Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + \cdots + 49172480 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-3.21799\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.21799 | 0.922419 | 0.461209 | − | 0.887291i | \(-0.347416\pi\) | ||||
0.461209 | + | 0.887291i | \(0.347416\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −4.77260 | −0.149144 | ||||||||
\(5\) | −21.6600 | −0.387466 | −0.193733 | − | 0.981054i | \(-0.562060\pi\) | ||||
−0.193733 | + | 0.981054i | \(0.562060\pi\) | |||||||
\(6\) | 46.9619 | 0.532559 | ||||||||
\(7\) | 150.168 | 1.15833 | 0.579164 | − | 0.815211i | \(-0.303379\pi\) | ||||
0.579164 | + | 0.815211i | \(0.303379\pi\) | |||||||
\(8\) | −191.879 | −1.05999 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −113.022 | −0.357406 | ||||||||
\(11\) | 527.794 | 1.31517 | 0.657587 | − | 0.753379i | \(-0.271577\pi\) | ||||
0.657587 | + | 0.753379i | \(0.271577\pi\) | |||||||
\(12\) | −42.9534 | −0.0861082 | ||||||||
\(13\) | 51.3772 | 0.0843165 | 0.0421582 | − | 0.999111i | \(-0.486577\pi\) | ||||
0.0421582 | + | 0.999111i | \(0.486577\pi\) | |||||||
\(14\) | 783.574 | 1.06846 | ||||||||
\(15\) | −194.940 | −0.223704 | ||||||||
\(16\) | −848.499 | −0.828612 | ||||||||
\(17\) | −968.342 | −0.812655 | −0.406328 | − | 0.913727i | \(-0.633191\pi\) | ||||
−0.406328 | + | 0.913727i | \(0.633191\pi\) | |||||||
\(18\) | 422.657 | 0.307473 | ||||||||
\(19\) | 2271.01 | 1.44323 | 0.721614 | − | 0.692296i | \(-0.243401\pi\) | ||||
0.721614 | + | 0.692296i | \(0.243401\pi\) | |||||||
\(20\) | 103.375 | 0.0577881 | ||||||||
\(21\) | 1351.51 | 0.668762 | ||||||||
\(22\) | 2754.02 | 1.21314 | ||||||||
\(23\) | 3803.24 | 1.49911 | 0.749556 | − | 0.661941i | \(-0.230267\pi\) | ||||
0.749556 | + | 0.661941i | \(0.230267\pi\) | |||||||
\(24\) | −1726.91 | −0.611986 | ||||||||
\(25\) | −2655.84 | −0.849870 | ||||||||
\(26\) | 268.086 | 0.0777751 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −716.691 | −0.172757 | ||||||||
\(29\) | 7264.82 | 1.60409 | 0.802047 | − | 0.597261i | \(-0.203744\pi\) | ||||
0.802047 | + | 0.597261i | \(0.203744\pi\) | |||||||
\(30\) | −1017.20 | −0.206348 | ||||||||
\(31\) | −513.041 | −0.0958843 | −0.0479422 | − | 0.998850i | \(-0.515266\pi\) | ||||
−0.0479422 | + | 0.998850i | \(0.515266\pi\) | |||||||
\(32\) | 1712.67 | 0.295664 | ||||||||
\(33\) | 4750.15 | 0.759316 | ||||||||
\(34\) | −5052.79 | −0.749608 | ||||||||
\(35\) | −3252.64 | −0.448813 | ||||||||
\(36\) | −386.581 | −0.0497146 | ||||||||
\(37\) | 11311.7 | 1.35839 | 0.679196 | − | 0.733957i | \(-0.262329\pi\) | ||||
0.679196 | + | 0.733957i | \(0.262329\pi\) | |||||||
\(38\) | 11850.1 | 1.33126 | ||||||||
\(39\) | 462.395 | 0.0486801 | ||||||||
\(40\) | 4156.10 | 0.410711 | ||||||||
\(41\) | 17019.0 | 1.58116 | 0.790579 | − | 0.612360i | \(-0.209780\pi\) | ||||
0.790579 | + | 0.612360i | \(0.209780\pi\) | |||||||
\(42\) | 7052.17 | 0.616878 | ||||||||
\(43\) | −7359.17 | −0.606956 | −0.303478 | − | 0.952838i | \(-0.598148\pi\) | ||||
−0.303478 | + | 0.952838i | \(0.598148\pi\) | |||||||
\(44\) | −2518.95 | −0.196150 | ||||||||
\(45\) | −1754.46 | −0.129155 | ||||||||
\(46\) | 19845.3 | 1.38281 | ||||||||
\(47\) | −15367.8 | −1.01477 | −0.507383 | − | 0.861720i | \(-0.669387\pi\) | ||||
−0.507383 | + | 0.861720i | \(0.669387\pi\) | |||||||
\(48\) | −7636.49 | −0.478400 | ||||||||
\(49\) | 5743.39 | 0.341726 | ||||||||
\(50\) | −13858.2 | −0.783936 | ||||||||
\(51\) | −8715.07 | −0.469187 | ||||||||
\(52\) | −245.203 | −0.0125753 | ||||||||
\(53\) | −32078.1 | −1.56862 | −0.784312 | − | 0.620367i | \(-0.786984\pi\) | ||||
−0.784312 | + | 0.620367i | \(0.786984\pi\) | |||||||
\(54\) | 3803.91 | 0.177520 | ||||||||
\(55\) | −11432.0 | −0.509585 | ||||||||
\(56\) | −28814.1 | −1.22782 | ||||||||
\(57\) | 20439.1 | 0.833248 | ||||||||
\(58\) | 37907.7 | 1.47965 | ||||||||
\(59\) | −3481.00 | −0.130189 | ||||||||
\(60\) | 930.371 | 0.0333640 | ||||||||
\(61\) | 13858.8 | 0.476872 | 0.238436 | − | 0.971158i | \(-0.423365\pi\) | ||||
0.238436 | + | 0.971158i | \(0.423365\pi\) | |||||||
\(62\) | −2677.04 | −0.0884455 | ||||||||
\(63\) | 12163.6 | 0.386110 | ||||||||
\(64\) | 36088.7 | 1.10134 | ||||||||
\(65\) | −1112.83 | −0.0326698 | ||||||||
\(66\) | 24786.2 | 0.700407 | ||||||||
\(67\) | −26206.8 | −0.713224 | −0.356612 | − | 0.934252i | \(-0.616068\pi\) | ||||
−0.356612 | + | 0.934252i | \(0.616068\pi\) | |||||||
\(68\) | 4621.51 | 0.121202 | ||||||||
\(69\) | 34229.2 | 0.865513 | ||||||||
\(70\) | −16972.2 | −0.413994 | ||||||||
\(71\) | −49223.6 | −1.15885 | −0.579426 | − | 0.815025i | \(-0.696723\pi\) | ||||
−0.579426 | + | 0.815025i | \(0.696723\pi\) | |||||||
\(72\) | −15542.2 | −0.353331 | ||||||||
\(73\) | −5312.00 | −0.116668 | −0.0583339 | − | 0.998297i | \(-0.518579\pi\) | ||||
−0.0583339 | + | 0.998297i | \(0.518579\pi\) | |||||||
\(74\) | 59024.5 | 1.25301 | ||||||||
\(75\) | −23902.6 | −0.490673 | ||||||||
\(76\) | −10838.6 | −0.215248 | ||||||||
\(77\) | 79257.7 | 1.52340 | ||||||||
\(78\) | 2412.77 | 0.0449035 | ||||||||
\(79\) | −41133.2 | −0.741524 | −0.370762 | − | 0.928728i | \(-0.620903\pi\) | ||||
−0.370762 | + | 0.928728i | \(0.620903\pi\) | |||||||
\(80\) | 18378.5 | 0.321059 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 88805.2 | 1.45849 | ||||||||
\(83\) | 60927.7 | 0.970777 | 0.485388 | − | 0.874299i | \(-0.338678\pi\) | ||||
0.485388 | + | 0.874299i | \(0.338678\pi\) | |||||||
\(84\) | −6450.22 | −0.0997416 | ||||||||
\(85\) | 20974.3 | 0.314876 | ||||||||
\(86\) | −38400.0 | −0.559868 | ||||||||
\(87\) | 65383.3 | 0.926124 | ||||||||
\(88\) | −101273. | −1.39407 | ||||||||
\(89\) | 4240.18 | 0.0567426 | 0.0283713 | − | 0.999597i | \(-0.490968\pi\) | ||||
0.0283713 | + | 0.999597i | \(0.490968\pi\) | |||||||
\(90\) | −9154.76 | −0.119135 | ||||||||
\(91\) | 7715.21 | 0.0976662 | ||||||||
\(92\) | −18151.3 | −0.223583 | ||||||||
\(93\) | −4617.37 | −0.0553588 | ||||||||
\(94\) | −80188.8 | −0.936040 | ||||||||
\(95\) | −49190.1 | −0.559202 | ||||||||
\(96\) | 15414.0 | 0.170702 | ||||||||
\(97\) | −4918.71 | −0.0530789 | −0.0265395 | − | 0.999648i | \(-0.508449\pi\) | ||||
−0.0265395 | + | 0.999648i | \(0.508449\pi\) | |||||||
\(98\) | 29968.9 | 0.315214 | ||||||||
\(99\) | 42751.3 | 0.438391 | ||||||||
\(100\) | 12675.3 | 0.126753 | ||||||||
\(101\) | −152708. | −1.48956 | −0.744780 | − | 0.667310i | \(-0.767446\pi\) | ||||
−0.744780 | + | 0.667310i | \(0.767446\pi\) | |||||||
\(102\) | −45475.2 | −0.432787 | ||||||||
\(103\) | 104142. | 0.967237 | 0.483619 | − | 0.875279i | \(-0.339322\pi\) | ||||
0.483619 | + | 0.875279i | \(0.339322\pi\) | |||||||
\(104\) | −9858.21 | −0.0893747 | ||||||||
\(105\) | −29273.7 | −0.259122 | ||||||||
\(106\) | −167383. | −1.44693 | ||||||||
\(107\) | 148892. | 1.25722 | 0.628611 | − | 0.777720i | \(-0.283624\pi\) | ||||
0.628611 | + | 0.777720i | \(0.283624\pi\) | |||||||
\(108\) | −3479.22 | −0.0287027 | ||||||||
\(109\) | −115623. | −0.932135 | −0.466067 | − | 0.884749i | \(-0.654330\pi\) | ||||
−0.466067 | + | 0.884749i | \(0.654330\pi\) | |||||||
\(110\) | −59652.2 | −0.470051 | ||||||||
\(111\) | 101806. | 0.784268 | ||||||||
\(112\) | −127417. | −0.959806 | ||||||||
\(113\) | −6712.64 | −0.0494535 | −0.0247268 | − | 0.999694i | \(-0.507872\pi\) | ||||
−0.0247268 | + | 0.999694i | \(0.507872\pi\) | |||||||
\(114\) | 106651. | 0.768603 | ||||||||
\(115\) | −82378.2 | −0.580855 | ||||||||
\(116\) | −34672.1 | −0.239240 | ||||||||
\(117\) | 4161.56 | 0.0281055 | ||||||||
\(118\) | −18163.8 | −0.120089 | ||||||||
\(119\) | −145414. | −0.941322 | ||||||||
\(120\) | 37404.9 | 0.237124 | ||||||||
\(121\) | 117516. | 0.729680 | ||||||||
\(122\) | 72315.2 | 0.439876 | ||||||||
\(123\) | 153171. | 0.912882 | ||||||||
\(124\) | 2448.54 | 0.0143005 | ||||||||
\(125\) | 125213. | 0.716762 | ||||||||
\(126\) | 63469.5 | 0.356155 | ||||||||
\(127\) | −254609. | −1.40076 | −0.700381 | − | 0.713769i | \(-0.746986\pi\) | ||||
−0.700381 | + | 0.713769i | \(0.746986\pi\) | |||||||
\(128\) | 133505. | 0.720231 | ||||||||
\(129\) | −66232.5 | −0.350426 | ||||||||
\(130\) | −5806.74 | −0.0301352 | ||||||||
\(131\) | −246062. | −1.25276 | −0.626379 | − | 0.779519i | \(-0.715464\pi\) | ||||
−0.626379 | + | 0.779519i | \(0.715464\pi\) | |||||||
\(132\) | −22670.6 | −0.113247 | ||||||||
\(133\) | 341032. | 1.67173 | ||||||||
\(134\) | −136747. | −0.657892 | ||||||||
\(135\) | −15790.2 | −0.0745679 | ||||||||
\(136\) | 185804. | 0.861408 | ||||||||
\(137\) | 171097. | 0.778827 | 0.389413 | − | 0.921063i | \(-0.372678\pi\) | ||||
0.389413 | + | 0.921063i | \(0.372678\pi\) | |||||||
\(138\) | 178607. | 0.798365 | ||||||||
\(139\) | −256672. | −1.12678 | −0.563392 | − | 0.826189i | \(-0.690504\pi\) | ||||
−0.563392 | + | 0.826189i | \(0.690504\pi\) | |||||||
\(140\) | 15523.5 | 0.0669377 | ||||||||
\(141\) | −138310. | −0.585876 | ||||||||
\(142\) | −256848. | −1.06895 | ||||||||
\(143\) | 27116.6 | 0.110891 | ||||||||
\(144\) | −68728.4 | −0.276204 | ||||||||
\(145\) | −157356. | −0.621532 | ||||||||
\(146\) | −27718.0 | −0.107617 | ||||||||
\(147\) | 51690.5 | 0.197296 | ||||||||
\(148\) | −53986.4 | −0.202596 | ||||||||
\(149\) | 122191. | 0.450894 | 0.225447 | − | 0.974255i | \(-0.427616\pi\) | ||||
0.225447 | + | 0.974255i | \(0.427616\pi\) | |||||||
\(150\) | −124723. | −0.452606 | ||||||||
\(151\) | −485698. | −1.73350 | −0.866750 | − | 0.498743i | \(-0.833795\pi\) | ||||
−0.866750 | + | 0.498743i | \(0.833795\pi\) | |||||||
\(152\) | −435759. | −1.52981 | ||||||||
\(153\) | −78435.7 | −0.270885 | ||||||||
\(154\) | 413566. | 1.40522 | ||||||||
\(155\) | 11112.5 | 0.0371519 | ||||||||
\(156\) | −2206.83 | −0.00726034 | ||||||||
\(157\) | −472070. | −1.52847 | −0.764235 | − | 0.644938i | \(-0.776883\pi\) | ||||
−0.764235 | + | 0.644938i | \(0.776883\pi\) | |||||||
\(158\) | −214633. | −0.683995 | ||||||||
\(159\) | −288703. | −0.905645 | ||||||||
\(160\) | −37096.4 | −0.114560 | ||||||||
\(161\) | 571124. | 1.73646 | ||||||||
\(162\) | 34235.2 | 0.102491 | ||||||||
\(163\) | 253916. | 0.748549 | 0.374275 | − | 0.927318i | \(-0.377892\pi\) | ||||
0.374275 | + | 0.927318i | \(0.377892\pi\) | |||||||
\(164\) | −81225.1 | −0.235820 | ||||||||
\(165\) | −102888. | −0.294209 | ||||||||
\(166\) | 317920. | 0.895463 | ||||||||
\(167\) | −79311.3 | −0.220061 | −0.110031 | − | 0.993928i | \(-0.535095\pi\) | ||||
−0.110031 | + | 0.993928i | \(0.535095\pi\) | |||||||
\(168\) | −259327. | −0.708882 | ||||||||
\(169\) | −368653. | −0.992891 | ||||||||
\(170\) | 109444. | 0.290448 | ||||||||
\(171\) | 183952. | 0.481076 | ||||||||
\(172\) | 35122.3 | 0.0905237 | ||||||||
\(173\) | 551760. | 1.40163 | 0.700817 | − | 0.713341i | \(-0.252819\pi\) | ||||
0.700817 | + | 0.713341i | \(0.252819\pi\) | |||||||
\(174\) | 341170. | 0.854274 | ||||||||
\(175\) | −398822. | −0.984429 | ||||||||
\(176\) | −447833. | −1.08977 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | 22125.2 | 0.0523405 | ||||||||
\(179\) | 738237. | 1.72212 | 0.861060 | − | 0.508504i | \(-0.169801\pi\) | ||||
0.861060 | + | 0.508504i | \(0.169801\pi\) | |||||||
\(180\) | 8373.34 | 0.0192627 | ||||||||
\(181\) | 663540. | 1.50546 | 0.752732 | − | 0.658327i | \(-0.228736\pi\) | ||||
0.752732 | + | 0.658327i | \(0.228736\pi\) | |||||||
\(182\) | 40257.9 | 0.0900891 | ||||||||
\(183\) | 124729. | 0.275322 | ||||||||
\(184\) | −729762. | −1.58905 | ||||||||
\(185\) | −245013. | −0.526331 | ||||||||
\(186\) | −24093.4 | −0.0510640 | ||||||||
\(187\) | −511085. | −1.06878 | ||||||||
\(188\) | 73344.2 | 0.151346 | ||||||||
\(189\) | 109472. | 0.222921 | ||||||||
\(190\) | −256673. | −0.515818 | ||||||||
\(191\) | −825937. | −1.63819 | −0.819093 | − | 0.573660i | \(-0.805523\pi\) | ||||
−0.819093 | + | 0.573660i | \(0.805523\pi\) | |||||||
\(192\) | 324798. | 0.635858 | ||||||||
\(193\) | −596260. | −1.15224 | −0.576120 | − | 0.817365i | \(-0.695434\pi\) | ||||
−0.576120 | + | 0.817365i | \(0.695434\pi\) | |||||||
\(194\) | −25665.8 | −0.0489610 | ||||||||
\(195\) | −10015.5 | −0.0188619 | ||||||||
\(196\) | −27410.9 | −0.0509663 | ||||||||
\(197\) | 847138. | 1.55521 | 0.777604 | − | 0.628754i | \(-0.216435\pi\) | ||||
0.777604 | + | 0.628754i | \(0.216435\pi\) | |||||||
\(198\) | 223076. | 0.404380 | ||||||||
\(199\) | −481833. | −0.862509 | −0.431254 | − | 0.902230i | \(-0.641929\pi\) | ||||
−0.431254 | + | 0.902230i | \(0.641929\pi\) | |||||||
\(200\) | 509601. | 0.900855 | ||||||||
\(201\) | −235861. | −0.411780 | ||||||||
\(202\) | −796828. | −1.37400 | ||||||||
\(203\) | 1.09094e6 | 1.85807 | ||||||||
\(204\) | 41593.6 | 0.0699762 | ||||||||
\(205\) | −368633. | −0.612645 | ||||||||
\(206\) | 543412. | 0.892198 | ||||||||
\(207\) | 308062. | 0.499704 | ||||||||
\(208\) | −43593.5 | −0.0698657 | ||||||||
\(209\) | 1.19863e6 | 1.89809 | ||||||||
\(210\) | −152750. | −0.239019 | ||||||||
\(211\) | 612379. | 0.946922 | 0.473461 | − | 0.880815i | \(-0.343005\pi\) | ||||
0.473461 | + | 0.880815i | \(0.343005\pi\) | |||||||
\(212\) | 153096. | 0.233950 | ||||||||
\(213\) | −443013. | −0.669063 | ||||||||
\(214\) | 776917. | 1.15969 | ||||||||
\(215\) | 159400. | 0.235175 | ||||||||
\(216\) | −139880. | −0.203995 | ||||||||
\(217\) | −77042.2 | −0.111066 | ||||||||
\(218\) | −603320. | −0.859818 | ||||||||
\(219\) | −47808.0 | −0.0673582 | ||||||||
\(220\) | 54560.5 | 0.0760014 | ||||||||
\(221\) | −49750.7 | −0.0685202 | ||||||||
\(222\) | 531221. | 0.723424 | ||||||||
\(223\) | 1.24590e6 | 1.67773 | 0.838865 | − | 0.544340i | \(-0.183220\pi\) | ||||
0.838865 | + | 0.544340i | \(0.183220\pi\) | |||||||
\(224\) | 257188. | 0.342476 | ||||||||
\(225\) | −215123. | −0.283290 | ||||||||
\(226\) | −35026.5 | −0.0456169 | ||||||||
\(227\) | −1.24352e6 | −1.60173 | −0.800864 | − | 0.598846i | \(-0.795626\pi\) | ||||
−0.800864 | + | 0.598846i | \(0.795626\pi\) | |||||||
\(228\) | −97547.5 | −0.124274 | ||||||||
\(229\) | 524991. | 0.661550 | 0.330775 | − | 0.943710i | \(-0.392690\pi\) | ||||
0.330775 | + | 0.943710i | \(0.392690\pi\) | |||||||
\(230\) | −429849. | −0.535792 | ||||||||
\(231\) | 713320. | 0.879537 | ||||||||
\(232\) | −1.39397e6 | −1.70033 | ||||||||
\(233\) | 529442. | 0.638894 | 0.319447 | − | 0.947604i | \(-0.396503\pi\) | ||||
0.319447 | + | 0.947604i | \(0.396503\pi\) | |||||||
\(234\) | 21714.9 | 0.0259250 | ||||||||
\(235\) | 332866. | 0.393188 | ||||||||
\(236\) | 16613.4 | 0.0194169 | ||||||||
\(237\) | −370199. | −0.428119 | ||||||||
\(238\) | −758767. | −0.868293 | ||||||||
\(239\) | −443263. | −0.501958 | −0.250979 | − | 0.967993i | \(-0.580752\pi\) | ||||
−0.250979 | + | 0.967993i | \(0.580752\pi\) | |||||||
\(240\) | 165407. | 0.185364 | ||||||||
\(241\) | −54132.2 | −0.0600362 | −0.0300181 | − | 0.999549i | \(-0.509556\pi\) | ||||
−0.0300181 | + | 0.999549i | \(0.509556\pi\) | |||||||
\(242\) | 613196. | 0.673071 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −66142.6 | −0.0711225 | ||||||||
\(245\) | −124402. | −0.132407 | ||||||||
\(246\) | 799246. | 0.842060 | ||||||||
\(247\) | 116678. | 0.121688 | ||||||||
\(248\) | 98441.7 | 0.101637 | ||||||||
\(249\) | 548349. | 0.560478 | ||||||||
\(250\) | 653361. | 0.661155 | ||||||||
\(251\) | 841171. | 0.842753 | 0.421376 | − | 0.906886i | \(-0.361547\pi\) | ||||
0.421376 | + | 0.906886i | \(0.361547\pi\) | |||||||
\(252\) | −58052.0 | −0.0575858 | ||||||||
\(253\) | 2.00733e6 | 1.97159 | ||||||||
\(254\) | −1.32855e6 | −1.29209 | ||||||||
\(255\) | 188769. | 0.181794 | ||||||||
\(256\) | −458211. | −0.436984 | ||||||||
\(257\) | −338918. | −0.320083 | −0.160041 | − | 0.987110i | \(-0.551163\pi\) | ||||
−0.160041 | + | 0.987110i | \(0.551163\pi\) | |||||||
\(258\) | −345600. | −0.323240 | ||||||||
\(259\) | 1.69866e6 | 1.57347 | ||||||||
\(260\) | 5311.10 | 0.00487249 | ||||||||
\(261\) | 588450. | 0.534698 | ||||||||
\(262\) | −1.28395e6 | −1.15557 | ||||||||
\(263\) | 2.18386e6 | 1.94686 | 0.973431 | − | 0.228981i | \(-0.0735395\pi\) | ||||
0.973431 | + | 0.228981i | \(0.0735395\pi\) | |||||||
\(264\) | −911454. | −0.804868 | ||||||||
\(265\) | 694812. | 0.607789 | ||||||||
\(266\) | 1.77950e6 | 1.54204 | ||||||||
\(267\) | 38161.6 | 0.0327604 | ||||||||
\(268\) | 125074. | 0.106373 | ||||||||
\(269\) | −104452. | −0.0880108 | −0.0440054 | − | 0.999031i | \(-0.514012\pi\) | ||||
−0.0440054 | + | 0.999031i | \(0.514012\pi\) | |||||||
\(270\) | −82392.8 | −0.0687828 | ||||||||
\(271\) | −263637. | −0.218063 | −0.109032 | − | 0.994038i | \(-0.534775\pi\) | ||||
−0.109032 | + | 0.994038i | \(0.534775\pi\) | |||||||
\(272\) | 821637. | 0.673376 | ||||||||
\(273\) | 69436.9 | 0.0563876 | ||||||||
\(274\) | 892782. | 0.718405 | ||||||||
\(275\) | −1.40174e6 | −1.11773 | ||||||||
\(276\) | −163362. | −0.129086 | ||||||||
\(277\) | 677687. | 0.530677 | 0.265338 | − | 0.964155i | \(-0.414516\pi\) | ||||
0.265338 | + | 0.964155i | \(0.414516\pi\) | |||||||
\(278\) | −1.33931e6 | −1.03937 | ||||||||
\(279\) | −41556.3 | −0.0319614 | ||||||||
\(280\) | 624113. | 0.475738 | ||||||||
\(281\) | 31956.5 | 0.0241431 | 0.0120716 | − | 0.999927i | \(-0.496157\pi\) | ||||
0.0120716 | + | 0.999927i | \(0.496157\pi\) | |||||||
\(282\) | −721700. | −0.540423 | ||||||||
\(283\) | 395858. | 0.293815 | 0.146907 | − | 0.989150i | \(-0.453068\pi\) | ||||
0.146907 | + | 0.989150i | \(0.453068\pi\) | |||||||
\(284\) | 234925. | 0.172835 | ||||||||
\(285\) | −442711. | −0.322855 | ||||||||
\(286\) | 141494. | 0.102288 | ||||||||
\(287\) | 2.55571e6 | 1.83150 | ||||||||
\(288\) | 138726. | 0.0985547 | ||||||||
\(289\) | −482172. | −0.339592 | ||||||||
\(290\) | −821082. | −0.573313 | ||||||||
\(291\) | −44268.4 | −0.0306451 | ||||||||
\(292\) | 25352.0 | 0.0174003 | ||||||||
\(293\) | 1.30735e6 | 0.889658 | 0.444829 | − | 0.895616i | \(-0.353264\pi\) | ||||
0.444829 | + | 0.895616i | \(0.353264\pi\) | |||||||
\(294\) | 269720. | 0.181989 | ||||||||
\(295\) | 75398.5 | 0.0504438 | ||||||||
\(296\) | −2.17049e6 | −1.43988 | ||||||||
\(297\) | 384762. | 0.253105 | ||||||||
\(298\) | 637593. | 0.415913 | ||||||||
\(299\) | 195400. | 0.126400 | ||||||||
\(300\) | 114077. | 0.0731807 | ||||||||
\(301\) | −1.10511e6 | −0.703055 | ||||||||
\(302\) | −2.53437e6 | −1.59901 | ||||||||
\(303\) | −1.37437e6 | −0.859998 | ||||||||
\(304\) | −1.92695e6 | −1.19588 | ||||||||
\(305\) | −300182. | −0.184772 | ||||||||
\(306\) | −409276. | −0.249869 | ||||||||
\(307\) | −2.11977e6 | −1.28364 | −0.641820 | − | 0.766856i | \(-0.721820\pi\) | ||||
−0.641820 | + | 0.766856i | \(0.721820\pi\) | |||||||
\(308\) | −378265. | −0.227206 | ||||||||
\(309\) | 937278. | 0.558435 | ||||||||
\(310\) | 57984.7 | 0.0342696 | ||||||||
\(311\) | 2.50058e6 | 1.46602 | 0.733009 | − | 0.680219i | \(-0.238115\pi\) | ||||
0.733009 | + | 0.680219i | \(0.238115\pi\) | |||||||
\(312\) | −88723.9 | −0.0516005 | ||||||||
\(313\) | −3.29921e6 | −1.90349 | −0.951743 | − | 0.306897i | \(-0.900709\pi\) | ||||
−0.951743 | + | 0.306897i | \(0.900709\pi\) | |||||||
\(314\) | −2.46325e6 | −1.40989 | ||||||||
\(315\) | −263464. | −0.149604 | ||||||||
\(316\) | 196312. | 0.110594 | ||||||||
\(317\) | −275609. | −0.154044 | −0.0770220 | − | 0.997029i | \(-0.524541\pi\) | ||||
−0.0770220 | + | 0.997029i | \(0.524541\pi\) | |||||||
\(318\) | −1.50645e6 | −0.835384 | ||||||||
\(319\) | 3.83433e6 | 2.10966 | ||||||||
\(320\) | −781681. | −0.426731 | ||||||||
\(321\) | 1.34003e6 | 0.725858 | ||||||||
\(322\) | 2.98012e6 | 1.60175 | ||||||||
\(323\) | −2.19911e6 | −1.17285 | ||||||||
\(324\) | −31313.0 | −0.0165715 | ||||||||
\(325\) | −136450. | −0.0716580 | ||||||||
\(326\) | 1.32493e6 | 0.690476 | ||||||||
\(327\) | −1.04061e6 | −0.538168 | ||||||||
\(328\) | −3.26560e6 | −1.67601 | ||||||||
\(329\) | −2.30775e6 | −1.17543 | ||||||||
\(330\) | −536870. | −0.271384 | ||||||||
\(331\) | −2.58017e6 | −1.29443 | −0.647215 | − | 0.762307i | \(-0.724067\pi\) | ||||
−0.647215 | + | 0.762307i | \(0.724067\pi\) | |||||||
\(332\) | −290783. | −0.144785 | ||||||||
\(333\) | 916251. | 0.452797 | ||||||||
\(334\) | −413846. | −0.202989 | ||||||||
\(335\) | 567639. | 0.276350 | ||||||||
\(336\) | −1.14676e6 | −0.554144 | ||||||||
\(337\) | 223512. | 0.107208 | 0.0536039 | − | 0.998562i | \(-0.482929\pi\) | ||||
0.0536039 | + | 0.998562i | \(0.482929\pi\) | |||||||
\(338\) | −1.92363e6 | −0.915861 | ||||||||
\(339\) | −60413.8 | −0.0285520 | ||||||||
\(340\) | −100102. | −0.0469618 | ||||||||
\(341\) | −270780. | −0.126104 | ||||||||
\(342\) | 959858. | 0.443753 | ||||||||
\(343\) | −1.66140e6 | −0.762498 | ||||||||
\(344\) | 1.41207e6 | 0.643369 | ||||||||
\(345\) | −741404. | −0.335357 | ||||||||
\(346\) | 2.87908e6 | 1.29289 | ||||||||
\(347\) | −2.39743e6 | −1.06886 | −0.534431 | − | 0.845212i | \(-0.679474\pi\) | ||||
−0.534431 | + | 0.845212i | \(0.679474\pi\) | |||||||
\(348\) | −312049. | −0.138126 | ||||||||
\(349\) | 1.79102e6 | 0.787113 | 0.393557 | − | 0.919300i | \(-0.371245\pi\) | ||||
0.393557 | + | 0.919300i | \(0.371245\pi\) | |||||||
\(350\) | −2.08105e6 | −0.908056 | ||||||||
\(351\) | 37454.0 | 0.0162267 | ||||||||
\(352\) | 903937. | 0.388849 | ||||||||
\(353\) | −883662. | −0.377441 | −0.188721 | − | 0.982031i | \(-0.560434\pi\) | ||||
−0.188721 | + | 0.982031i | \(0.560434\pi\) | |||||||
\(354\) | −163474. | −0.0693332 | ||||||||
\(355\) | 1.06618e6 | 0.449016 | ||||||||
\(356\) | −20236.7 | −0.00846281 | ||||||||
\(357\) | −1.30872e6 | −0.543472 | ||||||||
\(358\) | 3.85211e6 | 1.58851 | ||||||||
\(359\) | −597411. | −0.244645 | −0.122323 | − | 0.992490i | \(-0.539034\pi\) | ||||
−0.122323 | + | 0.992490i | \(0.539034\pi\) | |||||||
\(360\) | 336644. | 0.136904 | ||||||||
\(361\) | 2.68138e6 | 1.08291 | ||||||||
\(362\) | 3.46234e6 | 1.38867 | ||||||||
\(363\) | 1.05764e6 | 0.421281 | ||||||||
\(364\) | −36821.6 | −0.0145663 | ||||||||
\(365\) | 115058. | 0.0452048 | ||||||||
\(366\) | 650837. | 0.253962 | ||||||||
\(367\) | −2.44464e6 | −0.947437 | −0.473719 | − | 0.880676i | \(-0.657089\pi\) | ||||
−0.473719 | + | 0.880676i | \(0.657089\pi\) | |||||||
\(368\) | −3.22705e6 | −1.24218 | ||||||||
\(369\) | 1.37854e6 | 0.527053 | ||||||||
\(370\) | −1.27847e6 | −0.485498 | ||||||||
\(371\) | −4.81710e6 | −1.81698 | ||||||||
\(372\) | 22036.8 | 0.00825642 | ||||||||
\(373\) | −3.44062e6 | −1.28045 | −0.640227 | − | 0.768186i | \(-0.721160\pi\) | ||||
−0.640227 | + | 0.768186i | \(0.721160\pi\) | |||||||
\(374\) | −2.66684e6 | −0.985865 | ||||||||
\(375\) | 1.12692e6 | 0.413823 | ||||||||
\(376\) | 2.94875e6 | 1.07564 | ||||||||
\(377\) | 373246. | 0.135251 | ||||||||
\(378\) | 571226. | 0.205626 | ||||||||
\(379\) | −695527. | −0.248723 | −0.124361 | − | 0.992237i | \(-0.539688\pi\) | ||||
−0.124361 | + | 0.992237i | \(0.539688\pi\) | |||||||
\(380\) | 234765. | 0.0834014 | ||||||||
\(381\) | −2.29148e6 | −0.808730 | ||||||||
\(382\) | −4.30973e6 | −1.51109 | ||||||||
\(383\) | 453295. | 0.157901 | 0.0789503 | − | 0.996879i | \(-0.474843\pi\) | ||||
0.0789503 | + | 0.996879i | \(0.474843\pi\) | |||||||
\(384\) | 1.20154e6 | 0.415826 | ||||||||
\(385\) | −1.71672e6 | −0.590267 | ||||||||
\(386\) | −3.11128e6 | −1.06285 | ||||||||
\(387\) | −596092. | −0.202319 | ||||||||
\(388\) | 23475.1 | 0.00791639 | ||||||||
\(389\) | −5.66314e6 | −1.89751 | −0.948753 | − | 0.316017i | \(-0.897654\pi\) | ||||
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(390\) | −52260.7 | −0.0173986 | ||||||||
\(391\) | −3.68283e6 | −1.21826 | ||||||||
\(392\) | −1.10204e6 | −0.362227 | ||||||||
\(393\) | −2.21456e6 | −0.723280 | ||||||||
\(394\) | 4.42036e6 | 1.43455 | ||||||||
\(395\) | 890946. | 0.287315 | ||||||||
\(396\) | −204035. | −0.0653833 | ||||||||
\(397\) | 2.54465e6 | 0.810312 | 0.405156 | − | 0.914248i | \(-0.367217\pi\) | ||||
0.405156 | + | 0.914248i | \(0.367217\pi\) | |||||||
\(398\) | −2.51420e6 | −0.795594 | ||||||||
\(399\) | 3.06929e6 | 0.965175 | ||||||||
\(400\) | 2.25348e6 | 0.704213 | ||||||||
\(401\) | −168328. | −0.0522753 | −0.0261376 | − | 0.999658i | \(-0.508321\pi\) | ||||
−0.0261376 | + | 0.999658i | \(0.508321\pi\) | |||||||
\(402\) | −1.23072e6 | −0.379834 | ||||||||
\(403\) | −26358.6 | −0.00808462 | ||||||||
\(404\) | 728814. | 0.222159 | ||||||||
\(405\) | −142111. | −0.0430518 | ||||||||
\(406\) | 5.69252e6 | 1.71392 | ||||||||
\(407\) | 5.97027e6 | 1.78652 | ||||||||
\(408\) | 1.67224e6 | 0.497334 | ||||||||
\(409\) | 2.01773e6 | 0.596423 | 0.298212 | − | 0.954500i | \(-0.403610\pi\) | ||||
0.298212 | + | 0.954500i | \(0.403610\pi\) | |||||||
\(410\) | −1.92352e6 | −0.565116 | ||||||||
\(411\) | 1.53987e6 | 0.449656 | ||||||||
\(412\) | −497028. | −0.144257 | ||||||||
\(413\) | −522734. | −0.150802 | ||||||||
\(414\) | 1.60747e6 | 0.460936 | ||||||||
\(415\) | −1.31969e6 | −0.376143 | ||||||||
\(416\) | 87992.2 | 0.0249293 | ||||||||
\(417\) | −2.31005e6 | −0.650550 | ||||||||
\(418\) | 6.25441e6 | 1.75084 | ||||||||
\(419\) | 3.20396e6 | 0.891563 | 0.445782 | − | 0.895142i | \(-0.352926\pi\) | ||||
0.445782 | + | 0.895142i | \(0.352926\pi\) | |||||||
\(420\) | 139712. | 0.0386465 | ||||||||
\(421\) | 993569. | 0.273208 | 0.136604 | − | 0.990626i | \(-0.456381\pi\) | ||||
0.136604 | + | 0.990626i | \(0.456381\pi\) | |||||||
\(422\) | 3.19539e6 | 0.873458 | ||||||||
\(423\) | −1.24479e6 | −0.338256 | ||||||||
\(424\) | 6.15511e6 | 1.66273 | ||||||||
\(425\) | 2.57176e6 | 0.690651 | ||||||||
\(426\) | −2.31163e6 | −0.617156 | ||||||||
\(427\) | 2.08115e6 | 0.552375 | ||||||||
\(428\) | −710602. | −0.187507 | ||||||||
\(429\) | 244049. | 0.0640228 | ||||||||
\(430\) | 831746. | 0.216930 | ||||||||
\(431\) | −7.34140e6 | −1.90365 | −0.951823 | − | 0.306649i | \(-0.900792\pi\) | ||||
−0.951823 | + | 0.306649i | \(0.900792\pi\) | |||||||
\(432\) | −618556. | −0.159467 | ||||||||
\(433\) | −5.16376e6 | −1.32357 | −0.661784 | − | 0.749695i | \(-0.730200\pi\) | ||||
−0.661784 | + | 0.749695i | \(0.730200\pi\) | |||||||
\(434\) | −402005. | −0.102449 | ||||||||
\(435\) | −1.41620e6 | −0.358842 | ||||||||
\(436\) | 551823. | 0.139022 | ||||||||
\(437\) | 8.63719e6 | 2.16356 | ||||||||
\(438\) | −249462. | −0.0621324 | ||||||||
\(439\) | 335620. | 0.0831163 | 0.0415582 | − | 0.999136i | \(-0.486768\pi\) | ||||
0.0415582 | + | 0.999136i | \(0.486768\pi\) | |||||||
\(440\) | 2.19357e6 | 0.540156 | ||||||||
\(441\) | 465214. | 0.113909 | ||||||||
\(442\) | −259599. | −0.0632043 | ||||||||
\(443\) | 6.81650e6 | 1.65026 | 0.825129 | − | 0.564944i | \(-0.191102\pi\) | ||||
0.825129 | + | 0.564944i | \(0.191102\pi\) | |||||||
\(444\) | −485878. | −0.116969 | ||||||||
\(445\) | −91842.4 | −0.0219859 | ||||||||
\(446\) | 6.50111e6 | 1.54757 | ||||||||
\(447\) | 1.09972e6 | 0.260324 | ||||||||
\(448\) | 5.41936e6 | 1.27571 | ||||||||
\(449\) | 1.94054e6 | 0.454263 | 0.227132 | − | 0.973864i | \(-0.427065\pi\) | ||||
0.227132 | + | 0.973864i | \(0.427065\pi\) | |||||||
\(450\) | −1.12251e6 | −0.261312 | ||||||||
\(451\) | 8.98255e6 | 2.07950 | ||||||||
\(452\) | 32036.7 | 0.00737568 | ||||||||
\(453\) | −4.37128e6 | −1.00084 | ||||||||
\(454\) | −6.48868e6 | −1.47746 | ||||||||
\(455\) | −167112. | −0.0378423 | ||||||||
\(456\) | −3.92183e6 | −0.883236 | ||||||||
\(457\) | 4.70547e6 | 1.05393 | 0.526966 | − | 0.849887i | \(-0.323330\pi\) | ||||
0.526966 | + | 0.849887i | \(0.323330\pi\) | |||||||
\(458\) | 2.73939e6 | 0.610226 | ||||||||
\(459\) | −705921. | −0.156396 | ||||||||
\(460\) | 393158. | 0.0866309 | ||||||||
\(461\) | 1.04225e6 | 0.228413 | 0.114206 | − | 0.993457i | \(-0.463567\pi\) | ||||
0.114206 | + | 0.993457i | \(0.463567\pi\) | |||||||
\(462\) | 3.72209e6 | 0.811302 | ||||||||
\(463\) | 670929. | 0.145454 | 0.0727268 | − | 0.997352i | \(-0.476830\pi\) | ||||
0.0727268 | + | 0.997352i | \(0.476830\pi\) | |||||||
\(464\) | −6.16419e6 | −1.32917 | ||||||||
\(465\) | 100012. | 0.0214497 | ||||||||
\(466\) | 2.76262e6 | 0.589328 | ||||||||
\(467\) | −2.18853e6 | −0.464367 | −0.232183 | − | 0.972672i | \(-0.574587\pi\) | ||||
−0.232183 | + | 0.972672i | \(0.574587\pi\) | |||||||
\(468\) | −19861.4 | −0.00419176 | ||||||||
\(469\) | −3.93541e6 | −0.826149 | ||||||||
\(470\) | 1.73689e6 | 0.362684 | ||||||||
\(471\) | −4.24863e6 | −0.882463 | ||||||||
\(472\) | 667931. | 0.137999 | ||||||||
\(473\) | −3.88413e6 | −0.798253 | ||||||||
\(474\) | −1.93169e6 | −0.394905 | ||||||||
\(475\) | −6.03144e6 | −1.22656 | ||||||||
\(476\) | 694002. | 0.140392 | ||||||||
\(477\) | −2.59832e6 | −0.522875 | ||||||||
\(478\) | −2.31294e6 | −0.463015 | ||||||||
\(479\) | −4.83496e6 | −0.962840 | −0.481420 | − | 0.876490i | \(-0.659879\pi\) | ||||
−0.481420 | + | 0.876490i | \(0.659879\pi\) | |||||||
\(480\) | −333868. | −0.0661411 | ||||||||
\(481\) | 581166. | 0.114535 | ||||||||
\(482\) | −282461. | −0.0553785 | ||||||||
\(483\) | 5.14012e6 | 1.00255 | ||||||||
\(484\) | −560855. | −0.108827 | ||||||||
\(485\) | 106539. | 0.0205663 | ||||||||
\(486\) | 308117. | 0.0591732 | ||||||||
\(487\) | 7.05912e6 | 1.34874 | 0.674370 | − | 0.738394i | \(-0.264415\pi\) | ||||
0.674370 | + | 0.738394i | \(0.264415\pi\) | |||||||
\(488\) | −2.65922e6 | −0.505480 | ||||||||
\(489\) | 2.28524e6 | 0.432175 | ||||||||
\(490\) | −649128. | −0.122135 | ||||||||
\(491\) | 2.74825e6 | 0.514462 | 0.257231 | − | 0.966350i | \(-0.417190\pi\) | ||||
0.257231 | + | 0.966350i | \(0.417190\pi\) | |||||||
\(492\) | −731025. | −0.136151 | ||||||||
\(493\) | −7.03482e6 | −1.30357 | ||||||||
\(494\) | 608825. | 0.112247 | ||||||||
\(495\) | −925995. | −0.169862 | ||||||||
\(496\) | 435315. | 0.0794509 | ||||||||
\(497\) | −7.39181e6 | −1.34233 | ||||||||
\(498\) | 2.86128e6 | 0.516996 | ||||||||
\(499\) | −1.00805e7 | −1.81230 | −0.906149 | − | 0.422958i | \(-0.860992\pi\) | ||||
−0.906149 | + | 0.422958i | \(0.860992\pi\) | |||||||
\(500\) | −597592. | −0.106901 | ||||||||
\(501\) | −713802. | −0.127053 | ||||||||
\(502\) | 4.38922e6 | 0.777371 | ||||||||
\(503\) | 8.49561e6 | 1.49718 | 0.748591 | − | 0.663032i | \(-0.230731\pi\) | ||||
0.748591 | + | 0.663032i | \(0.230731\pi\) | |||||||
\(504\) | −2.33394e6 | −0.409273 | ||||||||
\(505\) | 3.30766e6 | 0.577154 | ||||||||
\(506\) | 1.04742e7 | 1.81863 | ||||||||
\(507\) | −3.31788e6 | −0.573246 | ||||||||
\(508\) | 1.21515e6 | 0.208915 | ||||||||
\(509\) | −6.16900e6 | −1.05541 | −0.527704 | − | 0.849428i | \(-0.676947\pi\) | ||||
−0.527704 | + | 0.849428i | \(0.676947\pi\) | |||||||
\(510\) | 984993. | 0.167690 | ||||||||
\(511\) | −797692. | −0.135140 | ||||||||
\(512\) | −6.66309e6 | −1.12331 | ||||||||
\(513\) | 1.65557e6 | 0.277749 | ||||||||
\(514\) | −1.76847e6 | −0.295250 | ||||||||
\(515\) | −2.25572e6 | −0.374772 | ||||||||
\(516\) | 316101. | 0.0522639 | ||||||||
\(517\) | −8.11102e6 | −1.33459 | ||||||||
\(518\) | 8.86359e6 | 1.45139 | ||||||||
\(519\) | 4.96584e6 | 0.809234 | ||||||||
\(520\) | 213529. | 0.0346297 | ||||||||
\(521\) | −4.98898e6 | −0.805225 | −0.402612 | − | 0.915371i | \(-0.631898\pi\) | ||||
−0.402612 | + | 0.915371i | \(0.631898\pi\) | |||||||
\(522\) | 3.07053e6 | 0.493215 | ||||||||
\(523\) | −2.82384e6 | −0.451425 | −0.225712 | − | 0.974194i | \(-0.572471\pi\) | ||||
−0.225712 | + | 0.974194i | \(0.572471\pi\) | |||||||
\(524\) | 1.17436e6 | 0.186841 | ||||||||
\(525\) | −3.58940e6 | −0.568360 | ||||||||
\(526\) | 1.13953e7 | 1.79582 | ||||||||
\(527\) | 496799. | 0.0779209 | ||||||||
\(528\) | −4.03050e6 | −0.629178 | ||||||||
\(529\) | 8.02829e6 | 1.24734 | ||||||||
\(530\) | 3.62552e6 | 0.560636 | ||||||||
\(531\) | −281961. | −0.0433963 | ||||||||
\(532\) | −1.62761e6 | −0.249328 | ||||||||
\(533\) | 874391. | 0.133318 | ||||||||
\(534\) | 199127. | 0.0302188 | ||||||||
\(535\) | −3.22501e6 | −0.487131 | ||||||||
\(536\) | 5.02853e6 | 0.756012 | ||||||||
\(537\) | 6.64413e6 | 0.994266 | ||||||||
\(538\) | −545029. | −0.0811829 | ||||||||
\(539\) | 3.03133e6 | 0.449429 | ||||||||
\(540\) | 75360.1 | 0.0111213 | ||||||||
\(541\) | −1.48508e6 | −0.218151 | −0.109075 | − | 0.994033i | \(-0.534789\pi\) | ||||
−0.109075 | + | 0.994033i | \(0.534789\pi\) | |||||||
\(542\) | −1.37565e6 | −0.201146 | ||||||||
\(543\) | 5.97186e6 | 0.869180 | ||||||||
\(544\) | −1.65845e6 | −0.240273 | ||||||||
\(545\) | 2.50440e6 | 0.361171 | ||||||||
\(546\) | 362321. | 0.0520130 | ||||||||
\(547\) | −1.20672e7 | −1.72440 | −0.862198 | − | 0.506571i | \(-0.830913\pi\) | ||||
−0.862198 | + | 0.506571i | \(0.830913\pi\) | |||||||
\(548\) | −816577. | −0.116157 | ||||||||
\(549\) | 1.12256e6 | 0.158957 | ||||||||
\(550\) | −7.31426e6 | −1.03101 | ||||||||
\(551\) | 1.64985e7 | 2.31507 | ||||||||
\(552\) | −6.56786e6 | −0.917436 | ||||||||
\(553\) | −6.17689e6 | −0.858928 | ||||||||
\(554\) | 3.53616e6 | 0.489506 | ||||||||
\(555\) | −2.20511e6 | −0.303877 | ||||||||
\(556\) | 1.22499e6 | 0.168053 | ||||||||
\(557\) | −1.54643e6 | −0.211199 | −0.105600 | − | 0.994409i | \(-0.533676\pi\) | ||||
−0.105600 | + | 0.994409i | \(0.533676\pi\) | |||||||
\(558\) | −216840. | −0.0294818 | ||||||||
\(559\) | −378094. | −0.0511764 | ||||||||
\(560\) | 2.75986e6 | 0.371892 | ||||||||
\(561\) | −4.59977e6 | −0.617062 | ||||||||
\(562\) | 166749. | 0.0222701 | ||||||||
\(563\) | 1.88354e6 | 0.250439 | 0.125220 | − | 0.992129i | \(-0.460036\pi\) | ||||
0.125220 | + | 0.992129i | \(0.460036\pi\) | |||||||
\(564\) | 660098. | 0.0873797 | ||||||||
\(565\) | 145396. | 0.0191616 | ||||||||
\(566\) | 2.06558e6 | 0.271020 | ||||||||
\(567\) | 985251. | 0.128703 | ||||||||
\(568\) | 9.44498e6 | 1.22837 | ||||||||
\(569\) | 1.00339e6 | 0.129924 | 0.0649622 | − | 0.997888i | \(-0.479307\pi\) | ||||
0.0649622 | + | 0.997888i | \(0.479307\pi\) | |||||||
\(570\) | −2.31006e6 | −0.297808 | ||||||||
\(571\) | 7.14637e6 | 0.917266 | 0.458633 | − | 0.888626i | \(-0.348339\pi\) | ||||
0.458633 | + | 0.888626i | \(0.348339\pi\) | |||||||
\(572\) | −129417. | −0.0165387 | ||||||||
\(573\) | −7.43343e6 | −0.945808 | ||||||||
\(574\) | 1.33357e7 | 1.68941 | ||||||||
\(575\) | −1.01008e7 | −1.27405 | ||||||||
\(576\) | 2.92318e6 | 0.367113 | ||||||||
\(577\) | −4.39566e6 | −0.549649 | −0.274824 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274824 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(578\) | −2.51597e6 | −0.313246 | ||||||||
\(579\) | −5.36634e6 | −0.665246 | ||||||||
\(580\) | 750997. | 0.0926976 | ||||||||
\(581\) | 9.14938e6 | 1.12448 | ||||||||
\(582\) | −230992. | −0.0282677 | ||||||||
\(583\) | −1.69306e7 | −2.06301 | ||||||||
\(584\) | 1.01926e6 | 0.123667 | ||||||||
\(585\) | −90139.4 | −0.0108899 | ||||||||
\(586\) | 6.82174e6 | 0.820637 | ||||||||
\(587\) | −9.07708e6 | −1.08730 | −0.543652 | − | 0.839311i | \(-0.682959\pi\) | ||||
−0.543652 | + | 0.839311i | \(0.682959\pi\) | |||||||
\(588\) | −246698. | −0.0294254 | ||||||||
\(589\) | −1.16512e6 | −0.138383 | ||||||||
\(590\) | 393429. | 0.0465303 | ||||||||
\(591\) | 7.62424e6 | 0.897900 | ||||||||
\(592\) | −9.59800e6 | −1.12558 | ||||||||
\(593\) | −2.24665e6 | −0.262360 | −0.131180 | − | 0.991359i | \(-0.541877\pi\) | ||||
−0.131180 | + | 0.991359i | \(0.541877\pi\) | |||||||
\(594\) | 2.00768e6 | 0.233469 | ||||||||
\(595\) | 3.14967e6 | 0.364730 | ||||||||
\(596\) | −583170. | −0.0672481 | ||||||||
\(597\) | −4.33649e6 | −0.497970 | ||||||||
\(598\) | 1.01959e6 | 0.116594 | ||||||||
\(599\) | 2.81454e6 | 0.320509 | 0.160255 | − | 0.987076i | \(-0.448768\pi\) | ||||
0.160255 | + | 0.987076i | \(0.448768\pi\) | |||||||
\(600\) | 4.58641e6 | 0.520109 | ||||||||
\(601\) | −7.44310e6 | −0.840557 | −0.420279 | − | 0.907395i | \(-0.638068\pi\) | ||||
−0.420279 | + | 0.907395i | \(0.638068\pi\) | |||||||
\(602\) | −5.76645e6 | −0.648511 | ||||||||
\(603\) | −2.12275e6 | −0.237741 | ||||||||
\(604\) | 2.31804e6 | 0.258541 | ||||||||
\(605\) | −2.54539e6 | −0.282726 | ||||||||
\(606\) | −7.17145e6 | −0.793278 | ||||||||
\(607\) | −1.48571e7 | −1.63667 | −0.818335 | − | 0.574742i | \(-0.805102\pi\) | ||||
−0.818335 | + | 0.574742i | \(0.805102\pi\) | |||||||
\(608\) | 3.88949e6 | 0.426710 | ||||||||
\(609\) | 9.81848e6 | 1.07276 | ||||||||
\(610\) | −1.56635e6 | −0.170437 | ||||||||
\(611\) | −789554. | −0.0855615 | ||||||||
\(612\) | 374342. | 0.0404008 | ||||||||
\(613\) | −8.75960e6 | −0.941528 | −0.470764 | − | 0.882259i | \(-0.656022\pi\) | ||||
−0.470764 | + | 0.882259i | \(0.656022\pi\) | |||||||
\(614\) | −1.10609e7 | −1.18405 | ||||||||
\(615\) | −3.31769e6 | −0.353711 | ||||||||
\(616\) | −1.52079e7 | −1.61479 | ||||||||
\(617\) | 1.22453e6 | 0.129496 | 0.0647478 | − | 0.997902i | \(-0.479376\pi\) | ||||
0.0647478 | + | 0.997902i | \(0.479376\pi\) | |||||||
\(618\) | 4.89071e6 | 0.515111 | ||||||||
\(619\) | 1.13512e7 | 1.19074 | 0.595369 | − | 0.803452i | \(-0.297006\pi\) | ||||
0.595369 | + | 0.803452i | \(0.297006\pi\) | |||||||
\(620\) | −53035.4 | −0.00554098 | ||||||||
\(621\) | 2.77256e6 | 0.288504 | ||||||||
\(622\) | 1.30480e7 | 1.35228 | ||||||||
\(623\) | 636739. | 0.0657266 | ||||||||
\(624\) | −392342. | −0.0403370 | ||||||||
\(625\) | 5.58739e6 | 0.572149 | ||||||||
\(626\) | −1.72153e7 | −1.75581 | ||||||||
\(627\) | 1.07876e7 | 1.09586 | ||||||||
\(628\) | 2.25300e6 | 0.227962 | ||||||||
\(629\) | −1.09536e7 | −1.10390 | ||||||||
\(630\) | −1.37475e6 | −0.137998 | ||||||||
\(631\) | 8.37476e6 | 0.837334 | 0.418667 | − | 0.908140i | \(-0.362497\pi\) | ||||
0.418667 | + | 0.908140i | \(0.362497\pi\) | |||||||
\(632\) | 7.89260e6 | 0.786009 | ||||||||
\(633\) | 5.51141e6 | 0.546706 | ||||||||
\(634\) | −1.43812e6 | −0.142093 | ||||||||
\(635\) | 5.51483e6 | 0.542748 | ||||||||
\(636\) | 1.37786e6 | 0.135071 | ||||||||
\(637\) | 295079. | 0.0288131 | ||||||||
\(638\) | 2.00075e7 | 1.94599 | ||||||||
\(639\) | −3.98711e6 | −0.386284 | ||||||||
\(640\) | −2.89172e6 | −0.279065 | ||||||||
\(641\) | 3.09372e6 | 0.297396 | 0.148698 | − | 0.988883i | \(-0.452492\pi\) | ||||
0.148698 | + | 0.988883i | \(0.452492\pi\) | |||||||
\(642\) | 6.99225e6 | 0.669545 | ||||||||
\(643\) | 3.68773e6 | 0.351748 | 0.175874 | − | 0.984413i | \(-0.443725\pi\) | ||||
0.175874 | + | 0.984413i | \(0.443725\pi\) | |||||||
\(644\) | −2.72575e6 | −0.258983 | ||||||||
\(645\) | 1.43460e6 | 0.135778 | ||||||||
\(646\) | −1.14749e7 | −1.08186 | ||||||||
\(647\) | 1.12690e7 | 1.05834 | 0.529171 | − | 0.848516i | \(-0.322503\pi\) | ||||
0.529171 | + | 0.848516i | \(0.322503\pi\) | |||||||
\(648\) | −1.25892e6 | −0.117777 | ||||||||
\(649\) | −1.83725e6 | −0.171221 | ||||||||
\(650\) | −711994. | −0.0660987 | ||||||||
\(651\) | −693380. | −0.0641237 | ||||||||
\(652\) | −1.21184e6 | −0.111641 | ||||||||
\(653\) | 9.48265e6 | 0.870255 | 0.435128 | − | 0.900369i | \(-0.356703\pi\) | ||||
0.435128 | + | 0.900369i | \(0.356703\pi\) | |||||||
\(654\) | −5.42988e6 | −0.496416 | ||||||||
\(655\) | 5.32972e6 | 0.485401 | ||||||||
\(656\) | −1.44406e7 | −1.31017 | ||||||||
\(657\) | −430272. | −0.0388893 | ||||||||
\(658\) | −1.20418e7 | −1.08424 | ||||||||
\(659\) | 1.67506e6 | 0.150251 | 0.0751255 | − | 0.997174i | \(-0.476064\pi\) | ||||
0.0751255 | + | 0.997174i | \(0.476064\pi\) | |||||||
\(660\) | 491045. | 0.0438794 | ||||||||
\(661\) | −1.47650e7 | −1.31441 | −0.657203 | − | 0.753714i | \(-0.728260\pi\) | ||||
−0.657203 | + | 0.753714i | \(0.728260\pi\) | |||||||
\(662\) | −1.34633e7 | −1.19401 | ||||||||
\(663\) | −447756. | −0.0395602 | ||||||||
\(664\) | −1.16907e7 | −1.02902 | ||||||||
\(665\) | −7.38677e6 | −0.647740 | ||||||||
\(666\) | 4.78099e6 | 0.417669 | ||||||||
\(667\) | 2.76298e7 | 2.40472 | ||||||||
\(668\) | 378521. | 0.0328208 | ||||||||
\(669\) | 1.12131e7 | 0.968638 | ||||||||
\(670\) | 2.96193e6 | 0.254911 | ||||||||
\(671\) | 7.31461e6 | 0.627169 | ||||||||
\(672\) | 2.31469e6 | 0.197729 | ||||||||
\(673\) | 4.22348e6 | 0.359445 | 0.179723 | − | 0.983717i | \(-0.442480\pi\) | ||||
0.179723 | + | 0.983717i | \(0.442480\pi\) | |||||||
\(674\) | 1.16628e6 | 0.0988904 | ||||||||
\(675\) | −1.93611e6 | −0.163558 | ||||||||
\(676\) | 1.75943e6 | 0.148083 | ||||||||
\(677\) | −5.35812e6 | −0.449304 | −0.224652 | − | 0.974439i | \(-0.572125\pi\) | ||||
−0.224652 | + | 0.974439i | \(0.572125\pi\) | |||||||
\(678\) | −315238. | −0.0263369 | ||||||||
\(679\) | −738633. | −0.0614829 | ||||||||
\(680\) | −4.02453e6 | −0.333766 | ||||||||
\(681\) | −1.11917e7 | −0.924758 | ||||||||
\(682\) | −1.41293e6 | −0.116321 | ||||||||
\(683\) | −3.41248e6 | −0.279910 | −0.139955 | − | 0.990158i | \(-0.544696\pi\) | ||||
−0.139955 | + | 0.990158i | \(0.544696\pi\) | |||||||
\(684\) | −877928. | −0.0717494 | ||||||||
\(685\) | −3.70596e6 | −0.301769 | ||||||||
\(686\) | −8.66916e6 | −0.703342 | ||||||||
\(687\) | 4.72492e6 | 0.381946 | ||||||||
\(688\) | 6.24425e6 | 0.502932 | ||||||||
\(689\) | −1.64808e6 | −0.132261 | ||||||||
\(690\) | −3.86864e6 | −0.309339 | ||||||||
\(691\) | −1.38499e7 | −1.10345 | −0.551724 | − | 0.834027i | \(-0.686030\pi\) | ||||
−0.551724 | + | 0.834027i | \(0.686030\pi\) | |||||||
\(692\) | −2.63333e6 | −0.209045 | ||||||||
\(693\) | 6.41988e6 | 0.507801 | ||||||||
\(694\) | −1.25097e7 | −0.985938 | ||||||||
\(695\) | 5.55951e6 | 0.436591 | ||||||||
\(696\) | −1.25457e7 | −0.981683 | ||||||||
\(697\) | −1.64802e7 | −1.28494 | ||||||||
\(698\) | 9.34553e6 | 0.726048 | ||||||||
\(699\) | 4.76498e6 | 0.368866 | ||||||||
\(700\) | 1.90342e6 | 0.146821 | ||||||||
\(701\) | −232405. | −0.0178628 | −0.00893142 | − | 0.999960i | \(-0.502843\pi\) | ||||
−0.00893142 | + | 0.999960i | \(0.502843\pi\) | |||||||
\(702\) | 195435. | 0.0149678 | ||||||||
\(703\) | 2.56891e7 | 1.96047 | ||||||||
\(704\) | 1.90474e7 | 1.44845 | ||||||||
\(705\) | 2.99580e6 | 0.227007 | ||||||||
\(706\) | −4.61094e6 | −0.348159 | ||||||||
\(707\) | −2.29318e7 | −1.72540 | ||||||||
\(708\) | 149521. | 0.0112103 | ||||||||
\(709\) | −3.14519e6 | −0.234981 | −0.117490 | − | 0.993074i | \(-0.537485\pi\) | ||||
−0.117490 | + | 0.993074i | \(0.537485\pi\) | |||||||
\(710\) | 5.56334e6 | 0.414181 | ||||||||
\(711\) | −3.33179e6 | −0.247175 | ||||||||
\(712\) | −813602. | −0.0601467 | ||||||||
\(713\) | −1.95122e6 | −0.143741 | ||||||||
\(714\) | −6.82891e6 | −0.501309 | ||||||||
\(715\) | −587346. | −0.0429664 | ||||||||
\(716\) | −3.52331e6 | −0.256843 | ||||||||
\(717\) | −3.98937e6 | −0.289805 | ||||||||
\(718\) | −3.11728e6 | −0.225665 | ||||||||
\(719\) | −8.47359e6 | −0.611287 | −0.305644 | − | 0.952146i | \(-0.598872\pi\) | ||||
−0.305644 | + | 0.952146i | \(0.598872\pi\) | |||||||
\(720\) | 1.48866e6 | 0.107020 | ||||||||
\(721\) | 1.56388e7 | 1.12038 | ||||||||
\(722\) | 1.39914e7 | 0.998892 | ||||||||
\(723\) | −487190. | −0.0346619 | ||||||||
\(724\) | −3.16681e6 | −0.224531 | ||||||||
\(725\) | −1.92942e7 | −1.36327 | ||||||||
\(726\) | 5.51876e6 | 0.388598 | ||||||||
\(727\) | −5.10460e6 | −0.358200 | −0.179100 | − | 0.983831i | \(-0.557319\pi\) | ||||
−0.179100 | + | 0.983831i | \(0.557319\pi\) | |||||||
\(728\) | −1.48039e6 | −0.103525 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 600371. | 0.0416978 | ||||||||
\(731\) | 7.12619e6 | 0.493246 | ||||||||
\(732\) | −595284. | −0.0410626 | ||||||||
\(733\) | −3.23461e6 | −0.222363 | −0.111181 | − | 0.993800i | \(-0.535463\pi\) | ||||
−0.111181 | + | 0.993800i | \(0.535463\pi\) | |||||||
\(734\) | −1.27561e7 | −0.873934 | ||||||||
\(735\) | −1.11962e6 | −0.0764454 | ||||||||
\(736\) | 6.51369e6 | 0.443234 | ||||||||
\(737\) | −1.38318e7 | −0.938014 | ||||||||
\(738\) | 7.19322e6 | 0.486163 | ||||||||
\(739\) | −2.43694e7 | −1.64147 | −0.820735 | − | 0.571309i | \(-0.806436\pi\) | ||||
−0.820735 | + | 0.571309i | \(0.806436\pi\) | |||||||
\(740\) | 1.16935e6 | 0.0784990 | ||||||||
\(741\) | 1.05010e6 | 0.0702565 | ||||||||
\(742\) | −2.51356e7 | −1.67602 | ||||||||
\(743\) | −1.35628e7 | −0.901315 | −0.450657 | − | 0.892697i | \(-0.648810\pi\) | ||||
−0.450657 | + | 0.892697i | \(0.648810\pi\) | |||||||
\(744\) | 885975. | 0.0586799 | ||||||||
\(745\) | −2.64667e6 | −0.174706 | ||||||||
\(746\) | −1.79531e7 | −1.18112 | ||||||||
\(747\) | 4.93514e6 | 0.323592 | ||||||||
\(748\) | 2.43920e6 | 0.159402 | ||||||||
\(749\) | 2.23588e7 | 1.45628 | ||||||||
\(750\) | 5.88025e6 | 0.381718 | ||||||||
\(751\) | −3.68893e6 | −0.238671 | −0.119336 | − | 0.992854i | \(-0.538076\pi\) | ||||
−0.119336 | + | 0.992854i | \(0.538076\pi\) | |||||||
\(752\) | 1.30395e7 | 0.840848 | ||||||||
\(753\) | 7.57054e6 | 0.486564 | ||||||||
\(754\) | 1.94759e6 | 0.124758 | ||||||||
\(755\) | 1.05202e7 | 0.671673 | ||||||||
\(756\) | −522468. | −0.0332472 | ||||||||
\(757\) | 4.79135e6 | 0.303892 | 0.151946 | − | 0.988389i | \(-0.451446\pi\) | ||||
0.151946 | + | 0.988389i | \(0.451446\pi\) | |||||||
\(758\) | −3.62925e6 | −0.229427 | ||||||||
\(759\) | 1.80660e7 | 1.13830 | ||||||||
\(760\) | 9.43854e6 | 0.592749 | ||||||||
\(761\) | 7.35535e6 | 0.460407 | 0.230203 | − | 0.973143i | \(-0.426061\pi\) | ||||
0.230203 | + | 0.973143i | \(0.426061\pi\) | |||||||
\(762\) | −1.19569e7 | −0.745988 | ||||||||
\(763\) | −1.73629e7 | −1.07972 | ||||||||
\(764\) | 3.94187e6 | 0.244325 | ||||||||
\(765\) | 1.69892e6 | 0.104959 | ||||||||
\(766\) | 2.36529e6 | 0.145650 | ||||||||
\(767\) | −178844. | −0.0109771 | ||||||||
\(768\) | −4.12390e6 | −0.252293 | ||||||||
\(769\) | −2.77997e7 | −1.69521 | −0.847607 | − | 0.530625i | \(-0.821957\pi\) | ||||
−0.847607 | + | 0.530625i | \(0.821957\pi\) | |||||||
\(770\) | −8.95784e6 | −0.544473 | ||||||||
\(771\) | −3.05026e6 | −0.184800 | ||||||||
\(772\) | 2.84571e6 | 0.171849 | ||||||||
\(773\) | 9.35408e6 | 0.563057 | 0.281529 | − | 0.959553i | \(-0.409159\pi\) | ||||
0.281529 | + | 0.959553i | \(0.409159\pi\) | |||||||
\(774\) | −3.11040e6 | −0.186623 | ||||||||
\(775\) | 1.36256e6 | 0.0814892 | ||||||||
\(776\) | 943798. | 0.0562632 | ||||||||
\(777\) | 1.52879e7 | 0.908441 | ||||||||
\(778\) | −2.95502e7 | −1.75030 | ||||||||
\(779\) | 3.86504e7 | 2.28197 | ||||||||
\(780\) | 47799.9 | 0.00281313 | ||||||||
\(781\) | −2.59799e7 | −1.52409 | ||||||||
\(782\) | −1.92170e7 | −1.12375 | ||||||||
\(783\) | 5.29605e6 | 0.308708 | ||||||||
\(784\) | −4.87326e6 | −0.283158 | ||||||||
\(785\) | 1.02250e7 | 0.592231 | ||||||||
\(786\) | −1.15556e7 | −0.667167 | ||||||||
\(787\) | 8.96042e6 | 0.515693 | 0.257847 | − | 0.966186i | \(-0.416987\pi\) | ||||
0.257847 | + | 0.966186i | \(0.416987\pi\) | |||||||
\(788\) | −4.04305e6 | −0.231950 | ||||||||
\(789\) | 1.96547e7 | 1.12402 | ||||||||
\(790\) | 4.64895e6 | 0.265025 | ||||||||
\(791\) | −1.00802e6 | −0.0572835 | ||||||||
\(792\) | −8.20308e6 | −0.464691 | ||||||||
\(793\) | 712028. | 0.0402082 | ||||||||
\(794\) | 1.32780e7 | 0.747447 | ||||||||
\(795\) | 6.25331e6 | 0.350907 | ||||||||
\(796\) | 2.29959e6 | 0.128638 | ||||||||
\(797\) | −1.17914e7 | −0.657536 | −0.328768 | − | 0.944411i | \(-0.606633\pi\) | ||||
−0.328768 | + | 0.944411i | \(0.606633\pi\) | |||||||
\(798\) | 1.60155e7 | 0.890295 | ||||||||
\(799\) | 1.48812e7 | 0.824655 | ||||||||
\(800\) | −4.54858e6 | −0.251276 | ||||||||
\(801\) | 343455. | 0.0189142 | ||||||||
\(802\) | −878336. | −0.0482197 | ||||||||
\(803\) | −2.80364e6 | −0.153438 | ||||||||
\(804\) | 1.12567e6 | 0.0614145 | ||||||||
\(805\) | −1.23706e7 | −0.672821 | ||||||||
\(806\) | −137539. | −0.00745741 | ||||||||
\(807\) | −940068. | −0.0508131 | ||||||||
\(808\) | 2.93014e7 | 1.57892 | ||||||||
\(809\) | 2.15179e7 | 1.15592 | 0.577960 | − | 0.816065i | \(-0.303849\pi\) | ||||
0.577960 | + | 0.816065i | \(0.303849\pi\) | |||||||
\(810\) | −741535. | −0.0397118 | ||||||||
\(811\) | 1.33906e7 | 0.714906 | 0.357453 | − | 0.933931i | \(-0.383645\pi\) | ||||
0.357453 | + | 0.933931i | \(0.383645\pi\) | |||||||
\(812\) | −5.20663e6 | −0.277119 | ||||||||
\(813\) | −2.37273e6 | −0.125899 | ||||||||
\(814\) | 3.11528e7 | 1.64792 | ||||||||
\(815\) | −5.49982e6 | −0.290038 | ||||||||
\(816\) | 7.39473e6 | 0.388774 | ||||||||
\(817\) | −1.67127e7 | −0.875976 | ||||||||
\(818\) | 1.05285e7 | 0.550152 | ||||||||
\(819\) | 624932. | 0.0325554 | ||||||||
\(820\) | 1.75934e6 | 0.0913722 | ||||||||
\(821\) | −8.26050e6 | −0.427709 | −0.213854 | − | 0.976866i | \(-0.568602\pi\) | ||||
−0.213854 | + | 0.976866i | \(0.568602\pi\) | |||||||
\(822\) | 8.03504e6 | 0.414771 | ||||||||
\(823\) | 3.28873e7 | 1.69250 | 0.846251 | − | 0.532784i | \(-0.178854\pi\) | ||||
0.846251 | + | 0.532784i | \(0.178854\pi\) | |||||||
\(824\) | −1.99827e7 | −1.02526 | ||||||||
\(825\) | −1.26156e7 | −0.645319 | ||||||||
\(826\) | −2.72762e6 | −0.139102 | ||||||||
\(827\) | −2.91579e6 | −0.148249 | −0.0741247 | − | 0.997249i | \(-0.523616\pi\) | ||||
−0.0741247 | + | 0.997249i | \(0.523616\pi\) | |||||||
\(828\) | −1.47026e6 | −0.0745277 | ||||||||
\(829\) | 1.16799e6 | 0.0590274 | 0.0295137 | − | 0.999564i | \(-0.490604\pi\) | ||||
0.0295137 | + | 0.999564i | \(0.490604\pi\) | |||||||
\(830\) | −6.88615e6 | −0.346961 | ||||||||
\(831\) | 6.09919e6 | 0.306386 | ||||||||
\(832\) | 1.85414e6 | 0.0928610 | ||||||||
\(833\) | −5.56156e6 | −0.277705 | ||||||||
\(834\) | −1.20538e7 | −0.600079 | ||||||||
\(835\) | 1.71788e6 | 0.0852664 | ||||||||
\(836\) | −5.72056e6 | −0.283089 | ||||||||
\(837\) | −374007. | −0.0184529 | ||||||||
\(838\) | 1.67182e7 | 0.822395 | ||||||||
\(839\) | 4.82533e6 | 0.236659 | 0.118329 | − | 0.992974i | \(-0.462246\pi\) | ||||
0.118329 | + | 0.992974i | \(0.462246\pi\) | |||||||
\(840\) | 5.61702e6 | 0.274668 | ||||||||
\(841\) | 3.22664e7 | 1.57312 | ||||||||
\(842\) | 5.18443e6 | 0.252012 | ||||||||
\(843\) | 287609. | 0.0139391 | ||||||||
\(844\) | −2.92264e6 | −0.141227 | ||||||||
\(845\) | 7.98504e6 | 0.384712 | ||||||||
\(846\) | −6.49530e6 | −0.312013 | ||||||||
\(847\) | 1.76471e7 | 0.845210 | ||||||||
\(848\) | 2.72182e7 | 1.29978 | ||||||||
\(849\) | 3.56273e6 | 0.169634 | ||||||||
\(850\) | 1.34194e7 | 0.637070 | ||||||||
\(851\) | 4.30213e7 | 2.03638 | ||||||||
\(852\) | 2.11432e6 | 0.0997866 | ||||||||
\(853\) | 2.55798e7 | 1.20372 | 0.601859 | − | 0.798603i | \(-0.294427\pi\) | ||||
0.601859 | + | 0.798603i | \(0.294427\pi\) | |||||||
\(854\) | 1.08594e7 | 0.509521 | ||||||||
\(855\) | −3.98440e6 | −0.186401 | ||||||||
\(856\) | −2.85693e7 | −1.33265 | ||||||||
\(857\) | −1.16798e7 | −0.543232 | −0.271616 | − | 0.962406i | \(-0.587558\pi\) | ||||
−0.271616 | + | 0.962406i | \(0.587558\pi\) | |||||||
\(858\) | 1.27345e6 | 0.0590558 | ||||||||
\(859\) | 1.36617e6 | 0.0631717 | 0.0315858 | − | 0.999501i | \(-0.489944\pi\) | ||||
0.0315858 | + | 0.999501i | \(0.489944\pi\) | |||||||
\(860\) | −760751. | −0.0350749 | ||||||||
\(861\) | 2.30014e7 | 1.05742 | ||||||||
\(862\) | −3.83074e7 | −1.75596 | ||||||||
\(863\) | −2.59879e7 | −1.18780 | −0.593901 | − | 0.804538i | \(-0.702413\pi\) | ||||
−0.593901 | + | 0.804538i | \(0.702413\pi\) | |||||||
\(864\) | 1.24854e6 | 0.0569006 | ||||||||
\(865\) | −1.19511e7 | −0.543086 | ||||||||
\(866\) | −2.69444e7 | −1.22088 | ||||||||
\(867\) | −4.33955e6 | −0.196063 | ||||||||
\(868\) | 367692. | 0.0165647 | ||||||||
\(869\) | −2.17099e7 | −0.975232 | ||||||||
\(870\) | −7.38974e6 | −0.331002 | ||||||||
\(871\) | −1.34643e6 | −0.0601366 | ||||||||
\(872\) | 2.21857e7 | 0.988055 | ||||||||
\(873\) | −398416. | −0.0176930 | ||||||||
\(874\) | 4.50688e7 | 1.99571 | ||||||||
\(875\) | 1.88030e7 | 0.830246 | ||||||||
\(876\) | 228168. | 0.0100460 | ||||||||
\(877\) | −3.18973e7 | −1.40041 | −0.700204 | − | 0.713943i | \(-0.746907\pi\) | ||||
−0.700204 | + | 0.713943i | \(0.746907\pi\) | |||||||
\(878\) | 1.75126e6 | 0.0766681 | ||||||||
\(879\) | 1.17662e7 | 0.513644 | ||||||||
\(880\) | 9.70007e6 | 0.422249 | ||||||||
\(881\) | 1.48478e7 | 0.644497 | 0.322249 | − | 0.946655i | \(-0.395561\pi\) | ||||
0.322249 | + | 0.946655i | \(0.395561\pi\) | |||||||
\(882\) | 2.42748e6 | 0.105071 | ||||||||
\(883\) | 2.11125e7 | 0.911249 | 0.455625 | − | 0.890172i | \(-0.349416\pi\) | ||||
0.455625 | + | 0.890172i | \(0.349416\pi\) | |||||||
\(884\) | 237440. | 0.0102194 | ||||||||
\(885\) | 678587. | 0.0291237 | ||||||||
\(886\) | 3.55684e7 | 1.52223 | ||||||||
\(887\) | −1.01713e7 | −0.434076 | −0.217038 | − | 0.976163i | \(-0.569640\pi\) | ||||
−0.217038 | + | 0.976163i | \(0.569640\pi\) | |||||||
\(888\) | −1.95344e7 | −0.831318 | ||||||||
\(889\) | −3.82341e7 | −1.62254 | ||||||||
\(890\) | −479233. | −0.0202802 | ||||||||
\(891\) | 3.46286e6 | 0.146130 | ||||||||
\(892\) | −5.94619e6 | −0.250223 | ||||||||
\(893\) | −3.49003e7 | −1.46454 | ||||||||
\(894\) | 5.73834e6 | 0.240128 | ||||||||
\(895\) | −1.59902e7 | −0.667263 | ||||||||
\(896\) | 2.00481e7 | 0.834265 | ||||||||
\(897\) | 1.75860e6 | 0.0729770 | ||||||||
\(898\) | 1.01257e7 | 0.419021 | ||||||||
\(899\) | −3.72715e6 | −0.153807 | ||||||||
\(900\) | 1.02670e6 | 0.0422509 | ||||||||
\(901\) | 3.10625e7 | 1.27475 | ||||||||
\(902\) | 4.68708e7 | 1.91817 | ||||||||
\(903\) | −9.94599e6 | −0.405909 | ||||||||
\(904\) | 1.28801e6 | 0.0524203 | ||||||||
\(905\) | −1.43723e7 | −0.583316 | ||||||||
\(906\) | −2.28093e7 | −0.923191 | ||||||||
\(907\) | −3.32335e7 | −1.34140 | −0.670700 | − | 0.741729i | \(-0.734006\pi\) | ||||
−0.670700 | + | 0.741729i | \(0.734006\pi\) | |||||||
\(908\) | 5.93483e6 | 0.238888 | ||||||||
\(909\) | −1.23693e7 | −0.496520 | ||||||||
\(910\) | −871986. | −0.0349065 | ||||||||
\(911\) | 701228. | 0.0279939 | 0.0139970 | − | 0.999902i | \(-0.495544\pi\) | ||||
0.0139970 | + | 0.999902i | \(0.495544\pi\) | |||||||
\(912\) | −1.73425e7 | −0.690439 | ||||||||
\(913\) | 3.21573e7 | 1.27674 | ||||||||
\(914\) | 2.45531e7 | 0.972166 | ||||||||
\(915\) | −2.70164e6 | −0.106678 | ||||||||
\(916\) | −2.50557e6 | −0.0986661 | ||||||||
\(917\) | −3.69507e7 | −1.45111 | ||||||||
\(918\) | −3.68349e6 | −0.144262 | ||||||||
\(919\) | 1.45028e7 | 0.566451 | 0.283226 | − | 0.959053i | \(-0.408595\pi\) | ||||
0.283226 | + | 0.959053i | \(0.408595\pi\) | |||||||
\(920\) | 1.58067e7 | 0.615702 | ||||||||
\(921\) | −1.90779e7 | −0.741109 | ||||||||
\(922\) | 5.43846e6 | 0.210692 | ||||||||
\(923\) | −2.52897e6 | −0.0977102 | ||||||||
\(924\) | −3.40439e6 | −0.131177 | ||||||||
\(925\) | −3.00422e7 | −1.15446 | ||||||||
\(926\) | 3.50090e6 | 0.134169 | ||||||||
\(927\) | 8.43550e6 | 0.322412 | ||||||||
\(928\) | 1.24422e7 | 0.474273 | ||||||||
\(929\) | −1.70226e7 | −0.647124 | −0.323562 | − | 0.946207i | \(-0.604880\pi\) | ||||
−0.323562 | + | 0.946207i | \(0.604880\pi\) | |||||||
\(930\) | 521863. | 0.0197856 | ||||||||
\(931\) | 1.30433e7 | 0.493188 | ||||||||
\(932\) | −2.52682e6 | −0.0952870 | ||||||||
\(933\) | 2.25052e7 | 0.846406 | ||||||||
\(934\) | −1.14197e7 | −0.428340 | ||||||||
\(935\) | 1.10701e7 | 0.414117 | ||||||||
\(936\) | −798515. | −0.0297916 | ||||||||
\(937\) | −2.02964e7 | −0.755214 | −0.377607 | − | 0.925966i | \(-0.623253\pi\) | ||||
−0.377607 | + | 0.925966i | \(0.623253\pi\) | |||||||
\(938\) | −2.05349e7 | −0.762055 | ||||||||
\(939\) | −2.96929e7 | −1.09898 | ||||||||
\(940\) | −1.58864e6 | −0.0586415 | ||||||||
\(941\) | 4.68227e7 | 1.72378 | 0.861891 | − | 0.507093i | \(-0.169280\pi\) | ||||
0.861891 | + | 0.507093i | \(0.169280\pi\) | |||||||
\(942\) | −2.21693e7 | −0.814000 | ||||||||
\(943\) | 6.47275e7 | 2.37033 | ||||||||
\(944\) | 2.95363e6 | 0.107876 | ||||||||
\(945\) | −2.37117e6 | −0.0863742 | ||||||||
\(946\) | −2.02673e7 | −0.736323 | ||||||||
\(947\) | 1.05919e7 | 0.383793 | 0.191897 | − | 0.981415i | \(-0.438536\pi\) | ||||
0.191897 | + | 0.981415i | \(0.438536\pi\) | |||||||
\(948\) | 1.76681e6 | 0.0638512 | ||||||||
\(949\) | −272916. | −0.00983701 | ||||||||
\(950\) | −3.14720e7 | −1.13140 | ||||||||
\(951\) | −2.48048e6 | −0.0889373 | ||||||||
\(952\) | 2.79018e7 | 0.997793 | ||||||||
\(953\) | 2.94030e7 | 1.04872 | 0.524360 | − | 0.851497i | \(-0.324305\pi\) | ||||
0.524360 | + | 0.851497i | \(0.324305\pi\) | |||||||
\(954\) | −1.35580e7 | −0.482309 | ||||||||
\(955\) | 1.78898e7 | 0.634742 | ||||||||
\(956\) | 2.11552e6 | 0.0748638 | ||||||||
\(957\) | 3.45090e7 | 1.21801 | ||||||||
\(958\) | −2.52288e7 | −0.888141 | ||||||||
\(959\) | 2.56933e7 | 0.902138 | ||||||||
\(960\) | −7.03513e6 | −0.246373 | ||||||||
\(961\) | −2.83659e7 | −0.990806 | ||||||||
\(962\) | 3.03252e6 | 0.105649 | ||||||||
\(963\) | 1.20603e7 | 0.419074 | ||||||||
\(964\) | 258351. | 0.00895402 | ||||||||
\(965\) | 1.29150e7 | 0.446454 | ||||||||
\(966\) | 2.68211e7 | 0.924770 | ||||||||
\(967\) | 4.00215e7 | 1.37635 | 0.688173 | − | 0.725547i | \(-0.258413\pi\) | ||||
0.688173 | + | 0.725547i | \(0.258413\pi\) | |||||||
\(968\) | −2.25488e7 | −0.773455 | ||||||||
\(969\) | −1.97920e7 | −0.677143 | ||||||||
\(970\) | 555922. | 0.0189707 | ||||||||
\(971\) | 3.43019e7 | 1.16753 | 0.583767 | − | 0.811921i | \(-0.301578\pi\) | ||||
0.583767 | + | 0.811921i | \(0.301578\pi\) | |||||||
\(972\) | −281817. | −0.00956757 | ||||||||
\(973\) | −3.85438e7 | −1.30519 | ||||||||
\(974\) | 3.68344e7 | 1.24410 | ||||||||
\(975\) | −1.22805e6 | −0.0413718 | ||||||||
\(976\) | −1.17592e7 | −0.395142 | ||||||||
\(977\) | −5.48788e7 | −1.83937 | −0.919684 | − | 0.392660i | \(-0.871555\pi\) | ||||
−0.919684 | + | 0.392660i | \(0.871555\pi\) | |||||||
\(978\) | 1.19244e7 | 0.398646 | ||||||||
\(979\) | 2.23794e6 | 0.0746264 | ||||||||
\(980\) | 593720. | 0.0197477 | ||||||||
\(981\) | −9.36548e6 | −0.310712 | ||||||||
\(982\) | 1.43404e7 | 0.474549 | ||||||||
\(983\) | 4.78986e7 | 1.58102 | 0.790512 | − | 0.612446i | \(-0.209814\pi\) | ||||
0.790512 | + | 0.612446i | \(0.209814\pi\) | |||||||
\(984\) | −2.93904e7 | −0.967648 | ||||||||
\(985\) | −1.83490e7 | −0.602591 | ||||||||
\(986\) | −3.67076e7 | −1.20244 | ||||||||
\(987\) | −2.07697e7 | −0.678637 | ||||||||
\(988\) | −556858. | −0.0181490 | ||||||||
\(989\) | −2.79887e7 | −0.909896 | ||||||||
\(990\) | −4.83183e6 | −0.156684 | ||||||||
\(991\) | 3.75136e7 | 1.21340 | 0.606702 | − | 0.794930i | \(-0.292492\pi\) | ||||
0.606702 | + | 0.794930i | \(0.292492\pi\) | |||||||
\(992\) | −878669. | −0.0283495 | ||||||||
\(993\) | −2.32216e7 | −0.747340 | ||||||||
\(994\) | −3.85704e7 | −1.23819 | ||||||||
\(995\) | 1.04365e7 | 0.334193 | ||||||||
\(996\) | −2.61705e6 | −0.0835918 | ||||||||
\(997\) | 3.98840e7 | 1.27075 | 0.635375 | − | 0.772203i | \(-0.280845\pi\) | ||||
0.635375 | + | 0.772203i | \(0.280845\pi\) | |||||||
\(998\) | −5.25998e7 | −1.67170 | ||||||||
\(999\) | 8.24626e6 | 0.261423 |
(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 | 177.6.a.c.1.8 | ✓ | 12 | |
3.2 | odd | 2 | 531.6.a.c.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.c.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial | |
531.6.a.c.1.5 | 12 | 3.2 | odd | 2 |