Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,6,Mod(1,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.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: | \(44.9074695476\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 1151x^{3} - 5642x^{2} + 193596x + 1258056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-7.03843\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 10.0384 | 0.643965 | 0.321983 | − | 0.946746i | \(-0.395651\pi\) | ||||
0.321983 | + | 0.946746i | \(0.395651\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −142.230 | −0.585308 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 422.924 | 1.05385 | 0.526927 | − | 0.849911i | \(-0.323344\pi\) | ||||
0.526927 | + | 0.849911i | \(0.323344\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −731.815 | −1.20100 | −0.600500 | − | 0.799625i | \(-0.705032\pi\) | ||||
−0.600500 | + | 0.799625i | \(0.705032\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 250.961 | 0.287990 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1498.36 | 1.25746 | 0.628729 | − | 0.777625i | \(-0.283575\pi\) | ||||
0.628729 | + | 0.777625i | \(0.283575\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1370.58 | 0.871004 | 0.435502 | − | 0.900188i | \(-0.356571\pi\) | ||||
0.435502 | + | 0.900188i | \(0.356571\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 491.883 | 0.243396 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2789.75 | 1.09963 | 0.549813 | − | 0.835288i | \(-0.314699\pi\) | ||||
0.549813 | + | 0.835288i | \(0.314699\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3867.10 | −1.02088 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6216.76 | −1.37268 | −0.686340 | − | 0.727281i | \(-0.740784\pi\) | ||||
−0.686340 | + | 0.727281i | \(0.740784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4080.91 | 0.762698 | 0.381349 | − | 0.924431i | \(-0.375460\pi\) | ||||
0.381349 | + | 0.924431i | \(0.375460\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4245.49 | 0.678645 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1225.00 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14739.6 | 1.77004 | 0.885018 | − | 0.465557i | \(-0.154146\pi\) | ||||
0.885018 | + | 0.465557i | \(0.154146\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7346.27 | −0.773402 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9008.85 | 0.836969 | 0.418485 | − | 0.908224i | \(-0.362561\pi\) | ||||
0.418485 | + | 0.908224i | \(0.362561\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2356.52 | 0.194357 | 0.0971784 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971784 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3555.75 | −0.261758 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6761.78 | −0.446495 | −0.223247 | − | 0.974762i | \(-0.571666\pi\) | ||||
−0.223247 | + | 0.974762i | \(0.571666\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15041.2 | 0.809760 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −25405.2 | −1.24232 | −0.621158 | − | 0.783685i | \(-0.713338\pi\) | ||||
−0.621158 | + | 0.783685i | \(0.713338\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10573.1 | 0.471298 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13758.5 | 0.560897 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16243.0 | 0.607487 | 0.303743 | − | 0.952754i | \(-0.401763\pi\) | ||||
0.303743 | + | 0.952754i | \(0.401763\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14602.7 | 0.502469 | 0.251234 | − | 0.967926i | \(-0.419164\pi\) | ||||
0.251234 | + | 0.967926i | \(0.419164\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6969.27 | −0.221226 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −18295.4 | −0.537103 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 49347.9 | 1.34302 | 0.671509 | − | 0.740996i | \(-0.265646\pi\) | ||||
0.671509 | + | 0.740996i | \(0.265646\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 28004.7 | 0.708121 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −36061.5 | −0.848981 | −0.424490 | − | 0.905432i | \(-0.639547\pi\) | ||||
−0.424490 | + | 0.905432i | \(0.639547\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2178.41 | −0.0478446 | −0.0239223 | − | 0.999714i | \(-0.507615\pi\) | ||||
−0.0239223 | + | 0.999714i | \(0.507615\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6274.02 | 0.128793 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20723.3 | 0.398319 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 108080. | 1.94841 | 0.974203 | − | 0.225673i | \(-0.0724581\pi\) | ||||
0.974203 | + | 0.225673i | \(0.0724581\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4257.76 | −0.0721056 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 28981.6 | 0.461771 | 0.230886 | − | 0.972981i | \(-0.425838\pi\) | ||||
0.230886 | + | 0.972981i | \(0.425838\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 37459.0 | 0.562352 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −62406.5 | −0.883959 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 53791.5 | 0.719845 | 0.359922 | − | 0.932982i | \(-0.382803\pi\) | ||||
0.359922 | + | 0.932982i | \(0.382803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −35858.9 | −0.453935 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 40965.9 | 0.491151 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 34264.5 | 0.389525 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −95770.6 | −1.03348 | −0.516741 | − | 0.856142i | \(-0.672855\pi\) | ||||
−0.516741 | + | 0.856142i | \(0.672855\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −60152.4 | −0.616829 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 103047. | 1.00515 | 0.502577 | − | 0.864532i | \(-0.332385\pi\) | ||||
0.502577 | + | 0.864532i | \(0.332385\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −110405. | −1.02541 | −0.512704 | − | 0.858565i | \(-0.671356\pi\) | ||||
−0.512704 | + | 0.858565i | \(0.671356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12297.1 | 0.108850 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −82760.3 | −0.698816 | −0.349408 | − | 0.936971i | \(-0.613617\pi\) | ||||
−0.349408 | + | 0.936971i | \(0.613617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 96804.8 | 0.780424 | 0.390212 | − | 0.920725i | \(-0.372402\pi\) | ||||
0.390212 | + | 0.920725i | \(0.372402\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 147963. | 1.13984 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 218042. | 1.60636 | 0.803182 | − | 0.595733i | \(-0.203138\pi\) | ||||
0.803182 | + | 0.595733i | \(0.203138\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 69743.6 | 0.491768 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 104086. | 0.702955 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 73419.6 | 0.475274 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17813.4 | 0.110607 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 90434.7 | 0.538979 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 234551. | 1.29041 | 0.645205 | − | 0.764010i | \(-0.276772\pi\) | ||||
0.645205 | + | 0.764010i | \(0.276772\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23655.8 | 0.125159 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −81880.4 | −0.416871 | −0.208435 | − | 0.978036i | \(-0.566837\pi\) | ||||
−0.208435 | + | 0.978036i | \(0.566837\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 67158.4 | 0.329209 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −96677.6 | −0.456553 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 136807. | 0.622739 | 0.311369 | − | 0.950289i | \(-0.399212\pi\) | ||||
0.311369 | + | 0.950289i | \(0.399212\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −287262. | −1.26107 | −0.630537 | − | 0.776159i | \(-0.717165\pi\) | ||||
−0.630537 | + | 0.776159i | \(0.717165\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −67877.6 | −0.287527 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −309502. | −1.26568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −155419. | −0.613881 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 24102.3 | 0.0919951 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 309740. | 1.14296 | 0.571480 | − | 0.820616i | \(-0.306369\pi\) | ||||
0.571480 | + | 0.820616i | \(0.306369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −486149. | −1.73511 | −0.867556 | − | 0.497340i | \(-0.834310\pi\) | ||||
−0.867556 | + | 0.497340i | \(0.834310\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −213111. | −0.736001 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 102023. | 0.341089 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 507730. | 1.64393 | 0.821966 | − | 0.569537i | \(-0.192877\pi\) | ||||
0.821966 | + | 0.569537i | \(0.192877\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −255028. | −0.800009 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 136698. | 0.415620 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −210698. | −0.621143 | −0.310571 | − | 0.950550i | \(-0.600520\pi\) | ||||
−0.310571 | + | 0.950550i | \(0.600520\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 106137. | 0.303499 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −454974. | −1.26240 | −0.631198 | − | 0.775622i | \(-0.717437\pi\) | ||||
−0.631198 | + | 0.775622i | \(0.717437\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 164260. | 0.442399 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −194937. | −0.509806 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −206691. | −0.525057 | −0.262529 | − | 0.964924i | \(-0.584556\pi\) | ||||
−0.262529 | + | 0.964924i | \(0.584556\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30625.0 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 163054. | 0.391200 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −235999. | −0.550526 | −0.275263 | − | 0.961369i | \(-0.588765\pi\) | ||||
−0.275263 | + | 0.961369i | \(0.588765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −365358. | −0.828939 | −0.414470 | − | 0.910063i | \(-0.636033\pi\) | ||||
−0.414470 | + | 0.910063i | \(0.636033\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 146588. | 0.323573 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 368490. | 0.791584 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 633691. | 1.32518 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189488. | −0.385858 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 143765. | 0.285148 | 0.142574 | − | 0.989784i | \(-0.454462\pi\) | ||||
0.142574 | + | 0.989784i | \(0.454462\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −615006. | −1.18846 | −0.594232 | − | 0.804294i | \(-0.702544\pi\) | ||||
−0.594232 | + | 0.804294i | \(0.702544\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −183657. | −0.345876 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −915222. | −1.68020 | −0.840099 | − | 0.542432i | \(-0.817503\pi\) | ||||
−0.840099 | + | 0.542432i | \(0.817503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −582204. | −1.04218 | −0.521089 | − | 0.853502i | \(-0.674474\pi\) | ||||
−0.521089 | + | 0.853502i | \(0.674474\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 495376. | 0.864858 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −304621. | −0.518824 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 225221. | 0.374304 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −396785. | −0.643620 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 579651. | 0.917911 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −862136. | −1.33312 | −0.666561 | − | 0.745451i | \(-0.732234\pi\) | ||||
−0.666561 | + | 0.745451i | \(0.732234\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −362001. | −0.546714 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 58913.0 | 0.0869190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 199964. | 0.288273 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −21867.8 | −0.0308103 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.09652e6 | −1.51021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −684947. | −0.922349 | −0.461174 | − | 0.887310i | \(-0.652572\pi\) | ||||
−0.461174 | + | 0.887310i | \(0.652572\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −88893.7 | −0.117062 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −160804. | −0.207125 | −0.103563 | − | 0.994623i | \(-0.533024\pi\) | ||||
−0.103563 | + | 0.994623i | \(0.533024\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.47603e6 | −1.85997 | −0.929987 | − | 0.367592i | \(-0.880182\pi\) | ||||
−0.929987 | + | 0.367592i | \(0.880182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 208029. | 0.256504 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.33729e6 | −1.61375 | −0.806874 | − | 0.590724i | \(-0.798842\pi\) | ||||
−0.806874 | + | 0.590724i | \(0.798842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −169044. | −0.199679 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.08496e6 | 1.25471 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −31064.0 | −0.0351773 | −0.0175886 | − | 0.999845i | \(-0.505599\pi\) | ||||
−0.0175886 | + | 0.999845i | \(0.505599\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 924703. | 1.02556 | 0.512779 | − | 0.858521i | \(-0.328616\pi\) | ||||
0.512779 | + | 0.858521i | \(0.328616\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 896965. | 0.974450 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 60025.0 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.00301e6 | −1.04608 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 290930. | 0.297365 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 561062. | 0.562117 | 0.281058 | − | 0.959691i | \(-0.409315\pi\) | ||||
0.281058 | + | 0.959691i | \(0.409315\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.17985e6 | 1.15884 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 376029. | 0.362135 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 316039. | 0.298475 | 0.149238 | − | 0.988801i | \(-0.452318\pi\) | ||||
0.149238 | + | 0.988801i | \(0.452318\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 722241. | 0.669010 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 884210. | 0.803441 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −262038. | −0.233601 | −0.116800 | − | 0.993155i | \(-0.537264\pi\) | ||||
−0.116800 | + | 0.993155i | \(0.537264\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −635129. | −0.555581 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 539982. | 0.463555 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.21153e6 | −1.02083 | −0.510413 | − | 0.859929i | \(-0.670507\pi\) | ||||
−0.510413 | + | 0.859929i | \(0.670507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 152730. | 0.126328 | 0.0631641 | − | 0.998003i | \(-0.479881\pi\) | ||||
0.0631641 | + | 0.998003i | \(0.479881\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −359967. | −0.292319 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 264327. | 0.210771 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 645375. | 0.505374 | 0.252687 | − | 0.967548i | \(-0.418686\pi\) | ||||
0.252687 | + | 0.967548i | \(0.418686\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −580427. | −0.446414 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 871336. | 0.658294 | 0.329147 | − | 0.944279i | \(-0.393239\pi\) | ||||
0.329147 | + | 0.944279i | \(0.393239\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.22474e6 | 0.909033 | 0.454516 | − | 0.890738i | \(-0.349812\pi\) | ||||
0.454516 | + | 0.890738i | \(0.349812\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 343962. | 0.250841 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 441433. | 0.316345 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 825222. | 0.581200 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −961386. | −0.665526 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 180700. | 0.122967 | 0.0614835 | − | 0.998108i | \(-0.480417\pi\) | ||||
0.0614835 | + | 0.998108i | \(0.480417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 406075. | 0.271676 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.63549e6 | −1.07586 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.04158e6 | −1.32065 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 115469. | 0.0734600 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.03443e6 | 0.647284 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 365068. | 0.224711 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.56849e6 | 1.55536 | 0.777682 | − | 0.628658i | \(-0.216395\pi\) | ||||
0.777682 | + | 0.628658i | \(0.216395\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.10830e6 | −0.660328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.83718e6 | −1.66336 | −0.831680 | − | 0.555255i | \(-0.812621\pi\) | ||||
−0.831680 | + | 0.555255i | \(0.812621\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.30062e6 | −0.750395 | −0.375197 | − | 0.926945i | \(-0.622425\pi\) | ||||
−0.375197 | + | 0.926945i | \(0.622425\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −174232. | −0.0989352 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.37328e6 | 1.32648 | 0.663241 | − | 0.748406i | \(-0.269180\pi\) | ||||
0.663241 | + | 0.748406i | \(0.269180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.62922e6 | −1.44660 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −830783. | −0.450013 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.05362e6 | 1.09525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −457384. | −0.240200 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 971768. | 0.502566 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −331327. | −0.168759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −462474. | −0.232016 | −0.116008 | − | 0.993248i | \(-0.537010\pi\) | ||||
−0.116008 | + | 0.993248i | \(0.537010\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.09642e6 | −1.03602 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.23370e6 | 0.600616 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.41385e6 | 1.63746 | 0.818729 | − | 0.574180i | \(-0.194679\pi\) | ||||
0.818729 | + | 0.574180i | \(0.194679\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.18880e6 | 1.03444 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.72591e6 | 0.803772 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 700116. | 0.316681 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.06822e6 | 0.476252 | 0.238126 | − | 0.971234i | \(-0.423467\pi\) | ||||
0.238126 | + | 0.971234i | \(0.423467\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.36926e6 | −1.48071 | −0.740356 | − | 0.672215i | \(-0.765343\pi\) | ||||
−0.740356 | + | 0.672215i | \(0.765343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.83000e6 | 1.22608 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.66070e6 | 1.56361 | 0.781803 | − | 0.623525i | \(-0.214300\pi\) | ||||
0.781803 | + | 0.623525i | \(0.214300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −901537. | −0.379676 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 737017. | 0.306060 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.67332e6 | −1.50426 | −0.752129 | − | 0.659016i | \(-0.770973\pi\) | ||||
−0.752129 | + | 0.659016i | \(0.770973\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −597611. | −0.241352 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 178819. | 0.0712273 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −54460.3 | −0.0213967 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.86123e6 | 0.721330 | 0.360665 | − | 0.932695i | \(-0.382550\pi\) | ||||
0.360665 | + | 0.932695i | \(0.382550\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.28133e6 | −0.489885 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.24485e6 | −0.469551 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.59890e6 | −1.33936 | −0.669681 | − | 0.742648i | \(-0.733569\pi\) | ||||
−0.669681 | + | 0.742648i | \(0.733569\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 156850. | 0.0575980 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.54952e6 | 1.64859 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.20715e6 | −0.789283 | −0.394642 | − | 0.918835i | \(-0.629131\pi\) | ||||
−0.394642 | + | 0.918835i | \(0.629131\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.35452e6 | 0.830979 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.51980e6 | 0.877746 | 0.438873 | − | 0.898549i | \(-0.355378\pi\) | ||||
0.438873 | + | 0.898549i | \(0.355378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 518081. | 0.178134 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −335168. | −0.113759 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −131011. | −0.0438970 | −0.0219485 | − | 0.999759i | \(-0.506987\pi\) | ||||
−0.0219485 | + | 0.999759i | \(0.506987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.18004e6 | 1.38273 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −821950. | −0.268450 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.70201e6 | 0.871354 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.86220e6 | −0.911431 | −0.455716 | − | 0.890125i | \(-0.650617\pi\) | ||||
−0.455716 | + | 0.890125i | \(0.650617\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 674165. | 0.211999 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.19911e6 | −0.682946 | −0.341473 | − | 0.939892i | \(-0.610926\pi\) | ||||
−0.341473 | + | 0.939892i | \(0.610926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.98647e6 | −0.916000 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −106444. | −0.0322466 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.23373e6 | 1.86536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.04568e6 | 1.19587 | 0.597934 | − | 0.801545i | \(-0.295989\pi\) | ||||
0.597934 | + | 0.801545i | \(0.295989\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.37332e6 | 0.401022 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 795908. | 0.229608 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 724540. | 0.206510 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.88365e6 | −0.812088 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.10057e6 | 1.14106 | 0.570531 | − | 0.821276i | \(-0.306737\pi\) | ||||
0.570531 | + | 0.821276i | \(0.306737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.28257e6 | −1.72755 | −0.863777 | − | 0.503873i | \(-0.831908\pi\) | ||||
−0.863777 | + | 0.503873i | \(0.831908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 961728. | 0.261337 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 936474. | 0.251492 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 715533. | 0.189915 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.10691e6 | −0.815053 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.76782e6 | 0.717703 | 0.358852 | − | 0.933395i | \(-0.383168\pi\) | ||||
0.358852 | + | 0.933395i | \(0.383168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.52060e6 | 0.389759 | 0.194879 | − | 0.980827i | \(-0.437568\pi\) | ||||
0.194879 | + | 0.980827i | \(0.437568\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.56016e6 | −0.395318 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.82357e6 | 0.957779 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.69329e6 | 0.419343 | 0.209671 | − | 0.977772i | \(-0.432761\pi\) | ||||
0.209671 | + | 0.977772i | \(0.432761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −341494. | −0.0836155 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −363356. | −0.0879677 | −0.0439839 | − | 0.999032i | \(-0.514005\pi\) | ||||
−0.0439839 | + | 0.999032i | \(0.514005\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.34479e6 | 0.321924 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.10930e6 | 0.736027 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 487162. | 0.114040 | 0.0570200 | − | 0.998373i | \(-0.481840\pi\) | ||||
0.0570200 | + | 0.998373i | \(0.481840\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.81005e6 | 0.882043 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.88018e6 | −1.11735 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −896473. | −0.203006 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.38947e6 | 1.20713 | 0.603567 | − | 0.797312i | \(-0.293746\pi\) | ||||
0.603567 | + | 0.797312i | \(0.293746\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.79431e6 | −1.28372 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.69670e6 | 0.371837 | 0.185919 | − | 0.982565i | \(-0.440474\pi\) | ||||
0.185919 | + | 0.982565i | \(0.440474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.84875e6 | −1.26797 | −0.633987 | − | 0.773344i | \(-0.718583\pi\) | ||||
−0.633987 | + | 0.773344i | \(0.718583\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.02415e6 | 0.219649 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.01745e6 | −0.215883 | −0.107942 | − | 0.994157i | \(-0.534426\pi\) | ||||
−0.107942 | + | 0.994157i | \(0.534426\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.41805e6 | 0.507613 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.09681e6 | 1.05864 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 996628. | 0.204824 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 856612. | 0.174201 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.61337e6 | 0.727138 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.29901e6 | −1.25439 | −0.627196 | − | 0.778861i | \(-0.715798\pi\) | ||||
−0.627196 | + | 0.778861i | \(0.715798\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.07867e7 | −2.12581 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.37223e6 | 0.267645 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.39426e6 | −0.462187 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −79494.0 | −0.0151884 | −0.00759420 | − | 0.999971i | \(-0.502417\pi\) | ||||
−0.00759420 | + | 0.999971i | \(0.502417\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.11508e6 | −0.399994 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.10200e6 | −0.393485 | −0.196743 | − | 0.980455i | \(-0.563036\pi\) | ||||
−0.196743 | + | 0.980455i | \(0.563036\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.31494e6 | −1.72609 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.50381e6 | −0.275854 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.76701e6 | −0.320885 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.02043e6 | −1.26215 | −0.631077 | − | 0.775720i | \(-0.717387\pi\) | ||||
−0.631077 | + | 0.775720i | \(0.717387\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.56723e6 | −0.812940 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.36878e6 | 1.65106 | 0.825530 | − | 0.564358i | \(-0.190876\pi\) | ||||
0.825530 | + | 0.564358i | \(0.190876\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.57618e6 | 0.449518 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.64891e6 | 0.284890 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.06864e6 | −1.03824 | −0.519119 | − | 0.854702i | \(-0.673740\pi\) | ||||
−0.519119 | + | 0.854702i | \(0.673740\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −106742. | −0.0180836 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.30017e6 | −0.889194 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.76013e6 | −0.458577 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.85972e6 | −0.470540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.07485e6 | −0.338119 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.15802e6 | 1.47811 | 0.739056 | − | 0.673644i | \(-0.235272\pi\) | ||||
0.739056 | + | 0.673644i | \(0.235272\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.72844e6 | 1.23549 | 0.617743 | − | 0.786380i | \(-0.288047\pi\) | ||||
0.617743 | + | 0.786380i | \(0.288047\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 307427. | 0.0486792 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.11466e6 | 0.959061 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.34634e6 | 0.209177 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.31024e6 | −0.355567 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.59281e6 | −1.00520 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.06901e6 | −0.312520 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.36906e6 | −0.354520 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.01544e6 | 0.150551 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.74918e6 | −1.13832 | −0.569158 | − | 0.822228i | \(-0.692731\pi\) | ||||
−0.569158 | + | 0.822228i | \(0.692731\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.66762e6 | −0.533808 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.42012e6 | 0.349016 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.29607e6 | −0.613907 | −0.306954 | − | 0.951725i | \(-0.599310\pi\) | ||||
−0.306954 | + | 0.951725i | \(0.599310\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.07694e6 | −0.294099 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.52057e6 | −1.19561 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.29594e6 | 0.736428 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.69907e6 | 0.509753 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.16671e7 | −1.59341 | −0.796703 | − | 0.604371i | \(-0.793424\pi\) | ||||
−0.796703 | + | 0.604371i | \(0.793424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.72454e6 | −0.233422 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.36126e6 | 0.853368 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.33119e6 | 0.974773 | 0.487386 | − | 0.873186i | \(-0.337950\pi\) | ||||
0.487386 | + | 0.873186i | \(0.337950\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.45105e6 | 0.718388 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −208630. | −0.0272533 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.23824e6 | −0.289818 | −0.144909 | − | 0.989445i | \(-0.546289\pi\) | ||||
−0.144909 | + | 0.989445i | \(0.546289\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.04904e7 | −1.34648 | −0.673240 | − | 0.739424i | \(-0.735098\pi\) | ||||
−0.673240 | + | 0.739424i | \(0.735098\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.44317e6 | 0.183625 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.74359e6 | 0.219925 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.40235e6 | 0.550484 | 0.275242 | − | 0.961375i | \(-0.411242\pi\) | ||||
0.275242 | + | 0.961375i | \(0.411242\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.17369e6 | −0.765329 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.42010e6 | 0.174533 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.07444e7 | −1.30922 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.60215e6 | 0.314371 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.01305e7 | 1.21349 | 0.606747 | − | 0.794895i | \(-0.292474\pi\) | ||||
0.606747 | + | 0.794895i | \(0.292474\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.59321e6 | 0.664313 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.18739e6 | −1.08199 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.52764e7 | −1.78396 | −0.891980 | − | 0.452074i | \(-0.850684\pi\) | ||||
−0.891980 | + | 0.452074i | \(0.850684\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.83549e6 | 0.212549 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.84441e6 | −0.671127 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.61379e7 | −1.83772 | −0.918862 | − | 0.394580i | \(-0.870890\pi\) | ||||
−0.918862 | + | 0.394580i | \(0.870890\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.52964e6 | 0.511538 | 0.255769 | − | 0.966738i | \(-0.417671\pi\) | ||||
0.255769 | + | 0.966738i | \(0.417671\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.01876e6 | −0.786080 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 445335. | 0.0494651 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.28753e6 | −0.251997 | −0.125999 | − | 0.992030i | \(-0.540213\pi\) | ||||
−0.125999 | + | 0.992030i | \(0.540213\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.05792e6 | −0.334105 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.94837e6 | 0.536240 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.62618e6 | −0.389761 | −0.194880 | − | 0.980827i | \(-0.562432\pi\) | ||||
−0.194880 | + | 0.980827i | \(0.562432\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.26087e6 | 0.241039 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.84457e6 | 0.829576 | 0.414788 | − | 0.909918i | \(-0.363856\pi\) | ||||
0.414788 | + | 0.909918i | \(0.363856\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.84380e6 | −0.717911 | −0.358955 | − | 0.933355i | \(-0.616867\pi\) | ||||
−0.358955 | + | 0.933355i | \(0.616867\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.07882e7 | −1.12259 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.63578e6 | 0.272076 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.81878e6 | 0.591103 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.20852e7 | 2.22575 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.57191e7 | 1.57165 | 0.785825 | − | 0.618449i | \(-0.212239\pi\) | ||||
0.785825 | + | 0.618449i | \(0.212239\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.65450e6 | −0.858485 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.86377e6 | 0.577089 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.75709e6 | −0.171571 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.12903e6 | 0.496916 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.46226e6 | −0.717340 | −0.358670 | − | 0.933464i | \(-0.616770\pi\) | ||||
−0.358670 | + | 0.933464i | \(0.616770\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.86336e7 | −1.77734 | −0.888668 | − | 0.458551i | \(-0.848369\pi\) | ||||
−0.888668 | + | 0.458551i | \(0.848369\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 591394. | 0.0559729 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.78598e7 | 1.67732 | 0.838661 | − | 0.544654i | \(-0.183339\pi\) | ||||
0.838661 | + | 0.544654i | \(0.183339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.86956e6 | 0.640202 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.00733e6 | 0.185638 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −549913. | −0.0504674 | −0.0252337 | − | 0.999682i | \(-0.508033\pi\) | ||||
−0.0252337 | + | 0.999682i | \(0.508033\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.04701e6 | −0.186430 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 309835. | 0.0280038 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.42882e6 | 0.756055 | 0.378027 | − | 0.925794i | \(-0.376603\pi\) | ||||
0.378027 | + | 0.925794i | \(0.376603\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.35056e6 | 0.654360 | 0.327180 | − | 0.944962i | \(-0.393902\pi\) | ||||
0.327180 | + | 0.944962i | \(0.393902\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.10073e7 | −0.972521 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.67896e6 | 0.147227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.73432e7 | −1.50943 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.87580e6 | −0.593961 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.17583e6 | 0.529529 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.31577e7 | 1.11981 | 0.559903 | − | 0.828558i | \(-0.310838\pi\) | ||||
0.559903 | + | 0.828558i | \(0.310838\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.41694e6 | −0.204177 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −739294. | −0.0619934 | −0.0309967 | − | 0.999519i | \(-0.509868\pi\) | ||||
−0.0309967 | + | 0.999519i | \(0.509868\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.69276e6 | −0.390619 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.61422e6 | −0.133382 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.02676e6 | 0.166246 | 0.0831228 | − | 0.996539i | \(-0.473511\pi\) | ||||
0.0831228 | + | 0.996539i | \(0.473511\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.42017e6 | 0.278497 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.48170e7 | −1.19776 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.85919e7 | 1.49202 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.86420e6 | −0.228196 | −0.114098 | − | 0.993470i | \(-0.536398\pi\) | ||||
−0.114098 | + | 0.993470i | \(0.536398\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.94747e6 | −0.233140 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.18154e6 | −0.563969 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.34985e7 | 1.05245 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.34243e7 | −1.03920 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.71236e6 | 0.515917 | 0.257959 | − | 0.966156i | \(-0.416950\pi\) | ||||
0.257959 | + | 0.966156i | \(0.416950\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.02018e7 | 1.54171 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.69694e6 | −0.128586 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.04931e6 | 0.379912 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.24637e6 | 0.466672 | 0.233336 | − | 0.972396i | \(-0.425036\pi\) | ||||
0.233336 | + | 0.972396i | \(0.425036\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.53723e7 | −1.14042 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.13847e7 | 0.838682 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.73754e6 | −0.566028 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −311833. | −0.0226530 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.33936e7 | 0.966215 | 0.483107 | − | 0.875561i | \(-0.339508\pi\) | ||||
0.483107 | + | 0.875561i | \(0.339508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.40986e6 | −0.387568 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.28257e6 | 0.660423 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.88548e6 | −0.274536 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.81735e7 | 1.27527 | 0.637635 | − | 0.770338i | \(-0.279913\pi\) | ||||
0.637635 | + | 0.770338i | \(0.279913\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00388e7 | 0.699618 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.53091e6 | 0.244396 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.72669e6 | 0.668660 | 0.334330 | − | 0.942456i | \(-0.391490\pi\) | ||||
0.334330 | + | 0.942456i | \(0.391490\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 602557. | 0.0411414 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.08704e7 | 1.41535 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.17199e7 | −0.789431 | −0.394716 | − | 0.918803i | \(-0.629157\pi\) | ||||
−0.394716 | + | 0.918803i | \(0.629157\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.00686e7 | −0.673637 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.66089e7 | −1.10374 | −0.551872 | − | 0.833929i | \(-0.686086\pi\) | ||||
−0.551872 | + | 0.833929i | \(0.686086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.74349e6 | 0.511147 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.12205e6 | −0.270279 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.05525e6 | −0.264127 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.81282e6 | 0.311386 | 0.155693 | − | 0.987805i | \(-0.450239\pi\) | ||||
0.155693 | + | 0.987805i | \(0.450239\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.63218e6 | 0.361984 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.21537e7 | −0.775965 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.44840e7 | 0.918645 | 0.459323 | − | 0.888270i | \(-0.348092\pi\) | ||||
0.459323 | + | 0.888270i | \(0.348092\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.18438e7 | 0.746256 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.97379e6 | 0.436523 | 0.218262 | − | 0.975890i | \(-0.429961\pi\) | ||||
0.218262 | + | 0.975890i | \(0.429961\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.74343e6 | 0.294972 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.32779e6 | −0.329150 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.18869e7 | −0.729591 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.57839e7 | 0.962494 | 0.481247 | − | 0.876585i | \(-0.340184\pi\) | ||||
0.481247 | + | 0.876585i | \(0.340184\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.17254e6 | 0.192208 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.86689e7 | 1.72569 | 0.862843 | − | 0.505472i | \(-0.168682\pi\) | ||||
0.862843 | + | 0.505472i | \(0.168682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.55057e6 | 0.152540 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.25017e6 | 0.430820 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.23473e7 | 0.729004 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.52513e7 | −0.894701 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.40409e7 | 1.40135 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.26933e7 | 0.735188 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.82453e7 | −1.62558 | −0.812791 | − | 0.582556i | \(-0.802053\pi\) | ||||
−0.812791 | + | 0.582556i | \(0.802053\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.63045e6 | −0.150431 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.06841e7 | 0.607149 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.06865e7 | −0.603465 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.37570e6 | −0.357775 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.95525e7 | −1.64797 | −0.823983 | − | 0.566615i | \(-0.808253\pi\) | ||||
−0.823983 | + | 0.566615i | \(0.808253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.01316e7 | −0.561448 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.65077e6 | −0.421331 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −921302. | −0.0504212 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.41744e6 | 0.185871 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.21618e7 | −0.657377 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.18511e7 | −0.636631 | −0.318316 | − | 0.947985i | \(-0.603117\pi\) | ||||
−0.318316 | + | 0.947985i | \(0.603117\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.41901e7 | 1.82536 | 0.912680 | − | 0.408676i | \(-0.134009\pi\) | ||||
0.912680 | + | 0.408676i | \(0.134009\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.53317e6 | 0.0813510 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.26745e6 | −0.277783 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.22980e6 | 0.169286 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.10021e6 | 0.265692 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.92970e7 | 0.999152 | 0.499576 | − | 0.866270i | \(-0.333489\pi\) | ||||
0.499576 | + | 0.866270i | \(0.333489\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.68887e7 | −0.869156 | −0.434578 | − | 0.900634i | \(-0.643103\pi\) | ||||
−0.434578 | + | 0.900634i | \(0.643103\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.65343e6 | 0.135729 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.80486e6 | −0.142609 | −0.0713046 | − | 0.997455i | \(-0.522716\pi\) | ||||
−0.0713046 | + | 0.997455i | \(0.522716\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.98746e6 | −0.403666 | −0.201833 | − | 0.979420i | \(-0.564690\pi\) | ||||
−0.201833 | + | 0.979420i | \(0.564690\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.47856e6 | 0.325444 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.59756e6 | 0.179637 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.13744e7 | −0.564561 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.57813e7 | −0.778626 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.93272e7 | −0.947901 | −0.473950 | − | 0.880552i | \(-0.657172\pi\) | ||||
−0.473950 | + | 0.880552i | \(0.657172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.81370e7 | 0.884251 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.74684e6 | 0.423918 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.10650e6 | 0.197847 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 872857. | 0.0418056 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.22945e7 | 0.585386 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.11198e7 | 1.94638 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.94339e7 | −1.85566 | −0.927828 | − | 0.373009i | \(-0.878326\pi\) | ||||
−0.927828 | + | 0.373009i | \(0.878326\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.87344e6 | −0.227992 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.72300e6 | 0.312688 | 0.156344 | − | 0.987703i | \(-0.450029\pi\) | ||||
0.156344 | + | 0.987703i | \(0.450029\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.35827e6 | −0.247766 | −0.123883 | − | 0.992297i | \(-0.539535\pi\) | ||||
−0.123883 | + | 0.992297i | \(0.539535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.43130e6 | 0.203715 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.33529e6 | 0.243855 | 0.121927 | − | 0.992539i | \(-0.461092\pi\) | ||||
0.121927 | + | 0.992539i | \(0.461092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.16728e6 | −0.234813 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.28393e6 | 0.374273 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.57098e7 | 2.05333 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.61136e7 | −1.61296 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.36214e7 | 0.604905 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 765625. | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.59912e7 | −0.702073 | −0.351036 | − | 0.936362i | \(-0.614171\pi\) | ||||
−0.351036 | + | 0.936362i | \(0.614171\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.81394e6 | 0.0791865 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.36775e6 | 0.189591 | 0.0947956 | − | 0.995497i | \(-0.469780\pi\) | ||||
0.0947956 | + | 0.995497i | \(0.469780\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.91052e7 | 1.25623 | 0.628114 | − | 0.778122i | \(-0.283827\pi\) | ||||
0.628114 | + | 0.778122i | \(0.283827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.07636e6 | 0.174950 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.99268e7 | 1.70395 | 0.851973 | − | 0.523586i | \(-0.175406\pi\) | ||||
0.851973 | + | 0.523586i | \(0.175406\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.14930e7 | 0.487729 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.80071e6 | −0.0759887 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.26756e6 | −0.388899 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.89998e6 | −0.246203 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.04942e7 | −0.850453 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.53700e7 | −1.04694 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.80660e7 | −1.56216 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.15913e6 | 0.0473057 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.13396e6 | −0.370713 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.59920e7 | −1.85637 | −0.928183 | − | 0.372123i | \(-0.878630\pi\) | ||||
−0.928183 | + | 0.372123i | \(0.878630\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.46564e7 | −0.588325 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.02730e7 | −0.809322 | −0.404661 | − | 0.914467i | \(-0.632610\pi\) | ||||
−0.404661 | + | 0.914467i | \(0.632610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.22570e7 | 0.486639 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.66471e6 | 0.144706 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.01214e6 | −0.157562 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.94257e7 | −0.758730 | −0.379365 | − | 0.925247i | \(-0.623858\pi\) | ||||
−0.379365 | + | 0.925247i | \(0.623858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.57836e7 | 1.00160 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.63903e7 | 1.01963 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.21226e6 | 0.354007 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.57029e7 | 0.600181 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.59308e7 | 1.74608 | 0.873040 | − | 0.487648i | \(-0.162145\pi\) | ||||
0.873040 | + | 0.487648i | \(0.162145\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.29076e6 | 0.124429 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.84809e7 | −1.07115 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.58423e7 | 0.592637 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.92867e6 | −0.295020 | −0.147510 | − | 0.989061i | \(-0.547126\pi\) | ||||
−0.147510 | + | 0.989061i | \(0.547126\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.30562e7 | −0.483228 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.31133e7 | −1.58722 | −0.793610 | − | 0.608426i | \(-0.791801\pi\) | ||||
−0.793610 | + | 0.608426i | \(0.791801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.51324e7 | 0.920353 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.73720e6 | −0.172561 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.33497e7 | 1.57077 | 0.785383 | − | 0.619011i | \(-0.212466\pi\) | ||||
0.785383 | + | 0.619011i | \(0.212466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.59419e6 | 0.0574613 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.38240e7 | 0.854209 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.08760e6 | 0.110126 | 0.0550628 | − | 0.998483i | \(-0.482464\pi\) | ||||
0.0550628 | + | 0.998483i | \(0.482464\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.59412e6 | 0.127522 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.63932e7 | −0.931563 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.70353e6 | 0.235373 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.19753e7 | −0.418292 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.17710e7 | 0.409023 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.53751e7 | −0.531497 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.37145e6 | −0.184725 | −0.0923623 | − | 0.995725i | \(-0.529442\pi\) | ||||
−0.0923623 | + | 0.995725i | \(0.529442\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.06151e7 | 0.705304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −588590. | −0.0200339 | −0.0100169 | − | 0.999950i | \(-0.503189\pi\) | ||||
−0.0100169 | + | 0.999950i | \(0.503189\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.40758e7 | −0.476641 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.59142e6 | −0.154680 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.96258e6 | −0.300398 | −0.150199 | − | 0.988656i | \(-0.547991\pi\) | ||||
−0.150199 | + | 0.988656i | \(0.547991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.27497e7 | 0.758611 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.37685e7 | −0.456789 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.47149e7 | 0.485705 | 0.242853 | − | 0.970063i | \(-0.421917\pi\) | ||||
0.242853 | + | 0.970063i | \(0.421917\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.28805e7 | −0.751408 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.32600e6 | −0.108675 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.57409e6 | 0.213720 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.67288e7 | −1.18802 | −0.594008 | − | 0.804459i | \(-0.702455\pi\) | ||||
−0.594008 | + | 0.804459i | \(0.702455\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.64251e6 | −0.149410 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.45551e7 | −0.466077 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.22158e6 | 0.0707821 | 0.0353910 | − | 0.999374i | \(-0.488732\pi\) | ||||
0.0353910 | + | 0.999374i | \(0.488732\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.69996e7 | −1.80700 |
(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 | 280.6.a.j.1.3 | ✓ | 5 | |
4.3 | odd | 2 | 560.6.a.y.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.6.a.j.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
560.6.a.y.1.3 | 5 | 4.3 | odd | 2 |