Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.53022 | −0.624061 | −0.312030 | − | 0.950072i | \(-0.601009\pi\) | ||||
−0.312030 | + | 0.950072i | \(0.601009\pi\) | |||||||
\(3\) | −7.27933 | −0.466969 | −0.233485 | − | 0.972361i | \(-0.575013\pi\) | ||||
−0.233485 | + | 0.972361i | \(0.575013\pi\) | |||||||
\(4\) | −19.5375 | −0.610548 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 25.6976 | 0.291417 | ||||||||
\(7\) | −171.265 | −1.32106 | −0.660531 | − | 0.750799i | \(-0.729669\pi\) | ||||
−0.660531 | + | 0.750799i | \(0.729669\pi\) | |||||||
\(8\) | 181.939 | 1.00508 | ||||||||
\(9\) | −190.011 | −0.781940 | ||||||||
\(10\) | 88.2555 | 0.279088 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 142.220 | 0.285107 | ||||||||
\(13\) | −544.583 | −0.893729 | −0.446865 | − | 0.894602i | \(-0.647459\pi\) | ||||
−0.446865 | + | 0.894602i | \(0.647459\pi\) | |||||||
\(14\) | 604.603 | 0.824423 | ||||||||
\(15\) | 181.983 | 0.208835 | ||||||||
\(16\) | −17.0833 | −0.0166829 | ||||||||
\(17\) | −539.710 | −0.452937 | −0.226469 | − | 0.974018i | \(-0.572718\pi\) | ||||
−0.226469 | + | 0.974018i | \(0.572718\pi\) | |||||||
\(18\) | 670.782 | 0.487978 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 488.438 | 0.273045 | ||||||||
\(21\) | 1246.69 | 0.616895 | ||||||||
\(22\) | 427.157 | 0.188161 | ||||||||
\(23\) | −1144.68 | −0.451197 | −0.225599 | − | 0.974220i | \(-0.572434\pi\) | ||||
−0.225599 | + | 0.974220i | \(0.572434\pi\) | |||||||
\(24\) | −1324.39 | −0.469341 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1922.50 | 0.557741 | ||||||||
\(27\) | 3152.03 | 0.832111 | ||||||||
\(28\) | 3346.10 | 0.806572 | ||||||||
\(29\) | −6290.66 | −1.38900 | −0.694499 | − | 0.719494i | \(-0.744374\pi\) | ||||
−0.694499 | + | 0.719494i | \(0.744374\pi\) | |||||||
\(30\) | −642.441 | −0.130326 | ||||||||
\(31\) | 1494.17 | 0.279251 | 0.139626 | − | 0.990204i | \(-0.455410\pi\) | ||||
0.139626 | + | 0.990204i | \(0.455410\pi\) | |||||||
\(32\) | −5761.74 | −0.994669 | ||||||||
\(33\) | 880.799 | 0.140796 | ||||||||
\(34\) | 1905.30 | 0.282660 | ||||||||
\(35\) | 4281.62 | 0.590797 | ||||||||
\(36\) | 3712.35 | 0.477412 | ||||||||
\(37\) | −6221.70 | −0.747145 | −0.373572 | − | 0.927601i | \(-0.621867\pi\) | ||||
−0.373572 | + | 0.927601i | \(0.621867\pi\) | |||||||
\(38\) | 1274.41 | 0.143169 | ||||||||
\(39\) | 3964.20 | 0.417344 | ||||||||
\(40\) | −4548.47 | −0.449485 | ||||||||
\(41\) | 12149.5 | 1.12875 | 0.564375 | − | 0.825518i | \(-0.309117\pi\) | ||||
0.564375 | + | 0.825518i | \(0.309117\pi\) | |||||||
\(42\) | −4401.10 | −0.384980 | ||||||||
\(43\) | 10982.9 | 0.905831 | 0.452915 | − | 0.891553i | \(-0.350384\pi\) | ||||
0.452915 | + | 0.891553i | \(0.350384\pi\) | |||||||
\(44\) | 2364.04 | 0.184087 | ||||||||
\(45\) | 4750.28 | 0.349694 | ||||||||
\(46\) | 4040.99 | 0.281574 | ||||||||
\(47\) | 13722.3 | 0.906111 | 0.453055 | − | 0.891482i | \(-0.350334\pi\) | ||||
0.453055 | + | 0.891482i | \(0.350334\pi\) | |||||||
\(48\) | 124.355 | 0.00779042 | ||||||||
\(49\) | 12524.7 | 0.745206 | ||||||||
\(50\) | −2206.39 | −0.124812 | ||||||||
\(51\) | 3928.72 | 0.211508 | ||||||||
\(52\) | 10639.8 | 0.545665 | ||||||||
\(53\) | 4411.40 | 0.215718 | 0.107859 | − | 0.994166i | \(-0.465600\pi\) | ||||
0.107859 | + | 0.994166i | \(0.465600\pi\) | |||||||
\(54\) | −11127.4 | −0.519288 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | −31159.8 | −1.32777 | ||||||||
\(57\) | 2627.84 | 0.107130 | ||||||||
\(58\) | 22207.4 | 0.866819 | ||||||||
\(59\) | 9974.23 | 0.373035 | 0.186517 | − | 0.982452i | \(-0.440280\pi\) | ||||
0.186517 | + | 0.982452i | \(0.440280\pi\) | |||||||
\(60\) | −3555.50 | −0.127504 | ||||||||
\(61\) | −44594.8 | −1.53447 | −0.767237 | − | 0.641363i | \(-0.778369\pi\) | ||||
−0.767237 | + | 0.641363i | \(0.778369\pi\) | |||||||
\(62\) | −5274.74 | −0.174270 | ||||||||
\(63\) | 32542.3 | 1.03299 | ||||||||
\(64\) | 20886.9 | 0.637417 | ||||||||
\(65\) | 13614.6 | 0.399688 | ||||||||
\(66\) | −3109.41 | −0.0878656 | ||||||||
\(67\) | −45465.7 | −1.23736 | −0.618681 | − | 0.785642i | \(-0.712333\pi\) | ||||
−0.618681 | + | 0.785642i | \(0.712333\pi\) | |||||||
\(68\) | 10544.6 | 0.276540 | ||||||||
\(69\) | 8332.54 | 0.210695 | ||||||||
\(70\) | −15115.1 | −0.368693 | ||||||||
\(71\) | 16382.9 | 0.385695 | 0.192847 | − | 0.981229i | \(-0.438228\pi\) | ||||
0.192847 | + | 0.981229i | \(0.438228\pi\) | |||||||
\(72\) | −34570.5 | −0.785912 | ||||||||
\(73\) | 40403.3 | 0.887381 | 0.443690 | − | 0.896180i | \(-0.353669\pi\) | ||||
0.443690 | + | 0.896180i | \(0.353669\pi\) | |||||||
\(74\) | 21964.0 | 0.466264 | ||||||||
\(75\) | −4549.58 | −0.0933938 | ||||||||
\(76\) | 7053.05 | 0.140069 | ||||||||
\(77\) | 20723.1 | 0.398315 | ||||||||
\(78\) | −13994.5 | −0.260448 | ||||||||
\(79\) | 75241.5 | 1.35641 | 0.678203 | − | 0.734875i | \(-0.262759\pi\) | ||||
0.678203 | + | 0.734875i | \(0.262759\pi\) | |||||||
\(80\) | 427.083 | 0.00746084 | ||||||||
\(81\) | 23228.1 | 0.393370 | ||||||||
\(82\) | −42890.3 | −0.704409 | ||||||||
\(83\) | 60170.0 | 0.958705 | 0.479353 | − | 0.877622i | \(-0.340871\pi\) | ||||
0.479353 | + | 0.877622i | \(0.340871\pi\) | |||||||
\(84\) | −24357.3 | −0.376644 | ||||||||
\(85\) | 13492.7 | 0.202560 | ||||||||
\(86\) | −38772.2 | −0.565294 | ||||||||
\(87\) | 45791.8 | 0.648619 | ||||||||
\(88\) | −22014.6 | −0.303043 | ||||||||
\(89\) | −25248.2 | −0.337874 | −0.168937 | − | 0.985627i | \(-0.554033\pi\) | ||||
−0.168937 | + | 0.985627i | \(0.554033\pi\) | |||||||
\(90\) | −16769.6 | −0.218230 | ||||||||
\(91\) | 93268.0 | 1.18067 | ||||||||
\(92\) | 22364.3 | 0.275478 | ||||||||
\(93\) | −10876.5 | −0.130402 | ||||||||
\(94\) | −48442.6 | −0.565468 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | 41941.6 | 0.464480 | ||||||||
\(97\) | 173936. | 1.87699 | 0.938493 | − | 0.345300i | \(-0.112223\pi\) | ||||
0.938493 | + | 0.345300i | \(0.112223\pi\) | |||||||
\(98\) | −44214.9 | −0.465054 | ||||||||
\(99\) | 22991.4 | 0.235764 | ||||||||
\(100\) | −12211.0 | −0.122110 | ||||||||
\(101\) | 56653.7 | 0.552618 | 0.276309 | − | 0.961069i | \(-0.410889\pi\) | ||||
0.276309 | + | 0.961069i | \(0.410889\pi\) | |||||||
\(102\) | −13869.3 | −0.131994 | ||||||||
\(103\) | 70057.7 | 0.650673 | 0.325337 | − | 0.945598i | \(-0.394522\pi\) | ||||
0.325337 | + | 0.945598i | \(0.394522\pi\) | |||||||
\(104\) | −99080.9 | −0.898269 | ||||||||
\(105\) | −31167.3 | −0.275884 | ||||||||
\(106\) | −15573.2 | −0.134621 | ||||||||
\(107\) | −80778.1 | −0.682078 | −0.341039 | − | 0.940049i | \(-0.610779\pi\) | ||||
−0.341039 | + | 0.940049i | \(0.610779\pi\) | |||||||
\(108\) | −61582.9 | −0.508044 | ||||||||
\(109\) | −87329.8 | −0.704038 | −0.352019 | − | 0.935993i | \(-0.614505\pi\) | ||||
−0.352019 | + | 0.935993i | \(0.614505\pi\) | |||||||
\(110\) | −10678.9 | −0.0841483 | ||||||||
\(111\) | 45289.8 | 0.348893 | ||||||||
\(112\) | 2925.78 | 0.0220392 | ||||||||
\(113\) | −156479. | −1.15282 | −0.576408 | − | 0.817162i | \(-0.695546\pi\) | ||||
−0.576408 | + | 0.817162i | \(0.695546\pi\) | |||||||
\(114\) | −9276.85 | −0.0668557 | ||||||||
\(115\) | 28617.1 | 0.201781 | ||||||||
\(116\) | 122904. | 0.848050 | ||||||||
\(117\) | 103477. | 0.698842 | ||||||||
\(118\) | −35211.2 | −0.232796 | ||||||||
\(119\) | 92433.4 | 0.598358 | ||||||||
\(120\) | 33109.8 | 0.209896 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 157430. | 0.957606 | ||||||||
\(123\) | −88440.0 | −0.527092 | ||||||||
\(124\) | −29192.4 | −0.170496 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −114881. | −0.644649 | ||||||||
\(127\) | −82327.7 | −0.452936 | −0.226468 | − | 0.974019i | \(-0.572718\pi\) | ||||
−0.226468 | + | 0.974019i | \(0.572718\pi\) | |||||||
\(128\) | 110640. | 0.596882 | ||||||||
\(129\) | −79948.3 | −0.422995 | ||||||||
\(130\) | −48062.5 | −0.249430 | ||||||||
\(131\) | 162054. | 0.825054 | 0.412527 | − | 0.910945i | \(-0.364646\pi\) | ||||
0.412527 | + | 0.910945i | \(0.364646\pi\) | |||||||
\(132\) | −17208.6 | −0.0859630 | ||||||||
\(133\) | 61826.6 | 0.303072 | ||||||||
\(134\) | 160504. | 0.772190 | ||||||||
\(135\) | −78800.8 | −0.372131 | ||||||||
\(136\) | −98194.2 | −0.455238 | ||||||||
\(137\) | −47031.1 | −0.214084 | −0.107042 | − | 0.994255i | \(-0.534138\pi\) | ||||
−0.107042 | + | 0.994255i | \(0.534138\pi\) | |||||||
\(138\) | −29415.7 | −0.131487 | ||||||||
\(139\) | 380873. | 1.67202 | 0.836012 | − | 0.548711i | \(-0.184881\pi\) | ||||
0.836012 | + | 0.548711i | \(0.184881\pi\) | |||||||
\(140\) | −83652.4 | −0.360710 | ||||||||
\(141\) | −99888.9 | −0.423126 | ||||||||
\(142\) | −57835.1 | −0.240697 | ||||||||
\(143\) | 65894.6 | 0.269469 | ||||||||
\(144\) | 3246.03 | 0.0130451 | ||||||||
\(145\) | 157267. | 0.621179 | ||||||||
\(146\) | −142633. | −0.553780 | ||||||||
\(147\) | −91171.2 | −0.347988 | ||||||||
\(148\) | 121557. | 0.456168 | ||||||||
\(149\) | −143872. | −0.530898 | −0.265449 | − | 0.964125i | \(-0.585520\pi\) | ||||
−0.265449 | + | 0.964125i | \(0.585520\pi\) | |||||||
\(150\) | 16061.0 | 0.0582834 | ||||||||
\(151\) | 35612.2 | 0.127103 | 0.0635515 | − | 0.997979i | \(-0.479757\pi\) | ||||
0.0635515 | + | 0.997979i | \(0.479757\pi\) | |||||||
\(152\) | −65679.9 | −0.230581 | ||||||||
\(153\) | 102551. | 0.354170 | ||||||||
\(154\) | −73157.0 | −0.248573 | ||||||||
\(155\) | −37354.2 | −0.124885 | ||||||||
\(156\) | −77450.7 | −0.254808 | ||||||||
\(157\) | 59316.4 | 0.192055 | 0.0960275 | − | 0.995379i | \(-0.469386\pi\) | ||||
0.0960275 | + | 0.995379i | \(0.469386\pi\) | |||||||
\(158\) | −265619. | −0.846480 | ||||||||
\(159\) | −32112.0 | −0.100734 | ||||||||
\(160\) | 144043. | 0.444829 | ||||||||
\(161\) | 196044. | 0.596060 | ||||||||
\(162\) | −82000.3 | −0.245487 | ||||||||
\(163\) | −272417. | −0.803092 | −0.401546 | − | 0.915839i | \(-0.631527\pi\) | ||||
−0.401546 | + | 0.915839i | \(0.631527\pi\) | |||||||
\(164\) | −237371. | −0.689156 | ||||||||
\(165\) | −22020.0 | −0.0629661 | ||||||||
\(166\) | −212414. | −0.598290 | ||||||||
\(167\) | 552431. | 1.53281 | 0.766403 | − | 0.642361i | \(-0.222045\pi\) | ||||
0.766403 | + | 0.642361i | \(0.222045\pi\) | |||||||
\(168\) | 226822. | 0.620029 | ||||||||
\(169\) | −74722.1 | −0.201248 | ||||||||
\(170\) | −47632.4 | −0.126410 | ||||||||
\(171\) | 68594.1 | 0.179389 | ||||||||
\(172\) | −214579. | −0.553053 | ||||||||
\(173\) | 538401. | 1.36770 | 0.683850 | − | 0.729623i | \(-0.260304\pi\) | ||||
0.683850 | + | 0.729623i | \(0.260304\pi\) | |||||||
\(174\) | −161655. | −0.404778 | ||||||||
\(175\) | −107041. | −0.264212 | ||||||||
\(176\) | 2067.08 | 0.00503010 | ||||||||
\(177\) | −72605.7 | −0.174196 | ||||||||
\(178\) | 89131.7 | 0.210854 | ||||||||
\(179\) | −235234. | −0.548740 | −0.274370 | − | 0.961624i | \(-0.588469\pi\) | ||||
−0.274370 | + | 0.961624i | \(0.588469\pi\) | |||||||
\(180\) | −92808.9 | −0.213505 | ||||||||
\(181\) | −88034.5 | −0.199736 | −0.0998680 | − | 0.995001i | \(-0.531842\pi\) | ||||
−0.0998680 | + | 0.995001i | \(0.531842\pi\) | |||||||
\(182\) | −329257. | −0.736811 | ||||||||
\(183\) | 324620. | 0.716552 | ||||||||
\(184\) | −208263. | −0.453489 | ||||||||
\(185\) | 155542. | 0.334133 | ||||||||
\(186\) | 38396.6 | 0.0813786 | ||||||||
\(187\) | 65304.9 | 0.136566 | ||||||||
\(188\) | −268099. | −0.553224 | ||||||||
\(189\) | −539832. | −1.09927 | ||||||||
\(190\) | −31860.2 | −0.0640273 | ||||||||
\(191\) | 729196. | 1.44631 | 0.723154 | − | 0.690686i | \(-0.242692\pi\) | ||||
0.723154 | + | 0.690686i | \(0.242692\pi\) | |||||||
\(192\) | −152042. | −0.297654 | ||||||||
\(193\) | −98341.9 | −0.190040 | −0.0950200 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950200 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(194\) | −614033. | −1.17135 | ||||||||
\(195\) | −99105.0 | −0.186642 | ||||||||
\(196\) | −244701. | −0.454984 | ||||||||
\(197\) | −231956. | −0.425833 | −0.212917 | − | 0.977070i | \(-0.568296\pi\) | ||||
−0.212917 | + | 0.977070i | \(0.568296\pi\) | |||||||
\(198\) | −81164.7 | −0.147131 | ||||||||
\(199\) | −282333. | −0.505393 | −0.252696 | − | 0.967546i | \(-0.581317\pi\) | ||||
−0.252696 | + | 0.967546i | \(0.581317\pi\) | |||||||
\(200\) | 113712. | 0.201016 | ||||||||
\(201\) | 330960. | 0.577810 | ||||||||
\(202\) | −200000. | −0.344867 | ||||||||
\(203\) | 1.07737e6 | 1.83495 | ||||||||
\(204\) | −76757.6 | −0.129136 | ||||||||
\(205\) | −303737. | −0.504793 | ||||||||
\(206\) | −247319. | −0.406060 | ||||||||
\(207\) | 217503. | 0.352809 | ||||||||
\(208\) | 9303.30 | 0.0149100 | ||||||||
\(209\) | 43681.0 | 0.0691714 | ||||||||
\(210\) | 110028. | 0.172168 | ||||||||
\(211\) | −604043. | −0.934032 | −0.467016 | − | 0.884249i | \(-0.654671\pi\) | ||||
−0.467016 | + | 0.884249i | \(0.654671\pi\) | |||||||
\(212\) | −86187.9 | −0.131706 | ||||||||
\(213\) | −119256. | −0.180108 | ||||||||
\(214\) | 285164. | 0.425658 | ||||||||
\(215\) | −274573. | −0.405100 | ||||||||
\(216\) | 573477. | 0.836338 | ||||||||
\(217\) | −255899. | −0.368908 | ||||||||
\(218\) | 308293. | 0.439362 | ||||||||
\(219\) | −294109. | −0.414379 | ||||||||
\(220\) | −59101.1 | −0.0823263 | ||||||||
\(221\) | 293917. | 0.404803 | ||||||||
\(222\) | −159883. | −0.217731 | ||||||||
\(223\) | −6340.45 | −0.00853804 | −0.00426902 | − | 0.999991i | \(-0.501359\pi\) | ||||
−0.00426902 | + | 0.999991i | \(0.501359\pi\) | |||||||
\(224\) | 986783. | 1.31402 | ||||||||
\(225\) | −118757. | −0.156388 | ||||||||
\(226\) | 552406. | 0.719428 | ||||||||
\(227\) | −650604. | −0.838015 | −0.419008 | − | 0.907983i | \(-0.637622\pi\) | ||||
−0.419008 | + | 0.907983i | \(0.637622\pi\) | |||||||
\(228\) | −51341.5 | −0.0654080 | ||||||||
\(229\) | −1.09283e6 | −1.37709 | −0.688545 | − | 0.725193i | \(-0.741750\pi\) | ||||
−0.688545 | + | 0.725193i | \(0.741750\pi\) | |||||||
\(230\) | −101025. | −0.125924 | ||||||||
\(231\) | −150850. | −0.186001 | ||||||||
\(232\) | −1.14452e6 | −1.39605 | ||||||||
\(233\) | 521341. | 0.629118 | 0.314559 | − | 0.949238i | \(-0.398143\pi\) | ||||
0.314559 | + | 0.949238i | \(0.398143\pi\) | |||||||
\(234\) | −365297. | −0.436120 | ||||||||
\(235\) | −343057. | −0.405225 | ||||||||
\(236\) | −194872. | −0.227756 | ||||||||
\(237\) | −547707. | −0.633399 | ||||||||
\(238\) | −326310. | −0.373412 | ||||||||
\(239\) | 196299. | 0.222292 | 0.111146 | − | 0.993804i | \(-0.464548\pi\) | ||||
0.111146 | + | 0.993804i | \(0.464548\pi\) | |||||||
\(240\) | −3108.88 | −0.00348398 | ||||||||
\(241\) | 19716.4 | 0.0218668 | 0.0109334 | − | 0.999940i | \(-0.496520\pi\) | ||||
0.0109334 | + | 0.999940i | \(0.496520\pi\) | |||||||
\(242\) | −51686.0 | −0.0567328 | ||||||||
\(243\) | −935029. | −1.01580 | ||||||||
\(244\) | 871273. | 0.936871 | ||||||||
\(245\) | −313117. | −0.333266 | ||||||||
\(246\) | 312213. | 0.328937 | ||||||||
\(247\) | 196595. | 0.205036 | ||||||||
\(248\) | 271847. | 0.280670 | ||||||||
\(249\) | −437997. | −0.447686 | ||||||||
\(250\) | 55159.7 | 0.0558177 | ||||||||
\(251\) | 643511. | 0.644721 | 0.322361 | − | 0.946617i | \(-0.395524\pi\) | ||||
0.322361 | + | 0.946617i | \(0.395524\pi\) | |||||||
\(252\) | −635796. | −0.630691 | ||||||||
\(253\) | 138507. | 0.136041 | ||||||||
\(254\) | 290635. | 0.282659 | ||||||||
\(255\) | −98218.1 | −0.0945891 | ||||||||
\(256\) | −1.05896e6 | −1.00991 | ||||||||
\(257\) | −119750. | −0.113095 | −0.0565475 | − | 0.998400i | \(-0.518009\pi\) | ||||
−0.0565475 | + | 0.998400i | \(0.518009\pi\) | |||||||
\(258\) | 282235. | 0.263975 | ||||||||
\(259\) | 1.06556e6 | 0.987025 | ||||||||
\(260\) | −265995. | −0.244029 | ||||||||
\(261\) | 1.19530e6 | 1.08611 | ||||||||
\(262\) | −572088. | −0.514884 | ||||||||
\(263\) | −356699. | −0.317990 | −0.158995 | − | 0.987279i | \(-0.550825\pi\) | ||||
−0.158995 | + | 0.987279i | \(0.550825\pi\) | |||||||
\(264\) | 160252. | 0.141512 | ||||||||
\(265\) | −110285. | −0.0964721 | ||||||||
\(266\) | −218262. | −0.189136 | ||||||||
\(267\) | 183790. | 0.157777 | ||||||||
\(268\) | 888288. | 0.755469 | ||||||||
\(269\) | 643644. | 0.542332 | 0.271166 | − | 0.962533i | \(-0.412591\pi\) | ||||
0.271166 | + | 0.962533i | \(0.412591\pi\) | |||||||
\(270\) | 278184. | 0.232233 | ||||||||
\(271\) | 430149. | 0.355792 | 0.177896 | − | 0.984049i | \(-0.443071\pi\) | ||||
0.177896 | + | 0.984049i | \(0.443071\pi\) | |||||||
\(272\) | 9220.05 | 0.00755633 | ||||||||
\(273\) | −678928. | −0.551337 | ||||||||
\(274\) | 166030. | 0.133601 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | −162797. | −0.128639 | ||||||||
\(277\) | −1.74029e6 | −1.36277 | −0.681384 | − | 0.731926i | \(-0.738622\pi\) | ||||
−0.681384 | + | 0.731926i | \(0.738622\pi\) | |||||||
\(278\) | −1.34456e6 | −1.04345 | ||||||||
\(279\) | −283909. | −0.218358 | ||||||||
\(280\) | 778994. | 0.593798 | ||||||||
\(281\) | −147401. | −0.111361 | −0.0556806 | − | 0.998449i | \(-0.517733\pi\) | ||||
−0.0556806 | + | 0.998449i | \(0.517733\pi\) | |||||||
\(282\) | 352630. | 0.264056 | ||||||||
\(283\) | −1.48493e6 | −1.10215 | −0.551074 | − | 0.834456i | \(-0.685782\pi\) | ||||
−0.551074 | + | 0.834456i | \(0.685782\pi\) | |||||||
\(284\) | −320081. | −0.235485 | ||||||||
\(285\) | −65695.9 | −0.0479100 | ||||||||
\(286\) | −232622. | −0.168165 | ||||||||
\(287\) | −2.08078e6 | −1.49115 | ||||||||
\(288\) | 1.09480e6 | 0.777771 | ||||||||
\(289\) | −1.12857e6 | −0.794848 | ||||||||
\(290\) | −555186. | −0.387653 | ||||||||
\(291\) | −1.26614e6 | −0.876494 | ||||||||
\(292\) | −789382. | −0.541789 | ||||||||
\(293\) | 908102. | 0.617967 | 0.308984 | − | 0.951067i | \(-0.400011\pi\) | ||||
0.308984 | + | 0.951067i | \(0.400011\pi\) | |||||||
\(294\) | 321855. | 0.217166 | ||||||||
\(295\) | −249356. | −0.166826 | ||||||||
\(296\) | −1.13197e6 | −0.750940 | ||||||||
\(297\) | −381396. | −0.250891 | ||||||||
\(298\) | 507900. | 0.331312 | ||||||||
\(299\) | 623376. | 0.403248 | ||||||||
\(300\) | 88887.6 | 0.0570214 | ||||||||
\(301\) | −1.88099e6 | −1.19666 | ||||||||
\(302\) | −125719. | −0.0793200 | ||||||||
\(303\) | −412401. | −0.258055 | ||||||||
\(304\) | 6167.09 | 0.00382733 | ||||||||
\(305\) | 1.11487e6 | 0.686238 | ||||||||
\(306\) | −362028. | −0.221023 | ||||||||
\(307\) | −1.96255e6 | −1.18843 | −0.594216 | − | 0.804305i | \(-0.702538\pi\) | ||||
−0.594216 | + | 0.804305i | \(0.702538\pi\) | |||||||
\(308\) | −404878. | −0.243191 | ||||||||
\(309\) | −509973. | −0.303844 | ||||||||
\(310\) | 131869. | 0.0779358 | ||||||||
\(311\) | 1.77468e6 | 1.04045 | 0.520224 | − | 0.854030i | \(-0.325849\pi\) | ||||
0.520224 | + | 0.854030i | \(0.325849\pi\) | |||||||
\(312\) | 721242. | 0.419464 | ||||||||
\(313\) | 175879. | 0.101474 | 0.0507369 | − | 0.998712i | \(-0.483843\pi\) | ||||
0.0507369 | + | 0.998712i | \(0.483843\pi\) | |||||||
\(314\) | −209400. | −0.119854 | ||||||||
\(315\) | −813557. | −0.461968 | ||||||||
\(316\) | −1.47003e6 | −0.828151 | ||||||||
\(317\) | 2.31567e6 | 1.29428 | 0.647140 | − | 0.762371i | \(-0.275965\pi\) | ||||
0.647140 | + | 0.762371i | \(0.275965\pi\) | |||||||
\(318\) | 113363. | 0.0628640 | ||||||||
\(319\) | 761170. | 0.418799 | ||||||||
\(320\) | −522172. | −0.285061 | ||||||||
\(321\) | 588010. | 0.318509 | ||||||||
\(322\) | −692080. | −0.371977 | ||||||||
\(323\) | 194835. | 0.103911 | ||||||||
\(324\) | −453820. | −0.240171 | ||||||||
\(325\) | −340365. | −0.178746 | ||||||||
\(326\) | 961692. | 0.501178 | ||||||||
\(327\) | 635702. | 0.328764 | ||||||||
\(328\) | 2.21046e6 | 1.13448 | ||||||||
\(329\) | −2.35014e6 | −1.19703 | ||||||||
\(330\) | 77735.3 | 0.0392947 | ||||||||
\(331\) | −2.29703e6 | −1.15238 | −0.576191 | − | 0.817315i | \(-0.695462\pi\) | ||||
−0.576191 | + | 0.817315i | \(0.695462\pi\) | |||||||
\(332\) | −1.17557e6 | −0.585336 | ||||||||
\(333\) | 1.18219e6 | 0.584222 | ||||||||
\(334\) | −1.95020e6 | −0.956564 | ||||||||
\(335\) | 1.13664e6 | 0.553365 | ||||||||
\(336\) | −21297.7 | −0.0102916 | ||||||||
\(337\) | 936024. | 0.448965 | 0.224482 | − | 0.974478i | \(-0.427931\pi\) | ||||
0.224482 | + | 0.974478i | \(0.427931\pi\) | |||||||
\(338\) | 263785. | 0.125591 | ||||||||
\(339\) | 1.13906e6 | 0.538330 | ||||||||
\(340\) | −263615. | −0.123672 | ||||||||
\(341\) | −180794. | −0.0841974 | ||||||||
\(342\) | −242152. | −0.111950 | ||||||||
\(343\) | 733412. | 0.336599 | ||||||||
\(344\) | 1.99822e6 | 0.910432 | ||||||||
\(345\) | −208313. | −0.0942257 | ||||||||
\(346\) | −1.90067e6 | −0.853528 | ||||||||
\(347\) | −1.50437e6 | −0.670702 | −0.335351 | − | 0.942093i | \(-0.608855\pi\) | ||||
−0.335351 | + | 0.942093i | \(0.608855\pi\) | |||||||
\(348\) | −894659. | −0.396013 | ||||||||
\(349\) | −3.65873e6 | −1.60793 | −0.803964 | − | 0.594679i | \(-0.797279\pi\) | ||||
−0.803964 | + | 0.594679i | \(0.797279\pi\) | |||||||
\(350\) | 377877. | 0.164885 | ||||||||
\(351\) | −1.71654e6 | −0.743682 | ||||||||
\(352\) | 697170. | 0.299904 | ||||||||
\(353\) | 1.05443e6 | 0.450380 | 0.225190 | − | 0.974315i | \(-0.427700\pi\) | ||||
0.225190 | + | 0.974315i | \(0.427700\pi\) | |||||||
\(354\) | 256314. | 0.108709 | ||||||||
\(355\) | −409572. | −0.172488 | ||||||||
\(356\) | 493287. | 0.206289 | ||||||||
\(357\) | −672853. | −0.279415 | ||||||||
\(358\) | 830426. | 0.342447 | ||||||||
\(359\) | −875247. | −0.358422 | −0.179211 | − | 0.983811i | \(-0.557354\pi\) | ||||
−0.179211 | + | 0.983811i | \(0.557354\pi\) | |||||||
\(360\) | 864262. | 0.351471 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 310781. | 0.124647 | ||||||||
\(363\) | −106577. | −0.0424517 | ||||||||
\(364\) | −1.82223e6 | −0.720857 | ||||||||
\(365\) | −1.01008e6 | −0.396849 | ||||||||
\(366\) | −1.14598e6 | −0.447172 | ||||||||
\(367\) | −910146. | −0.352733 | −0.176366 | − | 0.984325i | \(-0.556434\pi\) | ||||
−0.176366 | + | 0.984325i | \(0.556434\pi\) | |||||||
\(368\) | 19555.0 | 0.00752730 | ||||||||
\(369\) | −2.30854e6 | −0.882615 | ||||||||
\(370\) | −549099. | −0.208519 | ||||||||
\(371\) | −755518. | −0.284977 | ||||||||
\(372\) | 212501. | 0.0796165 | ||||||||
\(373\) | 726674. | 0.270438 | 0.135219 | − | 0.990816i | \(-0.456826\pi\) | ||||
0.135219 | + | 0.990816i | \(0.456826\pi\) | |||||||
\(374\) | −230541. | −0.0852253 | ||||||||
\(375\) | 113739. | 0.0417670 | ||||||||
\(376\) | 2.49661e6 | 0.910714 | ||||||||
\(377\) | 3.42579e6 | 1.24139 | ||||||||
\(378\) | 1.90573e6 | 0.686012 | ||||||||
\(379\) | −1.93968e6 | −0.693638 | −0.346819 | − | 0.937932i | \(-0.612738\pi\) | ||||
−0.346819 | + | 0.937932i | \(0.612738\pi\) | |||||||
\(380\) | −176326. | −0.0626409 | ||||||||
\(381\) | 599290. | 0.211507 | ||||||||
\(382\) | −2.57422e6 | −0.902585 | ||||||||
\(383\) | 2.87116e6 | 1.00014 | 0.500070 | − | 0.865985i | \(-0.333308\pi\) | ||||
0.500070 | + | 0.865985i | \(0.333308\pi\) | |||||||
\(384\) | −805387. | −0.278725 | ||||||||
\(385\) | −518076. | −0.178132 | ||||||||
\(386\) | 347169. | 0.118597 | ||||||||
\(387\) | −2.08688e6 | −0.708305 | ||||||||
\(388\) | −3.39829e6 | −1.14599 | ||||||||
\(389\) | −4.27230e6 | −1.43149 | −0.715744 | − | 0.698363i | \(-0.753912\pi\) | ||||
−0.715744 | + | 0.698363i | \(0.753912\pi\) | |||||||
\(390\) | 349863. | 0.116476 | ||||||||
\(391\) | 617798. | 0.204364 | ||||||||
\(392\) | 2.27873e6 | 0.748991 | ||||||||
\(393\) | −1.17965e6 | −0.385275 | ||||||||
\(394\) | 818855. | 0.265746 | ||||||||
\(395\) | −1.88104e6 | −0.606603 | ||||||||
\(396\) | −449195. | −0.143945 | ||||||||
\(397\) | −211399. | −0.0673172 | −0.0336586 | − | 0.999433i | \(-0.510716\pi\) | ||||
−0.0336586 | + | 0.999433i | \(0.510716\pi\) | |||||||
\(398\) | 996698. | 0.315396 | ||||||||
\(399\) | −450056. | −0.141525 | ||||||||
\(400\) | −10677.1 | −0.00333659 | ||||||||
\(401\) | −605610. | −0.188075 | −0.0940377 | − | 0.995569i | \(-0.529977\pi\) | ||||
−0.0940377 | + | 0.995569i | \(0.529977\pi\) | |||||||
\(402\) | −1.16836e6 | −0.360589 | ||||||||
\(403\) | −813699. | −0.249575 | ||||||||
\(404\) | −1.10687e6 | −0.337400 | ||||||||
\(405\) | −580702. | −0.175920 | ||||||||
\(406\) | −3.80335e6 | −1.14512 | ||||||||
\(407\) | 752826. | 0.225273 | ||||||||
\(408\) | 714788. | 0.212582 | ||||||||
\(409\) | 2.52166e6 | 0.745382 | 0.372691 | − | 0.927955i | \(-0.378435\pi\) | ||||
0.372691 | + | 0.927955i | \(0.378435\pi\) | |||||||
\(410\) | 1.07226e6 | 0.315021 | ||||||||
\(411\) | 342355. | 0.0999705 | ||||||||
\(412\) | −1.36876e6 | −0.397267 | ||||||||
\(413\) | −1.70823e6 | −0.492802 | ||||||||
\(414\) | −767834. | −0.220174 | ||||||||
\(415\) | −1.50425e6 | −0.428746 | ||||||||
\(416\) | 3.13775e6 | 0.888964 | ||||||||
\(417\) | −2.77250e6 | −0.780784 | ||||||||
\(418\) | −154204. | −0.0431672 | ||||||||
\(419\) | −4.00226e6 | −1.11371 | −0.556853 | − | 0.830611i | \(-0.687991\pi\) | ||||
−0.556853 | + | 0.830611i | \(0.687991\pi\) | |||||||
\(420\) | 608933. | 0.168440 | ||||||||
\(421\) | 1.03324e6 | 0.284117 | 0.142058 | − | 0.989858i | \(-0.454628\pi\) | ||||
0.142058 | + | 0.989858i | \(0.454628\pi\) | |||||||
\(422\) | 2.13240e6 | 0.582893 | ||||||||
\(423\) | −2.60739e6 | −0.708524 | ||||||||
\(424\) | 802605. | 0.216814 | ||||||||
\(425\) | −337319. | −0.0905875 | ||||||||
\(426\) | 421001. | 0.112398 | ||||||||
\(427\) | 7.63753e6 | 2.02714 | ||||||||
\(428\) | 1.57820e6 | 0.416441 | ||||||||
\(429\) | −479668. | −0.125834 | ||||||||
\(430\) | 969304. | 0.252807 | ||||||||
\(431\) | −3.33069e6 | −0.863656 | −0.431828 | − | 0.901956i | \(-0.642131\pi\) | ||||
−0.431828 | + | 0.901956i | \(0.642131\pi\) | |||||||
\(432\) | −53847.2 | −0.0138821 | ||||||||
\(433\) | 1.10574e6 | 0.283422 | 0.141711 | − | 0.989908i | \(-0.454740\pi\) | ||||
0.141711 | + | 0.989908i | \(0.454740\pi\) | |||||||
\(434\) | 903379. | 0.230221 | ||||||||
\(435\) | −1.14480e6 | −0.290071 | ||||||||
\(436\) | 1.70621e6 | 0.429849 | ||||||||
\(437\) | 413231. | 0.103512 | ||||||||
\(438\) | 1.03827e6 | 0.258598 | ||||||||
\(439\) | 6.42259e6 | 1.59056 | 0.795278 | − | 0.606245i | \(-0.207325\pi\) | ||||
0.795278 | + | 0.606245i | \(0.207325\pi\) | |||||||
\(440\) | 550365. | 0.135525 | ||||||||
\(441\) | −2.37983e6 | −0.582706 | ||||||||
\(442\) | −1.03759e6 | −0.252622 | ||||||||
\(443\) | −6.69493e6 | −1.62083 | −0.810414 | − | 0.585858i | \(-0.800758\pi\) | ||||
−0.810414 | + | 0.585858i | \(0.800758\pi\) | |||||||
\(444\) | −884851. | −0.213016 | ||||||||
\(445\) | 631205. | 0.151102 | ||||||||
\(446\) | 22383.2 | 0.00532825 | ||||||||
\(447\) | 1.04729e6 | 0.247913 | ||||||||
\(448\) | −3.57719e6 | −0.842067 | ||||||||
\(449\) | 1.94219e6 | 0.454648 | 0.227324 | − | 0.973819i | \(-0.427002\pi\) | ||||
0.227324 | + | 0.973819i | \(0.427002\pi\) | |||||||
\(450\) | 419239. | 0.0975956 | ||||||||
\(451\) | −1.47009e6 | −0.340331 | ||||||||
\(452\) | 3.05722e6 | 0.703850 | ||||||||
\(453\) | −259233. | −0.0593532 | ||||||||
\(454\) | 2.29677e6 | 0.522972 | ||||||||
\(455\) | −2.33170e6 | −0.528013 | ||||||||
\(456\) | 478106. | 0.107674 | ||||||||
\(457\) | −3.13746e6 | −0.702728 | −0.351364 | − | 0.936239i | \(-0.614282\pi\) | ||||
−0.351364 | + | 0.936239i | \(0.614282\pi\) | |||||||
\(458\) | 3.85792e6 | 0.859389 | ||||||||
\(459\) | −1.70118e6 | −0.376894 | ||||||||
\(460\) | −559108. | −0.123197 | ||||||||
\(461\) | −4.34869e6 | −0.953030 | −0.476515 | − | 0.879166i | \(-0.658100\pi\) | ||||
−0.476515 | + | 0.879166i | \(0.658100\pi\) | |||||||
\(462\) | 532534. | 0.116076 | ||||||||
\(463\) | 6.38906e6 | 1.38511 | 0.692555 | − | 0.721365i | \(-0.256485\pi\) | ||||
0.692555 | + | 0.721365i | \(0.256485\pi\) | |||||||
\(464\) | 107466. | 0.0231726 | ||||||||
\(465\) | 271913. | 0.0583174 | ||||||||
\(466\) | −1.84045e6 | −0.392608 | ||||||||
\(467\) | 1.31162e6 | 0.278303 | 0.139151 | − | 0.990271i | \(-0.455563\pi\) | ||||
0.139151 | + | 0.990271i | \(0.455563\pi\) | |||||||
\(468\) | −2.02169e6 | −0.426677 | ||||||||
\(469\) | 7.78668e6 | 1.63463 | ||||||||
\(470\) | 1.21107e6 | 0.252885 | ||||||||
\(471\) | −431784. | −0.0896838 | ||||||||
\(472\) | 1.81470e6 | 0.374930 | ||||||||
\(473\) | −1.32893e6 | −0.273118 | ||||||||
\(474\) | 1.93353e6 | 0.395280 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | −1.80592e6 | −0.365327 | ||||||||
\(477\) | −838216. | −0.168679 | ||||||||
\(478\) | −692980. | −0.138724 | ||||||||
\(479\) | −6.24610e6 | −1.24386 | −0.621928 | − | 0.783074i | \(-0.713650\pi\) | ||||
−0.621928 | + | 0.783074i | \(0.713650\pi\) | |||||||
\(480\) | −1.04854e6 | −0.207722 | ||||||||
\(481\) | 3.38823e6 | 0.667745 | ||||||||
\(482\) | −69603.2 | −0.0136462 | ||||||||
\(483\) | −1.42707e6 | −0.278341 | ||||||||
\(484\) | −286049. | −0.0555044 | ||||||||
\(485\) | −4.34841e6 | −0.839413 | ||||||||
\(486\) | 3.30086e6 | 0.633922 | ||||||||
\(487\) | 8.70883e6 | 1.66394 | 0.831970 | − | 0.554821i | \(-0.187213\pi\) | ||||
0.831970 | + | 0.554821i | \(0.187213\pi\) | |||||||
\(488\) | −8.11353e6 | −1.54227 | ||||||||
\(489\) | 1.98301e6 | 0.375019 | ||||||||
\(490\) | 1.10537e6 | 0.207978 | ||||||||
\(491\) | −3.78860e6 | −0.709209 | −0.354605 | − | 0.935016i | \(-0.615385\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(492\) | 1.72790e6 | 0.321815 | ||||||||
\(493\) | 3.39513e6 | 0.629129 | ||||||||
\(494\) | −694022. | −0.127955 | ||||||||
\(495\) | −574784. | −0.105437 | ||||||||
\(496\) | −25525.4 | −0.00465873 | ||||||||
\(497\) | −2.80581e6 | −0.509527 | ||||||||
\(498\) | 1.54623e6 | 0.279383 | ||||||||
\(499\) | −7.82596e6 | −1.40697 | −0.703487 | − | 0.710708i | \(-0.748375\pi\) | ||||
−0.703487 | + | 0.710708i | \(0.748375\pi\) | |||||||
\(500\) | 305274. | 0.0546091 | ||||||||
\(501\) | −4.02133e6 | −0.715773 | ||||||||
\(502\) | −2.27174e6 | −0.402345 | ||||||||
\(503\) | 1.08914e7 | 1.91938 | 0.959692 | − | 0.281053i | \(-0.0906838\pi\) | ||||
0.959692 | + | 0.281053i | \(0.0906838\pi\) | |||||||
\(504\) | 5.92071e6 | 1.03824 | ||||||||
\(505\) | −1.41634e6 | −0.247138 | ||||||||
\(506\) | −488960. | −0.0848979 | ||||||||
\(507\) | 543926. | 0.0939767 | ||||||||
\(508\) | 1.60848e6 | 0.276539 | ||||||||
\(509\) | 6.34375e6 | 1.08531 | 0.542653 | − | 0.839957i | \(-0.317420\pi\) | ||||
0.542653 | + | 0.839957i | \(0.317420\pi\) | |||||||
\(510\) | 346732. | 0.0590294 | ||||||||
\(511\) | −6.91967e6 | −1.17229 | ||||||||
\(512\) | 197890. | 0.0333617 | ||||||||
\(513\) | −1.13788e6 | −0.190899 | ||||||||
\(514\) | 422745. | 0.0705782 | ||||||||
\(515\) | −1.75144e6 | −0.290990 | ||||||||
\(516\) | 1.56199e6 | 0.258259 | ||||||||
\(517\) | −1.66039e6 | −0.273203 | ||||||||
\(518\) | −3.76166e6 | −0.615963 | ||||||||
\(519\) | −3.91920e6 | −0.638673 | ||||||||
\(520\) | 2.47702e6 | 0.401718 | ||||||||
\(521\) | −3.77648e6 | −0.609526 | −0.304763 | − | 0.952428i | \(-0.598577\pi\) | ||||
−0.304763 | + | 0.952428i | \(0.598577\pi\) | |||||||
\(522\) | −4.21967e6 | −0.677800 | ||||||||
\(523\) | −4.73171e6 | −0.756421 | −0.378210 | − | 0.925720i | \(-0.623460\pi\) | ||||
−0.378210 | + | 0.925720i | \(0.623460\pi\) | |||||||
\(524\) | −3.16614e6 | −0.503735 | ||||||||
\(525\) | 779183. | 0.123379 | ||||||||
\(526\) | 1.25923e6 | 0.198445 | ||||||||
\(527\) | −806417. | −0.126483 | ||||||||
\(528\) | −15047.0 | −0.00234890 | ||||||||
\(529\) | −5.12604e6 | −0.796421 | ||||||||
\(530\) | 389330. | 0.0602044 | ||||||||
\(531\) | −1.89522e6 | −0.291691 | ||||||||
\(532\) | −1.20794e6 | −0.185040 | ||||||||
\(533\) | −6.61640e6 | −1.00880 | ||||||||
\(534\) | −648819. | −0.0984624 | ||||||||
\(535\) | 2.01945e6 | 0.305035 | ||||||||
\(536\) | −8.27198e6 | −1.24365 | ||||||||
\(537\) | 1.71234e6 | 0.256245 | ||||||||
\(538\) | −2.27221e6 | −0.338448 | ||||||||
\(539\) | −1.51549e6 | −0.224688 | ||||||||
\(540\) | 1.53957e6 | 0.227204 | ||||||||
\(541\) | −9.01458e6 | −1.32420 | −0.662098 | − | 0.749417i | \(-0.730334\pi\) | ||||
−0.662098 | + | 0.749417i | \(0.730334\pi\) | |||||||
\(542\) | −1.51852e6 | −0.222036 | ||||||||
\(543\) | 640832. | 0.0932705 | ||||||||
\(544\) | 3.10967e6 | 0.450523 | ||||||||
\(545\) | 2.18324e6 | 0.314855 | ||||||||
\(546\) | 2.39677e6 | 0.344068 | ||||||||
\(547\) | −2.70367e6 | −0.386354 | −0.193177 | − | 0.981164i | \(-0.561879\pi\) | ||||
−0.193177 | + | 0.981164i | \(0.561879\pi\) | |||||||
\(548\) | 918872. | 0.130708 | ||||||||
\(549\) | 8.47352e6 | 1.19987 | ||||||||
\(550\) | 266973. | 0.0376323 | ||||||||
\(551\) | 2.27093e6 | 0.318658 | ||||||||
\(552\) | 1.51601e6 | 0.211765 | ||||||||
\(553\) | −1.28862e7 | −1.79190 | ||||||||
\(554\) | 6.14361e6 | 0.850451 | ||||||||
\(555\) | −1.13224e6 | −0.156030 | ||||||||
\(556\) | −7.44131e6 | −1.02085 | ||||||||
\(557\) | 6.35699e6 | 0.868187 | 0.434094 | − | 0.900868i | \(-0.357069\pi\) | ||||
0.434094 | + | 0.900868i | \(0.357069\pi\) | |||||||
\(558\) | 1.00226e6 | 0.136269 | ||||||||
\(559\) | −5.98112e6 | −0.809567 | ||||||||
\(560\) | −73144.4 | −0.00985624 | ||||||||
\(561\) | −475376. | −0.0637720 | ||||||||
\(562\) | 520357. | 0.0694961 | ||||||||
\(563\) | 9.06343e6 | 1.20510 | 0.602548 | − | 0.798083i | \(-0.294152\pi\) | ||||
0.602548 | + | 0.798083i | \(0.294152\pi\) | |||||||
\(564\) | 1.95158e6 | 0.258339 | ||||||||
\(565\) | 3.91198e6 | 0.515555 | ||||||||
\(566\) | 5.24214e6 | 0.687808 | ||||||||
\(567\) | −3.97816e6 | −0.519666 | ||||||||
\(568\) | 2.98068e6 | 0.387654 | ||||||||
\(569\) | 7.54997e6 | 0.977608 | 0.488804 | − | 0.872394i | \(-0.337433\pi\) | ||||
0.488804 | + | 0.872394i | \(0.337433\pi\) | |||||||
\(570\) | 231921. | 0.0298988 | ||||||||
\(571\) | 725296. | 0.0930947 | 0.0465473 | − | 0.998916i | \(-0.485178\pi\) | ||||
0.0465473 | + | 0.998916i | \(0.485178\pi\) | |||||||
\(572\) | −1.28742e6 | −0.164524 | ||||||||
\(573\) | −5.30806e6 | −0.675381 | ||||||||
\(574\) | 7.34561e6 | 0.930568 | ||||||||
\(575\) | −715428. | −0.0902394 | ||||||||
\(576\) | −3.96874e6 | −0.498422 | ||||||||
\(577\) | 4.17715e6 | 0.522324 | 0.261162 | − | 0.965295i | \(-0.415894\pi\) | ||||
0.261162 | + | 0.965295i | \(0.415894\pi\) | |||||||
\(578\) | 3.98410e6 | 0.496033 | ||||||||
\(579\) | 715863. | 0.0887428 | ||||||||
\(580\) | −3.07260e6 | −0.379259 | ||||||||
\(581\) | −1.03050e7 | −1.26651 | ||||||||
\(582\) | 4.46975e6 | 0.546986 | ||||||||
\(583\) | −533779. | −0.0650415 | ||||||||
\(584\) | 7.35094e6 | 0.891889 | ||||||||
\(585\) | −2.58693e6 | −0.312532 | ||||||||
\(586\) | −3.20580e6 | −0.385649 | ||||||||
\(587\) | −4.01299e6 | −0.480698 | −0.240349 | − | 0.970687i | \(-0.577262\pi\) | ||||
−0.240349 | + | 0.970687i | \(0.577262\pi\) | |||||||
\(588\) | 1.78126e6 | 0.212463 | ||||||||
\(589\) | −539395. | −0.0640646 | ||||||||
\(590\) | 880281. | 0.104110 | ||||||||
\(591\) | 1.68848e6 | 0.198851 | ||||||||
\(592\) | 106287. | 0.0124646 | ||||||||
\(593\) | −1.24992e6 | −0.145964 | −0.0729822 | − | 0.997333i | \(-0.523252\pi\) | ||||
−0.0729822 | + | 0.997333i | \(0.523252\pi\) | |||||||
\(594\) | 1.34641e6 | 0.156571 | ||||||||
\(595\) | −2.31083e6 | −0.267594 | ||||||||
\(596\) | 2.81091e6 | 0.324139 | ||||||||
\(597\) | 2.05520e6 | 0.236003 | ||||||||
\(598\) | −2.20066e6 | −0.251651 | ||||||||
\(599\) | 7.03447e6 | 0.801059 | 0.400530 | − | 0.916284i | \(-0.368826\pi\) | ||||
0.400530 | + | 0.916284i | \(0.368826\pi\) | |||||||
\(600\) | −827746. | −0.0938683 | ||||||||
\(601\) | 1.02684e7 | 1.15963 | 0.579813 | − | 0.814749i | \(-0.303125\pi\) | ||||
0.579813 | + | 0.814749i | \(0.303125\pi\) | |||||||
\(602\) | 6.64031e6 | 0.746788 | ||||||||
\(603\) | 8.63900e6 | 0.967543 | ||||||||
\(604\) | −695774. | −0.0776025 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | 1.45587e6 | 0.161042 | ||||||||
\(607\) | 5.27248e6 | 0.580823 | 0.290411 | − | 0.956902i | \(-0.406208\pi\) | ||||
0.290411 | + | 0.956902i | \(0.406208\pi\) | |||||||
\(608\) | 2.07999e6 | 0.228193 | ||||||||
\(609\) | −7.84253e6 | −0.856866 | ||||||||
\(610\) | −3.93574e6 | −0.428254 | ||||||||
\(611\) | −7.47292e6 | −0.809817 | ||||||||
\(612\) | −2.00359e6 | −0.216238 | ||||||||
\(613\) | 9.48094e6 | 1.01906 | 0.509531 | − | 0.860453i | \(-0.329819\pi\) | ||||
0.509531 | + | 0.860453i | \(0.329819\pi\) | |||||||
\(614\) | 6.92823e6 | 0.741654 | ||||||||
\(615\) | 2.21100e6 | 0.235723 | ||||||||
\(616\) | 3.77033e6 | 0.400339 | ||||||||
\(617\) | 4.81602e6 | 0.509302 | 0.254651 | − | 0.967033i | \(-0.418039\pi\) | ||||
0.254651 | + | 0.967033i | \(0.418039\pi\) | |||||||
\(618\) | 1.80032e6 | 0.189617 | ||||||||
\(619\) | 1.69971e7 | 1.78299 | 0.891496 | − | 0.453028i | \(-0.149656\pi\) | ||||
0.891496 | + | 0.453028i | \(0.149656\pi\) | |||||||
\(620\) | 729809. | 0.0762483 | ||||||||
\(621\) | −3.60808e6 | −0.375446 | ||||||||
\(622\) | −6.26503e6 | −0.649303 | ||||||||
\(623\) | 4.32413e6 | 0.446353 | ||||||||
\(624\) | −67721.8 | −0.00696253 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −620892. | −0.0633258 | ||||||||
\(627\) | −317968. | −0.0323009 | ||||||||
\(628\) | −1.15890e6 | −0.117259 | ||||||||
\(629\) | 3.35791e6 | 0.338410 | ||||||||
\(630\) | 2.87204e6 | 0.288296 | ||||||||
\(631\) | 7.54063e6 | 0.753935 | 0.376968 | − | 0.926226i | \(-0.376967\pi\) | ||||
0.376968 | + | 0.926226i | \(0.376967\pi\) | |||||||
\(632\) | 1.36894e7 | 1.36330 | ||||||||
\(633\) | 4.39703e6 | 0.436164 | ||||||||
\(634\) | −8.17483e6 | −0.807710 | ||||||||
\(635\) | 2.05819e6 | 0.202559 | ||||||||
\(636\) | 627390. | 0.0615028 | ||||||||
\(637\) | −6.82073e6 | −0.666012 | ||||||||
\(638\) | −2.68710e6 | −0.261356 | ||||||||
\(639\) | −3.11293e6 | −0.301590 | ||||||||
\(640\) | −2.76601e6 | −0.266934 | ||||||||
\(641\) | −9.66535e6 | −0.929122 | −0.464561 | − | 0.885541i | \(-0.653788\pi\) | ||||
−0.464561 | + | 0.885541i | \(0.653788\pi\) | |||||||
\(642\) | −2.07581e6 | −0.198769 | ||||||||
\(643\) | −2.20861e6 | −0.210664 | −0.105332 | − | 0.994437i | \(-0.533591\pi\) | ||||
−0.105332 | + | 0.994437i | \(0.533591\pi\) | |||||||
\(644\) | −3.83022e6 | −0.363923 | ||||||||
\(645\) | 1.99871e6 | 0.189169 | ||||||||
\(646\) | −687812. | −0.0648467 | ||||||||
\(647\) | 3.08586e6 | 0.289812 | 0.144906 | − | 0.989445i | \(-0.453712\pi\) | ||||
0.144906 | + | 0.989445i | \(0.453712\pi\) | |||||||
\(648\) | 4.22609e6 | 0.395368 | ||||||||
\(649\) | −1.20688e6 | −0.112474 | ||||||||
\(650\) | 1.20156e6 | 0.111548 | ||||||||
\(651\) | 1.86277e6 | 0.172269 | ||||||||
\(652\) | 5.32236e6 | 0.490326 | ||||||||
\(653\) | −1.20880e6 | −0.110936 | −0.0554679 | − | 0.998460i | \(-0.517665\pi\) | ||||
−0.0554679 | + | 0.998460i | \(0.517665\pi\) | |||||||
\(654\) | −2.24417e6 | −0.205169 | ||||||||
\(655\) | −4.05136e6 | −0.368976 | ||||||||
\(656\) | −207554. | −0.0188309 | ||||||||
\(657\) | −7.67709e6 | −0.693878 | ||||||||
\(658\) | 8.29652e6 | 0.747019 | ||||||||
\(659\) | 3.16858e6 | 0.284217 | 0.142109 | − | 0.989851i | \(-0.454612\pi\) | ||||
0.142109 | + | 0.989851i | \(0.454612\pi\) | |||||||
\(660\) | 430216. | 0.0384438 | ||||||||
\(661\) | 1.73420e7 | 1.54382 | 0.771909 | − | 0.635734i | \(-0.219302\pi\) | ||||
0.771909 | + | 0.635734i | \(0.219302\pi\) | |||||||
\(662\) | 8.10902e6 | 0.719157 | ||||||||
\(663\) | −2.13952e6 | −0.189031 | ||||||||
\(664\) | 1.09473e7 | 0.963576 | ||||||||
\(665\) | −1.54567e6 | −0.135538 | ||||||||
\(666\) | −4.17341e6 | −0.364590 | ||||||||
\(667\) | 7.20083e6 | 0.626712 | ||||||||
\(668\) | −1.07931e7 | −0.935851 | ||||||||
\(669\) | 46154.2 | 0.00398700 | ||||||||
\(670\) | −4.01260e6 | −0.345334 | ||||||||
\(671\) | 5.39597e6 | 0.462662 | ||||||||
\(672\) | −7.18312e6 | −0.613606 | ||||||||
\(673\) | −1.19365e7 | −1.01587 | −0.507936 | − | 0.861395i | \(-0.669591\pi\) | ||||
−0.507936 | + | 0.861395i | \(0.669591\pi\) | |||||||
\(674\) | −3.30437e6 | −0.280181 | ||||||||
\(675\) | 1.97002e6 | 0.166422 | ||||||||
\(676\) | 1.45989e6 | 0.122872 | ||||||||
\(677\) | 1.46589e7 | 1.22922 | 0.614611 | − | 0.788831i | \(-0.289313\pi\) | ||||
0.614611 | + | 0.788831i | \(0.289313\pi\) | |||||||
\(678\) | −4.02114e6 | −0.335950 | ||||||||
\(679\) | −2.97892e7 | −2.47961 | ||||||||
\(680\) | 2.45486e6 | 0.203589 | ||||||||
\(681\) | 4.73596e6 | 0.391327 | ||||||||
\(682\) | 638244. | 0.0525443 | ||||||||
\(683\) | 8.35322e6 | 0.685176 | 0.342588 | − | 0.939486i | \(-0.388696\pi\) | ||||
0.342588 | + | 0.939486i | \(0.388696\pi\) | |||||||
\(684\) | −1.34016e6 | −0.109526 | ||||||||
\(685\) | 1.17578e6 | 0.0957412 | ||||||||
\(686\) | −2.58911e6 | −0.210058 | ||||||||
\(687\) | 7.95504e6 | 0.643059 | ||||||||
\(688\) | −187625. | −0.0151119 | ||||||||
\(689\) | −2.40237e6 | −0.192794 | ||||||||
\(690\) | 735392. | 0.0588026 | ||||||||
\(691\) | 8.42488e6 | 0.671226 | 0.335613 | − | 0.942000i | \(-0.391057\pi\) | ||||
0.335613 | + | 0.942000i | \(0.391057\pi\) | |||||||
\(692\) | −1.05190e7 | −0.835046 | ||||||||
\(693\) | −3.93762e6 | −0.311459 | ||||||||
\(694\) | 5.31074e6 | 0.418559 | ||||||||
\(695\) | −9.52181e6 | −0.747752 | ||||||||
\(696\) | 8.33131e6 | 0.651914 | ||||||||
\(697\) | −6.55719e6 | −0.511253 | ||||||||
\(698\) | 1.29161e7 | 1.00344 | ||||||||
\(699\) | −3.79501e6 | −0.293779 | ||||||||
\(700\) | 2.09131e6 | 0.161314 | ||||||||
\(701\) | 3.60707e6 | 0.277242 | 0.138621 | − | 0.990345i | \(-0.455733\pi\) | ||||
0.138621 | + | 0.990345i | \(0.455733\pi\) | |||||||
\(702\) | 6.05978e6 | 0.464103 | ||||||||
\(703\) | 2.24603e6 | 0.171407 | ||||||||
\(704\) | −2.52731e6 | −0.192188 | ||||||||
\(705\) | 2.49722e6 | 0.189228 | ||||||||
\(706\) | −3.72235e6 | −0.281064 | ||||||||
\(707\) | −9.70279e6 | −0.730043 | ||||||||
\(708\) | 1.41854e6 | 0.106355 | ||||||||
\(709\) | 4.60024e6 | 0.343689 | 0.171844 | − | 0.985124i | \(-0.445027\pi\) | ||||
0.171844 | + | 0.985124i | \(0.445027\pi\) | |||||||
\(710\) | 1.44588e6 | 0.107643 | ||||||||
\(711\) | −1.42967e7 | −1.06063 | ||||||||
\(712\) | −4.59363e6 | −0.339591 | ||||||||
\(713\) | −1.71035e6 | −0.125997 | ||||||||
\(714\) | 2.37532e6 | 0.174372 | ||||||||
\(715\) | −1.64736e6 | −0.120510 | ||||||||
\(716\) | 4.59588e6 | 0.335032 | ||||||||
\(717\) | −1.42893e6 | −0.103803 | ||||||||
\(718\) | 3.08982e6 | 0.223677 | ||||||||
\(719\) | 2.39501e7 | 1.72777 | 0.863885 | − | 0.503690i | \(-0.168025\pi\) | ||||
0.863885 | + | 0.503690i | \(0.168025\pi\) | |||||||
\(720\) | −81150.7 | −0.00583393 | ||||||||
\(721\) | −1.19984e7 | −0.859580 | ||||||||
\(722\) | −460062. | −0.0328453 | ||||||||
\(723\) | −143522. | −0.0102111 | ||||||||
\(724\) | 1.71998e6 | 0.121948 | ||||||||
\(725\) | −3.93167e6 | −0.277800 | ||||||||
\(726\) | 376239. | 0.0264925 | ||||||||
\(727\) | −170934. | −0.0119948 | −0.00599739 | − | 0.999982i | \(-0.501909\pi\) | ||||
−0.00599739 | + | 0.999982i | \(0.501909\pi\) | |||||||
\(728\) | 1.69691e7 | 1.18667 | ||||||||
\(729\) | 1.16195e6 | 0.0809784 | ||||||||
\(730\) | 3.56582e6 | 0.247658 | ||||||||
\(731\) | −5.92760e6 | −0.410285 | ||||||||
\(732\) | −6.34228e6 | −0.437490 | ||||||||
\(733\) | 2.26600e7 | 1.55776 | 0.778880 | − | 0.627173i | \(-0.215788\pi\) | ||||
0.778880 | + | 0.627173i | \(0.215788\pi\) | |||||||
\(734\) | 3.21302e6 | 0.220127 | ||||||||
\(735\) | 2.27928e6 | 0.155625 | ||||||||
\(736\) | 6.59537e6 | 0.448792 | ||||||||
\(737\) | 5.50135e6 | 0.373079 | ||||||||
\(738\) | 8.14965e6 | 0.550805 | ||||||||
\(739\) | 1.59366e7 | 1.07346 | 0.536730 | − | 0.843754i | \(-0.319659\pi\) | ||||
0.536730 | + | 0.843754i | \(0.319659\pi\) | |||||||
\(740\) | −3.03892e6 | −0.204004 | ||||||||
\(741\) | −1.43108e6 | −0.0957452 | ||||||||
\(742\) | 2.66715e6 | 0.177843 | ||||||||
\(743\) | 1.56374e7 | 1.03918 | 0.519592 | − | 0.854415i | \(-0.326084\pi\) | ||||
0.519592 | + | 0.854415i | \(0.326084\pi\) | |||||||
\(744\) | −1.97887e6 | −0.131064 | ||||||||
\(745\) | 3.59680e6 | 0.237425 | ||||||||
\(746\) | −2.56532e6 | −0.168770 | ||||||||
\(747\) | −1.14330e7 | −0.749650 | ||||||||
\(748\) | −1.27590e6 | −0.0833799 | ||||||||
\(749\) | 1.38344e7 | 0.901068 | ||||||||
\(750\) | −401526. | −0.0260651 | ||||||||
\(751\) | −1.14499e7 | −0.740799 | −0.370399 | − | 0.928873i | \(-0.620779\pi\) | ||||
−0.370399 | + | 0.928873i | \(0.620779\pi\) | |||||||
\(752\) | −234422. | −0.0151166 | ||||||||
\(753\) | −4.68433e6 | −0.301065 | ||||||||
\(754\) | −1.20938e7 | −0.774701 | ||||||||
\(755\) | −890304. | −0.0568422 | ||||||||
\(756\) | 1.05470e7 | 0.671157 | ||||||||
\(757\) | 2.42052e7 | 1.53521 | 0.767606 | − | 0.640922i | \(-0.221448\pi\) | ||||
0.767606 | + | 0.640922i | \(0.221448\pi\) | |||||||
\(758\) | 6.84751e6 | 0.432872 | ||||||||
\(759\) | −1.00824e6 | −0.0635270 | ||||||||
\(760\) | 1.64200e6 | 0.103119 | ||||||||
\(761\) | 8.23734e6 | 0.515615 | 0.257807 | − | 0.966196i | \(-0.417000\pi\) | ||||
0.257807 | + | 0.966196i | \(0.417000\pi\) | |||||||
\(762\) | −2.11563e6 | −0.131993 | ||||||||
\(763\) | 1.49565e7 | 0.930078 | ||||||||
\(764\) | −1.42467e7 | −0.883041 | ||||||||
\(765\) | −2.56378e6 | −0.158390 | ||||||||
\(766\) | −1.01358e7 | −0.624148 | ||||||||
\(767\) | −5.43180e6 | −0.333392 | ||||||||
\(768\) | 7.70855e6 | 0.471596 | ||||||||
\(769\) | −4.22850e6 | −0.257852 | −0.128926 | − | 0.991654i | \(-0.541153\pi\) | ||||
−0.128926 | + | 0.991654i | \(0.541153\pi\) | |||||||
\(770\) | 1.82892e6 | 0.111165 | ||||||||
\(771\) | 871702. | 0.0528119 | ||||||||
\(772\) | 1.92136e6 | 0.116029 | ||||||||
\(773\) | 4.81751e6 | 0.289984 | 0.144992 | − | 0.989433i | \(-0.453684\pi\) | ||||
0.144992 | + | 0.989433i | \(0.453684\pi\) | |||||||
\(774\) | 7.36715e6 | 0.442026 | ||||||||
\(775\) | 933855. | 0.0558503 | ||||||||
\(776\) | 3.16458e7 | 1.88652 | ||||||||
\(777\) | −7.75655e6 | −0.460910 | ||||||||
\(778\) | 1.50822e7 | 0.893335 | ||||||||
\(779\) | −4.38596e6 | −0.258953 | ||||||||
\(780\) | 1.93627e6 | 0.113954 | ||||||||
\(781\) | −1.98233e6 | −0.116291 | ||||||||
\(782\) | −2.18096e6 | −0.127536 | ||||||||
\(783\) | −1.98284e7 | −1.15580 | ||||||||
\(784\) | −213963. | −0.0124322 | ||||||||
\(785\) | −1.48291e6 | −0.0858896 | ||||||||
\(786\) | 4.16442e6 | 0.240435 | ||||||||
\(787\) | −6675.36 | −0.000384183 0 | −0.000192091 | − | 1.00000i | \(-0.500061\pi\) | ||||
−0.000192091 | 1.00000i | \(0.500061\pi\) | ||||||||
\(788\) | 4.53185e6 | 0.259992 | ||||||||
\(789\) | 2.59653e6 | 0.148491 | ||||||||
\(790\) | 6.64048e6 | 0.378557 | ||||||||
\(791\) | 2.67994e7 | 1.52294 | ||||||||
\(792\) | 4.18303e6 | 0.236961 | ||||||||
\(793\) | 2.42856e7 | 1.37140 | ||||||||
\(794\) | 746284. | 0.0420100 | ||||||||
\(795\) | 802800. | 0.0450495 | ||||||||
\(796\) | 5.51609e6 | 0.308567 | ||||||||
\(797\) | 2.24867e7 | 1.25395 | 0.626975 | − | 0.779040i | \(-0.284293\pi\) | ||||
0.626975 | + | 0.779040i | \(0.284293\pi\) | |||||||
\(798\) | 1.58880e6 | 0.0883205 | ||||||||
\(799\) | −7.40604e6 | −0.410411 | ||||||||
\(800\) | −3.60109e6 | −0.198934 | ||||||||
\(801\) | 4.79744e6 | 0.264197 | ||||||||
\(802\) | 2.13794e6 | 0.117370 | ||||||||
\(803\) | −4.88880e6 | −0.267555 | ||||||||
\(804\) | −6.46614e6 | −0.352781 | ||||||||
\(805\) | −4.90111e6 | −0.266566 | ||||||||
\(806\) | 2.87254e6 | 0.155750 | ||||||||
\(807\) | −4.68530e6 | −0.253252 | ||||||||
\(808\) | 1.03075e7 | 0.555425 | ||||||||
\(809\) | 1.29089e6 | 0.0693456 | 0.0346728 | − | 0.999399i | \(-0.488961\pi\) | ||||
0.0346728 | + | 0.999399i | \(0.488961\pi\) | |||||||
\(810\) | 2.05001e6 | 0.109785 | ||||||||
\(811\) | 1.89391e7 | 1.01113 | 0.505566 | − | 0.862788i | \(-0.331284\pi\) | ||||
0.505566 | + | 0.862788i | \(0.331284\pi\) | |||||||
\(812\) | −2.10492e7 | −1.12033 | ||||||||
\(813\) | −3.13120e6 | −0.166144 | ||||||||
\(814\) | −2.65764e6 | −0.140584 | ||||||||
\(815\) | 6.81042e6 | 0.359153 | ||||||||
\(816\) | −67115.7 | −0.00352857 | ||||||||
\(817\) | −3.96484e6 | −0.207812 | ||||||||
\(818\) | −8.90203e6 | −0.465164 | ||||||||
\(819\) | −1.77220e7 | −0.923214 | ||||||||
\(820\) | 5.93427e6 | 0.308200 | ||||||||
\(821\) | −2.58220e7 | −1.33700 | −0.668500 | − | 0.743712i | \(-0.733063\pi\) | ||||
−0.668500 | + | 0.743712i | \(0.733063\pi\) | |||||||
\(822\) | −1.20859e6 | −0.0623877 | ||||||||
\(823\) | 1.13362e7 | 0.583404 | 0.291702 | − | 0.956509i | \(-0.405778\pi\) | ||||
0.291702 | + | 0.956509i | \(0.405778\pi\) | |||||||
\(824\) | 1.27462e7 | 0.653979 | ||||||||
\(825\) | 550499. | 0.0281593 | ||||||||
\(826\) | 6.03045e6 | 0.307538 | ||||||||
\(827\) | −1.33802e7 | −0.680299 | −0.340149 | − | 0.940371i | \(-0.610478\pi\) | ||||
−0.340149 | + | 0.940371i | \(0.610478\pi\) | |||||||
\(828\) | −4.24948e6 | −0.215407 | ||||||||
\(829\) | −9.29011e6 | −0.469499 | −0.234749 | − | 0.972056i | \(-0.575427\pi\) | ||||
−0.234749 | + | 0.972056i | \(0.575427\pi\) | |||||||
\(830\) | 5.31034e6 | 0.267564 | ||||||||
\(831\) | 1.26681e7 | 0.636371 | ||||||||
\(832\) | −1.13746e7 | −0.569678 | ||||||||
\(833\) | −6.75969e6 | −0.337531 | ||||||||
\(834\) | 9.78752e6 | 0.487257 | ||||||||
\(835\) | −1.38108e7 | −0.685491 | ||||||||
\(836\) | −853419. | −0.0422325 | ||||||||
\(837\) | 4.70966e6 | 0.232368 | ||||||||
\(838\) | 1.41289e7 | 0.695020 | ||||||||
\(839\) | −2.65341e7 | −1.30137 | −0.650684 | − | 0.759349i | \(-0.725518\pi\) | ||||
−0.650684 | + | 0.759349i | \(0.725518\pi\) | |||||||
\(840\) | −5.67055e6 | −0.277285 | ||||||||
\(841\) | 1.90613e7 | 0.929314 | ||||||||
\(842\) | −3.64757e6 | −0.177306 | ||||||||
\(843\) | 1.07298e6 | 0.0520022 | ||||||||
\(844\) | 1.18015e7 | 0.570271 | ||||||||
\(845\) | 1.86805e6 | 0.0900009 | ||||||||
\(846\) | 9.20465e6 | 0.442162 | ||||||||
\(847\) | −2.50749e6 | −0.120097 | ||||||||
\(848\) | −75361.4 | −0.00359881 | ||||||||
\(849\) | 1.08093e7 | 0.514669 | ||||||||
\(850\) | 1.19081e6 | 0.0565321 | ||||||||
\(851\) | 7.12188e6 | 0.337110 | ||||||||
\(852\) | 2.32997e6 | 0.109964 | ||||||||
\(853\) | 1.84210e7 | 0.866843 | 0.433421 | − | 0.901191i | \(-0.357306\pi\) | ||||
0.433421 | + | 0.901191i | \(0.357306\pi\) | |||||||
\(854\) | −2.69622e7 | −1.26506 | ||||||||
\(855\) | −1.71485e6 | −0.0802253 | ||||||||
\(856\) | −1.46967e7 | −0.685543 | ||||||||
\(857\) | −4.17414e7 | −1.94140 | −0.970700 | − | 0.240295i | \(-0.922756\pi\) | ||||
−0.970700 | + | 0.240295i | \(0.922756\pi\) | |||||||
\(858\) | 1.69333e6 | 0.0785280 | ||||||||
\(859\) | −1.41920e7 | −0.656237 | −0.328118 | − | 0.944637i | \(-0.606414\pi\) | ||||
−0.328118 | + | 0.944637i | \(0.606414\pi\) | |||||||
\(860\) | 5.36449e6 | 0.247333 | ||||||||
\(861\) | 1.51467e7 | 0.696321 | ||||||||
\(862\) | 1.17581e7 | 0.538974 | ||||||||
\(863\) | 3.73562e7 | 1.70740 | 0.853701 | − | 0.520764i | \(-0.174353\pi\) | ||||
0.853701 | + | 0.520764i | \(0.174353\pi\) | |||||||
\(864\) | −1.81612e7 | −0.827675 | ||||||||
\(865\) | −1.34600e7 | −0.611654 | ||||||||
\(866\) | −3.90351e6 | −0.176873 | ||||||||
\(867\) | 8.21523e6 | 0.371169 | ||||||||
\(868\) | 4.99963e6 | 0.225236 | ||||||||
\(869\) | −9.10422e6 | −0.408972 | ||||||||
\(870\) | 4.04138e6 | 0.181022 | ||||||||
\(871\) | 2.47599e7 | 1.10587 | ||||||||
\(872\) | −1.58887e7 | −0.707614 | ||||||||
\(873\) | −3.30499e7 | −1.46769 | ||||||||
\(874\) | −1.45880e6 | −0.0645976 | ||||||||
\(875\) | 2.67601e6 | 0.118159 | ||||||||
\(876\) | 5.74617e6 | 0.252999 | ||||||||
\(877\) | 1.76940e7 | 0.776831 | 0.388415 | − | 0.921484i | \(-0.373023\pi\) | ||||
0.388415 | + | 0.921484i | \(0.373023\pi\) | |||||||
\(878\) | −2.26732e7 | −0.992603 | ||||||||
\(879\) | −6.61037e6 | −0.288572 | ||||||||
\(880\) | −51677.1 | −0.00224953 | ||||||||
\(881\) | −2.42250e6 | −0.105154 | −0.0525768 | − | 0.998617i | \(-0.516743\pi\) | ||||
−0.0525768 | + | 0.998617i | \(0.516743\pi\) | |||||||
\(882\) | 8.40133e6 | 0.363644 | ||||||||
\(883\) | 3.44922e7 | 1.48874 | 0.744371 | − | 0.667767i | \(-0.232750\pi\) | ||||
0.744371 | + | 0.667767i | \(0.232750\pi\) | |||||||
\(884\) | −5.74241e6 | −0.247152 | ||||||||
\(885\) | 1.81514e6 | 0.0779027 | ||||||||
\(886\) | 2.36346e7 | 1.01149 | ||||||||
\(887\) | −1.34790e7 | −0.575240 | −0.287620 | − | 0.957745i | \(-0.592864\pi\) | ||||
−0.287620 | + | 0.957745i | \(0.592864\pi\) | |||||||
\(888\) | 8.23997e6 | 0.350666 | ||||||||
\(889\) | 1.40998e7 | 0.598356 | ||||||||
\(890\) | −2.22829e6 | −0.0942968 | ||||||||
\(891\) | −2.81060e6 | −0.118605 | ||||||||
\(892\) | 123877. | 0.00521288 | ||||||||
\(893\) | −4.95374e6 | −0.207876 | ||||||||
\(894\) | −3.69717e6 | −0.154713 | ||||||||
\(895\) | 5.88084e6 | 0.245404 | ||||||||
\(896\) | −1.89488e7 | −0.788518 | ||||||||
\(897\) | −4.53776e6 | −0.188304 | ||||||||
\(898\) | −6.85635e6 | −0.283728 | ||||||||
\(899\) | −9.39931e6 | −0.387879 | ||||||||
\(900\) | 2.32022e6 | 0.0954824 | ||||||||
\(901\) | −2.38088e6 | −0.0977068 | ||||||||
\(902\) | 5.18973e6 | 0.212387 | ||||||||
\(903\) | 1.36923e7 | 0.558803 | ||||||||
\(904\) | −2.84696e7 | −1.15867 | ||||||||
\(905\) | 2.20086e6 | 0.0893247 | ||||||||
\(906\) | 915149. | 0.0370400 | ||||||||
\(907\) | −1.96004e7 | −0.791128 | −0.395564 | − | 0.918438i | \(-0.629451\pi\) | ||||
−0.395564 | + | 0.918438i | \(0.629451\pi\) | |||||||
\(908\) | 1.27112e7 | 0.511648 | ||||||||
\(909\) | −1.07649e7 | −0.432114 | ||||||||
\(910\) | 8.23142e6 | 0.329512 | ||||||||
\(911\) | −2.63974e7 | −1.05382 | −0.526909 | − | 0.849922i | \(-0.676649\pi\) | ||||
−0.526909 | + | 0.849922i | \(0.676649\pi\) | |||||||
\(912\) | −44892.2 | −0.00178725 | ||||||||
\(913\) | −7.28058e6 | −0.289061 | ||||||||
\(914\) | 1.10759e7 | 0.438545 | ||||||||
\(915\) | −8.11551e6 | −0.320452 | ||||||||
\(916\) | 2.13511e7 | 0.840780 | ||||||||
\(917\) | −2.77542e7 | −1.08995 | ||||||||
\(918\) | 6.00555e6 | 0.235205 | ||||||||
\(919\) | −9.04770e6 | −0.353386 | −0.176693 | − | 0.984266i | \(-0.556540\pi\) | ||||
−0.176693 | + | 0.984266i | \(0.556540\pi\) | |||||||
\(920\) | 5.20657e6 | 0.202807 | ||||||||
\(921\) | 1.42860e7 | 0.554961 | ||||||||
\(922\) | 1.53518e7 | 0.594749 | ||||||||
\(923\) | −8.92183e6 | −0.344707 | ||||||||
\(924\) | 2.94724e6 | 0.113563 | ||||||||
\(925\) | −3.88856e6 | −0.149429 | ||||||||
\(926\) | −2.25548e7 | −0.864393 | ||||||||
\(927\) | −1.33118e7 | −0.508787 | ||||||||
\(928\) | 3.62452e7 | 1.38159 | ||||||||
\(929\) | −742447. | −0.0282245 | −0.0141122 | − | 0.999900i | \(-0.504492\pi\) | ||||
−0.0141122 | + | 0.999900i | \(0.504492\pi\) | |||||||
\(930\) | −959915. | −0.0363936 | ||||||||
\(931\) | −4.52141e6 | −0.170962 | ||||||||
\(932\) | −1.01857e7 | −0.384107 | ||||||||
\(933\) | −1.29185e7 | −0.485857 | ||||||||
\(934\) | −4.63032e6 | −0.173678 | ||||||||
\(935\) | −1.63262e6 | −0.0610740 | ||||||||
\(936\) | 1.88265e7 | 0.702393 | ||||||||
\(937\) | 2.41089e7 | 0.897076 | 0.448538 | − | 0.893764i | \(-0.351945\pi\) | ||||
0.448538 | + | 0.893764i | \(0.351945\pi\) | |||||||
\(938\) | −2.74887e7 | −1.02011 | ||||||||
\(939\) | −1.28028e6 | −0.0473851 | ||||||||
\(940\) | 6.70248e6 | 0.247409 | ||||||||
\(941\) | 4.02322e7 | 1.48115 | 0.740575 | − | 0.671973i | \(-0.234553\pi\) | ||||
0.740575 | + | 0.671973i | \(0.234553\pi\) | |||||||
\(942\) | 1.52429e6 | 0.0559681 | ||||||||
\(943\) | −1.39073e7 | −0.509289 | ||||||||
\(944\) | −170393. | −0.00622332 | ||||||||
\(945\) | 1.34958e7 | 0.491609 | ||||||||
\(946\) | 4.69143e6 | 0.170442 | ||||||||
\(947\) | −1.61467e7 | −0.585070 | −0.292535 | − | 0.956255i | \(-0.594499\pi\) | ||||
−0.292535 | + | 0.956255i | \(0.594499\pi\) | |||||||
\(948\) | 1.07009e7 | 0.386721 | ||||||||
\(949\) | −2.20030e7 | −0.793078 | ||||||||
\(950\) | 796506. | 0.0286339 | ||||||||
\(951\) | −1.68565e7 | −0.604389 | ||||||||
\(952\) | 1.68172e7 | 0.601398 | ||||||||
\(953\) | 2.46287e7 | 0.878434 | 0.439217 | − | 0.898381i | \(-0.355256\pi\) | ||||
0.439217 | + | 0.898381i | \(0.355256\pi\) | |||||||
\(954\) | 2.95909e6 | 0.105266 | ||||||||
\(955\) | −1.82299e7 | −0.646809 | ||||||||
\(956\) | −3.83520e6 | −0.135720 | ||||||||
\(957\) | −5.54081e6 | −0.195566 | ||||||||
\(958\) | 2.20501e7 | 0.776242 | ||||||||
\(959\) | 8.05478e6 | 0.282818 | ||||||||
\(960\) | 3.80106e6 | 0.133115 | ||||||||
\(961\) | −2.63966e7 | −0.922019 | ||||||||
\(962\) | −1.19612e7 | −0.416713 | ||||||||
\(963\) | 1.53488e7 | 0.533344 | ||||||||
\(964\) | −385209. | −0.0133507 | ||||||||
\(965\) | 2.45855e6 | 0.0849885 | ||||||||
\(966\) | 5.03788e6 | 0.173702 | ||||||||
\(967\) | −3.22241e7 | −1.10819 | −0.554095 | − | 0.832454i | \(-0.686935\pi\) | ||||
−0.554095 | + | 0.832454i | \(0.686935\pi\) | |||||||
\(968\) | 2.66377e6 | 0.0913709 | ||||||||
\(969\) | −1.41827e6 | −0.0485232 | ||||||||
\(970\) | 1.53508e7 | 0.523845 | ||||||||
\(971\) | −3.34985e7 | −1.14019 | −0.570095 | − | 0.821579i | \(-0.693094\pi\) | ||||
−0.570095 | + | 0.821579i | \(0.693094\pi\) | |||||||
\(972\) | 1.82682e7 | 0.620196 | ||||||||
\(973\) | −6.52301e7 | −2.20885 | ||||||||
\(974\) | −3.07441e7 | −1.03840 | ||||||||
\(975\) | 2.47762e6 | 0.0834688 | ||||||||
\(976\) | 761828. | 0.0255996 | ||||||||
\(977\) | −3.58506e6 | −0.120160 | −0.0600800 | − | 0.998194i | \(-0.519136\pi\) | ||||
−0.0600800 | + | 0.998194i | \(0.519136\pi\) | |||||||
\(978\) | −7.00047e6 | −0.234035 | ||||||||
\(979\) | 3.05503e6 | 0.101873 | ||||||||
\(980\) | 6.11753e6 | 0.203475 | ||||||||
\(981\) | 1.65936e7 | 0.550515 | ||||||||
\(982\) | 1.33746e7 | 0.442590 | ||||||||
\(983\) | 1.61808e7 | 0.534093 | 0.267047 | − | 0.963684i | \(-0.413952\pi\) | ||||
0.267047 | + | 0.963684i | \(0.413952\pi\) | |||||||
\(984\) | −1.60907e7 | −0.529769 | ||||||||
\(985\) | 5.79890e6 | 0.190438 | ||||||||
\(986\) | −1.19856e7 | −0.392615 | ||||||||
\(987\) | 1.71075e7 | 0.558975 | ||||||||
\(988\) | −3.84097e6 | −0.125184 | ||||||||
\(989\) | −1.25720e7 | −0.408708 | ||||||||
\(990\) | 2.02912e6 | 0.0657989 | ||||||||
\(991\) | −1.99244e7 | −0.644467 | −0.322233 | − | 0.946660i | \(-0.604434\pi\) | ||||
−0.322233 | + | 0.946660i | \(0.604434\pi\) | |||||||
\(992\) | −8.60900e6 | −0.277763 | ||||||||
\(993\) | 1.67208e7 | 0.538127 | ||||||||
\(994\) | 9.90513e6 | 0.317976 | ||||||||
\(995\) | 7.05833e6 | 0.226019 | ||||||||
\(996\) | 8.55739e6 | 0.273334 | ||||||||
\(997\) | 5.23056e7 | 1.66652 | 0.833260 | − | 0.552881i | \(-0.186472\pi\) | ||||
0.833260 | + | 0.552881i | \(0.186472\pi\) | |||||||
\(998\) | 2.76274e7 | 0.878037 | ||||||||
\(999\) | −1.96110e7 | −0.621707 |
(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 | 1045.6.a.c.1.15 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.c.1.15 | ✓ | 37 | 1.1 | even | 1 | trivial |