Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + 12724944 x^{10} + 71331230512 x^{9} + \cdots + 24\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-14.3045\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 14.3045 | 1.26435 | 0.632174 | − | 0.774826i | \(-0.282163\pi\) | ||||
0.632174 | + | 0.774826i | \(0.282163\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 76.6177 | 0.598576 | ||||||||
\(5\) | −348.885 | −1.24821 | −0.624105 | − | 0.781340i | \(-0.714536\pi\) | ||||
−0.624105 | + | 0.781340i | \(0.714536\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1316.66 | −1.45088 | −0.725441 | − | 0.688285i | \(-0.758364\pi\) | ||||
−0.725441 | + | 0.688285i | \(0.758364\pi\) | |||||||
\(8\) | −734.996 | −0.507540 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4990.62 | −1.57817 | ||||||||
\(11\) | −4994.84 | −1.13148 | −0.565740 | − | 0.824584i | \(-0.691409\pi\) | ||||
−0.565740 | + | 0.824584i | \(0.691409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3397.75 | 0.428933 | 0.214466 | − | 0.976731i | \(-0.431199\pi\) | ||||
0.214466 | + | 0.976731i | \(0.431199\pi\) | |||||||
\(14\) | −18834.2 | −1.83442 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −20320.8 | −1.24028 | ||||||||
\(17\) | −13080.3 | −0.645725 | −0.322863 | − | 0.946446i | \(-0.604645\pi\) | ||||
−0.322863 | + | 0.946446i | \(0.604645\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8796.50 | 0.294220 | 0.147110 | − | 0.989120i | \(-0.453003\pi\) | ||||
0.147110 | + | 0.989120i | \(0.453003\pi\) | |||||||
\(20\) | −26730.8 | −0.747149 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −71448.5 | −1.43058 | ||||||||
\(23\) | −107491. | −1.84215 | −0.921075 | − | 0.389385i | \(-0.872687\pi\) | ||||
−0.921075 | + | 0.389385i | \(0.872687\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 43596.1 | 0.558030 | ||||||||
\(26\) | 48603.0 | 0.542320 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −100880. | −0.868462 | ||||||||
\(29\) | −31901.3 | −0.242893 | −0.121447 | − | 0.992598i | \(-0.538753\pi\) | ||||
−0.121447 | + | 0.992598i | \(0.538753\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −154292. | −0.930200 | −0.465100 | − | 0.885258i | \(-0.653982\pi\) | ||||
−0.465100 | + | 0.885258i | \(0.653982\pi\) | |||||||
\(32\) | −196599. | −1.06061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −187107. | −0.816422 | ||||||||
\(35\) | 459365. | 1.81101 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −528856. | −1.71645 | −0.858225 | − | 0.513274i | \(-0.828432\pi\) | ||||
−0.858225 | + | 0.513274i | \(0.828432\pi\) | |||||||
\(38\) | 125829. | 0.371996 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 256430. | 0.633517 | ||||||||
\(41\) | 480637. | 1.08911 | 0.544557 | − | 0.838724i | \(-0.316698\pi\) | ||||
0.544557 | + | 0.838724i | \(0.316698\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −438138. | −0.840371 | −0.420186 | − | 0.907438i | \(-0.638035\pi\) | ||||
−0.420186 | + | 0.907438i | \(0.638035\pi\) | |||||||
\(44\) | −382693. | −0.677277 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.53760e6 | −2.32912 | ||||||||
\(47\) | −1.23501e6 | −1.73511 | −0.867555 | − | 0.497341i | \(-0.834310\pi\) | ||||
−0.867555 | + | 0.497341i | \(0.834310\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 910062. | 1.10506 | ||||||||
\(50\) | 623619. | 0.705544 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 260328. | 0.256749 | ||||||||
\(53\) | 1.18221e6 | 1.09076 | 0.545379 | − | 0.838190i | \(-0.316386\pi\) | ||||
0.545379 | + | 0.838190i | \(0.316386\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.74263e6 | 1.41233 | ||||||||
\(56\) | 967743. | 0.736380 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −456331. | −0.307102 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 873606. | 0.492789 | 0.246395 | − | 0.969170i | \(-0.420754\pi\) | ||||
0.246395 | + | 0.969170i | \(0.420754\pi\) | |||||||
\(62\) | −2.20706e6 | −1.17610 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −211175. | −0.100696 | ||||||||
\(65\) | −1.18542e6 | −0.535399 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −832263. | −0.338064 | −0.169032 | − | 0.985611i | \(-0.554064\pi\) | ||||
−0.169032 | + | 0.985611i | \(0.554064\pi\) | |||||||
\(68\) | −1.00219e6 | −0.386516 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.57097e6 | 2.28974 | ||||||||
\(71\) | −3.15545e6 | −1.04630 | −0.523152 | − | 0.852240i | \(-0.675244\pi\) | ||||
−0.523152 | + | 0.852240i | \(0.675244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.69697e6 | 0.811420 | 0.405710 | − | 0.914002i | \(-0.367024\pi\) | ||||
0.405710 | + | 0.914002i | \(0.367024\pi\) | |||||||
\(74\) | −7.56500e6 | −2.17019 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 673968. | 0.176113 | ||||||||
\(77\) | 6.57652e6 | 1.64164 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.93335e6 | 1.58215 | 0.791076 | − | 0.611718i | \(-0.209521\pi\) | ||||
0.791076 | + | 0.611718i | \(0.209521\pi\) | |||||||
\(80\) | 7.08963e6 | 1.54813 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.87525e6 | 1.37702 | ||||||||
\(83\) | 3.14360e6 | 0.603468 | 0.301734 | − | 0.953392i | \(-0.402435\pi\) | ||||
0.301734 | + | 0.953392i | \(0.402435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.56354e6 | 0.806001 | ||||||||
\(86\) | −6.26733e6 | −1.06252 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.67119e6 | 0.574271 | ||||||||
\(89\) | 470189. | 0.0706980 | 0.0353490 | − | 0.999375i | \(-0.488746\pi\) | ||||
0.0353490 | + | 0.999375i | \(0.488746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.47369e6 | −0.622331 | ||||||||
\(92\) | −8.23572e6 | −1.10267 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.76661e7 | −2.19378 | ||||||||
\(95\) | −3.06897e6 | −0.367249 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.03272e7 | 1.14890 | 0.574448 | − | 0.818541i | \(-0.305217\pi\) | ||||
0.574448 | + | 0.818541i | \(0.305217\pi\) | |||||||
\(98\) | 1.30179e7 | 1.39718 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.34023e6 | 0.334023 | ||||||||
\(101\) | 1.36297e7 | 1.31632 | 0.658159 | − | 0.752879i | \(-0.271336\pi\) | ||||
0.658159 | + | 0.752879i | \(0.271336\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.58162e6 | −0.142618 | −0.0713088 | − | 0.997454i | \(-0.522718\pi\) | ||||
−0.0713088 | + | 0.997454i | \(0.522718\pi\) | |||||||
\(104\) | −2.49733e6 | −0.217701 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.69109e7 | 1.37910 | ||||||||
\(107\) | −1.70106e7 | −1.34238 | −0.671191 | − | 0.741284i | \(-0.734217\pi\) | ||||
−0.671191 | + | 0.741284i | \(0.734217\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.78972e6 | −0.428218 | −0.214109 | − | 0.976810i | \(-0.568685\pi\) | ||||
−0.214109 | + | 0.976810i | \(0.568685\pi\) | |||||||
\(110\) | 2.49273e7 | 1.78567 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.67557e7 | 1.79950 | ||||||||
\(113\) | −2.12637e7 | −1.38632 | −0.693161 | − | 0.720783i | \(-0.743783\pi\) | ||||
−0.693161 | + | 0.720783i | \(0.743783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.75021e7 | 2.29939 | ||||||||
\(116\) | −2.44421e6 | −0.145390 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.93784e6 | 0.164604 | ||||||||
\(119\) | 1.72224e7 | 0.936871 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.46122e6 | 0.280247 | ||||||||
\(122\) | 1.24965e7 | 0.623057 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.18215e7 | −0.556795 | ||||||||
\(125\) | 1.20466e7 | 0.551672 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.24454e7 | 0.539132 | 0.269566 | − | 0.962982i | \(-0.413120\pi\) | ||||
0.269566 | + | 0.962982i | \(0.413120\pi\) | |||||||
\(128\) | 2.21439e7 | 0.933294 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.69569e7 | −0.676930 | ||||||||
\(131\) | −8.16356e6 | −0.317271 | −0.158635 | − | 0.987337i | \(-0.550709\pi\) | ||||
−0.158635 | + | 0.987337i | \(0.550709\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.15820e7 | −0.426878 | ||||||||
\(134\) | −1.19051e7 | −0.427430 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.61400e6 | 0.327731 | ||||||||
\(137\) | −4.91255e7 | −1.63224 | −0.816122 | − | 0.577880i | \(-0.803880\pi\) | ||||
−0.816122 | + | 0.577880i | \(0.803880\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.62822e6 | −0.0830060 | −0.0415030 | − | 0.999138i | \(-0.513215\pi\) | ||||
−0.0415030 | + | 0.999138i | \(0.513215\pi\) | |||||||
\(140\) | 3.51955e7 | 1.08402 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.51371e7 | −1.32289 | ||||||||
\(143\) | −1.69712e7 | −0.485329 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.11299e7 | 0.303182 | ||||||||
\(146\) | 3.85787e7 | 1.02592 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.05197e7 | −1.02743 | ||||||||
\(149\) | 1.97981e7 | 0.490311 | 0.245156 | − | 0.969484i | \(-0.421161\pi\) | ||||
0.245156 | + | 0.969484i | \(0.421161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.33779e7 | 0.316205 | 0.158103 | − | 0.987423i | \(-0.449462\pi\) | ||||
0.158103 | + | 0.987423i | \(0.449462\pi\) | |||||||
\(152\) | −6.46539e6 | −0.149328 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.40736e7 | 2.07561 | ||||||||
\(155\) | 5.38301e7 | 1.16109 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.96493e7 | −0.611457 | −0.305728 | − | 0.952119i | \(-0.598900\pi\) | ||||
−0.305728 | + | 0.952119i | \(0.598900\pi\) | |||||||
\(158\) | 9.91778e7 | 2.00039 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.85904e7 | 1.32386 | ||||||||
\(161\) | 1.41530e8 | 2.67274 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.91942e7 | −1.07059 | −0.535294 | − | 0.844666i | \(-0.679799\pi\) | ||||
−0.535294 | + | 0.844666i | \(0.679799\pi\) | |||||||
\(164\) | 3.68253e7 | 0.651918 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.49675e7 | 0.762993 | ||||||||
\(167\) | −1.03566e8 | −1.72071 | −0.860357 | − | 0.509692i | \(-0.829759\pi\) | ||||
−0.860357 | + | 0.509692i | \(0.829759\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.12038e7 | −0.816017 | ||||||||
\(170\) | 6.52790e7 | 1.01907 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.35691e7 | −0.503026 | ||||||||
\(173\) | −7.49114e7 | −1.09998 | −0.549992 | − | 0.835170i | \(-0.685369\pi\) | ||||
−0.549992 | + | 0.835170i | \(0.685369\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.74014e7 | −0.809635 | ||||||||
\(176\) | 1.01499e8 | 1.40336 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.72580e6 | 0.0893869 | ||||||||
\(179\) | −1.39539e8 | −1.81849 | −0.909244 | − | 0.416263i | \(-0.863339\pi\) | ||||
−0.909244 | + | 0.416263i | \(0.863339\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.39686e7 | 0.175096 | 0.0875480 | − | 0.996160i | \(-0.472097\pi\) | ||||
0.0875480 | + | 0.996160i | \(0.472097\pi\) | |||||||
\(182\) | −6.39938e7 | −0.786843 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.90055e7 | 0.934965 | ||||||||
\(185\) | 1.84510e8 | 2.14249 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.53342e7 | 0.730625 | ||||||||
\(188\) | −9.46235e7 | −1.03860 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.39000e7 | −0.464330 | ||||||||
\(191\) | 3.81975e7 | 0.396660 | 0.198330 | − | 0.980135i | \(-0.436448\pi\) | ||||
0.198330 | + | 0.980135i | \(0.436448\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.69244e7 | −0.369711 | −0.184856 | − | 0.982766i | \(-0.559182\pi\) | ||||
−0.184856 | + | 0.982766i | \(0.559182\pi\) | |||||||
\(194\) | 1.47725e8 | 1.45260 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.97268e7 | 0.661460 | ||||||||
\(197\) | −1.04700e8 | −0.975695 | −0.487847 | − | 0.872929i | \(-0.662218\pi\) | ||||
−0.487847 | + | 0.872929i | \(0.662218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.24096e8 | −1.11628 | −0.558138 | − | 0.829748i | \(-0.688484\pi\) | ||||
−0.558138 | + | 0.829748i | \(0.688484\pi\) | |||||||
\(200\) | −3.20430e7 | −0.283222 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.94965e8 | 1.66428 | ||||||||
\(203\) | 4.20033e7 | 0.352409 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.67687e8 | −1.35944 | ||||||||
\(206\) | −2.26243e7 | −0.180318 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.90449e7 | −0.531998 | ||||||||
\(209\) | −4.39371e7 | −0.332904 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.39750e7 | −0.615406 | −0.307703 | − | 0.951483i | \(-0.599560\pi\) | ||||
−0.307703 | + | 0.951483i | \(0.599560\pi\) | |||||||
\(212\) | 9.05781e7 | 0.652901 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.43327e8 | −1.69724 | ||||||||
\(215\) | 1.52860e8 | 1.04896 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.03150e8 | 1.34961 | ||||||||
\(218\) | −8.28188e7 | −0.541416 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.33516e8 | 0.845384 | ||||||||
\(221\) | −4.44437e7 | −0.276973 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.55405e8 | 1.54227 | 0.771137 | − | 0.636669i | \(-0.219688\pi\) | ||||
0.771137 | + | 0.636669i | \(0.219688\pi\) | |||||||
\(224\) | 2.58854e8 | 1.53882 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.04166e8 | −1.75279 | ||||||||
\(227\) | −2.94977e8 | −1.67377 | −0.836887 | − | 0.547375i | \(-0.815627\pi\) | ||||
−0.836887 | + | 0.547375i | \(0.815627\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.95841e7 | 0.217819 | 0.108910 | − | 0.994052i | \(-0.465264\pi\) | ||||
0.108910 | + | 0.994052i | \(0.465264\pi\) | |||||||
\(230\) | 5.36447e8 | 2.90723 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.34473e7 | 0.123278 | ||||||||
\(233\) | 1.72426e7 | 0.0893009 | 0.0446505 | − | 0.999003i | \(-0.485783\pi\) | ||||
0.0446505 | + | 0.999003i | \(0.485783\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.30876e8 | 2.16578 | ||||||||
\(236\) | 1.57357e7 | 0.0779279 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.46357e8 | 1.18453 | ||||||||
\(239\) | −3.47868e6 | −0.0164824 | −0.00824121 | − | 0.999966i | \(-0.502623\pi\) | ||||
−0.00824121 | + | 0.999966i | \(0.502623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.24809e8 | 1.03456 | 0.517279 | − | 0.855817i | \(-0.326945\pi\) | ||||
0.517279 | + | 0.855817i | \(0.326945\pi\) | |||||||
\(242\) | 7.81198e7 | 0.354330 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.69337e7 | 0.294972 | ||||||||
\(245\) | −3.17507e8 | −1.37934 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.98883e7 | 0.126201 | ||||||||
\(248\) | 1.13404e8 | 0.472113 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.72321e8 | 0.697505 | ||||||||
\(251\) | −4.20064e8 | −1.67671 | −0.838354 | − | 0.545127i | \(-0.816481\pi\) | ||||
−0.838354 | + | 0.545127i | \(0.816481\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.36900e8 | 2.08436 | ||||||||
\(254\) | 1.78024e8 | 0.681650 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.43787e8 | 1.28070 | ||||||||
\(257\) | −1.99799e8 | −0.734221 | −0.367111 | − | 0.930177i | \(-0.619653\pi\) | ||||
−0.367111 | + | 0.930177i | \(0.619653\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.96325e8 | 2.49036 | ||||||||
\(260\) | −9.08245e7 | −0.320477 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.16775e8 | −0.401141 | ||||||||
\(263\) | −5.10505e8 | −1.73043 | −0.865216 | − | 0.501399i | \(-0.832819\pi\) | ||||
−0.865216 | + | 0.501399i | \(0.832819\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.12455e8 | −1.36150 | ||||||||
\(266\) | −1.65675e8 | −0.539723 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.37661e7 | −0.202357 | ||||||||
\(269\) | 6.12082e8 | 1.91724 | 0.958621 | − | 0.284686i | \(-0.0918893\pi\) | ||||
0.958621 | + | 0.284686i | \(0.0918893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.95076e8 | 0.595404 | 0.297702 | − | 0.954659i | \(-0.403780\pi\) | ||||
0.297702 | + | 0.954659i | \(0.403780\pi\) | |||||||
\(272\) | 2.65803e8 | 0.800882 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.02714e8 | −2.06372 | ||||||||
\(275\) | −2.17755e8 | −0.631400 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.11429e8 | −1.16310 | −0.581548 | − | 0.813512i | \(-0.697553\pi\) | ||||
−0.581548 | + | 0.813512i | \(0.697553\pi\) | |||||||
\(278\) | −3.75953e7 | −0.104949 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.37632e8 | −0.919157 | ||||||||
\(281\) | 1.45356e8 | 0.390805 | 0.195403 | − | 0.980723i | \(-0.437399\pi\) | ||||
0.195403 | + | 0.980723i | \(0.437399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.33769e8 | −1.92445 | −0.962226 | − | 0.272252i | \(-0.912232\pi\) | ||||
−0.962226 | + | 0.272252i | \(0.912232\pi\) | |||||||
\(284\) | −2.41764e8 | −0.626292 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.42764e8 | −0.613625 | ||||||||
\(287\) | −6.32837e8 | −1.58018 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.39243e8 | −0.583039 | ||||||||
\(290\) | 1.59207e8 | 0.383328 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.06635e8 | 0.485696 | ||||||||
\(293\) | 3.59570e8 | 0.835117 | 0.417558 | − | 0.908650i | \(-0.362886\pi\) | ||||
0.417558 | + | 0.908650i | \(0.362886\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.16538e7 | −0.162503 | ||||||||
\(296\) | 3.88707e8 | 0.871167 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.83202e8 | 0.619924 | ||||||||
\(299\) | −3.65228e8 | −0.790159 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.76880e8 | 1.21928 | ||||||||
\(302\) | 1.91364e8 | 0.399794 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.78752e8 | −0.364916 | ||||||||
\(305\) | −3.04788e8 | −0.615105 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.59711e8 | −0.512278 | −0.256139 | − | 0.966640i | \(-0.582450\pi\) | ||||
−0.256139 | + | 0.966640i | \(0.582450\pi\) | |||||||
\(308\) | 5.03878e8 | 0.982648 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.70010e8 | 1.46802 | ||||||||
\(311\) | −4.42793e8 | −0.834717 | −0.417359 | − | 0.908742i | \(-0.637044\pi\) | ||||
−0.417359 | + | 0.908742i | \(0.637044\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.37731e7 | 0.0806867 | 0.0403433 | − | 0.999186i | \(-0.487155\pi\) | ||||
0.0403433 | + | 0.999186i | \(0.487155\pi\) | |||||||
\(314\) | −4.24117e8 | −0.773094 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.31217e8 | 0.947038 | ||||||||
\(317\) | −1.74353e8 | −0.307413 | −0.153706 | − | 0.988117i | \(-0.549121\pi\) | ||||
−0.153706 | + | 0.988117i | \(0.549121\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.59342e8 | 0.274829 | ||||||||
\(320\) | 7.36761e7 | 0.125690 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.02451e9 | 3.37927 | ||||||||
\(323\) | −1.15061e8 | −0.189985 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.48128e8 | 0.239357 | ||||||||
\(326\) | −8.46741e8 | −1.35360 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.53266e8 | −0.552769 | ||||||||
\(329\) | 1.62609e9 | 2.51744 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.19111e8 | 0.635231 | 0.317615 | − | 0.948220i | \(-0.397118\pi\) | ||||
0.317615 | + | 0.948220i | \(0.397118\pi\) | |||||||
\(332\) | 2.40856e8 | 0.361221 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.48145e9 | −2.17558 | ||||||||
\(335\) | 2.90364e8 | 0.421975 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.81583e8 | −0.827765 | −0.413882 | − | 0.910330i | \(-0.635827\pi\) | ||||
−0.413882 | + | 0.910330i | \(0.635827\pi\) | |||||||
\(338\) | −7.32443e8 | −1.03173 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.49648e8 | 0.482453 | ||||||||
\(341\) | 7.70661e8 | 1.05250 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.13916e8 | −0.152425 | ||||||||
\(344\) | 3.22030e8 | 0.426522 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.07157e9 | −1.39076 | ||||||||
\(347\) | −6.12801e8 | −0.787347 | −0.393673 | − | 0.919250i | \(-0.628796\pi\) | ||||
−0.393673 | + | 0.919250i | \(0.628796\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.26220e8 | 0.662642 | 0.331321 | − | 0.943518i | \(-0.392506\pi\) | ||||
0.331321 | + | 0.943518i | \(0.392506\pi\) | |||||||
\(350\) | −8.21096e8 | −1.02366 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.81978e8 | 1.20006 | ||||||||
\(353\) | −7.42142e8 | −0.897999 | −0.448999 | − | 0.893532i | \(-0.648219\pi\) | ||||
−0.448999 | + | 0.893532i | \(0.648219\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.10089e9 | 1.30601 | ||||||||
\(356\) | 3.60248e7 | 0.0423181 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.99603e9 | −2.29920 | ||||||||
\(359\) | −4.68258e8 | −0.534139 | −0.267070 | − | 0.963677i | \(-0.586055\pi\) | ||||
−0.267070 | + | 0.963677i | \(0.586055\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.16493e8 | −0.913435 | ||||||||
\(362\) | 1.99813e8 | 0.221382 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.42764e8 | −0.372512 | ||||||||
\(365\) | −9.40933e8 | −1.01282 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.07678e8 | 0.430513 | 0.215257 | − | 0.976558i | \(-0.430941\pi\) | ||||
0.215257 | + | 0.976558i | \(0.430941\pi\) | |||||||
\(368\) | 2.18430e9 | 2.28479 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.63932e9 | 2.70885 | ||||||||
\(371\) | −1.55657e9 | −1.58256 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.76997e9 | 1.76598 | 0.882989 | − | 0.469393i | \(-0.155527\pi\) | ||||
0.882989 | + | 0.469393i | \(0.155527\pi\) | |||||||
\(374\) | 9.34570e8 | 0.923765 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.07726e8 | 0.880638 | ||||||||
\(377\) | −1.08393e8 | −0.104185 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.03436e8 | −0.191951 | −0.0959757 | − | 0.995384i | \(-0.530597\pi\) | ||||
−0.0959757 | + | 0.995384i | \(0.530597\pi\) | |||||||
\(380\) | −2.35137e8 | −0.219826 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.46395e8 | 0.501516 | ||||||||
\(383\) | 1.58998e9 | 1.44609 | 0.723044 | − | 0.690802i | \(-0.242742\pi\) | ||||
0.723044 | + | 0.690802i | \(0.242742\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.29445e9 | −2.04912 | ||||||||
\(386\) | −5.28184e8 | −0.467444 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.91244e8 | 0.687701 | ||||||||
\(389\) | 6.10709e8 | 0.526030 | 0.263015 | − | 0.964792i | \(-0.415283\pi\) | ||||
0.263015 | + | 0.964792i | \(0.415283\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.40602e9 | 1.18952 | ||||||||
\(392\) | −6.68892e8 | −0.560860 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.49767e9 | −1.23362 | ||||||||
\(395\) | −2.41894e9 | −1.97486 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.32027e8 | 0.105900 | 0.0529501 | − | 0.998597i | \(-0.483138\pi\) | ||||
0.0529501 | + | 0.998597i | \(0.483138\pi\) | |||||||
\(398\) | −1.77513e9 | −1.41136 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.85907e8 | −0.692115 | ||||||||
\(401\) | −6.34337e8 | −0.491263 | −0.245632 | − | 0.969363i | \(-0.578995\pi\) | ||||
−0.245632 | + | 0.969363i | \(0.578995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.24244e8 | −0.398993 | ||||||||
\(404\) | 1.04427e9 | 0.787916 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00835e8 | 0.445568 | ||||||||
\(407\) | 2.64155e9 | 1.94213 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.45727e8 | 0.683493 | 0.341746 | − | 0.939792i | \(-0.388982\pi\) | ||||
0.341746 | + | 0.939792i | \(0.388982\pi\) | |||||||
\(410\) | −2.39868e9 | −1.71881 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.21180e8 | −0.0853675 | ||||||||
\(413\) | −2.70415e8 | −0.188889 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.09676e9 | −0.753255 | ||||||||
\(416\) | −6.67992e8 | −0.454930 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.28496e8 | −0.420907 | ||||||||
\(419\) | 1.99014e9 | 1.32170 | 0.660852 | − | 0.750517i | \(-0.270195\pi\) | ||||
0.660852 | + | 0.750517i | \(0.270195\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.39417e8 | 0.156375 | 0.0781875 | − | 0.996939i | \(-0.475087\pi\) | ||||
0.0781875 | + | 0.996939i | \(0.475087\pi\) | |||||||
\(422\) | −1.20122e9 | −0.778087 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.68918e8 | −0.553603 | ||||||||
\(425\) | −5.70252e8 | −0.360334 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.15025e9 | −0.714979 | ||||||||
\(428\) | −1.30331e9 | −0.803518 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.18658e9 | 1.32625 | ||||||||
\(431\) | 1.41644e9 | 0.852171 | 0.426086 | − | 0.904683i | \(-0.359892\pi\) | ||||
0.426086 | + | 0.904683i | \(0.359892\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.49096e9 | 1.47455 | 0.737273 | − | 0.675595i | \(-0.236113\pi\) | ||||
0.737273 | + | 0.675595i | \(0.236113\pi\) | |||||||
\(434\) | 2.90595e9 | 1.70638 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.43595e8 | −0.256321 | ||||||||
\(437\) | −9.45545e8 | −0.541997 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.29699e9 | 0.731661 | 0.365831 | − | 0.930681i | \(-0.380785\pi\) | ||||
0.365831 | + | 0.930681i | \(0.380785\pi\) | |||||||
\(440\) | −1.28082e9 | −0.716811 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.35743e8 | −0.350190 | ||||||||
\(443\) | 4.26015e8 | 0.232815 | 0.116408 | − | 0.993202i | \(-0.462862\pi\) | ||||
0.116408 | + | 0.993202i | \(0.462862\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.64042e8 | −0.0882460 | ||||||||
\(446\) | 3.65343e9 | 1.94997 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.78047e8 | 0.146098 | ||||||||
\(449\) | −3.29234e9 | −1.71649 | −0.858247 | − | 0.513236i | \(-0.828446\pi\) | ||||
−0.858247 | + | 0.513236i | \(0.828446\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.40070e9 | −1.23231 | ||||||||
\(452\) | −1.62918e9 | −0.829819 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.21948e9 | −2.11623 | ||||||||
\(455\) | 1.56081e9 | 0.776800 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.28524e8 | −0.210024 | −0.105012 | − | 0.994471i | \(-0.533488\pi\) | ||||
−0.105012 | + | 0.994471i | \(0.533488\pi\) | |||||||
\(458\) | 5.66229e8 | 0.275399 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.87332e9 | 1.37636 | ||||||||
\(461\) | 2.18183e9 | 1.03721 | 0.518605 | − | 0.855014i | \(-0.326452\pi\) | ||||
0.518605 | + | 0.855014i | \(0.326452\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.49857e9 | −1.63816 | −0.819082 | − | 0.573677i | \(-0.805517\pi\) | ||||
−0.819082 | + | 0.573677i | \(0.805517\pi\) | |||||||
\(464\) | 6.48260e8 | 0.301256 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.46646e8 | 0.112907 | ||||||||
\(467\) | −5.99769e8 | −0.272505 | −0.136253 | − | 0.990674i | \(-0.543506\pi\) | ||||
−0.136253 | + | 0.990674i | \(0.543506\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.09581e9 | 0.490490 | ||||||||
\(470\) | 6.16345e9 | 2.73830 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.50953e8 | −0.0660761 | ||||||||
\(473\) | 2.18843e9 | 0.950863 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.83493e8 | 0.164184 | ||||||||
\(476\) | 1.31954e9 | 0.560788 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.97606e7 | −0.0208395 | ||||||||
\(479\) | −1.04242e9 | −0.433381 | −0.216691 | − | 0.976240i | \(-0.569526\pi\) | ||||
−0.216691 | + | 0.976240i | \(0.569526\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.79692e9 | −0.736242 | ||||||||
\(482\) | 3.21578e9 | 1.30804 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.18426e8 | 0.167749 | ||||||||
\(485\) | −3.60300e9 | −1.43406 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.49609e9 | 1.76394 | 0.881970 | − | 0.471305i | \(-0.156217\pi\) | ||||
0.881970 | + | 0.471305i | \(0.156217\pi\) | |||||||
\(488\) | −6.42097e8 | −0.250110 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.54177e9 | −1.74397 | ||||||||
\(491\) | 3.34941e9 | 1.27698 | 0.638489 | − | 0.769631i | \(-0.279560\pi\) | ||||
0.638489 | + | 0.769631i | \(0.279560\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.17280e8 | 0.156842 | ||||||||
\(494\) | 4.27536e8 | 0.159562 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.13533e9 | 1.15371 | ||||||||
\(497\) | 4.15467e9 | 1.51806 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.53248e9 | −0.912419 | −0.456209 | − | 0.889872i | \(-0.650793\pi\) | ||||
−0.456209 | + | 0.889872i | \(0.650793\pi\) | |||||||
\(500\) | 9.22986e8 | 0.330217 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.00879e9 | −2.11994 | ||||||||
\(503\) | 2.14316e9 | 0.750874 | 0.375437 | − | 0.926848i | \(-0.377493\pi\) | ||||
0.375437 | + | 0.926848i | \(0.377493\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.75520e9 | −1.64304 | ||||||||
\(506\) | 7.68007e9 | 2.63535 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.53536e8 | 0.322711 | ||||||||
\(509\) | −3.85176e9 | −1.29463 | −0.647316 | − | 0.762222i | \(-0.724109\pi\) | ||||
−0.647316 | + | 0.762222i | \(0.724109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.55100e9 | −1.17727 | ||||||||
\(512\) | 2.08327e9 | 0.685962 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.85801e9 | −0.928311 | ||||||||
\(515\) | 5.51806e8 | 0.178017 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.16866e9 | 1.96324 | ||||||||
\(518\) | 9.96056e9 | 3.14869 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.71283e8 | 0.271736 | ||||||||
\(521\) | 4.67938e9 | 1.44963 | 0.724814 | − | 0.688945i | \(-0.241926\pi\) | ||||
0.724814 | + | 0.688945i | \(0.241926\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.37502e9 | 1.03162 | 0.515810 | − | 0.856703i | \(-0.327491\pi\) | ||||
0.515810 | + | 0.856703i | \(0.327491\pi\) | |||||||
\(524\) | −6.25474e8 | −0.189911 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.30250e9 | −2.18787 | ||||||||
\(527\) | 2.01819e9 | 0.600654 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.14951e9 | 2.39352 | ||||||||
\(530\) | −5.89995e9 | −1.72140 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.87389e8 | −0.255519 | ||||||||
\(533\) | 1.63308e9 | 0.467157 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.93475e9 | 1.67558 | ||||||||
\(536\) | 6.11710e8 | 0.171581 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.75551e9 | 2.42406 | ||||||||
\(539\) | −4.54561e9 | −1.25035 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.20625e9 | 0.870576 | 0.435288 | − | 0.900291i | \(-0.356647\pi\) | ||||
0.435288 | + | 0.900291i | \(0.356647\pi\) | |||||||
\(542\) | 2.79046e9 | 0.752798 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.57158e9 | 0.684862 | ||||||||
\(545\) | 2.01995e9 | 0.534506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.82907e8 | −0.126156 | −0.0630779 | − | 0.998009i | \(-0.520092\pi\) | ||||
−0.0630779 | + | 0.998009i | \(0.520092\pi\) | |||||||
\(548\) | −3.76388e9 | −0.977022 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.11487e9 | −0.798309 | ||||||||
\(551\) | −2.80620e8 | −0.0714641 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.12889e9 | −2.29551 | ||||||||
\(554\) | −5.88527e9 | −1.47056 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.01368e8 | −0.0496854 | ||||||||
\(557\) | 3.29285e9 | 0.807380 | 0.403690 | − | 0.914896i | \(-0.367727\pi\) | ||||
0.403690 | + | 0.914896i | \(0.367727\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.48868e9 | −0.360463 | ||||||||
\(560\) | −9.33466e9 | −2.24616 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.07924e9 | 0.494114 | ||||||||
\(563\) | −1.67347e9 | −0.395220 | −0.197610 | − | 0.980281i | \(-0.563318\pi\) | ||||
−0.197610 | + | 0.980281i | \(0.563318\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.41859e9 | 1.73042 | ||||||||
\(566\) | −1.04962e10 | −2.43318 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.31925e9 | 0.531041 | ||||||||
\(569\) | −5.59667e9 | −1.27361 | −0.636805 | − | 0.771025i | \(-0.719745\pi\) | ||||
−0.636805 | + | 0.771025i | \(0.719745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.50267e9 | −1.46172 | −0.730862 | − | 0.682525i | \(-0.760882\pi\) | ||||
−0.730862 | + | 0.682525i | \(0.760882\pi\) | |||||||
\(572\) | −1.30029e9 | −0.290506 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.05240e9 | −1.99789 | ||||||||
\(575\) | −4.68619e9 | −1.02797 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.50802e9 | −0.976945 | −0.488473 | − | 0.872579i | \(-0.662446\pi\) | ||||
−0.488473 | + | 0.872579i | \(0.662446\pi\) | |||||||
\(578\) | −3.42225e9 | −0.737164 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.52748e8 | 0.181477 | ||||||||
\(581\) | −4.13907e9 | −0.875560 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.90494e9 | −1.23417 | ||||||||
\(584\) | −1.98226e9 | −0.411828 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.14346e9 | 1.05588 | ||||||||
\(587\) | −6.96930e9 | −1.42218 | −0.711092 | − | 0.703099i | \(-0.751799\pi\) | ||||
−0.711092 | + | 0.703099i | \(0.751799\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.35723e9 | −0.273683 | ||||||||
\(590\) | −1.02497e9 | −0.205461 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.07468e10 | 2.12888 | ||||||||
\(593\) | −1.72102e9 | −0.338917 | −0.169459 | − | 0.985537i | \(-0.554202\pi\) | ||||
−0.169459 | + | 0.985537i | \(0.554202\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00865e9 | −1.16941 | ||||||||
\(596\) | 1.51689e9 | 0.293489 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.22438e9 | −0.999036 | ||||||||
\(599\) | −4.56819e9 | −0.868460 | −0.434230 | − | 0.900802i | \(-0.642979\pi\) | ||||
−0.434230 | + | 0.900802i | \(0.642979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.34532e9 | −0.440698 | −0.220349 | − | 0.975421i | \(-0.570720\pi\) | ||||
−0.220349 | + | 0.975421i | \(0.570720\pi\) | |||||||
\(602\) | 8.25197e9 | 1.54159 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.02499e9 | 0.189273 | ||||||||
\(605\) | −1.90534e9 | −0.349807 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.67032e9 | 0.666107 | 0.333053 | − | 0.942908i | \(-0.391921\pi\) | ||||
0.333053 | + | 0.942908i | \(0.391921\pi\) | |||||||
\(608\) | −1.72938e9 | −0.312052 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.35984e9 | −0.777706 | ||||||||
\(611\) | −4.19624e9 | −0.744246 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.62973e9 | 0.636447 | 0.318223 | − | 0.948016i | \(-0.396914\pi\) | ||||
0.318223 | + | 0.948016i | \(0.396914\pi\) | |||||||
\(614\) | −3.71502e9 | −0.647697 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.83372e9 | −0.833199 | ||||||||
\(617\) | −4.89208e9 | −0.838486 | −0.419243 | − | 0.907874i | \(-0.637704\pi\) | ||||
−0.419243 | + | 0.907874i | \(0.637704\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.57865e9 | −1.45379 | −0.726895 | − | 0.686749i | \(-0.759037\pi\) | ||||
−0.726895 | + | 0.686749i | \(0.759037\pi\) | |||||||
\(620\) | 4.12434e9 | 0.694997 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.33392e9 | −1.05537 | ||||||||
\(623\) | −6.19080e8 | −0.102574 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.60884e9 | −1.24663 | ||||||||
\(626\) | 6.26150e8 | 0.102016 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.27166e9 | −0.366003 | ||||||||
\(629\) | 6.91761e9 | 1.10836 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.81549e9 | 0.921475 | 0.460737 | − | 0.887537i | \(-0.347585\pi\) | ||||
0.460737 | + | 0.887537i | \(0.347585\pi\) | |||||||
\(632\) | −5.09598e9 | −0.803005 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.49403e9 | −0.388677 | ||||||||
\(635\) | −4.34201e9 | −0.672950 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.09216e9 | 0.473995 | ||||||||
\(638\) | 2.27930e9 | 0.347479 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.72567e9 | −1.16495 | ||||||||
\(641\) | 1.97168e6 | 0.000295688 0 | 0.000147844 | − | 1.00000i | \(-0.499953\pi\) | ||||
0.000147844 | 1.00000i | \(0.499953\pi\) | ||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.68675e9 | −0.843580 | −0.421790 | − | 0.906694i | \(-0.638598\pi\) | ||||
−0.421790 | + | 0.906694i | \(0.638598\pi\) | |||||||
\(644\) | 1.08437e10 | 1.59984 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.64589e9 | −0.240208 | ||||||||
\(647\) | −8.00900e9 | −1.16256 | −0.581278 | − | 0.813705i | \(-0.697447\pi\) | ||||
−0.581278 | + | 0.813705i | \(0.697447\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.02583e9 | −0.147306 | ||||||||
\(650\) | 2.11890e9 | 0.302631 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.53532e9 | −0.640828 | ||||||||
\(653\) | −4.57134e9 | −0.642462 | −0.321231 | − | 0.947001i | \(-0.604097\pi\) | ||||
−0.321231 | + | 0.947001i | \(0.604097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.84815e9 | 0.396021 | ||||||||
\(656\) | −9.76692e9 | −1.35081 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.32604e10 | 3.18292 | ||||||||
\(659\) | −1.31699e10 | −1.79260 | −0.896298 | − | 0.443452i | \(-0.853754\pi\) | ||||
−0.896298 | + | 0.443452i | \(0.853754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.04155e9 | −0.948338 | −0.474169 | − | 0.880434i | \(-0.657251\pi\) | ||||
−0.474169 | + | 0.880434i | \(0.657251\pi\) | |||||||
\(662\) | 5.99517e9 | 0.803153 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.31053e9 | −0.306284 | ||||||||
\(665\) | 4.04080e9 | 0.532834 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.42911e9 | 0.447446 | ||||||||
\(668\) | −7.93497e9 | −1.02998 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.15351e9 | 0.533523 | ||||||||
\(671\) | −4.36352e9 | −0.557581 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.33165e8 | 0.105361 | 0.0526803 | − | 0.998611i | \(-0.483224\pi\) | ||||
0.0526803 | + | 0.998611i | \(0.483224\pi\) | |||||||
\(674\) | −8.31923e9 | −1.04658 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.92312e9 | −0.488448 | ||||||||
\(677\) | −1.49936e10 | −1.85715 | −0.928573 | − | 0.371150i | \(-0.878964\pi\) | ||||
−0.928573 | + | 0.371150i | \(0.878964\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.35974e10 | −1.66691 | ||||||||
\(680\) | −3.35419e9 | −0.409078 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.10239e10 | 1.33073 | ||||||||
\(683\) | −6.61866e9 | −0.794873 | −0.397436 | − | 0.917630i | \(-0.630100\pi\) | ||||
−0.397436 | + | 0.917630i | \(0.630100\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.71392e10 | 2.03738 | ||||||||
\(686\) | −1.62951e9 | −0.192718 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.90331e9 | 1.04230 | ||||||||
\(689\) | 4.01684e9 | 0.467862 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.24311e9 | 0.835125 | 0.417563 | − | 0.908648i | \(-0.362884\pi\) | ||||
0.417563 | + | 0.908648i | \(0.362884\pi\) | |||||||
\(692\) | −5.73954e9 | −0.658424 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.76579e9 | −0.995480 | ||||||||
\(695\) | 9.16947e8 | 0.103609 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.28689e9 | −0.703269 | ||||||||
\(698\) | 7.52730e9 | 0.837810 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.39796e9 | −0.484628 | ||||||||
\(701\) | 2.33354e9 | 0.255860 | 0.127930 | − | 0.991783i | \(-0.459167\pi\) | ||||
0.127930 | + | 0.991783i | \(0.459167\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.65208e9 | −0.505014 | ||||||||
\(704\) | 1.05479e9 | 0.113936 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.06160e10 | −1.13538 | ||||||||
\(707\) | −1.79457e10 | −1.90982 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.23075e9 | 0.445816 | 0.222908 | − | 0.974839i | \(-0.428445\pi\) | ||||
0.222908 | + | 0.974839i | \(0.428445\pi\) | |||||||
\(710\) | 1.57477e10 | 1.65125 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.45587e8 | −0.0358820 | ||||||||
\(713\) | 1.65850e10 | 1.71357 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.92100e9 | 0.605793 | ||||||||
\(716\) | −1.06912e10 | −1.08850 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.69818e9 | −0.675338 | ||||||||
\(719\) | 1.25609e10 | 1.26029 | 0.630143 | − | 0.776479i | \(-0.282996\pi\) | ||||
0.630143 | + | 0.776479i | \(0.282996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.08247e9 | 0.206921 | ||||||||
\(722\) | −1.16795e10 | −1.15490 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.07024e9 | 0.104808 | ||||||||
\(725\) | −1.39077e9 | −0.135542 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.77361e9 | 0.943375 | 0.471688 | − | 0.881766i | \(-0.343645\pi\) | ||||
0.471688 | + | 0.881766i | \(0.343645\pi\) | |||||||
\(728\) | 3.28815e9 | 0.315858 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.34595e10 | −1.28056 | ||||||||
\(731\) | 5.73099e9 | 0.542649 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.89324e9 | −0.458915 | −0.229458 | − | 0.973319i | \(-0.573695\pi\) | ||||
−0.229458 | + | 0.973319i | \(0.573695\pi\) | |||||||
\(734\) | 5.83162e9 | 0.544318 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.11326e10 | 1.95380 | ||||||||
\(737\) | 4.15702e9 | 0.382512 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.16838e10 | −1.06495 | −0.532473 | − | 0.846447i | \(-0.678737\pi\) | ||||
−0.532473 | + | 0.846447i | \(0.678737\pi\) | |||||||
\(740\) | 1.41367e10 | 1.28244 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.22659e10 | −2.00091 | ||||||||
\(743\) | 2.02352e9 | 0.180987 | 0.0904934 | − | 0.995897i | \(-0.471156\pi\) | ||||
0.0904934 | + | 0.995897i | \(0.471156\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.90728e9 | −0.612012 | ||||||||
\(746\) | 2.53185e10 | 2.23281 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.00575e9 | 0.437335 | ||||||||
\(749\) | 2.23972e10 | 1.94764 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.88364e8 | −0.0506881 | −0.0253441 | − | 0.999679i | \(-0.508068\pi\) | ||||
−0.0253441 | + | 0.999679i | \(0.508068\pi\) | |||||||
\(752\) | 2.50963e10 | 2.15203 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.55050e9 | −0.131726 | ||||||||
\(755\) | −4.66736e9 | −0.394691 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.84565e10 | −1.54637 | −0.773185 | − | 0.634181i | \(-0.781337\pi\) | ||||
−0.773185 | + | 0.634181i | \(0.781337\pi\) | |||||||
\(758\) | −2.91005e9 | −0.242693 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.25568e9 | 0.186393 | ||||||||
\(761\) | −1.56129e10 | −1.28421 | −0.642105 | − | 0.766617i | \(-0.721939\pi\) | ||||
−0.642105 | + | 0.766617i | \(0.721939\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.62311e9 | 0.621293 | ||||||||
\(764\) | 2.92660e9 | 0.237431 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.27438e10 | 1.82836 | ||||||||
\(767\) | 6.97826e8 | 0.0558423 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.12983e10 | 1.68889 | 0.844446 | − | 0.535641i | \(-0.179930\pi\) | ||||
0.844446 | + | 0.535641i | \(0.179930\pi\) | |||||||
\(770\) | −3.28209e10 | −2.59080 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.82906e9 | −0.221300 | ||||||||
\(773\) | −1.58105e10 | −1.23116 | −0.615582 | − | 0.788073i | \(-0.711079\pi\) | ||||
−0.615582 | + | 0.788073i | \(0.711079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.72651e9 | −0.519079 | ||||||||
\(776\) | −7.59043e9 | −0.583110 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.73587e9 | 0.665086 | ||||||||
\(779\) | 4.22792e9 | 0.320439 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.57610e10 | 1.18387 | ||||||||
\(782\) | 2.01124e10 | 1.50397 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.84932e10 | −1.37058 | ||||||||
\(785\) | 1.03442e10 | 0.763227 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.69394e9 | 0.197005 | 0.0985024 | − | 0.995137i | \(-0.468595\pi\) | ||||
0.0985024 | + | 0.995137i | \(0.468595\pi\) | |||||||
\(788\) | −8.02186e9 | −0.584027 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.46017e10 | −2.49691 | ||||||||
\(791\) | 2.79971e10 | 2.01139 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.96829e9 | 0.211374 | ||||||||
\(794\) | 1.88858e9 | 0.133895 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.50795e9 | −0.668176 | ||||||||
\(797\) | −5.54182e9 | −0.387747 | −0.193873 | − | 0.981027i | \(-0.562105\pi\) | ||||
−0.193873 | + | 0.981027i | \(0.562105\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.61543e10 | 1.12040 | ||||||||
\(800\) | −8.57093e9 | −0.591852 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.07385e9 | −0.621128 | ||||||||
\(803\) | −1.34709e10 | −0.918106 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.93776e10 | −3.33614 | ||||||||
\(806\) | −7.49903e9 | −0.504466 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.00178e10 | −0.668084 | ||||||||
\(809\) | −1.56002e10 | −1.03589 | −0.517943 | − | 0.855415i | \(-0.673302\pi\) | ||||
−0.517943 | + | 0.855415i | \(0.673302\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.79846e9 | −0.513377 | −0.256688 | − | 0.966494i | \(-0.582631\pi\) | ||||
−0.256688 | + | 0.966494i | \(0.582631\pi\) | |||||||
\(812\) | 3.21820e9 | 0.210944 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.77859e10 | 2.45553 | ||||||||
\(815\) | 2.06520e10 | 1.33632 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.85408e9 | −0.247254 | ||||||||
\(818\) | 1.35281e10 | 0.864173 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.28478e10 | −0.813731 | ||||||||
\(821\) | −5.49348e9 | −0.346455 | −0.173227 | − | 0.984882i | \(-0.555420\pi\) | ||||
−0.173227 | + | 0.984882i | \(0.555420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.49423e10 | 1.55969 | 0.779843 | − | 0.625976i | \(-0.215299\pi\) | ||||
0.779843 | + | 0.625976i | \(0.215299\pi\) | |||||||
\(824\) | 1.16249e9 | 0.0723841 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.86814e9 | −0.238821 | ||||||||
\(827\) | 3.09149e10 | 1.90063 | 0.950317 | − | 0.311285i | \(-0.100759\pi\) | ||||
0.950317 | + | 0.311285i | \(0.100759\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.17903e8 | −0.0437648 | −0.0218824 | − | 0.999761i | \(-0.506966\pi\) | ||||
−0.0218824 | + | 0.999761i | \(0.506966\pi\) | |||||||
\(830\) | −1.56885e10 | −0.952376 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.17521e8 | −0.0431920 | ||||||||
\(833\) | −1.19039e10 | −0.713563 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.61326e10 | 2.14781 | ||||||||
\(836\) | −3.36636e9 | −0.199268 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.84678e10 | 1.67109 | ||||||||
\(839\) | 1.00495e10 | 0.587460 | 0.293730 | − | 0.955888i | \(-0.405103\pi\) | ||||
0.293730 | + | 0.955888i | \(0.405103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.62322e10 | −0.941003 | ||||||||
\(842\) | 3.42473e9 | 0.197713 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.43397e9 | −0.368367 | ||||||||
\(845\) | 1.78643e10 | 1.01856 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.19059e9 | −0.406605 | ||||||||
\(848\) | −2.40234e10 | −1.35285 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.15714e9 | −0.455588 | ||||||||
\(851\) | 5.68473e10 | 3.16196 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.41016e9 | 0.408795 | 0.204398 | − | 0.978888i | \(-0.434476\pi\) | ||||
0.204398 | + | 0.978888i | \(0.434476\pi\) | |||||||
\(854\) | −1.64536e10 | −0.903982 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.25027e10 | 0.681313 | ||||||||
\(857\) | −1.81207e10 | −0.983429 | −0.491714 | − | 0.870757i | \(-0.663630\pi\) | ||||
−0.491714 | + | 0.870757i | \(0.663630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.04208e10 | 0.560953 | 0.280477 | − | 0.959861i | \(-0.409508\pi\) | ||||
0.280477 | + | 0.959861i | \(0.409508\pi\) | |||||||
\(860\) | 1.17118e10 | 0.627882 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.02614e10 | 1.07744 | ||||||||
\(863\) | 2.49924e10 | 1.32364 | 0.661821 | − | 0.749662i | \(-0.269784\pi\) | ||||
0.661821 | + | 0.749662i | \(0.269784\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.61355e10 | 1.37301 | ||||||||
\(866\) | 3.56318e10 | 1.86434 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.55649e10 | 0.807843 | ||||||||
\(869\) | −3.46309e10 | −1.79017 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82782e9 | −0.145007 | ||||||||
\(872\) | 4.25542e9 | 0.217337 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.35255e10 | −0.685273 | ||||||||
\(875\) | −1.58614e10 | −0.800410 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.00470e10 | −0.502964 | −0.251482 | − | 0.967862i | \(-0.580918\pi\) | ||||
−0.251482 | + | 0.967862i | \(0.580918\pi\) | |||||||
\(878\) | 1.85527e10 | 0.925075 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.54115e10 | −1.75168 | ||||||||
\(881\) | 3.06184e10 | 1.50858 | 0.754288 | − | 0.656544i | \(-0.227982\pi\) | ||||
0.754288 | + | 0.656544i | \(0.227982\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.86608e9 | 0.286738 | 0.143369 | − | 0.989669i | \(-0.454206\pi\) | ||||
0.143369 | + | 0.989669i | \(0.454206\pi\) | |||||||
\(884\) | −3.40517e9 | −0.165789 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.09391e9 | 0.294359 | ||||||||
\(887\) | −1.17203e9 | −0.0563905 | −0.0281953 | − | 0.999602i | \(-0.508976\pi\) | ||||
−0.0281953 | + | 0.999602i | \(0.508976\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.63864e10 | −0.782217 | ||||||||
\(890\) | −2.34653e9 | −0.111574 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.95685e10 | 0.923168 | ||||||||
\(893\) | −1.08637e10 | −0.510504 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.86832e10 | 2.26986 | ||||||||
\(896\) | −2.91560e10 | −1.35410 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.70952e10 | −2.17025 | ||||||||
\(899\) | 4.92210e9 | 0.225939 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.54637e10 | −0.704330 | ||||||||
\(902\) | −3.43408e10 | −1.55807 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.56287e10 | 0.703614 | ||||||||
\(905\) | −4.87342e9 | −0.218557 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.61777e10 | 0.719932 | 0.359966 | − | 0.932965i | \(-0.382788\pi\) | ||||
0.359966 | + | 0.932965i | \(0.382788\pi\) | |||||||
\(908\) | −2.26004e10 | −1.00188 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.23265e10 | 0.982145 | ||||||||
\(911\) | 1.77685e10 | 0.778637 | 0.389319 | − | 0.921103i | \(-0.372710\pi\) | ||||
0.389319 | + | 0.921103i | \(0.372710\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.57018e10 | −0.682812 | ||||||||
\(914\) | −6.12981e9 | −0.265543 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.03284e9 | 0.130381 | ||||||||
\(917\) | 1.07487e10 | 0.460322 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.24473e10 | 0.954024 | 0.477012 | − | 0.878897i | \(-0.341720\pi\) | ||||
0.477012 | + | 0.878897i | \(0.341720\pi\) | |||||||
\(920\) | −2.75639e10 | −1.16703 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.12098e10 | 1.31139 | ||||||||
\(923\) | −1.07214e10 | −0.448794 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.30560e10 | −0.957830 | ||||||||
\(926\) | −5.00452e10 | −2.07121 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.27175e9 | 0.257615 | ||||||||
\(929\) | 2.97565e10 | 1.21766 | 0.608831 | − | 0.793300i | \(-0.291639\pi\) | ||||
0.608831 | + | 0.793300i | \(0.291639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00535e9 | 0.325130 | ||||||||
\(932\) | 1.32109e9 | 0.0534534 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.57937e9 | −0.344541 | ||||||||
\(935\) | −2.27941e10 | −0.911974 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.60896e9 | 0.103605 | 0.0518023 | − | 0.998657i | \(-0.483503\pi\) | ||||
0.0518023 | + | 0.998657i | \(0.483503\pi\) | |||||||
\(938\) | 1.56750e10 | 0.620151 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.30127e10 | 1.29639 | ||||||||
\(941\) | −3.46382e10 | −1.35516 | −0.677582 | − | 0.735447i | \(-0.736972\pi\) | ||||
−0.677582 | + | 0.735447i | \(0.736972\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.16642e10 | −2.00631 | ||||||||
\(944\) | −4.17346e9 | −0.161471 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.13043e10 | 1.20222 | ||||||||
\(947\) | 4.81487e10 | 1.84230 | 0.921149 | − | 0.389209i | \(-0.127252\pi\) | ||||
0.921149 | + | 0.389209i | \(0.127252\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.16362e9 | 0.348045 | ||||||||
\(950\) | 5.48566e9 | 0.207585 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.26584e10 | −0.475499 | ||||||||
\(953\) | 1.99375e9 | 0.0746182 | 0.0373091 | − | 0.999304i | \(-0.488121\pi\) | ||||
0.0373091 | + | 0.999304i | \(0.488121\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.33266e10 | −0.495115 | ||||||||
\(956\) | −2.66528e8 | −0.00986598 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.49113e10 | −0.547945 | ||||||||
\(959\) | 6.46818e10 | 2.36819 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.70674e9 | −0.134729 | ||||||||
\(962\) | −2.57039e10 | −0.930866 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.72244e10 | 0.619261 | ||||||||
\(965\) | 1.28824e10 | 0.461478 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.83920e9 | −0.278791 | −0.139396 | − | 0.990237i | \(-0.544516\pi\) | ||||
−0.139396 | + | 0.990237i | \(0.544516\pi\) | |||||||
\(968\) | −4.01398e9 | −0.142237 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.15390e10 | −1.81315 | ||||||||
\(971\) | 4.89013e10 | 1.71417 | 0.857084 | − | 0.515177i | \(-0.172274\pi\) | ||||
0.857084 | + | 0.515177i | \(0.172274\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.46048e9 | 0.120432 | ||||||||
\(974\) | 6.43142e10 | 2.23023 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.77524e10 | −0.611198 | ||||||||
\(977\) | 2.82603e10 | 0.969494 | 0.484747 | − | 0.874654i | \(-0.338912\pi\) | ||||
0.484747 | + | 0.874654i | \(0.338912\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.34852e9 | −0.0799934 | ||||||||
\(980\) | −2.43267e10 | −0.825642 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.79115e10 | 1.61454 | ||||||||
\(983\) | −4.62408e10 | −1.55270 | −0.776351 | − | 0.630301i | \(-0.782932\pi\) | ||||
−0.776351 | + | 0.630301i | \(0.782932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.65282e10 | 1.21787 | ||||||||
\(986\) | 5.96897e9 | 0.198303 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.28997e9 | 0.0755407 | ||||||||
\(989\) | 4.70959e10 | 1.54809 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.15771e10 | 0.377870 | 0.188935 | − | 0.981990i | \(-0.439497\pi\) | ||||
0.188935 | + | 0.981990i | \(0.439497\pi\) | |||||||
\(992\) | 3.03335e10 | 0.986578 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.94304e10 | 1.91936 | ||||||||
\(995\) | 4.32953e10 | 1.39335 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.71011e9 | 0.150521 | 0.0752607 | − | 0.997164i | \(-0.476021\pi\) | ||||
0.0752607 | + | 0.997164i | \(0.476021\pi\) | |||||||
\(998\) | −3.62258e10 | −1.15361 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 531.8.a.c.1.15 | 17 | ||
3.2 | odd | 2 | 177.8.a.c.1.3 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.c.1.3 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.c.1.15 | 17 | 1.1 | even | 1 | trivial |