Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,8,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(70.2866307339\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.0000 | −0.883883 | −0.441942 | − | 0.897044i | \(-0.645710\pi\) | ||||
−0.441942 | + | 0.897044i | \(0.645710\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −28.0000 | −0.218750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1170.00 | 1.28927 | 0.644633 | − | 0.764492i | \(-0.277010\pi\) | ||||
0.644633 | + | 0.764492i | \(0.277010\pi\) | |||||||
\(8\) | 1560.00 | 1.07723 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2650.00 | 0.600304 | 0.300152 | − | 0.953891i | \(-0.402963\pi\) | ||||
0.300152 | + | 0.953891i | \(0.402963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11180.0 | 1.41137 | 0.705684 | − | 0.708527i | \(-0.250640\pi\) | ||||
0.705684 | + | 0.708527i | \(0.250640\pi\) | |||||||
\(14\) | −11700.0 | −1.13956 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12016.0 | −0.733398 | ||||||||
\(17\) | 31070.0 | 1.53380 | 0.766902 | − | 0.641764i | \(-0.221797\pi\) | ||||
0.766902 | + | 0.641764i | \(0.221797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30316.0 | 1.01399 | 0.506996 | − | 0.861949i | \(-0.330756\pi\) | ||||
0.506996 | + | 0.861949i | \(0.330756\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −26500.0 | −0.530599 | ||||||||
\(23\) | 32760.0 | 0.561431 | 0.280716 | − | 0.959791i | \(-0.409428\pi\) | ||||
0.280716 | + | 0.959791i | \(0.409428\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −111800. | −1.24748 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −32760.0 | −0.282027 | ||||||||
\(29\) | −163150. | −1.24221 | −0.621104 | − | 0.783728i | \(-0.713315\pi\) | ||||
−0.621104 | + | 0.783728i | \(0.713315\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 136188. | 0.821056 | 0.410528 | − | 0.911848i | \(-0.365344\pi\) | ||||
0.410528 | + | 0.911848i | \(0.365344\pi\) | |||||||
\(32\) | −79520.0 | −0.428994 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −310700. | −1.35570 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −16640.0 | −0.0540067 | −0.0270033 | − | 0.999635i | \(-0.508596\pi\) | ||||
−0.0270033 | + | 0.999635i | \(0.508596\pi\) | |||||||
\(38\) | −303160. | −0.896250 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 483200. | 1.09492 | 0.547461 | − | 0.836831i | \(-0.315594\pi\) | ||||
0.547461 | + | 0.836831i | \(0.315594\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 141080. | 0.270599 | 0.135299 | − | 0.990805i | \(-0.456800\pi\) | ||||
0.135299 | + | 0.990805i | \(0.456800\pi\) | |||||||
\(44\) | −74200.0 | −0.131317 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −327600. | −0.496240 | ||||||||
\(47\) | −103240. | −0.145046 | −0.0725230 | − | 0.997367i | \(-0.523105\pi\) | ||||
−0.0725230 | + | 0.997367i | \(0.523105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 545357. | 0.662208 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −313040. | −0.308737 | ||||||||
\(53\) | −1.95013e6 | −1.79928 | −0.899638 | − | 0.436636i | \(-0.856170\pi\) | ||||
−0.899638 | + | 0.436636i | \(0.856170\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.82520e6 | 1.38884 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.63150e6 | 1.09797 | ||||||||
\(59\) | −2.64335e6 | −1.67561 | −0.837804 | − | 0.545971i | \(-0.816161\pi\) | ||||
−0.837804 | + | 0.545971i | \(0.816161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.82092e6 | 1.59124 | 0.795622 | − | 0.605794i | \(-0.207144\pi\) | ||||
0.795622 | + | 0.605794i | \(0.207144\pi\) | |||||||
\(62\) | −1.36188e6 | −0.725718 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.33325e6 | 1.11258 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 506220. | 0.205626 | 0.102813 | − | 0.994701i | \(-0.467216\pi\) | ||||
0.102813 | + | 0.994701i | \(0.467216\pi\) | |||||||
\(68\) | −869960. | −0.335520 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.89090e6 | −0.958581 | −0.479291 | − | 0.877656i | \(-0.659106\pi\) | ||||
−0.479291 | + | 0.877656i | \(0.659106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.87729e6 | 0.865673 | 0.432836 | − | 0.901473i | \(-0.357513\pi\) | ||||
0.432836 | + | 0.901473i | \(0.357513\pi\) | |||||||
\(74\) | 166400. | 0.0477356 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −848848. | −0.221811 | ||||||||
\(77\) | 3.10050e6 | 0.773952 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.71756e6 | −1.30471 | −0.652357 | − | 0.757911i | \(-0.726220\pi\) | ||||
−0.652357 | + | 0.757911i | \(0.726220\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.83200e6 | −0.967784 | ||||||||
\(83\) | 3.79038e6 | 0.727628 | 0.363814 | − | 0.931472i | \(-0.381474\pi\) | ||||
0.363814 | + | 0.931472i | \(0.381474\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.41080e6 | −0.239178 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.13400e6 | 0.646668 | ||||||||
\(89\) | −1.05645e7 | −1.58849 | −0.794244 | − | 0.607599i | \(-0.792133\pi\) | ||||
−0.794244 | + | 0.607599i | \(0.792133\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30806e7 | 1.81963 | ||||||||
\(92\) | −917280. | −0.122813 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.03240e6 | 0.128204 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.15813e6 | −0.240091 | −0.120046 | − | 0.992768i | \(-0.538304\pi\) | ||||
−0.120046 | + | 0.992768i | \(0.538304\pi\) | |||||||
\(98\) | −5.45357e6 | −0.585315 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.00565e6 | 0.483432 | 0.241716 | − | 0.970347i | \(-0.422290\pi\) | ||||
0.241716 | + | 0.970347i | \(0.422290\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.19448e7 | 1.97879 | 0.989397 | − | 0.145234i | \(-0.0463934\pi\) | ||||
0.989397 | + | 0.145234i | \(0.0463934\pi\) | |||||||
\(104\) | 1.74408e7 | 1.52037 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.95013e7 | 1.59035 | ||||||||
\(107\) | 8.47158e6 | 0.668530 | 0.334265 | − | 0.942479i | \(-0.391512\pi\) | ||||
0.334265 | + | 0.942479i | \(0.391512\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.68025e7 | 1.24274 | 0.621370 | − | 0.783517i | \(-0.286576\pi\) | ||||
0.621370 | + | 0.783517i | \(0.286576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.40587e7 | −0.945546 | ||||||||
\(113\) | 1.90436e7 | 1.24158 | 0.620789 | − | 0.783978i | \(-0.286812\pi\) | ||||
0.620789 | + | 0.783978i | \(0.286812\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.56820e6 | 0.271733 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.64335e7 | 1.48104 | ||||||||
\(119\) | 3.63519e7 | 1.97748 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.24647e7 | −0.639635 | ||||||||
\(122\) | −2.82092e7 | −1.40647 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.81326e6 | −0.179606 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.18507e7 | −0.513369 | −0.256685 | − | 0.966495i | \(-0.582630\pi\) | ||||
−0.256685 | + | 0.966495i | \(0.582630\pi\) | |||||||
\(128\) | −1.31539e7 | −0.554396 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.07226e7 | −0.805371 | −0.402685 | − | 0.915338i | \(-0.631923\pi\) | ||||
−0.402685 | + | 0.915338i | \(0.631923\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.54697e7 | 1.30731 | ||||||||
\(134\) | −5.06220e6 | −0.181749 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.84692e7 | 1.65226 | ||||||||
\(137\) | −1.29435e6 | −0.0430061 | −0.0215030 | − | 0.999769i | \(-0.506845\pi\) | ||||
−0.0215030 | + | 0.999769i | \(0.506845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.99420e6 | −0.126147 | −0.0630737 | − | 0.998009i | \(-0.520090\pi\) | ||||
−0.0630737 | + | 0.998009i | \(0.520090\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.89090e7 | 0.847274 | ||||||||
\(143\) | 2.96270e7 | 0.847250 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.87729e7 | −0.765154 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 465920. | 0.0118140 | ||||||||
\(149\) | 5.27315e6 | 0.130592 | 0.0652962 | − | 0.997866i | \(-0.479201\pi\) | ||||
0.0652962 | + | 0.997866i | \(0.479201\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.87634e7 | 1.62532 | 0.812659 | − | 0.582740i | \(-0.198019\pi\) | ||||
0.812659 | + | 0.582740i | \(0.198019\pi\) | |||||||
\(152\) | 4.72930e7 | 1.09231 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.10050e7 | −0.684084 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.43181e7 | −1.32643 | −0.663215 | − | 0.748429i | \(-0.730809\pi\) | ||||
−0.663215 | + | 0.748429i | \(0.730809\pi\) | |||||||
\(158\) | 5.71756e7 | 1.15322 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.83292e7 | 0.723834 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.10739e7 | −0.562004 | −0.281002 | − | 0.959707i | \(-0.590667\pi\) | ||||
−0.281002 | + | 0.959707i | \(0.590667\pi\) | |||||||
\(164\) | −1.35296e7 | −0.239514 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.79038e7 | −0.643138 | ||||||||
\(167\) | 8.07466e7 | 1.34158 | 0.670790 | − | 0.741648i | \(-0.265955\pi\) | ||||
0.670790 | + | 0.741648i | \(0.265955\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.22439e7 | 0.991958 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.95024e6 | −0.0591935 | ||||||||
\(173\) | −7.88638e7 | −1.15802 | −0.579011 | − | 0.815320i | \(-0.696561\pi\) | ||||
−0.579011 | + | 0.815320i | \(0.696561\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.18424e7 | −0.440262 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.05645e8 | 1.40404 | ||||||||
\(179\) | −1.25273e8 | −1.63256 | −0.816282 | − | 0.577653i | \(-0.803969\pi\) | ||||
−0.816282 | + | 0.577653i | \(0.803969\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.95947e7 | −0.747020 | −0.373510 | − | 0.927626i | \(-0.621846\pi\) | ||||
−0.373510 | + | 0.927626i | \(0.621846\pi\) | |||||||
\(182\) | −1.30806e8 | −1.60834 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.11056e7 | 0.604792 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.23355e7 | 0.920750 | ||||||||
\(188\) | 2.89072e6 | 0.0317288 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.40874e8 | 1.46290 | 0.731452 | − | 0.681893i | \(-0.238843\pi\) | ||||
0.731452 | + | 0.681893i | \(0.238843\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.43985e6 | 0.0544674 | 0.0272337 | − | 0.999629i | \(-0.491330\pi\) | ||||
0.0272337 | + | 0.999629i | \(0.491330\pi\) | |||||||
\(194\) | 2.15813e7 | 0.212213 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.52700e7 | −0.144858 | ||||||||
\(197\) | −9.05130e7 | −0.843489 | −0.421744 | − | 0.906715i | \(-0.638582\pi\) | ||||
−0.421744 | + | 0.906715i | \(0.638582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00226e8 | −0.901558 | −0.450779 | − | 0.892636i | \(-0.648854\pi\) | ||||
−0.450779 | + | 0.892636i | \(0.648854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.00565e7 | −0.427298 | ||||||||
\(203\) | −1.90886e8 | −1.60154 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.19448e8 | −1.74902 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.34339e8 | −1.03509 | ||||||||
\(209\) | 8.03374e7 | 0.608703 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.46103e6 | −0.0326924 | −0.0163462 | − | 0.999866i | \(-0.505203\pi\) | ||||
−0.0163462 | + | 0.999866i | \(0.505203\pi\) | |||||||
\(212\) | 5.46036e7 | 0.393592 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.47158e7 | −0.590903 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.59340e8 | 1.05856 | ||||||||
\(218\) | −1.68025e8 | −1.09844 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.47363e8 | 2.16476 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.13973e8 | −1.89594 | −0.947972 | − | 0.318353i | \(-0.896870\pi\) | ||||
−0.947972 | + | 0.318353i | \(0.896870\pi\) | |||||||
\(224\) | −9.30384e7 | −0.553088 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.90436e8 | −1.09741 | ||||||||
\(227\) | −6.07635e7 | −0.344788 | −0.172394 | − | 0.985028i | \(-0.555150\pi\) | ||||
−0.172394 | + | 0.985028i | \(0.555150\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.48864e7 | 0.357050 | 0.178525 | − | 0.983935i | \(-0.442867\pi\) | ||||
0.178525 | + | 0.983935i | \(0.442867\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.54514e8 | −1.33815 | ||||||||
\(233\) | 1.22649e8 | 0.635212 | 0.317606 | − | 0.948223i | \(-0.397121\pi\) | ||||
0.317606 | + | 0.948223i | \(0.397121\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.40138e7 | 0.366539 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.63519e8 | −1.74786 | ||||||||
\(239\) | −3.16220e8 | −1.49829 | −0.749146 | − | 0.662405i | \(-0.769536\pi\) | ||||
−0.749146 | + | 0.662405i | \(0.769536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.37644e8 | −0.633428 | −0.316714 | − | 0.948521i | \(-0.602579\pi\) | ||||
−0.316714 | + | 0.948521i | \(0.602579\pi\) | |||||||
\(242\) | 1.24647e8 | 0.565363 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.89858e7 | −0.348085 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.38933e8 | 1.43111 | ||||||||
\(248\) | 2.12453e8 | 0.884469 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.28522e8 | −0.912160 | −0.456080 | − | 0.889939i | \(-0.650747\pi\) | ||||
−0.456080 | + | 0.889939i | \(0.650747\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.68140e7 | 0.337030 | ||||||||
\(254\) | 1.18507e8 | 0.453759 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.67117e8 | −0.622558 | ||||||||
\(257\) | 2.83909e8 | 1.04331 | 0.521654 | − | 0.853157i | \(-0.325315\pi\) | ||||
0.521654 | + | 0.853157i | \(0.325315\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.94688e7 | −0.0696290 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.07226e8 | 0.711854 | ||||||||
\(263\) | 2.59380e8 | 0.879208 | 0.439604 | − | 0.898192i | \(-0.355119\pi\) | ||||
0.439604 | + | 0.898192i | \(0.355119\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.54697e8 | −1.15551 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.41742e7 | −0.0449806 | ||||||||
\(269\) | 3.45707e8 | 1.08287 | 0.541434 | − | 0.840743i | \(-0.317882\pi\) | ||||
0.541434 | + | 0.840743i | \(0.317882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.36373e8 | −1.02666 | −0.513332 | − | 0.858190i | \(-0.671589\pi\) | ||||
−0.513332 | + | 0.858190i | \(0.671589\pi\) | |||||||
\(272\) | −3.73337e8 | −1.12489 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.29435e7 | 0.0380124 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.09678e8 | 0.875448 | 0.437724 | − | 0.899109i | \(-0.355785\pi\) | ||||
0.437724 | + | 0.899109i | \(0.355785\pi\) | |||||||
\(278\) | 3.99420e7 | 0.111500 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.79386e8 | −0.482300 | −0.241150 | − | 0.970488i | \(-0.577525\pi\) | ||||
−0.241150 | + | 0.970488i | \(0.577525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.18903e8 | −1.09865 | −0.549327 | − | 0.835608i | \(-0.685116\pi\) | ||||
−0.549327 | + | 0.835608i | \(0.685116\pi\) | |||||||
\(284\) | 8.09452e7 | 0.209690 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.96270e8 | −0.748870 | ||||||||
\(287\) | 5.65344e8 | 1.41165 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.55006e8 | 1.35256 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.05641e7 | −0.189366 | ||||||||
\(293\) | −3.86471e7 | −0.0897595 | −0.0448797 | − | 0.998992i | \(-0.514290\pi\) | ||||
−0.0448797 | + | 0.998992i | \(0.514290\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.59584e7 | −0.0581778 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.27315e7 | −0.115429 | ||||||||
\(299\) | 3.66257e8 | 0.792386 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.65064e8 | 0.348874 | ||||||||
\(302\) | −6.87634e8 | −1.43659 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.64277e8 | −0.743660 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.28695e8 | −1.24010 | −0.620048 | − | 0.784564i | \(-0.712887\pi\) | ||||
−0.620048 | + | 0.784564i | \(0.712887\pi\) | |||||||
\(308\) | −8.68140e7 | −0.169302 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.04278e8 | 0.762112 | 0.381056 | − | 0.924552i | \(-0.375561\pi\) | ||||
0.381056 | + | 0.924552i | \(0.375561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.49782e8 | −1.19774 | −0.598870 | − | 0.800846i | \(-0.704383\pi\) | ||||
−0.598870 | + | 0.800846i | \(0.704383\pi\) | |||||||
\(314\) | 6.43181e8 | 1.17241 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.60092e8 | 0.285406 | ||||||||
\(317\) | −1.64523e8 | −0.290082 | −0.145041 | − | 0.989426i | \(-0.546331\pi\) | ||||
−0.145041 | + | 0.989426i | \(0.546331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.32347e8 | −0.745702 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.83292e8 | −0.639785 | ||||||||
\(323\) | 9.41918e8 | 1.55526 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.10739e8 | 0.496746 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.53792e8 | 1.17949 | ||||||||
\(329\) | −1.20791e8 | −0.187003 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.52532e7 | 0.0231187 | 0.0115593 | − | 0.999933i | \(-0.496320\pi\) | ||||
0.0115593 | + | 0.999933i | \(0.496320\pi\) | |||||||
\(332\) | −1.06131e8 | −0.159169 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.07466e8 | −1.18580 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.17071e9 | 1.66627 | 0.833136 | − | 0.553068i | \(-0.186543\pi\) | ||||
0.833136 | + | 0.553068i | \(0.186543\pi\) | |||||||
\(338\) | −6.22439e8 | −0.876775 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.60898e8 | 0.492884 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.25478e8 | −0.435504 | ||||||||
\(344\) | 2.20085e8 | 0.291498 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.88639e8 | 1.02356 | ||||||||
\(347\) | 8.86549e8 | 1.13907 | 0.569534 | − | 0.821968i | \(-0.307124\pi\) | ||||
0.569534 | + | 0.821968i | \(0.307124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.30443e8 | 1.17166 | 0.585829 | − | 0.810435i | \(-0.300769\pi\) | ||||
0.585829 | + | 0.810435i | \(0.300769\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.10728e8 | −0.257527 | ||||||||
\(353\) | −9.09069e8 | −1.09998 | −0.549991 | − | 0.835171i | \(-0.685369\pi\) | ||||
−0.549991 | + | 0.835171i | \(0.685369\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.95806e8 | 0.347482 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.25273e9 | 1.44300 | ||||||||
\(359\) | −1.07136e9 | −1.22209 | −0.611047 | − | 0.791594i | \(-0.709251\pi\) | ||||
−0.611047 | + | 0.791594i | \(0.709251\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.51881e7 | 0.0281787 | ||||||||
\(362\) | 5.95947e8 | 0.660279 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.66257e8 | −0.398044 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.38881e8 | −0.463463 | −0.231732 | − | 0.972780i | \(-0.574439\pi\) | ||||
−0.231732 | + | 0.972780i | \(0.574439\pi\) | |||||||
\(368\) | −3.93644e8 | −0.411753 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.28165e9 | −2.31975 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.86773e9 | 1.86352 | 0.931759 | − | 0.363077i | \(-0.118274\pi\) | ||||
0.931759 | + | 0.363077i | \(0.118274\pi\) | |||||||
\(374\) | −8.23355e8 | −0.813835 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.61054e8 | −0.156248 | ||||||||
\(377\) | −1.82402e9 | −1.75321 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.59566e9 | 1.50558 | 0.752788 | − | 0.658263i | \(-0.228708\pi\) | ||||
0.752788 | + | 0.658263i | \(0.228708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.40874e9 | −1.29304 | ||||||||
\(383\) | 1.19991e9 | 1.09132 | 0.545661 | − | 0.838006i | \(-0.316279\pi\) | ||||
0.545661 | + | 0.838006i | \(0.316279\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.43985e7 | −0.0481428 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.04276e7 | 0.0525200 | ||||||||
\(389\) | −9.25788e8 | −0.797421 | −0.398711 | − | 0.917077i | \(-0.630542\pi\) | ||||
−0.398711 | + | 0.917077i | \(0.630542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.01785e9 | 0.861126 | ||||||||
\(392\) | 8.50757e8 | 0.713353 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.05130e8 | 0.745546 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.87392e7 | −0.0791995 | −0.0395998 | − | 0.999216i | \(-0.512608\pi\) | ||||
−0.0395998 | + | 0.999216i | \(0.512608\pi\) | |||||||
\(398\) | 1.00226e9 | 0.796872 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.88875e9 | 1.46275 | 0.731373 | − | 0.681977i | \(-0.238880\pi\) | ||||
0.731373 | + | 0.681977i | \(0.238880\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.52258e9 | 1.15881 | ||||||||
\(404\) | −1.40158e8 | −0.105751 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.90886e9 | 1.41557 | ||||||||
\(407\) | −4.40960e7 | −0.0324204 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.19515e8 | 0.303191 | 0.151595 | − | 0.988443i | \(-0.451559\pi\) | ||||
0.151595 | + | 0.988443i | \(0.451559\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.14454e8 | −0.432861 | ||||||||
\(413\) | −3.09272e9 | −2.16031 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −8.89034e8 | −0.605468 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.03374e8 | −0.538023 | ||||||||
\(419\) | −8.54891e8 | −0.567756 | −0.283878 | − | 0.958860i | \(-0.591621\pi\) | ||||
−0.283878 | + | 0.958860i | \(0.591621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.65667e9 | 1.08205 | 0.541026 | − | 0.841006i | \(-0.318036\pi\) | ||||
0.541026 | + | 0.841006i | \(0.318036\pi\) | |||||||
\(422\) | 4.46103e7 | 0.0288962 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.04220e9 | −1.93824 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.30048e9 | 2.05154 | ||||||||
\(428\) | −2.37204e8 | −0.146241 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.57827e9 | 0.949536 | 0.474768 | − | 0.880111i | \(-0.342532\pi\) | ||||
0.474768 | + | 0.880111i | \(0.342532\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.85271e8 | 0.405653 | 0.202827 | − | 0.979215i | \(-0.434987\pi\) | ||||
0.202827 | + | 0.979215i | \(0.434987\pi\) | |||||||
\(434\) | −1.59340e9 | −0.935644 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.70469e8 | −0.271850 | ||||||||
\(437\) | 9.93152e8 | 0.569286 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.80243e8 | −0.440154 | −0.220077 | − | 0.975483i | \(-0.570631\pi\) | ||||
−0.220077 | + | 0.975483i | \(0.570631\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.47363e9 | −1.91340 | ||||||||
\(443\) | −7.41931e8 | −0.405462 | −0.202731 | − | 0.979234i | \(-0.564982\pi\) | ||||
−0.202731 | + | 0.979234i | \(0.564982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.13973e9 | 1.67579 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.72990e9 | 1.43441 | ||||||||
\(449\) | 2.86391e9 | 1.49313 | 0.746565 | − | 0.665312i | \(-0.231702\pi\) | ||||
0.746565 | + | 0.665312i | \(0.231702\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.28048e9 | 0.657287 | ||||||||
\(452\) | −5.33220e8 | −0.271595 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.07635e8 | 0.304753 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.37820e8 | 0.312602 | 0.156301 | − | 0.987709i | \(-0.450043\pi\) | ||||
0.156301 | + | 0.987709i | \(0.450043\pi\) | |||||||
\(458\) | −6.48864e8 | −0.315591 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.31053e9 | −1.09839 | −0.549196 | − | 0.835693i | \(-0.685066\pi\) | ||||
−0.549196 | + | 0.835693i | \(0.685066\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.74079e8 | −0.409277 | −0.204638 | − | 0.978838i | \(-0.565602\pi\) | ||||
−0.204638 | + | 0.978838i | \(0.565602\pi\) | |||||||
\(464\) | 1.96041e9 | 0.911033 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.22649e9 | −0.561454 | ||||||||
\(467\) | −2.81303e9 | −1.27810 | −0.639051 | − | 0.769164i | \(-0.720673\pi\) | ||||
−0.639051 | + | 0.769164i | \(0.720673\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.92277e8 | 0.265106 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.12363e9 | −1.80502 | ||||||||
\(473\) | 3.73862e8 | 0.162442 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.01785e9 | −0.432574 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.16220e9 | 1.32431 | ||||||||
\(479\) | 1.85406e9 | 0.770812 | 0.385406 | − | 0.922747i | \(-0.374061\pi\) | ||||
0.385406 | + | 0.922747i | \(0.374061\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.86035e8 | −0.0762232 | ||||||||
\(482\) | 1.37644e9 | 0.559876 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.49011e8 | 0.139920 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.78028e9 | 1.09078 | 0.545390 | − | 0.838183i | \(-0.316382\pi\) | ||||
0.545390 | + | 0.838183i | \(0.316382\pi\) | |||||||
\(488\) | 4.40064e9 | 1.71414 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.73954e9 | −0.663206 | −0.331603 | − | 0.943419i | \(-0.607589\pi\) | ||||
−0.331603 | + | 0.943419i | \(0.607589\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.06907e9 | −1.90530 | ||||||||
\(494\) | −3.38933e9 | −1.26494 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.63644e9 | −0.602161 | ||||||||
\(497\) | −3.38235e9 | −1.23587 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.39056e9 | 1.94215 | 0.971074 | − | 0.238778i | \(-0.0767470\pi\) | ||||
0.971074 | + | 0.238778i | \(0.0767470\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.28522e9 | 0.806243 | ||||||||
\(503\) | 6.05020e6 | 0.00211974 | 0.00105987 | − | 0.999999i | \(-0.499663\pi\) | ||||
0.00105987 | + | 0.999999i | \(0.499663\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.68140e8 | −0.297895 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.31819e8 | 0.112300 | ||||||||
\(509\) | 4.04539e9 | 1.35972 | 0.679858 | − | 0.733344i | \(-0.262041\pi\) | ||||
0.679858 | + | 0.733344i | \(0.262041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.36643e9 | 1.11608 | ||||||||
\(512\) | 3.35487e9 | 1.10466 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.83909e9 | −0.922163 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.73586e8 | −0.0870717 | ||||||||
\(518\) | 1.94688e8 | 0.0615439 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.47330e9 | −0.456413 | −0.228207 | − | 0.973613i | \(-0.573286\pi\) | ||||
−0.228207 | + | 0.973613i | \(0.573286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.56401e9 | 0.783725 | 0.391863 | − | 0.920024i | \(-0.371831\pi\) | ||||
0.391863 | + | 0.920024i | \(0.371831\pi\) | |||||||
\(524\) | 5.80234e8 | 0.176175 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.59380e9 | −0.777117 | ||||||||
\(527\) | 4.23136e9 | 1.25934 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.33161e9 | −0.684795 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.93152e8 | −0.285973 | ||||||||
\(533\) | 5.40218e9 | 1.54534 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.89703e8 | 0.221507 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.45707e9 | −0.957129 | ||||||||
\(539\) | 1.44520e9 | 0.397527 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.08476e9 | −1.38064 | −0.690320 | − | 0.723504i | \(-0.742530\pi\) | ||||
−0.690320 | + | 0.723504i | \(0.742530\pi\) | |||||||
\(542\) | 3.36373e9 | 0.907451 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.47069e9 | −0.657993 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.06578e9 | 0.800912 | 0.400456 | − | 0.916316i | \(-0.368852\pi\) | ||||
0.400456 | + | 0.916316i | \(0.368852\pi\) | |||||||
\(548\) | 3.62418e7 | 0.00940758 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.94606e9 | −1.25959 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.68954e9 | −1.68213 | ||||||||
\(554\) | −3.09678e9 | −0.773794 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.11838e8 | 0.0275948 | ||||||||
\(557\) | −2.13766e9 | −0.524137 | −0.262069 | − | 0.965049i | \(-0.584405\pi\) | ||||
−0.262069 | + | 0.965049i | \(0.584405\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.57727e9 | 0.381914 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.79386e9 | 0.426297 | ||||||||
\(563\) | 2.21110e9 | 0.522190 | 0.261095 | − | 0.965313i | \(-0.415916\pi\) | ||||
0.261095 | + | 0.965313i | \(0.415916\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.18903e9 | 0.971082 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.50980e9 | −1.03262 | ||||||||
\(569\) | −5.70449e8 | −0.129815 | −0.0649074 | − | 0.997891i | \(-0.520675\pi\) | ||||
−0.0649074 | + | 0.997891i | \(0.520675\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.58930e9 | −1.70599 | −0.852993 | − | 0.521922i | \(-0.825215\pi\) | ||||
−0.852993 | + | 0.521922i | \(0.825215\pi\) | |||||||
\(572\) | −8.29556e8 | −0.185336 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.65344e9 | −1.24773 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.22091e9 | 0.264587 | 0.132293 | − | 0.991211i | \(-0.457766\pi\) | ||||
0.132293 | + | 0.991211i | \(0.457766\pi\) | |||||||
\(578\) | −5.55006e9 | −1.19550 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.43474e9 | 0.938107 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.16784e9 | −1.08011 | ||||||||
\(584\) | 4.48857e9 | 0.932531 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.86471e8 | 0.0793369 | ||||||||
\(587\) | −4.95204e9 | −1.01053 | −0.505267 | − | 0.862963i | \(-0.668606\pi\) | ||||
−0.505267 | + | 0.862963i | \(0.668606\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.12868e9 | 0.832544 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.99946e8 | 0.0396084 | ||||||||
\(593\) | −7.15564e8 | −0.140915 | −0.0704575 | − | 0.997515i | \(-0.522446\pi\) | ||||
−0.0704575 | + | 0.997515i | \(0.522446\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.47648e8 | −0.0285671 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.66257e9 | −0.700376 | ||||||||
\(599\) | −7.09937e9 | −1.34966 | −0.674832 | − | 0.737971i | \(-0.735784\pi\) | ||||
−0.674832 | + | 0.737971i | \(0.735784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.34874e9 | −0.253435 | −0.126718 | − | 0.991939i | \(-0.540444\pi\) | ||||
−0.126718 | + | 0.991939i | \(0.540444\pi\) | |||||||
\(602\) | −1.65064e9 | −0.308364 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.92538e9 | −0.355538 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.16618e9 | 0.574613 | 0.287307 | − | 0.957839i | \(-0.407240\pi\) | ||||
0.287307 | + | 0.957839i | \(0.407240\pi\) | |||||||
\(608\) | −2.41073e9 | −0.434996 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.15422e9 | −0.204713 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.83727e9 | −0.322153 | −0.161076 | − | 0.986942i | \(-0.551497\pi\) | ||||
−0.161076 | + | 0.986942i | \(0.551497\pi\) | |||||||
\(614\) | 6.28695e9 | 1.09610 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.83678e9 | 0.833727 | ||||||||
\(617\) | 1.90555e9 | 0.326605 | 0.163302 | − | 0.986576i | \(-0.447785\pi\) | ||||
0.163302 | + | 0.986576i | \(0.447785\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.93437e9 | 1.17514 | 0.587570 | − | 0.809173i | \(-0.300085\pi\) | ||||
0.587570 | + | 0.809173i | \(0.300085\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.04278e9 | −0.673618 | ||||||||
\(623\) | −1.23605e10 | −2.04798 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.49782e9 | 1.05866 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.80091e9 | 0.290157 | ||||||||
\(629\) | −5.17005e8 | −0.0828357 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.23914e9 | −0.830152 | −0.415076 | − | 0.909787i | \(-0.636245\pi\) | ||||
−0.415076 | + | 0.909787i | \(0.636245\pi\) | |||||||
\(632\) | −8.91939e9 | −1.40548 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.64523e9 | 0.256398 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.09709e9 | 0.934619 | ||||||||
\(638\) | 4.32348e9 | 0.659114 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.00504e9 | −0.450657 | −0.225329 | − | 0.974283i | \(-0.572346\pi\) | ||||
−0.225329 | + | 0.974283i | \(0.572346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.72219e9 | 0.552154 | 0.276077 | − | 0.961136i | \(-0.410966\pi\) | ||||
0.276077 | + | 0.961136i | \(0.410966\pi\) | |||||||
\(644\) | −1.07322e9 | −0.158339 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.41918e9 | −1.37467 | ||||||||
\(647\) | 3.81203e9 | 0.553340 | 0.276670 | − | 0.960965i | \(-0.410769\pi\) | ||||
0.276670 | + | 0.960965i | \(0.410769\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.00488e9 | −1.00588 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.70069e8 | 0.122938 | ||||||||
\(653\) | 4.15124e8 | 0.0583420 | 0.0291710 | − | 0.999574i | \(-0.490713\pi\) | ||||
0.0291710 | + | 0.999574i | \(0.490713\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −5.80613e9 | −0.803015 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.20791e9 | 0.165289 | ||||||||
\(659\) | −5.54774e9 | −0.755122 | −0.377561 | − | 0.925985i | \(-0.623237\pi\) | ||||
−0.377561 | + | 0.925985i | \(0.623237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.32765e9 | −0.313482 | −0.156741 | − | 0.987640i | \(-0.550099\pi\) | ||||
−0.156741 | + | 0.987640i | \(0.550099\pi\) | |||||||
\(662\) | −1.52532e8 | −0.0204342 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.91299e9 | 0.783825 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.34479e9 | −0.697414 | ||||||||
\(668\) | −2.26090e9 | −0.293470 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.47544e9 | 0.955230 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.28697e9 | −0.795039 | −0.397520 | − | 0.917594i | \(-0.630129\pi\) | ||||
−0.397520 | + | 0.917594i | \(0.630129\pi\) | |||||||
\(674\) | −1.17071e10 | −1.47279 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.74283e9 | −0.216991 | ||||||||
\(677\) | 8.01998e9 | 0.993374 | 0.496687 | − | 0.867930i | \(-0.334550\pi\) | ||||
0.496687 | + | 0.867930i | \(0.334550\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.52501e9 | −0.309542 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.60898e9 | −0.435652 | ||||||||
\(683\) | 2.94863e9 | 0.354118 | 0.177059 | − | 0.984200i | \(-0.443342\pi\) | ||||
0.177059 | + | 0.984200i | \(0.443342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.25478e9 | 0.384934 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.69522e9 | −0.198457 | ||||||||
\(689\) | −2.18025e10 | −2.53944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.55069e7 | −0.00639991 | −0.00319996 | − | 0.999995i | \(-0.501019\pi\) | ||||
−0.00319996 | + | 0.999995i | \(0.501019\pi\) | |||||||
\(692\) | 2.20819e9 | 0.253317 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.86549e9 | −1.00680 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.50130e10 | 1.67940 | ||||||||
\(698\) | −9.30443e9 | −1.03561 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.99424e9 | −0.766880 | −0.383440 | − | 0.923566i | \(-0.625261\pi\) | ||||
−0.383440 | + | 0.923566i | \(0.625261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.04458e8 | −0.0547623 | ||||||||
\(704\) | 6.18311e9 | 0.667886 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.09069e9 | 0.972256 | ||||||||
\(707\) | 5.85661e9 | 0.623273 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.04433e9 | −0.636922 | −0.318461 | − | 0.947936i | \(-0.603166\pi\) | ||||
−0.318461 | + | 0.947936i | \(0.603166\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.64806e10 | −1.71117 | ||||||||
\(713\) | 4.46152e9 | 0.460967 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.50763e9 | 0.357123 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.07136e10 | 1.08019 | ||||||||
\(719\) | 1.82101e10 | 1.82710 | 0.913548 | − | 0.406731i | \(-0.133331\pi\) | ||||
0.913548 | + | 0.406731i | \(0.133331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.56754e10 | 2.55119 | ||||||||
\(722\) | −2.51881e8 | −0.0249067 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.66865e9 | 0.163411 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.18107e10 | −1.14000 | −0.570001 | − | 0.821644i | \(-0.693057\pi\) | ||||
−0.570001 | + | 0.821644i | \(0.693057\pi\) | |||||||
\(728\) | 2.04057e10 | 1.96016 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.38336e9 | 0.415046 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.95438e7 | 0.00277078 | 0.00138539 | − | 0.999999i | \(-0.499559\pi\) | ||||
0.00138539 | + | 0.999999i | \(0.499559\pi\) | |||||||
\(734\) | 4.38881e9 | 0.409647 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.60508e9 | −0.240851 | ||||||||
\(737\) | 1.34148e9 | 0.123438 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.04219e8 | 0.0277288 | 0.0138644 | − | 0.999904i | \(-0.495587\pi\) | ||||
0.0138644 | + | 0.999904i | \(0.495587\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.28165e10 | 2.05039 | ||||||||
\(743\) | 7.28471e9 | 0.651555 | 0.325778 | − | 0.945446i | \(-0.394374\pi\) | ||||
0.325778 | + | 0.945446i | \(0.394374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.86773e10 | −1.64713 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.30539e9 | −0.201414 | ||||||||
\(749\) | 9.91175e9 | 0.861914 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.35327e10 | 1.16586 | 0.582929 | − | 0.812523i | \(-0.301907\pi\) | ||||
0.582929 | + | 0.812523i | \(0.301907\pi\) | |||||||
\(752\) | 1.24053e9 | 0.106376 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.82402e10 | 1.54963 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.47276e10 | −1.23395 | −0.616974 | − | 0.786983i | \(-0.711642\pi\) | ||||
−0.616974 | + | 0.786983i | \(0.711642\pi\) | |||||||
\(758\) | −1.59566e10 | −1.33075 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.37523e9 | −0.195370 | −0.0976852 | − | 0.995217i | \(-0.531144\pi\) | ||||
−0.0976852 | + | 0.995217i | \(0.531144\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.96589e10 | 1.60222 | ||||||||
\(764\) | −3.94449e9 | −0.320010 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.19991e10 | −0.964602 | ||||||||
\(767\) | −2.95527e10 | −2.36490 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.41939e10 | 1.12554 | 0.562768 | − | 0.826615i | \(-0.309737\pi\) | ||||
0.562768 | + | 0.826615i | \(0.309737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.52316e8 | −0.0119147 | ||||||||
\(773\) | −7.82792e9 | −0.609562 | −0.304781 | − | 0.952422i | \(-0.598583\pi\) | ||||
−0.304781 | + | 0.952422i | \(0.598583\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.36668e9 | −0.258634 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.25788e9 | 0.704828 | ||||||||
\(779\) | 1.46487e10 | 1.11024 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.66088e9 | −0.575440 | ||||||||
\(782\) | −1.01785e10 | −0.761135 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.55301e9 | −0.485663 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.14353e8 | −0.0156754 | −0.00783769 | − | 0.999969i | \(-0.502495\pi\) | ||||
−0.00783769 | + | 0.999969i | \(0.502495\pi\) | |||||||
\(788\) | 2.53436e9 | 0.184513 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.22810e10 | 1.60072 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.15379e10 | 2.24583 | ||||||||
\(794\) | 9.87392e8 | 0.0700032 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.80632e9 | 0.197216 | ||||||||
\(797\) | 1.67153e10 | 1.16952 | 0.584762 | − | 0.811205i | \(-0.301188\pi\) | ||||
0.584762 | + | 0.811205i | \(0.301188\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.20767e9 | −0.222472 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.88875e10 | −1.29290 | ||||||||
\(803\) | 7.62482e9 | 0.519667 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.52258e10 | −1.02425 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.80881e9 | 0.520769 | ||||||||
\(809\) | −1.13448e9 | −0.0753313 | −0.0376657 | − | 0.999290i | \(-0.511992\pi\) | ||||
−0.0376657 | + | 0.999290i | \(0.511992\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.87794e9 | 0.518609 | 0.259304 | − | 0.965796i | \(-0.416507\pi\) | ||||
0.259304 | + | 0.965796i | \(0.416507\pi\) | |||||||
\(812\) | 5.34479e9 | 0.350336 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.40960e8 | 0.0286559 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.27698e9 | 0.274385 | ||||||||
\(818\) | −4.19515e9 | −0.267985 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.67119e10 | 1.05396 | 0.526981 | − | 0.849877i | \(-0.323324\pi\) | ||||
0.526981 | + | 0.849877i | \(0.323324\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.60135e8 | −0.0287730 | −0.0143865 | − | 0.999897i | \(-0.504580\pi\) | ||||
−0.0143865 | + | 0.999897i | \(0.504580\pi\) | |||||||
\(824\) | 3.42338e10 | 2.13162 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.09272e10 | 1.90946 | ||||||||
\(827\) | 1.80809e10 | 1.11160 | 0.555802 | − | 0.831315i | \(-0.312411\pi\) | ||||
0.555802 | + | 0.831315i | \(0.312411\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.31759e9 | −0.263209 | −0.131604 | − | 0.991302i | \(-0.542013\pi\) | ||||
−0.131604 | + | 0.991302i | \(0.542013\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.60857e10 | 1.57026 | ||||||||
\(833\) | 1.69442e10 | 1.01570 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.24945e9 | −0.133154 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.54891e9 | 0.501830 | ||||||||
\(839\) | 1.47269e10 | 0.860882 | 0.430441 | − | 0.902619i | \(-0.358358\pi\) | ||||
0.430441 | + | 0.902619i | \(0.358358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.36805e9 | 0.543079 | ||||||||
\(842\) | −1.65667e10 | −0.956408 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.24909e8 | 0.00715146 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.45837e10 | −0.824660 | ||||||||
\(848\) | 2.34328e10 | 1.31959 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.45126e8 | −0.0303210 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.33675e10 | −0.737444 | −0.368722 | − | 0.929540i | \(-0.620204\pi\) | ||||
−0.368722 | + | 0.929540i | \(0.620204\pi\) | |||||||
\(854\) | −3.30048e10 | −1.81332 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.32157e10 | 0.720163 | ||||||||
\(857\) | 9.72498e9 | 0.527784 | 0.263892 | − | 0.964552i | \(-0.414994\pi\) | ||||
0.263892 | + | 0.964552i | \(0.414994\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.19642e8 | −0.0387383 | −0.0193691 | − | 0.999812i | \(-0.506166\pi\) | ||||
−0.0193691 | + | 0.999812i | \(0.506166\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.57827e10 | −0.839279 | ||||||||
\(863\) | −1.73662e10 | −0.919743 | −0.459871 | − | 0.887985i | \(-0.652105\pi\) | ||||
−0.459871 | + | 0.887985i | \(0.652105\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.85271e9 | −0.358550 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.46152e9 | −0.231560 | ||||||||
\(869\) | −1.51515e10 | −0.783226 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.65954e9 | 0.290213 | ||||||||
\(872\) | 2.62119e10 | 1.33872 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.93152e9 | −0.503183 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.97495e10 | −1.48930 | −0.744649 | − | 0.667456i | \(-0.767383\pi\) | ||||
−0.744649 | + | 0.667456i | \(0.767383\pi\) | |||||||
\(878\) | 7.80243e9 | 0.389044 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.89920e9 | −0.339925 | −0.169962 | − | 0.985451i | \(-0.554365\pi\) | ||||
−0.169962 | + | 0.985451i | \(0.554365\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.12764e9 | 0.397285 | 0.198643 | − | 0.980072i | \(-0.436347\pi\) | ||||
0.198643 | + | 0.980072i | \(0.436347\pi\) | |||||||
\(884\) | −9.72615e9 | −0.473542 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.41931e9 | 0.358382 | ||||||||
\(887\) | −1.19176e10 | −0.573397 | −0.286698 | − | 0.958021i | \(-0.592558\pi\) | ||||
−0.286698 | + | 0.958021i | \(0.592558\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.38653e10 | −0.661870 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.79125e9 | 0.414738 | ||||||||
\(893\) | −3.12982e9 | −0.147075 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.53901e10 | −0.714765 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.86391e10 | −1.31975 | ||||||||
\(899\) | −2.22191e10 | −1.01992 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.05905e10 | −2.75974 | ||||||||
\(902\) | −1.28048e10 | −0.580965 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.97080e10 | 1.33747 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.67453e9 | 0.163522 | 0.0817611 | − | 0.996652i | \(-0.473946\pi\) | ||||
0.0817611 | + | 0.996652i | \(0.473946\pi\) | |||||||
\(908\) | 1.70138e9 | 0.0754224 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.49328e9 | −0.109259 | −0.0546294 | − | 0.998507i | \(-0.517398\pi\) | ||||
−0.0546294 | + | 0.998507i | \(0.517398\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.00445e10 | 0.436798 | ||||||||
\(914\) | −6.37820e9 | −0.276304 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.81682e9 | −0.0781048 | ||||||||
\(917\) | −2.42455e10 | −1.03834 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.51548e10 | −1.91911 | −0.959554 | − | 0.281526i | \(-0.909160\pi\) | ||||
−0.959554 | + | 0.281526i | \(0.909160\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.31053e10 | 0.970851 | ||||||||
\(923\) | −3.23203e10 | −1.35291 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.74079e9 | 0.361753 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.29737e10 | 0.532900 | ||||||||
\(929\) | −1.26182e10 | −0.516346 | −0.258173 | − | 0.966099i | \(-0.583120\pi\) | ||||
−0.258173 | + | 0.966099i | \(0.583120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.65330e10 | 0.671474 | ||||||||
\(932\) | −3.43418e9 | −0.138953 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.81303e10 | 1.12969 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.30706e10 | −0.916157 | −0.458079 | − | 0.888912i | \(-0.651462\pi\) | ||||
−0.458079 | + | 0.888912i | \(0.651462\pi\) | |||||||
\(938\) | −5.92277e9 | −0.234323 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.95344e10 | −1.15549 | −0.577743 | − | 0.816218i | \(-0.696067\pi\) | ||||
−0.577743 | + | 0.816218i | \(0.696067\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.58296e10 | 0.614724 | ||||||||
\(944\) | 3.17625e10 | 1.22889 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.73862e9 | −0.143579 | ||||||||
\(947\) | 3.33791e10 | 1.27717 | 0.638586 | − | 0.769551i | \(-0.279520\pi\) | ||||
0.638586 | + | 0.769551i | \(0.279520\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.21681e10 | 1.22178 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.67090e10 | 2.13021 | ||||||||
\(953\) | −5.59328e9 | −0.209335 | −0.104667 | − | 0.994507i | \(-0.533378\pi\) | ||||
−0.104667 | + | 0.994507i | \(0.533378\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.85415e9 | 0.327751 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.85406e10 | −0.681308 | ||||||||
\(959\) | −1.51439e9 | −0.0554463 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.96544e9 | −0.325867 | ||||||||
\(962\) | 1.86035e9 | 0.0673725 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.85403e9 | 0.138562 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.61612e9 | 0.235294 | 0.117647 | − | 0.993055i | \(-0.462465\pi\) | ||||
0.117647 | + | 0.993055i | \(0.462465\pi\) | |||||||
\(968\) | −1.94449e10 | −0.689036 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.48042e10 | 1.92108 | 0.960542 | − | 0.278136i | \(-0.0897165\pi\) | ||||
0.960542 | + | 0.278136i | \(0.0897165\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.67322e9 | −0.162638 | ||||||||
\(974\) | −2.78028e10 | −0.964122 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.38962e10 | −1.16702 | ||||||||
\(977\) | 2.89446e9 | 0.0992971 | 0.0496485 | − | 0.998767i | \(-0.484190\pi\) | ||||
0.0496485 | + | 0.998767i | \(0.484190\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.79959e10 | −0.953576 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.73954e10 | 0.586196 | ||||||||
\(983\) | 7.15494e9 | 0.240253 | 0.120127 | − | 0.992759i | \(-0.461670\pi\) | ||||
0.120127 | + | 0.992759i | \(0.461670\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.06907e10 | 1.68407 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.49012e9 | −0.313056 | ||||||||
\(989\) | 4.62178e9 | 0.151923 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.07992e9 | −0.0678872 | −0.0339436 | − | 0.999424i | \(-0.510807\pi\) | ||||
−0.0339436 | + | 0.999424i | \(0.510807\pi\) | |||||||
\(992\) | −1.08297e10 | −0.352228 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.38235e10 | 1.09236 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.10829e9 | −0.291074 | −0.145537 | − | 0.989353i | \(-0.546491\pi\) | ||||
−0.145537 | + | 0.989353i | \(0.546491\pi\) | |||||||
\(998\) | −5.39056e10 | −1.71663 | ||||||||
\(999\) | 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 | 225.8.a.d.1.1 | 1 | ||
3.2 | odd | 2 | 225.8.a.j.1.1 | 1 | |||
5.2 | odd | 4 | 225.8.b.e.199.1 | 2 | |||
5.3 | odd | 4 | 225.8.b.e.199.2 | 2 | |||
5.4 | even | 2 | 45.8.a.d.1.1 | yes | 1 | ||
15.2 | even | 4 | 225.8.b.d.199.2 | 2 | |||
15.8 | even | 4 | 225.8.b.d.199.1 | 2 | |||
15.14 | odd | 2 | 45.8.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.8.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
45.8.a.d.1.1 | yes | 1 | 5.4 | even | 2 | ||
225.8.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.8.a.j.1.1 | 1 | 3.2 | odd | 2 | |||
225.8.b.d.199.1 | 2 | 15.8 | even | 4 | |||
225.8.b.d.199.2 | 2 | 15.2 | even | 4 | |||
225.8.b.e.199.1 | 2 | 5.2 | odd | 4 | |||
225.8.b.e.199.2 | 2 | 5.3 | odd | 4 |