Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2732674592.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 113x^{2} + 882 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 392) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-10.2257\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | 8.21459 | 0.526966 | 0.263483 | − | 0.964664i | \(-0.415129\pi\) | ||||
0.263483 | + | 0.964664i | \(0.415129\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −57.1619 | −1.02254 | −0.511271 | − | 0.859419i | \(-0.670825\pi\) | ||||
−0.511271 | + | 0.859419i | \(0.670825\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −175.520 | −0.722307 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −176.520 | −0.439859 | −0.219929 | − | 0.975516i | \(-0.570583\pi\) | ||||
−0.219929 | + | 0.975516i | \(0.570583\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 252.951 | 0.415124 | 0.207562 | − | 0.978222i | \(-0.433447\pi\) | ||||
0.207562 | + | 0.978222i | \(0.433447\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −469.561 | −0.538846 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1946.23 | 1.63332 | 0.816659 | − | 0.577120i | \(-0.195824\pi\) | ||||
0.816659 | + | 0.577120i | \(0.195824\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −469.593 | −0.298427 | −0.149213 | − | 0.988805i | \(-0.547674\pi\) | ||||
−0.149213 | + | 0.988805i | \(0.547674\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −502.602 | −0.198109 | −0.0990547 | − | 0.995082i | \(-0.531582\pi\) | ||||
−0.0990547 | + | 0.995082i | \(0.531582\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 142.480 | 0.0455934 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3437.97 | −0.907598 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3926.33 | −0.866945 | −0.433473 | − | 0.901167i | \(-0.642712\pi\) | ||||
−0.433473 | + | 0.901167i | \(0.642712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3945.82 | −0.737451 | −0.368726 | − | 0.929538i | \(-0.620206\pi\) | ||||
−0.368726 | + | 0.929538i | \(0.620206\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1450.04 | −0.231791 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2351.04 | −0.282329 | −0.141165 | − | 0.989986i | \(-0.545085\pi\) | ||||
−0.141165 | + | 0.989986i | \(0.545085\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2077.89 | 0.218756 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10309.0 | −0.957758 | −0.478879 | − | 0.877881i | \(-0.658957\pi\) | ||||
−0.478879 | + | 0.877881i | \(0.658957\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4340.36 | 0.357976 | 0.178988 | − | 0.983851i | \(-0.442718\pi\) | ||||
0.178988 | + | 0.983851i | \(0.442718\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10033.1 | 0.738589 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −25000.3 | −1.65082 | −0.825410 | − | 0.564534i | \(-0.809056\pi\) | ||||
−0.825410 | + | 0.564534i | \(0.809056\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15987.5 | 0.860704 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13821.6 | 0.675879 | 0.337940 | − | 0.941168i | \(-0.390270\pi\) | ||||
0.337940 | + | 0.941168i | \(0.390270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10090.2 | 0.449774 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3857.51 | −0.157261 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 47285.8 | 1.76848 | 0.884242 | − | 0.467029i | \(-0.154676\pi\) | ||||
0.884242 | + | 0.467029i | \(0.154676\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11290.8 | −0.388509 | −0.194255 | − | 0.980951i | \(-0.562229\pi\) | ||||
−0.194255 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14459.2 | −0.424482 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −26445.6 | −0.719725 | −0.359862 | − | 0.933005i | \(-0.617176\pi\) | ||||
−0.359862 | + | 0.933005i | \(0.617176\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4128.67 | −0.104397 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 63078.1 | 1.48502 | 0.742510 | − | 0.669835i | \(-0.233635\pi\) | ||||
0.742510 | + | 0.669835i | \(0.233635\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10793.9 | 0.237067 | 0.118533 | − | 0.992950i | \(-0.462181\pi\) | ||||
0.118533 | + | 0.992950i | \(0.462181\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1170.41 | 0.0240262 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61419.5 | 1.10723 | 0.553616 | − | 0.832772i | \(-0.313248\pi\) | ||||
0.553616 | + | 0.832772i | \(0.313248\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14409.9 | 0.244033 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5383.09 | 0.0857702 | 0.0428851 | − | 0.999080i | \(-0.486345\pi\) | ||||
0.0428851 | + | 0.999080i | \(0.486345\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −111250. | −1.67014 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −32253.2 | −0.456851 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15237.3 | −0.203908 | −0.101954 | − | 0.994789i | \(-0.532509\pi\) | ||||
−0.101954 | + | 0.994789i | \(0.532509\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −32413.3 | −0.388612 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26842.8 | 0.305154 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 114148. | 1.23180 | 0.615898 | − | 0.787826i | \(-0.288793\pi\) | ||||
0.615898 | + | 0.787826i | \(0.288793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 30983.0 | 0.317713 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1671.49 | 0.0163042 | 0.00815212 | − | 0.999967i | \(-0.497405\pi\) | ||||
0.00815212 | + | 0.999967i | \(0.497405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 147637. | 1.37120 | 0.685601 | − | 0.727977i | \(-0.259539\pi\) | ||||
0.685601 | + | 0.727977i | \(0.259539\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 195451. | 1.65036 | 0.825179 | − | 0.564872i | \(-0.191074\pi\) | ||||
0.825179 | + | 0.564872i | \(0.191074\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 170850. | 1.37736 | 0.688680 | − | 0.725065i | \(-0.258190\pi\) | ||||
0.688680 | + | 0.725065i | \(0.258190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19312.8 | −0.148778 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −225942. | −1.66457 | −0.832283 | − | 0.554351i | \(-0.812967\pi\) | ||||
−0.832283 | + | 0.554351i | \(0.812967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28729.7 | 0.202575 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −44398.1 | −0.299847 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −129892. | −0.806524 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −84684.0 | −0.504706 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 170486. | 0.975921 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 161169. | 0.886688 | 0.443344 | − | 0.896352i | \(-0.353792\pi\) | ||||
0.443344 | + | 0.896352i | \(0.353792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 35654.3 | 0.188641 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −143042. | −0.728257 | −0.364129 | − | 0.931349i | \(-0.618633\pi\) | ||||
−0.364129 | + | 0.931349i | \(0.618633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 196521. | 0.928057 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 251450. | 1.14459 | 0.572295 | − | 0.820048i | \(-0.306053\pi\) | ||||
0.572295 | + | 0.820048i | \(0.306053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 405952. | 1.78212 | 0.891062 | − | 0.453881i | \(-0.149961\pi\) | ||||
0.891062 | + | 0.453881i | \(0.149961\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −205367. | −0.869927 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −44651.0 | −0.182596 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 224436. | 0.886488 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 77877.0 | 0.287371 | 0.143686 | − | 0.989623i | \(-0.454105\pi\) | ||||
0.143686 | + | 0.989623i | \(0.454105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 211478. | 0.754786 | 0.377393 | − | 0.926053i | \(-0.376821\pi\) | ||||
0.377393 | + | 0.926053i | \(0.376821\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −341602. | −1.17976 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 225551. | 0.754075 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −304925. | −0.987288 | −0.493644 | − | 0.869664i | \(-0.664335\pi\) | ||||
−0.493644 | + | 0.869664i | \(0.664335\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 113539. | 0.356166 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 537444. | 1.58440 | 0.792199 | − | 0.610263i | \(-0.208936\pi\) | ||||
0.792199 | + | 0.610263i | \(0.208936\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 82887.2 | 0.237016 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −542515. | −1.50529 | −0.752646 | − | 0.658425i | \(-0.771223\pi\) | ||||
−0.752646 | + | 0.658425i | \(0.771223\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −307309. | −0.827672 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 82423.2 | 0.215555 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 203550. | 0.517077 | 0.258539 | − | 0.966001i | \(-0.416759\pi\) | ||||
0.258539 | + | 0.966001i | \(0.416759\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 388434. | 0.931932 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 188519. | 0.439768 | 0.219884 | − | 0.975526i | \(-0.429432\pi\) | ||||
0.219884 | + | 0.975526i | \(0.429432\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −464405. | −1.05366 | −0.526830 | − | 0.849971i | \(-0.676620\pi\) | ||||
−0.526830 | + | 0.849971i | \(0.676620\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −92749.6 | −0.204731 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 134390. | 0.288694 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −343549. | −0.718430 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 638610. | 1.26664 | 0.633318 | − | 0.773891i | \(-0.281692\pi\) | ||||
0.633318 | + | 0.773891i | \(0.281692\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 504542. | 0.974998 | 0.487499 | − | 0.873123i | \(-0.337909\pi\) | ||||
0.487499 | + | 0.873123i | \(0.337909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −118776. | −0.223688 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −69194.6 | −0.127030 | −0.0635151 | − | 0.997981i | \(-0.520231\pi\) | ||||
−0.0635151 | + | 0.997981i | \(0.520231\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −846712. | −1.51566 | −0.757832 | − | 0.652449i | \(-0.773741\pi\) | ||||
−0.757832 | + | 0.652449i | \(0.773741\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −217240. | −0.379271 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 589280. | 0.979348 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 88217.0 | 0.143096 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 82892.8 | 0.131266 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −625421. | −0.967089 | −0.483544 | − | 0.875320i | \(-0.660651\pi\) | ||||
−0.483544 | + | 0.875320i | \(0.660651\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 518161. | 0.782556 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −248103. | −0.366046 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 88667.3 | 0.124926 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 492300. | 0.678030 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −584189. | −0.786667 | −0.393334 | − | 0.919396i | \(-0.628678\pi\) | ||||
−0.393334 | + | 0.919396i | \(0.628678\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25008.1 | −0.0329324 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 984064. | 1.26753 | 0.633766 | − | 0.773525i | \(-0.281508\pi\) | ||||
0.633766 | + | 0.773525i | \(0.281508\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.34694e6 | −1.69731 | −0.848653 | − | 0.528949i | \(-0.822586\pi\) | ||||
−0.848653 | + | 0.528949i | \(0.822586\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.14450e6 | 1.38111 | 0.690553 | − | 0.723282i | \(-0.257367\pi\) | ||||
0.690553 | + | 0.723282i | \(0.257367\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.42906e6 | 1.68803 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 504536. | 0.583474 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.42563e6 | −1.61441 | −0.807204 | − | 0.590272i | \(-0.799021\pi\) | ||||
−0.807204 | + | 0.590272i | \(0.799021\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −94563.3 | −0.104877 | −0.0524385 | − | 0.998624i | \(-0.516699\pi\) | ||||
−0.0524385 | + | 0.998624i | \(0.516699\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 953799. | 1.03619 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −118784. | −0.123884 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 44219.9 | 0.0451980 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −228497. | −0.228927 | −0.114463 | − | 0.993427i | \(-0.536515\pi\) | ||||
−0.114463 | + | 0.993427i | \(0.536515\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 88719.6 | 0.0871402 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −913873. | −0.880106 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.36203e6 | 1.28633 | 0.643165 | − | 0.765727i | \(-0.277621\pi\) | ||||
0.643165 | + | 0.765727i | \(0.277621\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 689151. | 0.626200 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.22988e6 | 1.09641 | 0.548206 | − | 0.836343i | \(-0.315311\pi\) | ||||
0.548206 | + | 0.836343i | \(0.315311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −790069. | −0.691115 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −125169. | −0.107453 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.87483e6 | −1.57972 | −0.789860 | − | 0.613287i | \(-0.789847\pi\) | ||||
−0.789860 | + | 0.613287i | \(0.789847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18097.8 | 0.0149693 | 0.00748465 | − | 0.999972i | \(-0.497618\pi\) | ||||
0.00748465 | + | 0.999972i | \(0.497618\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −25150.6 | −0.0200547 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 141825. | 0.111059 | 0.0555293 | − | 0.998457i | \(-0.482315\pi\) | ||||
0.0555293 | + | 0.998457i | \(0.482315\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 692573. | 0.532666 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.15247e6 | 0.870693 | 0.435346 | − | 0.900263i | \(-0.356626\pi\) | ||||
0.435346 | + | 0.900263i | \(0.356626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 957483. | 0.710665 | 0.355332 | − | 0.934740i | \(-0.384368\pi\) | ||||
0.355332 | + | 0.934740i | \(0.384368\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 220503. | 0.160806 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.36794e6 | 1.66773 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 937679. | 0.649115 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 440238. | 0.299584 | 0.149792 | − | 0.988718i | \(-0.452140\pi\) | ||||
0.149792 | + | 0.988718i | \(0.452140\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.70295e6 | −1.80835 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 606873. | 0.399215 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −127134. | −0.0822400 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13730.6 | 0.00859178 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 645405. | 0.397267 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.93780e6 | 1.17345 | 0.586724 | − | 0.809787i | \(-0.300417\pi\) | ||||
0.586724 | + | 0.809787i | \(0.300417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.21278e6 | 0.722577 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.70845e6 | 1.00162 | 0.500809 | − | 0.865558i | \(-0.333036\pi\) | ||||
0.500809 | + | 0.865558i | \(0.333036\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −383059. | −0.221006 | −0.110503 | − | 0.993876i | \(-0.535246\pi\) | ||||
−0.110503 | + | 0.993876i | \(0.535246\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.21790e6 | 1.79856 | 0.899280 | − | 0.437373i | \(-0.144091\pi\) | ||||
0.899280 | + | 0.437373i | \(0.144091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 693077. | 0.381333 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.60555e6 | 0.869683 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −913934. | −0.487426 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 36040.3 | 0.0189269 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.40346e6 | 0.725823 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.66097e6 | 0.833279 | 0.416640 | − | 0.909072i | \(-0.363208\pi\) | ||||
0.416640 | + | 0.909072i | \(0.363208\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 412656. | 0.203928 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.51168e6 | 0.735949 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.06508e6 | 0.510865 | 0.255433 | − | 0.966827i | \(-0.417782\pi\) | ||||
0.255433 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.85602e6 | −0.877170 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 696518. | 0.324374 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 236003. | 0.106750 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 178645. | 0.0796464 | 0.0398232 | − | 0.999207i | \(-0.487321\pi\) | ||||
0.0398232 | + | 0.999207i | \(0.487321\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.87153e6 | 0.822494 | 0.411247 | − | 0.911524i | \(-0.365093\pi\) | ||||
0.411247 | + | 0.911524i | \(0.365093\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −869639. | −0.376766 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.41481e6 | 1.45858 | 0.729290 | − | 0.684205i | \(-0.239851\pi\) | ||||
0.729290 | + | 0.684205i | \(0.239851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.60566e6 | −1.51850 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.58575e6 | −0.649380 | −0.324690 | − | 0.945820i | \(-0.605260\pi\) | ||||
−0.324690 | + | 0.945820i | \(0.605260\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.25558e6 | −0.910942 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.06701e6 | −0.425011 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −616998. | −0.242411 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −220985. | −0.0856443 | −0.0428221 | − | 0.999083i | \(-0.513635\pi\) | ||||
−0.0428221 | + | 0.999083i | \(0.513635\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.80944e6 | 0.691795 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −469456. | −0.174712 | −0.0873561 | − | 0.996177i | \(-0.527842\pi\) | ||||
−0.0873561 | + | 0.996177i | \(0.527842\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.40048e6 | 0.514278 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −993168. | −0.359890 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 527577. | 0.188664 | 0.0943318 | − | 0.995541i | \(-0.469929\pi\) | ||||
0.0943318 | + | 0.995541i | \(0.469929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.32393e6 | 0.467255 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 879752. | 0.306453 | 0.153226 | − | 0.988191i | \(-0.451034\pi\) | ||||
0.153226 | + | 0.988191i | \(0.451034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −761821. | −0.258569 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −33448.2 | −0.0112072 | −0.00560362 | − | 0.999984i | \(-0.501784\pi\) | ||||
−0.00560362 | + | 0.999984i | \(0.501784\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −978178. | −0.323576 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.17503e6 | −0.383767 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.51085e6 | −1.13219 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.49449e6 | −1.43121 | −0.715607 | − | 0.698503i | \(-0.753850\pi\) | ||||
−0.715607 | + | 0.698503i | \(0.753850\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.53668e6 | −0.477225 | −0.238613 | − | 0.971115i | \(-0.576693\pi\) | ||||
−0.238613 | + | 0.971115i | \(0.576693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −998100. | −0.306134 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −823698. | −0.249534 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 415007. | 0.124185 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.50479e6 | −0.740393 | −0.370197 | − | 0.928953i | \(-0.620710\pi\) | ||||
−0.370197 | + | 0.928953i | \(0.620710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.06556e6 | 0.603161 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −307707. | −0.0877036 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.33473e6 | 0.939120 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.32003e6 | −0.923862 | −0.461931 | − | 0.886916i | \(-0.652843\pi\) | ||||
−0.461931 | + | 0.886916i | \(0.652843\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 141680. | 0.0389587 | 0.0194793 | − | 0.999810i | \(-0.493799\pi\) | ||||
0.0194793 | + | 0.999810i | \(0.493799\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.38806e6 | 1.19240 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 277297. | 0.0744686 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −366790. | −0.0962220 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 155475. | 0.0403150 | 0.0201575 | − | 0.999797i | \(-0.493583\pi\) | ||||
0.0201575 | + | 0.999797i | \(0.493583\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.46000e6 | −0.886864 | −0.443432 | − | 0.896308i | \(-0.646239\pi\) | ||||
−0.443432 | + | 0.896308i | \(0.646239\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.84365e6 | 0.467149 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 236018. | 0.0591211 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.15172e6 | −1.52348 | −0.761738 | − | 0.647885i | \(-0.775654\pi\) | ||||
−0.761738 | + | 0.647885i | \(0.775654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.62933e6 | 0.636556 | 0.318278 | − | 0.947997i | \(-0.396896\pi\) | ||||
0.318278 | + | 0.947997i | \(0.396896\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 870995. | 0.208505 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 639728. | 0.151435 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.36346e6 | −0.787356 | −0.393678 | − | 0.919248i | \(-0.628797\pi\) | ||||
−0.393678 | + | 0.919248i | \(0.628797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.81974e6 | 0.421278 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.73721e6 | 0.397747 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.57232e6 | −1.69605 | −0.848025 | − | 0.529956i | \(-0.822208\pi\) | ||||
−0.848025 | + | 0.529956i | \(0.822208\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.69108e6 | −1.48240 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.61580e6 | −1.01157 | −0.505783 | − | 0.862660i | \(-0.668797\pi\) | ||||
−0.505783 | + | 0.862660i | \(0.668797\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.52659e6 | 0.547751 | 0.273875 | − | 0.961765i | \(-0.411694\pi\) | ||||
0.273875 | + | 0.961765i | \(0.411694\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.85281e6 | 0.397372 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.06866e6 | 0.863295 | 0.431647 | − | 0.902042i | \(-0.357932\pi\) | ||||
0.431647 | + | 0.902042i | \(0.357932\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.50483e6 | −0.520268 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −766162. | −0.157459 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −66907.4 | −0.0136063 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.42598e6 | −0.488192 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.93903e6 | 1.18271 | 0.591353 | − | 0.806413i | \(-0.298594\pi\) | ||||
0.591353 | + | 0.806413i | \(0.298594\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −594698. | −0.117202 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.52491e6 | −1.25956 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 160923. | 0.0307464 | 0.0153732 | − | 0.999882i | \(-0.495106\pi\) | ||||
0.0153732 | + | 0.999882i | \(0.495106\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.41488e6 | 0.834924 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.01033e7 | 1.89129 | 0.945647 | − | 0.325196i | \(-0.105430\pi\) | ||||
0.945647 | + | 0.325196i | \(0.105430\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.64152e6 | −1.41600 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.77104e6 | −0.324875 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.49005e6 | 1.34658 | 0.673292 | − | 0.739377i | \(-0.264880\pi\) | ||||
0.673292 | + | 0.739377i | \(0.264880\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.45654e6 | −0.793238 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.18116e6 | 0.560615 | 0.280308 | − | 0.959910i | \(-0.409563\pi\) | ||||
0.280308 | + | 0.959910i | \(0.409563\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −95545.5 | −0.0166718 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.52442e6 | −0.436155 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.32304e6 | −1.08176 | −0.540881 | − | 0.841099i | \(-0.681909\pi\) | ||||
−0.540881 | + | 0.841099i | \(0.681909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.61445e6 | 0.270851 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.43919e6 | −1.40211 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.41306e6 | 0.726128 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.67208e6 | 0.272482 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.16325e6 | −0.671952 | −0.335976 | − | 0.941870i | \(-0.609066\pi\) | ||||
−0.335976 | + | 0.941870i | \(0.609066\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.58604e6 | 0.892997 | 0.446498 | − | 0.894784i | \(-0.352671\pi\) | ||||
0.446498 | + | 0.894784i | \(0.352671\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.67946e6 | −1.20449 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.18373e6 | −0.960753 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.29964e6 | −1.27739 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.60766e6 | −0.397588 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.11723e7 | −1.68756 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.54861e6 | 0.231743 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.11301e7 | −1.63496 | −0.817480 | − | 0.575957i | \(-0.804630\pi\) | ||||
−0.817480 | + | 0.575957i | \(0.804630\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.81490e6 | −0.555244 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.76608e6 | −1.40841 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.20844e7 | 1.72686 | 0.863430 | − | 0.504468i | \(-0.168311\pi\) | ||||
0.863430 | + | 0.504468i | \(0.168311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.98177e6 | 0.280623 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.84378e6 | 0.258719 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.10396e6 | 0.152132 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.08796e6 | 0.421730 | 0.210865 | − | 0.977515i | \(-0.432372\pi\) | ||||
0.210865 | + | 0.977515i | \(0.432372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.09790e6 | 0.148605 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.82211e6 | −0.378588 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.93288e6 | −0.921813 | −0.460906 | − | 0.887449i | \(-0.652476\pi\) | ||||
−0.460906 | + | 0.887449i | \(0.652476\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.29153e7 | 1.70209 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.85938e6 | −0.888187 | −0.444093 | − | 0.895981i | \(-0.646474\pi\) | ||||
−0.444093 | + | 0.895981i | \(0.646474\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.03502e6 | −0.774619 | −0.387310 | − | 0.921950i | \(-0.626596\pi\) | ||||
−0.387310 | + | 0.921950i | \(0.626596\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.24592e6 | 0.667475 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −71610.5 | −0.00903249 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.63662e6 | 0.329691 | 0.164846 | − | 0.986319i | \(-0.447287\pi\) | ||||
0.164846 | + | 0.986319i | \(0.447287\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.14460e6 | 0.513791 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.43980e6 | −0.297291 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.53788e6 | 0.306606 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.90597e6 | 0.228307 | 0.114154 | − | 0.993463i | \(-0.463584\pi\) | ||||
0.114154 | + | 0.993463i | \(0.463584\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.85293e6 | 0.220075 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −568406. | −0.0669406 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 63087.3 | 0.00736724 | 0.00368362 | − | 0.999993i | \(-0.498827\pi\) | ||||
0.00368362 | + | 0.999993i | \(0.498827\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.95539e6 | −0.798704 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.34551e6 | −0.722602 | −0.361301 | − | 0.932449i | \(-0.617667\pi\) | ||||
−0.361301 | + | 0.932449i | \(0.617667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.44136e7 | 1.62774 | 0.813870 | − | 0.581046i | \(-0.197357\pi\) | ||||
0.813870 | + | 0.581046i | \(0.197357\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.64175e6 | 0.519862 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.42484e6 | 0.824705 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −53893.8 | −0.00593700 | −0.00296850 | − | 0.999996i | \(-0.500945\pi\) | ||||
−0.00296850 | + | 0.999996i | \(0.500945\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.32384e6 | −0.685295 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.14707e6 | −0.983175 | −0.491587 | − | 0.870828i | \(-0.663583\pi\) | ||||
−0.491587 | + | 0.870828i | \(0.663583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.84069e6 | 0.516083 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.57574e6 | 0.589643 | 0.294822 | − | 0.955552i | \(-0.404740\pi\) | ||||
0.294822 | + | 0.955552i | \(0.404740\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.70190e6 | 0.283428 | 0.141714 | − | 0.989908i | \(-0.454739\pi\) | ||||
0.141714 | + | 0.989908i | \(0.454739\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.72793e6 | 0.179804 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.01906e7 | −1.04351 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 680930. | 0.0691725 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.57566e6 | −0.461134 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.42258e7 | −1.42234 | −0.711170 | − | 0.703020i | \(-0.751834\pi\) | ||||
−0.711170 | + | 0.703020i | \(0.751834\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.13758e6 | −0.509623 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.21269e6 | −0.906676 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.10715e7 | −1.07264 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.92872e6 | 0.185407 | 0.0927033 | − | 0.995694i | \(-0.470449\pi\) | ||||
0.0927033 | + | 0.995694i | \(0.470449\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.13216e6 | 0.871056 | 0.435528 | − | 0.900175i | \(-0.356562\pi\) | ||||
0.435528 | + | 0.900175i | \(0.356562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.03806e6 | −0.192894 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.08021e7 | 1.01449 | 0.507245 | − | 0.861802i | \(-0.330664\pi\) | ||||
0.507245 | + | 0.861802i | \(0.330664\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.34692e6 | −0.777883 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.05977e6 | 0.189032 | 0.0945159 | − | 0.995523i | \(-0.469870\pi\) | ||||
0.0945159 | + | 0.995523i | \(0.469870\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.17654e6 | 0.744674 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.89455e6 | −0.171235 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.35721e7 | 1.21740 | 0.608700 | − | 0.793401i | \(-0.291691\pi\) | ||||
0.608700 | + | 0.793401i | \(0.291691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.14262e6 | 0.279762 | 0.139881 | − | 0.990168i | \(-0.455328\pi\) | ||||
0.139881 | + | 0.990168i | \(0.455328\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.04404e6 | 0.357299 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.97338e6 | 0.171750 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.79887e6 | −0.414547 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.99306e6 | 0.170889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.88424e6 | 0.500787 | 0.250393 | − | 0.968144i | \(-0.419440\pi\) | ||||
0.250393 | + | 0.968144i | \(0.419440\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −489841. | −0.0413805 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.17770e6 | 0.685740 | 0.342870 | − | 0.939383i | \(-0.388601\pi\) | ||||
0.342870 | + | 0.939383i | \(0.388601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.08369e6 | 0.667946 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.26901e6 | −0.268141 | −0.134071 | − | 0.990972i | \(-0.542805\pi\) | ||||
−0.134071 | + | 0.990972i | \(0.542805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.43733e7 | −1.17039 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.10646e7 | −0.894424 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.49619e6 | 0.280574 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.94889e7 | −1.55271 | −0.776357 | − | 0.630293i | \(-0.782935\pi\) | ||||
−0.776357 | + | 0.630293i | \(0.782935\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.32050e7 | −1.82230 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.00636e7 | −1.56432 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.40162e6 | 0.727796 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.07266e7 | 0.824453 | 0.412227 | − | 0.911081i | \(-0.364751\pi\) | ||||
0.412227 | + | 0.911081i | \(0.364751\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.10403e6 | 0.0842545 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.17392e7 | 0.889537 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.66490e6 | −0.199098 | −0.0995488 | − | 0.995033i | \(-0.531740\pi\) | ||||
−0.0995488 | + | 0.995033i | \(0.531740\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.07804e7 | −0.799761 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.98318e6 | 0.146096 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.55234e6 | 0.186712 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.17110e7 | −0.850739 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.01722e7 | 0.733825 | 0.366912 | − | 0.930255i | \(-0.380415\pi\) | ||||
0.366912 | + | 0.930255i | \(0.380415\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −776799. | −0.0552666 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −559421. | −0.0395270 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.80053e7 | −1.96519 | −0.982594 | − | 0.185766i | \(-0.940523\pi\) | ||||
−0.982594 | + | 0.185766i | \(0.940523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.33346e6 | 0.302007 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.44731e6 | 0.584689 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.55563e7 | −1.75687 | −0.878433 | − | 0.477866i | \(-0.841410\pi\) | ||||
−0.878433 | + | 0.477866i | \(0.841410\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.66819e6 | 0.316577 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.11853e6 | −0.0753421 | −0.0376710 | − | 0.999290i | \(-0.511994\pi\) | ||||
−0.0376710 | + | 0.999290i | \(0.511994\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −975762. | −0.0652827 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.08574e7 | −1.38608 | −0.693040 | − | 0.720899i | \(-0.743729\pi\) | ||||
−0.693040 | + | 0.720899i | \(0.743729\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.45159e6 | −0.293849 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −944842. | −0.0619523 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.32038e6 | −0.538324 | −0.269162 | − | 0.963095i | \(-0.586747\pi\) | ||||
−0.269162 | + | 0.963095i | \(0.586747\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.87701e6 | −0.120637 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.20885e7 | −0.771801 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.35804e7 | 1.49559 | 0.747793 | − | 0.663932i | \(-0.231114\pi\) | ||||
0.747793 | + | 0.663932i | \(0.231114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 728795. | 0.0459199 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.93273e7 | −1.83573 | −0.917867 | − | 0.396888i | \(-0.870090\pi\) | ||||
−0.917867 | + | 0.396888i | \(0.870090\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.95266e7 | 1.20635 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.19610e7 | 0.734140 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.35031e6 | −0.265280 | −0.132640 | − | 0.991164i | \(-0.542345\pi\) | ||||
−0.132640 | + | 0.991164i | \(0.542345\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.11885e7 | 0.677853 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.56420e7 | 1.54349 | 0.771744 | − | 0.635933i | \(-0.219385\pi\) | ||||
0.771744 | + | 0.635933i | \(0.219385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −562199. | −0.0336229 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.84102e6 | 0.285820 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.11346e7 | −0.653200 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.34986e7 | 0.786837 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.74301e7 | 1.00954 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.26920e7 | 1.30598 | 0.652988 | − | 0.757368i | \(-0.273515\pi\) | ||||
0.652988 | + | 0.757368i | \(0.273515\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.01030e7 | 0.577773 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.85603e6 | −0.161280 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.49010e6 | −0.364194 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.23986e7 | 1.80668 | 0.903338 | − | 0.428929i | \(-0.141109\pi\) | ||||
0.903338 | + | 0.428929i | \(0.141109\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.86561e7 | −2.69632 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.67447e6 | 0.147284 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.90534e6 | −0.104276 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.54009e7 | −0.832460 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.86367e6 | 0.476148 | 0.238074 | − | 0.971247i | \(-0.423484\pi\) | ||||
0.238074 | + | 0.971247i | \(0.423484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.45729e6 | 0.184580 | 0.0922898 | − | 0.995732i | \(-0.470581\pi\) | ||||
0.0922898 | + | 0.995732i | \(0.470581\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 148666. | 0.00788832 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.07213e7 | −1.62011 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.03820e6 | −0.106830 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.15406e7 | 1.63310 | 0.816548 | − | 0.577278i | \(-0.195885\pi\) | ||||
0.816548 | + | 0.577278i | \(0.195885\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.71909e7 | 1.91398 | 0.956988 | − | 0.290126i | \(-0.0936972\pi\) | ||||
0.956988 | + | 0.290126i | \(0.0936972\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −206602. | −0.0105681 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.55748e7 | 0.791879 | 0.395939 | − | 0.918277i | \(-0.370419\pi\) | ||||
0.395939 | + | 0.918277i | \(0.370419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.23547e7 | 1.12975 | 0.564876 | − | 0.825176i | \(-0.308924\pi\) | ||||
0.564876 | + | 0.825176i | \(0.308924\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.16503e6 | 0.0585242 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.10112e7 | 1.53923 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.35656e7 | 0.669309 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.65695e7 | −0.812652 | −0.406326 | − | 0.913728i | \(-0.633190\pi\) | ||||
−0.406326 | + | 0.913728i | \(0.633190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.09510e6 | −0.248406 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.46710e6 | 0.458826 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.75663e7 | 0.846330 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.86533e6 | 0.374496 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.18164e6 | 0.0559321 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.63671e7 | −1.24077 | −0.620384 | − | 0.784299i | \(-0.713023\pi\) | ||||
−0.620384 | + | 0.784299i | \(0.713023\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.71146e6 | −0.220415 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.81803e7 | −0.845570 | −0.422785 | − | 0.906230i | \(-0.638947\pi\) | ||||
−0.422785 | + | 0.906230i | \(0.638947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.13487e7 | 1.44956 | 0.724782 | − | 0.688979i | \(-0.241941\pi\) | ||||
0.724782 | + | 0.688979i | \(0.241941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.56999e7 | −1.63170 | −0.815850 | − | 0.578264i | \(-0.803730\pi\) | ||||
−0.815850 | + | 0.578264i | \(0.803730\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.16353e7 | −0.528733 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.94516e7 | 0.878837 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.08418e7 | −0.487026 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.68944e6 | −0.298775 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.00353e7 | −0.889735 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.81914e7 | −0.798672 | −0.399336 | − | 0.916805i | \(-0.630759\pi\) | ||||
−0.399336 | + | 0.916805i | \(0.630759\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.61638e6 | 0.157871 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.04023e7 | 0.885603 | 0.442802 | − | 0.896620i | \(-0.353985\pi\) | ||||
0.442802 | + | 0.896620i | \(0.353985\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.39975e6 | −0.189900 | −0.0949502 | − | 0.995482i | \(-0.530269\pi\) | ||||
−0.0949502 | + | 0.995482i | \(0.530269\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.22036e7 | −0.952940 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.39608e7 | −1.02257 | −0.511284 | − | 0.859412i | \(-0.670830\pi\) | ||||
−0.511284 | + | 0.859412i | \(0.670830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.54365e6 | −0.107340 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.17399e7 | 0.492649 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.07761e7 | −0.449681 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.04435e6 | −0.0433377 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.54926e7 | 0.639330 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.69000e7 | 1.10393 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.65463e7 | 1.07741 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.16278e7 | 0.469329 | 0.234665 | − | 0.972076i | \(-0.424601\pi\) | ||||
0.234665 | + | 0.972076i | \(0.424601\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −293381. | −0.0117767 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.46643e7 | −0.585417 | −0.292708 | − | 0.956202i | \(-0.594556\pi\) | ||||
−0.292708 | + | 0.956202i | \(0.594556\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −950225. | −0.0377268 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.30174e6 | 0.209346 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.14633e7 | 0.838315 | 0.419158 | − | 0.907914i | \(-0.362326\pi\) | ||||
0.419158 | + | 0.907914i | \(0.362326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.59183e7 | 0.618367 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.59557e7 | 0.616468 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −334975. | −0.0128724 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.59133e7 | −0.990428 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.12955e7 | 1.56987 | 0.784934 | − | 0.619579i | \(-0.212697\pi\) | ||||
0.784934 | + | 0.619579i | \(0.212697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.40342e7 | 0.527819 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.96379e7 | 0.734625 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.98623e7 | −0.739061 | −0.369530 | − | 0.929219i | \(-0.620481\pi\) | ||||
−0.369530 | + | 0.929219i | \(0.620481\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.14667e6 | −0.116463 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.90935e7 | −1.80738 | −0.903691 | − | 0.428186i | \(-0.859153\pi\) | ||||
−0.903691 | + | 0.428186i | \(0.859153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.18131e6 | 0.189741 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.27570e7 | 1.54929 | 0.774645 | − | 0.632396i | \(-0.217929\pi\) | ||||
0.774645 | + | 0.632396i | \(0.217929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.73032e6 | 0.0984121 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.64338e7 | 0.947781 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.11234e7 | −0.753409 | −0.376705 | − | 0.926333i | \(-0.622943\pi\) | ||||
−0.376705 | + | 0.926333i | \(0.622943\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.65041e7 | −1.29519 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.69335e6 | 0.200950 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.30596e7 | −0.456166 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.43056e7 | −1.19206 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.88406e7 | −0.996977 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.70026e7 | −0.928623 | −0.464312 | − | 0.885672i | \(-0.653698\pi\) | ||||
−0.464312 | + | 0.885672i | \(0.653698\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.50759e6 | −0.256857 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.61997e7 | −0.891761 | −0.445880 | − | 0.895093i | \(-0.647109\pi\) | ||||
−0.445880 | + | 0.895093i | \(0.647109\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 296057. | 0.00997386 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.00062e7 | 1.34088 | 0.670441 | − | 0.741963i | \(-0.266105\pi\) | ||||
0.670441 | + | 0.741963i | \(0.266105\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.68970e6 | 0.0896908 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.99876e7 | −0.994877 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.00329e6 | −0.0991319 | −0.0495659 | − | 0.998771i | \(-0.515784\pi\) | ||||
−0.0495659 | + | 0.998771i | \(0.515784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.95529e6 | 0.129894 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.18147e6 | −0.0709185 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.40747e7 | 1.10217 | 0.551083 | − | 0.834450i | \(-0.314215\pi\) | ||||
0.551083 | + | 0.834450i | \(0.314215\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.36442e7 | 0.439110 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.83996e7 | 1.54983 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.26699e7 | 1.67812 | 0.839062 | − | 0.544035i | \(-0.183104\pi\) | ||||
0.839062 | + | 0.544035i | \(0.183104\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.08282e6 | 0.256241 |
(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 | 784.6.a.bh.1.3 | 4 | ||
4.3 | odd | 2 | 392.6.a.h.1.2 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 784.6.a.bh.1.2 | 4 | ||
28.3 | even | 6 | 392.6.i.m.177.2 | 8 | |||
28.11 | odd | 6 | 392.6.i.m.177.3 | 8 | |||
28.19 | even | 6 | 392.6.i.m.361.2 | 8 | |||
28.23 | odd | 6 | 392.6.i.m.361.3 | 8 | |||
28.27 | even | 2 | 392.6.a.h.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.6.a.h.1.2 | ✓ | 4 | 4.3 | odd | 2 | ||
392.6.a.h.1.3 | yes | 4 | 28.27 | even | 2 | ||
392.6.i.m.177.2 | 8 | 28.3 | even | 6 | |||
392.6.i.m.177.3 | 8 | 28.11 | odd | 6 | |||
392.6.i.m.361.2 | 8 | 28.19 | even | 6 | |||
392.6.i.m.361.3 | 8 | 28.23 | odd | 6 | |||
784.6.a.bh.1.2 | 4 | 7.6 | odd | 2 | inner | ||
784.6.a.bh.1.3 | 4 | 1.1 | even | 1 | trivial |