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: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Root | \(-16.0158\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 15.0158 | 1.32723 | 0.663613 | − | 0.748076i | \(-0.269022\pi\) | ||||
0.663613 | + | 0.748076i | \(0.269022\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 97.4757 | 0.761529 | ||||||||
\(5\) | −6.55078 | −0.0234368 | −0.0117184 | − | 0.999931i | \(-0.503730\pi\) | ||||
−0.0117184 | + | 0.999931i | \(0.503730\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1466.16 | 1.61561 | 0.807807 | − | 0.589448i | \(-0.200655\pi\) | ||||
0.807807 | + | 0.589448i | \(0.200655\pi\) | |||||||
\(8\) | −458.348 | −0.316505 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −98.3656 | −0.0311059 | ||||||||
\(11\) | −4599.84 | −1.04200 | −0.521000 | − | 0.853556i | \(-0.674441\pi\) | ||||
−0.521000 | + | 0.853556i | \(0.674441\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15226.3 | 1.92217 | 0.961087 | − | 0.276246i | \(-0.0890903\pi\) | ||||
0.961087 | + | 0.276246i | \(0.0890903\pi\) | |||||||
\(14\) | 22015.6 | 2.14428 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19359.4 | −1.18160 | ||||||||
\(17\) | −38992.1 | −1.92489 | −0.962444 | − | 0.271481i | \(-0.912487\pi\) | ||||
−0.962444 | + | 0.271481i | \(0.912487\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −499.547 | −0.0167085 | −0.00835427 | − | 0.999965i | \(-0.502659\pi\) | ||||
−0.00835427 | + | 0.999965i | \(0.502659\pi\) | |||||||
\(20\) | −638.542 | −0.0178478 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −69070.4 | −1.38297 | ||||||||
\(23\) | −58259.9 | −0.998441 | −0.499220 | − | 0.866475i | \(-0.666380\pi\) | ||||
−0.499220 | + | 0.866475i | \(0.666380\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −78082.1 | −0.999451 | ||||||||
\(26\) | 228636. | 2.55116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 142915. | 1.23034 | ||||||||
\(29\) | −211255. | −1.60848 | −0.804238 | − | 0.594307i | \(-0.797426\pi\) | ||||
−0.804238 | + | 0.594307i | \(0.797426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 61846.8 | 0.372865 | 0.186432 | − | 0.982468i | \(-0.440307\pi\) | ||||
0.186432 | + | 0.982468i | \(0.440307\pi\) | |||||||
\(32\) | −232029. | −1.25175 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −585500. | −2.55476 | ||||||||
\(35\) | −9604.48 | −0.0378648 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −62940.4 | −0.204279 | −0.102139 | − | 0.994770i | \(-0.532569\pi\) | ||||
−0.102139 | + | 0.994770i | \(0.532569\pi\) | |||||||
\(38\) | −7501.12 | −0.0221760 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3002.54 | 0.00741785 | ||||||||
\(41\) | 619876. | 1.40463 | 0.702314 | − | 0.711867i | \(-0.252150\pi\) | ||||
0.702314 | + | 0.711867i | \(0.252150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −356192. | −0.683194 | −0.341597 | − | 0.939846i | \(-0.610968\pi\) | ||||
−0.341597 | + | 0.939846i | \(0.610968\pi\) | |||||||
\(44\) | −448372. | −0.793514 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −874822. | −1.32516 | ||||||||
\(47\) | 953515. | 1.33963 | 0.669815 | − | 0.742528i | \(-0.266373\pi\) | ||||
0.669815 | + | 0.742528i | \(0.266373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.32607e6 | 1.61021 | ||||||||
\(50\) | −1.17247e6 | −1.32650 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.48419e6 | 1.46379 | ||||||||
\(53\) | 1.97760e6 | 1.82462 | 0.912310 | − | 0.409501i | \(-0.134297\pi\) | ||||
0.912310 | + | 0.409501i | \(0.134297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30132.5 | 0.0244211 | ||||||||
\(56\) | −672010. | −0.511349 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.17218e6 | −2.13481 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.98506e6 | −1.68383 | −0.841917 | − | 0.539607i | \(-0.818573\pi\) | ||||
−0.841917 | + | 0.539607i | \(0.818573\pi\) | |||||||
\(62\) | 928683. | 0.494876 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00611e6 | −0.479751 | ||||||||
\(65\) | −99744.2 | −0.0450496 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.04862e6 | −0.425948 | −0.212974 | − | 0.977058i | \(-0.568315\pi\) | ||||
−0.212974 | + | 0.977058i | \(0.568315\pi\) | |||||||
\(68\) | −3.80078e6 | −1.46586 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −144219. | −0.0502551 | ||||||||
\(71\) | −4.10180e6 | −1.36010 | −0.680049 | − | 0.733166i | \(-0.738042\pi\) | ||||
−0.680049 | + | 0.733166i | \(0.738042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −260342. | −0.0783273 | −0.0391637 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391637 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(74\) | −945104. | −0.271124 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −48693.7 | −0.0127240 | ||||||||
\(77\) | −6.74408e6 | −1.68347 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.33466e6 | −0.304562 | −0.152281 | − | 0.988337i | \(-0.548662\pi\) | ||||
−0.152281 | + | 0.988337i | \(0.548662\pi\) | |||||||
\(80\) | 126819. | 0.0276930 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.30797e6 | 1.86426 | ||||||||
\(83\) | −8.30823e6 | −1.59491 | −0.797454 | − | 0.603380i | \(-0.793820\pi\) | ||||
−0.797454 | + | 0.603380i | \(0.793820\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 255429. | 0.0451132 | ||||||||
\(86\) | −5.34852e6 | −0.906753 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.10832e6 | 0.329798 | ||||||||
\(89\) | −3.49331e6 | −0.525257 | −0.262628 | − | 0.964897i | \(-0.584589\pi\) | ||||
−0.262628 | + | 0.964897i | \(0.584589\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.23242e7 | 3.10549 | ||||||||
\(92\) | −5.67893e6 | −0.760342 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.43178e7 | 1.77799 | ||||||||
\(95\) | 3272.42 | 0.000391594 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00211e7 | −1.11484 | −0.557420 | − | 0.830230i | \(-0.688209\pi\) | ||||
−0.557420 | + | 0.830230i | \(0.688209\pi\) | |||||||
\(98\) | 1.99121e7 | 2.13711 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.61111e6 | −0.761111 | ||||||||
\(101\) | −9.44535e6 | −0.912206 | −0.456103 | − | 0.889927i | \(-0.650755\pi\) | ||||
−0.456103 | + | 0.889927i | \(0.650755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.07761e6 | −0.367684 | −0.183842 | − | 0.982956i | \(-0.558854\pi\) | ||||
−0.183842 | + | 0.982956i | \(0.558854\pi\) | |||||||
\(104\) | −6.97894e6 | −0.608377 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.96953e7 | 2.42168 | ||||||||
\(107\) | 2.17048e7 | 1.71282 | 0.856410 | − | 0.516296i | \(-0.172690\pi\) | ||||
0.856410 | + | 0.516296i | \(0.172690\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.43849e6 | −0.328278 | −0.164139 | − | 0.986437i | \(-0.552485\pi\) | ||||
−0.164139 | + | 0.986437i | \(0.552485\pi\) | |||||||
\(110\) | 452465. | 0.0324124 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.83839e7 | −1.90901 | ||||||||
\(113\) | −7.13404e6 | −0.465116 | −0.232558 | − | 0.972583i | \(-0.574710\pi\) | ||||
−0.232558 | + | 0.972583i | \(0.574710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 381648. | 0.0234002 | ||||||||
\(116\) | −2.05923e7 | −1.22490 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.08394e6 | −0.172790 | ||||||||
\(119\) | −5.71686e7 | −3.10987 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.67132e6 | 0.0857652 | ||||||||
\(122\) | −4.48233e7 | −2.23483 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.02857e6 | 0.283948 | ||||||||
\(125\) | 1.02328e6 | 0.0468607 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.23488e7 | −0.534948 | −0.267474 | − | 0.963565i | \(-0.586189\pi\) | ||||
−0.267474 | + | 0.963565i | \(0.586189\pi\) | |||||||
\(128\) | 1.45921e7 | 0.615010 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.49774e6 | −0.0597910 | ||||||||
\(131\) | 1.76969e7 | 0.687779 | 0.343889 | − | 0.939010i | \(-0.388256\pi\) | ||||
0.343889 | + | 0.939010i | \(0.388256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −732414. | −0.0269945 | ||||||||
\(134\) | −1.57459e7 | −0.565329 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.78719e7 | 0.609236 | ||||||||
\(137\) | 2.34535e6 | 0.0779265 | 0.0389632 | − | 0.999241i | \(-0.487594\pi\) | ||||
0.0389632 | + | 0.999241i | \(0.487594\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.84954e7 | −0.584134 | −0.292067 | − | 0.956398i | \(-0.594343\pi\) | ||||
−0.292067 | + | 0.956398i | \(0.594343\pi\) | |||||||
\(140\) | −936203. | −0.0288351 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.15920e7 | −1.80516 | ||||||||
\(143\) | −7.00385e7 | −2.00291 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.38389e6 | 0.0376975 | ||||||||
\(146\) | −3.90925e6 | −0.103958 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.13516e6 | −0.155564 | ||||||||
\(149\) | 1.87066e7 | 0.463278 | 0.231639 | − | 0.972802i | \(-0.425591\pi\) | ||||
0.231639 | + | 0.972802i | \(0.425591\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.23257e7 | −0.764062 | −0.382031 | − | 0.924150i | \(-0.624775\pi\) | ||||
−0.382031 | + | 0.924150i | \(0.624775\pi\) | |||||||
\(152\) | 228966. | 0.00528833 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.01268e8 | −2.23435 | ||||||||
\(155\) | −405145. | −0.00873876 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.46991e7 | −1.12806 | −0.564029 | − | 0.825755i | \(-0.690749\pi\) | ||||
−0.564029 | + | 0.825755i | \(0.690749\pi\) | |||||||
\(158\) | −2.00411e7 | −0.404223 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.51997e6 | 0.0293370 | ||||||||
\(161\) | −8.54182e7 | −1.61309 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.22142e7 | −0.763487 | −0.381744 | − | 0.924268i | \(-0.624676\pi\) | ||||
−0.381744 | + | 0.924268i | \(0.624676\pi\) | |||||||
\(164\) | 6.04229e7 | 1.06967 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.24755e8 | −2.11680 | ||||||||
\(167\) | 8.74223e6 | 0.145250 | 0.0726248 | − | 0.997359i | \(-0.476862\pi\) | ||||
0.0726248 | + | 0.997359i | \(0.476862\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.69092e8 | 2.69475 | ||||||||
\(170\) | 3.83548e6 | 0.0598754 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.47201e7 | −0.520272 | ||||||||
\(173\) | −4.41610e7 | −0.648451 | −0.324225 | − | 0.945980i | \(-0.605104\pi\) | ||||
−0.324225 | + | 0.945980i | \(0.605104\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.14481e8 | −1.61473 | ||||||||
\(176\) | 8.90500e7 | 1.23123 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.24550e7 | −0.697135 | ||||||||
\(179\) | 3.77776e7 | 0.492322 | 0.246161 | − | 0.969229i | \(-0.420831\pi\) | ||||
0.246161 | + | 0.969229i | \(0.420831\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.26649e8 | 1.58755 | 0.793774 | − | 0.608213i | \(-0.208113\pi\) | ||||
0.793774 | + | 0.608213i | \(0.208113\pi\) | |||||||
\(182\) | 3.35216e8 | 4.12169 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.67033e7 | 0.316011 | ||||||||
\(185\) | 412309. | 0.00478764 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.79357e8 | 2.00573 | ||||||||
\(188\) | 9.29445e7 | 1.02017 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 49138.2 | 0.000519734 0 | ||||||||
\(191\) | 2.15055e7 | 0.223323 | 0.111661 | − | 0.993746i | \(-0.464383\pi\) | ||||
0.111661 | + | 0.993746i | \(0.464383\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.18519e7 | 0.218796 | 0.109398 | − | 0.993998i | \(-0.465108\pi\) | ||||
0.109398 | + | 0.993998i | \(0.465108\pi\) | |||||||
\(194\) | −1.50475e8 | −1.47965 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.29260e8 | 1.22622 | ||||||||
\(197\) | 8.73312e7 | 0.813837 | 0.406919 | − | 0.913464i | \(-0.366603\pi\) | ||||
0.406919 | + | 0.913464i | \(0.366603\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.03499e8 | −1.83053 | −0.915266 | − | 0.402850i | \(-0.868020\pi\) | ||||
−0.915266 | + | 0.402850i | \(0.868020\pi\) | |||||||
\(200\) | 3.57888e7 | 0.316331 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.41830e8 | −1.21070 | ||||||||
\(203\) | −3.09734e8 | −2.59868 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.06067e6 | −0.0329200 | ||||||||
\(206\) | −6.12288e7 | −0.488000 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.94772e8 | −2.27125 | ||||||||
\(209\) | 2.29783e6 | 0.0174103 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.64544e7 | −0.560291 | −0.280146 | − | 0.959958i | \(-0.590383\pi\) | ||||
−0.280146 | + | 0.959958i | \(0.590383\pi\) | |||||||
\(212\) | 1.92768e8 | 1.38950 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.25915e8 | 2.27330 | ||||||||
\(215\) | 2.33333e6 | 0.0160119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.06772e7 | 0.602406 | ||||||||
\(218\) | −6.66477e7 | −0.435700 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.93719e6 | 0.0185974 | ||||||||
\(221\) | −5.93706e8 | −3.69997 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.24257e7 | −0.316575 | −0.158288 | − | 0.987393i | \(-0.550597\pi\) | ||||
−0.158288 | + | 0.987393i | \(0.550597\pi\) | |||||||
\(224\) | −3.40191e8 | −2.02234 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.07124e8 | −0.617314 | ||||||||
\(227\) | −3.76491e6 | −0.0213631 | −0.0106816 | − | 0.999943i | \(-0.503400\pi\) | ||||
−0.0106816 | + | 0.999943i | \(0.503400\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.48786e8 | −0.818723 | −0.409362 | − | 0.912372i | \(-0.634249\pi\) | ||||
−0.409362 | + | 0.912372i | \(0.634249\pi\) | |||||||
\(230\) | 5.73077e6 | 0.0310574 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.68284e7 | 0.509090 | ||||||||
\(233\) | −1.35403e8 | −0.701265 | −0.350632 | − | 0.936513i | \(-0.614033\pi\) | ||||
−0.350632 | + | 0.936513i | \(0.614033\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.24627e6 | −0.0313966 | ||||||||
\(236\) | −2.00195e7 | −0.0991427 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.58434e8 | −4.12751 | ||||||||
\(239\) | 3.35966e8 | 1.59185 | 0.795926 | − | 0.605394i | \(-0.206984\pi\) | ||||
0.795926 | + | 0.605394i | \(0.206984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.48239e8 | −1.14238 | −0.571189 | − | 0.820818i | \(-0.693518\pi\) | ||||
−0.571189 | + | 0.820818i | \(0.693518\pi\) | |||||||
\(242\) | 2.50963e7 | 0.113830 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.90971e8 | −1.28229 | ||||||||
\(245\) | −8.68682e6 | −0.0377381 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.60625e6 | −0.0321167 | ||||||||
\(248\) | −2.83474e7 | −0.118014 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.53654e7 | 0.0621948 | ||||||||
\(251\) | −9.71369e7 | −0.387727 | −0.193864 | − | 0.981028i | \(-0.562102\pi\) | ||||
−0.193864 | + | 0.981028i | \(0.562102\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.67986e8 | 1.04038 | ||||||||
\(254\) | −1.85428e8 | −0.709997 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.47895e8 | 1.29601 | ||||||||
\(257\) | −5.01702e6 | −0.0184366 | −0.00921829 | − | 0.999958i | \(-0.502934\pi\) | ||||
−0.00921829 | + | 0.999958i | \(0.502934\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.22806e7 | −0.330036 | ||||||||
\(260\) | −9.72264e6 | −0.0343066 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.65735e8 | 0.912838 | ||||||||
\(263\) | 3.81564e8 | 1.29337 | 0.646685 | − | 0.762757i | \(-0.276155\pi\) | ||||
0.646685 | + | 0.762757i | \(0.276155\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.29548e7 | −0.0427632 | ||||||||
\(266\) | −1.09978e7 | −0.0358278 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.02215e8 | −0.324372 | ||||||||
\(269\) | 2.82835e8 | 0.885931 | 0.442965 | − | 0.896539i | \(-0.353926\pi\) | ||||
0.442965 | + | 0.896539i | \(0.353926\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.76884e7 | 0.0845095 | 0.0422547 | − | 0.999107i | \(-0.486546\pi\) | ||||
0.0422547 | + | 0.999107i | \(0.486546\pi\) | |||||||
\(272\) | 7.54863e8 | 2.27445 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.52174e7 | 0.103426 | ||||||||
\(275\) | 3.59165e8 | 1.04143 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.63786e7 | 0.0463018 | 0.0231509 | − | 0.999732i | \(-0.492630\pi\) | ||||
0.0231509 | + | 0.999732i | \(0.492630\pi\) | |||||||
\(278\) | −2.77725e8 | −0.775278 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.40219e6 | 0.0119844 | ||||||||
\(281\) | 1.44402e8 | 0.388240 | 0.194120 | − | 0.980978i | \(-0.437815\pi\) | ||||
0.194120 | + | 0.980978i | \(0.437815\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.29642e8 | 0.340011 | 0.170005 | − | 0.985443i | \(-0.445622\pi\) | ||||
0.170005 | + | 0.985443i | \(0.445622\pi\) | |||||||
\(284\) | −3.99826e8 | −1.03575 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.05169e9 | −2.65831 | ||||||||
\(287\) | 9.08836e8 | 2.26934 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.11005e9 | 2.70519 | ||||||||
\(290\) | 2.07802e7 | 0.0500331 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.53770e7 | −0.0596486 | ||||||||
\(293\) | 5.48210e8 | 1.27324 | 0.636620 | − | 0.771178i | \(-0.280332\pi\) | ||||
0.636620 | + | 0.771178i | \(0.280332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.34539e6 | 0.00305121 | ||||||||
\(296\) | 2.88486e7 | 0.0646553 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.80895e8 | 0.614875 | ||||||||
\(299\) | −8.87083e8 | −1.91918 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.22233e8 | −1.10378 | ||||||||
\(302\) | −4.85398e8 | −1.01408 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.67091e6 | 0.0197428 | ||||||||
\(305\) | 1.95545e7 | 0.0394637 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.57326e8 | 1.49382 | 0.746910 | − | 0.664925i | \(-0.231536\pi\) | ||||
0.746910 | + | 0.664925i | \(0.231536\pi\) | |||||||
\(308\) | −6.57384e8 | −1.28201 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.08360e6 | −0.0115983 | ||||||||
\(311\) | −3.48341e8 | −0.656665 | −0.328332 | − | 0.944562i | \(-0.606487\pi\) | ||||
−0.328332 | + | 0.944562i | \(0.606487\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.49639e8 | −1.38180 | −0.690902 | − | 0.722948i | \(-0.742787\pi\) | ||||
−0.690902 | + | 0.722948i | \(0.742787\pi\) | |||||||
\(314\) | −8.21354e8 | −1.49719 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.30097e8 | −0.231933 | ||||||||
\(317\) | −7.39103e7 | −0.130316 | −0.0651580 | − | 0.997875i | \(-0.520755\pi\) | ||||
−0.0651580 | + | 0.997875i | \(0.520755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.71740e8 | 1.67603 | ||||||||
\(320\) | 6.59082e6 | 0.0112438 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.28263e9 | −2.14094 | ||||||||
\(323\) | 1.94784e7 | 0.0321621 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.18890e9 | −1.92112 | ||||||||
\(326\) | −6.33882e8 | −1.01332 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.84119e8 | −0.444572 | ||||||||
\(329\) | 1.39800e9 | 2.16432 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.07136e8 | −0.920212 | −0.460106 | − | 0.887864i | \(-0.652189\pi\) | ||||
−0.460106 | + | 0.887864i | \(0.652189\pi\) | |||||||
\(332\) | −8.09851e8 | −1.21457 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.31272e8 | 0.192779 | ||||||||
\(335\) | 6.86928e6 | 0.00998285 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.21856e9 | 1.73437 | 0.867186 | − | 0.497985i | \(-0.165926\pi\) | ||||
0.867186 | + | 0.497985i | \(0.165926\pi\) | |||||||
\(338\) | 2.53906e9 | 3.57655 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.48981e7 | 0.0343550 | ||||||||
\(341\) | −2.84485e8 | −0.388526 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.36790e8 | 0.985858 | ||||||||
\(344\) | 1.63260e8 | 0.216234 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.63114e8 | −0.860641 | ||||||||
\(347\) | −8.27617e8 | −1.06335 | −0.531675 | − | 0.846948i | \(-0.678437\pi\) | ||||
−0.531675 | + | 0.846948i | \(0.678437\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.88709e8 | −1.24503 | −0.622515 | − | 0.782608i | \(-0.713889\pi\) | ||||
−0.622515 | + | 0.782608i | \(0.713889\pi\) | |||||||
\(350\) | −1.71902e9 | −2.14311 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.06730e9 | 1.30432 | ||||||||
\(353\) | −2.48535e7 | −0.0300730 | −0.0150365 | − | 0.999887i | \(-0.504786\pi\) | ||||
−0.0150365 | + | 0.999887i | \(0.504786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.68700e7 | 0.0318763 | ||||||||
\(356\) | −3.40513e8 | −0.399998 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.67263e8 | 0.653423 | ||||||||
\(359\) | −6.66922e8 | −0.760755 | −0.380377 | − | 0.924831i | \(-0.624206\pi\) | ||||
−0.380377 | + | 0.924831i | \(0.624206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.93622e8 | −0.999721 | ||||||||
\(362\) | 1.90174e9 | 2.10703 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.17606e9 | 2.36492 | ||||||||
\(365\) | 1.70544e6 | 0.00183574 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.68476e8 | 0.494716 | 0.247358 | − | 0.968924i | \(-0.420438\pi\) | ||||
0.247358 | + | 0.968924i | \(0.420438\pi\) | |||||||
\(368\) | 1.12788e9 | 1.17976 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.19117e6 | 0.00635429 | ||||||||
\(371\) | 2.89947e9 | 2.94788 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.89698e8 | 0.588368 | 0.294184 | − | 0.955749i | \(-0.404952\pi\) | ||||
0.294184 | + | 0.955749i | \(0.404952\pi\) | |||||||
\(374\) | 2.69320e9 | 2.66206 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.37041e8 | −0.423999 | ||||||||
\(377\) | −3.21664e9 | −3.09177 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.55066e8 | 0.712439 | 0.356220 | − | 0.934402i | \(-0.384066\pi\) | ||||
0.356220 | + | 0.934402i | \(0.384066\pi\) | |||||||
\(380\) | 318982. | 0.000298211 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.22924e8 | 0.296400 | ||||||||
\(383\) | 5.16218e8 | 0.469502 | 0.234751 | − | 0.972056i | \(-0.424573\pi\) | ||||
0.234751 | + | 0.972056i | \(0.424573\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.41790e7 | 0.0394551 | ||||||||
\(386\) | 3.28125e8 | 0.290392 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.76811e8 | −0.848984 | ||||||||
\(389\) | −2.02594e9 | −1.74503 | −0.872514 | − | 0.488589i | \(-0.837512\pi\) | ||||
−0.872514 | + | 0.488589i | \(0.837512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.27168e9 | 1.92189 | ||||||||
\(392\) | −6.07803e8 | −0.509638 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.31135e9 | 1.08015 | ||||||||
\(395\) | 8.74307e6 | 0.00713796 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.11905e9 | 0.897601 | 0.448801 | − | 0.893632i | \(-0.351851\pi\) | ||||
0.448801 | + | 0.893632i | \(0.351851\pi\) | |||||||
\(398\) | −3.05572e9 | −2.42953 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.51162e9 | 1.18095 | ||||||||
\(401\) | 2.75487e8 | 0.213352 | 0.106676 | − | 0.994294i | \(-0.465979\pi\) | ||||
0.106676 | + | 0.994294i | \(0.465979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.41699e8 | 0.716711 | ||||||||
\(404\) | −9.20692e8 | −0.694672 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.65091e9 | −3.44903 | ||||||||
\(407\) | 2.89516e8 | 0.212859 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.49535e8 | −0.541702 | −0.270851 | − | 0.962621i | \(-0.587305\pi\) | ||||
−0.270851 | + | 0.962621i | \(0.587305\pi\) | |||||||
\(410\) | −6.09745e7 | −0.0436923 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.97468e8 | −0.280002 | ||||||||
\(413\) | −3.01118e8 | −0.210335 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.44254e7 | 0.0373795 | ||||||||
\(416\) | −3.53294e9 | −2.40608 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.45039e7 | 0.0231074 | ||||||||
\(419\) | −2.09732e9 | −1.39289 | −0.696445 | − | 0.717611i | \(-0.745236\pi\) | ||||
−0.696445 | + | 0.717611i | \(0.745236\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.22045e8 | 0.536919 | 0.268459 | − | 0.963291i | \(-0.413486\pi\) | ||||
0.268459 | + | 0.963291i | \(0.413486\pi\) | |||||||
\(422\) | −1.14803e9 | −0.743633 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.06427e8 | −0.577501 | ||||||||
\(425\) | 3.04458e9 | 1.92383 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.37657e9 | −2.72042 | ||||||||
\(428\) | 2.11569e9 | 1.30436 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.50370e7 | 0.0212514 | ||||||||
\(431\) | 9.73123e8 | 0.585460 | 0.292730 | − | 0.956195i | \(-0.405436\pi\) | ||||
0.292730 | + | 0.956195i | \(0.405436\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.68877e9 | 1.59165 | 0.795823 | − | 0.605529i | \(-0.207039\pi\) | ||||
0.795823 | + | 0.605529i | \(0.207039\pi\) | |||||||
\(434\) | 1.36160e9 | 0.799528 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.32645e8 | −0.249994 | ||||||||
\(437\) | 2.91035e7 | 0.0166825 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.20359e9 | 1.24309 | 0.621547 | − | 0.783377i | \(-0.286504\pi\) | ||||
0.621547 | + | 0.783377i | \(0.286504\pi\) | |||||||
\(440\) | −1.38112e7 | −0.00772941 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.91499e9 | −4.91070 | ||||||||
\(443\) | 1.04965e9 | 0.573630 | 0.286815 | − | 0.957986i | \(-0.407403\pi\) | ||||
0.286815 | + | 0.957986i | \(0.407403\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.28839e7 | 0.0123103 | ||||||||
\(446\) | −7.87216e8 | −0.420167 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.47512e9 | −0.775093 | ||||||||
\(449\) | 2.02286e9 | 1.05464 | 0.527320 | − | 0.849667i | \(-0.323197\pi\) | ||||
0.527320 | + | 0.849667i | \(0.323197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.85133e9 | −1.46362 | ||||||||
\(452\) | −6.95396e8 | −0.354199 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.65334e7 | −0.0283537 | ||||||||
\(455\) | −1.46241e8 | −0.0727827 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.01761e9 | −1.47896 | −0.739480 | − | 0.673178i | \(-0.764929\pi\) | ||||
−0.739480 | + | 0.673178i | \(0.764929\pi\) | |||||||
\(458\) | −2.23414e9 | −1.08663 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.72014e7 | 0.0178200 | ||||||||
\(461\) | −3.13368e9 | −1.48971 | −0.744854 | − | 0.667228i | \(-0.767481\pi\) | ||||
−0.744854 | + | 0.667228i | \(0.767481\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.30769e9 | −1.08055 | −0.540275 | − | 0.841489i | \(-0.681680\pi\) | ||||
−0.540275 | + | 0.841489i | \(0.681680\pi\) | |||||||
\(464\) | 4.08977e9 | 1.90058 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.03319e9 | −0.930737 | ||||||||
\(467\) | 3.23147e9 | 1.46822 | 0.734110 | − | 0.679030i | \(-0.237600\pi\) | ||||
0.734110 | + | 0.679030i | \(0.237600\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.53744e9 | −0.688167 | ||||||||
\(470\) | −9.37930e7 | −0.0416704 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.41350e7 | 0.0412054 | ||||||||
\(473\) | 1.63842e9 | 0.711889 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.90056e7 | 0.0166994 | ||||||||
\(476\) | −5.57255e9 | −2.36826 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.04482e9 | 2.11275 | ||||||||
\(479\) | −3.12158e9 | −1.29778 | −0.648888 | − | 0.760884i | \(-0.724766\pi\) | ||||
−0.648888 | + | 0.760884i | \(0.724766\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.58350e8 | −0.392660 | ||||||||
\(482\) | −3.72752e9 | −1.51619 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.62913e8 | 0.0653127 | ||||||||
\(485\) | 6.56458e7 | 0.0261283 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.98211e9 | −0.777636 | −0.388818 | − | 0.921315i | \(-0.627116\pi\) | ||||
−0.388818 | + | 0.921315i | \(0.627116\pi\) | |||||||
\(488\) | 1.36820e9 | 0.532941 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.30440e8 | −0.0500870 | ||||||||
\(491\) | −2.49858e9 | −0.952594 | −0.476297 | − | 0.879285i | \(-0.658021\pi\) | ||||
−0.476297 | + | 0.879285i | \(0.658021\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.23729e9 | 3.09614 | ||||||||
\(494\) | −1.14214e8 | −0.0426261 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.19732e9 | −0.440578 | ||||||||
\(497\) | −6.01389e9 | −2.19739 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.80008e9 | 1.72940 | 0.864702 | − | 0.502285i | \(-0.167507\pi\) | ||||
0.864702 | + | 0.502285i | \(0.167507\pi\) | |||||||
\(500\) | 9.97448e7 | 0.0356858 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.45859e9 | −0.514602 | ||||||||
\(503\) | 3.37167e9 | 1.18129 | 0.590645 | − | 0.806931i | \(-0.298873\pi\) | ||||
0.590645 | + | 0.806931i | \(0.298873\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.18744e7 | 0.0213792 | ||||||||
\(506\) | 4.02404e9 | 1.38081 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.20371e9 | −0.407379 | ||||||||
\(509\) | 2.96439e9 | 0.996376 | 0.498188 | − | 0.867069i | \(-0.333999\pi\) | ||||
0.498188 | + | 0.867069i | \(0.333999\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.81702e8 | −0.126547 | ||||||||
\(512\) | 3.35615e9 | 1.10509 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.53349e7 | −0.0244695 | ||||||||
\(515\) | 2.67115e7 | 0.00861734 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.38601e9 | −1.39590 | ||||||||
\(518\) | −1.38567e9 | −0.438032 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.57175e7 | 0.0142584 | ||||||||
\(521\) | 2.91409e9 | 0.902757 | 0.451378 | − | 0.892333i | \(-0.350933\pi\) | ||||
0.451378 | + | 0.892333i | \(0.350933\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.99881e9 | −1.52796 | −0.763978 | − | 0.645243i | \(-0.776756\pi\) | ||||
−0.763978 | + | 0.645243i | \(0.776756\pi\) | |||||||
\(524\) | 1.72502e9 | 0.523763 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.72951e9 | 1.71659 | ||||||||
\(527\) | −2.41154e9 | −0.717723 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.06102e7 | −0.00311622 | ||||||||
\(530\) | −1.94527e8 | −0.0567565 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.13926e7 | −0.0205571 | ||||||||
\(533\) | 9.43842e9 | 2.69994 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.42183e8 | −0.0401430 | ||||||||
\(536\) | 4.80633e8 | 0.134814 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.24700e9 | 1.17583 | ||||||||
\(539\) | −6.09972e9 | −1.67784 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.32516e9 | −0.359813 | −0.179906 | − | 0.983684i | \(-0.557580\pi\) | ||||
−0.179906 | + | 0.983684i | \(0.557580\pi\) | |||||||
\(542\) | 4.15765e8 | 0.112163 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.04730e9 | 2.40948 | ||||||||
\(545\) | 2.90756e7 | 0.00769379 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.49203e9 | 0.389782 | 0.194891 | − | 0.980825i | \(-0.437565\pi\) | ||||
0.194891 | + | 0.980825i | \(0.437565\pi\) | |||||||
\(548\) | 2.28614e8 | 0.0593433 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.39316e9 | 1.38221 | ||||||||
\(551\) | 1.05532e8 | 0.0268753 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.95682e9 | −0.492055 | ||||||||
\(554\) | 2.45939e8 | 0.0614530 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.80286e9 | −0.444835 | ||||||||
\(557\) | 1.87638e9 | 0.460074 | 0.230037 | − | 0.973182i | \(-0.426115\pi\) | ||||
0.230037 | + | 0.973182i | \(0.426115\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.42348e9 | −1.31322 | ||||||||
\(560\) | 1.85937e8 | 0.0447411 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.16831e9 | 0.515282 | ||||||||
\(563\) | 2.13285e9 | 0.503711 | 0.251855 | − | 0.967765i | \(-0.418959\pi\) | ||||
0.251855 | + | 0.967765i | \(0.418959\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.67336e7 | 0.0109008 | ||||||||
\(566\) | 1.94668e9 | 0.451271 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.88005e9 | 0.430478 | ||||||||
\(569\) | 1.42082e9 | 0.323331 | 0.161666 | − | 0.986846i | \(-0.448313\pi\) | ||||
0.161666 | + | 0.986846i | \(0.448313\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.63133e9 | 0.366703 | 0.183352 | − | 0.983047i | \(-0.441305\pi\) | ||||
0.183352 | + | 0.983047i | \(0.441305\pi\) | |||||||
\(572\) | −6.82705e9 | −1.52527 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.36469e10 | 3.01192 | ||||||||
\(575\) | 4.54905e9 | 0.997892 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.83244e9 | 1.69739 | 0.848695 | − | 0.528882i | \(-0.177389\pi\) | ||||
0.848695 | + | 0.528882i | \(0.177389\pi\) | |||||||
\(578\) | 1.66683e10 | 3.59040 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.34895e8 | 0.0287078 | ||||||||
\(581\) | −1.21812e10 | −2.57675 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.09662e9 | −1.90125 | ||||||||
\(584\) | 1.19327e8 | 0.0247910 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.23184e9 | 1.68988 | ||||||||
\(587\) | −5.25336e9 | −1.07202 | −0.536011 | − | 0.844211i | \(-0.680069\pi\) | ||||
−0.536011 | + | 0.844211i | \(0.680069\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.08954e7 | −0.00623003 | ||||||||
\(590\) | 2.02022e7 | 0.00404965 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.21849e9 | 0.241377 | ||||||||
\(593\) | −3.96594e9 | −0.781007 | −0.390503 | − | 0.920601i | \(-0.627699\pi\) | ||||
−0.390503 | + | 0.920601i | \(0.627699\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.74499e8 | 0.0728855 | ||||||||
\(596\) | 1.82344e9 | 0.352800 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.33203e10 | −2.54718 | ||||||||
\(599\) | −4.82067e9 | −0.916461 | −0.458230 | − | 0.888833i | \(-0.651517\pi\) | ||||
−0.458230 | + | 0.888833i | \(0.651517\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.29063e9 | 0.242516 | 0.121258 | − | 0.992621i | \(-0.461307\pi\) | ||||
0.121258 | + | 0.992621i | \(0.461307\pi\) | |||||||
\(602\) | −7.84177e9 | −1.46496 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.15097e9 | −0.581855 | ||||||||
\(605\) | −1.09485e7 | −0.00201006 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.37737e9 | 1.33888 | 0.669440 | − | 0.742866i | \(-0.266534\pi\) | ||||
0.669440 | + | 0.742866i | \(0.266534\pi\) | |||||||
\(608\) | 1.15909e8 | 0.0209149 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.93627e8 | 0.0523772 | ||||||||
\(611\) | 1.45185e10 | 2.57500 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.76333e9 | −1.53659 | −0.768294 | − | 0.640097i | \(-0.778894\pi\) | ||||
−0.768294 | + | 0.640097i | \(0.778894\pi\) | |||||||
\(614\) | 1.13719e10 | 1.98264 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.09114e9 | 0.532826 | ||||||||
\(617\) | −9.05070e9 | −1.55126 | −0.775629 | − | 0.631189i | \(-0.782567\pi\) | ||||
−0.775629 | + | 0.631189i | \(0.782567\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.25987e9 | 1.23030 | 0.615151 | − | 0.788409i | \(-0.289095\pi\) | ||||
0.615151 | + | 0.788409i | \(0.289095\pi\) | |||||||
\(620\) | −3.94918e7 | −0.00665482 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.23064e9 | −0.871543 | ||||||||
\(623\) | −5.12174e9 | −0.848612 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.09346e9 | 0.998352 | ||||||||
\(626\) | −1.12565e10 | −1.83397 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.33184e9 | −0.859049 | ||||||||
\(629\) | 2.45418e9 | 0.393214 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.82668e9 | 1.08170 | 0.540850 | − | 0.841119i | \(-0.318103\pi\) | ||||
0.540850 | + | 0.841119i | \(0.318103\pi\) | |||||||
\(632\) | 6.11739e8 | 0.0963954 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.10983e9 | −0.172959 | ||||||||
\(635\) | 8.08943e7 | 0.0125375 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.01912e10 | 3.09510 | ||||||||
\(638\) | 1.45915e10 | 2.22448 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.55896e7 | −0.0144139 | ||||||||
\(641\) | −2.79576e9 | −0.419273 | −0.209637 | − | 0.977779i | \(-0.567228\pi\) | ||||
−0.209637 | + | 0.977779i | \(0.567228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.72738e9 | −0.404583 | −0.202292 | − | 0.979325i | \(-0.564839\pi\) | ||||
−0.202292 | + | 0.979325i | \(0.564839\pi\) | |||||||
\(644\) | −8.32620e9 | −1.22842 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.92484e8 | 0.0426863 | ||||||||
\(647\) | 4.23656e9 | 0.614962 | 0.307481 | − | 0.951554i | \(-0.400514\pi\) | ||||
0.307481 | + | 0.951554i | \(0.400514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.44710e8 | 0.135657 | ||||||||
\(650\) | −1.78524e10 | −2.54976 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.11486e9 | −0.581418 | ||||||||
\(653\) | 5.22693e9 | 0.734599 | 0.367300 | − | 0.930103i | \(-0.380282\pi\) | ||||
0.367300 | + | 0.930103i | \(0.380282\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.15929e8 | −0.0161193 | ||||||||
\(656\) | −1.20004e10 | −1.65971 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.09922e10 | 2.87255 | ||||||||
\(659\) | −3.27514e9 | −0.445791 | −0.222896 | − | 0.974842i | \(-0.571551\pi\) | ||||
−0.222896 | + | 0.974842i | \(0.571551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.03921e10 | 1.39958 | 0.699788 | − | 0.714351i | \(-0.253278\pi\) | ||||
0.699788 | + | 0.714351i | \(0.253278\pi\) | |||||||
\(662\) | −9.11666e9 | −1.22133 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.80806e9 | 0.504796 | ||||||||
\(665\) | 4.79788e6 | 0.000632665 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.23077e10 | 1.60597 | ||||||||
\(668\) | 8.52156e8 | 0.110612 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.03148e8 | 0.0132495 | ||||||||
\(671\) | 1.37308e10 | 1.75456 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.08020e10 | 1.36601 | 0.683003 | − | 0.730416i | \(-0.260674\pi\) | ||||
0.683003 | + | 0.730416i | \(0.260674\pi\) | |||||||
\(674\) | 1.82977e10 | 2.30190 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.64823e10 | 2.05213 | ||||||||
\(677\) | −1.40245e8 | −0.0173711 | −0.00868555 | − | 0.999962i | \(-0.502765\pi\) | ||||
−0.00868555 | + | 0.999962i | \(0.502765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.46925e10 | −1.80115 | ||||||||
\(680\) | −1.17075e8 | −0.0142785 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.27179e9 | −0.515661 | ||||||||
\(683\) | 5.38006e9 | 0.646122 | 0.323061 | − | 0.946378i | \(-0.395288\pi\) | ||||
0.323061 | + | 0.946378i | \(0.395288\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.53639e7 | −0.00182635 | ||||||||
\(686\) | 1.10635e10 | 1.30846 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.89565e9 | 0.807264 | ||||||||
\(689\) | 3.01115e10 | 3.50724 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.51475e9 | −0.981745 | −0.490873 | − | 0.871231i | \(-0.663322\pi\) | ||||
−0.490873 | + | 0.871231i | \(0.663322\pi\) | |||||||
\(692\) | −4.30462e9 | −0.493814 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.24274e10 | −1.41131 | ||||||||
\(695\) | 1.21160e8 | 0.0136902 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.41703e10 | −2.70375 | ||||||||
\(698\) | −1.48463e10 | −1.65244 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.11591e10 | −1.22966 | ||||||||
\(701\) | −1.29311e10 | −1.41782 | −0.708911 | − | 0.705298i | \(-0.750813\pi\) | ||||
−0.708911 | + | 0.705298i | \(0.750813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.14417e7 | 0.00341320 | ||||||||
\(704\) | 4.62795e9 | 0.499901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.73197e8 | −0.0399137 | ||||||||
\(707\) | −1.38484e10 | −1.47377 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.39507e9 | 0.568506 | 0.284253 | − | 0.958749i | \(-0.408254\pi\) | ||||
0.284253 | + | 0.958749i | \(0.408254\pi\) | |||||||
\(710\) | 4.03476e8 | 0.0423071 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.60115e9 | 0.166246 | ||||||||
\(713\) | −3.60319e9 | −0.372284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.58807e8 | 0.0469417 | ||||||||
\(716\) | 3.68240e9 | 0.374918 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.00144e10 | −1.00969 | ||||||||
\(719\) | 8.62160e9 | 0.865041 | 0.432521 | − | 0.901624i | \(-0.357624\pi\) | ||||
0.432521 | + | 0.901624i | \(0.357624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.97842e9 | −0.594036 | ||||||||
\(722\) | −1.34185e10 | −1.32686 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.23452e10 | 1.20896 | ||||||||
\(725\) | 1.64953e10 | 1.60759 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.76855e9 | −0.749841 | −0.374921 | − | 0.927057i | \(-0.622330\pi\) | ||||
−0.374921 | + | 0.927057i | \(0.622330\pi\) | |||||||
\(728\) | −1.02322e10 | −0.982902 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.56086e7 | 0.00243644 | ||||||||
\(731\) | 1.38887e10 | 1.31507 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.43007e9 | −0.227906 | −0.113953 | − | 0.993486i | \(-0.536351\pi\) | ||||
−0.113953 | + | 0.993486i | \(0.536351\pi\) | |||||||
\(734\) | 7.03456e9 | 0.656600 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.35180e10 | 1.24980 | ||||||||
\(737\) | 4.82348e9 | 0.443838 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.09023e9 | −0.646256 | −0.323128 | − | 0.946355i | \(-0.604734\pi\) | ||||
−0.323128 | + | 0.946355i | \(0.604734\pi\) | |||||||
\(740\) | 4.01901e7 | 0.00364593 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.35380e10 | 3.91250 | ||||||||
\(743\) | −6.11412e9 | −0.546857 | −0.273428 | − | 0.961892i | \(-0.588158\pi\) | ||||
−0.273428 | + | 0.961892i | \(0.588158\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.22543e8 | −0.0108578 | ||||||||
\(746\) | 8.85482e9 | 0.780897 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.74830e10 | 1.52743 | ||||||||
\(749\) | 3.18226e10 | 2.76726 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.01871e10 | 0.877629 | 0.438815 | − | 0.898578i | \(-0.355398\pi\) | ||||
0.438815 | + | 0.898578i | \(0.355398\pi\) | |||||||
\(752\) | −1.84594e10 | −1.58291 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.83005e10 | −4.10348 | ||||||||
\(755\) | 2.11759e8 | 0.0179072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.04917e10 | 1.71689 | 0.858446 | − | 0.512903i | \(-0.171430\pi\) | ||||
0.858446 | + | 0.512903i | \(0.171430\pi\) | |||||||
\(758\) | 1.13380e10 | 0.945568 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.49991e6 | −0.000123941 0 | ||||||||
\(761\) | −4.69491e9 | −0.386172 | −0.193086 | − | 0.981182i | \(-0.561850\pi\) | ||||
−0.193086 | + | 0.981182i | \(0.561850\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.50752e9 | −0.530371 | ||||||||
\(764\) | 2.09627e9 | 0.170067 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.75145e9 | 0.623135 | ||||||||
\(767\) | −3.12716e9 | −0.250246 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.90779e10 | 1.51282 | 0.756412 | − | 0.654095i | \(-0.226951\pi\) | ||||
0.756412 | + | 0.654095i | \(0.226951\pi\) | |||||||
\(770\) | 6.63386e8 | 0.0523659 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.13003e9 | 0.166619 | ||||||||
\(773\) | 1.43599e10 | 1.11821 | 0.559105 | − | 0.829097i | \(-0.311145\pi\) | ||||
0.559105 | + | 0.829097i | \(0.311145\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.82913e9 | −0.372660 | ||||||||
\(776\) | 4.59313e9 | 0.352852 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.04212e10 | −2.31605 | ||||||||
\(779\) | −3.09657e8 | −0.0234693 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.88676e10 | 1.41722 | ||||||||
\(782\) | 3.41111e10 | 2.55078 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.56720e10 | −1.90262 | ||||||||
\(785\) | 3.58322e8 | 0.0264381 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.56113e9 | −0.333550 | −0.166775 | − | 0.985995i | \(-0.553335\pi\) | ||||
−0.166775 | + | 0.985995i | \(0.553335\pi\) | |||||||
\(788\) | 8.51267e9 | 0.619761 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.31285e8 | 0.00947369 | ||||||||
\(791\) | −1.04596e10 | −0.751447 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.54515e10 | −3.23662 | ||||||||
\(794\) | 1.68035e10 | 1.19132 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.98363e10 | −1.39400 | ||||||||
\(797\) | −1.19252e10 | −0.834374 | −0.417187 | − | 0.908821i | \(-0.636984\pi\) | ||||
−0.417187 | + | 0.908821i | \(0.636984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.71795e10 | −2.57864 | ||||||||
\(800\) | 1.81173e10 | 1.25106 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.13667e9 | 0.283166 | ||||||||
\(803\) | 1.19753e9 | 0.0816171 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.59556e8 | 0.0378057 | ||||||||
\(806\) | 1.41404e10 | 0.951238 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.32925e9 | 0.288718 | ||||||||
\(809\) | 1.14473e10 | 0.760121 | 0.380061 | − | 0.924962i | \(-0.375903\pi\) | ||||
0.380061 | + | 0.924962i | \(0.375903\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.28875e10 | −0.848389 | −0.424195 | − | 0.905571i | \(-0.639443\pi\) | ||||
−0.424195 | + | 0.905571i | \(0.639443\pi\) | |||||||
\(812\) | −3.01915e10 | −1.97897 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.34732e9 | 0.282512 | ||||||||
\(815\) | 2.76536e8 | 0.0178937 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.77934e8 | 0.0114152 | ||||||||
\(818\) | −1.12549e10 | −0.718961 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.95817e8 | −0.0250695 | ||||||||
\(821\) | 1.25024e10 | 0.788481 | 0.394240 | − | 0.919007i | \(-0.371008\pi\) | ||||
0.394240 | + | 0.919007i | \(0.371008\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.32497e10 | 0.828528 | 0.414264 | − | 0.910157i | \(-0.364039\pi\) | ||||
0.414264 | + | 0.910157i | \(0.364039\pi\) | |||||||
\(824\) | 1.86896e9 | 0.116374 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.52154e9 | −0.279162 | ||||||||
\(827\) | −3.06111e9 | −0.188196 | −0.0940980 | − | 0.995563i | \(-0.529997\pi\) | ||||
−0.0940980 | + | 0.995563i | \(0.529997\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.74744e10 | −1.06527 | −0.532637 | − | 0.846344i | \(-0.678799\pi\) | ||||
−0.532637 | + | 0.846344i | \(0.678799\pi\) | |||||||
\(830\) | 8.17244e8 | 0.0496111 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.53194e10 | −0.922166 | ||||||||
\(833\) | −5.17064e10 | −3.09947 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.72685e7 | −0.00340418 | ||||||||
\(836\) | 2.23983e8 | 0.0132585 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.14931e10 | −1.84868 | ||||||||
\(839\) | 3.10592e9 | 0.181562 | 0.0907808 | − | 0.995871i | \(-0.471064\pi\) | ||||
0.0907808 | + | 0.995871i | \(0.471064\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.73789e10 | 1.58720 | ||||||||
\(842\) | 1.23437e10 | 0.712612 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.45245e9 | −0.426678 | ||||||||
\(845\) | −1.10768e9 | −0.0631564 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.45042e9 | 0.138563 | ||||||||
\(848\) | −3.82850e10 | −2.15597 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.57170e10 | 2.55336 | ||||||||
\(851\) | 3.66690e9 | 0.203960 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.91007e10 | 1.05372 | 0.526862 | − | 0.849951i | \(-0.323368\pi\) | ||||
0.526862 | + | 0.849951i | \(0.323368\pi\) | |||||||
\(854\) | −6.57180e10 | −3.61062 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.94833e9 | −0.542116 | ||||||||
\(857\) | −3.07421e9 | −0.166840 | −0.0834202 | − | 0.996514i | \(-0.526584\pi\) | ||||
−0.0834202 | + | 0.996514i | \(0.526584\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.57219e9 | −0.407610 | −0.203805 | − | 0.979011i | \(-0.565331\pi\) | ||||
−0.203805 | + | 0.979011i | \(0.565331\pi\) | |||||||
\(860\) | 2.27443e8 | 0.0121935 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.46123e10 | 0.777038 | ||||||||
\(863\) | −6.48477e9 | −0.343445 | −0.171722 | − | 0.985145i | \(-0.554933\pi\) | ||||
−0.171722 | + | 0.985145i | \(0.554933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.89289e8 | 0.0151976 | ||||||||
\(866\) | 4.03742e10 | 2.11247 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.83883e9 | 0.458749 | ||||||||
\(869\) | 6.13922e9 | 0.317354 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.59666e10 | −0.818746 | ||||||||
\(872\) | 2.03437e9 | 0.103902 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.37014e8 | 0.0221414 | ||||||||
\(875\) | 1.50029e9 | 0.0757088 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.00447e9 | −0.350652 | −0.175326 | − | 0.984510i | \(-0.556098\pi\) | ||||
−0.175326 | + | 0.984510i | \(0.556098\pi\) | |||||||
\(878\) | 3.30887e10 | 1.64987 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.83347e8 | −0.0288561 | ||||||||
\(881\) | 1.76566e10 | 0.869944 | 0.434972 | − | 0.900444i | \(-0.356758\pi\) | ||||
0.434972 | + | 0.900444i | \(0.356758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.27783e10 | −0.624610 | −0.312305 | − | 0.949982i | \(-0.601101\pi\) | ||||
−0.312305 | + | 0.949982i | \(0.601101\pi\) | |||||||
\(884\) | −5.78719e10 | −2.81763 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.57614e10 | 0.761337 | ||||||||
\(887\) | −3.30434e10 | −1.58983 | −0.794917 | − | 0.606719i | \(-0.792485\pi\) | ||||
−0.794917 | + | 0.606719i | \(0.792485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.81053e10 | −0.864270 | ||||||||
\(890\) | 3.43621e8 | 0.0163386 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.11023e9 | −0.241081 | ||||||||
\(893\) | −4.76325e8 | −0.0223833 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.47473e8 | −0.0115384 | ||||||||
\(896\) | 2.13943e10 | 0.993619 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.03750e10 | 1.39975 | ||||||||
\(899\) | −1.30655e10 | −0.599744 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.71107e10 | −3.51219 | ||||||||
\(902\) | −4.28151e10 | −1.94256 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.26987e9 | 0.147211 | ||||||||
\(905\) | −8.29650e8 | −0.0372070 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.42333e10 | −0.633401 | −0.316701 | − | 0.948526i | \(-0.602575\pi\) | ||||
−0.316701 | + | 0.948526i | \(0.602575\pi\) | |||||||
\(908\) | −3.66988e8 | −0.0162686 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.19593e9 | −0.0965991 | ||||||||
\(911\) | −8.60227e9 | −0.376963 | −0.188482 | − | 0.982077i | \(-0.560357\pi\) | ||||
−0.188482 | + | 0.982077i | \(0.560357\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.82165e10 | 1.66189 | ||||||||
\(914\) | −4.53120e10 | −1.96292 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.45030e10 | −0.623482 | ||||||||
\(917\) | 2.59465e10 | 1.11118 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.07267e10 | 0.880898 | 0.440449 | − | 0.897778i | \(-0.354819\pi\) | ||||
0.440449 | + | 0.897778i | \(0.354819\pi\) | |||||||
\(920\) | −1.74927e8 | −0.00740629 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.70548e10 | −1.97718 | ||||||||
\(923\) | −6.24553e10 | −2.61435 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.91452e9 | 0.204167 | ||||||||
\(926\) | −3.46520e10 | −1.43413 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.90174e10 | 2.01341 | ||||||||
\(929\) | 4.14549e10 | 1.69637 | 0.848186 | − | 0.529699i | \(-0.177695\pi\) | ||||
0.848186 | + | 0.529699i | \(0.177695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.62436e8 | −0.0269042 | ||||||||
\(932\) | −1.31985e10 | −0.534034 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.85233e10 | 1.94866 | ||||||||
\(935\) | −1.17493e9 | −0.0470080 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.37792e10 | −0.944296 | −0.472148 | − | 0.881519i | \(-0.656521\pi\) | ||||
−0.472148 | + | 0.881519i | \(0.656521\pi\) | |||||||
\(938\) | −2.30860e10 | −0.913353 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.08859e8 | −0.0239094 | ||||||||
\(941\) | 1.90527e10 | 0.745407 | 0.372703 | − | 0.927951i | \(-0.378431\pi\) | ||||
0.372703 | + | 0.927951i | \(0.378431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.61139e10 | −1.40244 | ||||||||
\(944\) | 3.97601e9 | 0.153832 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.46023e10 | 0.944838 | ||||||||
\(947\) | −2.17206e10 | −0.831089 | −0.415544 | − | 0.909573i | \(-0.636409\pi\) | ||||
−0.415544 | + | 0.909573i | \(0.636409\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.96404e9 | −0.150559 | ||||||||
\(950\) | 5.85703e8 | 0.0221638 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.62031e10 | 0.984290 | ||||||||
\(953\) | 2.72331e9 | 0.101923 | 0.0509614 | − | 0.998701i | \(-0.483771\pi\) | ||||
0.0509614 | + | 0.998701i | \(0.483771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.40878e8 | −0.00523397 | ||||||||
\(956\) | 3.27485e10 | 1.21224 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.68732e10 | −1.72244 | ||||||||
\(959\) | 3.43865e9 | 0.125899 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.36876e10 | −0.860972 | ||||||||
\(962\) | −1.43904e10 | −0.521148 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.41973e10 | −0.869955 | ||||||||
\(965\) | −1.43147e8 | −0.00512787 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.19767e10 | −0.425935 | −0.212967 | − | 0.977059i | \(-0.568313\pi\) | ||||
−0.212967 | + | 0.977059i | \(0.568313\pi\) | |||||||
\(968\) | −7.66047e8 | −0.0271451 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.85728e8 | 0.0346781 | ||||||||
\(971\) | −4.20855e9 | −0.147525 | −0.0737625 | − | 0.997276i | \(-0.523501\pi\) | ||||
−0.0737625 | + | 0.997276i | \(0.523501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.71172e10 | −0.943735 | ||||||||
\(974\) | −2.97631e10 | −1.03210 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.77890e10 | 1.98962 | ||||||||
\(977\) | −3.92707e10 | −1.34722 | −0.673608 | − | 0.739089i | \(-0.735256\pi\) | ||||
−0.673608 | + | 0.739089i | \(0.735256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.60686e10 | 0.547318 | ||||||||
\(980\) | −8.46754e8 | −0.0287386 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.75183e10 | −1.26431 | ||||||||
\(983\) | −2.85690e10 | −0.959308 | −0.479654 | − | 0.877458i | \(-0.659238\pi\) | ||||
−0.479654 | + | 0.877458i | \(0.659238\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.72087e8 | −0.0190737 | ||||||||
\(986\) | 1.23690e11 | 4.10927 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.41424e8 | −0.0244578 | ||||||||
\(989\) | 2.07517e10 | 0.682129 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.53806e10 | 0.828408 | 0.414204 | − | 0.910184i | \(-0.364060\pi\) | ||||
0.414204 | + | 0.910184i | \(0.364060\pi\) | |||||||
\(992\) | −1.43503e10 | −0.466733 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.03036e10 | −2.91644 | ||||||||
\(995\) | 1.33308e9 | 0.0429018 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.36748e9 | 0.299357 | 0.149679 | − | 0.988735i | \(-0.452176\pi\) | ||||
0.149679 | + | 0.988735i | \(0.452176\pi\) | |||||||
\(998\) | 7.20773e10 | 2.29531 | ||||||||
\(999\) | 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.e.1.15 | 18 | ||
3.2 | odd | 2 | 177.8.a.d.1.4 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.4 | ✓ | 18 | 3.2 | odd | 2 | ||
531.8.a.e.1.15 | 18 | 1.1 | even | 1 | trivial |