Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [495,6,Mod(1,495)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(495, 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("495.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 495 = 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 495.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: | \(79.3899908074\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.307532.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 76x + 168 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.91848\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 495.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.91848 | −1.75336 | −0.876678 | − | 0.481078i | \(-0.840245\pi\) | ||||
−0.876678 | + | 0.481078i | \(0.840245\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 66.3762 | 2.07426 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 92.6461 | 0.714631 | 0.357315 | − | 0.933984i | \(-0.383692\pi\) | ||||
0.357315 | + | 0.933984i | \(0.383692\pi\) | |||||||
\(8\) | −340.959 | −1.88355 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −247.962 | −0.784124 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 800.249 | 1.31331 | 0.656654 | − | 0.754192i | \(-0.271971\pi\) | ||||
0.656654 | + | 0.754192i | \(0.271971\pi\) | |||||||
\(14\) | −918.908 | −1.25300 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1257.76 | 1.22828 | ||||||||
\(17\) | 117.742 | 0.0988122 | 0.0494061 | − | 0.998779i | \(-0.484267\pi\) | ||||
0.0494061 | + | 0.998779i | \(0.484267\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 831.422 | 0.528369 | 0.264185 | − | 0.964472i | \(-0.414897\pi\) | ||||
0.264185 | + | 0.964472i | \(0.414897\pi\) | |||||||
\(20\) | 1659.40 | 0.927635 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1200.14 | 0.528657 | ||||||||
\(23\) | −2952.23 | −1.16367 | −0.581837 | − | 0.813306i | \(-0.697666\pi\) | ||||
−0.581837 | + | 0.813306i | \(0.697666\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −7937.25 | −2.30270 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6149.49 | 1.48233 | ||||||||
\(29\) | −5765.87 | −1.27312 | −0.636560 | − | 0.771227i | \(-0.719643\pi\) | ||||
−0.636560 | + | 0.771227i | \(0.719643\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −61.7803 | −0.0115464 | −0.00577319 | − | 0.999983i | \(-0.501838\pi\) | ||||
−0.00577319 | + | 0.999983i | \(0.501838\pi\) | |||||||
\(32\) | −1564.36 | −0.270061 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1167.83 | −0.173253 | ||||||||
\(35\) | 2316.15 | 0.319593 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10236.6 | −1.22928 | −0.614640 | − | 0.788808i | \(-0.710699\pi\) | ||||
−0.614640 | + | 0.788808i | \(0.710699\pi\) | |||||||
\(38\) | −8246.44 | −0.926419 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8523.98 | −0.842350 | ||||||||
\(41\) | −9599.21 | −0.891818 | −0.445909 | − | 0.895078i | \(-0.647119\pi\) | ||||
−0.445909 | + | 0.895078i | \(0.647119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −17473.2 | −1.44113 | −0.720563 | − | 0.693389i | \(-0.756117\pi\) | ||||
−0.720563 | + | 0.693389i | \(0.756117\pi\) | |||||||
\(44\) | −8031.52 | −0.625412 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 29281.7 | 2.04033 | ||||||||
\(47\) | −18748.3 | −1.23799 | −0.618995 | − | 0.785395i | \(-0.712460\pi\) | ||||
−0.618995 | + | 0.785395i | \(0.712460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8223.71 | −0.489303 | ||||||||
\(50\) | −6199.05 | −0.350671 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 53117.5 | 2.72414 | ||||||||
\(53\) | 9703.45 | 0.474500 | 0.237250 | − | 0.971449i | \(-0.423754\pi\) | ||||
0.237250 | + | 0.971449i | \(0.423754\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | −31588.5 | −1.34604 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 57188.6 | 2.23223 | ||||||||
\(59\) | 24401.4 | 0.912609 | 0.456305 | − | 0.889824i | \(-0.349173\pi\) | ||||
0.456305 | + | 0.889824i | \(0.349173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33910.3 | 1.16683 | 0.583413 | − | 0.812175i | \(-0.301717\pi\) | ||||
0.583413 | + | 0.812175i | \(0.301717\pi\) | |||||||
\(62\) | 612.766 | 0.0202449 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −24732.2 | −0.754768 | ||||||||
\(65\) | 20006.2 | 0.587329 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4989.24 | −0.135784 | −0.0678918 | − | 0.997693i | \(-0.521627\pi\) | ||||
−0.0678918 | + | 0.997693i | \(0.521627\pi\) | |||||||
\(68\) | 7815.29 | 0.204962 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −22972.7 | −0.560360 | ||||||||
\(71\) | 62961.6 | 1.48228 | 0.741140 | − | 0.671351i | \(-0.234286\pi\) | ||||
0.741140 | + | 0.671351i | \(0.234286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −54232.5 | −1.19111 | −0.595556 | − | 0.803314i | \(-0.703068\pi\) | ||||
−0.595556 | + | 0.803314i | \(0.703068\pi\) | |||||||
\(74\) | 101531. | 2.15537 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 55186.6 | 1.09597 | ||||||||
\(77\) | −11210.2 | −0.215469 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −56996.4 | −1.02750 | −0.513748 | − | 0.857941i | \(-0.671743\pi\) | ||||
−0.513748 | + | 0.857941i | \(0.671743\pi\) | |||||||
\(80\) | 31444.0 | 0.549304 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 95209.6 | 1.56367 | ||||||||
\(83\) | −49685.9 | −0.791659 | −0.395830 | − | 0.918324i | \(-0.629543\pi\) | ||||
−0.395830 | + | 0.918324i | \(0.629543\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2943.56 | 0.0441902 | ||||||||
\(86\) | 173308. | 2.52681 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 41256.1 | 0.567912 | ||||||||
\(89\) | 87990.1 | 1.17749 | 0.588747 | − | 0.808317i | \(-0.299621\pi\) | ||||
0.588747 | + | 0.808317i | \(0.299621\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 74139.9 | 0.938531 | ||||||||
\(92\) | −195958. | −2.41376 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 185954. | 2.17064 | ||||||||
\(95\) | 20785.5 | 0.236294 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −44817.9 | −0.483640 | −0.241820 | − | 0.970321i | \(-0.577744\pi\) | ||||
−0.241820 | + | 0.970321i | \(0.577744\pi\) | |||||||
\(98\) | 81566.7 | 0.857921 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 41485.1 | 0.414851 | ||||||||
\(101\) | −82871.7 | −0.808356 | −0.404178 | − | 0.914680i | \(-0.632442\pi\) | ||||
−0.404178 | + | 0.914680i | \(0.632442\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 153697. | 1.42749 | 0.713744 | − | 0.700406i | \(-0.246998\pi\) | ||||
0.713744 | + | 0.700406i | \(0.246998\pi\) | |||||||
\(104\) | −272852. | −2.47368 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −96243.5 | −0.831968 | ||||||||
\(107\) | −41662.3 | −0.351790 | −0.175895 | − | 0.984409i | \(-0.556282\pi\) | ||||
−0.175895 | + | 0.984409i | \(0.556282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 39745.0 | 0.320417 | 0.160209 | − | 0.987083i | \(-0.448783\pi\) | ||||
0.160209 | + | 0.987083i | \(0.448783\pi\) | |||||||
\(110\) | 30003.4 | 0.236422 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 116526. | 0.877768 | ||||||||
\(113\) | 191157. | 1.40829 | 0.704147 | − | 0.710054i | \(-0.251329\pi\) | ||||
0.704147 | + | 0.710054i | \(0.251329\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −73805.8 | −0.520411 | ||||||||
\(116\) | −382716. | −2.64078 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −242025. | −1.60013 | ||||||||
\(119\) | 10908.4 | 0.0706143 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −336338. | −2.04586 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4100.74 | −0.0239501 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −212879. | −1.17118 | −0.585590 | − | 0.810608i | \(-0.699137\pi\) | ||||
−0.585590 | + | 0.810608i | \(0.699137\pi\) | |||||||
\(128\) | 295366. | 1.59344 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −198431. | −1.02980 | ||||||||
\(131\) | 146592. | 0.746333 | 0.373166 | − | 0.927764i | \(-0.378272\pi\) | ||||
0.373166 | + | 0.927764i | \(0.378272\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 77027.9 | 0.377589 | ||||||||
\(134\) | 49485.7 | 0.238077 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −40145.4 | −0.186118 | ||||||||
\(137\) | −335075. | −1.52525 | −0.762623 | − | 0.646843i | \(-0.776089\pi\) | ||||
−0.762623 | + | 0.646843i | \(0.776089\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 30053.6 | 0.131935 | 0.0659674 | − | 0.997822i | \(-0.478987\pi\) | ||||
0.0659674 | + | 0.997822i | \(0.478987\pi\) | |||||||
\(140\) | 153737. | 0.662917 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −624483. | −2.59896 | ||||||||
\(143\) | −96830.1 | −0.395977 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −144147. | −0.569357 | ||||||||
\(146\) | 537904. | 2.08844 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −679466. | −2.54984 | ||||||||
\(149\) | −240256. | −0.886559 | −0.443280 | − | 0.896383i | \(-0.646185\pi\) | ||||
−0.443280 | + | 0.896383i | \(0.646185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 37997.8 | 0.135617 | 0.0678087 | − | 0.997698i | \(-0.478399\pi\) | ||||
0.0678087 | + | 0.997698i | \(0.478399\pi\) | |||||||
\(152\) | −283481. | −0.995211 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 111188. | 0.377794 | ||||||||
\(155\) | −1544.51 | −0.00516369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −260511. | −0.843483 | −0.421742 | − | 0.906716i | \(-0.638581\pi\) | ||||
−0.421742 | + | 0.906716i | \(0.638581\pi\) | |||||||
\(158\) | 565318. | 1.80157 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −39109.0 | −0.120775 | ||||||||
\(161\) | −273513. | −0.831597 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −364741. | −1.07527 | −0.537633 | − | 0.843179i | \(-0.680681\pi\) | ||||
−0.537633 | + | 0.843179i | \(0.680681\pi\) | |||||||
\(164\) | −637159. | −1.84986 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 492809. | 1.38806 | ||||||||
\(167\) | −70995.9 | −0.196989 | −0.0984945 | − | 0.995138i | \(-0.531403\pi\) | ||||
−0.0984945 | + | 0.995138i | \(0.531403\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 269105. | 0.724778 | ||||||||
\(170\) | −29195.6 | −0.0774811 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.15981e6 | −2.98927 | ||||||||
\(173\) | −295710. | −0.751192 | −0.375596 | − | 0.926783i | \(-0.622562\pi\) | ||||
−0.375596 | + | 0.926783i | \(0.622562\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 57903.8 | 0.142926 | ||||||||
\(176\) | −152189. | −0.370341 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −872727. | −2.06457 | ||||||||
\(179\) | 567691. | 1.32428 | 0.662139 | − | 0.749381i | \(-0.269649\pi\) | ||||
0.662139 | + | 0.749381i | \(0.269649\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −361118. | −0.819319 | −0.409660 | − | 0.912239i | \(-0.634352\pi\) | ||||
−0.409660 | + | 0.912239i | \(0.634352\pi\) | |||||||
\(182\) | −735355. | −1.64558 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00659e6 | 2.19184 | ||||||||
\(185\) | −255915. | −0.549751 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14246.8 | −0.0297930 | ||||||||
\(188\) | −1.24444e6 | −2.56791 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −206161. | −0.414307 | ||||||||
\(191\) | −334871. | −0.664193 | −0.332096 | − | 0.943245i | \(-0.607756\pi\) | ||||
−0.332096 | + | 0.943245i | \(0.607756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −286645. | −0.553926 | −0.276963 | − | 0.960881i | \(-0.589328\pi\) | ||||
−0.276963 | + | 0.960881i | \(0.589328\pi\) | |||||||
\(194\) | 444525. | 0.847992 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −545858. | −1.01494 | ||||||||
\(197\) | −402554. | −0.739024 | −0.369512 | − | 0.929226i | \(-0.620475\pi\) | ||||
−0.369512 | + | 0.929226i | \(0.620475\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 506857. | 0.907304 | 0.453652 | − | 0.891179i | \(-0.350121\pi\) | ||||
0.453652 | + | 0.891179i | \(0.350121\pi\) | |||||||
\(200\) | −213100. | −0.376710 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 821961. | 1.41734 | ||||||||
\(203\) | −534185. | −0.909812 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −239980. | −0.398833 | ||||||||
\(206\) | −1.52444e6 | −2.50289 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00652e6 | 1.61311 | ||||||||
\(209\) | −100602. | −0.159309 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 166764. | 0.257867 | 0.128934 | − | 0.991653i | \(-0.458845\pi\) | ||||
0.128934 | + | 0.991653i | \(0.458845\pi\) | |||||||
\(212\) | 644078. | 0.984235 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 413227. | 0.616813 | ||||||||
\(215\) | −436831. | −0.644492 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5723.70 | −0.00825140 | ||||||||
\(218\) | −394209. | −0.561805 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −200788. | −0.279693 | ||||||||
\(221\) | 94223.2 | 0.129771 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 556053. | 0.748780 | 0.374390 | − | 0.927271i | \(-0.377852\pi\) | ||||
0.374390 | + | 0.927271i | \(0.377852\pi\) | |||||||
\(224\) | −144932. | −0.192994 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.89598e6 | −2.46924 | ||||||||
\(227\) | −507849. | −0.654139 | −0.327069 | − | 0.945000i | \(-0.606061\pi\) | ||||
−0.327069 | + | 0.945000i | \(0.606061\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −627193. | −0.790337 | −0.395169 | − | 0.918609i | \(-0.629314\pi\) | ||||
−0.395169 | + | 0.918609i | \(0.629314\pi\) | |||||||
\(230\) | 732042. | 0.912465 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.96593e6 | 2.39799 | ||||||||
\(233\) | −955870. | −1.15348 | −0.576738 | − | 0.816929i | \(-0.695675\pi\) | ||||
−0.576738 | + | 0.816929i | \(0.695675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −468707. | −0.553646 | ||||||||
\(236\) | 1.61967e6 | 1.89298 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −108194. | −0.123812 | ||||||||
\(239\) | 509255. | 0.576687 | 0.288344 | − | 0.957527i | \(-0.406895\pi\) | ||||
0.288344 | + | 0.957527i | \(0.406895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −666125. | −0.738776 | −0.369388 | − | 0.929275i | \(-0.620433\pi\) | ||||
−0.369388 | + | 0.929275i | \(0.620433\pi\) | |||||||
\(242\) | −145216. | −0.159396 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.25083e6 | 2.42030 | ||||||||
\(245\) | −205593. | −0.218823 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 665344. | 0.693911 | ||||||||
\(248\) | 21064.6 | 0.0217482 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −154976. | −0.156825 | ||||||||
\(251\) | −505010. | −0.505960 | −0.252980 | − | 0.967472i | \(-0.581411\pi\) | ||||
−0.252980 | + | 0.967472i | \(0.581411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 357220. | 0.350861 | ||||||||
\(254\) | 2.11144e6 | 2.05349 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.13815e6 | −2.03909 | ||||||||
\(257\) | 2.02669e6 | 1.91405 | 0.957027 | − | 0.290000i | \(-0.0936552\pi\) | ||||
0.957027 | + | 0.290000i | \(0.0936552\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −948379. | −0.878482 | ||||||||
\(260\) | 1.32794e6 | 1.21827 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.45397e6 | −1.30859 | ||||||||
\(263\) | −1.57349e6 | −1.40273 | −0.701366 | − | 0.712801i | \(-0.747426\pi\) | ||||
−0.701366 | + | 0.712801i | \(0.747426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 242586. | 0.212203 | ||||||||
\(266\) | −764000. | −0.662048 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −331167. | −0.281650 | ||||||||
\(269\) | 1.55958e6 | 1.31409 | 0.657046 | − | 0.753850i | \(-0.271806\pi\) | ||||
0.657046 | + | 0.753850i | \(0.271806\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.35274e6 | 1.11890 | 0.559451 | − | 0.828864i | \(-0.311012\pi\) | ||||
0.559451 | + | 0.828864i | \(0.311012\pi\) | |||||||
\(272\) | 148092. | 0.121369 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.32343e6 | 2.67430 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.47205e6 | 1.93579 | 0.967895 | − | 0.251353i | \(-0.0808755\pi\) | ||||
0.967895 | + | 0.251353i | \(0.0808755\pi\) | |||||||
\(278\) | −298086. | −0.231328 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −789714. | −0.601970 | ||||||||
\(281\) | −769611. | −0.581441 | −0.290721 | − | 0.956808i | \(-0.593895\pi\) | ||||
−0.290721 | + | 0.956808i | \(0.593895\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.52887e6 | 1.87698 | 0.938490 | − | 0.345305i | \(-0.112225\pi\) | ||||
0.938490 | + | 0.345305i | \(0.112225\pi\) | |||||||
\(284\) | 4.17915e6 | 3.07463 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 960407. | 0.694289 | ||||||||
\(287\) | −889329. | −0.637320 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.40599e6 | −0.990236 | ||||||||
\(290\) | 1.42972e6 | 0.998285 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.59975e6 | −2.47067 | ||||||||
\(293\) | −2.06542e6 | −1.40553 | −0.702764 | − | 0.711423i | \(-0.748051\pi\) | ||||
−0.702764 | + | 0.711423i | \(0.748051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 610035. | 0.408131 | ||||||||
\(296\) | 3.49026e6 | 2.31541 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.38297e6 | 1.55445 | ||||||||
\(299\) | −2.36252e6 | −1.52826 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.61883e6 | −1.02987 | ||||||||
\(302\) | −376880. | −0.237786 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.04573e6 | 0.648986 | ||||||||
\(305\) | 847756. | 0.521821 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.17085e6 | −1.31457 | −0.657286 | − | 0.753641i | \(-0.728296\pi\) | ||||
−0.657286 | + | 0.753641i | \(0.728296\pi\) | |||||||
\(308\) | −744088. | −0.446939 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15319.2 | 0.00905379 | ||||||||
\(311\) | 198576. | 0.116420 | 0.0582098 | − | 0.998304i | \(-0.481461\pi\) | ||||
0.0582098 | + | 0.998304i | \(0.481461\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −483762. | −0.279107 | −0.139554 | − | 0.990215i | \(-0.544567\pi\) | ||||
−0.139554 | + | 0.990215i | \(0.544567\pi\) | |||||||
\(314\) | 2.58387e6 | 1.47893 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.78321e6 | −2.13129 | ||||||||
\(317\) | 1.68099e6 | 0.939542 | 0.469771 | − | 0.882788i | \(-0.344336\pi\) | ||||
0.469771 | + | 0.882788i | \(0.344336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 697670. | 0.383860 | ||||||||
\(320\) | −618306. | −0.337542 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.71283e6 | 1.45809 | ||||||||
\(323\) | 97893.6 | 0.0522093 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 500155. | 0.262662 | ||||||||
\(326\) | 3.61768e6 | 1.88532 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.27294e6 | 1.67979 | ||||||||
\(329\) | −1.73696e6 | −0.884706 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.18881e6 | −0.596407 | −0.298204 | − | 0.954502i | \(-0.596387\pi\) | ||||
−0.298204 | + | 0.954502i | \(0.596387\pi\) | |||||||
\(332\) | −3.29796e6 | −1.64210 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 704171. | 0.345392 | ||||||||
\(335\) | −124731. | −0.0607243 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.78561e6 | 0.856470 | 0.428235 | − | 0.903667i | \(-0.359135\pi\) | ||||
0.428235 | + | 0.903667i | \(0.359135\pi\) | |||||||
\(338\) | −2.66911e6 | −1.27079 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 195382. | 0.0916617 | ||||||||
\(341\) | 7475.41 | 0.00348136 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.31900e6 | −1.06430 | ||||||||
\(344\) | 5.95766e6 | 2.71444 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.93299e6 | 1.31711 | ||||||||
\(347\) | −2.71689e6 | −1.21129 | −0.605645 | − | 0.795735i | \(-0.707085\pi\) | ||||
−0.605645 | + | 0.795735i | \(0.707085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.87050e6 | −0.822044 | −0.411022 | − | 0.911626i | \(-0.634828\pi\) | ||||
−0.411022 | + | 0.911626i | \(0.634828\pi\) | |||||||
\(350\) | −574317. | −0.250600 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 189288. | 0.0814265 | ||||||||
\(353\) | 4.27952e6 | 1.82793 | 0.913963 | − | 0.405798i | \(-0.133006\pi\) | ||||
0.913963 | + | 0.405798i | \(0.133006\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.57404e6 | 0.662896 | ||||||||
\(356\) | 5.84045e6 | 2.44242 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.63063e6 | −2.32193 | ||||||||
\(359\) | 1.39681e6 | 0.572007 | 0.286003 | − | 0.958229i | \(-0.407673\pi\) | ||||
0.286003 | + | 0.958229i | \(0.407673\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.78484e6 | −0.720826 | ||||||||
\(362\) | 3.58174e6 | 1.43656 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.92112e6 | 1.94675 | ||||||||
\(365\) | −1.35581e6 | −0.532681 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.05674e6 | −1.95977 | −0.979885 | − | 0.199561i | \(-0.936049\pi\) | ||||
−0.979885 | + | 0.199561i | \(0.936049\pi\) | |||||||
\(368\) | −3.71320e6 | −1.42932 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.53828e6 | 0.963909 | ||||||||
\(371\) | 898987. | 0.339093 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.68117e6 | −1.74214 | −0.871069 | − | 0.491161i | \(-0.836573\pi\) | ||||
−0.871069 | + | 0.491161i | \(0.836573\pi\) | |||||||
\(374\) | 141307. | 0.0522377 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.39241e6 | 2.33182 | ||||||||
\(377\) | −4.61413e6 | −1.67200 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.76641e6 | −1.34688 | −0.673442 | − | 0.739240i | \(-0.735185\pi\) | ||||
−0.673442 | + | 0.739240i | \(0.735185\pi\) | |||||||
\(380\) | 1.37966e6 | 0.490134 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.32141e6 | 1.16457 | ||||||||
\(383\) | −4.17276e6 | −1.45354 | −0.726770 | − | 0.686881i | \(-0.758979\pi\) | ||||
−0.726770 | + | 0.686881i | \(0.758979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −280254. | −0.0963608 | ||||||||
\(386\) | 2.84308e6 | 0.971228 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.97484e6 | −1.00319 | ||||||||
\(389\) | 3.73222e6 | 1.25053 | 0.625265 | − | 0.780413i | \(-0.284991\pi\) | ||||
0.625265 | + | 0.780413i | \(0.284991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −347603. | −0.114985 | ||||||||
\(392\) | 2.80395e6 | 0.921627 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.99272e6 | 1.29577 | ||||||||
\(395\) | −1.42491e6 | −0.459510 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.71418e6 | 1.81961 | 0.909804 | − | 0.415038i | \(-0.136232\pi\) | ||||
0.909804 | + | 0.415038i | \(0.136232\pi\) | |||||||
\(398\) | −5.02725e6 | −1.59083 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 786100. | 0.245656 | ||||||||
\(401\) | −3.60785e6 | −1.12044 | −0.560219 | − | 0.828345i | \(-0.689283\pi\) | ||||
−0.560219 | + | 0.828345i | \(0.689283\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −49439.6 | −0.0151639 | ||||||||
\(404\) | −5.50070e6 | −1.67674 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.29830e6 | 1.59522 | ||||||||
\(407\) | 1.23863e6 | 0.370642 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.59452e6 | −1.35810 | −0.679050 | − | 0.734092i | \(-0.737608\pi\) | ||||
−0.679050 | + | 0.734092i | \(0.737608\pi\) | |||||||
\(410\) | 2.38024e6 | 0.699296 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.02018e7 | 2.96098 | ||||||||
\(413\) | 2.26069e6 | 0.652179 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.24215e6 | −0.354041 | ||||||||
\(416\) | −1.25188e6 | −0.354673 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 997819. | 0.279326 | ||||||||
\(419\) | −1.92383e6 | −0.535343 | −0.267671 | − | 0.963510i | \(-0.586254\pi\) | ||||
−0.267671 | + | 0.963510i | \(0.586254\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.28936e6 | −1.17947 | −0.589736 | − | 0.807596i | \(-0.700768\pi\) | ||||
−0.589736 | + | 0.807596i | \(0.700768\pi\) | |||||||
\(422\) | −1.65404e6 | −0.452133 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.30848e6 | −0.893746 | ||||||||
\(425\) | 73589.0 | 0.0197624 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.14165e6 | 0.833851 | ||||||||
\(428\) | −2.76538e6 | −0.729703 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.33270e6 | 1.13002 | ||||||||
\(431\) | −477444. | −0.123802 | −0.0619012 | − | 0.998082i | \(-0.519716\pi\) | ||||
−0.0619012 | + | 0.998082i | \(0.519716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.24919e6 | −1.60178 | −0.800892 | − | 0.598808i | \(-0.795641\pi\) | ||||
−0.800892 | + | 0.598808i | \(0.795641\pi\) | |||||||
\(434\) | 56770.4 | 0.0144676 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.63812e6 | 0.664627 | ||||||||
\(437\) | −2.45455e6 | −0.614849 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.45632e6 | 1.35126 | 0.675629 | − | 0.737241i | \(-0.263872\pi\) | ||||
0.675629 | + | 0.737241i | \(0.263872\pi\) | |||||||
\(440\) | 1.03140e6 | 0.253978 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −934551. | −0.227534 | ||||||||
\(443\) | 3.75783e6 | 0.909762 | 0.454881 | − | 0.890552i | \(-0.349682\pi\) | ||||
0.454881 | + | 0.890552i | \(0.349682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.19975e6 | 0.526591 | ||||||||
\(446\) | −5.51520e6 | −1.31288 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.29134e6 | −0.539380 | ||||||||
\(449\) | 7.17310e6 | 1.67916 | 0.839578 | − | 0.543239i | \(-0.182802\pi\) | ||||
0.839578 | + | 0.543239i | \(0.182802\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.16150e6 | 0.268893 | ||||||||
\(452\) | 1.26883e7 | 2.92116 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.03709e6 | 1.14694 | ||||||||
\(455\) | 1.85350e6 | 0.419724 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.21240e6 | −0.719513 | −0.359757 | − | 0.933046i | \(-0.617140\pi\) | ||||
−0.359757 | + | 0.933046i | \(0.617140\pi\) | |||||||
\(458\) | 6.22080e6 | 1.38574 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.89895e6 | −1.07946 | ||||||||
\(461\) | 5.17808e6 | 1.13479 | 0.567396 | − | 0.823445i | \(-0.307951\pi\) | ||||
0.567396 | + | 0.823445i | \(0.307951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.95142e6 | 0.639851 | 0.319926 | − | 0.947443i | \(-0.396342\pi\) | ||||
0.319926 | + | 0.947443i | \(0.396342\pi\) | |||||||
\(464\) | −7.25208e6 | −1.56375 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.48077e6 | 2.02245 | ||||||||
\(467\) | −7.26608e6 | −1.54173 | −0.770865 | − | 0.636999i | \(-0.780175\pi\) | ||||
−0.770865 | + | 0.636999i | \(0.780175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −462234. | −0.0970352 | ||||||||
\(470\) | 4.64886e6 | 0.970738 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.31989e6 | −1.71895 | ||||||||
\(473\) | 2.11426e6 | 0.434516 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 519639. | 0.105674 | ||||||||
\(476\) | 724056. | 0.146472 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.05103e6 | −1.01114 | ||||||||
\(479\) | 4.09584e6 | 0.815651 | 0.407826 | − | 0.913060i | \(-0.366287\pi\) | ||||
0.407826 | + | 0.913060i | \(0.366287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.19181e6 | −1.61442 | ||||||||
\(482\) | 6.60694e6 | 1.29534 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 971814. | 0.188569 | ||||||||
\(485\) | −1.12045e6 | −0.216290 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 218477. | 0.0417429 | 0.0208715 | − | 0.999782i | \(-0.493356\pi\) | ||||
0.0208715 | + | 0.999782i | \(0.493356\pi\) | |||||||
\(488\) | −1.15620e7 | −2.19778 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.03917e6 | 0.383674 | ||||||||
\(491\) | 3.49848e6 | 0.654901 | 0.327451 | − | 0.944868i | \(-0.393810\pi\) | ||||
0.327451 | + | 0.944868i | \(0.393810\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −678887. | −0.125800 | ||||||||
\(494\) | −6.59920e6 | −1.21667 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −77704.7 | −0.0141822 | ||||||||
\(497\) | 5.83315e6 | 1.05928 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.62715e6 | −0.652100 | −0.326050 | − | 0.945353i | \(-0.605718\pi\) | ||||
−0.326050 | + | 0.945353i | \(0.605718\pi\) | |||||||
\(500\) | 1.03713e6 | 0.185527 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.00893e6 | 0.887127 | ||||||||
\(503\) | −6.00845e6 | −1.05887 | −0.529435 | − | 0.848351i | \(-0.677596\pi\) | ||||
−0.529435 | + | 0.848351i | \(0.677596\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.07179e6 | −0.361508 | ||||||||
\(506\) | −3.54308e6 | −0.615184 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.41301e7 | −2.42933 | ||||||||
\(509\) | −4.28786e6 | −0.733578 | −0.366789 | − | 0.930304i | \(-0.619543\pi\) | ||||
−0.366789 | + | 0.930304i | \(0.619543\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.02443e6 | −0.851205 | ||||||||
\(512\) | 1.17554e7 | 1.98182 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.01017e7 | −3.35602 | ||||||||
\(515\) | 3.84243e6 | 0.638392 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.26854e6 | 0.373268 | ||||||||
\(518\) | 9.40648e6 | 1.54029 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.82131e6 | −1.10627 | ||||||||
\(521\) | −1.06243e7 | −1.71477 | −0.857386 | − | 0.514673i | \(-0.827913\pi\) | ||||
−0.857386 | + | 0.514673i | \(0.827913\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 123402. | 0.0197273 | 0.00986367 | − | 0.999951i | \(-0.496860\pi\) | ||||
0.00986367 | + | 0.999951i | \(0.496860\pi\) | |||||||
\(524\) | 9.73023e6 | 1.54809 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.56066e7 | 2.45949 | ||||||||
\(527\) | −7274.16 | −0.00114092 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.27934e6 | 0.354136 | ||||||||
\(530\) | −2.40609e6 | −0.372067 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.11282e6 | 0.783216 | ||||||||
\(533\) | −7.68176e6 | −1.17123 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.04156e6 | −0.157325 | ||||||||
\(536\) | 1.70113e6 | 0.255756 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.54686e7 | −2.30407 | ||||||||
\(539\) | 995069. | 0.147530 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.60908e6 | −0.823946 | −0.411973 | − | 0.911196i | \(-0.635160\pi\) | ||||
−0.411973 | + | 0.911196i | \(0.635160\pi\) | |||||||
\(542\) | −1.34171e7 | −1.96183 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −184192. | −0.0266853 | ||||||||
\(545\) | 993624. | 0.143295 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.72729e6 | 0.389729 | 0.194864 | − | 0.980830i | \(-0.437573\pi\) | ||||
0.194864 | + | 0.980830i | \(0.437573\pi\) | |||||||
\(548\) | −2.22410e7 | −3.16375 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 750085. | 0.105731 | ||||||||
\(551\) | −4.79387e6 | −0.672678 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.28050e6 | −0.734280 | ||||||||
\(554\) | −2.45190e7 | −3.39413 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.99484e6 | 0.273666 | ||||||||
\(557\) | −3.50042e6 | −0.478059 | −0.239030 | − | 0.971012i | \(-0.576829\pi\) | ||||
−0.239030 | + | 0.971012i | \(0.576829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.39829e7 | −1.89264 | ||||||||
\(560\) | 2.91316e6 | 0.392550 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.63337e6 | 1.01947 | ||||||||
\(563\) | −1.03320e7 | −1.37377 | −0.686886 | − | 0.726766i | \(-0.741023\pi\) | ||||
−0.686886 | + | 0.726766i | \(0.741023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.77892e6 | 0.629809 | ||||||||
\(566\) | −2.50825e7 | −3.29101 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.14674e7 | −2.79195 | ||||||||
\(569\) | 1.31943e7 | 1.70846 | 0.854229 | − | 0.519897i | \(-0.174030\pi\) | ||||
0.854229 | + | 0.519897i | \(0.174030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.98575e6 | −0.768295 | −0.384148 | − | 0.923272i | \(-0.625505\pi\) | ||||
−0.384148 | + | 0.923272i | \(0.625505\pi\) | |||||||
\(572\) | −6.42721e6 | −0.821358 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.82079e6 | 1.11745 | ||||||||
\(575\) | −1.84515e6 | −0.232735 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.74177e6 | 0.968056 | 0.484028 | − | 0.875052i | \(-0.339173\pi\) | ||||
0.484028 | + | 0.875052i | \(0.339173\pi\) | |||||||
\(578\) | 1.39453e7 | 1.73624 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9.56791e6 | −1.18099 | ||||||||
\(581\) | −4.60321e6 | −0.565744 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.17412e6 | −0.143067 | ||||||||
\(584\) | 1.84911e7 | 2.24352 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.04858e7 | 2.46439 | ||||||||
\(587\) | −1.19577e7 | −1.43236 | −0.716181 | − | 0.697915i | \(-0.754111\pi\) | ||||
−0.716181 | + | 0.697915i | \(0.754111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51365.5 | −0.00610075 | ||||||||
\(590\) | −6.05062e6 | −0.715599 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.28752e7 | −1.50990 | ||||||||
\(593\) | 1.08502e7 | 1.26707 | 0.633536 | − | 0.773713i | \(-0.281603\pi\) | ||||
0.633536 | + | 0.773713i | \(0.281603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 272709. | 0.0315797 | ||||||||
\(596\) | −1.59472e7 | −1.83895 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.34326e7 | 2.67959 | ||||||||
\(599\) | 1.23306e7 | 1.40416 | 0.702082 | − | 0.712096i | \(-0.252254\pi\) | ||||
0.702082 | + | 0.712096i | \(0.252254\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.17382e7 | 1.32561 | 0.662807 | − | 0.748790i | \(-0.269365\pi\) | ||||
0.662807 | + | 0.748790i | \(0.269365\pi\) | |||||||
\(602\) | 1.60563e7 | 1.80574 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.52215e6 | 0.281305 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.20559e6 | 1.01410 | 0.507049 | − | 0.861917i | \(-0.330736\pi\) | ||||
0.507049 | + | 0.861917i | \(0.330736\pi\) | |||||||
\(608\) | −1.30064e6 | −0.142692 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.40845e6 | −0.914938 | ||||||||
\(611\) | −1.50033e7 | −1.62586 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.83164e6 | 0.626815 | 0.313408 | − | 0.949619i | \(-0.398529\pi\) | ||||
0.313408 | + | 0.949619i | \(0.398529\pi\) | |||||||
\(614\) | 2.15316e7 | 2.30491 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.82221e6 | 0.405848 | ||||||||
\(617\) | 9.28462e6 | 0.981863 | 0.490932 | − | 0.871198i | \(-0.336656\pi\) | ||||
0.490932 | + | 0.871198i | \(0.336656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.47650e6 | 0.259784 | 0.129892 | − | 0.991528i | \(-0.458537\pi\) | ||||
0.129892 | + | 0.991528i | \(0.458537\pi\) | |||||||
\(620\) | −102518. | −0.0107108 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.96957e6 | −0.204125 | ||||||||
\(623\) | 8.15193e6 | 0.841474 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 4.79819e6 | 0.489374 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.72917e7 | −1.74960 | ||||||||
\(629\) | −1.20528e6 | −0.121468 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.58315e6 | 0.858170 | 0.429085 | − | 0.903264i | \(-0.358836\pi\) | ||||
0.429085 | + | 0.903264i | \(0.358836\pi\) | |||||||
\(632\) | 1.94335e7 | 1.93534 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.66728e7 | −1.64735 | ||||||||
\(635\) | −5.32197e6 | −0.523767 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.58101e6 | −0.642605 | ||||||||
\(638\) | −6.91982e6 | −0.673044 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.38414e6 | 0.712607 | ||||||||
\(641\) | −4.59033e6 | −0.441264 | −0.220632 | − | 0.975357i | \(-0.570812\pi\) | ||||
−0.220632 | + | 0.975357i | \(0.570812\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.70391e6 | 0.925592 | 0.462796 | − | 0.886465i | \(-0.346846\pi\) | ||||
0.462796 | + | 0.886465i | \(0.346846\pi\) | |||||||
\(644\) | −1.81547e7 | −1.72494 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −970955. | −0.0915415 | ||||||||
\(647\) | 9.01887e6 | 0.847015 | 0.423508 | − | 0.905892i | \(-0.360799\pi\) | ||||
0.423508 | + | 0.905892i | \(0.360799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.95257e6 | −0.275162 | ||||||||
\(650\) | −4.96078e6 | −0.460539 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.42101e7 | −2.23038 | ||||||||
\(653\) | −1.94337e6 | −0.178349 | −0.0891747 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891747 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.66481e6 | 0.333770 | ||||||||
\(656\) | −1.20735e7 | −1.09540 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.72279e7 | 1.55120 | ||||||||
\(659\) | 6.36990e6 | 0.571372 | 0.285686 | − | 0.958323i | \(-0.407779\pi\) | ||||
0.285686 | + | 0.958323i | \(0.407779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.88417e6 | −0.701863 | −0.350931 | − | 0.936401i | \(-0.614135\pi\) | ||||
−0.350931 | + | 0.936401i | \(0.614135\pi\) | |||||||
\(662\) | 1.17912e7 | 1.04571 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.69409e7 | 1.49113 | ||||||||
\(665\) | 1.92570e6 | 0.168863 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.70222e7 | 1.48150 | ||||||||
\(668\) | −4.71244e6 | −0.408606 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.23714e6 | 0.106471 | ||||||||
\(671\) | −4.10314e6 | −0.351812 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.51895e6 | −0.384592 | −0.192296 | − | 0.981337i | \(-0.561593\pi\) | ||||
−0.192296 | + | 0.981337i | \(0.561593\pi\) | |||||||
\(674\) | −1.77106e7 | −1.50170 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.78622e7 | 1.50337 | ||||||||
\(677\) | −1.17659e7 | −0.986624 | −0.493312 | − | 0.869852i | \(-0.664214\pi\) | ||||
−0.493312 | + | 0.869852i | \(0.664214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.15220e6 | −0.345624 | ||||||||
\(680\) | −1.00363e6 | −0.0832345 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −74144.7 | −0.00610407 | ||||||||
\(683\) | 1.27636e7 | 1.04694 | 0.523470 | − | 0.852044i | \(-0.324637\pi\) | ||||
0.523470 | + | 0.852044i | \(0.324637\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.37686e6 | −0.682111 | ||||||||
\(686\) | 2.30009e7 | 1.86610 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.19771e7 | −1.77011 | ||||||||
\(689\) | 7.76518e6 | 0.623165 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.94008e7 | 1.54570 | 0.772849 | − | 0.634590i | \(-0.218831\pi\) | ||||
0.772849 | + | 0.634590i | \(0.218831\pi\) | |||||||
\(692\) | −1.96281e7 | −1.55816 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.69474e7 | 2.12382 | ||||||||
\(695\) | 751339. | 0.0590030 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.13023e6 | −0.0881225 | ||||||||
\(698\) | 1.85525e7 | 1.44133 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.84343e6 | 0.296465 | ||||||||
\(701\) | −1.81026e7 | −1.39138 | −0.695690 | − | 0.718342i | \(-0.744901\pi\) | ||||
−0.695690 | + | 0.718342i | \(0.744901\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.51092e6 | −0.649514 | ||||||||
\(704\) | 2.99260e6 | 0.227571 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.24463e7 | −3.20500 | ||||||||
\(707\) | −7.67773e6 | −0.577676 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.55411e7 | 1.16109 | 0.580547 | − | 0.814227i | \(-0.302839\pi\) | ||||
0.580547 | + | 0.814227i | \(0.302839\pi\) | |||||||
\(710\) | −1.56121e7 | −1.16229 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00010e7 | −2.21787 | ||||||||
\(713\) | 182390. | 0.0134362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.42075e6 | −0.177086 | ||||||||
\(716\) | 3.76812e7 | 2.74689 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.38542e7 | −1.00293 | ||||||||
\(719\) | −8.88792e6 | −0.641177 | −0.320589 | − | 0.947219i | \(-0.603881\pi\) | ||||
−0.320589 | + | 0.947219i | \(0.603881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.42394e7 | 1.02013 | ||||||||
\(722\) | 1.77029e7 | 1.26386 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.39697e7 | −1.69948 | ||||||||
\(725\) | −3.60367e6 | −0.254624 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.73697e6 | −0.402575 | −0.201287 | − | 0.979532i | \(-0.564513\pi\) | ||||
−0.201287 | + | 0.979532i | \(0.564513\pi\) | |||||||
\(728\) | −2.52787e7 | −1.76777 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.34476e7 | 0.933980 | ||||||||
\(731\) | −2.05734e6 | −0.142401 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.77002e6 | 0.121680 | 0.0608399 | − | 0.998148i | \(-0.480622\pi\) | ||||
0.0608399 | + | 0.998148i | \(0.480622\pi\) | |||||||
\(734\) | 5.01551e7 | 3.43618 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.61836e6 | 0.314263 | ||||||||
\(737\) | 603698. | 0.0409403 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.53957e7 | 1.03702 | 0.518512 | − | 0.855070i | \(-0.326486\pi\) | ||||
0.518512 | + | 0.855070i | \(0.326486\pi\) | |||||||
\(740\) | −1.69866e7 | −1.14032 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.91658e6 | −0.594550 | ||||||||
\(743\) | −1.65861e7 | −1.10223 | −0.551115 | − | 0.834429i | \(-0.685798\pi\) | ||||
−0.551115 | + | 0.834429i | \(0.685798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00639e6 | −0.396481 | ||||||||
\(746\) | 4.64301e7 | 3.05459 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −945650. | −0.0617983 | ||||||||
\(749\) | −3.85985e6 | −0.251400 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.40157e6 | 0.608276 | 0.304138 | − | 0.952628i | \(-0.401632\pi\) | ||||
0.304138 | + | 0.952628i | \(0.401632\pi\) | |||||||
\(752\) | −2.35808e7 | −1.52060 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.57651e7 | 2.93161 | ||||||||
\(755\) | 949944. | 0.0606500 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.22686e7 | 0.778134 | 0.389067 | − | 0.921209i | \(-0.372797\pi\) | ||||
0.389067 | + | 0.921209i | \(0.372797\pi\) | |||||||
\(758\) | 3.73571e7 | 2.36157 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.08703e6 | −0.445072 | ||||||||
\(761\) | 2.14104e7 | 1.34018 | 0.670090 | − | 0.742280i | \(-0.266256\pi\) | ||||
0.670090 | + | 0.742280i | \(0.266256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.68221e6 | 0.228980 | ||||||||
\(764\) | −2.22275e7 | −1.37771 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.13875e7 | 2.54857 | ||||||||
\(767\) | 1.95272e7 | 1.19854 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.34064e6 | 0.508609 | 0.254304 | − | 0.967124i | \(-0.418154\pi\) | ||||
0.254304 | + | 0.967124i | \(0.418154\pi\) | |||||||
\(770\) | 2.77970e6 | 0.168955 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.90264e7 | −1.14898 | ||||||||
\(773\) | −3.00417e7 | −1.80832 | −0.904162 | − | 0.427191i | \(-0.859503\pi\) | ||||
−0.904162 | + | 0.427191i | \(0.859503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38612.7 | −0.00230927 | ||||||||
\(776\) | 1.52811e7 | 0.910960 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.70180e7 | −2.19262 | ||||||||
\(779\) | −7.98099e6 | −0.471209 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.61836e6 | −0.446924 | ||||||||
\(782\) | 3.44769e6 | 0.201610 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.03434e7 | −0.601001 | ||||||||
\(785\) | −6.51277e6 | −0.377217 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.55411e7 | −0.894427 | −0.447213 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447213 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(788\) | −2.67200e7 | −1.53292 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.41329e7 | 0.805684 | ||||||||
\(791\) | 1.77099e7 | 1.00641 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.71366e7 | 1.53240 | ||||||||
\(794\) | −5.66760e7 | −3.19042 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.36432e7 | 1.88198 | ||||||||
\(797\) | 2.13571e7 | 1.19096 | 0.595478 | − | 0.803371i | \(-0.296963\pi\) | ||||
0.595478 | + | 0.803371i | \(0.296963\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.20747e6 | −0.122328 | ||||||||
\(800\) | −977726. | −0.0540122 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.57844e7 | 1.96453 | ||||||||
\(803\) | 6.56213e6 | 0.359134 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.83782e6 | −0.371902 | ||||||||
\(806\) | 490365. | 0.0265878 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.82559e7 | 1.52258 | ||||||||
\(809\) | −9.58699e6 | −0.515004 | −0.257502 | − | 0.966278i | \(-0.582899\pi\) | ||||
−0.257502 | + | 0.966278i | \(0.582899\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.27762e6 | 0.121599 | 0.0607995 | − | 0.998150i | \(-0.480635\pi\) | ||||
0.0607995 | + | 0.998150i | \(0.480635\pi\) | |||||||
\(812\) | −3.54572e7 | −1.88718 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.22853e7 | −0.649867 | ||||||||
\(815\) | −9.11853e6 | −0.480874 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.45276e7 | −0.761447 | ||||||||
\(818\) | 4.55706e7 | 2.38123 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.59290e7 | −0.827282 | ||||||||
\(821\) | −2.31851e7 | −1.20047 | −0.600234 | − | 0.799824i | \(-0.704926\pi\) | ||||
−0.600234 | + | 0.799824i | \(0.704926\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.30629e7 | 1.70153 | 0.850767 | − | 0.525542i | \(-0.176138\pi\) | ||||
0.850767 | + | 0.525542i | \(0.176138\pi\) | |||||||
\(824\) | −5.24045e7 | −2.68875 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.24226e7 | −1.14350 | ||||||||
\(827\) | −2.84571e7 | −1.44686 | −0.723431 | − | 0.690396i | \(-0.757436\pi\) | ||||
−0.723431 | + | 0.690396i | \(0.757436\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.34334e7 | −1.68964 | −0.844821 | − | 0.535050i | \(-0.820293\pi\) | ||||
−0.844821 | + | 0.535050i | \(0.820293\pi\) | |||||||
\(830\) | 1.23202e7 | 0.620759 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.97919e7 | −0.991243 | ||||||||
\(833\) | −968279. | −0.0483491 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.77490e6 | −0.0880962 | ||||||||
\(836\) | −6.67758e6 | −0.330448 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.90815e7 | 0.938646 | ||||||||
\(839\) | 1.79019e7 | 0.877999 | 0.438999 | − | 0.898487i | \(-0.355333\pi\) | ||||
0.438999 | + | 0.898487i | \(0.355333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.27341e7 | 0.620837 | ||||||||
\(842\) | 4.25440e7 | 2.06803 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.10691e7 | 0.534882 | ||||||||
\(845\) | 6.72762e6 | 0.324130 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.35643e6 | 0.0649665 | ||||||||
\(848\) | 1.22046e7 | 0.582820 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −729891. | −0.0346506 | ||||||||
\(851\) | 3.02208e7 | 1.43048 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.79631e7 | −1.31587 | −0.657934 | − | 0.753076i | \(-0.728569\pi\) | ||||
−0.657934 | + | 0.753076i | \(0.728569\pi\) | |||||||
\(854\) | −3.11604e7 | −1.46204 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.42052e7 | 0.662615 | ||||||||
\(857\) | −9.24668e6 | −0.430065 | −0.215032 | − | 0.976607i | \(-0.568986\pi\) | ||||
−0.215032 | + | 0.976607i | \(0.568986\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.46860e7 | 0.679081 | 0.339540 | − | 0.940591i | \(-0.389728\pi\) | ||||
0.339540 | + | 0.940591i | \(0.389728\pi\) | |||||||
\(860\) | −2.89952e7 | −1.33684 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.73551e6 | 0.217070 | ||||||||
\(863\) | −1.14915e7 | −0.525231 | −0.262615 | − | 0.964901i | \(-0.584585\pi\) | ||||
−0.262615 | + | 0.964901i | \(0.584585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.39275e6 | −0.335943 | ||||||||
\(866\) | 6.19825e7 | 2.80850 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −379917. | −0.0171155 | ||||||||
\(869\) | 6.89657e6 | 0.309802 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.99263e6 | −0.178326 | ||||||||
\(872\) | −1.35514e7 | −0.603523 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.43454e7 | 1.07805 | ||||||||
\(875\) | 1.44759e6 | 0.0639185 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.92652e7 | 1.28485 | 0.642426 | − | 0.766348i | \(-0.277928\pi\) | ||||
0.642426 | + | 0.766348i | \(0.277928\pi\) | |||||||
\(878\) | −5.41184e7 | −2.36924 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.80472e6 | −0.165621 | ||||||||
\(881\) | 6.92950e6 | 0.300789 | 0.150395 | − | 0.988626i | \(-0.451946\pi\) | ||||
0.150395 | + | 0.988626i | \(0.451946\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.40887e7 | 1.90294 | 0.951470 | − | 0.307740i | \(-0.0995727\pi\) | ||||
0.951470 | + | 0.307740i | \(0.0995727\pi\) | |||||||
\(884\) | 6.25418e6 | 0.269178 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.72719e7 | −1.59514 | ||||||||
\(887\) | −4.26047e7 | −1.81823 | −0.909115 | − | 0.416545i | \(-0.863241\pi\) | ||||
−0.909115 | + | 0.416545i | \(0.863241\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.97224e7 | −0.836961 | ||||||||
\(890\) | −2.18182e7 | −0.923302 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.69087e7 | 1.55316 | ||||||||
\(893\) | −1.55877e7 | −0.654115 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.41923e7 | 0.592236 | ||||||||
\(896\) | 2.73645e7 | 1.13872 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.11462e7 | −2.94416 | ||||||||
\(899\) | 356217. | 0.0146999 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14251e6 | 0.0468864 | ||||||||
\(902\) | −1.15204e7 | −0.471465 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.51767e7 | −2.65260 | ||||||||
\(905\) | −9.02796e6 | −0.366411 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.03750e7 | 0.822392 | 0.411196 | − | 0.911547i | \(-0.365111\pi\) | ||||
0.411196 | + | 0.911547i | \(0.365111\pi\) | |||||||
\(908\) | −3.37091e7 | −1.35685 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.83839e7 | −0.735925 | ||||||||
\(911\) | −1.25015e7 | −0.499077 | −0.249538 | − | 0.968365i | \(-0.580279\pi\) | ||||
−0.249538 | + | 0.968365i | \(0.580279\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.01200e6 | 0.238694 | ||||||||
\(914\) | 3.18621e7 | 1.26156 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.16307e7 | −1.63936 | ||||||||
\(917\) | 1.35812e7 | 0.533353 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.12364e7 | 0.829455 | 0.414728 | − | 0.909946i | \(-0.363877\pi\) | ||||
0.414728 | + | 0.909946i | \(0.363877\pi\) | |||||||
\(920\) | 2.51648e7 | 0.980221 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.13586e7 | −1.98969 | ||||||||
\(923\) | 5.03850e7 | 1.94669 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.39787e6 | −0.245856 | ||||||||
\(926\) | −2.92736e7 | −1.12189 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.01990e6 | 0.343821 | ||||||||
\(929\) | −2.38747e7 | −0.907608 | −0.453804 | − | 0.891102i | \(-0.649933\pi\) | ||||
−0.453804 | + | 0.891102i | \(0.649933\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.83737e6 | −0.258532 | ||||||||
\(932\) | −6.34470e7 | −2.39261 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.20685e7 | 2.70320 | ||||||||
\(935\) | −356171. | −0.0133238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.33814e7 | −0.497914 | −0.248957 | − | 0.968515i | \(-0.580088\pi\) | ||||
−0.248957 | + | 0.968515i | \(0.580088\pi\) | |||||||
\(938\) | 4.58465e6 | 0.170137 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.11110e7 | −1.14840 | ||||||||
\(941\) | −5.91644e6 | −0.217814 | −0.108907 | − | 0.994052i | \(-0.534735\pi\) | ||||
−0.108907 | + | 0.994052i | \(0.534735\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.83391e7 | 1.03778 | ||||||||
\(944\) | 3.06911e7 | 1.12094 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.09703e7 | −0.761861 | ||||||||
\(947\) | 4.78035e7 | 1.73215 | 0.866074 | − | 0.499916i | \(-0.166636\pi\) | ||||
0.866074 | + | 0.499916i | \(0.166636\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.33995e7 | −1.56430 | ||||||||
\(950\) | −5.15402e6 | −0.185284 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.71931e6 | −0.133006 | ||||||||
\(953\) | 3.75680e7 | 1.33994 | 0.669971 | − | 0.742387i | \(-0.266306\pi\) | ||||
0.669971 | + | 0.742387i | \(0.266306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.37177e6 | −0.297036 | ||||||||
\(956\) | 3.38024e7 | 1.19620 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.06245e7 | −1.43013 | ||||||||
\(959\) | −3.10433e7 | −1.08999 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86253e7 | −0.999867 | ||||||||
\(962\) | 8.12503e7 | 2.83066 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.42148e7 | −1.53241 | ||||||||
\(965\) | −7.16613e6 | −0.247723 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.07684e7 | −0.714228 | −0.357114 | − | 0.934061i | \(-0.616239\pi\) | ||||
−0.357114 | + | 0.934061i | \(0.616239\pi\) | |||||||
\(968\) | −4.99199e6 | −0.171232 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.11131e7 | 0.379234 | ||||||||
\(971\) | −1.39451e7 | −0.474650 | −0.237325 | − | 0.971430i | \(-0.576271\pi\) | ||||
−0.237325 | + | 0.971430i | \(0.576271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.78434e6 | 0.0942846 | ||||||||
\(974\) | −2.16696e6 | −0.0731902 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.26510e7 | 1.43319 | ||||||||
\(977\) | −2.07797e7 | −0.696471 | −0.348236 | − | 0.937407i | \(-0.613219\pi\) | ||||
−0.348236 | + | 0.937407i | \(0.613219\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.06468e7 | −0.355028 | ||||||||
\(980\) | −1.36465e7 | −0.453894 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.46996e7 | −1.14828 | ||||||||
\(983\) | −1.16598e7 | −0.384864 | −0.192432 | − | 0.981310i | \(-0.561637\pi\) | ||||
−0.192432 | + | 0.981310i | \(0.561637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.00638e7 | −0.330501 | ||||||||
\(986\) | 6.73353e6 | 0.220572 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.41630e7 | 1.43935 | ||||||||
\(989\) | 5.15851e7 | 1.67700 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.35287e7 | −0.761050 | −0.380525 | − | 0.924771i | \(-0.624257\pi\) | ||||
−0.380525 | + | 0.924771i | \(0.624257\pi\) | |||||||
\(992\) | 96646.7 | 0.00311823 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.78559e7 | −1.85730 | ||||||||
\(995\) | 1.26714e7 | 0.405759 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.85989e7 | −1.54842 | −0.774210 | − | 0.632929i | \(-0.781853\pi\) | ||||
−0.774210 | + | 0.632929i | \(0.781853\pi\) | |||||||
\(998\) | 3.59758e7 | 1.14336 | ||||||||
\(999\) | 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 | 495.6.a.a.1.1 | 3 | ||
3.2 | odd | 2 | 165.6.a.e.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 825.6.a.f.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.e.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
495.6.a.a.1.1 | 3 | 1.1 | even | 1 | trivial | ||
825.6.a.f.1.1 | 3 | 15.14 | odd | 2 |