Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,6,Mod(1,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("504.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.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: | \(80.8334451857\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{249}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 62 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-7.38987\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 63.5595 | 1.13699 | 0.568493 | − | 0.822688i | \(-0.307527\pi\) | ||||
0.568493 | + | 0.822688i | \(0.307527\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −743.392 | −1.85241 | −0.926203 | − | 0.377025i | \(-0.876947\pi\) | ||||
−0.926203 | + | 0.377025i | \(0.876947\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 606.951 | 0.996083 | 0.498042 | − | 0.867153i | \(-0.334053\pi\) | ||||
0.498042 | + | 0.867153i | \(0.334053\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1457.53 | 1.22320 | 0.611598 | − | 0.791169i | \(-0.290527\pi\) | ||||
0.611598 | + | 0.791169i | \(0.290527\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2895.40 | −1.84003 | −0.920014 | − | 0.391884i | \(-0.871823\pi\) | ||||
−0.920014 | + | 0.391884i | \(0.871823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1770.72 | −0.697960 | −0.348980 | − | 0.937130i | \(-0.613472\pi\) | ||||
−0.348980 | + | 0.937130i | \(0.613472\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 914.806 | 0.292738 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −150.405 | −0.0332099 | −0.0166050 | − | 0.999862i | \(-0.505286\pi\) | ||||
−0.0166050 | + | 0.999862i | \(0.505286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6752.26 | −1.26196 | −0.630979 | − | 0.775800i | \(-0.717347\pi\) | ||||
−0.630979 | + | 0.775800i | \(0.717347\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3114.41 | 0.429740 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5552.80 | −0.666819 | −0.333409 | − | 0.942782i | \(-0.608199\pi\) | ||||
−0.333409 | + | 0.942782i | \(0.608199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −15482.1 | −1.43837 | −0.719183 | − | 0.694820i | \(-0.755484\pi\) | ||||
−0.719183 | + | 0.694820i | \(0.755484\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11432.3 | −0.942896 | −0.471448 | − | 0.881894i | \(-0.656269\pi\) | ||||
−0.471448 | + | 0.881894i | \(0.656269\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10111.4 | 0.667679 | 0.333839 | − | 0.942630i | \(-0.391656\pi\) | ||||
0.333839 | + | 0.942630i | \(0.391656\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13596.3 | 0.664859 | 0.332430 | − | 0.943128i | \(-0.392132\pi\) | ||||
0.332430 | + | 0.943128i | \(0.392132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −47249.6 | −2.10616 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 41467.6 | 1.55088 | 0.775440 | − | 0.631421i | \(-0.217528\pi\) | ||||
0.775440 | + | 0.631421i | \(0.217528\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10243.9 | 0.352486 | 0.176243 | − | 0.984347i | \(-0.443605\pi\) | ||||
0.176243 | + | 0.984347i | \(0.443605\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 38577.5 | 1.13253 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 45980.1 | 1.25136 | 0.625681 | − | 0.780079i | \(-0.284821\pi\) | ||||
0.625681 | + | 0.780079i | \(0.284821\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 48272.0 | 1.13645 | 0.568224 | − | 0.822874i | \(-0.307631\pi\) | ||||
0.568224 | + | 0.822874i | \(0.307631\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −27340.3 | −0.600477 | −0.300239 | − | 0.953864i | \(-0.597066\pi\) | ||||
−0.300239 | + | 0.953864i | \(0.597066\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −36426.2 | −0.700144 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −87096.9 | −1.57013 | −0.785063 | − | 0.619415i | \(-0.787370\pi\) | ||||
−0.785063 | + | 0.619415i | \(0.787370\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −91629.1 | −1.45995 | −0.729975 | − | 0.683474i | \(-0.760468\pi\) | ||||
−0.729975 | + | 0.683474i | \(0.760468\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 92640.0 | 1.39076 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 56598.5 | 0.757408 | 0.378704 | − | 0.925518i | \(-0.376370\pi\) | ||||
0.378704 | + | 0.925518i | \(0.376370\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 29740.6 | 0.376484 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −184030. | −2.09209 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −131388. | −1.41784 | −0.708921 | − | 0.705288i | \(-0.750818\pi\) | ||||
−0.708921 | + | 0.705288i | \(0.750818\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −189888. | −1.85223 | −0.926114 | − | 0.377243i | \(-0.876872\pi\) | ||||
−0.926114 | + | 0.377243i | \(0.876872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −179030. | −1.66277 | −0.831384 | − | 0.555698i | \(-0.812451\pi\) | ||||
−0.831384 | + | 0.555698i | \(0.812451\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 139871. | 1.18105 | 0.590526 | − | 0.807018i | \(-0.298920\pi\) | ||||
0.590526 | + | 0.807018i | \(0.298920\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27077.8 | −0.218297 | −0.109148 | − | 0.994025i | \(-0.534812\pi\) | ||||
−0.109148 | + | 0.994025i | \(0.534812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3694.91 | 0.0272212 | 0.0136106 | − | 0.999907i | \(-0.495667\pi\) | ||||
0.0136106 | + | 0.999907i | \(0.495667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −112546. | −0.793572 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 71419.1 | 0.462325 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 391581. | 2.43141 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −140479. | −0.804147 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −162019. | −0.891365 | −0.445683 | − | 0.895191i | \(-0.647039\pi\) | ||||
−0.445683 | + | 0.895191i | \(0.647039\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 23429.5 | 0.119285 | 0.0596424 | − | 0.998220i | \(-0.481004\pi\) | ||||
0.0596424 | + | 0.998220i | \(0.481004\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −141875. | −0.695466 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −220081. | −1.00180 | −0.500901 | − | 0.865505i | \(-0.666998\pi\) | ||||
−0.500901 | + | 0.865505i | \(0.666998\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 164108. | 0.720431 | 0.360216 | − | 0.932869i | \(-0.382703\pi\) | ||||
0.360216 | + | 0.932869i | \(0.382703\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −451203. | −1.84515 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9559.68 | −0.0377593 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −130408. | −0.481215 | −0.240607 | − | 0.970623i | \(-0.577347\pi\) | ||||
−0.240607 | + | 0.970623i | \(0.577347\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −316560. | −1.12983 | −0.564915 | − | 0.825149i | \(-0.691091\pi\) | ||||
−0.564915 | + | 0.825149i | \(0.691091\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −429170. | −1.43483 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −249308. | −0.807212 | −0.403606 | − | 0.914933i | \(-0.632243\pi\) | ||||
−0.403606 | + | 0.914933i | \(0.632243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −86765.4 | −0.263804 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 241804. | 0.712843 | 0.356422 | − | 0.934325i | \(-0.383997\pi\) | ||||
0.356422 | + | 0.934325i | \(0.383997\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 394733. | 1.09525 | 0.547624 | − | 0.836724i | \(-0.315532\pi\) | ||||
0.547624 | + | 0.836724i | \(0.315532\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2902.90 | −0.00781835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −55967.7 | −0.142175 | −0.0710873 | − | 0.997470i | \(-0.522647\pi\) | ||||
−0.0710873 | + | 0.997470i | \(0.522647\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 44825.5 | 0.110645 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −283606. | −0.661580 | −0.330790 | − | 0.943704i | \(-0.607315\pi\) | ||||
−0.330790 | + | 0.943704i | \(0.607315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −381796. | −0.866234 | −0.433117 | − | 0.901338i | \(-0.642586\pi\) | ||||
−0.433117 | + | 0.901338i | \(0.642586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −352933. | −0.758164 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.08352e6 | −2.26586 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 773789. | 1.53476 | 0.767378 | − | 0.641195i | \(-0.221561\pi\) | ||||
0.767378 | + | 0.641195i | \(0.221561\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −580648. | −1.12207 | −0.561035 | − | 0.827792i | \(-0.689597\pi\) | ||||
−0.561035 | + | 0.827792i | \(0.689597\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 301110. | 0.552789 | 0.276395 | − | 0.961044i | \(-0.410860\pi\) | ||||
0.276395 | + | 0.961044i | \(0.410860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 901241. | 1.61327 | 0.806637 | − | 0.591047i | \(-0.201285\pi\) | ||||
0.806637 | + | 0.591047i | \(0.201285\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7369.86 | −0.0125522 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −984033. | −1.63540 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.15242e6 | 3.40848 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −163082. | −0.252173 | −0.126087 | − | 0.992019i | \(-0.540242\pi\) | ||||
−0.126087 | + | 0.992019i | \(0.540242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −726633. | −1.07206 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −330861. | −0.476976 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 884652. | 1.21840 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −565625. | −0.761669 | −0.380835 | − | 0.924643i | \(-0.624363\pi\) | ||||
−0.380835 | + | 0.924643i | \(0.624363\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −334254. | −0.430538 | −0.215269 | − | 0.976555i | \(-0.569063\pi\) | ||||
−0.215269 | + | 0.976555i | \(0.569063\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 188123. | 0.237058 | 0.118529 | − | 0.992951i | \(-0.462182\pi\) | ||||
0.118529 | + | 0.992951i | \(0.462182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 588574. | 0.710250 | 0.355125 | − | 0.934819i | \(-0.384438\pi\) | ||||
0.355125 | + | 0.934819i | \(0.384438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 642676. | 0.759141 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.15364e6 | −1.30640 | −0.653201 | − | 0.757185i | \(-0.726574\pi\) | ||||
−0.653201 | + | 0.757185i | \(0.726574\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 599210. | 0.664564 | 0.332282 | − | 0.943180i | \(-0.392181\pi\) | ||||
0.332282 | + | 0.943180i | \(0.392181\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 152606. | 0.162427 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.75737e6 | −1.83282 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −442325. | −0.443156 | −0.221578 | − | 0.975143i | \(-0.571121\pi\) | ||||
−0.221578 | + | 0.975143i | \(0.571121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.31634e6 | 1.29291 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 177887. | 0.168001 | 0.0840003 | − | 0.996466i | \(-0.473230\pi\) | ||||
0.0840003 | + | 0.996466i | \(0.473230\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −272087. | −0.252034 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.26234e6 | −1.12535 | −0.562674 | − | 0.826679i | \(-0.690227\pi\) | ||||
−0.562674 | + | 0.826679i | \(0.690227\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 864171. | 0.755936 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 969188. | 0.816634 | 0.408317 | − | 0.912840i | \(-0.366116\pi\) | ||||
0.408317 | + | 0.912840i | \(0.366116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.17860e6 | −0.974860 | −0.487430 | − | 0.873162i | \(-0.662066\pi\) | ||||
−0.487430 | + | 0.873162i | \(0.662066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −680059. | −0.542269 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −158674. | −0.124253 | −0.0621265 | − | 0.998068i | \(-0.519788\pi\) | ||||
−0.0621265 | + | 0.998068i | \(0.519788\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −696402. | −0.526132 | −0.263066 | − | 0.964778i | \(-0.584734\pi\) | ||||
−0.263066 | + | 0.964778i | \(0.584734\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −951366. | −0.706125 | −0.353062 | − | 0.935600i | \(-0.614860\pi\) | ||||
−0.353062 | + | 0.935600i | \(0.614860\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −758622. | −0.543651 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 704545. | 0.496208 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −798149. | −0.543144 | −0.271572 | − | 0.962418i | \(-0.587543\pi\) | ||||
−0.271572 | + | 0.962418i | \(0.587543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.63566e6 | 1.76333 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.07474e6 | −0.695227 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −560184. | −0.356381 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 651099. | 0.400772 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 253169. | 0.153308 | 0.0766540 | − | 0.997058i | \(-0.475576\pi\) | ||||
0.0766540 | + | 0.997058i | \(0.475576\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 704729. | 0.413163 | 0.206581 | − | 0.978429i | \(-0.433766\pi\) | ||||
0.206581 | + | 0.978429i | \(0.433766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9154.82 | −0.00528189 | −0.00264094 | − | 0.999997i | \(-0.500841\pi\) | ||||
−0.00264094 | + | 0.999997i | \(0.500841\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.26957e6 | 0.709594 | 0.354797 | − | 0.934943i | \(-0.384550\pi\) | ||||
0.354797 | + | 0.934943i | \(0.384550\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 111810. | 0.0615183 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.22014e6 | −2.25072 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 555243. | 0.291591 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 495460. | 0.252359 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.52407e6 | 1.76797 | 0.883985 | − | 0.467515i | \(-0.154851\pi\) | ||||
0.883985 | + | 0.467515i | \(0.154851\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.92247e6 | 1.42278 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.72795e6 | 0.828815 | 0.414407 | − | 0.910092i | \(-0.363989\pi\) | ||||
0.414407 | + | 0.910092i | \(0.363989\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.01958e6 | 2.33766 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −620429. | −0.276610 | −0.138305 | − | 0.990390i | \(-0.544165\pi\) | ||||
−0.138305 | + | 0.990390i | \(0.544165\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −561993. | −0.246983 | −0.123492 | − | 0.992346i | \(-0.539409\pi\) | ||||
−0.123492 | + | 0.992346i | \(0.539409\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.30385e6 | −0.984051 | −0.492025 | − | 0.870581i | \(-0.663743\pi\) | ||||
−0.492025 | + | 0.870581i | \(0.663743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.06814e6 | 1.29213 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.45173e6 | 1.82303 | 0.911513 | − | 0.411272i | \(-0.134915\pi\) | ||||
0.911513 | + | 0.411272i | \(0.134915\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.90725e6 | 2.38571 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.73774e6 | −0.682734 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 929818. | 0.360357 | 0.180178 | − | 0.983634i | \(-0.442332\pi\) | ||||
0.180178 | + | 0.983634i | \(0.442332\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 666216. | 0.251293 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.91861e6 | 0.714026 | 0.357013 | − | 0.934099i | \(-0.383795\pi\) | ||||
0.357013 | + | 0.934099i | \(0.383795\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −91288.7 | −0.0330799 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.71768e6 | 1.32946 | 0.664728 | − | 0.747086i | \(-0.268548\pi\) | ||||
0.664728 | + | 0.747086i | \(0.268548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −236982. | −0.0825502 | −0.0412751 | − | 0.999148i | \(-0.513142\pi\) | ||||
−0.0412751 | + | 0.999148i | \(0.513142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.31523e6 | −0.796054 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.31064e6 | −1.10927 | −0.554636 | − | 0.832093i | \(-0.687142\pi\) | ||||
−0.554636 | + | 0.832093i | \(0.687142\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.58089e6 | −0.853742 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.53583e6 | −1.78521 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 159806. | 0.0508881 | 0.0254441 | − | 0.999676i | \(-0.491900\pi\) | ||||
0.0254441 | + | 0.999676i | \(0.491900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.39976e6 | 1.36637 | 0.683184 | − | 0.730246i | \(-0.260595\pi\) | ||||
0.683184 | + | 0.730246i | \(0.260595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.09830e6 | −1.25702 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.12791e6 | 1.23522 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.20429e6 | 0.947161 | 0.473581 | − | 0.880751i | \(-0.342961\pi\) | ||||
0.473581 | + | 0.880751i | \(0.342961\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.03191e6 | 0.586178 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.82390e6 | −1.65994 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −836895. | −0.232882 | −0.116441 | − | 0.993198i | \(-0.537149\pi\) | ||||
−0.116441 | + | 0.993198i | \(0.537149\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 397324. | 0.109255 | 0.0546273 | − | 0.998507i | \(-0.482603\pi\) | ||||
0.0546273 | + | 0.998507i | \(0.482603\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.33336e6 | 0.358076 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 501953. | 0.133227 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −693656. | −0.179867 | −0.0899334 | − | 0.995948i | \(-0.528665\pi\) | ||||
−0.0899334 | + | 0.995948i | \(0.528665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.19992e6 | −0.820200 | −0.410100 | − | 0.912041i | \(-0.634506\pi\) | ||||
−0.410100 | + | 0.912041i | \(0.634506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.12695e6 | 1.28427 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.58657e6 | −0.888215 | −0.444107 | − | 0.895974i | \(-0.646479\pi\) | ||||
−0.444107 | + | 0.895974i | \(0.646479\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.11515e6 | 0.269975 | 0.134988 | − | 0.990847i | \(-0.456900\pi\) | ||||
0.134988 | + | 0.990847i | \(0.456900\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.59737e6 | 0.861162 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.44703e6 | −1.50919 | −0.754595 | − | 0.656191i | \(-0.772167\pi\) | ||||
−0.754595 | + | 0.656191i | \(0.772167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.15093e7 | 2.66444 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.89030e6 | 0.428057 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.98008e6 | 1.78738 | 0.893690 | − | 0.448685i | \(-0.148107\pi\) | ||||
0.893690 | + | 0.448685i | \(0.148107\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.43839e6 | −0.753533 | −0.376767 | − | 0.926308i | \(-0.622964\pi\) | ||||
−0.376767 | + | 0.926308i | \(0.622964\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.36232e6 | 0.512137 | 0.256069 | − | 0.966659i | \(-0.417573\pi\) | ||||
0.256069 | + | 0.966659i | \(0.417573\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.00471e6 | 1.69845 | 0.849227 | − | 0.528029i | \(-0.177069\pi\) | ||||
0.849227 | + | 0.528029i | \(0.177069\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.25302e6 | 0.472970 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.49871e6 | 1.74663 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.64873e6 | −0.538646 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.36957e6 | 1.06930 | 0.534651 | − | 0.845073i | \(-0.320443\pi\) | ||||
0.534651 | + | 0.845073i | \(0.320443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.37028e6 | −0.664207 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.35098e6 | −1.61207 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.29649e6 | −1.58516 | −0.792578 | − | 0.609770i | \(-0.791262\pi\) | ||||
−0.792578 | + | 0.609770i | \(0.791262\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.94205e6 | 0.737936 | 0.368968 | − | 0.929442i | \(-0.379711\pi\) | ||||
0.368968 | + | 0.929442i | \(0.379711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −219221. | −0.0406223 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.36533e6 | 0.429537 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.47204e6 | −1.70291 | −0.851456 | − | 0.524426i | \(-0.824280\pi\) | ||||
−0.851456 | + | 0.524426i | \(0.824280\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 739396. | 0.130304 | 0.0651519 | − | 0.997875i | \(-0.479247\pi\) | ||||
0.0651519 | + | 0.997875i | \(0.479247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.20692e7 | −2.10596 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.12834e7 | 1.93039 | 0.965195 | − | 0.261532i | \(-0.0842277\pi\) | ||||
0.965195 | + | 0.261532i | \(0.0842277\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.33968e6 | −0.226959 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.13790e7 | −1.89054 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.51675e6 | −1.23681 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.31103e6 | −1.01860 | −0.509302 | − | 0.860588i | \(-0.670097\pi\) | ||||
−0.509302 | + | 0.860588i | \(0.670097\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.24140e6 | 0.198453 | 0.0992265 | − | 0.995065i | \(-0.468363\pi\) | ||||
0.0992265 | + | 0.995065i | \(0.468363\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.84165e6 | −1.54362 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.30089e6 | −0.512851 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.39687e6 | −1.43273 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.89015e6 | 1.34284 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.78488e6 | −0.264629 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.19933e6 | 1.05755 | 0.528773 | − | 0.848764i | \(-0.322652\pi\) | ||||
0.528773 | + | 0.848764i | \(0.322652\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.72105e6 | −0.248200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.09875e6 | −0.728610 | −0.364305 | − | 0.931280i | \(-0.618693\pi\) | ||||
−0.364305 | + | 0.931280i | \(0.618693\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 435484. | 0.0611073 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.26775e6 | −0.593452 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.08006e7 | 1.47506 | 0.737528 | − | 0.675317i | \(-0.235993\pi\) | ||||
0.737528 | + | 0.675317i | \(0.235993\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.93887e6 | −0.939203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −165192. | −0.0219643 | −0.0109822 | − | 0.999940i | \(-0.503496\pi\) | ||||
−0.0109822 | + | 0.999940i | \(0.503496\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 234846. | 0.0309501 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.21706e7 | −1.57590 | −0.787952 | − | 0.615737i | \(-0.788858\pi\) | ||||
−0.787952 | + | 0.615737i | \(0.788858\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.30513e6 | 0.295873 | 0.147936 | − | 0.988997i | \(-0.452737\pi\) | ||||
0.147936 | + | 0.988997i | \(0.452737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.61987e6 | −0.204319 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.54323e6 | 0.443058 | 0.221529 | − | 0.975154i | \(-0.428895\pi\) | ||||
0.221529 | + | 0.975154i | \(0.428895\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.48983e6 | −0.551809 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.01073e7 | −1.23159 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.26253e6 | 1.10952 | 0.554759 | − | 0.832011i | \(-0.312810\pi\) | ||||
0.554759 | + | 0.832011i | \(0.312810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.95505e7 | 2.32204 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.00317e7 | −1.17149 | −0.585743 | − | 0.810497i | \(-0.699197\pi\) | ||||
−0.585743 | + | 0.810497i | \(0.699197\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.53936e6 | 0.525657 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.22306e6 | −0.822535 | −0.411267 | − | 0.911515i | \(-0.634914\pi\) | ||||
−0.411267 | + | 0.911515i | \(0.634914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.34318e7 | 1.51687 | 0.758434 | − | 0.651749i | \(-0.225965\pi\) | ||||
0.758434 | + | 0.651749i | \(0.225965\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.48887e7 | 2.76448 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.63035e7 | 1.79602 | 0.898008 | − | 0.439979i | \(-0.145014\pi\) | ||||
0.898008 | + | 0.439979i | \(0.145014\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.13714e6 | 0.665063 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.13783e6 | 0.444755 | 0.222378 | − | 0.974961i | \(-0.428618\pi\) | ||||
0.222378 | + | 0.974961i | \(0.428618\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.91918e6 | 0.625962 | 0.312981 | − | 0.949759i | \(-0.398672\pi\) | ||||
0.312981 | + | 0.949759i | \(0.398672\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.91507e6 | 1.04009 | 0.520043 | − | 0.854140i | \(-0.325916\pi\) | ||||
0.520043 | + | 0.854140i | \(0.325916\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.77333e6 | 0.286273 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.17875e7 | −1.20704 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.09339e6 | −0.815650 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.19832e7 | −1.19812 | −0.599058 | − | 0.800705i | \(-0.704458\pi\) | ||||
−0.599058 | + | 0.800705i | \(0.704458\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.02978e7 | −1.01347 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.45729e6 | 0.142298 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.49041e7 | −1.43272 | −0.716359 | − | 0.697732i | \(-0.754193\pi\) | ||||
−0.716359 | + | 0.697732i | \(0.754193\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.98754e6 | 0.857261 | 0.428631 | − | 0.903480i | \(-0.358996\pi\) | ||||
0.428631 | + | 0.903480i | \(0.358996\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.81362e6 | 0.358160 | 0.179080 | − | 0.983835i | \(-0.442688\pi\) | ||||
0.179080 | + | 0.983835i | \(0.442688\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.08267e7 | −2.87286 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.78785e6 | 0.164077 | 0.0820387 | − | 0.996629i | \(-0.473857\pi\) | ||||
0.0820387 | + | 0.996629i | \(0.473857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.48917e6 | 0.135625 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.09551e7 | −0.982657 | −0.491328 | − | 0.870974i | \(-0.663489\pi\) | ||||
−0.491328 | + | 0.870974i | \(0.663489\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.95795e7 | −1.74300 | −0.871499 | − | 0.490397i | \(-0.836852\pi\) | ||||
−0.871499 | + | 0.490397i | \(0.836852\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.01748e6 | −0.790735 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 266326. | 0.0231792 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.61526e6 | −0.652948 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.28996e7 | −1.09784 | −0.548918 | − | 0.835876i | \(-0.684960\pi\) | ||||
−0.548918 | + | 0.835876i | \(0.684960\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.21099e6 | −0.185402 | −0.0927011 | − | 0.995694i | \(-0.529550\pi\) | ||||
−0.0927011 | + | 0.995694i | \(0.529550\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.43803e6 | −0.535894 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.34237e6 | 0.438210 | 0.219105 | − | 0.975701i | \(-0.429686\pi\) | ||||
0.219105 | + | 0.975701i | \(0.429686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.39883e7 | −1.13904 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.25227e6 | 0.662255 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.07335e6 | 0.324531 | 0.162266 | − | 0.986747i | \(-0.448120\pi\) | ||||
0.162266 | + | 0.986747i | \(0.448120\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.04306e7 | 0.819120 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.25656e7 | −1.75940 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.55148e7 | −1.19248 | −0.596241 | − | 0.802805i | \(-0.703340\pi\) | ||||
−0.596241 | + | 0.802805i | \(0.703340\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.60776e7 | 1.22697 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.30452e6 | −0.700077 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.11958e7 | 1.58356 | 0.791778 | − | 0.610809i | \(-0.209156\pi\) | ||||
0.791778 | + | 0.610809i | \(0.209156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.19564e7 | 0.880797 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.86782e7 | −2.09791 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.50416e6 | −0.685632 | −0.342816 | − | 0.939403i | \(-0.611381\pi\) | ||||
−0.342816 | + | 0.939403i | \(0.611381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.77245e6 | −0.628467 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −137592. | −0.00972181 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.70101e6 | 0.329879 | 0.164940 | − | 0.986304i | \(-0.447257\pi\) | ||||
0.164940 | + | 0.986304i | \(0.447257\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.66630e7 | −1.15335 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.14755e7 | 1.47633 | 0.738163 | − | 0.674622i | \(-0.235693\pi\) | ||||
0.738163 | + | 0.674622i | \(0.235693\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.41812e7 | −2.31803 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.32038e7 | 0.889379 | 0.444690 | − | 0.895685i | \(-0.353314\pi\) | ||||
0.444690 | + | 0.895685i | \(0.353314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.48906e6 | 0.431231 | 0.215616 | − | 0.976478i | \(-0.430824\pi\) | ||||
0.215616 | + | 0.976478i | \(0.430824\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.28867e6 | −0.547135 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.85370e6 | 0.446396 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.01859e7 | 1.30601 | 0.653007 | − | 0.757352i | \(-0.273507\pi\) | ||||
0.653007 | + | 0.757352i | \(0.273507\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.01204e7 | −1.28460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.86038e7 | −1.81420 | −0.907098 | − | 0.420920i | \(-0.861707\pi\) | ||||
−0.907098 | + | 0.420920i | \(0.861707\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.98907e6 | −0.562669 | −0.281335 | − | 0.959610i | \(-0.590777\pi\) | ||||
−0.281335 | + | 0.959610i | \(0.590777\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.32681e6 | −0.0825084 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.51688e7 | 1.54481 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.58860e6 | −0.157851 | −0.0789257 | − | 0.996880i | \(-0.525149\pi\) | ||||
−0.0789257 | + | 0.996880i | \(0.525149\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.40322e6 | 0.505821 | 0.252911 | − | 0.967490i | \(-0.418612\pi\) | ||||
0.252911 | + | 0.967490i | \(0.418612\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.17701e6 | −0.369423 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.48268e7 | 2.64664 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.58850e7 | −2.10516 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.58459e7 | −0.917789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.46380e7 | −1.41798 | −0.708988 | − | 0.705221i | \(-0.750848\pi\) | ||||
−0.708988 | + | 0.705221i | \(0.750848\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 181050. | 0.0102886 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.21757e6 | 0.351106 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.18021e7 | −0.658131 | −0.329066 | − | 0.944307i | \(-0.606734\pi\) | ||||
−0.329066 | + | 0.944307i | \(0.606734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.47377e7 | 0.816702 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.03246e7 | 1.11233 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.51476e6 | −0.299942 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.24938e6 | −0.120834 | −0.0604172 | − | 0.998173i | \(-0.519243\pi\) | ||||
−0.0604172 | + | 0.998173i | \(0.519243\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.67498e7 | −1.42813 | −0.714065 | − | 0.700080i | \(-0.753148\pi\) | ||||
−0.714065 | + | 0.700080i | \(0.753148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.53689e7 | 0.810493 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.31012e7 | 1.73496 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.87167e6 | 0.407577 | 0.203788 | − | 0.979015i | \(-0.434675\pi\) | ||||
0.203788 | + | 0.979015i | \(0.434675\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.72796e7 | −1.40390 | −0.701952 | − | 0.712224i | \(-0.747688\pi\) | ||||
−0.701952 | + | 0.712224i | \(0.747688\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.31252e7 | 1.17577 | 0.587884 | − | 0.808945i | \(-0.299961\pi\) | ||||
0.587884 | + | 0.808945i | \(0.299961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.79851e6 | 0.444655 | 0.222327 | − | 0.974972i | \(-0.428635\pi\) | ||||
0.222327 | + | 0.974972i | \(0.428635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.49954e6 | 0.174742 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.50890e7 | 1.24528 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.78911e6 | 0.185837 | 0.0929185 | − | 0.995674i | \(-0.470380\pi\) | ||||
0.0929185 | + | 0.995674i | \(0.470380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.04885e7 | −0.998897 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −184507. | −0.00888935 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.91875e7 | 0.918986 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.83247e6 | 0.465413 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.19644e7 | 1.03358 | 0.516792 | − | 0.856111i | \(-0.327126\pi\) | ||||
0.516792 | + | 0.856111i | \(0.327126\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.36376e7 | 0.634289 | 0.317145 | − | 0.948377i | \(-0.397276\pi\) | ||||
0.317145 | + | 0.948377i | \(0.397276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.89922e7 | 1.34060 | 0.670299 | − | 0.742091i | \(-0.266166\pi\) | ||||
0.670299 | + | 0.742091i | \(0.266166\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.76372e7 | 1.72024 | 0.860122 | − | 0.510088i | \(-0.170387\pi\) | ||||
0.860122 | + | 0.510088i | \(0.170387\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.55728e6 | −0.161651 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.47471e7 | 2.90851 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.79077e7 | 1.24646 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.88346e6 | −0.303939 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.58400e6 | −0.332966 | −0.166483 | − | 0.986044i | \(-0.553241\pi\) | ||||
−0.166483 | + | 0.986044i | \(0.553241\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.08299e7 | −1.33823 | −0.669117 | − | 0.743157i | \(-0.733328\pi\) | ||||
−0.669117 | + | 0.743157i | \(0.733328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.38308e7 | −1.89181 | −0.945905 | − | 0.324444i | \(-0.894823\pi\) | ||||
−0.945905 | + | 0.324444i | \(0.894823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.19743e7 | −1.36456 | −0.682279 | − | 0.731092i | \(-0.739011\pi\) | ||||
−0.682279 | + | 0.731092i | \(0.739011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.93892e6 | −0.336904 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.92766e7 | −1.22855 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.80258e7 | −0.752207 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.01558e6 | 0.0419096 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.98170e7 | 0.813253 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.42668e7 | −0.984897 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.24543e7 | −0.502693 | −0.251346 | − | 0.967897i | \(-0.580873\pi\) | ||||
−0.251346 | + | 0.967897i | \(0.580873\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.91131e7 | 0.763021 | 0.381510 | − | 0.924365i | \(-0.375404\pi\) | ||||
0.381510 | + | 0.924365i | \(0.375404\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.81163e7 | 2.70442 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.14805e6 | 0.0450854 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.34330e6 | 0.0524667 | 0.0262334 | − | 0.999656i | \(-0.491649\pi\) | ||||
0.0262334 | + | 0.999656i | \(0.491649\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.92988e7 | 1.13200 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.07974e6 | −0.195203 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.01419e7 | 0.385551 | 0.192775 | − | 0.981243i | \(-0.438251\pi\) | ||||
0.192775 | + | 0.981243i | \(0.438251\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.95186e6 | −0.262861 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.88678e7 | −2.57625 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.85233e7 | 1.43342 | 0.716711 | − | 0.697370i | \(-0.245647\pi\) | ||||
0.716711 | + | 0.697370i | \(0.245647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.36272e6 | −0.197429 | −0.0987146 | − | 0.995116i | \(-0.531473\pi\) | ||||
−0.0987146 | + | 0.995116i | \(0.531473\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.74145e7 | 1.00392 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.51394e7 | 0.548572 | 0.274286 | − | 0.961648i | \(-0.411559\pi\) | ||||
0.274286 | + | 0.961648i | \(0.411559\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.65943e7 | −0.598125 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 602459. | 0.0214880 | 0.0107440 | − | 0.999942i | \(-0.496580\pi\) | ||||
0.0107440 | + | 0.999942i | \(0.496580\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.91816e7 | 1.74500 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.07840e7 | −0.378646 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.69639e7 | 0.592540 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.69057e7 | −1.27578 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.51834e7 | −1.20996 | −0.604981 | − | 0.796240i | \(-0.706819\pi\) | ||||
−0.604981 | + | 0.796240i | \(0.706819\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.86560e7 | −0.975365 | −0.487683 | − | 0.873021i | \(-0.662158\pi\) | ||||
−0.487683 | + | 0.873021i | \(0.662158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.04129e6 | 0.272297 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.68769e7 | 0.900829 | 0.450414 | − | 0.892820i | \(-0.351276\pi\) | ||||
0.450414 | + | 0.892820i | \(0.351276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.20749e7 | −1.40303 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.59729e6 | −0.250770 | −0.125385 | − | 0.992108i | \(-0.540017\pi\) | ||||
−0.125385 | + | 0.992108i | \(0.540017\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.91384e7 | 0.628514 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.02435e7 | 0.658104 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.52583e7 | 1.46391 | 0.731954 | − | 0.681354i | \(-0.238609\pi\) | ||||
0.731954 | + | 0.681354i | \(0.238609\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.72824e7 | 1.83427 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.37777e7 | 0.757587 | 0.378793 | − | 0.925481i | \(-0.376339\pi\) | ||||
0.378793 | + | 0.925481i | \(0.376339\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.6.a.t.1.2 | 2 | ||
3.2 | odd | 2 | 168.6.a.h.1.1 | ✓ | 2 | ||
4.3 | odd | 2 | 1008.6.a.bu.1.2 | 2 | |||
12.11 | even | 2 | 336.6.a.w.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.6.a.h.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
336.6.a.w.1.1 | 2 | 12.11 | even | 2 | |||
504.6.a.t.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1008.6.a.bu.1.2 | 2 | 4.3 | odd | 2 |