Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,6,Mod(1,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.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: | \(3.52844403589\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{793}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 198 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-13.5801\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 28.5801 | 1.83342 | 0.916708 | − | 0.399558i | \(-0.130836\pi\) | ||||
0.916708 | + | 0.399558i | \(0.130836\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −76.9006 | −1.37564 | −0.687820 | − | 0.725881i | \(-0.741432\pi\) | ||||
−0.687820 | + | 0.725881i | \(0.741432\pi\) | |||||||
\(6\) | 114.321 | 1.29642 | ||||||||
\(7\) | −91.4808 | −0.705642 | −0.352821 | − | 0.935691i | \(-0.614778\pi\) | ||||
−0.352821 | + | 0.935691i | \(0.614778\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 573.824 | 2.36141 | ||||||||
\(10\) | −307.603 | −0.972725 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 457.282 | 0.916708 | ||||||||
\(13\) | −463.801 | −0.761156 | −0.380578 | − | 0.924749i | \(-0.624275\pi\) | ||||
−0.380578 | + | 0.924749i | \(0.624275\pi\) | |||||||
\(14\) | −365.923 | −0.498965 | ||||||||
\(15\) | −2197.83 | −2.52212 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 1641.94 | 1.37795 | 0.688976 | − | 0.724784i | \(-0.258061\pi\) | ||||
0.688976 | + | 0.724784i | \(0.258061\pi\) | |||||||
\(18\) | 2295.29 | 1.66977 | ||||||||
\(19\) | −1693.53 | −1.07624 | −0.538118 | − | 0.842869i | \(-0.680865\pi\) | ||||
−0.538118 | + | 0.842869i | \(0.680865\pi\) | |||||||
\(20\) | −1230.41 | −0.687820 | ||||||||
\(21\) | −2614.53 | −1.29374 | ||||||||
\(22\) | −484.000 | −0.213201 | ||||||||
\(23\) | 75.9391 | 0.0299327 | 0.0149663 | − | 0.999888i | \(-0.495236\pi\) | ||||
0.0149663 | + | 0.999888i | \(0.495236\pi\) | |||||||
\(24\) | 1829.13 | 0.648210 | ||||||||
\(25\) | 2788.71 | 0.892387 | ||||||||
\(26\) | −1855.21 | −0.538218 | ||||||||
\(27\) | 9454.98 | 2.49604 | ||||||||
\(28\) | −1463.69 | −0.352821 | ||||||||
\(29\) | −2942.33 | −0.649675 | −0.324837 | − | 0.945770i | \(-0.605310\pi\) | ||||
−0.324837 | + | 0.945770i | \(0.605310\pi\) | |||||||
\(30\) | −8791.32 | −1.78341 | ||||||||
\(31\) | 8443.63 | 1.57807 | 0.789033 | − | 0.614351i | \(-0.210582\pi\) | ||||
0.789033 | + | 0.614351i | \(0.210582\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −3458.20 | −0.552796 | ||||||||
\(34\) | 6567.74 | 0.974359 | ||||||||
\(35\) | 7034.93 | 0.970710 | ||||||||
\(36\) | 9181.18 | 1.18071 | ||||||||
\(37\) | −35.5610 | −0.00427041 | −0.00213520 | − | 0.999998i | \(-0.500680\pi\) | ||||
−0.00213520 | + | 0.999998i | \(0.500680\pi\) | |||||||
\(38\) | −6774.10 | −0.761014 | ||||||||
\(39\) | −13255.5 | −1.39552 | ||||||||
\(40\) | −4921.64 | −0.486362 | ||||||||
\(41\) | 9222.25 | 0.856796 | 0.428398 | − | 0.903590i | \(-0.359078\pi\) | ||||
0.428398 | + | 0.903590i | \(0.359078\pi\) | |||||||
\(42\) | −10458.1 | −0.914810 | ||||||||
\(43\) | −11516.7 | −0.949851 | −0.474925 | − | 0.880026i | \(-0.657525\pi\) | ||||
−0.474925 | + | 0.880026i | \(0.657525\pi\) | |||||||
\(44\) | −1936.00 | −0.150756 | ||||||||
\(45\) | −44127.4 | −3.24846 | ||||||||
\(46\) | 303.756 | 0.0211656 | ||||||||
\(47\) | 6179.00 | 0.408013 | 0.204006 | − | 0.978970i | \(-0.434604\pi\) | ||||
0.204006 | + | 0.978970i | \(0.434604\pi\) | |||||||
\(48\) | 7316.51 | 0.458354 | ||||||||
\(49\) | −8438.27 | −0.502069 | ||||||||
\(50\) | 11154.8 | 0.631013 | ||||||||
\(51\) | 46926.7 | 2.52636 | ||||||||
\(52\) | −7420.82 | −0.380578 | ||||||||
\(53\) | 25255.1 | 1.23498 | 0.617489 | − | 0.786579i | \(-0.288150\pi\) | ||||
0.617489 | + | 0.786579i | \(0.288150\pi\) | |||||||
\(54\) | 37819.9 | 1.76497 | ||||||||
\(55\) | 9304.98 | 0.414771 | ||||||||
\(56\) | −5854.77 | −0.249482 | ||||||||
\(57\) | −48401.2 | −1.97319 | ||||||||
\(58\) | −11769.3 | −0.459389 | ||||||||
\(59\) | 40786.8 | 1.52542 | 0.762711 | − | 0.646740i | \(-0.223868\pi\) | ||||
0.762711 | + | 0.646740i | \(0.223868\pi\) | |||||||
\(60\) | −35165.3 | −1.26106 | ||||||||
\(61\) | −7368.85 | −0.253557 | −0.126778 | − | 0.991931i | \(-0.540464\pi\) | ||||
−0.126778 | + | 0.991931i | \(0.540464\pi\) | |||||||
\(62\) | 33774.5 | 1.11586 | ||||||||
\(63\) | −52493.8 | −1.66631 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 35666.6 | 1.04708 | ||||||||
\(66\) | −13832.8 | −0.390886 | ||||||||
\(67\) | −11024.7 | −0.300041 | −0.150020 | − | 0.988683i | \(-0.547934\pi\) | ||||
−0.150020 | + | 0.988683i | \(0.547934\pi\) | |||||||
\(68\) | 26271.0 | 0.688976 | ||||||||
\(69\) | 2170.35 | 0.0548791 | ||||||||
\(70\) | 28139.7 | 0.686396 | ||||||||
\(71\) | −46964.9 | −1.10567 | −0.552837 | − | 0.833289i | \(-0.686455\pi\) | ||||
−0.552837 | + | 0.833289i | \(0.686455\pi\) | |||||||
\(72\) | 36724.7 | 0.834886 | ||||||||
\(73\) | −60727.5 | −1.33376 | −0.666880 | − | 0.745165i | \(-0.732371\pi\) | ||||
−0.666880 | + | 0.745165i | \(0.732371\pi\) | |||||||
\(74\) | −142.244 | −0.00301963 | ||||||||
\(75\) | 79701.6 | 1.63612 | ||||||||
\(76\) | −27096.4 | −0.538118 | ||||||||
\(77\) | 11069.2 | 0.212759 | ||||||||
\(78\) | −53022.0 | −0.986778 | ||||||||
\(79\) | 18386.1 | 0.331452 | 0.165726 | − | 0.986172i | \(-0.447003\pi\) | ||||
0.165726 | + | 0.986172i | \(0.447003\pi\) | |||||||
\(80\) | −19686.6 | −0.343910 | ||||||||
\(81\) | 130785. | 2.21486 | ||||||||
\(82\) | 36889.0 | 0.605846 | ||||||||
\(83\) | −59321.9 | −0.945192 | −0.472596 | − | 0.881279i | \(-0.656683\pi\) | ||||
−0.472596 | + | 0.881279i | \(0.656683\pi\) | |||||||
\(84\) | −41832.5 | −0.646868 | ||||||||
\(85\) | −126266. | −1.89557 | ||||||||
\(86\) | −46066.6 | −0.671646 | ||||||||
\(87\) | −84092.1 | −1.19112 | ||||||||
\(88\) | −7744.00 | −0.106600 | ||||||||
\(89\) | 5070.71 | 0.0678568 | 0.0339284 | − | 0.999424i | \(-0.489198\pi\) | ||||
0.0339284 | + | 0.999424i | \(0.489198\pi\) | |||||||
\(90\) | −176510. | −2.29701 | ||||||||
\(91\) | 42428.9 | 0.537104 | ||||||||
\(92\) | 1215.03 | 0.0149663 | ||||||||
\(93\) | 241320. | 2.89325 | ||||||||
\(94\) | 24716.0 | 0.288508 | ||||||||
\(95\) | 130233. | 1.48051 | ||||||||
\(96\) | 29266.1 | 0.324105 | ||||||||
\(97\) | −130795. | −1.41143 | −0.705717 | − | 0.708494i | \(-0.749375\pi\) | ||||
−0.705717 | + | 0.708494i | \(0.749375\pi\) | |||||||
\(98\) | −33753.1 | −0.355016 | ||||||||
\(99\) | −69432.7 | −0.711993 | ||||||||
\(100\) | 44619.3 | 0.446193 | ||||||||
\(101\) | −27114.8 | −0.264486 | −0.132243 | − | 0.991217i | \(-0.542218\pi\) | ||||
−0.132243 | + | 0.991217i | \(0.542218\pi\) | |||||||
\(102\) | 187707. | 1.78640 | ||||||||
\(103\) | −12802.9 | −0.118909 | −0.0594546 | − | 0.998231i | \(-0.518936\pi\) | ||||
−0.0594546 | + | 0.998231i | \(0.518936\pi\) | |||||||
\(104\) | −29683.3 | −0.269109 | ||||||||
\(105\) | 201059. | 1.77972 | ||||||||
\(106\) | 101020. | 0.873261 | ||||||||
\(107\) | −64131.5 | −0.541516 | −0.270758 | − | 0.962647i | \(-0.587274\pi\) | ||||
−0.270758 | + | 0.962647i | \(0.587274\pi\) | |||||||
\(108\) | 151280. | 1.24802 | ||||||||
\(109\) | −126630. | −1.02087 | −0.510434 | − | 0.859917i | \(-0.670515\pi\) | ||||
−0.510434 | + | 0.859917i | \(0.670515\pi\) | |||||||
\(110\) | 37219.9 | 0.293288 | ||||||||
\(111\) | −1016.34 | −0.00782943 | ||||||||
\(112\) | −23419.1 | −0.176411 | ||||||||
\(113\) | 131953. | 0.972130 | 0.486065 | − | 0.873923i | \(-0.338432\pi\) | ||||
0.486065 | + | 0.873923i | \(0.338432\pi\) | |||||||
\(114\) | −193605. | −1.39526 | ||||||||
\(115\) | −5839.77 | −0.0411766 | ||||||||
\(116\) | −47077.2 | −0.324837 | ||||||||
\(117\) | −266140. | −1.79740 | ||||||||
\(118\) | 163147. | 1.07864 | ||||||||
\(119\) | −150206. | −0.972341 | ||||||||
\(120\) | −140661. | −0.891705 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −29475.4 | −0.179292 | ||||||||
\(123\) | 263573. | 1.57086 | ||||||||
\(124\) | 135098. | 0.789033 | ||||||||
\(125\) | 25861.0 | 0.148037 | ||||||||
\(126\) | −209975. | −1.17826 | ||||||||
\(127\) | 118876. | 0.654013 | 0.327006 | − | 0.945022i | \(-0.393960\pi\) | ||||
0.327006 | + | 0.945022i | \(0.393960\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | −329148. | −1.74147 | ||||||||
\(130\) | 142666. | 0.740395 | ||||||||
\(131\) | 205935. | 1.04846 | 0.524229 | − | 0.851577i | \(-0.324353\pi\) | ||||
0.524229 | + | 0.851577i | \(0.324353\pi\) | |||||||
\(132\) | −55331.1 | −0.276398 | ||||||||
\(133\) | 154925. | 0.759438 | ||||||||
\(134\) | −44098.8 | −0.212161 | ||||||||
\(135\) | −727094. | −3.43365 | ||||||||
\(136\) | 105084. | 0.487179 | ||||||||
\(137\) | −196568. | −0.894769 | −0.447385 | − | 0.894342i | \(-0.647645\pi\) | ||||
−0.447385 | + | 0.894342i | \(0.647645\pi\) | |||||||
\(138\) | 8681.40 | 0.0388054 | ||||||||
\(139\) | −29936.4 | −0.131420 | −0.0657102 | − | 0.997839i | \(-0.520931\pi\) | ||||
−0.0657102 | + | 0.997839i | \(0.520931\pi\) | |||||||
\(140\) | 112559. | 0.485355 | ||||||||
\(141\) | 176597. | 0.748057 | ||||||||
\(142\) | −187859. | −0.781830 | ||||||||
\(143\) | 56120.0 | 0.229497 | ||||||||
\(144\) | 146899. | 0.590354 | ||||||||
\(145\) | 226267. | 0.893719 | ||||||||
\(146\) | −242910. | −0.943111 | ||||||||
\(147\) | −241167. | −0.920501 | ||||||||
\(148\) | −568.975 | −0.00213520 | ||||||||
\(149\) | −362800. | −1.33876 | −0.669379 | − | 0.742921i | \(-0.733440\pi\) | ||||
−0.669379 | + | 0.742921i | \(0.733440\pi\) | |||||||
\(150\) | 318807. | 1.15691 | ||||||||
\(151\) | 226244. | 0.807485 | 0.403742 | − | 0.914873i | \(-0.367709\pi\) | ||||
0.403742 | + | 0.914873i | \(0.367709\pi\) | |||||||
\(152\) | −108386. | −0.380507 | ||||||||
\(153\) | 942182. | 3.25391 | ||||||||
\(154\) | 44276.7 | 0.150443 | ||||||||
\(155\) | −649321. | −2.17085 | ||||||||
\(156\) | −212088. | −0.697758 | ||||||||
\(157\) | 392007. | 1.26924 | 0.634621 | − | 0.772824i | \(-0.281156\pi\) | ||||
0.634621 | + | 0.772824i | \(0.281156\pi\) | |||||||
\(158\) | 73544.2 | 0.234372 | ||||||||
\(159\) | 721794. | 2.26423 | ||||||||
\(160\) | −78746.3 | −0.243181 | ||||||||
\(161\) | −6946.97 | −0.0211218 | ||||||||
\(162\) | 523142. | 1.56615 | ||||||||
\(163\) | −84380.4 | −0.248755 | −0.124378 | − | 0.992235i | \(-0.539693\pi\) | ||||
−0.124378 | + | 0.992235i | \(0.539693\pi\) | |||||||
\(164\) | 147556. | 0.428398 | ||||||||
\(165\) | 265937. | 0.760448 | ||||||||
\(166\) | −237288. | −0.668352 | ||||||||
\(167\) | 543654. | 1.50845 | 0.754226 | − | 0.656615i | \(-0.228012\pi\) | ||||
0.754226 | + | 0.656615i | \(0.228012\pi\) | |||||||
\(168\) | −167330. | −0.457405 | ||||||||
\(169\) | −156181. | −0.420642 | ||||||||
\(170\) | −505064. | −1.34037 | ||||||||
\(171\) | −971785. | −2.54144 | ||||||||
\(172\) | −184267. | −0.474925 | ||||||||
\(173\) | 356699. | 0.906123 | 0.453061 | − | 0.891479i | \(-0.350332\pi\) | ||||
0.453061 | + | 0.891479i | \(0.350332\pi\) | |||||||
\(174\) | −336368. | −0.842252 | ||||||||
\(175\) | −255113. | −0.629706 | ||||||||
\(176\) | −30976.0 | −0.0753778 | ||||||||
\(177\) | 1.16569e6 | 2.79673 | ||||||||
\(178\) | 20282.8 | 0.0479820 | ||||||||
\(179\) | −521697. | −1.21699 | −0.608493 | − | 0.793559i | \(-0.708226\pi\) | ||||
−0.608493 | + | 0.793559i | \(0.708226\pi\) | |||||||
\(180\) | −706039. | −1.62423 | ||||||||
\(181\) | −698048. | −1.58376 | −0.791879 | − | 0.610678i | \(-0.790897\pi\) | ||||
−0.791879 | + | 0.610678i | \(0.790897\pi\) | |||||||
\(182\) | 169716. | 0.379790 | ||||||||
\(183\) | −210603. | −0.464875 | ||||||||
\(184\) | 4860.10 | 0.0105828 | ||||||||
\(185\) | 2734.66 | 0.00587454 | ||||||||
\(186\) | 965280. | 2.04584 | ||||||||
\(187\) | −198674. | −0.415468 | ||||||||
\(188\) | 98864.0 | 0.204006 | ||||||||
\(189\) | −864949. | −1.76131 | ||||||||
\(190\) | 520933. | 1.04688 | ||||||||
\(191\) | 612931. | 1.21571 | 0.607853 | − | 0.794050i | \(-0.292031\pi\) | ||||
0.607853 | + | 0.794050i | \(0.292031\pi\) | |||||||
\(192\) | 117064. | 0.229177 | ||||||||
\(193\) | −184465. | −0.356467 | −0.178234 | − | 0.983988i | \(-0.557038\pi\) | ||||
−0.178234 | + | 0.983988i | \(0.557038\pi\) | |||||||
\(194\) | −523178. | −0.998034 | ||||||||
\(195\) | 1.01936e6 | 1.91973 | ||||||||
\(196\) | −135012. | −0.251034 | ||||||||
\(197\) | −1.03211e6 | −1.89479 | −0.947393 | − | 0.320074i | \(-0.896292\pi\) | ||||
−0.947393 | + | 0.320074i | \(0.896292\pi\) | |||||||
\(198\) | −277731. | −0.503455 | ||||||||
\(199\) | 244463. | 0.437603 | 0.218801 | − | 0.975769i | \(-0.429785\pi\) | ||||
0.218801 | + | 0.975769i | \(0.429785\pi\) | |||||||
\(200\) | 178477. | 0.315506 | ||||||||
\(201\) | −315088. | −0.550099 | ||||||||
\(202\) | −108459. | −0.187020 | ||||||||
\(203\) | 269166. | 0.458438 | ||||||||
\(204\) | 750828. | 1.26318 | ||||||||
\(205\) | −709197. | −1.17864 | ||||||||
\(206\) | −51211.6 | −0.0840814 | ||||||||
\(207\) | 43575.7 | 0.0706835 | ||||||||
\(208\) | −118733. | −0.190289 | ||||||||
\(209\) | 204917. | 0.324498 | ||||||||
\(210\) | 804237. | 1.25845 | ||||||||
\(211\) | 1.12590e6 | 1.74098 | 0.870488 | − | 0.492190i | \(-0.163803\pi\) | ||||
0.870488 | + | 0.492190i | \(0.163803\pi\) | |||||||
\(212\) | 404081. | 0.617489 | ||||||||
\(213\) | −1.34226e6 | −2.02716 | ||||||||
\(214\) | −256526. | −0.382910 | ||||||||
\(215\) | 885639. | 1.30665 | ||||||||
\(216\) | 605119. | 0.882483 | ||||||||
\(217\) | −772430. | −1.11355 | ||||||||
\(218\) | −506519. | −0.721863 | ||||||||
\(219\) | −1.73560e6 | −2.44534 | ||||||||
\(220\) | 148880. | 0.207386 | ||||||||
\(221\) | −761532. | −1.04884 | ||||||||
\(222\) | −4065.35 | −0.00553624 | ||||||||
\(223\) | 72016.8 | 0.0969776 | 0.0484888 | − | 0.998824i | \(-0.484559\pi\) | ||||
0.0484888 | + | 0.998824i | \(0.484559\pi\) | |||||||
\(224\) | −93676.3 | −0.124741 | ||||||||
\(225\) | 1.60023e6 | 2.10729 | ||||||||
\(226\) | 527813. | 0.687400 | ||||||||
\(227\) | 1.13240e6 | 1.45860 | 0.729298 | − | 0.684196i | \(-0.239847\pi\) | ||||
0.729298 | + | 0.684196i | \(0.239847\pi\) | |||||||
\(228\) | −774419. | −0.986595 | ||||||||
\(229\) | −34423.7 | −0.0433779 | −0.0216890 | − | 0.999765i | \(-0.506904\pi\) | ||||
−0.0216890 | + | 0.999765i | \(0.506904\pi\) | |||||||
\(230\) | −23359.1 | −0.0291163 | ||||||||
\(231\) | 316358. | 0.390076 | ||||||||
\(232\) | −188309. | −0.229695 | ||||||||
\(233\) | 689707. | 0.832290 | 0.416145 | − | 0.909298i | \(-0.363381\pi\) | ||||
0.416145 | + | 0.909298i | \(0.363381\pi\) | |||||||
\(234\) | −1.06456e6 | −1.27096 | ||||||||
\(235\) | −475169. | −0.561279 | ||||||||
\(236\) | 652589. | 0.762711 | ||||||||
\(237\) | 525476. | 0.607690 | ||||||||
\(238\) | −600822. | −0.687549 | ||||||||
\(239\) | 289978. | 0.328375 | 0.164188 | − | 0.986429i | \(-0.447500\pi\) | ||||
0.164188 | + | 0.986429i | \(0.447500\pi\) | |||||||
\(240\) | −562645. | −0.630530 | ||||||||
\(241\) | 1.40673e6 | 1.56016 | 0.780078 | − | 0.625682i | \(-0.215179\pi\) | ||||
0.780078 | + | 0.625682i | \(0.215179\pi\) | |||||||
\(242\) | 58564.0 | 0.0642824 | ||||||||
\(243\) | 1.44030e6 | 1.56473 | ||||||||
\(244\) | −117902. | −0.126778 | ||||||||
\(245\) | 648908. | 0.690666 | ||||||||
\(246\) | 1.05429e6 | 1.11077 | ||||||||
\(247\) | 785459. | 0.819184 | ||||||||
\(248\) | 540392. | 0.557930 | ||||||||
\(249\) | −1.69543e6 | −1.73293 | ||||||||
\(250\) | 103444. | 0.104678 | ||||||||
\(251\) | 580131. | 0.581222 | 0.290611 | − | 0.956841i | \(-0.406141\pi\) | ||||
0.290611 | + | 0.956841i | \(0.406141\pi\) | |||||||
\(252\) | −839901. | −0.833157 | ||||||||
\(253\) | −9188.63 | −0.00902505 | ||||||||
\(254\) | 475505. | 0.462457 | ||||||||
\(255\) | −3.60870e6 | −3.47536 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −407104. | −0.384479 | −0.192240 | − | 0.981348i | \(-0.561575\pi\) | ||||
−0.192240 | + | 0.981348i | \(0.561575\pi\) | |||||||
\(258\) | −1.31659e6 | −1.23141 | ||||||||
\(259\) | 3253.14 | 0.00301338 | ||||||||
\(260\) | 570666. | 0.523538 | ||||||||
\(261\) | −1.68838e6 | −1.53415 | ||||||||
\(262\) | 823739. | 0.741372 | ||||||||
\(263\) | −1.57675e6 | −1.40564 | −0.702819 | − | 0.711369i | \(-0.748076\pi\) | ||||
−0.702819 | + | 0.711369i | \(0.748076\pi\) | |||||||
\(264\) | −221325. | −0.195443 | ||||||||
\(265\) | −1.94213e6 | −1.69889 | ||||||||
\(266\) | 619700. | 0.537004 | ||||||||
\(267\) | 144921. | 0.124410 | ||||||||
\(268\) | −176395. | −0.150020 | ||||||||
\(269\) | −752593. | −0.634132 | −0.317066 | − | 0.948404i | \(-0.602698\pi\) | ||||
−0.317066 | + | 0.948404i | \(0.602698\pi\) | |||||||
\(270\) | −2.90838e6 | −2.42796 | ||||||||
\(271\) | −208553. | −0.172501 | −0.0862507 | − | 0.996273i | \(-0.527489\pi\) | ||||
−0.0862507 | + | 0.996273i | \(0.527489\pi\) | |||||||
\(272\) | 420336. | 0.344488 | ||||||||
\(273\) | 1.21262e6 | 0.984735 | ||||||||
\(274\) | −786272. | −0.632698 | ||||||||
\(275\) | −337434. | −0.269065 | ||||||||
\(276\) | 34725.6 | 0.0274395 | ||||||||
\(277\) | 1.01926e6 | 0.798151 | 0.399075 | − | 0.916918i | \(-0.369331\pi\) | ||||
0.399075 | + | 0.916918i | \(0.369331\pi\) | |||||||
\(278\) | −119746. | −0.0929282 | ||||||||
\(279\) | 4.84516e6 | 3.72647 | ||||||||
\(280\) | 450235. | 0.343198 | ||||||||
\(281\) | 865597. | 0.653958 | 0.326979 | − | 0.945032i | \(-0.393969\pi\) | ||||
0.326979 | + | 0.945032i | \(0.393969\pi\) | |||||||
\(282\) | 706386. | 0.528956 | ||||||||
\(283\) | 1.72508e6 | 1.28040 | 0.640198 | − | 0.768210i | \(-0.278852\pi\) | ||||
0.640198 | + | 0.768210i | \(0.278852\pi\) | |||||||
\(284\) | −751438. | −0.552837 | ||||||||
\(285\) | 3.72208e6 | 2.71440 | ||||||||
\(286\) | 224480. | 0.162279 | ||||||||
\(287\) | −843658. | −0.604591 | ||||||||
\(288\) | 587595. | 0.417443 | ||||||||
\(289\) | 1.27610e6 | 0.898750 | ||||||||
\(290\) | 905067. | 0.631955 | ||||||||
\(291\) | −3.73813e6 | −2.58774 | ||||||||
\(292\) | −971639. | −0.666880 | ||||||||
\(293\) | 1.25254e6 | 0.852361 | 0.426181 | − | 0.904638i | \(-0.359859\pi\) | ||||
0.426181 | + | 0.904638i | \(0.359859\pi\) | |||||||
\(294\) | −964667. | −0.650892 | ||||||||
\(295\) | −3.13653e6 | −2.09843 | ||||||||
\(296\) | −2275.90 | −0.00150982 | ||||||||
\(297\) | −1.14405e6 | −0.752584 | ||||||||
\(298\) | −1.45120e6 | −0.946645 | ||||||||
\(299\) | −35220.7 | −0.0227834 | ||||||||
\(300\) | 1.27523e6 | 0.818058 | ||||||||
\(301\) | 1.05355e6 | 0.670255 | ||||||||
\(302\) | 904975. | 0.570978 | ||||||||
\(303\) | −774945. | −0.484914 | ||||||||
\(304\) | −433543. | −0.269059 | ||||||||
\(305\) | 566669. | 0.348803 | ||||||||
\(306\) | 3.76873e6 | 2.30086 | ||||||||
\(307\) | 2.69819e6 | 1.63390 | 0.816951 | − | 0.576707i | \(-0.195663\pi\) | ||||
0.816951 | + | 0.576707i | \(0.195663\pi\) | |||||||
\(308\) | 177107. | 0.106380 | ||||||||
\(309\) | −365908. | −0.218010 | ||||||||
\(310\) | −2.59728e6 | −1.53502 | ||||||||
\(311\) | −1.74373e6 | −1.02230 | −0.511150 | − | 0.859491i | \(-0.670780\pi\) | ||||
−0.511150 | + | 0.859491i | \(0.670780\pi\) | |||||||
\(312\) | −848352. | −0.493389 | ||||||||
\(313\) | −1.15038e6 | −0.663714 | −0.331857 | − | 0.943330i | \(-0.607675\pi\) | ||||
−0.331857 | + | 0.943330i | \(0.607675\pi\) | |||||||
\(314\) | 1.56803e6 | 0.897489 | ||||||||
\(315\) | 4.03681e6 | 2.29225 | ||||||||
\(316\) | 294177. | 0.165726 | ||||||||
\(317\) | −1.16110e6 | −0.648967 | −0.324484 | − | 0.945891i | \(-0.605190\pi\) | ||||
−0.324484 | + | 0.945891i | \(0.605190\pi\) | |||||||
\(318\) | 2.88717e6 | 1.60105 | ||||||||
\(319\) | 356022. | 0.195884 | ||||||||
\(320\) | −314985. | −0.171955 | ||||||||
\(321\) | −1.83289e6 | −0.992825 | ||||||||
\(322\) | −27787.9 | −0.0149354 | ||||||||
\(323\) | −2.78066e6 | −1.48300 | ||||||||
\(324\) | 2.09257e6 | 1.10743 | ||||||||
\(325\) | −1.29341e6 | −0.679245 | ||||||||
\(326\) | −337522. | −0.175897 | ||||||||
\(327\) | −3.61910e6 | −1.87168 | ||||||||
\(328\) | 590224. | 0.302923 | ||||||||
\(329\) | −565260. | −0.287911 | ||||||||
\(330\) | 1.06375e6 | 0.537718 | ||||||||
\(331\) | −2.31915e6 | −1.16348 | −0.581740 | − | 0.813375i | \(-0.697628\pi\) | ||||
−0.581740 | + | 0.813375i | \(0.697628\pi\) | |||||||
\(332\) | −949151. | −0.472596 | ||||||||
\(333\) | −20405.7 | −0.0100842 | ||||||||
\(334\) | 2.17462e6 | 1.06664 | ||||||||
\(335\) | 847807. | 0.412748 | ||||||||
\(336\) | −669320. | −0.323434 | ||||||||
\(337\) | 1.43786e6 | 0.689671 | 0.344835 | − | 0.938663i | \(-0.387935\pi\) | ||||
0.344835 | + | 0.938663i | \(0.387935\pi\) | |||||||
\(338\) | −624725. | −0.297439 | ||||||||
\(339\) | 3.77124e6 | 1.78232 | ||||||||
\(340\) | −2.02025e6 | −0.947783 | ||||||||
\(341\) | −1.02168e6 | −0.475805 | ||||||||
\(342\) | −3.88714e6 | −1.79707 | ||||||||
\(343\) | 2.30946e6 | 1.05992 | ||||||||
\(344\) | −737066. | −0.335823 | ||||||||
\(345\) | −166901. | −0.0754939 | ||||||||
\(346\) | 1.42680e6 | 0.640726 | ||||||||
\(347\) | 575629. | 0.256637 | 0.128318 | − | 0.991733i | \(-0.459042\pi\) | ||||
0.128318 | + | 0.991733i | \(0.459042\pi\) | |||||||
\(348\) | −1.34547e6 | −0.595562 | ||||||||
\(349\) | −2.77702e6 | −1.22044 | −0.610219 | − | 0.792233i | \(-0.708919\pi\) | ||||
−0.610219 | + | 0.792233i | \(0.708919\pi\) | |||||||
\(350\) | −1.02045e6 | −0.445269 | ||||||||
\(351\) | −4.38523e6 | −1.89987 | ||||||||
\(352\) | −123904. | −0.0533002 | ||||||||
\(353\) | 2.18172e6 | 0.931885 | 0.465942 | − | 0.884815i | \(-0.345715\pi\) | ||||
0.465942 | + | 0.884815i | \(0.345715\pi\) | |||||||
\(354\) | 4.66277e6 | 1.97759 | ||||||||
\(355\) | 3.61163e6 | 1.52101 | ||||||||
\(356\) | 81131.3 | 0.0339284 | ||||||||
\(357\) | −4.29289e6 | −1.78271 | ||||||||
\(358\) | −2.08679e6 | −0.860539 | ||||||||
\(359\) | −2.14848e6 | −0.879822 | −0.439911 | − | 0.898041i | \(-0.644990\pi\) | ||||
−0.439911 | + | 0.898041i | \(0.644990\pi\) | |||||||
\(360\) | −2.82415e6 | −1.14850 | ||||||||
\(361\) | 391930. | 0.158285 | ||||||||
\(362\) | −2.79219e6 | −1.11989 | ||||||||
\(363\) | 418442. | 0.166674 | ||||||||
\(364\) | 678862. | 0.268552 | ||||||||
\(365\) | 4.66998e6 | 1.83478 | ||||||||
\(366\) | −842411. | −0.328716 | ||||||||
\(367\) | 15838.0 | 0.00613813 | 0.00306907 | − | 0.999995i | \(-0.499023\pi\) | ||||
0.00306907 | + | 0.999995i | \(0.499023\pi\) | |||||||
\(368\) | 19440.4 | 0.00748317 | ||||||||
\(369\) | 5.29195e6 | 2.02325 | ||||||||
\(370\) | 10938.6 | 0.00415393 | ||||||||
\(371\) | −2.31035e6 | −0.871453 | ||||||||
\(372\) | 3.86112e6 | 1.44663 | ||||||||
\(373\) | −394343. | −0.146758 | −0.0733791 | − | 0.997304i | \(-0.523378\pi\) | ||||
−0.0733791 | + | 0.997304i | \(0.523378\pi\) | |||||||
\(374\) | −794697. | −0.293780 | ||||||||
\(375\) | 739112. | 0.271414 | ||||||||
\(376\) | 395456. | 0.144254 | ||||||||
\(377\) | 1.36465e6 | 0.494504 | ||||||||
\(378\) | −3.45980e6 | −1.24544 | ||||||||
\(379\) | 1.68501e6 | 0.602567 | 0.301283 | − | 0.953535i | \(-0.402585\pi\) | ||||
0.301283 | + | 0.953535i | \(0.402585\pi\) | |||||||
\(380\) | 2.08373e6 | 0.740257 | ||||||||
\(381\) | 3.39750e6 | 1.19908 | ||||||||
\(382\) | 2.45172e6 | 0.859633 | ||||||||
\(383\) | 3.94284e6 | 1.37345 | 0.686724 | − | 0.726918i | \(-0.259048\pi\) | ||||
0.686724 | + | 0.726918i | \(0.259048\pi\) | |||||||
\(384\) | 468257. | 0.162053 | ||||||||
\(385\) | −851226. | −0.292680 | ||||||||
\(386\) | −737859. | −0.252061 | ||||||||
\(387\) | −6.60853e6 | −2.24299 | ||||||||
\(388\) | −2.09271e6 | −0.705717 | ||||||||
\(389\) | −571118. | −0.191360 | −0.0956801 | − | 0.995412i | \(-0.530503\pi\) | ||||
−0.0956801 | + | 0.995412i | \(0.530503\pi\) | |||||||
\(390\) | 4.07743e6 | 1.35745 | ||||||||
\(391\) | 124687. | 0.0412458 | ||||||||
\(392\) | −540049. | −0.177508 | ||||||||
\(393\) | 5.88564e6 | 1.92226 | ||||||||
\(394\) | −4.12844e6 | −1.33982 | ||||||||
\(395\) | −1.41390e6 | −0.455959 | ||||||||
\(396\) | −1.11092e6 | −0.355997 | ||||||||
\(397\) | 6.17025e6 | 1.96484 | 0.982419 | − | 0.186689i | \(-0.0597756\pi\) | ||||
0.982419 | + | 0.186689i | \(0.0597756\pi\) | |||||||
\(398\) | 977851. | 0.309432 | ||||||||
\(399\) | 4.42778e6 | 1.39237 | ||||||||
\(400\) | 713909. | 0.223097 | ||||||||
\(401\) | 1.82838e6 | 0.567814 | 0.283907 | − | 0.958852i | \(-0.408369\pi\) | ||||
0.283907 | + | 0.958852i | \(0.408369\pi\) | |||||||
\(402\) | −1.26035e6 | −0.388979 | ||||||||
\(403\) | −3.91617e6 | −1.20115 | ||||||||
\(404\) | −433837. | −0.132243 | ||||||||
\(405\) | −1.00575e7 | −3.04686 | ||||||||
\(406\) | 1.07667e6 | 0.324165 | ||||||||
\(407\) | 4302.88 | 0.00128758 | ||||||||
\(408\) | 3.00331e6 | 0.893202 | ||||||||
\(409\) | −5.94235e6 | −1.75651 | −0.878254 | − | 0.478195i | \(-0.841291\pi\) | ||||
−0.878254 | + | 0.478195i | \(0.841291\pi\) | |||||||
\(410\) | −2.83679e6 | −0.833426 | ||||||||
\(411\) | −5.61794e6 | −1.64048 | ||||||||
\(412\) | −204846. | −0.0594546 | ||||||||
\(413\) | −3.73121e6 | −1.07640 | ||||||||
\(414\) | 174303. | 0.0499808 | ||||||||
\(415\) | 4.56189e6 | 1.30024 | ||||||||
\(416\) | −474933. | −0.134555 | ||||||||
\(417\) | −855586. | −0.240948 | ||||||||
\(418\) | 819666. | 0.229454 | ||||||||
\(419\) | −2.80473e6 | −0.780468 | −0.390234 | − | 0.920716i | \(-0.627606\pi\) | ||||
−0.390234 | + | 0.920716i | \(0.627606\pi\) | |||||||
\(420\) | 3.21695e6 | 0.889858 | ||||||||
\(421\) | 3.57571e6 | 0.983234 | 0.491617 | − | 0.870812i | \(-0.336406\pi\) | ||||
0.491617 | + | 0.870812i | \(0.336406\pi\) | |||||||
\(422\) | 4.50359e6 | 1.23106 | ||||||||
\(423\) | 3.54566e6 | 0.963487 | ||||||||
\(424\) | 1.61633e6 | 0.436631 | ||||||||
\(425\) | 4.57888e6 | 1.22967 | ||||||||
\(426\) | −5.36905e6 | −1.43342 | ||||||||
\(427\) | 674108. | 0.178920 | ||||||||
\(428\) | −1.02610e6 | −0.270758 | ||||||||
\(429\) | 1.60392e6 | 0.420764 | ||||||||
\(430\) | 3.54255e6 | 0.923943 | ||||||||
\(431\) | −2.82711e6 | −0.733078 | −0.366539 | − | 0.930403i | \(-0.619457\pi\) | ||||
−0.366539 | + | 0.930403i | \(0.619457\pi\) | |||||||
\(432\) | 2.42048e6 | 0.624010 | ||||||||
\(433\) | −765652. | −0.196251 | −0.0981254 | − | 0.995174i | \(-0.531285\pi\) | ||||
−0.0981254 | + | 0.995174i | \(0.531285\pi\) | |||||||
\(434\) | −3.08972e6 | −0.787399 | ||||||||
\(435\) | 6.46673e6 | 1.63856 | ||||||||
\(436\) | −2.02608e6 | −0.510434 | ||||||||
\(437\) | −128605. | −0.0322147 | ||||||||
\(438\) | −6.94239e6 | −1.72912 | ||||||||
\(439\) | 4.65788e6 | 1.15352 | 0.576762 | − | 0.816912i | \(-0.304316\pi\) | ||||
0.576762 | + | 0.816912i | \(0.304316\pi\) | |||||||
\(440\) | 595519. | 0.146644 | ||||||||
\(441\) | −4.84208e6 | −1.18559 | ||||||||
\(442\) | −3.04613e6 | −0.741639 | ||||||||
\(443\) | −4.99700e6 | −1.20976 | −0.604881 | − | 0.796316i | \(-0.706779\pi\) | ||||
−0.604881 | + | 0.796316i | \(0.706779\pi\) | |||||||
\(444\) | −16261.4 | −0.00391471 | ||||||||
\(445\) | −389941. | −0.0933466 | ||||||||
\(446\) | 288067. | 0.0685735 | ||||||||
\(447\) | −1.03689e7 | −2.45450 | ||||||||
\(448\) | −374705. | −0.0882053 | ||||||||
\(449\) | 165769. | 0.0388050 | 0.0194025 | − | 0.999812i | \(-0.493824\pi\) | ||||
0.0194025 | + | 0.999812i | \(0.493824\pi\) | |||||||
\(450\) | 6.40091e6 | 1.49008 | ||||||||
\(451\) | −1.11589e6 | −0.258334 | ||||||||
\(452\) | 2.11125e6 | 0.486065 | ||||||||
\(453\) | 6.46608e6 | 1.48046 | ||||||||
\(454\) | 4.52960e6 | 1.03138 | ||||||||
\(455\) | −3.26281e6 | −0.738862 | ||||||||
\(456\) | −3.09768e6 | −0.697628 | ||||||||
\(457\) | −8.07259e6 | −1.80810 | −0.904050 | − | 0.427428i | \(-0.859420\pi\) | ||||
−0.904050 | + | 0.427428i | \(0.859420\pi\) | |||||||
\(458\) | −137695. | −0.0306728 | ||||||||
\(459\) | 1.55245e7 | 3.43942 | ||||||||
\(460\) | −93436.3 | −0.0205883 | ||||||||
\(461\) | −5.87512e6 | −1.28755 | −0.643776 | − | 0.765214i | \(-0.722633\pi\) | ||||
−0.643776 | + | 0.765214i | \(0.722633\pi\) | |||||||
\(462\) | 1.26543e6 | 0.275825 | ||||||||
\(463\) | −1.02289e6 | −0.221757 | −0.110878 | − | 0.993834i | \(-0.535366\pi\) | ||||
−0.110878 | + | 0.993834i | \(0.535366\pi\) | |||||||
\(464\) | −753236. | −0.162419 | ||||||||
\(465\) | −1.85577e7 | −3.98007 | ||||||||
\(466\) | 2.75883e6 | 0.588518 | ||||||||
\(467\) | −6.17201e6 | −1.30959 | −0.654794 | − | 0.755807i | \(-0.727245\pi\) | ||||
−0.654794 | + | 0.755807i | \(0.727245\pi\) | |||||||
\(468\) | −4.25824e6 | −0.898702 | ||||||||
\(469\) | 1.00855e6 | 0.211721 | ||||||||
\(470\) | −1.90068e6 | −0.396884 | ||||||||
\(471\) | 1.12036e7 | 2.32705 | ||||||||
\(472\) | 2.61036e6 | 0.539318 | ||||||||
\(473\) | 1.39352e6 | 0.286391 | ||||||||
\(474\) | 2.10190e6 | 0.429702 | ||||||||
\(475\) | −4.72275e6 | −0.960419 | ||||||||
\(476\) | −2.40329e6 | −0.486170 | ||||||||
\(477\) | 1.44920e7 | 2.91629 | ||||||||
\(478\) | 1.15991e6 | 0.232196 | ||||||||
\(479\) | −7.00244e6 | −1.39447 | −0.697237 | − | 0.716841i | \(-0.745588\pi\) | ||||
−0.697237 | + | 0.716841i | \(0.745588\pi\) | |||||||
\(480\) | −2.25058e6 | −0.445852 | ||||||||
\(481\) | 16493.2 | 0.00325044 | ||||||||
\(482\) | 5.62692e6 | 1.10320 | ||||||||
\(483\) | −198545. | −0.0387250 | ||||||||
\(484\) | 234256. | 0.0454545 | ||||||||
\(485\) | 1.00582e7 | 1.94163 | ||||||||
\(486\) | 5.76122e6 | 1.10643 | ||||||||
\(487\) | 365769. | 0.0698852 | 0.0349426 | − | 0.999389i | \(-0.488875\pi\) | ||||
0.0349426 | + | 0.999389i | \(0.488875\pi\) | |||||||
\(488\) | −471607. | −0.0896459 | ||||||||
\(489\) | −2.41160e6 | −0.456072 | ||||||||
\(490\) | 2.59563e6 | 0.488375 | ||||||||
\(491\) | 5.00170e6 | 0.936297 | 0.468149 | − | 0.883650i | \(-0.344921\pi\) | ||||
0.468149 | + | 0.883650i | \(0.344921\pi\) | |||||||
\(492\) | 4.21717e6 | 0.785431 | ||||||||
\(493\) | −4.83111e6 | −0.895220 | ||||||||
\(494\) | 3.14184e6 | 0.579250 | ||||||||
\(495\) | 5.33942e6 | 0.979447 | ||||||||
\(496\) | 2.16157e6 | 0.394516 | ||||||||
\(497\) | 4.29638e6 | 0.780211 | ||||||||
\(498\) | −6.78171e6 | −1.22537 | ||||||||
\(499\) | −1.63517e6 | −0.293976 | −0.146988 | − | 0.989138i | \(-0.546958\pi\) | ||||
−0.146988 | + | 0.989138i | \(0.546958\pi\) | |||||||
\(500\) | 413777. | 0.0740186 | ||||||||
\(501\) | 1.55377e7 | 2.76562 | ||||||||
\(502\) | 2.32053e6 | 0.410986 | ||||||||
\(503\) | 5.20393e6 | 0.917088 | 0.458544 | − | 0.888672i | \(-0.348371\pi\) | ||||
0.458544 | + | 0.888672i | \(0.348371\pi\) | |||||||
\(504\) | −3.35961e6 | −0.589131 | ||||||||
\(505\) | 2.08515e6 | 0.363838 | ||||||||
\(506\) | −36754.5 | −0.00638167 | ||||||||
\(507\) | −4.46368e6 | −0.771212 | ||||||||
\(508\) | 1.90202e6 | 0.327006 | ||||||||
\(509\) | −8.62390e6 | −1.47540 | −0.737699 | − | 0.675130i | \(-0.764088\pi\) | ||||
−0.737699 | + | 0.675130i | \(0.764088\pi\) | |||||||
\(510\) | −1.44348e7 | −2.45745 | ||||||||
\(511\) | 5.55539e6 | 0.941158 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −1.60123e7 | −2.68633 | ||||||||
\(514\) | −1.62842e6 | −0.271868 | ||||||||
\(515\) | 984551. | 0.163576 | ||||||||
\(516\) | −5.26636e6 | −0.870736 | ||||||||
\(517\) | −747659. | −0.123020 | ||||||||
\(518\) | 13012.6 | 0.00213078 | ||||||||
\(519\) | 1.01945e7 | 1.66130 | ||||||||
\(520\) | 2.28266e6 | 0.370198 | ||||||||
\(521\) | 140764. | 0.0227194 | 0.0113597 | − | 0.999935i | \(-0.496384\pi\) | ||||
0.0113597 | + | 0.999935i | \(0.496384\pi\) | |||||||
\(522\) | −6.75351e6 | −1.08481 | ||||||||
\(523\) | −9.29900e6 | −1.48656 | −0.743279 | − | 0.668981i | \(-0.766731\pi\) | ||||
−0.743279 | + | 0.668981i | \(0.766731\pi\) | |||||||
\(524\) | 3.29496e6 | 0.524229 | ||||||||
\(525\) | −7.29117e6 | −1.15451 | ||||||||
\(526\) | −6.30700e6 | −0.993936 | ||||||||
\(527\) | 1.38639e7 | 2.17450 | ||||||||
\(528\) | −885298. | −0.138199 | ||||||||
\(529\) | −6.43058e6 | −0.999104 | ||||||||
\(530\) | −7.76853e6 | −1.20129 | ||||||||
\(531\) | 2.34044e7 | 3.60215 | ||||||||
\(532\) | 2.47880e6 | 0.379719 | ||||||||
\(533\) | −4.27729e6 | −0.652155 | ||||||||
\(534\) | 579686. | 0.0879710 | ||||||||
\(535\) | 4.93175e6 | 0.744932 | ||||||||
\(536\) | −705581. | −0.106080 | ||||||||
\(537\) | −1.49102e7 | −2.23124 | ||||||||
\(538\) | −3.01037e6 | −0.448399 | ||||||||
\(539\) | 1.02103e6 | 0.151379 | ||||||||
\(540\) | −1.16335e7 | −1.71683 | ||||||||
\(541\) | −4.98590e6 | −0.732403 | −0.366202 | − | 0.930536i | \(-0.619342\pi\) | ||||
−0.366202 | + | 0.930536i | \(0.619342\pi\) | |||||||
\(542\) | −834211. | −0.121977 | ||||||||
\(543\) | −1.99503e7 | −2.90369 | ||||||||
\(544\) | 1.68134e6 | 0.243590 | ||||||||
\(545\) | 9.73792e6 | 1.40435 | ||||||||
\(546\) | 4.85049e6 | 0.696313 | ||||||||
\(547\) | −3.57048e6 | −0.510221 | −0.255111 | − | 0.966912i | \(-0.582112\pi\) | ||||
−0.255111 | + | 0.966912i | \(0.582112\pi\) | |||||||
\(548\) | −3.14509e6 | −0.447385 | ||||||||
\(549\) | −4.22842e6 | −0.598753 | ||||||||
\(550\) | −1.34973e6 | −0.190257 | ||||||||
\(551\) | 4.98291e6 | 0.699204 | ||||||||
\(552\) | 138902. | 0.0194027 | ||||||||
\(553\) | −1.68197e6 | −0.233887 | ||||||||
\(554\) | 4.07703e6 | 0.564378 | ||||||||
\(555\) | 78156.9 | 0.0107705 | ||||||||
\(556\) | −478983. | −0.0657102 | ||||||||
\(557\) | 1.24799e7 | 1.70441 | 0.852206 | − | 0.523207i | \(-0.175264\pi\) | ||||
0.852206 | + | 0.523207i | \(0.175264\pi\) | |||||||
\(558\) | 1.93806e7 | 2.63501 | ||||||||
\(559\) | 5.34144e6 | 0.722984 | ||||||||
\(560\) | 1.80094e6 | 0.242678 | ||||||||
\(561\) | −5.67814e6 | −0.761726 | ||||||||
\(562\) | 3.46239e6 | 0.462418 | ||||||||
\(563\) | −5.12581e6 | −0.681540 | −0.340770 | − | 0.940147i | \(-0.610688\pi\) | ||||
−0.340770 | + | 0.940147i | \(0.610688\pi\) | |||||||
\(564\) | 2.82555e6 | 0.374028 | ||||||||
\(565\) | −1.01473e7 | −1.33730 | ||||||||
\(566\) | 6.90033e6 | 0.905376 | ||||||||
\(567\) | −1.19644e7 | −1.56290 | ||||||||
\(568\) | −3.00575e6 | −0.390915 | ||||||||
\(569\) | −1.09610e6 | −0.141929 | −0.0709645 | − | 0.997479i | \(-0.522608\pi\) | ||||
−0.0709645 | + | 0.997479i | \(0.522608\pi\) | |||||||
\(570\) | 1.48883e7 | 1.91937 | ||||||||
\(571\) | −1.08787e7 | −1.39632 | −0.698162 | − | 0.715940i | \(-0.745998\pi\) | ||||
−0.698162 | + | 0.715940i | \(0.745998\pi\) | |||||||
\(572\) | 897919. | 0.114749 | ||||||||
\(573\) | 1.75176e7 | 2.22889 | ||||||||
\(574\) | −3.37463e6 | −0.427511 | ||||||||
\(575\) | 211772. | 0.0267115 | ||||||||
\(576\) | 2.35038e6 | 0.295177 | ||||||||
\(577\) | 1.37408e7 | 1.71820 | 0.859101 | − | 0.511807i | \(-0.171024\pi\) | ||||
0.859101 | + | 0.511807i | \(0.171024\pi\) | |||||||
\(578\) | 5.10439e6 | 0.635512 | ||||||||
\(579\) | −5.27202e6 | −0.653553 | ||||||||
\(580\) | 3.62027e6 | 0.446859 | ||||||||
\(581\) | 5.42681e6 | 0.666967 | ||||||||
\(582\) | −1.49525e7 | −1.82981 | ||||||||
\(583\) | −3.05587e6 | −0.372360 | ||||||||
\(584\) | −3.88656e6 | −0.471556 | ||||||||
\(585\) | 2.04663e7 | 2.47258 | ||||||||
\(586\) | 5.01017e6 | 0.602711 | ||||||||
\(587\) | 7.50167e6 | 0.898593 | 0.449296 | − | 0.893383i | \(-0.351675\pi\) | ||||
0.449296 | + | 0.893383i | \(0.351675\pi\) | |||||||
\(588\) | −3.85867e6 | −0.460250 | ||||||||
\(589\) | −1.42995e7 | −1.69837 | ||||||||
\(590\) | −1.25461e7 | −1.48381 | ||||||||
\(591\) | −2.94978e7 | −3.47393 | ||||||||
\(592\) | −9103.60 | −0.00106760 | ||||||||
\(593\) | 1.23281e7 | 1.43966 | 0.719829 | − | 0.694151i | \(-0.244220\pi\) | ||||
0.719829 | + | 0.694151i | \(0.244220\pi\) | |||||||
\(594\) | −4.57621e6 | −0.532157 | ||||||||
\(595\) | 1.15509e7 | 1.33759 | ||||||||
\(596\) | −5.80481e6 | −0.669379 | ||||||||
\(597\) | 6.98677e6 | 0.802308 | ||||||||
\(598\) | −140883. | −0.0161103 | ||||||||
\(599\) | 3.71959e6 | 0.423573 | 0.211786 | − | 0.977316i | \(-0.432072\pi\) | ||||
0.211786 | + | 0.977316i | \(0.432072\pi\) | |||||||
\(600\) | 5.10090e6 | 0.578454 | ||||||||
\(601\) | −8.89207e6 | −1.00419 | −0.502096 | − | 0.864812i | \(-0.667437\pi\) | ||||
−0.502096 | + | 0.864812i | \(0.667437\pi\) | |||||||
\(602\) | 4.21421e6 | 0.473942 | ||||||||
\(603\) | −6.32624e6 | −0.708520 | ||||||||
\(604\) | 3.61990e6 | 0.403742 | ||||||||
\(605\) | −1.12590e6 | −0.125058 | ||||||||
\(606\) | −3.09978e6 | −0.342886 | ||||||||
\(607\) | 1.18740e7 | 1.30805 | 0.654027 | − | 0.756471i | \(-0.273078\pi\) | ||||
0.654027 | + | 0.756471i | \(0.273078\pi\) | |||||||
\(608\) | −1.73417e6 | −0.190254 | ||||||||
\(609\) | 7.69281e6 | 0.840508 | ||||||||
\(610\) | 2.26668e6 | 0.246641 | ||||||||
\(611\) | −2.86583e6 | −0.310561 | ||||||||
\(612\) | 1.50749e7 | 1.62696 | ||||||||
\(613\) | 9.08062e6 | 0.976033 | 0.488016 | − | 0.872834i | \(-0.337721\pi\) | ||||
0.488016 | + | 0.872834i | \(0.337721\pi\) | |||||||
\(614\) | 1.07927e7 | 1.15534 | ||||||||
\(615\) | −2.02689e7 | −2.16094 | ||||||||
\(616\) | 708427. | 0.0752217 | ||||||||
\(617\) | −9.98190e6 | −1.05560 | −0.527801 | − | 0.849368i | \(-0.676983\pi\) | ||||
−0.527801 | + | 0.849368i | \(0.676983\pi\) | |||||||
\(618\) | −1.46363e6 | −0.154156 | ||||||||
\(619\) | −3.86586e6 | −0.405527 | −0.202763 | − | 0.979228i | \(-0.564992\pi\) | ||||
−0.202763 | + | 0.979228i | \(0.564992\pi\) | |||||||
\(620\) | −1.03891e7 | −1.08543 | ||||||||
\(621\) | 718003. | 0.0747132 | ||||||||
\(622\) | −6.97492e6 | −0.722876 | ||||||||
\(623\) | −463872. | −0.0478827 | ||||||||
\(624\) | −3.39341e6 | −0.348879 | ||||||||
\(625\) | −1.07034e7 | −1.09603 | ||||||||
\(626\) | −4.60152e6 | −0.469316 | ||||||||
\(627\) | 5.85654e6 | 0.594939 | ||||||||
\(628\) | 6.27211e6 | 0.634621 | ||||||||
\(629\) | −58388.8 | −0.00588441 | ||||||||
\(630\) | 1.61472e7 | 1.62087 | ||||||||
\(631\) | 1.45626e7 | 1.45601 | 0.728007 | − | 0.685570i | \(-0.240447\pi\) | ||||
0.728007 | + | 0.685570i | \(0.240447\pi\) | |||||||
\(632\) | 1.17671e6 | 0.117186 | ||||||||
\(633\) | 3.21783e7 | 3.19193 | ||||||||
\(634\) | −4.64441e6 | −0.458889 | ||||||||
\(635\) | −9.14167e6 | −0.899686 | ||||||||
\(636\) | 1.15487e7 | 1.13211 | ||||||||
\(637\) | 3.91368e6 | 0.382153 | ||||||||
\(638\) | 1.42409e6 | 0.138511 | ||||||||
\(639\) | −2.69496e7 | −2.61096 | ||||||||
\(640\) | −1.25994e6 | −0.121591 | ||||||||
\(641\) | −1.34201e7 | −1.29006 | −0.645032 | − | 0.764155i | \(-0.723156\pi\) | ||||
−0.645032 | + | 0.764155i | \(0.723156\pi\) | |||||||
\(642\) | −7.33154e6 | −0.702033 | ||||||||
\(643\) | 1.50895e7 | 1.43929 | 0.719644 | − | 0.694344i | \(-0.244305\pi\) | ||||
0.719644 | + | 0.694344i | \(0.244305\pi\) | |||||||
\(644\) | −111151. | −0.0105609 | ||||||||
\(645\) | 2.53117e7 | 2.39564 | ||||||||
\(646\) | −1.11226e7 | −1.04864 | ||||||||
\(647\) | 1.42974e7 | 1.34275 | 0.671377 | − | 0.741116i | \(-0.265703\pi\) | ||||
0.671377 | + | 0.741116i | \(0.265703\pi\) | |||||||
\(648\) | 8.37027e6 | 0.783073 | ||||||||
\(649\) | −4.93520e6 | −0.459932 | ||||||||
\(650\) | −5.17363e6 | −0.480299 | ||||||||
\(651\) | −2.20761e7 | −2.04160 | ||||||||
\(652\) | −1.35009e6 | −0.124378 | ||||||||
\(653\) | −1.31607e6 | −0.120780 | −0.0603900 | − | 0.998175i | \(-0.519234\pi\) | ||||
−0.0603900 | + | 0.998175i | \(0.519234\pi\) | |||||||
\(654\) | −1.44764e7 | −1.32348 | ||||||||
\(655\) | −1.58365e7 | −1.44230 | ||||||||
\(656\) | 2.36090e6 | 0.214199 | ||||||||
\(657\) | −3.48469e7 | −3.14956 | ||||||||
\(658\) | −2.26104e6 | −0.203584 | ||||||||
\(659\) | 3.75917e6 | 0.337193 | 0.168596 | − | 0.985685i | \(-0.446077\pi\) | ||||
0.168596 | + | 0.985685i | \(0.446077\pi\) | |||||||
\(660\) | 4.25500e6 | 0.380224 | ||||||||
\(661\) | −8.95170e6 | −0.796896 | −0.398448 | − | 0.917191i | \(-0.630451\pi\) | ||||
−0.398448 | + | 0.917191i | \(0.630451\pi\) | |||||||
\(662\) | −9.27660e6 | −0.822705 | ||||||||
\(663\) | −2.17647e7 | −1.92295 | ||||||||
\(664\) | −3.79660e6 | −0.334176 | ||||||||
\(665\) | −1.19138e7 | −1.04471 | ||||||||
\(666\) | −81622.9 | −0.00713060 | ||||||||
\(667\) | −223438. | −0.0194465 | ||||||||
\(668\) | 8.69847e6 | 0.754226 | ||||||||
\(669\) | 2.05825e6 | 0.177800 | ||||||||
\(670\) | 3.39123e6 | 0.291857 | ||||||||
\(671\) | 891631. | 0.0764503 | ||||||||
\(672\) | −2.67728e6 | −0.228702 | ||||||||
\(673\) | −519050. | −0.0441745 | −0.0220873 | − | 0.999756i | \(-0.507031\pi\) | ||||
−0.0220873 | + | 0.999756i | \(0.507031\pi\) | |||||||
\(674\) | 5.75144e6 | 0.487671 | ||||||||
\(675\) | 2.63672e7 | 2.22743 | ||||||||
\(676\) | −2.49890e6 | −0.210321 | ||||||||
\(677\) | −4.12272e6 | −0.345711 | −0.172855 | − | 0.984947i | \(-0.555299\pi\) | ||||
−0.172855 | + | 0.984947i | \(0.555299\pi\) | |||||||
\(678\) | 1.50850e7 | 1.26029 | ||||||||
\(679\) | 1.19652e7 | 0.995967 | ||||||||
\(680\) | −8.08102e6 | −0.670184 | ||||||||
\(681\) | 3.23641e7 | 2.67421 | ||||||||
\(682\) | −4.08672e6 | −0.336445 | ||||||||
\(683\) | 8.35625e6 | 0.685425 | 0.342712 | − | 0.939440i | \(-0.388654\pi\) | ||||
0.342712 | + | 0.939440i | \(0.388654\pi\) | |||||||
\(684\) | −1.55486e7 | −1.27072 | ||||||||
\(685\) | 1.51162e7 | 1.23088 | ||||||||
\(686\) | 9.23783e6 | 0.749479 | ||||||||
\(687\) | −983834. | −0.0795298 | ||||||||
\(688\) | −2.94826e6 | −0.237463 | ||||||||
\(689\) | −1.17133e7 | −0.940011 | ||||||||
\(690\) | −667605. | −0.0533822 | ||||||||
\(691\) | 9.40353e6 | 0.749197 | 0.374598 | − | 0.927187i | \(-0.377781\pi\) | ||||
0.374598 | + | 0.927187i | \(0.377781\pi\) | |||||||
\(692\) | 5.70719e6 | 0.453061 | ||||||||
\(693\) | 6.35175e6 | 0.502413 | ||||||||
\(694\) | 2.30252e6 | 0.181470 | ||||||||
\(695\) | 2.30213e6 | 0.180787 | ||||||||
\(696\) | −5.38189e6 | −0.421126 | ||||||||
\(697\) | 1.51423e7 | 1.18062 | ||||||||
\(698\) | −1.11081e7 | −0.862980 | ||||||||
\(699\) | 1.97119e7 | 1.52593 | ||||||||
\(700\) | −4.08181e6 | −0.314853 | ||||||||
\(701\) | −1.76888e7 | −1.35957 | −0.679787 | − | 0.733410i | \(-0.737928\pi\) | ||||
−0.679787 | + | 0.733410i | \(0.737928\pi\) | |||||||
\(702\) | −1.75409e7 | −1.34341 | ||||||||
\(703\) | 60223.4 | 0.00459597 | ||||||||
\(704\) | −495616. | −0.0376889 | ||||||||
\(705\) | −1.35804e7 | −1.02906 | ||||||||
\(706\) | 8.72688e6 | 0.658942 | ||||||||
\(707\) | 2.48049e6 | 0.186633 | ||||||||
\(708\) | 1.86511e7 | 1.39837 | ||||||||
\(709\) | −1.11343e7 | −0.831853 | −0.415926 | − | 0.909398i | \(-0.636543\pi\) | ||||
−0.415926 | + | 0.909398i | \(0.636543\pi\) | |||||||
\(710\) | 1.44465e7 | 1.07552 | ||||||||
\(711\) | 1.05504e7 | 0.782696 | ||||||||
\(712\) | 324525. | 0.0239910 | ||||||||
\(713\) | 641202. | 0.0472358 | ||||||||
\(714\) | −1.71716e7 | −1.26056 | ||||||||
\(715\) | −4.31566e6 | −0.315706 | ||||||||
\(716\) | −8.34715e6 | −0.608493 | ||||||||
\(717\) | 8.28761e6 | 0.602048 | ||||||||
\(718\) | −8.59391e6 | −0.622128 | ||||||||
\(719\) | −9.55010e6 | −0.688947 | −0.344474 | − | 0.938796i | \(-0.611943\pi\) | ||||
−0.344474 | + | 0.938796i | \(0.611943\pi\) | |||||||
\(720\) | −1.12966e7 | −0.812114 | ||||||||
\(721\) | 1.17122e6 | 0.0839073 | ||||||||
\(722\) | 1.56772e6 | 0.111925 | ||||||||
\(723\) | 4.02045e7 | 2.86042 | ||||||||
\(724\) | −1.11688e7 | −0.791879 | ||||||||
\(725\) | −8.20529e6 | −0.579761 | ||||||||
\(726\) | 1.67377e6 | 0.117856 | ||||||||
\(727\) | −1.89994e7 | −1.33322 | −0.666612 | − | 0.745405i | \(-0.732256\pi\) | ||||
−0.666612 | + | 0.745405i | \(0.732256\pi\) | |||||||
\(728\) | 2.71545e6 | 0.189895 | ||||||||
\(729\) | 9.38322e6 | 0.653933 | ||||||||
\(730\) | 1.86799e7 | 1.29738 | ||||||||
\(731\) | −1.89096e7 | −1.30885 | ||||||||
\(732\) | −3.36964e6 | −0.232438 | ||||||||
\(733\) | −2.68111e7 | −1.84312 | −0.921561 | − | 0.388233i | \(-0.873086\pi\) | ||||
−0.921561 | + | 0.388233i | \(0.873086\pi\) | |||||||
\(734\) | 63352.2 | 0.00434032 | ||||||||
\(735\) | 1.85459e7 | 1.26628 | ||||||||
\(736\) | 77761.6 | 0.00529140 | ||||||||
\(737\) | 1.33399e6 | 0.0904657 | ||||||||
\(738\) | 2.11678e7 | 1.43065 | ||||||||
\(739\) | −6.41899e6 | −0.432370 | −0.216185 | − | 0.976352i | \(-0.569361\pi\) | ||||
−0.216185 | + | 0.976352i | \(0.569361\pi\) | |||||||
\(740\) | 43754.6 | 0.00293727 | ||||||||
\(741\) | 2.24485e7 | 1.50190 | ||||||||
\(742\) | −9.24142e6 | −0.616210 | ||||||||
\(743\) | 4.66177e6 | 0.309798 | 0.154899 | − | 0.987930i | \(-0.450495\pi\) | ||||
0.154899 | + | 0.987930i | \(0.450495\pi\) | |||||||
\(744\) | 1.54445e7 | 1.02292 | ||||||||
\(745\) | 2.78996e7 | 1.84165 | ||||||||
\(746\) | −1.57737e6 | −0.103774 | ||||||||
\(747\) | −3.40403e7 | −2.23199 | ||||||||
\(748\) | −3.17879e6 | −0.207734 | ||||||||
\(749\) | 5.86679e6 | 0.382117 | ||||||||
\(750\) | 2.95645e6 | 0.191919 | ||||||||
\(751\) | 2.39792e7 | 1.55144 | 0.775721 | − | 0.631076i | \(-0.217386\pi\) | ||||
0.775721 | + | 0.631076i | \(0.217386\pi\) | |||||||
\(752\) | 1.58182e6 | 0.102003 | ||||||||
\(753\) | 1.65802e7 | 1.06562 | ||||||||
\(754\) | 5.45862e6 | 0.349667 | ||||||||
\(755\) | −1.73983e7 | −1.11081 | ||||||||
\(756\) | −1.38392e7 | −0.880656 | ||||||||
\(757\) | 4.65197e6 | 0.295051 | 0.147526 | − | 0.989058i | \(-0.452869\pi\) | ||||
0.147526 | + | 0.989058i | \(0.452869\pi\) | |||||||
\(758\) | 6.74005e6 | 0.426079 | ||||||||
\(759\) | −262612. | −0.0165467 | ||||||||
\(760\) | 8.33492e6 | 0.523441 | ||||||||
\(761\) | −1.91952e7 | −1.20152 | −0.600760 | − | 0.799429i | \(-0.705135\pi\) | ||||
−0.600760 | + | 0.799429i | \(0.705135\pi\) | |||||||
\(762\) | 1.35900e7 | 0.847876 | ||||||||
\(763\) | 1.15842e7 | 0.720368 | ||||||||
\(764\) | 9.80690e6 | 0.607853 | ||||||||
\(765\) | −7.24544e7 | −4.47622 | ||||||||
\(766\) | 1.57714e7 | 0.971175 | ||||||||
\(767\) | −1.89170e7 | −1.16108 | ||||||||
\(768\) | 1.87303e6 | 0.114589 | ||||||||
\(769\) | 1.47548e7 | 0.899743 | 0.449871 | − | 0.893093i | \(-0.351470\pi\) | ||||
0.449871 | + | 0.893093i | \(0.351470\pi\) | |||||||
\(770\) | −3.40491e6 | −0.206956 | ||||||||
\(771\) | −1.16351e7 | −0.704910 | ||||||||
\(772\) | −2.95143e6 | −0.178234 | ||||||||
\(773\) | 1.48823e7 | 0.895820 | 0.447910 | − | 0.894079i | \(-0.352169\pi\) | ||||
0.447910 | + | 0.894079i | \(0.352169\pi\) | |||||||
\(774\) | −2.64341e7 | −1.58603 | ||||||||
\(775\) | 2.35468e7 | 1.40824 | ||||||||
\(776\) | −8.37085e6 | −0.499017 | ||||||||
\(777\) | 92975.2 | 0.00552478 | ||||||||
\(778\) | −2.28447e6 | −0.135312 | ||||||||
\(779\) | −1.56181e7 | −0.922115 | ||||||||
\(780\) | 1.63097e7 | 0.959864 | ||||||||
\(781\) | 5.68275e6 | 0.333373 | ||||||||
\(782\) | 498749. | 0.0291652 | ||||||||
\(783\) | −2.78197e7 | −1.62161 | ||||||||
\(784\) | −2.16020e6 | −0.125517 | ||||||||
\(785\) | −3.01456e7 | −1.74602 | ||||||||
\(786\) | 2.35426e7 | 1.35924 | ||||||||
\(787\) | 1.56041e7 | 0.898054 | 0.449027 | − | 0.893518i | \(-0.351771\pi\) | ||||
0.449027 | + | 0.893518i | \(0.351771\pi\) | |||||||
\(788\) | −1.65137e7 | −0.947393 | ||||||||
\(789\) | −4.50637e7 | −2.57712 | ||||||||
\(790\) | −5.65560e6 | −0.322412 | ||||||||
\(791\) | −1.20712e7 | −0.685976 | ||||||||
\(792\) | −4.44369e6 | −0.251728 | ||||||||
\(793\) | 3.41768e6 | 0.192996 | ||||||||
\(794\) | 2.46810e7 | 1.38935 | ||||||||
\(795\) | −5.55064e7 | −3.11476 | ||||||||
\(796\) | 3.91140e6 | 0.218801 | ||||||||
\(797\) | 2.19852e7 | 1.22599 | 0.612993 | − | 0.790088i | \(-0.289965\pi\) | ||||
0.612993 | + | 0.790088i | \(0.289965\pi\) | |||||||
\(798\) | 1.77111e7 | 0.984552 | ||||||||
\(799\) | 1.01455e7 | 0.562221 | ||||||||
\(800\) | 2.85564e6 | 0.157753 | ||||||||
\(801\) | 2.90969e6 | 0.160238 | ||||||||
\(802\) | 7.31353e6 | 0.401505 | ||||||||
\(803\) | 7.34802e6 | 0.402144 | ||||||||
\(804\) | −5.04140e6 | −0.275050 | ||||||||
\(805\) | 534226. | 0.0290560 | ||||||||
\(806\) | −1.56647e7 | −0.849344 | ||||||||
\(807\) | −2.15092e7 | −1.16263 | ||||||||
\(808\) | −1.73535e6 | −0.0935101 | ||||||||
\(809\) | 2.91738e7 | 1.56719 | 0.783596 | − | 0.621271i | \(-0.213383\pi\) | ||||
0.783596 | + | 0.621271i | \(0.213383\pi\) | |||||||
\(810\) | −4.02299e7 | −2.15445 | ||||||||
\(811\) | 2.59750e7 | 1.38677 | 0.693383 | − | 0.720569i | \(-0.256119\pi\) | ||||
0.693383 | + | 0.720569i | \(0.256119\pi\) | |||||||
\(812\) | 4.30666e6 | 0.229219 | ||||||||
\(813\) | −5.96046e6 | −0.316267 | ||||||||
\(814\) | 17211.5 | 0.000910453 0 | ||||||||
\(815\) | 6.48891e6 | 0.342198 | ||||||||
\(816\) | 1.20132e7 | 0.631590 | ||||||||
\(817\) | 1.95038e7 | 1.02226 | ||||||||
\(818\) | −2.37694e7 | −1.24204 | ||||||||
\(819\) | 2.43467e7 | 1.26832 | ||||||||
\(820\) | −1.13472e7 | −0.589321 | ||||||||
\(821\) | 3.42686e7 | 1.77435 | 0.887174 | − | 0.461436i | \(-0.152666\pi\) | ||||
0.887174 | + | 0.461436i | \(0.152666\pi\) | |||||||
\(822\) | −2.24717e7 | −1.16000 | ||||||||
\(823\) | −2.37132e7 | −1.22037 | −0.610184 | − | 0.792259i | \(-0.708905\pi\) | ||||
−0.610184 | + | 0.792259i | \(0.708905\pi\) | |||||||
\(824\) | −819385. | −0.0420407 | ||||||||
\(825\) | −9.64390e6 | −0.493308 | ||||||||
\(826\) | −1.49248e7 | −0.761131 | ||||||||
\(827\) | 1.83274e7 | 0.931833 | 0.465916 | − | 0.884829i | \(-0.345725\pi\) | ||||
0.465916 | + | 0.884829i | \(0.345725\pi\) | |||||||
\(828\) | 697211. | 0.0353418 | ||||||||
\(829\) | −2.66383e7 | −1.34623 | −0.673115 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673115 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(830\) | 1.82476e7 | 0.919411 | ||||||||
\(831\) | 2.91305e7 | 1.46334 | ||||||||
\(832\) | −1.89973e6 | −0.0951445 | ||||||||
\(833\) | −1.38551e7 | −0.691826 | ||||||||
\(834\) | −3.42235e6 | −0.170376 | ||||||||
\(835\) | −4.18074e7 | −2.07509 | ||||||||
\(836\) | 3.27867e6 | 0.162249 | ||||||||
\(837\) | 7.98344e7 | 3.93891 | ||||||||
\(838\) | −1.12189e7 | −0.551874 | ||||||||
\(839\) | 1.46709e7 | 0.719537 | 0.359768 | − | 0.933042i | \(-0.382856\pi\) | ||||
0.359768 | + | 0.933042i | \(0.382856\pi\) | |||||||
\(840\) | 1.28678e7 | 0.629225 | ||||||||
\(841\) | −1.18539e7 | −0.577923 | ||||||||
\(842\) | 1.43028e7 | 0.695251 | ||||||||
\(843\) | 2.47389e7 | 1.19898 | ||||||||
\(844\) | 1.80144e7 | 0.870488 | ||||||||
\(845\) | 1.20104e7 | 0.578652 | ||||||||
\(846\) | 1.41826e7 | 0.681288 | ||||||||
\(847\) | −1.33937e6 | −0.0641493 | ||||||||
\(848\) | 6.46530e6 | 0.308745 | ||||||||
\(849\) | 4.93031e7 | 2.34750 | ||||||||
\(850\) | 1.83155e7 | 0.869505 | ||||||||
\(851\) | −2700.47 | −0.000127825 0 | ||||||||
\(852\) | −2.14762e7 | −1.01358 | ||||||||
\(853\) | −1.74709e7 | −0.822133 | −0.411066 | − | 0.911605i | \(-0.634844\pi\) | ||||
−0.411066 | + | 0.911605i | \(0.634844\pi\) | |||||||
\(854\) | 2.69643e6 | 0.126516 | ||||||||
\(855\) | 7.47309e7 | 3.49611 | ||||||||
\(856\) | −4.10441e6 | −0.191455 | ||||||||
\(857\) | −2.49580e7 | −1.16080 | −0.580402 | − | 0.814330i | \(-0.697104\pi\) | ||||
−0.580402 | + | 0.814330i | \(0.697104\pi\) | |||||||
\(858\) | 6.41566e6 | 0.297525 | ||||||||
\(859\) | −1.42612e7 | −0.659439 | −0.329719 | − | 0.944079i | \(-0.606954\pi\) | ||||
−0.329719 | + | 0.944079i | \(0.606954\pi\) | |||||||
\(860\) | 1.41702e7 | 0.653327 | ||||||||
\(861\) | −2.41119e7 | −1.10847 | ||||||||
\(862\) | −1.13085e7 | −0.518364 | ||||||||
\(863\) | 494514. | 0.0226022 | 0.0113011 | − | 0.999936i | \(-0.496403\pi\) | ||||
0.0113011 | + | 0.999936i | \(0.496403\pi\) | |||||||
\(864\) | 9.68190e6 | 0.441242 | ||||||||
\(865\) | −2.74304e7 | −1.24650 | ||||||||
\(866\) | −3.06261e6 | −0.138770 | ||||||||
\(867\) | 3.64710e7 | 1.64778 | ||||||||
\(868\) | −1.23589e7 | −0.556775 | ||||||||
\(869\) | −2.22471e6 | −0.0999366 | ||||||||
\(870\) | 2.58669e7 | 1.15864 | ||||||||
\(871\) | 5.11327e6 | 0.228378 | ||||||||
\(872\) | −8.10431e6 | −0.360932 | ||||||||
\(873\) | −7.50530e7 | −3.33298 | ||||||||
\(874\) | −514419. | −0.0227792 | ||||||||
\(875\) | −2.36579e6 | −0.104461 | ||||||||
\(876\) | −2.77696e7 | −1.22267 | ||||||||
\(877\) | −8.07539e6 | −0.354539 | −0.177270 | − | 0.984162i | \(-0.556726\pi\) | ||||
−0.177270 | + | 0.984162i | \(0.556726\pi\) | |||||||
\(878\) | 1.86315e7 | 0.815665 | ||||||||
\(879\) | 3.57979e7 | 1.56273 | ||||||||
\(880\) | 2.38207e6 | 0.103693 | ||||||||
\(881\) | −5.24166e6 | −0.227525 | −0.113763 | − | 0.993508i | \(-0.536290\pi\) | ||||
−0.113763 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(882\) | −1.93683e7 | −0.838340 | ||||||||
\(883\) | −4.02805e7 | −1.73857 | −0.869287 | − | 0.494308i | \(-0.835422\pi\) | ||||
−0.869287 | + | 0.494308i | \(0.835422\pi\) | |||||||
\(884\) | −1.21845e7 | −0.524418 | ||||||||
\(885\) | −8.96425e7 | −3.84730 | ||||||||
\(886\) | −1.99880e7 | −0.855431 | ||||||||
\(887\) | 1.38423e7 | 0.590745 | 0.295373 | − | 0.955382i | \(-0.404556\pi\) | ||||
0.295373 | + | 0.955382i | \(0.404556\pi\) | |||||||
\(888\) | −65045.5 | −0.00276812 | ||||||||
\(889\) | −1.08749e7 | −0.461499 | ||||||||
\(890\) | −1.55976e6 | −0.0660060 | ||||||||
\(891\) | −1.58250e7 | −0.667807 | ||||||||
\(892\) | 1.15227e6 | 0.0484888 | ||||||||
\(893\) | −1.04643e7 | −0.439118 | ||||||||
\(894\) | −4.14755e7 | −1.73559 | ||||||||
\(895\) | 4.01188e7 | 1.67413 | ||||||||
\(896\) | −1.49882e6 | −0.0623706 | ||||||||
\(897\) | −1.00661e6 | −0.0417715 | ||||||||
\(898\) | 663076. | 0.0274393 | ||||||||
\(899\) | −2.48439e7 | −1.02523 | ||||||||
\(900\) | 2.56036e7 | 1.05365 | ||||||||
\(901\) | 4.14672e7 | 1.70174 | ||||||||
\(902\) | −4.46357e6 | −0.182669 | ||||||||
\(903\) | 3.01107e7 | 1.22886 | ||||||||
\(904\) | 8.44501e6 | 0.343700 | ||||||||
\(905\) | 5.36803e7 | 2.17868 | ||||||||
\(906\) | 2.58643e7 | 1.04684 | ||||||||
\(907\) | −5.53908e6 | −0.223573 | −0.111786 | − | 0.993732i | \(-0.535657\pi\) | ||||
−0.111786 | + | 0.993732i | \(0.535657\pi\) | |||||||
\(908\) | 1.81184e7 | 0.729298 | ||||||||
\(909\) | −1.55591e7 | −0.624562 | ||||||||
\(910\) | −1.30512e7 | −0.522454 | ||||||||
\(911\) | −1.76513e7 | −0.704660 | −0.352330 | − | 0.935876i | \(-0.614611\pi\) | ||||
−0.352330 | + | 0.935876i | \(0.614611\pi\) | |||||||
\(912\) | −1.23907e7 | −0.493297 | ||||||||
\(913\) | 7.17795e6 | 0.284986 | ||||||||
\(914\) | −3.22903e7 | −1.27852 | ||||||||
\(915\) | 1.61955e7 | 0.639501 | ||||||||
\(916\) | −550779. | −0.0216890 | ||||||||
\(917\) | −1.88391e7 | −0.739837 | ||||||||
\(918\) | 6.20979e7 | 2.43204 | ||||||||
\(919\) | −2.80718e7 | −1.09643 | −0.548215 | − | 0.836338i | \(-0.684692\pi\) | ||||
−0.548215 | + | 0.836338i | \(0.684692\pi\) | |||||||
\(920\) | −373745. | −0.0145581 | ||||||||
\(921\) | 7.71145e7 | 2.99562 | ||||||||
\(922\) | −2.35005e7 | −0.910436 | ||||||||
\(923\) | 2.17824e7 | 0.841591 | ||||||||
\(924\) | 5.06173e6 | 0.195038 | ||||||||
\(925\) | −99169.1 | −0.00381085 | ||||||||
\(926\) | −4.09156e6 | −0.156806 | ||||||||
\(927\) | −7.34660e6 | −0.280794 | ||||||||
\(928\) | −3.01294e6 | −0.114847 | ||||||||
\(929\) | −3.51046e6 | −0.133452 | −0.0667259 | − | 0.997771i | \(-0.521255\pi\) | ||||
−0.0667259 | + | 0.997771i | \(0.521255\pi\) | |||||||
\(930\) | −7.42307e7 | −2.81434 | ||||||||
\(931\) | 1.42904e7 | 0.540345 | ||||||||
\(932\) | 1.10353e7 | 0.416145 | ||||||||
\(933\) | −4.98361e7 | −1.87430 | ||||||||
\(934\) | −2.46881e7 | −0.926019 | ||||||||
\(935\) | 1.52782e7 | 0.571535 | ||||||||
\(936\) | −1.70330e7 | −0.635478 | ||||||||
\(937\) | −3.60265e7 | −1.34052 | −0.670260 | − | 0.742126i | \(-0.733818\pi\) | ||||
−0.670260 | + | 0.742126i | \(0.733818\pi\) | |||||||
\(938\) | 4.03420e6 | 0.149710 | ||||||||
\(939\) | −3.28780e7 | −1.21686 | ||||||||
\(940\) | −7.60270e6 | −0.280639 | ||||||||
\(941\) | 2.51917e7 | 0.927435 | 0.463717 | − | 0.885983i | \(-0.346515\pi\) | ||||
0.463717 | + | 0.885983i | \(0.346515\pi\) | |||||||
\(942\) | 4.48144e7 | 1.64547 | ||||||||
\(943\) | 700329. | 0.0256462 | ||||||||
\(944\) | 1.04414e7 | 0.381355 | ||||||||
\(945\) | 6.65151e7 | 2.42293 | ||||||||
\(946\) | 5.57406e6 | 0.202509 | ||||||||
\(947\) | 2.44815e6 | 0.0887082 | 0.0443541 | − | 0.999016i | \(-0.485877\pi\) | ||||
0.0443541 | + | 0.999016i | \(0.485877\pi\) | |||||||
\(948\) | 8.40761e6 | 0.303845 | ||||||||
\(949\) | 2.81655e7 | 1.01520 | ||||||||
\(950\) | −1.88910e7 | −0.679119 | ||||||||
\(951\) | −3.31845e7 | −1.18983 | ||||||||
\(952\) | −9.61316e6 | −0.343774 | ||||||||
\(953\) | −4.51778e7 | −1.61136 | −0.805681 | − | 0.592349i | \(-0.798200\pi\) | ||||
−0.805681 | + | 0.592349i | \(0.798200\pi\) | |||||||
\(954\) | 5.79679e7 | 2.06213 | ||||||||
\(955\) | −4.71348e7 | −1.67237 | ||||||||
\(956\) | 4.63965e6 | 0.164188 | ||||||||
\(957\) | 1.01751e7 | 0.359137 | ||||||||
\(958\) | −2.80098e7 | −0.986042 | ||||||||
\(959\) | 1.79822e7 | 0.631387 | ||||||||
\(960\) | −9.00231e6 | −0.315265 | ||||||||
\(961\) | 4.26658e7 | 1.49029 | ||||||||
\(962\) | 65972.9 | 0.00229841 | ||||||||
\(963\) | −3.68001e7 | −1.27874 | ||||||||
\(964\) | 2.25077e7 | 0.780078 | ||||||||
\(965\) | 1.41855e7 | 0.490371 | ||||||||
\(966\) | −794181. | −0.0273827 | ||||||||
\(967\) | −1.09821e7 | −0.377676 | −0.188838 | − | 0.982008i | \(-0.560472\pi\) | ||||
−0.188838 | + | 0.982008i | \(0.560472\pi\) | |||||||
\(968\) | 937024. | 0.0321412 | ||||||||
\(969\) | −7.94716e7 | −2.71896 | ||||||||
\(970\) | 4.02328e7 | 1.37294 | ||||||||
\(971\) | 8.62580e6 | 0.293597 | 0.146798 | − | 0.989166i | \(-0.453103\pi\) | ||||
0.146798 | + | 0.989166i | \(0.453103\pi\) | |||||||
\(972\) | 2.30449e7 | 0.782364 | ||||||||
\(973\) | 2.73861e6 | 0.0927358 | ||||||||
\(974\) | 1.46308e6 | 0.0494163 | ||||||||
\(975\) | −3.69657e7 | −1.24534 | ||||||||
\(976\) | −1.88643e6 | −0.0633892 | ||||||||
\(977\) | 1.06350e7 | 0.356451 | 0.178226 | − | 0.983990i | \(-0.442964\pi\) | ||||
0.178226 | + | 0.983990i | \(0.442964\pi\) | |||||||
\(978\) | −9.64641e6 | −0.322492 | ||||||||
\(979\) | −613556. | −0.0204596 | ||||||||
\(980\) | 1.03825e7 | 0.345333 | ||||||||
\(981\) | −7.26632e7 | −2.41069 | ||||||||
\(982\) | 2.00068e7 | 0.662062 | ||||||||
\(983\) | 2.66620e7 | 0.880053 | 0.440026 | − | 0.897985i | \(-0.354969\pi\) | ||||
0.440026 | + | 0.897985i | \(0.354969\pi\) | |||||||
\(984\) | 1.68687e7 | 0.555384 | ||||||||
\(985\) | 7.93698e7 | 2.60654 | ||||||||
\(986\) | −1.93244e7 | −0.633016 | ||||||||
\(987\) | −1.61552e7 | −0.527861 | ||||||||
\(988\) | 1.25673e7 | 0.409592 | ||||||||
\(989\) | −874565. | −0.0284316 | ||||||||
\(990\) | 2.13577e7 | 0.692573 | ||||||||
\(991\) | 2.56353e7 | 0.829190 | 0.414595 | − | 0.910006i | \(-0.363923\pi\) | ||||
0.414595 | + | 0.910006i | \(0.363923\pi\) | |||||||
\(992\) | 8.64628e6 | 0.278965 | ||||||||
\(993\) | −6.62816e7 | −2.13314 | ||||||||
\(994\) | 1.71855e7 | 0.551692 | ||||||||
\(995\) | −1.87993e7 | −0.601984 | ||||||||
\(996\) | −2.71268e7 | −0.866465 | ||||||||
\(997\) | −588022. | −0.0187351 | −0.00936754 | − | 0.999956i | \(-0.502982\pi\) | ||||
−0.00936754 | + | 0.999956i | \(0.502982\pi\) | |||||||
\(998\) | −6.54069e6 | −0.207873 | ||||||||
\(999\) | −336228. | −0.0106591 |
(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 | 22.6.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 198.6.a.k.1.2 | 2 | |||
4.3 | odd | 2 | 176.6.a.f.1.1 | 2 | |||
5.2 | odd | 4 | 550.6.b.j.199.3 | 4 | |||
5.3 | odd | 4 | 550.6.b.j.199.2 | 4 | |||
5.4 | even | 2 | 550.6.a.h.1.1 | 2 | |||
7.6 | odd | 2 | 1078.6.a.h.1.1 | 2 | |||
8.3 | odd | 2 | 704.6.a.p.1.2 | 2 | |||
8.5 | even | 2 | 704.6.a.k.1.1 | 2 | |||
11.10 | odd | 2 | 242.6.a.g.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.6.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
176.6.a.f.1.1 | 2 | 4.3 | odd | 2 | |||
198.6.a.k.1.2 | 2 | 3.2 | odd | 2 | |||
242.6.a.g.1.2 | 2 | 11.10 | odd | 2 | |||
550.6.a.h.1.1 | 2 | 5.4 | even | 2 | |||
550.6.b.j.199.2 | 4 | 5.3 | odd | 4 | |||
550.6.b.j.199.3 | 4 | 5.2 | odd | 4 | |||
704.6.a.k.1.1 | 2 | 8.5 | even | 2 | |||
704.6.a.p.1.2 | 2 | 8.3 | odd | 2 | |||
1078.6.a.h.1.1 | 2 | 7.6 | odd | 2 |