Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,8,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("570.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(178.059464526\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2087x^{2} + 44517x - 205110 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.63333\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 125.000 | 0.447214 | ||||||||
\(6\) | 216.000 | 0.408248 | ||||||||
\(7\) | −1226.02 | −1.35100 | −0.675499 | − | 0.737361i | \(-0.736072\pi\) | ||||
−0.675499 | + | 0.737361i | \(0.736072\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 1000.00 | 0.316228 | ||||||||
\(11\) | −4664.78 | −1.05671 | −0.528357 | − | 0.849022i | \(-0.677192\pi\) | ||||
−0.528357 | + | 0.849022i | \(0.677192\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | 9141.59 | 1.15404 | 0.577019 | − | 0.816731i | \(-0.304216\pi\) | ||||
0.577019 | + | 0.816731i | \(0.304216\pi\) | |||||||
\(14\) | −9808.17 | −0.955300 | ||||||||
\(15\) | 3375.00 | 0.258199 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −5655.69 | −0.279199 | −0.139600 | − | 0.990208i | \(-0.544582\pi\) | ||||
−0.139600 | + | 0.990208i | \(0.544582\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | −6859.00 | −0.229416 | ||||||||
\(20\) | 8000.00 | 0.223607 | ||||||||
\(21\) | −33102.6 | −0.779999 | ||||||||
\(22\) | −37318.3 | −0.747209 | ||||||||
\(23\) | 28546.1 | 0.489214 | 0.244607 | − | 0.969622i | \(-0.421341\pi\) | ||||
0.244607 | + | 0.969622i | \(0.421341\pi\) | |||||||
\(24\) | 13824.0 | 0.204124 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | 73132.7 | 0.816028 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −78465.3 | −0.675499 | ||||||||
\(29\) | −91499.2 | −0.696665 | −0.348333 | − | 0.937371i | \(-0.613252\pi\) | ||||
−0.348333 | + | 0.937371i | \(0.613252\pi\) | |||||||
\(30\) | 27000.0 | 0.182574 | ||||||||
\(31\) | 257718. | 1.55374 | 0.776871 | − | 0.629660i | \(-0.216806\pi\) | ||||
0.776871 | + | 0.629660i | \(0.216806\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | −125949. | −0.610094 | ||||||||
\(34\) | −45245.5 | −0.197424 | ||||||||
\(35\) | −153253. | −0.604185 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −349283. | −1.13363 | −0.566815 | − | 0.823845i | \(-0.691825\pi\) | ||||
−0.566815 | + | 0.823845i | \(0.691825\pi\) | |||||||
\(38\) | −54872.0 | −0.162221 | ||||||||
\(39\) | 246823. | 0.666284 | ||||||||
\(40\) | 64000.0 | 0.158114 | ||||||||
\(41\) | 16623.6 | 0.0376689 | 0.0188344 | − | 0.999823i | \(-0.494004\pi\) | ||||
0.0188344 | + | 0.999823i | \(0.494004\pi\) | |||||||
\(42\) | −264821. | −0.551543 | ||||||||
\(43\) | −873064. | −1.67458 | −0.837291 | − | 0.546757i | \(-0.815862\pi\) | ||||
−0.837291 | + | 0.546757i | \(0.815862\pi\) | |||||||
\(44\) | −298546. | −0.528357 | ||||||||
\(45\) | 91125.0 | 0.149071 | ||||||||
\(46\) | 228369. | 0.345927 | ||||||||
\(47\) | 927779. | 1.30347 | 0.651737 | − | 0.758445i | \(-0.274041\pi\) | ||||
0.651737 | + | 0.758445i | \(0.274041\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | 679585. | 0.825196 | ||||||||
\(50\) | 125000. | 0.141421 | ||||||||
\(51\) | −152704. | −0.161196 | ||||||||
\(52\) | 585062. | 0.577019 | ||||||||
\(53\) | −101382. | −0.0935399 | −0.0467700 | − | 0.998906i | \(-0.514893\pi\) | ||||
−0.0467700 | + | 0.998906i | \(0.514893\pi\) | |||||||
\(54\) | 157464. | 0.136083 | ||||||||
\(55\) | −583098. | −0.472577 | ||||||||
\(56\) | −627723. | −0.477650 | ||||||||
\(57\) | −185193. | −0.132453 | ||||||||
\(58\) | −731993. | −0.492617 | ||||||||
\(59\) | −985529. | −0.624723 | −0.312361 | − | 0.949963i | \(-0.601120\pi\) | ||||
−0.312361 | + | 0.949963i | \(0.601120\pi\) | |||||||
\(60\) | 216000. | 0.129099 | ||||||||
\(61\) | −756404. | −0.426677 | −0.213339 | − | 0.976978i | \(-0.568434\pi\) | ||||
−0.213339 | + | 0.976978i | \(0.568434\pi\) | |||||||
\(62\) | 2.06174e6 | 1.09866 | ||||||||
\(63\) | −893769. | −0.450333 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | 1.14270e6 | 0.516101 | ||||||||
\(66\) | −1.00759e6 | −0.431401 | ||||||||
\(67\) | −4.75212e6 | −1.93030 | −0.965151 | − | 0.261693i | \(-0.915719\pi\) | ||||
−0.965151 | + | 0.261693i | \(0.915719\pi\) | |||||||
\(68\) | −361964. | −0.139600 | ||||||||
\(69\) | 770744. | 0.282448 | ||||||||
\(70\) | −1.22602e6 | −0.427223 | ||||||||
\(71\) | −4.47915e6 | −1.48522 | −0.742612 | − | 0.669722i | \(-0.766413\pi\) | ||||
−0.742612 | + | 0.669722i | \(0.766413\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | −3.53609e6 | −1.06388 | −0.531941 | − | 0.846781i | \(-0.678537\pi\) | ||||
−0.531941 | + | 0.846781i | \(0.678537\pi\) | |||||||
\(74\) | −2.79427e6 | −0.801598 | ||||||||
\(75\) | 421875. | 0.115470 | ||||||||
\(76\) | −438976. | −0.114708 | ||||||||
\(77\) | 5.71912e6 | 1.42762 | ||||||||
\(78\) | 1.97458e6 | 0.471134 | ||||||||
\(79\) | −1.32434e6 | −0.302206 | −0.151103 | − | 0.988518i | \(-0.548283\pi\) | ||||
−0.151103 | + | 0.988518i | \(0.548283\pi\) | |||||||
\(80\) | 512000. | 0.111803 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 132989. | 0.0266359 | ||||||||
\(83\) | −71365.3 | −0.0136998 | −0.00684989 | − | 0.999977i | \(-0.502180\pi\) | ||||
−0.00684989 | + | 0.999977i | \(0.502180\pi\) | |||||||
\(84\) | −2.11856e6 | −0.390000 | ||||||||
\(85\) | −706962. | −0.124862 | ||||||||
\(86\) | −6.98451e6 | −1.18411 | ||||||||
\(87\) | −2.47048e6 | −0.402220 | ||||||||
\(88\) | −2.38837e6 | −0.373605 | ||||||||
\(89\) | −3.73761e6 | −0.561990 | −0.280995 | − | 0.959709i | \(-0.590664\pi\) | ||||
−0.280995 | + | 0.959709i | \(0.590664\pi\) | |||||||
\(90\) | 729000. | 0.105409 | ||||||||
\(91\) | −1.12078e7 | −1.55910 | ||||||||
\(92\) | 1.82695e6 | 0.244607 | ||||||||
\(93\) | 6.95839e6 | 0.897054 | ||||||||
\(94\) | 7.42223e6 | 0.921695 | ||||||||
\(95\) | −857375. | −0.102598 | ||||||||
\(96\) | 884736. | 0.102062 | ||||||||
\(97\) | −5.37895e6 | −0.598406 | −0.299203 | − | 0.954189i | \(-0.596721\pi\) | ||||
−0.299203 | + | 0.954189i | \(0.596721\pi\) | |||||||
\(98\) | 5.43668e6 | 0.583502 | ||||||||
\(99\) | −3.40063e6 | −0.352238 | ||||||||
\(100\) | 1.00000e6 | 0.100000 | ||||||||
\(101\) | −1.36707e7 | −1.32028 | −0.660139 | − | 0.751143i | \(-0.729503\pi\) | ||||
−0.660139 | + | 0.751143i | \(0.729503\pi\) | |||||||
\(102\) | −1.22163e6 | −0.113983 | ||||||||
\(103\) | 252601. | 0.0227775 | 0.0113887 | − | 0.999935i | \(-0.496375\pi\) | ||||
0.0113887 | + | 0.999935i | \(0.496375\pi\) | |||||||
\(104\) | 4.68049e6 | 0.408014 | ||||||||
\(105\) | −4.13782e6 | −0.348826 | ||||||||
\(106\) | −811059. | −0.0661427 | ||||||||
\(107\) | 656153. | 0.0517800 | 0.0258900 | − | 0.999665i | \(-0.491758\pi\) | ||||
0.0258900 | + | 0.999665i | \(0.491758\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | −8.93726e6 | −0.661016 | −0.330508 | − | 0.943803i | \(-0.607220\pi\) | ||||
−0.330508 | + | 0.943803i | \(0.607220\pi\) | |||||||
\(110\) | −4.66478e6 | −0.334162 | ||||||||
\(111\) | −9.43065e6 | −0.654502 | ||||||||
\(112\) | −5.02178e6 | −0.337750 | ||||||||
\(113\) | −4.69004e6 | −0.305775 | −0.152887 | − | 0.988244i | \(-0.548857\pi\) | ||||
−0.152887 | + | 0.988244i | \(0.548857\pi\) | |||||||
\(114\) | −1.48154e6 | −0.0936586 | ||||||||
\(115\) | 3.56826e6 | 0.218783 | ||||||||
\(116\) | −5.85595e6 | −0.348333 | ||||||||
\(117\) | 6.66422e6 | 0.384679 | ||||||||
\(118\) | −7.88423e6 | −0.441746 | ||||||||
\(119\) | 6.93400e6 | 0.377198 | ||||||||
\(120\) | 1.72800e6 | 0.0912871 | ||||||||
\(121\) | 2.27305e6 | 0.116643 | ||||||||
\(122\) | −6.05123e6 | −0.301706 | ||||||||
\(123\) | 448838. | 0.0217481 | ||||||||
\(124\) | 1.64940e7 | 0.776871 | ||||||||
\(125\) | 1.95312e6 | 0.0894427 | ||||||||
\(126\) | −7.15015e6 | −0.318433 | ||||||||
\(127\) | 3.91285e7 | 1.69504 | 0.847521 | − | 0.530762i | \(-0.178094\pi\) | ||||
0.847521 | + | 0.530762i | \(0.178094\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | −2.35727e7 | −0.966821 | ||||||||
\(130\) | 9.14159e6 | 0.364939 | ||||||||
\(131\) | −3.14409e7 | −1.22193 | −0.610963 | − | 0.791659i | \(-0.709218\pi\) | ||||
−0.610963 | + | 0.791659i | \(0.709218\pi\) | |||||||
\(132\) | −8.06075e6 | −0.305047 | ||||||||
\(133\) | 8.40928e6 | 0.309940 | ||||||||
\(134\) | −3.80169e7 | −1.36493 | ||||||||
\(135\) | 2.46038e6 | 0.0860663 | ||||||||
\(136\) | −2.89571e6 | −0.0987119 | ||||||||
\(137\) | −4.41045e7 | −1.46542 | −0.732709 | − | 0.680543i | \(-0.761744\pi\) | ||||
−0.732709 | + | 0.680543i | \(0.761744\pi\) | |||||||
\(138\) | 6.16595e6 | 0.199721 | ||||||||
\(139\) | 4.26450e7 | 1.34684 | 0.673421 | − | 0.739260i | \(-0.264824\pi\) | ||||
0.673421 | + | 0.739260i | \(0.264824\pi\) | |||||||
\(140\) | −9.80817e6 | −0.302092 | ||||||||
\(141\) | 2.50500e7 | 0.752561 | ||||||||
\(142\) | −3.58332e7 | −1.05021 | ||||||||
\(143\) | −4.26436e7 | −1.21949 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −1.14374e7 | −0.311558 | ||||||||
\(146\) | −2.82887e7 | −0.752278 | ||||||||
\(147\) | 1.83488e7 | 0.476427 | ||||||||
\(148\) | −2.23541e7 | −0.566815 | ||||||||
\(149\) | 8.55796e6 | 0.211943 | 0.105971 | − | 0.994369i | \(-0.466205\pi\) | ||||
0.105971 | + | 0.994369i | \(0.466205\pi\) | |||||||
\(150\) | 3.37500e6 | 0.0816497 | ||||||||
\(151\) | 4.01350e7 | 0.948645 | 0.474322 | − | 0.880351i | \(-0.342693\pi\) | ||||
0.474322 | + | 0.880351i | \(0.342693\pi\) | |||||||
\(152\) | −3.51181e6 | −0.0811107 | ||||||||
\(153\) | −4.12300e6 | −0.0930665 | ||||||||
\(154\) | 4.57530e7 | 1.00948 | ||||||||
\(155\) | 3.22148e7 | 0.694855 | ||||||||
\(156\) | 1.57967e7 | 0.333142 | ||||||||
\(157\) | 6.26893e7 | 1.29284 | 0.646419 | − | 0.762982i | \(-0.276266\pi\) | ||||
0.646419 | + | 0.762982i | \(0.276266\pi\) | |||||||
\(158\) | −1.05947e7 | −0.213692 | ||||||||
\(159\) | −2.73733e6 | −0.0540053 | ||||||||
\(160\) | 4.09600e6 | 0.0790569 | ||||||||
\(161\) | −3.49981e7 | −0.660928 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | 4.59226e7 | 0.830557 | 0.415279 | − | 0.909694i | \(-0.363684\pi\) | ||||
0.415279 | + | 0.909694i | \(0.363684\pi\) | |||||||
\(164\) | 1.06391e6 | 0.0188344 | ||||||||
\(165\) | −1.57436e7 | −0.272842 | ||||||||
\(166\) | −570922. | −0.00968721 | ||||||||
\(167\) | 2.20343e7 | 0.366093 | 0.183046 | − | 0.983104i | \(-0.441404\pi\) | ||||
0.183046 | + | 0.983104i | \(0.441404\pi\) | |||||||
\(168\) | −1.69485e7 | −0.275771 | ||||||||
\(169\) | 2.08202e7 | 0.331803 | ||||||||
\(170\) | −5.65569e6 | −0.0882906 | ||||||||
\(171\) | −5.00021e6 | −0.0764719 | ||||||||
\(172\) | −5.58761e7 | −0.837291 | ||||||||
\(173\) | −6.47515e7 | −0.950799 | −0.475400 | − | 0.879770i | \(-0.657696\pi\) | ||||
−0.475400 | + | 0.879770i | \(0.657696\pi\) | |||||||
\(174\) | −1.97638e7 | −0.284412 | ||||||||
\(175\) | −1.91566e7 | −0.270200 | ||||||||
\(176\) | −1.91070e7 | −0.264178 | ||||||||
\(177\) | −2.66093e7 | −0.360684 | ||||||||
\(178\) | −2.99008e7 | −0.397387 | ||||||||
\(179\) | 5.05932e7 | 0.659335 | 0.329668 | − | 0.944097i | \(-0.393063\pi\) | ||||
0.329668 | + | 0.944097i | \(0.393063\pi\) | |||||||
\(180\) | 5.83200e6 | 0.0745356 | ||||||||
\(181\) | −1.39134e8 | −1.74405 | −0.872026 | − | 0.489459i | \(-0.837194\pi\) | ||||
−0.872026 | + | 0.489459i | \(0.837194\pi\) | |||||||
\(182\) | −8.96623e7 | −1.10245 | ||||||||
\(183\) | −2.04229e7 | −0.246342 | ||||||||
\(184\) | 1.46156e7 | 0.172963 | ||||||||
\(185\) | −4.36604e7 | −0.506975 | ||||||||
\(186\) | 5.56671e7 | 0.634313 | ||||||||
\(187\) | 2.63826e7 | 0.295034 | ||||||||
\(188\) | 5.93779e7 | 0.651737 | ||||||||
\(189\) | −2.41318e7 | −0.260000 | ||||||||
\(190\) | −6.85900e6 | −0.0725476 | ||||||||
\(191\) | 6.61827e7 | 0.687270 | 0.343635 | − | 0.939103i | \(-0.388342\pi\) | ||||
0.343635 | + | 0.939103i | \(0.388342\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | −5.81508e7 | −0.582244 | −0.291122 | − | 0.956686i | \(-0.594029\pi\) | ||||
−0.291122 | + | 0.956686i | \(0.594029\pi\) | |||||||
\(194\) | −4.30316e7 | −0.423137 | ||||||||
\(195\) | 3.08529e7 | 0.297971 | ||||||||
\(196\) | 4.34934e7 | 0.412598 | ||||||||
\(197\) | 1.32939e8 | 1.23885 | 0.619426 | − | 0.785055i | \(-0.287366\pi\) | ||||
0.619426 | + | 0.785055i | \(0.287366\pi\) | |||||||
\(198\) | −2.72050e7 | −0.249070 | ||||||||
\(199\) | −7.83654e7 | −0.704918 | −0.352459 | − | 0.935827i | \(-0.614654\pi\) | ||||
−0.352459 | + | 0.935827i | \(0.614654\pi\) | |||||||
\(200\) | 8.00000e6 | 0.0707107 | ||||||||
\(201\) | −1.28307e8 | −1.11446 | ||||||||
\(202\) | −1.09365e8 | −0.933578 | ||||||||
\(203\) | 1.12180e8 | 0.941194 | ||||||||
\(204\) | −9.77304e6 | −0.0805979 | ||||||||
\(205\) | 2.07795e6 | 0.0168460 | ||||||||
\(206\) | 2.02081e6 | 0.0161061 | ||||||||
\(207\) | 2.08101e7 | 0.163071 | ||||||||
\(208\) | 3.74440e7 | 0.288509 | ||||||||
\(209\) | 3.19958e7 | 0.242427 | ||||||||
\(210\) | −3.31026e7 | −0.246657 | ||||||||
\(211\) | 5.07664e7 | 0.372039 | 0.186019 | − | 0.982546i | \(-0.440441\pi\) | ||||
0.186019 | + | 0.982546i | \(0.440441\pi\) | |||||||
\(212\) | −6.48847e6 | −0.0467700 | ||||||||
\(213\) | −1.20937e8 | −0.857494 | ||||||||
\(214\) | 5.24922e6 | 0.0366140 | ||||||||
\(215\) | −1.09133e8 | −0.748896 | ||||||||
\(216\) | 1.00777e7 | 0.0680414 | ||||||||
\(217\) | −3.15968e8 | −2.09910 | ||||||||
\(218\) | −7.14981e7 | −0.467409 | ||||||||
\(219\) | −9.54745e7 | −0.614233 | ||||||||
\(220\) | −3.73183e7 | −0.236288 | ||||||||
\(221\) | −5.17020e7 | −0.322207 | ||||||||
\(222\) | −7.54452e7 | −0.462803 | ||||||||
\(223\) | −1.46701e8 | −0.885861 | −0.442930 | − | 0.896556i | \(-0.646061\pi\) | ||||
−0.442930 | + | 0.896556i | \(0.646061\pi\) | |||||||
\(224\) | −4.01743e7 | −0.238825 | ||||||||
\(225\) | 1.13906e7 | 0.0666667 | ||||||||
\(226\) | −3.75203e7 | −0.216215 | ||||||||
\(227\) | −5.87583e7 | −0.333410 | −0.166705 | − | 0.986007i | \(-0.553313\pi\) | ||||
−0.166705 | + | 0.986007i | \(0.553313\pi\) | |||||||
\(228\) | −1.18524e7 | −0.0662266 | ||||||||
\(229\) | 3.04392e8 | 1.67498 | 0.837488 | − | 0.546456i | \(-0.184024\pi\) | ||||
0.837488 | + | 0.546456i | \(0.184024\pi\) | |||||||
\(230\) | 2.85461e7 | 0.154703 | ||||||||
\(231\) | 1.54416e8 | 0.824236 | ||||||||
\(232\) | −4.68476e7 | −0.246308 | ||||||||
\(233\) | −2.17333e8 | −1.12559 | −0.562793 | − | 0.826598i | \(-0.690273\pi\) | ||||
−0.562793 | + | 0.826598i | \(0.690273\pi\) | |||||||
\(234\) | 5.33138e7 | 0.272009 | ||||||||
\(235\) | 1.15972e8 | 0.582931 | ||||||||
\(236\) | −6.30739e7 | −0.312361 | ||||||||
\(237\) | −3.57571e7 | −0.174479 | ||||||||
\(238\) | 5.54720e7 | 0.266719 | ||||||||
\(239\) | 2.48827e8 | 1.17897 | 0.589487 | − | 0.807778i | \(-0.299330\pi\) | ||||
0.589487 | + | 0.807778i | \(0.299330\pi\) | |||||||
\(240\) | 1.38240e7 | 0.0645497 | ||||||||
\(241\) | −3.68119e8 | −1.69406 | −0.847030 | − | 0.531544i | \(-0.821612\pi\) | ||||
−0.847030 | + | 0.531544i | \(0.821612\pi\) | |||||||
\(242\) | 1.81844e7 | 0.0824793 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −4.84099e7 | −0.213339 | ||||||||
\(245\) | 8.49481e7 | 0.369039 | ||||||||
\(246\) | 3.59071e6 | 0.0153783 | ||||||||
\(247\) | −6.27022e7 | −0.264754 | ||||||||
\(248\) | 1.31952e8 | 0.549331 | ||||||||
\(249\) | −1.92686e6 | −0.00790957 | ||||||||
\(250\) | 1.56250e7 | 0.0632456 | ||||||||
\(251\) | −1.97259e8 | −0.787370 | −0.393685 | − | 0.919245i | \(-0.628800\pi\) | ||||
−0.393685 | + | 0.919245i | \(0.628800\pi\) | |||||||
\(252\) | −5.72012e7 | −0.225166 | ||||||||
\(253\) | −1.33161e8 | −0.516959 | ||||||||
\(254\) | 3.13028e8 | 1.19858 | ||||||||
\(255\) | −1.90880e7 | −0.0720890 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −2.06192e8 | −0.757713 | −0.378857 | − | 0.925455i | \(-0.623683\pi\) | ||||
−0.378857 | + | 0.925455i | \(0.623683\pi\) | |||||||
\(258\) | −1.88582e8 | −0.683646 | ||||||||
\(259\) | 4.28229e8 | 1.53153 | ||||||||
\(260\) | 7.31327e7 | 0.258051 | ||||||||
\(261\) | −6.67029e7 | −0.232222 | ||||||||
\(262\) | −2.51527e8 | −0.864032 | ||||||||
\(263\) | −1.32978e8 | −0.450749 | −0.225375 | − | 0.974272i | \(-0.572361\pi\) | ||||
−0.225375 | + | 0.974272i | \(0.572361\pi\) | |||||||
\(264\) | −6.44860e7 | −0.215701 | ||||||||
\(265\) | −1.26728e7 | −0.0418323 | ||||||||
\(266\) | 6.72742e7 | 0.219161 | ||||||||
\(267\) | −1.00915e8 | −0.324465 | ||||||||
\(268\) | −3.04136e8 | −0.965151 | ||||||||
\(269\) | 1.76304e8 | 0.552241 | 0.276120 | − | 0.961123i | \(-0.410951\pi\) | ||||
0.276120 | + | 0.961123i | \(0.410951\pi\) | |||||||
\(270\) | 1.96830e7 | 0.0608581 | ||||||||
\(271\) | −2.81735e8 | −0.859902 | −0.429951 | − | 0.902852i | \(-0.641469\pi\) | ||||
−0.429951 | + | 0.902852i | \(0.641469\pi\) | |||||||
\(272\) | −2.31657e7 | −0.0697999 | ||||||||
\(273\) | −3.02610e8 | −0.900149 | ||||||||
\(274\) | −3.52836e8 | −1.03621 | ||||||||
\(275\) | −7.28873e7 | −0.211343 | ||||||||
\(276\) | 4.93276e7 | 0.141224 | ||||||||
\(277\) | 3.32412e8 | 0.939718 | 0.469859 | − | 0.882742i | \(-0.344305\pi\) | ||||
0.469859 | + | 0.882742i | \(0.344305\pi\) | |||||||
\(278\) | 3.41160e8 | 0.952360 | ||||||||
\(279\) | 1.87877e8 | 0.517914 | ||||||||
\(280\) | −7.84653e7 | −0.213612 | ||||||||
\(281\) | 3.64016e8 | 0.978698 | 0.489349 | − | 0.872088i | \(-0.337234\pi\) | ||||
0.489349 | + | 0.872088i | \(0.337234\pi\) | |||||||
\(282\) | 2.00400e8 | 0.532141 | ||||||||
\(283\) | 4.69965e8 | 1.23257 | 0.616287 | − | 0.787522i | \(-0.288636\pi\) | ||||
0.616287 | + | 0.787522i | \(0.288636\pi\) | |||||||
\(284\) | −2.86666e8 | −0.742612 | ||||||||
\(285\) | −2.31491e7 | −0.0592349 | ||||||||
\(286\) | −3.41148e8 | −0.862308 | ||||||||
\(287\) | −2.03809e7 | −0.0508906 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −3.78352e8 | −0.922048 | ||||||||
\(290\) | −9.14992e7 | −0.220305 | ||||||||
\(291\) | −1.45232e8 | −0.345490 | ||||||||
\(292\) | −2.26310e8 | −0.531941 | ||||||||
\(293\) | −7.25312e8 | −1.68457 | −0.842284 | − | 0.539035i | \(-0.818789\pi\) | ||||
−0.842284 | + | 0.539035i | \(0.818789\pi\) | |||||||
\(294\) | 1.46790e8 | 0.336885 | ||||||||
\(295\) | −1.23191e8 | −0.279385 | ||||||||
\(296\) | −1.78833e8 | −0.400799 | ||||||||
\(297\) | −9.18170e7 | −0.203365 | ||||||||
\(298\) | 6.84636e7 | 0.149866 | ||||||||
\(299\) | 2.60957e8 | 0.564572 | ||||||||
\(300\) | 2.70000e7 | 0.0577350 | ||||||||
\(301\) | 1.07040e9 | 2.26236 | ||||||||
\(302\) | 3.21080e8 | 0.670793 | ||||||||
\(303\) | −3.69109e8 | −0.762263 | ||||||||
\(304\) | −2.80945e7 | −0.0573539 | ||||||||
\(305\) | −9.45505e7 | −0.190816 | ||||||||
\(306\) | −3.29840e7 | −0.0658079 | ||||||||
\(307\) | 1.97615e8 | 0.389795 | 0.194898 | − | 0.980824i | \(-0.437563\pi\) | ||||
0.194898 | + | 0.980824i | \(0.437563\pi\) | |||||||
\(308\) | 3.66024e8 | 0.713809 | ||||||||
\(309\) | 6.82023e6 | 0.0131506 | ||||||||
\(310\) | 2.57718e8 | 0.491337 | ||||||||
\(311\) | 8.09420e8 | 1.52585 | 0.762927 | − | 0.646485i | \(-0.223762\pi\) | ||||
0.762927 | + | 0.646485i | \(0.223762\pi\) | |||||||
\(312\) | 1.26373e8 | 0.235567 | ||||||||
\(313\) | −3.54187e8 | −0.652870 | −0.326435 | − | 0.945220i | \(-0.605847\pi\) | ||||
−0.326435 | + | 0.945220i | \(0.605847\pi\) | |||||||
\(314\) | 5.01514e8 | 0.914175 | ||||||||
\(315\) | −1.11721e8 | −0.201395 | ||||||||
\(316\) | −8.47576e7 | −0.151103 | ||||||||
\(317\) | 1.06264e9 | 1.87361 | 0.936803 | − | 0.349857i | \(-0.113770\pi\) | ||||
0.936803 | + | 0.349857i | \(0.113770\pi\) | |||||||
\(318\) | −2.18986e7 | −0.0381875 | ||||||||
\(319\) | 4.26824e8 | 0.736176 | ||||||||
\(320\) | 3.27680e7 | 0.0559017 | ||||||||
\(321\) | 1.77161e7 | 0.0298952 | ||||||||
\(322\) | −2.79985e8 | −0.467346 | ||||||||
\(323\) | 3.87924e7 | 0.0640527 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | 1.42837e8 | 0.230808 | ||||||||
\(326\) | 3.67381e8 | 0.587293 | ||||||||
\(327\) | −2.41306e8 | −0.381638 | ||||||||
\(328\) | 8.51130e6 | 0.0133180 | ||||||||
\(329\) | −1.13748e9 | −1.76099 | ||||||||
\(330\) | −1.25949e8 | −0.192929 | ||||||||
\(331\) | 2.26602e8 | 0.343452 | 0.171726 | − | 0.985145i | \(-0.445066\pi\) | ||||
0.171726 | + | 0.985145i | \(0.445066\pi\) | |||||||
\(332\) | −4.56738e6 | −0.00684989 | ||||||||
\(333\) | −2.54627e8 | −0.377877 | ||||||||
\(334\) | 1.76274e8 | 0.258867 | ||||||||
\(335\) | −5.94015e8 | −0.863258 | ||||||||
\(336\) | −1.35588e8 | −0.195000 | ||||||||
\(337\) | 3.83591e8 | 0.545964 | 0.272982 | − | 0.962019i | \(-0.411990\pi\) | ||||
0.272982 | + | 0.962019i | \(0.411990\pi\) | |||||||
\(338\) | 1.66561e8 | 0.234620 | ||||||||
\(339\) | −1.26631e8 | −0.176539 | ||||||||
\(340\) | −4.52455e7 | −0.0624309 | ||||||||
\(341\) | −1.20220e9 | −1.64186 | ||||||||
\(342\) | −4.00017e7 | −0.0540738 | ||||||||
\(343\) | 1.76496e8 | 0.236160 | ||||||||
\(344\) | −4.47009e8 | −0.592054 | ||||||||
\(345\) | 9.63430e7 | 0.126315 | ||||||||
\(346\) | −5.18012e8 | −0.672317 | ||||||||
\(347\) | 5.75945e8 | 0.739993 | 0.369997 | − | 0.929033i | \(-0.379359\pi\) | ||||
0.369997 | + | 0.929033i | \(0.379359\pi\) | |||||||
\(348\) | −1.58111e8 | −0.201110 | ||||||||
\(349\) | −1.03015e9 | −1.29721 | −0.648606 | − | 0.761124i | \(-0.724648\pi\) | ||||
−0.648606 | + | 0.761124i | \(0.724648\pi\) | |||||||
\(350\) | −1.53253e8 | −0.191060 | ||||||||
\(351\) | 1.79934e8 | 0.222095 | ||||||||
\(352\) | −1.52856e8 | −0.186802 | ||||||||
\(353\) | −8.91753e8 | −1.07903 | −0.539514 | − | 0.841976i | \(-0.681392\pi\) | ||||
−0.539514 | + | 0.841976i | \(0.681392\pi\) | |||||||
\(354\) | −2.12874e8 | −0.255042 | ||||||||
\(355\) | −5.59894e8 | −0.664212 | ||||||||
\(356\) | −2.39207e8 | −0.280995 | ||||||||
\(357\) | 1.87218e8 | 0.217775 | ||||||||
\(358\) | 4.04745e8 | 0.466220 | ||||||||
\(359\) | −1.42951e9 | −1.63063 | −0.815316 | − | 0.579017i | \(-0.803437\pi\) | ||||
−0.815316 | + | 0.579017i | \(0.803437\pi\) | |||||||
\(360\) | 4.66560e7 | 0.0527046 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | −1.11308e9 | −1.23323 | ||||||||
\(363\) | 6.13723e7 | 0.0673440 | ||||||||
\(364\) | −7.17298e8 | −0.779552 | ||||||||
\(365\) | −4.42011e8 | −0.475782 | ||||||||
\(366\) | −1.63383e8 | −0.174190 | ||||||||
\(367\) | −1.08198e9 | −1.14259 | −0.571293 | − | 0.820746i | \(-0.693558\pi\) | ||||
−0.571293 | + | 0.820746i | \(0.693558\pi\) | |||||||
\(368\) | 1.16925e8 | 0.122304 | ||||||||
\(369\) | 1.21186e7 | 0.0125563 | ||||||||
\(370\) | −3.49283e8 | −0.358486 | ||||||||
\(371\) | 1.24297e8 | 0.126372 | ||||||||
\(372\) | 4.45337e8 | 0.448527 | ||||||||
\(373\) | −1.41493e9 | −1.41174 | −0.705870 | − | 0.708341i | \(-0.749444\pi\) | ||||
−0.705870 | + | 0.708341i | \(0.749444\pi\) | |||||||
\(374\) | 2.11061e8 | 0.208620 | ||||||||
\(375\) | 5.27344e7 | 0.0516398 | ||||||||
\(376\) | 4.75023e8 | 0.460847 | ||||||||
\(377\) | −8.36448e8 | −0.803978 | ||||||||
\(378\) | −1.93054e8 | −0.183848 | ||||||||
\(379\) | −1.51393e8 | −0.142846 | −0.0714232 | − | 0.997446i | \(-0.522754\pi\) | ||||
−0.0714232 | + | 0.997446i | \(0.522754\pi\) | |||||||
\(380\) | −5.48720e7 | −0.0512989 | ||||||||
\(381\) | 1.05647e9 | 0.978633 | ||||||||
\(382\) | 5.29461e8 | 0.485973 | ||||||||
\(383\) | 5.80373e8 | 0.527851 | 0.263926 | − | 0.964543i | \(-0.414983\pi\) | ||||
0.263926 | + | 0.964543i | \(0.414983\pi\) | |||||||
\(384\) | 5.66231e7 | 0.0510310 | ||||||||
\(385\) | 7.14891e8 | 0.638450 | ||||||||
\(386\) | −4.65206e8 | −0.411709 | ||||||||
\(387\) | −6.36464e8 | −0.558194 | ||||||||
\(388\) | −3.44252e8 | −0.299203 | ||||||||
\(389\) | 1.59614e8 | 0.137482 | 0.0687411 | − | 0.997635i | \(-0.478102\pi\) | ||||
0.0687411 | + | 0.997635i | \(0.478102\pi\) | |||||||
\(390\) | 2.46823e8 | 0.210698 | ||||||||
\(391\) | −1.61448e8 | −0.136588 | ||||||||
\(392\) | 3.47947e8 | 0.291751 | ||||||||
\(393\) | −8.48904e8 | −0.705480 | ||||||||
\(394\) | 1.06351e9 | 0.876000 | ||||||||
\(395\) | −1.65542e8 | −0.135151 | ||||||||
\(396\) | −2.17640e8 | −0.176119 | ||||||||
\(397\) | 2.30750e8 | 0.185087 | 0.0925435 | − | 0.995709i | \(-0.470500\pi\) | ||||
0.0925435 | + | 0.995709i | \(0.470500\pi\) | |||||||
\(398\) | −6.26923e8 | −0.498453 | ||||||||
\(399\) | 2.27051e8 | 0.178944 | ||||||||
\(400\) | 6.40000e7 | 0.0500000 | ||||||||
\(401\) | −7.76649e8 | −0.601477 | −0.300739 | − | 0.953707i | \(-0.597233\pi\) | ||||
−0.300739 | + | 0.953707i | \(0.597233\pi\) | |||||||
\(402\) | −1.02646e9 | −0.788043 | ||||||||
\(403\) | 2.35595e9 | 1.79308 | ||||||||
\(404\) | −8.74924e8 | −0.660139 | ||||||||
\(405\) | 6.64301e7 | 0.0496904 | ||||||||
\(406\) | 8.97439e8 | 0.665524 | ||||||||
\(407\) | 1.62933e9 | 1.19792 | ||||||||
\(408\) | −7.81843e7 | −0.0569913 | ||||||||
\(409\) | 5.26460e8 | 0.380482 | 0.190241 | − | 0.981737i | \(-0.439073\pi\) | ||||
0.190241 | + | 0.981737i | \(0.439073\pi\) | |||||||
\(410\) | 1.66236e7 | 0.0119119 | ||||||||
\(411\) | −1.19082e9 | −0.846059 | ||||||||
\(412\) | 1.61665e7 | 0.0113887 | ||||||||
\(413\) | 1.20828e9 | 0.844000 | ||||||||
\(414\) | 1.66481e8 | 0.115309 | ||||||||
\(415\) | −8.92066e6 | −0.00612673 | ||||||||
\(416\) | 2.99552e8 | 0.204007 | ||||||||
\(417\) | 1.15142e9 | 0.777599 | ||||||||
\(418\) | 2.55966e8 | 0.171422 | ||||||||
\(419\) | −2.31838e9 | −1.53970 | −0.769850 | − | 0.638225i | \(-0.779669\pi\) | ||||
−0.769850 | + | 0.638225i | \(0.779669\pi\) | |||||||
\(420\) | −2.64821e8 | −0.174413 | ||||||||
\(421\) | −2.16319e9 | −1.41288 | −0.706442 | − | 0.707771i | \(-0.749701\pi\) | ||||
−0.706442 | + | 0.707771i | \(0.749701\pi\) | |||||||
\(422\) | 4.06131e8 | 0.263071 | ||||||||
\(423\) | 6.76351e8 | 0.434491 | ||||||||
\(424\) | −5.19078e7 | −0.0330714 | ||||||||
\(425\) | −8.83702e7 | −0.0558399 | ||||||||
\(426\) | −9.67497e8 | −0.606340 | ||||||||
\(427\) | 9.27368e8 | 0.576440 | ||||||||
\(428\) | 4.19938e7 | 0.0258900 | ||||||||
\(429\) | −1.15138e9 | −0.704071 | ||||||||
\(430\) | −8.73064e8 | −0.529550 | ||||||||
\(431\) | −2.19064e8 | −0.131796 | −0.0658979 | − | 0.997826i | \(-0.520991\pi\) | ||||
−0.0658979 | + | 0.997826i | \(0.520991\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | 3.08103e9 | 1.82384 | 0.911922 | − | 0.410363i | \(-0.134598\pi\) | ||||
0.911922 | + | 0.410363i | \(0.134598\pi\) | |||||||
\(434\) | −2.52774e9 | −1.48429 | ||||||||
\(435\) | −3.08810e8 | −0.179878 | ||||||||
\(436\) | −5.71985e8 | −0.330508 | ||||||||
\(437\) | −1.95798e8 | −0.112233 | ||||||||
\(438\) | −7.63796e8 | −0.434328 | ||||||||
\(439\) | 2.69086e9 | 1.51798 | 0.758988 | − | 0.651105i | \(-0.225694\pi\) | ||||
0.758988 | + | 0.651105i | \(0.225694\pi\) | |||||||
\(440\) | −2.98546e8 | −0.167081 | ||||||||
\(441\) | 4.95417e8 | 0.275065 | ||||||||
\(442\) | −4.13616e8 | −0.227835 | ||||||||
\(443\) | 3.73882e7 | 0.0204325 | 0.0102162 | − | 0.999948i | \(-0.496748\pi\) | ||||
0.0102162 | + | 0.999948i | \(0.496748\pi\) | |||||||
\(444\) | −6.03561e8 | −0.327251 | ||||||||
\(445\) | −4.67201e8 | −0.251330 | ||||||||
\(446\) | −1.17361e9 | −0.626398 | ||||||||
\(447\) | 2.31065e8 | 0.122365 | ||||||||
\(448\) | −3.21394e8 | −0.168875 | ||||||||
\(449\) | 1.53922e9 | 0.802489 | 0.401244 | − | 0.915971i | \(-0.368578\pi\) | ||||
0.401244 | + | 0.915971i | \(0.368578\pi\) | |||||||
\(450\) | 9.11250e7 | 0.0471405 | ||||||||
\(451\) | −7.75457e7 | −0.0398052 | ||||||||
\(452\) | −3.00162e8 | −0.152887 | ||||||||
\(453\) | 1.08364e9 | 0.547700 | ||||||||
\(454\) | −4.70066e8 | −0.235757 | ||||||||
\(455\) | −1.40097e9 | −0.697252 | ||||||||
\(456\) | −9.48188e7 | −0.0468293 | ||||||||
\(457\) | −3.29252e9 | −1.61370 | −0.806848 | − | 0.590759i | \(-0.798828\pi\) | ||||
−0.806848 | + | 0.590759i | \(0.798828\pi\) | |||||||
\(458\) | 2.43513e9 | 1.18439 | ||||||||
\(459\) | −1.11321e8 | −0.0537320 | ||||||||
\(460\) | 2.28369e8 | 0.109392 | ||||||||
\(461\) | 2.59005e9 | 1.23128 | 0.615638 | − | 0.788029i | \(-0.288898\pi\) | ||||
0.615638 | + | 0.788029i | \(0.288898\pi\) | |||||||
\(462\) | 1.23533e9 | 0.582823 | ||||||||
\(463\) | 2.10724e9 | 0.986689 | 0.493344 | − | 0.869834i | \(-0.335774\pi\) | ||||
0.493344 | + | 0.869834i | \(0.335774\pi\) | |||||||
\(464\) | −3.74781e8 | −0.174166 | ||||||||
\(465\) | 8.69799e8 | 0.401175 | ||||||||
\(466\) | −1.73866e9 | −0.795910 | ||||||||
\(467\) | 9.33516e8 | 0.424143 | 0.212072 | − | 0.977254i | \(-0.431979\pi\) | ||||
0.212072 | + | 0.977254i | \(0.431979\pi\) | |||||||
\(468\) | 4.26510e8 | 0.192340 | ||||||||
\(469\) | 5.82620e9 | 2.60784 | ||||||||
\(470\) | 9.27779e8 | 0.412194 | ||||||||
\(471\) | 1.69261e9 | 0.746421 | ||||||||
\(472\) | −5.04591e8 | −0.220873 | ||||||||
\(473\) | 4.07266e9 | 1.76955 | ||||||||
\(474\) | −2.86057e8 | −0.123375 | ||||||||
\(475\) | −1.07172e8 | −0.0458831 | ||||||||
\(476\) | 4.43776e8 | 0.188599 | ||||||||
\(477\) | −7.39078e7 | −0.0311800 | ||||||||
\(478\) | 1.99061e9 | 0.833660 | ||||||||
\(479\) | 9.27378e8 | 0.385552 | 0.192776 | − | 0.981243i | \(-0.438251\pi\) | ||||
0.192776 | + | 0.981243i | \(0.438251\pi\) | |||||||
\(480\) | 1.10592e8 | 0.0456435 | ||||||||
\(481\) | −3.19300e9 | −1.30825 | ||||||||
\(482\) | −2.94495e9 | −1.19788 | ||||||||
\(483\) | −9.44949e8 | −0.381587 | ||||||||
\(484\) | 1.45475e8 | 0.0583216 | ||||||||
\(485\) | −6.72368e8 | −0.267615 | ||||||||
\(486\) | 1.14791e8 | 0.0453609 | ||||||||
\(487\) | 3.59857e7 | 0.0141182 | 0.00705909 | − | 0.999975i | \(-0.497753\pi\) | ||||
0.00705909 | + | 0.999975i | \(0.497753\pi\) | |||||||
\(488\) | −3.87279e8 | −0.150853 | ||||||||
\(489\) | 1.23991e9 | 0.479523 | ||||||||
\(490\) | 6.79585e8 | 0.260950 | ||||||||
\(491\) | −4.85651e9 | −1.85157 | −0.925783 | − | 0.378056i | \(-0.876593\pi\) | ||||
−0.925783 | + | 0.378056i | \(0.876593\pi\) | |||||||
\(492\) | 2.87256e7 | 0.0108741 | ||||||||
\(493\) | 5.17491e8 | 0.194509 | ||||||||
\(494\) | −5.01617e8 | −0.187210 | ||||||||
\(495\) | −4.25079e8 | −0.157526 | ||||||||
\(496\) | 1.05561e9 | 0.388436 | ||||||||
\(497\) | 5.49154e9 | 2.00653 | ||||||||
\(498\) | −1.54149e7 | −0.00559291 | ||||||||
\(499\) | −5.20186e8 | −0.187416 | −0.0937080 | − | 0.995600i | \(-0.529872\pi\) | ||||
−0.0937080 | + | 0.995600i | \(0.529872\pi\) | |||||||
\(500\) | 1.25000e8 | 0.0447214 | ||||||||
\(501\) | 5.94926e8 | 0.211364 | ||||||||
\(502\) | −1.57807e9 | −0.556754 | ||||||||
\(503\) | −4.48316e8 | −0.157071 | −0.0785355 | − | 0.996911i | \(-0.525024\pi\) | ||||
−0.0785355 | + | 0.996911i | \(0.525024\pi\) | |||||||
\(504\) | −4.57610e8 | −0.159217 | ||||||||
\(505\) | −1.70884e9 | −0.590446 | ||||||||
\(506\) | −1.06529e9 | −0.365545 | ||||||||
\(507\) | 5.62144e8 | 0.191567 | ||||||||
\(508\) | 2.50423e9 | 0.847521 | ||||||||
\(509\) | −1.93635e9 | −0.650837 | −0.325419 | − | 0.945570i | \(-0.605505\pi\) | ||||
−0.325419 | + | 0.945570i | \(0.605505\pi\) | |||||||
\(510\) | −1.52704e8 | −0.0509746 | ||||||||
\(511\) | 4.33532e9 | 1.43730 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −1.35006e8 | −0.0441511 | ||||||||
\(514\) | −1.64953e9 | −0.535784 | ||||||||
\(515\) | 3.15752e7 | 0.0101864 | ||||||||
\(516\) | −1.50866e9 | −0.483410 | ||||||||
\(517\) | −4.32789e9 | −1.37740 | ||||||||
\(518\) | 3.42583e9 | 1.08296 | ||||||||
\(519\) | −1.74829e9 | −0.548944 | ||||||||
\(520\) | 5.85062e8 | 0.182469 | ||||||||
\(521\) | 3.32620e9 | 1.03042 | 0.515212 | − | 0.857063i | \(-0.327713\pi\) | ||||
0.515212 | + | 0.857063i | \(0.327713\pi\) | |||||||
\(522\) | −5.33623e8 | −0.164206 | ||||||||
\(523\) | −2.66642e9 | −0.815029 | −0.407515 | − | 0.913199i | \(-0.633604\pi\) | ||||
−0.407515 | + | 0.913199i | \(0.633604\pi\) | |||||||
\(524\) | −2.01222e9 | −0.610963 | ||||||||
\(525\) | −5.17228e8 | −0.156000 | ||||||||
\(526\) | −1.06382e9 | −0.318728 | ||||||||
\(527\) | −1.45757e9 | −0.433804 | ||||||||
\(528\) | −5.15888e8 | −0.152523 | ||||||||
\(529\) | −2.58995e9 | −0.760669 | ||||||||
\(530\) | −1.01382e8 | −0.0295799 | ||||||||
\(531\) | −7.18451e8 | −0.208241 | ||||||||
\(532\) | 5.38194e8 | 0.154970 | ||||||||
\(533\) | 1.51966e8 | 0.0434713 | ||||||||
\(534\) | −8.07323e8 | −0.229431 | ||||||||
\(535\) | 8.20191e7 | 0.0231567 | ||||||||
\(536\) | −2.43308e9 | −0.682465 | ||||||||
\(537\) | 1.36602e9 | 0.380667 | ||||||||
\(538\) | 1.41043e9 | 0.390493 | ||||||||
\(539\) | −3.17012e9 | −0.871996 | ||||||||
\(540\) | 1.57464e8 | 0.0430331 | ||||||||
\(541\) | 3.53887e9 | 0.960892 | 0.480446 | − | 0.877024i | \(-0.340475\pi\) | ||||
0.480446 | + | 0.877024i | \(0.340475\pi\) | |||||||
\(542\) | −2.25388e9 | −0.608042 | ||||||||
\(543\) | −3.75663e9 | −1.00693 | ||||||||
\(544\) | −1.85326e8 | −0.0493560 | ||||||||
\(545\) | −1.11716e9 | −0.295615 | ||||||||
\(546\) | −2.42088e9 | −0.636501 | ||||||||
\(547\) | 6.17856e9 | 1.61410 | 0.807052 | − | 0.590481i | \(-0.201062\pi\) | ||||
0.807052 | + | 0.590481i | \(0.201062\pi\) | |||||||
\(548\) | −2.82269e9 | −0.732709 | ||||||||
\(549\) | −5.51419e8 | −0.142226 | ||||||||
\(550\) | −5.83098e8 | −0.149442 | ||||||||
\(551\) | 6.27593e8 | 0.159826 | ||||||||
\(552\) | 3.94621e8 | 0.0998604 | ||||||||
\(553\) | 1.62367e9 | 0.408280 | ||||||||
\(554\) | 2.65930e9 | 0.664481 | ||||||||
\(555\) | −1.17883e9 | −0.292702 | ||||||||
\(556\) | 2.72928e9 | 0.673421 | ||||||||
\(557\) | 4.64096e8 | 0.113793 | 0.0568964 | − | 0.998380i | \(-0.481880\pi\) | ||||
0.0568964 | + | 0.998380i | \(0.481880\pi\) | |||||||
\(558\) | 1.50301e9 | 0.366221 | ||||||||
\(559\) | −7.98120e9 | −1.93253 | ||||||||
\(560\) | −6.27723e8 | −0.151046 | ||||||||
\(561\) | 7.12330e8 | 0.170338 | ||||||||
\(562\) | 2.91213e9 | 0.692044 | ||||||||
\(563\) | 6.20879e9 | 1.46632 | 0.733158 | − | 0.680059i | \(-0.238046\pi\) | ||||
0.733158 | + | 0.680059i | \(0.238046\pi\) | |||||||
\(564\) | 1.60320e9 | 0.376280 | ||||||||
\(565\) | −5.86255e8 | −0.136747 | ||||||||
\(566\) | 3.75972e9 | 0.871561 | ||||||||
\(567\) | −6.51558e8 | −0.150111 | ||||||||
\(568\) | −2.29333e9 | −0.525106 | ||||||||
\(569\) | −3.12134e8 | −0.0710311 | −0.0355155 | − | 0.999369i | \(-0.511307\pi\) | ||||
−0.0355155 | + | 0.999369i | \(0.511307\pi\) | |||||||
\(570\) | −1.85193e8 | −0.0418854 | ||||||||
\(571\) | 5.24046e9 | 1.17799 | 0.588997 | − | 0.808135i | \(-0.299523\pi\) | ||||
0.588997 | + | 0.808135i | \(0.299523\pi\) | |||||||
\(572\) | −2.72919e9 | −0.609744 | ||||||||
\(573\) | 1.78693e9 | 0.396796 | ||||||||
\(574\) | −1.63047e8 | −0.0359851 | ||||||||
\(575\) | 4.46033e8 | 0.0978429 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | −6.89035e9 | −1.49323 | −0.746614 | − | 0.665257i | \(-0.768322\pi\) | ||||
−0.746614 | + | 0.665257i | \(0.768322\pi\) | |||||||
\(578\) | −3.02681e9 | −0.651986 | ||||||||
\(579\) | −1.57007e9 | −0.336159 | ||||||||
\(580\) | −7.31993e8 | −0.155779 | ||||||||
\(581\) | 8.74954e7 | 0.0185084 | ||||||||
\(582\) | −1.16185e9 | −0.244298 | ||||||||
\(583\) | 4.72927e8 | 0.0988449 | ||||||||
\(584\) | −1.81048e9 | −0.376139 | ||||||||
\(585\) | 8.33027e8 | 0.172034 | ||||||||
\(586\) | −5.80250e9 | −1.19117 | ||||||||
\(587\) | 1.37892e9 | 0.281388 | 0.140694 | − | 0.990053i | \(-0.455067\pi\) | ||||
0.140694 | + | 0.990053i | \(0.455067\pi\) | |||||||
\(588\) | 1.17432e9 | 0.238214 | ||||||||
\(589\) | −1.76769e9 | −0.356453 | ||||||||
\(590\) | −9.85529e8 | −0.197555 | ||||||||
\(591\) | 3.58934e9 | 0.715251 | ||||||||
\(592\) | −1.43066e9 | −0.283408 | ||||||||
\(593\) | −3.35153e9 | −0.660012 | −0.330006 | − | 0.943979i | \(-0.607051\pi\) | ||||
−0.330006 | + | 0.943979i | \(0.607051\pi\) | |||||||
\(594\) | −7.34536e8 | −0.143800 | ||||||||
\(595\) | 8.66750e8 | 0.168688 | ||||||||
\(596\) | 5.47709e8 | 0.105971 | ||||||||
\(597\) | −2.11587e9 | −0.406985 | ||||||||
\(598\) | 2.08765e9 | 0.399213 | ||||||||
\(599\) | 6.74203e9 | 1.28173 | 0.640865 | − | 0.767654i | \(-0.278576\pi\) | ||||
0.640865 | + | 0.767654i | \(0.278576\pi\) | |||||||
\(600\) | 2.16000e8 | 0.0408248 | ||||||||
\(601\) | 4.63680e9 | 0.871281 | 0.435640 | − | 0.900121i | \(-0.356522\pi\) | ||||
0.435640 | + | 0.900121i | \(0.356522\pi\) | |||||||
\(602\) | 8.56316e9 | 1.59973 | ||||||||
\(603\) | −3.46429e9 | −0.643434 | ||||||||
\(604\) | 2.56864e9 | 0.474322 | ||||||||
\(605\) | 2.84131e8 | 0.0521645 | ||||||||
\(606\) | −2.95287e9 | −0.539001 | ||||||||
\(607\) | −4.15246e9 | −0.753607 | −0.376804 | − | 0.926293i | \(-0.622977\pi\) | ||||
−0.376804 | + | 0.926293i | \(0.622977\pi\) | |||||||
\(608\) | −2.24756e8 | −0.0405554 | ||||||||
\(609\) | 3.02886e9 | 0.543398 | ||||||||
\(610\) | −7.56404e8 | −0.134927 | ||||||||
\(611\) | 8.48138e9 | 1.50426 | ||||||||
\(612\) | −2.63872e8 | −0.0465332 | ||||||||
\(613\) | −5.87720e9 | −1.03053 | −0.515263 | − | 0.857032i | \(-0.672306\pi\) | ||||
−0.515263 | + | 0.857032i | \(0.672306\pi\) | |||||||
\(614\) | 1.58092e9 | 0.275627 | ||||||||
\(615\) | 5.61048e7 | 0.00972606 | ||||||||
\(616\) | 2.92819e9 | 0.504739 | ||||||||
\(617\) | 4.26910e9 | 0.731709 | 0.365854 | − | 0.930672i | \(-0.380777\pi\) | ||||
0.365854 | + | 0.930672i | \(0.380777\pi\) | |||||||
\(618\) | 5.45619e7 | 0.00929886 | ||||||||
\(619\) | 6.08008e9 | 1.03037 | 0.515183 | − | 0.857080i | \(-0.327724\pi\) | ||||
0.515183 | + | 0.857080i | \(0.327724\pi\) | |||||||
\(620\) | 2.06174e9 | 0.347427 | ||||||||
\(621\) | 5.61873e8 | 0.0941493 | ||||||||
\(622\) | 6.47536e9 | 1.07894 | ||||||||
\(623\) | 4.58238e9 | 0.759247 | ||||||||
\(624\) | 1.01099e9 | 0.166571 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | −2.83349e9 | −0.461649 | ||||||||
\(627\) | 8.63886e8 | 0.139965 | ||||||||
\(628\) | 4.01211e9 | 0.646419 | ||||||||
\(629\) | 1.97544e9 | 0.316509 | ||||||||
\(630\) | −8.93769e8 | −0.142408 | ||||||||
\(631\) | −2.76268e9 | −0.437751 | −0.218876 | − | 0.975753i | \(-0.570239\pi\) | ||||
−0.218876 | + | 0.975753i | \(0.570239\pi\) | |||||||
\(632\) | −6.78061e8 | −0.106846 | ||||||||
\(633\) | 1.37069e9 | 0.214797 | ||||||||
\(634\) | 8.50111e9 | 1.32484 | ||||||||
\(635\) | 4.89107e9 | 0.758046 | ||||||||
\(636\) | −1.75189e8 | −0.0270027 | ||||||||
\(637\) | 6.21248e9 | 0.952308 | ||||||||
\(638\) | 3.41459e9 | 0.520555 | ||||||||
\(639\) | −3.26530e9 | −0.495074 | ||||||||
\(640\) | 2.62144e8 | 0.0395285 | ||||||||
\(641\) | −4.56044e9 | −0.683918 | −0.341959 | − | 0.939715i | \(-0.611090\pi\) | ||||
−0.341959 | + | 0.939715i | \(0.611090\pi\) | |||||||
\(642\) | 1.41729e8 | 0.0211391 | ||||||||
\(643\) | −5.32233e9 | −0.789521 | −0.394760 | − | 0.918784i | \(-0.629172\pi\) | ||||
−0.394760 | + | 0.918784i | \(0.629172\pi\) | |||||||
\(644\) | −2.23988e9 | −0.330464 | ||||||||
\(645\) | −2.94659e9 | −0.432375 | ||||||||
\(646\) | 3.10339e8 | 0.0452921 | ||||||||
\(647\) | 3.18208e9 | 0.461897 | 0.230949 | − | 0.972966i | \(-0.425817\pi\) | ||||
0.230949 | + | 0.972966i | \(0.425817\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | 4.59728e9 | 0.660153 | ||||||||
\(650\) | 1.14270e9 | 0.163206 | ||||||||
\(651\) | −8.53113e9 | −1.21192 | ||||||||
\(652\) | 2.93905e9 | 0.415279 | ||||||||
\(653\) | 9.07611e9 | 1.27557 | 0.637784 | − | 0.770215i | \(-0.279851\pi\) | ||||
0.637784 | + | 0.770215i | \(0.279851\pi\) | |||||||
\(654\) | −1.93045e9 | −0.269859 | ||||||||
\(655\) | −3.93011e9 | −0.546462 | ||||||||
\(656\) | 6.80904e7 | 0.00941722 | ||||||||
\(657\) | −2.57781e9 | −0.354627 | ||||||||
\(658\) | −9.09981e9 | −1.24521 | ||||||||
\(659\) | 5.36153e9 | 0.729777 | 0.364888 | − | 0.931051i | \(-0.381107\pi\) | ||||
0.364888 | + | 0.931051i | \(0.381107\pi\) | |||||||
\(660\) | −1.00759e9 | −0.136421 | ||||||||
\(661\) | 6.20884e9 | 0.836191 | 0.418096 | − | 0.908403i | \(-0.362698\pi\) | ||||
0.418096 | + | 0.908403i | \(0.362698\pi\) | |||||||
\(662\) | 1.81282e9 | 0.242857 | ||||||||
\(663\) | −1.39595e9 | −0.186026 | ||||||||
\(664\) | −3.65390e7 | −0.00484361 | ||||||||
\(665\) | 1.05116e9 | 0.138609 | ||||||||
\(666\) | −2.03702e9 | −0.267199 | ||||||||
\(667\) | −2.61194e9 | −0.340819 | ||||||||
\(668\) | 1.41019e9 | 0.183046 | ||||||||
\(669\) | −3.96092e9 | −0.511452 | ||||||||
\(670\) | −4.75212e9 | −0.610415 | ||||||||
\(671\) | 3.52846e9 | 0.450876 | ||||||||
\(672\) | −1.08470e9 | −0.137886 | ||||||||
\(673\) | 3.64417e9 | 0.460836 | 0.230418 | − | 0.973092i | \(-0.425991\pi\) | ||||
0.230418 | + | 0.973092i | \(0.425991\pi\) | |||||||
\(674\) | 3.06873e9 | 0.386055 | ||||||||
\(675\) | 3.07547e8 | 0.0384900 | ||||||||
\(676\) | 1.33249e9 | 0.165902 | ||||||||
\(677\) | 9.03739e9 | 1.11939 | 0.559697 | − | 0.828697i | \(-0.310918\pi\) | ||||
0.559697 | + | 0.828697i | \(0.310918\pi\) | |||||||
\(678\) | −1.01305e9 | −0.124832 | ||||||||
\(679\) | 6.59470e9 | 0.808446 | ||||||||
\(680\) | −3.61964e8 | −0.0441453 | ||||||||
\(681\) | −1.58647e9 | −0.192494 | ||||||||
\(682\) | −9.61760e9 | −1.16097 | ||||||||
\(683\) | −4.80985e9 | −0.577643 | −0.288821 | − | 0.957383i | \(-0.593263\pi\) | ||||
−0.288821 | + | 0.957383i | \(0.593263\pi\) | |||||||
\(684\) | −3.20014e8 | −0.0382360 | ||||||||
\(685\) | −5.51307e9 | −0.655354 | ||||||||
\(686\) | 1.41197e9 | 0.166990 | ||||||||
\(687\) | 8.21857e9 | 0.967047 | ||||||||
\(688\) | −3.57607e9 | −0.418646 | ||||||||
\(689\) | −9.26797e8 | −0.107949 | ||||||||
\(690\) | 7.70744e8 | 0.0893179 | ||||||||
\(691\) | 8.74228e9 | 1.00798 | 0.503990 | − | 0.863710i | \(-0.331865\pi\) | ||||
0.503990 | + | 0.863710i | \(0.331865\pi\) | |||||||
\(692\) | −4.14410e9 | −0.475400 | ||||||||
\(693\) | 4.16924e9 | 0.475873 | ||||||||
\(694\) | 4.60756e9 | 0.523254 | ||||||||
\(695\) | 5.33063e9 | 0.602326 | ||||||||
\(696\) | −1.26488e9 | −0.142206 | ||||||||
\(697\) | −9.40182e7 | −0.0105171 | ||||||||
\(698\) | −8.24120e9 | −0.917268 | ||||||||
\(699\) | −5.86798e9 | −0.649858 | ||||||||
\(700\) | −1.22602e9 | −0.135100 | ||||||||
\(701\) | 1.06528e10 | 1.16803 | 0.584013 | − | 0.811744i | \(-0.301482\pi\) | ||||
0.584013 | + | 0.811744i | \(0.301482\pi\) | |||||||
\(702\) | 1.43947e9 | 0.157045 | ||||||||
\(703\) | 2.39573e9 | 0.260073 | ||||||||
\(704\) | −1.22285e9 | −0.132089 | ||||||||
\(705\) | 3.13125e9 | 0.336555 | ||||||||
\(706\) | −7.13402e9 | −0.762988 | ||||||||
\(707\) | 1.67605e10 | 1.78369 | ||||||||
\(708\) | −1.70299e9 | −0.180342 | ||||||||
\(709\) | 1.03896e10 | 1.09481 | 0.547403 | − | 0.836869i | \(-0.315617\pi\) | ||||
0.547403 | + | 0.836869i | \(0.315617\pi\) | |||||||
\(710\) | −4.47915e9 | −0.469669 | ||||||||
\(711\) | −9.65442e8 | −0.100735 | ||||||||
\(712\) | −1.91365e9 | −0.198693 | ||||||||
\(713\) | 7.35684e9 | 0.760113 | ||||||||
\(714\) | 1.49774e9 | 0.153990 | ||||||||
\(715\) | −5.33044e9 | −0.545371 | ||||||||
\(716\) | 3.23796e9 | 0.329668 | ||||||||
\(717\) | 6.71832e9 | 0.680681 | ||||||||
\(718\) | −1.14361e10 | −1.15303 | ||||||||
\(719\) | 7.96840e9 | 0.799503 | 0.399752 | − | 0.916624i | \(-0.369096\pi\) | ||||
0.399752 | + | 0.916624i | \(0.369096\pi\) | |||||||
\(720\) | 3.73248e8 | 0.0372678 | ||||||||
\(721\) | −3.09694e8 | −0.0307723 | ||||||||
\(722\) | 3.76367e8 | 0.0372161 | ||||||||
\(723\) | −9.93922e9 | −0.978066 | ||||||||
\(724\) | −8.90460e9 | −0.872026 | ||||||||
\(725\) | −1.42967e9 | −0.139333 | ||||||||
\(726\) | 4.90978e8 | 0.0476194 | ||||||||
\(727\) | 1.46339e10 | 1.41251 | 0.706253 | − | 0.707960i | \(-0.250384\pi\) | ||||
0.706253 | + | 0.707960i | \(0.250384\pi\) | |||||||
\(728\) | −5.73838e9 | −0.551226 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −3.53609e9 | −0.336429 | ||||||||
\(731\) | 4.93778e9 | 0.467543 | ||||||||
\(732\) | −1.30707e9 | −0.123171 | ||||||||
\(733\) | 1.27362e10 | 1.19447 | 0.597234 | − | 0.802067i | \(-0.296266\pi\) | ||||
0.597234 | + | 0.802067i | \(0.296266\pi\) | |||||||
\(734\) | −8.65586e9 | −0.807930 | ||||||||
\(735\) | 2.29360e9 | 0.213065 | ||||||||
\(736\) | 9.35398e8 | 0.0864817 | ||||||||
\(737\) | 2.21676e10 | 2.03978 | ||||||||
\(738\) | 9.69491e7 | 0.00887864 | ||||||||
\(739\) | −1.95071e10 | −1.77802 | −0.889009 | − | 0.457890i | \(-0.848605\pi\) | ||||
−0.889009 | + | 0.457890i | \(0.848605\pi\) | |||||||
\(740\) | −2.79427e9 | −0.253488 | ||||||||
\(741\) | −1.69296e9 | −0.152856 | ||||||||
\(742\) | 9.94376e8 | 0.0893587 | ||||||||
\(743\) | 1.07928e10 | 0.965326 | 0.482663 | − | 0.875806i | \(-0.339670\pi\) | ||||
0.482663 | + | 0.875806i | \(0.339670\pi\) | |||||||
\(744\) | 3.56270e9 | 0.317156 | ||||||||
\(745\) | 1.06974e9 | 0.0947836 | ||||||||
\(746\) | −1.13195e10 | −0.998251 | ||||||||
\(747\) | −5.20253e7 | −0.00456660 | ||||||||
\(748\) | 1.68849e9 | 0.147517 | ||||||||
\(749\) | −8.04457e8 | −0.0699547 | ||||||||
\(750\) | 4.21875e8 | 0.0365148 | ||||||||
\(751\) | 1.57746e10 | 1.35899 | 0.679497 | − | 0.733679i | \(-0.262198\pi\) | ||||
0.679497 | + | 0.733679i | \(0.262198\pi\) | |||||||
\(752\) | 3.80018e9 | 0.325868 | ||||||||
\(753\) | −5.32599e9 | −0.454588 | ||||||||
\(754\) | −6.69158e9 | −0.568498 | ||||||||
\(755\) | 5.01687e9 | 0.424247 | ||||||||
\(756\) | −1.54443e9 | −0.130000 | ||||||||
\(757\) | −1.16114e9 | −0.0972855 | −0.0486427 | − | 0.998816i | \(-0.515490\pi\) | ||||
−0.0486427 | + | 0.998816i | \(0.515490\pi\) | |||||||
\(758\) | −1.21115e9 | −0.101008 | ||||||||
\(759\) | −3.59536e9 | −0.298467 | ||||||||
\(760\) | −4.38976e8 | −0.0362738 | ||||||||
\(761\) | −7.77889e9 | −0.639840 | −0.319920 | − | 0.947445i | \(-0.603656\pi\) | ||||
−0.319920 | + | 0.947445i | \(0.603656\pi\) | |||||||
\(762\) | 8.45176e9 | 0.691998 | ||||||||
\(763\) | 1.09573e10 | 0.893031 | ||||||||
\(764\) | 4.23569e9 | 0.343635 | ||||||||
\(765\) | −5.15375e8 | −0.0416206 | ||||||||
\(766\) | 4.64299e9 | 0.373247 | ||||||||
\(767\) | −9.00930e9 | −0.720954 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | 6.68999e9 | 0.530497 | 0.265249 | − | 0.964180i | \(-0.414546\pi\) | ||||
0.265249 | + | 0.964180i | \(0.414546\pi\) | |||||||
\(770\) | 5.71912e9 | 0.451452 | ||||||||
\(771\) | −5.56717e9 | −0.437466 | ||||||||
\(772\) | −3.72165e9 | −0.291122 | ||||||||
\(773\) | −2.23508e10 | −1.74046 | −0.870230 | − | 0.492645i | \(-0.836030\pi\) | ||||
−0.870230 | + | 0.492645i | \(0.836030\pi\) | |||||||
\(774\) | −5.09171e9 | −0.394703 | ||||||||
\(775\) | 4.02685e9 | 0.310748 | ||||||||
\(776\) | −2.75402e9 | −0.211569 | ||||||||
\(777\) | 1.15622e10 | 0.884231 | ||||||||
\(778\) | 1.27691e9 | 0.0972147 | ||||||||
\(779\) | −1.14022e8 | −0.00864183 | ||||||||
\(780\) | 1.97458e9 | 0.148986 | ||||||||
\(781\) | 2.08943e10 | 1.56946 | ||||||||
\(782\) | −1.29158e9 | −0.0965826 | ||||||||
\(783\) | −1.80098e9 | −0.134073 | ||||||||
\(784\) | 2.78358e9 | 0.206299 | ||||||||
\(785\) | 7.83616e9 | 0.578175 | ||||||||
\(786\) | −6.79123e9 | −0.498849 | ||||||||
\(787\) | −9.69306e9 | −0.708841 | −0.354421 | − | 0.935086i | \(-0.615322\pi\) | ||||
−0.354421 | + | 0.935086i | \(0.615322\pi\) | |||||||
\(788\) | 8.50807e9 | 0.619426 | ||||||||
\(789\) | −3.59041e9 | −0.260240 | ||||||||
\(790\) | −1.32434e9 | −0.0955661 | ||||||||
\(791\) | 5.75008e9 | 0.413101 | ||||||||
\(792\) | −1.74112e9 | −0.124535 | ||||||||
\(793\) | −6.91474e9 | −0.492402 | ||||||||
\(794\) | 1.84600e9 | 0.130876 | ||||||||
\(795\) | −3.42166e8 | −0.0241519 | ||||||||
\(796\) | −5.01539e9 | −0.352459 | ||||||||
\(797\) | 1.58293e10 | 1.10754 | 0.553769 | − | 0.832670i | \(-0.313189\pi\) | ||||
0.553769 | + | 0.832670i | \(0.313189\pi\) | |||||||
\(798\) | 1.81640e9 | 0.126533 | ||||||||
\(799\) | −5.24723e9 | −0.363929 | ||||||||
\(800\) | 5.12000e8 | 0.0353553 | ||||||||
\(801\) | −2.72471e9 | −0.187330 | ||||||||
\(802\) | −6.21319e9 | −0.425309 | ||||||||
\(803\) | 1.64951e10 | 1.12422 | ||||||||
\(804\) | −8.21166e9 | −0.557230 | ||||||||
\(805\) | −4.37476e9 | −0.295576 | ||||||||
\(806\) | 1.88476e10 | 1.26790 | ||||||||
\(807\) | 4.76020e9 | 0.318836 | ||||||||
\(808\) | −6.99939e9 | −0.466789 | ||||||||
\(809\) | −7.03323e9 | −0.467020 | −0.233510 | − | 0.972354i | \(-0.575021\pi\) | ||||
−0.233510 | + | 0.972354i | \(0.575021\pi\) | |||||||
\(810\) | 5.31441e8 | 0.0351364 | ||||||||
\(811\) | −2.22464e10 | −1.46449 | −0.732244 | − | 0.681042i | \(-0.761527\pi\) | ||||
−0.732244 | + | 0.681042i | \(0.761527\pi\) | |||||||
\(812\) | 7.17951e9 | 0.470597 | ||||||||
\(813\) | −7.60685e9 | −0.496464 | ||||||||
\(814\) | 1.30346e10 | 0.847059 | ||||||||
\(815\) | 5.74032e9 | 0.371437 | ||||||||
\(816\) | −6.25474e8 | −0.0402990 | ||||||||
\(817\) | 5.98835e9 | 0.384176 | ||||||||
\(818\) | 4.21168e9 | 0.269041 | ||||||||
\(819\) | −8.17047e9 | −0.519701 | ||||||||
\(820\) | 1.32989e8 | 0.00842301 | ||||||||
\(821\) | 1.45023e10 | 0.914611 | 0.457305 | − | 0.889310i | \(-0.348815\pi\) | ||||
0.457305 | + | 0.889310i | \(0.348815\pi\) | |||||||
\(822\) | −9.52658e9 | −0.598254 | ||||||||
\(823\) | −1.39647e9 | −0.0873237 | −0.0436619 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436619 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(824\) | 1.29332e8 | 0.00805305 | ||||||||
\(825\) | −1.96796e9 | −0.122019 | ||||||||
\(826\) | 9.66624e9 | 0.596798 | ||||||||
\(827\) | 6.31315e9 | 0.388130 | 0.194065 | − | 0.980989i | \(-0.437833\pi\) | ||||
0.194065 | + | 0.980989i | \(0.437833\pi\) | |||||||
\(828\) | 1.33185e9 | 0.0815357 | ||||||||
\(829\) | −2.65187e9 | −0.161663 | −0.0808317 | − | 0.996728i | \(-0.525758\pi\) | ||||
−0.0808317 | + | 0.996728i | \(0.525758\pi\) | |||||||
\(830\) | −7.13653e7 | −0.00433225 | ||||||||
\(831\) | 8.97512e9 | 0.542546 | ||||||||
\(832\) | 2.39641e9 | 0.144255 | ||||||||
\(833\) | −3.84352e9 | −0.230394 | ||||||||
\(834\) | 9.21132e9 | 0.549846 | ||||||||
\(835\) | 2.75429e9 | 0.163722 | ||||||||
\(836\) | 2.04773e9 | 0.121213 | ||||||||
\(837\) | 5.07267e9 | 0.299018 | ||||||||
\(838\) | −1.85471e10 | −1.08873 | ||||||||
\(839\) | 2.35103e10 | 1.37433 | 0.687165 | − | 0.726502i | \(-0.258855\pi\) | ||||
0.687165 | + | 0.726502i | \(0.258855\pi\) | |||||||
\(840\) | −2.11856e9 | −0.123329 | ||||||||
\(841\) | −8.87778e9 | −0.514657 | ||||||||
\(842\) | −1.73055e10 | −0.999060 | ||||||||
\(843\) | 9.82844e9 | 0.565051 | ||||||||
\(844\) | 3.24905e9 | 0.186019 | ||||||||
\(845\) | 2.60252e9 | 0.148387 | ||||||||
\(846\) | 5.41081e9 | 0.307232 | ||||||||
\(847\) | −2.78680e9 | −0.157585 | ||||||||
\(848\) | −4.15262e8 | −0.0233850 | ||||||||
\(849\) | 1.26890e10 | 0.711627 | ||||||||
\(850\) | −7.06962e8 | −0.0394848 | ||||||||
\(851\) | −9.97067e9 | −0.554588 | ||||||||
\(852\) | −7.73998e9 | −0.428747 | ||||||||
\(853\) | 1.25648e10 | 0.693160 | 0.346580 | − | 0.938020i | \(-0.387343\pi\) | ||||
0.346580 | + | 0.938020i | \(0.387343\pi\) | |||||||
\(854\) | 7.41894e9 | 0.407605 | ||||||||
\(855\) | −6.25026e8 | −0.0341993 | ||||||||
\(856\) | 3.35950e8 | 0.0183070 | ||||||||
\(857\) | 2.24742e10 | 1.21970 | 0.609848 | − | 0.792519i | \(-0.291231\pi\) | ||||
0.609848 | + | 0.792519i | \(0.291231\pi\) | |||||||
\(858\) | −9.21101e9 | −0.497854 | ||||||||
\(859\) | −1.20621e10 | −0.649302 | −0.324651 | − | 0.945834i | \(-0.605247\pi\) | ||||
−0.324651 | + | 0.945834i | \(0.605247\pi\) | |||||||
\(860\) | −6.98451e9 | −0.374448 | ||||||||
\(861\) | −5.50285e8 | −0.0293817 | ||||||||
\(862\) | −1.75252e9 | −0.0931937 | ||||||||
\(863\) | −3.12352e10 | −1.65427 | −0.827136 | − | 0.562001i | \(-0.810032\pi\) | ||||
−0.827136 | + | 0.562001i | \(0.810032\pi\) | |||||||
\(864\) | 6.44973e8 | 0.0340207 | ||||||||
\(865\) | −8.09394e9 | −0.425210 | ||||||||
\(866\) | 2.46482e10 | 1.28965 | ||||||||
\(867\) | −1.02155e10 | −0.532344 | ||||||||
\(868\) | −2.02219e10 | −1.04955 | ||||||||
\(869\) | 6.17775e9 | 0.319346 | ||||||||
\(870\) | −2.47048e9 | −0.127193 | ||||||||
\(871\) | −4.34419e10 | −2.22764 | ||||||||
\(872\) | −4.57588e9 | −0.233704 | ||||||||
\(873\) | −3.92125e9 | −0.199469 | ||||||||
\(874\) | −1.56638e9 | −0.0793610 | ||||||||
\(875\) | −2.39457e9 | −0.120837 | ||||||||
\(876\) | −6.11037e9 | −0.307116 | ||||||||
\(877\) | −1.16277e10 | −0.582096 | −0.291048 | − | 0.956709i | \(-0.594004\pi\) | ||||
−0.291048 | + | 0.956709i | \(0.594004\pi\) | |||||||
\(878\) | 2.15268e10 | 1.07337 | ||||||||
\(879\) | −1.95834e10 | −0.972585 | ||||||||
\(880\) | −2.38837e9 | −0.118144 | ||||||||
\(881\) | −6.80837e9 | −0.335450 | −0.167725 | − | 0.985834i | \(-0.553642\pi\) | ||||
−0.167725 | + | 0.985834i | \(0.553642\pi\) | |||||||
\(882\) | 3.96334e9 | 0.194501 | ||||||||
\(883\) | −4.66300e8 | −0.0227931 | −0.0113965 | − | 0.999935i | \(-0.503628\pi\) | ||||
−0.0113965 | + | 0.999935i | \(0.503628\pi\) | |||||||
\(884\) | −3.30893e9 | −0.161103 | ||||||||
\(885\) | −3.32616e9 | −0.161303 | ||||||||
\(886\) | 2.99105e8 | 0.0144480 | ||||||||
\(887\) | −3.49184e10 | −1.68005 | −0.840025 | − | 0.542548i | \(-0.817460\pi\) | ||||
−0.840025 | + | 0.542548i | \(0.817460\pi\) | |||||||
\(888\) | −4.82849e9 | −0.231401 | ||||||||
\(889\) | −4.79724e10 | −2.29000 | ||||||||
\(890\) | −3.73761e9 | −0.177717 | ||||||||
\(891\) | −2.47906e9 | −0.117413 | ||||||||
\(892\) | −9.38885e9 | −0.442930 | ||||||||
\(893\) | −6.36364e9 | −0.299037 | ||||||||
\(894\) | 1.84852e9 | 0.0865252 | ||||||||
\(895\) | 6.32414e9 | 0.294864 | ||||||||
\(896\) | −2.57115e9 | −0.119413 | ||||||||
\(897\) | 7.04583e9 | 0.325956 | ||||||||
\(898\) | 1.23138e10 | 0.567445 | ||||||||
\(899\) | −2.35810e10 | −1.08244 | ||||||||
\(900\) | 7.29000e8 | 0.0333333 | ||||||||
\(901\) | 5.73388e8 | 0.0261163 | ||||||||
\(902\) | −6.20366e8 | −0.0281465 | ||||||||
\(903\) | 2.89007e10 | 1.30617 | ||||||||
\(904\) | −2.40130e9 | −0.108108 | ||||||||
\(905\) | −1.73918e10 | −0.779964 | ||||||||
\(906\) | 8.66915e9 | 0.387283 | ||||||||
\(907\) | −9.65664e9 | −0.429735 | −0.214867 | − | 0.976643i | \(-0.568932\pi\) | ||||
−0.214867 | + | 0.976643i | \(0.568932\pi\) | |||||||
\(908\) | −3.76053e9 | −0.166705 | ||||||||
\(909\) | −9.96593e9 | −0.440093 | ||||||||
\(910\) | −1.12078e10 | −0.493032 | ||||||||
\(911\) | 5.54939e8 | 0.0243182 | 0.0121591 | − | 0.999926i | \(-0.496130\pi\) | ||||
0.0121591 | + | 0.999926i | \(0.496130\pi\) | |||||||
\(912\) | −7.58551e8 | −0.0331133 | ||||||||
\(913\) | 3.32904e8 | 0.0144767 | ||||||||
\(914\) | −2.63402e10 | −1.14106 | ||||||||
\(915\) | −2.55286e9 | −0.110168 | ||||||||
\(916\) | 1.94811e10 | 0.837488 | ||||||||
\(917\) | 3.85472e10 | 1.65082 | ||||||||
\(918\) | −8.90568e8 | −0.0379942 | ||||||||
\(919\) | −9.56305e9 | −0.406436 | −0.203218 | − | 0.979134i | \(-0.565140\pi\) | ||||
−0.203218 | + | 0.979134i | \(0.565140\pi\) | |||||||
\(920\) | 1.82695e9 | 0.0773516 | ||||||||
\(921\) | 5.33562e9 | 0.225048 | ||||||||
\(922\) | 2.07204e10 | 0.870644 | ||||||||
\(923\) | −4.09466e10 | −1.71400 | ||||||||
\(924\) | 9.88265e9 | 0.412118 | ||||||||
\(925\) | −5.45755e9 | −0.226726 | ||||||||
\(926\) | 1.68579e10 | 0.697694 | ||||||||
\(927\) | 1.84146e8 | 0.00759249 | ||||||||
\(928\) | −2.99824e9 | −0.123154 | ||||||||
\(929\) | −2.73541e10 | −1.11935 | −0.559677 | − | 0.828711i | \(-0.689075\pi\) | ||||
−0.559677 | + | 0.828711i | \(0.689075\pi\) | |||||||
\(930\) | 6.95839e9 | 0.283673 | ||||||||
\(931\) | −4.66127e9 | −0.189313 | ||||||||
\(932\) | −1.39093e10 | −0.562793 | ||||||||
\(933\) | 2.18543e10 | 0.880952 | ||||||||
\(934\) | 7.46812e9 | 0.299915 | ||||||||
\(935\) | 3.29782e9 | 0.131943 | ||||||||
\(936\) | 3.41208e9 | 0.136005 | ||||||||
\(937\) | −1.94603e10 | −0.772787 | −0.386394 | − | 0.922334i | \(-0.626279\pi\) | ||||
−0.386394 | + | 0.922334i | \(0.626279\pi\) | |||||||
\(938\) | 4.66096e10 | 1.84402 | ||||||||
\(939\) | −9.56304e9 | −0.376935 | ||||||||
\(940\) | 7.42223e9 | 0.291465 | ||||||||
\(941\) | 1.34447e10 | 0.526002 | 0.263001 | − | 0.964796i | \(-0.415288\pi\) | ||||
0.263001 | + | 0.964796i | \(0.415288\pi\) | |||||||
\(942\) | 1.35409e10 | 0.527799 | ||||||||
\(943\) | 4.74540e8 | 0.0184281 | ||||||||
\(944\) | −4.03673e9 | −0.156181 | ||||||||
\(945\) | −3.01647e9 | −0.116275 | ||||||||
\(946\) | 3.25813e10 | 1.25126 | ||||||||
\(947\) | 8.81228e9 | 0.337181 | 0.168591 | − | 0.985686i | \(-0.446078\pi\) | ||||
0.168591 | + | 0.985686i | \(0.446078\pi\) | |||||||
\(948\) | −2.28845e9 | −0.0872395 | ||||||||
\(949\) | −3.23255e10 | −1.22776 | ||||||||
\(950\) | −8.57375e8 | −0.0324443 | ||||||||
\(951\) | 2.86912e10 | 1.08173 | ||||||||
\(952\) | 3.55021e9 | 0.133360 | ||||||||
\(953\) | 2.10715e10 | 0.788623 | 0.394312 | − | 0.918977i | \(-0.370983\pi\) | ||||
0.394312 | + | 0.918977i | \(0.370983\pi\) | |||||||
\(954\) | −5.91262e8 | −0.0220476 | ||||||||
\(955\) | 8.27283e9 | 0.307356 | ||||||||
\(956\) | 1.59249e10 | 0.589487 | ||||||||
\(957\) | 1.15242e10 | 0.425031 | ||||||||
\(958\) | 7.41903e9 | 0.272626 | ||||||||
\(959\) | 5.40731e10 | 1.97978 | ||||||||
\(960\) | 8.84736e8 | 0.0322749 | ||||||||
\(961\) | 3.89060e10 | 1.41412 | ||||||||
\(962\) | −2.55440e10 | −0.925074 | ||||||||
\(963\) | 4.78336e8 | 0.0172600 | ||||||||
\(964\) | −2.35596e10 | −0.847030 | ||||||||
\(965\) | −7.26885e9 | −0.260387 | ||||||||
\(966\) | −7.55959e9 | −0.269823 | ||||||||
\(967\) | −8.38176e9 | −0.298087 | −0.149043 | − | 0.988831i | \(-0.547619\pi\) | ||||
−0.149043 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(968\) | 1.16380e9 | 0.0412396 | ||||||||
\(969\) | 1.04739e9 | 0.0369809 | ||||||||
\(970\) | −5.37895e9 | −0.189233 | ||||||||
\(971\) | 1.05194e10 | 0.368742 | 0.184371 | − | 0.982857i | \(-0.440975\pi\) | ||||
0.184371 | + | 0.982857i | \(0.440975\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | −5.22837e10 | −1.81958 | ||||||||
\(974\) | 2.87886e8 | 0.00998306 | ||||||||
\(975\) | 3.85661e9 | 0.133257 | ||||||||
\(976\) | −3.09823e9 | −0.106669 | ||||||||
\(977\) | 1.62963e10 | 0.559059 | 0.279529 | − | 0.960137i | \(-0.409822\pi\) | ||||
0.279529 | + | 0.960137i | \(0.409822\pi\) | |||||||
\(978\) | 9.91928e9 | 0.339074 | ||||||||
\(979\) | 1.74351e10 | 0.593862 | ||||||||
\(980\) | 5.43668e9 | 0.184519 | ||||||||
\(981\) | −6.51527e9 | −0.220339 | ||||||||
\(982\) | −3.88521e10 | −1.30925 | ||||||||
\(983\) | 3.02334e9 | 0.101519 | 0.0507597 | − | 0.998711i | \(-0.483836\pi\) | ||||
0.0507597 | + | 0.998711i | \(0.483836\pi\) | |||||||
\(984\) | 2.29805e8 | 0.00768913 | ||||||||
\(985\) | 1.66173e10 | 0.554031 | ||||||||
\(986\) | 4.13993e9 | 0.137538 | ||||||||
\(987\) | −3.07119e10 | −1.01671 | ||||||||
\(988\) | −4.01294e9 | −0.132377 | ||||||||
\(989\) | −2.49226e10 | −0.819230 | ||||||||
\(990\) | −3.40063e9 | −0.111387 | ||||||||
\(991\) | −3.28205e10 | −1.07124 | −0.535620 | − | 0.844459i | \(-0.679922\pi\) | ||||
−0.535620 | + | 0.844459i | \(0.679922\pi\) | |||||||
\(992\) | 8.44491e9 | 0.274665 | ||||||||
\(993\) | 6.11825e9 | 0.198292 | ||||||||
\(994\) | 4.39323e10 | 1.41883 | ||||||||
\(995\) | −9.79568e9 | −0.315249 | ||||||||
\(996\) | −1.23319e8 | −0.00395479 | ||||||||
\(997\) | −4.27161e10 | −1.36508 | −0.682541 | − | 0.730848i | \(-0.739125\pi\) | ||||
−0.682541 | + | 0.730848i | \(0.739125\pi\) | |||||||
\(998\) | −4.16149e9 | −0.132523 | ||||||||
\(999\) | −6.87494e9 | −0.218167 |
(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 | 570.8.a.c.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.8.a.c.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |