Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(1,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, 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("400.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.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: | \(64.1535279252\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 400.1 |
$q$-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 | ||||||||
\(3\) | −2.00000 | −0.128300 | −0.0641500 | − | 0.997940i | \(-0.520434\pi\) | ||||
−0.0641500 | + | 0.997940i | \(0.520434\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −62.0000 | −0.478241 | −0.239120 | − | 0.970990i | \(-0.576859\pi\) | ||||
−0.239120 | + | 0.970990i | \(0.576859\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −239.000 | −0.983539 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 144.000 | 0.358823 | 0.179412 | − | 0.983774i | \(-0.442581\pi\) | ||||
0.179412 | + | 0.983774i | \(0.442581\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 654.000 | 1.07330 | 0.536648 | − | 0.843806i | \(-0.319690\pi\) | ||||
0.536648 | + | 0.843806i | \(0.319690\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1190.00 | 0.998676 | 0.499338 | − | 0.866407i | \(-0.333577\pi\) | ||||
0.499338 | + | 0.866407i | \(0.333577\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −556.000 | −0.353338 | −0.176669 | − | 0.984270i | \(-0.556532\pi\) | ||||
−0.176669 | + | 0.984270i | \(0.556532\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 124.000 | 0.0613583 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2182.00 | 0.860073 | 0.430036 | − | 0.902812i | \(-0.358501\pi\) | ||||
0.430036 | + | 0.902812i | \(0.358501\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 964.000 | 0.254488 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1578.00 | −0.348427 | −0.174214 | − | 0.984708i | \(-0.555738\pi\) | ||||
−0.174214 | + | 0.984708i | \(0.555738\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9660.00 | −1.80540 | −0.902699 | − | 0.430273i | \(-0.858417\pi\) | ||||
−0.902699 | + | 0.430273i | \(0.858417\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −288.000 | −0.0460371 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3534.00 | 0.424387 | 0.212194 | − | 0.977228i | \(-0.431939\pi\) | ||||
0.212194 | + | 0.977228i | \(0.431939\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1308.00 | −0.137704 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7462.00 | 0.693259 | 0.346630 | − | 0.938002i | \(-0.387326\pi\) | ||||
0.346630 | + | 0.938002i | \(0.387326\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7114.00 | −0.586736 | −0.293368 | − | 0.956000i | \(-0.594776\pi\) | ||||
−0.293368 | + | 0.956000i | \(0.594776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −28294.0 | −1.86831 | −0.934157 | − | 0.356863i | \(-0.883846\pi\) | ||||
−0.934157 | + | 0.356863i | \(0.883846\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12963.0 | −0.771286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2380.00 | −0.128130 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13046.0 | 0.637952 | 0.318976 | − | 0.947763i | \(-0.396661\pi\) | ||||
0.318976 | + | 0.947763i | \(0.396661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1112.00 | 0.0453333 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 37092.0 | 1.38724 | 0.693618 | − | 0.720343i | \(-0.256016\pi\) | ||||
0.693618 | + | 0.720343i | \(0.256016\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39570.0 | 1.36157 | 0.680787 | − | 0.732481i | \(-0.261638\pi\) | ||||
0.680787 | + | 0.732481i | \(0.261638\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 14818.0 | 0.470368 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −56734.0 | −1.54403 | −0.772016 | − | 0.635603i | \(-0.780752\pi\) | ||||
−0.772016 | + | 0.635603i | \(0.780752\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4364.00 | −0.110347 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −45588.0 | −1.07326 | −0.536630 | − | 0.843818i | \(-0.680303\pi\) | ||||
−0.536630 | + | 0.843818i | \(0.680303\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11842.0 | −0.260087 | −0.130043 | − | 0.991508i | \(-0.541512\pi\) | ||||
−0.130043 | + | 0.991508i | \(0.541512\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8928.00 | −0.171604 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −94216.0 | −1.69847 | −0.849233 | − | 0.528018i | \(-0.822935\pi\) | ||||
−0.849233 | + | 0.528018i | \(0.822935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 56149.0 | 0.950888 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −31482.0 | −0.501611 | −0.250806 | − | 0.968037i | \(-0.580695\pi\) | ||||
−0.250806 | + | 0.968037i | \(0.580695\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3156.00 | 0.0447032 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −94054.0 | −1.25864 | −0.629321 | − | 0.777145i | \(-0.716667\pi\) | ||||
−0.629321 | + | 0.777145i | \(0.716667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −40548.0 | −0.513294 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19320.0 | 0.231633 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −23714.0 | −0.255903 | −0.127952 | − | 0.991780i | \(-0.540840\pi\) | ||||
−0.127952 | + | 0.991780i | \(0.540840\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −34416.0 | −0.352917 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −129674. | −1.26488 | −0.632440 | − | 0.774609i | \(-0.717947\pi\) | ||||
−0.632440 | + | 0.774609i | \(0.717947\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 136846. | 1.27098 | 0.635490 | − | 0.772109i | \(-0.280798\pi\) | ||||
0.635490 | + | 0.772109i | \(0.280798\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −193190. | −1.63127 | −0.815634 | − | 0.578569i | \(-0.803612\pi\) | ||||
−0.815634 | + | 0.578569i | \(0.803612\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −120046. | −0.967791 | −0.483895 | − | 0.875126i | \(-0.660778\pi\) | ||||
−0.483895 | + | 0.875126i | \(0.660778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7068.00 | −0.0544489 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 152646. | 1.12458 | 0.562289 | − | 0.826941i | \(-0.309921\pi\) | ||||
0.562289 | + | 0.826941i | \(0.309921\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −156306. | −1.05563 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −73780.0 | −0.477608 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −140315. | −0.871246 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14924.0 | −0.0889452 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 107906. | 0.593658 | 0.296829 | − | 0.954931i | \(-0.404071\pi\) | ||||
0.296829 | + | 0.954931i | \(0.404071\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14228.0 | 0.0752783 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 233072. | 1.18662 | 0.593310 | − | 0.804974i | \(-0.297821\pi\) | ||||
0.593310 | + | 0.804974i | \(0.297821\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 34472.0 | 0.168981 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −356082. | −1.62087 | −0.810436 | − | 0.585827i | \(-0.800770\pi\) | ||||
−0.810436 | + | 0.585827i | \(0.800770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −312204. | −1.37057 | −0.685285 | − | 0.728275i | \(-0.740323\pi\) | ||||
−0.685285 | + | 0.728275i | \(0.740323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 56588.0 | 0.239705 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 94176.0 | 0.385124 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 25926.0 | 0.0989560 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 27498.0 | 0.101469 | 0.0507347 | − | 0.998712i | \(-0.483844\pi\) | ||||
0.0507347 | + | 0.998712i | \(0.483844\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 136908. | 0.488637 | 0.244319 | − | 0.969695i | \(-0.421436\pi\) | ||||
0.244319 | + | 0.969695i | \(0.421436\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −284410. | −0.982237 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −406714. | −1.31686 | −0.658431 | − | 0.752641i | \(-0.728779\pi\) | ||||
−0.658431 | + | 0.752641i | \(0.728779\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −26092.0 | −0.0818492 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −135284. | −0.411322 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13642.0 | −0.0402169 | −0.0201085 | − | 0.999798i | \(-0.506401\pi\) | ||||
−0.0201085 | + | 0.999798i | \(0.506401\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −203438. | −0.564470 | −0.282235 | − | 0.959345i | \(-0.591076\pi\) | ||||
−0.282235 | + | 0.959345i | \(0.591076\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 56423.0 | 0.151964 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 132884. | 0.347522 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −127242. | −0.323233 | −0.161616 | − | 0.986854i | \(-0.551671\pi\) | ||||
−0.161616 | + | 0.986854i | \(0.551671\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −74184.0 | −0.177982 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 94684.0 | 0.220874 | 0.110437 | − | 0.993883i | \(-0.464775\pi\) | ||||
0.110437 | + | 0.993883i | \(0.464775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −517018. | −1.17303 | −0.586515 | − | 0.809938i | \(-0.699501\pi\) | ||||
−0.586515 | + | 0.809938i | \(0.699501\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −79140.0 | −0.174690 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 171360. | 0.358348 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −59768.0 | −0.121707 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 412300. | 0.817768 | 0.408884 | − | 0.912586i | \(-0.365918\pi\) | ||||
0.408884 | + | 0.912586i | \(0.365918\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 771654. | 1.49118 | 0.745589 | − | 0.666406i | \(-0.232168\pi\) | ||||
0.745589 | + | 0.666406i | \(0.232168\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 190238. | 0.349246 | 0.174623 | − | 0.984635i | \(-0.444129\pi\) | ||||
0.174623 | + | 0.984635i | \(0.444129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −132072. | −0.236417 | −0.118208 | − | 0.992989i | \(-0.537715\pi\) | ||||
−0.118208 | + | 0.992989i | \(0.537715\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 113468. | 0.198099 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 97836.0 | 0.166632 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −521498. | −0.845915 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −80064.0 | −0.126786 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −928704. | −1.43606 | −0.718028 | − | 0.696015i | \(-0.754955\pi\) | ||||
−0.718028 | + | 0.696015i | \(0.754955\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 91176.0 | 0.137699 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 598920. | 0.863415 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 23684.0 | 0.0333691 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 778260. | 1.07187 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 421494. | 0.567583 | 0.283791 | − | 0.958886i | \(-0.408408\pi\) | ||||
0.283791 | + | 0.958886i | \(0.408408\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 991962. | 1.27770 | 0.638852 | − | 0.769329i | \(-0.279410\pi\) | ||||
0.638852 | + | 0.769329i | \(0.279410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −266946. | −0.336384 | −0.168192 | − | 0.985754i | \(-0.553793\pi\) | ||||
−0.168192 | + | 0.985754i | \(0.553793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17856.0 | 0.0220168 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −960314. | −1.15884 | −0.579420 | − | 0.815029i | \(-0.696721\pi\) | ||||
−0.579420 | + | 0.815029i | \(0.696721\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 188432. | 0.217913 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 492696. | 0.557936 | 0.278968 | − | 0.960300i | \(-0.410008\pi\) | ||||
0.278968 | + | 0.960300i | \(0.410008\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 56078.0 | 0.0621942 | 0.0310971 | − | 0.999516i | \(-0.490100\pi\) | ||||
0.0310971 | + | 0.999516i | \(0.490100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −346550. | −0.376487 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −363624. | −0.379237 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 62964.0 | 0.0643567 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.96792e6 | −1.97162 | −0.985810 | − | 0.167866i | \(-0.946312\pi\) | ||||
−0.985810 | + | 0.167866i | \(0.946312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 314208. | 0.308614 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 971910. | 0.917896 | 0.458948 | − | 0.888463i | \(-0.348227\pi\) | ||||
0.458948 | + | 0.888463i | \(0.348227\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −219108. | −0.202959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 377142. | 0.342692 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −154770. | −0.137974 | −0.0689870 | − | 0.997618i | \(-0.521977\pi\) | ||||
−0.0689870 | + | 0.997618i | \(0.521977\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 188108. | 0.161484 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.02371e6 | 0.862577 | 0.431289 | − | 0.902214i | \(-0.358059\pi\) | ||||
0.431289 | + | 0.902214i | \(0.358059\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.14776e6 | 0.949350 | 0.474675 | − | 0.880161i | \(-0.342566\pi\) | ||||
0.474675 | + | 0.880161i | \(0.342566\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 81096.0 | 0.0658556 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.49676e6 | 1.95514 | 0.977568 | − | 0.210619i | \(-0.0675481\pi\) | ||||
0.977568 | + | 0.210619i | \(0.0675481\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.30874e6 | 1.77568 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.69540e6 | 1.28087 | 0.640436 | − | 0.768011i | \(-0.278754\pi\) | ||||
0.640436 | + | 0.768011i | \(0.278754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.12395e6 | −1.57645 | −0.788223 | − | 0.615390i | \(-0.788999\pi\) | ||||
−0.788223 | + | 0.615390i | \(0.788999\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −462644. | −0.331545 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3757.00 | −0.00264604 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 47428.0 | 0.0328324 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −992722. | −0.675552 | −0.337776 | − | 0.941227i | \(-0.609675\pi\) | ||||
−0.337776 | + | 0.941227i | \(0.609675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 138816. | 0.0913163 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.42703e6 | 0.923112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 441068. | 0.280601 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 259348. | 0.162284 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 487522. | 0.295222 | 0.147611 | − | 0.989046i | \(-0.452842\pi\) | ||||
0.147611 | + | 0.989046i | \(0.452842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −273692. | −0.163067 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 444116. | 0.260373 | 0.130186 | − | 0.991490i | \(-0.458442\pi\) | ||||
0.130186 | + | 0.991490i | \(0.458442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −47242.0 | −0.0272563 | −0.0136282 | − | 0.999907i | \(-0.504338\pi\) | ||||
−0.0136282 | + | 0.999907i | \(0.504338\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −694058. | −0.387925 | −0.193962 | − | 0.981009i | \(-0.562134\pi\) | ||||
−0.193962 | + | 0.981009i | \(0.562134\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −227232. | −0.125024 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 386380. | 0.209292 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −661640. | −0.352871 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 240092. | 0.124168 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.75423e6 | 0.893504 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −82168.0 | −0.0412223 | −0.0206112 | − | 0.999788i | \(-0.506561\pi\) | ||||
−0.0206112 | + | 0.999788i | \(0.506561\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −844626. | −0.417401 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 727934. | 0.349154 | 0.174577 | − | 0.984644i | \(-0.444144\pi\) | ||||
0.174577 | + | 0.984644i | \(0.444144\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −305292. | −0.144283 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.39104e6 | −0.647819 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.84574e6 | 0.847101 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.02298e6 | 0.901919 | 0.450959 | − | 0.892544i | \(-0.351082\pi\) | ||||
0.450959 | + | 0.892544i | \(0.351082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.40858e6 | 1.93747 | 0.968736 | − | 0.248095i | \(-0.0798044\pi\) | ||||
0.968736 | + | 0.248095i | \(0.0798044\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 630456. | 0.273141 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.06965e6 | −0.456883 | −0.228441 | − | 0.973558i | \(-0.573363\pi\) | ||||
−0.228441 | + | 0.973558i | \(0.573363\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 147560. | 0.0612771 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32968.0 | 0.0135007 | 0.00675035 | − | 0.999977i | \(-0.497851\pi\) | ||||
0.00675035 | + | 0.999977i | \(0.497851\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.16696e6 | −0.875152 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 280630. | 0.111781 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.64081e6 | 1.41102 | 0.705509 | − | 0.708700i | \(-0.250718\pi\) | ||||
0.705509 | + | 0.708700i | \(0.250718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.78342e6 | −0.681847 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −808852. | −0.305094 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.17311e6 | 1.18090 | 0.590450 | − | 0.807074i | \(-0.298950\pi\) | ||||
0.590450 | + | 0.807074i | \(0.298950\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.03201e6 | −0.373965 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.60498e6 | −0.573947 | −0.286973 | − | 0.957939i | \(-0.592649\pi\) | ||||
−0.286973 | + | 0.957939i | \(0.592649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −215812. | −0.0761664 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.98925e6 | 0.692936 | 0.346468 | − | 0.938062i | \(-0.387381\pi\) | ||||
0.346468 | + | 0.938062i | \(0.387381\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.70025e6 | 0.577078 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.16495e6 | −1.73058 | −0.865291 | − | 0.501270i | \(-0.832866\pi\) | ||||
−0.865291 | + | 0.501270i | \(0.832866\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.59658e6 | 0.858934 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −466144. | −0.152243 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −937586. | −0.298562 | −0.149281 | − | 0.988795i | \(-0.547696\pi\) | ||||
−0.149281 | + | 0.988795i | \(0.547696\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −68944.0 | −0.0216802 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.63657e6 | −1.75047 | −0.875234 | − | 0.483699i | \(-0.839293\pi\) | ||||
−0.875234 | + | 0.483699i | \(0.839293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.31764e6 | −1.93773 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 508896. | 0.152280 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.06137e6 | 1.20051 | 0.600254 | − | 0.799810i | \(-0.295066\pi\) | ||||
0.600254 | + | 0.799810i | \(0.295066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 712164. | 0.207958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.29970e6 | −0.663433 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 624408. | 0.175844 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 976108. | 0.271621 | 0.135810 | − | 0.990735i | \(-0.456636\pi\) | ||||
0.135810 | + | 0.990735i | \(0.456636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.62706e6 | −0.447403 | −0.223701 | − | 0.974658i | \(-0.571814\pi\) | ||||
−0.223701 | + | 0.974658i | \(0.571814\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.76227e6 | 1.83756 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.45334e6 | −0.651161 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −188352. | −0.0494114 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.27900e6 | 1.10956 | 0.554778 | − | 0.831998i | \(-0.312803\pi\) | ||||
0.554778 | + | 0.831998i | \(0.312803\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.20195e6 | 0.820720 | 0.410360 | − | 0.911924i | \(-0.365403\pi\) | ||||
0.410360 | + | 0.911924i | \(0.365403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.21319e6 | −0.303897 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.09246e6 | −1.26115 | −0.630574 | − | 0.776129i | \(-0.717180\pi\) | ||||
−0.630574 | + | 0.776129i | \(0.717180\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.09816e6 | 0.758590 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.43551e6 | −1.31593 | −0.657963 | − | 0.753050i | \(-0.728582\pi\) | ||||
−0.657963 | + | 0.753050i | \(0.728582\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −54996.0 | −0.0130185 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.99007e6 | −0.699948 | −0.349974 | − | 0.936759i | \(-0.613810\pi\) | ||||
−0.349974 | + | 0.936759i | \(0.613810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.07453e6 | 0.248758 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −273816. | −0.0626922 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.01759e6 | −1.79578 | −0.897891 | − | 0.440218i | \(-0.854901\pi\) | ||||
−0.897891 | + | 0.440218i | \(0.854901\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.14716e6 | 0.254151 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.58462e6 | 0.566428 | 0.283214 | − | 0.959057i | \(-0.408599\pi\) | ||||
0.283214 | + | 0.959057i | \(0.408599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.14261e6 | 1.33168 | 0.665840 | − | 0.746094i | \(-0.268073\pi\) | ||||
0.665840 | + | 0.746094i | \(0.268073\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.59270e6 | −0.337942 | −0.168971 | − | 0.985621i | \(-0.554044\pi\) | ||||
−0.168971 | + | 0.985621i | \(0.554044\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.51751e6 | 0.738419 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 813428. | 0.168953 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.02442e6 | −0.210535 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.11799e6 | −0.627450 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −863592. | −0.171977 | −0.0859884 | − | 0.996296i | \(-0.527405\pi\) | ||||
−0.0859884 | + | 0.996296i | \(0.527405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.31124e6 | 0.455493 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 270568. | 0.0527726 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.20714e6 | −1.56808 | −0.784042 | − | 0.620707i | \(-0.786846\pi\) | ||||
−0.784042 | + | 0.620707i | \(0.786846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27284.0 | 0.00515984 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.93394e6 | −1.67240 | −0.836198 | − | 0.548428i | \(-0.815227\pi\) | ||||
−0.836198 | + | 0.548428i | \(0.815227\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.87782e6 | −0.347966 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.82646e6 | 0.513276 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.11960e6 | −0.201284 | −0.100642 | − | 0.994923i | \(-0.532090\pi\) | ||||
−0.100642 | + | 0.994923i | \(0.532090\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 406876. | 0.0724215 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.68177e6 | 0.648839 | 0.324420 | − | 0.945913i | \(-0.394831\pi\) | ||||
0.324420 | + | 0.945913i | \(0.394831\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −112846. | −0.0194969 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.73483e6 | −1.15221 | −0.576105 | − | 0.817375i | \(-0.695428\pi\) | ||||
−0.576105 | + | 0.817375i | \(0.695428\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 734204. | 0.124384 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −535984. | −0.0899204 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.07434e6 | −0.670395 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 254484. | 0.0414708 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 441370. | 0.0712375 | 0.0356187 | − | 0.999365i | \(-0.488660\pi\) | ||||
0.0356187 | + | 0.999365i | \(0.488660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.17300e7 | −1.87518 | −0.937589 | − | 0.347744i | \(-0.886948\pi\) | ||||
−0.937589 | + | 0.347744i | \(0.886948\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.14954e7 | −1.80301 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.67522e6 | −0.260275 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.86499e6 | −1.36440 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.88015e6 | 0.744072 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −189368. | −0.0283381 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.86667e6 | −0.276755 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 744158. | 0.109313 | 0.0546565 | − | 0.998505i | \(-0.482594\pi\) | ||||
0.0546565 | + | 0.998505i | \(0.482594\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.03404e6 | 0.150500 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.24801e6 | −0.464139 | −0.232070 | − | 0.972699i | \(-0.574550\pi\) | ||||
−0.232070 | + | 0.972699i | \(0.574550\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.45723e6 | −1.33916 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 877368. | 0.123113 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.84139e6 | 0.812276 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.94446e6 | 1.35814 | 0.679068 | − | 0.734075i | \(-0.262384\pi\) | ||||
0.679068 | + | 0.734075i | \(0.262384\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.65256e6 | −0.629741 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −342720. | −0.0459761 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.89374e6 | 0.517721 | 0.258861 | − | 0.965915i | \(-0.416653\pi\) | ||||
0.258861 | + | 0.965915i | \(0.416653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.48124e6 | −0.454754 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.11951e7 | −1.44960 | −0.724801 | − | 0.688958i | \(-0.758068\pi\) | ||||
−0.724801 | + | 0.688958i | \(0.758068\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 844040. | 0.108336 | 0.0541680 | − | 0.998532i | \(-0.482749\pi\) | ||||
0.0541680 | + | 0.998532i | \(0.482749\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −824600. | −0.104920 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.13378e6 | 0.641945 | 0.320973 | − | 0.947088i | \(-0.395990\pi\) | ||||
0.320973 | + | 0.947088i | \(0.395990\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.54331e6 | −0.191318 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.95188e6 | 0.239891 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.87862e6 | 0.228912 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.76156e6 | 1.16929 | 0.584647 | − | 0.811287i | \(-0.301233\pi\) | ||||
0.584647 | + | 0.811287i | \(0.301233\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.37096e6 | 0.637916 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −380476. | −0.0448083 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −966226. | −0.112835 | −0.0564173 | − | 0.998407i | \(-0.517968\pi\) | ||||
−0.0564173 | + | 0.998407i | \(0.517968\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 264144. | 0.0303323 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.90000e6 | 0.899622 | 0.449811 | − | 0.893124i | \(-0.351491\pi\) | ||||
0.449811 | + | 0.893124i | \(0.351491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.03126e7 | 1.16461 | 0.582307 | − | 0.812969i | \(-0.302150\pi\) | ||||
0.582307 | + | 0.812969i | \(0.302150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.35594e7 | 1.51862 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.70767e6 | −1.06941 | −0.534704 | − | 0.845040i | \(-0.679577\pi\) | ||||
−0.534704 | + | 0.845040i | \(0.679577\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −195672. | −0.0213789 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.85043e7 | −2.00525 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.10568e7 | 1.18844 | 0.594219 | − | 0.804304i | \(-0.297461\pi\) | ||||
0.594219 | + | 0.804304i | \(0.297461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.31174e6 | −0.878980 | −0.439490 | − | 0.898248i | \(-0.644841\pi\) | ||||
−0.439490 | + | 0.898248i | \(0.644841\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.15451e7 | −1.21108 | −0.605539 | − | 0.795816i | \(-0.707042\pi\) | ||||
−0.605539 | + | 0.795816i | \(0.707042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.10345e6 | 0.218878 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.83135e6 | 0.601934 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 160128. | 0.0162667 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.20546e6 | 0.423825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.20262e6 | 0.820123 | 0.410062 | − | 0.912058i | \(-0.365507\pi\) | ||||
0.410062 | + | 0.912058i | \(0.365507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.85741e6 | 0.184246 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.47780e6 | −0.827818 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.08955e7 | 1.05559 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.39695e6 | −0.518804 | −0.259402 | − | 0.965769i | \(-0.583525\pi\) | ||||
−0.259402 | + | 0.965769i | \(0.583525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.33896e7 | −1.27715 | −0.638573 | − | 0.769561i | \(-0.720475\pi\) | ||||
−0.638573 | + | 0.769561i | \(0.720475\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.48254e6 | 0.608814 | 0.304407 | − | 0.952542i | \(-0.401542\pi\) | ||||
0.304407 | + | 0.952542i | \(0.401542\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.34125e6 | 0.497773 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.19784e6 | −0.110776 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.44907e7 | −1.32986 | −0.664931 | − | 0.746904i | \(-0.731539\pi\) | ||||
−0.664931 | + | 0.746904i | \(0.731539\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.83024e6 | 0.255805 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.59080e6 | −0.591187 | −0.295593 | − | 0.955314i | \(-0.595517\pi\) | ||||
−0.295593 | + | 0.955314i | \(0.595517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.25233e6 | −0.289528 | −0.144764 | − | 0.989466i | \(-0.546242\pi\) | ||||
−0.144764 | + | 0.989466i | \(0.546242\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.55652e6 | −0.137522 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.44320e6 | −0.299673 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −842988. | −0.0728209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.69808e6 | 0.488565 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.86655e6 | −0.329068 | −0.164534 | − | 0.986371i | \(-0.552612\pi\) | ||||
−0.164534 | + | 0.986371i | \(0.552612\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.23856e6 | −0.103859 | −0.0519297 | − | 0.998651i | \(-0.516537\pi\) | ||||
−0.0519297 | + | 0.998651i | \(0.516537\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.47027e6 | 0.122383 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.98392e6 | −0.163930 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.31376e7 | −1.07762 | −0.538810 | − | 0.842427i | \(-0.681126\pi\) | ||||
−0.538810 | + | 0.842427i | \(0.681126\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 533892. | 0.0431580 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.53208e6 | 0.684711 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.23841e7 | 0.986664 | 0.493332 | − | 0.869841i | \(-0.335779\pi\) | ||||
0.493332 | + | 0.869841i | \(0.335779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.13379e6 | 0.168779 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.87978e6 | 0.692341 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.92063e6 | 0.148679 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.78952e6 | −0.752430 | −0.376215 | − | 0.926532i | \(-0.622775\pi\) | ||||
−0.376215 | + | 0.926532i | \(0.622775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.96490e6 | −0.149952 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.03979e6 | 0.604917 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.22257e7 | 0.913397 | 0.456699 | − | 0.889622i | \(-0.349032\pi\) | ||||
0.456699 | + | 0.889622i | \(0.349032\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.25176e7 | 1.67051 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.10781e7 | −1.55277 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −985392. | −0.0715832 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.35053e7 | 0.974276 | 0.487138 | − | 0.873325i | \(-0.338041\pi\) | ||||
0.487138 | + | 0.873325i | \(0.338041\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.48445e6 | −0.607835 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −112156. | −0.00797952 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.17271e7 | 0.822916 | 0.411458 | − | 0.911429i | \(-0.365020\pi\) | ||||
0.411458 | + | 0.911429i | \(0.365020\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.29511e7 | −0.902585 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.46566e6 | −0.585959 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.16512e7 | 0.800960 | 0.400480 | − | 0.916305i | \(-0.368843\pi\) | ||||
0.400480 | + | 0.916305i | \(0.368843\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.16970e6 | −0.554035 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.26808e7 | 0.854155 | 0.427077 | − | 0.904215i | \(-0.359543\pi\) | ||||
0.427077 | + | 0.904215i | \(0.359543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 727248. | 0.0486561 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −197370. | −0.0131162 | −0.00655812 | − | 0.999978i | \(-0.502088\pi\) | ||||
−0.00655812 | + | 0.999978i | \(0.502088\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.52420e6 | 0.493354 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.19778e7 | 0.780139 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.33282e7 | 0.862326 | 0.431163 | − | 0.902274i | \(-0.358103\pi\) | ||||
0.431163 | + | 0.902274i | \(0.358103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.93584e6 | 0.252959 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.86122e6 | 0.244898 | 0.122449 | − | 0.992475i | \(-0.460925\pi\) | ||||
0.122449 | + | 0.992475i | \(0.460925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −628416. | −0.0395952 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.31756e6 | −0.520636 | −0.260318 | − | 0.965523i | \(-0.583827\pi\) | ||||
−0.260318 | + | 0.965523i | \(0.583827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.44285e6 | 0.462837 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.42582e7 | 1.48891 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.76358e7 | 1.68522 | 0.842609 | − | 0.538527i | \(-0.181019\pi\) | ||||
0.842609 | + | 0.538527i | \(0.181019\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.94382e6 | −0.117766 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.78842e7 | −1.07652 | −0.538259 | − | 0.842780i | \(-0.680918\pi\) | ||||
−0.538259 | + | 0.842780i | \(0.680918\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 438216. | 0.0260397 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.14887e6 | −0.244955 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.56467e6 | −0.385111 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.52119e6 | −0.0886706 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.15691e7 | 1.24135 | 0.620676 | − | 0.784067i | \(-0.286858\pi\) | ||||
0.620676 | + | 0.784067i | \(0.286858\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 309540. | 0.0177021 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.46405e6 | −0.537819 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.58788e7 | 1.46137 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.03060e7 | 0.574705 | 0.287353 | − | 0.957825i | \(-0.407225\pi\) | ||||
0.287353 | + | 0.957825i | \(0.407225\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.36699e7 | −1.86584 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.24789e7 | 1.23792 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.70525e6 | −0.0933251 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.04743e6 | −0.110669 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 372378. | 0.0200038 | 0.0100019 | − | 0.999950i | \(-0.496816\pi\) | ||||
0.0100019 | + | 0.999950i | \(0.496816\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.94795e7 | 1.03998 | 0.519990 | − | 0.854173i | \(-0.325936\pi\) | ||||
0.519990 | + | 0.854173i | \(0.325936\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.29551e6 | −0.121802 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.95538e6 | 0.207316 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.69097e6 | 0.504844 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −469318. | −0.0243002 | −0.0121501 | − | 0.999926i | \(-0.503868\pi\) | ||||
−0.0121501 | + | 0.999926i | \(0.503868\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.78622e7 | 0.919253 | 0.459626 | − | 0.888112i | \(-0.347983\pi\) | ||||
0.459626 | + | 0.888112i | \(0.347983\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.42560e6 | 0.479231 | 0.239616 | − | 0.970868i | \(-0.422979\pi\) | ||||
0.239616 | + | 0.970868i | \(0.422979\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.48622e7 | −0.751098 | −0.375549 | − | 0.926803i | \(-0.622546\pi\) | ||||
−0.375549 | + | 0.926803i | \(0.622546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.99352e6 | −0.250844 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.54260e7 | −0.770265 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.31224e6 | −0.459452 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.71170e6 | 0.231085 | 0.115543 | − | 0.993303i | \(-0.463139\pi\) | ||||
0.115543 | + | 0.993303i | \(0.463139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.80211e7 | −0.878599 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.39080e6 | −0.164336 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.69953e6 | 0.416665 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.24791e6 | 0.202258 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.71119e6 | 0.365004 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.62685e7 | −0.765552 | −0.382776 | − | 0.923841i | \(-0.625032\pi\) | ||||
−0.382776 | + | 0.923841i | \(0.625032\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.92667e7 | 1.36120 | 0.680600 | − | 0.732656i | \(-0.261719\pi\) | ||||
0.680600 | + | 0.732656i | \(0.261719\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.31062e7 | 1.53083 | 0.765413 | − | 0.643539i | \(-0.222535\pi\) | ||||
0.765413 | + | 0.643539i | \(0.222535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 925288. | 0.0425372 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.58052e7 | −0.722391 | −0.361196 | − | 0.932490i | \(-0.617631\pi\) | ||||
−0.361196 | + | 0.932490i | \(0.617631\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7514.00 | 0.000339487 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.35671e7 | −0.609449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.71040e7 | −1.65720 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.66765e6 | 0.251691 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.26834e7 | 1.87396 | 0.936980 | − | 0.349384i | \(-0.113609\pi\) | ||||
0.936980 | + | 0.349384i | \(0.113609\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.98544e6 | 0.0866733 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.57397e6 | −0.155135 | −0.0775677 | − | 0.996987i | \(-0.524715\pi\) | ||||
−0.0775677 | + | 0.996987i | \(0.524715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.68471e7 | −0.727149 | −0.363574 | − | 0.931565i | \(-0.618444\pi\) | ||||
−0.363574 | + | 0.931565i | \(0.618444\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.36792e6 | −0.357115 | −0.178558 | − | 0.983929i | \(-0.557143\pi\) | ||||
−0.178558 | + | 0.983929i | \(0.557143\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.69017e6 | −0.283911 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.08546e6 | 0.341201 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.57315e7 | 0.660147 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.85406e6 | −0.118435 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.52435e7 | 0.629050 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.55247e7 | 0.637107 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −882136. | −0.0360011 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.57230e7 | −1.03825 | −0.519127 | − | 0.854697i | \(-0.673743\pi\) | ||||
−0.519127 | + | 0.854697i | \(0.673743\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.09921e7 | 1.24406 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.42108e7 | −1.36574 | −0.682869 | − | 0.730540i | \(-0.739268\pi\) | ||||
−0.682869 | + | 0.730540i | \(0.739268\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.53341e6 | −0.179990 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.44505e7 | −0.567490 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.44034e6 | −0.0953149 | −0.0476575 | − | 0.998864i | \(-0.515176\pi\) | ||||
−0.0476575 | + | 0.998864i | \(0.515176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −975044. | −0.0378770 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.98146e7 | −1.15192 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.27062e7 | −1.25006 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.34361e7 | 0.510781 | 0.255390 | − | 0.966838i | \(-0.417796\pi\) | ||||
0.255390 | + | 0.966838i | \(0.417796\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.20743e6 | 0.272525 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −888232. | −0.0334058 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.96529e6 | −0.296383 | −0.148191 | − | 0.988959i | \(-0.547345\pi\) | ||||
−0.148191 | + | 0.988959i | \(0.547345\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 94484.0 | 0.00349699 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.08025e6 | 0.334290 | 0.167145 | − | 0.985932i | \(-0.446545\pi\) | ||||
0.167145 | + | 0.985932i | \(0.446545\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.62821e7 | 0.596253 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.21769e7 | −1.16592 | −0.582961 | − | 0.812500i | \(-0.698106\pi\) | ||||
−0.582961 | + | 0.812500i | \(0.698106\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.74467e6 | −0.279150 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.38812e6 | 0.0497708 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.33807e6 | −0.190394 | −0.0951968 | − | 0.995458i | \(-0.530348\pi\) | ||||
−0.0951968 | + | 0.995458i | \(0.530348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 454464. | 0.0160406 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.20771e7 | 0.775167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.46864e7 | 2.25946 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.61724e7 | 1.60442 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.71522e7 | 1.27767 | 0.638834 | − | 0.769345i | \(-0.279417\pi\) | ||||
0.638834 | + | 0.769345i | \(0.279417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.32328e6 | 0.0452733 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.09865e7 | 0.373949 | 0.186975 | − | 0.982365i | \(-0.440132\pi\) | ||||
0.186975 | + | 0.982365i | \(0.440132\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.93566e7 | 0.655463 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.65054e7 | 0.888379 | 0.444190 | − | 0.895933i | \(-0.353492\pi\) | ||||
0.444190 | + | 0.895933i | \(0.353492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.35438e7 | −0.451630 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.86910e7 | 0.951860 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.75726e7 | −1.57027 | −0.785133 | − | 0.619327i | \(-0.787406\pi\) | ||||
−0.785133 | + | 0.619327i | \(0.787406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.50846e6 | −0.114637 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.55227e7 | −0.504636 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.22149e7 | −1.04201 | −0.521006 | − | 0.853553i | \(-0.674443\pi\) | ||||
−0.521006 | + | 0.853553i | \(0.674443\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 164336. | 0.00528883 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.87072e7 | −1.23326 | −0.616630 | − | 0.787253i | \(-0.711502\pi\) | ||||
−0.616630 | + | 0.787253i | \(0.711502\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.40678e6 | 0.108002 |
(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 | 400.6.a.h.1.1 | 1 | ||
4.3 | odd | 2 | 200.6.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 400.6.c.k.49.2 | 2 | |||
5.3 | odd | 4 | 400.6.c.k.49.1 | 2 | |||
5.4 | even | 2 | 80.6.a.d.1.1 | 1 | |||
15.14 | odd | 2 | 720.6.a.t.1.1 | 1 | |||
20.3 | even | 4 | 200.6.c.d.49.2 | 2 | |||
20.7 | even | 4 | 200.6.c.d.49.1 | 2 | |||
20.19 | odd | 2 | 40.6.a.c.1.1 | ✓ | 1 | ||
40.19 | odd | 2 | 320.6.a.i.1.1 | 1 | |||
40.29 | even | 2 | 320.6.a.h.1.1 | 1 | |||
60.59 | even | 2 | 360.6.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.a.c.1.1 | ✓ | 1 | 20.19 | odd | 2 | ||
80.6.a.d.1.1 | 1 | 5.4 | even | 2 | |||
200.6.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
200.6.c.d.49.1 | 2 | 20.7 | even | 4 | |||
200.6.c.d.49.2 | 2 | 20.3 | even | 4 | |||
320.6.a.h.1.1 | 1 | 40.29 | even | 2 | |||
320.6.a.i.1.1 | 1 | 40.19 | odd | 2 | |||
360.6.a.f.1.1 | 1 | 60.59 | even | 2 | |||
400.6.a.h.1.1 | 1 | 1.1 | even | 1 | trivial | ||
400.6.c.k.49.1 | 2 | 5.3 | odd | 4 | |||
400.6.c.k.49.2 | 2 | 5.2 | odd | 4 | |||
720.6.a.t.1.1 | 1 | 15.14 | odd | 2 |