Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{79}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 79 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.88819\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −24.7764 | −1.58941 | −0.794703 | − | 0.606998i | \(-0.792373\pi\) | ||||
−0.794703 | + | 0.606998i | \(0.792373\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −36.1056 | −0.645876 | −0.322938 | − | 0.946420i | \(-0.604671\pi\) | ||||
−0.322938 | + | 0.946420i | \(0.604671\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 370.869 | 1.52621 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −155.435 | −0.387317 | −0.193658 | − | 0.981069i | \(-0.562035\pi\) | ||||
−0.193658 | + | 0.981069i | \(0.562035\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1158.87 | 1.90185 | 0.950925 | − | 0.309422i | \(-0.100136\pi\) | ||||
0.950925 | + | 0.309422i | \(0.100136\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 894.565 | 1.02656 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1238.08 | 1.03903 | 0.519513 | − | 0.854462i | \(-0.326113\pi\) | ||||
0.519513 | + | 0.854462i | \(0.326113\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 280.279 | 0.178118 | 0.0890588 | − | 0.996026i | \(-0.471614\pi\) | ||||
0.0890588 | + | 0.996026i | \(0.471614\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3482.39 | 1.37264 | 0.686322 | − | 0.727298i | \(-0.259224\pi\) | ||||
0.686322 | + | 0.727298i | \(0.259224\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1821.39 | −0.582844 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3168.14 | −0.836364 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5656.78 | −1.24903 | −0.624517 | − | 0.781011i | \(-0.714704\pi\) | ||||
−0.624517 | + | 0.781011i | \(0.714704\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2314.70 | 0.432604 | 0.216302 | − | 0.976326i | \(-0.430600\pi\) | ||||
0.216302 | + | 0.976326i | \(0.430600\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3851.11 | 0.615604 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2333.18 | −0.280184 | −0.140092 | − | 0.990139i | \(-0.544740\pi\) | ||||
−0.140092 | + | 0.990139i | \(0.544740\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −28712.6 | −3.02281 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3812.61 | 0.354211 | 0.177106 | − | 0.984192i | \(-0.443327\pi\) | ||||
0.177106 | + | 0.984192i | \(0.443327\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3925.73 | −0.323780 | −0.161890 | − | 0.986809i | \(-0.551759\pi\) | ||||
−0.161890 | + | 0.986809i | \(0.551759\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13390.4 | −0.985743 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11116.5 | 0.734043 | 0.367022 | − | 0.930212i | \(-0.380378\pi\) | ||||
0.367022 | + | 0.930212i | \(0.380378\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −30675.2 | −1.65143 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11186.2 | −0.547007 | −0.273504 | − | 0.961871i | \(-0.588183\pi\) | ||||
−0.273504 | + | 0.961871i | \(0.588183\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5612.06 | 0.250159 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6944.31 | −0.283101 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6010.35 | 0.224786 | 0.112393 | − | 0.993664i | \(-0.464148\pi\) | ||||
0.112393 | + | 0.993664i | \(0.464148\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14838.7 | −0.510589 | −0.255295 | − | 0.966863i | \(-0.582172\pi\) | ||||
−0.255295 | + | 0.966863i | \(0.582172\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −41841.6 | −1.22836 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42983.9 | 1.16982 | 0.584909 | − | 0.811099i | \(-0.301130\pi\) | ||||
0.584909 | + | 0.811099i | \(0.301130\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −86281.1 | −2.18169 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 19962.4 | 0.469967 | 0.234984 | − | 0.971999i | \(-0.424496\pi\) | ||||
0.234984 | + | 0.971999i | \(0.424496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 45550.6 | 1.00043 | 0.500215 | − | 0.865901i | \(-0.333254\pi\) | ||||
0.500215 | + | 0.865901i | \(0.333254\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 45127.4 | 0.926376 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −108992. | −1.96484 | −0.982419 | − | 0.186687i | \(-0.940225\pi\) | ||||
−0.982419 | + | 0.186687i | \(0.940225\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11626.1 | −0.196890 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −55829.0 | −0.889538 | −0.444769 | − | 0.895645i | \(-0.646714\pi\) | ||||
−0.444769 | + | 0.895645i | \(0.646714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −44701.6 | −0.671082 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 140155. | 1.98522 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −95545.8 | −1.27861 | −0.639303 | − | 0.768955i | \(-0.720777\pi\) | ||||
−0.639303 | + | 0.768955i | \(0.720777\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −57349.9 | −0.687584 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10119.6 | −0.115042 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15004.9 | 0.161922 | 0.0809609 | − | 0.996717i | \(-0.474201\pi\) | ||||
0.0809609 | + | 0.996717i | \(0.474201\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −57646.0 | −0.591127 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 26876.1 | 0.262158 | 0.131079 | − | 0.991372i | \(-0.458156\pi\) | ||||
0.131079 | + | 0.991372i | \(0.458156\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 51915.2 | 0.482171 | 0.241086 | − | 0.970504i | \(-0.422497\pi\) | ||||
0.241086 | + | 0.970504i | \(0.422497\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 24974.8 | 0.210883 | 0.105442 | − | 0.994425i | \(-0.466374\pi\) | ||||
0.105442 | + | 0.994425i | \(0.466374\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3636.14 | −0.0293140 | −0.0146570 | − | 0.999893i | \(-0.504666\pi\) | ||||
−0.0146570 | + | 0.999893i | \(0.504666\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 57807.7 | 0.445326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 62175.0 | 0.458057 | 0.229028 | − | 0.973420i | \(-0.426445\pi\) | ||||
0.229028 | + | 0.973420i | \(0.426445\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −125734. | −0.886557 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 429789. | 2.90262 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −136891. | −0.849986 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −94462.7 | −0.562986 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 178592. | 1.02232 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −63550.3 | −0.349630 | −0.174815 | − | 0.984601i | \(-0.555933\pi\) | ||||
−0.174815 | + | 0.984601i | \(0.555933\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 97265.5 | 0.514617 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −136297. | −0.693918 | −0.346959 | − | 0.937880i | \(-0.612786\pi\) | ||||
−0.346959 | + | 0.937880i | \(0.612786\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 114388. | 0.540187 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 335303. | 1.52629 | 0.763144 | − | 0.646228i | \(-0.223655\pi\) | ||||
0.763144 | + | 0.646228i | \(0.223655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −58195.2 | −0.255476 | −0.127738 | − | 0.991808i | \(-0.540772\pi\) | ||||
−0.127738 | + | 0.991808i | \(0.540772\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −275426. | −1.16669 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −180129. | −0.736618 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 204241. | 0.806721 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 283058. | 1.04450 | 0.522251 | − | 0.852792i | \(-0.325092\pi\) | ||||
0.522251 | + | 0.852792i | \(0.325092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 241558. | 0.862142 | 0.431071 | − | 0.902318i | \(-0.358136\pi\) | ||||
0.431071 | + | 0.902318i | \(0.358136\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 459166. | 1.58577 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −83573.6 | −0.279409 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −214029. | −0.692984 | −0.346492 | − | 0.938053i | \(-0.612627\pi\) | ||||
−0.346492 | + | 0.938053i | \(0.612627\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 277154. | 0.869417 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −64466.0 | −0.190047 | −0.0950237 | − | 0.995475i | \(-0.530293\pi\) | ||||
−0.0950237 | + | 0.995475i | \(0.530293\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −139047. | −0.397604 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 442694. | 1.22832 | 0.614162 | − | 0.789180i | \(-0.289494\pi\) | ||||
0.614162 | + | 0.789180i | \(0.289494\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 971685. | 2.61703 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 103947. | 0.271845 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −78599.0 | −0.199665 | −0.0998325 | − | 0.995004i | \(-0.531831\pi\) | ||||
−0.0998325 | + | 0.995004i | \(0.531831\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −148915. | −0.357277 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 510427. | 1.19070 | 0.595348 | − | 0.803468i | \(-0.297014\pi\) | ||||
0.595348 | + | 0.803468i | \(0.297014\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22051.8 | −0.0500319 | −0.0250160 | − | 0.999687i | \(-0.507964\pi\) | ||||
−0.0250160 | + | 0.999687i | \(0.507964\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 367650. | 0.811534 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 84240.6 | 0.180964 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −192441. | −0.402432 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 558152. | 1.10706 | 0.553528 | − | 0.832831i | \(-0.313281\pi\) | ||||
0.553528 | + | 0.832831i | \(0.313281\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −49316.3 | −0.0953009 | −0.0476504 | − | 0.998864i | \(-0.515173\pi\) | ||||
−0.0476504 | + | 0.998864i | \(0.515173\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.03668e6 | 1.95236 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −941509. | −1.72846 | −0.864229 | − | 0.503099i | \(-0.832193\pi\) | ||||
−0.864229 | + | 0.503099i | \(0.832193\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −640012. | −1.14566 | −0.572830 | − | 0.819675i | \(-0.694154\pi\) | ||||
−0.572830 | + | 0.819675i | \(0.694154\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.06499e6 | −1.85932 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −137656. | −0.228777 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.29151e6 | 2.09495 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −43565.1 | −0.0689879 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −921869. | −1.42549 | −0.712743 | − | 0.701425i | \(-0.752548\pi\) | ||||
−0.712743 | + | 0.701425i | \(0.752548\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −494597. | −0.746969 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 141741. | 0.209121 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.12858e6 | −1.59009 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.43477e6 | 1.97607 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 837700. | 1.12805 | 0.564023 | − | 0.825759i | \(-0.309253\pi\) | ||||
0.564023 | + | 0.825759i | \(0.309253\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −675497. | −0.889544 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.33069e6 | 1.71400 | 0.857002 | − | 0.515313i | \(-0.172324\pi\) | ||||
0.857002 | + | 0.515313i | \(0.172324\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.01063e6 | 1.27352 | 0.636759 | − | 0.771063i | \(-0.280275\pi\) | ||||
0.636759 | + | 0.771063i | \(0.280275\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.48610e6 | 1.79332 | 0.896661 | − | 0.442718i | \(-0.145986\pi\) | ||||
0.896661 | + | 0.442718i | \(0.145986\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −401366. | −0.474101 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.70043e6 | 3.12293 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −875637. | −0.991584 | −0.495792 | − | 0.868441i | \(-0.665122\pi\) | ||||
−0.495792 | + | 0.868441i | \(0.665122\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.45294e6 | 1.61141 | 0.805706 | − | 0.592316i | \(-0.201786\pi\) | ||||
0.805706 | + | 0.592316i | \(0.201786\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.05791e6 | 1.14930 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 324807. | 0.338753 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.38324e6 | 1.41384 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 198384. | 0.198757 | 0.0993786 | − | 0.995050i | \(-0.468315\pi\) | ||||
0.0993786 | + | 0.995050i | \(0.468315\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −541284. | −0.531648 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.10754e6 | 1.06662 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 479572. | 0.452919 | 0.226460 | − | 0.974021i | \(-0.427285\pi\) | ||||
0.226460 | + | 0.974021i | \(0.427285\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.09793e6 | −1.90629 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −454943. | −0.405572 | −0.202786 | − | 0.979223i | \(-0.565000\pi\) | ||||
−0.202786 | + | 0.979223i | \(0.565000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 403884. | 0.353299 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.36728e6 | 2.03222 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −860136. | −0.724747 | −0.362374 | − | 0.932033i | \(-0.618034\pi\) | ||||
−0.362374 | + | 0.932033i | \(0.618034\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.30558e6 | −1.07989 | −0.539946 | − | 0.841700i | \(-0.681555\pi\) | ||||
−0.539946 | + | 0.841700i | \(0.681555\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 283107. | 0.225745 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −543109. | −0.425292 | −0.212646 | − | 0.977129i | \(-0.568208\pi\) | ||||
−0.212646 | + | 0.977129i | \(0.568208\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 858452. | 0.660246 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 998089. | 0.754055 | 0.377028 | − | 0.926202i | \(-0.376946\pi\) | ||||
0.377028 | + | 0.926202i | \(0.376946\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.77732e6 | −1.31917 | −0.659583 | − | 0.751632i | \(-0.729267\pi\) | ||||
−0.659583 | + | 0.751632i | \(0.729267\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 250728. | 0.182848 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 112986. | 0.0795759 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −371768. | −0.257359 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.63987e6 | −1.11594 | −0.557969 | − | 0.829862i | \(-0.688419\pi\) | ||||
−0.557969 | + | 0.829862i | \(0.688419\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −217007. | −0.145184 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 492439. | 0.323938 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.03564e6 | 2.61056 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −665894. | −0.416676 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 535760. | 0.329777 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.38130e6 | −1.44201 | −0.721006 | − | 0.692928i | \(-0.756320\pi\) | ||||
−0.721006 | + | 0.692928i | \(0.756320\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.28627e6 | −0.766366 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.24513e6 | 0.729983 | 0.364992 | − | 0.931011i | \(-0.381072\pi\) | ||||
0.364992 | + | 0.931011i | \(0.381072\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.66299e6 | 0.959465 | 0.479732 | − | 0.877415i | \(-0.340734\pi\) | ||||
0.479732 | + | 0.877415i | \(0.340734\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.62486e6 | −1.46709 | −0.733547 | − | 0.679639i | \(-0.762136\pi\) | ||||
−0.733547 | + | 0.679639i | \(0.762136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 879260. | 0.483772 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −618784. | −0.335179 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 347008. | 0.185069 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.11075e6 | −1.10848 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 90090.5 | 0.0465918 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.73886e6 | −0.872355 | −0.436178 | − | 0.899861i | \(-0.643668\pi\) | ||||
−0.436178 | + | 0.899861i | \(0.643668\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −865303. | −0.427620 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.55196e6 | −0.755558 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 853564. | 0.409413 | 0.204706 | − | 0.978823i | \(-0.434376\pi\) | ||||
0.204706 | + | 0.978823i | \(0.434376\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.54047e6 | −0.728038 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −359785. | −0.167555 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.11523e6 | 1.40910 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.98500e6 | 1.33082 | 0.665411 | − | 0.746477i | \(-0.268256\pi\) | ||||
0.665411 | + | 0.746477i | \(0.268256\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.87467e6 | 1.26335 | 0.631676 | − | 0.775233i | \(-0.282367\pi\) | ||||
0.631676 | + | 0.775233i | \(0.282367\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.67146e6 | −1.59064 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.47109e6 | 0.628352 | 0.314176 | − | 0.949365i | \(-0.398272\pi\) | ||||
0.314176 | + | 0.949365i | \(0.398272\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −720755. | −0.303540 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.07799e6 | −1.26047 | −0.630233 | − | 0.776406i | \(-0.717041\pi\) | ||||
−0.630233 | + | 0.776406i | \(0.717041\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.39754e6 | −0.968274 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.39167e6 | 1.35097 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.64463e6 | −0.646154 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.61670e6 | −0.626561 | −0.313281 | − | 0.949661i | \(-0.601428\pi\) | ||||
−0.313281 | + | 0.949661i | \(0.601428\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.41398e6 | 0.540602 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.76119e6 | −1.77192 | −0.885958 | − | 0.463766i | \(-0.846498\pi\) | ||||
−0.885958 | + | 0.463766i | \(0.846498\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.42487e6 | −1.62488 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.55547e6 | −2.37548 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.00193e6 | −0.358294 | −0.179147 | − | 0.983822i | \(-0.557334\pi\) | ||||
−0.179147 | + | 0.983822i | \(0.557334\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.57455e6 | 0.555704 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.82152e6 | 0.982849 | 0.491424 | − | 0.870920i | \(-0.336476\pi\) | ||||
0.491424 | + | 0.870920i | \(0.336476\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.45593e6 | −0.494156 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.24240e6 | −0.416281 | −0.208140 | − | 0.978099i | \(-0.566741\pi\) | ||||
−0.208140 | + | 0.978099i | \(0.566741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.31148e6 | 1.42621 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.37695e6 | 1.10292 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.93522e6 | 1.26904 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.74562e6 | 0.874308 | 0.437154 | − | 0.899387i | \(-0.355986\pi\) | ||||
0.437154 | + | 0.899387i | \(0.355986\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.71335e6 | −1.15320 | −0.576601 | − | 0.817026i | \(-0.695621\pi\) | ||||
−0.576601 | + | 0.817026i | \(0.695621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.68244e6 | 0.822748 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 419768. | 0.127166 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 362656. | 0.108520 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.75940e6 | 1.11125 | 0.555623 | − | 0.831434i | \(-0.312480\pi\) | ||||
0.555623 | + | 0.831434i | \(0.312480\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.30761e6 | −2.42589 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.01574e6 | 0.574531 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.44187e6 | 0.406055 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.60027e6 | −1.28011 | −0.640056 | − | 0.768328i | \(-0.721089\pi\) | ||||
−0.640056 | + | 0.768328i | \(0.721089\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −404864. | −0.111328 | −0.0556639 | − | 0.998450i | \(-0.517728\pi\) | ||||
−0.0556639 | + | 0.998450i | \(0.517728\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.12275e6 | 1.12031 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.25503e6 | −0.605591 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.46293e6 | 1.17079 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −94758.5 | −0.0245711 | −0.0122856 | − | 0.999925i | \(-0.503911\pi\) | ||||
−0.0122856 | + | 0.999925i | \(0.503911\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.31727e6 | 1.10660 | 0.553298 | − | 0.832983i | \(-0.313369\pi\) | ||||
0.553298 | + | 0.832983i | \(0.313369\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.06036e6 | −1.28221 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 976041. | 0.244492 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.22367e6 | 0.550693 | 0.275346 | − | 0.961345i | \(-0.411207\pi\) | ||||
0.275346 | + | 0.961345i | \(0.411207\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.68425e6 | 1.13405 | 0.567024 | − | 0.823701i | \(-0.308095\pi\) | ||||
0.567024 | + | 0.823701i | \(0.308095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.44973e6 | 0.825821 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.01315e6 | −1.66014 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 897932. | 0.210198 | 0.105099 | − | 0.994462i | \(-0.466484\pi\) | ||||
0.105099 | + | 0.994462i | \(0.466484\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −592612. | −0.137192 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.98493e6 | −1.37029 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.98181e6 | 1.33981 | 0.669903 | − | 0.742448i | \(-0.266336\pi\) | ||||
0.669903 | + | 0.742448i | \(0.266336\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.92242e6 | −0.869004 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.62507e6 | 0.356138 | 0.178069 | − | 0.984018i | \(-0.443015\pi\) | ||||
0.178069 | + | 0.984018i | \(0.443015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.46295e6 | 1.83472 | 0.917359 | − | 0.398060i | \(-0.130317\pi\) | ||||
0.917359 | + | 0.398060i | \(0.130317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.07065e6 | 0.444094 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.66594e6 | −1.62657 | −0.813286 | − | 0.581864i | \(-0.802324\pi\) | ||||
−0.813286 | + | 0.581864i | \(0.802324\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.30286e6 | 1.10143 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 610195. | 0.125405 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −510497. | −0.103815 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.14862e6 | −0.834849 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.40292e6 | 0.478521 | 0.239261 | − | 0.970955i | \(-0.423095\pi\) | ||||
0.239261 | + | 0.970955i | \(0.423095\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.70385e6 | −0.532867 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −541762. | −0.104581 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 170302. | 0.0325384 | 0.0162692 | − | 0.999868i | \(-0.494821\pi\) | ||||
0.0162692 | + | 0.999868i | \(0.494821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.59724e6 | 0.302063 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.77628e6 | 1.08130 | 0.540648 | − | 0.841249i | \(-0.318179\pi\) | ||||
0.540648 | + | 0.841249i | \(0.318179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.00355e6 | −1.29778 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.08134e6 | 0.381795 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −543602. | −0.0977303 | −0.0488652 | − | 0.998805i | \(-0.515560\pi\) | ||||
−0.0488652 | + | 0.998805i | \(0.515560\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.09684e7 | −1.95230 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.40086e6 | 0.951794 | 0.475897 | − | 0.879501i | \(-0.342124\pi\) | ||||
0.475897 | + | 0.879501i | \(0.342124\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −970378. | −0.169322 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.40749e7 | −4.15953 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.34418e6 | 1.42754 | 0.713772 | − | 0.700378i | \(-0.246985\pi\) | ||||
0.713772 | + | 0.700378i | \(0.246985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −887964. | −0.148971 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.87443e6 | −0.311423 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.72788e6 | −0.284307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.94740e6 | 0.317349 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.14784e7 | −1.85262 | −0.926310 | − | 0.376762i | \(-0.877037\pi\) | ||||
−0.926310 | + | 0.376762i | \(0.877037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.38734e6 | 0.701370 | 0.350685 | − | 0.936494i | \(-0.385949\pi\) | ||||
0.350685 | + | 0.936494i | \(0.385949\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.86579e6 | 0.449487 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.69070e6 | 0.884151 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.22906e6 | 0.343071 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.41832e6 | 0.673657 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −901728. | −0.136204 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.26465e7 | −1.89250 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.22306e6 | 1.06103 | 0.530515 | − | 0.847675i | \(-0.321998\pi\) | ||||
0.530515 | + | 0.847675i | \(0.321998\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 546364. | 0.0795211 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 131285. | 0.0189332 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.54529e6 | −0.506622 | −0.253311 | − | 0.967385i | \(-0.581520\pi\) | ||||
−0.253311 | + | 0.967385i | \(0.581520\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.50323e6 | −0.779267 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.58548e6 | −0.222475 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.08718e6 | −0.287625 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.03663e7 | 1.41575 | 0.707873 | − | 0.706340i | \(-0.249655\pi\) | ||||
0.707873 | + | 0.706340i | \(0.249655\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.54941e6 | −0.615780 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.76799e6 | 0.639628 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.48282e6 | 0.596047 | 0.298023 | − | 0.954559i | \(-0.403673\pi\) | ||||
0.298023 | + | 0.954559i | \(0.403673\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.24486e6 | −0.295848 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.49335e6 | 0.840792 | 0.420396 | − | 0.907341i | \(-0.361891\pi\) | ||||
0.420396 | + | 0.907341i | \(0.361891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 497508. | 0.0638571 | 0.0319286 | − | 0.999490i | \(-0.489835\pi\) | ||||
0.0319286 | + | 0.999490i | \(0.489835\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.38290e7 | −1.75956 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.34279e6 | −0.800038 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.55123e6 | −0.819187 | −0.409594 | − | 0.912268i | \(-0.634330\pi\) | ||||
−0.409594 | + | 0.912268i | \(0.634330\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.22188e6 | 0.151472 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.73873e6 | 0.211865 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.55178e7 | −1.87474 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30793.5 | 0.00368862 | 0.00184431 | − | 0.999998i | \(-0.499413\pi\) | ||||
0.00184431 | + | 0.999998i | \(0.499413\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 648763. | 0.0770544 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.33272e7 | 2.74722 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 570937. | 0.0666732 | 0.0333366 | − | 0.999444i | \(-0.489387\pi\) | ||||
0.0333366 | + | 0.999444i | \(0.489387\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.58572e7 | 1.82092 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.07111e6 | −1.03298 | −0.516492 | − | 0.856292i | \(-0.672762\pi\) | ||||
−0.516492 | + | 0.856292i | \(0.672762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.36309e7 | −1.53936 | −0.769679 | − | 0.638431i | \(-0.779584\pi\) | ||||
−0.769679 | + | 0.638431i | \(0.779584\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.59414e7 | 1.78539 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.94253e6 | 0.548985 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.95651e6 | 0.435853 | 0.217927 | − | 0.975965i | \(-0.430071\pi\) | ||||
0.217927 | + | 0.975965i | \(0.430071\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.28825e7 | 1.39604 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.32310e6 | 0.142214 | 0.0711070 | − | 0.997469i | \(-0.477347\pi\) | ||||
0.0711070 | + | 0.997469i | \(0.477347\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.41063e6 | 0.363619 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.26370e6 | 0.979651 | 0.489826 | − | 0.871820i | \(-0.337060\pi\) | ||||
0.489826 | + | 0.871820i | \(0.337060\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −669385. | −0.0702182 | −0.0351091 | − | 0.999383i | \(-0.511178\pi\) | ||||
−0.0351091 | + | 0.999383i | \(0.511178\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.10327e7 | −1.14803 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −756327. | −0.0774479 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.07939e6 | 0.109650 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.88866e6 | −0.291118 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 666246. | 0.0666133 | 0.0333067 | − | 0.999445i | \(-0.489396\pi\) | ||||
0.0333067 | + | 0.999445i | \(0.489396\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.28406e7 | 2.26568 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.29452e6 | 0.225817 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.40345e6 | 0.717269 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.10877e6 | −0.202714 | −0.101357 | − | 0.994850i | \(-0.532318\pi\) | ||||
−0.101357 | + | 0.994850i | \(0.532318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.25977e7 | −1.20161 | −0.600806 | − | 0.799395i | \(-0.705154\pi\) | ||||
−0.600806 | + | 0.799395i | \(0.705154\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.51182e6 | −0.332379 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.71299e7 | −1.60877 | −0.804386 | − | 0.594107i | \(-0.797506\pi\) | ||||
−0.804386 | + | 0.594107i | \(0.797506\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −934217. | −0.0870635 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.25525e6 | −0.757613 | −0.378806 | − | 0.925476i | \(-0.623665\pi\) | ||||
−0.378806 | + | 0.925476i | \(0.623665\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.92108e6 | 0.448185 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.68933e7 | 1.52687 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.05417e7 | 0.945581 | 0.472790 | − | 0.881175i | \(-0.343247\pi\) | ||||
0.472790 | + | 0.881175i | \(0.343247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.47640e6 | 0.398498 | 0.199249 | − | 0.979949i | \(-0.436150\pi\) | ||||
0.199249 | + | 0.979949i | \(0.436150\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.55485e7 | −3.14078 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.96991e7 | −1.71448 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.07552e7 | −1.79292 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.30645e6 | 0.197760 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.87165e7 | −1.59289 | −0.796447 | − | 0.604708i | \(-0.793290\pi\) | ||||
−0.796447 | + | 0.604708i | \(0.793290\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.77042e6 | 0.487470 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.16232e6 | 0.349031 | 0.174515 | − | 0.984654i | \(-0.444164\pi\) | ||||
0.174515 | + | 0.984654i | \(0.444164\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.29697e7 | −2.72425 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.28691e7 | 1.05559 | 0.527796 | − | 0.849371i | \(-0.323019\pi\) | ||||
0.527796 | + | 0.849371i | \(0.323019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.21063e7 | −0.985793 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.50398e7 | −2.02414 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.29634e7 | −1.04033 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.29037e6 | 0.740181 | 0.370090 | − | 0.928996i | \(-0.379327\pi\) | ||||
0.370090 | + | 0.928996i | \(0.379327\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.10117e6 | 0.165006 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.72032e6 | 0.368035 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.68202e7 | −2.85032 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.50809e7 | 1.92774 | 0.963870 | − | 0.266375i | \(-0.0858258\pi\) | ||||
0.963870 | + | 0.266375i | \(0.0858258\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −653940. | −0.0499057 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.94439e6 | 0.753539 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.93780e6 | 0.742463 | 0.371231 | − | 0.928540i | \(-0.378936\pi\) | ||||
0.371231 | + | 0.928540i | \(0.378936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.04218e7 | −2.99876 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.06069e6 | 0.593811 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.50364e6 | 0.475764 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.16951e7 | 1.57603 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.40009e7 | 1.01003 | 0.505016 | − | 0.863110i | \(-0.331487\pi\) | ||||
0.505016 | + | 0.863110i | \(0.331487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.59987e7 | −2.56119 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.03032e7 | 0.727993 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.27315e6 | −0.580544 | −0.290272 | − | 0.956944i | \(-0.593746\pi\) | ||||
−0.290272 | + | 0.956944i | \(0.593746\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.33861e7 | −1.62982 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.86037e6 | −0.336416 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.28591e6 | −0.225889 | −0.112945 | − | 0.993601i | \(-0.536028\pi\) | ||||
−0.112945 | + | 0.993601i | \(0.536028\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.68119e6 | −0.453090 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.00913e7 | −0.679728 | −0.339864 | − | 0.940475i | \(-0.610381\pi\) | ||||
−0.339864 | + | 0.940475i | \(0.610381\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.04754e6 | −0.538416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.73443e7 | −1.15261 | −0.576307 | − | 0.817233i | \(-0.695507\pi\) | ||||
−0.576307 | + | 0.817233i | \(0.695507\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.02200e7 | −0.674619 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.07053e7 | −1.35762 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.75971e7 | 1.13852 | 0.569262 | − | 0.822156i | \(-0.307229\pi\) | ||||
0.569262 | + | 0.822156i | \(0.307229\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.91525e6 | −0.315906 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.72158e6 | −0.556836 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.66480e6 | −0.295865 | −0.147932 | − | 0.988997i | \(-0.547262\pi\) | ||||
−0.147932 | + | 0.988997i | \(0.547262\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.34111e7 | 0.845005 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.82717e7 | 1.14371 | 0.571857 | − | 0.820353i | \(-0.306223\pi\) | ||||
0.571857 | + | 0.820353i | \(0.306223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.65785e7 | −1.02421 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.96521e6 | 0.427510 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.31895e7 | −1.41409 | −0.707043 | − | 0.707171i | \(-0.749971\pi\) | ||||
−0.707043 | + | 0.707171i | \(0.749971\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.18821e7 | −0.719873 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.02149e6 | 0.121681 | 0.0608405 | − | 0.998148i | \(-0.480622\pi\) | ||||
0.0608405 | + | 0.998148i | \(0.480622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.21597e6 | −0.252141 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.06859e6 | 0.0630913 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.10285e6 | −0.182026 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.79215e7 | 1.04465 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.72763e6 | 0.447582 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.57744e7 | −0.907856 | −0.453928 | − | 0.891038i | \(-0.649978\pi\) | ||||
−0.453928 | + | 0.891038i | \(0.649978\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.12718e7 | 0.644618 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.71961e7 | −0.971064 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.00068e7 | −0.561535 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.22436e6 | 0.0682750 | 0.0341375 | − | 0.999417i | \(-0.489132\pi\) | ||||
0.0341375 | + | 0.999417i | \(0.489132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.37631e7 | 0.762690 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.54350e7 | −1.95142 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.08014e6 | −0.387483 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.13111e7 | 1.15192 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.77325e7 | −1.48976 | −0.744882 | − | 0.667196i | \(-0.767494\pi\) | ||||
−0.744882 | + | 0.667196i | \(0.767494\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.19246e7 | 0.636636 | 0.318318 | − | 0.947984i | \(-0.396882\pi\) | ||||
0.318318 | + | 0.947984i | \(0.396882\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.23476e7 | 1.71639 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.32758e6 | 0.122747 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.10030e6 | −0.0576709 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.60462e7 | 0.830836 | 0.415418 | − | 0.909631i | \(-0.363635\pi\) | ||||
0.415418 | + | 0.909631i | \(0.363635\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.12307e7 | 0.577970 | 0.288985 | − | 0.957334i | \(-0.406682\pi\) | ||||
0.288985 | + | 0.957334i | \(0.406682\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.01437e6 | −0.358801 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.68427e7 | 1.36478 | 0.682389 | − | 0.730989i | \(-0.260941\pi\) | ||||
0.682389 | + | 0.730989i | \(0.260941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.80419e7 | 1.41717 | 0.708584 | − | 0.705626i | \(-0.249334\pi\) | ||||
0.708584 | + | 0.705626i | \(0.249334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.34563e7 | 0.675962 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.59837e7 | −0.793344 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.33331e6 | −0.361815 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.30603e7 | 1.62145 | 0.810723 | − | 0.585430i | \(-0.199074\pi\) | ||||
0.810723 | + | 0.585430i | \(0.199074\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.14880e7 | 0.560086 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.47290e7 | −1.19850 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.50832e7 | −1.69028 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.40356e7 | 2.09669 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.12503e6 | −0.384593 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.73897e7 | 1.28889 | 0.644444 | − | 0.764652i | \(-0.277089\pi\) | ||||
0.644444 | + | 0.764652i | \(0.277089\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.75306e6 | −0.175578 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.96721e6 | −0.138005 | −0.0690027 | − | 0.997616i | \(-0.521982\pi\) | ||||
−0.0690027 | + | 0.997616i | \(0.521982\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.97960e7 | 1.84016 | 0.920081 | − | 0.391729i | \(-0.128123\pi\) | ||||
0.920081 | + | 0.391729i | \(0.128123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.19597e6 | −0.328899 | −0.164450 | − | 0.986385i | \(-0.552585\pi\) | ||||
−0.164450 | + | 0.986385i | \(0.552585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.83786e6 | 0.128959 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.79940e6 | −0.126478 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.69411e7 | 0.761015 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.98127e7 | 2.22482 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.56488e6 | 0.247127 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.51242e7 | 1.10305 | 0.551523 | − | 0.834160i | \(-0.314047\pi\) | ||||
0.551523 | + | 0.834160i | \(0.314047\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.06300e7 | 1.77368 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 120262. | 0.00522022 | 0.00261011 | − | 0.999997i | \(-0.499169\pi\) | ||||
0.00261011 | + | 0.999997i | \(0.499169\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.43497e7 | −1.05097 | −0.525487 | − | 0.850802i | \(-0.676117\pi\) | ||||
−0.525487 | + | 0.850802i | \(0.676117\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.37665e6 | 0.230756 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.82766e7 | 1.20675 | 0.603377 | − | 0.797456i | \(-0.293821\pi\) | ||||
0.603377 | + | 0.797456i | \(0.293821\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.80710e6 | 0.0762586 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.11571e6 | 0.130746 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.84293e7 | −0.769042 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.99885e7 | −4.14924 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.30938e7 | −0.540337 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.38494e7 | −0.568355 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 796192. | 0.0323144 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.43168e7 | 0.981496 | 0.490748 | − | 0.871302i | \(-0.336724\pi\) | ||||
0.490748 | + | 0.871302i | \(0.336724\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.96754e6 | 0.400109 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.36224e7 | 1.34225 | 0.671123 | − | 0.741346i | \(-0.265812\pi\) | ||||
0.671123 | + | 0.741346i | \(0.265812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.67777e6 | 0.344533 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.32742e7 | −0.524150 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.13749e6 | 0.317835 | 0.158917 | − | 0.987292i | \(-0.449200\pi\) | ||||
0.158917 | + | 0.987292i | \(0.449200\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.90001e7 | 2.29194 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.31338e7 | 0.893807 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.24962e6 | 0.163304 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.92538e7 | 0.735896 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.58054e7 | 1.36116 | 0.680580 | − | 0.732674i | \(-0.261728\pi\) | ||||
0.680580 | + | 0.732674i | \(0.261728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.08498e7 | −1.16024 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.94818e6 | 0.259921 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.65849e7 | 1.73339 | 0.866694 | − | 0.498840i | \(-0.166241\pi\) | ||||
0.866694 | + | 0.498840i | \(0.166241\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.12029e7 | −1.52498 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.06725e6 | −0.0761059 | −0.0380529 | − | 0.999276i | \(-0.512116\pi\) | ||||
−0.0380529 | + | 0.999276i | \(0.512116\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.32770e7 | 0.486206 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.36773e7 | −0.857940 | −0.428970 | − | 0.903319i | \(-0.641123\pi\) | ||||
−0.428970 | + | 0.903319i | \(0.641123\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.27872e7 | 1.90267 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.50345e7 | 2.33181 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.40521e6 | −0.121454 | −0.0607270 | − | 0.998154i | \(-0.519342\pi\) | ||||
−0.0607270 | + | 0.998154i | \(0.519342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.01524e7 | −0.715020 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.17849e7 | −0.768910 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.32713e7 | −0.812854 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.26238e6 | 0.321852 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.78059e6 | 0.0615525 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.44238e6 | −0.0496036 | −0.0248018 | − | 0.999692i | \(-0.507895\pi\) | ||||
−0.0248018 | + | 0.999692i | \(0.507895\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.59761e6 | −0.294150 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.15954e6 | 0.175616 | 0.0878078 | − | 0.996137i | \(-0.472014\pi\) | ||||
0.0878078 | + | 0.996137i | \(0.472014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.22968e7 | 1.76183 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.97650e6 | −0.233831 | −0.116915 | − | 0.993142i | \(-0.537301\pi\) | ||||
−0.116915 | + | 0.993142i | \(0.537301\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.48511e7 | 0.495225 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.34853e6 | −0.0447394 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.81568e7 | 0.929393 | 0.464696 | − | 0.885470i | \(-0.346163\pi\) | ||||
0.464696 | + | 0.885470i | \(0.346163\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.39937e7 | 1.11637 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.36709e7 | −0.444434 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.34043e7 | 0.757028 | 0.378514 | − | 0.925596i | \(-0.376435\pi\) | ||||
0.378514 | + | 0.925596i | \(0.376435\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.30825e7 | 1.38653 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.31080e7 | 0.739954 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.30284e7 | −1.37094 | −0.685468 | − | 0.728103i | \(-0.740402\pi\) | ||||
−0.685468 | + | 0.728103i | \(0.740402\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.39183e6 | 0.234336 |
(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 | 784.6.a.s.1.1 | 2 | ||
4.3 | odd | 2 | 98.6.a.h.1.2 | 2 | |||
7.2 | even | 3 | 112.6.i.d.81.2 | 4 | |||
7.4 | even | 3 | 112.6.i.d.65.2 | 4 | |||
7.6 | odd | 2 | 784.6.a.bb.1.2 | 2 | |||
12.11 | even | 2 | 882.6.a.ba.1.2 | 2 | |||
28.3 | even | 6 | 98.6.c.e.79.2 | 4 | |||
28.11 | odd | 6 | 14.6.c.a.9.1 | ✓ | 4 | ||
28.19 | even | 6 | 98.6.c.e.67.2 | 4 | |||
28.23 | odd | 6 | 14.6.c.a.11.1 | yes | 4 | ||
28.27 | even | 2 | 98.6.a.g.1.1 | 2 | |||
84.11 | even | 6 | 126.6.g.j.37.1 | 4 | |||
84.23 | even | 6 | 126.6.g.j.109.1 | 4 | |||
84.83 | odd | 2 | 882.6.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.c.a.9.1 | ✓ | 4 | 28.11 | odd | 6 | ||
14.6.c.a.11.1 | yes | 4 | 28.23 | odd | 6 | ||
98.6.a.g.1.1 | 2 | 28.27 | even | 2 | |||
98.6.a.h.1.2 | 2 | 4.3 | odd | 2 | |||
98.6.c.e.67.2 | 4 | 28.19 | even | 6 | |||
98.6.c.e.79.2 | 4 | 28.3 | even | 6 | |||
112.6.i.d.65.2 | 4 | 7.4 | even | 3 | |||
112.6.i.d.81.2 | 4 | 7.2 | even | 3 | |||
126.6.g.j.37.1 | 4 | 84.11 | even | 6 | |||
126.6.g.j.109.1 | 4 | 84.23 | even | 6 | |||
784.6.a.s.1.1 | 2 | 1.1 | even | 1 | trivial | ||
784.6.a.bb.1.2 | 2 | 7.6 | odd | 2 | |||
882.6.a.ba.1.2 | 2 | 12.11 | even | 2 | |||
882.6.a.bi.1.1 | 2 | 84.83 | odd | 2 |