Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,6,Mod(1,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.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: | \(35.9259756381\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{61}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 15 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.40512\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.1 |
$q$-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 | ||||||||
\(3\) | 14.8102 | 0.950078 | 0.475039 | − | 0.879965i | \(-0.342434\pi\) | ||||
0.475039 | + | 0.879965i | \(0.342434\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −37.6717 | −0.673893 | −0.336946 | − | 0.941524i | \(-0.609394\pi\) | ||||
−0.336946 | + | 0.941524i | \(0.609394\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −23.6565 | −0.0973519 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 149.271 | 0.371959 | 0.185980 | − | 0.982554i | \(-0.440454\pi\) | ||||
0.185980 | + | 0.982554i | \(0.440454\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −627.702 | −1.03014 | −0.515069 | − | 0.857149i | \(-0.672234\pi\) | ||||
−0.515069 | + | 0.857149i | \(0.672234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −557.928 | −0.640251 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −637.343 | −0.534874 | −0.267437 | − | 0.963575i | \(-0.586177\pi\) | ||||
−0.267437 | + | 0.963575i | \(0.586177\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1306.13 | 0.830048 | 0.415024 | − | 0.909811i | \(-0.363773\pi\) | ||||
0.415024 | + | 0.909811i | \(0.363773\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 725.702 | 0.359096 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 376.964 | 0.148587 | 0.0742934 | − | 0.997236i | \(-0.476330\pi\) | ||||
0.0742934 | + | 0.997236i | \(0.476330\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1705.84 | −0.545869 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3949.25 | −1.04257 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6216.40 | −1.37260 | −0.686300 | − | 0.727319i | \(-0.740766\pi\) | ||||
−0.686300 | + | 0.727319i | \(0.740766\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6036.18 | −1.12813 | −0.564063 | − | 0.825731i | \(-0.690763\pi\) | ||||
−0.564063 | + | 0.825731i | \(0.690763\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2210.75 | 0.353390 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1845.92 | −0.254708 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3634.66 | −0.436475 | −0.218237 | − | 0.975896i | \(-0.570031\pi\) | ||||
−0.218237 | + | 0.975896i | \(0.570031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9296.43 | −0.978711 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12772.8 | 1.18666 | 0.593331 | − | 0.804958i | \(-0.297812\pi\) | ||||
0.593331 | + | 0.804958i | \(0.297812\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3347.17 | 0.276062 | 0.138031 | − | 0.990428i | \(-0.455923\pi\) | ||||
0.138031 | + | 0.990428i | \(0.455923\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 891.182 | 0.0656047 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −14347.3 | −0.947382 | −0.473691 | − | 0.880691i | \(-0.657079\pi\) | ||||
−0.473691 | + | 0.880691i | \(0.657079\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9439.22 | −0.508172 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4587.95 | −0.224352 | −0.112176 | − | 0.993688i | \(-0.535782\pi\) | ||||
−0.112176 | + | 0.993688i | \(0.535782\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5623.32 | −0.250660 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 19344.1 | 0.788610 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11398.0 | −0.426284 | −0.213142 | − | 0.977021i | \(-0.568370\pi\) | ||||
−0.213142 | + | 0.977021i | \(0.568370\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3085.32 | 0.106164 | 0.0530818 | − | 0.998590i | \(-0.483096\pi\) | ||||
0.0530818 | + | 0.998590i | \(0.483096\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1159.17 | −0.0367955 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23646.6 | 0.694202 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −35278.7 | −0.960120 | −0.480060 | − | 0.877236i | \(-0.659385\pi\) | ||||
−0.480060 | + | 0.877236i | \(0.659385\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5582.93 | 0.141169 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −48903.1 | −1.15131 | −0.575653 | − | 0.817694i | \(-0.695252\pi\) | ||||
−0.575653 | + | 0.817694i | \(0.695252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15156.6 | 0.332885 | 0.166443 | − | 0.986051i | \(-0.446772\pi\) | ||||
0.166443 | + | 0.986051i | \(0.446772\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −25263.9 | −0.518618 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7314.30 | 0.140587 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −23630.2 | −0.425991 | −0.212996 | − | 0.977053i | \(-0.568322\pi\) | ||||
−0.212996 | + | 0.977053i | \(0.568322\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −52740.8 | −0.893171 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 28021.0 | 0.446466 | 0.223233 | − | 0.974765i | \(-0.428339\pi\) | ||||
0.223233 | + | 0.974765i | \(0.428339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24009.8 | 0.360447 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −92066.4 | −1.30408 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −121536. | −1.62642 | −0.813208 | − | 0.581973i | \(-0.802281\pi\) | ||||
−0.813208 | + | 0.581973i | \(0.802281\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −30757.4 | −0.389355 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −89397.3 | −1.07181 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −49204.3 | −0.559363 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −646.205 | −0.00697335 | −0.00348667 | − | 0.999994i | \(-0.501110\pi\) | ||||
−0.00348667 | + | 0.999994i | \(0.501110\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3531.24 | −0.0362109 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 73325.8 | 0.715243 | 0.357621 | − | 0.933867i | \(-0.383588\pi\) | ||||
0.357621 | + | 0.933867i | \(0.383588\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −179916. | −1.67101 | −0.835503 | − | 0.549486i | \(-0.814824\pi\) | ||||
−0.835503 | + | 0.549486i | \(0.814824\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −27338.5 | −0.241992 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 229269. | 1.93591 | 0.967957 | − | 0.251115i | \(-0.0807971\pi\) | ||||
0.967957 | + | 0.251115i | \(0.0807971\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −38061.4 | −0.306844 | −0.153422 | − | 0.988161i | \(-0.549029\pi\) | ||||
−0.153422 | + | 0.988161i | \(0.549029\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −53830.2 | −0.414685 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 50424.1 | 0.371485 | 0.185743 | − | 0.982598i | \(-0.440531\pi\) | ||||
0.185743 | + | 0.982598i | \(0.440531\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14200.9 | −0.100132 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14849.2 | 0.100286 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −31229.8 | −0.202163 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −138769. | −0.861646 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 189169. | 1.12742 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 181986. | 1.04175 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 163141. | 0.897541 | 0.448771 | − | 0.893647i | \(-0.351862\pi\) | ||||
0.448771 | + | 0.893647i | \(0.351862\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 49572.5 | 0.262281 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 147002. | 0.748417 | 0.374208 | − | 0.927345i | \(-0.377914\pi\) | ||||
0.374208 | + | 0.927345i | \(0.377914\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 64000.5 | 0.313728 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 148775. | 0.702580 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5291.80 | 0.0240881 | 0.0120440 | − | 0.999927i | \(-0.496166\pi\) | ||||
0.0120440 | + | 0.999927i | \(0.496166\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 173621. | 0.762195 | 0.381097 | − | 0.924535i | \(-0.375546\pi\) | ||||
0.381097 | + | 0.924535i | \(0.375546\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −212487. | −0.900087 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −93698.0 | −0.383169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 234183. | 0.924985 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 35559.4 | 0.135725 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 352741. | 1.30164 | 0.650820 | − | 0.759232i | \(-0.274425\pi\) | ||||
0.650820 | + | 0.759232i | \(0.274425\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −474621. | −1.69397 | −0.846983 | − | 0.531619i | \(-0.821584\pi\) | ||||
−0.846983 | + | 0.531619i | \(0.821584\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15077.3 | 0.0520710 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 227393. | 0.760237 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −79394.0 | −0.257062 | −0.128531 | − | 0.991705i | \(-0.541026\pi\) | ||||
−0.128531 | + | 0.991705i | \(0.541026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −67948.7 | −0.213151 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18471.2 | 0.0561605 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 566730. | 1.67073 | 0.835367 | − | 0.549692i | \(-0.185255\pi\) | ||||
0.835367 | + | 0.549692i | \(0.185255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −83282.7 | −0.238147 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 537999. | 1.49276 | 0.746381 | − | 0.665519i | \(-0.231790\pi\) | ||||
0.746381 | + | 0.665519i | \(0.231790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22717.1 | 0.0611837 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −30898.5 | −0.0808067 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −182499. | −0.463603 | −0.231801 | − | 0.972763i | \(-0.574462\pi\) | ||||
−0.231801 | + | 0.972763i | \(0.574462\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −83586.1 | −0.206319 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −168807. | −0.405003 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 270286. | 0.630510 | 0.315255 | − | 0.949007i | \(-0.397910\pi\) | ||||
0.315255 | + | 0.949007i | \(0.397910\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 391356. | 0.887924 | 0.443962 | − | 0.896046i | \(-0.353573\pi\) | ||||
0.443962 | + | 0.896046i | \(0.353573\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 45694.4 | 0.100864 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 136924. | 0.294137 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −95137.2 | −0.198951 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −193513. | −0.394054 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 489469. | 0.970826 | 0.485413 | − | 0.874285i | \(-0.338669\pi\) | ||||
0.485413 | + | 0.874285i | \(0.338669\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 620214. | 1.19853 | 0.599265 | − | 0.800551i | \(-0.295460\pi\) | ||||
0.599265 | + | 0.800551i | \(0.295460\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 350213. | 0.659546 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −614756. | −1.12859 | −0.564296 | − | 0.825572i | \(-0.690853\pi\) | ||||
−0.564296 | + | 0.825572i | \(0.690853\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6443.77 | −0.0115347 | −0.00576736 | − | 0.999983i | \(-0.501836\pi\) | ||||
−0.00576736 | + | 0.999983i | \(0.501836\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −522486. | −0.912189 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −304603. | −0.518794 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −481175. | −0.799683 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8917.65 | −0.0144652 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 194968. | 0.308744 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 533104. | 0.824340 | 0.412170 | − | 0.911107i | \(-0.364771\pi\) | ||||
0.412170 | + | 0.911107i | \(0.364771\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −724268. | −1.09383 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −126094. | −0.186036 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −295773. | −0.426392 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 224473. | 0.316267 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 400062. | 0.550994 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 67470.5 | 0.0908556 | 0.0454278 | − | 0.998968i | \(-0.485535\pi\) | ||||
0.0454278 | + | 0.998968i | \(0.485535\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 40354.2 | 0.0531413 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −489721. | −0.630788 | −0.315394 | − | 0.948961i | \(-0.602137\pi\) | ||||
−0.315394 | + | 0.948961i | \(0.602137\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 373971. | 0.471248 | 0.235624 | − | 0.971844i | \(-0.424287\pi\) | ||||
0.235624 | + | 0.971844i | \(0.424287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 108327. | 0.133569 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −579217. | −0.698958 | −0.349479 | − | 0.936944i | \(-0.613641\pi\) | ||||
−0.349479 | + | 0.936944i | \(0.613641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 540487. | 0.638434 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −349970. | −0.404725 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −165669. | −0.187605 | −0.0938027 | − | 0.995591i | \(-0.529902\pi\) | ||||
−0.0938027 | + | 0.995591i | \(0.529902\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 574223. | 0.636851 | 0.318426 | − | 0.947948i | \(-0.396846\pi\) | ||||
0.318426 | + | 0.947948i | \(0.396846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 178563. | 0.193988 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −90449.9 | −0.0962704 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −819862. | −0.855063 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 414998. | 0.424178 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −940094. | −0.941861 | −0.470931 | − | 0.882170i | \(-0.656082\pi\) | ||||
−0.470931 | + | 0.882170i | \(0.656082\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 56270.0 | 0.0552682 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 355592. | 0.342453 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 129585. | 0.122383 | 0.0611915 | − | 0.998126i | \(-0.480510\pi\) | ||||
0.0611915 | + | 0.998126i | \(0.480510\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −178098. | −0.164972 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 147058. | 0.133625 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.42670e6 | −1.27187 | −0.635936 | − | 0.771742i | \(-0.719386\pi\) | ||||
−0.635936 | + | 0.771742i | \(0.719386\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 172836. | 0.151189 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.79999e6 | −1.54522 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.00662e6 | 0.848173 | 0.424087 | − | 0.905622i | \(-0.360595\pi\) | ||||
0.424087 | + | 0.905622i | \(0.360595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.14104e6 | −0.943793 | −0.471897 | − | 0.881654i | \(-0.656430\pi\) | ||||
−0.471897 | + | 0.881654i | \(0.656430\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −455525. | −0.369918 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −254633. | −0.203041 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.20121e6 | 1.72370 | 0.861850 | − | 0.507163i | \(-0.169306\pi\) | ||||
0.861850 | + | 0.507163i | \(0.169306\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 142795. | 0.109825 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 359913. | 0.271914 | 0.135957 | − | 0.990715i | \(-0.456589\pi\) | ||||
0.135957 | + | 0.990715i | \(0.456589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.10587e6 | −1.56302 | −0.781510 | − | 0.623893i | \(-0.785550\pi\) | ||||
−0.781510 | + | 0.623893i | \(0.785550\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −728727. | −0.531438 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 625868. | 0.448516 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.01365e6 | −0.713910 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9570.46 | −0.00662522 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.47171e6 | 1.68201 | 0.841003 | − | 0.541030i | \(-0.181965\pi\) | ||||
0.841003 | + | 0.541030i | \(0.181965\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 429383. | 0.287269 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −589510. | −0.387793 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −236621. | −0.153065 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 164011. | 0.104342 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.08597e6 | 0.679537 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −116229. | −0.0715429 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.46333e6 | −1.49169 | −0.745843 | − | 0.666122i | \(-0.767953\pi\) | ||||
−0.745843 | + | 0.666122i | \(0.767953\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.66461e6 | −1.58759 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.87297e6 | 1.09807 | 0.549036 | − | 0.835799i | \(-0.314995\pi\) | ||||
0.549036 | + | 0.835799i | \(0.314995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −482265. | −0.278244 | −0.139122 | − | 0.990275i | \(-0.544428\pi\) | ||||
−0.139122 | + | 0.990275i | \(0.544428\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 43667.9 | 0.0247963 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −790018. | −0.441559 | −0.220780 | − | 0.975324i | \(-0.570860\pi\) | ||||
−0.220780 | + | 0.975324i | \(0.570860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −927931. | −0.510551 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.39553e6 | 1.83927 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −832455. | −0.443971 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.07076e6 | 0.562320 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −563698. | −0.291526 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −703017. | −0.358077 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.54749e6 | −1.77972 | −0.889859 | − | 0.456236i | \(-0.849197\pi\) | ||||
−0.889859 | + | 0.456236i | \(0.849197\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 85983.3 | 0.0424916 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.32901e6 | 0.647018 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.78817e6 | −1.81700 | −0.908500 | − | 0.417884i | \(-0.862772\pi\) | ||||
−0.908500 | + | 0.417884i | \(0.862772\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 746793. | 0.352940 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −901030. | −0.419617 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −210319. | −0.0951328 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 352917. | 0.157344 | 0.0786719 | − | 0.996901i | \(-0.474932\pi\) | ||||
0.0786719 | + | 0.996901i | \(0.474932\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.43108e6 | 0.628926 | 0.314463 | − | 0.949270i | \(-0.398176\pi\) | ||||
0.314463 | + | 0.949270i | \(0.398176\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.47895e6 | 1.07399 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.23269e6 | −0.953657 | −0.476828 | − | 0.878996i | \(-0.658214\pi\) | ||||
−0.476828 | + | 0.878996i | \(0.658214\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.84227e6 | 0.775857 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −462522. | −0.192071 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.95264e6 | −1.61864 | −0.809322 | − | 0.587365i | \(-0.800165\pi\) | ||||
−0.809322 | + | 0.587365i | \(0.800165\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −770119. | −0.311021 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.05520e6 | −0.818631 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −570975. | −0.224329 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.67542e6 | 0.649320 | 0.324660 | − | 0.945831i | \(-0.394750\pi\) | ||||
0.324660 | + | 0.945831i | \(0.394750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −302160. | −0.115524 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −224810. | −0.0847969 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.64764e6 | −1.35750 | −0.678751 | − | 0.734369i | \(-0.737478\pi\) | ||||
−0.678751 | + | 0.734369i | \(0.737478\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.69526e6 | 0.989743 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.90205e6 | 1.41397 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.23267e6 | −1.51362 | −0.756809 | − | 0.653636i | \(-0.773243\pi\) | ||||
−0.756809 | + | 0.653636i | \(0.773243\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.41616e6 | 0.852734 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.11709e6 | 1.43415 | 0.717074 | − | 0.696997i | \(-0.245481\pi\) | ||||
0.717074 | + | 0.696997i | \(0.245481\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −275543. | −0.0947408 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −79182.4 | −0.0268752 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.41160e6 | −0.472974 | −0.236487 | − | 0.971635i | \(-0.575996\pi\) | ||||
−0.236487 | + | 0.971635i | \(0.575996\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −240256. | −0.0794752 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.17713e6 | 0.711054 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 890193. | 0.287072 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.99388e6 | −1.27180 | −0.635900 | − | 0.771771i | \(-0.719371\pi\) | ||||
−0.635900 | + | 0.771771i | \(0.719371\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 947863. | 0.298067 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.72629e6 | −0.536110 | −0.268055 | − | 0.963404i | \(-0.586381\pi\) | ||||
−0.268055 | + | 0.963404i | \(0.586381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.78892e6 | 1.16213 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.98684e6 | 0.601901 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −542551. | −0.162351 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.99081e6 | 1.47524 | 0.737620 | − | 0.675216i | \(-0.235949\pi\) | ||||
0.737620 | + | 0.675216i | \(0.235949\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 78372.9 | 0.0228855 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −558502. | −0.161120 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.05560e6 | −0.300870 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.57137e6 | 0.724144 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.02457e6 | 0.285105 | 0.142553 | − | 0.989787i | \(-0.454469\pi\) | ||||
0.142553 | + | 0.989787i | \(0.454469\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 118203. | 0.0325029 | 0.0162514 | − | 0.999868i | \(-0.494827\pi\) | ||||
0.0162514 | + | 0.999868i | \(0.494827\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 339407. | 0.0922294 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.08721e6 | 0.291971 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 151181. | 0.0401261 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.38769e6 | −0.364040 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −99057.3 | −0.0256858 | −0.0128429 | − | 0.999918i | \(-0.504088\pi\) | ||||
−0.0128429 | + | 0.999918i | \(0.504088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.05998e6 | 1.04065 | 0.520325 | − | 0.853968i | \(-0.325811\pi\) | ||||
0.520325 | + | 0.853968i | \(0.325811\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.46830e6 | 0.878807 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 492365. | 0.123334 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.77648e6 | 0.439946 | 0.219973 | − | 0.975506i | \(-0.429403\pi\) | ||||
0.219973 | + | 0.975506i | \(0.429403\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −56799.3 | −0.0139074 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.49343e6 | 0.845752 | 0.422876 | − | 0.906188i | \(-0.361021\pi\) | ||||
0.422876 | + | 0.906188i | \(0.361021\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.57849e6 | 1.09603 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.22419e6 | 1.23666 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.18634e6 | −0.979983 | −0.489991 | − | 0.871727i | \(-0.663000\pi\) | ||||
−0.489991 | + | 0.871727i | \(0.663000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.90662e6 | 0.441390 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.02926e6 | −1.60940 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.15869e6 | 0.262384 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.42202e6 | −1.88636 | −0.943182 | − | 0.332275i | \(-0.892184\pi\) | ||||
−0.943182 | + | 0.332275i | \(0.892184\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.51703e6 | 0.557643 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.99005e6 | 1.97020 | 0.985099 | − | 0.171988i | \(-0.0550192\pi\) | ||||
0.985099 | + | 0.171988i | \(0.0550192\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 990479. | 0.214730 | 0.107365 | − | 0.994220i | \(-0.465759\pi\) | ||||
0.107365 | + | 0.994220i | \(0.465759\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.36775e6 | 0.722284 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.43975e6 | 1.15422 | 0.577108 | − | 0.816668i | \(-0.304181\pi\) | ||||
0.577108 | + | 0.816668i | \(0.304181\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.72866e6 | −0.362891 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.17584e6 | −0.244229 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 499637. | 0.102684 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.22805e6 | −0.453097 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 108535. | 0.0218410 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.32397e6 | 1.65765 | 0.828823 | − | 0.559512i | \(-0.189011\pi\) | ||||
0.828823 | + | 0.559512i | \(0.189011\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.28148e6 | 0.449629 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 273564. | 0.0533569 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24343.7 | 0.00469929 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.77528e6 | −1.48557 | −0.742786 | − | 0.669529i | \(-0.766496\pi\) | ||||
−0.742786 | + | 0.669529i | \(0.766496\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.39342e6 | 1.58733 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.72471e6 | 1.07164 | 0.535821 | − | 0.844332i | \(-0.320002\pi\) | ||||
0.535821 | + | 0.844332i | \(0.320002\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.96198e6 | 0.734167 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 133028. | 0.0244023 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.39625e6 | −0.435153 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.43278e6 | −0.796938 | −0.398469 | − | 0.917182i | \(-0.630458\pi\) | ||||
−0.398469 | + | 0.917182i | \(0.630458\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.96790e6 | 1.41824 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.69126e6 | −1.00297 | −0.501485 | − | 0.865166i | \(-0.667213\pi\) | ||||
−0.501485 | + | 0.865166i | \(0.667213\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.76231e6 | −0.481997 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 336446. | 0.0581293 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.16835e6 | −1.39746 | −0.698731 | − | 0.715384i | \(-0.746252\pi\) | ||||
−0.698731 | + | 0.715384i | \(0.746252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 742673. | 0.125819 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.15824e6 | −0.865383 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.77777e6 | 1.12608 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.14164e6 | −0.352387 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.70286e6 | −0.440459 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.28498e6 | −0.853000 | −0.426500 | − | 0.904488i | \(-0.640254\pi\) | ||||
−0.426500 | + | 0.904488i | \(0.640254\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.45225e6 | −1.03147 | −0.515736 | − | 0.856748i | \(-0.672481\pi\) | ||||
−0.515736 | + | 0.856748i | \(0.672481\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.23793e6 | −0.196019 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.84712e6 | 0.603405 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.29424e6 | −0.977922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 269637. | 0.0414995 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.01753e6 | −1.22243 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.63697e6 | −1.30460 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.00301e6 | 0.599033 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 358401. | 0.0531370 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 850524. | 0.124938 | 0.0624688 | − | 0.998047i | \(-0.480103\pi\) | ||||
0.0624688 | + | 0.998047i | \(0.480103\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.79608e6 | 0.843597 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.43384e6 | 0.206780 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.85068e6 | −0.836061 | −0.418030 | − | 0.908433i | \(-0.637279\pi\) | ||||
−0.418030 | + | 0.908433i | \(0.637279\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −72987.9 | −0.0103352 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.11943e6 | −1.13932 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.15788e6 | −0.161009 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.02788e6 | 0.279453 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.50904e6 | 0.479238 | 0.239619 | − | 0.970867i | \(-0.422978\pi\) | ||||
0.239619 | + | 0.970867i | \(0.422978\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.10103e6 | −0.284382 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.40901e6 | −0.189019 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.04945e6 | 0.405462 | 0.202731 | − | 0.979234i | \(-0.435018\pi\) | ||||
0.202731 | + | 0.979234i | \(0.435018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.89956e6 | −0.250341 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.58430e6 | −0.337587 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.30346e6 | −0.427748 | −0.213874 | − | 0.976861i | \(-0.568608\pi\) | ||||
−0.213874 | + | 0.976861i | \(0.568608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.43527e7 | −1.84222 | −0.921112 | − | 0.389297i | \(-0.872718\pi\) | ||||
−0.921112 | + | 0.389297i | \(0.872718\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.24915e6 | 0.922361 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −643040. | −0.0811089 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.11546e7 | −1.39481 | −0.697404 | − | 0.716679i | \(-0.745661\pi\) | ||||
−0.697404 | + | 0.716679i | \(0.745661\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.18553e6 | 1.13870 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.37303e6 | 0.168748 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −684850. | −0.0834496 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −559397. | −0.0675819 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.85459e6 | 1.06065 | 0.530326 | − | 0.847794i | \(-0.322069\pi\) | ||||
0.530326 | + | 0.847794i | \(0.322069\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.88405e6 | −0.936399 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.10469e6 | −1.07225 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.01381e6 | 0.585505 | 0.292753 | − | 0.956188i | \(-0.405429\pi\) | ||||
0.292753 | + | 0.956188i | \(0.405429\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.17648e6 | 0.136236 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −95433.8 | −0.0109589 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.15050e6 | −0.131014 | −0.0655072 | − | 0.997852i | \(-0.520867\pi\) | ||||
−0.0655072 | + | 0.997852i | \(0.520867\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.59933e7 | 1.80614 | 0.903072 | − | 0.429489i | \(-0.141306\pi\) | ||||
0.903072 | + | 0.429489i | \(0.141306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 834570. | 0.0934694 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.22767e6 | 0.580657 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.17435e7 | −1.29367 | −0.646836 | − | 0.762629i | \(-0.723908\pi\) | ||||
−0.646836 | + | 0.762629i | \(0.723908\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.51125e6 | −0.492894 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.00582e6 | 0.975934 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.45792e7 | 1.56705 | 0.783526 | − | 0.621359i | \(-0.213419\pi\) | ||||
0.783526 | + | 0.621359i | \(0.213419\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.12632e6 | −0.759761 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.55808e7 | −1.64769 | −0.823845 | − | 0.566815i | \(-0.808175\pi\) | ||||
−0.823845 | + | 0.566815i | \(0.808175\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.31769e7 | −1.38225 | −0.691125 | − | 0.722735i | \(-0.742885\pi\) | ||||
−0.691125 | + | 0.722735i | \(0.742885\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.48872e6 | −0.154912 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.95529e6 | −0.614728 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.52499e6 | −0.156159 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.88753e6 | 0.293331 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.31652e6 | 0.233459 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.39854e7 | −1.39830 | −0.699150 | − | 0.714975i | \(-0.746438\pi\) | ||||
−0.699150 | + | 0.714975i | \(0.746438\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.89541e6 | 0.783187 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.14582e6 | −0.604847 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.50711e6 | −0.147163 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.15688e6 | 0.112082 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.99947e7 | 1.92208 | 0.961038 | − | 0.276416i | \(-0.0891467\pi\) | ||||
0.961038 | + | 0.276416i | \(0.0891467\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.12846e7 | 1.07637 | 0.538183 | − | 0.842828i | \(-0.319111\pi\) | ||||
0.538183 | + | 0.842828i | \(0.319111\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.86748e6 | −0.176749 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.66736e6 | −0.626172 | −0.313086 | − | 0.949725i | \(-0.601363\pi\) | ||||
−0.313086 | + | 0.949725i | \(0.601363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.70140e6 | −0.158560 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.38047e6 | −0.405106 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.11346e6 | −0.377506 | −0.188753 | − | 0.982025i | \(-0.560445\pi\) | ||||
−0.188753 | + | 0.982025i | \(0.560445\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.53780e6 | −0.504353 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −358552. | −0.0324070 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.01860e7 | 0.913673 | 0.456836 | − | 0.889551i | \(-0.348982\pi\) | ||||
0.456836 | + | 0.889551i | \(0.348982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.38745e6 | 0.746666 | 0.373333 | − | 0.927697i | \(-0.378215\pi\) | ||||
0.373333 | + | 0.927697i | \(0.378215\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.92502e6 | 0.523487 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.41101e6 | −0.211419 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.34336e6 | −0.203950 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 999255. | 0.0863199 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 460550. | 0.0394885 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.98643e7 | 1.69058 | 0.845290 | − | 0.534308i | \(-0.179428\pi\) | ||||
0.845290 | + | 0.534308i | \(0.179428\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.73679e6 | 0.569106 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.35862e6 | −0.449346 | −0.224673 | − | 0.974434i | \(-0.572131\pi\) | ||||
−0.224673 | + | 0.974434i | \(0.572131\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −31664.1 | −0.00263568 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.25288e6 | −0.599298 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.18486e7 | −0.971889 | −0.485945 | − | 0.873990i | \(-0.661524\pi\) | ||||
−0.485945 | + | 0.873990i | \(0.661524\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −199351. | −0.0162328 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.53860e6 | 0.447722 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.87987e6 | 0.231113 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.79391e7 | −1.42924 | −0.714619 | − | 0.699513i | \(-0.753400\pi\) | ||||
−0.714619 | + | 0.699513i | \(0.753400\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −173031. | −0.0136864 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.54062e6 | −0.513638 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.14068e6 | −0.634715 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.57834e6 | −0.664065 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.47768e7 | −1.13575 | −0.567877 | − | 0.823114i | \(-0.692235\pi\) | ||||
−0.567877 | + | 0.823114i | \(0.692235\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.74734e6 | −0.362295 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.00475e6 | 0.606562 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.59297e6 | 0.270336 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.09017e6 | −0.156159 | −0.0780794 | − | 0.996947i | \(-0.524879\pi\) | ||||
−0.0780794 | + | 0.996947i | \(0.524879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 559009. | 0.0414710 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.27542e6 | −0.167625 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.52977e6 | 0.258215 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.45359e6 | −0.178240 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.23653e6 | −0.0892037 | −0.0446019 | − | 0.999005i | \(-0.514202\pi\) | ||||
−0.0446019 | + | 0.999005i | \(0.514202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.81591e6 | −0.631581 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.50438e6 | 0.605058 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.06042e7 | 0.749259 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.50721e6 | −0.526796 | −0.263398 | − | 0.964687i | \(-0.584843\pi\) | ||||
−0.263398 | + | 0.964687i | \(0.584843\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.54606e7 | 1.07747 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.13330e6 | −0.147658 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.22220e7 | −1.52765 | −0.763823 | − | 0.645425i | \(-0.776680\pi\) | ||||
−0.763823 | + | 0.645425i | \(0.776680\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.33959e6 | −0.0914644 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.26610e6 | −0.357125 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.52607e7 | −1.02793 | −0.513964 | − | 0.857812i | \(-0.671824\pi\) | ||||
−0.513964 | + | 0.857812i | \(0.671824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.21424e7 | −0.812377 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.74605e6 | 0.381854 | 0.190927 | − | 0.981604i | \(-0.438851\pi\) | ||||
0.190927 | + | 0.981604i | \(0.438851\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.32884e7 | −0.877165 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −662879. | −0.0434643 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.12342e7 | 0.731707 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.64874e7 | 1.71372 | 0.856858 | − | 0.515553i | \(-0.172413\pi\) | ||||
0.856858 | + | 0.515553i | \(0.172413\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.39230e7 | −0.894842 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.78798e7 | 1.14155 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.06970e6 | −0.194695 | −0.0973477 | − | 0.995250i | \(-0.531036\pi\) | ||||
−0.0973477 | + | 0.995250i | \(0.531036\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 833372. | 0.0525091 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.03017e7 | 1.27078 | 0.635390 | − | 0.772191i | \(-0.280839\pi\) | ||||
0.635390 | + | 0.772191i | \(0.280839\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.86501e6 | −0.115976 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −567989. | −0.0350902 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.15455e6 | 0.439131 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.07950e7 | 0.658274 | 0.329137 | − | 0.944282i | \(-0.393242\pi\) | ||||
0.329137 | + | 0.944282i | \(0.393242\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.91918e6 | 0.116273 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.21883e6 | 0.0733662 | 0.0366831 | − | 0.999327i | \(-0.488321\pi\) | ||||
0.0366831 | + | 0.999327i | \(0.488321\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.02968e7 | 0.615809 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.63768e6 | −0.156736 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.66830e7 | 0.984986 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.29984e6 | −0.428239 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.45501e7 | 1.43103 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.99091e6 | 0.173232 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.06011e6 | 0.463878 | 0.231939 | − | 0.972730i | \(-0.425493\pi\) | ||||
0.231939 | + | 0.972730i | \(0.425493\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.11298e7 | −1.20838 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.47078e6 | 0.140408 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.93666e6 | −0.109363 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.55975e6 | 0.143641 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.16016e6 | 0.455043 | 0.227522 | − | 0.973773i | \(-0.426938\pi\) | ||||
0.227522 | + | 0.973773i | \(0.426938\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.14415e6 | 0.506730 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.87513e6 | 0.158335 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.26245e6 | 0.123820 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −695844. | −0.0378462 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.49083e7 | 0.805831 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.78986e7 | −1.49869 | −0.749343 | − | 0.662182i | \(-0.769631\pi\) | ||||
−0.749343 | + | 0.662182i | \(0.769631\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.61578e6 | −0.246429 | −0.123215 | − | 0.992380i | \(-0.539320\pi\) | ||||
−0.123215 | + | 0.992380i | \(0.539320\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.68991e7 | −0.896677 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.13497e7 | −1.12590 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.37185e6 | 0.229145 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 727613. | 0.0379045 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.87016e7 | 1.48610 | 0.743050 | − | 0.669236i | \(-0.233378\pi\) | ||||
0.743050 | + | 0.669236i | \(0.233378\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.90189e7 | 1.49342 | 0.746710 | − | 0.665150i | \(-0.231633\pi\) | ||||
0.746710 | + | 0.665150i | \(0.231633\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.77118e6 | −0.192905 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.18186e6 | −0.212621 | −0.106310 | − | 0.994333i | \(-0.533904\pi\) | ||||
−0.106310 | + | 0.994333i | \(0.533904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.54599e6 | 0.229743 | 0.114871 | − | 0.993380i | \(-0.463354\pi\) | ||||
0.114871 | + | 0.993380i | \(0.463354\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.26004e7 | 1.63765 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.53026e6 | −0.0764105 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.02674e7 | −1.00596 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.38384e7 | 1.17615 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 544689. | 0.0267143 | 0.0133571 | − | 0.999911i | \(-0.495748\pi\) | ||||
0.0133571 | + | 0.999911i | \(0.495748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.81324e7 | 0.884028 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.33041e6 | 0.258340 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −855793. | −0.0412313 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.79968e6 | −0.325672 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.11884e7 | −1.48499 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.37013e6 | −0.0648544 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.73893e6 | 0.411231 | 0.205615 | − | 0.978633i | \(-0.434080\pi\) | ||||
0.205615 | + | 0.978633i | \(0.434080\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.16400e6 | 0.0544550 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.09388e6 | −0.0508768 | −0.0254384 | − | 0.999676i | \(-0.508098\pi\) | ||||
−0.0254384 | + | 0.999676i | \(0.508098\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.98806e7 | −0.919276 | −0.459638 | − | 0.888106i | \(-0.652021\pi\) | ||||
−0.459638 | + | 0.888106i | \(0.652021\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.26927e6 | 0.426125 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.53027e7 | 0.699424 | 0.349712 | − | 0.936857i | \(-0.386279\pi\) | ||||
0.349712 | + | 0.936857i | \(0.386279\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.87507e6 | 0.312419 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.50124e7 | −0.678270 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.52732e6 | −0.158451 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.21445e7 | 0.989055 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15287.0 | 0.000678868 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.91732e6 | 0.393744 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.51846e7 | 1.54474 | 0.772368 | − | 0.635176i | \(-0.219072\pi\) | ||||
0.772368 | + | 0.635176i | \(0.219072\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.66066e7 | 1.59804 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.04493e7 | 0.453572 | 0.226786 | − | 0.973945i | \(-0.427178\pi\) | ||||
0.226786 | + | 0.973945i | \(0.427178\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.42290e6 | 0.104577 | 0.0522883 | − | 0.998632i | \(-0.483349\pi\) | ||||
0.0522883 | + | 0.998632i | \(0.483349\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.35926e6 | 0.272928 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.69859e6 | −0.371227 | −0.185614 | − | 0.982623i | \(-0.559427\pi\) | ||||
−0.185614 | + | 0.982623i | \(0.559427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.99392e6 | 0.339239 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.87270e6 | −0.332223 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.87394e7 | −0.786372 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.01822e7 | −0.424896 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.50442e6 | −0.145424 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.75233e7 | 1.54847 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.92410e6 | 0.120000 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.42905e6 | 0.0991327 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.47431e7 | −0.598365 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.66178e7 | −0.670743 | −0.335372 | − | 0.942086i | \(-0.608862\pi\) | ||||
−0.335372 | + | 0.942086i | \(0.608862\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.73463e6 | −0.0696302 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.78722e6 | −0.310876 | −0.155438 | − | 0.987846i | \(-0.549679\pi\) | ||||
−0.155438 | + | 0.987846i | \(0.549679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.18274e6 | 0.166067 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.72139e6 | −0.0679713 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.20307e6 | 0.282875 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.61606e7 | −1.41236 | −0.706181 | − | 0.708031i | \(-0.749584\pi\) | ||||
−0.706181 | + | 0.708031i | \(0.749584\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.64826e7 | −1.41722 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.06966e7 | 1.18600 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.20014e6 | 0.238258 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.25620e6 | 0.162676 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.64147e7 | 1.76448 | 0.882240 | − | 0.470801i | \(-0.156035\pi\) | ||||
0.882240 | + | 0.470801i | \(0.156035\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.13602e6 | 0.118578 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.77392e7 | 1.04325 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.58398e6 | 0.134072 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.63671e7 | −0.981100 | −0.490550 | − | 0.871413i | \(-0.663204\pi\) | ||||
−0.490550 | + | 0.871413i | \(0.663204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.14247e6 | −0.264353 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.40567e6 | −0.125380 | −0.0626900 | − | 0.998033i | \(-0.519968\pi\) | ||||
−0.0626900 | + | 0.998033i | \(0.519968\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.81489e6 | 0.176322 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.28998e6 | 0.265550 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.15081e7 | −1.50403 | −0.752017 | − | 0.659144i | \(-0.770919\pi\) | ||||
−0.752017 | + | 0.659144i | \(0.770919\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.51382e6 | −0.342917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.17004e7 | −0.419516 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.02395e7 | 1.07855 | 0.539277 | − | 0.842128i | \(-0.318697\pi\) | ||||
0.539277 | + | 0.842128i | \(0.318697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.84391e7 | −0.654233 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.37429e7 | −0.485063 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 259298. | 0.00910444 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.80632e6 | 0.272670 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.42371e6 | −0.188465 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.33646e7 | −0.807680 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.09163e6 | 0.209492 | 0.104746 | − | 0.994499i | \(-0.466597\pi\) | ||||
0.104746 | + | 0.994499i | \(0.466597\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.23289e7 | −0.421807 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.12760e7 | 0.724171 | 0.362086 | − | 0.932145i | \(-0.382065\pi\) | ||||
0.362086 | + | 0.932145i | \(0.382065\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.50744e6 | 0.288083 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.58582e7 | 0.534248 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.66948e7 | −0.559559 | −0.279779 | − | 0.960064i | \(-0.590261\pi\) | ||||
−0.279779 | + | 0.960064i | \(0.590261\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.81419e7 | −0.604960 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 900399. | 0.0298719 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.55038e7 | 1.17190 | 0.585951 | − | 0.810347i | \(-0.300721\pi\) | ||||
0.585951 | + | 0.810347i | \(0.300721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.31589e7 | 0.760551 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.04119e7 | −0.340201 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.26176e6 | 0.0410192 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.44851e7 | −0.791988 | −0.395994 | − | 0.918253i | \(-0.629600\pi\) | ||||
−0.395994 | + | 0.918253i | \(0.629600\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.25392e7 | −1.69087 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 242748. | 0.00777316 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.11209e6 | −0.226600 | −0.113300 | − | 0.993561i | \(-0.536142\pi\) | ||||
−0.113300 | + | 0.993561i | \(0.536142\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.43542e7 | 0.455055 |
(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 | 224.6.a.d.1.2 | yes | 2 | |
4.3 | odd | 2 | 224.6.a.c.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 448.6.a.y.1.2 | 2 | |||
8.5 | even | 2 | 448.6.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.6.a.c.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
224.6.a.d.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
448.6.a.s.1.1 | 2 | 8.5 | even | 2 | |||
448.6.a.y.1.2 | 2 | 8.3 | odd | 2 |