Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,6,Mod(1,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, 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("576.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.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: | \(92.3810802123\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 96) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 576.1 |
$q$-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 | ||||||||
\(5\) | −14.0000 | −0.250440 | −0.125220 | − | 0.992129i | \(-0.539964\pi\) | ||||
−0.125220 | + | 0.992129i | \(0.539964\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 100.000 | 0.771356 | 0.385678 | − | 0.922633i | \(-0.373968\pi\) | ||||
0.385678 | + | 0.922633i | \(0.373968\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 220.000 | 0.548202 | 0.274101 | − | 0.961701i | \(-0.411620\pi\) | ||||
0.274101 | + | 0.961701i | \(0.411620\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 818.000 | 1.34244 | 0.671220 | − | 0.741258i | \(-0.265771\pi\) | ||||
0.671220 | + | 0.741258i | \(0.265771\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 774.000 | 0.649559 | 0.324780 | − | 0.945790i | \(-0.394710\pi\) | ||||
0.324780 | + | 0.945790i | \(0.394710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1436.00 | 0.912579 | 0.456289 | − | 0.889831i | \(-0.349178\pi\) | ||||
0.456289 | + | 0.889831i | \(0.349178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −192.000 | −0.0756801 | −0.0378400 | − | 0.999284i | \(-0.512048\pi\) | ||||
−0.0378400 | + | 0.999284i | \(0.512048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2929.00 | −0.937280 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7022.00 | −1.55048 | −0.775239 | − | 0.631668i | \(-0.782371\pi\) | ||||
−0.775239 | + | 0.631668i | \(0.782371\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1436.00 | 0.268380 | 0.134190 | − | 0.990956i | \(-0.457157\pi\) | ||||
0.134190 | + | 0.990956i | \(0.457157\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1400.00 | −0.193178 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3410.00 | 0.409496 | 0.204748 | − | 0.978815i | \(-0.434362\pi\) | ||||
0.204748 | + | 0.978815i | \(0.434362\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7838.00 | 0.728192 | 0.364096 | − | 0.931362i | \(-0.381378\pi\) | ||||
0.364096 | + | 0.931362i | \(0.381378\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16036.0 | 1.32259 | 0.661295 | − | 0.750126i | \(-0.270007\pi\) | ||||
0.661295 | + | 0.750126i | \(0.270007\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −22712.0 | −1.49972 | −0.749861 | − | 0.661595i | \(-0.769880\pi\) | ||||
−0.749861 | + | 0.661595i | \(0.769880\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6807.00 | −0.405010 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 27578.0 | 1.34857 | 0.674284 | − | 0.738472i | \(-0.264452\pi\) | ||||
0.674284 | + | 0.738472i | \(0.264452\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3080.00 | −0.137292 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −28828.0 | −1.07816 | −0.539082 | − | 0.842254i | \(-0.681229\pi\) | ||||
−0.539082 | + | 0.842254i | \(0.681229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12438.0 | −0.427982 | −0.213991 | − | 0.976836i | \(-0.568646\pi\) | ||||
−0.213991 | + | 0.976836i | \(0.568646\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −11452.0 | −0.336200 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 70948.0 | 1.93087 | 0.965435 | − | 0.260643i | \(-0.0839345\pi\) | ||||
0.965435 | + | 0.260643i | \(0.0839345\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −58832.0 | −1.38506 | −0.692529 | − | 0.721390i | \(-0.743503\pi\) | ||||
−0.692529 | + | 0.721390i | \(0.743503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 79386.0 | 1.74356 | 0.871780 | − | 0.489898i | \(-0.162966\pi\) | ||||
0.871780 | + | 0.489898i | \(0.162966\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22000.0 | 0.422859 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −46948.0 | −0.846349 | −0.423174 | − | 0.906048i | \(-0.639084\pi\) | ||||
−0.423174 | + | 0.906048i | \(0.639084\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 67284.0 | 1.07205 | 0.536027 | − | 0.844201i | \(-0.319925\pi\) | ||||
0.536027 | + | 0.844201i | \(0.319925\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10836.0 | −0.162675 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16106.0 | −0.215532 | −0.107766 | − | 0.994176i | \(-0.534370\pi\) | ||||
−0.107766 | + | 0.994176i | \(0.534370\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 81800.0 | 1.03550 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20104.0 | −0.228546 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4238.00 | −0.0457332 | −0.0228666 | − | 0.999739i | \(-0.507279\pi\) | ||||
−0.0228666 | + | 0.999739i | \(0.507279\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 51690.0 | 0.504200 | 0.252100 | − | 0.967701i | \(-0.418879\pi\) | ||||
0.252100 | + | 0.967701i | \(0.418879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −63828.0 | −0.592814 | −0.296407 | − | 0.955062i | \(-0.595788\pi\) | ||||
−0.296407 | + | 0.955062i | \(0.595788\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3428.00 | 0.0289455 | 0.0144728 | − | 0.999895i | \(-0.495393\pi\) | ||||
0.0144728 | + | 0.999895i | \(0.495393\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 153250. | 1.23548 | 0.617738 | − | 0.786384i | \(-0.288049\pi\) | ||||
0.617738 | + | 0.786384i | \(0.288049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 263870. | 1.94399 | 0.971995 | − | 0.235003i | \(-0.0755099\pi\) | ||||
0.971995 | + | 0.235003i | \(0.0755099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2688.00 | 0.0189533 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 77400.0 | 0.501041 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −112651. | −0.699474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 84756.0 | 0.485172 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −297484. | −1.63664 | −0.818322 | − | 0.574760i | \(-0.805095\pi\) | ||||
−0.818322 | + | 0.574760i | \(0.805095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 277468. | 1.41265 | 0.706325 | − | 0.707888i | \(-0.250352\pi\) | ||||
0.706325 | + | 0.707888i | \(0.250352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 143600. | 0.703923 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 290958. | 1.32443 | 0.662215 | − | 0.749314i | \(-0.269617\pi\) | ||||
0.662215 | + | 0.749314i | \(0.269617\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10100.0 | −0.0443388 | −0.0221694 | − | 0.999754i | \(-0.507057\pi\) | ||||
−0.0221694 | + | 0.999754i | \(0.507057\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 179960. | 0.735929 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 98308.0 | 0.388301 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 96450.0 | 0.355907 | 0.177954 | − | 0.984039i | \(-0.443052\pi\) | ||||
0.177954 | + | 0.984039i | \(0.443052\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 210900. | 0.752721 | 0.376361 | − | 0.926473i | \(-0.377175\pi\) | ||||
0.376361 | + | 0.926473i | \(0.377175\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20104.0 | −0.0672130 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −130310. | −0.421919 | −0.210959 | − | 0.977495i | \(-0.567659\pi\) | ||||
−0.210959 | + | 0.977495i | \(0.567659\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19200.0 | −0.0583763 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −633700. | −1.86816 | −0.934081 | − | 0.357060i | \(-0.883779\pi\) | ||||
−0.934081 | + | 0.357060i | \(0.883779\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −133880. | −0.371471 | −0.185735 | − | 0.982600i | \(-0.559467\pi\) | ||||
−0.185735 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 297831. | 0.802145 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 373578. | 0.949000 | 0.474500 | − | 0.880256i | \(-0.342629\pi\) | ||||
0.474500 | + | 0.880256i | \(0.342629\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −292900. | −0.722977 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −130836. | −0.305207 | −0.152604 | − | 0.988287i | \(-0.548766\pi\) | ||||
−0.152604 | + | 0.988287i | \(0.548766\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 214426. | 0.486498 | 0.243249 | − | 0.969964i | \(-0.421787\pi\) | ||||
0.243249 | + | 0.969964i | \(0.421787\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −47740.0 | −0.102554 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 170280. | 0.356090 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 466176. | 0.924627 | 0.462313 | − | 0.886717i | \(-0.347020\pi\) | ||||
0.462313 | + | 0.886717i | \(0.347020\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 584850. | 1.13019 | 0.565095 | − | 0.825026i | \(-0.308840\pi\) | ||||
0.565095 | + | 0.825026i | \(0.308840\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 771418. | 1.41620 | 0.708099 | − | 0.706113i | \(-0.249553\pi\) | ||||
0.708099 | + | 0.706113i | \(0.249553\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 704540. | 1.26117 | 0.630584 | − | 0.776121i | \(-0.282815\pi\) | ||||
0.630584 | + | 0.776121i | \(0.282815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −702200. | −1.19597 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −109732. | −0.182368 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 315920. | 0.500278 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −790732. | −1.22271 | −0.611355 | − | 0.791357i | \(-0.709375\pi\) | ||||
−0.611355 | + | 0.791357i | \(0.709375\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −224504. | −0.331229 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 143600. | 0.207017 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 633132. | 0.871994 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.22890e6 | 1.65483 | 0.827417 | − | 0.561588i | \(-0.189809\pi\) | ||||
0.827417 | + | 0.561588i | \(0.189809\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 367572. | 0.473454 | 0.236727 | − | 0.971576i | \(-0.423925\pi\) | ||||
0.236727 | + | 0.971576i | \(0.423925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 513754. | 0.647391 | 0.323695 | − | 0.946161i | \(-0.395075\pi\) | ||||
0.323695 | + | 0.946161i | \(0.395075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.10717e6 | 1.33606 | 0.668030 | − | 0.744134i | \(-0.267138\pi\) | ||||
0.668030 | + | 0.744134i | \(0.267138\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 317968. | 0.375590 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 886656. | 1.00406 | 0.502031 | − | 0.864850i | \(-0.332586\pi\) | ||||
0.502031 | + | 0.864850i | \(0.332586\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −250958. | −0.278329 | −0.139164 | − | 0.990269i | \(-0.544442\pi\) | ||||
−0.139164 | + | 0.990269i | \(0.544442\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 95298.0 | 0.101431 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.17465e6 | 1.22508 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.14076e6 | −1.14290 | −0.571450 | − | 0.820637i | \(-0.693619\pi\) | ||||
−0.571450 | + | 0.820637i | \(0.693619\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42240.0 | −0.0414880 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 726014. | 0.685665 | 0.342833 | − | 0.939396i | \(-0.388614\pi\) | ||||
0.342833 | + | 0.939396i | \(0.388614\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 341000. | 0.315868 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.09052e6 | −1.86365 | −0.931826 | − | 0.362905i | \(-0.881785\pi\) | ||||
−0.931826 | + | 0.362905i | \(0.881785\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −386092. | −0.337735 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.05059e6 | −1.72782 | −0.863909 | − | 0.503647i | \(-0.831991\pi\) | ||||
−0.863909 | + | 0.503647i | \(0.831991\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −544044. | −0.449998 | −0.224999 | − | 0.974359i | \(-0.572238\pi\) | ||||
−0.224999 | + | 0.974359i | \(0.572238\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −644380. | −0.513819 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 697082. | 0.545864 | 0.272932 | − | 0.962033i | \(-0.412007\pi\) | ||||
0.272932 | + | 0.962033i | \(0.412007\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −583002. | −0.440458 | −0.220229 | − | 0.975448i | \(-0.570680\pi\) | ||||
−0.220229 | + | 0.975448i | \(0.570680\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 890812. | 0.661180 | 0.330590 | − | 0.943774i | \(-0.392752\pi\) | ||||
0.330590 | + | 0.943774i | \(0.392752\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 783800. | 0.561695 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −820781. | −0.578073 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 514794. | 0.350320 | 0.175160 | − | 0.984540i | \(-0.443956\pi\) | ||||
0.175160 | + | 0.984540i | \(0.443956\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 403592. | 0.270015 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −157056. | −0.101596 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.60360e6 | 1.02019 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 174132. | 0.107184 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.15326e6 | −0.698363 | −0.349182 | − | 0.937055i | \(-0.613540\pi\) | ||||
−0.349182 | + | 0.937055i | \(0.613540\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −783000. | −0.459051 | −0.229525 | − | 0.973303i | \(-0.573717\pi\) | ||||
−0.229525 | + | 0.973303i | \(0.573717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −205718. | −0.118689 | −0.0593446 | − | 0.998238i | \(-0.518901\pi\) | ||||
−0.0593446 | + | 0.998238i | \(0.518901\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 515874. | 0.288334 | 0.144167 | − | 0.989553i | \(-0.453950\pi\) | ||||
0.144167 | + | 0.989553i | \(0.453950\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.54484e6 | −0.849976 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.11146e6 | 0.592774 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.39592e6 | −1.25824 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.27120e6 | −1.15682 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 641212. | 0.321686 | 0.160843 | − | 0.986980i | \(-0.448579\pi\) | ||||
0.160843 | + | 0.986980i | \(0.448579\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −993272. | −0.483566 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.41978e6 | 1.16065 | 0.580324 | − | 0.814385i | \(-0.302926\pi\) | ||||
0.580324 | + | 0.814385i | \(0.302926\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 315920. | 0.147127 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.36140e6 | −1.08376 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.60123e6 | 0.713887 | 0.356944 | − | 0.934126i | \(-0.383819\pi\) | ||||
0.356944 | + | 0.934126i | \(0.383819\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.41356e6 | −1.06070 | −0.530352 | − | 0.847778i | \(-0.677940\pi\) | ||||
−0.530352 | + | 0.847778i | \(0.677940\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 581902. | 0.248550 | 0.124275 | − | 0.992248i | \(-0.460340\pi\) | ||||
0.124275 | + | 0.992248i | \(0.460340\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 823648. | 0.346873 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.45614e6 | 1.00581 | 0.502907 | − | 0.864341i | \(-0.332264\pi\) | ||||
0.502907 | + | 0.864341i | \(0.332264\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −414003. | −0.167200 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.11140e6 | −0.436656 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.74831e6 | −1.45268 | −0.726340 | − | 0.687335i | \(-0.758780\pi\) | ||||
−0.726340 | + | 0.687335i | \(0.758780\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.75780e6 | 1.04023 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.63989e6 | −0.610297 | −0.305149 | − | 0.952305i | \(-0.598706\pi\) | ||||
−0.305149 | + | 0.952305i | \(0.598706\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.74400e6 | −2.08142 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.67642e6 | 0.599494 | 0.299747 | − | 0.954019i | \(-0.403098\pi\) | ||||
0.299747 | + | 0.954019i | \(0.403098\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 464416. | 0.161775 | 0.0808873 | − | 0.996723i | \(-0.474225\pi\) | ||||
0.0808873 | + | 0.996723i | \(0.474225\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −308000. | −0.105901 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.35377e6 | −0.453599 | −0.226800 | − | 0.973941i | \(-0.572826\pi\) | ||||
−0.226800 | + | 0.973941i | \(0.572826\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −148608. | −0.0491587 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 657272. | 0.211959 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.44535e6 | −0.460253 | −0.230127 | − | 0.973161i | \(-0.573914\pi\) | ||||
−0.230127 | + | 0.973161i | \(0.573914\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 554614. | 0.172238 | 0.0861192 | − | 0.996285i | \(-0.472553\pi\) | ||||
0.0861192 | + | 0.996285i | \(0.472553\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.17465e6 | 0.360284 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 750200. | 0.224487 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.96815e6 | −1.17295 | −0.586475 | − | 0.809967i | \(-0.699485\pi\) | ||||
−0.586475 | + | 0.809967i | \(0.699485\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.88280e6 | −0.831648 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −941976. | −0.268485 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.95621e6 | 1.10089 | 0.550446 | − | 0.834871i | \(-0.314458\pi\) | ||||
0.550446 | + | 0.834871i | \(0.314458\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.47057e6 | 0.679347 | 0.339674 | − | 0.940543i | \(-0.389683\pi\) | ||||
0.339674 | + | 0.940543i | \(0.389683\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.26705e6 | −0.608819 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.24380e6 | −0.330127 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −197928. | −0.0513232 | −0.0256616 | − | 0.999671i | \(-0.508169\pi\) | ||||
−0.0256616 | + | 0.999671i | \(0.508169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.22817e6 | −0.571123 | −0.285561 | − | 0.958360i | \(-0.592180\pi\) | ||||
−0.285561 | + | 0.958360i | \(0.592180\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −275712. | −0.0690641 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.72212e6 | −1.16943 | −0.584717 | − | 0.811238i | \(-0.698794\pi\) | ||||
−0.584717 | + | 0.811238i | \(0.698794\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.30366e6 | 0.799809 | 0.399904 | − | 0.916557i | \(-0.369043\pi\) | ||||
0.399904 | + | 0.916557i | \(0.369043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 225484. | 0.0539779 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.08543e6 | 0.488180 | 0.244090 | − | 0.969753i | \(-0.421511\pi\) | ||||
0.244090 | + | 0.969753i | \(0.421511\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.72436e6 | 0.399196 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.14520e6 | −0.259330 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.04724e6 | −0.234561 | −0.117280 | − | 0.993099i | \(-0.537418\pi\) | ||||
−0.117280 | + | 0.993099i | \(0.537418\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.15929e6 | −1.78813 | −0.894067 | − | 0.447934i | \(-0.852160\pi\) | ||||
−0.894067 | + | 0.447934i | \(0.852160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.65324e6 | 0.358412 | 0.179206 | − | 0.983812i | \(-0.442647\pi\) | ||||
0.179206 | + | 0.983812i | \(0.442647\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.64288e6 | −1.83386 | −0.916930 | − | 0.399049i | \(-0.869340\pi\) | ||||
−0.916930 | + | 0.399049i | \(0.869340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.09480e6 | 1.48939 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.52792e6 | 0.725047 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.20604e6 | −0.855342 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.67209e6 | −1.72697 | −0.863485 | − | 0.504374i | \(-0.831723\pi\) | ||||
−0.863485 | + | 0.504374i | \(0.831723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.78938e6 | 0.549724 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 59332.0 | 0.0114534 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.93066e6 | 0.942069 | 0.471034 | − | 0.882115i | \(-0.343881\pi\) | ||||
0.471034 | + | 0.882115i | \(0.343881\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.59340e6 | −1.42145 | −0.710727 | − | 0.703468i | \(-0.751634\pi\) | ||||
−0.710727 | + | 0.703468i | \(0.751634\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.43503e6 | −1.00713 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.88320e6 | −1.06837 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.56008e6 | 0.280477 | 0.140238 | − | 0.990118i | \(-0.455213\pi\) | ||||
0.140238 | + | 0.990118i | \(0.455213\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.79648e6 | 1.55020 | 0.775102 | − | 0.631836i | \(-0.217698\pi\) | ||||
0.775102 | + | 0.631836i | \(0.217698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −723660. | −0.126272 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.17251e6 | −1.39817 | −0.699087 | − | 0.715037i | \(-0.746410\pi\) | ||||
−0.699087 | + | 0.715037i | \(0.746410\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.93860e6 | 1.34491 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 893592. | 0.148464 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.99664e6 | −0.822151 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.66202e6 | −1.23666 | −0.618328 | − | 0.785920i | \(-0.712190\pi\) | ||||
−0.618328 | + | 0.785920i | \(0.712190\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 691092. | 0.110479 | 0.0552397 | − | 0.998473i | \(-0.482408\pi\) | ||||
0.0552397 | + | 0.998473i | \(0.482408\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.11146e6 | 0.174329 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.39948e6 | −0.994273 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.41148e6 | 0.977554 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −47992.0 | −0.00724911 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.49754e6 | −0.222027 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.26056e6 | −0.772749 | −0.386375 | − | 0.922342i | \(-0.626273\pi\) | ||||
−0.386375 | + | 0.922342i | \(0.626273\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.14550e6 | −0.309412 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.98897e6 | 0.427124 | 0.213562 | − | 0.976930i | \(-0.431494\pi\) | ||||
0.213562 | + | 0.976930i | \(0.431494\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00836e7 | −1.41493 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.69480e6 | −0.652836 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.72780e6 | 0.782258 | 0.391129 | − | 0.920336i | \(-0.372085\pi\) | ||||
0.391129 | + | 0.920336i | \(0.372085\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.31174e7 | 1.77550 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.01894e7 | −1.35480 | −0.677401 | − | 0.735614i | \(-0.736894\pi\) | ||||
−0.677401 | + | 0.735614i | \(0.736894\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.69418e6 | −0.486852 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 994190. | 0.128733 | 0.0643663 | − | 0.997926i | \(-0.479497\pi\) | ||||
0.0643663 | + | 0.997926i | \(0.479497\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.46040e6 | −0.957573 | −0.478787 | − | 0.877931i | \(-0.658923\pi\) | ||||
−0.478787 | + | 0.877931i | \(0.658923\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 562368. | 0.0709334 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.42449e7 | 1.78123 | 0.890614 | − | 0.454761i | \(-0.150275\pi\) | ||||
0.890614 | + | 0.454761i | \(0.150275\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.72840e6 | 0.826935 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.06716e6 | 0.739289 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.50084e7 | 1.79779 | 0.898895 | − | 0.438165i | \(-0.144371\pi\) | ||||
0.898895 | + | 0.438165i | \(0.144371\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.06210e6 | 0.244918 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.45853e6 | 1.10455 | 0.552277 | − | 0.833661i | \(-0.313759\pi\) | ||||
0.552277 | + | 0.833661i | \(0.313759\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.08360e6 | −0.125481 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.38815e7 | 1.58077 | 0.790387 | − | 0.612607i | \(-0.209879\pi\) | ||||
0.790387 | + | 0.612607i | \(0.209879\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.83787e6 | 0.320484 | 0.160242 | − | 0.987078i | \(-0.448773\pi\) | ||||
0.160242 | + | 0.987078i | \(0.448773\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.57711e6 | 0.175176 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.38418e6 | 0.593127 | 0.296564 | − | 0.955013i | \(-0.404159\pi\) | ||||
0.296564 | + | 0.955013i | \(0.404159\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.85784e7 | −2.01329 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.47139e6 | 0.910550 | 0.455275 | − | 0.890351i | \(-0.349541\pi\) | ||||
0.455275 | + | 0.890351i | \(0.349541\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.50297e7 | −1.58942 | −0.794708 | − | 0.606992i | \(-0.792376\pi\) | ||||
−0.794708 | + | 0.606992i | \(0.792376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.24601e7 | −1.30706 | −0.653530 | − | 0.756901i | \(-0.726713\pi\) | ||||
−0.653530 | + | 0.756901i | \(0.726713\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.61060e6 | −0.166252 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.96654e6 | 0.815774 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.63934e6 | 0.265992 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.24849e7 | −1.24828 | −0.624138 | − | 0.781314i | \(-0.714550\pi\) | ||||
−0.624138 | + | 0.781314i | \(0.714550\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.16478e6 | 0.409881 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.56813e6 | −0.543701 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.85191e7 | 1.78022 | 0.890112 | − | 0.455742i | \(-0.150626\pi\) | ||||
0.890112 | + | 0.455742i | \(0.150626\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.22232e6 | 0.498122 | 0.249061 | − | 0.968488i | \(-0.419878\pi\) | ||||
0.249061 | + | 0.968488i | \(0.419878\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.94424e6 | 0.464343 | 0.232171 | − | 0.972675i | \(-0.425417\pi\) | ||||
0.232171 | + | 0.972675i | \(0.425417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.34216e6 | −0.591052 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.20663e6 | −0.753151 | −0.376575 | − | 0.926386i | \(-0.622898\pi\) | ||||
−0.376575 | + | 0.926386i | \(0.622898\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.88455e6 | −0.353784 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.46992e7 | 1.31850 | 0.659250 | − | 0.751924i | \(-0.270874\pi\) | ||||
0.659250 | + | 0.751924i | \(0.270874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.27866e7 | 1.13828 | 0.569141 | − | 0.822240i | \(-0.307276\pi\) | ||||
0.569141 | + | 0.822240i | \(0.307276\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.01040e6 | −0.176290 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.34822e6 | 0.117340 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.73636e6 | −0.234621 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.86969e6 | −0.669762 | −0.334881 | − | 0.942261i | \(-0.608696\pi\) | ||||
−0.334881 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.88522e6 | 0.577359 | 0.288680 | − | 0.957426i | \(-0.406784\pi\) | ||||
0.288680 | + | 0.957426i | \(0.406784\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −423800. | −0.0352766 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.00604e6 | −0.492647 | −0.246324 | − | 0.969188i | \(-0.579223\pi\) | ||||
−0.246324 | + | 0.969188i | \(0.579223\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.07341e6 | −0.331690 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.25588e7 | 1.81037 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.58485e6 | −0.683971 | −0.341986 | − | 0.939705i | \(-0.611099\pi\) | ||||
−0.341986 | + | 0.939705i | \(0.611099\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 141400. | 0.0111042 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.06661e6 | 0.473003 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.39556e7 | −1.07263 | −0.536317 | − | 0.844016i | \(-0.680185\pi\) | ||||
−0.536317 | + | 0.844016i | \(0.680185\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89676e6 | 0.373698 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.16900e6 | 0.388918 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.61567e7 | 1.20709 | 0.603543 | − | 0.797331i | \(-0.293755\pi\) | ||||
0.603543 | + | 0.797331i | \(0.293755\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −275712. | −0.0203110 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.51944e6 | −0.184306 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.03861e7 | 1.47066 | 0.735330 | − | 0.677709i | \(-0.237027\pi\) | ||||
0.735330 | + | 0.677709i | \(0.237027\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.38280e6 | −0.457270 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.05674e7 | 1.45323 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.27446e7 | −1.59604 | −0.798018 | − | 0.602634i | \(-0.794118\pi\) | ||||
−0.798018 | + | 0.602634i | \(0.794118\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.24119e7 | 0.859100 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.67512e7 | 1.83901 | 0.919503 | − | 0.393082i | \(-0.128591\pi\) | ||||
0.919503 | + | 0.393082i | \(0.128591\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.56086e7 | 1.05851 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.28027e6 | −0.557742 | −0.278871 | − | 0.960329i | \(-0.589960\pi\) | ||||
−0.278871 | + | 0.960329i | \(0.589960\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.79877e7 | −1.19537 | −0.597686 | − | 0.801730i | \(-0.703913\pi\) | ||||
−0.597686 | + | 0.801730i | \(0.703913\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.35030e6 | −0.0891332 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 342800. | 0.0223273 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.78553e7 | −1.15523 | −0.577615 | − | 0.816310i | \(-0.696016\pi\) | ||||
−0.577615 | + | 0.816310i | \(0.696016\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.95260e6 | −0.188511 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.74527e7 | −1.10693 | −0.553467 | − | 0.832871i | \(-0.686696\pi\) | ||||
−0.553467 | + | 0.832871i | \(0.686696\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.20819e6 | −0.200816 | −0.100408 | − | 0.994946i | \(-0.532015\pi\) | ||||
−0.100408 | + | 0.994946i | \(0.532015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.53250e7 | 0.952992 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.35813e7 | −1.44737 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.87050e7 | 1.14062 | 0.570311 | − | 0.821429i | \(-0.306823\pi\) | ||||
0.570311 | + | 0.821429i | \(0.306823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.06368e7 | 1.24221 | 0.621104 | − | 0.783728i | \(-0.286685\pi\) | ||||
0.621104 | + | 0.783728i | \(0.286685\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.20604e6 | −0.251547 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.12554e7 | 0.664532 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.29430e7 | −0.759292 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.82434e6 | 0.105665 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.28794e7 | 1.31676 | 0.658382 | − | 0.752684i | \(-0.271241\pi\) | ||||
0.658382 | + | 0.752684i | \(0.271241\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.63870e7 | 1.49951 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.01743e7 | −0.574541 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.66035e7 | 0.925880 | 0.462940 | − | 0.886390i | \(-0.346795\pi\) | ||||
0.462940 | + | 0.886390i | \(0.346795\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.75791e7 | −0.974158 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.74649e7 | 0.955824 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 268800. | 0.0146197 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.78923e7 | 1.49835 | 0.749174 | − | 0.662374i | \(-0.230451\pi\) | ||||
0.749174 | + | 0.662374i | \(0.230451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.33062e7 | 0.710401 | 0.355200 | − | 0.934790i | \(-0.384413\pi\) | ||||
0.355200 | + | 0.934790i | \(0.384413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.87180e6 | 0.467862 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.30277e7 | 1.20697 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.27230e7 | 1.17654 | 0.588272 | − | 0.808663i | \(-0.299808\pi\) | ||||
0.588272 | + | 0.808663i | \(0.299808\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.29782e6 | −0.0667905 | −0.0333953 | − | 0.999442i | \(-0.510632\pi\) | ||||
−0.0333953 | + | 0.999442i | \(0.510632\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.28396e7 | −0.652810 | −0.326405 | − | 0.945230i | \(-0.605837\pi\) | ||||
−0.326405 | + | 0.945230i | \(0.605837\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.98277e6 | −0.352891 | −0.176446 | − | 0.984310i | \(-0.556460\pi\) | ||||
−0.176446 | + | 0.984310i | \(0.556460\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.26862e6 | −0.263078 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.87432e6 | 0.0930310 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.63449e7 | −1.78254 | −0.891268 | − | 0.453478i | \(-0.850183\pi\) | ||||
−0.891268 | + | 0.453478i | \(0.850183\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.87973e7 | 1.40398 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.16963e6 | −0.200889 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.12651e7 | −0.539544 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −654720. | −0.0309907 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.31369e6 | −0.202991 | −0.101495 | − | 0.994836i | \(-0.532363\pi\) | ||||
−0.101495 | + | 0.994836i | \(0.532363\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.74751e7 | −1.74297 | −0.871486 | − | 0.490420i | \(-0.836844\pi\) | ||||
−0.871486 | + | 0.490420i | \(0.836844\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.42986e6 | 0.112357 | 0.0561783 | − | 0.998421i | \(-0.482108\pi\) | ||||
0.0561783 | + | 0.998421i | \(0.482108\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.34998e6 | −0.335938 | −0.167969 | − | 0.985792i | \(-0.553721\pi\) | ||||
−0.167969 | + | 0.985792i | \(0.553721\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.23009e6 | −0.237667 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.03286e7 | −0.463970 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.80355e7 | 2.59208 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.47560e6 | 0.374240 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.06809e7 | −0.468932 | −0.234466 | − | 0.972124i | \(-0.575334\pi\) | ||||
−0.234466 | + | 0.972124i | \(0.575334\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.18750e7 | −0.515460 | −0.257730 | − | 0.966217i | \(-0.582974\pi\) | ||||
−0.257730 | + | 0.966217i | \(0.582974\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.59380e6 | 0.370923 | 0.185461 | − | 0.982652i | \(-0.440622\pi\) | ||||
0.185461 | + | 0.982652i | \(0.440622\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.10692e7 | 0.472397 | 0.236199 | − | 0.971705i | \(-0.424098\pi\) | ||||
0.236199 | + | 0.971705i | \(0.424098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.97484e7 | −1.26244 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.26144e7 | −1.36861 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.83170e6 | 0.0764360 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.00836e7 | −0.416118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.13454e7 | 0.875975 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.00196e6 | −0.121838 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.73654e7 | 1.50818 | 0.754088 | − | 0.656774i | \(-0.228079\pi\) | ||||
0.754088 | + | 0.656774i | \(0.228079\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.15898e7 | −1.26110 | −0.630551 | − | 0.776148i | \(-0.717171\pi\) | ||||
−0.630551 | + | 0.776148i | \(0.717171\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.48025e7 | 0.587703 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.77468e7 | 1.08966 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.45760e7 | −1.35047 | −0.675237 | − | 0.737601i | \(-0.735958\pi\) | ||||
−0.675237 | + | 0.737601i | \(0.735958\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.81246e7 | −1.85936 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.98789e6 | −0.383813 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.19448e7 | 1.21440 | 0.607198 | − | 0.794550i | \(-0.292293\pi\) | ||||
0.607198 | + | 0.794550i | \(0.292293\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.77485e6 | −0.369603 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.38392e6 | −0.0891790 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.33625e6 | −0.161349 | −0.0806743 | − | 0.996741i | \(-0.525707\pi\) | ||||
−0.0806743 | + | 0.996741i | \(0.525707\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.46316e6 | −0.0538663 | −0.0269332 | − | 0.999637i | \(-0.508574\pi\) | ||||
−0.0269332 | + | 0.999637i | \(0.508574\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.50490e6 | −0.0551096 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.39115e7 | 1.22878 | 0.614388 | − | 0.789004i | \(-0.289403\pi\) | ||||
0.614388 | + | 0.789004i | \(0.289403\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.49377e7 | 2.34062 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.49099e6 | −0.267182 | −0.133591 | − | 0.991037i | \(-0.542651\pi\) | ||||
−0.133591 | + | 0.991037i | \(0.542651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.52646e6 | −0.231563 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.90958e7 | 1.02161 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.65671e7 | −0.927972 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.18790e6 | −0.283044 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.52251e7 | 1.55530 | 0.777649 | − | 0.628699i | \(-0.216412\pi\) | ||||
0.777649 | + | 0.628699i | \(0.216412\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.70782e7 | −1.60240 | −0.801202 | − | 0.598394i | \(-0.795806\pi\) | ||||
−0.801202 | + | 0.598394i | \(0.795806\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.01000e6 | −0.0342010 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.50439e7 | 1.50973 | 0.754865 | − | 0.655880i | \(-0.227702\pi\) | ||||
0.754865 | + | 0.655880i | \(0.227702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.54332e6 | −0.118155 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.65491e7 | −1.20640 | −0.603202 | − | 0.797588i | \(-0.706109\pi\) | ||||
−0.603202 | + | 0.797588i | \(0.706109\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.07999e7 | −0.354672 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.07891e6 | −0.100094 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.80715e7 | 1.23145 | 0.615724 | − | 0.787962i | \(-0.288864\pi\) | ||||
0.615724 | + | 0.787962i | \(0.288864\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.86356e6 | −0.315846 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.19349e7 | −1.65471 | −0.827354 | − | 0.561681i | \(-0.810155\pi\) | ||||
−0.827354 | + | 0.561681i | \(0.810155\pi\) | |||||||
\(998\) | 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 | 576.6.a.p.1.1 | 1 | ||
3.2 | odd | 2 | 192.6.a.m.1.1 | 1 | |||
4.3 | odd | 2 | 576.6.a.o.1.1 | 1 | |||
8.3 | odd | 2 | 288.6.a.f.1.1 | 1 | |||
8.5 | even | 2 | 288.6.a.g.1.1 | 1 | |||
12.11 | even | 2 | 192.6.a.e.1.1 | 1 | |||
24.5 | odd | 2 | 96.6.a.b.1.1 | ✓ | 1 | ||
24.11 | even | 2 | 96.6.a.e.1.1 | yes | 1 | ||
48.5 | odd | 4 | 768.6.d.g.385.1 | 2 | |||
48.11 | even | 4 | 768.6.d.l.385.2 | 2 | |||
48.29 | odd | 4 | 768.6.d.g.385.2 | 2 | |||
48.35 | even | 4 | 768.6.d.l.385.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.6.a.b.1.1 | ✓ | 1 | 24.5 | odd | 2 | ||
96.6.a.e.1.1 | yes | 1 | 24.11 | even | 2 | ||
192.6.a.e.1.1 | 1 | 12.11 | even | 2 | |||
192.6.a.m.1.1 | 1 | 3.2 | odd | 2 | |||
288.6.a.f.1.1 | 1 | 8.3 | odd | 2 | |||
288.6.a.g.1.1 | 1 | 8.5 | even | 2 | |||
576.6.a.o.1.1 | 1 | 4.3 | odd | 2 | |||
576.6.a.p.1.1 | 1 | 1.1 | even | 1 | trivial | ||
768.6.d.g.385.1 | 2 | 48.5 | odd | 4 | |||
768.6.d.g.385.2 | 2 | 48.29 | odd | 4 | |||
768.6.d.l.385.1 | 2 | 48.35 | even | 4 | |||
768.6.d.l.385.2 | 2 | 48.11 | even | 4 |