Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,6,Mod(165,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.165");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.e (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(31.4352286833\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 177.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.177 |
Dual form | 196.6.e.a.165.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −13.0000 | − | 22.5167i | −0.833950 | − | 1.44444i | −0.894882 | − | 0.446303i | \(-0.852741\pi\) |
0.0609318 | − | 0.998142i | \(-0.480593\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.00000 | + | 13.8564i | −0.143108 | + | 0.247871i | −0.928666 | − | 0.370918i | \(-0.879043\pi\) |
0.785557 | + | 0.618789i | \(0.212376\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −216.500 | + | 374.989i | −0.890947 | + | 1.54316i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | − | 6.92820i | −0.00996732 | − | 0.0172639i | 0.860999 | − | 0.508607i | \(-0.169839\pi\) |
−0.870966 | + | 0.491343i | \(0.836506\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 684.000 | 1.12253 | 0.561265 | − | 0.827636i | \(-0.310315\pi\) | ||||
0.561265 | + | 0.827636i | \(0.310315\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 416.000 | 0.477381 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1109.00 | + | 1920.84i | 0.930699 | + | 1.61202i | 0.782129 | + | 0.623116i | \(0.214134\pi\) |
0.148570 | + | 0.988902i | \(0.452533\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1349.00 | − | 2336.54i | 0.857290 | − | 1.48487i | −0.0172134 | − | 0.999852i | \(-0.505479\pi\) |
0.874504 | − | 0.485019i | \(-0.161187\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1672.00 | + | 2895.99i | −0.659047 | + | 1.14150i | 0.321815 | + | 0.946803i | \(0.395707\pi\) |
−0.980863 | + | 0.194701i | \(0.937626\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1434.50 | + | 2484.63i | 0.459040 | + | 0.795081i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4940.00 | 1.30412 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3254.00 | −0.718493 | −0.359247 | − | 0.933243i | \(-0.616966\pi\) | ||||
−0.359247 | + | 0.933243i | \(0.616966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2394.00 | − | 4146.53i | −0.447425 | − | 0.774962i | 0.550793 | − | 0.834642i | \(-0.314325\pi\) |
−0.998218 | + | 0.0596797i | \(0.980992\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −104.000 | + | 180.133i | −0.0166245 | + | 0.0287945i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5735.00 | − | 9933.31i | 0.688698 | − | 1.19286i | −0.283561 | − | 0.958954i | \(-0.591516\pi\) |
0.972259 | − | 0.233906i | \(-0.0751509\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8892.00 | − | 15401.4i | −0.936134 | − | 1.62143i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13350.0 | 1.24029 | 0.620143 | − | 0.784489i | \(-0.287075\pi\) | ||||
0.620143 | + | 0.784489i | \(0.287075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −928.000 | −0.0765380 | −0.0382690 | − | 0.999267i | \(-0.512184\pi\) | ||||
−0.0382690 | + | 0.999267i | \(0.512184\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3464.00 | − | 5999.82i | −0.255004 | − | 0.441679i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −606.000 | + | 1049.62i | −0.0400155 | + | 0.0693088i | −0.885340 | − | 0.464945i | \(-0.846074\pi\) |
0.845324 | + | 0.534254i | \(0.179407\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 28834.0 | − | 49942.0i | 1.55231 | − | 2.68869i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6555.00 | − | 11353.6i | −0.320541 | − | 0.555193i | 0.660059 | − | 0.751214i | \(-0.270531\pi\) |
−0.980600 | + | 0.196021i | \(0.937198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 128.000 | 0.00570563 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −70148.0 | −2.85975 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −17351.0 | − | 30052.8i | −0.648925 | − | 1.12397i | −0.983380 | − | 0.181559i | \(-0.941886\pi\) |
0.334455 | − | 0.942412i | \(-0.391448\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 516.000 | − | 893.738i | 0.0177552 | − | 0.0307529i | −0.857011 | − | 0.515298i | \(-0.827681\pi\) |
0.874766 | + | 0.484545i | \(0.161015\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5472.00 | + | 9477.78i | −0.160643 | + | 0.278242i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5054.00 | − | 8753.78i | −0.137546 | − | 0.238237i | 0.789021 | − | 0.614366i | \(-0.210588\pi\) |
−0.926567 | + | 0.376129i | \(0.877255\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 86944.0 | 2.19845 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 62720.0 | 1.47659 | 0.738295 | − | 0.674477i | \(-0.235631\pi\) | ||||
0.738295 | + | 0.674477i | \(0.235631\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9463.00 | + | 16390.4i | 0.207836 | + | 0.359983i | 0.951033 | − | 0.309090i | \(-0.100024\pi\) |
−0.743196 | + | 0.669073i | \(0.766691\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 37297.0 | − | 64600.3i | 0.765633 | − | 1.32612i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5700.00 | + | 9872.69i | −0.102756 | + | 0.177979i | −0.912819 | − | 0.408364i | \(-0.866099\pi\) |
0.810063 | + | 0.586343i | \(0.199433\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11610.5 | − | 20110.0i | −0.196625 | − | 0.340564i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 88958.0 | 1.41739 | 0.708696 | − | 0.705514i | \(-0.249284\pi\) | ||||
0.708696 | + | 0.705514i | \(0.249284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −35488.0 | −0.532763 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 42302.0 | + | 73269.2i | 0.599188 | + | 1.03782i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9861.00 | + | 17079.8i | −0.131961 | + | 0.228563i | −0.924432 | − | 0.381346i | \(-0.875461\pi\) |
0.792471 | + | 0.609909i | \(0.208794\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −62244.0 | + | 107810.i | −0.746260 | + | 1.29256i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21584.0 | + | 37384.6i | 0.245371 | + | 0.424995i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17062.0 | 0.184120 | 0.0920599 | − | 0.995753i | \(-0.470655\pi\) | ||||
0.0920599 | + | 0.995753i | \(0.470655\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3464.00 | 0.0355214 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −22952.0 | − | 39754.0i | −0.223881 | − | 0.387773i | 0.732102 | − | 0.681195i | \(-0.238539\pi\) |
−0.955983 | + | 0.293422i | \(0.905206\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 68006.0 | − | 117790.i | 0.631618 | − | 1.09399i | −0.355604 | − | 0.934637i | \(-0.615725\pi\) |
0.987221 | − | 0.159357i | \(-0.0509420\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 34578.0 | − | 59890.9i | 0.291971 | − | 0.505709i | −0.682304 | − | 0.731068i | \(-0.739022\pi\) |
0.974276 | + | 0.225359i | \(0.0723554\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 73207.0 | + | 126798.i | 0.590183 | + | 1.02223i | 0.994207 | + | 0.107478i | \(0.0342776\pi\) |
−0.404025 | + | 0.914748i | \(0.632389\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −298220. | −2.29736 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −80186.0 | −0.590748 | −0.295374 | − | 0.955382i | \(-0.595444\pi\) | ||||
−0.295374 | + | 0.955382i | \(0.595444\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26752.0 | − | 46335.8i | −0.188630 | − | 0.326717i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −148086. | + | 256492.i | −1.00011 | + | 1.73225i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 80493.5 | − | 139419.i | 0.499801 | − | 0.865681i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −173550. | − | 300597.i | −1.03434 | − | 1.79152i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −95904.0 | −0.548987 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 274800. | 1.51185 | 0.755923 | − | 0.654661i | \(-0.227189\pi\) | ||||
0.755923 | + | 0.654661i | \(0.227189\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12064.0 | + | 20895.5i | 0.0638289 | + | 0.110555i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −90371.0 | + | 156527.i | −0.460099 | + | 0.796914i | −0.998965 | − | 0.0454769i | \(-0.985519\pi\) |
0.538867 | + | 0.842391i | \(0.318853\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −39520.0 | + | 68450.6i | −0.186630 | + | 0.323253i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 104839. | + | 181586.i | 0.477223 | + | 0.826575i | 0.999659 | − | 0.0261038i | \(-0.00831003\pi\) |
−0.522436 | + | 0.852678i | \(0.674977\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17242.0 | 0.0756921 | 0.0378461 | − | 0.999284i | \(-0.487950\pi\) | ||||
0.0378461 | + | 0.999284i | \(0.487950\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 31512.0 | 0.133484 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2736.00 | − | 4738.89i | −0.0111886 | − | 0.0193792i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 26032.0 | − | 45088.7i | 0.102822 | − | 0.178094i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −29679.0 | + | 51405.5i | −0.109518 | + | 0.189690i | −0.915575 | − | 0.402147i | \(-0.868264\pi\) |
0.806057 | + | 0.591837i | \(0.201597\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 168172. | + | 291282.i | 0.600221 | + | 1.03961i | 0.992787 | + | 0.119890i | \(0.0382541\pi\) |
−0.392566 | + | 0.919724i | \(0.628413\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −960394. | −3.31681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 76608.0 | 0.256121 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −232294. | − | 402345.i | −0.752123 | − | 1.30272i | −0.946792 | − | 0.321846i | \(-0.895697\pi\) |
0.194669 | − | 0.980869i | \(-0.437637\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −170430. | + | 295193.i | −0.534630 | + | 0.926006i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −157396. | + | 272618.i | −0.464007 | + | 0.803684i | −0.999156 | − | 0.0410737i | \(-0.986922\pi\) |
0.535149 | + | 0.844758i | \(0.320255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1664.00 | − | 2882.13i | −0.00475821 | − | 0.00824146i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 285724. | 0.792785 | 0.396393 | − | 0.918081i | \(-0.370262\pi\) | ||||
0.396393 | + | 0.918081i | \(0.370262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 96563.0 | 0.260072 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 584117. | + | 1.01172e6i | 1.52760 | + | 2.64588i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 354574. | − | 614140.i | 0.900724 | − | 1.56010i | 0.0741671 | − | 0.997246i | \(-0.476370\pi\) |
0.826557 | − | 0.562854i | \(-0.190296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −451126. | + | 781373.i | −1.08234 | + | 1.87467i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 308574. | + | 534466.i | 0.719825 | + | 1.24677i | 0.961069 | + | 0.276309i | \(0.0891112\pi\) |
−0.241244 | + | 0.970464i | \(0.577555\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 237828. | 0.539593 | 0.269797 | − | 0.962917i | \(-0.413044\pi\) | ||||
0.269797 | + | 0.962917i | \(0.413044\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26832.0 | −0.0592278 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 91760.0 | + | 158933.i | 0.197117 | + | 0.341417i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8872.00 | − | 15366.8i | 0.0185531 | − | 0.0321350i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 66756.0 | − | 115625.i | 0.132406 | − | 0.229334i | −0.792198 | − | 0.610265i | \(-0.791063\pi\) |
0.924603 | + | 0.380931i | \(0.124396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −135223. | − | 234213.i | −0.261311 | − | 0.452604i | 0.705280 | − | 0.708929i | \(-0.250821\pi\) |
−0.966590 | + | 0.256326i | \(0.917488\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 284544. | 0.535874 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 875102. | 1.60655 | 0.803273 | − | 0.595611i | \(-0.203090\pi\) | ||||
0.803273 | + | 0.595611i | \(0.203090\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 173810. | + | 301048.i | 0.311130 | + | 0.538893i | 0.978607 | − | 0.205737i | \(-0.0659592\pi\) |
−0.667477 | + | 0.744630i | \(0.732626\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −131404. | + | 227598.i | −0.229413 | + | 0.397355i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −106800. | + | 184983.i | −0.177495 | + | 0.307431i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −723976. | − | 1.25396e6i | −1.17435 | − | 2.03404i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21584.0 | −0.0341795 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −425380. | −0.657765 | −0.328883 | − | 0.944371i | \(-0.606672\pi\) | ||||
−0.328883 | + | 0.944371i | \(0.606672\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −815360. | − | 1.41224e6i | −1.23140 | − | 2.13285i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7424.00 | − | 12858.7i | 0.0109532 | − | 0.0189715i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 246038. | − | 426150.i | 0.346651 | − | 0.600416i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 758556. | + | 1.31386e6i | 1.04474 | + | 1.80954i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 481592. | 0.648511 | 0.324255 | − | 0.945970i | \(-0.394886\pi\) | ||||
0.324255 | + | 0.945970i | \(0.394886\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.24228e6 | −1.63592 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3021.00 | + | 5232.53i | 0.00389122 | + | 0.00673980i | 0.867964 | − | 0.496626i | \(-0.165428\pi\) |
−0.864073 | + | 0.503366i | \(0.832095\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −902.000 | + | 1562.31i | −0.00113663 | + | 0.00196870i | −0.866593 | − | 0.499015i | \(-0.833695\pi\) |
0.865457 | + | 0.500984i | \(0.167028\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 805763. | − | 1.39562e6i | 0.972339 | − | 1.68414i | 0.283887 | − | 0.958858i | \(-0.408376\pi\) |
0.688452 | − | 0.725282i | \(-0.258291\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9696.00 | − | 16794.0i | −0.0114531 | − | 0.0198373i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 296400. | 0.342774 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −987096. | −1.11780 | −0.558901 | − | 0.829235i | \(-0.688777\pi\) | ||||
−0.558901 | + | 0.829235i | \(0.688777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −446755. | − | 773802.i | −0.495481 | − | 0.858198i | 0.504506 | − | 0.863408i | \(-0.331675\pi\) |
−0.999986 | + | 0.00521050i | \(0.998341\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 298337. | − | 516735.i | 0.324109 | − | 0.561374i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 922716. | − | 1.59819e6i | 0.962334 | − | 1.66681i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.15645e6 | − | 2.00304e6i | −1.18203 | − | 2.04734i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 365946. | 0.366634 | 0.183317 | − | 0.983054i | \(-0.441317\pi\) | ||||
0.183317 | + | 0.983054i | \(0.441317\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 26752.0 | 0.0262757 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 461344. | + | 799071.i | 0.444298 | + | 0.769547i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −702297. | + | 1.21641e6i | −0.663266 | + | 1.14881i | 0.316486 | + | 0.948597i | \(0.397497\pi\) |
−0.979752 | + | 0.200214i | \(0.935836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 704491. | − | 1.22021e6i | 0.640139 | − | 1.10875i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −549840. | − | 952351.i | −0.490170 | − | 0.849000i | 0.509766 | − | 0.860313i | \(-0.329732\pi\) |
−0.999936 | + | 0.0113135i | \(0.996399\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 209760. | 0.183488 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 512772. | 0.440196 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −407474. | − | 705766.i | −0.343336 | − | 0.594675i | 0.641714 | − | 0.766944i | \(-0.278224\pi\) |
−0.985050 | + | 0.172269i | \(0.944890\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 849528. | − | 1.47143e6i | 0.702675 | − | 1.21707i | −0.264849 | − | 0.964290i | \(-0.585322\pi\) |
0.967524 | − | 0.252779i | \(-0.0813445\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11476.0 | − | 19877.0i | 0.00915079 | − | 0.0158496i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 682541. | + | 1.18220e6i | 0.534477 | + | 0.925742i | 0.999188 | + | 0.0402796i | \(0.0128249\pi\) |
−0.464711 | + | 0.885462i | \(0.653842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.07320e6 | 1.59453 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −715846. | −0.540821 | −0.270411 | − | 0.962745i | \(-0.587159\pi\) | ||||
−0.270411 | + | 0.962745i | \(0.587159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −108863. | − | 188556.i | −0.0808005 | − | 0.139951i | 0.822793 | − | 0.568340i | \(-0.192414\pi\) |
−0.903594 | + | 0.428390i | \(0.859081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 561184. | − | 971999.i | 0.409254 | − | 0.708849i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.74983e6 | + | 3.03080e6i | −1.23240 | + | 2.13458i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −221806. | − | 384179.i | −0.153547 | − | 0.265951i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.50708e6 | 1.02557 | 0.512787 | − | 0.858516i | \(-0.328613\pi\) | ||||
0.512787 | + | 0.858516i | \(0.328613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 555232. | 0.371466 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19760.0 | − | 34225.3i | −0.0129986 | − | 0.0225142i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.14365e6 | + | 1.98086e6i | −0.739800 | + | 1.28137i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −596752. | + | 1.03360e6i | −0.373411 | + | 0.646767i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8256.00 | + | 14299.8i | 0.00508183 | + | 0.00880199i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12502.0 | 0.00757066 | 0.00378533 | − | 0.999993i | \(-0.498795\pi\) | ||||
0.00378533 | + | 0.999993i | \(0.498795\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.53631e6 | −2.10695 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 323716. | + | 560693.i | 0.189786 | + | 0.328718i | 0.945179 | − | 0.326554i | \(-0.105887\pi\) |
−0.755393 | + | 0.655272i | \(0.772554\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 467989. | − | 810581.i | 0.270007 | − | 0.467666i | −0.698856 | − | 0.715262i | \(-0.746307\pi\) |
0.968863 | + | 0.247596i | \(0.0796407\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −352971. | + | 611364.i | −0.197284 | + | 0.341705i | −0.947647 | − | 0.319321i | \(-0.896545\pi\) |
0.750363 | + | 0.661026i | \(0.229879\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13016.0 | + | 22544.4i | 0.00716145 | + | 0.0124040i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.79806e6 | −0.973959 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.98416e6 | 3.19152 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 981198. | + | 1.69948e6i | 0.515286 | + | 0.892501i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.90338e6 | − | 3.29675e6i | 0.984366 | − | 1.70497i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 571520. | − | 989902.i | 0.286722 | − | 0.496618i | −0.686303 | − | 0.727316i | \(-0.740768\pi\) |
0.973025 | + | 0.230698i | \(0.0741010\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.48326e6 | + | 4.30112e6i | 1.22719 | + | 2.12555i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 161728. | 0.0787360 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.36402e6 | −1.13390 | −0.566952 | − | 0.823751i | \(-0.691877\pi\) | ||||
−0.566952 | + | 0.823751i | \(0.691877\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.04242e6 | + | 1.80552e6i | 0.492655 | + | 0.853303i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19152.0 | + | 33172.2i | −0.00891925 | + | 0.0154486i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −695552. | + | 1.20473e6i | −0.314617 | + | 0.544932i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −363120. | − | 628942.i | −0.161892 | − | 0.280406i | 0.773655 | − | 0.633607i | \(-0.218426\pi\) |
−0.935547 | + | 0.353201i | \(0.885093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 136180. | 0.0598480 | 0.0299240 | − | 0.999552i | \(-0.490473\pi\) | ||||
0.0299240 | + | 0.999552i | \(0.490473\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.37896e6 | 1.46391 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 584535. | + | 1.01244e6i | 0.249674 | + | 0.432448i | 0.963435 | − | 0.267941i | \(-0.0863431\pi\) |
−0.713761 | + | 0.700389i | \(0.753010\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −501760. | + | 869074.i | −0.211312 | + | 0.366004i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2140.00 | − | 3706.59i | 0.000876350 | − | 0.00151788i | −0.865587 | − | 0.500759i | \(-0.833054\pi\) |
0.866463 | + | 0.499241i | \(0.166388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.40155e6 | − | 4.15961e6i | −0.969894 | − | 1.67990i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.18566e6 | −1.66724 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −302816. | −0.118973 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.22398e6 | − | 2.12000e6i | −0.474361 | − | 0.821618i | 0.525208 | − | 0.850974i | \(-0.323988\pi\) |
−0.999569 | + | 0.0293563i | \(0.990654\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.89028e6 | + | 5.00610e6i | −1.10503 | + | 1.91396i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 452257. | − | 783332.i | 0.168311 | − | 0.291524i | −0.769515 | − | 0.638629i | \(-0.779502\pi\) |
0.937826 | + | 0.347105i | \(0.112835\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.24675e6 | + | 2.15944e6i | 0.457828 | + | 0.792981i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.22574e6 | −0.806530 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.23034e6 | −1.51279 | −0.756393 | − | 0.654117i | \(-0.773040\pi\) | ||||
−0.756393 | + | 0.654117i | \(0.773040\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.57240e6 | − | 6.18758e6i | −1.26080 | − | 2.18378i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.27700e6 | + | 3.94388e6i | −0.793169 | + | 1.37381i | 0.130826 | + | 0.991405i | \(0.458237\pi\) |
−0.923995 | + | 0.382404i | \(0.875096\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 200912. | − | 347990.i | 0.0681912 | − | 0.118111i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.99270e6 | + | 3.45146e6i | 0.667680 | + | 1.15646i | 0.978551 | + | 0.206004i | \(0.0660460\pi\) |
−0.310871 | + | 0.950452i | \(0.600621\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.41699e6 | −2.45350 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.69929e6 | 1.53480 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −91200.0 | − | 157963.i | −0.0294105 | − | 0.0509404i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −276210. | + | 478410.i | −0.0879555 | + | 0.152343i | −0.906647 | − | 0.421890i | \(-0.861367\pi\) |
0.818691 | + | 0.574234i | \(0.194700\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19095.0 | + | 33073.5i | −0.00593006 | + | 0.0102712i | −0.868975 | − | 0.494856i | \(-0.835221\pi\) |
0.863045 | + | 0.505127i | \(0.168554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.63750e6 | − | 2.83623e6i | −0.502247 | − | 0.869918i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 371536. | 0.112555 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −91760.0 | −0.0274579 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.96238e6 | + | 3.39894e6i | 0.580062 | + | 1.00470i | 0.995471 | + | 0.0950619i | \(0.0303049\pi\) |
−0.415410 | + | 0.909634i | \(0.636362\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.72581e6 | − | 4.72125e6i | 0.795961 | − | 1.37864i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −711664. | + | 1.23264e6i | −0.202841 | + | 0.351330i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −224146. | − | 388232.i | −0.0631235 | − | 0.109333i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 598386. | 0.166512 | 0.0832562 | − | 0.996528i | \(-0.473468\pi\) | ||||
0.0832562 | + | 0.996528i | \(0.473468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.61597e6 | 1.26928 | 0.634641 | − | 0.772807i | \(-0.281148\pi\) | ||||
0.634641 | + | 0.772807i | \(0.281148\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −262398. | − | 454487.i | −0.0713033 | − | 0.123501i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.18172e6 | + | 5.51090e6i | −0.854456 | + | 1.47996i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −71136.0 | + | 123211.i | −0.0186615 | + | 0.0323226i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30780.0 | + | 53312.5i | 0.00798133 | + | 0.0138241i | 0.869988 | − | 0.493072i | \(-0.164126\pi\) |
−0.862007 | + | 0.506896i | \(0.830793\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.79727e6 | −0.973310 | −0.486655 | − | 0.873594i | \(-0.661783\pi\) | ||||
−0.486655 | + | 0.873594i | \(0.661783\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.35366e6 | −0.342995 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.51106e6 | + | 7.81338e6i | 1.12999 | + | 1.95720i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.14426e6 | − | 1.98192e6i | 0.283376 | − | 0.490822i | −0.688838 | − | 0.724915i | \(-0.741879\pi\) |
0.972214 | + | 0.234093i | \(0.0752122\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.37988e6 | − | 4.12207e6i | 0.576163 | − | 0.997944i | −0.419751 | − | 0.907639i | \(-0.637883\pi\) |
0.995914 | − | 0.0903044i | \(-0.0287840\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −157776. | − | 273276.i | −0.0377695 | − | 0.0654186i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.54331e6 | 0.365329 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.36715e6 | −1.02231 | −0.511155 | − | 0.859489i | \(-0.670782\pi\) | ||||
−0.511155 | + | 0.859489i | \(0.670782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53400.0 | − | 92491.5i | −0.0123623 | − | 0.0214122i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.37247e6 | − | 7.57334e6i | 1.00111 | − | 1.73397i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.72497e6 | + | 4.71979e6i | −0.610339 | + | 1.05714i | 0.380844 | + | 0.924639i | \(0.375634\pi\) |
−0.991183 | + | 0.132499i | \(0.957700\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.47846e6 | + | 9.48897e6i | 1.21374 | + | 2.10226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.66966e6 | 0.365911 | 0.182956 | − | 0.983121i | \(-0.441434\pi\) | ||||
0.182956 | + | 0.983121i | \(0.441434\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 70768.0 | 0.0153421 | 0.00767104 | − | 0.999971i | \(-0.497558\pi\) | ||||
0.00767104 | + | 0.999971i | \(0.497558\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −995904. | − | 1.72496e6i | −0.213592 | − | 0.369952i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.83041e6 | + | 4.90242e6i | −0.600562 | + | 1.04020i | 0.392174 | + | 0.919891i | \(0.371723\pi\) |
−0.992736 | + | 0.120313i | \(0.961610\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.03964e6 | + | 1.04610e7i | −1.25447 | + | 2.17280i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3712.00 | + | 6429.37i | 0.000762878 | + | 0.00132134i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.74056e6 | 1.57412 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.67663e6 | 1.14234 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 724742. | + | 1.25529e6i | 0.144326 | + | 0.249980i | 0.929121 | − | 0.369775i | \(-0.120565\pi\) |
−0.784795 | + | 0.619755i | \(0.787232\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.92274e6 | − | 6.79438e6i | 0.773084 | − | 1.33902i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −136496. | + | 236418.i | −0.0263491 | + | 0.0456380i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.03752e6 | − | 3.52909e6i | −0.389296 | − | 0.674280i | 0.603059 | − | 0.797696i | \(-0.293948\pi\) |
−0.992355 | + | 0.123417i | \(0.960615\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.18459e6 | 1.54784 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 986100. | 0.184594 | 0.0922969 | − | 0.995732i | \(-0.470579\pi\) | ||||
0.0922969 | + | 0.995732i | \(0.470579\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.60869e6 | − | 6.25043e6i | −0.668701 | − | 1.15822i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27712.0 | + | 47998.6i | −0.00508341 | + | 0.00880472i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.99171e6 | + | 5.18179e6i | −0.537859 | + | 0.931598i | 0.461160 | + | 0.887317i | \(0.347433\pi\) |
−0.999019 | + | 0.0442817i | \(0.985900\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.71441e6 | − | 6.43355e6i | −0.661144 | − | 1.14513i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.49373e6 | −0.615700 | −0.307850 | − | 0.951435i | \(-0.599609\pi\) | ||||
−0.307850 | + | 0.951435i | \(0.599609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 734464. | 0.128157 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.25532e6 | − | 2.17428e6i | −0.216887 | − | 0.375660i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.07855e6 | + | 1.86811e6i | −0.184522 | + | 0.319601i | −0.943415 | − | 0.331614i | \(-0.892407\pi\) |
0.758894 | + | 0.651215i | \(0.225740\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.66406e6 | − | 1.15425e7i | 1.11801 | − | 1.93645i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.08810e6 | + | 1.88464e6i | 0.180779 | + | 0.313119i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9696.00 | 0.00159539 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.84378e7 | −3.00464 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.32908e6 | + | 5.76614e6i | 0.537317 | + | 0.930660i | 0.999047 | + | 0.0436400i | \(0.0138955\pi\) |
−0.461730 | + | 0.887020i | \(0.652771\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.97611e6 | + | 5.15478e6i | −0.475768 | + | 0.824055i | −0.999615 | − | 0.0277579i | \(-0.991163\pi\) |
0.523846 | + | 0.851813i | \(0.324497\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.30989e6 | − | 9.19700e6i | 0.832835 | − | 1.44251i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.37300e6 | − | 4.11015e6i | −0.368687 | − | 0.638585i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.50260e7 | 2.31263 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.13140e6 | 1.39226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 553248. | + | 958254.i | 0.0835671 | + | 0.144742i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.02292e6 | − | 1.38961e7i | 1.20060 | − | 2.07949i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.19840e6 | − | 5.53980e6i | 0.469830 | − | 0.813769i | −0.529575 | − | 0.848263i | \(-0.677649\pi\) |
0.999405 | + | 0.0344943i | \(0.0109821\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.09176e6 | − | 5.35509e6i | −0.449994 | − | 0.779413i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.34262e6 | −0.337840 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.51851e6 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 223428. | + | 386989.i | 0.0316378 | + | 0.0547983i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.38965e6 | + | 7.60309e6i | −0.615957 | + | 1.06687i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.38576e6 | − | 4.13226e6i | 0.328772 | − | 0.569449i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.01080e6 | − | 1.75075e6i | −0.138046 | − | 0.239103i | 0.788711 | − | 0.614765i | \(-0.210749\pi\) |
−0.926757 | + | 0.375661i | \(0.877416\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −634752. | −0.0859161 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −461344. | −0.0618896 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.07339e6 | − | 7.05532e6i | −0.541608 | − | 0.938092i | −0.998812 | − | 0.0487304i | \(-0.984482\pi\) |
0.457204 | − | 0.889362i | \(-0.348851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 641488. | − | 1.11109e6i | 0.0845410 | − | 0.146429i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.99121e6 | − | 1.03771e7i | 0.775772 | − | 1.34368i | −0.158588 | − | 0.987345i | \(-0.550694\pi\) |
0.934360 | − | 0.356332i | \(-0.115973\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −697908. | − | 1.20881e6i | −0.0895793 | − | 0.155156i | 0.817754 | − | 0.575568i | \(-0.195219\pi\) |
−0.907333 | + | 0.420412i | \(0.861886\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.47131e6 | −0.441679 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.59394e6 | −1.21012 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −983921. | − | 1.70420e6i | −0.123033 | − | 0.213099i | 0.797930 | − | 0.602751i | \(-0.205929\pi\) |
−0.920962 | + | 0.389652i | \(0.872595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.51580e6 | + | 6.08954e6i | −0.435840 | + | 0.754898i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −52440.0 | + | 90828.7i | −0.00638986 | + | 0.0110676i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.36938e6 | − | 4.10388e6i | −0.286249 | − | 0.495798i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.18897e6 | −0.381993 | −0.190997 | − | 0.981591i | \(-0.561172\pi\) | ||||
−0.190997 | + | 0.981591i | \(0.561172\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.29180e7 | −1.53429 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.13763e7 | − | 1.97044e7i | −1.33978 | − | 2.32057i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −837501. | + | 1.45059e6i | −0.0978022 | + | 0.169398i | −0.910775 | − | 0.412904i | \(-0.864515\pi\) |
0.812972 | + | 0.582302i | \(0.197848\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.51906e6 | − | 7.82724e6i | 0.518934 | − | 0.898820i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.03173e6 | + | 8.71522e6i | 0.572994 | + | 0.992456i | 0.996256 | + | 0.0864482i | \(0.0275517\pi\) |
−0.423262 | + | 0.906007i | \(0.639115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.72798e6 | 0.195143 | 0.0975713 | − | 0.995229i | \(-0.468893\pi\) | ||||
0.0975713 | + | 0.995229i | \(0.468893\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.37676e6 | 0.490185 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.28790e6 | + | 2.23070e6i | 0.143051 | + | 0.247772i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.47613e6 | − | 1.46811e7i | 0.933740 | − | 1.61728i | 0.156873 | − | 0.987619i | \(-0.449859\pi\) |
0.776866 | − | 0.629666i | \(-0.216808\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −414504. | + | 717942.i | −0.0449185 | + | 0.0778012i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.09708e6 | − | 8.82840e6i | −0.547861 | − | 0.948923i | −0.998421 | − | 0.0561768i | \(-0.982109\pi\) |
0.450560 | − | 0.892746i | \(-0.351224\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.55360e6 | 0.592089 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.57452e7 | 1.66508 | 0.832540 | − | 0.553965i | \(-0.186886\pi\) | ||||
0.832540 | + | 0.553965i | \(0.186886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 166345. | + | 288118.i | 0.0174495 | + | 0.0302234i | 0.874618 | − | 0.484812i | \(-0.161112\pi\) |
−0.857169 | + | 0.515036i | \(0.827779\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.25968e6 | + | 1.43062e7i | −0.859477 | + | 1.48866i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.71558e6 | + | 6.43557e6i | −0.380475 | + | 0.659003i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 280592. | + | 486000.i | 0.0285040 | + | 0.0493704i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.54405e7 | 2.56388 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.59720e6 | 0.359659 | 0.179830 | − | 0.983698i | \(-0.442445\pi\) | ||||
0.179830 | + | 0.983698i | \(0.442445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.52994e6 | + | 9.57814e6i | 0.548544 | + | 0.950105i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.19840e6 | + | 3.80774e6i | −0.216358 | + | 0.374743i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.35789e7 | + | 2.35193e7i | −1.31556 | + | 2.27862i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.31946e6 | + | 1.26777e7i | 0.703614 | + | 1.21869i | 0.967190 | + | 0.254056i | \(0.0817647\pi\) |
−0.263576 | + | 0.964639i | \(0.584902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.38386e7 | −1.31997 | −0.659987 | − | 0.751277i | \(-0.729438\pi\) | ||||
−0.659987 | + | 0.751277i | \(0.729438\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −386048. | −0.0365378 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.01791e6 | + | 1.21554e7i | 0.659093 | + | 1.14158i | 0.980851 | + | 0.194761i | \(0.0623931\pi\) |
−0.321758 | + | 0.946822i | \(0.604274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −138808. | + | 240423.i | −0.0129361 | + | 0.0224060i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.05314e6 | + | 1.39484e7i | −0.739064 | + | 1.28010i | 0.213853 | + | 0.976866i | \(0.431399\pi\) |
−0.952917 | + | 0.303231i | \(0.901935\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.44594e6 | − | 2.50443e6i | −0.131688 | − | 0.228090i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.19496e6 | −0.740685 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.80075e6 | 0.430622 | 0.215311 | − | 0.976546i | \(-0.430924\pi\) | ||||
0.215311 | + | 0.976546i | \(0.430924\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.82824e6 | + | 1.52910e7i | 0.785905 | + | 1.36123i | 0.928457 | + | 0.371441i | \(0.121136\pi\) |
−0.142551 | + | 0.989787i | \(0.545531\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.97225e7 | − | 3.41603e7i | 1.74252 | − | 3.01813i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.44069e6 | − | 9.42355e6i | 0.473521 | − | 0.820162i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.26070e6 | − | 1.08438e7i | −0.540826 | − | 0.936738i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8256.00 | −0.000707886 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.59225e6 | 0.561043 | 0.280521 | − | 0.959848i | \(-0.409493\pi\) | ||||
0.280521 | + | 0.959848i | \(0.409493\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.08643e6 | + | 1.22741e7i | 0.598643 | + | 1.03688i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.88589e6 | + | 8.46261e6i | −0.409706 | + | 0.709631i | −0.994857 | − | 0.101293i | \(-0.967702\pi\) |
0.585151 | + | 0.810924i | \(0.301035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 78546.0 | − | 136046.i | 0.00649017 | − | 0.0112413i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.43316e6 | + | 1.63387e7i | 0.773758 | + | 1.34019i | 0.935490 | + | 0.353354i | \(0.114959\pi\) |
−0.161731 | + | 0.986835i | \(0.551708\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.35485e6 | −0.273178 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46904.0 | 0.00379156 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.48362e6 | − | 7.76586e6i | −0.359816 | − | 0.623220i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.33509e6 | + | 7.50860e6i | −0.345385 | + | 0.598224i | −0.985424 | − | 0.170119i | \(-0.945585\pi\) |
0.640039 | + | 0.768343i | \(0.278918\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −137936. | + | 238912.i | −0.0108322 | + | 0.0187619i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.48052e7 | + | 2.56433e7i | 1.15433 | + | 1.99936i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.18997e7 | −3.24353 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.93482e6 | 0.609877 | 0.304938 | − | 0.952372i | \(-0.401364\pi\) | ||||
0.304938 | + | 0.952372i | \(0.401364\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.54730e7 | − | 2.68001e7i | −1.18083 | − | 2.04526i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −252096. | + | 436643.i | −0.0191026 | + | 0.0330867i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.31300e7 | + | 2.27419e7i | −0.980956 | + | 1.69907i | −0.322272 | + | 0.946647i | \(0.604446\pi\) |
−0.658685 | + | 0.752419i | \(0.728887\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.46810e6 | − | 4.27487e6i | −0.183100 | − | 0.317139i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.60111e7 | 1.17950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 87552.0 | 0.00640473 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.28322e7 | + | 2.22261e7i | 0.932191 | + | 1.61460i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.10381e7 | + | 1.91186e7i | −0.796295 | + | 1.37922i | 0.125719 | + | 0.992066i | \(0.459876\pi\) |
−0.922014 | + | 0.387157i | \(0.873457\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.16156e7 | + | 2.01189e7i | −0.826413 | + | 1.43139i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.66786e6 | − | 8.08498e6i | −0.329817 | − | 0.571260i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.49245e6 | 0.595933 | 0.297966 | − | 0.954576i | \(-0.403692\pi\) | ||||
0.297966 | + | 0.954576i | \(0.403692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.11562e7 | −1.47441 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.02915e6 | − | 1.78254e6i | −0.0712338 | − | 0.123381i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.53564e6 | − | 1.65162e7i | 0.655526 | − | 1.13540i | −0.326235 | − | 0.945289i | \(-0.605780\pi\) |
0.981762 | − | 0.190116i | \(-0.0608865\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40432.0 | + | 70030.3i | −0.00274193 | + | 0.00474916i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.34161e6 | + | 1.27160e7i | 0.494516 | + | 0.856527i | 0.999980 | − | 0.00632086i | \(-0.00201201\pi\) |
−0.505464 | + | 0.862848i | \(0.668679\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.79812e7 | −3.21015 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.64265e7 | 1.09162 | 0.545812 | − | 0.837908i | \(-0.316221\pi\) | ||||
0.545812 | + | 0.837908i | \(0.316221\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −474864. | − | 822489.i | −0.0313457 | − | 0.0542924i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.92594e7 | + | 3.33583e7i | −1.26282 | + | 2.18727i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.22178e7 | − | 2.11619e7i | 0.790486 | − | 1.36916i | −0.135180 | − | 0.990821i | \(-0.543161\pi\) |
0.925666 | − | 0.378342i | \(-0.123506\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.75730e6 | − | 8.23988e6i | −0.305755 | − | 0.529582i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.38150e6 | −0.343587 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −295566. | −0.0187463 | −0.00937313 | − | 0.999956i | \(-0.502984\pi\) | ||||
−0.00937313 | + | 0.999956i | \(0.502984\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −347776. | − | 602366.i | −0.0219127 | − | 0.0379538i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 236921. | − | 410359.i | 0.0148300 | − | 0.0256864i | −0.858515 | − | 0.512788i | \(-0.828613\pi\) |
0.873345 | + | 0.487102i | \(0.161946\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.68315e6 | − | 1.33076e7i | 0.474664 | − | 0.822141i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.18681e7 | − | 2.05561e7i | −0.728437 | − | 1.26169i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.33241e7 | 1.42229 | 0.711145 | − | 0.703045i | \(-0.248177\pi\) | ||||
0.711145 | + | 0.703045i | \(0.248177\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.65194e7 | 2.21253 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.77914e6 | − | 1.34739e7i | −0.468255 | − | 0.811042i | 0.531086 | − | 0.847318i | \(-0.321784\pi\) |
−0.999342 | + | 0.0362754i | \(0.988451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.86839e6 | − | 1.18964e7i | 0.410772 | − | 0.711477i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.80092e7 | − | 3.11928e7i | 1.06328 | − | 1.84166i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −250880. | − | 434537.i | −0.0147176 | − | 0.0254917i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.60748e7 | −0.937001 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.43341e6 | 0.430540 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.33422e6 | − | 5.77503e6i | −0.191892 | − | 0.332367i | 0.753985 | − | 0.656891i | \(-0.228129\pi\) |
−0.945877 | + | 0.324525i | \(0.894796\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.42958e7 | + | 2.47611e7i | −0.817555 | + | 1.41605i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 352944. | − | 611317.i | 0.0199307 | − | 0.0345210i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.72688e6 | − | 4.72309e6i | −0.153020 | − | 0.265038i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.22461e7 | −0.682892 | −0.341446 | − | 0.939901i | \(-0.610917\pi\) | ||||
−0.341446 | + | 0.939901i | \(0.610917\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.68822e6 | −0.148969 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.26981e6 | − | 7.39553e6i | −0.235141 | − | 0.407275i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 75704.0 | − | 131123.i | 0.00414314 | − | 0.00717613i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.05943e7 | + | 1.83499e7i | −0.572650 | + | 0.991859i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.45747e7 | + | 2.52442e7i | 0.782941 | + | 1.35609i | 0.930221 | + | 0.367000i | \(0.119615\pi\) |
−0.147280 | + | 0.989095i | \(0.547052\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.58849e6 | 0.405138 | 0.202569 | − | 0.979268i | \(-0.435071\pi\) | ||||
0.202569 | + | 0.979268i | \(0.435071\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.41755e7 | −2.34398 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.51834e6 | − | 4.36189e6i | −0.132807 | − | 0.230028i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.25187e6 | + | 2.16831e6i | −0.0656152 | + | 0.113649i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.99424e6 | − | 5.18618e6i | 0.155035 | − | 0.268528i | −0.778037 | − | 0.628219i | \(-0.783784\pi\) |
0.933072 | + | 0.359690i | \(0.117118\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −408980. | − | 708374.i | −0.0210476 | − | 0.0364555i | 0.855310 | − | 0.518117i | \(-0.173367\pi\) |
−0.876357 | + | 0.481661i | \(0.840033\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −596752. | −0.0305252 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.51963e6 | 0.128107 | 0.0640535 | − | 0.997946i | \(-0.479597\pi\) | ||||
0.0640535 | + | 0.997946i | \(0.479597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.05030e6 | + | 1.39435e7i | 0.406842 | + | 0.704671i | 0.994534 | − | 0.104414i | \(-0.0332966\pi\) |
−0.587692 | + | 0.809085i | \(0.699963\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.77461e7 | − | 3.07371e7i | 0.891455 | − | 1.54405i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.28579e6 | + | 3.95911e6i | −0.113454 | + | 0.196508i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.18264e7 | − | 2.04839e7i | −0.583495 | − | 1.01064i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.58167e7 | −1.26618 | −0.633091 | − | 0.774077i | \(-0.718214\pi\) | ||||
−0.633091 | + | 0.774077i | \(0.718214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.92263e6 | −0.483768 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.30600e6 | + | 1.61185e7i | 0.451018 | + | 0.781186i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −772504. | + | 1.33802e6i | −0.0372185 | + | 0.0644643i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.83044e6 | + | 4.90246e6i | −0.134767 | + | 0.233424i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.91778e7 | + | 3.32170e7i | 0.907770 | + | 1.57230i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.54270e7 | −0.725954 | −0.362977 | − | 0.931798i | \(-0.618240\pi\) | ||||
−0.362977 | + | 0.931798i | \(0.618240\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.86917e7 | −0.874449 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.80258e6 | − | 3.12217e6i | −0.0838384 | − | 0.145212i | 0.821057 | − | 0.570846i | \(-0.193385\pi\) |
−0.904896 | + | 0.425633i | \(0.860051\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.03497e6 | + | 3.52468e6i | −0.0940970 | + | 0.162981i | −0.909231 | − | 0.416291i | \(-0.863330\pi\) |
0.815134 | + | 0.579272i | \(0.196663\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.62556e6 | + | 6.27965e6i | −0.165710 | + | 0.287017i | −0.936907 | − | 0.349579i | \(-0.886325\pi\) |
0.771197 | + | 0.636596i | \(0.219658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.67318e6 | + | 9.82624e6i | 0.257802 | + | 0.446526i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.09913e7 | 4.11105 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 91200.0 | 0.00409681 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.45694e6 | − | 5.98759e6i | −0.154400 | − | 0.267428i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.69392e6 | + | 6.39806e6i | −0.164041 | + | 0.284127i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.18707e6 | + | 2.05606e6i | −0.0521167 | + | 0.0902688i | −0.890907 | − | 0.454186i | \(-0.849930\pi\) |
0.838790 | + | 0.544455i | \(0.183263\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.95920e7 | − | 3.39344e7i | −0.855278 | − | 1.48139i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.03558e7 | 1.31766 | 0.658828 | − | 0.752293i | \(-0.271052\pi\) | ||||
0.658828 | + | 0.752293i | \(0.271052\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.53338e6 | 0.0661832 | 0.0330916 | − | 0.999452i | \(-0.489465\pi\) | ||||
0.0330916 | + | 0.999452i | \(0.489465\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.21802e6 | − | 1.25020e7i | −0.309784 | − | 0.536562i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.46189e7 | − | 2.53207e7i | 0.623888 | − | 1.08061i | −0.364867 | − | 0.931060i | \(-0.618885\pi\) |
0.988755 | − | 0.149546i | \(-0.0477812\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −92884.0 | + | 160880.i | −0.00391964 | + | 0.00678902i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.63499e6 | + | 2.83188e6i | 0.0686098 | + | 0.118836i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.87437e6 | −0.412052 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.94697e7 | 2.46783 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.79008e6 | + | 1.34928e7i | 0.321471 | + | 0.556805i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.45390e7 | − | 2.51823e7i | 0.596654 | − | 1.03343i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.90262e6 | + | 3.29544e6i | −0.0772203 | + | 0.133749i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.24114e7 | − | 3.88176e7i | −0.904587 | − | 1.56679i | −0.821471 | − | 0.570250i | \(-0.806846\pi\) |
−0.0831160 | − | 0.996540i | \(-0.526487\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.98764e7 | 0.797864 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.62906e7 | −1.44877 | −0.724384 | − | 0.689397i | \(-0.757876\pi\) | ||||
−0.724384 | + | 0.689397i | \(0.757876\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −355832. | − | 616319.i | −0.0141276 | − | 0.0244697i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 214656. | − | 371795.i | 0.00847599 | − | 0.0146808i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.62675e7 | + | 2.81762e7i | −0.635378 | + | 1.10051i | 0.351057 | + | 0.936354i | \(0.385822\pi\) |
−0.986435 | + | 0.164153i | \(0.947511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −162526. | − | 281503.i | −0.00631355 | − | 0.0109354i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.29005e7 | 1.65752 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.29074e7 | 1.26456 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.94466e7 | + | 5.10030e7i | 1.12547 | + | 1.94938i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.23338e7 | − | 3.86833e7i | 0.849030 | − | 1.47056i | −0.0330440 | − | 0.999454i | \(-0.510520\pi\) |
0.882074 | − | 0.471110i | \(-0.156147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.41662e6 | − | 1.45780e7i | 0.316544 | − | 0.548269i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 141952. | + | 245868.i | 0.00531022 | + | 0.00919757i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.56680e7 | 0.582995 | 0.291498 | − | 0.956572i | \(-0.405846\pi\) | ||||
0.291498 | + | 0.956572i | \(0.405846\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.43354e7 | −0.900689 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.00587e7 | + | 1.74222e7i | 0.370313 | + | 0.641402i | 0.989614 | − | 0.143753i | \(-0.0459169\pi\) |
−0.619300 | + | 0.785154i | \(0.712584\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.23212e7 | + | 3.86615e7i | −0.817407 | + | 1.41579i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.42259e6 | − | 7.66015e6i | 0.160251 | − | 0.277564i | −0.774707 | − | 0.632320i | \(-0.782103\pi\) |
0.934959 | + | 0.354756i | \(0.115436\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.47269e6 | + | 1.12110e7i | 0.233303 | + | 0.404092i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.83545e7 | 0.658099 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.14364e7 | −1.12124 | −0.560622 | − | 0.828072i | \(-0.689438\pi\) | ||||
−0.560622 | + | 0.828072i | \(0.689438\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.06810e6 | + | 1.85000e6i | 0.0378967 | + | 0.0656391i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 338416. | − | 586154.i | 0.0119446 | − | 0.0206886i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.85210e6 | − | 4.93999e6i | 0.0996224 | − | 0.172551i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.49723e7 | + | 2.59327e7i | 0.520262 | + | 0.901120i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.32714e6 | 0.149583 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.52158e6 | −0.327449 | −0.163724 | − | 0.986506i | \(-0.552351\pi\) | ||||
−0.163724 | + | 0.986506i | \(0.552351\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.77941e7 | − | 1.34743e8i | −2.66157 | − | 4.60997i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.32602e6 | + | 9.22494e6i | −0.181282 | + | 0.313990i | −0.942317 | − | 0.334721i | \(-0.891358\pi\) |
0.761035 | + | 0.648710i | \(0.224691\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.55111e7 | − | 4.41866e7i | 0.859446 | − | 1.48860i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.36465e7 | − | 2.36365e7i | −0.457389 | − | 0.792222i | 0.541433 | − | 0.840744i | \(-0.317882\pi\) |
−0.998822 | + | 0.0485223i | \(0.984549\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 157776. | 0.00526119 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.33973e7 | −2.10328 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.23819e6 | − | 9.07280e6i | −0.172901 | − | 0.299473i | 0.766532 | − | 0.642206i | \(-0.221981\pi\) |
−0.939433 | + | 0.342733i | \(0.888647\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.00082e6 | + | 1.21258e7i | −0.229910 | + | 0.398216i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.55162e6 | − | 2.68748e6i | 0.0504421 | − | 0.0873684i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −941152. | − | 1.63012e6i | −0.0304422 | − | 0.0527274i | 0.850403 | − | 0.526132i | \(-0.176358\pi\) |
−0.880845 | + | 0.473405i | \(0.843025\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.97190e7 | −0.956449 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.56192e6 | −0.178101 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.35759e7 | − | 2.35142e7i | −0.432545 | − | 0.749190i | 0.564547 | − | 0.825401i | \(-0.309051\pi\) |
−0.997092 | + | 0.0762113i | \(0.975718\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.83309e7 | − | 4.90706e7i | 0.898145 | − | 1.55563i |
(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 | 196.6.e.a.177.1 | 2 | ||
7.2 | even | 3 | 28.6.a.b.1.1 | ✓ | 1 | ||
7.3 | odd | 6 | 196.6.e.i.165.1 | 2 | |||
7.4 | even | 3 | inner | 196.6.e.a.165.1 | 2 | ||
7.5 | odd | 6 | 196.6.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 196.6.e.i.177.1 | 2 | |||
21.2 | odd | 6 | 252.6.a.a.1.1 | 1 | |||
28.19 | even | 6 | 784.6.a.m.1.1 | 1 | |||
28.23 | odd | 6 | 112.6.a.b.1.1 | 1 | |||
35.2 | odd | 12 | 700.6.e.b.449.1 | 2 | |||
35.9 | even | 6 | 700.6.a.b.1.1 | 1 | |||
35.23 | odd | 12 | 700.6.e.b.449.2 | 2 | |||
56.37 | even | 6 | 448.6.a.b.1.1 | 1 | |||
56.51 | odd | 6 | 448.6.a.o.1.1 | 1 | |||
84.23 | even | 6 | 1008.6.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.6.a.b.1.1 | ✓ | 1 | 7.2 | even | 3 | ||
112.6.a.b.1.1 | 1 | 28.23 | odd | 6 | |||
196.6.a.a.1.1 | 1 | 7.5 | odd | 6 | |||
196.6.e.a.165.1 | 2 | 7.4 | even | 3 | inner | ||
196.6.e.a.177.1 | 2 | 1.1 | even | 1 | trivial | ||
196.6.e.i.165.1 | 2 | 7.3 | odd | 6 | |||
196.6.e.i.177.1 | 2 | 7.6 | odd | 2 | |||
252.6.a.a.1.1 | 1 | 21.2 | odd | 6 | |||
448.6.a.b.1.1 | 1 | 56.37 | even | 6 | |||
448.6.a.o.1.1 | 1 | 56.51 | odd | 6 | |||
700.6.a.b.1.1 | 1 | 35.9 | even | 6 | |||
700.6.e.b.449.1 | 2 | 35.2 | odd | 12 | |||
700.6.e.b.449.2 | 2 | 35.23 | odd | 12 | |||
784.6.a.m.1.1 | 1 | 28.19 | even | 6 | |||
1008.6.a.l.1.1 | 1 | 84.23 | even | 6 |