Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(1,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.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: | \(53.8889634572\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 336.1 |
$q$-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 | ||||||||
\(5\) | 26.0000 | 0.465102 | 0.232551 | − | 0.972584i | \(-0.425293\pi\) | ||||
0.232551 | + | 0.972584i | \(0.425293\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −664.000 | −1.65457 | −0.827287 | − | 0.561779i | \(-0.810117\pi\) | ||||
−0.827287 | + | 0.561779i | \(0.810117\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 318.000 | 0.521878 | 0.260939 | − | 0.965355i | \(-0.415968\pi\) | ||||
0.260939 | + | 0.965355i | \(0.415968\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −234.000 | −0.268527 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1582.00 | 1.32765 | 0.663826 | − | 0.747887i | \(-0.268932\pi\) | ||||
0.663826 | + | 0.747887i | \(0.268932\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −236.000 | −0.149978 | −0.0749891 | − | 0.997184i | \(-0.523892\pi\) | ||||
−0.0749891 | + | 0.997184i | \(0.523892\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −441.000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2212.00 | −0.871898 | −0.435949 | − | 0.899971i | \(-0.643587\pi\) | ||||
−0.435949 | + | 0.899971i | \(0.643587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2449.00 | −0.783680 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4954.00 | −1.09386 | −0.546929 | − | 0.837179i | \(-0.684203\pi\) | ||||
−0.546929 | + | 0.837179i | \(0.684203\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7128.00 | 1.33218 | 0.666091 | − | 0.745871i | \(-0.267966\pi\) | ||||
0.666091 | + | 0.745871i | \(0.267966\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5976.00 | 0.955269 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1274.00 | 0.175792 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4358.00 | 0.523339 | 0.261669 | − | 0.965158i | \(-0.415727\pi\) | ||||
0.261669 | + | 0.965158i | \(0.415727\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2862.00 | −0.301306 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10542.0 | 0.979407 | 0.489704 | − | 0.871889i | \(-0.337105\pi\) | ||||
0.489704 | + | 0.871889i | \(0.337105\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8452.00 | 0.697089 | 0.348545 | − | 0.937292i | \(-0.386676\pi\) | ||||
0.348545 | + | 0.937292i | \(0.386676\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2106.00 | 0.155034 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5352.00 | −0.353404 | −0.176702 | − | 0.984264i | \(-0.556543\pi\) | ||||
−0.176702 | + | 0.984264i | \(0.556543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14238.0 | −0.766520 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −33354.0 | −1.63102 | −0.815508 | − | 0.578746i | \(-0.803542\pi\) | ||||
−0.815508 | + | 0.578746i | \(0.803542\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17264.0 | −0.769546 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2124.00 | 0.0865899 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15436.0 | 0.577304 | 0.288652 | − | 0.957434i | \(-0.406793\pi\) | ||||
0.288652 | + | 0.957434i | \(0.406793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36762.0 | −1.26495 | −0.632477 | − | 0.774579i | \(-0.717962\pi\) | ||||
−0.632477 | + | 0.774579i | \(0.717962\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3969.00 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8268.00 | 0.242726 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −40972.0 | −1.11506 | −0.557532 | − | 0.830155i | \(-0.688252\pi\) | ||||
−0.557532 | + | 0.830155i | \(0.688252\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19908.0 | 0.503390 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9092.00 | 0.214049 | 0.107025 | − | 0.994256i | \(-0.465868\pi\) | ||||
0.107025 | + | 0.994256i | \(0.465868\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −73454.0 | −1.61327 | −0.806637 | − | 0.591047i | \(-0.798715\pi\) | ||||
−0.806637 | + | 0.591047i | \(0.798715\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22041.0 | 0.452458 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −32536.0 | −0.625370 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −89400.0 | −1.61165 | −0.805823 | − | 0.592156i | \(-0.798277\pi\) | ||||
−0.805823 | + | 0.592156i | \(0.798277\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6428.00 | 0.102419 | 0.0512095 | − | 0.998688i | \(-0.483692\pi\) | ||||
0.0512095 | + | 0.998688i | \(0.483692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41132.0 | 0.617494 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 44586.0 | 0.631539 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −122658. | −1.64142 | −0.820712 | − | 0.571342i | \(-0.806423\pi\) | ||||
−0.820712 | + | 0.571342i | \(0.806423\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15582.0 | 0.197251 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −64152.0 | −0.769135 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6136.00 | −0.0697552 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 21370.0 | 0.230608 | 0.115304 | − | 0.993330i | \(-0.463216\pi\) | ||||
0.115304 | + | 0.993330i | \(0.463216\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −53784.0 | −0.551525 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −36814.0 | −0.359095 | −0.179548 | − | 0.983749i | \(-0.557463\pi\) | ||||
−0.179548 | + | 0.983749i | \(0.557463\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −104528. | −0.970822 | −0.485411 | − | 0.874286i | \(-0.661330\pi\) | ||||
−0.485411 | + | 0.874286i | \(0.661330\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11466.0 | −0.101494 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −214440. | −1.81070 | −0.905350 | − | 0.424667i | \(-0.860391\pi\) | ||||
−0.905350 | + | 0.424667i | \(0.860391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 28798.0 | 0.232165 | 0.116082 | − | 0.993240i | \(-0.462966\pi\) | ||||
0.116082 | + | 0.993240i | \(0.462966\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −39222.0 | −0.302150 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −56014.0 | −0.412668 | −0.206334 | − | 0.978482i | \(-0.566153\pi\) | ||||
−0.206334 | + | 0.978482i | \(0.566153\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −57512.0 | −0.405521 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 25758.0 | 0.173959 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 77518.0 | 0.501805 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 279845. | 1.73762 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −94878.0 | −0.565461 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −144924. | −0.829593 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −185400. | −1.02000 | −0.510000 | − | 0.860174i | \(-0.670355\pi\) | ||||
−0.510000 | + | 0.860174i | \(0.670355\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −76068.0 | −0.402465 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −64532.0 | −0.328547 | −0.164273 | − | 0.986415i | \(-0.552528\pi\) | ||||
−0.164273 | + | 0.986415i | \(0.552528\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11564.0 | −0.0566864 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −18954.0 | −0.0895089 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 152930. | 0.696131 | 0.348066 | − | 0.937470i | \(-0.386839\pi\) | ||||
0.348066 | + | 0.937470i | \(0.386839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 343460. | 1.50778 | 0.753892 | − | 0.656998i | \(-0.228174\pi\) | ||||
0.753892 | + | 0.656998i | \(0.228174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 48168.0 | 0.204038 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −211152. | −0.863486 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −128804. | −0.508756 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −21609.0 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −174858. | −0.645238 | −0.322619 | − | 0.946529i | \(-0.604563\pi\) | ||||
−0.322619 | + | 0.946529i | \(0.604563\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 452552. | 1.61520 | 0.807600 | − | 0.589731i | \(-0.200766\pi\) | ||||
0.807600 | + | 0.589731i | \(0.200766\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 128142. | 0.442551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 185328. | 0.619601 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −499066. | −1.61588 | −0.807940 | − | 0.589265i | \(-0.799417\pi\) | ||||
−0.807940 | + | 0.589265i | \(0.799417\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 300186. | 0.941668 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −108388. | −0.329546 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 475588. | 1.40204 | 0.701022 | − | 0.713139i | \(-0.252727\pi\) | ||||
0.701022 | + | 0.713139i | \(0.252727\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 155376. | 0.444298 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −120224. | −0.333580 | −0.166790 | − | 0.985992i | \(-0.553340\pi\) | ||||
−0.166790 | + | 0.985992i | \(0.553340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −270169. | −0.727644 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19116.0 | −0.0499927 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 508874. | 1.29269 | 0.646346 | − | 0.763045i | \(-0.276296\pi\) | ||||
0.646346 | + | 0.763045i | \(0.276296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −120001. | −0.296203 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −138924. | −0.333307 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −487560. | −1.13735 | −0.568677 | − | 0.822561i | \(-0.692544\pi\) | ||||
−0.568677 | + | 0.822561i | \(0.692544\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −544410. | −1.23518 | −0.617589 | − | 0.786501i | \(-0.711891\pi\) | ||||
−0.617589 | + | 0.786501i | \(0.711891\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 330858. | 0.730321 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 113308. | 0.243406 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.05045e6 | −2.19670 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −376404. | −0.746570 | −0.373285 | − | 0.927717i | \(-0.621769\pi\) | ||||
−0.373285 | + | 0.927717i | \(0.621769\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 844946. | 1.63281 | 0.816405 | − | 0.577480i | \(-0.195964\pi\) | ||||
0.816405 | + | 0.577480i | \(0.195964\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −74412.0 | −0.140138 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −492794. | −0.904690 | −0.452345 | − | 0.891843i | \(-0.649412\pi\) | ||||
−0.452345 | + | 0.891843i | \(0.649412\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 914776. | 1.63750 | 0.818751 | − | 0.574148i | \(-0.194667\pi\) | ||||
0.818751 | + | 0.574148i | \(0.194667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 368748. | 0.643783 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −242746. | −0.413440 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 274092. | 0.455524 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −179172. | −0.290633 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 156704. | 0.248150 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −311780. | −0.482106 | −0.241053 | − | 0.970512i | \(-0.577493\pi\) | ||||
−0.241053 | + | 0.970512i | \(0.577493\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −81828.0 | −0.123581 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 219752. | 0.324218 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 349272. | 0.503517 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 661086. | 0.931425 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 503076. | 0.692872 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.28776e6 | 1.73409 | 0.867047 | − | 0.498226i | \(-0.166015\pi\) | ||||
0.867047 | + | 0.498226i | \(0.166015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −198369. | −0.261227 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.28905e6 | −1.66037 | −0.830187 | − | 0.557485i | \(-0.811766\pi\) | ||||
−0.830187 | + | 0.557485i | \(0.811766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 678214. | 0.854630 | 0.427315 | − | 0.904103i | \(-0.359460\pi\) | ||||
0.427315 | + | 0.904103i | \(0.359460\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 292824. | 0.361058 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.11731e6 | −1.34829 | −0.674146 | − | 0.738598i | \(-0.735488\pi\) | ||||
−0.674146 | + | 0.738598i | \(0.735488\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −139152. | −0.164369 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 804600. | 0.930485 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.26196e6 | 1.42906 | 0.714528 | − | 0.699606i | \(-0.246641\pi\) | ||||
0.714528 | + | 0.699606i | \(0.246641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 948218. | 1.05164 | 0.525818 | − | 0.850597i | \(-0.323759\pi\) | ||||
0.525818 | + | 0.850597i | \(0.323759\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 62426.0 | 0.0664432 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −75048.0 | −0.0782703 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −57852.0 | −0.0591317 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 486396. | 0.487310 | 0.243655 | − | 0.969862i | \(-0.421653\pi\) | ||||
0.243655 | + | 0.969862i | \(0.421653\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.46877e6 | 1.44262 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −370188. | −0.356510 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.03910e6 | −0.981349 | −0.490675 | − | 0.871343i | \(-0.663250\pi\) | ||||
−0.490675 | + | 0.871343i | \(0.663250\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 213542. | 0.197803 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −401274. | −0.364619 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.35104e6 | −1.20443 | −0.602213 | − | 0.798335i | \(-0.705714\pi\) | ||||
−0.602213 | + | 0.798335i | \(0.705714\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −867204. | −0.758589 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.10392e6 | 0.947677 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.11811e6 | −0.942115 | −0.471057 | − | 0.882103i | \(-0.656128\pi\) | ||||
−0.471057 | + | 0.882103i | \(0.656128\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 190104. | 0.157242 | 0.0786209 | − | 0.996905i | \(-0.474948\pi\) | ||||
0.0786209 | + | 0.996905i | \(0.474948\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −140238. | −0.113883 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.62614e6 | 1.29666 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −200506. | −0.157010 | −0.0785051 | − | 0.996914i | \(-0.525015\pi\) | ||||
−0.0785051 | + | 0.996914i | \(0.525015\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 577368. | 0.444061 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.09237e6 | 0.825285 | 0.412643 | − | 0.910893i | \(-0.364606\pi\) | ||||
0.412643 | + | 0.910893i | \(0.364606\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.81258e6 | −1.34534 | −0.672669 | − | 0.739944i | \(-0.734852\pi\) | ||||
−0.672669 | + | 0.739944i | \(0.734852\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 55224.0 | 0.0402732 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 516558. | 0.370181 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.08287e6 | 0.762659 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −192330. | −0.133142 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.10031e6 | 1.42927 | 0.714634 | − | 0.699499i | \(-0.246593\pi\) | ||||
0.714634 | + | 0.699499i | \(0.246593\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 401336. | 0.268505 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 484056. | 0.318423 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −703416. | −0.455024 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 414148. | 0.263475 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 331326. | 0.207324 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −955812. | −0.588333 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.64104e6 | 0.993743 | 0.496872 | − | 0.867824i | \(-0.334482\pi\) | ||||
0.496872 | + | 0.867824i | \(0.334482\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 940752. | 0.560504 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 945232. | 0.554163 | 0.277081 | − | 0.960846i | \(-0.410633\pi\) | ||||
0.277081 | + | 0.960846i | \(0.410633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 415354. | 0.239639 | 0.119820 | − | 0.992796i | \(-0.461768\pi\) | ||||
0.119820 | + | 0.992796i | \(0.461768\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 103194. | 0.0585974 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.18481e6 | 0.662220 | 0.331110 | − | 0.943592i | \(-0.392577\pi\) | ||||
0.331110 | + | 0.943592i | \(0.392577\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.28946e6 | 1.80987 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.92996e6 | 1.04541 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −373352. | −0.199119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −778782. | −0.408985 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −259182. | −0.134040 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −262248. | −0.133574 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.37155e6 | −0.688083 | −0.344042 | − | 0.938954i | \(-0.611796\pi\) | ||||
−0.344042 | + | 0.938954i | \(0.611796\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 352998. | 0.174446 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.06527e6 | −0.518619 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 963522. | 0.462154 | 0.231077 | − | 0.972935i | \(-0.425775\pi\) | ||||
0.231077 | + | 0.972935i | \(0.425775\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 504126. | 0.238254 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.73299e6 | −2.20419 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 517608. | 0.234128 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.57731e6 | −1.14906 | −0.574531 | − | 0.818483i | \(-0.694815\pi\) | ||||
−0.574531 | + | 0.818483i | \(0.694815\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.06751e6 | −1.34810 | −0.674051 | − | 0.738684i | \(-0.735447\pi\) | ||||
−0.674051 | + | 0.738684i | \(0.735447\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −231822. | −0.100435 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.10144e6 | −1.32473 | −0.662364 | − | 0.749182i | \(-0.730447\pi\) | ||||
−0.662364 | + | 0.749182i | \(0.730447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 236392. | 0.0995547 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −697662. | −0.289717 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 327508. | 0.134118 | 0.0670588 | − | 0.997749i | \(-0.478638\pi\) | ||||
0.0670588 | + | 0.997749i | \(0.478638\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.42040e6 | −0.977507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.51860e6 | −1.00321 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.90980e6 | −0.750337 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.86739e6 | 1.11128 | 0.555638 | − | 0.831424i | \(-0.312474\pi\) | ||||
0.555638 | + | 0.831424i | \(0.312474\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 853902. | 0.326469 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.63435e6 | −0.616466 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.58029e6 | 1.33244 | 0.666218 | − | 0.745757i | \(-0.267912\pi\) | ||||
0.666218 | + | 0.745757i | \(0.267912\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.30432e6 | 0.478966 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.57537e6 | −0.570860 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.64235e6 | −0.587310 | −0.293655 | − | 0.955912i | \(-0.594872\pi\) | ||||
−0.293655 | + | 0.955912i | \(0.594872\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.66860e6 | 0.588898 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.05698e6 | 0.716527 | 0.358263 | − | 0.933621i | \(-0.383369\pi\) | ||||
0.358263 | + | 0.933621i | \(0.383369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −845936. | −0.290861 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 684612. | 0.232363 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 616142. | 0.206446 | 0.103223 | − | 0.994658i | \(-0.467084\pi\) | ||||
0.103223 | + | 0.994658i | \(0.467084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.49938e6 | −1.15758 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 580788. | 0.189686 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.32440e6 | −0.749580 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.19212e6 | 0.698052 | 0.349026 | − | 0.937113i | \(-0.386513\pi\) | ||||
0.349026 | + | 0.937113i | \(0.386513\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 104076. | 0.0327279 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.28454e6 | 1.02003 | 0.510015 | − | 0.860165i | \(-0.329640\pi\) | ||||
0.510015 | + | 0.860165i | \(0.329640\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.26670e6 | 0.695236 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 170586. | 0.0516780 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.89371e6 | −0.865903 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.61219e6 | −1.06773 | −0.533866 | − | 0.845569i | \(-0.679261\pi\) | ||||
−0.533866 | + | 0.845569i | \(0.679261\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.37637e6 | −0.401912 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 756364. | 0.218200 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 167128. | 0.0476353 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.09114e6 | −0.870520 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.41489e6 | −1.50680 | −0.753398 | − | 0.657564i | \(-0.771587\pi\) | ||||
−0.753398 | + | 0.657564i | \(0.771587\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.60629e6 | 0.991644 | 0.495822 | − | 0.868424i | \(-0.334867\pi\) | ||||
0.495822 | + | 0.868424i | \(0.334867\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −433512. | −0.117801 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.87432e6 | −1.04045 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.80134e6 | −0.478107 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.90037e6 | 0.498534 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.78214e6 | 0.721416 | 0.360708 | − | 0.932679i | \(-0.382535\pi\) | ||||
0.360708 | + | 0.932679i | \(0.382535\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.27619e6 | 1.60871 | 0.804353 | − | 0.594152i | \(-0.202512\pi\) | ||||
0.804353 | + | 0.594152i | \(0.202512\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.15924e6 | 0.293730 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 522032. | 0.130766 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −641592. | −0.158890 | −0.0794452 | − | 0.996839i | \(-0.525315\pi\) | ||||
−0.0794452 | + | 0.996839i | \(0.525315\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.05546e6 | −1.46601 | −0.733006 | − | 0.680222i | \(-0.761883\pi\) | ||||
−0.733006 | + | 0.680222i | \(0.761883\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.18911e6 | −0.763430 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.57372e6 | 0.372528 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.16681e6 | −1.20950 | −0.604752 | − | 0.796414i | \(-0.706728\pi\) | ||||
−0.604752 | + | 0.796414i | \(0.706728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.99989e6 | −1.62050 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.07297e6 | −0.932536 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 405132. | 0.0917420 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −227798. | −0.0510222 | −0.0255111 | − | 0.999675i | \(-0.508121\pi\) | ||||
−0.0255111 | + | 0.999675i | \(0.508121\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.15328e6 | −0.255507 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 585146. | 0.128237 | 0.0641183 | − | 0.997942i | \(-0.479577\pi\) | ||||
0.0641183 | + | 0.997942i | \(0.479577\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.41454e6 | 0.740251 | 0.370126 | − | 0.928982i | \(-0.379315\pi\) | ||||
0.370126 | + | 0.928982i | \(0.379315\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.66795e6 | −0.357727 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −716300. | −0.151986 | −0.0759929 | − | 0.997108i | \(-0.524213\pi\) | ||||
−0.0759929 | + | 0.997108i | \(0.524213\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.00763e6 | −0.421455 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.49159e6 | 0.932928 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.61213e6 | −1.15339 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 577964. | 0.117535 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.70167e6 | −0.543672 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.24092e6 | −1.04368 | −0.521842 | − | 0.853042i | \(-0.674755\pi\) | ||||
−0.521842 | + | 0.853042i | \(0.674755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.38584e6 | 0.273119 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 975492. | 0.190264 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 555620. | 0.107256 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.11702e6 | −0.213421 | −0.106710 | − | 0.994290i | \(-0.534032\pi\) | ||||
−0.106710 | + | 0.994290i | \(0.534032\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.28029e6 | −0.809471 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.34458e6 | −0.251699 | −0.125850 | − | 0.992049i | \(-0.540166\pi\) | ||||
−0.125850 | + | 0.992049i | \(0.540166\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.83723e6 | −1.45226 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.39838e6 | −0.256515 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 445508. | 0.0809030 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.54648e6 | 1.17695 | 0.588473 | − | 0.808517i | \(-0.299729\pi\) | ||||
0.588473 | + | 0.808517i | \(0.299729\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.08202e6 | 0.192592 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.22050e6 | 1.44870 | 0.724350 | − | 0.689432i | \(-0.242140\pi\) | ||||
0.724350 | + | 0.689432i | \(0.242140\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −957164. | −0.167016 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.43152e6 | 0.420105 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.11045e6 | −0.874308 | −0.437154 | − | 0.899387i | \(-0.644013\pi\) | ||||
−0.437154 | + | 0.899387i | \(0.644013\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.59925e6 | −0.609760 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 172044. | 0.0288633 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.71773e6 | −0.451531 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.55373e6 | 0.584733 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.57987e6 | −0.746336 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.69999e6 | 1.56559 | 0.782793 | − | 0.622282i | \(-0.213794\pi\) | ||||
0.782793 | + | 0.622282i | \(0.213794\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.17295e6 | 0.507234 | 0.253617 | − | 0.967305i | \(-0.418380\pi\) | ||||
0.253617 | + | 0.967305i | \(0.418380\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.08001e6 | 0.171013 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.12765e7 | 1.76867 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.54340e6 | −0.239794 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.25032e6 | 0.192435 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.35236e6 | 0.511131 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.57544e6 | −0.842160 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.38804e6 | 0.656651 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.59426e6 | −0.236368 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.62575e6 | −0.973289 | −0.486644 | − | 0.873600i | \(-0.661779\pi\) | ||||
−0.486644 | + | 0.873600i | \(0.661779\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.89969e6 | 0.713131 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 748748. | 0.107980 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.84707e6 | −0.549745 | −0.274873 | − | 0.961481i | \(-0.588636\pi\) | ||||
−0.274873 | + | 0.961481i | \(0.588636\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.97772e6 | −0.421651 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.16914e6 | 0.164055 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.38060e6 | −0.609145 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.01977e6 | −0.140531 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.00176e6 | 0.683101 | 0.341550 | − | 0.939863i | \(-0.389048\pi\) | ||||
0.341550 | + | 0.939863i | \(0.389048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.68774e6 | 0.363795 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.45403e6 | 1.26826 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.27772e6 | −0.302852 | −0.151426 | − | 0.988469i | \(-0.548386\pi\) | ||||
−0.151426 | + | 0.988469i | \(0.548386\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.45636e6 | −0.191933 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 321489. | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.86979e6 | 1.14850 | 0.574252 | − | 0.818678i | \(-0.305293\pi\) | ||||
0.574252 | + | 0.818678i | \(0.305293\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.40102e7 | −1.79826 | −0.899132 | − | 0.437678i | \(-0.855801\pi\) | ||||
−0.899132 | + | 0.437678i | \(0.855801\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.38764e6 | 0.431033 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.41719e6 | 0.683289 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.75327e6 | 1.09454 | 0.547269 | − | 0.836957i | \(-0.315668\pi\) | ||||
0.547269 | + | 0.836957i | \(0.315668\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.60451e6 | −0.942703 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 314972. | 0.0387108 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.21471e7 | 2.69864 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 669708. | 0.0809088 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.06117e7 | 1.27113 | 0.635564 | − | 0.772048i | \(-0.280768\pi\) | ||||
0.635564 | + | 0.772048i | \(0.280768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.68221e6 | −0.199798 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.43515e6 | 0.522323 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.88552e6 | 0.220188 | 0.110094 | − | 0.993921i | \(-0.464885\pi\) | ||||
0.110094 | + | 0.993921i | \(0.464885\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.01547e6 | 0.233391 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.23298e6 | −0.945413 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.27256e7 | −1.44915 | −0.724573 | − | 0.689198i | \(-0.757963\pi\) | ||||
−0.724573 | + | 0.689198i | \(0.757963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.18846e6 | 0.811801 | 0.405900 | − | 0.913917i | \(-0.366958\pi\) | ||||
0.405900 | + | 0.913917i | \(0.366958\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.31873e6 | −0.371688 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.27597e6 | 0.808170 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.08494e7 | −1.19519 | −0.597593 | − | 0.801800i | \(-0.703876\pi\) | ||||
−0.597593 | + | 0.801800i | \(0.703876\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.18471e6 | 0.238699 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.70194e6 | −0.184434 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.90511e6 | −0.527227 | −0.263614 | − | 0.964628i | \(-0.584914\pi\) | ||||
−0.263614 | + | 0.964628i | \(0.584914\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.46683e6 | −0.262997 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.58445e6 | 0.273310 | 0.136655 | − | 0.990619i | \(-0.456365\pi\) | ||||
0.136655 | + | 0.990619i | \(0.456365\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.99336e6 | 0.523801 | 0.261901 | − | 0.965095i | \(-0.415651\pi\) | ||||
0.261901 | + | 0.965095i | \(0.415651\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.61255e6 | 0.167797 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.01024e6 | −0.620400 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.88510e6 | 0.397834 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.41034e6 | −0.143269 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.89436e6 | 0.694812 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.18219e7 | 1.18199 | 0.590997 | − | 0.806674i | \(-0.298735\pi\) | ||||
0.590997 | + | 0.806674i | \(0.298735\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.80602e6 | 0.278344 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.82040e6 | −0.474404 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 763518. | 0.0745540 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 736452. | 0.0713497 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.47007e6 | −0.525833 | −0.262916 | − | 0.964819i | \(-0.584684\pi\) | ||||
−0.262916 | + | 0.964819i | \(0.584684\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.64934e6 | −0.920386 | −0.460193 | − | 0.887819i | \(-0.652220\pi\) | ||||
−0.460193 | + | 0.887819i | \(0.652220\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.97777e6 | −0.187187 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −292368. | −0.0274580 | −0.0137290 | − | 0.999906i | \(-0.504370\pi\) | ||||
−0.0137290 | + | 0.999906i | \(0.504370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.02495e7 | −0.955193 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.14345e6 | −0.290706 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.94081e6 | 0.636982 | 0.318491 | − | 0.947926i | \(-0.396824\pi\) | ||||
0.318491 | + | 0.947926i | \(0.396824\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.67783e6 | −0.152808 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.94977e6 | −0.537758 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.32912e7 | 1.19221 | 0.596104 | − | 0.802908i | \(-0.296715\pi\) | ||||
0.596104 | + | 0.802908i | \(0.296715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.05219e6 | 0.182690 | 0.0913448 | − | 0.995819i | \(-0.470883\pi\) | ||||
0.0913448 | + | 0.995819i | \(0.470883\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.52768e6 | −0.400030 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −300664. | −0.0263650 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.09582e7 | 0.953732 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.15898e7 | −1.00118 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.44100e7 | 2.09296 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.57039e7 | −1.33650 | −0.668252 | − | 0.743935i | \(-0.732957\pi\) | ||||
−0.668252 | + | 0.743935i | \(0.732957\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.78532e6 | 0.150819 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −969534. | −0.0813002 | −0.0406501 | − | 0.999173i | \(-0.512943\pi\) | ||||
−0.0406501 | + | 0.999173i | \(0.512943\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.04713e6 | 0.0871618 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.16015e7 | 0.958617 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.49908e7 | 1.22962 | 0.614812 | − | 0.788673i | \(-0.289232\pi\) | ||||
0.614812 | + | 0.788673i | \(0.289232\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.97618e6 | 0.323772 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.10393e6 | −0.493421 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.06066e7 | −0.851191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.16038e6 | 0.570481 | 0.285240 | − | 0.958456i | \(-0.407927\pi\) | ||||
0.285240 | + | 0.958456i | \(0.407927\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.63542e6 | −0.208457 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.92996e6 | 0.701274 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.66774e7 | 1.30031 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.00558e7 | 0.778437 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −91834.0 | −0.00705844 | −0.00352922 | − | 0.999994i | \(-0.501123\pi\) | ||||
−0.00352922 | + | 0.999994i | \(0.501123\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.02849e6 | −0.0784894 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.25237e6 | 0.0948985 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.80389e6 | −0.135725 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.20981e7 | 1.65097 | 0.825487 | − | 0.564422i | \(-0.190901\pi\) | ||||
0.825487 | + | 0.564422i | \(0.190901\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.24140e6 | −0.537216 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.57671e7 | −1.16153 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.48995e6 | −0.401609 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.13576e7 | −0.825066 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.58388e7 | −1.14262 | −0.571308 | − | 0.820736i | \(-0.693564\pi\) | ||||
−0.571308 | + | 0.820736i | \(0.693564\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.12187e6 | −0.366936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.53396e6 | −0.607163 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.21323e7 | 0.857235 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.31418e6 | −0.443078 | −0.221539 | − | 0.975151i | \(-0.571108\pi\) | ||||
−0.221539 | + | 0.975151i | \(0.571108\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.33711e7 | 0.925492 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.93003e6 | 0.476404 | 0.238202 | − | 0.971216i | \(-0.423442\pi\) | ||||
0.238202 | + | 0.971216i | \(0.423442\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −561834. | −0.0383610 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.72054e7 | 1.84496 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.42331e7 | −0.958714 | −0.479357 | − | 0.877620i | \(-0.659130\pi\) | ||||
−0.479357 | + | 0.877620i | \(0.659130\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 675432. | 0.0451894 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.94460e6 | 0.395048 | 0.197524 | − | 0.980298i | \(-0.436710\pi\) | ||||
0.197524 | + | 0.980298i | \(0.436710\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.54631e6 | −0.300102 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 520668. | 0.0341397 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.05076e7 | −0.684380 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 682752. | 0.0441736 | 0.0220868 | − | 0.999756i | \(-0.492969\pi\) | ||||
0.0220868 | + | 0.999756i | \(0.492969\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.37756e6 | −0.281349 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.17664e7 | 0.751233 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.46333e7 | 0.928116 | 0.464058 | − | 0.885805i | \(-0.346393\pi\) | ||||
0.464058 | + | 0.885805i | \(0.346393\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.32189e7 | −0.832897 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.16367e7 | −0.728399 | −0.364200 | − | 0.931321i | \(-0.618657\pi\) | ||||
−0.364200 | + | 0.931321i | \(0.618657\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.41110e6 | 0.0877500 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.33169e6 | 0.205831 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.90865e6 | 0.301282 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.91472e7 | 1.16759 | 0.583793 | − | 0.811902i | \(-0.301568\pi\) | ||||
0.583793 | + | 0.811902i | \(0.301568\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.35188e6 | 0.566582 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.39261e6 | −0.324601 | −0.162301 | − | 0.986741i | \(-0.551891\pi\) | ||||
−0.162301 | + | 0.986741i | \(0.551891\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.74565e7 | −1.04400 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.92188e6 | −0.114202 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.48791e6 | −0.146890 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.03709e6 | −0.354160 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.61147e6 | 0.210513 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.29757e7 | −0.751549 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.04348e6 | −0.175159 | −0.0875796 | − | 0.996158i | \(-0.527913\pi\) | ||||
−0.0875796 | + | 0.996158i | \(0.527913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.21594e7 | 0.695376 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.74469e6 | −0.155974 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.16903e7 | −0.660151 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.80484e6 | 0.437972 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.29652e7 | 1.28063 | 0.640316 | − | 0.768111i | \(-0.278803\pi\) | ||||
0.640316 | + | 0.768111i | \(0.278803\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.46686e6 | −0.469197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.93530e6 | −0.547141 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.87735e7 | 2.66928 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.81809e6 | −0.153273 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.00630e7 | 0.543930 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.90787e7 | 1.02489 | 0.512445 | − | 0.858720i | \(-0.328740\pi\) | ||||
0.512445 | + | 0.858720i | \(0.328740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.09414e7 | −0.584147 | −0.292074 | − | 0.956396i | \(-0.594345\pi\) | ||||
−0.292074 | + | 0.956396i | \(0.594345\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.71094e6 | −0.0907836 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.23653e7 | 0.652094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.99467e6 | −0.104548 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.26214e6 | 0.0657504 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.12594e7 | 1.10076 | 0.550380 | − | 0.834914i | \(-0.314483\pi\) | ||||
0.550380 | + | 0.834914i | \(0.314483\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.42256e7 | 0.732103 | 0.366052 | − | 0.930595i | \(-0.380709\pi\) | ||||
0.366052 | + | 0.930595i | \(0.380709\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.46352e7 | −0.748625 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.76103e6 | −0.140381 | −0.0701904 | − | 0.997534i | \(-0.522361\pi\) | ||||
−0.0701904 | + | 0.997534i | \(0.522361\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.82147e7 | −1.93127 | −0.965637 | − | 0.259895i | \(-0.916312\pi\) | ||||
−0.965637 | + | 0.259895i | \(0.916312\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.80455e6 | 0.0906499 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.79838e6 | 0.189665 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.12582e6 | −0.155149 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.19631e6 | −0.256378 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.06044e7 | −0.520094 | −0.260047 | − | 0.965596i | \(-0.583738\pi\) | ||||
−0.260047 | + | 0.965596i | \(0.583738\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.03097e6 | 0.196526 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.83133e6 | −0.476479 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.02439e6 | −0.338429 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.37124e7 | 0.656758 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.63132e7 | 0.776731 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.63990e6 | −0.456298 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.07009e7 | −1.91527 | −0.957637 | − | 0.287977i | \(-0.907017\pi\) | ||||
−0.957637 | + | 0.287977i | \(0.907017\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −497016. | −0.0232517 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.10120e7 | −1.44237 | −0.721187 | − | 0.692741i | \(-0.756403\pi\) | ||||
−0.721187 | + | 0.692741i | \(0.756403\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.09104e7 | −0.504495 | −0.252247 | − | 0.967663i | \(-0.581170\pi\) | ||||
−0.252247 | + | 0.967663i | \(0.581170\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.64902e6 | −0.213724 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.04089e7 | −0.475751 | −0.237875 | − | 0.971296i | \(-0.576451\pi\) | ||||
−0.237875 | + | 0.971296i | \(0.576451\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.32307e7 | 0.601234 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.74580e6 | −0.440321 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.93616e7 | 2.66659 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.30291e7 | −0.581928 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.73097e6 | 0.0768695 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.10128e6 | −0.313557 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.64064e7 | 0.720299 | 0.360150 | − | 0.932895i | \(-0.382726\pi\) | ||||
0.360150 | + | 0.932895i | \(0.382726\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.89028e7 | −0.825188 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.48577e7 | 0.644927 | 0.322464 | − | 0.946582i | \(-0.395489\pi\) | ||||
0.322464 | + | 0.946582i | \(0.395489\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.72018e7 | 1.17407 | 0.587037 | − | 0.809560i | \(-0.300294\pi\) | ||||
0.587037 | + | 0.809560i | \(0.300294\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.61202e6 | −0.155022 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.71242e7 | −1.15757 | −0.578785 | − | 0.815480i | \(-0.696473\pi\) | ||||
−0.578785 | + | 0.815480i | \(0.696473\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.08460e6 | −0.385524 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.35650e6 | −0.183842 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.26307e6 | 0.0530029 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.26766e7 | −0.528986 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.33074e6 | 0.262708 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.53121e7 | −1.45722 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.27660e7 | −2.16542 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.72733e6 | −0.152117 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.41547e7 | −0.574484 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.42269e6 | 0.339964 | 0.169982 | − | 0.985447i | \(-0.445629\pi\) | ||||
0.169982 | + | 0.985447i | \(0.445629\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.98193e6 | −0.119698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.08637e7 | −1.23212 | −0.616060 | − | 0.787700i | \(-0.711272\pi\) | ||||
−0.616060 | + | 0.787700i | \(0.711272\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.26819e6 | −0.169460 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.60231e6 | 0.339674 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.16207e6 | −0.124179 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.93895e6 | −0.192906 | −0.0964531 | − | 0.995338i | \(-0.530750\pi\) | ||||
−0.0964531 | + | 0.995338i | \(0.530750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.47694e7 | −0.573738 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.89126e6 | 0.111707 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.06727e7 | −0.410130 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.46677e6 | −0.323607 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.62575e6 | 0.213866 | 0.106933 | − | 0.994266i | \(-0.465897\pi\) | ||||
0.106933 | + | 0.994266i | \(0.465897\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −566636. | −0.0214255 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.50709e6 | −0.319946 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.73116e7 | −1.02169 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.60073e7 | 0.967714 | 0.483857 | − | 0.875147i | \(-0.339236\pi\) | ||||
0.483857 | + | 0.875147i | \(0.339236\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.73819e6 | −0.138356 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.02160e6 | 0.111241 | 0.0556203 | − | 0.998452i | \(-0.482286\pi\) | ||||
0.0556203 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.33189e7 | −0.853943 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −928746. | −0.0338312 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.48282e7 | 1.26199 | 0.630995 | − | 0.775787i | \(-0.282647\pi\) | ||||
0.630995 | + | 0.775787i | \(0.282647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.33584e7 | −0.841932 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.06633e7 | −0.382333 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.39009e6 | −0.334917 | −0.167459 | − | 0.985879i | \(-0.553556\pi\) | ||||
−0.167459 | + | 0.985879i | \(0.553556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.78650e6 | −0.347232 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.96051e7 | −1.04493 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.49357e6 | 0.263113 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.21792e7 | 0.774708 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.73696e7 | −0.603566 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.19686e7 | 0.759423 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.44768e7 | −0.497860 | −0.248930 | − | 0.968521i | \(-0.580079\pi\) | ||||
−0.248930 | + | 0.968521i | \(0.580079\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.36017e6 | 0.114961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.24976e6 | −0.314834 | −0.157417 | − | 0.987532i | \(-0.550317\pi\) | ||||
−0.157417 | + | 0.987532i | \(0.550317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.68295e7 | 0.569889 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.00904e6 | 0.236128 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.97780e7 | −1.66840 | −0.834202 | − | 0.551459i | \(-0.814071\pi\) | ||||
−0.834202 | + | 0.551459i | \(0.814071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.14449e7 | 2.71586 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.33264e6 | 0.0773882 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.95601e6 | 0.295618 | 0.147809 | − | 0.989016i | \(-0.452778\pi\) | ||||
0.147809 | + | 0.989016i | \(0.452778\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.28126e7 | −0.420773 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.36023e6 | 0.0771191 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.86958e7 | −0.607790 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.62400e7 | −0.848751 | −0.424376 | − | 0.905486i | \(-0.639506\pi\) | ||||
−0.424376 | + | 0.905486i | \(0.639506\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.23439e7 | 0.397265 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.37842e7 | 0.761606 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.80506e7 | 0.893727 | 0.446863 | − | 0.894602i | \(-0.352541\pi\) | ||||
0.446863 | + | 0.894602i | \(0.352541\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.17698e6 | −0.100717 |
(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 | 336.6.a.h.1.1 | 1 | ||
3.2 | odd | 2 | 1008.6.a.j.1.1 | 1 | |||
4.3 | odd | 2 | 42.6.a.d.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 126.6.a.i.1.1 | 1 | |||
20.3 | even | 4 | 1050.6.g.i.799.2 | 2 | |||
20.7 | even | 4 | 1050.6.g.i.799.1 | 2 | |||
20.19 | odd | 2 | 1050.6.a.k.1.1 | 1 | |||
28.3 | even | 6 | 294.6.e.p.79.1 | 2 | |||
28.11 | odd | 6 | 294.6.e.i.79.1 | 2 | |||
28.19 | even | 6 | 294.6.e.p.67.1 | 2 | |||
28.23 | odd | 6 | 294.6.e.i.67.1 | 2 | |||
28.27 | even | 2 | 294.6.a.b.1.1 | 1 | |||
84.83 | odd | 2 | 882.6.a.s.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.6.a.d.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
126.6.a.i.1.1 | 1 | 12.11 | even | 2 | |||
294.6.a.b.1.1 | 1 | 28.27 | even | 2 | |||
294.6.e.i.67.1 | 2 | 28.23 | odd | 6 | |||
294.6.e.i.79.1 | 2 | 28.11 | odd | 6 | |||
294.6.e.p.67.1 | 2 | 28.19 | even | 6 | |||
294.6.e.p.79.1 | 2 | 28.3 | even | 6 | |||
336.6.a.h.1.1 | 1 | 1.1 | even | 1 | trivial | ||
882.6.a.s.1.1 | 1 | 84.83 | odd | 2 | |||
1008.6.a.j.1.1 | 1 | 3.2 | odd | 2 | |||
1050.6.a.k.1.1 | 1 | 20.19 | odd | 2 | |||
1050.6.g.i.799.1 | 2 | 20.7 | even | 4 | |||
1050.6.g.i.799.2 | 2 | 20.3 | even | 4 |