Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,6,Mod(1,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.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: | \(80.8334451857\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{37}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.54138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.1 |
$q$-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 | ||||||||
\(5\) | 84.8276 | 1.51744 | 0.758721 | − | 0.651415i | \(-0.225824\pi\) | ||||
0.758721 | + | 0.651415i | \(0.225824\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 634.124 | 1.58013 | 0.790065 | − | 0.613023i | \(-0.210047\pi\) | ||||
0.790065 | + | 0.613023i | \(0.210047\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 895.242 | 1.46920 | 0.734602 | − | 0.678498i | \(-0.237369\pi\) | ||||
0.734602 | + | 0.678498i | \(0.237369\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2057.46 | −1.72667 | −0.863335 | − | 0.504630i | \(-0.831629\pi\) | ||||
−0.863335 | + | 0.504630i | \(0.831629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2451.95 | 1.55821 | 0.779106 | − | 0.626892i | \(-0.215673\pi\) | ||||
0.779106 | + | 0.626892i | \(0.215673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 569.186 | 0.224354 | 0.112177 | − | 0.993688i | \(-0.464218\pi\) | ||||
0.112177 | + | 0.993688i | \(0.464218\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4070.73 | 1.30263 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1471.78 | −0.324974 | −0.162487 | − | 0.986711i | \(-0.551951\pi\) | ||||
−0.162487 | + | 0.986711i | \(0.551951\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2006.65 | −0.375031 | −0.187515 | − | 0.982262i | \(-0.560043\pi\) | ||||
−0.187515 | + | 0.982262i | \(0.560043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4156.55 | −0.573539 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4860.54 | 0.583687 | 0.291844 | − | 0.956466i | \(-0.405731\pi\) | ||||
0.291844 | + | 0.956466i | \(0.405731\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 17228.4 | 1.60061 | 0.800307 | − | 0.599591i | \(-0.204670\pi\) | ||||
0.800307 | + | 0.599591i | \(0.204670\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15481.3 | −1.27684 | −0.638420 | − | 0.769689i | \(-0.720412\pi\) | ||||
−0.638420 | + | 0.769689i | \(0.720412\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5006.40 | −0.330583 | −0.165292 | − | 0.986245i | \(-0.552857\pi\) | ||||
−0.165292 | + | 0.986245i | \(0.552857\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19560.3 | 0.956504 | 0.478252 | − | 0.878223i | \(-0.341271\pi\) | ||||
0.478252 | + | 0.878223i | \(0.341271\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 53791.3 | 2.39776 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14515.6 | −0.542881 | −0.271441 | − | 0.962455i | \(-0.587500\pi\) | ||||
−0.271441 | + | 0.962455i | \(0.587500\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3572.67 | 0.122933 | 0.0614664 | − | 0.998109i | \(-0.480422\pi\) | ||||
0.0614664 | + | 0.998109i | \(0.480422\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 75941.3 | 2.22943 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −41480.7 | −1.12891 | −0.564455 | − | 0.825464i | \(-0.690914\pi\) | ||||
−0.564455 | + | 0.825464i | \(0.690914\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9247.05 | −0.217700 | −0.108850 | − | 0.994058i | \(-0.534717\pi\) | ||||
−0.108850 | + | 0.994058i | \(0.534717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −41350.0 | −0.908172 | −0.454086 | − | 0.890958i | \(-0.650034\pi\) | ||||
−0.454086 | + | 0.890958i | \(0.650034\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −31072.1 | −0.597233 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −37962.2 | −0.684359 | −0.342179 | − | 0.939635i | \(-0.611165\pi\) | ||||
−0.342179 | + | 0.939635i | \(0.611165\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −79211.1 | −1.26209 | −0.631046 | − | 0.775746i | \(-0.717374\pi\) | ||||
−0.631046 | + | 0.775746i | \(0.717374\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −174530. | −2.62012 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 92538.5 | 1.23836 | 0.619181 | − | 0.785248i | \(-0.287465\pi\) | ||||
0.619181 | + | 0.785248i | \(0.287465\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −43866.9 | −0.555307 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 207993. | 2.36450 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 175419. | 1.89299 | 0.946495 | − | 0.322720i | \(-0.104597\pi\) | ||||
0.946495 | + | 0.322720i | \(0.104597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −56163.2 | −0.547834 | −0.273917 | − | 0.961753i | \(-0.588319\pi\) | ||||
−0.273917 | + | 0.961753i | \(0.588319\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −158376. | −1.47095 | −0.735474 | − | 0.677553i | \(-0.763040\pi\) | ||||
−0.735474 | + | 0.677553i | \(0.763040\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 23496.4 | 0.198400 | 0.0992001 | − | 0.995068i | \(-0.468372\pi\) | ||||
0.0992001 | + | 0.995068i | \(0.468372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 205342. | 1.65543 | 0.827715 | − | 0.561148i | \(-0.189640\pi\) | ||||
0.827715 | + | 0.561148i | \(0.189640\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 185993. | 1.37025 | 0.685125 | − | 0.728426i | \(-0.259748\pi\) | ||||
0.685125 | + | 0.728426i | \(0.259748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 48282.7 | 0.340445 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 100816. | 0.652620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 241063. | 1.49681 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 80223.7 | 0.459227 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 348363. | 1.91656 | 0.958281 | − | 0.285828i | \(-0.0922685\pi\) | ||||
0.958281 | + | 0.285828i | \(0.0922685\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 294849. | 1.50114 | 0.750571 | − | 0.660790i | \(-0.229779\pi\) | ||||
0.750571 | + | 0.660790i | \(0.229779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −120145. | −0.588949 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −119607. | −0.544446 | −0.272223 | − | 0.962234i | \(-0.587759\pi\) | ||||
−0.272223 | + | 0.962234i | \(0.587759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 145630. | 0.639312 | 0.319656 | − | 0.947534i | \(-0.396433\pi\) | ||||
0.319656 | + | 0.947534i | \(0.396433\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 567695. | 2.32153 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −124848. | −0.493129 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −49750.8 | −0.183584 | −0.0917919 | − | 0.995778i | \(-0.529259\pi\) | ||||
−0.0917919 | + | 0.995778i | \(0.529259\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −214254. | −0.764691 | −0.382346 | − | 0.924019i | \(-0.624884\pi\) | ||||
−0.382346 | + | 0.924019i | \(0.624884\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −170219. | −0.569088 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −197114. | −0.638217 | −0.319108 | − | 0.947718i | \(-0.603383\pi\) | ||||
−0.319108 | + | 0.947718i | \(0.603383\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27890.1 | −0.0847980 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 103013. | 0.303686 | 0.151843 | − | 0.988405i | \(-0.451479\pi\) | ||||
0.151843 | + | 0.988405i | \(0.451479\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 231396. | 0.642044 | 0.321022 | − | 0.947072i | \(-0.395974\pi\) | ||||
0.321022 | + | 0.947072i | \(0.395974\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 430165. | 1.15856 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 207599. | 0.527365 | 0.263682 | − | 0.964610i | \(-0.415063\pi\) | ||||
0.263682 | + | 0.964610i | \(0.415063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −199466. | −0.492349 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 713483. | 1.66438 | 0.832188 | − | 0.554494i | \(-0.187088\pi\) | ||||
0.832188 | + | 0.554494i | \(0.187088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 241894. | 0.548818 | 0.274409 | − | 0.961613i | \(-0.411518\pi\) | ||||
0.274409 | + | 0.961613i | \(0.411518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 412308. | 0.885712 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.30469e6 | −2.72836 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 220340. | 0.437029 | 0.218515 | − | 0.975834i | \(-0.429879\pi\) | ||||
0.218515 | + | 0.975834i | \(0.429879\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −736048. | −1.42237 | −0.711185 | − | 0.703005i | \(-0.751841\pi\) | ||||
−0.711185 | + | 0.703005i | \(0.751841\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 586422. | 1.07658 | 0.538288 | − | 0.842761i | \(-0.319071\pi\) | ||||
0.538288 | + | 0.842761i | \(0.319071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −680230. | −1.21765 | −0.608826 | − | 0.793304i | \(-0.708359\pi\) | ||||
−0.608826 | + | 0.793304i | \(0.708359\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 72117.3 | 0.122828 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.46145e6 | 2.42884 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.55484e6 | 2.46218 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 142662. | 0.220598 | 0.110299 | − | 0.993898i | \(-0.464819\pi\) | ||||
0.110299 | + | 0.993898i | \(0.464819\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.31324e6 | −1.93753 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 98325.8 | 0.141748 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.84193e6 | −2.53683 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.41803e6 | −1.90952 | −0.954760 | − | 0.297377i | \(-0.903888\pi\) | ||||
−0.954760 | + | 0.297377i | \(0.903888\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −75557.1 | −0.0973219 | −0.0486610 | − | 0.998815i | \(-0.515495\pi\) | ||||
−0.0486610 | + | 0.998815i | \(0.515495\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.29149e6 | 1.62743 | 0.813714 | − | 0.581265i | \(-0.197442\pi\) | ||||
0.813714 | + | 0.581265i | \(0.197442\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 112997. | 0.136357 | 0.0681783 | − | 0.997673i | \(-0.478281\pi\) | ||||
0.0681783 | + | 0.997673i | \(0.478281\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −424681. | −0.501641 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 473209. | 0.535869 | 0.267935 | − | 0.963437i | \(-0.413659\pi\) | ||||
0.267935 | + | 0.963437i | \(0.413659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.39122e6 | −1.54296 | −0.771478 | − | 0.636256i | \(-0.780482\pi\) | ||||
−0.771478 | + | 0.636256i | \(0.780482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 203671. | 0.216778 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.19508e6 | 2.28933 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −776017. | −0.777476 | −0.388738 | − | 0.921348i | \(-0.627089\pi\) | ||||
−0.388738 | + | 0.921348i | \(0.627089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 360935. | 0.354509 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 955090. | 0.902011 | 0.451005 | − | 0.892521i | \(-0.351066\pi\) | ||||
0.451005 | + | 0.892521i | \(0.351066\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −238166. | −0.220613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −190821. | −0.170113 | −0.0850566 | − | 0.996376i | \(-0.527107\pi\) | ||||
−0.0850566 | + | 0.996376i | \(0.527107\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.65926e6 | 1.45144 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 224114. | 0.188837 | 0.0944186 | − | 0.995533i | \(-0.469901\pi\) | ||||
0.0944186 | + | 0.995533i | \(0.469901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 687404. | 0.568577 | 0.284288 | − | 0.958739i | \(-0.408243\pi\) | ||||
0.284288 | + | 0.958739i | \(0.408243\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.58135e6 | 2.05833 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.14588e6 | −0.897302 | −0.448651 | − | 0.893707i | \(-0.648095\pi\) | ||||
−0.448651 | + | 0.893707i | \(0.648095\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 755908. | 0.571088 | 0.285544 | − | 0.958366i | \(-0.407826\pi\) | ||||
0.285544 | + | 0.958366i | \(0.407826\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.92464e6 | −1.42851 | −0.714257 | − | 0.699884i | \(-0.753235\pi\) | ||||
−0.714257 | + | 0.699884i | \(0.753235\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −844194. | −0.604975 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.81329e6 | 1.98139 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.46185e6 | −0.994795 | −0.497398 | − | 0.867523i | \(-0.665711\pi\) | ||||
−0.497398 | + | 0.867523i | \(0.665711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.23132e6 | −0.823791 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 509559. | 0.329622 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 758584. | 0.482600 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 303061. | 0.186544 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.06474e6 | 0.644756 | 0.322378 | − | 0.946611i | \(-0.395518\pi\) | ||||
0.322378 | + | 0.946611i | \(0.395518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.59214e6 | −1.51970 | −0.759850 | − | 0.650098i | \(-0.774728\pi\) | ||||
−0.759850 | + | 0.650098i | \(0.774728\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.14280e6 | −1.23629 | −0.618147 | − | 0.786063i | \(-0.712116\pi\) | ||||
−0.618147 | + | 0.786063i | \(0.712116\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.02229e6 | −1.68923 | −0.844613 | − | 0.535377i | \(-0.820170\pi\) | ||||
−0.844613 | + | 0.535377i | \(0.820170\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −933292. | −0.513501 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.04478e6 | −2.69052 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.64428e6 | 1.91383 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 245314. | 0.124949 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.03801e6 | −0.520751 | −0.260376 | − | 0.965507i | \(-0.583846\pi\) | ||||
−0.260376 | + | 0.965507i | \(0.583846\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.51871e6 | −1.71306 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.23059e6 | 1.06991 | 0.534953 | − | 0.844882i | \(-0.320329\pi\) | ||||
0.534953 | + | 0.844882i | \(0.320329\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.27246e6 | −0.592598 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.57483e6 | 1.14795 | 0.573977 | − | 0.818872i | \(-0.305400\pi\) | ||||
0.573977 | + | 0.818872i | \(0.305400\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 311098. | 0.136721 | 0.0683604 | − | 0.997661i | \(-0.478223\pi\) | ||||
0.0683604 | + | 0.997661i | \(0.478223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.77642e6 | 1.61303 | 0.806517 | − | 0.591212i | \(-0.201350\pi\) | ||||
0.806517 | + | 0.591212i | \(0.201350\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −784406. | −0.330347 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −996020. | −0.407880 | −0.203940 | − | 0.978983i | \(-0.565375\pi\) | ||||
−0.203940 | + | 0.978983i | \(0.565375\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.53594e6 | 1.42803 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.50762e6 | −1.37810 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.83928e6 | −1.48794 | −0.743969 | − | 0.668214i | \(-0.767059\pi\) | ||||
−0.743969 | + | 0.668214i | \(0.767059\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −958457. | −0.361525 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.05517e6 | −1.88132 | −0.940662 | − | 0.339344i | \(-0.889795\pi\) | ||||
−0.940662 | + | 0.339344i | \(0.889795\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.31760e6 | −0.477453 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.46825e6 | −1.24026 | −0.620129 | − | 0.784500i | \(-0.712920\pi\) | ||||
−0.620129 | + | 0.784500i | \(0.712920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.58445e6 | 1.24861 | 0.624304 | − | 0.781182i | \(-0.285383\pi\) | ||||
0.624304 | + | 0.781182i | \(0.285383\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.63577e6 | −0.906267 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.86098e6 | −1.29367 | −0.646834 | − | 0.762630i | \(-0.723908\pi\) | ||||
−0.646834 | + | 0.762630i | \(0.723908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.17108e6 | −0.387386 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.22025e6 | −1.03848 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.20136e6 | −0.382559 | −0.191280 | − | 0.981536i | \(-0.561264\pi\) | ||||
−0.191280 | + | 0.981536i | \(0.561264\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.88850e6 | −1.20760 | −0.603798 | − | 0.797138i | \(-0.706347\pi\) | ||||
−0.603798 | + | 0.797138i | \(0.706347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.79644e6 | −0.550997 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.08219e6 | 0.922301 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.63640e6 | 0.779296 | 0.389648 | − | 0.920964i | \(-0.372597\pi\) | ||||
0.389648 | + | 0.920964i | \(0.372597\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 711264. | 0.205190 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.71929e6 | −1.91515 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 432053. | 0.120227 | 0.0601134 | − | 0.998192i | \(-0.480854\pi\) | ||||
0.0601134 | + | 0.998192i | \(0.480854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.31215e6 | 0.910763 | 0.455381 | − | 0.890296i | \(-0.349503\pi\) | ||||
0.455381 | + | 0.890296i | \(0.349503\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.37537e6 | −2.24922 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −175061. | −0.0464642 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.30508e6 | 1.37562 | 0.687811 | − | 0.725890i | \(-0.258572\pi\) | ||||
0.687811 | + | 0.725890i | \(0.258572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.86645e6 | −0.734723 | −0.367362 | − | 0.930078i | \(-0.619739\pi\) | ||||
−0.367362 | + | 0.930078i | \(0.619739\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.39561e6 | 0.349592 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 758493. | 0.187841 | 0.0939205 | − | 0.995580i | \(-0.470060\pi\) | ||||
0.0939205 | + | 0.995580i | \(0.470060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.02230e6 | −0.731693 | −0.365846 | − | 0.930675i | \(-0.619220\pi\) | ||||
−0.365846 | + | 0.930675i | \(0.619220\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.84982e6 | 1.87914 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.55957e6 | −1.30144 | −0.650721 | − | 0.759317i | \(-0.725533\pi\) | ||||
−0.650721 | + | 0.759317i | \(0.725533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.09250e7 | 2.52918 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.72112e6 | −0.842646 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.48117e6 | 0.331752 | 0.165876 | − | 0.986147i | \(-0.446955\pi\) | ||||
0.165876 | + | 0.986147i | \(0.446955\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12329.0 | −0.00270193 | −0.00135097 | − | 0.999999i | \(-0.500430\pi\) | ||||
−0.00135097 | + | 0.999999i | \(0.500430\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.27201e6 | −0.275765 | −0.137882 | − | 0.990449i | \(-0.544030\pi\) | ||||
−0.137882 | + | 0.990449i | \(0.544030\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.15829e6 | 1.51886 | 0.759429 | − | 0.650590i | \(-0.225479\pi\) | ||||
0.759429 | + | 0.650590i | \(0.225479\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.03256e6 | 0.426688 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.81707e6 | −2.01757 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.98120e6 | 2.02978 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.01478e6 | 0.998649 | 0.499325 | − | 0.866415i | \(-0.333582\pi\) | ||||
0.499325 | + | 0.866415i | \(0.333582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.35136e6 | 0.857555 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.48804e7 | 2.87250 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.46712e6 | 1.23563 | 0.617815 | − | 0.786323i | \(-0.288018\pi\) | ||||
0.617815 | + | 0.786323i | \(0.288018\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.89564e6 | −1.29084 | −0.645418 | − | 0.763829i | \(-0.723317\pi\) | ||||
−0.645418 | + | 0.763829i | \(0.723317\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.02813e6 | 0.561123 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 453106. | 0.0822827 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.00230e7 | −1.80196 | −0.900979 | − | 0.433862i | \(-0.857151\pi\) | ||||
−0.900979 | + | 0.433862i | \(0.857151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.02505e7 | −1.80644 | −0.903220 | − | 0.429178i | \(-0.858803\pi\) | ||||
−0.903220 | + | 0.429178i | \(0.858803\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.76419e6 | −0.831306 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.95058e6 | −0.333710 | −0.166855 | − | 0.985981i | \(-0.553361\pi\) | ||||
−0.166855 | + | 0.985981i | \(0.553361\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.02615e6 | 0.343257 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.34347e7 | −2.23208 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.17468e6 | −0.522364 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.02692e6 | 0.811349 | 0.405674 | − | 0.914018i | \(-0.367037\pi\) | ||||
0.405674 | + | 0.914018i | \(0.367037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −356811. | −0.0570405 | −0.0285203 | − | 0.999593i | \(-0.509080\pi\) | ||||
−0.0285203 | + | 0.999593i | \(0.509080\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.12860e6 | 0.647555 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.11237e6 | −0.949665 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.54236e7 | 2.35163 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.99314e6 | 0.301061 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.52253e6 | 0.225733 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.16485e7 | −1.71111 | −0.855555 | − | 0.517712i | \(-0.826784\pi\) | ||||
−0.855555 | + | 0.517712i | \(0.826784\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.74187e7 | 2.51202 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.56657e6 | −0.366763 | −0.183382 | − | 0.983042i | \(-0.558704\pi\) | ||||
−0.183382 | + | 0.983042i | \(0.558704\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.60873e6 | −0.506378 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.86015e6 | 0.258663 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.19382e6 | −1.25562 | −0.627809 | − | 0.778367i | \(-0.716048\pi\) | ||||
−0.627809 | + | 0.778367i | \(0.716048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.38595e7 | −1.87594 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.73412e6 | 0.363535 | 0.181768 | − | 0.983342i | \(-0.441818\pi\) | ||||
0.181768 | + | 0.983342i | \(0.441818\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.57773e7 | 2.07927 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.51619e6 | 0.714264 | 0.357132 | − | 0.934054i | \(-0.383755\pi\) | ||||
0.357132 | + | 0.934054i | \(0.383755\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.15557e7 | −1.48322 | −0.741612 | − | 0.670829i | \(-0.765938\pi\) | ||||
−0.741612 | + | 0.670829i | \(0.765938\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.31700e6 | 0.292251 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.36955e6 | −1.17160 | −0.585800 | − | 0.810456i | \(-0.699220\pi\) | ||||
−0.585800 | + | 0.810456i | \(0.699220\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.88134e6 | 0.477026 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.24037e7 | 1.51140 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.61313e6 | 0.432801 | 0.216400 | − | 0.976305i | \(-0.430568\pi\) | ||||
0.216400 | + | 0.976305i | \(0.430568\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.92019e6 | −0.584378 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.65554e6 | −1.12756 | −0.563780 | − | 0.825925i | \(-0.690654\pi\) | ||||
−0.563780 | + | 0.825925i | \(0.690654\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.55195e6 | 0.990314 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.36706e6 | 0.838932 | 0.419466 | − | 0.907771i | \(-0.362217\pi\) | ||||
0.419466 | + | 0.907771i | \(0.362217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.04647e6 | −1.02163 | −0.510814 | − | 0.859691i | \(-0.670656\pi\) | ||||
−0.510814 | + | 0.859691i | \(0.670656\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.04488e7 | 2.27132 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.07723e7 | 1.18669 | 0.593345 | − | 0.804948i | \(-0.297807\pi\) | ||||
0.593345 | + | 0.804948i | \(0.297807\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.48194e6 | −0.485694 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.64815e6 | 0.607093 | 0.303547 | − | 0.952817i | \(-0.401829\pi\) | ||||
0.303547 | + | 0.952817i | \(0.401829\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.21062e7 | −1.28025 | −0.640123 | − | 0.768272i | \(-0.721117\pi\) | ||||
−0.640123 | + | 0.768272i | \(0.721117\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.22164e6 | −0.337948 | −0.168974 | − | 0.985620i | \(-0.554045\pi\) | ||||
−0.168974 | + | 0.985620i | \(0.554045\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.53439e6 | −0.468057 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.91583e6 | −0.605781 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.00004e7 | −1.00784 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.59962e6 | −0.859816 | −0.429908 | − | 0.902873i | \(-0.641454\pi\) | ||||
−0.429908 | + | 0.902873i | \(0.641454\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.95508e7 | 2.90827 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.14948e6 | 0.209886 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.89346e6 | 0.854920 | 0.427460 | − | 0.904034i | \(-0.359408\pi\) | ||||
0.427460 | + | 0.904034i | \(0.359408\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.57628e6 | −0.627268 | −0.313634 | − | 0.949544i | \(-0.601546\pi\) | ||||
−0.313634 | + | 0.949544i | \(0.601546\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.16128e7 | 1.09063 | 0.545313 | − | 0.838232i | \(-0.316411\pi\) | ||||
0.545313 | + | 0.838232i | \(0.316411\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.20470e6 | −0.857823 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.03391e6 | 0.645527 | 0.322763 | − | 0.946480i | \(-0.395388\pi\) | ||||
0.322763 | + | 0.946480i | \(0.395388\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.50114e7 | 2.27790 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.10193e7 | −0.988422 | −0.494211 | − | 0.869342i | \(-0.664543\pi\) | ||||
−0.494211 | + | 0.869342i | \(0.664543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.37812e6 | 0.300726 | 0.150363 | − | 0.988631i | \(-0.451956\pi\) | ||||
0.150363 | + | 0.988631i | \(0.451956\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.01916e7 | −0.893696 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −837717. | −0.0729093 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.26552e6 | 0.194250 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.46735e6 | −0.295094 | −0.147547 | − | 0.989055i | \(-0.547138\pi\) | ||||
−0.147547 | + | 0.989055i | \(0.547138\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.81353e7 | 1.52074 | 0.760369 | − | 0.649492i | \(-0.225018\pi\) | ||||
0.760369 | + | 0.649492i | \(0.225018\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.59555e6 | −0.715483 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.60726e7 | 1.31836 | 0.659182 | − | 0.751983i | \(-0.270903\pi\) | ||||
0.659182 | + | 0.751983i | \(0.270903\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.01460e7 | −0.826166 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.75112e7 | 1.40530 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 779272. | 0.0620860 | 0.0310430 | − | 0.999518i | \(-0.490117\pi\) | ||||
0.0310430 | + | 0.999518i | \(0.490117\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.23534e7 | 0.970120 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.54469e7 | −2.76373 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −616669. | −0.0473977 | −0.0236989 | − | 0.999719i | \(-0.507544\pi\) | ||||
−0.0236989 | + | 0.999719i | \(0.507544\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.19178e7 | 0.909509 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.75200e6 | 0.207062 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.94867e7 | 1.45587 | 0.727935 | − | 0.685646i | \(-0.240480\pi\) | ||||
0.727935 | + | 0.685646i | \(0.240480\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.14216e6 | −0.0841398 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.81562e7 | 3.52279 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.07365e6 | −0.438155 | −0.219078 | − | 0.975707i | \(-0.570305\pi\) | ||||
−0.219078 | + | 0.975707i | \(0.570305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.76044e6 | 0.555966 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.99122e6 | −0.423321 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.38803e6 | 0.658777 | 0.329389 | − | 0.944194i | \(-0.393157\pi\) | ||||
0.329389 | + | 0.944194i | \(0.393157\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.18522e7 | 2.20468 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.87253e6 | 0.472451 | 0.236226 | − | 0.971698i | \(-0.424090\pi\) | ||||
0.236226 | + | 0.971698i | \(0.424090\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.63040e7 | −1.78383 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.13208e6 | 0.210970 | 0.105485 | − | 0.994421i | \(-0.466360\pi\) | ||||
0.105485 | + | 0.994421i | \(0.466360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.05007e6 | −0.534968 | −0.267484 | − | 0.963562i | \(-0.586192\pi\) | ||||
−0.267484 | + | 0.963562i | \(0.586192\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.22024e6 | −0.278578 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.15132e6 | −0.0749882 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.51621e7 | −0.980976 | −0.490488 | − | 0.871448i | \(-0.663181\pi\) | ||||
−0.490488 | + | 0.871448i | \(0.663181\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.81746e7 | −1.16037 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.86111e6 | 0.244891 | 0.122445 | − | 0.992475i | \(-0.460926\pi\) | ||||
0.122445 | + | 0.992475i | \(0.460926\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.74204e7 | 1.71638 | 0.858188 | − | 0.513335i | \(-0.171590\pi\) | ||||
0.858188 | + | 0.513335i | \(0.171590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.00617e7 | −0.625694 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.29950e7 | −0.797603 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.96097e6 | 0.485456 | 0.242728 | − | 0.970094i | \(-0.421958\pi\) | ||||
0.242728 | + | 0.970094i | \(0.421958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.09621e6 | −0.246566 | −0.123283 | − | 0.992372i | \(-0.539342\pi\) | ||||
−0.123283 | + | 0.992372i | \(0.539342\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.16852e6 | −0.488527 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.22432e7 | 2.49410 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.86378e6 | −0.343994 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.67207e7 | −0.968457 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.43564e7 | 0.826244 | 0.413122 | − | 0.910676i | \(-0.364438\pi\) | ||||
0.413122 | + | 0.910676i | \(0.364438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.11364e6 | −0.517906 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.19840e6 | 0.180613 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.61963e7 | −1.46081 | −0.730407 | − | 0.683012i | \(-0.760670\pi\) | ||||
−0.730407 | + | 0.683012i | \(0.760670\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.03005e7 | 0.570809 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.62210e7 | −1.43503 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.36585e6 | −0.128676 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.31159e6 | −0.177896 | −0.0889478 | − | 0.996036i | \(-0.528350\pi\) | ||||
−0.0889478 | + | 0.996036i | \(0.528350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.43440e6 | 0.343523 | 0.171761 | − | 0.985139i | \(-0.445054\pi\) | ||||
0.171761 | + | 0.985139i | \(0.445054\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.73839e6 | 0.460826 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.79593e7 | −1.98959 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.12076e7 | 1.09808 | 0.549039 | − | 0.835796i | \(-0.314994\pi\) | ||||
0.549039 | + | 0.835796i | \(0.314994\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.96206e7 | 1.00975 | 0.504875 | − | 0.863193i | \(-0.331539\pi\) | ||||
0.504875 | + | 0.863193i | \(0.331539\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.34210e6 | −0.474986 | −0.237493 | − | 0.971389i | \(-0.576326\pi\) | ||||
−0.237493 | + | 0.971389i | \(0.576326\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.15436e6 | −0.412101 | −0.206050 | − | 0.978541i | \(-0.566061\pi\) | ||||
−0.206050 | + | 0.978541i | \(0.566061\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.93997e6 | −0.246667 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.96288e7 | 0.974265 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.14558e6 | 0.203320 | 0.101660 | − | 0.994819i | \(-0.467585\pi\) | ||||
0.101660 | + | 0.994819i | \(0.467585\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.83450e7 | −0.894392 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.64899e7 | 1.75805 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.18121e7 | −0.565741 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.76655e6 | 0.130953 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.40559e6 | 0.160258 | 0.0801291 | − | 0.996784i | \(-0.474467\pi\) | ||||
0.0801291 | + | 0.996784i | \(0.474467\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.26615e6 | 0.105399 | 0.0526996 | − | 0.998610i | \(-0.483217\pi\) | ||||
0.0526996 | + | 0.998610i | \(0.483217\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.45799e7 | −0.674174 | −0.337087 | − | 0.941474i | \(-0.609442\pi\) | ||||
−0.337087 | + | 0.941474i | \(0.609442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.37184e7 | 1.54113 | 0.770567 | − | 0.637359i | \(-0.219973\pi\) | ||||
0.770567 | + | 0.637359i | \(0.219973\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.76102e7 | 0.800245 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.40728e7 | −1.08138 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.71353e7 | −1.65860 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.93096e6 | −0.173572 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.34267e7 | 0.589481 | 0.294740 | − | 0.955577i | \(-0.404767\pi\) | ||||
0.294740 | + | 0.955577i | \(0.404767\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.01261e6 | −0.260990 | −0.130495 | − | 0.991449i | \(-0.541657\pi\) | ||||
−0.130495 | + | 0.991449i | \(0.541657\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.30820e7 | −1.85949 | −0.929747 | − | 0.368200i | \(-0.879974\pi\) | ||||
−0.929747 | + | 0.368200i | \(0.879974\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.82279e7 | −1.20467 | −0.602336 | − | 0.798242i | \(-0.705763\pi\) | ||||
−0.602336 | + | 0.798242i | \(0.705763\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.70698e7 | −0.724392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.22754e7 | −0.515119 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.05231e7 | 2.52559 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.95335e6 | 0.121875 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.02447e7 | −1.65157 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.05193e7 | 0.832799 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.56044e7 | −0.629836 | −0.314918 | − | 0.949119i | \(-0.601977\pi\) | ||||
−0.314918 | + | 0.949119i | \(0.601977\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.33384e6 | 0.252855 | 0.126427 | − | 0.991976i | \(-0.459649\pi\) | ||||
0.126427 | + | 0.991976i | \(0.459649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.02297e7 | −1.99427 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.44476e7 | −0.567378 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.11662e7 | 0.826713 | 0.413357 | − | 0.910569i | \(-0.364356\pi\) | ||||
0.413357 | + | 0.910569i | \(0.364356\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.27835e6 | −0.319845 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.97859e7 | 0.760330 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.25377e6 | 0.123694 | 0.0618468 | − | 0.998086i | \(-0.480301\pi\) | ||||
0.0618468 | + | 0.998086i | \(0.480301\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.88712e6 | 0.222602 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.10674e8 | −4.14014 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.00930e7 | −0.375555 | −0.187777 | − | 0.982212i | \(-0.560128\pi\) | ||||
−0.187777 | + | 0.982212i | \(0.560128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.04029e7 | 1.11929 | 0.559643 | − | 0.828734i | \(-0.310938\pi\) | ||||
0.559643 | + | 0.828734i | \(0.310938\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.80619e6 | 0.359105 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.37126e7 | −1.58391 | −0.791957 | − | 0.610577i | \(-0.790938\pi\) | ||||
−0.791957 | + | 0.610577i | \(0.790938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.70182e7 | −1.33429 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.31900e7 | −0.827120 | −0.413560 | − | 0.910477i | \(-0.635715\pi\) | ||||
−0.413560 | + | 0.910477i | \(0.635715\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.86909e7 | 0.663167 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.86074e6 | 0.205781 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.46025e7 | −0.859352 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.24372e7 | −2.15837 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.78623e7 | −0.958188 | −0.479094 | − | 0.877764i | \(-0.659035\pi\) | ||||
−0.479094 | + | 0.877764i | \(0.659035\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.65933e7 | −1.24553 | −0.622763 | − | 0.782410i | \(-0.713990\pi\) | ||||
−0.622763 | + | 0.782410i | \(0.713990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.13586e6 | −0.241637 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.83769e7 | −0.615938 | −0.307969 | − | 0.951396i | \(-0.599649\pi\) | ||||
−0.307969 | + | 0.951396i | \(0.599649\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.86809e7 | 1.95677 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.09387e7 | 1.68137 | 0.840687 | − | 0.541522i | \(-0.182152\pi\) | ||||
0.840687 | + | 0.541522i | \(0.182152\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.97448e7 | 1.63364 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.81174e6 | −0.286465 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −946169. | −0.0306044 | −0.0153022 | − | 0.999883i | \(-0.504871\pi\) | ||||
−0.0153022 | + | 0.999883i | \(0.504871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.77023e7 | −1.84772 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.61505e6 | 0.274486 | 0.137243 | − | 0.990537i | \(-0.456176\pi\) | ||||
0.137243 | + | 0.990537i | \(0.456176\pi\) | |||||||
\(998\) | 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 | 504.6.a.r.1.2 | yes | 2 | |
3.2 | odd | 2 | 504.6.a.l.1.1 | ✓ | 2 | ||
4.3 | odd | 2 | 1008.6.a.bs.1.2 | 2 | |||
12.11 | even | 2 | 1008.6.a.bh.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.6.a.l.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
504.6.a.r.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
1008.6.a.bh.1.1 | 2 | 12.11 | even | 2 | |||
1008.6.a.bs.1.2 | 2 | 4.3 | odd | 2 |