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: | \( x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | 1.11 | ||
Root | \(-4.85375\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.85375 | 0.605791 | 0.302896 | − | 0.953024i | \(-0.402047\pi\) | ||||
0.302896 | + | 0.953024i | \(0.402047\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −81.0262 | −0.633017 | ||||||||
\(5\) | 190.727 | 0.682367 | 0.341183 | − | 0.939997i | \(-0.389172\pi\) | ||||
0.341183 | + | 0.939997i | \(0.389172\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −799.288 | −0.880765 | −0.440383 | − | 0.897810i | \(-0.645157\pi\) | ||||
−0.440383 | + | 0.897810i | \(0.645157\pi\) | |||||||
\(8\) | −1432.61 | −0.989267 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1307.20 | 0.413372 | ||||||||
\(11\) | −972.348 | −0.220266 | −0.110133 | − | 0.993917i | \(-0.535128\pi\) | ||||
−0.110133 | + | 0.993917i | \(0.535128\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1278.77 | −0.161432 | −0.0807161 | − | 0.996737i | \(-0.525721\pi\) | ||||
−0.0807161 | + | 0.996737i | \(0.525721\pi\) | |||||||
\(14\) | −5478.12 | −0.533560 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 552.586 | 0.0337272 | ||||||||
\(17\) | −36467.5 | −1.80026 | −0.900128 | − | 0.435625i | \(-0.856527\pi\) | ||||
−0.900128 | + | 0.435625i | \(0.856527\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1900.72 | 0.0635742 | 0.0317871 | − | 0.999495i | \(-0.489880\pi\) | ||||
0.0317871 | + | 0.999495i | \(0.489880\pi\) | |||||||
\(20\) | −15453.9 | −0.431950 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6664.23 | −0.133435 | ||||||||
\(23\) | −80181.7 | −1.37413 | −0.687065 | − | 0.726596i | \(-0.741101\pi\) | ||||
−0.687065 | + | 0.726596i | \(0.741101\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −41748.1 | −0.534376 | ||||||||
\(26\) | −8764.35 | −0.0977942 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 64763.2 | 0.557539 | ||||||||
\(29\) | 201337. | 1.53296 | 0.766479 | − | 0.642270i | \(-0.222007\pi\) | ||||
0.766479 | + | 0.642270i | \(0.222007\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 106900. | 0.644484 | 0.322242 | − | 0.946657i | \(-0.395564\pi\) | ||||
0.322242 | + | 0.946657i | \(0.395564\pi\) | |||||||
\(32\) | 187162. | 1.00970 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −249939. | −1.09058 | ||||||||
\(35\) | −152446. | −0.601005 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −246438. | −0.799838 | −0.399919 | − | 0.916550i | \(-0.630962\pi\) | ||||
−0.399919 | + | 0.916550i | \(0.630962\pi\) | |||||||
\(38\) | 13027.1 | 0.0385127 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −273238. | −0.675043 | ||||||||
\(41\) | 348348. | 0.789350 | 0.394675 | − | 0.918821i | \(-0.370857\pi\) | ||||
0.394675 | + | 0.918821i | \(0.370857\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 303791. | 0.582687 | 0.291343 | − | 0.956619i | \(-0.405898\pi\) | ||||
0.291343 | + | 0.956619i | \(0.405898\pi\) | |||||||
\(44\) | 78785.6 | 0.139432 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −549545. | −0.832436 | ||||||||
\(47\) | −1.12223e6 | −1.57666 | −0.788330 | − | 0.615252i | \(-0.789054\pi\) | ||||
−0.788330 | + | 0.615252i | \(0.789054\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −184682. | −0.224253 | ||||||||
\(50\) | −286131. | −0.323720 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 103614. | 0.102189 | ||||||||
\(53\) | −534787. | −0.493418 | −0.246709 | − | 0.969090i | \(-0.579349\pi\) | ||||
−0.246709 | + | 0.969090i | \(0.579349\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −185453. | −0.150302 | ||||||||
\(56\) | 1.14507e6 | 0.871312 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.37991e6 | 0.928652 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.14348e6 | −1.20911 | −0.604555 | − | 0.796564i | \(-0.706649\pi\) | ||||
−0.604555 | + | 0.796564i | \(0.706649\pi\) | |||||||
\(62\) | 732666. | 0.390423 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.21203e6 | 0.577940 | ||||||||
\(65\) | −243896. | −0.110156 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −158432. | −0.0643548 | −0.0321774 | − | 0.999482i | \(-0.510244\pi\) | ||||
−0.0321774 | + | 0.999482i | \(0.510244\pi\) | |||||||
\(68\) | 2.95482e6 | 1.13959 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.04483e6 | −0.364084 | ||||||||
\(71\) | 3.94945e6 | 1.30958 | 0.654790 | − | 0.755811i | \(-0.272757\pi\) | ||||
0.654790 | + | 0.755811i | \(0.272757\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.25842e6 | 0.980342 | 0.490171 | − | 0.871626i | \(-0.336934\pi\) | ||||
0.490171 | + | 0.871626i | \(0.336934\pi\) | |||||||
\(74\) | −1.68903e6 | −0.484535 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −154008. | −0.0402435 | ||||||||
\(77\) | 777186. | 0.194003 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.28930e6 | −1.20699 | −0.603494 | − | 0.797367i | \(-0.706225\pi\) | ||||
−0.603494 | + | 0.797367i | \(0.706225\pi\) | |||||||
\(80\) | 105393. | 0.0230143 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.38749e6 | 0.478181 | ||||||||
\(83\) | 3.63337e6 | 0.697487 | 0.348744 | − | 0.937218i | \(-0.386608\pi\) | ||||
0.348744 | + | 0.937218i | \(0.386608\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.95534e6 | −1.22844 | ||||||||
\(86\) | 2.08211e6 | 0.352987 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.39300e6 | 0.217902 | ||||||||
\(89\) | 1.34439e6 | 0.202143 | 0.101072 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101072 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.02210e6 | 0.142184 | ||||||||
\(92\) | 6.49682e6 | 0.869848 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.69146e6 | −0.955128 | ||||||||
\(95\) | 362519. | 0.0433809 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.79048e6 | 0.310441 | 0.155220 | − | 0.987880i | \(-0.450391\pi\) | ||||
0.155220 | + | 0.987880i | \(0.450391\pi\) | |||||||
\(98\) | −1.26576e6 | −0.135850 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.38269e6 | 0.338269 | ||||||||
\(101\) | 1.43415e7 | 1.38506 | 0.692532 | − | 0.721387i | \(-0.256495\pi\) | ||||
0.692532 | + | 0.721387i | \(0.256495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.62771e6 | 0.146773 | 0.0733867 | − | 0.997304i | \(-0.476619\pi\) | ||||
0.0733867 | + | 0.997304i | \(0.476619\pi\) | |||||||
\(104\) | 1.83198e6 | 0.159700 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.66529e6 | −0.298908 | ||||||||
\(107\) | 7.86386e6 | 0.620572 | 0.310286 | − | 0.950643i | \(-0.399575\pi\) | ||||
0.310286 | + | 0.950643i | \(0.399575\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.63958e6 | 0.195228 | 0.0976141 | − | 0.995224i | \(-0.468879\pi\) | ||||
0.0976141 | + | 0.995224i | \(0.468879\pi\) | |||||||
\(110\) | −1.27105e6 | −0.0910518 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −441675. | −0.0297057 | ||||||||
\(113\) | 2.91448e7 | 1.90015 | 0.950074 | − | 0.312026i | \(-0.101008\pi\) | ||||
0.950074 | + | 0.312026i | \(0.101008\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.52928e7 | −0.937661 | ||||||||
\(116\) | −1.63135e7 | −0.970388 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.40762e6 | 0.0788673 | ||||||||
\(119\) | 2.91480e7 | 1.58560 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.85417e7 | −0.951483 | ||||||||
\(122\) | −1.46909e7 | −0.732468 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.66170e6 | −0.407969 | ||||||||
\(125\) | −2.28631e7 | −1.04701 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.71615e7 | −1.60983 | −0.804915 | − | 0.593390i | \(-0.797789\pi\) | ||||
−0.804915 | + | 0.593390i | \(0.797789\pi\) | |||||||
\(128\) | −1.56498e7 | −0.659588 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.67160e6 | −0.0667315 | ||||||||
\(131\) | −1.50104e7 | −0.583369 | −0.291684 | − | 0.956515i | \(-0.594216\pi\) | ||||
−0.291684 | + | 0.956515i | \(0.594216\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.51922e6 | −0.0559939 | ||||||||
\(134\) | −1.08585e6 | −0.0389856 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.22437e7 | 1.78094 | ||||||||
\(137\) | −1.75306e7 | −0.582470 | −0.291235 | − | 0.956652i | \(-0.594066\pi\) | ||||
−0.291235 | + | 0.956652i | \(0.594066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.16871e7 | −0.369110 | −0.184555 | − | 0.982822i | \(-0.559084\pi\) | ||||
−0.184555 | + | 0.982822i | \(0.559084\pi\) | |||||||
\(140\) | 1.23521e7 | 0.380446 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.70685e7 | 0.793332 | ||||||||
\(143\) | 1.24341e6 | 0.0355580 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.84004e7 | 1.04604 | ||||||||
\(146\) | 2.23324e7 | 0.593883 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.99679e7 | 0.506311 | ||||||||
\(149\) | 6.76391e7 | 1.67512 | 0.837559 | − | 0.546346i | \(-0.183982\pi\) | ||||
0.837559 | + | 0.546346i | \(0.183982\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.31830e7 | 1.02069 | 0.510345 | − | 0.859970i | \(-0.329518\pi\) | ||||
0.510345 | + | 0.859970i | \(0.329518\pi\) | |||||||
\(152\) | −2.72300e6 | −0.0628919 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.32664e6 | 0.117525 | ||||||||
\(155\) | 2.03888e7 | 0.439775 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.62920e7 | 0.954679 | 0.477340 | − | 0.878719i | \(-0.341601\pi\) | ||||
0.477340 | + | 0.878719i | \(0.341601\pi\) | |||||||
\(158\) | −3.62515e7 | −0.731183 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.56968e7 | 0.688985 | ||||||||
\(161\) | 6.40883e7 | 1.21029 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.22501e7 | 1.30672 | 0.653359 | − | 0.757048i | \(-0.273359\pi\) | ||||
0.653359 | + | 0.757048i | \(0.273359\pi\) | |||||||
\(164\) | −2.82253e7 | −0.499672 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.49022e7 | 0.422532 | ||||||||
\(167\) | −3.24667e7 | −0.539425 | −0.269713 | − | 0.962941i | \(-0.586929\pi\) | ||||
−0.269713 | + | 0.962941i | \(0.586929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.11133e7 | −0.973940 | ||||||||
\(170\) | −4.76702e7 | −0.744175 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.46150e7 | −0.368851 | ||||||||
\(173\) | −1.31381e7 | −0.192918 | −0.0964589 | − | 0.995337i | \(-0.530752\pi\) | ||||
−0.0964589 | + | 0.995337i | \(0.530752\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.33687e7 | 0.470659 | ||||||||
\(176\) | −537306. | −0.00742895 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.21409e6 | 0.122457 | ||||||||
\(179\) | 1.99708e7 | 0.260261 | 0.130131 | − | 0.991497i | \(-0.458460\pi\) | ||||
0.130131 | + | 0.991497i | \(0.458460\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.38499e7 | 1.17641 | 0.588205 | − | 0.808712i | \(-0.299835\pi\) | ||||
0.588205 | + | 0.808712i | \(0.299835\pi\) | |||||||
\(182\) | 7.00524e6 | 0.0861337 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.14869e8 | 1.35938 | ||||||||
\(185\) | −4.70025e7 | −0.545783 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.54591e7 | 0.396535 | ||||||||
\(188\) | 9.09298e7 | 0.998053 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.48462e6 | 0.0262798 | ||||||||
\(191\) | 7.50591e7 | 0.779447 | 0.389724 | − | 0.920932i | \(-0.372571\pi\) | ||||
0.389724 | + | 0.920932i | \(0.372571\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.13691e7 | −0.714594 | −0.357297 | − | 0.933991i | \(-0.616302\pi\) | ||||
−0.357297 | + | 0.933991i | \(0.616302\pi\) | |||||||
\(194\) | 1.91253e7 | 0.188062 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.49641e7 | 0.141956 | ||||||||
\(197\) | 1.40656e8 | 1.31077 | 0.655384 | − | 0.755296i | \(-0.272507\pi\) | ||||
0.655384 | + | 0.755296i | \(0.272507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.79140e7 | 0.251094 | 0.125547 | − | 0.992088i | \(-0.459931\pi\) | ||||
0.125547 | + | 0.992088i | \(0.459931\pi\) | |||||||
\(200\) | 5.98088e7 | 0.528640 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.82931e7 | 0.839060 | ||||||||
\(203\) | −1.60926e8 | −1.35018 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.64394e7 | 0.538626 | ||||||||
\(206\) | 1.11559e7 | 0.0889140 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −706629. | −0.00544465 | ||||||||
\(209\) | −1.84816e6 | −0.0140032 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.66531e8 | 1.22041 | 0.610207 | − | 0.792242i | \(-0.291086\pi\) | ||||
0.610207 | + | 0.792242i | \(0.291086\pi\) | |||||||
\(212\) | 4.33317e7 | 0.312342 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.38969e7 | 0.375937 | ||||||||
\(215\) | 5.79412e7 | 0.397606 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.54439e7 | −0.567639 | ||||||||
\(218\) | 1.80910e7 | 0.118268 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.50266e7 | 0.0951438 | ||||||||
\(221\) | 4.66334e7 | 0.290619 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.94297e6 | 0.0540026 | 0.0270013 | − | 0.999635i | \(-0.491404\pi\) | ||||
0.0270013 | + | 0.999635i | \(0.491404\pi\) | |||||||
\(224\) | −1.49596e8 | −0.889308 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.99751e8 | 1.15109 | ||||||||
\(227\) | 6.88172e7 | 0.390487 | 0.195243 | − | 0.980755i | \(-0.437450\pi\) | ||||
0.195243 | + | 0.980755i | \(0.437450\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.97507e8 | 1.08682 | 0.543411 | − | 0.839467i | \(-0.317132\pi\) | ||||
0.543411 | + | 0.839467i | \(0.317132\pi\) | |||||||
\(230\) | −1.04813e8 | −0.568027 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.88438e8 | −1.51651 | ||||||||
\(233\) | −2.46365e8 | −1.27595 | −0.637973 | − | 0.770058i | \(-0.720227\pi\) | ||||
−0.637973 | + | 0.770058i | \(0.720227\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.14039e8 | −1.07586 | ||||||||
\(236\) | −1.66411e7 | −0.0824118 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.99773e8 | 0.960545 | ||||||||
\(239\) | 3.78259e8 | 1.79224 | 0.896120 | − | 0.443812i | \(-0.146374\pi\) | ||||
0.896120 | + | 0.443812i | \(0.146374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.71983e8 | −1.25165 | −0.625824 | − | 0.779964i | \(-0.715237\pi\) | ||||
−0.625824 | + | 0.779964i | \(0.715237\pi\) | |||||||
\(242\) | −1.27080e8 | −0.576400 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.73678e8 | 0.765387 | ||||||||
\(245\) | −3.52239e7 | −0.153023 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.43058e6 | −0.0102629 | ||||||||
\(248\) | −1.53146e8 | −0.637567 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.56698e8 | −0.634268 | ||||||||
\(251\) | −1.67816e8 | −0.669847 | −0.334923 | − | 0.942245i | \(-0.608710\pi\) | ||||
−0.334923 | + | 0.942245i | \(0.608710\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.79645e7 | 0.302674 | ||||||||
\(254\) | −2.54695e8 | −0.975221 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.62399e8 | −0.977513 | ||||||||
\(257\) | 3.77370e8 | 1.38676 | 0.693381 | − | 0.720571i | \(-0.256120\pi\) | ||||
0.693381 | + | 0.720571i | \(0.256120\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.96975e8 | 0.704470 | ||||||||
\(260\) | 1.97619e7 | 0.0697305 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.02878e8 | −0.353400 | ||||||||
\(263\) | 2.37395e8 | 0.804686 | 0.402343 | − | 0.915489i | \(-0.368196\pi\) | ||||
0.402343 | + | 0.915489i | \(0.368196\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.01998e8 | −0.336692 | ||||||||
\(266\) | −1.04124e7 | −0.0339206 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.28371e7 | 0.0407377 | ||||||||
\(269\) | −2.56851e8 | −0.804542 | −0.402271 | − | 0.915521i | \(-0.631779\pi\) | ||||
−0.402271 | + | 0.915521i | \(0.631779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.99436e8 | −0.913927 | −0.456964 | − | 0.889485i | \(-0.651063\pi\) | ||||
−0.456964 | + | 0.889485i | \(0.651063\pi\) | |||||||
\(272\) | −2.01514e7 | −0.0607176 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.20150e8 | −0.352855 | ||||||||
\(275\) | 4.05937e7 | 0.117705 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.07342e8 | −0.303453 | −0.151727 | − | 0.988422i | \(-0.548483\pi\) | ||||
−0.151727 | + | 0.988422i | \(0.548483\pi\) | |||||||
\(278\) | −8.01006e7 | −0.223604 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.18396e8 | 0.594555 | ||||||||
\(281\) | −1.26999e8 | −0.341451 | −0.170726 | − | 0.985319i | \(-0.554611\pi\) | ||||
−0.170726 | + | 0.985319i | \(0.554611\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.79420e8 | 1.78191 | 0.890955 | − | 0.454091i | \(-0.150036\pi\) | ||||
0.890955 | + | 0.454091i | \(0.150036\pi\) | |||||||
\(284\) | −3.20009e8 | −0.828986 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.52200e6 | 0.0215407 | ||||||||
\(287\) | −2.78430e8 | −0.695232 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.19537e8 | 2.24092 | ||||||||
\(290\) | 2.63187e8 | 0.633682 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.64018e8 | −0.620573 | ||||||||
\(293\) | −3.54246e8 | −0.822752 | −0.411376 | − | 0.911466i | \(-0.634952\pi\) | ||||
−0.411376 | + | 0.911466i | \(0.634952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.91714e7 | 0.0888366 | ||||||||
\(296\) | 3.53051e8 | 0.791254 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.63581e8 | 1.01477 | ||||||||
\(299\) | 1.02534e8 | 0.221829 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.42816e8 | −0.513210 | ||||||||
\(302\) | 2.95966e8 | 0.618325 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.05031e6 | 0.00214418 | ||||||||
\(305\) | −4.08821e8 | −0.825056 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.47178e8 | −0.882056 | −0.441028 | − | 0.897493i | \(-0.645386\pi\) | ||||
−0.441028 | + | 0.897493i | \(0.645386\pi\) | |||||||
\(308\) | −6.29724e7 | −0.122807 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.39739e8 | 0.266412 | ||||||||
\(311\) | 1.03177e9 | 1.94501 | 0.972506 | − | 0.232879i | \(-0.0748145\pi\) | ||||
0.972506 | + | 0.232879i | \(0.0748145\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.47667e8 | −0.272194 | −0.136097 | − | 0.990695i | \(-0.543456\pi\) | ||||
−0.136097 | + | 0.990695i | \(0.543456\pi\) | |||||||
\(314\) | 3.17274e8 | 0.578336 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.28571e8 | 0.764044 | ||||||||
\(317\) | 8.08129e8 | 1.42486 | 0.712431 | − | 0.701742i | \(-0.247594\pi\) | ||||
0.712431 | + | 0.701742i | \(0.247594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.95769e8 | −0.337658 | ||||||||
\(320\) | 2.31167e8 | 0.394367 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.39245e8 | 0.733181 | ||||||||
\(323\) | −6.93145e7 | −0.114450 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.33861e7 | 0.0862654 | ||||||||
\(326\) | 4.95184e8 | 0.791599 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.99047e8 | −0.780878 | ||||||||
\(329\) | 8.96983e8 | 1.38867 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.71934e8 | −0.260594 | −0.130297 | − | 0.991475i | \(-0.541593\pi\) | ||||
−0.130297 | + | 0.991475i | \(0.541593\pi\) | |||||||
\(332\) | −2.94398e8 | −0.441521 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.22519e8 | −0.326779 | ||||||||
\(335\) | −3.02173e7 | −0.0439136 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.64986e8 | 0.377154 | 0.188577 | − | 0.982058i | \(-0.439613\pi\) | ||||
0.188577 | + | 0.982058i | \(0.439613\pi\) | |||||||
\(338\) | −4.18855e8 | −0.590004 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.63565e8 | 0.777620 | ||||||||
\(341\) | −1.03944e8 | −0.141958 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.05862e8 | 1.07828 | ||||||||
\(344\) | −4.35215e8 | −0.576433 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00455e7 | −0.116868 | ||||||||
\(347\) | −5.14421e8 | −0.660945 | −0.330473 | − | 0.943816i | \(-0.607208\pi\) | ||||
−0.330473 | + | 0.943816i | \(0.607208\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.09218e7 | −0.0767157 | −0.0383578 | − | 0.999264i | \(-0.512213\pi\) | ||||
−0.0383578 | + | 0.999264i | \(0.512213\pi\) | |||||||
\(350\) | 2.28701e8 | 0.285121 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.81986e8 | −0.222402 | ||||||||
\(353\) | 1.90611e8 | 0.230641 | 0.115320 | − | 0.993328i | \(-0.463211\pi\) | ||||
0.115320 | + | 0.993328i | \(0.463211\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.53268e8 | 0.893614 | ||||||||
\(356\) | −1.08931e8 | −0.127960 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.36875e8 | 0.157664 | ||||||||
\(359\) | 1.39955e9 | 1.59646 | 0.798229 | − | 0.602354i | \(-0.205770\pi\) | ||||
0.798229 | + | 0.602354i | \(0.205770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.90259e8 | −0.995958 | ||||||||
\(362\) | 6.43224e8 | 0.712659 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.28171e7 | −0.0900047 | ||||||||
\(365\) | 6.21471e8 | 0.668953 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50266e9 | −1.58683 | −0.793413 | − | 0.608684i | \(-0.791698\pi\) | ||||
−0.793413 | + | 0.608684i | \(0.791698\pi\) | |||||||
\(368\) | −4.43073e7 | −0.0463455 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.22143e8 | −0.330631 | ||||||||
\(371\) | 4.27449e8 | 0.434585 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.89561e7 | 0.0887554 | 0.0443777 | − | 0.999015i | \(-0.485869\pi\) | ||||
0.0443777 | + | 0.999015i | \(0.485869\pi\) | |||||||
\(374\) | 2.43027e8 | 0.240218 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.60772e9 | 1.55974 | ||||||||
\(377\) | −2.57463e8 | −0.247469 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.27075e8 | −0.686028 | −0.343014 | − | 0.939330i | \(-0.611448\pi\) | ||||
−0.343014 | + | 0.939330i | \(0.611448\pi\) | |||||||
\(380\) | −2.93736e7 | −0.0274608 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.14436e8 | 0.472182 | ||||||||
\(383\) | −2.06745e9 | −1.88036 | −0.940178 | − | 0.340683i | \(-0.889342\pi\) | ||||
−0.940178 | + | 0.340683i | \(0.889342\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.48231e8 | 0.132381 | ||||||||
\(386\) | −4.89145e8 | −0.432895 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.26102e8 | −0.196514 | ||||||||
\(389\) | 8.24531e7 | 0.0710205 | 0.0355102 | − | 0.999369i | \(-0.488694\pi\) | ||||
0.0355102 | + | 0.999369i | \(0.488694\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.92402e9 | 2.47379 | ||||||||
\(392\) | 2.64578e8 | 0.221846 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.64019e8 | 0.794051 | ||||||||
\(395\) | −1.00881e9 | −0.823609 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.60792e8 | 0.209183 | 0.104592 | − | 0.994515i | \(-0.466646\pi\) | ||||
0.104592 | + | 0.994515i | \(0.466646\pi\) | |||||||
\(398\) | 1.91316e8 | 0.152111 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.30694e7 | −0.0180230 | ||||||||
\(401\) | 5.57165e8 | 0.431498 | 0.215749 | − | 0.976449i | \(-0.430781\pi\) | ||||
0.215749 | + | 0.976449i | \(0.430781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.36700e8 | −0.104040 | ||||||||
\(404\) | −1.16204e9 | −0.876769 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.10295e9 | −0.817925 | ||||||||
\(407\) | 2.39624e8 | 0.176177 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.59001e9 | −1.14913 | −0.574564 | − | 0.818460i | \(-0.694828\pi\) | ||||
−0.574564 | + | 0.818460i | \(0.694828\pi\) | |||||||
\(410\) | 4.55359e8 | 0.326295 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.31887e8 | −0.0929100 | ||||||||
\(413\) | −1.64157e8 | −0.114666 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.92983e8 | 0.475942 | ||||||||
\(416\) | −2.39336e8 | −0.162998 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.26668e7 | −0.00848303 | ||||||||
\(419\) | −5.88021e8 | −0.390520 | −0.195260 | − | 0.980751i | \(-0.562555\pi\) | ||||
−0.195260 | + | 0.980751i | \(0.562555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.50924e8 | −0.490466 | −0.245233 | − | 0.969464i | \(-0.578864\pi\) | ||||
−0.245233 | + | 0.969464i | \(0.578864\pi\) | |||||||
\(422\) | 1.14136e9 | 0.739316 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.66142e8 | 0.488123 | ||||||||
\(425\) | 1.52245e9 | 0.962013 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.71326e9 | 1.06494 | ||||||||
\(428\) | −6.37178e8 | −0.392833 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.97114e8 | 0.240866 | ||||||||
\(431\) | 2.36435e9 | 1.42247 | 0.711233 | − | 0.702957i | \(-0.248137\pi\) | ||||
0.711233 | + | 0.702957i | \(0.248137\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.97398e7 | 0.0412832 | 0.0206416 | − | 0.999787i | \(-0.493429\pi\) | ||||
0.0206416 | + | 0.999787i | \(0.493429\pi\) | |||||||
\(434\) | −5.85611e8 | −0.343871 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.13875e8 | −0.123583 | ||||||||
\(437\) | −1.52403e8 | −0.0873592 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.54774e9 | −1.43724 | −0.718620 | − | 0.695403i | \(-0.755226\pi\) | ||||
−0.718620 | + | 0.695403i | \(0.755226\pi\) | |||||||
\(440\) | 2.65683e8 | 0.148689 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.19614e8 | 0.176055 | ||||||||
\(443\) | −1.15431e9 | −0.630825 | −0.315412 | − | 0.948955i | \(-0.602143\pi\) | ||||
−0.315412 | + | 0.948955i | \(0.602143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.56411e8 | 0.137936 | ||||||||
\(446\) | 6.12929e7 | 0.0327143 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.68759e8 | −0.509029 | ||||||||
\(449\) | −5.55994e8 | −0.289873 | −0.144937 | − | 0.989441i | \(-0.546298\pi\) | ||||
−0.144937 | + | 0.989441i | \(0.546298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.38715e8 | −0.173867 | ||||||||
\(452\) | −2.36150e9 | −1.20283 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.71655e8 | 0.236554 | ||||||||
\(455\) | 1.94943e8 | 0.0970215 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.93559e8 | 0.192887 | 0.0964435 | − | 0.995338i | \(-0.469253\pi\) | ||||
0.0964435 | + | 0.995338i | \(0.469253\pi\) | |||||||
\(458\) | 1.35366e9 | 0.658388 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.23912e9 | 0.593555 | ||||||||
\(461\) | 2.99382e9 | 1.42322 | 0.711611 | − | 0.702574i | \(-0.247966\pi\) | ||||
0.711611 | + | 0.702574i | \(0.247966\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.18369e9 | −0.554248 | −0.277124 | − | 0.960834i | \(-0.589381\pi\) | ||||
−0.277124 | + | 0.960834i | \(0.589381\pi\) | |||||||
\(464\) | 1.11256e8 | 0.0517023 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.68852e9 | −0.772957 | ||||||||
\(467\) | −3.15650e9 | −1.43416 | −0.717079 | − | 0.696992i | \(-0.754521\pi\) | ||||
−0.717079 | + | 0.696992i | \(0.754521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.26633e8 | 0.0566815 | ||||||||
\(470\) | −1.46697e9 | −0.651747 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.94228e8 | −0.128792 | ||||||||
\(473\) | −2.95390e8 | −0.128346 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.93515e7 | −0.0339725 | ||||||||
\(476\) | −2.36175e9 | −1.00371 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.59249e9 | 1.08572 | ||||||||
\(479\) | −2.27050e9 | −0.943945 | −0.471972 | − | 0.881613i | \(-0.656458\pi\) | ||||
−0.471972 | + | 0.881613i | \(0.656458\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.15137e8 | 0.129120 | ||||||||
\(482\) | −1.86410e9 | −0.758238 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.50236e9 | 0.602305 | ||||||||
\(485\) | 5.32222e8 | 0.211834 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.04995e8 | 0.0804252 | 0.0402126 | − | 0.999191i | \(-0.487196\pi\) | ||||
0.0402126 | + | 0.999191i | \(0.487196\pi\) | |||||||
\(488\) | 3.07078e9 | 1.19613 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.41416e8 | −0.0926999 | ||||||||
\(491\) | −1.08333e9 | −0.413023 | −0.206512 | − | 0.978444i | \(-0.566211\pi\) | ||||
−0.206512 | + | 0.978444i | \(0.566211\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.34224e9 | −2.75972 | ||||||||
\(494\) | −1.66586e7 | −0.00621718 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.90715e7 | 0.0217366 | ||||||||
\(497\) | −3.15675e9 | −1.15343 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.23774e9 | 0.445942 | 0.222971 | − | 0.974825i | \(-0.428425\pi\) | ||||
0.222971 | + | 0.974825i | \(0.428425\pi\) | |||||||
\(500\) | 1.85251e9 | 0.662773 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.15017e9 | −0.405787 | ||||||||
\(503\) | −3.42069e9 | −1.19847 | −0.599234 | − | 0.800574i | \(-0.704528\pi\) | ||||
−0.599234 | + | 0.800574i | \(0.704528\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.73532e9 | 0.945122 | ||||||||
\(506\) | 5.34349e8 | 0.183357 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.01105e9 | 1.01905 | ||||||||
\(509\) | 3.62806e9 | 1.21944 | 0.609722 | − | 0.792616i | \(-0.291281\pi\) | ||||
0.609722 | + | 0.792616i | \(0.291281\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.60442e9 | −0.863451 | ||||||||
\(512\) | 2.04753e8 | 0.0674195 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.58640e9 | 0.840088 | ||||||||
\(515\) | 3.10449e8 | 0.100153 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.09120e9 | 0.347285 | ||||||||
\(518\) | 1.35002e9 | 0.426762 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.49408e8 | 0.108974 | ||||||||
\(521\) | 1.36162e9 | 0.421817 | 0.210909 | − | 0.977506i | \(-0.432358\pi\) | ||||
0.210909 | + | 0.977506i | \(0.432358\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.07415e9 | 0.328329 | 0.164165 | − | 0.986433i | \(-0.447507\pi\) | ||||
0.164165 | + | 0.986433i | \(0.447507\pi\) | |||||||
\(524\) | 1.21624e9 | 0.369282 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.62705e9 | 0.487472 | ||||||||
\(527\) | −3.89838e9 | −1.16024 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.02428e9 | 0.888234 | ||||||||
\(530\) | −6.99072e8 | −0.203965 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.23097e8 | 0.0354451 | ||||||||
\(533\) | −4.45456e8 | −0.127426 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.49985e9 | 0.423458 | ||||||||
\(536\) | 2.26972e8 | 0.0636642 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.76039e9 | −0.487385 | ||||||||
\(539\) | 1.79575e8 | 0.0493953 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.13348e9 | −1.66539 | −0.832696 | − | 0.553730i | \(-0.813204\pi\) | ||||
−0.832696 | + | 0.553730i | \(0.813204\pi\) | |||||||
\(542\) | −2.05226e9 | −0.553649 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.82531e9 | −1.81772 | ||||||||
\(545\) | 5.03440e8 | 0.133217 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.39180e9 | −1.66981 | −0.834906 | − | 0.550392i | \(-0.814478\pi\) | ||||
−0.834906 | + | 0.550392i | \(0.814478\pi\) | |||||||
\(548\) | 1.42043e9 | 0.368713 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.78219e8 | 0.0713045 | ||||||||
\(551\) | 3.82685e8 | 0.0974565 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.22767e9 | 1.06307 | ||||||||
\(554\) | −7.35697e8 | −0.183829 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.46963e8 | 0.233653 | ||||||||
\(557\) | −5.20568e9 | −1.27639 | −0.638197 | − | 0.769873i | \(-0.720319\pi\) | ||||
−0.638197 | + | 0.769873i | \(0.720319\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.88478e8 | −0.0940643 | ||||||||
\(560\) | −8.42396e7 | −0.0202702 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.70420e8 | −0.206848 | ||||||||
\(563\) | −3.32429e9 | −0.785089 | −0.392545 | − | 0.919733i | \(-0.628405\pi\) | ||||
−0.392545 | + | 0.919733i | \(0.628405\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.55872e9 | 1.29660 | ||||||||
\(566\) | 4.65657e9 | 1.07947 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.65803e9 | −1.29553 | ||||||||
\(569\) | −1.61858e9 | −0.368333 | −0.184166 | − | 0.982895i | \(-0.558959\pi\) | ||||
−0.184166 | + | 0.982895i | \(0.558959\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.26853e8 | −0.140909 | −0.0704546 | − | 0.997515i | \(-0.522445\pi\) | ||||
−0.0704546 | + | 0.997515i | \(0.522445\pi\) | |||||||
\(572\) | −1.00749e8 | −0.0225088 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.90829e9 | −0.421165 | ||||||||
\(575\) | 3.34743e9 | 0.734302 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.33845e9 | 0.506772 | 0.253386 | − | 0.967365i | \(-0.418456\pi\) | ||||
0.253386 | + | 0.967365i | \(0.418456\pi\) | |||||||
\(578\) | 6.30228e9 | 1.35753 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.11144e9 | −0.662161 | ||||||||
\(581\) | −2.90411e9 | −0.614323 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.19999e8 | 0.108683 | ||||||||
\(584\) | −4.66806e9 | −0.969820 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.42791e9 | −0.498416 | ||||||||
\(587\) | 5.68734e9 | 1.16058 | 0.580291 | − | 0.814409i | \(-0.302939\pi\) | ||||
0.580291 | + | 0.814409i | \(0.302939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.03187e8 | 0.0409725 | ||||||||
\(590\) | 2.68471e8 | 0.0538164 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.36178e8 | −0.0269763 | ||||||||
\(593\) | 6.92748e9 | 1.36422 | 0.682109 | − | 0.731250i | \(-0.261063\pi\) | ||||
0.682109 | + | 0.731250i | \(0.261063\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.55932e9 | 1.08196 | ||||||||
\(596\) | −5.48053e9 | −1.06038 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.02741e8 | 0.134382 | ||||||||
\(599\) | −1.04577e7 | −0.00198812 | −0.000994062 | − | 1.00000i | \(-0.500316\pi\) | ||||
−0.000994062 | 1.00000i | \(0.500316\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.50968e9 | 1.03530 | 0.517649 | − | 0.855593i | \(-0.326807\pi\) | ||||
0.517649 | + | 0.855593i | \(0.326807\pi\) | |||||||
\(602\) | −1.66420e9 | −0.310898 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.49896e9 | −0.646114 | ||||||||
\(605\) | −3.53641e9 | −0.649260 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.08515e10 | −1.96939 | −0.984693 | − | 0.174298i | \(-0.944234\pi\) | ||||
−0.984693 | + | 0.174298i | \(0.944234\pi\) | |||||||
\(608\) | 3.55742e8 | 0.0641908 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.80195e9 | −0.499812 | ||||||||
\(611\) | 1.43507e9 | 0.254524 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.00263e9 | −0.877177 | −0.438588 | − | 0.898688i | \(-0.644521\pi\) | ||||
−0.438588 | + | 0.898688i | \(0.644521\pi\) | |||||||
\(614\) | −3.06485e9 | −0.534342 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.11341e9 | −0.191920 | ||||||||
\(617\) | −1.47593e9 | −0.252970 | −0.126485 | − | 0.991969i | \(-0.540370\pi\) | ||||
−0.126485 | + | 0.991969i | \(0.540370\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.36559e9 | −1.58715 | −0.793575 | − | 0.608472i | \(-0.791783\pi\) | ||||
−0.793575 | + | 0.608472i | \(0.791783\pi\) | |||||||
\(620\) | −1.65202e9 | −0.278385 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7.07150e9 | 1.17827 | ||||||||
\(623\) | −1.07455e9 | −0.178041 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.09904e9 | −0.180067 | ||||||||
\(626\) | −1.01207e9 | −0.164893 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.75087e9 | −0.604328 | ||||||||
\(629\) | 8.98698e9 | 1.43991 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.19966e10 | −1.90088 | −0.950438 | − | 0.310914i | \(-0.899365\pi\) | ||||
−0.950438 | + | 0.310914i | \(0.899365\pi\) | |||||||
\(632\) | 7.57751e9 | 1.19403 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.53871e9 | 0.863170 | ||||||||
\(635\) | −7.08771e9 | −1.09849 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.36165e8 | 0.0362016 | ||||||||
\(638\) | −1.34175e9 | −0.204551 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.98484e9 | −0.450081 | ||||||||
\(641\) | 1.25626e10 | 1.88398 | 0.941989 | − | 0.335644i | \(-0.108954\pi\) | ||||
0.941989 | + | 0.335644i | \(0.108954\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.11211e9 | −0.609995 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(644\) | −5.19283e9 | −0.766131 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.75064e8 | −0.0693327 | ||||||||
\(647\) | 8.36038e9 | 1.21356 | 0.606780 | − | 0.794870i | \(-0.292461\pi\) | ||||
0.606780 | + | 0.794870i | \(0.292461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.99700e8 | −0.0286762 | ||||||||
\(650\) | 3.65895e8 | 0.0522588 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.85415e9 | −0.827175 | ||||||||
\(653\) | −5.92578e8 | −0.0832817 | −0.0416409 | − | 0.999133i | \(-0.513259\pi\) | ||||
−0.0416409 | + | 0.999133i | \(0.513259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.86290e9 | −0.398072 | ||||||||
\(656\) | 1.92492e8 | 0.0266225 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.14769e9 | 0.841243 | ||||||||
\(659\) | −3.61916e9 | −0.492617 | −0.246308 | − | 0.969192i | \(-0.579218\pi\) | ||||
−0.246308 | + | 0.969192i | \(0.579218\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.49686e9 | 0.201593 | 0.100797 | − | 0.994907i | \(-0.467861\pi\) | ||||
0.100797 | + | 0.994907i | \(0.467861\pi\) | |||||||
\(662\) | −1.17839e9 | −0.157866 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.20521e9 | −0.690002 | ||||||||
\(665\) | −2.89757e8 | −0.0382084 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.61435e10 | −2.10648 | ||||||||
\(668\) | 2.63066e9 | 0.341465 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.07102e8 | −0.0266025 | ||||||||
\(671\) | 2.08421e9 | 0.266326 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.55009e10 | 1.96022 | 0.980109 | − | 0.198461i | \(-0.0635943\pi\) | ||||
0.980109 | + | 0.198461i | \(0.0635943\pi\) | |||||||
\(674\) | 1.81615e9 | 0.228476 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.95177e9 | 0.616520 | ||||||||
\(677\) | 7.97429e9 | 0.987715 | 0.493857 | − | 0.869543i | \(-0.335586\pi\) | ||||
0.493857 | + | 0.869543i | \(0.335586\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.23040e9 | −0.273425 | ||||||||
\(680\) | 9.96431e9 | 1.21525 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.12407e8 | −0.0859969 | ||||||||
\(683\) | −7.37364e9 | −0.885542 | −0.442771 | − | 0.896635i | \(-0.646005\pi\) | ||||
−0.442771 | + | 0.896635i | \(0.646005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.34356e9 | −0.397458 | ||||||||
\(686\) | 5.52317e9 | 0.653212 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.67871e8 | 0.0196524 | ||||||||
\(689\) | 6.83868e8 | 0.0796535 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.70889e9 | 0.658232 | 0.329116 | − | 0.944290i | \(-0.393249\pi\) | ||||
0.329116 | + | 0.944290i | \(0.393249\pi\) | |||||||
\(692\) | 1.06453e9 | 0.122120 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.52571e9 | −0.400395 | ||||||||
\(695\) | −2.22905e9 | −0.251868 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.27034e10 | −1.42103 | ||||||||
\(698\) | −4.17543e8 | −0.0464737 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.70374e9 | −0.297935 | ||||||||
\(701\) | −1.23928e10 | −1.35880 | −0.679402 | − | 0.733767i | \(-0.737761\pi\) | ||||
−0.679402 | + | 0.733767i | \(0.737761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.68410e8 | −0.0508491 | ||||||||
\(704\) | −1.17851e9 | −0.127300 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.30640e9 | 0.139720 | ||||||||
\(707\) | −1.14630e10 | −1.21992 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.39979e10 | 1.47504 | 0.737518 | − | 0.675328i | \(-0.235998\pi\) | ||||
0.737518 | + | 0.675328i | \(0.235998\pi\) | |||||||
\(710\) | 5.16271e9 | 0.541344 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.92599e9 | −0.199974 | ||||||||
\(713\) | −8.57143e9 | −0.885605 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.37152e8 | 0.0242636 | ||||||||
\(716\) | −1.61815e9 | −0.164750 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.59215e9 | 0.967120 | ||||||||
\(719\) | −7.66012e9 | −0.768572 | −0.384286 | − | 0.923214i | \(-0.625552\pi\) | ||||
−0.384286 | + | 0.923214i | \(0.625552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.30101e9 | −0.129273 | ||||||||
\(722\) | −6.10161e9 | −0.603343 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.60430e9 | −0.744688 | ||||||||
\(725\) | −8.40543e9 | −0.819175 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.02618e10 | 0.990493 | 0.495247 | − | 0.868752i | \(-0.335078\pi\) | ||||
0.495247 | + | 0.868752i | \(0.335078\pi\) | |||||||
\(728\) | −1.46428e9 | −0.140658 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.25940e9 | 0.405246 | ||||||||
\(731\) | −1.10785e10 | −1.04899 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.67714e10 | −1.57292 | −0.786459 | − | 0.617643i | \(-0.788088\pi\) | ||||
−0.786459 | + | 0.617643i | \(0.788088\pi\) | |||||||
\(734\) | −1.02988e10 | −0.961285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.50069e10 | −1.38746 | ||||||||
\(737\) | 1.54051e8 | 0.0141752 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.49527e9 | 0.500880 | 0.250440 | − | 0.968132i | \(-0.419425\pi\) | ||||
0.250440 | + | 0.968132i | \(0.419425\pi\) | |||||||
\(740\) | 3.80843e9 | 0.345490 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.92962e9 | 0.263268 | ||||||||
\(743\) | 1.77986e9 | 0.159193 | 0.0795966 | − | 0.996827i | \(-0.474637\pi\) | ||||
0.0795966 | + | 0.996827i | \(0.474637\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.29006e10 | 1.14305 | ||||||||
\(746\) | 6.09683e8 | 0.0537673 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.87311e9 | −0.251013 | ||||||||
\(749\) | −6.28548e9 | −0.546578 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.12062e9 | −0.613448 | −0.306724 | − | 0.951798i | \(-0.599233\pi\) | ||||
−0.306724 | + | 0.951798i | \(0.599233\pi\) | |||||||
\(752\) | −6.20127e8 | −0.0531763 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.76459e9 | −0.149914 | ||||||||
\(755\) | 8.23619e9 | 0.696485 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.43143e9 | 0.538855 | 0.269428 | − | 0.963021i | \(-0.413166\pi\) | ||||
0.269428 | + | 0.963021i | \(0.413166\pi\) | |||||||
\(758\) | −4.98319e9 | −0.415590 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.19350e8 | −0.0429153 | ||||||||
\(761\) | −1.46912e10 | −1.20840 | −0.604202 | − | 0.796831i | \(-0.706508\pi\) | ||||
−0.604202 | + | 0.796831i | \(0.706508\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.10979e9 | −0.171950 | ||||||||
\(764\) | −6.08175e9 | −0.493403 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.41698e10 | −1.13910 | ||||||||
\(767\) | −2.62632e8 | −0.0210167 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.24049e10 | 0.983677 | 0.491838 | − | 0.870687i | \(-0.336325\pi\) | ||||
0.491838 | + | 0.870687i | \(0.336325\pi\) | |||||||
\(770\) | 1.01594e9 | 0.0801952 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.78276e9 | 0.452350 | ||||||||
\(773\) | 2.65186e9 | 0.206501 | 0.103250 | − | 0.994655i | \(-0.467076\pi\) | ||||
0.103250 | + | 0.994655i | \(0.467076\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.46287e9 | −0.344396 | ||||||||
\(776\) | −3.99768e9 | −0.307109 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.65113e8 | 0.0430236 | ||||||||
\(779\) | 6.62112e8 | 0.0501823 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.84024e9 | −0.288456 | ||||||||
\(782\) | 2.00405e10 | 1.49860 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.02053e8 | −0.00756342 | ||||||||
\(785\) | 8.82916e9 | 0.651441 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.05957e9 | −0.296871 | −0.148436 | − | 0.988922i | \(-0.547424\pi\) | ||||
−0.148436 | + | 0.988922i | \(0.547424\pi\) | |||||||
\(788\) | −1.13968e10 | −0.829738 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.91415e9 | −0.498935 | ||||||||
\(791\) | −2.32951e10 | −1.67358 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.74102e9 | 0.195189 | ||||||||
\(794\) | 1.78740e9 | 0.126721 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.26177e9 | −0.158947 | ||||||||
\(797\) | −2.36833e10 | −1.65706 | −0.828530 | − | 0.559944i | \(-0.810823\pi\) | ||||
−0.828530 | + | 0.559944i | \(0.810823\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.09248e10 | 2.83839 | ||||||||
\(800\) | −7.81364e9 | −0.539558 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.81867e9 | 0.261398 | ||||||||
\(803\) | −3.16832e9 | −0.215936 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.22234e10 | 0.825859 | ||||||||
\(806\) | −9.36910e8 | −0.0630268 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.05458e10 | −1.37020 | ||||||||
\(809\) | 9.66394e9 | 0.641704 | 0.320852 | − | 0.947129i | \(-0.396031\pi\) | ||||
0.320852 | + | 0.947129i | \(0.396031\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.27359e10 | 0.838413 | 0.419207 | − | 0.907891i | \(-0.362308\pi\) | ||||
0.419207 | + | 0.907891i | \(0.362308\pi\) | |||||||
\(812\) | 1.30392e10 | 0.854684 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.64232e9 | 0.106727 | ||||||||
\(815\) | 1.37801e10 | 0.891661 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.77422e8 | 0.0370438 | ||||||||
\(818\) | −1.08975e10 | −0.696132 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.38333e9 | −0.340959 | ||||||||
\(821\) | −1.18429e10 | −0.746893 | −0.373446 | − | 0.927652i | \(-0.621824\pi\) | ||||
−0.373446 | + | 0.927652i | \(0.621824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.12076e10 | 0.700829 | 0.350415 | − | 0.936595i | \(-0.386041\pi\) | ||||
0.350415 | + | 0.936595i | \(0.386041\pi\) | |||||||
\(824\) | −2.33188e9 | −0.145198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.12509e9 | −0.0694636 | ||||||||
\(827\) | 1.69838e10 | 1.04416 | 0.522078 | − | 0.852898i | \(-0.325157\pi\) | ||||
0.522078 | + | 0.852898i | \(0.325157\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.59293e9 | −0.279994 | −0.139997 | − | 0.990152i | \(-0.544709\pi\) | ||||
−0.139997 | + | 0.990152i | \(0.544709\pi\) | |||||||
\(830\) | 4.74953e9 | 0.288322 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.54990e9 | −0.0932980 | ||||||||
\(833\) | 6.73488e9 | 0.403713 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.19230e9 | −0.368086 | ||||||||
\(836\) | 1.49749e8 | 0.00886428 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.03015e9 | −0.236574 | ||||||||
\(839\) | 2.30945e10 | 1.35002 | 0.675012 | − | 0.737806i | \(-0.264138\pi\) | ||||
0.675012 | + | 0.737806i | \(0.264138\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.32866e10 | 1.34996 | ||||||||
\(842\) | −5.14664e9 | −0.297120 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.34934e10 | −0.772542 | ||||||||
\(845\) | −1.16560e10 | −0.664584 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.48202e10 | 0.838033 | ||||||||
\(848\) | −2.95516e8 | −0.0166416 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.04345e10 | 0.582779 | ||||||||
\(851\) | 1.97598e10 | 1.09908 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.22496e10 | 1.22744 | 0.613721 | − | 0.789523i | \(-0.289672\pi\) | ||||
0.613721 | + | 0.789523i | \(0.289672\pi\) | |||||||
\(854\) | 1.17422e10 | 0.645132 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.12659e10 | −0.613912 | ||||||||
\(857\) | −1.07105e10 | −0.581270 | −0.290635 | − | 0.956834i | \(-0.593867\pi\) | ||||
−0.290635 | + | 0.956834i | \(0.593867\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.19391e10 | 1.71928 | 0.859639 | − | 0.510902i | \(-0.170688\pi\) | ||||
0.859639 | + | 0.510902i | \(0.170688\pi\) | |||||||
\(860\) | −4.69475e9 | −0.251691 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.62047e10 | 0.861717 | ||||||||
\(863\) | −2.90663e10 | −1.53940 | −0.769700 | − | 0.638406i | \(-0.779594\pi\) | ||||
−0.769700 | + | 0.638406i | \(0.779594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.50580e9 | −0.131641 | ||||||||
\(866\) | 4.77979e8 | 0.0250090 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.92319e9 | 0.359325 | ||||||||
\(869\) | 5.14304e9 | 0.265858 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.02598e8 | 0.0103889 | ||||||||
\(872\) | −3.78150e9 | −0.193133 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.04453e9 | −0.0529215 | ||||||||
\(875\) | 1.82742e10 | 0.922167 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.87443e9 | −0.0938364 | −0.0469182 | − | 0.998899i | \(-0.514940\pi\) | ||||
−0.0469182 | + | 0.998899i | \(0.514940\pi\) | |||||||
\(878\) | −1.74616e10 | −0.870668 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.02479e8 | −0.00506927 | ||||||||
\(881\) | 3.84330e10 | 1.89360 | 0.946802 | − | 0.321818i | \(-0.104294\pi\) | ||||
0.946802 | + | 0.321818i | \(0.104294\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.17045e10 | 0.572125 | 0.286063 | − | 0.958211i | \(-0.407653\pi\) | ||||
0.286063 | + | 0.958211i | \(0.407653\pi\) | |||||||
\(884\) | −3.77853e9 | −0.183967 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.91134e9 | −0.382148 | ||||||||
\(887\) | −3.09354e9 | −0.148841 | −0.0744205 | − | 0.997227i | \(-0.523711\pi\) | ||||
−0.0744205 | + | 0.997227i | \(0.523711\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.97027e10 | 1.41788 | ||||||||
\(890\) | 1.75738e9 | 0.0835604 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.24615e8 | −0.0341846 | ||||||||
\(893\) | −2.13304e9 | −0.100235 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.80897e9 | 0.177594 | ||||||||
\(896\) | 1.25087e10 | 0.580942 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.81064e9 | −0.175603 | ||||||||
\(899\) | 2.15229e10 | 0.987967 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.95023e10 | 0.888279 | ||||||||
\(902\) | −2.32147e9 | −0.105327 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.17533e10 | −1.87975 | ||||||||
\(905\) | 1.78997e10 | 0.802744 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.95597e9 | −0.265050 | −0.132525 | − | 0.991180i | \(-0.542308\pi\) | ||||
−0.132525 | + | 0.991180i | \(0.542308\pi\) | |||||||
\(908\) | −5.57599e9 | −0.247185 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.33609e9 | 0.0587748 | ||||||||
\(911\) | 4.08258e10 | 1.78904 | 0.894521 | − | 0.447026i | \(-0.147517\pi\) | ||||
0.894521 | + | 0.447026i | \(0.147517\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.53290e9 | −0.153633 | ||||||||
\(914\) | 2.69735e9 | 0.116849 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.60032e10 | −0.687977 | ||||||||
\(917\) | 1.19976e10 | 0.513811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.12519e10 | −0.478214 | −0.239107 | − | 0.970993i | \(-0.576855\pi\) | ||||
−0.239107 | + | 0.970993i | \(0.576855\pi\) | |||||||
\(920\) | 2.19087e10 | 0.927598 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.05189e10 | 0.862176 | ||||||||
\(923\) | −5.05043e9 | −0.211408 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.02883e10 | 0.427414 | ||||||||
\(926\) | −8.11271e9 | −0.335759 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.76825e10 | 1.54783 | ||||||||
\(929\) | −1.44429e10 | −0.591018 | −0.295509 | − | 0.955340i | \(-0.595489\pi\) | ||||
−0.295509 | + | 0.955340i | \(0.595489\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.51029e8 | −0.0142567 | ||||||||
\(932\) | 1.99620e10 | 0.807696 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.16339e10 | −0.868801 | ||||||||
\(935\) | 6.76301e9 | 0.270582 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.43718e10 | 0.967829 | 0.483915 | − | 0.875115i | \(-0.339215\pi\) | ||||
0.483915 | + | 0.875115i | \(0.339215\pi\) | |||||||
\(938\) | 8.67909e8 | 0.0343372 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.73428e10 | 0.681038 | ||||||||
\(941\) | 1.04613e10 | 0.409280 | 0.204640 | − | 0.978837i | \(-0.434398\pi\) | ||||
0.204640 | + | 0.978837i | \(0.434398\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.79311e10 | −1.08467 | ||||||||
\(944\) | 1.13490e8 | 0.00439090 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.02453e9 | −0.0777509 | ||||||||
\(947\) | 6.80097e9 | 0.260223 | 0.130112 | − | 0.991499i | \(-0.458466\pi\) | ||||
0.130112 | + | 0.991499i | \(0.458466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.16677e9 | −0.158259 | ||||||||
\(950\) | −5.43855e8 | −0.0205802 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.17578e10 | −1.56859 | ||||||||
\(953\) | 9.17306e8 | 0.0343312 | 0.0171656 | − | 0.999853i | \(-0.494536\pi\) | ||||
0.0171656 | + | 0.999853i | \(0.494536\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.43158e10 | 0.531869 | ||||||||
\(956\) | −3.06488e10 | −1.13452 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.55614e10 | −0.571833 | ||||||||
\(959\) | 1.40120e10 | 0.513019 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.60850e10 | −0.584640 | ||||||||
\(962\) | 2.15987e9 | 0.0782195 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.20377e10 | 0.792314 | ||||||||
\(965\) | −1.36120e10 | −0.487615 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.69970e10 | −1.31575 | −0.657875 | − | 0.753127i | \(-0.728544\pi\) | ||||
−0.657875 | + | 0.753127i | \(0.728544\pi\) | |||||||
\(968\) | 2.65631e10 | 0.941271 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.64771e9 | 0.128327 | ||||||||
\(971\) | 1.31210e10 | 0.459937 | 0.229968 | − | 0.973198i | \(-0.426138\pi\) | ||||
0.229968 | + | 0.973198i | \(0.426138\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.34138e9 | 0.325099 | ||||||||
\(974\) | 1.40498e9 | 0.0487209 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.18446e9 | −0.0407798 | ||||||||
\(977\) | 3.90962e10 | 1.34123 | 0.670615 | − | 0.741806i | \(-0.266030\pi\) | ||||
0.670615 | + | 0.741806i | \(0.266030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.30721e9 | −0.0445253 | ||||||||
\(980\) | 2.85406e9 | 0.0968660 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.42485e9 | −0.250206 | ||||||||
\(983\) | 3.75059e10 | 1.25940 | 0.629699 | − | 0.776840i | \(-0.283178\pi\) | ||||
0.629699 | + | 0.776840i | \(0.283178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.68269e10 | 0.894424 | ||||||||
\(986\) | −5.03219e10 | −1.67181 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.96941e8 | 0.00649660 | ||||||||
\(989\) | −2.43585e10 | −0.800688 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.39247e10 | 1.76007 | 0.880036 | − | 0.474907i | \(-0.157518\pi\) | ||||
0.880036 | + | 0.474907i | \(0.157518\pi\) | |||||||
\(992\) | 2.00076e10 | 0.650735 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.16355e10 | −0.698739 | ||||||||
\(995\) | 5.32397e9 | 0.171338 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.01581e10 | 0.644192 | 0.322096 | − | 0.946707i | \(-0.395613\pi\) | ||||
0.322096 | + | 0.946707i | \(0.395613\pi\) | |||||||
\(998\) | 8.48317e9 | 0.270148 | ||||||||
\(999\) | 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.d.1.11 | 17 | ||
3.2 | odd | 2 | 177.8.a.b.1.7 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.7 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.d.1.11 | 17 | 1.1 | even | 1 | trivial |