Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,6,Mod(1,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("324.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.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: | \(51.9643576194\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 110x^{3} + 39x^{2} + 2214x - 1944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{7} \) |
Twist minimal: | no (minimal twist has level 36) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(4.43077\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.1 |
$q$-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 | ||||||||
\(5\) | 9.76844 | 0.174743 | 0.0873716 | − | 0.996176i | \(-0.472153\pi\) | ||||
0.0873716 | + | 0.996176i | \(0.472153\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 136.668 | 1.05420 | 0.527099 | − | 0.849804i | \(-0.323280\pi\) | ||||
0.527099 | + | 0.849804i | \(0.323280\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −653.321 | −1.62796 | −0.813982 | − | 0.580890i | \(-0.802705\pi\) | ||||
−0.813982 | + | 0.580890i | \(0.802705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 250.494 | 0.411092 | 0.205546 | − | 0.978647i | \(-0.434103\pi\) | ||||
0.205546 | + | 0.978647i | \(0.434103\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −249.768 | −0.209611 | −0.104806 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104806 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1754.03 | −1.11469 | −0.557343 | − | 0.830282i | \(-0.688179\pi\) | ||||
−0.557343 | + | 0.830282i | \(0.688179\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1654.88 | 0.652300 | 0.326150 | − | 0.945318i | \(-0.394249\pi\) | ||||
0.326150 | + | 0.945318i | \(0.394249\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3029.58 | −0.969465 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4247.92 | −0.937954 | −0.468977 | − | 0.883211i | \(-0.655377\pi\) | ||||
−0.468977 | + | 0.883211i | \(0.655377\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8987.43 | 1.67970 | 0.839849 | − | 0.542820i | \(-0.182643\pi\) | ||||
0.839849 | + | 0.542820i | \(0.182643\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1335.03 | 0.184214 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6000.33 | −0.720561 | −0.360280 | − | 0.932844i | \(-0.617319\pi\) | ||||
−0.360280 | + | 0.932844i | \(0.617319\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10745.2 | 0.998285 | 0.499142 | − | 0.866520i | \(-0.333648\pi\) | ||||
0.499142 | + | 0.866520i | \(0.333648\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10046.6 | 0.828606 | 0.414303 | − | 0.910139i | \(-0.364025\pi\) | ||||
0.414303 | + | 0.910139i | \(0.364025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −23486.6 | −1.55087 | −0.775435 | − | 0.631427i | \(-0.782469\pi\) | ||||
−0.775435 | + | 0.631427i | \(0.782469\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1871.16 | 0.111332 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9411.34 | −0.460216 | −0.230108 | − | 0.973165i | \(-0.573908\pi\) | ||||
−0.230108 | + | 0.973165i | \(0.573908\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6381.93 | −0.284476 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −44166.8 | −1.65183 | −0.825915 | − | 0.563794i | \(-0.809341\pi\) | ||||
−0.825915 | + | 0.563794i | \(0.809341\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22404.9 | −0.770935 | −0.385467 | − | 0.922721i | \(-0.625960\pi\) | ||||
−0.385467 | + | 0.922721i | \(0.625960\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2446.93 | 0.0718355 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −36003.0 | −0.979832 | −0.489916 | − | 0.871770i | \(-0.662973\pi\) | ||||
−0.489916 | + | 0.871770i | \(0.662973\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −78538.5 | −1.84900 | −0.924499 | − | 0.381184i | \(-0.875517\pi\) | ||||
−0.924499 | + | 0.381184i | \(0.875517\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 61305.5 | 1.34646 | 0.673229 | − | 0.739434i | \(-0.264907\pi\) | ||||
0.673229 | + | 0.739434i | \(0.264907\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −89288.1 | −1.71620 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 27490.1 | 0.495574 | 0.247787 | − | 0.968815i | \(-0.420297\pi\) | ||||
0.247787 | + | 0.968815i | \(0.420297\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 64806.4 | 1.03258 | 0.516289 | − | 0.856415i | \(-0.327313\pi\) | ||||
0.516289 | + | 0.856415i | \(0.327313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2439.85 | −0.0366282 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 34652.4 | 0.463722 | 0.231861 | − | 0.972749i | \(-0.425518\pi\) | ||||
0.231861 | + | 0.972749i | \(0.425518\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 34234.5 | 0.433372 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17134.1 | −0.194784 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16112.3 | 0.173871 | 0.0869356 | − | 0.996214i | \(-0.472293\pi\) | ||||
0.0869356 | + | 0.996214i | \(0.472293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −186939. | −1.82346 | −0.911731 | − | 0.410787i | \(-0.865254\pi\) | ||||
−0.911731 | + | 0.410787i | \(0.865254\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −168588. | −1.56579 | −0.782893 | − | 0.622156i | \(-0.786257\pi\) | ||||
−0.782893 | + | 0.622156i | \(0.786257\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −155131. | −1.30991 | −0.654953 | − | 0.755669i | \(-0.727312\pi\) | ||||
−0.654953 | + | 0.755669i | \(0.727312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −115289. | −0.929439 | −0.464720 | − | 0.885458i | \(-0.653845\pi\) | ||||
−0.464720 | + | 0.885458i | \(0.653845\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −125388. | −0.923759 | −0.461880 | − | 0.886943i | \(-0.652825\pi\) | ||||
−0.461880 | + | 0.886943i | \(0.652825\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16165.6 | 0.113985 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −34135.4 | −0.220972 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 265777. | 1.65027 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −60120.6 | −0.344151 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17459.4 | 0.0960548 | 0.0480274 | − | 0.998846i | \(-0.484707\pi\) | ||||
0.0480274 | + | 0.998846i | \(0.484707\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 28928.1 | 0.147279 | 0.0736395 | − | 0.997285i | \(-0.476539\pi\) | ||||
0.0736395 | + | 0.997285i | \(0.476539\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −239720. | −1.17510 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −408554. | −1.85972 | −0.929862 | − | 0.367910i | \(-0.880074\pi\) | ||||
−0.929862 | + | 0.367910i | \(0.880074\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 289155. | 1.26939 | 0.634693 | − | 0.772765i | \(-0.281127\pi\) | ||||
0.634693 | + | 0.772765i | \(0.281127\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −163653. | −0.669243 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −41495.6 | −0.163901 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 339.345 | 0.00125221 | 0.000626104 | − | 1.00000i | \(-0.499801\pi\) | ||||
0.000626104 | 1.00000i | \(0.499801\pi\) | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 357474. | 1.27586 | 0.637928 | − | 0.770096i | \(-0.279792\pi\) | ||||
0.637928 | + | 0.770096i | \(0.279792\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 87793.2 | 0.293516 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −752.621 | −0.00243684 | −0.00121842 | − | 0.999999i | \(-0.500388\pi\) | ||||
−0.00121842 | + | 0.999999i | \(0.500388\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 226169. | 0.687653 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −358488. | −1.05683 | −0.528416 | − | 0.848986i | \(-0.677214\pi\) | ||||
−0.528416 | + | 0.848986i | \(0.677214\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 493751. | 1.36999 | 0.684994 | − | 0.728549i | \(-0.259805\pi\) | ||||
0.684994 | + | 0.728549i | \(0.259805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −308546. | −0.831004 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −167849. | −0.426387 | −0.213193 | − | 0.977010i | \(-0.568386\pi\) | ||||
−0.213193 | + | 0.977010i | \(0.568386\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −414047. | −1.02201 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 483862. | 1.12873 | 0.564364 | − | 0.825526i | \(-0.309122\pi\) | ||||
0.564364 | + | 0.825526i | \(0.309122\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 74732.3 | 0.169555 | 0.0847777 | − | 0.996400i | \(-0.472982\pi\) | ||||
0.0847777 | + | 0.996400i | \(0.472982\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −58613.8 | −0.125913 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 163179. | 0.341240 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 594260. | 1.17867 | 0.589337 | − | 0.807888i | \(-0.299389\pi\) | ||||
0.589337 | + | 0.807888i | \(0.299389\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −89899.6 | −0.173726 | −0.0868630 | − | 0.996220i | \(-0.527684\pi\) | ||||
−0.0868630 | + | 0.996220i | \(0.527684\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −425161. | −0.780527 | −0.390263 | − | 0.920703i | \(-0.627616\pi\) | ||||
−0.390263 | + | 0.920703i | \(0.627616\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 374339. | 0.670089 | 0.335044 | − | 0.942202i | \(-0.391249\pi\) | ||||
0.335044 | + | 0.942202i | \(0.391249\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −580555. | −0.988788 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 104964. | 0.174443 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.14594e6 | 1.81467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −164605. | −0.254529 | −0.127265 | − | 0.991869i | \(-0.540620\pi\) | ||||
−0.127265 | + | 0.991869i | \(0.540620\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 98139.7 | 0.144793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.22829e6 | 1.77073 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −62565.4 | −0.0861695 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −324678. | −0.437211 | −0.218605 | − | 0.975813i | \(-0.570151\pi\) | ||||
−0.218605 | + | 0.975813i | \(0.570151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 709768. | 0.914222 | 0.457111 | − | 0.889410i | \(-0.348884\pi\) | ||||
0.457111 | + | 0.889410i | \(0.348884\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −253906. | −0.319952 | −0.159976 | − | 0.987121i | \(-0.551142\pi\) | ||||
−0.159976 | + | 0.987121i | \(0.551142\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 557666. | 0.672952 | 0.336476 | − | 0.941692i | \(-0.390765\pi\) | ||||
0.336476 | + | 0.941692i | \(0.390765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −229427. | −0.271004 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 532295. | 0.602778 | 0.301389 | − | 0.953501i | \(-0.402550\pi\) | ||||
0.301389 | + | 0.953501i | \(0.402550\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 665089. | 0.737627 | 0.368814 | − | 0.929503i | \(-0.379764\pi\) | ||||
0.368814 | + | 0.929503i | \(0.379764\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18278.3 | 0.0194546 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −439373. | −0.458238 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 906446. | 0.908150 | 0.454075 | − | 0.890963i | \(-0.349970\pi\) | ||||
0.454075 | + | 0.890963i | \(0.349970\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.08117e6 | −1.06192 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 724841. | 0.684557 | 0.342279 | − | 0.939598i | \(-0.388801\pi\) | ||||
0.342279 | + | 0.939598i | \(0.388801\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −820053. | −0.759613 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −252523. | −0.225119 | −0.112560 | − | 0.993645i | \(-0.535905\pi\) | ||||
−0.112560 | + | 0.993645i | \(0.535905\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −91934.2 | −0.0804197 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 191107. | 0.161026 | 0.0805131 | − | 0.996754i | \(-0.474344\pi\) | ||||
0.0805131 | + | 0.996754i | \(0.474344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 86694.8 | 0.0717084 | 0.0358542 | − | 0.999357i | \(-0.488585\pi\) | ||||
0.0358542 | + | 0.999357i | \(0.488585\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.97929e6 | 1.57825 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.27048e6 | 0.994873 | 0.497437 | − | 0.867500i | \(-0.334275\pi\) | ||||
0.497437 | + | 0.867500i | \(0.334275\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 56829.7 | 0.0429348 | 0.0214674 | − | 0.999770i | \(-0.493166\pi\) | ||||
0.0214674 | + | 0.999770i | \(0.493166\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.35360e6 | 1.00467 | 0.502335 | − | 0.864673i | \(-0.332475\pi\) | ||||
0.502335 | + | 0.864673i | \(0.332475\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.46852e6 | 1.05239 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.35747e6 | −0.956063 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 527702. | 0.359103 | 0.179552 | − | 0.983749i | \(-0.442535\pi\) | ||||
0.179552 | + | 0.983749i | \(0.442535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −431440. | −0.288646 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 414537. | 0.268155 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.37305e6 | 0.873515 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −218861. | −0.134716 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.15348e6 | 0.698497 | 0.349249 | − | 0.937030i | \(-0.386437\pi\) | ||||
0.349249 | + | 0.937030i | \(0.386437\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.51767e6 | 0.889765 | 0.444883 | − | 0.895589i | \(-0.353245\pi\) | ||||
0.444883 | + | 0.895589i | \(0.353245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.95992e6 | −1.13078 | −0.565388 | − | 0.824825i | \(-0.691274\pi\) | ||||
−0.565388 | + | 0.824825i | \(0.691274\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.83228e6 | −1.02410 | −0.512052 | − | 0.858955i | \(-0.671114\pi\) | ||||
−0.512052 | + | 0.858955i | \(0.671114\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.77525e6 | 1.52695 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 438100. | 0.233651 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −758891. | −0.398539 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.20987e6 | −1.63492 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −720112. | −0.361269 | −0.180634 | − | 0.983550i | \(-0.557815\pi\) | ||||
−0.180634 | + | 0.983550i | \(0.557815\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −351693. | −0.171219 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.10867e6 | −1.49107 | −0.745537 | − | 0.666464i | \(-0.767807\pi\) | ||||
−0.745537 | + | 0.666464i | \(0.767807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.87168e6 | −2.73449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.04125e6 | −0.936831 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −272068. | −0.121298 | −0.0606490 | − | 0.998159i | \(-0.519317\pi\) | ||||
−0.0606490 | + | 0.998159i | \(0.519317\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.02049e6 | 1.32744 | 0.663718 | − | 0.747983i | \(-0.268978\pi\) | ||||
0.663718 | + | 0.747983i | \(0.268978\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.05389e6 | −0.450151 | −0.225075 | − | 0.974341i | \(-0.572263\pi\) | ||||
−0.225075 | + | 0.974341i | \(0.572263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −767198. | −0.323100 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.26085e6 | 1.74486 | 0.872430 | − | 0.488739i | \(-0.162543\pi\) | ||||
0.872430 | + | 0.488739i | \(0.162543\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 600514. | 0.242524 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 598860. | 0.235284 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −311300. | −0.120646 | −0.0603231 | − | 0.998179i | \(-0.519213\pi\) | ||||
−0.0603231 | + | 0.998179i | \(0.519213\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.28623e6 | −0.485159 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.27536e6 | −0.846794 | −0.423397 | − | 0.905944i | \(-0.639162\pi\) | ||||
−0.423397 | + | 0.905944i | \(0.639162\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.06408e6 | −0.385585 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.28710e6 | 1.17548 | 0.587739 | − | 0.809050i | \(-0.300018\pi\) | ||||
0.587739 | + | 0.809050i | \(0.300018\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.24672e6 | −0.782621 | −0.391311 | − | 0.920259i | \(-0.627978\pi\) | ||||
−0.391311 | + | 0.920259i | \(0.627978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −872206. | −0.299893 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.36745e6 | 0.458180 | 0.229090 | − | 0.973405i | \(-0.426425\pi\) | ||||
0.229090 | + | 0.973405i | \(0.426425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −413337. | −0.136729 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 268535. | 0.0865982 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.52652e6 | 0.486099 | 0.243050 | − | 0.970014i | \(-0.421852\pi\) | ||||
0.243050 | + | 0.970014i | \(0.421852\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.73997e6 | −1.47202 | −0.736011 | − | 0.676969i | \(-0.763293\pi\) | ||||
−0.736011 | + | 0.676969i | \(0.763293\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.25130e6 | 0.690510 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.92014e6 | 1.17305 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 956937. | 0.282862 | 0.141431 | − | 0.989948i | \(-0.454830\pi\) | ||||
0.141431 | + | 0.989948i | \(0.454830\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.03619e6 | −1.74136 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 633057. | 0.180436 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.77084e6 | −0.492769 | −0.246384 | − | 0.969172i | \(-0.579243\pi\) | ||||
−0.246384 | + | 0.969172i | \(0.579243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.08529e6 | 0.848381 | 0.424190 | − | 0.905573i | \(-0.360559\pi\) | ||||
0.424190 | + | 0.905573i | \(0.360559\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 756692. | 0.203211 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.06203e6 | −0.812718 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.16873e6 | −0.562356 | −0.281178 | − | 0.959656i | \(-0.590725\pi\) | ||||
−0.281178 | + | 0.959656i | \(0.590725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.69677e6 | 1.71651 | 0.858253 | − | 0.513226i | \(-0.171550\pi\) | ||||
0.858253 | + | 0.513226i | \(0.171550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.90271e6 | −0.727109 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.46259e6 | −1.60046 | −0.800231 | − | 0.599691i | \(-0.795290\pi\) | ||||
−0.800231 | + | 0.599691i | \(0.795290\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.75472e6 | −0.424815 | −0.212407 | − | 0.977181i | \(-0.568130\pi\) | ||||
−0.212407 | + | 0.977181i | \(0.568130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 338500. | 0.0810323 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 515131. | 0.120587 | 0.0602937 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602937 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.02006e6 | −1.62517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 334418. | 0.0757288 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.93389e6 | −1.10509 | −0.552546 | − | 0.833482i | \(-0.686344\pi\) | ||||
−0.552546 | + | 0.833482i | \(0.686344\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.25863e6 | −1.80991 | −0.904953 | − | 0.425512i | \(-0.860094\pi\) | ||||
−0.904953 | + | 0.425512i | \(0.860094\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.19085e6 | 0.474964 | 0.237482 | − | 0.971392i | \(-0.423678\pi\) | ||||
0.237482 | + | 0.971392i | \(0.423678\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.29374e6 | −0.486691 | −0.243345 | − | 0.969940i | \(-0.578245\pi\) | ||||
−0.243345 | + | 0.969940i | \(0.578245\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.92046e6 | −1.03294 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.56366e6 | −1.34894 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.31396e6 | 1.08065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −92886.5 | −0.0184975 | −0.00924876 | − | 0.999957i | \(-0.502944\pi\) | ||||
−0.00924876 | + | 0.999957i | \(0.502944\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50304e6 | −0.296217 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 157392. | 0.0303828 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.13899e6 | −0.217620 | −0.108810 | − | 0.994063i | \(-0.534704\pi\) | ||||
−0.108810 | + | 0.994063i | \(0.534704\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.72946e6 | 1.63412 | 0.817060 | − | 0.576553i | \(-0.195603\pi\) | ||||
0.817060 | + | 0.576553i | \(0.195603\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.06100e6 | 0.196606 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.07337e7 | −1.94921 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.47762e6 | −0.265651 | −0.132825 | − | 0.991139i | \(-0.542405\pi\) | ||||
−0.132825 | + | 0.991139i | \(0.542405\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 743514. | 0.131029 | 0.0655147 | − | 0.997852i | \(-0.479131\pi\) | ||||
0.0655147 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.82610e6 | −0.318638 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.87120e6 | 1.51771 | 0.758854 | − | 0.651261i | \(-0.225760\pi\) | ||||
0.758854 | + | 0.651261i | \(0.225760\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.37851e6 | 1.41943 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.64684e6 | −0.273610 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.53443e7 | 2.52476 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.00935e6 | 0.324311 | 0.162155 | − | 0.986765i | \(-0.448155\pi\) | ||||
0.162155 | + | 0.986765i | \(0.448155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.39895e6 | 1.02295 | 0.511475 | − | 0.859298i | \(-0.329099\pi\) | ||||
0.511475 | + | 0.859298i | \(0.329099\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.24478e6 | −0.352084 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.69771e6 | −0.574505 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.69160e6 | 0.410387 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.51539e6 | −0.228897 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.22247e6 | −0.181245 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.26335e7 | −1.85580 | −0.927899 | − | 0.372832i | \(-0.878387\pi\) | ||||
−0.927899 | + | 0.372832i | \(0.878387\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.12619e6 | −0.162413 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.10355e7 | −1.57697 | −0.788487 | − | 0.615052i | \(-0.789135\pi\) | ||||
−0.788487 | + | 0.615052i | \(0.789135\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.45097e6 | 1.04552 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.75702e6 | 0.522433 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.08374e7 | 1.48009 | 0.740046 | − | 0.672557i | \(-0.234804\pi\) | ||||
0.740046 | + | 0.672557i | \(0.234804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.51661e6 | 0.340633 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.31377e6 | 0.440607 | 0.220303 | − | 0.975431i | \(-0.429295\pi\) | ||||
0.220303 | + | 0.975431i | \(0.429295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.22484e6 | −0.161421 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.54951e6 | 0.200639 | 0.100319 | − | 0.994955i | \(-0.468014\pi\) | ||||
0.100319 | + | 0.994955i | \(0.468014\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.19114e6 | 0.409595 | 0.204798 | − | 0.978804i | \(-0.434346\pi\) | ||||
0.204798 | + | 0.978804i | \(0.434346\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.01359e6 | −0.632381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.55234e6 | 1.19446 | 0.597228 | − | 0.802072i | \(-0.296269\pi\) | ||||
0.597228 | + | 0.802072i | \(0.296269\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.85696e6 | 1.08854 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.14863e6 | 0.749216 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.12882e7 | 1.35217 | 0.676083 | − | 0.736826i | \(-0.263676\pi\) | ||||
0.676083 | + | 0.736826i | \(0.263676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.57642e7 | −1.87234 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.91815e6 | 0.924671 | 0.462336 | − | 0.886705i | \(-0.347012\pi\) | ||||
0.462336 | + | 0.886705i | \(0.347012\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −333449. | −0.0386133 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.21828e6 | 0.366485 | 0.183242 | − | 0.983068i | \(-0.441341\pi\) | ||||
0.183242 | + | 0.983068i | \(0.441341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.48609e6 | −0.845413 | −0.422706 | − | 0.906267i | \(-0.638920\pi\) | ||||
−0.422706 | + | 0.906267i | \(0.638920\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.59623e6 | 0.288373 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.01212e7 | −1.11497 | −0.557483 | − | 0.830189i | \(-0.688233\pi\) | ||||
−0.557483 | + | 0.830189i | \(0.688233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.88325e6 | −0.637550 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.34715e6 | −0.467254 | −0.233627 | − | 0.972326i | \(-0.575059\pi\) | ||||
−0.233627 | + | 0.972326i | \(0.575059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.85918e7 | −1.96611 | −0.983056 | − | 0.183305i | \(-0.941320\pi\) | ||||
−0.983056 | + | 0.183305i | \(0.941320\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.36603e7 | 1.43296 | 0.716478 | − | 0.697610i | \(-0.245753\pi\) | ||||
0.716478 | + | 0.697610i | \(0.245753\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.73588e6 | 0.488855 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.88015e6 | 0.909327 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.49869e6 | 0.151038 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.33121e6 | −0.333065 | −0.166532 | − | 0.986036i | \(-0.553257\pi\) | ||||
−0.166532 | + | 0.986036i | \(0.553257\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 170551. | 0.0167849 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 468715. | 0.0457678 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.28954e6 | −0.220091 | −0.110046 | − | 0.993927i | \(-0.535100\pi\) | ||||
−0.110046 | + | 0.993927i | \(0.535100\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.81039e6 | −0.649597 | −0.324799 | − | 0.945783i | \(-0.605297\pi\) | ||||
−0.324799 | + | 0.945783i | \(0.605297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.48250e7 | 1.39231 | 0.696153 | − | 0.717894i | \(-0.254894\pi\) | ||||
0.696153 | + | 0.717894i | \(0.254894\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.88551e7 | 2.68912 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.12712e6 | 0.745854 | 0.372927 | − | 0.927861i | \(-0.378354\pi\) | ||||
0.372927 | + | 0.927861i | \(0.378354\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 282582. | 0.0257360 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.15231e6 | 0.731253 | 0.365626 | − | 0.930762i | \(-0.380855\pi\) | ||||
0.365626 | + | 0.930762i | \(0.380855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.75916e6 | −0.779756 | −0.389878 | − | 0.920867i | \(-0.627483\pi\) | ||||
−0.389878 | + | 0.920867i | \(0.627483\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.34169e6 | −0.205341 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.02980e6 | −0.611827 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.46376e7 | 1.25505 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.53489e6 | 0.726374 | 0.363187 | − | 0.931716i | \(-0.381689\pi\) | ||||
0.363187 | + | 0.931716i | \(0.381689\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.51632e7 | 1.27151 | 0.635755 | − | 0.771891i | \(-0.280689\pi\) | ||||
0.635755 | + | 0.771891i | \(0.280689\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.20203e6 | 0.183295 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.33221e7 | 1.09275 | 0.546376 | − | 0.837540i | \(-0.316007\pi\) | ||||
0.546376 | + | 0.837540i | \(0.316007\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.99094e6 | −0.324974 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.35748e6 | −0.189191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.96348e6 | −0.156434 | −0.0782169 | − | 0.996936i | \(-0.524923\pi\) | ||||
−0.0782169 | + | 0.996936i | \(0.524923\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.82459e6 | 0.221816 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.68381e6 | −0.209252 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.36605e7 | −1.81856 | −0.909282 | − | 0.416180i | \(-0.863369\pi\) | ||||
−0.909282 | + | 0.416180i | \(0.863369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.05247e7 | 0.803199 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.55486e7 | −1.92229 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.67839e7 | −1.25394 | −0.626970 | − | 0.779043i | \(-0.715705\pi\) | ||||
−0.626970 | + | 0.779043i | \(0.715705\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.48731e7 | 1.09567 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.59863e6 | −0.116946 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.89621e6 | 0.425355 | 0.212677 | − | 0.977123i | \(-0.431782\pi\) | ||||
0.212677 | + | 0.977123i | \(0.431782\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.30405e7 | −1.65065 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.28694e7 | 0.909313 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.03092e7 | −0.723415 | −0.361708 | − | 0.932292i | \(-0.617806\pi\) | ||||
−0.361708 | + | 0.932292i | \(0.617806\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.50932e6 | −0.173685 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.53374e7 | 1.05436 | 0.527182 | − | 0.849752i | \(-0.323249\pi\) | ||||
0.527182 | + | 0.849752i | \(0.323249\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.35215e7 | 1.59513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.97929e6 | −0.133321 | −0.0666606 | − | 0.997776i | \(-0.521234\pi\) | ||||
−0.0666606 | + | 0.997776i | \(0.521234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.89747e7 | 1.92552 | 0.962758 | − | 0.270363i | \(-0.0871437\pi\) | ||||
0.962758 | + | 0.270363i | \(0.0871437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3314.88 | 0.000218815 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.12015e7 | −1.38090 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.04365e7 | 0.675238 | 0.337619 | − | 0.941283i | \(-0.390379\pi\) | ||||
0.337619 | + | 0.941283i | \(0.390379\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.49196e6 | 0.222947 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.51464e7 | 0.960661 | 0.480331 | − | 0.877087i | \(-0.340517\pi\) | ||||
0.480331 | + | 0.877087i | \(0.340517\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.21800e7 | 1.38835 | 0.694176 | − | 0.719806i | \(-0.255769\pi\) | ||||
0.694176 | + | 0.719806i | \(0.255769\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.57563e7 | −0.979812 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.10635e7 | −0.679054 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.42382e6 | −0.391722 | −0.195861 | − | 0.980632i | \(-0.562750\pi\) | ||||
−0.195861 | + | 0.980632i | \(0.562750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.34346e6 | −0.141062 | −0.0705308 | − | 0.997510i | \(-0.522469\pi\) | ||||
−0.0705308 | + | 0.997510i | \(0.522469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.72281e7 | −1.62841 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.88474e7 | −1.11277 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.13108e7 | 3.01010 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7351.93 | −0.000425821 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.85081e7 | 1.64071 | 0.820354 | − | 0.571856i | \(-0.193776\pi\) | ||||
0.820354 | + | 0.571856i | \(0.193776\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.71365e7 | −0.973824 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.61228e6 | −0.316925 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.54995e6 | −0.421016 | −0.210508 | − | 0.977592i | \(-0.567512\pi\) | ||||
−0.210508 | + | 0.977592i | \(0.567512\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.86621e6 | 0.325080 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.00522e7 | −2.19198 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.20932e6 | 0.120163 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.98225e6 | −0.321361 | −0.160680 | − | 0.987006i | \(-0.551369\pi\) | ||||
−0.160680 | + | 0.987006i | \(0.551369\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.22339e6 | 0.492423 | 0.246212 | − | 0.969216i | \(-0.420814\pi\) | ||||
0.246212 | + | 0.969216i | \(0.420814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.50187e6 | −0.184674 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.76220e7 | −0.923636 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.29602e7 | −0.671049 | −0.335525 | − | 0.942031i | \(-0.608914\pi\) | ||||
−0.335525 | + | 0.942031i | \(0.608914\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.53351e6 | −0.387702 | −0.193851 | − | 0.981031i | \(-0.562098\pi\) | ||||
−0.193851 | + | 0.981031i | \(0.562098\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.59694e7 | −0.811942 | −0.405971 | − | 0.913886i | \(-0.633067\pi\) | ||||
−0.405971 | + | 0.913886i | \(0.633067\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.71049e7 | −1.36981 | −0.684907 | − | 0.728631i | \(-0.740157\pi\) | ||||
−0.684907 | + | 0.728631i | \(0.740157\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −467357. | −0.0233365 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.82318e6 | 0.239396 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.76275e7 | −1.35499 | −0.677497 | − | 0.735526i | \(-0.736935\pi\) | ||||
−0.677497 | + | 0.735526i | \(0.736935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.46633e6 | −0.120243 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.01401e6 | −0.145212 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.63233e7 | 1.73971 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.92982e6 | −0.470021 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.93396e7 | −0.910072 | −0.455036 | − | 0.890473i | \(-0.650374\pi\) | ||||
−0.455036 | + | 0.890473i | \(0.650374\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.74898e7 | 1.27855 | 0.639277 | − | 0.768977i | \(-0.279234\pi\) | ||||
0.639277 | + | 0.768977i | \(0.279234\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.66389e6 | 0.215658 | 0.107829 | − | 0.994169i | \(-0.465610\pi\) | ||||
0.107829 | + | 0.994169i | \(0.465610\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.10059e6 | 0.141716 | 0.0708578 | − | 0.997486i | \(-0.477426\pi\) | ||||
0.0708578 | + | 0.997486i | \(0.477426\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.63962e6 | −0.0745082 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.79599e7 | −0.806777 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.01853e6 | −0.402801 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.21657e6 | −0.362803 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.64543e7 | −0.722405 | −0.361202 | − | 0.932487i | \(-0.617634\pi\) | ||||
−0.361202 | + | 0.932487i | \(0.617634\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.06332e6 | −0.0895626 | −0.0447813 | − | 0.998997i | \(-0.514259\pi\) | ||||
−0.0447813 | + | 0.998997i | \(0.514259\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00336e7 | −0.864683 | −0.432342 | − | 0.901710i | \(-0.642313\pi\) | ||||
−0.432342 | + | 0.901710i | \(0.642313\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.83243e7 | −1.20879 | −0.604393 | − | 0.796686i | \(-0.706584\pi\) | ||||
−0.604393 | + | 0.796686i | \(0.706584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.38614e6 | 0.101261 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.11961e7 | 1.72873 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.72658e6 | 0.197237 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.81779e7 | −1.57548 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.35066e6 | 0.0964666 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 730018. | 0.0296287 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.80750e7 | −1.13319 | −0.566593 | − | 0.823998i | \(-0.691739\pi\) | ||||
−0.566593 | + | 0.823998i | \(0.691739\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.71729e7 | 1.08477 | 0.542387 | − | 0.840128i | \(-0.317520\pi\) | ||||
0.542387 | + | 0.840128i | \(0.317520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.23394e7 | −1.68100 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.95354e6 | 0.155261 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.48360e7 | 1.75121 | 0.875604 | − | 0.483029i | \(-0.160464\pi\) | ||||
0.875604 | + | 0.483029i | \(0.160464\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.96734e7 | −0.760108 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.81785e7 | 0.698558 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.57318e6 | 0.0598054 | 0.0299027 | − | 0.999553i | \(-0.490480\pi\) | ||||
0.0299027 | + | 0.999553i | \(0.490480\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.28207e6 | −0.124101 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.59400e6 | 0.0596293 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.08278e6 | 0.0774986 | 0.0387493 | − | 0.999249i | \(-0.487663\pi\) | ||||
0.0387493 | + | 0.999249i | \(0.487663\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.30903e6 | 0.305898 | 0.152949 | − | 0.988234i | \(-0.451123\pi\) | ||||
0.152949 | + | 0.988234i | \(0.451123\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.77820e7 | 0.651181 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.69140e7 | −1.69992 | −0.849958 | − | 0.526851i | \(-0.823373\pi\) | ||||
−0.849958 | + | 0.526851i | \(0.823373\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.53567e7 | 0.553517 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.19875e7 | −0.427559 | −0.213779 | − | 0.976882i | \(-0.568577\pi\) | ||||
−0.213779 | + | 0.976882i | \(0.568577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.80500e6 | 0.205965 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.58363e7 | −1.96052 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.21448e7 | 1.82139 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −878179. | −0.0303574 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.88381e7 | −0.991745 | −0.495872 | − | 0.868395i | \(-0.665152\pi\) | ||||
−0.495872 | + | 0.868395i | \(0.665152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.30199e7 | −0.443158 | −0.221579 | − | 0.975142i | \(-0.571121\pi\) | ||||
−0.221579 | + | 0.975142i | \(0.571121\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.95182e7 | 1.33818 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.82908e7 | 0.613050 | 0.306525 | − | 0.951863i | \(-0.400834\pi\) | ||||
0.306525 | + | 0.951863i | \(0.400834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.26391e7 | −0.754924 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −969801. | −0.0320110 | −0.0160055 | − | 0.999872i | \(-0.505095\pi\) | ||||
−0.0160055 | + | 0.999872i | \(0.505095\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.15316e6 | −0.136392 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.66259e7 | 0.540500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.04589e7 | −1.63213 | −0.816063 | − | 0.577962i | \(-0.803848\pi\) | ||||
−0.816063 | + | 0.577962i | \(0.803848\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.65671e6 | 0.117093 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.78125e7 | 0.567528 | 0.283764 | − | 0.958894i | \(-0.408417\pi\) | ||||
0.283764 | + | 0.958894i | \(0.408417\pi\) | |||||||
\(998\) | 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 | 324.6.a.d.1.3 | 5 | ||
3.2 | odd | 2 | 324.6.a.e.1.3 | 5 | |||
9.2 | odd | 6 | 36.6.e.a.13.2 | ✓ | 10 | ||
9.4 | even | 3 | 108.6.e.a.73.3 | 10 | |||
9.5 | odd | 6 | 36.6.e.a.25.2 | yes | 10 | ||
9.7 | even | 3 | 108.6.e.a.37.3 | 10 | |||
36.7 | odd | 6 | 432.6.i.d.145.3 | 10 | |||
36.11 | even | 6 | 144.6.i.d.49.4 | 10 | |||
36.23 | even | 6 | 144.6.i.d.97.4 | 10 | |||
36.31 | odd | 6 | 432.6.i.d.289.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.e.a.13.2 | ✓ | 10 | 9.2 | odd | 6 | ||
36.6.e.a.25.2 | yes | 10 | 9.5 | odd | 6 | ||
108.6.e.a.37.3 | 10 | 9.7 | even | 3 | |||
108.6.e.a.73.3 | 10 | 9.4 | even | 3 | |||
144.6.i.d.49.4 | 10 | 36.11 | even | 6 | |||
144.6.i.d.97.4 | 10 | 36.23 | even | 6 | |||
324.6.a.d.1.3 | 5 | 1.1 | even | 1 | trivial | ||
324.6.a.e.1.3 | 5 | 3.2 | odd | 2 | |||
432.6.i.d.145.3 | 10 | 36.7 | odd | 6 | |||
432.6.i.d.289.3 | 10 | 36.31 | odd | 6 |