Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,6,Mod(1,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(69.2858101592\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 54) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 432.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 33.0000 | 0.590322 | 0.295161 | − | 0.955448i | \(-0.404627\pi\) | ||||
0.295161 | + | 0.955448i | \(0.404627\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −59.0000 | −0.455100 | −0.227550 | − | 0.973766i | \(-0.573072\pi\) | ||||
−0.227550 | + | 0.973766i | \(0.573072\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −147.000 | −0.366299 | −0.183149 | − | 0.983085i | \(-0.558629\pi\) | ||||
−0.183149 | + | 0.983085i | \(0.558629\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 836.000 | 1.37198 | 0.685990 | − | 0.727611i | \(-0.259369\pi\) | ||||
0.685990 | + | 0.727611i | \(0.259369\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1080.00 | −0.906362 | −0.453181 | − | 0.891419i | \(-0.649711\pi\) | ||||
−0.453181 | + | 0.891419i | \(0.649711\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2882.00 | −1.83151 | −0.915756 | − | 0.401734i | \(-0.868408\pi\) | ||||
−0.915756 | + | 0.401734i | \(0.868408\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4386.00 | 1.72882 | 0.864409 | − | 0.502790i | \(-0.167693\pi\) | ||||
0.864409 | + | 0.502790i | \(0.167693\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2036.00 | −0.651520 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1866.00 | 0.412018 | 0.206009 | − | 0.978550i | \(-0.433952\pi\) | ||||
0.206009 | + | 0.978550i | \(0.433952\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3295.00 | 0.615816 | 0.307908 | − | 0.951416i | \(-0.400371\pi\) | ||||
0.307908 | + | 0.951416i | \(0.400371\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1947.00 | −0.268656 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3958.00 | −0.475304 | −0.237652 | − | 0.971350i | \(-0.576378\pi\) | ||||
−0.237652 | + | 0.971350i | \(0.576378\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −20586.0 | −1.91255 | −0.956274 | − | 0.292472i | \(-0.905522\pi\) | ||||
−0.956274 | + | 0.292472i | \(0.905522\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8770.00 | 0.723317 | 0.361658 | − | 0.932311i | \(-0.382211\pi\) | ||||
0.361658 | + | 0.932311i | \(0.382211\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12666.0 | −0.836363 | −0.418182 | − | 0.908363i | \(-0.637332\pi\) | ||||
−0.418182 | + | 0.908363i | \(0.637332\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13326.0 | −0.792884 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9621.00 | −0.470468 | −0.235234 | − | 0.971939i | \(-0.575586\pi\) | ||||
−0.235234 | + | 0.971939i | \(0.575586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4851.00 | −0.216234 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 21468.0 | 0.802900 | 0.401450 | − | 0.915881i | \(-0.368506\pi\) | ||||
0.401450 | + | 0.915881i | \(0.368506\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36248.0 | 1.24727 | 0.623634 | − | 0.781717i | \(-0.285656\pi\) | ||||
0.623634 | + | 0.781717i | \(0.285656\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 27588.0 | 0.809910 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5174.00 | −0.140812 | −0.0704060 | − | 0.997518i | \(-0.522429\pi\) | ||||
−0.0704060 | + | 0.997518i | \(0.522429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −63720.0 | −1.50013 | −0.750067 | − | 0.661362i | \(-0.769979\pi\) | ||||
−0.750067 | + | 0.661362i | \(0.769979\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 57953.0 | 1.27283 | 0.636413 | − | 0.771349i | \(-0.280418\pi\) | ||||
0.636413 | + | 0.771349i | \(0.280418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8673.00 | 0.166703 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16448.0 | −0.296514 | −0.148257 | − | 0.988949i | \(-0.547366\pi\) | ||||
−0.148257 | + | 0.988949i | \(0.547366\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −69267.0 | −1.10365 | −0.551825 | − | 0.833960i | \(-0.686068\pi\) | ||||
−0.551825 | + | 0.833960i | \(0.686068\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −35640.0 | −0.535045 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −54198.0 | −0.725284 | −0.362642 | − | 0.931928i | \(-0.618125\pi\) | ||||
−0.362642 | + | 0.931928i | \(0.618125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −49324.0 | −0.624388 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −95106.0 | −1.08118 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −132961. | −1.43481 | −0.717406 | − | 0.696655i | \(-0.754671\pi\) | ||||
−0.717406 | + | 0.696655i | \(0.754671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −171033. | −1.66831 | −0.834154 | − | 0.551531i | \(-0.814044\pi\) | ||||
−0.834154 | + | 0.551531i | \(0.814044\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 120844. | 1.12236 | 0.561180 | − | 0.827694i | \(-0.310348\pi\) | ||||
0.561180 | + | 0.827694i | \(0.310348\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −30879.0 | −0.260738 | −0.130369 | − | 0.991466i | \(-0.541616\pi\) | ||||
−0.130369 | + | 0.991466i | \(0.541616\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 39962.0 | 0.322167 | 0.161083 | − | 0.986941i | \(-0.448501\pi\) | ||||
0.161083 | + | 0.986941i | \(0.448501\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 70134.0 | 0.516693 | 0.258346 | − | 0.966052i | \(-0.416822\pi\) | ||||
0.258346 | + | 0.966052i | \(0.416822\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 144738. | 1.02056 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 63720.0 | 0.412485 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139442. | −0.865825 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −170313. | −0.974929 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −181613. | −0.999166 | −0.499583 | − | 0.866266i | \(-0.666513\pi\) | ||||
−0.499583 | + | 0.866266i | \(0.666513\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −320055. | −1.62947 | −0.814735 | − | 0.579833i | \(-0.803118\pi\) | ||||
−0.814735 | + | 0.579833i | \(0.803118\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 170038. | 0.833522 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −312414. | −1.42210 | −0.711048 | − | 0.703143i | \(-0.751779\pi\) | ||||
−0.711048 | + | 0.703143i | \(0.751779\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −205676. | −0.902914 | −0.451457 | − | 0.892293i | \(-0.649096\pi\) | ||||
−0.451457 | + | 0.892293i | \(0.649096\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −122892. | −0.502555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 61578.0 | 0.243224 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −346647. | −1.27915 | −0.639575 | − | 0.768728i | \(-0.720890\pi\) | ||||
−0.639575 | + | 0.768728i | \(0.720890\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −185117. | −0.660699 | −0.330350 | − | 0.943859i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943859i | \(0.607167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 108735. | 0.363530 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 65996.0 | 0.213682 | 0.106841 | − | 0.994276i | \(-0.465926\pi\) | ||||
0.106841 | + | 0.994276i | \(0.465926\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −258774. | −0.786785 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 271060. | 0.799091 | 0.399546 | − | 0.916713i | \(-0.369168\pi\) | ||||
0.399546 | + | 0.916713i | \(0.369168\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 104826. | 0.290856 | 0.145428 | − | 0.989369i | \(-0.453544\pi\) | ||||
0.145428 | + | 0.989369i | \(0.453544\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 327603. | 0.882330 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 210405. | 0.534491 | 0.267246 | − | 0.963628i | \(-0.413886\pi\) | ||||
0.267246 | + | 0.963628i | \(0.413886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 120124. | 0.296507 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −74961.0 | −0.174865 | −0.0874325 | − | 0.996170i | \(-0.527866\pi\) | ||||
−0.0874325 | + | 0.996170i | \(0.527866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 30944.0 | 0.0702069 | 0.0351035 | − | 0.999384i | \(-0.488824\pi\) | ||||
0.0351035 | + | 0.999384i | \(0.488824\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −130614. | −0.280582 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 158760. | 0.331999 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −936948. | −1.85837 | −0.929185 | − | 0.369616i | \(-0.879489\pi\) | ||||
−0.929185 | + | 0.369616i | \(0.879489\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −335395. | −0.648132 | −0.324066 | − | 0.946035i | \(-0.605050\pi\) | ||||
−0.324066 | + | 0.946035i | \(0.605050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 445059. | 0.817056 | 0.408528 | − | 0.912746i | \(-0.366042\pi\) | ||||
0.408528 | + | 0.912746i | \(0.366042\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 616867. | 1.10423 | 0.552114 | − | 0.833769i | \(-0.313821\pi\) | ||||
0.552114 | + | 0.833769i | \(0.313821\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −110094. | −0.187510 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −679338. | −1.12902 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 423654. | 0.670881 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −655658. | −1.01384 | −0.506922 | − | 0.861992i | \(-0.669217\pi\) | ||||
−0.506922 | + | 0.861992i | \(0.669217\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 289410. | 0.426990 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −194405. | −0.280258 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −902880. | −1.24351 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 906592. | 1.22081 | 0.610407 | − | 0.792088i | \(-0.291006\pi\) | ||||
0.610407 | + | 0.792088i | \(0.291006\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −449868. | −0.579456 | −0.289728 | − | 0.957109i | \(-0.593565\pi\) | ||||
−0.289728 | + | 0.957109i | \(0.593565\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −218386. | −0.275192 | −0.137596 | − | 0.990488i | \(-0.543938\pi\) | ||||
−0.137596 | + | 0.990488i | \(0.543938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.05860e6 | 1.27744 | 0.638721 | − | 0.769438i | \(-0.279464\pi\) | ||||
0.638721 | + | 0.769438i | \(0.279464\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −417978. | −0.493723 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 699510. | 0.792135 | 0.396067 | − | 0.918221i | \(-0.370375\pi\) | ||||
0.396067 | + | 0.918221i | \(0.370375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.56839e6 | 1.73945 | 0.869724 | − | 0.493538i | \(-0.164297\pi\) | ||||
0.869724 | + | 0.493538i | \(0.164297\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −439758. | −0.468057 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.40935e6 | −2.51280 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −568080. | −0.569148 | −0.284574 | − | 0.958654i | \(-0.591852\pi\) | ||||
−0.284574 | + | 0.958654i | \(0.591852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −644742. | −0.633264 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 843612. | 0.796728 | 0.398364 | − | 0.917227i | \(-0.369578\pi\) | ||||
0.398364 | + | 0.917227i | \(0.369578\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 233522. | 0.216311 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 751290. | 0.669759 | 0.334879 | − | 0.942261i | \(-0.391304\pi\) | ||||
0.334879 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −317493. | −0.277728 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.48088e6 | −1.24778 | −0.623891 | − | 0.781512i | \(-0.714449\pi\) | ||||
−0.623891 | + | 0.781512i | \(0.714449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12395.0 | −0.0102523 | −0.00512617 | − | 0.999987i | \(-0.501632\pi\) | ||||
−0.00512617 | + | 0.999987i | \(0.501632\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 299292. | 0.238651 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.87225e6 | 1.46610 | 0.733051 | − | 0.680174i | \(-0.238096\pi\) | ||||
0.733051 | + | 0.680174i | \(0.238096\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.89422e6 | 1.43109 | 0.715543 | − | 0.698569i | \(-0.246179\pi\) | ||||
0.715543 | + | 0.698569i | \(0.246179\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 676306. | 0.501969 | 0.250985 | − | 0.967991i | \(-0.419246\pi\) | ||||
0.250985 | + | 0.967991i | \(0.419246\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.21457e6 | 0.870401 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −253457. | −0.178509 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.98821e6 | 1.35299 | 0.676494 | − | 0.736448i | \(-0.263498\pi\) | ||||
0.676494 | + | 0.736448i | \(0.263498\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 708444. | 0.473970 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.66670e6 | 2.37190 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −517430. | −0.329181 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.19618e6 | 0.736289 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.57214e6 | 0.952016 | 0.476008 | − | 0.879441i | \(-0.342083\pi\) | ||||
0.476008 | + | 0.879441i | \(0.342083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 185826. | 0.108945 | 0.0544723 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544723 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.06718e6 | −0.615710 | −0.307855 | − | 0.951433i | \(-0.599611\pi\) | ||||
−0.307855 | + | 0.951433i | \(0.599611\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.39367e6 | −1.33788 | −0.668939 | − | 0.743317i | \(-0.733251\pi\) | ||||
−0.668939 | + | 0.743317i | \(0.733251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −274302. | −0.150922 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.11256e6 | 1.66001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.70210e6 | −0.893873 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 747294. | 0.380629 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 396850. | 0.199093 | 0.0995466 | − | 0.995033i | \(-0.468261\pi\) | ||||
0.0995466 | + | 0.995033i | \(0.468261\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −170742. | −0.0831244 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.28762e6 | −0.617609 | −0.308805 | − | 0.951126i | \(-0.599929\pi\) | ||||
−0.308805 | + | 0.951126i | \(0.599929\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −484365. | −0.225573 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.77785e6 | 0.815942 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.33329e6 | −0.594432 | −0.297216 | − | 0.954810i | \(-0.596058\pi\) | ||||
−0.297216 | + | 0.954810i | \(0.596058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.69259e6 | 0.743855 | 0.371927 | − | 0.928262i | \(-0.378697\pi\) | ||||
0.371927 | + | 0.928262i | \(0.378697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 798906. | 0.341239 | 0.170620 | − | 0.985337i | \(-0.445423\pi\) | ||||
0.170620 | + | 0.985337i | \(0.445423\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.10276e6 | −0.885562 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.72080e6 | −1.52370 | −0.761851 | − | 0.647752i | \(-0.775709\pi\) | ||||
−0.761851 | + | 0.647752i | \(0.775709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.82982e6 | 2.35444 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.91245e6 | 0.751377 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.34640e6 | 0.909363 | 0.454682 | − | 0.890654i | \(-0.349753\pi\) | ||||
0.454682 | + | 0.890654i | \(0.349753\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 567639. | 0.214110 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.47321e6 | −1.66474 | −0.832371 | − | 0.554219i | \(-0.813017\pi\) | ||||
−0.832371 | + | 0.554219i | \(0.813017\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.55998e6 | 0.565281 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.40850e6 | −1.21889 | −0.609446 | − | 0.792828i | \(-0.708608\pi\) | ||||
−0.609446 | + | 0.792828i | \(0.708608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.94982e6 | 1.37588 | 0.687940 | − | 0.725767i | \(-0.258515\pi\) | ||||
0.687940 | + | 0.725767i | \(0.258515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 286209. | 0.0984082 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.50501e6 | 0.839335 | 0.419667 | − | 0.907678i | \(-0.362147\pi\) | ||||
0.419667 | + | 0.907678i | \(0.362147\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.73688e6 | −1.56693 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −542784. | −0.175039 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.42550e6 | 1.40924 | 0.704622 | − | 0.709583i | \(-0.251117\pi\) | ||||
0.704622 | + | 0.709583i | \(0.251117\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.63557e6 | 1.75016 | 0.875079 | − | 0.483981i | \(-0.160810\pi\) | ||||
0.875079 | + | 0.483981i | \(0.160810\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.75462e6 | 0.844888 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 581826. | 0.174103 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.52038e6 | −1.33618 | −0.668092 | − | 0.744079i | \(-0.732889\pi\) | ||||
−0.668092 | + | 0.744079i | \(0.732889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.26661e6 | −0.365400 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.28581e6 | −0.651508 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 488028. | 0.135803 | 0.0679015 | − | 0.997692i | \(-0.478370\pi\) | ||||
0.0679015 | + | 0.997692i | \(0.478370\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.54769e6 | 0.975529 | 0.487764 | − | 0.872975i | \(-0.337812\pi\) | ||||
0.487764 | + | 0.872975i | \(0.337812\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.19888e6 | 0.590513 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.13863e6 | −0.567631 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.90608e6 | 0.753555 | 0.376777 | − | 0.926304i | \(-0.377032\pi\) | ||||
0.376777 | + | 0.926304i | \(0.377032\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.07157e6 | −1.04362 | −0.521810 | − | 0.853062i | \(-0.674743\pi\) | ||||
−0.521810 | + | 0.853062i | \(0.674743\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.26405e7 | −3.16635 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 121999. | 0.0302131 | 0.0151065 | − | 0.999886i | \(-0.495191\pi\) | ||||
0.0151065 | + | 0.999886i | \(0.495191\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.59731e6 | −1.83929 | −0.919645 | − | 0.392750i | \(-0.871524\pi\) | ||||
−0.919645 | + | 0.392750i | \(0.871524\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.78853e6 | −0.428151 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.09200e6 | 1.19199 | 0.595995 | − | 0.802988i | \(-0.296758\pi\) | ||||
0.595995 | + | 0.802988i | \(0.296758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.02614e6 | 0.700564 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.62769e6 | −0.368590 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.36968e6 | 0.306781 | 0.153390 | − | 0.988166i | \(-0.450981\pi\) | ||||
0.153390 | + | 0.988166i | \(0.450981\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −659391. | −0.144508 | −0.0722538 | − | 0.997386i | \(-0.523019\pi\) | ||||
−0.0722538 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.32679e6 | 1.58841 | 0.794203 | − | 0.607653i | \(-0.207889\pi\) | ||||
0.794203 | + | 0.607653i | \(0.207889\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.45508e6 | −0.520924 | −0.260462 | − | 0.965484i | \(-0.583875\pi\) | ||||
−0.260462 | + | 0.965484i | \(0.583875\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 305266. | 0.0640835 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.28919e6 | −0.264950 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.86775e6 | 1.19327 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.24387e6 | −0.247705 | −0.123853 | − | 0.992301i | \(-0.539525\pi\) | ||||
−0.123853 | + | 0.992301i | \(0.539525\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.30889e6 | −0.652108 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.38771e6 | −0.847001 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.15882e6 | −0.221409 | −0.110704 | − | 0.993853i | \(-0.535311\pi\) | ||||
−0.110704 | + | 0.993853i | \(0.535311\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.98739e6 | 0.559227 | 0.279614 | − | 0.960113i | \(-0.409794\pi\) | ||||
0.279614 | + | 0.960113i | \(0.409794\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.01528e6 | −0.373438 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.75948e6 | 0.682711 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.98173e6 | −0.715848 | −0.357924 | − | 0.933751i | \(-0.616515\pi\) | ||||
−0.357924 | + | 0.933751i | \(0.616515\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.90964e6 | 0.336536 | 0.168268 | − | 0.985741i | \(-0.446183\pi\) | ||||
0.168268 | + | 0.985741i | \(0.446183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.64409e6 | −0.984839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.29440e6 | −1.07686 | −0.538431 | − | 0.842669i | \(-0.680983\pi\) | ||||
−0.538431 | + | 0.842669i | \(0.680983\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.41923e6 | −0.579263 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.98785e6 | 0.662554 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.86190e6 | 0.306359 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.34932e6 | 0.217781 | 0.108890 | − | 0.994054i | \(-0.465270\pi\) | ||||
0.108890 | + | 0.994054i | \(0.465270\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.18866e6 | −0.829471 | −0.414736 | − | 0.909942i | \(-0.636126\pi\) | ||||
−0.414736 | + | 0.909942i | \(0.636126\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.55860e6 | −0.558152 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.28007e7 | 1.98881 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.72099e7 | −2.62398 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.01901e6 | −0.153919 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.95892e6 | 0.290433 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.40250e6 | 1.38118 | 0.690590 | − | 0.723247i | \(-0.257351\pi\) | ||||
0.690590 | + | 0.723247i | \(0.257351\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.31875e6 | 0.190182 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.46643e6 | 0.924052 | 0.462026 | − | 0.886866i | \(-0.347123\pi\) | ||||
0.462026 | + | 0.886866i | \(0.347123\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.37781e6 | −0.754617 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 970432. | 0.134944 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.12306e7 | −1.53379 | −0.766895 | − | 0.641773i | \(-0.778199\pi\) | ||||
−0.766895 | + | 0.641773i | \(0.778199\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.33172e6 | 0.992376 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.15199e7 | −1.53171 | −0.765854 | − | 0.643015i | \(-0.777683\pi\) | ||||
−0.765854 | + | 0.643015i | \(0.777683\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.31442e6 | 0.305015 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.00381e6 | −0.129979 | −0.0649893 | − | 0.997886i | \(-0.520701\pi\) | ||||
−0.0649893 | + | 0.997886i | \(0.520701\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.35620e7 | −1.74074 | −0.870371 | − | 0.492396i | \(-0.836121\pi\) | ||||
−0.870371 | + | 0.492396i | \(0.836121\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.92990e6 | −1.12636 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.66252e6 | 0.207887 | 0.103943 | − | 0.994583i | \(-0.466854\pi\) | ||||
0.103943 | + | 0.994583i | \(0.466854\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.08675e6 | 0.502271 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.41429e6 | 0.172332 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.83917e6 | 0.340092 | 0.170046 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170046 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.49619e6 | −1.12788 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.56588e6 | −0.299640 | −0.149820 | − | 0.988713i | \(-0.547869\pi\) | ||||
−0.149820 | + | 0.988713i | \(0.547869\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.10276e6 | 0.243499 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.72454e6 | −0.538012 | −0.269006 | − | 0.963138i | \(-0.586695\pi\) | ||||
−0.269006 | + | 0.963138i | \(0.586695\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.60032e6 | −0.745382 | −0.372691 | − | 0.927955i | \(-0.621565\pi\) | ||||
−0.372691 | + | 0.927955i | \(0.621565\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.60159e6 | −0.511116 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.48098e7 | −1.63147 | −0.815734 | − | 0.578428i | \(-0.803667\pi\) | ||||
−0.815734 | + | 0.578428i | \(0.803667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.05888e7 | −1.14747 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.44259e6 | −0.692484 | −0.346242 | − | 0.938145i | \(-0.612542\pi\) | ||||
−0.346242 | + | 0.938145i | \(0.612542\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.02261e7 | 1.08142 | 0.540711 | − | 0.841208i | \(-0.318155\pi\) | ||||
0.540711 | + | 0.841208i | \(0.318155\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.70327e6 | 0.598270 | 0.299135 | − | 0.954211i | \(-0.403302\pi\) | ||||
0.299135 | + | 0.954211i | \(0.403302\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.19768e6 | 0.330077 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 742171. | 0.0759983 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.27464e6 | 0.430797 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.09132e6 | 0.509046 | 0.254523 | − | 0.967067i | \(-0.418081\pi\) | ||||
0.254523 | + | 0.967067i | \(0.418081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.99323e6 | −0.589830 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.11405e7 | −1.08782 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.81898e6 | 0.367115 | 0.183558 | − | 0.983009i | \(-0.441239\pi\) | ||||
0.183558 | + | 0.983009i | \(0.441239\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.36716e7 | 1.30404 | 0.652022 | − | 0.758200i | \(-0.273921\pi\) | ||||
0.652022 | + | 0.758200i | \(0.273921\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.93384e6 | 0.932946 | 0.466473 | − | 0.884535i | \(-0.345524\pi\) | ||||
0.466473 | + | 0.884535i | \(0.345524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.15580e6 | −0.294101 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.31301e6 | −0.304046 | −0.152023 | − | 0.988377i | \(-0.548579\pi\) | ||||
−0.152023 | + | 0.988377i | \(0.548579\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.05618e7 | −0.961912 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.77763e6 | −0.159451 | −0.0797256 | − | 0.996817i | \(-0.525404\pi\) | ||||
−0.0797256 | + | 0.996817i | \(0.525404\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −55306.0 | −0.00492344 | −0.00246172 | − | 0.999997i | \(-0.500784\pi\) | ||||
−0.00246172 | + | 0.999997i | \(0.500784\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.61125e6 | 0.492046 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.18428e6 | 0.712304 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.32846e6 | −0.456873 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.65070e6 | 0.395805 | 0.197902 | − | 0.980222i | \(-0.436587\pi\) | ||||
0.197902 | + | 0.980222i | \(0.436587\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.49270e6 | −0.376735 | −0.188367 | − | 0.982099i | \(-0.560320\pi\) | ||||
−0.188367 | + | 0.982099i | \(0.560320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.84470e6 | 0.652983 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.68760e6 | 0.384502 | 0.192251 | − | 0.981346i | \(-0.438421\pi\) | ||||
0.192251 | + | 0.981346i | \(0.438421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.03097e7 | −0.839495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.04316e6 | −0.645474 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.09452e6 | −0.644906 | −0.322453 | − | 0.946586i | \(-0.604507\pi\) | ||||
−0.322453 | + | 0.946586i | \(0.604507\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.78731e6 | −0.533010 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.22329e7 | 1.73346 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.62894e6 | −0.509506 | −0.254753 | − | 0.967006i | \(-0.581994\pi\) | ||||
−0.254753 | + | 0.967006i | \(0.581994\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.14070e7 | 0.870525 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.00909e7 | 0.759248 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.23483e7 | 0.922552 | 0.461276 | − | 0.887257i | \(-0.347392\pi\) | ||||
0.461276 | + | 0.887257i | \(0.347392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.44519e7 | 1.06463 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.05544e6 | −0.296669 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.91464e6 | −0.570964 | −0.285482 | − | 0.958384i | \(-0.592154\pi\) | ||||
−0.285482 | + | 0.958384i | \(0.592154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.12980e6 | −0.510786 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.79918e6 | −0.268438 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.19607e7 | −0.839306 | −0.419653 | − | 0.907685i | \(-0.637848\pi\) | ||||
−0.419653 | + | 0.907685i | \(0.637848\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.47160e6 | −0.655586 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.84911e7 | 1.27117 | 0.635585 | − | 0.772031i | \(-0.280759\pi\) | ||||
0.635585 | + | 0.772031i | \(0.280759\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 760578. | 0.0515793 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.86031e7 | −1.92664 | −0.963322 | − | 0.268348i | \(-0.913522\pi\) | ||||
−0.963322 | + | 0.268348i | \(0.913522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.08559e6 | 0.337963 | 0.168981 | − | 0.985619i | \(-0.445952\pi\) | ||||
0.168981 | + | 0.985619i | \(0.445952\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.14394e7 | −0.755111 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.82186e6 | 0.118662 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.40296e7 | 0.907705 | 0.453853 | − | 0.891077i | \(-0.350049\pi\) | ||||
0.453853 | + | 0.891077i | \(0.350049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.10886e6 | −0.390025 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.23984e6 | −0.0786367 | −0.0393183 | − | 0.999227i | \(-0.512519\pi\) | ||||
−0.0393183 | + | 0.999227i | \(0.512519\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.50752e7 | 0.943627 | 0.471814 | − | 0.881698i | \(-0.343599\pi\) | ||||
0.471814 | + | 0.881698i | \(0.343599\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.35776e6 | −0.146618 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.79472e7 | 1.10156 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.99071e6 | −0.121393 | −0.0606963 | − | 0.998156i | \(-0.519332\pi\) | ||||
−0.0606963 | + | 0.998156i | \(0.519332\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.24623e7 | −0.750153 | −0.375077 | − | 0.926994i | \(-0.622384\pi\) | ||||
−0.375077 | + | 0.926994i | \(0.622384\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.70862e6 | −0.401217 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.93289e7 | 3.50286 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.36684e6 | 0.549497 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.17787e6 | 0.126141 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.30237e6 | 0.362716 | 0.181358 | − | 0.983417i | \(-0.441951\pi\) | ||||
0.181358 | + | 0.983417i | \(0.441951\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.13791e6 | −0.235147 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.03033e7 | 1.71123 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.95260e7 | −1.08885 | −0.544423 | − | 0.838811i | \(-0.683252\pi\) | ||||
−0.544423 | + | 0.838811i | \(0.683252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.36793e7 | 0.758047 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.51909e6 | −0.466234 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.53954e6 | −0.464456 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.56364e7 | 0.839975 | 0.419988 | − | 0.907530i | \(-0.362034\pi\) | ||||
0.419988 | + | 0.907530i | \(0.362034\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.53900e7 | 0.821649 | 0.410825 | − | 0.911714i | \(-0.365241\pi\) | ||||
0.410825 | + | 0.911714i | \(0.365241\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.94498e6 | 0.471721 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.52751e7 | −1.32476 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.65043e6 | 0.396121 | 0.198060 | − | 0.980190i | \(-0.436536\pi\) | ||||
0.198060 | + | 0.980190i | \(0.436536\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.11099e6 | −0.365957 | −0.182979 | − | 0.983117i | \(-0.558574\pi\) | ||||
−0.182979 | + | 0.983117i | \(0.558574\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.50690e7 | 1.27460 | 0.637298 | − | 0.770617i | \(-0.280052\pi\) | ||||
0.637298 | + | 0.770617i | \(0.280052\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.64584e6 | −0.487476 | −0.243738 | − | 0.969841i | \(-0.578374\pi\) | ||||
−0.243738 | + | 0.969841i | \(0.578374\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.43921e7 | 0.718639 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.45926e6 | 0.171699 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.41135e7 | 0.692199 | 0.346099 | − | 0.938198i | \(-0.387506\pi\) | ||||
0.346099 | + | 0.938198i | \(0.387506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.70292e7 | −0.830241 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.08109e7 | 0.520859 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.22708e6 | 0.394037 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.73598e7 | −0.821714 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.62546e7 | −1.70605 | −0.853024 | − | 0.521872i | \(-0.825234\pi\) | ||||
−0.853024 | + | 0.521872i | \(0.825234\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.65814e7 | 0.771205 | 0.385603 | − | 0.922665i | \(-0.373994\pi\) | ||||
0.385603 | + | 0.922665i | \(0.373994\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.77808e7 | 1.28458 | 0.642290 | − | 0.766462i | \(-0.277984\pi\) | ||||
0.642290 | + | 0.766462i | \(0.277984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.94274e7 | 0.887950 | 0.443975 | − | 0.896039i | \(-0.353568\pi\) | ||||
0.443975 | + | 0.896039i | \(0.353568\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.94336e6 | 0.315522 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.41786e6 | 0.108613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.32546e6 | −0.193191 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00485e7 | 0.443690 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.12534e6 | 0.181118 | 0.0905588 | − | 0.995891i | \(-0.471135\pi\) | ||||
0.0905588 | + | 0.995891i | \(0.471135\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.32293e7 | 1.00832 | 0.504158 | − | 0.863611i | \(-0.331803\pi\) | ||||
0.504158 | + | 0.863611i | \(0.331803\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.86906e7 | −1.66995 | −0.834976 | − | 0.550286i | \(-0.814519\pi\) | ||||
−0.834976 | + | 0.550286i | \(0.814519\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.52681e7 | −0.651592 | −0.325796 | − | 0.945440i | \(-0.605632\pi\) | ||||
−0.325796 | + | 0.945440i | \(0.605632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.07152e7 | 0.454721 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.65034e7 | 1.53181 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.47371e6 | −0.103227 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.14847e6 | 0.253728 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.03907e7 | 0.426415 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.02115e6 | 0.0414447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.19149e6 | 0.128818 | 0.0644089 | − | 0.997924i | \(-0.479484\pi\) | ||||
0.0644089 | + | 0.997924i | \(0.479484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.33880e7 | 0.534465 | 0.267232 | − | 0.963632i | \(-0.413891\pi\) | ||||
0.267232 | + | 0.963632i | \(0.413891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.01822e7 | 0.404266 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.88832e7 | 0.741572 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.44593e6 | −0.212708 | −0.106354 | − | 0.994328i | \(-0.533918\pi\) | ||||
−0.106354 | + | 0.994328i | \(0.533918\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.32699e7 | −2.05815 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.05849e6 | 0.309670 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.44241e7 | −1.68881 | −0.844403 | − | 0.535709i | \(-0.820044\pi\) | ||||
−0.844403 | + | 0.535709i | \(0.820044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.84055e7 | 1.45218 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.23908e6 | 0.195986 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.42388e7 | −0.901907 | −0.450954 | − | 0.892547i | \(-0.648916\pi\) | ||||
−0.450954 | + | 0.892547i | \(0.648916\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.67337e7 | 1.35235 | 0.676177 | − | 0.736739i | \(-0.263635\pi\) | ||||
0.676177 | + | 0.736739i | \(0.263635\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.02902e7 | −3.30645 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 215259. | 0.00779985 | 0.00389993 | − | 0.999992i | \(-0.498759\pi\) | ||||
0.00389993 | + | 0.999992i | \(0.498759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.84487e7 | 1.74629 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.04947e7 | −1.80100 | −0.900500 | − | 0.434856i | \(-0.856799\pi\) | ||||
−0.900500 | + | 0.434856i | \(0.856799\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.09193e7 | −1.09704 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.84324e7 | 0.647196 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.77721e7 | −0.620770 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.10680e7 | −0.382606 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.08587e7 | 1.74904 | 0.874518 | − | 0.484993i | \(-0.161178\pi\) | ||||
0.874518 | + | 0.484993i | \(0.161178\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.81634e7 | −0.958599 | −0.479300 | − | 0.877651i | \(-0.659109\pi\) | ||||
−0.479300 | + | 0.877651i | \(0.659109\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.21349e7 | 0.410916 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.89210e6 | 0.231002 | 0.115501 | − | 0.993307i | \(-0.463153\pi\) | ||||
0.115501 | + | 0.993307i | \(0.463153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.96711e6 | 0.265671 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.47833e7 | 0.487965 | 0.243982 | − | 0.969780i | \(-0.421546\pi\) | ||||
0.243982 | + | 0.969780i | \(0.421546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.46869e7 | 0.482326 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.84652e7 | 1.25048 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.62721e7 | 0.526333 | 0.263166 | − | 0.964750i | \(-0.415233\pi\) | ||||
0.263166 | + | 0.964750i | \(0.415233\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.03566e7 | 0.651850 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.05805e7 | −0.337109 | −0.168554 | − | 0.985692i | \(-0.553910\pi\) | ||||
−0.168554 | + | 0.985692i | \(0.553910\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.6.a.i.1.1 | 1 | ||
3.2 | odd | 2 | 432.6.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 54.6.a.f.1.1 | yes | 1 | ||
12.11 | even | 2 | 54.6.a.a.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 162.6.c.b.109.1 | 2 | |||
36.11 | even | 6 | 162.6.c.k.109.1 | 2 | |||
36.23 | even | 6 | 162.6.c.k.55.1 | 2 | |||
36.31 | odd | 6 | 162.6.c.b.55.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.6.a.a.1.1 | ✓ | 1 | 12.11 | even | 2 | ||
54.6.a.f.1.1 | yes | 1 | 4.3 | odd | 2 | ||
162.6.c.b.55.1 | 2 | 36.31 | odd | 6 | |||
162.6.c.b.109.1 | 2 | 36.7 | odd | 6 | |||
162.6.c.k.55.1 | 2 | 36.23 | even | 6 | |||
162.6.c.k.109.1 | 2 | 36.11 | even | 6 | |||
432.6.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
432.6.a.i.1.1 | 1 | 1.1 | even | 1 | trivial |