Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,6,Mod(1,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, 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("1014.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.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: | \(162.629193290\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 2192x^{2} - 12432x + 55224 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 78) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-42.7585\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.1 |
$q$-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 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 83.5169 | 1.49400 | 0.746998 | − | 0.664826i | \(-0.231494\pi\) | ||||
0.746998 | + | 0.664826i | \(0.231494\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 187.367 | 1.44527 | 0.722633 | − | 0.691232i | \(-0.242932\pi\) | ||||
0.722633 | + | 0.691232i | \(0.242932\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −334.068 | −1.05642 | ||||||||
\(11\) | −786.334 | −1.95941 | −0.979705 | − | 0.200447i | \(-0.935761\pi\) | ||||
−0.979705 | + | 0.200447i | \(0.935761\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −749.468 | −1.02196 | ||||||||
\(15\) | 751.652 | 0.862559 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −923.787 | −0.775264 | −0.387632 | − | 0.921814i | \(-0.626707\pi\) | ||||
−0.387632 | + | 0.921814i | \(0.626707\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | 434.886 | 0.276370 | 0.138185 | − | 0.990406i | \(-0.455873\pi\) | ||||
0.138185 | + | 0.990406i | \(0.455873\pi\) | |||||||
\(20\) | 1336.27 | 0.746998 | ||||||||
\(21\) | 1686.30 | 0.834425 | ||||||||
\(22\) | 3145.33 | 1.38551 | ||||||||
\(23\) | −3790.69 | −1.49416 | −0.747082 | − | 0.664732i | \(-0.768546\pi\) | ||||
−0.747082 | + | 0.664732i | \(0.768546\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 3850.08 | 1.23203 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 2997.87 | 0.722633 | ||||||||
\(29\) | −3735.14 | −0.824731 | −0.412365 | − | 0.911019i | \(-0.635297\pi\) | ||||
−0.412365 | + | 0.911019i | \(0.635297\pi\) | |||||||
\(30\) | −3006.61 | −0.609921 | ||||||||
\(31\) | 2690.43 | 0.502826 | 0.251413 | − | 0.967880i | \(-0.419105\pi\) | ||||
0.251413 | + | 0.967880i | \(0.419105\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −7077.00 | −1.13127 | ||||||||
\(34\) | 3695.15 | 0.548195 | ||||||||
\(35\) | 15648.3 | 2.15922 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −1734.37 | −0.208275 | −0.104138 | − | 0.994563i | \(-0.533208\pi\) | ||||
−0.104138 | + | 0.994563i | \(0.533208\pi\) | |||||||
\(38\) | −1739.54 | −0.195423 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5345.08 | −0.528208 | ||||||||
\(41\) | −12144.6 | −1.12830 | −0.564150 | − | 0.825672i | \(-0.690796\pi\) | ||||
−0.564150 | + | 0.825672i | \(0.690796\pi\) | |||||||
\(42\) | −6745.21 | −0.590027 | ||||||||
\(43\) | −1808.26 | −0.149138 | −0.0745690 | − | 0.997216i | \(-0.523758\pi\) | ||||
−0.0745690 | + | 0.997216i | \(0.523758\pi\) | |||||||
\(44\) | −12581.3 | −0.979705 | ||||||||
\(45\) | 6764.87 | 0.497999 | ||||||||
\(46\) | 15162.8 | 1.05653 | ||||||||
\(47\) | −5647.45 | −0.372913 | −0.186457 | − | 0.982463i | \(-0.559700\pi\) | ||||
−0.186457 | + | 0.982463i | \(0.559700\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | 18299.4 | 1.08879 | ||||||||
\(50\) | −15400.3 | −0.871174 | ||||||||
\(51\) | −8314.09 | −0.447599 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −30508.2 | −1.49186 | −0.745929 | − | 0.666026i | \(-0.767994\pi\) | ||||
−0.745929 | + | 0.666026i | \(0.767994\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | −65672.2 | −2.92735 | ||||||||
\(56\) | −11991.5 | −0.510979 | ||||||||
\(57\) | 3913.97 | 0.159563 | ||||||||
\(58\) | 14940.6 | 0.583173 | ||||||||
\(59\) | −38919.0 | −1.45556 | −0.727782 | − | 0.685808i | \(-0.759449\pi\) | ||||
−0.727782 | + | 0.685808i | \(0.759449\pi\) | |||||||
\(60\) | 12026.4 | 0.431280 | ||||||||
\(61\) | 9010.71 | 0.310052 | 0.155026 | − | 0.987910i | \(-0.450454\pi\) | ||||
0.155026 | + | 0.987910i | \(0.450454\pi\) | |||||||
\(62\) | −10761.7 | −0.355551 | ||||||||
\(63\) | 15176.7 | 0.481755 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 28308.0 | 0.799925 | ||||||||
\(67\) | −28172.0 | −0.766709 | −0.383355 | − | 0.923601i | \(-0.625231\pi\) | ||||
−0.383355 | + | 0.923601i | \(0.625231\pi\) | |||||||
\(68\) | −14780.6 | −0.387632 | ||||||||
\(69\) | −34116.2 | −0.862656 | ||||||||
\(70\) | −62593.3 | −1.52680 | ||||||||
\(71\) | −80313.2 | −1.89078 | −0.945390 | − | 0.325941i | \(-0.894319\pi\) | ||||
−0.945390 | + | 0.325941i | \(0.894319\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | −5864.17 | −0.128795 | −0.0643975 | − | 0.997924i | \(-0.520513\pi\) | ||||
−0.0643975 | + | 0.997924i | \(0.520513\pi\) | |||||||
\(74\) | 6937.48 | 0.147273 | ||||||||
\(75\) | 34650.7 | 0.711310 | ||||||||
\(76\) | 6958.18 | 0.138185 | ||||||||
\(77\) | −147333. | −2.83187 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17250.7 | −0.310985 | −0.155492 | − | 0.987837i | \(-0.549696\pi\) | ||||
−0.155492 | + | 0.987837i | \(0.549696\pi\) | |||||||
\(80\) | 21380.3 | 0.373499 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 48578.5 | 0.797829 | ||||||||
\(83\) | 74769.4 | 1.19132 | 0.595661 | − | 0.803236i | \(-0.296890\pi\) | ||||
0.595661 | + | 0.803236i | \(0.296890\pi\) | |||||||
\(84\) | 26980.8 | 0.417212 | ||||||||
\(85\) | −77151.9 | −1.15824 | ||||||||
\(86\) | 7233.02 | 0.105457 | ||||||||
\(87\) | −33616.3 | −0.476158 | ||||||||
\(88\) | 50325.4 | 0.692756 | ||||||||
\(89\) | 45780.6 | 0.612641 | 0.306320 | − | 0.951928i | \(-0.400902\pi\) | ||||
0.306320 | + | 0.951928i | \(0.400902\pi\) | |||||||
\(90\) | −27059.5 | −0.352138 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −60651.0 | −0.747082 | ||||||||
\(93\) | 24213.9 | 0.290307 | ||||||||
\(94\) | 22589.8 | 0.263690 | ||||||||
\(95\) | 36320.4 | 0.412896 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | −77912.8 | −0.840774 | −0.420387 | − | 0.907345i | \(-0.638106\pi\) | ||||
−0.420387 | + | 0.907345i | \(0.638106\pi\) | |||||||
\(98\) | −73197.5 | −0.769894 | ||||||||
\(99\) | −63693.0 | −0.653136 | ||||||||
\(100\) | 61601.3 | 0.616013 | ||||||||
\(101\) | −17140.1 | −0.167190 | −0.0835949 | − | 0.996500i | \(-0.526640\pi\) | ||||
−0.0835949 | + | 0.996500i | \(0.526640\pi\) | |||||||
\(102\) | 33256.3 | 0.316500 | ||||||||
\(103\) | 102916. | 0.955848 | 0.477924 | − | 0.878401i | \(-0.341390\pi\) | ||||
0.477924 | + | 0.878401i | \(0.341390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 140835. | 1.24663 | ||||||||
\(106\) | 122033. | 1.05490 | ||||||||
\(107\) | 133735. | 1.12924 | 0.564619 | − | 0.825352i | \(-0.309023\pi\) | ||||
0.564619 | + | 0.825352i | \(0.309023\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | −237067. | −1.91120 | −0.955598 | − | 0.294674i | \(-0.904789\pi\) | ||||
−0.955598 | + | 0.294674i | \(0.904789\pi\) | |||||||
\(110\) | 262689. | 2.06995 | ||||||||
\(111\) | −15609.3 | −0.120248 | ||||||||
\(112\) | 47965.9 | 0.361317 | ||||||||
\(113\) | 138273. | 1.01869 | 0.509343 | − | 0.860564i | \(-0.329889\pi\) | ||||
0.509343 | + | 0.860564i | \(0.329889\pi\) | |||||||
\(114\) | −15655.9 | −0.112828 | ||||||||
\(115\) | −316587. | −2.23228 | ||||||||
\(116\) | −59762.3 | −0.412365 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 155676. | 1.02924 | ||||||||
\(119\) | −173087. | −1.12046 | ||||||||
\(120\) | −48105.8 | −0.304961 | ||||||||
\(121\) | 457270. | 2.83928 | ||||||||
\(122\) | −36042.8 | −0.219240 | ||||||||
\(123\) | −109302. | −0.651425 | ||||||||
\(124\) | 43046.9 | 0.251413 | ||||||||
\(125\) | 60556.4 | 0.346645 | ||||||||
\(126\) | −60706.9 | −0.340653 | ||||||||
\(127\) | −283497. | −1.55969 | −0.779847 | − | 0.625970i | \(-0.784703\pi\) | ||||
−0.779847 | + | 0.625970i | \(0.784703\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −16274.3 | −0.0861049 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 101624. | 0.517391 | 0.258695 | − | 0.965959i | \(-0.416707\pi\) | ||||
0.258695 | + | 0.965959i | \(0.416707\pi\) | |||||||
\(132\) | −113232. | −0.565633 | ||||||||
\(133\) | 81483.3 | 0.399429 | ||||||||
\(134\) | 112688. | 0.542145 | ||||||||
\(135\) | 60883.8 | 0.287520 | ||||||||
\(136\) | 59122.4 | 0.274097 | ||||||||
\(137\) | 136816. | 0.622781 | 0.311390 | − | 0.950282i | \(-0.399205\pi\) | ||||
0.311390 | + | 0.950282i | \(0.399205\pi\) | |||||||
\(138\) | 136465. | 0.609990 | ||||||||
\(139\) | 122457. | 0.537585 | 0.268793 | − | 0.963198i | \(-0.413375\pi\) | ||||
0.268793 | + | 0.963198i | \(0.413375\pi\) | |||||||
\(140\) | 250373. | 1.07961 | ||||||||
\(141\) | −50827.1 | −0.215302 | ||||||||
\(142\) | 321253. | 1.33698 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −311948. | −1.23214 | ||||||||
\(146\) | 23456.7 | 0.0910718 | ||||||||
\(147\) | 164694. | 0.628616 | ||||||||
\(148\) | −27749.9 | −0.104138 | ||||||||
\(149\) | −247858. | −0.914613 | −0.457307 | − | 0.889309i | \(-0.651186\pi\) | ||||
−0.457307 | + | 0.889309i | \(0.651186\pi\) | |||||||
\(150\) | −138603. | −0.502972 | ||||||||
\(151\) | −324290. | −1.15742 | −0.578711 | − | 0.815533i | \(-0.696444\pi\) | ||||
−0.578711 | + | 0.815533i | \(0.696444\pi\) | |||||||
\(152\) | −27832.7 | −0.0977117 | ||||||||
\(153\) | −74826.8 | −0.258421 | ||||||||
\(154\) | 589332. | 2.00243 | ||||||||
\(155\) | 224696. | 0.751220 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 407075. | 1.31803 | 0.659014 | − | 0.752130i | \(-0.270974\pi\) | ||||
0.659014 | + | 0.752130i | \(0.270974\pi\) | |||||||
\(158\) | 69002.8 | 0.219900 | ||||||||
\(159\) | −274574. | −0.861324 | ||||||||
\(160\) | −85521.3 | −0.264104 | ||||||||
\(161\) | −710250. | −2.15947 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | 192942. | 0.568799 | 0.284399 | − | 0.958706i | \(-0.408206\pi\) | ||||
0.284399 | + | 0.958706i | \(0.408206\pi\) | |||||||
\(164\) | −194314. | −0.564150 | ||||||||
\(165\) | −591050. | −1.69011 | ||||||||
\(166\) | −299078. | −0.842391 | ||||||||
\(167\) | 358847. | 0.995675 | 0.497838 | − | 0.867270i | \(-0.334128\pi\) | ||||
0.497838 | + | 0.867270i | \(0.334128\pi\) | |||||||
\(168\) | −107923. | −0.295014 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 308608. | 0.819001 | ||||||||
\(171\) | 35225.8 | 0.0921235 | ||||||||
\(172\) | −28932.1 | −0.0745690 | ||||||||
\(173\) | −575252. | −1.46131 | −0.730656 | − | 0.682746i | \(-0.760786\pi\) | ||||
−0.730656 | + | 0.682746i | \(0.760786\pi\) | |||||||
\(174\) | 134465. | 0.336695 | ||||||||
\(175\) | 721378. | 1.78060 | ||||||||
\(176\) | −201301. | −0.489852 | ||||||||
\(177\) | −350271. | −0.840371 | ||||||||
\(178\) | −183122. | −0.433203 | ||||||||
\(179\) | 730150. | 1.70326 | 0.851628 | − | 0.524147i | \(-0.175616\pi\) | ||||
0.851628 | + | 0.524147i | \(0.175616\pi\) | |||||||
\(180\) | 108238. | 0.248999 | ||||||||
\(181\) | −18004.4 | −0.0408490 | −0.0204245 | − | 0.999791i | \(-0.506502\pi\) | ||||
−0.0204245 | + | 0.999791i | \(0.506502\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 81096.4 | 0.179009 | ||||||||
\(184\) | 242604. | 0.528267 | ||||||||
\(185\) | −144849. | −0.311162 | ||||||||
\(186\) | −96855.5 | −0.205278 | ||||||||
\(187\) | 726405. | 1.51906 | ||||||||
\(188\) | −90359.3 | −0.186457 | ||||||||
\(189\) | 136591. | 0.278142 | ||||||||
\(190\) | −145281. | −0.291962 | ||||||||
\(191\) | 718887. | 1.42586 | 0.712930 | − | 0.701235i | \(-0.247368\pi\) | ||||
0.712930 | + | 0.701235i | \(0.247368\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | −163524. | −0.316001 | −0.158000 | − | 0.987439i | \(-0.550505\pi\) | ||||
−0.158000 | + | 0.987439i | \(0.550505\pi\) | |||||||
\(194\) | 311651. | 0.594517 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 292790. | 0.544397 | ||||||||
\(197\) | 41747.3 | 0.0766412 | 0.0383206 | − | 0.999265i | \(-0.487799\pi\) | ||||
0.0383206 | + | 0.999265i | \(0.487799\pi\) | |||||||
\(198\) | 254772. | 0.461837 | ||||||||
\(199\) | −159023. | −0.284661 | −0.142331 | − | 0.989819i | \(-0.545460\pi\) | ||||
−0.142331 | + | 0.989819i | \(0.545460\pi\) | |||||||
\(200\) | −246405. | −0.435587 | ||||||||
\(201\) | −253548. | −0.442660 | ||||||||
\(202\) | 68560.4 | 0.118221 | ||||||||
\(203\) | −699842. | −1.19196 | ||||||||
\(204\) | −133025. | −0.223800 | ||||||||
\(205\) | −1.01428e6 | −1.68568 | ||||||||
\(206\) | −411663. | −0.675886 | ||||||||
\(207\) | −307046. | −0.498055 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −341966. | −0.541523 | ||||||||
\(210\) | −563339. | −0.881499 | ||||||||
\(211\) | −323039. | −0.499516 | −0.249758 | − | 0.968308i | \(-0.580351\pi\) | ||||
−0.249758 | + | 0.968308i | \(0.580351\pi\) | |||||||
\(212\) | −488132. | −0.745929 | ||||||||
\(213\) | −722819. | −1.09164 | ||||||||
\(214\) | −534940. | −0.798492 | ||||||||
\(215\) | −151020. | −0.222812 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 504098. | 0.726717 | ||||||||
\(218\) | 948269. | 1.35142 | ||||||||
\(219\) | −52777.5 | −0.0743598 | ||||||||
\(220\) | −1.05075e6 | −1.46368 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 62437.3 | 0.0850280 | ||||||||
\(223\) | −1.20727e6 | −1.62570 | −0.812852 | − | 0.582470i | \(-0.802086\pi\) | ||||
−0.812852 | + | 0.582470i | \(0.802086\pi\) | |||||||
\(224\) | −191864. | −0.255489 | ||||||||
\(225\) | 311856. | 0.410675 | ||||||||
\(226\) | −553090. | −0.720319 | ||||||||
\(227\) | 885255. | 1.14026 | 0.570130 | − | 0.821555i | \(-0.306893\pi\) | ||||
0.570130 | + | 0.821555i | \(0.306893\pi\) | |||||||
\(228\) | 62623.6 | 0.0797813 | ||||||||
\(229\) | 473761. | 0.596995 | 0.298498 | − | 0.954410i | \(-0.403515\pi\) | ||||
0.298498 | + | 0.954410i | \(0.403515\pi\) | |||||||
\(230\) | 1.26635e6 | 1.57846 | ||||||||
\(231\) | −1.32600e6 | −1.63498 | ||||||||
\(232\) | 239049. | 0.291586 | ||||||||
\(233\) | −169230. | −0.204215 | −0.102107 | − | 0.994773i | \(-0.532559\pi\) | ||||
−0.102107 | + | 0.994773i | \(0.532559\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −471658. | −0.557131 | ||||||||
\(236\) | −622704. | −0.727782 | ||||||||
\(237\) | −155256. | −0.179547 | ||||||||
\(238\) | 692349. | 0.792287 | ||||||||
\(239\) | 1.46535e6 | 1.65939 | 0.829694 | − | 0.558219i | \(-0.188515\pi\) | ||||
0.829694 | + | 0.558219i | \(0.188515\pi\) | |||||||
\(240\) | 192423. | 0.215640 | ||||||||
\(241\) | −34983.5 | −0.0387990 | −0.0193995 | − | 0.999812i | \(-0.506175\pi\) | ||||
−0.0193995 | + | 0.999812i | \(0.506175\pi\) | |||||||
\(242\) | −1.82908e6 | −2.00768 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 144171. | 0.155026 | ||||||||
\(245\) | 1.52831e6 | 1.62666 | ||||||||
\(246\) | 437207. | 0.460627 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −172188. | −0.177776 | ||||||||
\(249\) | 672925. | 0.687810 | ||||||||
\(250\) | −242226. | −0.245115 | ||||||||
\(251\) | 629330. | 0.630513 | 0.315256 | − | 0.949007i | \(-0.397909\pi\) | ||||
0.315256 | + | 0.949007i | \(0.397909\pi\) | |||||||
\(252\) | 242828. | 0.240878 | ||||||||
\(253\) | 2.98075e6 | 2.92768 | ||||||||
\(254\) | 1.13399e6 | 1.10287 | ||||||||
\(255\) | −694367. | −0.668711 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 829748. | 0.783634 | 0.391817 | − | 0.920043i | \(-0.371847\pi\) | ||||
0.391817 | + | 0.920043i | \(0.371847\pi\) | |||||||
\(258\) | 65097.2 | 0.0608854 | ||||||||
\(259\) | −324964. | −0.301013 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −302546. | −0.274910 | ||||||||
\(262\) | −406497. | −0.365850 | ||||||||
\(263\) | −209606. | −0.186859 | −0.0934294 | − | 0.995626i | \(-0.529783\pi\) | ||||
−0.0934294 | + | 0.995626i | \(0.529783\pi\) | |||||||
\(264\) | 452928. | 0.399963 | ||||||||
\(265\) | −2.54795e6 | −2.22883 | ||||||||
\(266\) | −325933. | −0.282439 | ||||||||
\(267\) | 412025. | 0.353708 | ||||||||
\(268\) | −450752. | −0.383355 | ||||||||
\(269\) | 1.68780e6 | 1.42213 | 0.711066 | − | 0.703125i | \(-0.248213\pi\) | ||||
0.711066 | + | 0.703125i | \(0.248213\pi\) | |||||||
\(270\) | −243535. | −0.203307 | ||||||||
\(271\) | 1.42123e6 | 1.17555 | 0.587774 | − | 0.809025i | \(-0.300004\pi\) | ||||
0.587774 | + | 0.809025i | \(0.300004\pi\) | |||||||
\(272\) | −236490. | −0.193816 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −547264. | −0.440372 | ||||||||
\(275\) | −3.02745e6 | −2.41404 | ||||||||
\(276\) | −545859. | −0.431328 | ||||||||
\(277\) | 428628. | 0.335646 | 0.167823 | − | 0.985817i | \(-0.446326\pi\) | ||||
0.167823 | + | 0.985817i | \(0.446326\pi\) | |||||||
\(278\) | −489829. | −0.380130 | ||||||||
\(279\) | 217925. | 0.167609 | ||||||||
\(280\) | −1.00149e6 | −0.763401 | ||||||||
\(281\) | −243338. | −0.183842 | −0.0919208 | − | 0.995766i | \(-0.529301\pi\) | ||||
−0.0919208 | + | 0.995766i | \(0.529301\pi\) | |||||||
\(282\) | 203308. | 0.152241 | ||||||||
\(283\) | 1.53845e6 | 1.14187 | 0.570937 | − | 0.820994i | \(-0.306580\pi\) | ||||
0.570937 | + | 0.820994i | \(0.306580\pi\) | |||||||
\(284\) | −1.28501e6 | −0.945390 | ||||||||
\(285\) | 326883. | 0.238386 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.27550e6 | −1.63070 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | −566474. | −0.398965 | ||||||||
\(290\) | 1.24779e6 | 0.871258 | ||||||||
\(291\) | −701215. | −0.485421 | ||||||||
\(292\) | −93826.7 | −0.0643975 | ||||||||
\(293\) | −1.02136e6 | −0.695038 | −0.347519 | − | 0.937673i | \(-0.612976\pi\) | ||||
−0.347519 | + | 0.937673i | \(0.612976\pi\) | |||||||
\(294\) | −658777. | −0.444499 | ||||||||
\(295\) | −3.25040e6 | −2.17461 | ||||||||
\(296\) | 111000. | 0.0736364 | ||||||||
\(297\) | −573237. | −0.377088 | ||||||||
\(298\) | 991432. | 0.646729 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 554411. | 0.355655 | ||||||||
\(301\) | −338807. | −0.215544 | ||||||||
\(302\) | 1.29716e6 | 0.818420 | ||||||||
\(303\) | −154261. | −0.0965271 | ||||||||
\(304\) | 111331. | 0.0690926 | ||||||||
\(305\) | 752547. | 0.463217 | ||||||||
\(306\) | 299307. | 0.182732 | ||||||||
\(307\) | −535631. | −0.324354 | −0.162177 | − | 0.986762i | \(-0.551852\pi\) | ||||
−0.162177 | + | 0.986762i | \(0.551852\pi\) | |||||||
\(308\) | −2.35733e6 | −1.41593 | ||||||||
\(309\) | 926241. | 0.551859 | ||||||||
\(310\) | −898786. | −0.531193 | ||||||||
\(311\) | −2.97584e6 | −1.74465 | −0.872325 | − | 0.488926i | \(-0.837389\pi\) | ||||
−0.872325 | + | 0.488926i | \(0.837389\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16412.0 | 0.00946893 | 0.00473447 | − | 0.999989i | \(-0.498493\pi\) | ||||
0.00473447 | + | 0.999989i | \(0.498493\pi\) | |||||||
\(314\) | −1.62830e6 | −0.931987 | ||||||||
\(315\) | 1.26751e6 | 0.719741 | ||||||||
\(316\) | −276011. | −0.155492 | ||||||||
\(317\) | −2.98387e6 | −1.66775 | −0.833876 | − | 0.551951i | \(-0.813884\pi\) | ||||
−0.833876 | + | 0.551951i | \(0.813884\pi\) | |||||||
\(318\) | 1.09830e6 | 0.609048 | ||||||||
\(319\) | 2.93707e6 | 1.61598 | ||||||||
\(320\) | 342085. | 0.186750 | ||||||||
\(321\) | 1.20361e6 | 0.651966 | ||||||||
\(322\) | 2.84100e6 | 1.52697 | ||||||||
\(323\) | −401742. | −0.214260 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −771770. | −0.402202 | ||||||||
\(327\) | −2.13360e6 | −1.10343 | ||||||||
\(328\) | 777257. | 0.398915 | ||||||||
\(329\) | −1.05815e6 | −0.538959 | ||||||||
\(330\) | 2.36420e6 | 1.19509 | ||||||||
\(331\) | 848266. | 0.425561 | 0.212781 | − | 0.977100i | \(-0.431748\pi\) | ||||
0.212781 | + | 0.977100i | \(0.431748\pi\) | |||||||
\(332\) | 1.19631e6 | 0.595661 | ||||||||
\(333\) | −140484. | −0.0694251 | ||||||||
\(334\) | −1.43539e6 | −0.704049 | ||||||||
\(335\) | −2.35284e6 | −1.14546 | ||||||||
\(336\) | 431693. | 0.208606 | ||||||||
\(337\) | −403049. | −0.193323 | −0.0966615 | − | 0.995317i | \(-0.530816\pi\) | ||||
−0.0966615 | + | 0.995317i | \(0.530816\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.24445e6 | 0.588138 | ||||||||
\(340\) | −1.23443e6 | −0.579121 | ||||||||
\(341\) | −2.11558e6 | −0.985241 | ||||||||
\(342\) | −140903. | −0.0651411 | ||||||||
\(343\) | 279621. | 0.128332 | ||||||||
\(344\) | 115728. | 0.0527283 | ||||||||
\(345\) | −2.84928e6 | −1.28881 | ||||||||
\(346\) | 2.30101e6 | 1.03330 | ||||||||
\(347\) | −455097. | −0.202899 | −0.101450 | − | 0.994841i | \(-0.532348\pi\) | ||||
−0.101450 | + | 0.994841i | \(0.532348\pi\) | |||||||
\(348\) | −537860. | −0.238079 | ||||||||
\(349\) | 2.55559e6 | 1.12312 | 0.561562 | − | 0.827435i | \(-0.310201\pi\) | ||||
0.561562 | + | 0.827435i | \(0.310201\pi\) | |||||||
\(350\) | −2.88551e6 | −1.25908 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 805206. | 0.346378 | ||||||||
\(353\) | 492691. | 0.210445 | 0.105222 | − | 0.994449i | \(-0.466445\pi\) | ||||
0.105222 | + | 0.994449i | \(0.466445\pi\) | |||||||
\(354\) | 1.40108e6 | 0.594232 | ||||||||
\(355\) | −6.70751e6 | −2.82482 | ||||||||
\(356\) | 732489. | 0.306320 | ||||||||
\(357\) | −1.55779e6 | −0.646900 | ||||||||
\(358\) | −2.92060e6 | −1.20438 | ||||||||
\(359\) | −2.17485e6 | −0.890623 | −0.445311 | − | 0.895376i | \(-0.646907\pi\) | ||||
−0.445311 | + | 0.895376i | \(0.646907\pi\) | |||||||
\(360\) | −432952. | −0.176069 | ||||||||
\(361\) | −2.28697e6 | −0.923619 | ||||||||
\(362\) | 72017.4 | 0.0288846 | ||||||||
\(363\) | 4.11543e6 | 1.63926 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −489757. | −0.192419 | ||||||||
\(366\) | −324386. | −0.126578 | ||||||||
\(367\) | 741107. | 0.287221 | 0.143610 | − | 0.989634i | \(-0.454129\pi\) | ||||
0.143610 | + | 0.989634i | \(0.454129\pi\) | |||||||
\(368\) | −970416. | −0.373541 | ||||||||
\(369\) | −983716. | −0.376100 | ||||||||
\(370\) | 579397. | 0.220025 | ||||||||
\(371\) | −5.71623e6 | −2.15613 | ||||||||
\(372\) | 387422. | 0.145153 | ||||||||
\(373\) | −3.42043e6 | −1.27294 | −0.636471 | − | 0.771300i | \(-0.719607\pi\) | ||||
−0.636471 | + | 0.771300i | \(0.719607\pi\) | |||||||
\(374\) | −2.90562e6 | −1.07414 | ||||||||
\(375\) | 545008. | 0.200136 | ||||||||
\(376\) | 361437. | 0.131845 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −546362. | −0.196676 | ||||||||
\(379\) | −2.40039e6 | −0.858387 | −0.429193 | − | 0.903213i | \(-0.641202\pi\) | ||||
−0.429193 | + | 0.903213i | \(0.641202\pi\) | |||||||
\(380\) | 581126. | 0.206448 | ||||||||
\(381\) | −2.55148e6 | −0.900490 | ||||||||
\(382\) | −2.87555e6 | −1.00824 | ||||||||
\(383\) | −70722.4 | −0.0246354 | −0.0123177 | − | 0.999924i | \(-0.503921\pi\) | ||||
−0.0123177 | + | 0.999924i | \(0.503921\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | −1.23048e7 | −4.23080 | ||||||||
\(386\) | 654096. | 0.223446 | ||||||||
\(387\) | −146469. | −0.0497127 | ||||||||
\(388\) | −1.24660e6 | −0.420387 | ||||||||
\(389\) | 3.95890e6 | 1.32648 | 0.663240 | − | 0.748406i | \(-0.269181\pi\) | ||||
0.663240 | + | 0.748406i | \(0.269181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.50179e6 | 1.15837 | ||||||||
\(392\) | −1.17116e6 | −0.384947 | ||||||||
\(393\) | 914617. | 0.298716 | ||||||||
\(394\) | −166989. | −0.0541935 | ||||||||
\(395\) | −1.44073e6 | −0.464610 | ||||||||
\(396\) | −1.01909e6 | −0.326568 | ||||||||
\(397\) | 559732. | 0.178240 | 0.0891198 | − | 0.996021i | \(-0.471595\pi\) | ||||
0.0891198 | + | 0.996021i | \(0.471595\pi\) | |||||||
\(398\) | 636094. | 0.201286 | ||||||||
\(399\) | 733349. | 0.230610 | ||||||||
\(400\) | 985620. | 0.308006 | ||||||||
\(401\) | −731268. | −0.227099 | −0.113550 | − | 0.993532i | \(-0.536222\pi\) | ||||
−0.113550 | + | 0.993532i | \(0.536222\pi\) | |||||||
\(402\) | 1.01419e6 | 0.313008 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −274242. | −0.0835949 | ||||||||
\(405\) | 547955. | 0.166000 | ||||||||
\(406\) | 2.79937e6 | 0.842840 | ||||||||
\(407\) | 1.36379e6 | 0.408096 | ||||||||
\(408\) | 532102. | 0.158250 | ||||||||
\(409\) | 4.10605e6 | 1.21371 | 0.606856 | − | 0.794812i | \(-0.292431\pi\) | ||||
0.606856 | + | 0.794812i | \(0.292431\pi\) | |||||||
\(410\) | 4.05713e6 | 1.19195 | ||||||||
\(411\) | 1.23134e6 | 0.359563 | ||||||||
\(412\) | 1.64665e6 | 0.477924 | ||||||||
\(413\) | −7.29213e6 | −2.10368 | ||||||||
\(414\) | 1.22818e6 | 0.352178 | ||||||||
\(415\) | 6.24451e6 | 1.77983 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.10211e6 | 0.310375 | ||||||||
\(418\) | 1.36786e6 | 0.382914 | ||||||||
\(419\) | −2.16620e6 | −0.602787 | −0.301393 | − | 0.953500i | \(-0.597452\pi\) | ||||
−0.301393 | + | 0.953500i | \(0.597452\pi\) | |||||||
\(420\) | 2.25336e6 | 0.623314 | ||||||||
\(421\) | −5.73337e6 | −1.57654 | −0.788270 | − | 0.615330i | \(-0.789023\pi\) | ||||
−0.788270 | + | 0.615330i | \(0.789023\pi\) | |||||||
\(422\) | 1.29216e6 | 0.353211 | ||||||||
\(423\) | −457444. | −0.124304 | ||||||||
\(424\) | 1.95253e6 | 0.527451 | ||||||||
\(425\) | −3.55665e6 | −0.955145 | ||||||||
\(426\) | 2.89128e6 | 0.771908 | ||||||||
\(427\) | 1.68831e6 | 0.448108 | ||||||||
\(428\) | 2.13976e6 | 0.564619 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 604080. | 0.157552 | ||||||||
\(431\) | −943230. | −0.244582 | −0.122291 | − | 0.992494i | \(-0.539024\pi\) | ||||
−0.122291 | + | 0.992494i | \(0.539024\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | −907853. | −0.232700 | −0.116350 | − | 0.993208i | \(-0.537119\pi\) | ||||
−0.116350 | + | 0.993208i | \(0.537119\pi\) | |||||||
\(434\) | −2.01639e6 | −0.513867 | ||||||||
\(435\) | −2.80753e6 | −0.711379 | ||||||||
\(436\) | −3.79307e6 | −0.955598 | ||||||||
\(437\) | −1.64852e6 | −0.412943 | ||||||||
\(438\) | 211110. | 0.0525803 | ||||||||
\(439\) | 801162. | 0.198408 | 0.0992039 | − | 0.995067i | \(-0.468370\pi\) | ||||
0.0992039 | + | 0.995067i | \(0.468370\pi\) | |||||||
\(440\) | 4.20302e6 | 1.03497 | ||||||||
\(441\) | 1.48225e6 | 0.362932 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.98329e6 | −1.44854 | −0.724270 | − | 0.689516i | \(-0.757823\pi\) | ||||
−0.724270 | + | 0.689516i | \(0.757823\pi\) | |||||||
\(444\) | −249749. | −0.0601239 | ||||||||
\(445\) | 3.82345e6 | 0.915283 | ||||||||
\(446\) | 4.82907e6 | 1.14955 | ||||||||
\(447\) | −2.23072e6 | −0.528052 | ||||||||
\(448\) | 767455. | 0.180658 | ||||||||
\(449\) | 674540. | 0.157904 | 0.0789518 | − | 0.996878i | \(-0.474843\pi\) | ||||
0.0789518 | + | 0.996878i | \(0.474843\pi\) | |||||||
\(450\) | −1.24743e6 | −0.290391 | ||||||||
\(451\) | 9.54974e6 | 2.21080 | ||||||||
\(452\) | 2.21236e6 | 0.509343 | ||||||||
\(453\) | −2.91861e6 | −0.668237 | ||||||||
\(454\) | −3.54102e6 | −0.806286 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −250494. | −0.0564139 | ||||||||
\(457\) | 2.44421e6 | 0.547455 | 0.273728 | − | 0.961807i | \(-0.411743\pi\) | ||||
0.273728 | + | 0.961807i | \(0.411743\pi\) | |||||||
\(458\) | −1.89504e6 | −0.422139 | ||||||||
\(459\) | −673441. | −0.149200 | ||||||||
\(460\) | −5.06539e6 | −1.11614 | ||||||||
\(461\) | 858805. | 0.188210 | 0.0941049 | − | 0.995562i | \(-0.470001\pi\) | ||||
0.0941049 | + | 0.995562i | \(0.470001\pi\) | |||||||
\(462\) | 5.30399e6 | 1.15611 | ||||||||
\(463\) | 7.81981e6 | 1.69529 | 0.847645 | − | 0.530564i | \(-0.178020\pi\) | ||||
0.847645 | + | 0.530564i | \(0.178020\pi\) | |||||||
\(464\) | −956196. | −0.206183 | ||||||||
\(465\) | 2.02227e6 | 0.433717 | ||||||||
\(466\) | 676919. | 0.144402 | ||||||||
\(467\) | 6.27959e6 | 1.33241 | 0.666207 | − | 0.745767i | \(-0.267917\pi\) | ||||
0.666207 | + | 0.745767i | \(0.267917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.27850e6 | −1.10810 | ||||||||
\(470\) | 1.88663e6 | 0.393951 | ||||||||
\(471\) | 3.66367e6 | 0.760964 | ||||||||
\(472\) | 2.49082e6 | 0.514620 | ||||||||
\(473\) | 1.42189e6 | 0.292223 | ||||||||
\(474\) | 621026. | 0.126959 | ||||||||
\(475\) | 1.67435e6 | 0.340495 | ||||||||
\(476\) | −2.76940e6 | −0.560232 | ||||||||
\(477\) | −2.47117e6 | −0.497286 | ||||||||
\(478\) | −5.86142e6 | −1.17336 | ||||||||
\(479\) | 2.29110e6 | 0.456252 | 0.228126 | − | 0.973632i | \(-0.426740\pi\) | ||||
0.228126 | + | 0.973632i | \(0.426740\pi\) | |||||||
\(480\) | −769692. | −0.152480 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 139934. | 0.0274350 | ||||||||
\(483\) | −6.39225e6 | −1.24677 | ||||||||
\(484\) | 7.31631e6 | 1.41964 | ||||||||
\(485\) | −6.50704e6 | −1.25611 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | −4.05799e6 | −0.775333 | −0.387666 | − | 0.921800i | \(-0.626719\pi\) | ||||
−0.387666 | + | 0.921800i | \(0.626719\pi\) | |||||||
\(488\) | −576686. | −0.109620 | ||||||||
\(489\) | 1.73648e6 | 0.328396 | ||||||||
\(490\) | −6.11323e6 | −1.15022 | ||||||||
\(491\) | 609711. | 0.114135 | 0.0570677 | − | 0.998370i | \(-0.481825\pi\) | ||||
0.0570677 | + | 0.998370i | \(0.481825\pi\) | |||||||
\(492\) | −1.74883e6 | −0.325712 | ||||||||
\(493\) | 3.45048e6 | 0.639384 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.31945e6 | −0.975783 | ||||||||
\(496\) | 688750. | 0.125706 | ||||||||
\(497\) | −1.50480e7 | −2.73268 | ||||||||
\(498\) | −2.69170e6 | −0.486355 | ||||||||
\(499\) | 9.43555e6 | 1.69635 | 0.848176 | − | 0.529715i | \(-0.177701\pi\) | ||||
0.848176 | + | 0.529715i | \(0.177701\pi\) | |||||||
\(500\) | 968903. | 0.173323 | ||||||||
\(501\) | 3.22962e6 | 0.574853 | ||||||||
\(502\) | −2.51732e6 | −0.445840 | ||||||||
\(503\) | −4.48965e6 | −0.791211 | −0.395606 | − | 0.918421i | \(-0.629465\pi\) | ||||
−0.395606 | + | 0.918421i | \(0.629465\pi\) | |||||||
\(504\) | −971310. | −0.170326 | ||||||||
\(505\) | −1.43149e6 | −0.249781 | ||||||||
\(506\) | −1.19230e7 | −2.07018 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.53596e6 | −0.779847 | ||||||||
\(509\) | −4.48242e6 | −0.766863 | −0.383432 | − | 0.923569i | \(-0.625258\pi\) | ||||
−0.383432 | + | 0.923569i | \(0.625258\pi\) | |||||||
\(510\) | 2.77747e6 | 0.472850 | ||||||||
\(511\) | −1.09875e6 | −0.186143 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 317032. | 0.0531875 | ||||||||
\(514\) | −3.31899e6 | −0.554113 | ||||||||
\(515\) | 8.59521e6 | 1.42803 | ||||||||
\(516\) | −260389. | −0.0430525 | ||||||||
\(517\) | 4.44078e6 | 0.730690 | ||||||||
\(518\) | 1.29985e6 | 0.212848 | ||||||||
\(519\) | −5.17727e6 | −0.843689 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.38286e6 | 1.19160 | 0.595799 | − | 0.803133i | \(-0.296835\pi\) | ||||
0.595799 | + | 0.803133i | \(0.296835\pi\) | |||||||
\(522\) | 1.21019e6 | 0.194391 | ||||||||
\(523\) | 2.71336e6 | 0.433764 | 0.216882 | − | 0.976198i | \(-0.430411\pi\) | ||||
0.216882 | + | 0.976198i | \(0.430411\pi\) | |||||||
\(524\) | 1.62599e6 | 0.258695 | ||||||||
\(525\) | 6.49240e6 | 1.02803 | ||||||||
\(526\) | 838422. | 0.132129 | ||||||||
\(527\) | −2.48539e6 | −0.389823 | ||||||||
\(528\) | −1.81171e6 | −0.282816 | ||||||||
\(529\) | 7.93297e6 | 1.23253 | ||||||||
\(530\) | 1.01918e7 | 1.57602 | ||||||||
\(531\) | −3.15244e6 | −0.485188 | ||||||||
\(532\) | 1.30373e6 | 0.199714 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.64810e6 | −0.250110 | ||||||||
\(535\) | 1.11691e7 | 1.68708 | ||||||||
\(536\) | 1.80301e6 | 0.271073 | ||||||||
\(537\) | 6.57135e6 | 0.983375 | ||||||||
\(538\) | −6.75119e6 | −1.00560 | ||||||||
\(539\) | −1.43894e7 | −2.13339 | ||||||||
\(540\) | 974142. | 0.143760 | ||||||||
\(541\) | −4.37688e6 | −0.642942 | −0.321471 | − | 0.946920i | \(-0.604177\pi\) | ||||
−0.321471 | + | 0.946920i | \(0.604177\pi\) | |||||||
\(542\) | −5.68491e6 | −0.831238 | ||||||||
\(543\) | −162039. | −0.0235842 | ||||||||
\(544\) | 945958. | 0.137049 | ||||||||
\(545\) | −1.97991e7 | −2.85532 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.72786e6 | 0.389811 | 0.194905 | − | 0.980822i | \(-0.437560\pi\) | ||||
0.194905 | + | 0.980822i | \(0.437560\pi\) | |||||||
\(548\) | 2.18905e6 | 0.311390 | ||||||||
\(549\) | 729868. | 0.103351 | ||||||||
\(550\) | 1.21098e7 | 1.70699 | ||||||||
\(551\) | −1.62436e6 | −0.227931 | ||||||||
\(552\) | 2.18344e6 | 0.304995 | ||||||||
\(553\) | −3.23221e6 | −0.449456 | ||||||||
\(554\) | −1.71451e6 | −0.237338 | ||||||||
\(555\) | −1.30364e6 | −0.179650 | ||||||||
\(556\) | 1.95932e6 | 0.268793 | ||||||||
\(557\) | −1.11073e7 | −1.51694 | −0.758472 | − | 0.651706i | \(-0.774054\pi\) | ||||
−0.758472 | + | 0.651706i | \(0.774054\pi\) | |||||||
\(558\) | −871699. | −0.118517 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 4.00597e6 | 0.539806 | ||||||||
\(561\) | 6.53765e6 | 0.877030 | ||||||||
\(562\) | 973351. | 0.129996 | ||||||||
\(563\) | −1.20957e7 | −1.60827 | −0.804137 | − | 0.594444i | \(-0.797372\pi\) | ||||
−0.804137 | + | 0.594444i | \(0.797372\pi\) | |||||||
\(564\) | −813233. | −0.107651 | ||||||||
\(565\) | 1.15481e7 | 1.52191 | ||||||||
\(566\) | −6.15381e6 | −0.807427 | ||||||||
\(567\) | 1.22931e6 | 0.160585 | ||||||||
\(568\) | 5.14004e6 | 0.668492 | ||||||||
\(569\) | 1.25640e7 | 1.62685 | 0.813426 | − | 0.581669i | \(-0.197600\pi\) | ||||
0.813426 | + | 0.581669i | \(0.197600\pi\) | |||||||
\(570\) | −1.30753e6 | −0.168564 | ||||||||
\(571\) | −1.01907e7 | −1.30802 | −0.654009 | − | 0.756487i | \(-0.726914\pi\) | ||||
−0.654009 | + | 0.756487i | \(0.726914\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.46998e6 | 0.823221 | ||||||||
\(574\) | 9.10201e6 | 1.15308 | ||||||||
\(575\) | −1.45944e7 | −1.84085 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | 396134. | 0.0495340 | 0.0247670 | − | 0.999693i | \(-0.492116\pi\) | ||||
0.0247670 | + | 0.999693i | \(0.492116\pi\) | |||||||
\(578\) | 2.26590e6 | 0.282111 | ||||||||
\(579\) | −1.47172e6 | −0.182443 | ||||||||
\(580\) | −4.99116e6 | −0.616072 | ||||||||
\(581\) | 1.40093e7 | 1.72178 | ||||||||
\(582\) | 2.80486e6 | 0.343245 | ||||||||
\(583\) | 2.39896e7 | 2.92316 | ||||||||
\(584\) | 375307. | 0.0455359 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.08543e6 | 0.491466 | ||||||||
\(587\) | −4.04427e6 | −0.484446 | −0.242223 | − | 0.970221i | \(-0.577876\pi\) | ||||
−0.242223 | + | 0.970221i | \(0.577876\pi\) | |||||||
\(588\) | 2.63511e6 | 0.314308 | ||||||||
\(589\) | 1.17003e6 | 0.138966 | ||||||||
\(590\) | 1.30016e7 | 1.53768 | ||||||||
\(591\) | 375725. | 0.0442488 | ||||||||
\(592\) | −443999. | −0.0520688 | ||||||||
\(593\) | −3.61298e6 | −0.421918 | −0.210959 | − | 0.977495i | \(-0.567659\pi\) | ||||
−0.210959 | + | 0.977495i | \(0.567659\pi\) | |||||||
\(594\) | 2.29295e6 | 0.266642 | ||||||||
\(595\) | −1.44557e7 | −1.67397 | ||||||||
\(596\) | −3.96573e6 | −0.457307 | ||||||||
\(597\) | −1.43121e6 | −0.164349 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.13849e7 | 1.29647 | 0.648235 | − | 0.761441i | \(-0.275508\pi\) | ||||
0.648235 | + | 0.761441i | \(0.275508\pi\) | |||||||
\(600\) | −2.21765e6 | −0.251486 | ||||||||
\(601\) | −1.38080e7 | −1.55935 | −0.779677 | − | 0.626181i | \(-0.784617\pi\) | ||||
−0.779677 | + | 0.626181i | \(0.784617\pi\) | |||||||
\(602\) | 1.35523e6 | 0.152413 | ||||||||
\(603\) | −2.28193e6 | −0.255570 | ||||||||
\(604\) | −5.18864e6 | −0.578711 | ||||||||
\(605\) | 3.81898e7 | 4.24188 | ||||||||
\(606\) | 617043. | 0.0682550 | ||||||||
\(607\) | −4.80008e6 | −0.528782 | −0.264391 | − | 0.964416i | \(-0.585171\pi\) | ||||
−0.264391 | + | 0.964416i | \(0.585171\pi\) | |||||||
\(608\) | −445323. | −0.0488558 | ||||||||
\(609\) | −6.29858e6 | −0.688176 | ||||||||
\(610\) | −3.01019e6 | −0.327544 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.19723e6 | −0.129211 | ||||||||
\(613\) | −8.26464e6 | −0.888327 | −0.444163 | − | 0.895946i | \(-0.646499\pi\) | ||||
−0.444163 | + | 0.895946i | \(0.646499\pi\) | |||||||
\(614\) | 2.14252e6 | 0.229353 | ||||||||
\(615\) | −9.12855e6 | −0.973226 | ||||||||
\(616\) | 9.42931e6 | 1.00122 | ||||||||
\(617\) | −6.25819e6 | −0.661814 | −0.330907 | − | 0.943663i | \(-0.607355\pi\) | ||||
−0.330907 | + | 0.943663i | \(0.607355\pi\) | |||||||
\(618\) | −3.70497e6 | −0.390223 | ||||||||
\(619\) | 1.49773e7 | 1.57111 | 0.785556 | − | 0.618791i | \(-0.212377\pi\) | ||||
0.785556 | + | 0.618791i | \(0.212377\pi\) | |||||||
\(620\) | 3.59514e6 | 0.375610 | ||||||||
\(621\) | −2.76341e6 | −0.287552 | ||||||||
\(622\) | 1.19034e7 | 1.23365 | ||||||||
\(623\) | 8.57776e6 | 0.885429 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.97401e6 | −0.714139 | ||||||||
\(626\) | −65648.0 | −0.00669554 | ||||||||
\(627\) | −3.07769e6 | −0.312648 | ||||||||
\(628\) | 6.51319e6 | 0.659014 | ||||||||
\(629\) | 1.60219e6 | 0.161468 | ||||||||
\(630\) | −5.07005e6 | −0.508934 | ||||||||
\(631\) | −9.45858e6 | −0.945698 | −0.472849 | − | 0.881143i | \(-0.656774\pi\) | ||||
−0.472849 | + | 0.881143i | \(0.656774\pi\) | |||||||
\(632\) | 1.10405e6 | 0.109950 | ||||||||
\(633\) | −2.90735e6 | −0.288396 | ||||||||
\(634\) | 1.19355e7 | 1.17928 | ||||||||
\(635\) | −2.36768e7 | −2.33018 | ||||||||
\(636\) | −4.39318e6 | −0.430662 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.17483e7 | −1.14267 | ||||||||
\(639\) | −6.50537e6 | −0.630260 | ||||||||
\(640\) | −1.36834e6 | −0.132052 | ||||||||
\(641\) | 8.37531e6 | 0.805111 | 0.402556 | − | 0.915395i | \(-0.368122\pi\) | ||||
0.402556 | + | 0.915395i | \(0.368122\pi\) | |||||||
\(642\) | −4.81446e6 | −0.461009 | ||||||||
\(643\) | 627456. | 0.0598489 | 0.0299244 | − | 0.999552i | \(-0.490473\pi\) | ||||
0.0299244 | + | 0.999552i | \(0.490473\pi\) | |||||||
\(644\) | −1.13640e7 | −1.07973 | ||||||||
\(645\) | −1.35918e6 | −0.128640 | ||||||||
\(646\) | 1.60697e6 | 0.151505 | ||||||||
\(647\) | −9.06494e6 | −0.851343 | −0.425671 | − | 0.904878i | \(-0.639962\pi\) | ||||
−0.425671 | + | 0.904878i | \(0.639962\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 3.06033e7 | 2.85205 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.53688e6 | 0.419570 | ||||||||
\(652\) | 3.08708e6 | 0.284399 | ||||||||
\(653\) | 4.92251e6 | 0.451756 | 0.225878 | − | 0.974156i | \(-0.427475\pi\) | ||||
0.225878 | + | 0.974156i | \(0.427475\pi\) | |||||||
\(654\) | 8.53442e6 | 0.780242 | ||||||||
\(655\) | 8.48734e6 | 0.772980 | ||||||||
\(656\) | −3.10903e6 | −0.282075 | ||||||||
\(657\) | −474997. | −0.0429317 | ||||||||
\(658\) | 4.23258e6 | 0.381102 | ||||||||
\(659\) | 1.00268e7 | 0.899389 | 0.449694 | − | 0.893182i | \(-0.351533\pi\) | ||||
0.449694 | + | 0.893182i | \(0.351533\pi\) | |||||||
\(660\) | −9.45679e6 | −0.845053 | ||||||||
\(661\) | 97629.5 | 0.00869116 | 0.00434558 | − | 0.999991i | \(-0.498617\pi\) | ||||
0.00434558 | + | 0.999991i | \(0.498617\pi\) | |||||||
\(662\) | −3.39306e6 | −0.300917 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.78524e6 | −0.421196 | ||||||||
\(665\) | 6.80523e6 | 0.596745 | ||||||||
\(666\) | 561936. | 0.0490909 | ||||||||
\(667\) | 1.41588e7 | 1.23228 | ||||||||
\(668\) | 5.74155e6 | 0.497838 | ||||||||
\(669\) | −1.08654e7 | −0.938601 | ||||||||
\(670\) | 9.41136e6 | 0.809963 | ||||||||
\(671\) | −7.08543e6 | −0.607519 | ||||||||
\(672\) | −1.72677e6 | −0.147507 | ||||||||
\(673\) | −7.82943e6 | −0.666334 | −0.333167 | − | 0.942868i | \(-0.608117\pi\) | ||||
−0.333167 | + | 0.942868i | \(0.608117\pi\) | |||||||
\(674\) | 1.61220e6 | 0.136700 | ||||||||
\(675\) | 2.80671e6 | 0.237103 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.24465e6 | −0.523644 | −0.261822 | − | 0.965116i | \(-0.584323\pi\) | ||||
−0.261822 | + | 0.965116i | \(0.584323\pi\) | |||||||
\(678\) | −4.97781e6 | −0.415876 | ||||||||
\(679\) | −1.45983e7 | −1.21514 | ||||||||
\(680\) | 4.93772e6 | 0.409500 | ||||||||
\(681\) | 7.96730e6 | 0.658329 | ||||||||
\(682\) | 8.46230e6 | 0.696671 | ||||||||
\(683\) | −1.22265e7 | −1.00288 | −0.501441 | − | 0.865192i | \(-0.667197\pi\) | ||||
−0.501441 | + | 0.865192i | \(0.667197\pi\) | |||||||
\(684\) | 563612. | 0.0460617 | ||||||||
\(685\) | 1.14264e7 | 0.930432 | ||||||||
\(686\) | −1.11848e6 | −0.0907444 | ||||||||
\(687\) | 4.26385e6 | 0.344675 | ||||||||
\(688\) | −462913. | −0.0372845 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.13971e7 | 0.911323 | ||||||||
\(691\) | 1.33096e7 | 1.06040 | 0.530198 | − | 0.847874i | \(-0.322117\pi\) | ||||
0.530198 | + | 0.847874i | \(0.322117\pi\) | |||||||
\(692\) | −9.20403e6 | −0.730656 | ||||||||
\(693\) | −1.19340e7 | −0.943956 | ||||||||
\(694\) | 1.82039e6 | 0.143471 | ||||||||
\(695\) | 1.02273e7 | 0.803150 | ||||||||
\(696\) | 2.15144e6 | 0.168347 | ||||||||
\(697\) | 1.12191e7 | 0.874731 | ||||||||
\(698\) | −1.02224e7 | −0.794169 | ||||||||
\(699\) | −1.52307e6 | −0.117903 | ||||||||
\(700\) | 1.15420e7 | 0.890302 | ||||||||
\(701\) | 8.08924e6 | 0.621745 | 0.310873 | − | 0.950452i | \(-0.399379\pi\) | ||||
0.310873 | + | 0.950452i | \(0.399379\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −754254. | −0.0575611 | ||||||||
\(704\) | −3.22082e6 | −0.244926 | ||||||||
\(705\) | −4.24492e6 | −0.321660 | ||||||||
\(706\) | −1.97076e6 | −0.148807 | ||||||||
\(707\) | −3.21149e6 | −0.241634 | ||||||||
\(708\) | −5.60433e6 | −0.420185 | ||||||||
\(709\) | −1.44669e7 | −1.08084 | −0.540418 | − | 0.841397i | \(-0.681734\pi\) | ||||
−0.540418 | + | 0.841397i | \(0.681734\pi\) | |||||||
\(710\) | 2.68301e7 | 1.99745 | ||||||||
\(711\) | −1.39731e6 | −0.103662 | ||||||||
\(712\) | −2.92996e6 | −0.216601 | ||||||||
\(713\) | −1.01986e7 | −0.751304 | ||||||||
\(714\) | 6.23114e6 | 0.457427 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.16824e7 | 0.851628 | ||||||||
\(717\) | 1.31882e7 | 0.958048 | ||||||||
\(718\) | 8.69941e6 | 0.629765 | ||||||||
\(719\) | −1.10888e7 | −0.799950 | −0.399975 | − | 0.916526i | \(-0.630981\pi\) | ||||
−0.399975 | + | 0.916526i | \(0.630981\pi\) | |||||||
\(720\) | 1.73181e6 | 0.124500 | ||||||||
\(721\) | 1.92830e7 | 1.38145 | ||||||||
\(722\) | 9.14789e6 | 0.653098 | ||||||||
\(723\) | −314851. | −0.0224006 | ||||||||
\(724\) | −288070. | −0.0204245 | ||||||||
\(725\) | −1.43806e7 | −1.01609 | ||||||||
\(726\) | −1.64617e7 | −1.15913 | ||||||||
\(727\) | 1.58622e7 | 1.11308 | 0.556542 | − | 0.830819i | \(-0.312128\pi\) | ||||
0.556542 | + | 0.830819i | \(0.312128\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.95903e6 | 0.136061 | ||||||||
\(731\) | 1.67044e6 | 0.115621 | ||||||||
\(732\) | 1.29754e6 | 0.0895043 | ||||||||
\(733\) | −1.25058e7 | −0.859711 | −0.429856 | − | 0.902898i | \(-0.641436\pi\) | ||||
−0.429856 | + | 0.902898i | \(0.641436\pi\) | |||||||
\(734\) | −2.96443e6 | −0.203096 | ||||||||
\(735\) | 1.37548e7 | 0.939150 | ||||||||
\(736\) | 3.88166e6 | 0.264133 | ||||||||
\(737\) | 2.21526e7 | 1.50230 | ||||||||
\(738\) | 3.93486e6 | 0.265943 | ||||||||
\(739\) | −1.10338e7 | −0.743217 | −0.371609 | − | 0.928389i | \(-0.621194\pi\) | ||||
−0.371609 | + | 0.928389i | \(0.621194\pi\) | |||||||
\(740\) | −2.31759e6 | −0.155581 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.28649e7 | 1.52461 | ||||||||
\(743\) | 2.80392e7 | 1.86335 | 0.931674 | − | 0.363296i | \(-0.118349\pi\) | ||||
0.931674 | + | 0.363296i | \(0.118349\pi\) | |||||||
\(744\) | −1.54969e6 | −0.102639 | ||||||||
\(745\) | −2.07003e7 | −1.36643 | ||||||||
\(746\) | 1.36817e7 | 0.900107 | ||||||||
\(747\) | 6.05632e6 | 0.397107 | ||||||||
\(748\) | 1.16225e7 | 0.759530 | ||||||||
\(749\) | 2.50575e7 | 1.63205 | ||||||||
\(750\) | −2.18003e6 | −0.141517 | ||||||||
\(751\) | −3.13111e6 | −0.202581 | −0.101291 | − | 0.994857i | \(-0.532297\pi\) | ||||
−0.101291 | + | 0.994857i | \(0.532297\pi\) | |||||||
\(752\) | −1.44575e6 | −0.0932284 | ||||||||
\(753\) | 5.66397e6 | 0.364027 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.70837e7 | −1.72918 | ||||||||
\(756\) | 2.18545e6 | 0.139071 | ||||||||
\(757\) | −4.09411e6 | −0.259669 | −0.129834 | − | 0.991536i | \(-0.541445\pi\) | ||||
−0.129834 | + | 0.991536i | \(0.541445\pi\) | |||||||
\(758\) | 9.60154e6 | 0.606971 | ||||||||
\(759\) | 2.68267e7 | 1.69030 | ||||||||
\(760\) | −2.32450e6 | −0.145981 | ||||||||
\(761\) | 7.05171e6 | 0.441400 | 0.220700 | − | 0.975342i | \(-0.429166\pi\) | ||||
0.220700 | + | 0.975342i | \(0.429166\pi\) | |||||||
\(762\) | 1.02059e7 | 0.636743 | ||||||||
\(763\) | −4.44185e7 | −2.76219 | ||||||||
\(764\) | 1.15022e7 | 0.712930 | ||||||||
\(765\) | −6.24930e6 | −0.386081 | ||||||||
\(766\) | 282890. | 0.0174199 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | 1.49719e7 | 0.912977 | 0.456488 | − | 0.889729i | \(-0.349107\pi\) | ||||
0.456488 | + | 0.889729i | \(0.349107\pi\) | |||||||
\(770\) | 4.92192e7 | 2.99163 | ||||||||
\(771\) | 7.46773e6 | 0.452431 | ||||||||
\(772\) | −2.61638e6 | −0.158000 | ||||||||
\(773\) | −2.67527e7 | −1.61035 | −0.805173 | − | 0.593040i | \(-0.797928\pi\) | ||||
−0.805173 | + | 0.593040i | \(0.797928\pi\) | |||||||
\(774\) | 585875. | 0.0351522 | ||||||||
\(775\) | 1.03584e7 | 0.619494 | ||||||||
\(776\) | 4.98642e6 | 0.297259 | ||||||||
\(777\) | −2.92467e6 | −0.173790 | ||||||||
\(778\) | −1.58356e7 | −0.937963 | ||||||||
\(779\) | −5.28153e6 | −0.311829 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.31530e7 | 3.70481 | ||||||||
\(782\) | −1.40072e7 | −0.819093 | ||||||||
\(783\) | −2.72292e6 | −0.158719 | ||||||||
\(784\) | 4.68464e6 | 0.272199 | ||||||||
\(785\) | 3.39976e7 | 1.96913 | ||||||||
\(786\) | −3.65847e6 | −0.211224 | ||||||||
\(787\) | −1.16234e7 | −0.668956 | −0.334478 | − | 0.942404i | \(-0.608560\pi\) | ||||
−0.334478 | + | 0.942404i | \(0.608560\pi\) | |||||||
\(788\) | 667956. | 0.0383206 | ||||||||
\(789\) | −1.88645e6 | −0.107883 | ||||||||
\(790\) | 5.76291e6 | 0.328529 | ||||||||
\(791\) | 2.59077e7 | 1.47227 | ||||||||
\(792\) | 4.07635e6 | 0.230919 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −2.23893e6 | −0.126034 | ||||||||
\(795\) | −2.29316e7 | −1.28682 | ||||||||
\(796\) | −2.54437e6 | −0.142331 | ||||||||
\(797\) | 2.45692e7 | 1.37008 | 0.685040 | − | 0.728505i | \(-0.259785\pi\) | ||||
0.685040 | + | 0.728505i | \(0.259785\pi\) | |||||||
\(798\) | −2.93340e6 | −0.163066 | ||||||||
\(799\) | 5.21705e6 | 0.289106 | ||||||||
\(800\) | −3.94248e6 | −0.217793 | ||||||||
\(801\) | 3.70822e6 | 0.204214 | ||||||||
\(802\) | 2.92507e6 | 0.160583 | ||||||||
\(803\) | 4.61119e6 | 0.252362 | ||||||||
\(804\) | −4.05677e6 | −0.221330 | ||||||||
\(805\) | −5.93179e7 | −3.22623 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.51902e7 | 0.821068 | ||||||||
\(808\) | 1.09697e6 | 0.0591105 | ||||||||
\(809\) | 2.45251e7 | 1.31747 | 0.658734 | − | 0.752376i | \(-0.271092\pi\) | ||||
0.658734 | + | 0.752376i | \(0.271092\pi\) | |||||||
\(810\) | −2.19182e6 | −0.117379 | ||||||||
\(811\) | −6.07437e6 | −0.324302 | −0.162151 | − | 0.986766i | \(-0.551843\pi\) | ||||
−0.162151 | + | 0.986766i | \(0.551843\pi\) | |||||||
\(812\) | −1.11975e7 | −0.595978 | ||||||||
\(813\) | 1.27910e7 | 0.678703 | ||||||||
\(814\) | −5.45518e6 | −0.288568 | ||||||||
\(815\) | 1.61140e7 | 0.849783 | ||||||||
\(816\) | −2.12841e6 | −0.111900 | ||||||||
\(817\) | −786385. | −0.0412174 | ||||||||
\(818\) | −1.64242e7 | −0.858224 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.62285e7 | −0.842839 | ||||||||
\(821\) | −7.25192e6 | −0.375487 | −0.187744 | − | 0.982218i | \(-0.560117\pi\) | ||||
−0.187744 | + | 0.982218i | \(0.560117\pi\) | |||||||
\(822\) | −4.92537e6 | −0.254249 | ||||||||
\(823\) | −3.62080e7 | −1.86340 | −0.931699 | − | 0.363233i | \(-0.881673\pi\) | ||||
−0.931699 | + | 0.363233i | \(0.881673\pi\) | |||||||
\(824\) | −6.58661e6 | −0.337943 | ||||||||
\(825\) | −2.72470e7 | −1.39375 | ||||||||
\(826\) | 2.91685e7 | 1.48753 | ||||||||
\(827\) | −1.58515e7 | −0.805946 | −0.402973 | − | 0.915212i | \(-0.632023\pi\) | ||||
−0.402973 | + | 0.915212i | \(0.632023\pi\) | |||||||
\(828\) | −4.91273e6 | −0.249027 | ||||||||
\(829\) | 8.06150e6 | 0.407408 | 0.203704 | − | 0.979033i | \(-0.434702\pi\) | ||||
0.203704 | + | 0.979033i | \(0.434702\pi\) | |||||||
\(830\) | −2.49781e7 | −1.25853 | ||||||||
\(831\) | 3.85765e6 | 0.193785 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.69047e7 | −0.844104 | ||||||||
\(834\) | −4.40846e6 | −0.219468 | ||||||||
\(835\) | 2.99698e7 | 1.48754 | ||||||||
\(836\) | −5.47145e6 | −0.270761 | ||||||||
\(837\) | 1.96132e6 | 0.0967688 | ||||||||
\(838\) | 8.66480e6 | 0.426235 | ||||||||
\(839\) | −1.60489e7 | −0.787118 | −0.393559 | − | 0.919299i | \(-0.628756\pi\) | ||||
−0.393559 | + | 0.919299i | \(0.628756\pi\) | |||||||
\(840\) | −9.01343e6 | −0.440749 | ||||||||
\(841\) | −6.55987e6 | −0.319820 | ||||||||
\(842\) | 2.29335e7 | 1.11478 | ||||||||
\(843\) | −2.19004e6 | −0.106141 | ||||||||
\(844\) | −5.16863e6 | −0.249758 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.82977e6 | 0.0878965 | ||||||||
\(847\) | 8.56772e7 | 4.10352 | ||||||||
\(848\) | −7.81010e6 | −0.372964 | ||||||||
\(849\) | 1.38461e7 | 0.659262 | ||||||||
\(850\) | 1.42266e7 | 0.675390 | ||||||||
\(851\) | 6.57446e6 | 0.311197 | ||||||||
\(852\) | −1.15651e7 | −0.545821 | ||||||||
\(853\) | 1.48875e7 | 0.700566 | 0.350283 | − | 0.936644i | \(-0.386085\pi\) | ||||
0.350283 | + | 0.936644i | \(0.386085\pi\) | |||||||
\(854\) | −6.75324e6 | −0.316860 | ||||||||
\(855\) | 2.94195e6 | 0.137632 | ||||||||
\(856\) | −8.55904e6 | −0.399246 | ||||||||
\(857\) | 1.30374e7 | 0.606369 | 0.303185 | − | 0.952932i | \(-0.401950\pi\) | ||||
0.303185 | + | 0.952932i | \(0.401950\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.33964e7 | −0.619448 | −0.309724 | − | 0.950826i | \(-0.600237\pi\) | ||||
−0.309724 | + | 0.950826i | \(0.600237\pi\) | |||||||
\(860\) | −2.41632e6 | −0.111406 | ||||||||
\(861\) | −2.04795e7 | −0.941482 | ||||||||
\(862\) | 3.77292e6 | 0.172946 | ||||||||
\(863\) | 2.38224e7 | 1.08882 | 0.544412 | − | 0.838818i | \(-0.316753\pi\) | ||||
0.544412 | + | 0.838818i | \(0.316753\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | −4.80433e7 | −2.18319 | ||||||||
\(866\) | 3.63141e6 | 0.164544 | ||||||||
\(867\) | −5.09826e6 | −0.230343 | ||||||||
\(868\) | 8.06556e6 | 0.363359 | ||||||||
\(869\) | 1.35648e7 | 0.609347 | ||||||||
\(870\) | 1.12301e7 | 0.503021 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.51723e7 | 0.675710 | ||||||||
\(873\) | −6.31093e6 | −0.280258 | ||||||||
\(874\) | 6.59407e6 | 0.291995 | ||||||||
\(875\) | 1.13463e7 | 0.500995 | ||||||||
\(876\) | −844440. | −0.0371799 | ||||||||
\(877\) | −2.72239e7 | −1.19523 | −0.597616 | − | 0.801783i | \(-0.703885\pi\) | ||||
−0.597616 | + | 0.801783i | \(0.703885\pi\) | |||||||
\(878\) | −3.20465e6 | −0.140296 | ||||||||
\(879\) | −9.19221e6 | −0.401280 | ||||||||
\(880\) | −1.68121e7 | −0.731838 | ||||||||
\(881\) | −1.21240e7 | −0.526268 | −0.263134 | − | 0.964759i | \(-0.584756\pi\) | ||||
−0.263134 | + | 0.964759i | \(0.584756\pi\) | |||||||
\(882\) | −5.92900e6 | −0.256631 | ||||||||
\(883\) | 5.51350e6 | 0.237972 | 0.118986 | − | 0.992896i | \(-0.462036\pi\) | ||||
0.118986 | + | 0.992896i | \(0.462036\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.92536e7 | −1.25551 | ||||||||
\(886\) | 2.39332e7 | 1.02427 | ||||||||
\(887\) | 2.79700e7 | 1.19367 | 0.596835 | − | 0.802364i | \(-0.296425\pi\) | ||||
0.596835 | + | 0.802364i | \(0.296425\pi\) | |||||||
\(888\) | 998998. | 0.0425140 | ||||||||
\(889\) | −5.31180e7 | −2.25417 | ||||||||
\(890\) | −1.52938e7 | −0.647203 | ||||||||
\(891\) | −5.15914e6 | −0.217712 | ||||||||
\(892\) | −1.93163e7 | −0.812852 | ||||||||
\(893\) | −2.45600e6 | −0.103062 | ||||||||
\(894\) | 8.92289e6 | 0.373389 | ||||||||
\(895\) | 6.09799e7 | 2.54466 | ||||||||
\(896\) | −3.06982e6 | −0.127745 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.69816e6 | −0.111655 | ||||||||
\(899\) | −1.00491e7 | −0.414696 | ||||||||
\(900\) | 4.98970e6 | 0.205338 | ||||||||
\(901\) | 2.81831e7 | 1.15658 | ||||||||
\(902\) | −3.81989e7 | −1.56327 | ||||||||
\(903\) | −3.04927e6 | −0.124445 | ||||||||
\(904\) | −8.84944e6 | −0.360160 | ||||||||
\(905\) | −1.50367e6 | −0.0610282 | ||||||||
\(906\) | 1.16744e7 | 0.472515 | ||||||||
\(907\) | −5.29278e6 | −0.213632 | −0.106816 | − | 0.994279i | \(-0.534066\pi\) | ||||
−0.106816 | + | 0.994279i | \(0.534066\pi\) | |||||||
\(908\) | 1.41641e7 | 0.570130 | ||||||||
\(909\) | −1.38835e6 | −0.0557299 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.21671e7 | −0.884939 | −0.442469 | − | 0.896784i | \(-0.645897\pi\) | ||||
−0.442469 | + | 0.896784i | \(0.645897\pi\) | |||||||
\(912\) | 1.00198e6 | 0.0398906 | ||||||||
\(913\) | −5.87937e7 | −2.33429 | ||||||||
\(914\) | −9.77685e6 | −0.387109 | ||||||||
\(915\) | 6.77292e6 | 0.267438 | ||||||||
\(916\) | 7.58018e6 | 0.298498 | ||||||||
\(917\) | 1.90410e7 | 0.747767 | ||||||||
\(918\) | 2.69376e6 | 0.105500 | ||||||||
\(919\) | 2.94503e7 | 1.15027 | 0.575136 | − | 0.818058i | \(-0.304949\pi\) | ||||
0.575136 | + | 0.818058i | \(0.304949\pi\) | |||||||
\(920\) | 2.02615e7 | 0.789229 | ||||||||
\(921\) | −4.82068e6 | −0.187266 | ||||||||
\(922\) | −3.43522e6 | −0.133084 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.12159e7 | −0.817490 | ||||||||
\(925\) | −6.67747e6 | −0.256600 | ||||||||
\(926\) | −3.12793e7 | −1.19875 | ||||||||
\(927\) | 8.33617e6 | 0.318616 | ||||||||
\(928\) | 3.82478e6 | 0.145793 | ||||||||
\(929\) | −3.97704e7 | −1.51189 | −0.755945 | − | 0.654635i | \(-0.772822\pi\) | ||||
−0.755945 | + | 0.654635i | \(0.772822\pi\) | |||||||
\(930\) | −8.08907e6 | −0.306684 | ||||||||
\(931\) | 7.95814e6 | 0.300911 | ||||||||
\(932\) | −2.70768e6 | −0.102107 | ||||||||
\(933\) | −2.67825e7 | −1.00727 | ||||||||
\(934\) | −2.51184e7 | −0.942159 | ||||||||
\(935\) | 6.06671e7 | 2.26947 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.09277e7 | −1.52289 | −0.761445 | − | 0.648229i | \(-0.775510\pi\) | ||||
−0.761445 | + | 0.648229i | \(0.775510\pi\) | |||||||
\(938\) | 2.11140e7 | 0.783544 | ||||||||
\(939\) | 147708. | 0.00546689 | ||||||||
\(940\) | −7.54653e6 | −0.278566 | ||||||||
\(941\) | 3.05137e7 | 1.12337 | 0.561683 | − | 0.827353i | \(-0.310154\pi\) | ||||
0.561683 | + | 0.827353i | \(0.310154\pi\) | |||||||
\(942\) | −1.46547e7 | −0.538083 | ||||||||
\(943\) | 4.60365e7 | 1.68587 | ||||||||
\(944\) | −9.96326e6 | −0.363891 | ||||||||
\(945\) | 1.14076e7 | 0.415543 | ||||||||
\(946\) | −5.68757e6 | −0.206633 | ||||||||
\(947\) | −3.50278e7 | −1.26922 | −0.634611 | − | 0.772831i | \(-0.718840\pi\) | ||||
−0.634611 | + | 0.772831i | \(0.718840\pi\) | |||||||
\(948\) | −2.48410e6 | −0.0897736 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.69738e6 | −0.240767 | ||||||||
\(951\) | −2.68548e7 | −0.962878 | ||||||||
\(952\) | 1.10776e7 | 0.396144 | ||||||||
\(953\) | −3.97551e7 | −1.41795 | −0.708974 | − | 0.705234i | \(-0.750842\pi\) | ||||
−0.708974 | + | 0.705234i | \(0.750842\pi\) | |||||||
\(954\) | 9.88466e6 | 0.351634 | ||||||||
\(955\) | 6.00392e7 | 2.13023 | ||||||||
\(956\) | 2.34457e7 | 0.829694 | ||||||||
\(957\) | 2.64336e7 | 0.932989 | ||||||||
\(958\) | −9.16439e6 | −0.322619 | ||||||||
\(959\) | 2.56348e7 | 0.900084 | ||||||||
\(960\) | 3.07877e6 | 0.107820 | ||||||||
\(961\) | −2.13907e7 | −0.747166 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.08325e7 | 0.376413 | ||||||||
\(964\) | −559735. | −0.0193995 | ||||||||
\(965\) | −1.36570e7 | −0.472104 | ||||||||
\(966\) | 2.55690e7 | 0.881598 | ||||||||
\(967\) | −1.45550e7 | −0.500547 | −0.250274 | − | 0.968175i | \(-0.580521\pi\) | ||||
−0.250274 | + | 0.968175i | \(0.580521\pi\) | |||||||
\(968\) | −2.92653e7 | −1.00384 | ||||||||
\(969\) | −3.61568e6 | −0.123703 | ||||||||
\(970\) | 2.60281e7 | 0.888206 | ||||||||
\(971\) | −1.10708e7 | −0.376818 | −0.188409 | − | 0.982091i | \(-0.560333\pi\) | ||||
−0.188409 | + | 0.982091i | \(0.560333\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 2.29444e7 | 0.776954 | ||||||||
\(974\) | 1.62319e7 | 0.548243 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.30674e6 | 0.0775130 | ||||||||
\(977\) | 1.10774e7 | 0.371280 | 0.185640 | − | 0.982618i | \(-0.440564\pi\) | ||||
0.185640 | + | 0.982618i | \(0.440564\pi\) | |||||||
\(978\) | −6.94593e6 | −0.232211 | ||||||||
\(979\) | −3.59988e7 | −1.20041 | ||||||||
\(980\) | 2.44529e7 | 0.813328 | ||||||||
\(981\) | −1.92024e7 | −0.637065 | ||||||||
\(982\) | −2.43885e6 | −0.0807060 | ||||||||
\(983\) | 3.48354e7 | 1.14984 | 0.574919 | − | 0.818210i | \(-0.305033\pi\) | ||||
0.574919 | + | 0.818210i | \(0.305033\pi\) | |||||||
\(984\) | 6.99531e6 | 0.230313 | ||||||||
\(985\) | 3.48660e6 | 0.114502 | ||||||||
\(986\) | −1.38019e7 | −0.452113 | ||||||||
\(987\) | −9.52331e6 | −0.311168 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.85453e6 | 0.222837 | ||||||||
\(990\) | 2.12778e7 | 0.689983 | ||||||||
\(991\) | 1.08055e7 | 0.349512 | 0.174756 | − | 0.984612i | \(-0.444086\pi\) | ||||
0.174756 | + | 0.984612i | \(0.444086\pi\) | |||||||
\(992\) | −2.75500e6 | −0.0888879 | ||||||||
\(993\) | 7.63439e6 | 0.245698 | ||||||||
\(994\) | 6.01922e7 | 1.93230 | ||||||||
\(995\) | −1.32811e7 | −0.425283 | ||||||||
\(996\) | 1.07668e7 | 0.343905 | ||||||||
\(997\) | −2.76495e6 | −0.0880945 | −0.0440473 | − | 0.999029i | \(-0.514025\pi\) | ||||
−0.0440473 | + | 0.999029i | \(0.514025\pi\) | |||||||
\(998\) | −3.77422e7 | −1.19950 | ||||||||
\(999\) | −1.26436e6 | −0.0400826 |
(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 | 1014.6.a.t.1.4 | 4 | ||
13.5 | odd | 4 | 78.6.b.b.25.5 | yes | 8 | ||
13.8 | odd | 4 | 78.6.b.b.25.4 | ✓ | 8 | ||
13.12 | even | 2 | 1014.6.a.u.1.1 | 4 | |||
39.5 | even | 4 | 234.6.b.d.181.4 | 8 | |||
39.8 | even | 4 | 234.6.b.d.181.5 | 8 | |||
52.31 | even | 4 | 624.6.c.f.337.2 | 8 | |||
52.47 | even | 4 | 624.6.c.f.337.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.6.b.b.25.4 | ✓ | 8 | 13.8 | odd | 4 | ||
78.6.b.b.25.5 | yes | 8 | 13.5 | odd | 4 | ||
234.6.b.d.181.4 | 8 | 39.5 | even | 4 | |||
234.6.b.d.181.5 | 8 | 39.8 | even | 4 | |||
624.6.c.f.337.2 | 8 | 52.31 | even | 4 | |||
624.6.c.f.337.7 | 8 | 52.47 | even | 4 | |||
1014.6.a.t.1.4 | 4 | 1.1 | even | 1 | trivial | ||
1014.6.a.u.1.1 | 4 | 13.12 | even | 2 |