(0.647446\pi\) | |||||||
\(572\) | 1.16468e13 | 4.54908 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.46692e11 | −0.210203 | ||||||||
\(575\) | 2.63461e11 | 0.100510 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.93038e12 | −0.725021 | −0.362511 | − | 0.931980i | \(-0.618080\pi\) | ||||
−0.362511 | + | 0.931980i | \(0.618080\pi\) | |||||||
\(578\) | −3.00804e11 | −0.112101 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.09146e11 | 0.0767402 | ||||||||
\(581\) | 5.94251e11 | 0.216360 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.23312e12 | 1.15908 | ||||||||
\(584\) | 7.05036e12 | 2.50815 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.82119e12 | −1.33863 | ||||||||
\(587\) | −2.62778e12 | −0.913518 | −0.456759 | − | 0.889590i | \(-0.650990\pi\) | ||||
−0.456759 | + | 0.889590i | \(0.650990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.07049e12 | −0.366492 | ||||||||
\(590\) | −6.36507e12 | −2.16256 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.82393e12 | −1.61419 | ||||||||
\(593\) | −5.85157e12 | −1.94324 | −0.971620 | − | 0.236548i | \(-0.923984\pi\) | ||||
−0.971620 | + | 0.236548i | \(0.923984\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.88471e11 | 0.127067 | ||||||||
\(596\) | −2.51997e12 | −0.818064 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.64500e12 | 1.48535 | ||||||||
\(599\) | −4.56968e11 | −0.145033 | −0.0725163 | − | 0.997367i | \(-0.523103\pi\) | ||||
−0.0725163 | + | 0.997367i | \(0.523103\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.72333e12 | −1.47677 | −0.738385 | − | 0.674379i | \(-0.764411\pi\) | ||||
−0.738385 | + | 0.674379i | \(0.764411\pi\) | |||||||
\(602\) | 1.25360e12 | 0.389023 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.15063e12 | −2.49187 | ||||||||
\(605\) | −5.25894e11 | −0.159588 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.89920e12 | 0.567836 | 0.283918 | − | 0.958849i | \(-0.408366\pi\) | ||||
0.283918 | + | 0.958849i | \(0.408366\pi\) | |||||||
\(608\) | 1.94477e13 | 5.77168 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.23794e13 | −3.62005 | ||||||||
\(611\) | 6.62553e12 | 1.92325 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.38704e12 | −1.54091 | −0.770456 | − | 0.637493i | \(-0.779971\pi\) | ||||
−0.770456 | + | 0.637493i | \(0.779971\pi\) | |||||||
\(614\) | 7.32756e12 | 2.08066 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.66794e12 | 1.58603 | ||||||||
\(617\) | 5.80011e11 | 0.161121 | 0.0805607 | − | 0.996750i | \(-0.474329\pi\) | ||||
0.0805607 | + | 0.996750i | \(0.474329\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.58371e12 | −0.433579 | −0.216790 | − | 0.976218i | \(-0.569559\pi\) | ||||
−0.216790 | + | 0.976218i | \(0.569559\pi\) | |||||||
\(620\) | −2.14133e12 | −0.581997 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.11685e12 | 1.37071 | ||||||||
\(623\) | 1.19054e12 | 0.316626 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.44378e12 | −1.16491 | ||||||||
\(626\) | −1.08710e13 | −2.82934 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.91695e12 | 2.03114 | ||||||||
\(629\) | 4.66549e11 | 0.118842 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.36740e12 | 0.845595 | 0.422797 | − | 0.906224i | \(-0.361048\pi\) | ||||
0.422797 | + | 0.906224i | \(0.361048\pi\) | |||||||
\(632\) | −9.82191e12 | −2.44889 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.25344e12 | 0.799727 | ||||||||
\(635\) | −7.13908e11 | −0.174245 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.18752e12 | 1.24834 | ||||||||
\(638\) | −2.26403e11 | −0.0540990 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.61205e12 | 2.26468 | ||||||||
\(641\) | 7.80868e12 | 1.82691 | 0.913454 | − | 0.406943i | \(-0.133405\pi\) | ||||
0.913454 | + | 0.406943i | \(0.133405\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.11639e12 | −0.488255 | −0.244128 | − | 0.969743i | \(-0.578502\pi\) | ||||
−0.244128 | + | 0.969743i | \(0.578502\pi\) | |||||||
\(644\) | 2.64196e12 | 0.605257 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.72693e12 | −0.841985 | ||||||||
\(647\) | −3.18454e12 | −0.714460 | −0.357230 | − | 0.934016i | \(-0.616279\pi\) | ||||
−0.357230 | + | 0.934016i | \(0.616279\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.99302e12 | 1.10475 | ||||||||
\(650\) | 2.91806e12 | 0.641186 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.60794e13 | 3.48462 | ||||||||
\(653\) | −1.82854e12 | −0.393545 | −0.196772 | − | 0.980449i | \(-0.563046\pi\) | ||||
−0.196772 | + | 0.980449i | \(0.563046\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.23104e12 | 1.53502 | ||||||||
\(656\) | 3.61609e12 | 0.762382 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.20036e12 | 1.08148 | ||||||||
\(659\) | −7.92252e11 | −0.163636 | −0.0818181 | − | 0.996647i | \(-0.526073\pi\) | ||||
−0.0818181 | + | 0.996647i | \(0.526073\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.49133e11 | −0.152634 | −0.0763172 | − | 0.997084i | \(-0.524316\pi\) | ||||
−0.0763172 | + | 0.997084i | \(0.524316\pi\) | |||||||
\(662\) | 1.03279e13 | 2.09002 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.07081e12 | −1.41160 | ||||||||
\(665\) | 4.81311e12 | 0.954396 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.54319e10 | −0.0128004 | ||||||||
\(668\) | −2.85309e12 | −0.554398 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.47545e12 | 0.474589 | ||||||||
\(671\) | 9.71091e12 | 1.84931 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.01486e12 | 1.31811 | 0.659055 | − | 0.752095i | \(-0.270957\pi\) | ||||
0.659055 | + | 0.752095i | \(0.270957\pi\) | |||||||
\(674\) | −3.47435e12 | −0.648490 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.29923e13 | 4.23471 | ||||||||
\(677\) | −7.71992e12 | −1.41242 | −0.706210 | − | 0.708002i | \(-0.749597\pi\) | ||||
−0.706210 | + | 0.708002i | \(0.749597\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.65069e12 | 0.478570 | ||||||||
\(680\) | −4.62229e12 | −0.829025 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.31802e12 | 0.410286 | ||||||||
\(683\) | 4.25216e12 | 0.747680 | 0.373840 | − | 0.927493i | \(-0.378041\pi\) | ||||
0.373840 | + | 0.927493i | \(0.378041\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.28614e12 | 1.09088 | ||||||||
\(686\) | 9.34014e12 | 1.61026 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.29195e12 | −1.41094 | ||||||||
\(689\) | 1.03492e13 | 1.74953 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.49111e12 | −0.415664 | −0.207832 | − | 0.978165i | \(-0.566641\pi\) | ||||
−0.207832 | + | 0.978165i | \(0.566641\pi\) | |||||||
\(692\) | −5.89539e12 | −0.977317 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.64679e13 | −2.69476 | ||||||||
\(695\) | 7.09286e11 | 0.115316 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.49732e11 | −0.0561291 | ||||||||
\(698\) | 1.23459e13 | 1.96867 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.65972e12 | 0.261272 | ||||||||
\(701\) | 3.08136e11 | 0.0481961 | 0.0240980 | − | 0.999710i | \(-0.492329\pi\) | ||||
0.0240980 | + | 0.999710i | \(0.492329\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.78049e12 | 0.892619 | ||||||||
\(704\) | −1.91355e13 | −2.93605 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.65255e12 | 0.250342 | ||||||||
\(707\) | −8.38630e11 | −0.126236 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.98388e12 | −1.03798 | −0.518990 | − | 0.854780i | \(-0.673692\pi\) | ||||
−0.518990 | + | 0.854780i | \(0.673692\pi\) | |||||||
\(710\) | −1.35530e13 | −2.00158 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.41658e13 | −2.06577 | ||||||||
\(713\) | 6.69922e11 | 0.0970781 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.32784e13 | −1.90007 | ||||||||
\(716\) | −2.86724e12 | −0.407714 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.64876e12 | −0.512373 | ||||||||
\(719\) | 1.30686e13 | 1.82368 | 0.911842 | − | 0.410540i | \(-0.134660\pi\) | ||||
0.911842 | + | 0.410540i | \(0.134660\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.65895e11 | −0.0228626 | ||||||||
\(722\) | −3.22615e13 | −4.41842 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.43209e13 | 3.28970 | ||||||||
\(725\) | −4.11053e10 | −0.00552557 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.13650e12 | −0.150891 | −0.0754456 | − | 0.997150i | \(-0.524038\pi\) | ||||
−0.0754456 | + | 0.997150i | \(0.524038\pi\) | |||||||
\(728\) | 1.81431e13 | 2.39398 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.29642e13 | −1.68963 | ||||||||
\(731\) | 8.01960e11 | 0.103878 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.78287e12 | 0.739904 | 0.369952 | − | 0.929051i | \(-0.379374\pi\) | ||||
0.369952 | + | 0.929051i | \(0.379374\pi\) | |||||||
\(734\) | −2.81507e13 | −3.57978 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.21705e13 | −1.52883 | ||||||||
\(737\) | −1.94185e12 | −0.242444 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.05562e13 | −1.30199 | −0.650996 | − | 0.759081i | \(-0.725649\pi\) | ||||
−0.650996 | + | 0.759081i | \(0.725649\pi\) | |||||||
\(740\) | 1.15628e13 | 1.41750 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.12308e12 | 0.983792 | ||||||||
\(743\) | −1.33049e13 | −1.60163 | −0.800815 | − | 0.598912i | \(-0.795600\pi\) | ||||
−0.800815 | + | 0.598912i | \(0.795600\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.87300e12 | 0.341690 | ||||||||
\(746\) | 4.18020e12 | 0.494165 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.84805e12 | 0.683053 | ||||||||
\(749\) | −4.03729e12 | −0.468729 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.33606e12 | −0.267982 | −0.133991 | − | 0.990983i | \(-0.542779\pi\) | ||||
−0.133991 | + | 0.990983i | \(0.542779\pi\) | |||||||
\(752\) | −3.43977e13 | −3.92238 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.24716e11 | −0.0816576 | ||||||||
\(755\) | 9.29248e12 | 1.04081 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.17644e13 | −1.30208 | −0.651039 | − | 0.759045i | \(-0.725666\pi\) | ||||
−0.651039 | + | 0.759045i | \(0.725666\pi\) | |||||||
\(758\) | 2.93509e13 | 3.22931 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.72697e13 | −6.22679 | ||||||||
\(761\) | −3.21795e12 | −0.347815 | −0.173907 | − | 0.984762i | \(-0.555639\pi\) | ||||
−0.173907 | + | 0.984762i | \(0.555639\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.13225e12 | −0.227760 | ||||||||
\(764\) | 8.51281e11 | 0.0903968 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.74991e12 | 0.708384 | ||||||||
\(767\) | 1.59827e13 | 1.66752 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.65995e12 | −0.996108 | −0.498054 | − | 0.867146i | \(-0.665952\pi\) | ||||
−0.498054 | + | 0.867146i | \(0.665952\pi\) | |||||||
\(770\) | −1.04222e13 | −1.06844 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.04802e13 | 2.07518 | ||||||||
\(773\) | 3.02219e12 | 0.304449 | 0.152224 | − | 0.988346i | \(-0.451356\pi\) | ||||
0.152224 | + | 0.988346i | \(0.451356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.20855e11 | 0.0419059 | ||||||||
\(776\) | −3.15398e13 | −3.12235 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.39658e13 | −2.34522 | ||||||||
\(779\) | −4.33315e12 | −0.421585 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.06315e13 | 1.02251 | ||||||||
\(782\) | 2.33234e12 | 0.223029 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.69320e13 | −2.54593 | ||||||||
\(785\) | −9.02606e12 | −0.848369 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.47037e13 | −1.36628 | −0.683141 | − | 0.730286i | \(-0.739387\pi\) | ||||
−0.683141 | + | 0.730286i | \(0.739387\pi\) | |||||||
\(788\) | 3.54734e13 | 3.27744 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.80605e13 | 1.64971 | ||||||||
\(791\) | −4.25106e12 | −0.386103 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.10846e13 | 2.79136 | ||||||||
\(794\) | 1.12723e13 | 1.00652 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.58430e13 | 4.04729 | ||||||||
\(797\) | 1.44405e13 | 1.26771 | 0.633856 | − | 0.773451i | \(-0.281471\pi\) | ||||
0.633856 | + | 0.773451i | \(0.281471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.32680e12 | 0.288779 | ||||||||
\(800\) | −7.64569e12 | −0.659951 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.47017e12 | 0.296187 | ||||||||
\(803\) | 1.01696e13 | 0.863148 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.01208e12 | −0.252805 | ||||||||
\(806\) | 7.41997e12 | 0.619291 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.97860e12 | 0.823604 | ||||||||
\(809\) | −1.10265e13 | −0.905041 | −0.452521 | − | 0.891754i | \(-0.649475\pi\) | ||||
−0.452521 | + | 0.891754i | \(0.649475\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.97221e12 | 0.160088 | 0.0800440 | − | 0.996791i | \(-0.474494\pi\) | ||||
0.0800440 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(812\) | −4.12200e11 | −0.0332741 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.25169e13 | −0.999282 | ||||||||
\(815\) | −1.83320e13 | −1.45546 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.93621e12 | 0.780228 | ||||||||
\(818\) | −2.14173e13 | −1.67253 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.66769e12 | −0.669485 | ||||||||
\(821\) | 1.24725e13 | 0.958093 | 0.479047 | − | 0.877789i | \(-0.340982\pi\) | ||||
0.479047 | + | 0.877789i | \(0.340982\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.63904e12 | 0.428455 | 0.214228 | − | 0.976784i | \(-0.431277\pi\) | ||||
0.214228 | + | 0.976784i | \(0.431277\pi\) | |||||||
\(824\) | 1.97394e12 | 0.149163 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.25448e13 | 0.937674 | ||||||||
\(827\) | 6.43118e12 | 0.478097 | 0.239048 | − | 0.971008i | \(-0.423165\pi\) | ||||
0.239048 | + | 0.971008i | \(0.423165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.51844e12 | −0.332272 | −0.166136 | − | 0.986103i | \(-0.553129\pi\) | ||||
−0.166136 | + | 0.986103i | \(0.553129\pi\) | |||||||
\(830\) | 1.30018e13 | 0.950936 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.12529e13 | −4.43171 | ||||||||
\(833\) | 2.60475e12 | 0.187440 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.25279e12 | 0.231562 | ||||||||
\(836\) | 7.24568e13 | 5.13039 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.15647e13 | 1.51058 | ||||||||
\(839\) | −1.73764e13 | −1.21068 | −0.605342 | − | 0.795965i | \(-0.706964\pi\) | ||||
−0.605342 | + | 0.795965i | \(0.706964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.44969e13 | −0.999296 | ||||||||
\(842\) | −4.08530e13 | −2.80104 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.09802e13 | −2.10157 | ||||||||
\(845\) | −2.62134e13 | −1.76876 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.03647e12 | 0.0691962 | ||||||||
\(848\) | −5.37301e13 | −3.56809 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.46521e12 | 0.0962752 | ||||||||
\(851\) | −3.61747e12 | −0.236441 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.23489e12 | −0.209213 | −0.104607 | − | 0.994514i | \(-0.533358\pi\) | ||||
−0.104607 | + | 0.994514i | \(0.533358\pi\) | |||||||
\(854\) | 2.43982e13 | 1.56963 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.80384e13 | 3.05814 | ||||||||
\(857\) | −6.56773e12 | −0.415912 | −0.207956 | − | 0.978138i | \(-0.566681\pi\) | ||||
−0.207956 | + | 0.978138i | \(0.566681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.06597e13 | −0.668001 | −0.334000 | − | 0.942573i | \(-0.608399\pi\) | ||||
−0.334000 | + | 0.942573i | \(0.608399\pi\) | |||||||
\(860\) | 1.98756e13 | 1.23902 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.19649e13 | −1.35502 | ||||||||
\(863\) | 2.96333e12 | 0.181857 | 0.0909287 | − | 0.995857i | \(-0.471016\pi\) | ||||
0.0909287 | + | 0.995857i | \(0.471016\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.72130e12 | 0.408207 | ||||||||
\(866\) | −5.39466e13 | −3.25937 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.22029e12 | 0.252350 | ||||||||
\(869\) | −1.41674e13 | −0.842755 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.21585e12 | −0.365948 | ||||||||
\(872\) | 2.53710e13 | 1.48598 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.88974e13 | 1.67516 | ||||||||
\(875\) | 7.19209e12 | 0.414781 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.22652e13 | −0.700128 | −0.350064 | − | 0.936726i | \(-0.613840\pi\) | ||||
−0.350064 | + | 0.936726i | \(0.613840\pi\) | |||||||
\(878\) | 4.97019e13 | 2.82259 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.89375e13 | 3.87511 | ||||||||
\(881\) | −2.36185e13 | −1.32087 | −0.660435 | − | 0.750883i | \(-0.729628\pi\) | ||||
−0.660435 | + | 0.750883i | \(0.729628\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.46792e13 | 1.36618 | 0.683089 | − | 0.730335i | \(-0.260636\pi\) | ||||
0.683089 | + | 0.730335i | \(0.260636\pi\) | |||||||
\(884\) | 1.87196e13 | 1.03101 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.79663e13 | 3.70546 | ||||||||
\(887\) | 8.49974e12 | 0.461051 | 0.230526 | − | 0.973066i | \(-0.425955\pi\) | ||||
0.230526 | + | 0.973066i | \(0.425955\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.40702e12 | 0.0755516 | ||||||||
\(890\) | 2.60481e13 | 1.39162 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.83694e13 | −4.14481 | ||||||||
\(893\) | 4.12186e13 | 2.16901 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.26892e12 | 0.170295 | ||||||||
\(896\) | −1.89442e13 | −0.981950 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.03201e13 | −3.09541 | ||||||||
\(899\) | −1.04522e11 | −0.00533689 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.19653e12 | 0.262695 | ||||||||
\(902\) | 9.38288e12 | 0.471962 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.05821e13 | 2.51906 | ||||||||
\(905\) | −2.77281e13 | −1.37405 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.51717e13 | −0.744390 | −0.372195 | − | 0.928155i | \(-0.621395\pi\) | ||||
−0.372195 | + | 0.928155i | \(0.621395\pi\) | |||||||
\(908\) | 8.57645e12 | 0.418718 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.33614e13 | −1.61272 | ||||||||
\(911\) | 2.65044e12 | 0.127493 | 0.0637464 | − | 0.997966i | \(-0.479695\pi\) | ||||
0.0637464 | + | 0.997966i | \(0.479695\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.01991e13 | −0.485786 | ||||||||
\(914\) | −1.62340e13 | −0.769425 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.77348e13 | −4.58690 | ||||||||
\(917\) | −1.42515e13 | −0.665576 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.10783e13 | −0.512336 | −0.256168 | − | 0.966632i | \(-0.582460\pi\) | ||||
−0.256168 | + | 0.966632i | \(0.582460\pi\) | |||||||
\(920\) | 3.58398e13 | 1.64938 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.79656e12 | 0.400889 | ||||||||
\(923\) | 3.40315e13 | 1.54338 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.27255e12 | −0.102065 | ||||||||
\(926\) | 5.13860e13 | 2.29665 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.89885e12 | 0.0840475 | ||||||||
\(929\) | 1.10570e13 | 0.487044 | 0.243522 | − | 0.969895i | \(-0.421697\pi\) | ||||
0.243522 | + | 0.969895i | \(0.421697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.22725e13 | 1.40786 | ||||||||
\(932\) | 1.09597e14 | 4.75804 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.17655e13 | −2.22577 | ||||||||
\(935\) | −6.66733e12 | −0.285299 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.12152e13 | −1.32293 | −0.661466 | − | 0.749975i | \(-0.730065\pi\) | ||||
−0.661466 | + | 0.749975i | \(0.730065\pi\) | |||||||
\(938\) | −4.87880e12 | −0.205779 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.24505e13 | 3.44444 | ||||||||
\(941\) | −3.48495e13 | −1.44891 | −0.724457 | − | 0.689320i | \(-0.757910\pi\) | ||||
−0.724457 | + | 0.689320i | \(0.757910\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.71171e12 | 0.111671 | ||||||||
\(944\) | −8.29772e13 | −3.40083 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.15156e13 | −0.873460 | ||||||||
\(947\) | −2.89060e13 | −1.16792 | −0.583960 | − | 0.811783i | \(-0.698497\pi\) | ||||
−0.583960 | + | 0.811783i | \(0.698497\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.25530e13 | 1.30285 | ||||||||
\(950\) | 1.81538e13 | 0.723121 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.10996e12 | 0.359460 | ||||||||
\(953\) | −1.17377e13 | −0.460963 | −0.230482 | − | 0.973077i | \(-0.574030\pi\) | ||||
−0.230482 | + | 0.973077i | \(0.574030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.70540e11 | −0.0377571 | ||||||||
\(956\) | −1.00877e14 | −3.90598 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.63328e12 | −0.0626494 | ||||||||
\(959\) | −1.23892e13 | −0.472998 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.53695e13 | −0.959525 | ||||||||
\(962\) | −4.00667e13 | −1.50833 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.43173e13 | −0.533969 | ||||||||
\(965\) | −2.33493e13 | −0.866765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.64159e13 | 1.70705 | 0.853527 | − | 0.521048i | \(-0.174459\pi\) | ||||
0.853527 | + | 0.521048i | \(0.174459\pi\) | |||||||
\(968\) | −1.23327e13 | −0.451458 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.79952e13 | 2.10339 | ||||||||
\(971\) | 3.56315e12 | 0.128632 | 0.0643158 | − | 0.997930i | \(-0.479514\pi\) | ||||
0.0643158 | + | 0.997930i | \(0.479514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.39791e12 | −0.0500003 | ||||||||
\(974\) | −8.10986e13 | −2.88734 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.61382e14 | −5.69287 | ||||||||
\(977\) | 1.39593e13 | 0.490160 | 0.245080 | − | 0.969503i | \(-0.421186\pi\) | ||||
0.245080 | + | 0.969503i | \(0.421186\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.04332e13 | −0.710909 | ||||||||
\(980\) | 6.45554e13 | 2.23571 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.04731e13 | −0.359395 | ||||||||
\(983\) | 6.28271e12 | 0.214613 | 0.107306 | − | 0.994226i | \(-0.465777\pi\) | ||||
0.107306 | + | 0.994226i | \(0.465777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.04429e13 | −1.36893 | ||||||||
\(986\) | −3.63893e11 | −0.0122610 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.31934e14 | 7.74388 | ||||||||
\(989\) | −6.21815e12 | −0.206670 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.49640e13 | −1.48093 | −0.740463 | − | 0.672097i | \(-0.765394\pi\) | ||||
−0.740463 | + | 0.672097i | \(0.765394\pi\) | |||||||
\(992\) | −1.94413e13 | −0.637416 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.67112e13 | 0.867871 | ||||||||
\(995\) | −5.22653e13 | −1.69048 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.21770e13 | −0.390311 | −0.195156 | − | 0.980772i | \(-0.562521\pi\) | ||||
−0.195156 | + | 0.980772i | \(0.562521\pi\) | |||||||
\(998\) | −3.40075e13 | −1.08514 | ||||||||
\(999\) | 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 | 153.10.a.f.1.1 | 7 | ||
3.2 | odd | 2 | 17.10.a.b.1.7 | ✓ | 7 | ||
12.11 | even | 2 | 272.10.a.g.1.6 | 7 | |||
51.50 | odd | 2 | 289.10.a.b.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.b.1.7 | ✓ | 7 | 3.2 | odd | 2 | ||
153.10.a.f.1.1 | 7 | 1.1 | even | 1 | trivial | ||
272.10.a.g.1.6 | 7 | 12.11 | even | 2 | |||
289.10.a.b.1.7 | 7 | 51.50 | odd | 2 |