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: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −13.0000 | −1.14905 | −0.574524 | − | 0.818488i | \(-0.694813\pi\) | ||||
−0.574524 | + | 0.818488i | \(0.694813\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 41.0000 | 0.320312 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1380.00 | −1.52067 | −0.760337 | − | 0.649529i | \(-0.774966\pi\) | ||||
−0.760337 | + | 0.649529i | \(0.774966\pi\) | |||||||
\(8\) | 1131.00 | 0.780994 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3304.00 | 0.748455 | 0.374227 | − | 0.927337i | \(-0.377908\pi\) | ||||
0.374227 | + | 0.927337i | \(0.377908\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8506.00 | −1.07380 | −0.536900 | − | 0.843646i | \(-0.680405\pi\) | ||||
−0.536900 | + | 0.843646i | \(0.680405\pi\) | |||||||
\(14\) | 17940.0 | 1.74733 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19951.0 | −1.21771 | ||||||||
\(17\) | −9994.00 | −0.493365 | −0.246682 | − | 0.969096i | \(-0.579340\pi\) | ||||
−0.246682 | + | 0.969096i | \(0.579340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 41236.0 | 1.37924 | 0.689619 | − | 0.724173i | \(-0.257778\pi\) | ||||
0.689619 | + | 0.724173i | \(0.257778\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −42952.0 | −0.860011 | ||||||||
\(23\) | 84120.0 | 1.44162 | 0.720812 | − | 0.693131i | \(-0.243769\pi\) | ||||
0.720812 | + | 0.693131i | \(0.243769\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 110578. | 1.23385 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −56580.0 | −0.487091 | ||||||||
\(29\) | −132802. | −1.01114 | −0.505570 | − | 0.862785i | \(-0.668718\pi\) | ||||
−0.505570 | + | 0.862785i | \(0.668718\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −55800.0 | −0.336410 | −0.168205 | − | 0.985752i | \(-0.553797\pi\) | ||||
−0.168205 | + | 0.985752i | \(0.553797\pi\) | |||||||
\(32\) | 114595. | 0.618217 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 129922. | 0.566900 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −228170. | −0.740547 | −0.370273 | − | 0.928923i | \(-0.620736\pi\) | ||||
−0.370273 | + | 0.928923i | \(0.620736\pi\) | |||||||
\(38\) | −536068. | −1.58481 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 139670. | 0.316490 | 0.158245 | − | 0.987400i | \(-0.449416\pi\) | ||||
0.158245 | + | 0.987400i | \(0.449416\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 755492. | 1.44907 | 0.724537 | − | 0.689236i | \(-0.242054\pi\) | ||||
0.724537 | + | 0.689236i | \(0.242054\pi\) | |||||||
\(44\) | 135464. | 0.239739 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.09356e6 | −1.65650 | ||||||||
\(47\) | 836984. | 1.17591 | 0.587956 | − | 0.808893i | \(-0.299933\pi\) | ||||
0.587956 | + | 0.808893i | \(0.299933\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.08086e6 | 1.31245 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −348746. | −0.343952 | ||||||||
\(53\) | 1.64165e6 | 1.51466 | 0.757330 | − | 0.653033i | \(-0.226504\pi\) | ||||
0.757330 | + | 0.653033i | \(0.226504\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.56078e6 | −1.18764 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.72643e6 | 1.16185 | ||||||||
\(59\) | 989656. | 0.627339 | 0.313669 | − | 0.949532i | \(-0.398442\pi\) | ||||
0.313669 | + | 0.949532i | \(0.398442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.65816e6 | −0.935347 | −0.467673 | − | 0.883901i | \(-0.654908\pi\) | ||||
−0.467673 | + | 0.883901i | \(0.654908\pi\) | |||||||
\(62\) | 725400. | 0.386551 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.06399e6 | 0.507351 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.52384e6 | 1.83758 | 0.918789 | − | 0.394749i | \(-0.129168\pi\) | ||||
0.918789 | + | 0.394749i | \(0.129168\pi\) | |||||||
\(68\) | −409754. | −0.158031 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 389408. | 0.129122 | 0.0645611 | − | 0.997914i | \(-0.479435\pi\) | ||||
0.0645611 | + | 0.997914i | \(0.479435\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.61733e6 | −1.69005 | −0.845026 | − | 0.534726i | \(-0.820415\pi\) | ||||
−0.845026 | + | 0.534726i | \(0.820415\pi\) | |||||||
\(74\) | 2.96621e6 | 0.850924 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.69068e6 | 0.441787 | ||||||||
\(77\) | −4.55952e6 | −1.13816 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.90108e6 | 0.890205 | 0.445103 | − | 0.895480i | \(-0.353167\pi\) | ||||
0.445103 | + | 0.895480i | \(0.353167\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.81571e6 | −0.363662 | ||||||||
\(83\) | −9.39412e6 | −1.80336 | −0.901680 | − | 0.432403i | \(-0.857666\pi\) | ||||
−0.901680 | + | 0.432403i | \(0.857666\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.82140e6 | −1.66506 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.73682e6 | 0.584539 | ||||||||
\(89\) | −2.80375e6 | −0.421574 | −0.210787 | − | 0.977532i | \(-0.567603\pi\) | ||||
−0.210787 | + | 0.977532i | \(0.567603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.17383e7 | 1.63290 | ||||||||
\(92\) | 3.44892e6 | 0.461770 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.08808e7 | −1.35118 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.09943e6 | −0.567310 | −0.283655 | − | 0.958926i | \(-0.591547\pi\) | ||||
−0.283655 | + | 0.958926i | \(0.591547\pi\) | |||||||
\(98\) | −1.40511e7 | −1.50807 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.51723e7 | −1.46530 | −0.732648 | − | 0.680607i | \(-0.761716\pi\) | ||||
−0.732648 | + | 0.680607i | \(0.761716\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.70527e6 | −0.424281 | −0.212141 | − | 0.977239i | \(-0.568044\pi\) | ||||
−0.212141 | + | 0.977239i | \(0.568044\pi\) | |||||||
\(104\) | −9.62029e6 | −0.838632 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.13414e7 | −1.74042 | ||||||||
\(107\) | 2.63120e6 | 0.207640 | 0.103820 | − | 0.994596i | \(-0.466893\pi\) | ||||
0.103820 | + | 0.994596i | \(0.466893\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.30059e6 | −0.318080 | −0.159040 | − | 0.987272i | \(-0.550840\pi\) | ||||
−0.159040 | + | 0.987272i | \(0.550840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.75324e7 | 1.85174 | ||||||||
\(113\) | 3.98233e6 | 0.259635 | 0.129817 | − | 0.991538i | \(-0.458561\pi\) | ||||
0.129817 | + | 0.991538i | \(0.458561\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.44488e6 | −0.323881 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.28655e7 | −0.720843 | ||||||||
\(119\) | 1.37917e7 | 0.750247 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.57076e6 | −0.439815 | ||||||||
\(122\) | 2.15561e7 | 1.07476 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.28780e6 | −0.107756 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.80177e7 | −1.21372 | −0.606861 | − | 0.794808i | \(-0.707571\pi\) | ||||
−0.606861 | + | 0.794808i | \(0.707571\pi\) | |||||||
\(128\) | −2.85001e7 | −1.20119 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.19919e6 | 0.318656 | 0.159328 | − | 0.987226i | \(-0.449067\pi\) | ||||
0.159328 | + | 0.987226i | \(0.449067\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.69057e7 | −2.09737 | ||||||||
\(134\) | −5.88100e7 | −2.11147 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.13032e7 | −0.385315 | ||||||||
\(137\) | −1.66646e6 | −0.0553697 | −0.0276849 | − | 0.999617i | \(-0.508813\pi\) | ||||
−0.0276849 | + | 0.999617i | \(0.508813\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.87456e7 | −1.85534 | −0.927670 | − | 0.373401i | \(-0.878192\pi\) | ||||
−0.927670 | + | 0.373401i | \(0.878192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.06230e6 | −0.148368 | ||||||||
\(143\) | −2.81038e7 | −0.803691 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.30253e7 | 1.94195 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.35497e6 | −0.237206 | ||||||||
\(149\) | 1.93697e7 | 0.479702 | 0.239851 | − | 0.970810i | \(-0.422901\pi\) | ||||
0.239851 | + | 0.970810i | \(0.422901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.33952e7 | −1.26207 | −0.631034 | − | 0.775755i | \(-0.717369\pi\) | ||||
−0.631034 | + | 0.775755i | \(0.717369\pi\) | |||||||
\(152\) | 4.66379e7 | 1.07718 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.92738e7 | 1.30780 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.04529e7 | −0.421800 | −0.210900 | − | 0.977508i | \(-0.567639\pi\) | ||||
−0.210900 | + | 0.977508i | \(0.567639\pi\) | |||||||
\(158\) | −5.07140e7 | −1.02289 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.16086e8 | −2.19224 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 733588. | 0.0132677 | 0.00663385 | − | 0.999978i | \(-0.497888\pi\) | ||||
0.00663385 | + | 0.999978i | \(0.497888\pi\) | |||||||
\(164\) | 5.72647e6 | 0.101376 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.22124e8 | 2.07215 | ||||||||
\(167\) | 1.68925e7 | 0.280664 | 0.140332 | − | 0.990105i | \(-0.455183\pi\) | ||||
0.140332 | + | 0.990105i | \(0.455183\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.60352e6 | 0.153048 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.09752e7 | 0.464156 | ||||||||
\(173\) | 1.18186e7 | 0.173541 | 0.0867707 | − | 0.996228i | \(-0.472345\pi\) | ||||
0.0867707 | + | 0.996228i | \(0.472345\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.59181e7 | −0.911403 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.64487e7 | 0.484409 | ||||||||
\(179\) | 3.13746e7 | 0.408877 | 0.204439 | − | 0.978879i | \(-0.434463\pi\) | ||||
0.204439 | + | 0.978879i | \(0.434463\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.83555e7 | −0.731488 | −0.365744 | − | 0.930716i | \(-0.619185\pi\) | ||||
−0.365744 | + | 0.930716i | \(0.619185\pi\) | |||||||
\(182\) | −1.52598e8 | −1.87628 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.51397e7 | 1.12590 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.30202e7 | −0.369261 | ||||||||
\(188\) | 3.43163e7 | 0.376659 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.06166e6 | −0.0421780 | −0.0210890 | − | 0.999778i | \(-0.506713\pi\) | ||||
−0.0210890 | + | 0.999778i | \(0.506713\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.33221e8 | 1.33389 | 0.666946 | − | 0.745106i | \(-0.267601\pi\) | ||||
0.666946 | + | 0.745106i | \(0.267601\pi\) | |||||||
\(194\) | 6.62925e7 | 0.651866 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.43151e7 | 0.420393 | ||||||||
\(197\) | 1.30771e7 | 0.121866 | 0.0609328 | − | 0.998142i | \(-0.480592\pi\) | ||||
0.0609328 | + | 0.998142i | \(0.480592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.98502e7 | −0.628322 | −0.314161 | − | 0.949370i | \(-0.601723\pi\) | ||||
−0.314161 | + | 0.949370i | \(0.601723\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.97239e8 | 1.68370 | ||||||||
\(203\) | 1.83267e8 | 1.53761 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.11685e7 | 0.487520 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.69703e8 | 1.30758 | ||||||||
\(209\) | 1.36244e8 | 1.03230 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.28535e7 | 0.240765 | 0.120382 | − | 0.992728i | \(-0.461588\pi\) | ||||
0.120382 | + | 0.992728i | \(0.461588\pi\) | |||||||
\(212\) | 6.73076e7 | 0.485164 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.42057e7 | −0.238589 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.70040e7 | 0.511569 | ||||||||
\(218\) | 5.59077e7 | 0.365489 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.50090e7 | 0.529775 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.95194e7 | −0.419796 | −0.209898 | − | 0.977723i | \(-0.567313\pi\) | ||||
−0.209898 | + | 0.977723i | \(0.567313\pi\) | |||||||
\(224\) | −1.58141e8 | −0.940106 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.17703e7 | −0.298333 | ||||||||
\(227\) | −2.30779e8 | −1.30950 | −0.654750 | − | 0.755845i | \(-0.727226\pi\) | ||||
−0.654750 | + | 0.755845i | \(0.727226\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.46157e8 | 0.804258 | 0.402129 | − | 0.915583i | \(-0.368270\pi\) | ||||
0.402129 | + | 0.915583i | \(0.368270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.50199e8 | −0.789695 | ||||||||
\(233\) | 3.11907e8 | 1.61540 | 0.807700 | − | 0.589594i | \(-0.200712\pi\) | ||||
0.807700 | + | 0.589594i | \(0.200712\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.05759e7 | 0.200944 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.79292e8 | −0.862070 | ||||||||
\(239\) | −2.27310e8 | −1.07703 | −0.538513 | − | 0.842617i | \(-0.681014\pi\) | ||||
−0.538513 | + | 0.842617i | \(0.681014\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.98483e8 | −0.913404 | −0.456702 | − | 0.889620i | \(-0.650969\pi\) | ||||
−0.456702 | + | 0.889620i | \(0.650969\pi\) | |||||||
\(242\) | 1.11420e8 | 0.505369 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.79846e7 | −0.299603 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.50753e8 | −1.48103 | ||||||||
\(248\) | −6.31098e7 | −0.262734 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.32536e8 | 0.529024 | 0.264512 | − | 0.964382i | \(-0.414789\pi\) | ||||
0.264512 | + | 0.964382i | \(0.414789\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.77932e8 | 1.07899 | ||||||||
\(254\) | 3.64230e8 | 1.39463 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.34310e8 | 0.872872 | ||||||||
\(257\) | −3.58642e7 | −0.131794 | −0.0658970 | − | 0.997826i | \(-0.520991\pi\) | ||||
−0.0658970 | + | 0.997826i | \(0.520991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.14875e8 | 1.12613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.06589e8 | −0.366151 | ||||||||
\(263\) | −4.79640e8 | −1.62581 | −0.812907 | − | 0.582394i | \(-0.802116\pi\) | ||||
−0.812907 | + | 0.582394i | \(0.802116\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.39774e8 | 2.40998 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.85478e8 | 0.588599 | ||||||||
\(269\) | 7.08764e7 | 0.222008 | 0.111004 | − | 0.993820i | \(-0.464593\pi\) | ||||
0.111004 | + | 0.993820i | \(0.464593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.07490e8 | 1.24373 | 0.621863 | − | 0.783126i | \(-0.286376\pi\) | ||||
0.621863 | + | 0.783126i | \(0.286376\pi\) | |||||||
\(272\) | 1.99390e8 | 0.600776 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.16640e7 | 0.0636225 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.93477e7 | 0.224313 | 0.112157 | − | 0.993691i | \(-0.464224\pi\) | ||||
0.112157 | + | 0.993691i | \(0.464224\pi\) | |||||||
\(278\) | 7.63693e8 | 2.13188 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.70068e7 | 0.233928 | 0.116964 | − | 0.993136i | \(-0.462684\pi\) | ||||
0.116964 | + | 0.993136i | \(0.462684\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.77612e8 | −0.728091 | −0.364045 | − | 0.931381i | \(-0.618605\pi\) | ||||
−0.364045 | + | 0.931381i | \(0.618605\pi\) | |||||||
\(284\) | 1.59657e7 | 0.0413594 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.65350e8 | 0.923480 | ||||||||
\(287\) | −1.92745e8 | −0.481278 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.10459e8 | −0.756591 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.30311e8 | −0.541345 | ||||||||
\(293\) | 2.46490e8 | 0.572484 | 0.286242 | − | 0.958157i | \(-0.407594\pi\) | ||||
0.286242 | + | 0.958157i | \(0.407594\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.58060e8 | −0.578363 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.51807e8 | −0.551201 | ||||||||
\(299\) | −7.15525e8 | −1.54802 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.04258e9 | −2.20357 | ||||||||
\(302\) | 6.94138e8 | 1.45018 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.22699e8 | −1.67951 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.84965e8 | −0.759340 | −0.379670 | − | 0.925122i | \(-0.623963\pi\) | ||||
−0.379670 | + | 0.925122i | \(0.623963\pi\) | |||||||
\(308\) | −1.86940e8 | −0.364565 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.64435e7 | −0.0875514 | −0.0437757 | − | 0.999041i | \(-0.513939\pi\) | ||||
−0.0437757 | + | 0.999041i | \(0.513939\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.10558e8 | −0.388120 | −0.194060 | − | 0.980990i | \(-0.562166\pi\) | ||||
−0.194060 | + | 0.980990i | \(0.562166\pi\) | |||||||
\(314\) | 2.65888e8 | 0.484669 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.59944e8 | 0.285144 | ||||||||
\(317\) | −9.60971e8 | −1.69435 | −0.847175 | − | 0.531314i | \(-0.821698\pi\) | ||||
−0.847175 | + | 0.531314i | \(0.821698\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.38778e8 | −0.756793 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.50911e9 | 2.51899 | ||||||||
\(323\) | −4.12113e8 | −0.680467 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.53664e6 | −0.0152452 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.57967e8 | 0.247177 | ||||||||
\(329\) | −1.15504e9 | −1.78818 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.99923e8 | 0.606147 | 0.303074 | − | 0.952967i | \(-0.401987\pi\) | ||||
0.303074 | + | 0.952967i | \(0.401987\pi\) | |||||||
\(332\) | −3.85159e8 | −0.577639 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.19603e8 | −0.322497 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.69185e8 | −0.383129 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(338\) | −1.24846e8 | −0.175859 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.84363e8 | −0.251787 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.55093e8 | −0.475131 | ||||||||
\(344\) | 8.54461e8 | 1.13172 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.53641e8 | −0.199407 | ||||||||
\(347\) | −8.21868e8 | −1.05596 | −0.527982 | − | 0.849256i | \(-0.677051\pi\) | ||||
−0.527982 | + | 0.849256i | \(0.677051\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.48354e8 | 0.816438 | 0.408219 | − | 0.912884i | \(-0.366150\pi\) | ||||
0.408219 | + | 0.912884i | \(0.366150\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.78622e8 | 0.462707 | ||||||||
\(353\) | 6.52666e8 | 0.789732 | 0.394866 | − | 0.918739i | \(-0.370791\pi\) | ||||
0.394866 | + | 0.918739i | \(0.370791\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.14954e8 | −0.135035 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.07870e8 | −0.469820 | ||||||||
\(359\) | 8.77431e8 | 1.00088 | 0.500440 | − | 0.865771i | \(-0.333171\pi\) | ||||
0.500440 | + | 0.865771i | \(0.333171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.06536e8 | 0.902295 | ||||||||
\(362\) | 7.58622e8 | 0.840515 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.81269e8 | 0.523038 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.86989e8 | −0.303064 | −0.151532 | − | 0.988452i | \(-0.548421\pi\) | ||||
−0.151532 | + | 0.988452i | \(0.548421\pi\) | |||||||
\(368\) | −1.67828e9 | −1.75548 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.26548e9 | −2.30330 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.77013e9 | 1.76614 | 0.883069 | − | 0.469242i | \(-0.155473\pi\) | ||||
0.883069 | + | 0.469242i | \(0.155473\pi\) | |||||||
\(374\) | 4.29262e8 | 0.424299 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.46629e8 | 0.918380 | ||||||||
\(377\) | 1.12961e9 | 1.08576 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.46311e9 | 1.38051 | 0.690257 | − | 0.723565i | \(-0.257498\pi\) | ||||
0.690257 | + | 0.723565i | \(0.257498\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.28015e7 | 0.0484646 | ||||||||
\(383\) | −9.90456e8 | −0.900823 | −0.450412 | − | 0.892821i | \(-0.648723\pi\) | ||||
−0.450412 | + | 0.892821i | \(0.648723\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.73187e9 | −1.53271 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.09076e8 | −0.181716 | ||||||||
\(389\) | 7.96901e8 | 0.686406 | 0.343203 | − | 0.939261i | \(-0.388488\pi\) | ||||
0.343203 | + | 0.939261i | \(0.388488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.40695e8 | −0.711246 | ||||||||
\(392\) | 1.22245e9 | 1.02501 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.70003e8 | −0.140029 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.95584e8 | −0.638145 | −0.319073 | − | 0.947730i | \(-0.603371\pi\) | ||||
−0.319073 | + | 0.947730i | \(0.603371\pi\) | |||||||
\(398\) | 9.08053e8 | 0.721972 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.01632e9 | 1.56154 | 0.780771 | − | 0.624817i | \(-0.214826\pi\) | ||||
0.780771 | + | 0.624817i | \(0.214826\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.74635e8 | 0.361237 | ||||||||
\(404\) | −6.22063e8 | −0.469353 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.38247e9 | −1.76679 | ||||||||
\(407\) | −7.53874e8 | −0.554266 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.48030e7 | −0.0396070 | −0.0198035 | − | 0.999804i | \(-0.506304\pi\) | ||||
−0.0198035 | + | 0.999804i | \(0.506304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.92916e8 | −0.135903 | ||||||||
\(413\) | −1.36573e9 | −0.953978 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.74745e8 | −0.663841 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.77117e9 | −1.18616 | ||||||||
\(419\) | −1.10925e8 | −0.0736679 | −0.0368340 | − | 0.999321i | \(-0.511727\pi\) | ||||
−0.0368340 | + | 0.999321i | \(0.511727\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.12064e9 | −1.38509 | −0.692547 | − | 0.721373i | \(-0.743511\pi\) | ||||
−0.692547 | + | 0.721373i | \(0.743511\pi\) | |||||||
\(422\) | −4.27096e8 | −0.276650 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.85671e9 | 1.18294 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.28826e9 | 1.42236 | ||||||||
\(428\) | 1.07879e8 | 0.0665097 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.48533e9 | 1.49525 | 0.747624 | − | 0.664123i | \(-0.231195\pi\) | ||||
0.747624 | + | 0.664123i | \(0.231195\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.99956e7 | −0.0177562 | −0.00887811 | − | 0.999961i | \(-0.502826\pi\) | ||||
−0.00887811 | + | 0.999961i | \(0.502826\pi\) | |||||||
\(434\) | −1.00105e9 | −0.587818 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.76324e8 | −0.101885 | ||||||||
\(437\) | 3.46877e9 | 1.98834 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.04873e9 | −0.591616 | −0.295808 | − | 0.955247i | \(-0.595589\pi\) | ||||
−0.295808 | + | 0.955247i | \(0.595589\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.10512e9 | −0.608738 | ||||||||
\(443\) | 2.04679e8 | 0.111856 | 0.0559282 | − | 0.998435i | \(-0.482188\pi\) | ||||
0.0559282 | + | 0.998435i | \(0.482188\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.03752e8 | 0.482366 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.46831e9 | −0.771516 | ||||||||
\(449\) | −2.63962e9 | −1.37619 | −0.688097 | − | 0.725619i | \(-0.741554\pi\) | ||||
−0.688097 | + | 0.725619i | \(0.741554\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.61470e8 | 0.236878 | ||||||||
\(452\) | 1.63276e8 | 0.0831643 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.00013e9 | 1.50468 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.83738e9 | −0.900519 | −0.450260 | − | 0.892898i | \(-0.648669\pi\) | ||||
−0.450260 | + | 0.892898i | \(0.648669\pi\) | |||||||
\(458\) | −1.90004e9 | −0.924132 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.57678e9 | −1.70035 | −0.850176 | − | 0.526499i | \(-0.823505\pi\) | ||||
−0.850176 | + | 0.526499i | \(0.823505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.28068e9 | −0.599662 | −0.299831 | − | 0.953992i | \(-0.596930\pi\) | ||||
−0.299831 | + | 0.953992i | \(0.596930\pi\) | |||||||
\(464\) | 2.64953e9 | 1.23128 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.05480e9 | −1.85617 | ||||||||
\(467\) | −4.19984e9 | −1.90820 | −0.954100 | − | 0.299490i | \(-0.903184\pi\) | ||||
−0.954100 | + | 0.299490i | \(0.903184\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.24290e9 | −2.79436 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.11930e9 | 0.489948 | ||||||||
\(473\) | 2.49615e9 | 1.08457 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.65461e8 | 0.240313 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.95503e9 | 1.23756 | ||||||||
\(479\) | −2.48202e9 | −1.03188 | −0.515942 | − | 0.856623i | \(-0.672558\pi\) | ||||
−0.515942 | + | 0.856623i | \(0.672558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.94081e9 | 0.795200 | ||||||||
\(482\) | 2.58027e9 | 1.04955 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.51401e8 | −0.140878 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.08065e9 | 0.423970 | 0.211985 | − | 0.977273i | \(-0.432007\pi\) | ||||
0.211985 | + | 0.977273i | \(0.432007\pi\) | |||||||
\(488\) | −1.87538e9 | −0.730500 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.47787e8 | 0.361348 | 0.180674 | − | 0.983543i | \(-0.442172\pi\) | ||||
0.180674 | + | 0.983543i | \(0.442172\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.32722e9 | 0.498861 | ||||||||
\(494\) | 4.55979e9 | 1.70177 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.11327e9 | 0.409650 | ||||||||
\(497\) | −5.37383e8 | −0.196353 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.07692e9 | −0.748286 | −0.374143 | − | 0.927371i | \(-0.622063\pi\) | ||||
−0.374143 | + | 0.927371i | \(0.622063\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.72297e9 | −0.607875 | ||||||||
\(503\) | 2.73265e9 | 0.957408 | 0.478704 | − | 0.877976i | \(-0.341107\pi\) | ||||
0.478704 | + | 0.877976i | \(0.341107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.61312e9 | −1.23981 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.14872e9 | −0.388770 | ||||||||
\(509\) | −4.52470e9 | −1.52082 | −0.760409 | − | 0.649444i | \(-0.775002\pi\) | ||||
−0.760409 | + | 0.649444i | \(0.775002\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.75192e9 | 2.57002 | ||||||||
\(512\) | 6.01982e8 | 0.198216 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.66235e8 | 0.151438 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.76540e9 | 0.880117 | ||||||||
\(518\) | −4.09337e9 | −1.29398 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.79533e8 | 0.0865965 | 0.0432983 | − | 0.999062i | \(-0.486213\pi\) | ||||
0.0432983 | + | 0.999062i | \(0.486213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.46376e9 | −0.447419 | −0.223710 | − | 0.974656i | \(-0.571817\pi\) | ||||
−0.223710 | + | 0.974656i | \(0.571817\pi\) | |||||||
\(524\) | 3.36167e8 | 0.102069 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.23533e9 | 1.86814 | ||||||||
\(527\) | 5.57665e8 | 0.165973 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.67135e9 | 1.07828 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.33313e9 | −0.671814 | ||||||||
\(533\) | −1.18803e9 | −0.339847 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.11647e9 | 1.43514 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.21393e8 | −0.255098 | ||||||||
\(539\) | 3.57115e9 | 0.982308 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.72194e9 | −0.739073 | −0.369537 | − | 0.929216i | \(-0.620484\pi\) | ||||
−0.369537 | + | 0.929216i | \(0.620484\pi\) | |||||||
\(542\) | −5.29737e9 | −1.42910 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.14526e9 | −0.305006 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.73048e8 | 0.175829 | 0.0879145 | − | 0.996128i | \(-0.471980\pi\) | ||||
0.0879145 | + | 0.996128i | \(0.471980\pi\) | |||||||
\(548\) | −6.83248e7 | −0.0177356 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.47622e9 | −1.39460 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.38349e9 | −1.35371 | ||||||||
\(554\) | −1.03152e9 | −0.257747 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.40857e9 | −0.594289 | ||||||||
\(557\) | −7.19994e9 | −1.76537 | −0.882685 | − | 0.469964i | \(-0.844267\pi\) | ||||
−0.882685 | + | 0.469964i | \(0.844267\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.42621e9 | −1.55602 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.13109e9 | −0.268794 | ||||||||
\(563\) | 5.80114e9 | 1.37004 | 0.685021 | − | 0.728524i | \(-0.259793\pi\) | ||||
0.685021 | + | 0.728524i | \(0.259793\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.60895e9 | 0.836612 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.40420e8 | 0.100844 | ||||||||
\(569\) | 1.67069e9 | 0.380192 | 0.190096 | − | 0.981766i | \(-0.439120\pi\) | ||||
0.190096 | + | 0.981766i | \(0.439120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.70139e9 | 1.28160 | 0.640802 | − | 0.767706i | \(-0.278602\pi\) | ||||
0.640802 | + | 0.767706i | \(0.278602\pi\) | |||||||
\(572\) | −1.15226e9 | −0.257432 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.50568e9 | 0.553011 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.43063e9 | −0.526750 | −0.263375 | − | 0.964694i | \(-0.584836\pi\) | ||||
−0.263375 | + | 0.964694i | \(0.584836\pi\) | |||||||
\(578\) | 4.03596e9 | 0.869360 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.29639e10 | 2.74232 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.42401e9 | 1.13365 | ||||||||
\(584\) | −6.35320e9 | −1.31992 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.20438e9 | −0.657812 | ||||||||
\(587\) | −3.33378e9 | −0.680305 | −0.340153 | − | 0.940370i | \(-0.610479\pi\) | ||||
−0.340153 | + | 0.940370i | \(0.610479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.30097e9 | −0.463988 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.55222e9 | 0.901773 | ||||||||
\(593\) | 3.42280e9 | 0.674048 | 0.337024 | − | 0.941496i | \(-0.390580\pi\) | ||||
0.337024 | + | 0.941496i | \(0.390580\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.94159e8 | 0.153655 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.30182e9 | 1.77875 | ||||||||
\(599\) | 9.28661e8 | 0.176548 | 0.0882741 | − | 0.996096i | \(-0.471865\pi\) | ||||
0.0882741 | + | 0.996096i | \(0.471865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.56974e9 | −1.23449 | −0.617245 | − | 0.786771i | \(-0.711751\pi\) | ||||
−0.617245 | + | 0.786771i | \(0.711751\pi\) | |||||||
\(602\) | 1.35535e10 | 2.53201 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.18920e9 | −0.404256 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.50790e9 | 0.636629 | 0.318315 | − | 0.947985i | \(-0.396883\pi\) | ||||
0.318315 | + | 0.947985i | \(0.396883\pi\) | |||||||
\(608\) | 4.72544e9 | 0.852667 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.11939e9 | −1.26269 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.63970e9 | −0.638196 | −0.319098 | − | 0.947722i | \(-0.603380\pi\) | ||||
−0.319098 | + | 0.947722i | \(0.603380\pi\) | |||||||
\(614\) | 5.00454e9 | 0.872519 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.15682e9 | −0.888892 | ||||||||
\(617\) | 7.82559e9 | 1.34128 | 0.670639 | − | 0.741784i | \(-0.266020\pi\) | ||||
0.670639 | + | 0.741784i | \(0.266020\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.35173e9 | 1.41533 | 0.707667 | − | 0.706546i | \(-0.249748\pi\) | ||||
0.707667 | + | 0.706546i | \(0.249748\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.03765e8 | 0.100601 | ||||||||
\(623\) | 3.86917e9 | 0.641076 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.73725e9 | 0.445969 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.38570e8 | −0.135108 | ||||||||
\(629\) | 2.28033e9 | 0.365360 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.16820e7 | −0.00343555 | −0.00171777 | − | 0.999999i | \(-0.500547\pi\) | ||||
−0.00171777 | + | 0.999999i | \(0.500547\pi\) | |||||||
\(632\) | 4.41212e9 | 0.695245 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.24926e10 | 1.94689 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.19377e9 | −1.40931 | ||||||||
\(638\) | 5.70411e9 | 0.869592 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.85361e9 | 1.17779 | 0.588893 | − | 0.808211i | \(-0.299564\pi\) | ||||
0.588893 | + | 0.808211i | \(0.299564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.81820e9 | 1.30810 | 0.654051 | − | 0.756451i | \(-0.273068\pi\) | ||||
0.654051 | + | 0.756451i | \(0.273068\pi\) | |||||||
\(644\) | −4.75951e9 | −0.702201 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.35746e9 | 0.781890 | ||||||||
\(647\) | −8.71997e9 | −1.26576 | −0.632878 | − | 0.774252i | \(-0.718127\pi\) | ||||
−0.632878 | + | 0.774252i | \(0.718127\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.26982e9 | 0.469535 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.00771e7 | 0.00424981 | ||||||||
\(653\) | −6.65755e8 | −0.0935661 | −0.0467830 | − | 0.998905i | \(-0.514897\pi\) | ||||
−0.0467830 | + | 0.998905i | \(0.514897\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.78656e9 | −0.385393 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.50155e10 | 2.05470 | ||||||||
\(659\) | 9.99513e9 | 1.36047 | 0.680236 | − | 0.732994i | \(-0.261877\pi\) | ||||
0.680236 | + | 0.732994i | \(0.261877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.89160e9 | −0.389434 | −0.194717 | − | 0.980859i | \(-0.562379\pi\) | ||||
−0.194717 | + | 0.980859i | \(0.562379\pi\) | |||||||
\(662\) | −5.19900e9 | −0.696493 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.06247e10 | −1.40841 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.11713e10 | −1.45768 | ||||||||
\(668\) | 6.92593e8 | 0.0899002 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.47857e9 | −0.700065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.83236e9 | 0.737550 | 0.368775 | − | 0.929519i | \(-0.379777\pi\) | ||||
0.368775 | + | 0.929519i | \(0.379777\pi\) | |||||||
\(674\) | 3.49940e9 | 0.440234 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.93744e8 | 0.0490231 | ||||||||
\(677\) | −1.22524e10 | −1.51762 | −0.758808 | − | 0.651315i | \(-0.774218\pi\) | ||||
−0.758808 | + | 0.651315i | \(0.774218\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.03721e9 | 0.862693 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.39672e9 | 0.289316 | ||||||||
\(683\) | −9.69293e9 | −1.16408 | −0.582040 | − | 0.813160i | \(-0.697745\pi\) | ||||
−0.582040 | + | 0.813160i | \(0.697745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 4.61621e9 | 0.545948 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.50728e10 | −1.76455 | ||||||||
\(689\) | −1.39639e10 | −1.62644 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.33285e9 | 0.384276 | 0.192138 | − | 0.981368i | \(-0.438458\pi\) | ||||
0.192138 | + | 0.981368i | \(0.438458\pi\) | |||||||
\(692\) | 4.84561e8 | 0.0555875 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.06843e10 | 1.21335 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.39586e9 | −0.156145 | ||||||||
\(698\) | −8.42860e9 | −0.938127 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.73199e9 | 0.299548 | 0.149774 | − | 0.988720i | \(-0.452145\pi\) | ||||
0.149774 | + | 0.988720i | \(0.452145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.40882e9 | −1.02139 | ||||||||
\(704\) | 3.51543e9 | 0.379730 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.48466e9 | −0.907440 | ||||||||
\(707\) | 2.09377e10 | 2.22824 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.44620e8 | 0.0363144 | 0.0181572 | − | 0.999835i | \(-0.494220\pi\) | ||||
0.0181572 | + | 0.999835i | \(0.494220\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.17104e9 | −0.329247 | ||||||||
\(713\) | −4.69390e9 | −0.484976 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.28636e9 | 0.130969 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.14066e10 | −1.15006 | ||||||||
\(719\) | −3.35749e9 | −0.336871 | −0.168436 | − | 0.985713i | \(-0.553872\pi\) | ||||
−0.168436 | + | 0.985713i | \(0.553872\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.49327e9 | 0.645194 | ||||||||
\(722\) | −1.04850e10 | −1.03678 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.39258e9 | −0.234305 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.32017e10 | 1.27426 | 0.637132 | − | 0.770755i | \(-0.280121\pi\) | ||||
0.637132 | + | 0.770755i | \(0.280121\pi\) | |||||||
\(728\) | 1.32760e10 | 1.27528 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.55039e9 | −0.714922 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.30179e9 | −0.403446 | −0.201723 | − | 0.979443i | \(-0.564654\pi\) | ||||
−0.201723 | + | 0.979443i | \(0.564654\pi\) | |||||||
\(734\) | 3.73086e9 | 0.348235 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.63973e9 | 0.891236 | ||||||||
\(737\) | 1.49468e10 | 1.37534 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.82414e10 | −1.66266 | −0.831330 | − | 0.555780i | \(-0.812420\pi\) | ||||
−0.831330 | + | 0.555780i | \(0.812420\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.94512e10 | 2.64661 | ||||||||
\(743\) | −2.36847e8 | −0.0211840 | −0.0105920 | − | 0.999944i | \(-0.503372\pi\) | ||||
−0.0105920 | + | 0.999944i | \(0.503372\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.30117e10 | −2.02938 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.35383e9 | −0.118279 | ||||||||
\(749\) | −3.63106e9 | −0.315753 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.44326e10 | −1.24338 | −0.621690 | − | 0.783264i | \(-0.713553\pi\) | ||||
−0.621690 | + | 0.783264i | \(0.713553\pi\) | |||||||
\(752\) | −1.66987e10 | −1.43192 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.46850e10 | −1.24760 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.64934e10 | −1.38189 | −0.690945 | − | 0.722907i | \(-0.742805\pi\) | ||||
−0.690945 | + | 0.722907i | \(0.742805\pi\) | |||||||
\(758\) | −1.90205e10 | −1.58628 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.96845e9 | 0.244165 | 0.122083 | − | 0.992520i | \(-0.461043\pi\) | ||||
0.122083 | + | 0.992520i | \(0.461043\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.93482e9 | 0.483695 | ||||||||
\(764\) | −1.66528e8 | −0.0135102 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.28759e10 | 1.03509 | ||||||||
\(767\) | −8.41801e9 | −0.673637 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.15400e9 | 0.646590 | 0.323295 | − | 0.946298i | \(-0.395209\pi\) | ||||
0.323295 | + | 0.946298i | \(0.395209\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.46204e9 | 0.427262 | ||||||||
\(773\) | −2.78059e9 | −0.216525 | −0.108263 | − | 0.994122i | \(-0.534529\pi\) | ||||
−0.108263 | + | 0.994122i | \(0.534529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.76745e9 | −0.443065 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.03597e10 | −0.788713 | ||||||||
\(779\) | 5.75943e9 | 0.436514 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.28660e9 | 0.0966421 | ||||||||
\(782\) | 1.09290e10 | 0.817256 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.15642e10 | −1.59818 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.20982e9 | 0.600374 | 0.300187 | − | 0.953880i | \(-0.402951\pi\) | ||||
0.300187 | + | 0.953880i | \(0.402951\pi\) | |||||||
\(788\) | 5.36163e8 | 0.0390351 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.49562e9 | −0.394820 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.41043e10 | 1.00438 | ||||||||
\(794\) | 1.03426e10 | 0.733260 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.86386e9 | −0.201259 | ||||||||
\(797\) | −5.47916e7 | −0.00383363 | −0.00191681 | − | 0.999998i | \(-0.500610\pi\) | ||||
−0.00191681 | + | 0.999998i | \(0.500610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.36482e9 | −0.580153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.62121e10 | −1.79429 | ||||||||
\(803\) | −1.85597e10 | −1.26493 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.17025e9 | −0.415079 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.71598e10 | −1.14439 | ||||||||
\(809\) | −2.04973e9 | −0.136106 | −0.0680529 | − | 0.997682i | \(-0.521679\pi\) | ||||
−0.0680529 | + | 0.997682i | \(0.521679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.59471e10 | −1.04981 | −0.524903 | − | 0.851162i | \(-0.675899\pi\) | ||||
−0.524903 | + | 0.851162i | \(0.675899\pi\) | |||||||
\(812\) | 7.51394e9 | 0.492517 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.80036e9 | 0.636878 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.11535e10 | 1.99862 | ||||||||
\(818\) | 7.12439e8 | 0.0455104 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.65923e9 | −0.609174 | −0.304587 | − | 0.952484i | \(-0.598518\pi\) | ||||
−0.304587 | + | 0.952484i | \(0.598518\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.90398e9 | −0.244123 | −0.122061 | − | 0.992523i | \(-0.538950\pi\) | ||||
−0.122061 | + | 0.992523i | \(0.538950\pi\) | |||||||
\(824\) | −5.32166e9 | −0.331361 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.77544e10 | 1.09617 | ||||||||
\(827\) | −1.32224e10 | −0.812910 | −0.406455 | − | 0.913671i | \(-0.633235\pi\) | ||||
−0.406455 | + | 0.913671i | \(0.633235\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.20482e10 | 0.734484 | 0.367242 | − | 0.930125i | \(-0.380302\pi\) | ||||
0.367242 | + | 0.930125i | \(0.380302\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9.05032e9 | −0.544794 | ||||||||
\(833\) | −1.08021e10 | −0.647515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.58599e9 | 0.330658 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.44202e9 | 0.0846480 | ||||||||
\(839\) | −3.10603e10 | −1.81568 | −0.907839 | − | 0.419319i | \(-0.862269\pi\) | ||||
−0.907839 | + | 0.419319i | \(0.862269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.86495e8 | 0.0224057 | ||||||||
\(842\) | 2.75683e10 | 1.59154 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.34699e9 | 0.0771200 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.18276e10 | 0.668815 | ||||||||
\(848\) | −3.27526e10 | −1.84442 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.91937e10 | −1.06759 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.52157e10 | −1.39107 | −0.695536 | − | 0.718491i | \(-0.744833\pi\) | ||||
−0.695536 | + | 0.718491i | \(0.744833\pi\) | |||||||
\(854\) | −2.97474e10 | −1.63436 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.97589e9 | 0.162166 | ||||||||
\(857\) | 2.25314e10 | 1.22280 | 0.611401 | − | 0.791321i | \(-0.290606\pi\) | ||||
0.611401 | + | 0.791321i | \(0.290606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.07863e9 | 0.219552 | 0.109776 | − | 0.993956i | \(-0.464987\pi\) | ||||
0.109776 | + | 0.993956i | \(0.464987\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.23092e10 | −1.71811 | ||||||||
\(863\) | −1.10643e10 | −0.585986 | −0.292993 | − | 0.956115i | \(-0.594651\pi\) | ||||
−0.292993 | + | 0.956115i | \(0.594651\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.89943e8 | 0.0204028 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.15716e9 | 0.163862 | ||||||||
\(869\) | 1.28892e10 | 0.666278 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.84798e10 | −1.97319 | ||||||||
\(872\) | −4.86397e9 | −0.248418 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.50940e10 | −2.28470 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.60595e10 | −1.80518 | −0.902590 | − | 0.430501i | \(-0.858337\pi\) | ||||
−0.902590 | + | 0.430501i | \(0.858337\pi\) | |||||||
\(878\) | 1.36336e10 | 0.679795 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.62954e10 | 1.29558 | 0.647789 | − | 0.761820i | \(-0.275694\pi\) | ||||
0.647789 | + | 0.761820i | \(0.275694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.78873e9 | −0.136315 | −0.0681575 | − | 0.997675i | \(-0.521712\pi\) | ||||
−0.0681575 | + | 0.997675i | \(0.521712\pi\) | |||||||
\(884\) | 3.48537e9 | 0.169694 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.66083e9 | −0.128528 | ||||||||
\(887\) | −1.82970e10 | −0.880332 | −0.440166 | − | 0.897916i | \(-0.645080\pi\) | ||||
−0.440166 | + | 0.897916i | \(0.645080\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.86644e10 | 1.84567 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.85029e9 | −0.134466 | ||||||||
\(893\) | 3.45139e10 | 1.62186 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.93301e10 | 1.82661 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.43151e10 | 1.58131 | ||||||||
\(899\) | 7.41035e9 | 0.340157 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.64067e10 | −0.747280 | ||||||||
\(902\) | −5.99911e9 | −0.272185 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.50402e9 | 0.202773 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.21245e9 | 0.0539559 | 0.0269780 | − | 0.999636i | \(-0.491412\pi\) | ||||
0.0269780 | + | 0.999636i | \(0.491412\pi\) | |||||||
\(908\) | −9.46193e9 | −0.419449 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.09181e10 | 0.916659 | 0.458329 | − | 0.888782i | \(-0.348448\pi\) | ||||
0.458329 | + | 0.888782i | \(0.348448\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.10382e10 | −1.34973 | ||||||||
\(914\) | 2.38860e10 | 1.03474 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.99244e9 | 0.257614 | ||||||||
\(917\) | −1.13149e10 | −0.484571 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.81545e10 | −0.771577 | −0.385789 | − | 0.922587i | \(-0.626071\pi\) | ||||
−0.385789 | + | 0.922587i | \(0.626071\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.64981e10 | 1.95379 | ||||||||
\(923\) | −3.31230e9 | −0.138651 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.66488e10 | 0.689040 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.52184e10 | −0.625104 | ||||||||
\(929\) | 3.39225e10 | 1.38814 | 0.694069 | − | 0.719908i | \(-0.255816\pi\) | ||||
0.694069 | + | 0.719908i | \(0.255816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.45702e10 | 1.81018 | ||||||||
\(932\) | 1.27882e10 | 0.517433 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.45979e10 | 2.19261 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.64023e10 | −1.44557 | −0.722786 | − | 0.691072i | \(-0.757139\pi\) | ||||
−0.722786 | + | 0.691072i | \(0.757139\pi\) | |||||||
\(938\) | 8.11578e10 | 3.21085 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.07117e10 | −1.98401 | −0.992007 | − | 0.126181i | \(-0.959728\pi\) | ||||
−0.992007 | + | 0.126181i | \(0.959728\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.17490e10 | 0.456259 | ||||||||
\(944\) | −1.97446e10 | −0.763918 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.24499e10 | −1.24622 | ||||||||
\(947\) | 2.30994e10 | 0.883845 | 0.441922 | − | 0.897053i | \(-0.354297\pi\) | ||||
0.441922 | + | 0.897053i | \(0.354297\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.77810e10 | 1.81478 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.55984e10 | 0.585938 | ||||||||
\(953\) | −4.16368e9 | −0.155830 | −0.0779151 | − | 0.996960i | \(-0.524826\pi\) | ||||
−0.0779151 | + | 0.996960i | \(0.524826\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.31972e9 | −0.344985 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.22663e10 | 1.18569 | ||||||||
\(959\) | 2.29971e9 | 0.0841993 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.43990e10 | −0.886829 | ||||||||
\(962\) | −2.52306e10 | −0.913723 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.13779e9 | −0.292575 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.20468e10 | 1.85098 | 0.925489 | − | 0.378775i | \(-0.123655\pi\) | ||||
0.925489 | + | 0.378775i | \(0.123655\pi\) | |||||||
\(968\) | −9.69352e9 | −0.343493 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.64573e8 | 0.0127796 | 0.00638979 | − | 0.999980i | \(-0.497966\pi\) | ||||
0.00638979 | + | 0.999980i | \(0.497966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.10689e10 | 2.82137 | ||||||||
\(974\) | −1.40485e10 | −0.487162 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.30820e10 | 1.13898 | ||||||||
\(977\) | −1.81785e10 | −0.623631 | −0.311816 | − | 0.950143i | \(-0.600937\pi\) | ||||
−0.311816 | + | 0.950143i | \(0.600937\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.26358e9 | −0.315529 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.23212e10 | −0.415206 | ||||||||
\(983\) | −1.85778e10 | −0.623816 | −0.311908 | − | 0.950112i | \(-0.600968\pi\) | ||||
−0.311908 | + | 0.950112i | \(0.600968\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.72539e10 | −0.573216 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.43809e10 | −0.474391 | ||||||||
\(989\) | 6.35520e10 | 2.08902 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.82520e10 | 0.595735 | 0.297867 | − | 0.954607i | \(-0.403725\pi\) | ||||
0.297867 | + | 0.954607i | \(0.403725\pi\) | |||||||
\(992\) | −6.39440e9 | −0.207974 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.98598e9 | 0.225619 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.24534e9 | 0.0397975 | 0.0198987 | − | 0.999802i | \(-0.493666\pi\) | ||||
0.0198987 | + | 0.999802i | \(0.493666\pi\) | |||||||
\(998\) | 2.70000e10 | 0.859817 | ||||||||
\(999\) | 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.c.1.1 | 1 | ||
3.2 | odd | 2 | 75.8.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 225.8.b.c.199.1 | 2 | |||
5.3 | odd | 4 | 225.8.b.c.199.2 | 2 | |||
5.4 | even | 2 | 45.8.a.e.1.1 | 1 | |||
15.2 | even | 4 | 75.8.b.b.49.2 | 2 | |||
15.8 | even | 4 | 75.8.b.b.49.1 | 2 | |||
15.14 | odd | 2 | 15.8.a.b.1.1 | ✓ | 1 | ||
60.59 | even | 2 | 240.8.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.8.a.b.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
45.8.a.e.1.1 | 1 | 5.4 | even | 2 | |||
75.8.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
75.8.b.b.49.1 | 2 | 15.8 | even | 4 | |||
75.8.b.b.49.2 | 2 | 15.2 | even | 4 | |||
225.8.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.8.b.c.199.1 | 2 | 5.2 | odd | 4 | |||
225.8.b.c.199.2 | 2 | 5.3 | odd | 4 | |||
240.8.a.h.1.1 | 1 | 60.59 | even | 2 |