Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,6,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, 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("1080.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(173.214525398\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.15881.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 29x - 55 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.82250\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −177.292 | −1.36756 | −0.683778 | − | 0.729690i | \(-0.739664\pi\) | ||||
−0.683778 | + | 0.729690i | \(0.739664\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −778.539 | −1.93999 | −0.969993 | − | 0.243133i | \(-0.921825\pi\) | ||||
−0.969993 | + | 0.243133i | \(0.921825\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 132.539 | 0.217513 | 0.108756 | − | 0.994068i | \(-0.465313\pi\) | ||||
0.108756 | + | 0.994068i | \(0.465313\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1634.72 | 1.37190 | 0.685949 | − | 0.727650i | \(-0.259387\pi\) | ||||
0.685949 | + | 0.727650i | \(0.259387\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 345.079 | 0.219298 | 0.109649 | − | 0.993970i | \(-0.465027\pi\) | ||||
0.109649 | + | 0.993970i | \(0.465027\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 959.441 | 0.378180 | 0.189090 | − | 0.981960i | \(-0.439446\pi\) | ||||
0.189090 | + | 0.981960i | \(0.439446\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2573.30 | 0.568193 | 0.284096 | − | 0.958796i | \(-0.408306\pi\) | ||||
0.284096 | + | 0.958796i | \(0.408306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4123.80 | 0.770715 | 0.385358 | − | 0.922767i | \(-0.374078\pi\) | ||||
0.385358 | + | 0.922767i | \(0.374078\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4432.31 | −0.611589 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7188.70 | 0.863269 | 0.431635 | − | 0.902049i | \(-0.357937\pi\) | ||||
0.431635 | + | 0.902049i | \(0.357937\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 19345.5 | 1.79729 | 0.898647 | − | 0.438672i | \(-0.144551\pi\) | ||||
0.898647 | + | 0.438672i | \(0.144551\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1526.17 | 0.125873 | 0.0629365 | − | 0.998018i | \(-0.479953\pi\) | ||||
0.0629365 | + | 0.998018i | \(0.479953\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3415.76 | −0.225550 | −0.112775 | − | 0.993621i | \(-0.535974\pi\) | ||||
−0.112775 | + | 0.993621i | \(0.535974\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14625.6 | 0.870208 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 17770.0 | 0.868955 | 0.434477 | − | 0.900683i | \(-0.356933\pi\) | ||||
0.434477 | + | 0.900683i | \(0.356933\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19463.5 | −0.867588 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 17443.5 | 0.652385 | 0.326192 | − | 0.945303i | \(-0.394234\pi\) | ||||
0.326192 | + | 0.945303i | \(0.394234\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18471.9 | −0.635603 | −0.317802 | − | 0.948157i | \(-0.602945\pi\) | ||||
−0.317802 | + | 0.948157i | \(0.602945\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3313.47 | 0.0972747 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −54149.5 | −1.47369 | −0.736847 | − | 0.676059i | \(-0.763686\pi\) | ||||
−0.736847 | + | 0.676059i | \(0.763686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −66498.8 | −1.56555 | −0.782776 | − | 0.622303i | \(-0.786197\pi\) | ||||
−0.782776 | + | 0.622303i | \(0.786197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −28937.5 | −0.635556 | −0.317778 | − | 0.948165i | \(-0.602937\pi\) | ||||
−0.317778 | + | 0.948165i | \(0.602937\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 138029. | 2.65304 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −88015.0 | −1.58668 | −0.793339 | − | 0.608780i | \(-0.791659\pi\) | ||||
−0.793339 | + | 0.608780i | \(0.791659\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −68424.7 | −1.09023 | −0.545114 | − | 0.838362i | \(-0.683514\pi\) | ||||
−0.545114 | + | 0.838362i | \(0.683514\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 40868.1 | 0.613531 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −116101. | −1.55368 | −0.776838 | − | 0.629701i | \(-0.783177\pi\) | ||||
−0.776838 | + | 0.629701i | \(0.783177\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −23498.1 | −0.297461 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8626.98 | 0.0980731 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −47803.9 | −0.515863 | −0.257931 | − | 0.966163i | \(-0.583041\pi\) | ||||
−0.257931 | + | 0.966163i | \(0.583041\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −184461. | −1.79929 | −0.899643 | − | 0.436626i | \(-0.856173\pi\) | ||||
−0.899643 | + | 0.436626i | \(0.856173\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 36260.9 | 0.336780 | 0.168390 | − | 0.985720i | \(-0.446143\pi\) | ||||
0.168390 | + | 0.985720i | \(0.446143\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 194715. | 1.64414 | 0.822072 | − | 0.569383i | \(-0.192818\pi\) | ||||
0.822072 | + | 0.569383i | \(0.192818\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 35234.0 | 0.284051 | 0.142025 | − | 0.989863i | \(-0.454639\pi\) | ||||
0.142025 | + | 0.989863i | \(0.454639\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −138170. | −1.01793 | −0.508965 | − | 0.860787i | \(-0.669972\pi\) | ||||
−0.508965 | + | 0.860787i | \(0.669972\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23986.0 | 0.169127 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −289824. | −1.87615 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 445072. | 2.76355 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 37441.3 | 0.205988 | 0.102994 | − | 0.994682i | \(-0.467158\pi\) | ||||
0.102994 | + | 0.994682i | \(0.467158\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −50118.6 | −0.255165 | −0.127582 | − | 0.991828i | \(-0.540722\pi\) | ||||
−0.127582 | + | 0.991828i | \(0.540722\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −61179.9 | −0.299902 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 73408.5 | 0.334153 | 0.167076 | − | 0.985944i | \(-0.446567\pi\) | ||||
0.167076 | + | 0.985944i | \(0.446567\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −32460.7 | −0.142502 | −0.0712510 | − | 0.997458i | \(-0.522699\pi\) | ||||
−0.0712510 | + | 0.997458i | \(0.522699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −103187. | −0.421972 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 64332.5 | 0.254103 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −301999. | −1.11440 | −0.557198 | − | 0.830380i | \(-0.688123\pi\) | ||||
−0.557198 | + | 0.830380i | \(0.688123\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 239797. | 0.855858 | 0.427929 | − | 0.903812i | \(-0.359243\pi\) | ||||
0.427929 | + | 0.903812i | \(0.359243\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 103095. | 0.344674 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 312913. | 1.01315 | 0.506577 | − | 0.862195i | \(-0.330911\pi\) | ||||
0.506577 | + | 0.862195i | \(0.330911\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −170101. | −0.517182 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 219202. | 0.646214 | 0.323107 | − | 0.946362i | \(-0.395273\pi\) | ||||
0.323107 | + | 0.946362i | \(0.395273\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −186815. | −0.518346 | −0.259173 | − | 0.965831i | \(-0.583450\pi\) | ||||
−0.259173 | + | 0.965831i | \(0.583450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −353726. | −0.952688 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 35108.1 | 0.0891851 | 0.0445926 | − | 0.999005i | \(-0.485801\pi\) | ||||
0.0445926 | + | 0.999005i | \(0.485801\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −110808. | −0.273511 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 250525. | 0.584410 | 0.292205 | − | 0.956356i | \(-0.405611\pi\) | ||||
0.292205 | + | 0.956356i | \(0.405611\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −541712. | −1.22906 | −0.614529 | − | 0.788894i | \(-0.710654\pi\) | ||||
−0.614529 | + | 0.788894i | \(0.710654\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 179718. | 0.386066 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.27270e6 | −2.66146 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −180536. | −0.358081 | −0.179040 | − | 0.983842i | \(-0.557299\pi\) | ||||
−0.179040 | + | 0.983842i | \(0.557299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −531938. | −1.02794 | −0.513970 | − | 0.857808i | \(-0.671826\pi\) | ||||
−0.513970 | + | 0.857808i | \(0.671826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 488199. | 0.896255 | 0.448127 | − | 0.893970i | \(-0.352091\pi\) | ||||
0.448127 | + | 0.893970i | \(0.352091\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 41226.6 | 0.0737980 | 0.0368990 | − | 0.999319i | \(-0.488252\pi\) | ||||
0.0368990 | + | 0.999319i | \(0.488252\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −456227. | −0.777035 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 483636. | 0.803775 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −268658. | −0.425435 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 727442. | 1.12484 | 0.562422 | − | 0.826851i | \(-0.309870\pi\) | ||||
0.562422 | + | 0.826851i | \(0.309870\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 38154.3 | 0.0562921 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −731119. | −1.05400 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 216664. | 0.298405 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.05221e6 | 1.41691 | 0.708453 | − | 0.705758i | \(-0.249394\pi\) | ||||
0.708453 | + | 0.705758i | \(0.249394\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −70140.8 | −0.0903454 | −0.0451727 | − | 0.998979i | \(-0.514384\pi\) | ||||
−0.0451727 | + | 0.998979i | \(0.514384\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 331611. | 0.417868 | 0.208934 | − | 0.977930i | \(-0.433001\pi\) | ||||
0.208934 | + | 0.977930i | \(0.433001\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.18857e6 | −1.43429 | −0.717143 | − | 0.696926i | \(-0.754550\pi\) | ||||
−0.717143 | + | 0.696926i | \(0.754550\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −85394.0 | −0.100869 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.65354e6 | −1.87249 | −0.936246 | − | 0.351345i | \(-0.885724\pi\) | ||||
−0.936246 | + | 0.351345i | \(0.885724\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.28873e6 | 1.42929 | 0.714643 | − | 0.699489i | \(-0.246589\pi\) | ||||
0.714643 | + | 0.699489i | \(0.246589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 365639. | 0.389169 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 45736.4 | 0.0477002 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.01541e6 | 1.01732 | 0.508662 | − | 0.860967i | \(-0.330140\pi\) | ||||
0.508662 | + | 0.860967i | \(0.330140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −746962. | −0.733664 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −560979. | −0.529802 | −0.264901 | − | 0.964276i | \(-0.585339\pi\) | ||||
−0.264901 | + | 0.964276i | \(0.585339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.27450e6 | −1.18057 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −695106. | −0.619672 | −0.309836 | − | 0.950790i | \(-0.600274\pi\) | ||||
−0.309836 | + | 0.950790i | \(0.600274\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 444249. | 0.388608 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.70042e6 | −1.43277 | −0.716383 | − | 0.697707i | \(-0.754204\pi\) | ||||
−0.716383 | + | 0.697707i | \(0.754204\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.57912e6 | 1.30615 | 0.653074 | − | 0.757294i | \(-0.273479\pi\) | ||||
0.653074 | + | 0.757294i | \(0.273479\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −486587. | −0.387997 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −640171. | −0.501299 | −0.250649 | − | 0.968078i | \(-0.580644\pi\) | ||||
−0.250649 | + | 0.968078i | \(0.580644\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −468521. | −0.353968 | −0.176984 | − | 0.984214i | \(-0.556634\pi\) | ||||
−0.176984 | + | 0.984214i | \(0.556634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −669897. | −0.497212 | −0.248606 | − | 0.968605i | \(-0.579972\pi\) | ||||
−0.248606 | + | 0.968605i | \(0.579972\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.42980e6 | −2.45790 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.25246e6 | 0.882104 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −223700. | −0.152229 | −0.0761145 | − | 0.997099i | \(-0.524251\pi\) | ||||
−0.0761145 | + | 0.997099i | \(0.524251\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 436088. | 0.291755 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 127163. | 0.0822590 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −270579. | −0.172138 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −461796. | −0.284250 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.09907e6 | −0.665547 | −0.332774 | − | 0.943007i | \(-0.607984\pi\) | ||||
−0.332774 | + | 0.943007i | \(0.607984\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.84743e6 | −1.08310 | −0.541548 | − | 0.840670i | \(-0.682162\pi\) | ||||
−0.541548 | + | 0.840670i | \(0.682162\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 84378.0 | 0.0486820 | 0.0243410 | − | 0.999704i | \(-0.492251\pi\) | ||||
0.0243410 | + | 0.999704i | \(0.492251\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.19843e6 | −1.78768 | −0.893838 | − | 0.448389i | \(-0.851998\pi\) | ||||
−0.893838 | + | 0.448389i | \(0.851998\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00341e6 | −1.10229 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 564109. | 0.300855 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 82836.8 | 0.0435026 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 605588. | 0.308452 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 798314. | 0.400501 | 0.200251 | − | 0.979745i | \(-0.435824\pi\) | ||||
0.200251 | + | 0.979745i | \(0.435824\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.35374e6 | −0.659056 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −721479. | −0.346058 | −0.173029 | − | 0.984917i | \(-0.555355\pi\) | ||||
−0.173029 | + | 0.984917i | \(0.555355\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.21054e6 | −1.49518 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 386749. | 0.177498 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.83135e6 | −0.816483 | −0.408242 | − | 0.912874i | \(-0.633858\pi\) | ||||
−0.408242 | + | 0.912874i | \(0.633858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.63801e6 | 1.15935 | 0.579673 | − | 0.814849i | \(-0.303180\pi\) | ||||
0.579673 | + | 0.814849i | \(0.303180\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −640229. | −0.273463 | −0.136732 | − | 0.990608i | \(-0.543660\pi\) | ||||
−0.136732 | + | 0.990608i | \(0.543660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.66247e6 | −0.700136 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.88403e6 | 1.59055 | 0.795273 | − | 0.606252i | \(-0.207328\pi\) | ||||
0.795273 | + | 0.606252i | \(0.207328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.35702e6 | −0.951908 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −723437. | −0.284229 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.89439e6 | −1.12174 | −0.560870 | − | 0.827904i | \(-0.689533\pi\) | ||||
−0.560870 | + | 0.827904i | \(0.689533\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.15048e6 | −1.18834 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.55971e6 | −1.32478 | −0.662389 | − | 0.749160i | \(-0.730457\pi\) | ||||
−0.662389 | + | 0.749160i | \(0.730457\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 341062. | 0.123589 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.33127e6 | −1.90648 | −0.953242 | − | 0.302209i | \(-0.902276\pi\) | ||||
−0.953242 | + | 0.302209i | \(0.902276\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 988098. | 0.344194 | 0.172097 | − | 0.985080i | \(-0.444946\pi\) | ||||
0.172097 | + | 0.985080i | \(0.444946\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.45072e6 | 1.18647 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.45055e6 | −0.821088 | −0.410544 | − | 0.911841i | \(-0.634661\pi\) | ||||
−0.410544 | + | 0.911841i | \(0.634661\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.56842e6 | 0.518824 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.20038e6 | −0.709584 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.03254e6 | 1.60255 | 0.801273 | − | 0.598299i | \(-0.204156\pi\) | ||||
0.801273 | + | 0.598299i | \(0.204156\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 421036. | 0.130755 | 0.0653775 | − | 0.997861i | \(-0.479175\pi\) | ||||
0.0653775 | + | 0.997861i | \(0.479175\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 546564. | 0.167640 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.59668e6 | −1.67473 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.26037e6 | 1.55492 | 0.777459 | − | 0.628933i | \(-0.216508\pi\) | ||||
0.777459 | + | 0.628933i | \(0.216508\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.09260e6 | −0.892172 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.71062e6 | −0.487565 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.27635e6 | 1.46825 | 0.734123 | − | 0.679016i | \(-0.237593\pi\) | ||||
0.734123 | + | 0.679016i | \(0.237593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.85695e6 | 1.88550 | 0.942748 | − | 0.333506i | \(-0.108232\pi\) | ||||
0.942748 | + | 0.333506i | \(0.108232\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.02170e6 | 0.274380 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.27492e6 | 0.869222 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.34747e6 | 1.38661 | 0.693306 | − | 0.720643i | \(-0.256153\pi\) | ||||
0.693306 | + | 0.720643i | \(0.256153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.48030e6 | 1.40470 | 0.702351 | − | 0.711831i | \(-0.252134\pi\) | ||||
0.702351 | + | 0.711831i | \(0.252134\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 331083. | 0.0829342 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.88107e6 | −0.465848 | −0.232924 | − | 0.972495i | \(-0.574829\pi\) | ||||
−0.232924 | + | 0.972495i | \(0.574829\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.74311e6 | 1.63249 | 0.816245 | − | 0.577706i | \(-0.196052\pi\) | ||||
0.816245 | + | 0.577706i | \(0.196052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.90252e6 | −0.694825 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.56671e6 | −0.366751 | −0.183376 | − | 0.983043i | \(-0.558702\pi\) | ||||
−0.183376 | + | 0.983043i | \(0.558702\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.50612e7 | −3.48673 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −587453. | −0.133029 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.65144e6 | −1.26581 | −0.632905 | − | 0.774229i | \(-0.718138\pi\) | ||||
−0.632905 | + | 0.774229i | \(0.718138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.08271e6 | −1.55220 | −0.776099 | − | 0.630611i | \(-0.782804\pi\) | ||||
−0.776099 | + | 0.630611i | \(0.782804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.96223e6 | 0.425400 | 0.212700 | − | 0.977118i | \(-0.431774\pi\) | ||||
0.212700 | + | 0.977118i | \(0.431774\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.00128e6 | −0.848999 | −0.424500 | − | 0.905428i | \(-0.639550\pi\) | ||||
−0.424500 | + | 0.905428i | \(0.639550\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.60029e6 | 2.01536 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.18818e6 | −0.244192 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 215675. | 0.0438596 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.02033e6 | 0.999755 | 0.499878 | − | 0.866096i | \(-0.333378\pi\) | ||||
0.499878 | + | 0.866096i | \(0.333378\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 952782. | 0.187772 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.19510e6 | −0.230701 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.44446e6 | 0.849174 | 0.424587 | − | 0.905387i | \(-0.360419\pi\) | ||||
0.424587 | + | 0.905387i | \(0.360419\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.94382e6 | −1.48705 | −0.743525 | − | 0.668708i | \(-0.766847\pi\) | ||||
−0.743525 | + | 0.668708i | \(0.766847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.20663e6 | 0.779502 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.17897e7 | 2.14098 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.40214e6 | 0.791430 | 0.395715 | − | 0.918373i | \(-0.370497\pi\) | ||||
0.395715 | + | 0.918373i | \(0.370497\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.09339e7 | −1.92689 | −0.963445 | − | 0.267907i | \(-0.913668\pi\) | ||||
−0.963445 | + | 0.267907i | \(0.913668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.61152e6 | −0.804665 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.82803e6 | −0.825992 | −0.412996 | − | 0.910733i | \(-0.635518\pi\) | ||||
−0.412996 | + | 0.910733i | \(0.635518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.13039e6 | 0.869157 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 906524. | 0.150613 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.65930e6 | 0.437564 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.13830e6 | 0.667924 | 0.333962 | − | 0.942586i | \(-0.391614\pi\) | ||||
0.333962 | + | 0.942586i | \(0.391614\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.79480e6 | −1.56582 | −0.782909 | − | 0.622136i | \(-0.786265\pi\) | ||||
−0.782909 | + | 0.622136i | \(0.786265\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.74128e6 | 1.05734 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.51582e6 | −0.856980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.56402e6 | 0.390935 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.86788e6 | 0.735284 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.13866e7 | −1.68819 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.01186e6 | −0.736216 | −0.368108 | − | 0.929783i | \(-0.619994\pi\) | ||||
−0.368108 | + | 0.929783i | \(0.619994\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 880850. | 0.127031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.87207e6 | −0.553318 | −0.276659 | − | 0.960968i | \(-0.589227\pi\) | ||||
−0.276659 | + | 0.960968i | \(0.589227\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 887993. | 0.124604 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.56044e7 | 2.16987 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.83098e6 | 0.932921 | 0.466461 | − | 0.884542i | \(-0.345529\pi\) | ||||
0.466461 | + | 0.884542i | \(0.345529\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 202277. | 0.0273790 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.10042e7 | −1.46314 | −0.731571 | − | 0.681765i | \(-0.761213\pi\) | ||||
−0.731571 | + | 0.681765i | \(0.761213\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.45425e6 | −0.455232 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.90980e6 | −1.02420 | −0.512100 | − | 0.858926i | \(-0.671132\pi\) | ||||
−0.512100 | + | 0.858926i | \(0.671132\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.27065e6 | −0.676509 | −0.338255 | − | 0.941055i | \(-0.609836\pi\) | ||||
−0.338255 | + | 0.941055i | \(0.609836\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 599650. | 0.0756360 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16853.3 | 0.00210740 | 0.00105370 | − | 0.999999i | \(-0.499665\pi\) | ||||
0.00105370 | + | 0.999999i | \(0.499665\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.21312e7 | 1.49095 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.38346e7 | −1.68576 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.46707e7 | −1.75733 | −0.878667 | − | 0.477435i | \(-0.841567\pi\) | ||||
−0.878667 | + | 0.477435i | \(0.841567\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.42304e6 | 0.169016 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.22349e6 | −0.259656 | −0.129828 | − | 0.991537i | \(-0.541443\pi\) | ||||
−0.129828 | + | 0.991537i | \(0.541443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.24560e6 | −0.839038 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.24066e7 | −1.41281 | −0.706405 | − | 0.707807i | \(-0.749684\pi\) | ||||
−0.706405 | + | 0.707807i | \(0.749684\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.44445e6 | −0.163124 | −0.0815618 | − | 0.996668i | \(-0.525991\pi\) | ||||
−0.0815618 | + | 0.996668i | \(0.525991\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.11268e7 | 1.23590 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.21724e6 | −0.684898 | −0.342449 | − | 0.939536i | \(-0.611256\pi\) | ||||
−0.342449 | + | 0.939536i | \(0.611256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −452721. | −0.0490600 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.57737e6 | −0.814455 | −0.407228 | − | 0.913327i | \(-0.633504\pi\) | ||||
−0.407228 | + | 0.913327i | \(0.633504\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.51893e7 | −1.60629 | −0.803147 | − | 0.595782i | \(-0.796842\pi\) | ||||
−0.803147 | + | 0.595782i | \(0.796842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.86181e6 | 0.510001 | 0.255001 | − | 0.966941i | \(-0.417924\pi\) | ||||
0.255001 | + | 0.966941i | \(0.417924\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.05838e7 | 2.12474 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.17515e7 | 1.18432 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.62841e7 | −1.62813 | −0.814065 | − | 0.580773i | \(-0.802750\pi\) | ||||
−0.814065 | + | 0.580773i | \(0.802750\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 936033. | 0.0921206 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.93846e6 | 0.189281 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.64531e6 | −0.254292 | −0.127146 | − | 0.991884i | \(-0.540582\pi\) | ||||
−0.127146 | + | 0.991884i | \(0.540582\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.43973e7 | 1.37326 | 0.686630 | − | 0.727007i | \(-0.259089\pi\) | ||||
0.686630 | + | 0.727007i | \(0.259089\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.26066e6 | 0.494060 | 0.247030 | − | 0.969008i | \(-0.420545\pi\) | ||||
0.247030 | + | 0.969008i | \(0.420545\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.35805e7 | −1.26562 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.57874e6 | −0.879074 | −0.439537 | − | 0.898225i | \(-0.644857\pi\) | ||||
−0.439537 | + | 0.898225i | \(0.644857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.25297e6 | −0.114113 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.87271e6 | 0.795871 | 0.397936 | − | 0.917413i | \(-0.369727\pi\) | ||||
0.397936 | + | 0.917413i | \(0.369727\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −262438. | −0.0233627 | −0.0116814 | − | 0.999932i | \(-0.503718\pi\) | ||||
−0.0116814 | + | 0.999932i | \(0.503718\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.52950e6 | −0.134120 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.46893e6 | 0.214879 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.43811e7 | 1.23306 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.01759e6 | 0.427029 | 0.213514 | − | 0.976940i | \(-0.431509\pi\) | ||||
0.213514 | + | 0.976940i | \(0.431509\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.24406e7 | 1.04320 | 0.521602 | − | 0.853189i | \(-0.325335\pi\) | ||||
0.521602 | + | 0.853189i | \(0.325335\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.47527e6 | 0.705471 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.34912e6 | 0.274712 | 0.137356 | − | 0.990522i | \(-0.456139\pi\) | ||||
0.137356 | + | 0.990522i | \(0.456139\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.83521e6 | 0.149438 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.35521e6 | 0.189009 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.44577e7 | −1.15188 | −0.575938 | − | 0.817494i | \(-0.695363\pi\) | ||||
−0.575938 | + | 0.817494i | \(0.695363\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −811517. | −0.0637288 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.16245e7 | 2.46570 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.17953e6 | 0.705546 | 0.352773 | − | 0.935709i | \(-0.385239\pi\) | ||||
0.352773 | + | 0.935709i | \(0.385239\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.48067e6 | 0.189313 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.27035e7 | 2.46062 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.55235e7 | 1.15977 | 0.579887 | − | 0.814697i | \(-0.303097\pi\) | ||||
0.579887 | + | 0.814697i | \(0.303097\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.95655e6 | 0.291469 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.57967e6 | −0.188712 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.96476e6 | 0.430299 | 0.215150 | − | 0.976581i | \(-0.430976\pi\) | ||||
0.215150 | + | 0.976581i | \(0.430976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.42879e6 | −0.460565 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.60831e6 | 0.113639 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.08552e6 | −0.427033 | −0.213517 | − | 0.976939i | \(-0.568492\pi\) | ||||
−0.213517 | + | 0.976939i | \(0.568492\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.49487e6 | 0.172685 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.96004e7 | 1.34742 | 0.673712 | − | 0.738994i | \(-0.264699\pi\) | ||||
0.673712 | + | 0.738994i | \(0.264699\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.21575e7 | 2.85895 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.81747e7 | 1.22421 | 0.612106 | − | 0.790776i | \(-0.290323\pi\) | ||||
0.612106 | + | 0.790776i | \(0.290323\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.94965e7 | 1.29564 | 0.647820 | − | 0.761793i | \(-0.275681\pi\) | ||||
0.647820 | + | 0.761793i | \(0.275681\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.54996e6 | −0.498373 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.45215e7 | −2.24846 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.80428e6 | 0.310834 | 0.155417 | − | 0.987849i | \(-0.450328\pi\) | ||||
0.155417 | + | 0.987849i | \(0.450328\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.99493e6 | 0.382751 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.51641e7 | −0.961780 | −0.480890 | − | 0.876781i | \(-0.659686\pi\) | ||||
−0.480890 | + | 0.876781i | \(0.659686\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.65799e6 | −0.354161 | −0.177080 | − | 0.984196i | \(-0.556665\pi\) | ||||
−0.177080 | + | 0.984196i | \(0.556665\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.24672e6 | −0.388455 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.31194e6 | 0.141902 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.26224e7 | 1.98930 | 0.994650 | − | 0.103299i | \(-0.0329398\pi\) | ||||
0.994650 | + | 0.103299i | \(0.0329398\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.93469e6 | −0.417425 | −0.208712 | − | 0.977977i | \(-0.566927\pi\) | ||||
−0.208712 | + | 0.977977i | \(0.566927\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.57738e6 | 0.154143 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.67572e6 | 0.394143 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.17719e7 | 3.03715 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.82284e6 | 0.453096 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.48568e7 | −1.43057 | −0.715285 | − | 0.698833i | \(-0.753703\pi\) | ||||
−0.715285 | + | 0.698833i | \(0.753703\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.44965e7 | 1.39208 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.44824e6 | −0.138252 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.45001e6 | 0.0808583 | 0.0404292 | − | 0.999182i | \(-0.487127\pi\) | ||||
0.0404292 | + | 0.999182i | \(0.487127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.58382e6 | −0.309431 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.25289e7 | 1.23297 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.25254e6 | −0.231291 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.88981e6 | 0.477552 | 0.238776 | − | 0.971075i | \(-0.423254\pi\) | ||||
0.238776 | + | 0.971075i | \(0.423254\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.16694e6 | 0.436021 | 0.218011 | − | 0.975946i | \(-0.430043\pi\) | ||||
0.218011 | + | 0.975946i | \(0.430043\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.48006e6 | 0.288996 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 526651. | 0.0276037 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.76397e7 | −0.913339 | −0.456670 | − | 0.889636i | \(-0.650958\pi\) | ||||
−0.456670 | + | 0.889636i | \(0.650958\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.01825e7 | −1.55330 | −0.776651 | − | 0.629931i | \(-0.783083\pi\) | ||||
−0.776651 | + | 0.629931i | \(0.783083\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.94875e7 | −0.990817 | −0.495408 | − | 0.868660i | \(-0.664982\pi\) | ||||
−0.495408 | + | 0.868660i | \(0.664982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.29876e7 | −1.16174 | −0.580868 | − | 0.813998i | \(-0.697287\pi\) | ||||
−0.580868 | + | 0.813998i | \(0.697287\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.39088e7 | 1.19384 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.67037e6 | −0.231811 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.59410e7 | 0.781827 | 0.390913 | − | 0.920427i | \(-0.372159\pi\) | ||||
0.390913 | + | 0.920427i | \(0.372159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.38893e7 | −0.677157 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.84316e6 | −0.426055 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.89078e7 | −3.77930 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.89713e6 | 0.326471 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.10065e7 | 0.517938 | 0.258969 | − | 0.965886i | \(-0.416617\pi\) | ||||
0.258969 | + | 0.965886i | \(0.416617\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.02680e7 | −0.942667 | −0.471334 | − | 0.881955i | \(-0.656227\pi\) | ||||
−0.471334 | + | 0.881955i | \(0.656227\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.35167e6 | 0.432420 | 0.216210 | − | 0.976347i | \(-0.430630\pi\) | ||||
0.216210 | + | 0.976347i | \(0.430630\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.37371e7 | −1.54199 | −0.770993 | − | 0.636843i | \(-0.780240\pi\) | ||||
−0.770993 | + | 0.636843i | \(0.780240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 877703. | 0.0398848 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.85231e7 | 3.07813 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.17691e6 | −0.320547 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.77019e6 | −0.122318 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.27863e6 | 0.231751 | 0.115876 | − | 0.993264i | \(-0.463033\pi\) | ||||
0.115876 | + | 0.993264i | \(0.463033\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.46500e6 | 0.410848 | 0.205424 | − | 0.978673i | \(-0.434143\pi\) | ||||
0.205424 | + | 0.978673i | \(0.434143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.19136e7 | −1.37744 | −0.688722 | − | 0.725026i | \(-0.741828\pi\) | ||||
−0.688722 | + | 0.725026i | \(0.741828\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.25237e7 | 0.534469 | 0.267235 | − | 0.963631i | \(-0.413890\pi\) | ||||
0.267235 | + | 0.963631i | \(0.413890\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.63806e6 | −0.281700 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.17871e6 | −0.0494627 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.26311e6 | 0.261356 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.06118e7 | 0.437915 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.90490e7 | 1.19212 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.35428e7 | −0.549651 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.30028e7 | 0.928458 | 0.464229 | − | 0.885715i | \(-0.346331\pi\) | ||||
0.464229 | + | 0.885715i | \(0.346331\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.53237e7 | −1.41017 | −0.705084 | − | 0.709124i | \(-0.749091\pi\) | ||||
−0.705084 | + | 0.709124i | \(0.749091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.32713e7 | 2.11503 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.88565e6 | 0.348952 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.41122e7 | −0.551195 | −0.275598 | − | 0.961273i | \(-0.588876\pi\) | ||||
−0.275598 | + | 0.961273i | \(0.588876\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.81367e6 | −0.340528 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.49294e6 | 0.172654 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.42561e7 | 1.68242 | 0.841209 | − | 0.540709i | \(-0.181844\pi\) | ||||
0.841209 | + | 0.540709i | \(0.181844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.04698e6 | 0.190835 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.18174e7 | −1.19024 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.43783e7 | −1.65128 | −0.825642 | − | 0.564194i | \(-0.809187\pi\) | ||||
−0.825642 | + | 0.564194i | \(0.809187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.55733e6 | 0.130964 | 0.0654818 | − | 0.997854i | \(-0.479142\pi\) | ||||
0.0654818 | + | 0.997854i | \(0.479142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.85608e7 | 0.679701 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.69862e6 | −0.242723 | −0.121361 | − | 0.992608i | \(-0.538726\pi\) | ||||
−0.121361 | + | 0.992608i | \(0.538726\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.83534e6 | −0.138241 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.31129e7 | 0.467698 | 0.233849 | − | 0.972273i | \(-0.424868\pi\) | ||||
0.233849 | + | 0.972273i | \(0.424868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.51341e6 | −0.160139 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.30148e7 | −0.456972 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.16234e7 | −0.405998 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.32984e7 | −0.459708 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.15407e7 | −1.77249 | −0.886246 | − | 0.463215i | \(-0.846696\pi\) | ||||
−0.886246 | + | 0.463215i | \(0.846696\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.13728e6 | 0.242932 | 0.121466 | − | 0.992596i | \(-0.461240\pi\) | ||||
0.121466 | + | 0.992596i | \(0.461240\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.75503e6 | 0.194879 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.94348e7 | −1.99207 | −0.996034 | − | 0.0889707i | \(-0.971642\pi\) | ||||
−0.996034 | + | 0.0889707i | \(0.971642\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.03890e7 | 3.01411 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.29387e7 | 0.427078 | 0.213539 | − | 0.976934i | \(-0.431501\pi\) | ||||
0.213539 | + | 0.976934i | \(0.431501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.22050e7 | 0.400817 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.46427e6 | 0.0476026 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.39160e7 | 1.09704 | 0.548518 | − | 0.836139i | \(-0.315192\pi\) | ||||
0.548518 | + | 0.836139i | \(0.315192\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.03066e6 | 0.0330035 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.25463e7 | 0.399739 | 0.199869 | − | 0.979823i | \(-0.435948\pi\) | ||||
0.199869 | + | 0.979823i | \(0.435948\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1080.6.a.g.1.1 | yes | 3 | |
3.2 | odd | 2 | 1080.6.a.e.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.6.a.e.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
1080.6.a.g.1.1 | yes | 3 | 1.1 | even | 1 | trivial |