Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,10,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(22.1465409550\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} - 11474166224 x^{9} + 47465836576 x^{8} + 5986976782464 x^{7} + \cdots + 52\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(16.4876\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −18.4876 | −0.817043 | −0.408521 | − | 0.912749i | \(-0.633955\pi\) | ||||
−0.408521 | + | 0.912749i | \(0.633955\pi\) | |||||||
\(3\) | −262.112 | −1.86827 | −0.934137 | − | 0.356914i | \(-0.883829\pi\) | ||||
−0.934137 | + | 0.356914i | \(0.883829\pi\) | |||||||
\(4\) | −170.210 | −0.332441 | ||||||||
\(5\) | −2363.43 | −1.69113 | −0.845567 | − | 0.533870i | \(-0.820737\pi\) | ||||
−0.845567 | + | 0.533870i | \(0.820737\pi\) | |||||||
\(6\) | 4845.81 | 1.52646 | ||||||||
\(7\) | 7025.62 | 1.10597 | 0.552985 | − | 0.833191i | \(-0.313489\pi\) | ||||
0.552985 | + | 0.833191i | \(0.313489\pi\) | |||||||
\(8\) | 12612.4 | 1.08866 | ||||||||
\(9\) | 49019.5 | 2.49045 | ||||||||
\(10\) | 43694.1 | 1.38173 | ||||||||
\(11\) | −59098.5 | −1.21705 | −0.608526 | − | 0.793534i | \(-0.708239\pi\) | ||||
−0.608526 | + | 0.793534i | \(0.708239\pi\) | |||||||
\(12\) | 44614.0 | 0.621091 | ||||||||
\(13\) | −84020.4 | −0.815905 | −0.407952 | − | 0.913003i | \(-0.633757\pi\) | ||||
−0.407952 | + | 0.913003i | \(0.633757\pi\) | |||||||
\(14\) | −129887. | −0.903625 | ||||||||
\(15\) | 619483. | 3.15950 | ||||||||
\(16\) | −146025. | −0.557042 | ||||||||
\(17\) | 199182. | 0.578402 | 0.289201 | − | 0.957268i | \(-0.406610\pi\) | ||||
0.289201 | + | 0.957268i | \(0.406610\pi\) | |||||||
\(18\) | −906252. | −2.03480 | ||||||||
\(19\) | 293458. | 0.516600 | 0.258300 | − | 0.966065i | \(-0.416838\pi\) | ||||
0.258300 | + | 0.966065i | \(0.416838\pi\) | |||||||
\(20\) | 402279. | 0.562202 | ||||||||
\(21\) | −1.84150e6 | −2.06626 | ||||||||
\(22\) | 1.09259e6 | 0.994384 | ||||||||
\(23\) | 366554. | 0.273126 | 0.136563 | − | 0.990631i | \(-0.456394\pi\) | ||||
0.136563 | + | 0.990631i | \(0.456394\pi\) | |||||||
\(24\) | −3.30586e6 | −2.03392 | ||||||||
\(25\) | 3.63268e6 | 1.85993 | ||||||||
\(26\) | 1.55333e6 | 0.666629 | ||||||||
\(27\) | −7.68944e6 | −2.78457 | ||||||||
\(28\) | −1.19583e6 | −0.367670 | ||||||||
\(29\) | −1.87481e6 | −0.492228 | −0.246114 | − | 0.969241i | \(-0.579154\pi\) | ||||
−0.246114 | + | 0.969241i | \(0.579154\pi\) | |||||||
\(30\) | −1.14527e7 | −2.58145 | ||||||||
\(31\) | 3.91740e6 | 0.761852 | 0.380926 | − | 0.924605i | \(-0.375605\pi\) | ||||
0.380926 | + | 0.924605i | \(0.375605\pi\) | |||||||
\(32\) | −3.75790e6 | −0.633534 | ||||||||
\(33\) | 1.54904e7 | 2.27379 | ||||||||
\(34\) | −3.68239e6 | −0.472579 | ||||||||
\(35\) | −1.66046e7 | −1.87034 | ||||||||
\(36\) | −8.34360e6 | −0.827928 | ||||||||
\(37\) | 2.22050e7 | 1.94779 | 0.973895 | − | 0.226997i | \(-0.0728907\pi\) | ||||
0.973895 | + | 0.226997i | \(0.0728907\pi\) | |||||||
\(38\) | −5.42532e6 | −0.422084 | ||||||||
\(39\) | 2.20227e7 | 1.52433 | ||||||||
\(40\) | −2.98085e7 | −1.84107 | ||||||||
\(41\) | 3.33190e6 | 0.184147 | 0.0920736 | − | 0.995752i | \(-0.470650\pi\) | ||||
0.0920736 | + | 0.995752i | \(0.470650\pi\) | |||||||
\(42\) | 3.40448e7 | 1.68822 | ||||||||
\(43\) | −3.41880e6 | −0.152499 | ||||||||
\(44\) | 1.00591e7 | 0.404598 | ||||||||
\(45\) | −1.15854e8 | −4.21168 | ||||||||
\(46\) | −6.77669e6 | −0.223156 | ||||||||
\(47\) | −4.54124e7 | −1.35748 | −0.678741 | − | 0.734378i | \(-0.737474\pi\) | ||||
−0.678741 | + | 0.734378i | \(0.737474\pi\) | |||||||
\(48\) | 3.82749e7 | 1.04071 | ||||||||
\(49\) | 9.00569e6 | 0.223169 | ||||||||
\(50\) | −6.71594e7 | −1.51964 | ||||||||
\(51\) | −5.22079e7 | −1.08061 | ||||||||
\(52\) | 1.43011e7 | 0.271240 | ||||||||
\(53\) | 4.88629e7 | 0.850624 | 0.425312 | − | 0.905047i | \(-0.360164\pi\) | ||||
0.425312 | + | 0.905047i | \(0.360164\pi\) | |||||||
\(54\) | 1.42159e8 | 2.27511 | ||||||||
\(55\) | 1.39675e8 | 2.05820 | ||||||||
\(56\) | 8.86099e7 | 1.20403 | ||||||||
\(57\) | −7.69187e7 | −0.965150 | ||||||||
\(58\) | 3.46607e7 | 0.402172 | ||||||||
\(59\) | 1.66035e8 | 1.78387 | 0.891937 | − | 0.452159i | \(-0.149346\pi\) | ||||
0.891937 | + | 0.452159i | \(0.149346\pi\) | |||||||
\(60\) | −1.05442e8 | −1.05035 | ||||||||
\(61\) | −1.65599e8 | −1.53135 | −0.765673 | − | 0.643230i | \(-0.777594\pi\) | ||||
−0.765673 | + | 0.643230i | \(0.777594\pi\) | |||||||
\(62\) | −7.24233e7 | −0.622466 | ||||||||
\(63\) | 3.44392e8 | 2.75436 | ||||||||
\(64\) | 1.44239e8 | 1.07467 | ||||||||
\(65\) | 1.98576e8 | 1.37980 | ||||||||
\(66\) | −2.86380e8 | −1.85778 | ||||||||
\(67\) | 1.13400e7 | 0.0687507 | 0.0343753 | − | 0.999409i | \(-0.489056\pi\) | ||||
0.0343753 | + | 0.999409i | \(0.489056\pi\) | |||||||
\(68\) | −3.39027e7 | −0.192285 | ||||||||
\(69\) | −9.60781e7 | −0.510274 | ||||||||
\(70\) | 3.06978e8 | 1.52815 | ||||||||
\(71\) | −2.09329e8 | −0.977611 | −0.488806 | − | 0.872393i | \(-0.662567\pi\) | ||||
−0.488806 | + | 0.872393i | \(0.662567\pi\) | |||||||
\(72\) | 6.18254e8 | 2.71126 | ||||||||
\(73\) | 7.39810e6 | 0.0304907 | 0.0152453 | − | 0.999884i | \(-0.495147\pi\) | ||||
0.0152453 | + | 0.999884i | \(0.495147\pi\) | |||||||
\(74\) | −4.10516e8 | −1.59143 | ||||||||
\(75\) | −9.52167e8 | −3.47486 | ||||||||
\(76\) | −4.99494e7 | −0.171739 | ||||||||
\(77\) | −4.15204e8 | −1.34602 | ||||||||
\(78\) | −4.07146e8 | −1.24545 | ||||||||
\(79\) | 5.09343e8 | 1.47126 | 0.735629 | − | 0.677385i | \(-0.236887\pi\) | ||||
0.735629 | + | 0.677385i | \(0.236887\pi\) | |||||||
\(80\) | 3.45120e8 | 0.942032 | ||||||||
\(81\) | 1.05064e9 | 2.71189 | ||||||||
\(82\) | −6.15988e7 | −0.150456 | ||||||||
\(83\) | −4.59491e8 | −1.06274 | −0.531369 | − | 0.847141i | \(-0.678322\pi\) | ||||
−0.531369 | + | 0.847141i | \(0.678322\pi\) | |||||||
\(84\) | 3.13441e8 | 0.686908 | ||||||||
\(85\) | −4.70753e8 | −0.978155 | ||||||||
\(86\) | 6.32053e7 | 0.124598 | ||||||||
\(87\) | 4.91410e8 | 0.919618 | ||||||||
\(88\) | −7.45374e8 | −1.32496 | ||||||||
\(89\) | −2.28949e8 | −0.386798 | −0.193399 | − | 0.981120i | \(-0.561951\pi\) | ||||
−0.193399 | + | 0.981120i | \(0.561951\pi\) | |||||||
\(90\) | 2.14186e9 | 3.44112 | ||||||||
\(91\) | −5.90295e8 | −0.902366 | ||||||||
\(92\) | −6.23911e7 | −0.0907983 | ||||||||
\(93\) | −1.02680e9 | −1.42335 | ||||||||
\(94\) | 8.39565e8 | 1.10912 | ||||||||
\(95\) | −6.93567e8 | −0.873639 | ||||||||
\(96\) | 9.84989e8 | 1.18362 | ||||||||
\(97\) | −9.54121e8 | −1.09429 | −0.547143 | − | 0.837039i | \(-0.684285\pi\) | ||||
−0.547143 | + | 0.837039i | \(0.684285\pi\) | |||||||
\(98\) | −1.66493e8 | −0.182339 | ||||||||
\(99\) | −2.89698e9 | −3.03101 | ||||||||
\(100\) | −6.18318e8 | −0.618318 | ||||||||
\(101\) | 1.29443e9 | 1.23775 | 0.618876 | − | 0.785489i | \(-0.287588\pi\) | ||||
0.618876 | + | 0.785489i | \(0.287588\pi\) | |||||||
\(102\) | 9.65198e8 | 0.882908 | ||||||||
\(103\) | 5.67850e8 | 0.497126 | 0.248563 | − | 0.968616i | \(-0.420042\pi\) | ||||
0.248563 | + | 0.968616i | \(0.420042\pi\) | |||||||
\(104\) | −1.05970e9 | −0.888244 | ||||||||
\(105\) | 4.35225e9 | 3.49431 | ||||||||
\(106\) | −9.03356e8 | −0.694996 | ||||||||
\(107\) | 4.53655e8 | 0.334579 | 0.167290 | − | 0.985908i | \(-0.446499\pi\) | ||||
0.167290 | + | 0.985908i | \(0.446499\pi\) | |||||||
\(108\) | 1.30882e9 | 0.925705 | ||||||||
\(109\) | 9.29530e8 | 0.630731 | 0.315365 | − | 0.948970i | \(-0.397873\pi\) | ||||
0.315365 | + | 0.948970i | \(0.397873\pi\) | |||||||
\(110\) | −2.58226e9 | −1.68164 | ||||||||
\(111\) | −5.82018e9 | −3.63901 | ||||||||
\(112\) | −1.02592e9 | −0.616071 | ||||||||
\(113\) | −3.79267e7 | −0.0218822 | −0.0109411 | − | 0.999940i | \(-0.503483\pi\) | ||||
−0.0109411 | + | 0.999940i | \(0.503483\pi\) | |||||||
\(114\) | 1.42204e9 | 0.788569 | ||||||||
\(115\) | −8.66325e8 | −0.461892 | ||||||||
\(116\) | 3.19111e8 | 0.163637 | ||||||||
\(117\) | −4.11864e9 | −2.03197 | ||||||||
\(118\) | −3.06957e9 | −1.45750 | ||||||||
\(119\) | 1.39938e9 | 0.639696 | ||||||||
\(120\) | 7.81316e9 | 3.43963 | ||||||||
\(121\) | 1.13469e9 | 0.481218 | ||||||||
\(122\) | 3.06152e9 | 1.25118 | ||||||||
\(123\) | −8.73331e8 | −0.344038 | ||||||||
\(124\) | −6.66781e8 | −0.253271 | ||||||||
\(125\) | −3.96951e9 | −1.45426 | ||||||||
\(126\) | −6.36698e9 | −2.25043 | ||||||||
\(127\) | −3.97458e9 | −1.35573 | −0.677867 | − | 0.735185i | \(-0.737095\pi\) | ||||
−0.677867 | + | 0.735185i | \(0.737095\pi\) | |||||||
\(128\) | −7.42589e8 | −0.244514 | ||||||||
\(129\) | 8.96108e8 | 0.284909 | ||||||||
\(130\) | −3.67119e9 | −1.12736 | ||||||||
\(131\) | −1.80701e9 | −0.536093 | −0.268047 | − | 0.963406i | \(-0.586378\pi\) | ||||
−0.268047 | + | 0.963406i | \(0.586378\pi\) | |||||||
\(132\) | −2.63662e9 | −0.755901 | ||||||||
\(133\) | 2.06172e9 | 0.571344 | ||||||||
\(134\) | −2.09649e8 | −0.0561722 | ||||||||
\(135\) | 1.81735e10 | 4.70908 | ||||||||
\(136\) | 2.51216e9 | 0.629684 | ||||||||
\(137\) | −2.82788e9 | −0.685834 | −0.342917 | − | 0.939366i | \(-0.611415\pi\) | ||||
−0.342917 | + | 0.939366i | \(0.611415\pi\) | |||||||
\(138\) | 1.77625e9 | 0.416916 | ||||||||
\(139\) | 6.82579e9 | 1.55091 | 0.775454 | − | 0.631404i | \(-0.217521\pi\) | ||||
0.775454 | + | 0.631404i | \(0.217521\pi\) | |||||||
\(140\) | 2.82626e9 | 0.621779 | ||||||||
\(141\) | 1.19031e10 | 2.53615 | ||||||||
\(142\) | 3.86998e9 | 0.798750 | ||||||||
\(143\) | 4.96548e9 | 0.992999 | ||||||||
\(144\) | −7.15808e9 | −1.38728 | ||||||||
\(145\) | 4.43099e9 | 0.832424 | ||||||||
\(146\) | −1.36773e8 | −0.0249122 | ||||||||
\(147\) | −2.36050e9 | −0.416942 | ||||||||
\(148\) | −3.77950e9 | −0.647526 | ||||||||
\(149\) | −9.22449e9 | −1.53322 | −0.766610 | − | 0.642113i | \(-0.778058\pi\) | ||||
−0.766610 | + | 0.642113i | \(0.778058\pi\) | |||||||
\(150\) | 1.76033e10 | 2.83911 | ||||||||
\(151\) | 7.71760e9 | 1.20805 | 0.604027 | − | 0.796964i | \(-0.293562\pi\) | ||||
0.604027 | + | 0.796964i | \(0.293562\pi\) | |||||||
\(152\) | 3.70121e9 | 0.562402 | ||||||||
\(153\) | 9.76381e9 | 1.44048 | ||||||||
\(154\) | 7.67610e9 | 1.09976 | ||||||||
\(155\) | −9.25851e9 | −1.28839 | ||||||||
\(156\) | −3.74848e9 | −0.506751 | ||||||||
\(157\) | −1.03691e10 | −1.36205 | −0.681027 | − | 0.732259i | \(-0.738466\pi\) | ||||
−0.681027 | + | 0.732259i | \(0.738466\pi\) | |||||||
\(158\) | −9.41652e9 | −1.20208 | ||||||||
\(159\) | −1.28075e10 | −1.58920 | ||||||||
\(160\) | 8.88153e9 | 1.07139 | ||||||||
\(161\) | 2.57527e9 | 0.302069 | ||||||||
\(162\) | −1.94238e10 | −2.21573 | ||||||||
\(163\) | 1.24179e10 | 1.37786 | 0.688929 | − | 0.724829i | \(-0.258081\pi\) | ||||
0.688929 | + | 0.724829i | \(0.258081\pi\) | |||||||
\(164\) | −5.67123e8 | −0.0612181 | ||||||||
\(165\) | −3.66105e10 | −3.84528 | ||||||||
\(166\) | 8.49488e9 | 0.868302 | ||||||||
\(167\) | 8.49813e8 | 0.0845472 | 0.0422736 | − | 0.999106i | \(-0.486540\pi\) | ||||
0.0422736 | + | 0.999106i | \(0.486540\pi\) | |||||||
\(168\) | −2.32257e10 | −2.24945 | ||||||||
\(169\) | −3.54508e9 | −0.334300 | ||||||||
\(170\) | 8.70308e9 | 0.799195 | ||||||||
\(171\) | 1.43852e10 | 1.28657 | ||||||||
\(172\) | 5.81914e8 | 0.0506968 | ||||||||
\(173\) | −2.05242e10 | −1.74204 | −0.871022 | − | 0.491244i | \(-0.836542\pi\) | ||||
−0.871022 | + | 0.491244i | \(0.836542\pi\) | |||||||
\(174\) | −9.08498e9 | −0.751367 | ||||||||
\(175\) | 2.55218e10 | 2.05703 | ||||||||
\(176\) | 8.62987e9 | 0.677949 | ||||||||
\(177\) | −4.35196e10 | −3.33277 | ||||||||
\(178\) | 4.23271e9 | 0.316030 | ||||||||
\(179\) | 2.24623e8 | 0.0163537 | 0.00817684 | − | 0.999967i | \(-0.497397\pi\) | ||||
0.00817684 | + | 0.999967i | \(0.497397\pi\) | |||||||
\(180\) | 1.97195e10 | 1.40014 | ||||||||
\(181\) | 1.28374e10 | 0.889043 | 0.444522 | − | 0.895768i | \(-0.353374\pi\) | ||||
0.444522 | + | 0.895768i | \(0.353374\pi\) | |||||||
\(182\) | 1.09131e10 | 0.737272 | ||||||||
\(183\) | 4.34054e10 | 2.86097 | ||||||||
\(184\) | 4.62313e9 | 0.297342 | ||||||||
\(185\) | −5.24799e10 | −3.29397 | ||||||||
\(186\) | 1.89830e10 | 1.16294 | ||||||||
\(187\) | −1.17714e10 | −0.703946 | ||||||||
\(188\) | 7.72964e9 | 0.451283 | ||||||||
\(189\) | −5.40231e10 | −3.07965 | ||||||||
\(190\) | 1.28224e10 | 0.713801 | ||||||||
\(191\) | 1.84958e9 | 0.100560 | 0.0502798 | − | 0.998735i | \(-0.483989\pi\) | ||||
0.0502798 | + | 0.998735i | \(0.483989\pi\) | |||||||
\(192\) | −3.78068e10 | −2.00777 | ||||||||
\(193\) | 7.73188e9 | 0.401123 | 0.200561 | − | 0.979681i | \(-0.435723\pi\) | ||||
0.200561 | + | 0.979681i | \(0.435723\pi\) | |||||||
\(194\) | 1.76394e10 | 0.894078 | ||||||||
\(195\) | −5.20492e10 | −2.57785 | ||||||||
\(196\) | −1.53286e9 | −0.0741907 | ||||||||
\(197\) | 2.41118e10 | 1.14060 | 0.570298 | − | 0.821438i | \(-0.306828\pi\) | ||||
0.570298 | + | 0.821438i | \(0.306828\pi\) | |||||||
\(198\) | 5.35581e10 | 2.47646 | ||||||||
\(199\) | 2.46274e10 | 1.11322 | 0.556609 | − | 0.830775i | \(-0.312102\pi\) | ||||
0.556609 | + | 0.830775i | \(0.312102\pi\) | |||||||
\(200\) | 4.58168e10 | 2.02484 | ||||||||
\(201\) | −2.97235e9 | −0.128445 | ||||||||
\(202\) | −2.39309e10 | −1.01130 | ||||||||
\(203\) | −1.31717e10 | −0.544390 | ||||||||
\(204\) | 8.88630e9 | 0.359241 | ||||||||
\(205\) | −7.87472e9 | −0.311417 | ||||||||
\(206\) | −1.04982e10 | −0.406173 | ||||||||
\(207\) | 1.79683e10 | 0.680206 | ||||||||
\(208\) | 1.22691e10 | 0.454493 | ||||||||
\(209\) | −1.73429e10 | −0.628729 | ||||||||
\(210\) | −8.04625e10 | −2.85500 | ||||||||
\(211\) | −1.54470e10 | −0.536504 | −0.268252 | − | 0.963349i | \(-0.586446\pi\) | ||||
−0.268252 | + | 0.963349i | \(0.586446\pi\) | |||||||
\(212\) | −8.31695e9 | −0.282782 | ||||||||
\(213\) | 5.48675e10 | 1.82645 | ||||||||
\(214\) | −8.38698e9 | −0.273365 | ||||||||
\(215\) | 8.08010e9 | 0.257895 | ||||||||
\(216\) | −9.69823e10 | −3.03145 | ||||||||
\(217\) | 2.75222e10 | 0.842586 | ||||||||
\(218\) | −1.71847e10 | −0.515334 | ||||||||
\(219\) | −1.93913e9 | −0.0569650 | ||||||||
\(220\) | −2.37741e10 | −0.684230 | ||||||||
\(221\) | −1.67353e10 | −0.471921 | ||||||||
\(222\) | 1.07601e11 | 2.97323 | ||||||||
\(223\) | −6.69002e10 | −1.81157 | −0.905786 | − | 0.423736i | \(-0.860718\pi\) | ||||
−0.905786 | + | 0.423736i | \(0.860718\pi\) | |||||||
\(224\) | −2.64016e10 | −0.700670 | ||||||||
\(225\) | 1.78072e11 | 4.63207 | ||||||||
\(226\) | 7.01172e8 | 0.0178787 | ||||||||
\(227\) | −2.18215e10 | −0.545466 | −0.272733 | − | 0.962090i | \(-0.587928\pi\) | ||||
−0.272733 | + | 0.962090i | \(0.587928\pi\) | |||||||
\(228\) | 1.30923e10 | 0.320856 | ||||||||
\(229\) | −4.48901e9 | −0.107868 | −0.0539338 | − | 0.998545i | \(-0.517176\pi\) | ||||
−0.0539338 | + | 0.998545i | \(0.517176\pi\) | |||||||
\(230\) | 1.60162e10 | 0.377386 | ||||||||
\(231\) | 1.08830e11 | 2.51474 | ||||||||
\(232\) | −2.36459e10 | −0.535870 | ||||||||
\(233\) | 2.75398e9 | 0.0612151 | 0.0306076 | − | 0.999531i | \(-0.490256\pi\) | ||||
0.0306076 | + | 0.999531i | \(0.490256\pi\) | |||||||
\(234\) | 7.61436e10 | 1.66021 | ||||||||
\(235\) | 1.07329e11 | 2.29568 | ||||||||
\(236\) | −2.82607e10 | −0.593033 | ||||||||
\(237\) | −1.33505e11 | −2.74871 | ||||||||
\(238\) | −2.58711e10 | −0.522659 | ||||||||
\(239\) | 2.52877e10 | 0.501324 | 0.250662 | − | 0.968075i | \(-0.419352\pi\) | ||||
0.250662 | + | 0.968075i | \(0.419352\pi\) | |||||||
\(240\) | −9.04601e10 | −1.75997 | ||||||||
\(241\) | 1.07229e10 | 0.204755 | 0.102377 | − | 0.994746i | \(-0.467355\pi\) | ||||
0.102377 | + | 0.994746i | \(0.467355\pi\) | |||||||
\(242\) | −2.09776e10 | −0.393176 | ||||||||
\(243\) | −1.24034e11 | −2.28198 | ||||||||
\(244\) | 2.81866e10 | 0.509082 | ||||||||
\(245\) | −2.12843e10 | −0.377409 | ||||||||
\(246\) | 1.61458e10 | 0.281093 | ||||||||
\(247\) | −2.46564e10 | −0.421496 | ||||||||
\(248\) | 4.94079e10 | 0.829399 | ||||||||
\(249\) | 1.20438e11 | 1.98549 | ||||||||
\(250\) | 7.33866e10 | 1.18819 | ||||||||
\(251\) | 4.66245e10 | 0.741451 | 0.370725 | − | 0.928743i | \(-0.379109\pi\) | ||||
0.370725 | + | 0.928743i | \(0.379109\pi\) | |||||||
\(252\) | −5.86190e10 | −0.915663 | ||||||||
\(253\) | −2.16628e10 | −0.332409 | ||||||||
\(254\) | 7.34803e10 | 1.10769 | ||||||||
\(255\) | 1.23390e11 | 1.82746 | ||||||||
\(256\) | −6.01218e10 | −0.874888 | ||||||||
\(257\) | −2.77809e10 | −0.397234 | −0.198617 | − | 0.980077i | \(-0.563645\pi\) | ||||
−0.198617 | + | 0.980077i | \(0.563645\pi\) | |||||||
\(258\) | −1.65668e10 | −0.232783 | ||||||||
\(259\) | 1.56004e11 | 2.15420 | ||||||||
\(260\) | −3.37996e10 | −0.458703 | ||||||||
\(261\) | −9.19024e10 | −1.22587 | ||||||||
\(262\) | 3.34073e10 | 0.438011 | ||||||||
\(263\) | −7.66179e10 | −0.987482 | −0.493741 | − | 0.869609i | \(-0.664371\pi\) | ||||
−0.493741 | + | 0.869609i | \(0.664371\pi\) | |||||||
\(264\) | 1.95371e11 | 2.47539 | ||||||||
\(265\) | −1.15484e11 | −1.43852 | ||||||||
\(266\) | −3.81162e10 | −0.466812 | ||||||||
\(267\) | 6.00102e10 | 0.722645 | ||||||||
\(268\) | −1.93018e9 | −0.0228556 | ||||||||
\(269\) | −5.82715e10 | −0.678533 | −0.339266 | − | 0.940690i | \(-0.610179\pi\) | ||||
−0.339266 | + | 0.940690i | \(0.610179\pi\) | |||||||
\(270\) | −3.35983e11 | −3.84752 | ||||||||
\(271\) | 5.01640e10 | 0.564977 | 0.282488 | − | 0.959271i | \(-0.408840\pi\) | ||||
0.282488 | + | 0.959271i | \(0.408840\pi\) | |||||||
\(272\) | −2.90856e10 | −0.322194 | ||||||||
\(273\) | 1.54723e11 | 1.68587 | ||||||||
\(274\) | 5.22807e10 | 0.560356 | ||||||||
\(275\) | −2.14686e11 | −2.26364 | ||||||||
\(276\) | 1.63534e10 | 0.169636 | ||||||||
\(277\) | −6.47834e10 | −0.661157 | −0.330579 | − | 0.943778i | \(-0.607244\pi\) | ||||
−0.330579 | + | 0.943778i | \(0.607244\pi\) | |||||||
\(278\) | −1.26192e11 | −1.26716 | ||||||||
\(279\) | 1.92029e11 | 1.89735 | ||||||||
\(280\) | −2.09423e11 | −2.03617 | ||||||||
\(281\) | 5.01006e10 | 0.479363 | 0.239682 | − | 0.970852i | \(-0.422957\pi\) | ||||
0.239682 | + | 0.970852i | \(0.422957\pi\) | |||||||
\(282\) | −2.20060e11 | −2.07214 | ||||||||
\(283\) | 2.09526e11 | 1.94177 | 0.970887 | − | 0.239540i | \(-0.0769966\pi\) | ||||
0.970887 | + | 0.239540i | \(0.0769966\pi\) | |||||||
\(284\) | 3.56298e10 | 0.324998 | ||||||||
\(285\) | 1.81792e11 | 1.63220 | ||||||||
\(286\) | −9.17996e10 | −0.811323 | ||||||||
\(287\) | 2.34087e10 | 0.203661 | ||||||||
\(288\) | −1.84210e11 | −1.57779 | ||||||||
\(289\) | −7.89144e10 | −0.665451 | ||||||||
\(290\) | −8.19182e10 | −0.680126 | ||||||||
\(291\) | 2.50086e11 | 2.04443 | ||||||||
\(292\) | −1.25923e9 | −0.0101364 | ||||||||
\(293\) | −2.20081e11 | −1.74453 | −0.872264 | − | 0.489035i | \(-0.837349\pi\) | ||||
−0.872264 | + | 0.489035i | \(0.837349\pi\) | |||||||
\(294\) | 4.36398e10 | 0.340659 | ||||||||
\(295\) | −3.92411e11 | −3.01677 | ||||||||
\(296\) | 2.80058e11 | 2.12048 | ||||||||
\(297\) | 4.54435e11 | 3.38897 | ||||||||
\(298\) | 1.70538e11 | 1.25271 | ||||||||
\(299\) | −3.07980e10 | −0.222845 | ||||||||
\(300\) | 1.62068e11 | 1.15519 | ||||||||
\(301\) | −2.40192e10 | −0.168659 | ||||||||
\(302\) | −1.42680e11 | −0.987031 | ||||||||
\(303\) | −3.39286e11 | −2.31246 | ||||||||
\(304\) | −4.28522e10 | −0.287768 | ||||||||
\(305\) | 3.91382e11 | 2.58971 | ||||||||
\(306\) | −1.80509e11 | −1.17694 | ||||||||
\(307\) | 4.15422e10 | 0.266911 | 0.133455 | − | 0.991055i | \(-0.457393\pi\) | ||||
0.133455 | + | 0.991055i | \(0.457393\pi\) | |||||||
\(308\) | 7.06717e10 | 0.447474 | ||||||||
\(309\) | −1.48840e11 | −0.928767 | ||||||||
\(310\) | 1.71167e11 | 1.05267 | ||||||||
\(311\) | 7.16229e10 | 0.434140 | 0.217070 | − | 0.976156i | \(-0.430350\pi\) | ||||
0.217070 | + | 0.976156i | \(0.430350\pi\) | |||||||
\(312\) | 2.77759e11 | 1.65948 | ||||||||
\(313\) | −1.61891e11 | −0.953398 | −0.476699 | − | 0.879067i | \(-0.658167\pi\) | ||||
−0.476699 | + | 0.879067i | \(0.658167\pi\) | |||||||
\(314\) | 1.91700e11 | 1.11286 | ||||||||
\(315\) | −8.13947e11 | −4.65799 | ||||||||
\(316\) | −8.66953e10 | −0.489107 | ||||||||
\(317\) | −7.64203e9 | −0.0425052 | −0.0212526 | − | 0.999774i | \(-0.506765\pi\) | ||||
−0.0212526 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(318\) | 2.36780e11 | 1.29844 | ||||||||
\(319\) | 1.10799e11 | 0.599068 | ||||||||
\(320\) | −3.40900e11 | −1.81740 | ||||||||
\(321\) | −1.18908e11 | −0.625085 | ||||||||
\(322\) | −4.76105e10 | −0.246803 | ||||||||
\(323\) | 5.84515e10 | 0.298803 | ||||||||
\(324\) | −1.78829e11 | −0.901543 | ||||||||
\(325\) | −3.05219e11 | −1.51753 | ||||||||
\(326\) | −2.29577e11 | −1.12577 | ||||||||
\(327\) | −2.43641e11 | −1.17838 | ||||||||
\(328\) | 4.20233e10 | 0.200474 | ||||||||
\(329\) | −3.19050e11 | −1.50133 | ||||||||
\(330\) | 6.76839e11 | 3.14176 | ||||||||
\(331\) | 1.41081e11 | 0.646014 | 0.323007 | − | 0.946396i | \(-0.395306\pi\) | ||||
0.323007 | + | 0.946396i | \(0.395306\pi\) | |||||||
\(332\) | 7.82100e10 | 0.353298 | ||||||||
\(333\) | 1.08848e12 | 4.85087 | ||||||||
\(334\) | −1.57110e10 | −0.0690787 | ||||||||
\(335\) | −2.68013e10 | −0.116267 | ||||||||
\(336\) | 2.68905e11 | 1.15099 | ||||||||
\(337\) | 1.00695e11 | 0.425279 | 0.212640 | − | 0.977131i | \(-0.431794\pi\) | ||||
0.212640 | + | 0.977131i | \(0.431794\pi\) | |||||||
\(338\) | 6.55399e10 | 0.273137 | ||||||||
\(339\) | 9.94103e9 | 0.0408820 | ||||||||
\(340\) | 8.01268e10 | 0.325179 | ||||||||
\(341\) | −2.31513e11 | −0.927215 | ||||||||
\(342\) | −2.65947e11 | −1.05118 | ||||||||
\(343\) | −2.20238e11 | −0.859151 | ||||||||
\(344\) | −4.31193e10 | −0.166019 | ||||||||
\(345\) | 2.27074e11 | 0.862941 | ||||||||
\(346\) | 3.79443e11 | 1.42332 | ||||||||
\(347\) | −2.91880e11 | −1.08074 | −0.540370 | − | 0.841428i | \(-0.681716\pi\) | ||||
−0.540370 | + | 0.841428i | \(0.681716\pi\) | |||||||
\(348\) | −8.36428e10 | −0.305719 | ||||||||
\(349\) | −7.88123e10 | −0.284367 | −0.142184 | − | 0.989840i | \(-0.545412\pi\) | ||||
−0.142184 | + | 0.989840i | \(0.545412\pi\) | |||||||
\(350\) | −4.71836e11 | −1.68068 | ||||||||
\(351\) | 6.46070e11 | 2.27194 | ||||||||
\(352\) | 2.22086e11 | 0.771045 | ||||||||
\(353\) | −4.57862e11 | −1.56945 | −0.784726 | − | 0.619842i | \(-0.787197\pi\) | ||||
−0.784726 | + | 0.619842i | \(0.787197\pi\) | |||||||
\(354\) | 8.04571e11 | 2.72301 | ||||||||
\(355\) | 4.94734e11 | 1.65327 | ||||||||
\(356\) | 3.89694e10 | 0.128588 | ||||||||
\(357\) | −3.66793e11 | −1.19513 | ||||||||
\(358\) | −4.15273e9 | −0.0133617 | ||||||||
\(359\) | −6.39676e10 | −0.203252 | −0.101626 | − | 0.994823i | \(-0.532405\pi\) | ||||
−0.101626 | + | 0.994823i | \(0.532405\pi\) | |||||||
\(360\) | −1.46120e12 | −4.58510 | ||||||||
\(361\) | −2.36570e11 | −0.733125 | ||||||||
\(362\) | −2.37332e11 | −0.726387 | ||||||||
\(363\) | −2.97415e11 | −0.899047 | ||||||||
\(364\) | 1.00474e11 | 0.299984 | ||||||||
\(365\) | −1.74849e10 | −0.0515638 | ||||||||
\(366\) | −8.02461e11 | −2.33754 | ||||||||
\(367\) | 5.56082e10 | 0.160008 | 0.0800039 | − | 0.996795i | \(-0.474507\pi\) | ||||
0.0800039 | + | 0.996795i | \(0.474507\pi\) | |||||||
\(368\) | −5.35261e10 | −0.152143 | ||||||||
\(369\) | 1.63328e11 | 0.458609 | ||||||||
\(370\) | 9.70226e11 | 2.69132 | ||||||||
\(371\) | 3.43292e11 | 0.940765 | ||||||||
\(372\) | 1.74771e11 | 0.473180 | ||||||||
\(373\) | −2.47592e11 | −0.662289 | −0.331145 | − | 0.943580i | \(-0.607435\pi\) | ||||
−0.331145 | + | 0.943580i | \(0.607435\pi\) | |||||||
\(374\) | 2.17624e11 | 0.575154 | ||||||||
\(375\) | 1.04045e12 | 2.71696 | ||||||||
\(376\) | −5.72759e11 | −1.47784 | ||||||||
\(377\) | 1.57522e11 | 0.401612 | ||||||||
\(378\) | 9.98755e11 | 2.51620 | ||||||||
\(379\) | 2.02764e11 | 0.504794 | 0.252397 | − | 0.967624i | \(-0.418781\pi\) | ||||
0.252397 | + | 0.967624i | \(0.418781\pi\) | |||||||
\(380\) | 1.18052e11 | 0.290434 | ||||||||
\(381\) | 1.04178e12 | 2.53288 | ||||||||
\(382\) | −3.41943e10 | −0.0821615 | ||||||||
\(383\) | −7.84097e10 | −0.186198 | −0.0930990 | − | 0.995657i | \(-0.529677\pi\) | ||||
−0.0930990 | + | 0.995657i | \(0.529677\pi\) | |||||||
\(384\) | 1.94641e11 | 0.456819 | ||||||||
\(385\) | 9.81305e11 | 2.27631 | ||||||||
\(386\) | −1.42944e11 | −0.327734 | ||||||||
\(387\) | −1.67588e11 | −0.379790 | ||||||||
\(388\) | 1.62401e11 | 0.363786 | ||||||||
\(389\) | 2.70312e11 | 0.598539 | 0.299270 | − | 0.954169i | \(-0.403257\pi\) | ||||
0.299270 | + | 0.954169i | \(0.403257\pi\) | |||||||
\(390\) | 9.62262e11 | 2.10622 | ||||||||
\(391\) | 7.30110e10 | 0.157977 | ||||||||
\(392\) | 1.13583e11 | 0.242956 | ||||||||
\(393\) | 4.73639e11 | 1.00157 | ||||||||
\(394\) | −4.45769e11 | −0.931915 | ||||||||
\(395\) | −1.20380e12 | −2.48809 | ||||||||
\(396\) | 4.93095e11 | 1.00763 | ||||||||
\(397\) | −6.70016e11 | −1.35372 | −0.676859 | − | 0.736113i | \(-0.736659\pi\) | ||||
−0.676859 | + | 0.736113i | \(0.736659\pi\) | |||||||
\(398\) | −4.55301e11 | −0.909546 | ||||||||
\(399\) | −5.40401e11 | −1.06743 | ||||||||
\(400\) | −5.30463e11 | −1.03606 | ||||||||
\(401\) | 3.58493e11 | 0.692359 | 0.346179 | − | 0.938168i | \(-0.387479\pi\) | ||||
0.346179 | + | 0.938168i | \(0.387479\pi\) | |||||||
\(402\) | 5.49515e10 | 0.104945 | ||||||||
\(403\) | −3.29142e11 | −0.621599 | ||||||||
\(404\) | −2.20325e11 | −0.411480 | ||||||||
\(405\) | −2.48312e12 | −4.58616 | ||||||||
\(406\) | 2.43513e11 | 0.444790 | ||||||||
\(407\) | −1.31228e12 | −2.37056 | ||||||||
\(408\) | −6.58467e11 | −1.17642 | ||||||||
\(409\) | −2.93226e11 | −0.518140 | −0.259070 | − | 0.965859i | \(-0.583416\pi\) | ||||
−0.259070 | + | 0.965859i | \(0.583416\pi\) | |||||||
\(410\) | 1.45584e11 | 0.254441 | ||||||||
\(411\) | 7.41221e11 | 1.28133 | ||||||||
\(412\) | −9.66537e10 | −0.165265 | ||||||||
\(413\) | 1.16649e12 | 1.97291 | ||||||||
\(414\) | −3.32190e11 | −0.555757 | ||||||||
\(415\) | 1.08598e12 | 1.79723 | ||||||||
\(416\) | 3.15740e11 | 0.516904 | ||||||||
\(417\) | −1.78912e12 | −2.89752 | ||||||||
\(418\) | 3.20628e11 | 0.513699 | ||||||||
\(419\) | −2.52617e11 | −0.400404 | −0.200202 | − | 0.979755i | \(-0.564160\pi\) | ||||
−0.200202 | + | 0.979755i | \(0.564160\pi\) | |||||||
\(420\) | −7.40796e11 | −1.16165 | ||||||||
\(421\) | 1.22137e11 | 0.189486 | 0.0947429 | − | 0.995502i | \(-0.469797\pi\) | ||||
0.0947429 | + | 0.995502i | \(0.469797\pi\) | |||||||
\(422\) | 2.85578e11 | 0.438347 | ||||||||
\(423\) | −2.22609e12 | −3.38074 | ||||||||
\(424\) | 6.16278e11 | 0.926042 | ||||||||
\(425\) | 7.23564e11 | 1.07579 | ||||||||
\(426\) | −1.01437e12 | −1.49228 | ||||||||
\(427\) | −1.16343e12 | −1.69362 | ||||||||
\(428\) | −7.72166e10 | −0.111228 | ||||||||
\(429\) | −1.30151e12 | −1.85519 | ||||||||
\(430\) | −1.49381e11 | −0.210712 | ||||||||
\(431\) | 1.01246e12 | 1.41329 | 0.706643 | − | 0.707571i | \(-0.250209\pi\) | ||||
0.706643 | + | 0.707571i | \(0.250209\pi\) | |||||||
\(432\) | 1.12285e12 | 1.55112 | ||||||||
\(433\) | −9.36722e11 | −1.28061 | −0.640303 | − | 0.768123i | \(-0.721191\pi\) | ||||
−0.640303 | + | 0.768123i | \(0.721191\pi\) | |||||||
\(434\) | −5.08818e11 | −0.688429 | ||||||||
\(435\) | −1.16141e12 | −1.55520 | ||||||||
\(436\) | −1.58215e11 | −0.209681 | ||||||||
\(437\) | 1.07568e11 | 0.141097 | ||||||||
\(438\) | 3.58498e10 | 0.0465428 | ||||||||
\(439\) | −5.85451e10 | −0.0752316 | −0.0376158 | − | 0.999292i | \(-0.511976\pi\) | ||||
−0.0376158 | + | 0.999292i | \(0.511976\pi\) | |||||||
\(440\) | 1.76164e12 | 2.24068 | ||||||||
\(441\) | 4.41455e11 | 0.555792 | ||||||||
\(442\) | 3.09396e11 | 0.385580 | ||||||||
\(443\) | 1.20731e12 | 1.48936 | 0.744681 | − | 0.667421i | \(-0.232602\pi\) | ||||
0.744681 | + | 0.667421i | \(0.232602\pi\) | |||||||
\(444\) | 9.90652e11 | 1.20976 | ||||||||
\(445\) | 5.41105e11 | 0.654127 | ||||||||
\(446\) | 1.23682e12 | 1.48013 | ||||||||
\(447\) | 2.41785e12 | 2.86447 | ||||||||
\(448\) | 1.01337e12 | 1.18855 | ||||||||
\(449\) | −1.34315e11 | −0.155961 | −0.0779807 | − | 0.996955i | \(-0.524847\pi\) | ||||
−0.0779807 | + | 0.996955i | \(0.524847\pi\) | |||||||
\(450\) | −3.29212e12 | −3.78460 | ||||||||
\(451\) | −1.96911e11 | −0.224117 | ||||||||
\(452\) | 6.45550e9 | 0.00727456 | ||||||||
\(453\) | −2.02287e12 | −2.25698 | ||||||||
\(454\) | 4.03426e11 | 0.445669 | ||||||||
\(455\) | 1.39512e12 | 1.52602 | ||||||||
\(456\) | −9.70129e11 | −1.05072 | ||||||||
\(457\) | 6.04169e11 | 0.647941 | 0.323970 | − | 0.946067i | \(-0.394982\pi\) | ||||
0.323970 | + | 0.946067i | \(0.394982\pi\) | |||||||
\(458\) | 8.29909e10 | 0.0881325 | ||||||||
\(459\) | −1.53160e12 | −1.61060 | ||||||||
\(460\) | 1.47457e11 | 0.153552 | ||||||||
\(461\) | −7.96508e11 | −0.821364 | −0.410682 | − | 0.911779i | \(-0.634709\pi\) | ||||
−0.410682 | + | 0.911779i | \(0.634709\pi\) | |||||||
\(462\) | −2.01200e12 | −2.05465 | ||||||||
\(463\) | 1.60119e12 | 1.61930 | 0.809652 | − | 0.586910i | \(-0.199656\pi\) | ||||
0.809652 | + | 0.586910i | \(0.199656\pi\) | |||||||
\(464\) | 2.73770e11 | 0.274192 | ||||||||
\(465\) | 2.42676e12 | 2.40707 | ||||||||
\(466\) | −5.09144e10 | −0.0500154 | ||||||||
\(467\) | 1.97526e11 | 0.192176 | 0.0960879 | − | 0.995373i | \(-0.469367\pi\) | ||||
0.0960879 | + | 0.995373i | \(0.469367\pi\) | |||||||
\(468\) | 7.01033e11 | 0.675510 | ||||||||
\(469\) | 7.96706e10 | 0.0760362 | ||||||||
\(470\) | −1.98425e12 | −1.87567 | ||||||||
\(471\) | 2.71787e12 | 2.54469 | ||||||||
\(472\) | 2.09409e12 | 1.94204 | ||||||||
\(473\) | 2.02046e11 | 0.185599 | ||||||||
\(474\) | 2.46818e12 | 2.24582 | ||||||||
\(475\) | 1.06604e12 | 0.960841 | ||||||||
\(476\) | −2.38188e11 | −0.212661 | ||||||||
\(477\) | 2.39524e12 | 2.11844 | ||||||||
\(478\) | −4.67508e11 | −0.409604 | ||||||||
\(479\) | −1.31380e12 | −1.14030 | −0.570149 | − | 0.821541i | \(-0.693115\pi\) | ||||
−0.570149 | + | 0.821541i | \(0.693115\pi\) | |||||||
\(480\) | −2.32795e12 | −2.00165 | ||||||||
\(481\) | −1.86567e12 | −1.58921 | ||||||||
\(482\) | −1.98240e11 | −0.167293 | ||||||||
\(483\) | −6.75008e11 | −0.564348 | ||||||||
\(484\) | −1.93135e11 | −0.159977 | ||||||||
\(485\) | 2.25500e12 | 1.85058 | ||||||||
\(486\) | 2.29309e12 | 1.86448 | ||||||||
\(487\) | −1.13531e12 | −0.914604 | −0.457302 | − | 0.889312i | \(-0.651184\pi\) | ||||
−0.457302 | + | 0.889312i | \(0.651184\pi\) | |||||||
\(488\) | −2.08860e12 | −1.66712 | ||||||||
\(489\) | −3.25488e12 | −2.57422 | ||||||||
\(490\) | 3.93495e11 | 0.308360 | ||||||||
\(491\) | −2.16799e11 | −0.168341 | −0.0841707 | − | 0.996451i | \(-0.526824\pi\) | ||||
−0.0841707 | + | 0.996451i | \(0.526824\pi\) | |||||||
\(492\) | 1.48650e11 | 0.114372 | ||||||||
\(493\) | −3.73429e11 | −0.284706 | ||||||||
\(494\) | 4.55837e11 | 0.344380 | ||||||||
\(495\) | 6.84681e12 | 5.12584 | ||||||||
\(496\) | −5.72040e11 | −0.424384 | ||||||||
\(497\) | −1.47066e12 | −1.08121 | ||||||||
\(498\) | −2.22661e12 | −1.62223 | ||||||||
\(499\) | −1.61040e12 | −1.16274 | −0.581368 | − | 0.813641i | \(-0.697482\pi\) | ||||
−0.581368 | + | 0.813641i | \(0.697482\pi\) | |||||||
\(500\) | 6.75650e11 | 0.483456 | ||||||||
\(501\) | −2.22746e11 | −0.157957 | ||||||||
\(502\) | −8.61973e11 | −0.605797 | ||||||||
\(503\) | −1.85720e12 | −1.29361 | −0.646803 | − | 0.762657i | \(-0.723894\pi\) | ||||
−0.646803 | + | 0.762657i | \(0.723894\pi\) | |||||||
\(504\) | 4.34361e12 | 2.99857 | ||||||||
\(505\) | −3.05930e12 | −2.09320 | ||||||||
\(506\) | 4.00493e11 | 0.271592 | ||||||||
\(507\) | 9.29207e11 | 0.624563 | ||||||||
\(508\) | 6.76513e11 | 0.450702 | ||||||||
\(509\) | 1.23771e11 | 0.0817312 | 0.0408656 | − | 0.999165i | \(-0.486988\pi\) | ||||
0.0408656 | + | 0.999165i | \(0.486988\pi\) | |||||||
\(510\) | −2.28118e12 | −1.49312 | ||||||||
\(511\) | 5.19762e10 | 0.0337218 | ||||||||
\(512\) | 1.49171e12 | 0.959335 | ||||||||
\(513\) | −2.25653e12 | −1.43851 | ||||||||
\(514\) | 5.13601e11 | 0.324557 | ||||||||
\(515\) | −1.34207e12 | −0.840705 | ||||||||
\(516\) | −1.52526e11 | −0.0947155 | ||||||||
\(517\) | 2.68380e12 | 1.65213 | ||||||||
\(518\) | −2.88413e12 | −1.76007 | ||||||||
\(519\) | 5.37964e12 | 3.25462 | ||||||||
\(520\) | 2.50452e12 | 1.50214 | ||||||||
\(521\) | −3.54135e11 | −0.210571 | −0.105286 | − | 0.994442i | \(-0.533576\pi\) | ||||
−0.105286 | + | 0.994442i | \(0.533576\pi\) | |||||||
\(522\) | 1.69905e12 | 1.00159 | ||||||||
\(523\) | −9.79180e11 | −0.572275 | −0.286138 | − | 0.958188i | \(-0.592371\pi\) | ||||
−0.286138 | + | 0.958188i | \(0.592371\pi\) | |||||||
\(524\) | 3.07571e11 | 0.178219 | ||||||||
\(525\) | −6.68956e12 | −3.84309 | ||||||||
\(526\) | 1.41648e12 | 0.806815 | ||||||||
\(527\) | 7.80277e11 | 0.440657 | ||||||||
\(528\) | −2.26199e12 | −1.26660 | ||||||||
\(529\) | −1.66679e12 | −0.925402 | ||||||||
\(530\) | 2.13502e12 | 1.17533 | ||||||||
\(531\) | 8.13893e12 | 4.44265 | ||||||||
\(532\) | −3.50925e11 | −0.189938 | ||||||||
\(533\) | −2.79948e11 | −0.150247 | ||||||||
\(534\) | −1.10944e12 | −0.590431 | ||||||||
\(535\) | −1.07218e12 | −0.565818 | ||||||||
\(536\) | 1.43025e11 | 0.0748462 | ||||||||
\(537\) | −5.88763e10 | −0.0305532 | ||||||||
\(538\) | 1.07730e12 | 0.554390 | ||||||||
\(539\) | −5.32223e11 | −0.271609 | ||||||||
\(540\) | −3.09330e12 | −1.56549 | ||||||||
\(541\) | −1.88732e12 | −0.947234 | −0.473617 | − | 0.880731i | \(-0.657052\pi\) | ||||
−0.473617 | + | 0.880731i | \(0.657052\pi\) | |||||||
\(542\) | −9.27411e11 | −0.461610 | ||||||||
\(543\) | −3.36483e12 | −1.66098 | ||||||||
\(544\) | −7.48506e11 | −0.366438 | ||||||||
\(545\) | −2.19688e12 | −1.06665 | ||||||||
\(546\) | −2.86045e12 | −1.37743 | ||||||||
\(547\) | −9.25517e11 | −0.442020 | −0.221010 | − | 0.975272i | \(-0.570935\pi\) | ||||
−0.221010 | + | 0.975272i | \(0.570935\pi\) | |||||||
\(548\) | 4.81334e11 | 0.227999 | ||||||||
\(549\) | −8.11758e12 | −3.81374 | ||||||||
\(550\) | 3.96902e12 | 1.84949 | ||||||||
\(551\) | −5.50178e11 | −0.254285 | ||||||||
\(552\) | −1.21178e12 | −0.555516 | ||||||||
\(553\) | 3.57845e12 | 1.62717 | ||||||||
\(554\) | 1.19769e12 | 0.540194 | ||||||||
\(555\) | 1.37556e13 | 6.15405 | ||||||||
\(556\) | −1.16182e12 | −0.515586 | ||||||||
\(557\) | 4.04068e12 | 1.77871 | 0.889356 | − | 0.457215i | \(-0.151153\pi\) | ||||
0.889356 | + | 0.457215i | \(0.151153\pi\) | |||||||
\(558\) | −3.55015e12 | −1.55022 | ||||||||
\(559\) | 2.87249e11 | 0.124424 | ||||||||
\(560\) | 2.42468e12 | 1.04186 | ||||||||
\(561\) | 3.08541e12 | 1.31516 | ||||||||
\(562\) | −9.26239e11 | −0.391660 | ||||||||
\(563\) | −1.31953e12 | −0.553517 | −0.276758 | − | 0.960940i | \(-0.589260\pi\) | ||||
−0.276758 | + | 0.960940i | \(0.589260\pi\) | |||||||
\(564\) | −2.02603e12 | −0.843120 | ||||||||
\(565\) | 8.96371e10 | 0.0370058 | ||||||||
\(566\) | −3.87362e12 | −1.58651 | ||||||||
\(567\) | 7.38140e12 | 2.99927 | ||||||||
\(568\) | −2.64014e12 | −1.06429 | ||||||||
\(569\) | −1.40113e12 | −0.560366 | −0.280183 | − | 0.959947i | \(-0.590395\pi\) | ||||
−0.280183 | + | 0.959947i | \(0.590395\pi\) | |||||||
\(570\) | −3.36089e12 | −1.33358 | ||||||||
\(571\) | −7.55062e11 | −0.297249 | −0.148624 | − | 0.988894i | \(-0.547485\pi\) | ||||
−0.148624 | + | 0.988894i | \(0.547485\pi\) | |||||||
\(572\) | −8.45173e11 | −0.330114 | ||||||||
\(573\) | −4.84797e11 | −0.187873 | ||||||||
\(574\) | −4.32770e11 | −0.166400 | ||||||||
\(575\) | 1.33157e12 | 0.507995 | ||||||||
\(576\) | 7.07054e12 | 2.67640 | ||||||||
\(577\) | 2.44025e12 | 0.916521 | 0.458261 | − | 0.888818i | \(-0.348473\pi\) | ||||
0.458261 | + | 0.888818i | \(0.348473\pi\) | |||||||
\(578\) | 1.45894e12 | 0.543702 | ||||||||
\(579\) | −2.02662e12 | −0.749407 | ||||||||
\(580\) | −7.54198e11 | −0.276732 | ||||||||
\(581\) | −3.22821e12 | −1.17536 | ||||||||
\(582\) | −4.62349e12 | −1.67038 | ||||||||
\(583\) | −2.88772e12 | −1.03525 | ||||||||
\(584\) | 9.33078e10 | 0.0331940 | ||||||||
\(585\) | 9.73411e12 | 3.43633 | ||||||||
\(586\) | 4.06876e12 | 1.42535 | ||||||||
\(587\) | −5.63814e12 | −1.96004 | −0.980019 | − | 0.198906i | \(-0.936261\pi\) | ||||
−0.980019 | + | 0.198906i | \(0.936261\pi\) | |||||||
\(588\) | 4.01780e11 | 0.138609 | ||||||||
\(589\) | 1.14959e12 | 0.393573 | ||||||||
\(590\) | 7.25473e12 | 2.46483 | ||||||||
\(591\) | −6.31998e12 | −2.13095 | ||||||||
\(592\) | −3.24248e12 | −1.08500 | ||||||||
\(593\) | 2.07785e12 | 0.690031 | 0.345016 | − | 0.938597i | \(-0.387874\pi\) | ||||
0.345016 | + | 0.938597i | \(0.387874\pi\) | |||||||
\(594\) | −8.40139e12 | −2.76893 | ||||||||
\(595\) | −3.30733e12 | −1.08181 | ||||||||
\(596\) | 1.57010e12 | 0.509705 | ||||||||
\(597\) | −6.45513e12 | −2.07980 | ||||||||
\(598\) | 5.69380e11 | 0.182074 | ||||||||
\(599\) | 2.05195e12 | 0.651248 | 0.325624 | − | 0.945499i | \(-0.394426\pi\) | ||||
0.325624 | + | 0.945499i | \(0.394426\pi\) | |||||||
\(600\) | −1.20091e13 | −3.78295 | ||||||||
\(601\) | −3.93140e12 | −1.22917 | −0.614586 | − | 0.788850i | \(-0.710677\pi\) | ||||
−0.614586 | + | 0.788850i | \(0.710677\pi\) | |||||||
\(602\) | 4.44056e11 | 0.137801 | ||||||||
\(603\) | 5.55882e11 | 0.171220 | ||||||||
\(604\) | −1.31361e12 | −0.401607 | ||||||||
\(605\) | −2.68175e12 | −0.813803 | ||||||||
\(606\) | 6.27257e12 | 1.88938 | ||||||||
\(607\) | 2.33530e12 | 0.698221 | 0.349110 | − | 0.937082i | \(-0.386484\pi\) | ||||
0.349110 | + | 0.937082i | \(0.386484\pi\) | |||||||
\(608\) | −1.10278e12 | −0.327284 | ||||||||
\(609\) | 3.45246e12 | 1.01707 | ||||||||
\(610\) | −7.23569e12 | −2.11590 | ||||||||
\(611\) | 3.81557e12 | 1.10758 | ||||||||
\(612\) | −1.66190e12 | −0.478875 | ||||||||
\(613\) | 1.39331e12 | 0.398544 | 0.199272 | − | 0.979944i | \(-0.436142\pi\) | ||||
0.199272 | + | 0.979944i | \(0.436142\pi\) | |||||||
\(614\) | −7.68013e11 | −0.218078 | ||||||||
\(615\) | 2.06406e12 | 0.581813 | ||||||||
\(616\) | −5.23671e12 | −1.46536 | ||||||||
\(617\) | 6.75919e11 | 0.187764 | 0.0938818 | − | 0.995583i | \(-0.470072\pi\) | ||||
0.0938818 | + | 0.995583i | \(0.470072\pi\) | |||||||
\(618\) | 2.75169e12 | 0.758842 | ||||||||
\(619\) | −3.04638e12 | −0.834019 | −0.417010 | − | 0.908902i | \(-0.636922\pi\) | ||||
−0.417010 | + | 0.908902i | \(0.636922\pi\) | |||||||
\(620\) | 1.57589e12 | 0.428315 | ||||||||
\(621\) | −2.81860e12 | −0.760538 | ||||||||
\(622\) | −1.32413e12 | −0.354711 | ||||||||
\(623\) | −1.60851e12 | −0.427787 | ||||||||
\(624\) | −3.21587e12 | −0.849118 | ||||||||
\(625\) | 2.28658e12 | 0.599414 | ||||||||
\(626\) | 2.99298e12 | 0.778967 | ||||||||
\(627\) | 4.54578e12 | 1.17464 | ||||||||
\(628\) | 1.76493e12 | 0.452802 | ||||||||
\(629\) | 4.42283e12 | 1.12661 | ||||||||
\(630\) | 1.50479e13 | 3.80578 | ||||||||
\(631\) | −5.72611e12 | −1.43790 | −0.718948 | − | 0.695064i | \(-0.755376\pi\) | ||||
−0.718948 | + | 0.695064i | \(0.755376\pi\) | |||||||
\(632\) | 6.42404e12 | 1.60170 | ||||||||
\(633\) | 4.04884e12 | 1.00234 | ||||||||
\(634\) | 1.41283e11 | 0.0347286 | ||||||||
\(635\) | 9.39364e12 | 2.29273 | ||||||||
\(636\) | 2.17997e12 | 0.528315 | ||||||||
\(637\) | −7.56661e11 | −0.182085 | ||||||||
\(638\) | −2.04840e12 | −0.489464 | ||||||||
\(639\) | −1.02612e13 | −2.43469 | ||||||||
\(640\) | 1.75506e12 | 0.413506 | ||||||||
\(641\) | 7.81185e10 | 0.0182765 | 0.00913825 | − | 0.999958i | \(-0.497091\pi\) | ||||
0.00913825 | + | 0.999958i | \(0.497091\pi\) | |||||||
\(642\) | 2.19832e12 | 0.510722 | ||||||||
\(643\) | −1.63383e12 | −0.376927 | −0.188464 | − | 0.982080i | \(-0.560351\pi\) | ||||
−0.188464 | + | 0.982080i | \(0.560351\pi\) | |||||||
\(644\) | −4.38336e11 | −0.100420 | ||||||||
\(645\) | −2.11789e12 | −0.481819 | ||||||||
\(646\) | −1.08063e12 | −0.244134 | ||||||||
\(647\) | 4.02702e12 | 0.903471 | 0.451735 | − | 0.892152i | \(-0.350805\pi\) | ||||
0.451735 | + | 0.892152i | \(0.350805\pi\) | |||||||
\(648\) | 1.32511e13 | 2.95233 | ||||||||
\(649\) | −9.81239e12 | −2.17107 | ||||||||
\(650\) | 5.64276e12 | 1.23988 | ||||||||
\(651\) | −7.21389e12 | −1.57418 | ||||||||
\(652\) | −2.11365e12 | −0.458057 | ||||||||
\(653\) | 5.84257e12 | 1.25746 | 0.628730 | − | 0.777623i | \(-0.283575\pi\) | ||||
0.628730 | + | 0.777623i | \(0.283575\pi\) | |||||||
\(654\) | 4.50432e12 | 0.962785 | ||||||||
\(655\) | 4.27075e12 | 0.906605 | ||||||||
\(656\) | −4.86542e11 | −0.102578 | ||||||||
\(657\) | 3.62651e11 | 0.0759355 | ||||||||
\(658\) | 5.89846e12 | 1.22665 | ||||||||
\(659\) | 4.19256e11 | 0.0865955 | 0.0432977 | − | 0.999062i | \(-0.486214\pi\) | ||||
0.0432977 | + | 0.999062i | \(0.486214\pi\) | |||||||
\(660\) | 6.23147e12 | 1.27833 | ||||||||
\(661\) | −4.51791e12 | −0.920515 | −0.460258 | − | 0.887785i | \(-0.652243\pi\) | ||||
−0.460258 | + | 0.887785i | \(0.652243\pi\) | |||||||
\(662\) | −2.60824e12 | −0.527821 | ||||||||
\(663\) | 4.38653e12 | 0.881678 | ||||||||
\(664\) | −5.79529e12 | −1.15696 | ||||||||
\(665\) | −4.87274e12 | −0.966219 | ||||||||
\(666\) | −2.01233e13 | −3.96337 | ||||||||
\(667\) | −6.87220e11 | −0.134440 | ||||||||
\(668\) | −1.44647e11 | −0.0281070 | ||||||||
\(669\) | 1.75353e13 | 3.38451 | ||||||||
\(670\) | 4.95492e11 | 0.0949948 | ||||||||
\(671\) | 9.78665e12 | 1.86373 | ||||||||
\(672\) | 6.92016e12 | 1.30904 | ||||||||
\(673\) | −3.13452e12 | −0.588983 | −0.294492 | − | 0.955654i | \(-0.595150\pi\) | ||||
−0.294492 | + | 0.955654i | \(0.595150\pi\) | |||||||
\(674\) | −1.86161e12 | −0.347471 | ||||||||
\(675\) | −2.79333e13 | −5.17911 | ||||||||
\(676\) | 6.03407e11 | 0.111135 | ||||||||
\(677\) | 9.08025e12 | 1.66130 | 0.830651 | − | 0.556793i | \(-0.187968\pi\) | ||||
0.830651 | + | 0.556793i | \(0.187968\pi\) | |||||||
\(678\) | −1.83785e11 | −0.0334024 | ||||||||
\(679\) | −6.70329e12 | −1.21025 | ||||||||
\(680\) | −5.93732e12 | −1.06488 | ||||||||
\(681\) | 5.71966e12 | 1.01908 | ||||||||
\(682\) | 4.28011e12 | 0.757574 | ||||||||
\(683\) | 9.92561e12 | 1.74528 | 0.872638 | − | 0.488367i | \(-0.162407\pi\) | ||||
0.872638 | + | 0.488367i | \(0.162407\pi\) | |||||||
\(684\) | −2.44850e12 | −0.427707 | ||||||||
\(685\) | 6.68351e12 | 1.15984 | ||||||||
\(686\) | 4.07167e12 | 0.701963 | ||||||||
\(687\) | 1.17662e12 | 0.201526 | ||||||||
\(688\) | 4.99231e11 | 0.0849481 | ||||||||
\(689\) | −4.10548e12 | −0.694028 | ||||||||
\(690\) | −4.19804e12 | −0.705060 | ||||||||
\(691\) | 2.83695e12 | 0.473370 | 0.236685 | − | 0.971586i | \(-0.423939\pi\) | ||||
0.236685 | + | 0.971586i | \(0.423939\pi\) | |||||||
\(692\) | 3.49342e12 | 0.579127 | ||||||||
\(693\) | −2.03531e13 | −3.35220 | ||||||||
\(694\) | 5.39614e12 | 0.883011 | ||||||||
\(695\) | −1.61323e13 | −2.62279 | ||||||||
\(696\) | 6.19786e12 | 1.00115 | ||||||||
\(697\) | 6.63655e11 | 0.106511 | ||||||||
\(698\) | 1.45705e12 | 0.232340 | ||||||||
\(699\) | −7.21850e11 | −0.114367 | ||||||||
\(700\) | −4.34406e12 | −0.683841 | ||||||||
\(701\) | −9.36363e11 | −0.146458 | −0.0732290 | − | 0.997315i | \(-0.523330\pi\) | ||||
−0.0732290 | + | 0.997315i | \(0.523330\pi\) | |||||||
\(702\) | −1.19443e13 | −1.85627 | ||||||||
\(703\) | 6.51622e12 | 1.00623 | ||||||||
\(704\) | −8.52433e12 | −1.30793 | ||||||||
\(705\) | −2.81322e13 | −4.28896 | ||||||||
\(706\) | 8.46475e12 | 1.28231 | ||||||||
\(707\) | 9.09420e12 | 1.36892 | ||||||||
\(708\) | 7.40746e12 | 1.10795 | ||||||||
\(709\) | 5.31394e12 | 0.789785 | 0.394892 | − | 0.918727i | \(-0.370782\pi\) | ||||
0.394892 | + | 0.918727i | \(0.370782\pi\) | |||||||
\(710\) | −9.14643e12 | −1.35079 | ||||||||
\(711\) | 2.49678e13 | 3.66409 | ||||||||
\(712\) | −2.88760e12 | −0.421092 | ||||||||
\(713\) | 1.43594e12 | 0.208082 | ||||||||
\(714\) | 6.78111e12 | 0.976470 | ||||||||
\(715\) | −1.17356e13 | −1.67929 | ||||||||
\(716\) | −3.82330e10 | −0.00543663 | ||||||||
\(717\) | −6.62820e12 | −0.936612 | ||||||||
\(718\) | 1.18261e12 | 0.166066 | ||||||||
\(719\) | 6.83793e12 | 0.954212 | 0.477106 | − | 0.878846i | \(-0.341686\pi\) | ||||
0.477106 | + | 0.878846i | \(0.341686\pi\) | |||||||
\(720\) | 1.69176e13 | 2.34608 | ||||||||
\(721\) | 3.98950e12 | 0.549806 | ||||||||
\(722\) | 4.37361e12 | 0.598994 | ||||||||
\(723\) | −2.81059e12 | −0.382538 | ||||||||
\(724\) | −2.18505e12 | −0.295555 | ||||||||
\(725\) | −6.81059e12 | −0.915511 | ||||||||
\(726\) | 5.49847e12 | 0.734560 | ||||||||
\(727\) | 6.36741e12 | 0.845392 | 0.422696 | − | 0.906272i | \(-0.361084\pi\) | ||||
0.422696 | + | 0.906272i | \(0.361084\pi\) | |||||||
\(728\) | −7.44504e12 | −0.982371 | ||||||||
\(729\) | 1.18310e13 | 1.55148 | ||||||||
\(730\) | 3.23253e11 | 0.0421299 | ||||||||
\(731\) | −6.80964e11 | −0.0882055 | ||||||||
\(732\) | −7.38803e12 | −0.951106 | ||||||||
\(733\) | 5.47275e12 | 0.700226 | 0.350113 | − | 0.936708i | \(-0.386143\pi\) | ||||
0.350113 | + | 0.936708i | \(0.386143\pi\) | |||||||
\(734\) | −1.02806e12 | −0.130733 | ||||||||
\(735\) | 5.57887e12 | 0.705104 | ||||||||
\(736\) | −1.37747e12 | −0.173035 | ||||||||
\(737\) | −6.70178e11 | −0.0836732 | ||||||||
\(738\) | −3.01954e12 | −0.374703 | ||||||||
\(739\) | −1.09212e13 | −1.34701 | −0.673503 | − | 0.739185i | \(-0.735211\pi\) | ||||
−0.673503 | + | 0.739185i | \(0.735211\pi\) | |||||||
\(740\) | 8.93260e12 | 1.09505 | ||||||||
\(741\) | 6.46274e12 | 0.787471 | ||||||||
\(742\) | −6.34663e12 | −0.768645 | ||||||||
\(743\) | 1.41066e11 | 0.0169813 | 0.00849066 | − | 0.999964i | \(-0.497297\pi\) | ||||
0.00849066 | + | 0.999964i | \(0.497297\pi\) | |||||||
\(744\) | −1.29504e13 | −1.54955 | ||||||||
\(745\) | 2.18014e13 | 2.59288 | ||||||||
\(746\) | 4.57738e12 | 0.541118 | ||||||||
\(747\) | −2.25240e13 | −2.64669 | ||||||||
\(748\) | 2.00360e12 | 0.234021 | ||||||||
\(749\) | 3.18721e12 | 0.370034 | ||||||||
\(750\) | −1.92355e13 | −2.21987 | ||||||||
\(751\) | 1.07431e13 | 1.23240 | 0.616200 | − | 0.787590i | \(-0.288671\pi\) | ||||
0.616200 | + | 0.787590i | \(0.288671\pi\) | |||||||
\(752\) | 6.63135e12 | 0.756174 | ||||||||
\(753\) | −1.22208e13 | −1.38523 | ||||||||
\(754\) | −2.91221e12 | −0.328134 | ||||||||
\(755\) | −1.82400e13 | −2.04298 | ||||||||
\(756\) | 9.19526e12 | 1.02380 | ||||||||
\(757\) | −3.92377e12 | −0.434282 | −0.217141 | − | 0.976140i | \(-0.569673\pi\) | ||||
−0.217141 | + | 0.976140i | \(0.569673\pi\) | |||||||
\(758\) | −3.74861e12 | −0.412438 | ||||||||
\(759\) | 5.67807e12 | 0.621031 | ||||||||
\(760\) | −8.74754e12 | −0.951097 | ||||||||
\(761\) | 2.65761e12 | 0.287250 | 0.143625 | − | 0.989632i | \(-0.454124\pi\) | ||||
0.143625 | + | 0.989632i | \(0.454124\pi\) | |||||||
\(762\) | −1.92600e13 | −2.06947 | ||||||||
\(763\) | 6.53052e12 | 0.697569 | ||||||||
\(764\) | −3.14817e11 | −0.0334302 | ||||||||
\(765\) | −2.30761e13 | −2.43605 | ||||||||
\(766\) | 1.44960e12 | 0.152132 | ||||||||
\(767\) | −1.39503e13 | −1.45547 | ||||||||
\(768\) | 1.57586e13 | 1.63453 | ||||||||
\(769\) | 3.14923e12 | 0.324740 | 0.162370 | − | 0.986730i | \(-0.448086\pi\) | ||||
0.162370 | + | 0.986730i | \(0.448086\pi\) | |||||||
\(770\) | −1.81419e13 | −1.85984 | ||||||||
\(771\) | 7.28169e12 | 0.742143 | ||||||||
\(772\) | −1.31604e12 | −0.133350 | ||||||||
\(773\) | 3.67725e11 | 0.0370438 | 0.0185219 | − | 0.999828i | \(-0.494104\pi\) | ||||
0.0185219 | + | 0.999828i | \(0.494104\pi\) | |||||||
\(774\) | 3.09829e12 | 0.310305 | ||||||||
\(775\) | 1.42307e13 | 1.41699 | ||||||||
\(776\) | −1.20338e13 | −1.19131 | ||||||||
\(777\) | −4.08904e13 | −4.02463 | ||||||||
\(778\) | −4.99742e12 | −0.489032 | ||||||||
\(779\) | 9.77773e11 | 0.0951304 | ||||||||
\(780\) | 8.85928e12 | 0.856984 | ||||||||
\(781\) | 1.23710e13 | 1.18980 | ||||||||
\(782\) | −1.34980e12 | −0.129074 | ||||||||
\(783\) | 1.44163e13 | 1.37064 | ||||||||
\(784\) | −1.31506e12 | −0.124315 | ||||||||
\(785\) | 2.45067e13 | 2.30341 | ||||||||
\(786\) | −8.75643e12 | −0.818325 | ||||||||
\(787\) | −1.46553e13 | −1.36179 | −0.680895 | − | 0.732381i | \(-0.738409\pi\) | ||||
−0.680895 | + | 0.732381i | \(0.738409\pi\) | |||||||
\(788\) | −4.10407e12 | −0.379181 | ||||||||
\(789\) | 2.00824e13 | 1.84489 | ||||||||
\(790\) | 2.22553e13 | 2.03288 | ||||||||
\(791\) | −2.66458e11 | −0.0242011 | ||||||||
\(792\) | −3.65379e13 | −3.29974 | ||||||||
\(793\) | 1.39137e13 | 1.24943 | ||||||||
\(794\) | 1.23870e13 | 1.10604 | ||||||||
\(795\) | 3.02697e13 | 2.68755 | ||||||||
\(796\) | −4.19183e12 | −0.370079 | ||||||||
\(797\) | −2.07106e13 | −1.81815 | −0.909075 | − | 0.416633i | \(-0.863210\pi\) | ||||
−0.909075 | + | 0.416633i | \(0.863210\pi\) | |||||||
\(798\) | 9.99070e12 | 0.872134 | ||||||||
\(799\) | −9.04533e12 | −0.785171 | ||||||||
\(800\) | −1.36512e13 | −1.17833 | ||||||||
\(801\) | −1.12230e13 | −0.963300 | ||||||||
\(802\) | −6.62767e12 | −0.565687 | ||||||||
\(803\) | −4.37217e11 | −0.0371088 | ||||||||
\(804\) | 5.05923e11 | 0.0427004 | ||||||||
\(805\) | −6.08647e12 | −0.510839 | ||||||||
\(806\) | 6.08503e12 | 0.507873 | ||||||||
\(807\) | 1.52736e13 | 1.26768 | ||||||||
\(808\) | 1.63259e13 | 1.34749 | ||||||||
\(809\) | 1.94599e12 | 0.159725 | 0.0798623 | − | 0.996806i | \(-0.474552\pi\) | ||||
0.0798623 | + | 0.996806i | \(0.474552\pi\) | |||||||
\(810\) | 4.59068e13 | 3.74709 | ||||||||
\(811\) | 1.32679e11 | 0.0107698 | 0.00538491 | − | 0.999986i | \(-0.498286\pi\) | ||||
0.00538491 | + | 0.999986i | \(0.498286\pi\) | |||||||
\(812\) | 2.24196e12 | 0.180978 | ||||||||
\(813\) | −1.31486e13 | −1.05553 | ||||||||
\(814\) | 2.42609e13 | 1.93685 | ||||||||
\(815\) | −2.93489e13 | −2.33014 | ||||||||
\(816\) | 7.62367e12 | 0.601947 | ||||||||
\(817\) | −1.00327e12 | −0.0787807 | ||||||||
\(818\) | 5.42103e12 | 0.423343 | ||||||||
\(819\) | −2.89360e13 | −2.24730 | ||||||||
\(820\) | 1.34036e12 | 0.103528 | ||||||||
\(821\) | 1.39889e13 | 1.07458 | 0.537290 | − | 0.843398i | \(-0.319448\pi\) | ||||
0.537290 | + | 0.843398i | \(0.319448\pi\) | |||||||
\(822\) | −1.37034e13 | −1.04690 | ||||||||
\(823\) | −2.70521e12 | −0.205543 | −0.102771 | − | 0.994705i | \(-0.532771\pi\) | ||||
−0.102771 | + | 0.994705i | \(0.532771\pi\) | |||||||
\(824\) | 7.16195e12 | 0.541201 | ||||||||
\(825\) | 5.62717e13 | 4.22909 | ||||||||
\(826\) | −2.15657e13 | −1.61195 | ||||||||
\(827\) | −7.17939e11 | −0.0533719 | −0.0266859 | − | 0.999644i | \(-0.508495\pi\) | ||||
−0.0266859 | + | 0.999644i | \(0.508495\pi\) | |||||||
\(828\) | −3.05838e12 | −0.226128 | ||||||||
\(829\) | −1.65304e12 | −0.121559 | −0.0607796 | − | 0.998151i | \(-0.519359\pi\) | ||||
−0.0607796 | + | 0.998151i | \(0.519359\pi\) | |||||||
\(830\) | −2.00771e13 | −1.46841 | ||||||||
\(831\) | 1.69805e13 | 1.23522 | ||||||||
\(832\) | −1.21190e13 | −0.876825 | ||||||||
\(833\) | 1.79377e12 | 0.129082 | ||||||||
\(834\) | 3.30764e13 | 2.36740 | ||||||||
\(835\) | −2.00848e12 | −0.142981 | ||||||||
\(836\) | 2.95193e12 | 0.209016 | ||||||||
\(837\) | −3.01227e13 | −2.12143 | ||||||||
\(838\) | 4.67027e12 | 0.327148 | ||||||||
\(839\) | 1.51228e13 | 1.05366 | 0.526832 | − | 0.849969i | \(-0.323380\pi\) | ||||
0.526832 | + | 0.849969i | \(0.323380\pi\) | |||||||
\(840\) | 5.48923e13 | 3.80412 | ||||||||
\(841\) | −1.09922e13 | −0.757711 | ||||||||
\(842\) | −2.25801e12 | −0.154818 | ||||||||
\(843\) | −1.31320e13 | −0.895582 | ||||||||
\(844\) | 2.62923e12 | 0.178356 | ||||||||
\(845\) | 8.37855e12 | 0.565345 | ||||||||
\(846\) | 4.11550e13 | 2.76221 | ||||||||
\(847\) | 7.97187e12 | 0.532212 | ||||||||
\(848\) | −7.13521e12 | −0.473833 | ||||||||
\(849\) | −5.49191e13 | −3.62776 | ||||||||
\(850\) | −1.33769e13 | −0.878965 | ||||||||
\(851\) | 8.13932e12 | 0.531992 | ||||||||
\(852\) | −9.33899e12 | −0.607186 | ||||||||
\(853\) | −1.14817e13 | −0.742568 | −0.371284 | − | 0.928519i | \(-0.621082\pi\) | ||||
−0.371284 | + | 0.928519i | \(0.621082\pi\) | |||||||
\(854\) | 2.15091e13 | 1.38376 | ||||||||
\(855\) | −3.39983e13 | −2.17575 | ||||||||
\(856\) | 5.72168e12 | 0.364243 | ||||||||
\(857\) | 1.99397e13 | 1.26271 | 0.631356 | − | 0.775493i | \(-0.282499\pi\) | ||||
0.631356 | + | 0.775493i | \(0.282499\pi\) | |||||||
\(858\) | 2.40617e13 | 1.51577 | ||||||||
\(859\) | 1.38539e13 | 0.868164 | 0.434082 | − | 0.900873i | \(-0.357073\pi\) | ||||
0.434082 | + | 0.900873i | \(0.357073\pi\) | |||||||
\(860\) | −1.37531e12 | −0.0857350 | ||||||||
\(861\) | −6.13569e12 | −0.380495 | ||||||||
\(862\) | −1.87179e13 | −1.15471 | ||||||||
\(863\) | −2.96018e13 | −1.81664 | −0.908321 | − | 0.418275i | \(-0.862635\pi\) | ||||
−0.908321 | + | 0.418275i | \(0.862635\pi\) | |||||||
\(864\) | 2.88961e13 | 1.76412 | ||||||||
\(865\) | 4.85076e13 | 2.94603 | ||||||||
\(866\) | 1.73177e13 | 1.04631 | ||||||||
\(867\) | 2.06844e13 | 1.24324 | ||||||||
\(868\) | −4.68455e12 | −0.280110 | ||||||||
\(869\) | −3.01014e13 | −1.79060 | ||||||||
\(870\) | 2.14717e13 | 1.27066 | ||||||||
\(871\) | −9.52792e11 | −0.0560940 | ||||||||
\(872\) | 1.17236e13 | 0.686652 | ||||||||
\(873\) | −4.67706e13 | −2.72526 | ||||||||
\(874\) | −1.98867e12 | −0.115282 | ||||||||
\(875\) | −2.78883e13 | −1.60837 | ||||||||
\(876\) | 3.30059e11 | 0.0189375 | ||||||||
\(877\) | −5.98845e12 | −0.341835 | −0.170918 | − | 0.985285i | \(-0.554673\pi\) | ||||
−0.170918 | + | 0.985285i | \(0.554673\pi\) | |||||||
\(878\) | 1.08236e12 | 0.0614674 | ||||||||
\(879\) | 5.76858e13 | 3.25926 | ||||||||
\(880\) | −2.03961e13 | −1.14650 | ||||||||
\(881\) | 4.47788e10 | 0.00250427 | 0.00125213 | − | 0.999999i | \(-0.499601\pi\) | ||||
0.00125213 | + | 0.999999i | \(0.499601\pi\) | |||||||
\(882\) | −8.16142e12 | −0.454106 | ||||||||
\(883\) | 1.82152e13 | 1.00835 | 0.504175 | − | 0.863601i | \(-0.331797\pi\) | ||||
0.504175 | + | 0.863601i | \(0.331797\pi\) | |||||||
\(884\) | 2.84852e12 | 0.156886 | ||||||||
\(885\) | 1.02856e14 | 5.63615 | ||||||||
\(886\) | −2.23201e13 | −1.21687 | ||||||||
\(887\) | −1.08674e13 | −0.589483 | −0.294741 | − | 0.955577i | \(-0.595234\pi\) | ||||
−0.294741 | + | 0.955577i | \(0.595234\pi\) | |||||||
\(888\) | −7.34064e13 | −3.96165 | ||||||||
\(889\) | −2.79239e13 | −1.49940 | ||||||||
\(890\) | −1.00037e13 | −0.534450 | ||||||||
\(891\) | −6.20913e13 | −3.30051 | ||||||||
\(892\) | 1.13871e13 | 0.602241 | ||||||||
\(893\) | −1.33266e13 | −0.701275 | ||||||||
\(894\) | −4.47001e13 | −2.34040 | ||||||||
\(895\) | −5.30881e11 | −0.0276562 | ||||||||
\(896\) | −5.21715e12 | −0.270425 | ||||||||
\(897\) | 8.07252e12 | 0.416335 | ||||||||
\(898\) | 2.48316e12 | 0.127427 | ||||||||
\(899\) | −7.34440e12 | −0.375005 | ||||||||
\(900\) | −3.03096e13 | −1.53989 | ||||||||
\(901\) | 9.73261e12 | 0.492003 | ||||||||
\(902\) | 3.64040e12 | 0.183113 | ||||||||
\(903\) | 6.29571e12 | 0.315101 | ||||||||
\(904\) | −4.78347e11 | −0.0238224 | ||||||||
\(905\) | −3.03403e13 | −1.50349 | ||||||||
\(906\) | 3.73980e13 | 1.84405 | ||||||||
\(907\) | −2.21516e13 | −1.08686 | −0.543429 | − | 0.839455i | \(-0.682874\pi\) | ||||
−0.543429 | + | 0.839455i | \(0.682874\pi\) | |||||||
\(908\) | 3.71423e12 | 0.181335 | ||||||||
\(909\) | 6.34525e13 | 3.08256 | ||||||||
\(910\) | −2.57924e13 | −1.24682 | ||||||||
\(911\) | 8.34279e12 | 0.401309 | 0.200654 | − | 0.979662i | \(-0.435693\pi\) | ||||
0.200654 | + | 0.979662i | \(0.435693\pi\) | |||||||
\(912\) | 1.12321e13 | 0.537629 | ||||||||
\(913\) | 2.71553e13 | 1.29341 | ||||||||
\(914\) | −1.11696e13 | −0.529395 | ||||||||
\(915\) | −1.02586e14 | −4.83829 | ||||||||
\(916\) | 7.64074e11 | 0.0358596 | ||||||||
\(917\) | −1.26954e13 | −0.592903 | ||||||||
\(918\) | 2.83155e13 | 1.31593 | ||||||||
\(919\) | −1.73492e13 | −0.802341 | −0.401170 | − | 0.916003i | \(-0.631396\pi\) | ||||
−0.401170 | + | 0.916003i | \(0.631396\pi\) | |||||||
\(920\) | −1.09264e13 | −0.502844 | ||||||||
\(921\) | −1.08887e13 | −0.498663 | ||||||||
\(922\) | 1.47255e13 | 0.671090 | ||||||||
\(923\) | 1.75879e13 | 0.797638 | ||||||||
\(924\) | −1.85239e13 | −0.836004 | ||||||||
\(925\) | 8.06635e13 | 3.62276 | ||||||||
\(926\) | −2.96021e13 | −1.32304 | ||||||||
\(927\) | 2.78357e13 | 1.23807 | ||||||||
\(928\) | 7.04535e12 | 0.311844 | ||||||||
\(929\) | −1.11298e13 | −0.490247 | −0.245124 | − | 0.969492i | \(-0.578829\pi\) | ||||
−0.245124 | + | 0.969492i | \(0.578829\pi\) | |||||||
\(930\) | −4.48650e13 | −1.96668 | ||||||||
\(931\) | 2.64279e12 | 0.115289 | ||||||||
\(932\) | −4.68754e11 | −0.0203504 | ||||||||
\(933\) | −1.87732e13 | −0.811093 | ||||||||
\(934\) | −3.65178e12 | −0.157016 | ||||||||
\(935\) | 2.78208e13 | 1.19047 | ||||||||
\(936\) | −5.19459e13 | −2.21213 | ||||||||
\(937\) | −2.31541e13 | −0.981297 | −0.490648 | − | 0.871358i | \(-0.663240\pi\) | ||||
−0.490648 | + | 0.871358i | \(0.663240\pi\) | |||||||
\(938\) | −1.47292e12 | −0.0621248 | ||||||||
\(939\) | 4.24336e13 | 1.78121 | ||||||||
\(940\) | −1.82685e13 | −0.763179 | ||||||||
\(941\) | 6.27432e12 | 0.260864 | 0.130432 | − | 0.991457i | \(-0.458364\pi\) | ||||
0.130432 | + | 0.991457i | \(0.458364\pi\) | |||||||
\(942\) | −5.02468e13 | −2.07912 | ||||||||
\(943\) | 1.22132e12 | 0.0502954 | ||||||||
\(944\) | −2.42452e13 | −0.993693 | ||||||||
\(945\) | 1.27680e14 | 5.20810 | ||||||||
\(946\) | −3.73534e12 | −0.151642 | ||||||||
\(947\) | −1.95848e12 | −0.0791305 | −0.0395652 | − | 0.999217i | \(-0.512597\pi\) | ||||
−0.0395652 | + | 0.999217i | \(0.512597\pi\) | |||||||
\(948\) | 2.27238e13 | 0.913785 | ||||||||
\(949\) | −6.21591e11 | −0.0248775 | ||||||||
\(950\) | −1.97084e13 | −0.785048 | ||||||||
\(951\) | 2.00306e12 | 0.0794114 | ||||||||
\(952\) | 1.76495e13 | 0.696412 | ||||||||
\(953\) | −3.01343e13 | −1.18343 | −0.591716 | − | 0.806146i | \(-0.701549\pi\) | ||||
−0.591716 | + | 0.806146i | \(0.701549\pi\) | |||||||
\(954\) | −4.42821e13 | −1.73085 | ||||||||
\(955\) | −4.37136e12 | −0.170060 | ||||||||
\(956\) | −4.30422e12 | −0.166661 | ||||||||
\(957\) | −2.90416e13 | −1.11922 | ||||||||
\(958\) | 2.42889e13 | 0.931672 | ||||||||
\(959\) | −1.98676e13 | −0.758512 | ||||||||
\(960\) | 8.93537e13 | 3.39541 | ||||||||
\(961\) | −1.10936e13 | −0.419581 | ||||||||
\(962\) | 3.44917e13 | 1.29845 | ||||||||
\(963\) | 2.22379e13 | 0.833252 | ||||||||
\(964\) | −1.82514e12 | −0.0680689 | ||||||||
\(965\) | −1.82738e13 | −0.678352 | ||||||||
\(966\) | 1.24793e13 | 0.461096 | ||||||||
\(967\) | −4.59576e13 | −1.69020 | −0.845099 | − | 0.534609i | \(-0.820459\pi\) | ||||
−0.845099 | + | 0.534609i | \(0.820459\pi\) | |||||||
\(968\) | 1.43111e13 | 0.523883 | ||||||||
\(969\) | −1.53208e13 | −0.558245 | ||||||||
\(970\) | −4.16895e13 | −1.51201 | ||||||||
\(971\) | 5.92518e11 | 0.0213902 | 0.0106951 | − | 0.999943i | \(-0.496596\pi\) | ||||
0.0106951 | + | 0.999943i | \(0.496596\pi\) | |||||||
\(972\) | 2.11118e13 | 0.758625 | ||||||||
\(973\) | 4.79554e13 | 1.71526 | ||||||||
\(974\) | 2.09891e13 | 0.747270 | ||||||||
\(975\) | 8.00015e13 | 2.83516 | ||||||||
\(976\) | 2.41816e13 | 0.853024 | ||||||||
\(977\) | −3.04374e13 | −1.06876 | −0.534382 | − | 0.845243i | \(-0.679456\pi\) | ||||
−0.534382 | + | 0.845243i | \(0.679456\pi\) | |||||||
\(978\) | 6.01748e13 | 2.10325 | ||||||||
\(979\) | 1.35306e13 | 0.470753 | ||||||||
\(980\) | 3.62280e12 | 0.125466 | ||||||||
\(981\) | 4.55651e13 | 1.57080 | ||||||||
\(982\) | 4.00809e12 | 0.137542 | ||||||||
\(983\) | 2.48900e13 | 0.850225 | 0.425113 | − | 0.905140i | \(-0.360235\pi\) | ||||
0.425113 | + | 0.905140i | \(0.360235\pi\) | |||||||
\(984\) | −1.10148e13 | −0.374540 | ||||||||
\(985\) | −5.69866e13 | −1.92890 | ||||||||
\(986\) | 6.90379e12 | 0.232617 | ||||||||
\(987\) | 8.36267e13 | 2.80490 | ||||||||
\(988\) | 4.19677e12 | 0.140123 | ||||||||
\(989\) | −1.25318e12 | −0.0416513 | ||||||||
\(990\) | −1.26581e14 | −4.18803 | ||||||||
\(991\) | 7.06033e12 | 0.232538 | 0.116269 | − | 0.993218i | \(-0.462907\pi\) | ||||
0.116269 | + | 0.993218i | \(0.462907\pi\) | |||||||
\(992\) | −1.47212e13 | −0.482660 | ||||||||
\(993\) | −3.69789e13 | −1.20693 | ||||||||
\(994\) | 2.71890e13 | 0.883394 | ||||||||
\(995\) | −5.82052e13 | −1.88260 | ||||||||
\(996\) | −2.04997e13 | −0.660057 | ||||||||
\(997\) | −1.27122e13 | −0.407468 | −0.203734 | − | 0.979026i | \(-0.565308\pi\) | ||||
−0.203734 | + | 0.979026i | \(0.565308\pi\) | |||||||
\(998\) | 2.97724e13 | 0.950005 | ||||||||
\(999\) | −1.70744e14 | −5.42376 |
(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 | 43.10.a.a.1.5 | ✓ | 15 | |
3.2 | odd | 2 | 387.10.a.c.1.11 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.10.a.a.1.5 | ✓ | 15 | 1.1 | even | 1 | trivial | |
387.10.a.c.1.11 | 15 | 3.2 | odd | 2 |