Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + 1488374176 x^{9} + 42885295136 x^{8} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-13.0039\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −13.0039 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 41.1009 | 0.321101 | ||||||||
\(5\) | −167.303 | −0.598562 | −0.299281 | − | 0.954165i | \(-0.596747\pi\) | ||||
−0.299281 | + | 0.954165i | \(0.596747\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 887.373 | 0.977829 | 0.488915 | − | 0.872332i | \(-0.337393\pi\) | ||||
0.488915 | + | 0.872332i | \(0.337393\pi\) | |||||||
\(8\) | 1130.03 | 0.780321 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2175.59 | 0.687982 | ||||||||
\(11\) | 7784.37 | 1.76339 | 0.881696 | − | 0.471818i | \(-0.156402\pi\) | ||||
0.881696 | + | 0.471818i | \(0.156402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4609.99 | 0.581967 | 0.290983 | − | 0.956728i | \(-0.406018\pi\) | ||||
0.290983 | + | 0.956728i | \(0.406018\pi\) | |||||||
\(14\) | −11539.3 | −1.12391 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19955.6 | −1.21800 | ||||||||
\(17\) | 6055.74 | 0.298948 | 0.149474 | − | 0.988766i | \(-0.452242\pi\) | ||||
0.149474 | + | 0.988766i | \(0.452242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13552.7 | 0.453304 | 0.226652 | − | 0.973976i | \(-0.427222\pi\) | ||||
0.226652 | + | 0.973976i | \(0.427222\pi\) | |||||||
\(20\) | −6876.32 | −0.192199 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −101227. | −2.02683 | ||||||||
\(23\) | −35274.4 | −0.604523 | −0.302261 | − | 0.953225i | \(-0.597742\pi\) | ||||
−0.302261 | + | 0.953225i | \(0.597742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −50134.6 | −0.641723 | ||||||||
\(26\) | −59947.7 | −0.668907 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 36471.8 | 0.313982 | ||||||||
\(29\) | −78335.1 | −0.596435 | −0.298218 | − | 0.954498i | \(-0.596392\pi\) | ||||
−0.298218 | + | 0.954498i | \(0.596392\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −170575. | −1.02837 | −0.514184 | − | 0.857680i | \(-0.671905\pi\) | ||||
−0.514184 | + | 0.857680i | \(0.671905\pi\) | |||||||
\(32\) | 114857. | 0.619632 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −78748.2 | −0.343609 | ||||||||
\(35\) | −148460. | −0.585292 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −263573. | −0.855451 | −0.427726 | − | 0.903909i | \(-0.640685\pi\) | ||||
−0.427726 | + | 0.903909i | \(0.640685\pi\) | |||||||
\(38\) | −176238. | −0.521024 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −189057. | −0.467071 | ||||||||
\(41\) | 198905. | 0.450714 | 0.225357 | − | 0.974276i | \(-0.427645\pi\) | ||||
0.225357 | + | 0.974276i | \(0.427645\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −444435. | −0.852449 | −0.426225 | − | 0.904617i | \(-0.640157\pi\) | ||||
−0.426225 | + | 0.904617i | \(0.640157\pi\) | |||||||
\(44\) | 319945. | 0.566227 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 458704. | 0.694833 | ||||||||
\(47\) | 531622. | 0.746896 | 0.373448 | − | 0.927651i | \(-0.378175\pi\) | ||||
0.373448 | + | 0.927651i | \(0.378175\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −36112.2 | −0.0438499 | ||||||||
\(50\) | 651945. | 0.737591 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 189475. | 0.186870 | ||||||||
\(53\) | 1.00107e6 | 0.923631 | 0.461816 | − | 0.886976i | \(-0.347198\pi\) | ||||
0.461816 | + | 0.886976i | \(0.347198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.30235e6 | −1.05550 | ||||||||
\(56\) | 1.00275e6 | 0.763021 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.01866e6 | 0.685538 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.77312e6 | −1.00019 | −0.500097 | − | 0.865969i | \(-0.666702\pi\) | ||||
−0.500097 | + | 0.865969i | \(0.666702\pi\) | |||||||
\(62\) | 2.21813e6 | 1.18200 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.06073e6 | 0.505795 | ||||||||
\(65\) | −771266. | −0.348343 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.37225e6 | −0.963606 | −0.481803 | − | 0.876280i | \(-0.660018\pi\) | ||||
−0.481803 | + | 0.876280i | \(0.660018\pi\) | |||||||
\(68\) | 248897. | 0.0959926 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.93056e6 | 0.672729 | ||||||||
\(71\) | 5.87275e6 | 1.94732 | 0.973659 | − | 0.228008i | \(-0.0732212\pi\) | ||||
0.973659 | + | 0.228008i | \(0.0732212\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.90906e6 | −0.875232 | −0.437616 | − | 0.899162i | \(-0.644177\pi\) | ||||
−0.437616 | + | 0.899162i | \(0.644177\pi\) | |||||||
\(74\) | 3.42748e6 | 0.983249 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 557030. | 0.145556 | ||||||||
\(77\) | 6.90764e6 | 1.72430 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.66441e6 | −0.379808 | −0.189904 | − | 0.981803i | \(-0.560818\pi\) | ||||
−0.189904 | + | 0.981803i | \(0.560818\pi\) | |||||||
\(80\) | 3.33864e6 | 0.729046 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.58653e6 | −0.518047 | ||||||||
\(83\) | −8.18425e6 | −1.57111 | −0.785553 | − | 0.618794i | \(-0.787621\pi\) | ||||
−0.785553 | + | 0.618794i | \(0.787621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.01315e6 | −0.178939 | ||||||||
\(86\) | 5.77938e6 | 0.979798 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.79653e6 | 1.37601 | ||||||||
\(89\) | −1.13356e7 | −1.70444 | −0.852219 | − | 0.523185i | \(-0.824744\pi\) | ||||
−0.852219 | + | 0.523185i | \(0.824744\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.09078e6 | 0.569064 | ||||||||
\(92\) | −1.44981e6 | −0.194113 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.91315e6 | −0.858476 | ||||||||
\(95\) | −2.26742e6 | −0.271331 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 243947. | 0.0271390 | 0.0135695 | − | 0.999908i | \(-0.495681\pi\) | ||||
0.0135695 | + | 0.999908i | \(0.495681\pi\) | |||||||
\(98\) | 469599. | 0.0504006 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.06058e6 | −0.206058 | ||||||||
\(101\) | −1.91745e7 | −1.85183 | −0.925913 | − | 0.377736i | \(-0.876703\pi\) | ||||
−0.925913 | + | 0.377736i | \(0.876703\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.63345e6 | 0.778492 | 0.389246 | − | 0.921134i | \(-0.372736\pi\) | ||||
0.389246 | + | 0.921134i | \(0.372736\pi\) | |||||||
\(104\) | 5.20940e6 | 0.454121 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.30178e7 | −1.06161 | ||||||||
\(107\) | 1.22715e7 | 0.968397 | 0.484199 | − | 0.874958i | \(-0.339111\pi\) | ||||
0.484199 | + | 0.874958i | \(0.339111\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.90858e6 | −0.510971 | −0.255485 | − | 0.966813i | \(-0.582235\pi\) | ||||
−0.255485 | + | 0.966813i | \(0.582235\pi\) | |||||||
\(110\) | 1.69356e7 | 1.21318 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.77081e7 | −1.19099 | ||||||||
\(113\) | −9.23590e6 | −0.602150 | −0.301075 | − | 0.953601i | \(-0.597345\pi\) | ||||
−0.301075 | + | 0.953601i | \(0.597345\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.90153e6 | 0.361844 | ||||||||
\(116\) | −3.21964e6 | −0.191516 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.67072e6 | 0.149638 | ||||||||
\(119\) | 5.37370e6 | 0.292320 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.11092e7 | 2.10955 | ||||||||
\(122\) | 2.30575e7 | 1.14961 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.01078e6 | −0.330210 | ||||||||
\(125\) | 2.14583e7 | 0.982674 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.43987e6 | 0.149015 | 0.0745073 | − | 0.997220i | \(-0.476262\pi\) | ||||
0.0745073 | + | 0.997220i | \(0.476262\pi\) | |||||||
\(128\) | −2.84953e7 | −1.20099 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.00295e7 | 0.400383 | ||||||||
\(131\) | 2.36186e6 | 0.0917919 | 0.0458960 | − | 0.998946i | \(-0.485386\pi\) | ||||
0.0458960 | + | 0.998946i | \(0.485386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.20263e7 | 0.443254 | ||||||||
\(134\) | 3.08485e7 | 1.10756 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.84314e6 | 0.233276 | ||||||||
\(137\) | −3.14805e6 | −0.104597 | −0.0522985 | − | 0.998631i | \(-0.516655\pi\) | ||||
−0.0522985 | + | 0.998631i | \(0.516655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.60628e7 | 0.507305 | 0.253652 | − | 0.967295i | \(-0.418368\pi\) | ||||
0.253652 | + | 0.967295i | \(0.418368\pi\) | |||||||
\(140\) | −6.10186e6 | −0.187938 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.63685e7 | −2.23823 | ||||||||
\(143\) | 3.58858e7 | 1.02624 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.31057e7 | 0.357004 | ||||||||
\(146\) | 3.78291e7 | 1.00598 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.08331e7 | −0.274686 | ||||||||
\(149\) | 3.30906e7 | 0.819506 | 0.409753 | − | 0.912196i | \(-0.365615\pi\) | ||||
0.409753 | + | 0.912196i | \(0.365615\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.23311e7 | −1.94601 | −0.973003 | − | 0.230791i | \(-0.925869\pi\) | ||||
−0.973003 | + | 0.230791i | \(0.925869\pi\) | |||||||
\(152\) | 1.53149e7 | 0.353722 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.98261e7 | −1.98189 | ||||||||
\(155\) | 2.85377e7 | 0.615543 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.06660e7 | 1.45734 | 0.728671 | − | 0.684863i | \(-0.240138\pi\) | ||||
0.728671 | + | 0.684863i | \(0.240138\pi\) | |||||||
\(158\) | 2.16437e7 | 0.436548 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.92160e7 | −0.370889 | ||||||||
\(161\) | −3.13016e7 | −0.591120 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.37840e7 | −0.972740 | −0.486370 | − | 0.873753i | \(-0.661679\pi\) | ||||
−0.486370 | + | 0.873753i | \(0.661679\pi\) | |||||||
\(164\) | 8.17516e6 | 0.144725 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.06427e8 | 1.80582 | ||||||||
\(167\) | −4.12989e7 | −0.686169 | −0.343084 | − | 0.939305i | \(-0.611472\pi\) | ||||
−0.343084 | + | 0.939305i | \(0.611472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.14965e7 | −0.661315 | ||||||||
\(170\) | 1.31748e7 | 0.205671 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.82667e7 | −0.273722 | ||||||||
\(173\) | −5.36462e7 | −0.787731 | −0.393865 | − | 0.919168i | \(-0.628862\pi\) | ||||
−0.393865 | + | 0.919168i | \(0.628862\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.44881e7 | −0.627496 | ||||||||
\(176\) | −1.55342e8 | −2.14780 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.47407e8 | 1.95907 | ||||||||
\(179\) | 3.62629e7 | 0.472581 | 0.236291 | − | 0.971682i | \(-0.424068\pi\) | ||||
0.236291 | + | 0.971682i | \(0.424068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.64625e7 | −0.206358 | −0.103179 | − | 0.994663i | \(-0.532901\pi\) | ||||
−0.103179 | + | 0.994663i | \(0.532901\pi\) | |||||||
\(182\) | −5.31960e7 | −0.654077 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.98610e7 | −0.471722 | ||||||||
\(185\) | 4.40967e7 | 0.512041 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.71401e7 | 0.527163 | ||||||||
\(188\) | 2.18501e7 | 0.239829 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.94852e7 | 0.311865 | ||||||||
\(191\) | 7.01561e7 | 0.728532 | 0.364266 | − | 0.931295i | \(-0.381320\pi\) | ||||
0.364266 | + | 0.931295i | \(0.381320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.06871e7 | 0.908019 | 0.454010 | − | 0.890997i | \(-0.349993\pi\) | ||||
0.454010 | + | 0.890997i | \(0.349993\pi\) | |||||||
\(194\) | −3.17225e6 | −0.0311933 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.48425e6 | −0.0140802 | ||||||||
\(197\) | 3.02563e7 | 0.281958 | 0.140979 | − | 0.990013i | \(-0.454975\pi\) | ||||
0.140979 | + | 0.990013i | \(0.454975\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.78612e8 | 1.60666 | 0.803332 | − | 0.595532i | \(-0.203059\pi\) | ||||
0.803332 | + | 0.595532i | \(0.203059\pi\) | |||||||
\(200\) | −5.66534e7 | −0.500750 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.49343e8 | 2.12847 | ||||||||
\(203\) | −6.95125e7 | −0.583212 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.32774e7 | −0.269781 | ||||||||
\(206\) | −1.12268e8 | −0.894792 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.19952e7 | −0.708832 | ||||||||
\(209\) | 1.05499e8 | 0.799352 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.01493e8 | −0.743786 | −0.371893 | − | 0.928276i | \(-0.621291\pi\) | ||||
−0.371893 | + | 0.928276i | \(0.621291\pi\) | |||||||
\(212\) | 4.11449e7 | 0.296579 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.59577e8 | −1.11307 | ||||||||
\(215\) | 7.43554e7 | 0.510244 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.51363e8 | −1.00557 | ||||||||
\(218\) | 8.98383e7 | 0.587305 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.35278e7 | −0.338922 | ||||||||
\(221\) | 2.79169e7 | 0.173978 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.17677e8 | 0.710600 | 0.355300 | − | 0.934752i | \(-0.384379\pi\) | ||||
0.355300 | + | 0.934752i | \(0.384379\pi\) | |||||||
\(224\) | 1.01921e8 | 0.605895 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.20102e8 | 0.692106 | ||||||||
\(227\) | −2.17121e8 | −1.23200 | −0.616000 | − | 0.787746i | \(-0.711248\pi\) | ||||
−0.616000 | + | 0.787746i | \(0.711248\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.89428e7 | 0.379372 | 0.189686 | − | 0.981845i | \(-0.439253\pi\) | ||||
0.189686 | + | 0.981845i | \(0.439253\pi\) | |||||||
\(230\) | −7.67427e7 | −0.415901 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.85207e7 | −0.465411 | ||||||||
\(233\) | −2.42127e8 | −1.25400 | −0.627000 | − | 0.779019i | \(-0.715718\pi\) | ||||
−0.627000 | + | 0.779019i | \(0.715718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.89421e7 | −0.447064 | ||||||||
\(236\) | −8.44126e6 | −0.0418038 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.98790e7 | −0.335991 | ||||||||
\(239\) | −1.66165e8 | −0.787312 | −0.393656 | − | 0.919258i | \(-0.628790\pi\) | ||||
−0.393656 | + | 0.919258i | \(0.628790\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.91718e7 | 0.134247 | 0.0671233 | − | 0.997745i | \(-0.478618\pi\) | ||||
0.0671233 | + | 0.997745i | \(0.478618\pi\) | |||||||
\(242\) | −5.34579e8 | −2.42470 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.28769e7 | −0.321163 | ||||||||
\(245\) | 6.04170e6 | 0.0262469 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.24779e7 | 0.263808 | ||||||||
\(248\) | −1.92754e8 | −0.802458 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.79041e8 | −1.12948 | ||||||||
\(251\) | −2.96094e8 | −1.18188 | −0.590938 | − | 0.806717i | \(-0.701242\pi\) | ||||
−0.590938 | + | 0.806717i | \(0.701242\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.74589e8 | −1.06601 | ||||||||
\(254\) | −4.47317e7 | −0.171276 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.34777e8 | 0.874611 | ||||||||
\(257\) | −2.67505e8 | −0.983027 | −0.491514 | − | 0.870870i | \(-0.663556\pi\) | ||||
−0.491514 | + | 0.870870i | \(0.663556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.33888e8 | −0.836485 | ||||||||
\(260\) | −3.16997e7 | −0.111853 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.07133e7 | −0.105505 | ||||||||
\(263\) | −2.10348e8 | −0.713006 | −0.356503 | − | 0.934294i | \(-0.616031\pi\) | ||||
−0.356503 | + | 0.934294i | \(0.616031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.67482e8 | −0.552851 | ||||||||
\(266\) | −1.56389e8 | −0.509472 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.75018e7 | −0.309415 | ||||||||
\(269\) | 4.76854e8 | 1.49366 | 0.746831 | − | 0.665014i | \(-0.231574\pi\) | ||||
0.746831 | + | 0.665014i | \(0.231574\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.49889e8 | −0.762701 | −0.381350 | − | 0.924431i | \(-0.624541\pi\) | ||||
−0.381350 | + | 0.924431i | \(0.624541\pi\) | |||||||
\(272\) | −1.20846e8 | −0.364118 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.09368e7 | 0.120223 | ||||||||
\(275\) | −3.90266e8 | −1.13161 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.02351e8 | −0.572039 | −0.286020 | − | 0.958224i | \(-0.592332\pi\) | ||||
−0.286020 | + | 0.958224i | \(0.592332\pi\) | |||||||
\(278\) | −2.08879e8 | −0.583092 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.67764e8 | −0.456715 | ||||||||
\(281\) | 2.77424e8 | 0.745885 | 0.372942 | − | 0.927855i | \(-0.378349\pi\) | ||||
0.372942 | + | 0.927855i | \(0.378349\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.44360e8 | −0.903151 | −0.451575 | − | 0.892233i | \(-0.649138\pi\) | ||||
−0.451575 | + | 0.892233i | \(0.649138\pi\) | |||||||
\(284\) | 2.41375e8 | 0.625286 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.66655e8 | −1.17955 | ||||||||
\(287\) | 1.76503e8 | 0.440722 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.73667e8 | −0.910630 | ||||||||
\(290\) | −1.70425e8 | −0.410337 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.19565e8 | −0.281038 | ||||||||
\(293\) | 3.56077e8 | 0.827004 | 0.413502 | − | 0.910503i | \(-0.364306\pi\) | ||||
0.413502 | + | 0.910503i | \(0.364306\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.43606e7 | 0.0779262 | ||||||||
\(296\) | −2.97845e8 | −0.667527 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.30306e8 | −0.941934 | ||||||||
\(299\) | −1.62615e8 | −0.351812 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.94379e8 | −0.833550 | ||||||||
\(302\) | 1.07062e9 | 2.23672 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.70453e8 | −0.552122 | ||||||||
\(305\) | 2.96649e8 | 0.598679 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.96195e8 | −0.386993 | −0.193496 | − | 0.981101i | \(-0.561983\pi\) | ||||
−0.193496 | + | 0.981101i | \(0.561983\pi\) | |||||||
\(308\) | 2.83910e8 | 0.553673 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.71101e8 | −0.707500 | ||||||||
\(311\) | −5.23320e7 | −0.0986519 | −0.0493260 | − | 0.998783i | \(-0.515707\pi\) | ||||
−0.0493260 | + | 0.998783i | \(0.515707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.12015e8 | −0.575136 | −0.287568 | − | 0.957760i | \(-0.592847\pi\) | ||||
−0.287568 | + | 0.957760i | \(0.592847\pi\) | |||||||
\(314\) | −9.18932e8 | −1.67506 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.84086e7 | −0.121957 | ||||||||
\(317\) | −5.38220e8 | −0.948970 | −0.474485 | − | 0.880264i | \(-0.657366\pi\) | ||||
−0.474485 | + | 0.880264i | \(0.657366\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.09789e8 | −1.05175 | ||||||||
\(320\) | −1.77463e8 | −0.302750 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.07042e8 | 0.679428 | ||||||||
\(323\) | 8.20719e7 | 0.135514 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.31120e8 | −0.373461 | ||||||||
\(326\) | 6.99401e8 | 1.11806 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.24767e8 | 0.351702 | ||||||||
\(329\) | 4.71747e8 | 0.730337 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.08848e8 | −1.07437 | −0.537187 | − | 0.843463i | \(-0.680513\pi\) | ||||
−0.537187 | + | 0.843463i | \(0.680513\pi\) | |||||||
\(332\) | −3.36380e8 | −0.504483 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.37046e8 | 0.788676 | ||||||||
\(335\) | 3.96886e8 | 0.576778 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.28631e8 | 0.183079 | 0.0915397 | − | 0.995801i | \(-0.470821\pi\) | ||||
0.0915397 | + | 0.995801i | \(0.470821\pi\) | |||||||
\(338\) | 5.39616e8 | 0.760110 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.16412e7 | −0.0574575 | ||||||||
\(341\) | −1.32782e9 | −1.81342 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.62835e8 | −1.02071 | ||||||||
\(344\) | −5.02223e8 | −0.665184 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.97609e8 | 0.905411 | ||||||||
\(347\) | 6.00582e7 | 0.0771648 | 0.0385824 | − | 0.999255i | \(-0.487716\pi\) | ||||
0.0385824 | + | 0.999255i | \(0.487716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.11674e9 | 1.40625 | 0.703124 | − | 0.711067i | \(-0.251788\pi\) | ||||
0.703124 | + | 0.711067i | \(0.251788\pi\) | |||||||
\(350\) | 5.78518e8 | 0.721238 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.94092e8 | 1.09265 | ||||||||
\(353\) | −3.99147e8 | −0.482971 | −0.241486 | − | 0.970404i | \(-0.577635\pi\) | ||||
−0.241486 | + | 0.970404i | \(0.577635\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.82530e8 | −1.16559 | ||||||||
\(356\) | −4.65905e8 | −0.547296 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.71558e8 | −0.543181 | ||||||||
\(359\) | 6.35935e8 | 0.725408 | 0.362704 | − | 0.931904i | \(-0.381854\pi\) | ||||
0.362704 | + | 0.931904i | \(0.381854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.10195e8 | −0.794516 | ||||||||
\(362\) | 2.14077e8 | 0.237186 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.68135e8 | 0.182727 | ||||||||
\(365\) | 4.86696e8 | 0.523881 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.61675e8 | −0.276332 | −0.138166 | − | 0.990409i | \(-0.544121\pi\) | ||||
−0.138166 | + | 0.990409i | \(0.544121\pi\) | |||||||
\(368\) | 7.03923e8 | 0.736305 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.73428e8 | −0.588536 | ||||||||
\(371\) | 8.88322e8 | 0.903154 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.69724e9 | 1.69341 | 0.846706 | − | 0.532060i | \(-0.178582\pi\) | ||||
0.846706 | + | 0.532060i | \(0.178582\pi\) | |||||||
\(374\) | −6.13004e8 | −0.605917 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00746e8 | 0.582819 | ||||||||
\(377\) | −3.61124e8 | −0.347106 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.10612e9 | 1.04367 | 0.521837 | − | 0.853045i | \(-0.325247\pi\) | ||||
0.521837 | + | 0.853045i | \(0.325247\pi\) | |||||||
\(380\) | −9.31929e7 | −0.0871245 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.12301e8 | −0.837368 | ||||||||
\(383\) | 6.71833e8 | 0.611034 | 0.305517 | − | 0.952187i | \(-0.401171\pi\) | ||||
0.305517 | + | 0.952187i | \(0.401171\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.15567e9 | −1.03210 | ||||||||
\(386\) | −1.17928e9 | −1.04367 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.00264e7 | 0.00871435 | ||||||||
\(389\) | −1.16525e9 | −1.00368 | −0.501839 | − | 0.864961i | \(-0.667343\pi\) | ||||
−0.501839 | + | 0.864961i | \(0.667343\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.13613e8 | −0.180721 | ||||||||
\(392\) | −4.08077e7 | −0.0342170 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.93450e8 | −0.324080 | ||||||||
\(395\) | 2.78460e8 | 0.227339 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.93011e8 | 0.555870 | 0.277935 | − | 0.960600i | \(-0.410350\pi\) | ||||
0.277935 | + | 0.960600i | \(0.410350\pi\) | |||||||
\(398\) | −2.32265e9 | −1.84669 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00047e9 | 0.781616 | ||||||||
\(401\) | 2.25957e9 | 1.74993 | 0.874965 | − | 0.484186i | \(-0.160884\pi\) | ||||
0.874965 | + | 0.484186i | \(0.160884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.86348e8 | −0.598476 | ||||||||
\(404\) | −7.88091e8 | −0.594623 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.03932e8 | 0.670339 | ||||||||
\(407\) | −2.05175e9 | −1.50850 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.72327e7 | 0.0630446 | 0.0315223 | − | 0.999503i | \(-0.489964\pi\) | ||||
0.0315223 | + | 0.999503i | \(0.489964\pi\) | |||||||
\(410\) | 4.32735e8 | 0.310084 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.54843e8 | 0.249974 | ||||||||
\(413\) | −1.82248e8 | −0.127303 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.36925e9 | 0.940405 | ||||||||
\(416\) | 5.29491e8 | 0.360605 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.37190e9 | −0.918769 | ||||||||
\(419\) | 8.24265e8 | 0.547416 | 0.273708 | − | 0.961813i | \(-0.411750\pi\) | ||||
0.273708 | + | 0.961813i | \(0.411750\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.82215e9 | −1.19014 | −0.595068 | − | 0.803675i | \(-0.702875\pi\) | ||||
−0.595068 | + | 0.803675i | \(0.702875\pi\) | |||||||
\(422\) | 1.31980e9 | 0.854901 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.13123e9 | 0.720729 | ||||||||
\(425\) | −3.03602e8 | −0.191842 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.57342e9 | −0.978019 | ||||||||
\(428\) | 5.04369e8 | 0.310953 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.66909e8 | −0.586470 | ||||||||
\(431\) | −3.24182e9 | −1.95038 | −0.975189 | − | 0.221375i | \(-0.928946\pi\) | ||||
−0.975189 | + | 0.221375i | \(0.928946\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.71326e9 | 1.01418 | 0.507090 | − | 0.861893i | \(-0.330721\pi\) | ||||
0.507090 | + | 0.861893i | \(0.330721\pi\) | |||||||
\(434\) | 1.96831e9 | 1.15579 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.83949e8 | −0.164073 | ||||||||
\(437\) | −4.78065e8 | −0.274032 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.70403e9 | −0.961283 | −0.480642 | − | 0.876917i | \(-0.659596\pi\) | ||||
−0.480642 | + | 0.876917i | \(0.659596\pi\) | |||||||
\(440\) | −1.47169e9 | −0.823629 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.63028e8 | −0.199969 | ||||||||
\(443\) | −8.96154e7 | −0.0489745 | −0.0244872 | − | 0.999700i | \(-0.507795\pi\) | ||||
−0.0244872 | + | 0.999700i | \(0.507795\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.89649e9 | 1.02021 | ||||||||
\(446\) | −1.53026e9 | −0.816757 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.41262e8 | 0.494581 | ||||||||
\(449\) | 2.38975e9 | 1.24592 | 0.622959 | − | 0.782255i | \(-0.285930\pi\) | ||||
0.622959 | + | 0.782255i | \(0.285930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.54835e9 | 0.794786 | ||||||||
\(452\) | −3.79604e8 | −0.193351 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.82341e9 | 1.41605 | ||||||||
\(455\) | −6.84401e8 | −0.340620 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.10251e9 | 1.52057 | 0.760286 | − | 0.649588i | \(-0.225059\pi\) | ||||
0.760286 | + | 0.649588i | \(0.225059\pi\) | |||||||
\(458\) | −8.96525e8 | −0.436047 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.42558e8 | 0.116189 | ||||||||
\(461\) | 9.42015e8 | 0.447821 | 0.223911 | − | 0.974610i | \(-0.428118\pi\) | ||||
0.223911 | + | 0.974610i | \(0.428118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.76277e9 | −1.29363 | −0.646817 | − | 0.762645i | \(-0.723900\pi\) | ||||
−0.646817 | + | 0.762645i | \(0.723900\pi\) | |||||||
\(464\) | 1.56323e9 | 0.726455 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.14859e9 | 1.44134 | ||||||||
\(467\) | −602426. | −0.000273712 0 | −0.000136856 | − | 1.00000i | \(-0.500044\pi\) | ||||
−0.000136856 | 1.00000i | \(0.500044\pi\) | ||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.10507e9 | −0.942242 | ||||||||
\(470\) | 1.15659e9 | 0.513852 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.32083e8 | −0.101589 | ||||||||
\(473\) | −3.45964e9 | −1.50320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.79461e8 | −0.290896 | ||||||||
\(476\) | 2.20864e8 | 0.0938643 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.16079e9 | 0.904930 | ||||||||
\(479\) | 2.45402e9 | 1.02024 | 0.510121 | − | 0.860103i | \(-0.329601\pi\) | ||||
0.510121 | + | 0.860103i | \(0.329601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.21507e9 | −0.497844 | ||||||||
\(482\) | −3.79346e8 | −0.154302 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.68963e9 | 0.677379 | ||||||||
\(485\) | −4.08131e7 | −0.0162444 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.78601e9 | −0.700701 | −0.350350 | − | 0.936619i | \(-0.613937\pi\) | ||||
−0.350350 | + | 0.936619i | \(0.613937\pi\) | |||||||
\(488\) | −2.00367e9 | −0.780472 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.85655e7 | −0.0301679 | ||||||||
\(491\) | 2.06965e9 | 0.789063 | 0.394532 | − | 0.918882i | \(-0.370907\pi\) | ||||
0.394532 | + | 0.918882i | \(0.370907\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.74377e8 | −0.178303 | ||||||||
\(494\) | −8.12456e8 | −0.303218 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.40393e9 | 1.25255 | ||||||||
\(497\) | 5.21132e9 | 1.90415 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.63444e9 | −0.588866 | −0.294433 | − | 0.955672i | \(-0.595131\pi\) | ||||
−0.294433 | + | 0.955672i | \(0.595131\pi\) | |||||||
\(500\) | 8.81954e8 | 0.315537 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.85037e9 | 1.35844 | ||||||||
\(503\) | 1.96230e9 | 0.687507 | 0.343754 | − | 0.939060i | \(-0.388301\pi\) | ||||
0.343754 | + | 0.939060i | \(0.388301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.20796e9 | 1.10843 | ||||||||
\(506\) | 3.57072e9 | 1.22526 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.41382e8 | 0.0478487 | ||||||||
\(509\) | 1.74020e8 | 0.0584906 | 0.0292453 | − | 0.999572i | \(-0.490690\pi\) | ||||
0.0292453 | + | 0.999572i | \(0.490690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.58142e9 | −0.855827 | ||||||||
\(512\) | 5.94396e8 | 0.195718 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.47860e9 | 1.12988 | ||||||||
\(515\) | −1.44440e9 | −0.465976 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.13834e9 | 1.31707 | ||||||||
\(518\) | 3.04145e9 | 0.961449 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.71550e8 | −0.271820 | ||||||||
\(521\) | 1.04646e9 | 0.324184 | 0.162092 | − | 0.986776i | \(-0.448176\pi\) | ||||
0.162092 | + | 0.986776i | \(0.448176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.71160e9 | −1.13450 | −0.567252 | − | 0.823545i | \(-0.691993\pi\) | ||||
−0.567252 | + | 0.823545i | \(0.691993\pi\) | |||||||
\(524\) | 9.70745e7 | 0.0294745 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.73534e9 | 0.819523 | ||||||||
\(527\) | −1.03296e9 | −0.307429 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.16054e9 | −0.634553 | ||||||||
\(530\) | 2.17792e9 | 0.635442 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.94293e8 | 0.142329 | ||||||||
\(533\) | 9.16948e8 | 0.262301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.05306e9 | −0.579646 | ||||||||
\(536\) | −2.68071e9 | −0.751922 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.20095e9 | −1.71680 | ||||||||
\(539\) | −2.81111e8 | −0.0773245 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.26372e9 | 0.886180 | 0.443090 | − | 0.896477i | \(-0.353882\pi\) | ||||
0.443090 | + | 0.896477i | \(0.353882\pi\) | |||||||
\(542\) | 3.24952e9 | 0.876642 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.95547e8 | 0.185238 | ||||||||
\(545\) | 1.15583e9 | 0.305848 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.46387e8 | 0.194988 | 0.0974941 | − | 0.995236i | \(-0.468917\pi\) | ||||
0.0974941 | + | 0.995236i | \(0.468917\pi\) | |||||||
\(548\) | −1.29388e8 | −0.0335862 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.07498e9 | 1.30066 | ||||||||
\(551\) | −1.06166e9 | −0.270366 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.47695e9 | −0.371388 | ||||||||
\(554\) | 2.63135e9 | 0.657497 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.60195e8 | 0.162896 | ||||||||
\(557\) | −5.33461e9 | −1.30801 | −0.654003 | − | 0.756492i | \(-0.726912\pi\) | ||||
−0.654003 | + | 0.756492i | \(0.726912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.04884e9 | −0.496097 | ||||||||
\(560\) | 2.96262e9 | 0.712883 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.60759e9 | −0.857313 | ||||||||
\(563\) | −7.90248e9 | −1.86631 | −0.933156 | − | 0.359472i | \(-0.882957\pi\) | ||||
−0.933156 | + | 0.359472i | \(0.882957\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.54520e9 | 0.360424 | ||||||||
\(566\) | 4.47802e9 | 1.03807 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.63635e9 | 1.51953 | ||||||||
\(569\) | −5.54526e9 | −1.26191 | −0.630956 | − | 0.775819i | \(-0.717337\pi\) | ||||
−0.630956 | + | 0.775819i | \(0.717337\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.09241e9 | 1.14471 | 0.572357 | − | 0.820004i | \(-0.306029\pi\) | ||||
0.572357 | + | 0.820004i | \(0.306029\pi\) | |||||||
\(572\) | 1.47494e9 | 0.329525 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.29522e9 | −0.506562 | ||||||||
\(575\) | 1.76847e9 | 0.387936 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.69420e9 | 0.367154 | 0.183577 | − | 0.983005i | \(-0.441232\pi\) | ||||
0.183577 | + | 0.983005i | \(0.441232\pi\) | |||||||
\(578\) | 4.85912e9 | 1.04667 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.38657e8 | 0.114634 | ||||||||
\(581\) | −7.26248e9 | −1.53627 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.79269e9 | 1.62872 | ||||||||
\(584\) | −3.28732e9 | −0.682962 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.63039e9 | −0.950551 | ||||||||
\(587\) | 8.65701e9 | 1.76659 | 0.883293 | − | 0.468821i | \(-0.155321\pi\) | ||||
0.883293 | + | 0.468821i | \(0.155321\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.31175e9 | −0.466163 | ||||||||
\(590\) | −4.46821e8 | −0.0895677 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.25977e9 | 1.04194 | ||||||||
\(593\) | 7.39803e9 | 1.45688 | 0.728441 | − | 0.685108i | \(-0.240245\pi\) | ||||
0.728441 | + | 0.685108i | \(0.240245\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.99038e8 | −0.174972 | ||||||||
\(596\) | 1.36005e9 | 0.263144 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.11462e9 | 0.404370 | ||||||||
\(599\) | −4.39303e9 | −0.835162 | −0.417581 | − | 0.908640i | \(-0.637122\pi\) | ||||
−0.417581 | + | 0.908640i | \(0.637122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.08818e9 | −0.204475 | −0.102238 | − | 0.994760i | \(-0.532600\pi\) | ||||
−0.102238 | + | 0.994760i | \(0.532600\pi\) | |||||||
\(602\) | 5.12846e9 | 0.958075 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.38388e9 | −0.624864 | ||||||||
\(605\) | −6.87770e9 | −1.26270 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.98074e9 | −1.08541 | −0.542706 | − | 0.839923i | \(-0.682600\pi\) | ||||
−0.542706 | + | 0.839923i | \(0.682600\pi\) | |||||||
\(608\) | 1.55663e9 | 0.280882 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.85759e9 | −0.688116 | ||||||||
\(611\) | 2.45077e9 | 0.434669 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.60656e9 | −0.983070 | −0.491535 | − | 0.870858i | \(-0.663564\pi\) | ||||
−0.491535 | + | 0.870858i | \(0.663564\pi\) | |||||||
\(614\) | 2.55129e9 | 0.444806 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.80580e9 | 1.34550 | ||||||||
\(617\) | 9.07967e9 | 1.55622 | 0.778112 | − | 0.628126i | \(-0.216178\pi\) | ||||
0.778112 | + | 0.628126i | \(0.216178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.61181e9 | −0.612079 | −0.306040 | − | 0.952019i | \(-0.599004\pi\) | ||||
−0.306040 | + | 0.952019i | \(0.599004\pi\) | |||||||
\(620\) | 1.17293e9 | 0.197651 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.80518e8 | 0.113390 | ||||||||
\(623\) | −1.00589e10 | −1.66665 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.26731e8 | 0.0535316 | ||||||||
\(626\) | 4.05741e9 | 0.661056 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.90444e9 | 0.467954 | ||||||||
\(629\) | −1.59613e9 | −0.255736 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.73746e9 | 0.433756 | 0.216878 | − | 0.976199i | \(-0.430413\pi\) | ||||
0.216878 | + | 0.976199i | \(0.430413\pi\) | |||||||
\(632\) | −1.88082e9 | −0.296372 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.99895e9 | 1.09074 | ||||||||
\(635\) | −5.75502e8 | −0.0891946 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.66477e8 | −0.0255191 | ||||||||
\(638\) | 7.92963e9 | 1.20887 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.76736e9 | 0.718867 | ||||||||
\(641\) | 7.16076e9 | 1.07388 | 0.536940 | − | 0.843620i | \(-0.319580\pi\) | ||||
0.536940 | + | 0.843620i | \(0.319580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.59933e9 | −0.237247 | −0.118623 | − | 0.992939i | \(-0.537848\pi\) | ||||
−0.118623 | + | 0.992939i | \(0.537848\pi\) | |||||||
\(644\) | −1.28652e9 | −0.189809 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.06725e9 | −0.155759 | ||||||||
\(647\) | 1.56410e9 | 0.227038 | 0.113519 | − | 0.993536i | \(-0.463788\pi\) | ||||
0.113519 | + | 0.993536i | \(0.463788\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.59875e9 | −0.229574 | ||||||||
\(650\) | 3.00546e9 | 0.429253 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.21057e9 | −0.312348 | ||||||||
\(653\) | −1.10948e10 | −1.55928 | −0.779639 | − | 0.626229i | \(-0.784598\pi\) | ||||
−0.779639 | + | 0.626229i | \(0.784598\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.95147e8 | −0.0549432 | ||||||||
\(656\) | −3.96927e9 | −0.548968 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.13454e9 | −0.839443 | ||||||||
\(659\) | −8.31935e9 | −1.13238 | −0.566188 | − | 0.824276i | \(-0.691582\pi\) | ||||
−0.566188 | + | 0.824276i | \(0.691582\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.78095e9 | 0.778563 | 0.389282 | − | 0.921119i | \(-0.372723\pi\) | ||||
0.389282 | + | 0.921119i | \(0.372723\pi\) | |||||||
\(662\) | 9.21778e9 | 1.23488 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.24841e9 | −1.22597 | ||||||||
\(665\) | −2.01204e9 | −0.265315 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.76323e9 | 0.360559 | ||||||||
\(668\) | −1.69742e9 | −0.220329 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.16106e9 | −0.662944 | ||||||||
\(671\) | −1.38026e10 | −1.76373 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.94500e9 | −0.878252 | −0.439126 | − | 0.898425i | \(-0.644712\pi\) | ||||
−0.439126 | + | 0.898425i | \(0.644712\pi\) | |||||||
\(674\) | −1.67270e9 | −0.210430 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.70554e9 | −0.212349 | ||||||||
\(677\) | −2.90331e9 | −0.359611 | −0.179806 | − | 0.983702i | \(-0.557547\pi\) | ||||
−0.179806 | + | 0.983702i | \(0.557547\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.16472e8 | 0.0265373 | ||||||||
\(680\) | −1.14488e9 | −0.139630 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.72668e10 | 2.08433 | ||||||||
\(683\) | 4.42751e9 | 0.531726 | 0.265863 | − | 0.964011i | \(-0.414343\pi\) | ||||
0.265863 | + | 0.964011i | \(0.414343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.26679e8 | 0.0626078 | ||||||||
\(686\) | 9.91981e9 | 1.17319 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.86898e9 | 1.03828 | ||||||||
\(689\) | 4.61492e9 | 0.537523 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.87979e9 | 0.447337 | 0.223669 | − | 0.974665i | \(-0.428197\pi\) | ||||
0.223669 | + | 0.974665i | \(0.428197\pi\) | |||||||
\(692\) | −2.20491e9 | −0.252941 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.80989e8 | −0.0886925 | ||||||||
\(695\) | −2.68736e9 | −0.303654 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.20451e9 | 0.134740 | ||||||||
\(698\) | −1.45219e10 | −1.61633 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.82850e9 | −0.201489 | ||||||||
\(701\) | 1.56016e10 | 1.71063 | 0.855315 | − | 0.518108i | \(-0.173364\pi\) | ||||
0.855315 | + | 0.518108i | \(0.173364\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.57214e9 | −0.387779 | ||||||||
\(704\) | 8.25710e9 | 0.891915 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.19046e9 | 0.555123 | ||||||||
\(707\) | −1.70150e10 | −1.81077 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.35775e10 | 1.43073 | 0.715364 | − | 0.698752i | \(-0.246261\pi\) | ||||
0.715364 | + | 0.698752i | \(0.246261\pi\) | |||||||
\(710\) | 1.27767e10 | 1.33972 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.28096e10 | −1.33001 | ||||||||
\(713\) | 6.01693e9 | 0.621672 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.00382e9 | −0.614266 | ||||||||
\(716\) | 1.49044e9 | 0.151746 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.26963e9 | −0.833778 | ||||||||
\(719\) | −1.51786e10 | −1.52293 | −0.761466 | − | 0.648205i | \(-0.775520\pi\) | ||||
−0.761466 | + | 0.648205i | \(0.775520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.66109e9 | 0.761232 | ||||||||
\(722\) | 9.23529e9 | 0.913210 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.76625e8 | −0.0662618 | ||||||||
\(725\) | 3.92730e9 | 0.382746 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.49034e10 | −1.43852 | −0.719260 | − | 0.694741i | \(-0.755519\pi\) | ||||
−0.719260 | + | 0.694741i | \(0.755519\pi\) | |||||||
\(728\) | 4.62268e9 | 0.444053 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.32893e9 | −0.602144 | ||||||||
\(731\) | −2.69138e9 | −0.254838 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.05230e10 | 0.986905 | 0.493453 | − | 0.869773i | \(-0.335735\pi\) | ||||
0.493453 | + | 0.869773i | \(0.335735\pi\) | |||||||
\(734\) | 3.40279e9 | 0.317614 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.05153e9 | −0.374582 | ||||||||
\(737\) | −1.84665e10 | −1.69921 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.82290e10 | 1.66153 | 0.830764 | − | 0.556624i | \(-0.187904\pi\) | ||||
0.830764 | + | 0.556624i | \(0.187904\pi\) | |||||||
\(740\) | 1.81241e9 | 0.164417 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.15516e10 | −1.03808 | ||||||||
\(743\) | 1.41694e9 | 0.126733 | 0.0633667 | − | 0.997990i | \(-0.479816\pi\) | ||||
0.0633667 | + | 0.997990i | \(0.479816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.53616e9 | −0.490526 | ||||||||
\(746\) | −2.20707e10 | −1.94639 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.93750e9 | 0.169273 | ||||||||
\(749\) | 1.08894e10 | 0.946927 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.51027e10 | −1.30111 | −0.650554 | − | 0.759460i | \(-0.725463\pi\) | ||||
−0.650554 | + | 0.759460i | \(0.725463\pi\) | |||||||
\(752\) | −1.06088e10 | −0.909716 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.69601e9 | 0.398960 | ||||||||
\(755\) | 1.37743e10 | 1.16481 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.01056e9 | −0.671162 | −0.335581 | − | 0.942011i | \(-0.608933\pi\) | ||||
−0.335581 | + | 0.942011i | \(0.608933\pi\) | |||||||
\(758\) | −1.43838e10 | −1.19959 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.56224e9 | −0.211725 | ||||||||
\(761\) | −9.09051e9 | −0.747725 | −0.373863 | − | 0.927484i | \(-0.621967\pi\) | ||||
−0.373863 | + | 0.927484i | \(0.621967\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.13049e9 | −0.499642 | ||||||||
\(764\) | 2.88348e9 | 0.233932 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.73643e9 | −0.702317 | ||||||||
\(767\) | −9.46795e8 | −0.0757656 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.56881e10 | −1.24402 | −0.622009 | − | 0.783010i | \(-0.713683\pi\) | ||||
−0.622009 | + | 0.783010i | \(0.713683\pi\) | |||||||
\(770\) | 1.50282e10 | 1.18629 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.72732e9 | 0.291566 | ||||||||
\(773\) | −2.02623e10 | −1.57783 | −0.788916 | − | 0.614502i | \(-0.789357\pi\) | ||||
−0.788916 | + | 0.614502i | \(0.789357\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.55170e9 | 0.659928 | ||||||||
\(776\) | 2.75666e8 | 0.0211771 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.51527e10 | 1.15362 | ||||||||
\(779\) | 2.69570e9 | 0.204310 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.57156e10 | 3.43389 | ||||||||
\(782\) | 2.77780e9 | 0.207719 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.20643e8 | 0.0534089 | ||||||||
\(785\) | −1.18227e10 | −0.872311 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.40184e9 | 0.175644 | 0.0878219 | − | 0.996136i | \(-0.472009\pi\) | ||||
0.0878219 | + | 0.996136i | \(0.472009\pi\) | |||||||
\(788\) | 1.24356e9 | 0.0905370 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.62107e9 | −0.261301 | ||||||||
\(791\) | −8.19568e9 | −0.588800 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.17407e9 | −0.582080 | ||||||||
\(794\) | −9.01184e9 | −0.638913 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.34111e9 | 0.515901 | ||||||||
\(797\) | −2.37890e9 | −0.166446 | −0.0832228 | − | 0.996531i | \(-0.526521\pi\) | ||||
−0.0832228 | + | 0.996531i | \(0.526521\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.21936e9 | 0.223283 | ||||||||
\(800\) | −5.75833e9 | −0.397632 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.93832e10 | −2.01136 | ||||||||
\(803\) | −2.26452e10 | −1.54338 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.23685e9 | 0.353822 | ||||||||
\(806\) | 1.02256e10 | 0.687884 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.16677e10 | −1.44502 | ||||||||
\(809\) | −1.39600e10 | −0.926967 | −0.463483 | − | 0.886106i | \(-0.653401\pi\) | ||||
−0.463483 | + | 0.886106i | \(0.653401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.88244e10 | −1.23922 | −0.619611 | − | 0.784909i | \(-0.712710\pi\) | ||||
−0.619611 | + | 0.784909i | \(0.712710\pi\) | |||||||
\(812\) | −2.85703e9 | −0.187270 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.66807e10 | 1.73385 | ||||||||
\(815\) | 8.99825e9 | 0.582246 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.02331e9 | −0.386418 | ||||||||
\(818\) | −1.13436e9 | −0.0724629 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.36773e9 | −0.0866268 | ||||||||
\(821\) | −7.81215e9 | −0.492685 | −0.246343 | − | 0.969183i | \(-0.579229\pi\) | ||||
−0.246343 | + | 0.969183i | \(0.579229\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.87867e10 | −1.17476 | −0.587381 | − | 0.809310i | \(-0.699841\pi\) | ||||
−0.587381 | + | 0.809310i | \(0.699841\pi\) | |||||||
\(824\) | 9.75602e9 | 0.607474 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.36993e9 | 0.146320 | ||||||||
\(827\) | 1.42506e10 | 0.876119 | 0.438059 | − | 0.898946i | \(-0.355666\pi\) | ||||
0.438059 | + | 0.898946i | \(0.355666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.49011e8 | 0.0456612 | 0.0228306 | − | 0.999739i | \(-0.492732\pi\) | ||||
0.0228306 | + | 0.999739i | \(0.492732\pi\) | |||||||
\(830\) | −1.78056e10 | −1.08089 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.88995e9 | 0.294356 | ||||||||
\(833\) | −2.18686e8 | −0.0131088 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.90944e9 | 0.410715 | ||||||||
\(836\) | 4.33612e9 | 0.256673 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.07186e10 | −0.629196 | ||||||||
\(839\) | 2.65131e10 | 1.54987 | 0.774933 | − | 0.632043i | \(-0.217783\pi\) | ||||
0.774933 | + | 0.632043i | \(0.217783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.11135e10 | −0.644265 | ||||||||
\(842\) | 2.36950e10 | 1.36793 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.17146e9 | −0.238830 | ||||||||
\(845\) | 6.94250e9 | 0.395838 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.64792e10 | 2.06278 | ||||||||
\(848\) | −1.99770e10 | −1.12498 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.94801e9 | 0.220502 | ||||||||
\(851\) | 9.29739e9 | 0.517140 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.34893e10 | −0.744163 | −0.372081 | − | 0.928200i | \(-0.621356\pi\) | ||||
−0.372081 | + | 0.928200i | \(0.621356\pi\) | |||||||
\(854\) | 2.04606e10 | 1.12413 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.38671e10 | 0.755660 | ||||||||
\(857\) | −2.26740e10 | −1.23054 | −0.615269 | − | 0.788317i | \(-0.710953\pi\) | ||||
−0.615269 | + | 0.788317i | \(0.710953\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.97914e10 | −1.06537 | −0.532685 | − | 0.846314i | \(-0.678817\pi\) | ||||
−0.532685 | + | 0.846314i | \(0.678817\pi\) | |||||||
\(860\) | 3.05607e9 | 0.163840 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.21563e10 | 2.24175 | ||||||||
\(863\) | 1.08103e10 | 0.572534 | 0.286267 | − | 0.958150i | \(-0.407585\pi\) | ||||
0.286267 | + | 0.958150i | \(0.407585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.97519e9 | 0.471506 | ||||||||
\(866\) | −2.22790e10 | −1.16569 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.22117e9 | −0.322889 | ||||||||
\(869\) | −1.29563e10 | −0.669751 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.09361e10 | −0.560786 | ||||||||
\(872\) | −7.80687e9 | −0.398721 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.21670e9 | 0.314970 | ||||||||
\(875\) | 1.90415e10 | 0.960887 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.46440e7 | −0.00423738 | −0.00211869 | − | 0.999998i | \(-0.500674\pi\) | ||||
−0.00211869 | + | 0.999998i | \(0.500674\pi\) | |||||||
\(878\) | 2.21590e10 | 1.10489 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.59892e10 | 1.28559 | ||||||||
\(881\) | 3.78092e10 | 1.86286 | 0.931432 | − | 0.363915i | \(-0.118560\pi\) | ||||
0.931432 | + | 0.363915i | \(0.118560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.77215e10 | 1.84385 | 0.921927 | − | 0.387364i | \(-0.126614\pi\) | ||||
0.921927 | + | 0.387364i | \(0.126614\pi\) | |||||||
\(884\) | 1.14741e9 | 0.0558645 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.16535e9 | 0.0562908 | ||||||||
\(887\) | −1.24757e10 | −0.600250 | −0.300125 | − | 0.953900i | \(-0.597028\pi\) | ||||
−0.300125 | + | 0.953900i | \(0.597028\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.05245e9 | 0.145711 | ||||||||
\(890\) | −2.46617e10 | −1.17262 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.83664e9 | 0.228174 | ||||||||
\(893\) | 7.20493e9 | 0.338571 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.06689e9 | −0.282869 | ||||||||
\(896\) | −2.52860e10 | −1.17436 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.10760e10 | −1.43205 | ||||||||
\(899\) | 1.33620e10 | 0.613356 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.06222e9 | 0.276118 | ||||||||
\(902\) | −2.01345e10 | −0.913520 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.04368e10 | −0.469870 | ||||||||
\(905\) | 2.75424e9 | 0.123518 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.59259e8 | 0.00708725 | 0.00354363 | − | 0.999994i | \(-0.498872\pi\) | ||||
0.00354363 | + | 0.999994i | \(0.498872\pi\) | |||||||
\(908\) | −8.92386e9 | −0.395596 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.89986e9 | 0.391506 | ||||||||
\(911\) | −2.28968e10 | −1.00337 | −0.501683 | − | 0.865051i | \(-0.667286\pi\) | ||||
−0.501683 | + | 0.865051i | \(0.667286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.37092e10 | −2.77048 | ||||||||
\(914\) | −4.03447e10 | −1.74773 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.83361e9 | 0.121817 | ||||||||
\(917\) | 2.09585e9 | 0.0897568 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.19936e10 | −0.509734 | −0.254867 | − | 0.966976i | \(-0.582032\pi\) | ||||
−0.254867 | + | 0.966976i | \(0.582032\pi\) | |||||||
\(920\) | 6.66887e9 | 0.282355 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.22498e10 | −0.514722 | ||||||||
\(923\) | 2.70733e10 | 1.13327 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.32141e10 | 0.548963 | ||||||||
\(926\) | 3.59268e10 | 1.48689 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.99737e9 | −0.369571 | ||||||||
\(929\) | 5.52148e9 | 0.225944 | 0.112972 | − | 0.993598i | \(-0.463963\pi\) | ||||
0.112972 | + | 0.993598i | \(0.463963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.89420e8 | −0.0198773 | ||||||||
\(932\) | −9.95165e9 | −0.402661 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.83387e6 | 0.000314603 0 | ||||||||
\(935\) | −7.88670e9 | −0.315540 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.28153e10 | 1.70024 | 0.850120 | − | 0.526589i | \(-0.176529\pi\) | ||||
0.850120 | + | 0.526589i | \(0.176529\pi\) | |||||||
\(938\) | 2.73741e10 | 1.08300 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.65560e9 | −0.143553 | ||||||||
\(941\) | −4.62683e10 | −1.81017 | −0.905087 | − | 0.425227i | \(-0.860194\pi\) | ||||
−0.905087 | + | 0.425227i | \(0.860194\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.01624e9 | −0.272467 | ||||||||
\(944\) | 4.09847e9 | 0.158569 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.49888e10 | 1.72777 | ||||||||
\(947\) | −1.84946e10 | −0.707651 | −0.353826 | − | 0.935311i | \(-0.615119\pi\) | ||||
−0.353826 | + | 0.935311i | \(0.615119\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.34107e10 | −0.509356 | ||||||||
\(950\) | 8.83563e9 | 0.334353 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.07242e9 | 0.228104 | ||||||||
\(953\) | 1.08055e10 | 0.404409 | 0.202205 | − | 0.979343i | \(-0.435189\pi\) | ||||
0.202205 | + | 0.979343i | \(0.435189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.17373e10 | −0.436072 | ||||||||
\(956\) | −6.82953e9 | −0.252807 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.19117e10 | −1.17266 | ||||||||
\(959\) | −2.79349e9 | −0.102278 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.58314e9 | 0.0575423 | ||||||||
\(962\) | 1.58006e10 | 0.572218 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.19899e9 | 0.0431067 | ||||||||
\(965\) | −1.51723e10 | −0.543506 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.41210e10 | 0.857834 | 0.428917 | − | 0.903344i | \(-0.358895\pi\) | ||||
0.428917 | + | 0.903344i | \(0.358895\pi\) | |||||||
\(968\) | 4.64544e10 | 1.64613 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.30728e8 | 0.0186712 | ||||||||
\(971\) | 3.65187e10 | 1.28011 | 0.640057 | − | 0.768328i | \(-0.278911\pi\) | ||||
0.640057 | + | 0.768328i | \(0.278911\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.42537e10 | 0.496058 | ||||||||
\(974\) | 2.32251e10 | 0.805379 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.53838e10 | 1.21823 | ||||||||
\(977\) | −1.82046e10 | −0.624524 | −0.312262 | − | 0.949996i | \(-0.601087\pi\) | ||||
−0.312262 | + | 0.949996i | \(0.601087\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.82408e10 | −3.00559 | ||||||||
\(980\) | 2.48319e8 | 0.00842789 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.69135e10 | −0.906942 | ||||||||
\(983\) | 4.38690e10 | 1.47306 | 0.736531 | − | 0.676404i | \(-0.236463\pi\) | ||||
0.736531 | + | 0.676404i | \(0.236463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.06199e9 | −0.168770 | ||||||||
\(986\) | 6.16875e9 | 0.204940 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.56790e9 | 0.0847089 | ||||||||
\(989\) | 1.56772e10 | 0.515325 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.39803e10 | −0.782702 | −0.391351 | − | 0.920242i | \(-0.627992\pi\) | ||||
−0.391351 | + | 0.920242i | \(0.627992\pi\) | |||||||
\(992\) | −1.95918e10 | −0.637210 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.77673e10 | −2.18861 | ||||||||
\(995\) | −2.98824e10 | −0.961688 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.54581e10 | 1.77228 | 0.886139 | − | 0.463419i | \(-0.153378\pi\) | ||||
0.886139 | + | 0.463419i | \(0.153378\pi\) | |||||||
\(998\) | 2.12540e10 | 0.676837 | ||||||||
\(999\) | 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 | 531.8.a.b.1.5 | 16 | ||
3.2 | odd | 2 | 177.8.a.a.1.12 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.12 | ✓ | 16 | 3.2 | odd | 2 | ||
531.8.a.b.1.5 | 16 | 1.1 | even | 1 | trivial |