Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,6,Mod(1,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, 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("432.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.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: | \(69.2858101592\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 108) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −88.1816 | −1.57744 | −0.788720 | − | 0.614752i | \(-0.789256\pi\) | ||||
−0.788720 | + | 0.614752i | \(0.789256\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.0000 | −0.223693 | −0.111847 | − | 0.993725i | \(-0.535677\pi\) | ||||
−0.111847 | + | 0.993725i | \(0.535677\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 88.1816 | 0.219734 | 0.109867 | − | 0.993946i | \(-0.464958\pi\) | ||||
0.109867 | + | 0.993946i | \(0.464958\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 329.000 | 0.539930 | 0.269965 | − | 0.962870i | \(-0.412988\pi\) | ||||
0.269965 | + | 0.962870i | \(0.412988\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2204.54 | 1.85010 | 0.925051 | − | 0.379842i | \(-0.124022\pi\) | ||||
0.925051 | + | 0.379842i | \(0.124022\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1799.00 | −1.14327 | −0.571633 | − | 0.820510i | \(-0.693690\pi\) | ||||
−0.571633 | + | 0.820510i | \(0.693690\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3615.45 | 1.42509 | 0.712545 | − | 0.701626i | \(-0.247542\pi\) | ||||
0.712545 | + | 0.701626i | \(0.247542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4651.00 | 1.48832 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1410.91 | −0.311532 | −0.155766 | − | 0.987794i | \(-0.549785\pi\) | ||||
−0.155766 | + | 0.987794i | \(0.549785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5228.00 | −0.977083 | −0.488541 | − | 0.872541i | \(-0.662471\pi\) | ||||
−0.488541 | + | 0.872541i | \(0.662471\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2557.27 | 0.352863 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8783.00 | 1.05472 | 0.527362 | − | 0.849641i | \(-0.323181\pi\) | ||||
0.527362 | + | 0.849641i | \(0.323181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15520.0 | 1.44189 | 0.720943 | − | 0.692994i | \(-0.243709\pi\) | ||||
0.720943 | + | 0.692994i | \(0.243709\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19976.0 | −1.64755 | −0.823773 | − | 0.566920i | \(-0.808135\pi\) | ||||
−0.823773 | + | 0.566920i | \(0.808135\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10846.3 | −0.716207 | −0.358104 | − | 0.933682i | \(-0.616577\pi\) | ||||
−0.358104 | + | 0.933682i | \(0.616577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15966.0 | −0.949961 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −29452.7 | −1.44024 | −0.720120 | − | 0.693849i | \(-0.755913\pi\) | ||||
−0.720120 | + | 0.693849i | \(0.755913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7776.00 | −0.346617 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5731.81 | 0.214369 | 0.107184 | − | 0.994239i | \(-0.465816\pi\) | ||||
0.107184 | + | 0.994239i | \(0.465816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1069.00 | −0.0367835 | −0.0183918 | − | 0.999831i | \(-0.505855\pi\) | ||||
−0.0183918 | + | 0.999831i | \(0.505855\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −29011.8 | −0.851708 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 62077.0 | 1.68944 | 0.844722 | − | 0.535206i | \(-0.179766\pi\) | ||||
0.844722 | + | 0.535206i | \(0.179766\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −46383.5 | −1.09199 | −0.545994 | − | 0.837789i | \(-0.683848\pi\) | ||||
−0.545994 | + | 0.837789i | \(0.683848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −48079.0 | −1.05596 | −0.527981 | − | 0.849256i | \(-0.677051\pi\) | ||||
−0.527981 | + | 0.849256i | \(0.677051\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2557.27 | −0.0491529 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −49979.0 | −0.900990 | −0.450495 | − | 0.892779i | \(-0.648752\pi\) | ||||
−0.450495 | + | 0.892779i | \(0.648752\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −57670.8 | −0.918884 | −0.459442 | − | 0.888208i | \(-0.651951\pi\) | ||||
−0.459442 | + | 0.888208i | \(0.651951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −194400. | −2.91843 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 87917.1 | 1.17652 | 0.588259 | − | 0.808673i | \(-0.299814\pi\) | ||||
0.588259 | + | 0.808673i | \(0.299814\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9541.00 | −0.120779 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 158639. | 1.80343 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12917.0 | 0.139390 | 0.0696951 | − | 0.997568i | \(-0.477797\pi\) | ||||
0.0696951 | + | 0.997568i | \(0.477797\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −112872. | −1.10099 | −0.550497 | − | 0.834837i | \(-0.685562\pi\) | ||||
−0.550497 | + | 0.834837i | \(0.685562\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 77503.0 | 0.719823 | 0.359911 | − | 0.932987i | \(-0.382807\pi\) | ||||
0.359911 | + | 0.932987i | \(0.382807\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 111726. | 0.943399 | 0.471699 | − | 0.881759i | \(-0.343641\pi\) | ||||
0.471699 | + | 0.881759i | \(0.343641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17710.0 | −0.142775 | −0.0713875 | − | 0.997449i | \(-0.522743\pi\) | ||||
−0.0713875 | + | 0.997449i | \(0.522743\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 251582. | 1.85346 | 0.926731 | − | 0.375725i | \(-0.122606\pi\) | ||||
0.926731 | + | 0.375725i | \(0.122606\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −318816. | −2.24800 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −63931.7 | −0.413855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −153275. | −0.951717 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −134565. | −0.770296 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −269444. | −1.48238 | −0.741189 | − | 0.671296i | \(-0.765738\pi\) | ||||
−0.741189 | + | 0.671296i | \(0.765738\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −154141. | −0.784768 | −0.392384 | − | 0.919801i | \(-0.628350\pi\) | ||||
−0.392384 | + | 0.919801i | \(0.628350\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 52171.0 | 0.255741 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 271864. | 1.23751 | 0.618757 | − | 0.785582i | \(-0.287636\pi\) | ||||
0.618757 | + | 0.785582i | \(0.287636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −182705. | −0.802072 | −0.401036 | − | 0.916062i | \(-0.631350\pi\) | ||||
−0.401036 | + | 0.916062i | \(0.631350\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29011.8 | 0.118641 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 124416. | 0.491424 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −347259. | −1.28141 | −0.640705 | − | 0.767787i | \(-0.721358\pi\) | ||||
−0.640705 | + | 0.767787i | \(0.721358\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −434351. | −1.55024 | −0.775119 | − | 0.631815i | \(-0.782310\pi\) | ||||
−0.775119 | + | 0.631815i | \(0.782310\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 461014. | 1.54129 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22978.0 | −0.0743983 | −0.0371992 | − | 0.999308i | \(-0.511844\pi\) | ||||
−0.0371992 | + | 0.999308i | \(0.511844\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −104848. | −0.318783 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −109961. | −0.324168 | −0.162084 | − | 0.986777i | \(-0.551821\pi\) | ||||
−0.162084 | + | 0.986777i | \(0.551821\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −307137. | −0.852198 | −0.426099 | − | 0.904677i | \(-0.640112\pi\) | ||||
−0.426099 | + | 0.904677i | \(0.640112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −263052. | −0.708476 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4232.72 | 0.0107524 | 0.00537618 | − | 0.999986i | \(-0.498289\pi\) | ||||
0.00537618 | + | 0.999986i | \(0.498289\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −134879. | −0.332927 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −831906. | −1.94062 | −0.970312 | − | 0.241856i | \(-0.922244\pi\) | ||||
−0.970312 | + | 0.241856i | \(0.922244\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −327187. | −0.742334 | −0.371167 | − | 0.928566i | \(-0.621042\pi\) | ||||
−0.371167 | + | 0.928566i | \(0.621042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −774499. | −1.66376 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 194400. | 0.406530 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −468862. | −0.929954 | −0.464977 | − | 0.885323i | \(-0.653937\pi\) | ||||
−0.464977 | + | 0.885323i | \(0.653937\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 152231. | 0.294178 | 0.147089 | − | 0.989123i | \(-0.453010\pi\) | ||||
0.147089 | + | 0.989123i | \(0.453010\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 653514. | 1.19975 | 0.599873 | − | 0.800095i | \(-0.295218\pi\) | ||||
0.599873 | + | 0.800095i | \(0.295218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 645895. | 1.15619 | 0.578095 | − | 0.815969i | \(-0.303796\pi\) | ||||
0.578095 | + | 0.815969i | \(0.303796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 40916.3 | 0.0696877 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.36858e6 | −2.27449 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −158639. | −0.251214 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −169637. | −0.262310 | −0.131155 | − | 0.991362i | \(-0.541869\pi\) | ||||
−0.131155 | + | 0.991362i | \(0.541869\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.76152e6 | 2.59891 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 151612. | 0.218567 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 725294. | 0.998926 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 691276. | 0.930871 | 0.465435 | − | 0.885082i | \(-0.345898\pi\) | ||||
0.465435 | + | 0.885082i | \(0.345898\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 989927. | 1.27508 | 0.637542 | − | 0.770416i | \(-0.279951\pi\) | ||||
0.637542 | + | 0.770416i | \(0.279951\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 352250. | 0.443877 | 0.221938 | − | 0.975061i | \(-0.428762\pi\) | ||||
0.221938 | + | 0.975061i | \(0.428762\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −381297. | −0.460123 | −0.230062 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230062 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 956448. | 1.12977 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −785698. | −0.889736 | −0.444868 | − | 0.895596i | \(-0.646749\pi\) | ||||
−0.444868 | + | 0.895596i | \(0.646749\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.20262e6 | −1.33379 | −0.666894 | − | 0.745152i | \(-0.732377\pi\) | ||||
−0.666894 | + | 0.745152i | \(0.732377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.40791e6 | 1.49851 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −591871. | −0.617284 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −416570. | −0.417353 | −0.208677 | − | 0.977985i | \(-0.566916\pi\) | ||||
−0.208677 | + | 0.977985i | \(0.566916\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 318816. | 0.313140 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 44972.6 | 0.0424732 | 0.0212366 | − | 0.999774i | \(-0.493240\pi\) | ||||
0.0212366 | + | 0.999774i | \(0.493240\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −254707. | −0.235935 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −515157. | −0.459251 | −0.229626 | − | 0.973279i | \(-0.573750\pi\) | ||||
−0.229626 | + | 0.973279i | \(0.573750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.59718e6 | 2.27189 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −197439. | −0.166361 | −0.0831805 | − | 0.996534i | \(-0.526508\pi\) | ||||
−0.0831805 | + | 0.996534i | \(0.526508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.01499e6 | 0.839530 | 0.419765 | − | 0.907633i | \(-0.362112\pi\) | ||||
0.419765 | + | 0.907633i | \(0.362112\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 410133. | 0.327034 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −379318. | −0.297033 | −0.148516 | − | 0.988910i | \(-0.547450\pi\) | ||||
−0.148516 | + | 0.988910i | \(0.547450\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −955889. | −0.722174 | −0.361087 | − | 0.932532i | \(-0.617594\pi\) | ||||
−0.361087 | + | 0.932532i | \(0.617594\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −662912. | −0.492028 | −0.246014 | − | 0.969266i | \(-0.579121\pi\) | ||||
−0.246014 | + | 0.969266i | \(0.579121\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −450079. | −0.322540 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.44014e6 | 2.42288 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −447522. | −0.304541 | −0.152270 | − | 0.988339i | \(-0.548658\pi\) | ||||
−0.152270 | + | 0.988339i | \(0.548658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −505440. | −0.338154 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.18948e6 | 0.769449 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 579304. | 0.368545 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 94266.2 | 0.0580238 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.17362e6 | 0.710690 | 0.355345 | − | 0.934735i | \(-0.384363\pi\) | ||||
0.355345 | + | 0.934735i | \(0.384363\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.41221e6 | 1.41421 | 0.707105 | − | 0.707109i | \(-0.250001\pi\) | ||||
0.707105 | + | 0.707109i | \(0.250001\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.72967e6 | 0.997934 | 0.498967 | − | 0.866621i | \(-0.333713\pi\) | ||||
0.498967 | + | 0.866621i | \(0.333713\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.17476e6 | −0.656598 | −0.328299 | − | 0.944574i | \(-0.606475\pi\) | ||||
−0.328299 | + | 0.944574i | \(0.606475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −124416. | −0.0684541 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.96597e6 | −2.11516 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.53018e6 | 0.803589 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 314544. | 0.160211 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −451001. | −0.226260 | −0.113130 | − | 0.993580i | \(-0.536088\pi\) | ||||
−0.113130 | + | 0.993580i | \(0.536088\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.47405e6 | −2.66500 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.17937e6 | 1.04534 | 0.522669 | − | 0.852536i | \(-0.324936\pi\) | ||||
0.522669 | + | 0.852536i | \(0.324936\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −461014. | −0.214698 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 950417. | 0.436193 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −381474. | −0.170075 | −0.0850376 | − | 0.996378i | \(-0.527101\pi\) | ||||
−0.0850376 | + | 0.996378i | \(0.527101\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.29596e6 | −1.00902 | −0.504511 | − | 0.863405i | \(-0.668327\pi\) | ||||
−0.504511 | + | 0.863405i | \(0.668327\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.24103e6 | −1.38435 | −0.692175 | − | 0.721730i | \(-0.743347\pi\) | ||||
−0.692175 | + | 0.721730i | \(0.743347\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.09018e6 | 1.72255 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.15044e6 | 1.69965 | 0.849823 | − | 0.527068i | \(-0.176709\pi\) | ||||
0.849823 | + | 0.527068i | \(0.176709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 760302. | 0.307056 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.23968e6 | 1.66572 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.39911e6 | −1.31735 | −0.658674 | − | 0.752429i | \(-0.728882\pi\) | ||||
−0.658674 | + | 0.752429i | \(0.728882\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 854127. | 0.322172 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.14494e6 | −1.17041 | −0.585207 | − | 0.810884i | \(-0.698987\pi\) | ||||
−0.585207 | + | 0.810884i | \(0.698987\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −464188. | −0.168206 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.76635e6 | 0.989257 | 0.494628 | − | 0.869105i | \(-0.335304\pi\) | ||||
0.494628 | + | 0.869105i | \(0.335304\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.24898e6 | 0.783411 | 0.391705 | − | 0.920091i | \(-0.371885\pi\) | ||||
0.391705 | + | 0.920091i | \(0.371885\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 225504. | 0.0775358 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −555985. | −0.186290 | −0.0931449 | − | 0.995653i | \(-0.529692\pi\) | ||||
−0.0931449 | + | 0.995653i | \(0.529692\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.97040e6 | 2.63656 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.40723e6 | 1.42126 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 836174. | 0.266269 | 0.133134 | − | 0.991098i | \(-0.457496\pi\) | ||||
0.133134 | + | 0.991098i | \(0.457496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.01283e6 | 0.625096 | 0.312548 | − | 0.949902i | \(-0.398817\pi\) | ||||
0.312548 | + | 0.949902i | \(0.398817\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.72001e6 | −0.527556 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 774499. | 0.231758 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.37271e6 | −0.405762 | −0.202881 | − | 0.979203i | \(-0.565030\pi\) | ||||
−0.202881 | + | 0.979203i | \(0.565030\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −166222. | −0.0479528 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.08550e6 | 1.44949 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.54305e6 | −0.985921 | −0.492961 | − | 0.870052i | \(-0.664085\pi\) | ||||
−0.492961 | + | 0.870052i | \(0.664085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.48884e6 | −0.959347 | −0.479673 | − | 0.877447i | \(-0.659245\pi\) | ||||
−0.479673 | + | 0.877447i | \(0.659245\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.02533e7 | 2.75354 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31001.0 | 0.00822822 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.43754e6 | −1.40997 | −0.704985 | − | 0.709223i | \(-0.749046\pi\) | ||||
−0.704985 | + | 0.709223i | \(0.749046\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.96023e6 | 1.27140 | 0.635699 | − | 0.771937i | \(-0.280712\pi\) | ||||
0.635699 | + | 0.771937i | \(0.280712\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.50419e6 | −1.62926 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.75071e6 | −1.42416 | −0.712082 | − | 0.702096i | \(-0.752248\pi\) | ||||
−0.712082 | + | 0.702096i | \(0.752248\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.63110e6 | 1.36328 | 0.681639 | − | 0.731689i | \(-0.261268\pi\) | ||||
0.681639 | + | 0.731689i | \(0.261268\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.75267e6 | −1.85589 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.45310e6 | 0.808340 | 0.404170 | − | 0.914684i | \(-0.367560\pi\) | ||||
0.404170 | + | 0.914684i | \(0.367560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.36858e6 | 0.316831 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 841341. | 0.190521 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.96799e6 | 0.440791 | 0.220395 | − | 0.975411i | \(-0.429265\pi\) | ||||
0.220395 | + | 0.975411i | \(0.429265\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.63329e6 | −1.45371 | −0.726853 | − | 0.686793i | \(-0.759018\pi\) | ||||
−0.726853 | + | 0.686793i | \(0.759018\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.62568e6 | 0.352439 | 0.176219 | − | 0.984351i | \(-0.443613\pi\) | ||||
0.176219 | + | 0.984351i | \(0.443613\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.48346e6 | −0.526944 | −0.263472 | − | 0.964667i | \(-0.584868\pi\) | ||||
−0.263472 | + | 0.964667i | \(0.584868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.80023e6 | −0.377917 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.76152e6 | −0.362021 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.36715e6 | −1.70155 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.59626e6 | 0.317882 | 0.158941 | − | 0.987288i | \(-0.449192\pi\) | ||||
0.158941 | + | 0.987288i | \(0.449192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.88961e6 | 0.569477 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.13904e6 | −0.219880 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.95245e6 | −1.51942 | −0.759712 | − | 0.650260i | \(-0.774660\pi\) | ||||
−0.759712 | + | 0.650260i | \(0.774660\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.05595e6 | 0.384866 | 0.192433 | − | 0.981310i | \(-0.438362\pi\) | ||||
0.192433 | + | 0.981310i | \(0.438362\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.11040e6 | −0.576367 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.34512e6 | 0.244270 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.93539e6 | −0.887300 | −0.443650 | − | 0.896200i | \(-0.646317\pi\) | ||||
−0.443650 | + | 0.896200i | \(0.646317\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 836755. | 0.147461 | 0.0737307 | − | 0.997278i | \(-0.476509\pi\) | ||||
0.0737307 | + | 0.997278i | \(0.476509\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.95328e6 | 1.73675 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.90156e6 | −1.00965 | −0.504826 | − | 0.863221i | \(-0.668443\pi\) | ||||
−0.504826 | + | 0.863221i | \(0.668443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39429e6 | 0.236212 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.83434e6 | −1.13548 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −956448. | −0.157375 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 163577. | 0.0264014 | 0.0132007 | − | 0.999913i | \(-0.495798\pi\) | ||||
0.0132007 | + | 0.999913i | \(0.495798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.95232e6 | 0.471965 | 0.235983 | − | 0.971757i | \(-0.424169\pi\) | ||||
0.235983 | + | 0.971757i | \(0.424169\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.15253e7 | −1.80770 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.63511e6 | 1.03088 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.10607e6 | 0.778518 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.85219e6 | −1.48816 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.40791e6 | −0.208738 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.58390e6 | −1.40783 | −0.703913 | − | 0.710286i | \(-0.748566\pi\) | ||||
−0.703913 | + | 0.710286i | \(0.748566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.56170e6 | 0.225219 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.21781e7 | −1.74025 | −0.870127 | − | 0.492827i | \(-0.835964\pi\) | ||||
−0.870127 | + | 0.492827i | \(0.835964\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.53822e6 | 0.356164 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.44939e6 | 0.201545 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.32679e6 | −0.727491 | −0.363745 | − | 0.931498i | \(-0.618502\pi\) | ||||
−0.363745 | + | 0.931498i | \(0.618502\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.57210e6 | −0.889559 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.23899e6 | −1.09548 | −0.547738 | − | 0.836650i | \(-0.684511\pi\) | ||||
−0.547738 | + | 0.836650i | \(0.684511\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.21849e7 | −2.92373 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.42410e6 | −0.961309 | −0.480655 | − | 0.876910i | \(-0.659601\pi\) | ||||
−0.480655 | + | 0.876910i | \(0.659601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 288553. | 0.0370370 | 0.0185185 | − | 0.999829i | \(-0.494105\pi\) | ||||
0.0185185 | + | 0.999829i | \(0.494105\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.68154e7 | 2.12099 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 933299. | 0.116703 | 0.0583514 | − | 0.998296i | \(-0.481416\pi\) | ||||
0.0583514 | + | 0.998296i | \(0.481416\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.67245e6 | 0.205548 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.59718e6 | −0.316469 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.15424e6 | 0.976761 | 0.488381 | − | 0.872631i | \(-0.337588\pi\) | ||||
0.488381 | + | 0.872631i | \(0.337588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.40517e6 | 1.11707 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.18214e6 | −0.254828 | −0.127414 | − | 0.991850i | \(-0.540668\pi\) | ||||
−0.127414 | + | 0.991850i | \(0.540668\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.63760e6 | 0.652833 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.85991e6 | 0.325675 | 0.162838 | − | 0.986653i | \(-0.447935\pi\) | ||||
0.162838 | + | 0.986653i | \(0.447935\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.52613e7 | −1.72347 | −0.861737 | − | 0.507355i | \(-0.830623\pi\) | ||||
−0.861737 | + | 0.507355i | \(0.830623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.35160e7 | 1.50128 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.37356e6 | −0.261474 | −0.130737 | − | 0.991417i | \(-0.541734\pi\) | ||||
−0.130737 | + | 0.991417i | \(0.541734\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.56845e6 | −0.386702 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.21002e6 | −0.452515 | −0.226258 | − | 0.974068i | \(-0.572649\pi\) | ||||
−0.226258 | + | 0.974068i | \(0.572649\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.19579e6 | −0.337960 | −0.168980 | − | 0.985619i | \(-0.554047\pi\) | ||||
−0.168980 | + | 0.985619i | \(0.554047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.30206e7 | 1.36586 | 0.682930 | − | 0.730484i | \(-0.260706\pi\) | ||||
0.682930 | + | 0.730484i | \(0.260706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.54960e6 | −0.263179 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.66820e6 | −0.273224 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.93625e7 | 1.95135 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.44185e7 | 1.44161 | 0.720803 | − | 0.693140i | \(-0.243773\pi\) | ||||
0.720803 | + | 0.693140i | \(0.243773\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.37600e7 | 2.33837 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.25281e6 | −0.512913 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.40822e6 | −0.327629 | −0.163815 | − | 0.986491i | \(-0.552380\pi\) | ||||
−0.163815 | + | 0.986491i | \(0.552380\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.43017e7 | −1.36414 | −0.682070 | − | 0.731287i | \(-0.738920\pi\) | ||||
−0.682070 | + | 0.731287i | \(0.738920\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.59891e7 | −1.50163 | −0.750815 | − | 0.660512i | \(-0.770339\pi\) | ||||
−0.750815 | + | 0.660512i | \(0.770339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 505440. | 0.0471040 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.83032e7 | 1.67974 | 0.839872 | − | 0.542785i | \(-0.182630\pi\) | ||||
0.839872 | + | 0.542785i | \(0.182630\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.35924e7 | 1.23793 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.82724e6 | −0.432997 | −0.216499 | − | 0.976283i | \(-0.569464\pi\) | ||||
−0.216499 | + | 0.976283i | \(0.569464\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.45127e7 | −1.29195 | −0.645973 | − | 0.763360i | \(-0.723548\pi\) | ||||
−0.645973 | + | 0.763360i | \(0.723548\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.60052e6 | −0.403416 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.10106e6 | −0.443962 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −94266.2 | −0.00808257 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.23273e6 | −0.445339 | −0.222670 | − | 0.974894i | \(-0.571477\pi\) | ||||
−0.222670 | + | 0.974894i | \(0.571477\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.31889e6 | −0.278305 | −0.139153 | − | 0.990271i | \(-0.544438\pi\) | ||||
−0.139153 | + | 0.990271i | \(0.544438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −374593. | −0.0311807 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 350257. | 0.0287300 | 0.0143650 | − | 0.999897i | \(-0.495427\pi\) | ||||
0.0143650 | + | 0.999897i | \(0.495427\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.39734e7 | −1.95211 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.68993e6 | −0.777629 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.62745e6 | 0.767037 | 0.383518 | − | 0.923533i | \(-0.374712\pi\) | ||||
0.383518 | + | 0.923533i | \(0.374712\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.61112e7 | 1.26522 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.42144e7 | 2.66764 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.75325e7 | −1.34756 | −0.673782 | − | 0.738930i | \(-0.735332\pi\) | ||||
−0.673782 | + | 0.738930i | \(0.735332\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.58006e7 | −1.20583 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.27330e6 | 0.246285 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.32158e6 | 0.397581 | 0.198790 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198790 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.89016e7 | −1.39243 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.55830e6 | −0.187149 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.74700e7 | −1.26029 | −0.630146 | − | 0.776477i | \(-0.717005\pi\) | ||||
−0.630146 | + | 0.776477i | \(0.717005\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.24759e6 | −0.161019 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.56212e6 | −0.463660 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.86973e6 | 0.411891 | 0.205945 | − | 0.978563i | \(-0.433973\pi\) | ||||
0.205945 | + | 0.978563i | \(0.433973\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.40379e7 | −3.04813 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.60294e6 | −0.385173 | −0.192587 | − | 0.981280i | \(-0.561688\pi\) | ||||
−0.192587 | + | 0.981280i | \(0.561688\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.47405e6 | 0.371227 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.56792e6 | 0.375044 | 0.187522 | − | 0.982260i | \(-0.439954\pi\) | ||||
0.187522 | + | 0.982260i | \(0.439954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.78484e6 | 0.251522 | 0.125761 | − | 0.992061i | \(-0.459863\pi\) | ||||
0.125761 | + | 0.992061i | \(0.459863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.06219e7 | 2.02135 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.24006e6 | −0.211032 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.76657e6 | 0.437793 | 0.218897 | − | 0.975748i | \(-0.429754\pi\) | ||||
0.218897 | + | 0.975748i | \(0.429754\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.83018e7 | 2.44541 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.46970e7 | 1.56640 | 0.783202 | − | 0.621768i | \(-0.213585\pi\) | ||||
0.783202 | + | 0.621768i | \(0.213585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.00870e7 | 1.88329 | 0.941644 | − | 0.336611i | \(-0.109281\pi\) | ||||
0.941644 | + | 0.336611i | \(0.109281\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 513590. | 0.0319378 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.88576e6 | 0.115744 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.25118e6 | 0.198256 | 0.0991278 | − | 0.995075i | \(-0.468395\pi\) | ||||
0.0991278 | + | 0.995075i | \(0.468395\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.30628e6 | 0.199017 | 0.0995087 | − | 0.995037i | \(-0.468273\pi\) | ||||
0.0995087 | + | 0.995037i | \(0.468273\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.43154e7 | −1.45421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.79204e7 | −1.64846 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.09018e6 | −0.239946 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.02624e6 | 0.117359 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.70156e7 | −0.979286 | −0.489643 | − | 0.871923i | \(-0.662873\pi\) | ||||
−0.489643 | + | 0.871923i | \(0.662873\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.29588e6 | −0.414607 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −351701. | −0.0198605 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.31267e7 | 0.731999 | 0.365999 | − | 0.930615i | \(-0.380727\pi\) | ||||
0.365999 | + | 0.930615i | \(0.380727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.39112e7 | −1.32506 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.23968e6 | −0.232030 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.24566e6 | 0.502862 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.90313e7 | −1.55954 | −0.779768 | − | 0.626068i | \(-0.784663\pi\) | ||||
−0.779768 | + | 0.626068i | \(0.784663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.70345e7 | 1.44333 | 0.721666 | − | 0.692241i | \(-0.243377\pi\) | ||||
0.721666 | + | 0.692241i | \(0.243377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.69654e6 | 0.511355 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.59368e7 | 1.88358 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.14836e7 | −1.11237 | −0.556185 | − | 0.831059i | \(-0.687735\pi\) | ||||
−0.556185 | + | 0.831059i | \(0.687735\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.46282e7 | 1.26745 | 0.633727 | − | 0.773557i | \(-0.281524\pi\) | ||||
0.633727 | + | 0.773557i | \(0.281524\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.10933e6 | 0.259777 | 0.129888 | − | 0.991529i | \(-0.458538\pi\) | ||||
0.129888 | + | 0.991529i | \(0.458538\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.04805e7 | 1.54041 | 0.770205 | − | 0.637797i | \(-0.220154\pi\) | ||||
0.770205 | + | 0.637797i | \(0.220154\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.51977e7 | −1.75753 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.70838e7 | 1.34429 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.36807e7 | 0.670969 | 0.335485 | − | 0.942046i | \(-0.391100\pi\) | ||||
0.335485 | + | 0.942046i | \(0.391100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.85205e7 | −0.902948 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.31964e7 | 1.11758 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.44498e6 | 0.212893 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.17545e7 | 1.50308 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.44079e7 | 1.61914 | 0.809572 | − | 0.587020i | \(-0.199699\pi\) | ||||
0.809572 | + | 0.587020i | \(0.199699\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.73555e7 | 1.27231 | 0.636155 | − | 0.771561i | \(-0.280524\pi\) | ||||
0.636155 | + | 0.771561i | \(0.280524\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.37818e6 | 0.248687 | 0.124343 | − | 0.992239i | \(-0.460318\pi\) | ||||
0.124343 | + | 0.992239i | \(0.460318\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.64604e7 | −1.20940 | −0.604699 | − | 0.796454i | \(-0.706707\pi\) | ||||
−0.604699 | + | 0.796454i | \(0.706707\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −373248. | −0.0169612 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.40723e6 | −0.197978 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.04233e7 | 0.912181 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.90239e6 | 0.172310 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.77108e7 | −0.777571 | −0.388785 | − | 0.921328i | \(-0.627105\pi\) | ||||
−0.388785 | + | 0.921328i | \(0.627105\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.04035e7 | 1.31973 | 0.659864 | − | 0.751385i | \(-0.270614\pi\) | ||||
0.659864 | + | 0.751385i | \(0.270614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.93557e7 | −1.26704 | −0.633521 | − | 0.773726i | \(-0.718391\pi\) | ||||
−0.633521 | + | 0.773726i | \(0.718391\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.64563e6 | −0.112907 | −0.0564533 | − | 0.998405i | \(-0.517979\pi\) | ||||
−0.0564533 | + | 0.998405i | \(0.517979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.81388e6 | 0.331598 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.95126e7 | 0.818815 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.33588e7 | 3.06122 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.37622e6 | 0.304393 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.49296e7 | −2.66459 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.88519e7 | 1.17099 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.07393e7 | −0.837095 | −0.418548 | − | 0.908195i | \(-0.637461\pi\) | ||||
−0.418548 | + | 0.908195i | \(0.637461\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.55091e7 | 1.81678 | 0.908390 | − | 0.418123i | \(-0.137312\pi\) | ||||
0.908390 | + | 0.418123i | \(0.137312\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.08550e6 | −0.201910 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.47010e6 | 0.175547 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.89012e7 | −0.738247 | −0.369123 | − | 0.929380i | \(-0.620342\pi\) | ||||
−0.369123 | + | 0.929380i | \(0.620342\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.52602e7 | −0.589597 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.08497e7 | 1.56977 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.08391e7 | 1.17236 | 0.586181 | − | 0.810180i | \(-0.300631\pi\) | ||||
0.586181 | + | 0.810180i | \(0.300631\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.87228e7 | 1.08606 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.71425e7 | −0.641277 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.36296e6 | −0.199552 | −0.0997758 | − | 0.995010i | \(-0.531813\pi\) | ||||
−0.0997758 | + | 0.995010i | \(0.531813\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.76785e7 | −1.38714 | −0.693569 | − | 0.720390i | \(-0.743963\pi\) | ||||
−0.693569 | + | 0.720390i | \(0.743963\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.61116e7 | 2.05482 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.96221e7 | 0.711001 | 0.355501 | − | 0.934676i | \(-0.384310\pi\) | ||||
0.355501 | + | 0.934676i | \(0.384310\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.58180e7 | −0.570146 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.36730e7 | −0.487676 | −0.243838 | − | 0.969816i | \(-0.578407\pi\) | ||||
−0.243838 | + | 0.969816i | \(0.578407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.13450e7 | 1.46695 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.88406e6 | −0.276824 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.29717e6 | −0.0453093 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.34240e7 | −0.464048 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.63824e7 | −1.25119 | −0.625597 | − | 0.780146i | \(-0.715145\pi\) | ||||
−0.625597 | + | 0.780146i | \(0.715145\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.46886e6 | 0.322292 | 0.161146 | − | 0.986931i | \(-0.448481\pi\) | ||||
0.161146 | + | 0.986931i | \(0.448481\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.29844e6 | 0.179418 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.59889e7 | −1.20623 | −0.603117 | − | 0.797653i | \(-0.706075\pi\) | ||||
−0.603117 | + | 0.797653i | \(0.706075\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.75267e6 | 0.258520 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.60556e7 | −0.860039 | −0.430019 | − | 0.902820i | \(-0.641493\pi\) | ||||
−0.430019 | + | 0.902820i | \(0.641493\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.76279e7 | −1.89253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.22222e7 | −2.34790 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.92232e7 | −0.621788 | −0.310894 | − | 0.950445i | \(-0.600628\pi\) | ||||
−0.310894 | + | 0.950445i | \(0.600628\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.69561e7 | −1.82382 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.93287e7 | 0.934448 | 0.467224 | − | 0.884139i | \(-0.345254\pi\) | ||||
0.467224 | + | 0.884139i | \(0.345254\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.6.a.p.1.1 | 2 | ||
3.2 | odd | 2 | inner | 432.6.a.p.1.2 | 2 | ||
4.3 | odd | 2 | 108.6.a.d.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 108.6.a.d.1.2 | yes | 2 | ||
36.7 | odd | 6 | 324.6.e.e.109.2 | 4 | |||
36.11 | even | 6 | 324.6.e.e.109.1 | 4 | |||
36.23 | even | 6 | 324.6.e.e.217.1 | 4 | |||
36.31 | odd | 6 | 324.6.e.e.217.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.a.d.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
108.6.a.d.1.2 | yes | 2 | 12.11 | even | 2 | ||
324.6.e.e.109.1 | 4 | 36.11 | even | 6 | |||
324.6.e.e.109.2 | 4 | 36.7 | odd | 6 | |||
324.6.e.e.217.1 | 4 | 36.23 | even | 6 | |||
324.6.e.e.217.2 | 4 | 36.31 | odd | 6 | |||
432.6.a.p.1.1 | 2 | 1.1 | even | 1 | trivial | ||
432.6.a.p.1.2 | 2 | 3.2 | odd | 2 | inner |