Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,6,Mod(1,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, 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("300.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.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: | \(48.1151459439\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 300.1 |
$q$-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 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 91.0000 | 0.701934 | 0.350967 | − | 0.936388i | \(-0.385853\pi\) | ||||
0.350967 | + | 0.936388i | \(0.385853\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −174.000 | −0.433578 | −0.216789 | − | 0.976218i | \(-0.569558\pi\) | ||||
−0.216789 | + | 0.976218i | \(0.569558\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −785.000 | −1.28828 | −0.644142 | − | 0.764906i | \(-0.722785\pi\) | ||||
−0.644142 | + | 0.764906i | \(0.722785\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1794.00 | −1.50557 | −0.752784 | − | 0.658268i | \(-0.771289\pi\) | ||||
−0.752784 | + | 0.658268i | \(0.771289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −925.000 | −0.587838 | −0.293919 | − | 0.955830i | \(-0.594960\pi\) | ||||
−0.293919 | + | 0.955830i | \(0.594960\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 819.000 | 0.405262 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2346.00 | 0.924716 | 0.462358 | − | 0.886693i | \(-0.347003\pi\) | ||||
0.462358 | + | 0.886693i | \(0.347003\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −726.000 | −0.160303 | −0.0801515 | − | 0.996783i | \(-0.525540\pi\) | ||||
−0.0801515 | + | 0.996783i | \(0.525540\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −811.000 | −0.151571 | −0.0757856 | − | 0.997124i | \(-0.524146\pi\) | ||||
−0.0757856 | + | 0.997124i | \(0.524146\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1566.00 | −0.250327 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7922.00 | −0.951329 | −0.475664 | − | 0.879627i | \(-0.657792\pi\) | ||||
−0.475664 | + | 0.879627i | \(0.657792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7065.00 | −0.743791 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −360.000 | −0.0334459 | −0.0167229 | − | 0.999860i | \(-0.505323\pi\) | ||||
−0.0167229 | + | 0.999860i | \(0.505323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4951.00 | 0.408340 | 0.204170 | − | 0.978935i | \(-0.434550\pi\) | ||||
0.204170 | + | 0.978935i | \(0.434550\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9906.00 | −0.654114 | −0.327057 | − | 0.945005i | \(-0.606057\pi\) | ||||
−0.327057 | + | 0.945005i | \(0.606057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8526.00 | −0.507289 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16146.0 | −0.869240 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8292.00 | 0.405480 | 0.202740 | − | 0.979233i | \(-0.435015\pi\) | ||||
0.202740 | + | 0.979233i | \(0.435015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8325.00 | −0.339388 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7014.00 | 0.262323 | 0.131161 | − | 0.991361i | \(-0.458129\pi\) | ||||
0.131161 | + | 0.991361i | \(0.458129\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −51433.0 | −1.76977 | −0.884886 | − | 0.465808i | \(-0.845764\pi\) | ||||
−0.884886 | + | 0.465808i | \(0.845764\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7371.00 | 0.233978 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −581.000 | −0.0158121 | −0.00790604 | − | 0.999969i | \(-0.502517\pi\) | ||||
−0.00790604 | + | 0.999969i | \(0.502517\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21114.0 | 0.533885 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −56520.0 | −1.33063 | −0.665313 | − | 0.746564i | \(-0.731702\pi\) | ||||
−0.665313 | + | 0.746564i | \(0.731702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 42478.0 | 0.932947 | 0.466473 | − | 0.884535i | \(-0.345524\pi\) | ||||
0.466473 | + | 0.884535i | \(0.345524\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15834.0 | −0.304343 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −28912.0 | −0.521207 | −0.260604 | − | 0.965446i | \(-0.583922\pi\) | ||||
−0.260604 | + | 0.965446i | \(0.583922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 104586. | 1.66640 | 0.833198 | − | 0.552974i | \(-0.186507\pi\) | ||||
0.833198 | + | 0.552974i | \(0.186507\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6534.00 | −0.0925510 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −118080. | −1.58016 | −0.790080 | − | 0.613003i | \(-0.789961\pi\) | ||||
−0.790080 | + | 0.613003i | \(0.789961\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −71435.0 | −0.904290 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7299.00 | −0.0875097 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −110273. | −1.18998 | −0.594990 | − | 0.803733i | \(-0.702844\pi\) | ||||
−0.594990 | + | 0.803733i | \(0.702844\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14094.0 | −0.144526 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −193332. | −1.88582 | −0.942910 | − | 0.333047i | \(-0.891923\pi\) | ||||
−0.942910 | + | 0.333047i | \(0.891923\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 37684.0 | 0.349997 | 0.174998 | − | 0.984569i | \(-0.444008\pi\) | ||||
0.174998 | + | 0.984569i | \(0.444008\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17292.0 | −0.146011 | −0.0730055 | − | 0.997332i | \(-0.523259\pi\) | ||||
−0.0730055 | + | 0.997332i | \(0.523259\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 142133. | 1.14585 | 0.572926 | − | 0.819607i | \(-0.305808\pi\) | ||||
0.572926 | + | 0.819607i | \(0.305808\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −71298.0 | −0.549250 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 68388.0 | 0.503830 | 0.251915 | − | 0.967749i | \(-0.418940\pi\) | ||||
0.251915 | + | 0.967749i | \(0.418940\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −63585.0 | −0.429428 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −163254. | −1.05681 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −130775. | −0.812010 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3240.00 | −0.0193100 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −185384. | −1.01991 | −0.509956 | − | 0.860200i | \(-0.670338\pi\) | ||||
−0.509956 | + | 0.860200i | \(0.670338\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 44559.0 | 0.235755 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 329772. | 1.67894 | 0.839471 | − | 0.543405i | \(-0.182865\pi\) | ||||
0.839471 | + | 0.543405i | \(0.182865\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −84175.0 | −0.412624 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −143982. | −0.655401 | −0.327700 | − | 0.944782i | \(-0.606274\pi\) | ||||
−0.327700 | + | 0.944782i | \(0.606274\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −365644. | −1.60517 | −0.802586 | − | 0.596537i | \(-0.796543\pi\) | ||||
−0.802586 | + | 0.596537i | \(0.796543\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −89154.0 | −0.377653 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 136590. | 0.558572 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −76734.0 | −0.292883 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 155178. | 0.572617 | 0.286309 | − | 0.958137i | \(-0.407572\pi\) | ||||
0.286309 | + | 0.958137i | \(0.407572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −227185. | −0.810844 | −0.405422 | − | 0.914130i | \(-0.632875\pi\) | ||||
−0.405422 | + | 0.914130i | \(0.632875\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −145314. | −0.501856 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 171277. | 0.554562 | 0.277281 | − | 0.960789i | \(-0.410567\pi\) | ||||
0.277281 | + | 0.960789i | \(0.410567\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 74628.0 | 0.234104 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 213486. | 0.649090 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −110675. | −0.326273 | −0.163136 | − | 0.986604i | \(-0.552161\pi\) | ||||
−0.163136 | + | 0.986604i | \(0.552161\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 440628. | 1.22259 | 0.611295 | − | 0.791403i | \(-0.290649\pi\) | ||||
0.611295 | + | 0.791403i | \(0.290649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 244932. | 0.659673 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −74925.0 | −0.195946 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 699834. | 1.77779 | 0.888894 | − | 0.458114i | \(-0.151475\pi\) | ||||
0.888894 | + | 0.458114i | \(0.151475\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 63126.0 | 0.151452 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −309786. | −0.722652 | −0.361326 | − | 0.932440i | \(-0.617676\pi\) | ||||
−0.361326 | + | 0.932440i | \(0.617676\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 628625. | 1.42625 | 0.713124 | − | 0.701038i | \(-0.247280\pi\) | ||||
0.713124 | + | 0.701038i | \(0.247280\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −462897. | −1.02178 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 312156. | 0.652781 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 66339.0 | 0.135087 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 192774. | 0.382353 | 0.191177 | − | 0.981556i | \(-0.438770\pi\) | ||||
0.191177 | + | 0.981556i | \(0.438770\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −708971. | −1.37005 | −0.685023 | − | 0.728521i | \(-0.740208\pi\) | ||||
−0.685023 | + | 0.728521i | \(0.740208\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 119154. | 0.218747 | 0.109374 | − | 0.994001i | \(-0.465115\pi\) | ||||
0.109374 | + | 0.994001i | \(0.465115\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.01864e6 | 1.82343 | 0.911715 | − | 0.410822i | \(-0.134758\pi\) | ||||
0.911715 | + | 0.410822i | \(0.134758\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5229.00 | −0.00912911 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −66066.0 | −0.112522 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 190026. | 0.308239 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 160950. | 0.254874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −32245.0 | −0.0498605 | −0.0249302 | − | 0.999689i | \(-0.507936\pi\) | ||||
−0.0249302 | + | 0.999689i | \(0.507936\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −508680. | −0.768238 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −73801.0 | −0.106393 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 382302. | 0.538637 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.40829e6 | 1.93960 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −815765. | −1.09851 | −0.549254 | − | 0.835656i | \(-0.685088\pi\) | ||||
−0.549254 | + | 0.835656i | \(0.685088\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.45908e6 | 1.87938 | 0.939690 | − | 0.342028i | \(-0.111114\pi\) | ||||
0.939690 | + | 0.342028i | \(0.111114\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 406241. | 0.511912 | 0.255956 | − | 0.966688i | \(-0.417610\pi\) | ||||
0.255956 | + | 0.966688i | \(0.417610\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −142506. | −0.175713 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 901080. | 1.08736 | 0.543680 | − | 0.839292i | \(-0.317030\pi\) | ||||
0.543680 | + | 0.839292i | \(0.317030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −260208. | −0.300919 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.36513e6 | −1.54589 | −0.772947 | − | 0.634470i | \(-0.781218\pi\) | ||||
−0.772947 | + | 0.634470i | \(0.781218\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −180247. | −0.199906 | −0.0999529 | − | 0.994992i | \(-0.531869\pi\) | ||||
−0.0999529 | + | 0.994992i | \(0.531869\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 726125. | 0.757302 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 941274. | 0.962094 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.87739e6 | 1.88092 | 0.940459 | − | 0.339908i | \(-0.110396\pi\) | ||||
0.940459 | + | 0.339908i | \(0.110396\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −408204. | −0.400937 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 825108. | 0.779252 | 0.389626 | − | 0.920973i | \(-0.372604\pi\) | ||||
0.389626 | + | 0.920973i | \(0.372604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −720902. | −0.667770 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −58806.0 | −0.0534343 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −196944. | −0.175571 | −0.0877856 | − | 0.996139i | \(-0.527979\pi\) | ||||
−0.0877856 | + | 0.996139i | \(0.527979\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.06272e6 | −0.912306 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20874.0 | −0.0175883 | −0.00879417 | − | 0.999961i | \(-0.502799\pi\) | ||||
−0.00879417 | + | 0.999961i | \(0.502799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 770024. | 0.636914 | 0.318457 | − | 0.947937i | \(-0.396835\pi\) | ||||
0.318457 | + | 0.947937i | \(0.396835\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −642915. | −0.522092 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.75169e6 | −1.37170 | −0.685849 | − | 0.727744i | \(-0.740569\pi\) | ||||
−0.685849 | + | 0.727744i | \(0.740569\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −65691.0 | −0.0505237 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.72693e6 | 1.30469 | 0.652346 | − | 0.757921i | \(-0.273785\pi\) | ||||
0.652346 | + | 0.757921i | \(0.273785\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.20061e6 | −1.63334 | −0.816670 | − | 0.577105i | \(-0.804182\pi\) | ||||
−0.816670 | + | 0.577105i | \(0.804182\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −32760.0 | −0.0234768 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.79858e6 | 1.26673 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −992457. | −0.687036 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.04086e6 | 1.38881 | 0.694406 | − | 0.719583i | \(-0.255667\pi\) | ||||
0.694406 | + | 0.719583i | \(0.255667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −126846. | −0.0834422 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.84161e6 | −1.19130 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 450541. | 0.286628 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.73999e6 | −1.08878 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 433153. | 0.262298 | 0.131149 | − | 0.991363i | \(-0.458133\pi\) | ||||
0.131149 | + | 0.991363i | \(0.458133\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 339156. | 0.202071 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.20663e6 | −1.29368 | −0.646841 | − | 0.762625i | \(-0.723910\pi\) | ||||
−0.646841 | + | 0.762625i | \(0.723910\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.17607e6 | 1.25549 | 0.627743 | − | 0.778421i | \(-0.283979\pi\) | ||||
0.627743 | + | 0.778421i | \(0.283979\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 380136. | 0.212467 | 0.106233 | − | 0.994341i | \(-0.466121\pi\) | ||||
0.106233 | + | 0.994341i | \(0.466121\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 126324. | 0.0695039 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −155628. | −0.0842995 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.65945e6 | 0.885030 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.27920e6 | 0.661558 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −901446. | −0.459145 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.43599e6 | −1.72378 | −0.861890 | − | 0.507096i | \(-0.830719\pi\) | ||||
−0.861890 | + | 0.507096i | \(0.830719\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −641682. | −0.317110 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.57718e6 | −0.756494 | −0.378247 | − | 0.925705i | \(-0.623473\pi\) | ||||
−0.378247 | + | 0.925705i | \(0.623473\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 615492. | 0.290886 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 141114. | 0.0657180 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.30530e6 | −1.05802 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.08744e6 | −0.930659 | −0.465330 | − | 0.885137i | \(-0.654064\pi\) | ||||
−0.465330 | + | 0.885137i | \(0.654064\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 542426. | 0.238384 | 0.119192 | − | 0.992871i | \(-0.461970\pi\) | ||||
0.119192 | + | 0.992871i | \(0.461970\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −572265. | −0.247930 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.16054e6 | 1.77710 | 0.888552 | − | 0.458776i | \(-0.151712\pi\) | ||||
0.888552 | + | 0.458776i | \(0.151712\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.46929e6 | −0.610149 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.69018e6 | −0.692143 | −0.346071 | − | 0.938208i | \(-0.612485\pi\) | ||||
−0.346071 | + | 0.938208i | \(0.612485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.62047e6 | −0.654446 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.17698e6 | −0.468814 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 846061. | 0.327896 | 0.163948 | − | 0.986469i | \(-0.447577\pi\) | ||||
0.163948 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −29160.0 | −0.0111486 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 754572. | 0.284620 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.25910e6 | 0.468585 | 0.234293 | − | 0.972166i | \(-0.424723\pi\) | ||||
0.234293 | + | 0.972166i | \(0.424723\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 569910. | 0.206516 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.37437e6 | −1.56429 | −0.782145 | − | 0.623097i | \(-0.785874\pi\) | ||||
−0.782145 | + | 0.623097i | \(0.785874\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.66846e6 | −0.588847 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.77827e6 | 1.66446 | 0.832230 | − | 0.554430i | \(-0.187064\pi\) | ||||
0.832230 | + | 0.554430i | \(0.187064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 401031. | 0.136113 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.98618e6 | 1.00056 | 0.500278 | − | 0.865865i | \(-0.333231\pi\) | ||||
0.500278 | + | 0.865865i | \(0.333231\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.20872e6 | −1.39222 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.96795e6 | 0.969337 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 238633. | 0.0759896 | 0.0379948 | − | 0.999278i | \(-0.487903\pi\) | ||||
0.0379948 | + | 0.999278i | \(0.487903\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −757575. | −0.238228 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.66856e6 | −0.518182 | −0.259091 | − | 0.965853i | \(-0.583423\pi\) | ||||
−0.259091 | + | 0.965853i | \(0.583423\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 636635. | 0.195267 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.37843e6 | 0.412475 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.05242e6 | 0.902269 | 0.451135 | − | 0.892456i | \(-0.351019\pi\) | ||||
0.451135 | + | 0.892456i | \(0.351019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.29584e6 | −0.378396 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 638274. | 0.184133 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.29080e6 | −0.926746 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.16223e6 | −0.879950 | −0.439975 | − | 0.898010i | \(-0.645013\pi\) | ||||
−0.439975 | + | 0.898010i | \(0.645013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.76169e6 | −0.759398 | −0.379699 | − | 0.925110i | \(-0.623973\pi\) | ||||
−0.379699 | + | 0.925110i | \(0.623973\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −802386. | −0.218038 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.68040e6 | −1.24226 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.22931e6 | 0.322491 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.46832e6 | −0.640042 | −0.320021 | − | 0.947410i | \(-0.603690\pi\) | ||||
−0.320021 | + | 0.947410i | \(0.603690\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −838931. | −0.215034 | −0.107517 | − | 0.994203i | \(-0.534290\pi\) | ||||
−0.107517 | + | 0.994203i | \(0.534290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.17005e6 | −0.543583 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −481867. | −0.119334 | −0.0596672 | − | 0.998218i | \(-0.519004\pi\) | ||||
−0.0596672 | + | 0.998218i | \(0.519004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −690606. | −0.169096 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.83550e6 | −1.17066 | −0.585331 | − | 0.810794i | \(-0.699036\pi\) | ||||
−0.585331 | + | 0.810794i | \(0.699036\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.39660e6 | 0.330601 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.64449e6 | −0.384960 | −0.192480 | − | 0.981301i | \(-0.561653\pi\) | ||||
−0.192480 | + | 0.981301i | \(0.561653\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 62640.0 | 0.0145014 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.04466e6 | −0.468141 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.59903e6 | −1.47805 | −0.739026 | − | 0.673677i | \(-0.764714\pi\) | ||||
−0.739026 | + | 0.673677i | \(0.764714\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.30783e6 | −0.289747 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 253836. | 0.0556290 | 0.0278145 | − | 0.999613i | \(-0.491145\pi\) | ||||
0.0278145 | + | 0.999613i | \(0.491145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.03985e6 | 1.09261 | 0.546305 | − | 0.837586i | \(-0.316034\pi\) | ||||
0.546305 | + | 0.837586i | \(0.316034\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 419958. | 0.0891074 | 0.0445537 | − | 0.999007i | \(-0.485813\pi\) | ||||
0.0445537 | + | 0.999007i | \(0.485813\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −52871.0 | −0.0110990 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.54149e6 | 0.320176 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −861474. | −0.177047 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 671652. | 0.135160 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.28623e6 | −1.45099 | −0.725494 | − | 0.688228i | \(-0.758389\pi\) | ||||
−0.725494 | + | 0.688228i | \(0.758389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.21877e6 | 1.22558 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.92137e6 | 0.374752 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.48420e6 | 1.42996 | 0.714978 | − | 0.699147i | \(-0.246437\pi\) | ||||
0.714978 | + | 0.699147i | \(0.246437\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −996075. | −0.188374 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −339816. | −0.0636122 | −0.0318061 | − | 0.999494i | \(-0.510126\pi\) | ||||
−0.0318061 | + | 0.999494i | \(0.510126\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.30244e6 | 0.241347 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.14332e6 | −0.934012 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 280499. | 0.0504290 | 0.0252145 | − | 0.999682i | \(-0.491973\pi\) | ||||
0.0252145 | + | 0.999682i | \(0.491973\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.96565e6 | 0.705863 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.41522e6 | −0.425634 | −0.212817 | − | 0.977092i | \(-0.568264\pi\) | ||||
−0.212817 | + | 0.977092i | \(0.568264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.20439e6 | 0.380862 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.09746e6 | 1.38533 | 0.692667 | − | 0.721258i | \(-0.256436\pi\) | ||||
0.692667 | + | 0.721258i | \(0.256436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.86550e6 | 0.654867 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −674325. | −0.113129 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.72364e6 | 0.283610 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.29851e6 | 1.02641 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.52334e6 | −0.568670 | −0.284335 | − | 0.958725i | \(-0.591773\pi\) | ||||
−0.284335 | + | 0.958725i | \(0.591773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.27241e6 | −0.682996 | −0.341498 | − | 0.939882i | \(-0.610934\pi\) | ||||
−0.341498 | + | 0.939882i | \(0.610934\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.45493e6 | 0.228201 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −932627. | −0.144900 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 568134. | 0.0874409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 282600. | 0.0430878 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.78807e6 | −0.417223 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.48352e6 | 0.219949 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.80585e6 | 0.559061 | 0.279530 | − | 0.960137i | \(-0.409821\pi\) | ||||
0.279530 | + | 0.960137i | \(0.409821\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.65762e6 | 0.823445 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.46327e6 | 1.06650 | 0.533250 | − | 0.845958i | \(-0.320970\pi\) | ||||
0.533250 | + | 0.845958i | \(0.320970\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.16607e6 | −0.589924 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 671550. | 0.0942322 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.63099e6 | −0.365853 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.26290e6 | 0.855338 | 0.427669 | − | 0.903935i | \(-0.359335\pi\) | ||||
0.427669 | + | 0.903935i | \(0.359335\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.88654e6 | −0.526057 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.80940e6 | 0.376883 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.34426e7 | −1.78735 | −0.893677 | − | 0.448710i | \(-0.851883\pi\) | ||||
−0.893677 | + | 0.448710i | \(0.851883\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 597051. | 0.0779927 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.25046e7 | 1.61916 | 0.809579 | − | 0.587011i | \(-0.199695\pi\) | ||||
0.809579 | + | 0.587011i | \(0.199695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.80272e6 | 0.873156 | 0.436578 | − | 0.899666i | \(-0.356190\pi\) | ||||
0.436578 | + | 0.899666i | \(0.356190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.73497e6 | 0.220752 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 375517. | 0.0469559 | 0.0234779 | − | 0.999724i | \(-0.492526\pi\) | ||||
0.0234779 | + | 0.999724i | \(0.492526\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.38074e6 | −0.790997 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.51733e6 | 1.16970 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.44281e6 | −0.175807 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.36164e6 | −0.402677 | −0.201338 | − | 0.979522i | \(-0.564529\pi\) | ||||
−0.201338 | + | 0.979522i | \(0.564529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 750175. | 0.0890993 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.07239e6 | 0.126294 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.31214e6 | −1.08746 | −0.543730 | − | 0.839260i | \(-0.682988\pi\) | ||||
−0.543730 | + | 0.839260i | \(0.682988\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.16779e6 | 1.05276 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.03007e7 | 1.17301 | 0.586503 | − | 0.809947i | \(-0.300504\pi\) | ||||
0.586503 | + | 0.809947i | \(0.300504\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.14328e6 | −0.467905 | −0.233953 | − | 0.972248i | \(-0.575166\pi\) | ||||
−0.233953 | + | 0.972248i | \(0.575166\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −47061.0 | −0.00527069 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.42729e6 | 0.708037 | 0.354019 | − | 0.935238i | \(-0.384815\pi\) | ||||
0.354019 | + | 0.935238i | \(0.384815\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −594594. | −0.0649647 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.77621e6 | 0.842684 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.11824e6 | 0.227679 | 0.113840 | − | 0.993499i | \(-0.463685\pi\) | ||||
0.113840 | + | 0.993499i | \(0.463685\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.53399e7 | 1.62222 | 0.811111 | − | 0.584892i | \(-0.198863\pi\) | ||||
0.811111 | + | 0.584892i | \(0.198863\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.04124e7 | 1.09226 | 0.546128 | − | 0.837702i | \(-0.316101\pi\) | ||||
0.546128 | + | 0.837702i | \(0.316101\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.71023e6 | 0.177962 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.07453e7 | −1.10917 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.44855e6 | 0.147151 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.42121e7 | 1.43229 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.88626e6 | 0.288577 | 0.144288 | − | 0.989536i | \(-0.453911\pi\) | ||||
0.144288 | + | 0.989536i | \(0.453911\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −290205. | −0.0287869 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.69291e6 | 0.653531 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.57812e6 | −0.443542 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.48587e7 | −1.42835 | −0.714176 | − | 0.699967i | \(-0.753198\pi\) | ||||
−0.714176 | + | 0.699967i | \(0.753198\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.59676e6 | 0.915371 | 0.457686 | − | 0.889114i | \(-0.348678\pi\) | ||||
0.457686 | + | 0.889114i | \(0.348678\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.08529e7 | −1.01926 | −0.509632 | − | 0.860393i | \(-0.670218\pi\) | ||||
−0.509632 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.22044e6 | −0.113737 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −664209. | −0.0614260 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.20352e7 | −1.10451 | −0.552254 | − | 0.833676i | \(-0.686232\pi\) | ||||
−0.552254 | + | 0.833676i | \(0.686232\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.44072e6 | 0.310982 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.80711e6 | −0.520891 | −0.260445 | − | 0.965489i | \(-0.583869\pi\) | ||||
−0.260445 | + | 0.965489i | \(0.583869\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.91093e7 | 1.70114 | 0.850570 | − | 0.525861i | \(-0.176257\pi\) | ||||
0.850570 | + | 0.525861i | \(0.176257\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.26746e7 | 1.11983 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.70320e6 | −0.148235 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.34189e6 | −0.634223 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.94934e6 | 0.767335 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.15545e6 | 0.183443 | 0.0917213 | − | 0.995785i | \(-0.470763\pi\) | ||||
0.0917213 | + | 0.995785i | \(0.470763\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.69543e6 | −0.729155 | −0.364577 | − | 0.931173i | \(-0.618786\pi\) | ||||
−0.364577 | + | 0.931173i | \(0.618786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.00348e7 | −0.835288 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.31317e7 | 1.08506 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −781896. | −0.0641353 | −0.0320677 | − | 0.999486i | \(-0.510209\pi\) | ||||
−0.0320677 | + | 0.999486i | \(0.510209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.65617e6 | 0.295552 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.50922e6 | −0.522373 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.13518e7 | 0.904416 | 0.452208 | − | 0.891912i | \(-0.350636\pi\) | ||||
0.452208 | + | 0.891912i | \(0.350636\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.28255e6 | −0.101448 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 645840. | 0.0503550 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.10972e6 | 0.627788 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.99404e7 | −1.53263 | −0.766317 | − | 0.642462i | \(-0.777913\pi\) | ||||
−0.766317 | + | 0.642462i | \(0.777913\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.32785e6 | 0.559227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.75932e7 | −1.32372 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.75367e7 | −1.31018 | −0.655092 | − | 0.755549i | \(-0.727370\pi\) | ||||
−0.655092 | + | 0.755549i | \(0.727370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.34187e6 | −0.173736 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.90261e6 | −0.140160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.22862e7 | −0.892523 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.78220e7 | 1.28568 | 0.642842 | − | 0.765999i | \(-0.277755\pi\) | ||||
0.642842 | + | 0.765999i | \(0.277755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.42924e6 | 0.245675 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.62222e6 | −0.115416 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.29063e6 | 0.581770 | 0.290885 | − | 0.956758i | \(-0.406050\pi\) | ||||
0.290885 | + | 0.956758i | \(0.406050\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.88209e6 | −0.614783 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.69219e7 | −1.16330 | −0.581648 | − | 0.813441i | \(-0.697592\pi\) | ||||
−0.581648 | + | 0.813441i | \(0.697592\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 101094. | 0.00685578 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.40718e6 | 0.633648 | 0.316824 | − | 0.948484i | \(-0.397383\pi\) | ||||
0.316824 | + | 0.948484i | \(0.397383\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.53512e6 | 0.437228 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.81581e7 | −1.20670 | −0.603348 | − | 0.797478i | \(-0.706167\pi\) | ||||
−0.603348 | + | 0.797478i | \(0.706167\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.47147e6 | 0.555465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.57357e6 | −0.102490 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.81468e7 | −1.82108 | −0.910541 | − | 0.413420i | \(-0.864334\pi\) | ||||
−0.910541 | + | 0.413420i | \(0.864334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.68965e7 | 1.08595 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.50436e6 | −0.475964 | −0.237982 | − | 0.971270i | \(-0.576486\pi\) | ||||
−0.237982 | + | 0.971270i | \(0.576486\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.67384e6 | −0.231481 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.18499e7 | −1.99364 | −0.996820 | − | 0.0796919i | \(-0.974606\pi\) | ||||
−0.996820 | + | 0.0796919i | \(0.974606\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.29341e7 | 0.804313 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.50599e6 | −0.337946 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.38750e7 | −1.45588 | −0.727942 | − | 0.685638i | \(-0.759523\pi\) | ||||
−0.727942 | + | 0.685638i | \(0.759523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.42597e6 | 0.449901 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.43665e6 | −0.507833 | −0.253917 | − | 0.967226i | \(-0.581719\pi\) | ||||
−0.253917 | + | 0.967226i | \(0.581719\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.48812e6 | −0.385537 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 333000. | 0.0196608 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.83448e6 | 0.576931 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −529254. | −0.0308503 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.55971e7 | −1.47317 | −0.736587 | − | 0.676343i | \(-0.763564\pi\) | ||||
−0.736587 | + | 0.676343i | \(0.763564\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.77250e6 | −0.101366 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.22331e6 | 0.353655 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.03749e7 | 2.27997 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.22343e7 | 0.682231 | 0.341116 | − | 0.940021i | \(-0.389195\pi\) | ||||
0.341116 | + | 0.940021i | \(0.389195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.77714e7 | 0.984813 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.56448e6 | −0.526720 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.39117e6 | −0.404506 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −187866. | −0.0101546 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.82538e7 | −1.51777 | −0.758885 | − | 0.651224i | \(-0.774256\pi\) | ||||
−0.758885 | + | 0.651224i | \(0.774256\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.02221e7 | −1.07963 | −0.539815 | − | 0.841784i | \(-0.681506\pi\) | ||||
−0.539815 | + | 0.841784i | \(0.681506\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.93022e6 | 0.367723 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.57968e6 | −0.240038 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.78624e6 | −0.301430 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.92645e6 | 0.151524 | 0.0757622 | − | 0.997126i | \(-0.475861\pi\) | ||||
0.0757622 | + | 0.997126i | \(0.475861\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.19976e7 | 0.617439 | 0.308720 | − | 0.951153i | \(-0.400100\pi\) | ||||
0.308720 | + | 0.951153i | \(0.400100\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.87877e7 | −1.46367 | −0.731836 | − | 0.681481i | \(-0.761336\pi\) | ||||
−0.731836 | + | 0.681481i | \(0.761336\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.76584e6 | 0.341929 | 0.170964 | − | 0.985277i | \(-0.445312\pi\) | ||||
0.170964 | + | 0.985277i | \(0.445312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.57652e7 | −0.791950 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.52956e7 | 0.763757 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −591219. | −0.0291699 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.64443e7 | 0.806512 | 0.403256 | − | 0.915087i | \(-0.367878\pi\) | ||||
0.403256 | + | 0.915087i | \(0.367878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.99841e7 | −0.974303 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.55423e7 | 0.753264 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.19005e7 | −0.569977 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.98055e7 | −0.943009 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.85850e7 | −0.879709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.17440e7 | −0.552642 | −0.276321 | − | 0.961065i | \(-0.589115\pi\) | ||||
−0.276321 | + | 0.961065i | \(0.589115\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.59380e7 | 1.20638 | 0.603191 | − | 0.797597i | \(-0.293896\pi\) | ||||
0.603191 | + | 0.797597i | \(0.293896\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.81132e6 | −0.222475 | −0.111238 | − | 0.993794i | \(-0.535481\pi\) | ||||
−0.111238 | + | 0.993794i | \(0.535481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −294840. | −0.0135543 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.80123e6 | 0.402269 | 0.201134 | − | 0.979564i | \(-0.435537\pi\) | ||||
0.201134 | + | 0.979564i | \(0.435537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.61872e7 | 0.731348 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.03069e6 | 0.225984 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 456085. | 0.0203704 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.93211e6 | −0.396660 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.47823e7 | 0.648998 | 0.324499 | − | 0.945886i | \(-0.394804\pi\) | ||||
0.324499 | + | 0.945886i | \(0.394804\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.83677e7 | 0.801831 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.47219e7 | −1.07311 | −0.536553 | − | 0.843867i | \(-0.680274\pi\) | ||||
−0.536553 | + | 0.843867i | \(0.680274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.63912e7 | 0.707470 | 0.353735 | − | 0.935346i | \(-0.384911\pi\) | ||||
0.353735 | + | 0.935346i | \(0.384911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.47481e7 | −1.48293 | −0.741467 | − | 0.670989i | \(-0.765870\pi\) | ||||
−0.741467 | + | 0.670989i | \(0.765870\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.68699e7 | −0.715911 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.14161e6 | −0.0481754 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.16305e6 | 0.384513 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.65745e7 | −0.687795 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 588786. | 0.0242973 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.48758e7 | −0.610478 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.05487e6 | 0.165485 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.42672e7 | 1.78675 | 0.893375 | − | 0.449312i | \(-0.148331\pi\) | ||||
0.893375 | + | 0.449312i | \(0.148331\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.56599e7 | −0.628607 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.78972e6 | 0.231133 | 0.115566 | − | 0.993300i | \(-0.463132\pi\) | ||||
0.115566 | + | 0.993300i | \(0.463132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.81980e7 | −0.722513 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.00093e7 | 1.17851 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.95894e6 | 0.271803 | 0.135902 | − | 0.990722i | \(-0.456607\pi\) | ||||
0.135902 | + | 0.990722i | \(0.456607\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.89838e6 | 0.151438 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.43682e7 | 1.71422 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.05240e6 | 0.116666 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.13281e7 | 0.430643 | 0.215321 | − | 0.976543i | \(-0.430920\pi\) | ||||
0.215321 | + | 0.976543i | \(0.430920\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.88655e6 | 0.298204 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.98596e7 | −0.746908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.38002e7 | −1.25768 | −0.628840 | − | 0.777534i | \(-0.716470\pi\) | ||||
−0.628840 | + | 0.777534i | \(0.716470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.95846e7 | 0.724855 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.01912e7 | −0.375190 | −0.187595 | − | 0.982246i | \(-0.560069\pi\) | ||||
−0.187595 | + | 0.982246i | \(0.560069\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −844560. | −0.0309280 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.78585e7 | −1.00944 | −0.504722 | − | 0.863282i | \(-0.668405\pi\) | ||||
−0.504722 | + | 0.863282i | \(0.668405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.33452e7 | −1.20190 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.42122e6 | 0.122668 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.26828e7 | −0.452358 | −0.226179 | − | 0.974086i | \(-0.572623\pi\) | ||||
−0.226179 | + | 0.974086i | \(0.572623\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.13692e6 | 0.0401281 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.31024e7 | −0.460048 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.79714e7 | −0.977026 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.40065e6 | −0.0486704 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.17434e7 | −1.09166 | −0.545831 | − | 0.837896i | \(-0.683786\pi\) | ||||
−0.545831 | + | 0.837896i | \(0.683786\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.49350e7 | 0.510972 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.81895e7 | 0.619117 | 0.309558 | − | 0.950880i | \(-0.399819\pi\) | ||||
0.309558 | + | 0.950880i | \(0.399819\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.32736e7 | −1.12672 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.61267e7 | −0.875684 | −0.437842 | − | 0.899052i | \(-0.644257\pi\) | ||||
−0.437842 | + | 0.899052i | \(0.644257\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.05459e7 | 0.685123 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.15128e7 | 0.381951 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.44653e6 | −0.212786 | −0.106393 | − | 0.994324i | \(-0.533930\pi\) | ||||
−0.106393 | + | 0.994324i | \(0.533930\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.11301e6 | −0.265088 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.16150e7 | 0.377598 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.16146e7 | 0.699139 | 0.349570 | − | 0.936910i | \(-0.386328\pi\) | ||||
0.349570 | + | 0.936910i | \(0.386328\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.09239e7 | −0.995224 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.16105e7 | 0.688538 | 0.344269 | − | 0.938871i | \(-0.388127\pi\) | ||||
0.344269 | + | 0.938871i | \(0.388127\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.77514e6 | −0.183083 |
(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 | 300.6.a.f.1.1 | yes | 1 | |
3.2 | odd | 2 | 900.6.a.i.1.1 | 1 | |||
5.2 | odd | 4 | 300.6.d.b.49.1 | 2 | |||
5.3 | odd | 4 | 300.6.d.b.49.2 | 2 | |||
5.4 | even | 2 | 300.6.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 900.6.d.g.649.2 | 2 | |||
15.8 | even | 4 | 900.6.d.g.649.1 | 2 | |||
15.14 | odd | 2 | 900.6.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.6.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
300.6.a.f.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
300.6.d.b.49.1 | 2 | 5.2 | odd | 4 | |||
300.6.d.b.49.2 | 2 | 5.3 | odd | 4 | |||
900.6.a.d.1.1 | 1 | 15.14 | odd | 2 | |||
900.6.a.i.1.1 | 1 | 3.2 | odd | 2 | |||
900.6.d.g.649.1 | 2 | 15.8 | even | 4 | |||
900.6.d.g.649.2 | 2 | 15.2 | even | 4 |