Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,6,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, 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("69.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(11.0664835671\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 113x^{3} - 257x^{2} + 1404x + 2197 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-5.17654\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.27315 | 1.63928 | 0.819639 | − | 0.572881i | \(-0.194174\pi\) | ||||
0.819639 | + | 0.572881i | \(0.194174\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 53.9914 | 1.68723 | ||||||||
\(5\) | −37.4928 | −0.670691 | −0.335345 | − | 0.942095i | \(-0.608853\pi\) | ||||
−0.335345 | + | 0.942095i | \(0.608853\pi\) | |||||||
\(6\) | 83.4584 | 0.946437 | ||||||||
\(7\) | 154.850 | 1.19445 | 0.597224 | − | 0.802075i | \(-0.296270\pi\) | ||||
0.597224 | + | 0.802075i | \(0.296270\pi\) | |||||||
\(8\) | 203.929 | 1.12656 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −347.676 | −1.09945 | ||||||||
\(11\) | 521.289 | 1.29896 | 0.649482 | − | 0.760377i | \(-0.274986\pi\) | ||||
0.649482 | + | 0.760377i | \(0.274986\pi\) | |||||||
\(12\) | 485.922 | 0.974123 | ||||||||
\(13\) | −28.8511 | −0.0473483 | −0.0236741 | − | 0.999720i | \(-0.507536\pi\) | ||||
−0.0236741 | + | 0.999720i | \(0.507536\pi\) | |||||||
\(14\) | 1435.95 | 1.95803 | ||||||||
\(15\) | −337.435 | −0.387224 | ||||||||
\(16\) | 163.344 | 0.159516 | ||||||||
\(17\) | −428.492 | −0.359601 | −0.179800 | − | 0.983703i | \(-0.557545\pi\) | ||||
−0.179800 | + | 0.983703i | \(0.557545\pi\) | |||||||
\(18\) | 751.125 | 0.546426 | ||||||||
\(19\) | −2563.67 | −1.62921 | −0.814606 | − | 0.580015i | \(-0.803047\pi\) | ||||
−0.814606 | + | 0.580015i | \(0.803047\pi\) | |||||||
\(20\) | −2024.29 | −1.13161 | ||||||||
\(21\) | 1393.65 | 0.689615 | ||||||||
\(22\) | 4834.00 | 2.12936 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | 1835.36 | 0.650420 | ||||||||
\(25\) | −1719.29 | −0.550174 | ||||||||
\(26\) | −267.541 | −0.0776169 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 8360.58 | 2.01531 | ||||||||
\(29\) | −2401.11 | −0.530172 | −0.265086 | − | 0.964225i | \(-0.585400\pi\) | ||||
−0.265086 | + | 0.964225i | \(0.585400\pi\) | |||||||
\(30\) | −3129.09 | −0.634767 | ||||||||
\(31\) | −2130.21 | −0.398124 | −0.199062 | − | 0.979987i | \(-0.563789\pi\) | ||||
−0.199062 | + | 0.979987i | \(0.563789\pi\) | |||||||
\(32\) | −5011.02 | −0.865071 | ||||||||
\(33\) | 4691.60 | 0.749957 | ||||||||
\(34\) | −3973.47 | −0.589485 | ||||||||
\(35\) | −5805.77 | −0.801105 | ||||||||
\(36\) | 4373.30 | 0.562410 | ||||||||
\(37\) | 3651.58 | 0.438507 | 0.219253 | − | 0.975668i | \(-0.429638\pi\) | ||||
0.219253 | + | 0.975668i | \(0.429638\pi\) | |||||||
\(38\) | −23773.3 | −2.67073 | ||||||||
\(39\) | −259.660 | −0.0273365 | ||||||||
\(40\) | −7645.87 | −0.755574 | ||||||||
\(41\) | 16198.0 | 1.50488 | 0.752440 | − | 0.658661i | \(-0.228877\pi\) | ||||
0.752440 | + | 0.658661i | \(0.228877\pi\) | |||||||
\(42\) | 12923.6 | 1.13047 | ||||||||
\(43\) | 6503.63 | 0.536395 | 0.268197 | − | 0.963364i | \(-0.413572\pi\) | ||||
0.268197 | + | 0.963364i | \(0.413572\pi\) | |||||||
\(44\) | 28145.1 | 2.19165 | ||||||||
\(45\) | −3036.91 | −0.223564 | ||||||||
\(46\) | −4905.50 | −0.341813 | ||||||||
\(47\) | −20712.3 | −1.36768 | −0.683838 | − | 0.729633i | \(-0.739691\pi\) | ||||
−0.683838 | + | 0.729633i | \(0.739691\pi\) | |||||||
\(48\) | 1470.10 | 0.0920964 | ||||||||
\(49\) | 7171.64 | 0.426706 | ||||||||
\(50\) | −15943.3 | −0.901887 | ||||||||
\(51\) | −3856.43 | −0.207615 | ||||||||
\(52\) | −1557.71 | −0.0798874 | ||||||||
\(53\) | 34393.6 | 1.68185 | 0.840926 | − | 0.541149i | \(-0.182011\pi\) | ||||
0.840926 | + | 0.541149i | \(0.182011\pi\) | |||||||
\(54\) | 6760.13 | 0.315479 | ||||||||
\(55\) | −19544.6 | −0.871203 | ||||||||
\(56\) | 31578.5 | 1.34562 | ||||||||
\(57\) | −23073.0 | −0.940626 | ||||||||
\(58\) | −22265.9 | −0.869099 | ||||||||
\(59\) | −18299.4 | −0.684393 | −0.342197 | − | 0.939628i | \(-0.611171\pi\) | ||||
−0.342197 | + | 0.939628i | \(0.611171\pi\) | |||||||
\(60\) | −18218.6 | −0.653335 | ||||||||
\(61\) | −26509.8 | −0.912183 | −0.456092 | − | 0.889933i | \(-0.650751\pi\) | ||||
−0.456092 | + | 0.889933i | \(0.650751\pi\) | |||||||
\(62\) | −19753.7 | −0.652635 | ||||||||
\(63\) | 12542.9 | 0.398149 | ||||||||
\(64\) | −51695.0 | −1.57761 | ||||||||
\(65\) | 1081.71 | 0.0317560 | ||||||||
\(66\) | 43506.0 | 1.22939 | ||||||||
\(67\) | −26313.7 | −0.716136 | −0.358068 | − | 0.933696i | \(-0.616564\pi\) | ||||
−0.358068 | + | 0.933696i | \(0.616564\pi\) | |||||||
\(68\) | −23134.9 | −0.606729 | ||||||||
\(69\) | −4761.00 | −0.120386 | ||||||||
\(70\) | −53837.8 | −1.31323 | ||||||||
\(71\) | 39459.2 | 0.928971 | 0.464486 | − | 0.885581i | \(-0.346239\pi\) | ||||
0.464486 | + | 0.885581i | \(0.346239\pi\) | |||||||
\(72\) | 16518.3 | 0.375520 | ||||||||
\(73\) | −37484.5 | −0.823273 | −0.411637 | − | 0.911348i | \(-0.635043\pi\) | ||||
−0.411637 | + | 0.911348i | \(0.635043\pi\) | |||||||
\(74\) | 33861.6 | 0.718834 | ||||||||
\(75\) | −15473.6 | −0.317643 | ||||||||
\(76\) | −138416. | −2.74886 | ||||||||
\(77\) | 80721.9 | 1.55154 | ||||||||
\(78\) | −2407.87 | −0.0448122 | ||||||||
\(79\) | 37368.8 | 0.673660 | 0.336830 | − | 0.941565i | \(-0.390645\pi\) | ||||
0.336830 | + | 0.941565i | \(0.390645\pi\) | |||||||
\(80\) | −6124.22 | −0.106986 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 150206. | 2.46691 | ||||||||
\(83\) | 76901.5 | 1.22529 | 0.612646 | − | 0.790357i | \(-0.290105\pi\) | ||||
0.612646 | + | 0.790357i | \(0.290105\pi\) | |||||||
\(84\) | 75245.3 | 1.16354 | ||||||||
\(85\) | 16065.3 | 0.241181 | ||||||||
\(86\) | 60309.1 | 0.879300 | ||||||||
\(87\) | −21610.0 | −0.306095 | ||||||||
\(88\) | 106306. | 1.46336 | ||||||||
\(89\) | 62991.4 | 0.842959 | 0.421480 | − | 0.906838i | \(-0.361511\pi\) | ||||
0.421480 | + | 0.906838i | \(0.361511\pi\) | |||||||
\(90\) | −28161.8 | −0.366483 | ||||||||
\(91\) | −4467.60 | −0.0565550 | ||||||||
\(92\) | −28561.4 | −0.351812 | ||||||||
\(93\) | −19171.9 | −0.229857 | ||||||||
\(94\) | −192068. | −2.24200 | ||||||||
\(95\) | 96118.9 | 1.09270 | ||||||||
\(96\) | −45099.2 | −0.499449 | ||||||||
\(97\) | 61484.7 | 0.663495 | 0.331748 | − | 0.943368i | \(-0.392362\pi\) | ||||
0.331748 | + | 0.943368i | \(0.392362\pi\) | |||||||
\(98\) | 66503.7 | 0.699489 | ||||||||
\(99\) | 42224.4 | 0.432988 | ||||||||
\(100\) | −92827.0 | −0.928270 | ||||||||
\(101\) | −89228.8 | −0.870365 | −0.435183 | − | 0.900342i | \(-0.643316\pi\) | ||||
−0.435183 | + | 0.900342i | \(0.643316\pi\) | |||||||
\(102\) | −35761.2 | −0.340339 | ||||||||
\(103\) | 76234.9 | 0.708045 | 0.354023 | − | 0.935237i | \(-0.384814\pi\) | ||||
0.354023 | + | 0.935237i | \(0.384814\pi\) | |||||||
\(104\) | −5883.59 | −0.0533407 | ||||||||
\(105\) | −52251.9 | −0.462518 | ||||||||
\(106\) | 318937. | 2.75702 | ||||||||
\(107\) | −98757.7 | −0.833895 | −0.416947 | − | 0.908931i | \(-0.636900\pi\) | ||||
−0.416947 | + | 0.908931i | \(0.636900\pi\) | |||||||
\(108\) | 39359.7 | 0.324708 | ||||||||
\(109\) | 242295. | 1.95334 | 0.976672 | − | 0.214738i | \(-0.0688898\pi\) | ||||
0.976672 | + | 0.214738i | \(0.0688898\pi\) | |||||||
\(110\) | −181240. | −1.42814 | ||||||||
\(111\) | 32864.2 | 0.253172 | ||||||||
\(112\) | 25293.9 | 0.190533 | ||||||||
\(113\) | 218460. | 1.60945 | 0.804723 | − | 0.593650i | \(-0.202314\pi\) | ||||
0.804723 | + | 0.593650i | \(0.202314\pi\) | |||||||
\(114\) | −213959. | −1.54195 | ||||||||
\(115\) | 19833.7 | 0.139849 | ||||||||
\(116\) | −129639. | −0.894523 | ||||||||
\(117\) | −2336.94 | −0.0157828 | ||||||||
\(118\) | −169693. | −1.12191 | ||||||||
\(119\) | −66352.1 | −0.429524 | ||||||||
\(120\) | −68812.9 | −0.436231 | ||||||||
\(121\) | 110692. | 0.687307 | ||||||||
\(122\) | −245830. | −1.49532 | ||||||||
\(123\) | 145782. | 0.868842 | ||||||||
\(124\) | −115013. | −0.671726 | ||||||||
\(125\) | 181626. | 1.03969 | ||||||||
\(126\) | 116312. | 0.652677 | ||||||||
\(127\) | −199105. | −1.09540 | −0.547700 | − | 0.836675i | \(-0.684496\pi\) | ||||
−0.547700 | + | 0.836675i | \(0.684496\pi\) | |||||||
\(128\) | −319023. | −1.72106 | ||||||||
\(129\) | 58532.6 | 0.309688 | ||||||||
\(130\) | 10030.8 | 0.0520570 | ||||||||
\(131\) | 236710. | 1.20514 | 0.602572 | − | 0.798064i | \(-0.294142\pi\) | ||||
0.602572 | + | 0.798064i | \(0.294142\pi\) | |||||||
\(132\) | 253306. | 1.26535 | ||||||||
\(133\) | −396985. | −1.94601 | ||||||||
\(134\) | −244011. | −1.17395 | ||||||||
\(135\) | −27332.2 | −0.129075 | ||||||||
\(136\) | −87382.1 | −0.405112 | ||||||||
\(137\) | −308407. | −1.40386 | −0.701929 | − | 0.712247i | \(-0.747678\pi\) | ||||
−0.701929 | + | 0.712247i | \(0.747678\pi\) | |||||||
\(138\) | −44149.5 | −0.197346 | ||||||||
\(139\) | −99198.8 | −0.435481 | −0.217741 | − | 0.976007i | \(-0.569869\pi\) | ||||
−0.217741 | + | 0.976007i | \(0.569869\pi\) | |||||||
\(140\) | −313461. | −1.35165 | ||||||||
\(141\) | −186411. | −0.789629 | ||||||||
\(142\) | 365911. | 1.52284 | ||||||||
\(143\) | −15039.8 | −0.0615037 | ||||||||
\(144\) | 13230.9 | 0.0531719 | ||||||||
\(145\) | 90024.2 | 0.355582 | ||||||||
\(146\) | −347599. | −1.34957 | ||||||||
\(147\) | 64544.8 | 0.246359 | ||||||||
\(148\) | 197154. | 0.739862 | ||||||||
\(149\) | −10925.0 | −0.0403140 | −0.0201570 | − | 0.999797i | \(-0.506417\pi\) | ||||
−0.0201570 | + | 0.999797i | \(0.506417\pi\) | |||||||
\(150\) | −143489. | −0.520705 | ||||||||
\(151\) | −488685. | −1.74416 | −0.872081 | − | 0.489362i | \(-0.837230\pi\) | ||||
−0.872081 | + | 0.489362i | \(0.837230\pi\) | |||||||
\(152\) | −522807. | −1.83541 | ||||||||
\(153\) | −34707.8 | −0.119867 | ||||||||
\(154\) | 748546. | 2.54341 | ||||||||
\(155\) | 79867.4 | 0.267018 | ||||||||
\(156\) | −14019.4 | −0.0461230 | ||||||||
\(157\) | −589168. | −1.90761 | −0.953806 | − | 0.300423i | \(-0.902872\pi\) | ||||
−0.953806 | + | 0.300423i | \(0.902872\pi\) | |||||||
\(158\) | 346526. | 1.10432 | ||||||||
\(159\) | 309542. | 0.971018 | ||||||||
\(160\) | 187877. | 0.580195 | ||||||||
\(161\) | −81915.9 | −0.249060 | ||||||||
\(162\) | 60841.2 | 0.182142 | ||||||||
\(163\) | 598674. | 1.76490 | 0.882452 | − | 0.470402i | \(-0.155891\pi\) | ||||
0.882452 | + | 0.470402i | \(0.155891\pi\) | |||||||
\(164\) | 874552. | 2.53908 | ||||||||
\(165\) | −175901. | −0.502989 | ||||||||
\(166\) | 713119. | 2.00859 | ||||||||
\(167\) | 222576. | 0.617570 | 0.308785 | − | 0.951132i | \(-0.400078\pi\) | ||||
0.308785 | + | 0.951132i | \(0.400078\pi\) | |||||||
\(168\) | 284207. | 0.776893 | ||||||||
\(169\) | −370461. | −0.997758 | ||||||||
\(170\) | 148976. | 0.395362 | ||||||||
\(171\) | −207657. | −0.543071 | ||||||||
\(172\) | 351140. | 0.905021 | ||||||||
\(173\) | 438731. | 1.11451 | 0.557253 | − | 0.830343i | \(-0.311855\pi\) | ||||
0.557253 | + | 0.830343i | \(0.311855\pi\) | |||||||
\(174\) | −200393. | −0.501775 | ||||||||
\(175\) | −266233. | −0.657154 | ||||||||
\(176\) | 85149.5 | 0.207205 | ||||||||
\(177\) | −164694. | −0.395135 | ||||||||
\(178\) | 584129. | 1.38184 | ||||||||
\(179\) | 159561. | 0.372216 | 0.186108 | − | 0.982529i | \(-0.440413\pi\) | ||||
0.186108 | + | 0.982529i | \(0.440413\pi\) | |||||||
\(180\) | −163967. | −0.377203 | ||||||||
\(181\) | 448958. | 1.01861 | 0.509306 | − | 0.860585i | \(-0.329902\pi\) | ||||
0.509306 | + | 0.860585i | \(0.329902\pi\) | |||||||
\(182\) | −41428.8 | −0.0927094 | ||||||||
\(183\) | −238588. | −0.526649 | ||||||||
\(184\) | −107879. | −0.234904 | ||||||||
\(185\) | −136908. | −0.294103 | ||||||||
\(186\) | −177784. | −0.376799 | ||||||||
\(187\) | −223368. | −0.467108 | ||||||||
\(188\) | −1.11829e6 | −2.30759 | ||||||||
\(189\) | 112886. | 0.229872 | ||||||||
\(190\) | 891326. | 1.79123 | ||||||||
\(191\) | 170763. | 0.338696 | 0.169348 | − | 0.985556i | \(-0.445834\pi\) | ||||
0.169348 | + | 0.985556i | \(0.445834\pi\) | |||||||
\(192\) | −465255. | −0.910831 | ||||||||
\(193\) | 211013. | 0.407771 | 0.203885 | − | 0.978995i | \(-0.434643\pi\) | ||||
0.203885 | + | 0.978995i | \(0.434643\pi\) | |||||||
\(194\) | 570157. | 1.08765 | ||||||||
\(195\) | 9735.37 | 0.0183344 | ||||||||
\(196\) | 387207. | 0.719951 | ||||||||
\(197\) | −429130. | −0.787813 | −0.393906 | − | 0.919151i | \(-0.628877\pi\) | ||||
−0.393906 | + | 0.919151i | \(0.628877\pi\) | |||||||
\(198\) | 391554. | 0.709787 | ||||||||
\(199\) | −646856. | −1.15791 | −0.578955 | − | 0.815359i | \(-0.696539\pi\) | ||||
−0.578955 | + | 0.815359i | \(0.696539\pi\) | |||||||
\(200\) | −350614. | −0.619804 | ||||||||
\(201\) | −236824. | −0.413461 | ||||||||
\(202\) | −827432. | −1.42677 | ||||||||
\(203\) | −371813. | −0.633263 | ||||||||
\(204\) | −208214. | −0.350295 | ||||||||
\(205\) | −607308. | −1.00931 | ||||||||
\(206\) | 706938. | 1.16068 | ||||||||
\(207\) | −42849.0 | −0.0695048 | ||||||||
\(208\) | −4712.66 | −0.00755279 | ||||||||
\(209\) | −1.33641e6 | −2.11629 | ||||||||
\(210\) | −484540. | −0.758196 | ||||||||
\(211\) | 282510. | 0.436845 | 0.218422 | − | 0.975854i | \(-0.429909\pi\) | ||||
0.218422 | + | 0.975854i | \(0.429909\pi\) | |||||||
\(212\) | 1.85696e6 | 2.83767 | ||||||||
\(213\) | 355133. | 0.536342 | ||||||||
\(214\) | −915795. | −1.36699 | ||||||||
\(215\) | −243839. | −0.359755 | ||||||||
\(216\) | 148664. | 0.216807 | ||||||||
\(217\) | −329864. | −0.475538 | ||||||||
\(218\) | 2.24684e6 | 3.20207 | ||||||||
\(219\) | −337360. | −0.475317 | ||||||||
\(220\) | −1.05524e6 | −1.46992 | ||||||||
\(221\) | 12362.5 | 0.0170265 | ||||||||
\(222\) | 304755. | 0.415019 | ||||||||
\(223\) | −637440. | −0.858375 | −0.429187 | − | 0.903215i | \(-0.641200\pi\) | ||||
−0.429187 | + | 0.903215i | \(0.641200\pi\) | |||||||
\(224\) | −775959. | −1.03328 | ||||||||
\(225\) | −139263. | −0.183391 | ||||||||
\(226\) | 2.02582e6 | 2.63833 | ||||||||
\(227\) | 687712. | 0.885813 | 0.442906 | − | 0.896568i | \(-0.353947\pi\) | ||||
0.442906 | + | 0.896568i | \(0.353947\pi\) | |||||||
\(228\) | −1.24574e6 | −1.58705 | ||||||||
\(229\) | −606450. | −0.764199 | −0.382100 | − | 0.924121i | \(-0.624799\pi\) | ||||
−0.382100 | + | 0.924121i | \(0.624799\pi\) | |||||||
\(230\) | 183921. | 0.229251 | ||||||||
\(231\) | 726497. | 0.895785 | ||||||||
\(232\) | −489657. | −0.597271 | ||||||||
\(233\) | 1.44933e6 | 1.74895 | 0.874475 | − | 0.485070i | \(-0.161206\pi\) | ||||
0.874475 | + | 0.485070i | \(0.161206\pi\) | |||||||
\(234\) | −21670.8 | −0.0258723 | ||||||||
\(235\) | 776561. | 0.917289 | ||||||||
\(236\) | −988007. | −1.15473 | ||||||||
\(237\) | 336319. | 0.388938 | ||||||||
\(238\) | −615294. | −0.704109 | ||||||||
\(239\) | 1.10668e6 | 1.25322 | 0.626610 | − | 0.779333i | \(-0.284442\pi\) | ||||
0.626610 | + | 0.779333i | \(0.284442\pi\) | |||||||
\(240\) | −55118.0 | −0.0617682 | ||||||||
\(241\) | −1.02594e6 | −1.13784 | −0.568919 | − | 0.822394i | \(-0.692638\pi\) | ||||
−0.568919 | + | 0.822394i | \(0.692638\pi\) | |||||||
\(242\) | 1.02646e6 | 1.12669 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −1.43130e6 | −1.53906 | ||||||||
\(245\) | −268885. | −0.286188 | ||||||||
\(246\) | 1.35186e6 | 1.42427 | ||||||||
\(247\) | 73964.6 | 0.0771403 | ||||||||
\(248\) | −434412. | −0.448510 | ||||||||
\(249\) | 692114. | 0.707423 | ||||||||
\(250\) | 1.68424e6 | 1.70434 | ||||||||
\(251\) | −1.07943e6 | −1.08146 | −0.540730 | − | 0.841196i | \(-0.681852\pi\) | ||||
−0.540730 | + | 0.841196i | \(0.681852\pi\) | |||||||
\(252\) | 677207. | 0.671770 | ||||||||
\(253\) | −275762. | −0.270853 | ||||||||
\(254\) | −1.84633e6 | −1.79566 | ||||||||
\(255\) | 144588. | 0.139246 | ||||||||
\(256\) | −1.30411e6 | −1.24369 | ||||||||
\(257\) | 1.24866e6 | 1.17926 | 0.589631 | − | 0.807673i | \(-0.299273\pi\) | ||||
0.589631 | + | 0.807673i | \(0.299273\pi\) | |||||||
\(258\) | 542782. | 0.507664 | ||||||||
\(259\) | 565448. | 0.523774 | ||||||||
\(260\) | 58402.9 | 0.0535798 | ||||||||
\(261\) | −194490. | −0.176724 | ||||||||
\(262\) | 2.19505e6 | 1.97557 | ||||||||
\(263\) | 53460.0 | 0.0476584 | 0.0238292 | − | 0.999716i | \(-0.492414\pi\) | ||||
0.0238292 | + | 0.999716i | \(0.492414\pi\) | |||||||
\(264\) | 956756. | 0.844873 | ||||||||
\(265\) | −1.28951e6 | −1.12800 | ||||||||
\(266\) | −3.68130e6 | −3.19005 | ||||||||
\(267\) | 566923. | 0.486683 | ||||||||
\(268\) | −1.42071e6 | −1.20829 | ||||||||
\(269\) | −1.19910e6 | −1.01035 | −0.505177 | − | 0.863016i | \(-0.668573\pi\) | ||||
−0.505177 | + | 0.863016i | \(0.668573\pi\) | |||||||
\(270\) | −253456. | −0.211589 | ||||||||
\(271\) | 595615. | 0.492654 | 0.246327 | − | 0.969187i | \(-0.420776\pi\) | ||||
0.246327 | + | 0.969187i | \(0.420776\pi\) | |||||||
\(272\) | −69991.6 | −0.0573619 | ||||||||
\(273\) | −40208.4 | −0.0326521 | ||||||||
\(274\) | −2.85991e6 | −2.30131 | ||||||||
\(275\) | −896249. | −0.714656 | ||||||||
\(276\) | −257053. | −0.203119 | ||||||||
\(277\) | 2.14463e6 | 1.67940 | 0.839698 | − | 0.543053i | \(-0.182732\pi\) | ||||
0.839698 | + | 0.543053i | \(0.182732\pi\) | |||||||
\(278\) | −919886. | −0.713875 | ||||||||
\(279\) | −172547. | −0.132708 | ||||||||
\(280\) | −1.18397e6 | −0.902494 | ||||||||
\(281\) | −1.27455e6 | −0.962921 | −0.481461 | − | 0.876468i | \(-0.659894\pi\) | ||||
−0.481461 | + | 0.876468i | \(0.659894\pi\) | |||||||
\(282\) | −1.72861e6 | −1.29442 | ||||||||
\(283\) | 1.33116e6 | 0.988014 | 0.494007 | − | 0.869458i | \(-0.335532\pi\) | ||||
0.494007 | + | 0.869458i | \(0.335532\pi\) | |||||||
\(284\) | 2.13046e6 | 1.56739 | ||||||||
\(285\) | 865070. | 0.630869 | ||||||||
\(286\) | −139466. | −0.100822 | ||||||||
\(287\) | 2.50827e6 | 1.79750 | ||||||||
\(288\) | −405893. | −0.288357 | ||||||||
\(289\) | −1.23625e6 | −0.870687 | ||||||||
\(290\) | 834808. | 0.582897 | ||||||||
\(291\) | 553362. | 0.383069 | ||||||||
\(292\) | −2.02384e6 | −1.38905 | ||||||||
\(293\) | −543720. | −0.370004 | −0.185002 | − | 0.982738i | \(-0.559229\pi\) | ||||
−0.185002 | + | 0.982738i | \(0.559229\pi\) | |||||||
\(294\) | 598534. | 0.403850 | ||||||||
\(295\) | 686093. | 0.459016 | ||||||||
\(296\) | 744664. | 0.494005 | ||||||||
\(297\) | 380020. | 0.249986 | ||||||||
\(298\) | −101309. | −0.0660858 | ||||||||
\(299\) | 15262.2 | 0.00987279 | ||||||||
\(300\) | −835443. | −0.535937 | ||||||||
\(301\) | 1.00709e6 | 0.640695 | ||||||||
\(302\) | −4.53165e6 | −2.85917 | ||||||||
\(303\) | −803059. | −0.502506 | ||||||||
\(304\) | −418760. | −0.259885 | ||||||||
\(305\) | 993926. | 0.611793 | ||||||||
\(306\) | −321851. | −0.196495 | ||||||||
\(307\) | 2.16140e6 | 1.30885 | 0.654424 | − | 0.756127i | \(-0.272911\pi\) | ||||
0.654424 | + | 0.756127i | \(0.272911\pi\) | |||||||
\(308\) | 4.35828e6 | 2.61781 | ||||||||
\(309\) | 686114. | 0.408790 | ||||||||
\(310\) | 740623. | 0.437716 | ||||||||
\(311\) | −2.27827e6 | −1.33569 | −0.667843 | − | 0.744302i | \(-0.732782\pi\) | ||||
−0.667843 | + | 0.744302i | \(0.732782\pi\) | |||||||
\(312\) | −52952.3 | −0.0307963 | ||||||||
\(313\) | −2.34170e6 | −1.35105 | −0.675524 | − | 0.737338i | \(-0.736083\pi\) | ||||
−0.675524 | + | 0.737338i | \(0.736083\pi\) | |||||||
\(314\) | −5.46345e6 | −3.12711 | ||||||||
\(315\) | −470267. | −0.267035 | ||||||||
\(316\) | 2.01759e6 | 1.13662 | ||||||||
\(317\) | 1.70927e6 | 0.955348 | 0.477674 | − | 0.878537i | \(-0.341480\pi\) | ||||
0.477674 | + | 0.878537i | \(0.341480\pi\) | |||||||
\(318\) | 2.87043e6 | 1.59177 | ||||||||
\(319\) | −1.25167e6 | −0.688675 | ||||||||
\(320\) | 1.93819e6 | 1.05809 | ||||||||
\(321\) | −888819. | −0.481449 | ||||||||
\(322\) | −759618. | −0.408278 | ||||||||
\(323\) | 1.09851e6 | 0.585865 | ||||||||
\(324\) | 354237. | 0.187470 | ||||||||
\(325\) | 49603.5 | 0.0260498 | ||||||||
\(326\) | 5.55159e6 | 2.89317 | ||||||||
\(327\) | 2.18066e6 | 1.12776 | ||||||||
\(328\) | 3.30325e6 | 1.69534 | ||||||||
\(329\) | −3.20731e6 | −1.63362 | ||||||||
\(330\) | −1.63116e6 | −0.824539 | ||||||||
\(331\) | 3.09295e6 | 1.55168 | 0.775840 | − | 0.630930i | \(-0.217326\pi\) | ||||
0.775840 | + | 0.630930i | \(0.217326\pi\) | |||||||
\(332\) | 4.15202e6 | 2.06735 | ||||||||
\(333\) | 295778. | 0.146169 | ||||||||
\(334\) | 2.06398e6 | 1.01237 | ||||||||
\(335\) | 986575. | 0.480306 | ||||||||
\(336\) | 227645. | 0.110004 | ||||||||
\(337\) | −691524. | −0.331690 | −0.165845 | − | 0.986152i | \(-0.553035\pi\) | ||||
−0.165845 | + | 0.986152i | \(0.553035\pi\) | |||||||
\(338\) | −3.43534e6 | −1.63560 | ||||||||
\(339\) | 1.96614e6 | 0.929214 | ||||||||
\(340\) | 867390. | 0.406928 | ||||||||
\(341\) | −1.11045e6 | −0.517148 | ||||||||
\(342\) | −1.92563e6 | −0.890243 | ||||||||
\(343\) | −1.49204e6 | −0.684770 | ||||||||
\(344\) | 1.32628e6 | 0.604281 | ||||||||
\(345\) | 178503. | 0.0807417 | ||||||||
\(346\) | 4.06842e6 | 1.82699 | ||||||||
\(347\) | −4.15931e6 | −1.85437 | −0.927187 | − | 0.374599i | \(-0.877780\pi\) | ||||
−0.927187 | + | 0.374599i | \(0.877780\pi\) | |||||||
\(348\) | −1.16675e6 | −0.516453 | ||||||||
\(349\) | −3.44531e6 | −1.51414 | −0.757068 | − | 0.653337i | \(-0.773369\pi\) | ||||
−0.757068 | + | 0.653337i | \(0.773369\pi\) | |||||||
\(350\) | −2.46882e6 | −1.07726 | ||||||||
\(351\) | −21032.5 | −0.00911218 | ||||||||
\(352\) | −2.61219e6 | −1.12370 | ||||||||
\(353\) | −2.27651e6 | −0.972373 | −0.486186 | − | 0.873855i | \(-0.661612\pi\) | ||||
−0.486186 | + | 0.873855i | \(0.661612\pi\) | |||||||
\(354\) | −1.52723e6 | −0.647735 | ||||||||
\(355\) | −1.47943e6 | −0.623053 | ||||||||
\(356\) | 3.40099e6 | 1.42227 | ||||||||
\(357\) | −597169. | −0.247986 | ||||||||
\(358\) | 1.47964e6 | 0.610165 | ||||||||
\(359\) | −602616. | −0.246777 | −0.123388 | − | 0.992358i | \(-0.539376\pi\) | ||||
−0.123388 | + | 0.992358i | \(0.539376\pi\) | |||||||
\(360\) | −619316. | −0.251858 | ||||||||
\(361\) | 4.09629e6 | 1.65433 | ||||||||
\(362\) | 4.16326e6 | 1.66979 | ||||||||
\(363\) | 996224. | 0.396817 | ||||||||
\(364\) | −241212. | −0.0954214 | ||||||||
\(365\) | 1.40540e6 | 0.552162 | ||||||||
\(366\) | −2.21247e6 | −0.863324 | ||||||||
\(367\) | 2.69133e6 | 1.04304 | 0.521521 | − | 0.853238i | \(-0.325365\pi\) | ||||
0.521521 | + | 0.853238i | \(0.325365\pi\) | |||||||
\(368\) | −86409.0 | −0.0332613 | ||||||||
\(369\) | 1.31204e6 | 0.501626 | ||||||||
\(370\) | −1.26957e6 | −0.482116 | ||||||||
\(371\) | 5.32586e6 | 2.00889 | ||||||||
\(372\) | −1.03512e6 | −0.387821 | ||||||||
\(373\) | −2.93803e6 | −1.09341 | −0.546707 | − | 0.837324i | \(-0.684119\pi\) | ||||
−0.546707 | + | 0.837324i | \(0.684119\pi\) | |||||||
\(374\) | −2.07133e6 | −0.765720 | ||||||||
\(375\) | 1.63463e6 | 0.600264 | ||||||||
\(376\) | −4.22384e6 | −1.54077 | ||||||||
\(377\) | 69274.6 | 0.0251027 | ||||||||
\(378\) | 1.04681e6 | 0.376823 | ||||||||
\(379\) | 2.78962e6 | 0.997578 | 0.498789 | − | 0.866723i | \(-0.333778\pi\) | ||||
0.498789 | + | 0.866723i | \(0.333778\pi\) | |||||||
\(380\) | 5.18959e6 | 1.84363 | ||||||||
\(381\) | −1.79194e6 | −0.632429 | ||||||||
\(382\) | 1.58351e6 | 0.555216 | ||||||||
\(383\) | 3.28779e6 | 1.14527 | 0.572634 | − | 0.819811i | \(-0.305922\pi\) | ||||
0.572634 | + | 0.819811i | \(0.305922\pi\) | |||||||
\(384\) | −2.87121e6 | −0.993657 | ||||||||
\(385\) | −3.02649e6 | −1.04061 | ||||||||
\(386\) | 1.95676e6 | 0.668450 | ||||||||
\(387\) | 526794. | 0.178798 | ||||||||
\(388\) | 3.31964e6 | 1.11947 | ||||||||
\(389\) | −2.17987e6 | −0.730392 | −0.365196 | − | 0.930931i | \(-0.618998\pi\) | ||||
−0.365196 | + | 0.930931i | \(0.618998\pi\) | |||||||
\(390\) | 90277.5 | 0.0300551 | ||||||||
\(391\) | 226672. | 0.0749819 | ||||||||
\(392\) | 1.46251e6 | 0.480710 | ||||||||
\(393\) | 2.13039e6 | 0.695791 | ||||||||
\(394\) | −3.97939e6 | −1.29144 | ||||||||
\(395\) | −1.40106e6 | −0.451818 | ||||||||
\(396\) | 2.27976e6 | 0.730550 | ||||||||
\(397\) | −3.30454e6 | −1.05229 | −0.526144 | − | 0.850396i | \(-0.676363\pi\) | ||||
−0.526144 | + | 0.850396i | \(0.676363\pi\) | |||||||
\(398\) | −5.99839e6 | −1.89814 | ||||||||
\(399\) | −3.57286e6 | −1.12353 | ||||||||
\(400\) | −280836. | −0.0877613 | ||||||||
\(401\) | 3.56153e6 | 1.10605 | 0.553026 | − | 0.833164i | \(-0.313473\pi\) | ||||
0.553026 | + | 0.833164i | \(0.313473\pi\) | |||||||
\(402\) | −2.19610e6 | −0.677778 | ||||||||
\(403\) | 61458.9 | 0.0188505 | ||||||||
\(404\) | −4.81758e6 | −1.46851 | ||||||||
\(405\) | −245990. | −0.0745212 | ||||||||
\(406\) | −3.44788e6 | −1.03809 | ||||||||
\(407\) | 1.90353e6 | 0.569605 | ||||||||
\(408\) | −786439. | −0.233892 | ||||||||
\(409\) | −2.96716e6 | −0.877066 | −0.438533 | − | 0.898715i | \(-0.644502\pi\) | ||||
−0.438533 | + | 0.898715i | \(0.644502\pi\) | |||||||
\(410\) | −5.63166e6 | −1.65454 | ||||||||
\(411\) | −2.77567e6 | −0.810518 | ||||||||
\(412\) | 4.11603e6 | 1.19464 | ||||||||
\(413\) | −2.83366e6 | −0.817472 | ||||||||
\(414\) | −397345. | −0.113938 | ||||||||
\(415\) | −2.88325e6 | −0.821792 | ||||||||
\(416\) | 144574. | 0.0409596 | ||||||||
\(417\) | −892789. | −0.251425 | ||||||||
\(418\) | −1.23928e7 | −3.46918 | ||||||||
\(419\) | −1.51390e6 | −0.421272 | −0.210636 | − | 0.977565i | \(-0.567553\pi\) | ||||
−0.210636 | + | 0.977565i | \(0.567553\pi\) | |||||||
\(420\) | −2.82115e6 | −0.780375 | ||||||||
\(421\) | 746530. | 0.205278 | 0.102639 | − | 0.994719i | \(-0.467271\pi\) | ||||
0.102639 | + | 0.994719i | \(0.467271\pi\) | |||||||
\(422\) | 2.61975e6 | 0.716109 | ||||||||
\(423\) | −1.67770e6 | −0.455892 | ||||||||
\(424\) | 7.01386e6 | 1.89471 | ||||||||
\(425\) | 736703. | 0.197843 | ||||||||
\(426\) | 3.29320e6 | 0.879213 | ||||||||
\(427\) | −4.10506e6 | −1.08956 | ||||||||
\(428\) | −5.33206e6 | −1.40697 | ||||||||
\(429\) | −135358. | −0.0355092 | ||||||||
\(430\) | −2.26116e6 | −0.589738 | ||||||||
\(431\) | 2.15954e6 | 0.559976 | 0.279988 | − | 0.960004i | \(-0.409670\pi\) | ||||
0.279988 | + | 0.960004i | \(0.409670\pi\) | |||||||
\(432\) | 119078. | 0.0306988 | ||||||||
\(433\) | 5.74239e6 | 1.47188 | 0.735941 | − | 0.677045i | \(-0.236740\pi\) | ||||
0.735941 | + | 0.677045i | \(0.236740\pi\) | |||||||
\(434\) | −3.05888e6 | −0.779538 | ||||||||
\(435\) | 810218. | 0.205295 | ||||||||
\(436\) | 1.30818e7 | 3.29574 | ||||||||
\(437\) | 1.35618e6 | 0.339714 | ||||||||
\(438\) | −3.12839e6 | −0.779176 | ||||||||
\(439\) | 3.04352e6 | 0.753728 | 0.376864 | − | 0.926269i | \(-0.377002\pi\) | ||||
0.376864 | + | 0.926269i | \(0.377002\pi\) | |||||||
\(440\) | −3.98571e6 | −0.981464 | ||||||||
\(441\) | 580903. | 0.142235 | ||||||||
\(442\) | 114639. | 0.0279111 | ||||||||
\(443\) | −2.95192e6 | −0.714652 | −0.357326 | − | 0.933980i | \(-0.616311\pi\) | ||||
−0.357326 | + | 0.933980i | \(0.616311\pi\) | |||||||
\(444\) | 1.77438e6 | 0.427160 | ||||||||
\(445\) | −2.36172e6 | −0.565365 | ||||||||
\(446\) | −5.91108e6 | −1.40711 | ||||||||
\(447\) | −98325.1 | −0.0232753 | ||||||||
\(448\) | −8.00499e6 | −1.88437 | ||||||||
\(449\) | 3.29085e6 | 0.770356 | 0.385178 | − | 0.922842i | \(-0.374140\pi\) | ||||
0.385178 | + | 0.922842i | \(0.374140\pi\) | |||||||
\(450\) | −1.29140e6 | −0.300629 | ||||||||
\(451\) | 8.44384e6 | 1.95478 | ||||||||
\(452\) | 1.17950e7 | 2.71551 | ||||||||
\(453\) | −4.39817e6 | −1.00699 | ||||||||
\(454\) | 6.37726e6 | 1.45209 | ||||||||
\(455\) | 167503. | 0.0379309 | ||||||||
\(456\) | −4.70526e6 | −1.05967 | ||||||||
\(457\) | 5.82436e6 | 1.30454 | 0.652271 | − | 0.757986i | \(-0.273816\pi\) | ||||
0.652271 | + | 0.757986i | \(0.273816\pi\) | |||||||
\(458\) | −5.62371e6 | −1.25273 | ||||||||
\(459\) | −312371. | −0.0692052 | ||||||||
\(460\) | 1.07085e6 | 0.235957 | ||||||||
\(461\) | −1.73714e6 | −0.380700 | −0.190350 | − | 0.981716i | \(-0.560962\pi\) | ||||
−0.190350 | + | 0.981716i | \(0.560962\pi\) | |||||||
\(462\) | 6.73692e6 | 1.46844 | ||||||||
\(463\) | 3.08948e6 | 0.669780 | 0.334890 | − | 0.942257i | \(-0.391301\pi\) | ||||
0.334890 | + | 0.942257i | \(0.391301\pi\) | |||||||
\(464\) | −392207. | −0.0845708 | ||||||||
\(465\) | 718807. | 0.154163 | ||||||||
\(466\) | 1.34399e7 | 2.86702 | ||||||||
\(467\) | −1.75231e6 | −0.371808 | −0.185904 | − | 0.982568i | \(-0.559521\pi\) | ||||
−0.185904 | + | 0.982568i | \(0.559521\pi\) | |||||||
\(468\) | −126175. | −0.0266291 | ||||||||
\(469\) | −4.07469e6 | −0.855387 | ||||||||
\(470\) | 7.20117e6 | 1.50369 | ||||||||
\(471\) | −5.30251e6 | −1.10136 | ||||||||
\(472\) | −3.73178e6 | −0.771011 | ||||||||
\(473\) | 3.39027e6 | 0.696757 | ||||||||
\(474\) | 3.11874e6 | 0.637577 | ||||||||
\(475\) | 4.40769e6 | 0.896349 | ||||||||
\(476\) | −3.58244e6 | −0.724706 | ||||||||
\(477\) | 2.78588e6 | 0.560618 | ||||||||
\(478\) | 1.02624e7 | 2.05438 | ||||||||
\(479\) | −5.38341e6 | −1.07206 | −0.536030 | − | 0.844199i | \(-0.680076\pi\) | ||||
−0.536030 | + | 0.844199i | \(0.680076\pi\) | |||||||
\(480\) | 1.69089e6 | 0.334976 | ||||||||
\(481\) | −105352. | −0.0207625 | ||||||||
\(482\) | −9.51372e6 | −1.86523 | ||||||||
\(483\) | −737243. | −0.143795 | ||||||||
\(484\) | 5.97639e6 | 1.15965 | ||||||||
\(485\) | −2.30523e6 | −0.445000 | ||||||||
\(486\) | 547570. | 0.105160 | ||||||||
\(487\) | −6.11771e6 | −1.16887 | −0.584436 | − | 0.811440i | \(-0.698684\pi\) | ||||
−0.584436 | + | 0.811440i | \(0.698684\pi\) | |||||||
\(488\) | −5.40613e6 | −1.02763 | ||||||||
\(489\) | 5.38806e6 | 1.01897 | ||||||||
\(490\) | −2.49341e6 | −0.469141 | ||||||||
\(491\) | 5.22411e6 | 0.977932 | 0.488966 | − | 0.872303i | \(-0.337374\pi\) | ||||
0.488966 | + | 0.872303i | \(0.337374\pi\) | |||||||
\(492\) | 7.87097e6 | 1.46594 | ||||||||
\(493\) | 1.02886e6 | 0.190650 | ||||||||
\(494\) | 685885. | 0.126454 | ||||||||
\(495\) | −1.58311e6 | −0.290401 | ||||||||
\(496\) | −347957. | −0.0635070 | ||||||||
\(497\) | 6.11027e6 | 1.10961 | ||||||||
\(498\) | 6.41808e6 | 1.15966 | ||||||||
\(499\) | 8.89404e6 | 1.59900 | 0.799498 | − | 0.600668i | \(-0.205099\pi\) | ||||
0.799498 | + | 0.600668i | \(0.205099\pi\) | |||||||
\(500\) | 9.80623e6 | 1.75419 | ||||||||
\(501\) | 2.00318e6 | 0.356554 | ||||||||
\(502\) | −1.00097e7 | −1.77281 | ||||||||
\(503\) | −3.62219e6 | −0.638339 | −0.319170 | − | 0.947698i | \(-0.603404\pi\) | ||||
−0.319170 | + | 0.947698i | \(0.603404\pi\) | |||||||
\(504\) | 2.55786e6 | 0.448539 | ||||||||
\(505\) | 3.34543e6 | 0.583746 | ||||||||
\(506\) | −2.55718e6 | −0.444003 | ||||||||
\(507\) | −3.33415e6 | −0.576056 | ||||||||
\(508\) | −1.07499e7 | −1.84819 | ||||||||
\(509\) | 454923. | 0.0778294 | 0.0389147 | − | 0.999243i | \(-0.487610\pi\) | ||||
0.0389147 | + | 0.999243i | \(0.487610\pi\) | |||||||
\(510\) | 1.34079e6 | 0.228263 | ||||||||
\(511\) | −5.80448e6 | −0.983357 | ||||||||
\(512\) | −1.88446e6 | −0.317696 | ||||||||
\(513\) | −1.86891e6 | −0.313542 | ||||||||
\(514\) | 1.15790e7 | 1.93314 | ||||||||
\(515\) | −2.85826e6 | −0.474879 | ||||||||
\(516\) | 3.16026e6 | 0.522514 | ||||||||
\(517\) | −1.07971e7 | −1.77656 | ||||||||
\(518\) | 5.24349e6 | 0.858610 | ||||||||
\(519\) | 3.94857e6 | 0.643461 | ||||||||
\(520\) | 220592. | 0.0357751 | ||||||||
\(521\) | 4.46566e6 | 0.720761 | 0.360380 | − | 0.932805i | \(-0.382647\pi\) | ||||
0.360380 | + | 0.932805i | \(0.382647\pi\) | |||||||
\(522\) | −1.80353e6 | −0.289700 | ||||||||
\(523\) | −2.91793e6 | −0.466467 | −0.233234 | − | 0.972421i | \(-0.574931\pi\) | ||||
−0.233234 | + | 0.972421i | \(0.574931\pi\) | |||||||
\(524\) | 1.27803e7 | 2.03336 | ||||||||
\(525\) | −2.39610e6 | −0.379408 | ||||||||
\(526\) | 495743. | 0.0781254 | ||||||||
\(527\) | 912777. | 0.143165 | ||||||||
\(528\) | 766346. | 0.119630 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −1.19578e7 | −1.84911 | ||||||||
\(531\) | −1.48225e6 | −0.228131 | ||||||||
\(532\) | −2.14337e7 | −3.28336 | ||||||||
\(533\) | −467330. | −0.0712534 | ||||||||
\(534\) | 5.25716e6 | 0.797808 | ||||||||
\(535\) | 3.70270e6 | 0.559286 | ||||||||
\(536\) | −5.36614e6 | −0.806771 | ||||||||
\(537\) | 1.43605e6 | 0.214899 | ||||||||
\(538\) | −1.11194e7 | −1.65625 | ||||||||
\(539\) | 3.73850e6 | 0.554275 | ||||||||
\(540\) | −1.47570e6 | −0.217778 | ||||||||
\(541\) | −2.73195e6 | −0.401310 | −0.200655 | − | 0.979662i | \(-0.564307\pi\) | ||||
−0.200655 | + | 0.979662i | \(0.564307\pi\) | |||||||
\(542\) | 5.52323e6 | 0.807597 | ||||||||
\(543\) | 4.04062e6 | 0.588096 | ||||||||
\(544\) | 2.14718e6 | 0.311080 | ||||||||
\(545\) | −9.08432e6 | −1.31009 | ||||||||
\(546\) | −372859. | −0.0535258 | ||||||||
\(547\) | −5.55388e6 | −0.793648 | −0.396824 | − | 0.917895i | \(-0.629888\pi\) | ||||
−0.396824 | + | 0.917895i | \(0.629888\pi\) | |||||||
\(548\) | −1.66513e7 | −2.36863 | ||||||||
\(549\) | −2.14730e6 | −0.304061 | ||||||||
\(550\) | −8.31105e6 | −1.17152 | ||||||||
\(551\) | 6.15564e6 | 0.863763 | ||||||||
\(552\) | −970908. | −0.135622 | ||||||||
\(553\) | 5.78657e6 | 0.804652 | ||||||||
\(554\) | 1.98875e7 | 2.75300 | ||||||||
\(555\) | −1.23217e6 | −0.169800 | ||||||||
\(556\) | −5.35588e6 | −0.734757 | ||||||||
\(557\) | −1.69772e6 | −0.231862 | −0.115931 | − | 0.993257i | \(-0.536985\pi\) | ||||
−0.115931 | + | 0.993257i | \(0.536985\pi\) | |||||||
\(558\) | −1.60005e6 | −0.217545 | ||||||||
\(559\) | −187637. | −0.0253974 | ||||||||
\(560\) | −948338. | −0.127789 | ||||||||
\(561\) | −2.01031e6 | −0.269685 | ||||||||
\(562\) | −1.18191e7 | −1.57849 | ||||||||
\(563\) | 4.59153e6 | 0.610501 | 0.305250 | − | 0.952272i | \(-0.401260\pi\) | ||||
0.305250 | + | 0.952272i | \(0.401260\pi\) | |||||||
\(564\) | −1.00646e7 | −1.33229 | ||||||||
\(565\) | −8.19068e6 | −1.07944 | ||||||||
\(566\) | 1.23440e7 | 1.61963 | ||||||||
\(567\) | 1.01597e6 | 0.132716 | ||||||||
\(568\) | 8.04689e6 | 1.04654 | ||||||||
\(569\) | −1.10517e7 | −1.43103 | −0.715517 | − | 0.698595i | \(-0.753809\pi\) | ||||
−0.715517 | + | 0.698595i | \(0.753809\pi\) | |||||||
\(570\) | 8.02193e6 | 1.03417 | ||||||||
\(571\) | −1.35952e7 | −1.74500 | −0.872500 | − | 0.488613i | \(-0.837503\pi\) | ||||
−0.872500 | + | 0.488613i | \(0.837503\pi\) | |||||||
\(572\) | −812018. | −0.103771 | ||||||||
\(573\) | 1.53686e6 | 0.195546 | ||||||||
\(574\) | 2.32595e7 | 2.94660 | ||||||||
\(575\) | 909506. | 0.114719 | ||||||||
\(576\) | −4.18730e6 | −0.525869 | ||||||||
\(577\) | 4.14819e6 | 0.518703 | 0.259351 | − | 0.965783i | \(-0.416491\pi\) | ||||
0.259351 | + | 0.965783i | \(0.416491\pi\) | |||||||
\(578\) | −1.14640e7 | −1.42730 | ||||||||
\(579\) | 1.89912e6 | 0.235427 | ||||||||
\(580\) | 4.86053e6 | 0.599948 | ||||||||
\(581\) | 1.19082e7 | 1.46355 | ||||||||
\(582\) | 5.13141e6 | 0.627956 | ||||||||
\(583\) | 1.79290e7 | 2.18467 | ||||||||
\(584\) | −7.64418e6 | −0.927468 | ||||||||
\(585\) | 87618.3 | 0.0105853 | ||||||||
\(586\) | −5.04200e6 | −0.606539 | ||||||||
\(587\) | −55407.2 | −0.00663699 | −0.00331849 | − | 0.999994i | \(-0.501056\pi\) | ||||
−0.00331849 | + | 0.999994i | \(0.501056\pi\) | |||||||
\(588\) | 3.48486e6 | 0.415664 | ||||||||
\(589\) | 5.46114e6 | 0.648628 | ||||||||
\(590\) | 6.36225e6 | 0.752455 | ||||||||
\(591\) | −3.86217e6 | −0.454844 | ||||||||
\(592\) | 596464. | 0.0699487 | ||||||||
\(593\) | −1.44004e7 | −1.68166 | −0.840829 | − | 0.541300i | \(-0.817932\pi\) | ||||
−0.840829 | + | 0.541300i | \(0.817932\pi\) | |||||||
\(594\) | 3.52398e6 | 0.409796 | ||||||||
\(595\) | 2.48773e6 | 0.288078 | ||||||||
\(596\) | −589856. | −0.0680190 | ||||||||
\(597\) | −5.82170e6 | −0.668520 | ||||||||
\(598\) | 141529. | 0.0161842 | ||||||||
\(599\) | 1.33225e6 | 0.151712 | 0.0758559 | − | 0.997119i | \(-0.475831\pi\) | ||||
0.0758559 | + | 0.997119i | \(0.475831\pi\) | |||||||
\(600\) | −3.15553e6 | −0.357844 | ||||||||
\(601\) | −4.11211e6 | −0.464386 | −0.232193 | − | 0.972670i | \(-0.574590\pi\) | ||||
−0.232193 | + | 0.972670i | \(0.574590\pi\) | |||||||
\(602\) | 9.33889e6 | 1.05028 | ||||||||
\(603\) | −2.13141e6 | −0.238712 | ||||||||
\(604\) | −2.63848e7 | −2.94280 | ||||||||
\(605\) | −4.15013e6 | −0.460971 | ||||||||
\(606\) | −7.44689e6 | −0.823746 | ||||||||
\(607\) | −5.38575e6 | −0.593300 | −0.296650 | − | 0.954986i | \(-0.595869\pi\) | ||||
−0.296650 | + | 0.954986i | \(0.595869\pi\) | |||||||
\(608\) | 1.28466e7 | 1.40938 | ||||||||
\(609\) | −3.34631e6 | −0.365615 | ||||||||
\(610\) | 9.21683e6 | 1.00290 | ||||||||
\(611\) | 597572. | 0.0647571 | ||||||||
\(612\) | −1.87392e6 | −0.202243 | ||||||||
\(613\) | −2.17889e6 | −0.234199 | −0.117100 | − | 0.993120i | \(-0.537360\pi\) | ||||
−0.117100 | + | 0.993120i | \(0.537360\pi\) | |||||||
\(614\) | 2.00430e7 | 2.14557 | ||||||||
\(615\) | −5.46577e6 | −0.582725 | ||||||||
\(616\) | 1.64616e7 | 1.74791 | ||||||||
\(617\) | 1.40873e7 | 1.48976 | 0.744880 | − | 0.667199i | \(-0.232507\pi\) | ||||
0.744880 | + | 0.667199i | \(0.232507\pi\) | |||||||
\(618\) | 6.36244e6 | 0.670120 | ||||||||
\(619\) | −5.63132e6 | −0.590722 | −0.295361 | − | 0.955386i | \(-0.595440\pi\) | ||||
−0.295361 | + | 0.955386i | \(0.595440\pi\) | |||||||
\(620\) | 4.31215e6 | 0.450521 | ||||||||
\(621\) | −385641. | −0.0401286 | ||||||||
\(622\) | −2.11268e7 | −2.18956 | ||||||||
\(623\) | 9.75425e6 | 1.00687 | ||||||||
\(624\) | −42413.9 | −0.00436061 | ||||||||
\(625\) | −1.43687e6 | −0.147135 | ||||||||
\(626\) | −2.17150e7 | −2.21474 | ||||||||
\(627\) | −1.20277e7 | −1.22184 | ||||||||
\(628\) | −3.18100e7 | −3.21858 | ||||||||
\(629\) | −1.56467e6 | −0.157687 | ||||||||
\(630\) | −4.36086e6 | −0.437745 | ||||||||
\(631\) | −1.47000e7 | −1.46976 | −0.734878 | − | 0.678200i | \(-0.762760\pi\) | ||||
−0.734878 | + | 0.678200i | \(0.762760\pi\) | |||||||
\(632\) | 7.62059e6 | 0.758919 | ||||||||
\(633\) | 2.54259e6 | 0.252212 | ||||||||
\(634\) | 1.58503e7 | 1.56608 | ||||||||
\(635\) | 7.46499e6 | 0.734675 | ||||||||
\(636\) | 1.67126e7 | 1.63833 | ||||||||
\(637\) | −206910. | −0.0202038 | ||||||||
\(638\) | −1.16070e7 | −1.12893 | ||||||||
\(639\) | 3.19619e6 | 0.309657 | ||||||||
\(640\) | 1.19610e7 | 1.15430 | ||||||||
\(641\) | −1.20465e7 | −1.15802 | −0.579012 | − | 0.815319i | \(-0.696561\pi\) | ||||
−0.579012 | + | 0.815319i | \(0.696561\pi\) | |||||||
\(642\) | −8.24215e6 | −0.789229 | ||||||||
\(643\) | 4.72652e6 | 0.450831 | 0.225416 | − | 0.974263i | \(-0.427626\pi\) | ||||
0.225416 | + | 0.974263i | \(0.427626\pi\) | |||||||
\(644\) | −4.42275e6 | −0.420221 | ||||||||
\(645\) | −2.19455e6 | −0.207705 | ||||||||
\(646\) | 1.01867e7 | 0.960396 | ||||||||
\(647\) | −1.24621e7 | −1.17039 | −0.585196 | − | 0.810892i | \(-0.698982\pi\) | ||||
−0.585196 | + | 0.810892i | \(0.698982\pi\) | |||||||
\(648\) | 1.33798e6 | 0.125173 | ||||||||
\(649\) | −9.53926e6 | −0.889002 | ||||||||
\(650\) | 459981. | 0.0427028 | ||||||||
\(651\) | −2.96877e6 | −0.274552 | ||||||||
\(652\) | 3.23232e7 | 2.97780 | ||||||||
\(653\) | −7.75118e6 | −0.711353 | −0.355676 | − | 0.934609i | \(-0.615749\pi\) | ||||
−0.355676 | + | 0.934609i | \(0.615749\pi\) | |||||||
\(654\) | 2.02216e7 | 1.84872 | ||||||||
\(655\) | −8.87493e6 | −0.808280 | ||||||||
\(656\) | 2.64585e6 | 0.240052 | ||||||||
\(657\) | −3.03624e6 | −0.274424 | ||||||||
\(658\) | −2.97418e7 | −2.67795 | ||||||||
\(659\) | 1.52713e7 | 1.36981 | 0.684907 | − | 0.728630i | \(-0.259843\pi\) | ||||
0.684907 | + | 0.728630i | \(0.259843\pi\) | |||||||
\(660\) | −9.49715e6 | −0.848659 | ||||||||
\(661\) | 2.21977e7 | 1.97608 | 0.988041 | − | 0.154190i | \(-0.0492767\pi\) | ||||
0.988041 | + | 0.154190i | \(0.0492767\pi\) | |||||||
\(662\) | 2.86814e7 | 2.54363 | ||||||||
\(663\) | 111262. | 0.00983023 | ||||||||
\(664\) | 1.56825e7 | 1.38037 | ||||||||
\(665\) | 1.48841e7 | 1.30517 | ||||||||
\(666\) | 2.74279e6 | 0.239611 | ||||||||
\(667\) | 1.27019e6 | 0.110549 | ||||||||
\(668\) | 1.20172e7 | 1.04198 | ||||||||
\(669\) | −5.73696e6 | −0.495583 | ||||||||
\(670\) | 9.14866e6 | 0.787355 | ||||||||
\(671\) | −1.38193e7 | −1.18489 | ||||||||
\(672\) | −6.98363e6 | −0.596565 | ||||||||
\(673\) | 6.38649e6 | 0.543531 | 0.271766 | − | 0.962363i | \(-0.412392\pi\) | ||||
0.271766 | + | 0.962363i | \(0.412392\pi\) | |||||||
\(674\) | −6.41261e6 | −0.543732 | ||||||||
\(675\) | −1.25336e6 | −0.105881 | ||||||||
\(676\) | −2.00017e7 | −1.68345 | ||||||||
\(677\) | 6.89077e6 | 0.577825 | 0.288913 | − | 0.957356i | \(-0.406706\pi\) | ||||
0.288913 | + | 0.957356i | \(0.406706\pi\) | |||||||
\(678\) | 1.82323e7 | 1.52324 | ||||||||
\(679\) | 9.52093e6 | 0.792510 | ||||||||
\(680\) | 3.27620e6 | 0.271705 | ||||||||
\(681\) | 6.18941e6 | 0.511424 | ||||||||
\(682\) | −1.02974e7 | −0.847749 | ||||||||
\(683\) | −2.36161e7 | −1.93712 | −0.968558 | − | 0.248788i | \(-0.919968\pi\) | ||||
−0.968558 | + | 0.248788i | \(0.919968\pi\) | |||||||
\(684\) | −1.12117e7 | −0.916285 | ||||||||
\(685\) | 1.15630e7 | 0.941555 | ||||||||
\(686\) | −1.38359e7 | −1.12253 | ||||||||
\(687\) | −5.45805e6 | −0.441211 | ||||||||
\(688\) | 1.06233e6 | 0.0855634 | ||||||||
\(689\) | −992293. | −0.0796328 | ||||||||
\(690\) | 1.65529e6 | 0.132358 | ||||||||
\(691\) | 1.22060e7 | 0.972472 | 0.486236 | − | 0.873828i | \(-0.338370\pi\) | ||||
0.486236 | + | 0.873828i | \(0.338370\pi\) | |||||||
\(692\) | 2.36877e7 | 1.88043 | ||||||||
\(693\) | 6.53847e6 | 0.517182 | ||||||||
\(694\) | −3.85699e7 | −3.03983 | ||||||||
\(695\) | 3.71924e6 | 0.292073 | ||||||||
\(696\) | −4.40691e6 | −0.344835 | ||||||||
\(697\) | −6.94071e6 | −0.541155 | ||||||||
\(698\) | −3.19489e7 | −2.48209 | ||||||||
\(699\) | 1.30440e7 | 1.00976 | ||||||||
\(700\) | −1.43743e7 | −1.10877 | ||||||||
\(701\) | 6.09955e6 | 0.468816 | 0.234408 | − | 0.972138i | \(-0.424685\pi\) | ||||
0.234408 | + | 0.972138i | \(0.424685\pi\) | |||||||
\(702\) | −195037. | −0.0149374 | ||||||||
\(703\) | −9.36143e6 | −0.714420 | ||||||||
\(704\) | −2.69481e7 | −2.04925 | ||||||||
\(705\) | 6.98905e6 | 0.529597 | ||||||||
\(706\) | −2.11104e7 | −1.59399 | ||||||||
\(707\) | −1.38171e7 | −1.03961 | ||||||||
\(708\) | −8.89207e6 | −0.666683 | ||||||||
\(709\) | 2.32369e7 | 1.73605 | 0.868026 | − | 0.496518i | \(-0.165388\pi\) | ||||
0.868026 | + | 0.496518i | \(0.165388\pi\) | |||||||
\(710\) | −1.37190e7 | −1.02136 | ||||||||
\(711\) | 3.02687e6 | 0.224553 | ||||||||
\(712\) | 1.28458e7 | 0.949645 | ||||||||
\(713\) | 1.12688e6 | 0.0830145 | ||||||||
\(714\) | −5.53764e6 | −0.406518 | ||||||||
\(715\) | 563883. | 0.0412500 | ||||||||
\(716\) | 8.61493e6 | 0.628014 | ||||||||
\(717\) | 9.96012e6 | 0.723547 | ||||||||
\(718\) | −5.58815e6 | −0.404536 | ||||||||
\(719\) | −1.64452e7 | −1.18636 | −0.593179 | − | 0.805071i | \(-0.702127\pi\) | ||||
−0.593179 | + | 0.805071i | \(0.702127\pi\) | |||||||
\(720\) | −496062. | −0.0356619 | ||||||||
\(721\) | 1.18050e7 | 0.845723 | ||||||||
\(722\) | 3.79855e7 | 2.71191 | ||||||||
\(723\) | −9.23348e6 | −0.656931 | ||||||||
\(724\) | 2.42399e7 | 1.71863 | ||||||||
\(725\) | 4.12821e6 | 0.291687 | ||||||||
\(726\) | 9.23814e6 | 0.650493 | ||||||||
\(727\) | −3.66575e6 | −0.257233 | −0.128617 | − | 0.991694i | \(-0.541054\pi\) | ||||
−0.128617 | + | 0.991694i | \(0.541054\pi\) | |||||||
\(728\) | −911076. | −0.0637127 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.30324e7 | 0.905146 | ||||||||
\(731\) | −2.78675e6 | −0.192888 | ||||||||
\(732\) | −1.28817e7 | −0.888579 | ||||||||
\(733\) | −2.15654e7 | −1.48251 | −0.741256 | − | 0.671223i | \(-0.765769\pi\) | ||||
−0.741256 | + | 0.671223i | \(0.765769\pi\) | |||||||
\(734\) | 2.49571e7 | 1.70984 | ||||||||
\(735\) | −2.41996e6 | −0.165231 | ||||||||
\(736\) | 2.65083e6 | 0.180380 | ||||||||
\(737\) | −1.37171e7 | −0.930235 | ||||||||
\(738\) | 1.21667e7 | 0.822305 | ||||||||
\(739\) | 2.21913e7 | 1.49476 | 0.747380 | − | 0.664397i | \(-0.231311\pi\) | ||||
0.747380 | + | 0.664397i | \(0.231311\pi\) | |||||||
\(740\) | −7.39184e6 | −0.496219 | ||||||||
\(741\) | 665681. | 0.0445370 | ||||||||
\(742\) | 4.93875e7 | 3.29312 | ||||||||
\(743\) | −6.61440e6 | −0.439560 | −0.219780 | − | 0.975549i | \(-0.570534\pi\) | ||||
−0.219780 | + | 0.975549i | \(0.570534\pi\) | |||||||
\(744\) | −3.90971e6 | −0.258948 | ||||||||
\(745\) | 409609. | 0.0270382 | ||||||||
\(746\) | −2.72448e7 | −1.79241 | ||||||||
\(747\) | 6.22902e6 | 0.408431 | ||||||||
\(748\) | −1.20600e7 | −0.788119 | ||||||||
\(749\) | −1.52927e7 | −0.996044 | ||||||||
\(750\) | 1.51582e7 | 0.983999 | ||||||||
\(751\) | −8.17370e6 | −0.528834 | −0.264417 | − | 0.964409i | \(-0.585179\pi\) | ||||
−0.264417 | + | 0.964409i | \(0.585179\pi\) | |||||||
\(752\) | −3.38323e6 | −0.218166 | ||||||||
\(753\) | −9.71487e6 | −0.624381 | ||||||||
\(754\) | 642394. | 0.0411503 | ||||||||
\(755\) | 1.83222e7 | 1.16979 | ||||||||
\(756\) | 6.09487e6 | 0.387846 | ||||||||
\(757\) | −6.07796e6 | −0.385495 | −0.192747 | − | 0.981248i | \(-0.561740\pi\) | ||||
−0.192747 | + | 0.981248i | \(0.561740\pi\) | |||||||
\(758\) | 2.58686e7 | 1.63531 | ||||||||
\(759\) | −2.48186e6 | −0.156377 | ||||||||
\(760\) | 1.96015e7 | 1.23099 | ||||||||
\(761\) | 2.93696e6 | 0.183838 | 0.0919192 | − | 0.995766i | \(-0.470700\pi\) | ||||
0.0919192 | + | 0.995766i | \(0.470700\pi\) | |||||||
\(762\) | −1.66170e7 | −1.03673 | ||||||||
\(763\) | 3.75195e7 | 2.33317 | ||||||||
\(764\) | 9.21971e6 | 0.571457 | ||||||||
\(765\) | 1.30129e6 | 0.0803936 | ||||||||
\(766\) | 3.04882e7 | 1.87741 | ||||||||
\(767\) | 527957. | 0.0324048 | ||||||||
\(768\) | −1.17370e7 | −0.718047 | ||||||||
\(769\) | 6.47116e6 | 0.394608 | 0.197304 | − | 0.980342i | \(-0.436781\pi\) | ||||
0.197304 | + | 0.980342i | \(0.436781\pi\) | |||||||
\(770\) | −2.80651e7 | −1.70584 | ||||||||
\(771\) | 1.12379e7 | 0.680847 | ||||||||
\(772\) | 1.13929e7 | 0.688003 | ||||||||
\(773\) | 2.52231e7 | 1.51827 | 0.759136 | − | 0.650932i | \(-0.225622\pi\) | ||||
0.759136 | + | 0.650932i | \(0.225622\pi\) | |||||||
\(774\) | 4.88504e6 | 0.293100 | ||||||||
\(775\) | 3.66245e6 | 0.219037 | ||||||||
\(776\) | 1.25385e7 | 0.747468 | ||||||||
\(777\) | 5.08904e6 | 0.302401 | ||||||||
\(778\) | −2.02143e7 | −1.19732 | ||||||||
\(779\) | −4.15263e7 | −2.45177 | ||||||||
\(780\) | 525626. | 0.0309343 | ||||||||
\(781\) | 2.05697e7 | 1.20670 | ||||||||
\(782\) | 2.10197e6 | 0.122916 | ||||||||
\(783\) | −1.75041e6 | −0.102032 | ||||||||
\(784\) | 1.17145e6 | 0.0680663 | ||||||||
\(785\) | 2.20895e7 | 1.27942 | ||||||||
\(786\) | 1.97555e7 | 1.14059 | ||||||||
\(787\) | −1.74674e7 | −1.00529 | −0.502644 | − | 0.864493i | \(-0.667639\pi\) | ||||
−0.502644 | + | 0.864493i | \(0.667639\pi\) | |||||||
\(788\) | −2.31693e7 | −1.32922 | ||||||||
\(789\) | 481140. | 0.0275156 | ||||||||
\(790\) | −1.29922e7 | −0.740655 | ||||||||
\(791\) | 3.38287e7 | 1.92240 | ||||||||
\(792\) | 8.61080e6 | 0.487787 | ||||||||
\(793\) | 764838. | 0.0431903 | ||||||||
\(794\) | −3.06435e7 | −1.72499 | ||||||||
\(795\) | −1.16056e7 | −0.651253 | ||||||||
\(796\) | −3.49246e7 | −1.95366 | ||||||||
\(797\) | 2.12790e6 | 0.118660 | 0.0593302 | − | 0.998238i | \(-0.481104\pi\) | ||||
0.0593302 | + | 0.998238i | \(0.481104\pi\) | |||||||
\(798\) | −3.31317e7 | −1.84177 | ||||||||
\(799\) | 8.87505e6 | 0.491817 | ||||||||
\(800\) | 8.61542e6 | 0.475939 | ||||||||
\(801\) | 5.10231e6 | 0.280986 | ||||||||
\(802\) | 3.30266e7 | 1.81312 | ||||||||
\(803\) | −1.95402e7 | −1.06940 | ||||||||
\(804\) | −1.27864e7 | −0.697604 | ||||||||
\(805\) | 3.07125e6 | 0.167042 | ||||||||
\(806\) | 569917. | 0.0309011 | ||||||||
\(807\) | −1.07919e7 | −0.583328 | ||||||||
\(808\) | −1.81964e7 | −0.980519 | ||||||||
\(809\) | −5.17917e6 | −0.278220 | −0.139110 | − | 0.990277i | \(-0.544424\pi\) | ||||
−0.139110 | + | 0.990277i | \(0.544424\pi\) | |||||||
\(810\) | −2.28110e6 | −0.122161 | ||||||||
\(811\) | 2.72737e7 | 1.45610 | 0.728050 | − | 0.685524i | \(-0.240427\pi\) | ||||
0.728050 | + | 0.685524i | \(0.240427\pi\) | |||||||
\(812\) | −2.00747e7 | −1.06846 | ||||||||
\(813\) | 5.36053e6 | 0.284434 | ||||||||
\(814\) | 1.76517e7 | 0.933740 | ||||||||
\(815\) | −2.24459e7 | −1.18371 | ||||||||
\(816\) | −629925. | −0.0331179 | ||||||||
\(817\) | −1.66731e7 | −0.873900 | ||||||||
\(818\) | −2.75149e7 | −1.43775 | ||||||||
\(819\) | −361876. | −0.0188517 | ||||||||
\(820\) | −3.27894e7 | −1.70294 | ||||||||
\(821\) | 2.28417e7 | 1.18269 | 0.591346 | − | 0.806418i | \(-0.298597\pi\) | ||||
0.591346 | + | 0.806418i | \(0.298597\pi\) | |||||||
\(822\) | −2.57392e7 | −1.32866 | ||||||||
\(823\) | 1.38673e7 | 0.713664 | 0.356832 | − | 0.934169i | \(-0.383857\pi\) | ||||
0.356832 | + | 0.934169i | \(0.383857\pi\) | |||||||
\(824\) | 1.55465e7 | 0.797656 | ||||||||
\(825\) | −8.06624e6 | −0.412607 | ||||||||
\(826\) | −2.62770e7 | −1.34006 | ||||||||
\(827\) | −7.98777e6 | −0.406127 | −0.203064 | − | 0.979166i | \(-0.565090\pi\) | ||||
−0.203064 | + | 0.979166i | \(0.565090\pi\) | |||||||
\(828\) | −2.31348e6 | −0.117271 | ||||||||
\(829\) | −8.88714e6 | −0.449134 | −0.224567 | − | 0.974459i | \(-0.572097\pi\) | ||||
−0.224567 | + | 0.974459i | \(0.572097\pi\) | |||||||
\(830\) | −2.67368e7 | −1.34715 | ||||||||
\(831\) | 1.93017e7 | 0.969600 | ||||||||
\(832\) | 1.49146e6 | 0.0746969 | ||||||||
\(833\) | −3.07299e6 | −0.153444 | ||||||||
\(834\) | −8.27897e6 | −0.412156 | ||||||||
\(835\) | −8.34498e6 | −0.414199 | ||||||||
\(836\) | −7.21547e7 | −3.57066 | ||||||||
\(837\) | −1.55292e6 | −0.0766189 | ||||||||
\(838\) | −1.40386e7 | −0.690581 | ||||||||
\(839\) | −2.25661e7 | −1.10676 | −0.553379 | − | 0.832930i | \(-0.686662\pi\) | ||||
−0.553379 | + | 0.832930i | \(0.686662\pi\) | |||||||
\(840\) | −1.06557e7 | −0.521055 | ||||||||
\(841\) | −1.47458e7 | −0.718917 | ||||||||
\(842\) | 6.92268e6 | 0.336507 | ||||||||
\(843\) | −1.14709e7 | −0.555943 | ||||||||
\(844\) | 1.52531e7 | 0.737057 | ||||||||
\(845\) | 1.38896e7 | 0.669187 | ||||||||
\(846\) | −1.55575e7 | −0.747334 | ||||||||
\(847\) | 1.71406e7 | 0.820953 | ||||||||
\(848\) | 5.61799e6 | 0.268282 | ||||||||
\(849\) | 1.19804e7 | 0.570430 | ||||||||
\(850\) | 6.83156e6 | 0.324319 | ||||||||
\(851\) | −1.93169e6 | −0.0914350 | ||||||||
\(852\) | 1.91741e7 | 0.904932 | ||||||||
\(853\) | −3.35094e7 | −1.57686 | −0.788431 | − | 0.615124i | \(-0.789106\pi\) | ||||
−0.788431 | + | 0.615124i | \(0.789106\pi\) | |||||||
\(854\) | −3.80668e7 | −1.78608 | ||||||||
\(855\) | 7.78563e6 | 0.364232 | ||||||||
\(856\) | −2.01396e7 | −0.939433 | ||||||||
\(857\) | −1.84965e7 | −0.860276 | −0.430138 | − | 0.902763i | \(-0.641535\pi\) | ||||
−0.430138 | + | 0.902763i | \(0.641535\pi\) | |||||||
\(858\) | −1.25519e6 | −0.0582094 | ||||||||
\(859\) | 3.55324e7 | 1.64302 | 0.821508 | − | 0.570198i | \(-0.193133\pi\) | ||||
0.821508 | + | 0.570198i | \(0.193133\pi\) | |||||||
\(860\) | −1.31652e7 | −0.606989 | ||||||||
\(861\) | 2.25744e7 | 1.03779 | ||||||||
\(862\) | 2.00258e7 | 0.917955 | ||||||||
\(863\) | −1.37196e7 | −0.627067 | −0.313534 | − | 0.949577i | \(-0.601513\pi\) | ||||
−0.313534 | + | 0.949577i | \(0.601513\pi\) | |||||||
\(864\) | −3.65304e6 | −0.166483 | ||||||||
\(865\) | −1.64492e7 | −0.747489 | ||||||||
\(866\) | 5.32501e7 | 2.41282 | ||||||||
\(867\) | −1.11263e7 | −0.502692 | ||||||||
\(868\) | −1.78098e7 | −0.802342 | ||||||||
\(869\) | 1.94799e7 | 0.875060 | ||||||||
\(870\) | 7.51327e6 | 0.336536 | ||||||||
\(871\) | 759180. | 0.0339078 | ||||||||
\(872\) | 4.94111e7 | 2.20056 | ||||||||
\(873\) | 4.98026e6 | 0.221165 | ||||||||
\(874\) | 1.25761e7 | 0.556886 | ||||||||
\(875\) | 2.81248e7 | 1.24185 | ||||||||
\(876\) | −1.82145e7 | −0.801969 | ||||||||
\(877\) | −1.74346e7 | −0.765443 | −0.382721 | − | 0.923864i | \(-0.625013\pi\) | ||||
−0.382721 | + | 0.923864i | \(0.625013\pi\) | |||||||
\(878\) | 2.82230e7 | 1.23557 | ||||||||
\(879\) | −4.89348e6 | −0.213622 | ||||||||
\(880\) | −3.19249e6 | −0.138971 | ||||||||
\(881\) | 3.33087e7 | 1.44583 | 0.722916 | − | 0.690936i | \(-0.242801\pi\) | ||||
0.722916 | + | 0.690936i | \(0.242801\pi\) | |||||||
\(882\) | 5.38680e6 | 0.233163 | ||||||||
\(883\) | 3.36375e6 | 0.145185 | 0.0725925 | − | 0.997362i | \(-0.476873\pi\) | ||||
0.0725925 | + | 0.997362i | \(0.476873\pi\) | |||||||
\(884\) | 667466. | 0.0287276 | ||||||||
\(885\) | 6.17484e6 | 0.265013 | ||||||||
\(886\) | −2.73736e7 | −1.17151 | ||||||||
\(887\) | −1.07106e7 | −0.457095 | −0.228547 | − | 0.973533i | \(-0.573398\pi\) | ||||
−0.228547 | + | 0.973533i | \(0.573398\pi\) | |||||||
\(888\) | 6.70198e6 | 0.285214 | ||||||||
\(889\) | −3.08315e7 | −1.30840 | ||||||||
\(890\) | −2.19006e7 | −0.926790 | ||||||||
\(891\) | 3.42018e6 | 0.144329 | ||||||||
\(892\) | −3.44162e7 | −1.44828 | ||||||||
\(893\) | 5.30994e7 | 2.22824 | ||||||||
\(894\) | −911783. | −0.0381547 | ||||||||
\(895\) | −5.98239e6 | −0.249642 | ||||||||
\(896\) | −4.94008e7 | −2.05572 | ||||||||
\(897\) | 137360. | 0.00570006 | ||||||||
\(898\) | 3.05165e7 | 1.26283 | ||||||||
\(899\) | 5.11486e6 | 0.211074 | ||||||||
\(900\) | −7.51898e6 | −0.309423 | ||||||||
\(901\) | −1.47374e7 | −0.604795 | ||||||||
\(902\) | 7.83010e7 | 3.20443 | ||||||||
\(903\) | 9.06380e6 | 0.369906 | ||||||||
\(904\) | 4.45505e7 | 1.81314 | ||||||||
\(905\) | −1.68327e7 | −0.683174 | ||||||||
\(906\) | −4.07849e7 | −1.65074 | ||||||||
\(907\) | 1.90456e7 | 0.768735 | 0.384367 | − | 0.923180i | \(-0.374420\pi\) | ||||
0.384367 | + | 0.923180i | \(0.374420\pi\) | |||||||
\(908\) | 3.71305e7 | 1.49457 | ||||||||
\(909\) | −7.22753e6 | −0.290122 | ||||||||
\(910\) | 1.55328e6 | 0.0621793 | ||||||||
\(911\) | 1.05019e6 | 0.0419249 | 0.0209624 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209624 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(912\) | −3.76884e6 | −0.150045 | ||||||||
\(913\) | 4.00879e7 | 1.59161 | ||||||||
\(914\) | 5.40102e7 | 2.13851 | ||||||||
\(915\) | 8.94534e6 | 0.353219 | ||||||||
\(916\) | −3.27431e7 | −1.28938 | ||||||||
\(917\) | 3.66547e7 | 1.43948 | ||||||||
\(918\) | −2.89666e6 | −0.113446 | ||||||||
\(919\) | −1.19851e7 | −0.468114 | −0.234057 | − | 0.972223i | \(-0.575200\pi\) | ||||
−0.234057 | + | 0.972223i | \(0.575200\pi\) | |||||||
\(920\) | 4.04467e6 | 0.157548 | ||||||||
\(921\) | 1.94526e7 | 0.755664 | ||||||||
\(922\) | −1.61088e7 | −0.624073 | ||||||||
\(923\) | −1.13844e6 | −0.0439852 | ||||||||
\(924\) | 3.92246e7 | 1.51140 | ||||||||
\(925\) | −6.27813e6 | −0.241255 | ||||||||
\(926\) | 2.86492e7 | 1.09796 | ||||||||
\(927\) | 6.17503e6 | 0.236015 | ||||||||
\(928\) | 1.20320e7 | 0.458636 | ||||||||
\(929\) | 1.29362e7 | 0.491777 | 0.245888 | − | 0.969298i | \(-0.420920\pi\) | ||||
0.245888 | + | 0.969298i | \(0.420920\pi\) | |||||||
\(930\) | 6.66560e6 | 0.252716 | ||||||||
\(931\) | −1.83857e7 | −0.695194 | ||||||||
\(932\) | 7.82513e7 | 2.95088 | ||||||||
\(933\) | −2.05044e7 | −0.771159 | ||||||||
\(934\) | −1.62494e7 | −0.609496 | ||||||||
\(935\) | 8.37469e6 | 0.313285 | ||||||||
\(936\) | −476570. | −0.0177802 | ||||||||
\(937\) | −1.25390e7 | −0.466567 | −0.233283 | − | 0.972409i | \(-0.574947\pi\) | ||||
−0.233283 | + | 0.972409i | \(0.574947\pi\) | |||||||
\(938\) | −3.77852e7 | −1.40222 | ||||||||
\(939\) | −2.10753e7 | −0.780028 | ||||||||
\(940\) | 4.19276e7 | 1.54768 | ||||||||
\(941\) | −2.45328e7 | −0.903178 | −0.451589 | − | 0.892226i | \(-0.649143\pi\) | ||||
−0.451589 | + | 0.892226i | \(0.649143\pi\) | |||||||
\(942\) | −4.91710e7 | −1.80544 | ||||||||
\(943\) | −8.56874e6 | −0.313789 | ||||||||
\(944\) | −2.98909e6 | −0.109171 | ||||||||
\(945\) | −4.23241e6 | −0.154173 | ||||||||
\(946\) | 3.14385e7 | 1.14218 | ||||||||
\(947\) | −2.08008e7 | −0.753713 | −0.376856 | − | 0.926272i | \(-0.622995\pi\) | ||||
−0.376856 | + | 0.926272i | \(0.622995\pi\) | |||||||
\(948\) | 1.81583e7 | 0.656228 | ||||||||
\(949\) | 1.08147e6 | 0.0389806 | ||||||||
\(950\) | 4.08732e7 | 1.46937 | ||||||||
\(951\) | 1.53834e7 | 0.551570 | ||||||||
\(952\) | −1.35311e7 | −0.483885 | ||||||||
\(953\) | −9.76608e6 | −0.348328 | −0.174164 | − | 0.984717i | \(-0.555722\pi\) | ||||
−0.174164 | + | 0.984717i | \(0.555722\pi\) | |||||||
\(954\) | 2.58339e7 | 0.919008 | ||||||||
\(955\) | −6.40236e6 | −0.227160 | ||||||||
\(956\) | 5.97512e7 | 2.11447 | ||||||||
\(957\) | −1.12651e7 | −0.397606 | ||||||||
\(958\) | −4.99212e7 | −1.75740 | ||||||||
\(959\) | −4.77570e7 | −1.67684 | ||||||||
\(960\) | 1.74437e7 | 0.610886 | ||||||||
\(961\) | −2.40914e7 | −0.841498 | ||||||||
\(962\) | −976946. | −0.0340356 | ||||||||
\(963\) | −7.99937e6 | −0.277965 | ||||||||
\(964\) | −5.53920e7 | −1.91979 | ||||||||
\(965\) | −7.91147e6 | −0.273488 | ||||||||
\(966\) | −6.83656e6 | −0.235719 | ||||||||
\(967\) | −2.35516e7 | −0.809942 | −0.404971 | − | 0.914329i | \(-0.632718\pi\) | ||||
−0.404971 | + | 0.914329i | \(0.632718\pi\) | |||||||
\(968\) | 2.25733e7 | 0.774294 | ||||||||
\(969\) | 9.88659e6 | 0.338250 | ||||||||
\(970\) | −2.13768e7 | −0.729479 | ||||||||
\(971\) | 2.32199e7 | 0.790336 | 0.395168 | − | 0.918609i | \(-0.370686\pi\) | ||||
0.395168 | + | 0.918609i | \(0.370686\pi\) | |||||||
\(972\) | 3.18814e6 | 0.108236 | ||||||||
\(973\) | −1.53610e7 | −0.520160 | ||||||||
\(974\) | −5.67305e7 | −1.91610 | ||||||||
\(975\) | 446431. | 0.0150398 | ||||||||
\(976\) | −4.33022e6 | −0.145508 | ||||||||
\(977\) | −3.29920e7 | −1.10579 | −0.552895 | − | 0.833251i | \(-0.686477\pi\) | ||||
−0.552895 | + | 0.833251i | \(0.686477\pi\) | |||||||
\(978\) | 4.99643e7 | 1.67037 | ||||||||
\(979\) | 3.28368e7 | 1.09497 | ||||||||
\(980\) | −1.45175e7 | −0.482864 | ||||||||
\(981\) | 1.96259e7 | 0.651114 | ||||||||
\(982\) | 4.84440e7 | 1.60310 | ||||||||
\(983\) | −2.82144e7 | −0.931294 | −0.465647 | − | 0.884970i | \(-0.654178\pi\) | ||||
−0.465647 | + | 0.884970i | \(0.654178\pi\) | |||||||
\(984\) | 2.97292e7 | 0.978804 | ||||||||
\(985\) | 1.60893e7 | 0.528379 | ||||||||
\(986\) | 9.54074e6 | 0.312529 | ||||||||
\(987\) | −2.88658e7 | −0.943170 | ||||||||
\(988\) | 3.99345e6 | 0.130153 | ||||||||
\(989\) | −3.44042e6 | −0.111846 | ||||||||
\(990\) | −1.46804e7 | −0.476048 | ||||||||
\(991\) | −3.77541e7 | −1.22118 | −0.610590 | − | 0.791947i | \(-0.709068\pi\) | ||||
−0.610590 | + | 0.791947i | \(0.709068\pi\) | |||||||
\(992\) | 1.06745e7 | 0.344405 | ||||||||
\(993\) | 2.78365e7 | 0.895863 | ||||||||
\(994\) | 5.66615e7 | 1.81896 | ||||||||
\(995\) | 2.42524e7 | 0.776600 | ||||||||
\(996\) | 3.73682e7 | 1.19359 | ||||||||
\(997\) | 3.33776e7 | 1.06345 | 0.531726 | − | 0.846917i | \(-0.321544\pi\) | ||||
0.531726 | + | 0.846917i | \(0.321544\pi\) | |||||||
\(998\) | 8.24758e7 | 2.62120 | ||||||||
\(999\) | 2.66200e6 | 0.0843907 |
(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 | 69.6.a.e.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 207.6.a.f.1.2 | 5 | |||
4.3 | odd | 2 | 1104.6.a.r.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.6.a.e.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
207.6.a.f.1.2 | 5 | 3.2 | odd | 2 | |||
1104.6.a.r.1.2 | 5 | 4.3 | odd | 2 |