Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,8,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.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: | \(170.562223914\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 302081x^{4} - 2628147x^{3} + 19116974952x^{2} - 78725393748x - 5138711063280 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-14.4733\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 7.47333 | 0.0267374 | 0.0133687 | − | 0.999911i | \(-0.495744\pi\) | ||||
0.0133687 | + | 0.999911i | \(0.495744\pi\) | |||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −59.7866 | −0.0189062 | ||||||||
\(11\) | 5391.75 | 1.22139 | 0.610696 | − | 0.791865i | \(-0.290890\pi\) | ||||
0.610696 | + | 0.791865i | \(0.290890\pi\) | |||||||
\(12\) | 1728.00 | 0.288675 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | −2744.00 | −0.267261 | ||||||||
\(15\) | 201.780 | 0.0154368 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 23811.5 | 1.17548 | 0.587740 | − | 0.809050i | \(-0.300018\pi\) | ||||
0.587740 | + | 0.809050i | \(0.300018\pi\) | |||||||
\(18\) | −5832.00 | −0.235702 | ||||||||
\(19\) | 46865.1 | 1.56752 | 0.783758 | − | 0.621066i | \(-0.213300\pi\) | ||||
0.783758 | + | 0.621066i | \(0.213300\pi\) | |||||||
\(20\) | 478.293 | 0.0133687 | ||||||||
\(21\) | 9261.00 | 0.218218 | ||||||||
\(22\) | −43134.0 | −0.863654 | ||||||||
\(23\) | 73930.3 | 1.26699 | 0.633497 | − | 0.773745i | \(-0.281619\pi\) | ||||
0.633497 | + | 0.773745i | \(0.281619\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | −78069.1 | −0.999285 | ||||||||
\(26\) | 17576.0 | 0.196116 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 21952.0 | 0.188982 | ||||||||
\(29\) | −175803. | −1.33854 | −0.669272 | − | 0.743018i | \(-0.733394\pi\) | ||||
−0.669272 | + | 0.743018i | \(0.733394\pi\) | |||||||
\(30\) | −1614.24 | −0.0109155 | ||||||||
\(31\) | 277477. | 1.67286 | 0.836432 | − | 0.548071i | \(-0.184638\pi\) | ||||
0.836432 | + | 0.548071i | \(0.184638\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | 145577. | 0.705171 | ||||||||
\(34\) | −190492. | −0.831190 | ||||||||
\(35\) | 2563.35 | 0.0101058 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | 241049. | 0.782345 | 0.391173 | − | 0.920317i | \(-0.372070\pi\) | ||||
0.391173 | + | 0.920317i | \(0.372070\pi\) | |||||||
\(38\) | −374921. | −1.10840 | ||||||||
\(39\) | −59319.0 | −0.160128 | ||||||||
\(40\) | −3826.34 | −0.00945309 | ||||||||
\(41\) | −78727.1 | −0.178394 | −0.0891972 | − | 0.996014i | \(-0.528430\pi\) | ||||
−0.0891972 | + | 0.996014i | \(0.528430\pi\) | |||||||
\(42\) | −74088.0 | −0.154303 | ||||||||
\(43\) | −199540. | −0.382729 | −0.191364 | − | 0.981519i | \(-0.561291\pi\) | ||||
−0.191364 | + | 0.981519i | \(0.561291\pi\) | |||||||
\(44\) | 345072. | 0.610696 | ||||||||
\(45\) | 5448.06 | 0.00891246 | ||||||||
\(46\) | −591442. | −0.895901 | ||||||||
\(47\) | 142125. | 0.199677 | 0.0998383 | − | 0.995004i | \(-0.468167\pi\) | ||||
0.0998383 | + | 0.995004i | \(0.468167\pi\) | |||||||
\(48\) | 110592. | 0.144338 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 624553. | 0.706601 | ||||||||
\(51\) | 642910. | 0.678664 | ||||||||
\(52\) | −140608. | −0.138675 | ||||||||
\(53\) | −854767. | −0.788646 | −0.394323 | − | 0.918972i | \(-0.629021\pi\) | ||||
−0.394323 | + | 0.918972i | \(0.629021\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | 40294.3 | 0.0326568 | ||||||||
\(56\) | −175616. | −0.133631 | ||||||||
\(57\) | 1.26536e6 | 0.905006 | ||||||||
\(58\) | 1.40642e6 | 0.946493 | ||||||||
\(59\) | −533880. | −0.338424 | −0.169212 | − | 0.985580i | \(-0.554122\pi\) | ||||
−0.169212 | + | 0.985580i | \(0.554122\pi\) | |||||||
\(60\) | 12913.9 | 0.00771842 | ||||||||
\(61\) | 3.35232e6 | 1.89100 | 0.945499 | − | 0.325624i | \(-0.105574\pi\) | ||||
0.945499 | + | 0.325624i | \(0.105574\pi\) | |||||||
\(62\) | −2.21981e6 | −1.18289 | ||||||||
\(63\) | 250047. | 0.125988 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −16418.9 | −0.00741562 | ||||||||
\(66\) | −1.16462e6 | −0.498631 | ||||||||
\(67\) | −4.13096e6 | −1.67799 | −0.838994 | − | 0.544141i | \(-0.816856\pi\) | ||||
−0.838994 | + | 0.544141i | \(0.816856\pi\) | |||||||
\(68\) | 1.52393e6 | 0.587740 | ||||||||
\(69\) | 1.99612e6 | 0.731500 | ||||||||
\(70\) | −20506.8 | −0.00714587 | ||||||||
\(71\) | −2.83222e6 | −0.939122 | −0.469561 | − | 0.882900i | \(-0.655588\pi\) | ||||
−0.469561 | + | 0.882900i | \(0.655588\pi\) | |||||||
\(72\) | −373248. | −0.117851 | ||||||||
\(73\) | 3.21360e6 | 0.966857 | 0.483429 | − | 0.875384i | \(-0.339391\pi\) | ||||
0.483429 | + | 0.875384i | \(0.339391\pi\) | |||||||
\(74\) | −1.92839e6 | −0.553202 | ||||||||
\(75\) | −2.10787e6 | −0.576938 | ||||||||
\(76\) | 2.99937e6 | 0.783758 | ||||||||
\(77\) | 1.84937e6 | 0.461643 | ||||||||
\(78\) | 474552. | 0.113228 | ||||||||
\(79\) | −8.08645e6 | −1.84528 | −0.922641 | − | 0.385659i | \(-0.873974\pi\) | ||||
−0.922641 | + | 0.385659i | \(0.873974\pi\) | |||||||
\(80\) | 30610.7 | 0.00668435 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 629817. | 0.126144 | ||||||||
\(83\) | 6.07145e6 | 1.16552 | 0.582760 | − | 0.812645i | \(-0.301973\pi\) | ||||
0.582760 | + | 0.812645i | \(0.301973\pi\) | |||||||
\(84\) | 592704. | 0.109109 | ||||||||
\(85\) | 177951. | 0.0314293 | ||||||||
\(86\) | 1.59632e6 | 0.270630 | ||||||||
\(87\) | −4.74667e6 | −0.772809 | ||||||||
\(88\) | −2.76057e6 | −0.431827 | ||||||||
\(89\) | 7.87841e6 | 1.18460 | 0.592302 | − | 0.805716i | \(-0.298219\pi\) | ||||
0.592302 | + | 0.805716i | \(0.298219\pi\) | |||||||
\(90\) | −43584.4 | −0.00630206 | ||||||||
\(91\) | −753571. | −0.104828 | ||||||||
\(92\) | 4.73154e6 | 0.633497 | ||||||||
\(93\) | 7.49187e6 | 0.965828 | ||||||||
\(94\) | −1.13700e6 | −0.141193 | ||||||||
\(95\) | 350238. | 0.0419113 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | 1.58135e6 | 0.175924 | 0.0879622 | − | 0.996124i | \(-0.471965\pi\) | ||||
0.0879622 | + | 0.996124i | \(0.471965\pi\) | |||||||
\(98\) | −941192. | −0.101015 | ||||||||
\(99\) | 3.93058e6 | 0.407131 | ||||||||
\(100\) | −4.99643e6 | −0.499643 | ||||||||
\(101\) | 9.21450e6 | 0.889912 | 0.444956 | − | 0.895553i | \(-0.353219\pi\) | ||||
0.444956 | + | 0.895553i | \(0.353219\pi\) | |||||||
\(102\) | −5.14328e6 | −0.479888 | ||||||||
\(103\) | 1.38313e7 | 1.24719 | 0.623596 | − | 0.781747i | \(-0.285671\pi\) | ||||
0.623596 | + | 0.781747i | \(0.285671\pi\) | |||||||
\(104\) | 1.12486e6 | 0.0980581 | ||||||||
\(105\) | 69210.5 | 0.00583458 | ||||||||
\(106\) | 6.83813e6 | 0.557657 | ||||||||
\(107\) | 1.47082e7 | 1.16069 | 0.580343 | − | 0.814372i | \(-0.302918\pi\) | ||||
0.580343 | + | 0.814372i | \(0.302918\pi\) | |||||||
\(108\) | 1.25971e6 | 0.0962250 | ||||||||
\(109\) | −6.12182e6 | −0.452781 | −0.226390 | − | 0.974037i | \(-0.572692\pi\) | ||||
−0.226390 | + | 0.974037i | \(0.572692\pi\) | |||||||
\(110\) | −322354. | −0.0230919 | ||||||||
\(111\) | 6.50831e6 | 0.451687 | ||||||||
\(112\) | 1.40493e6 | 0.0944911 | ||||||||
\(113\) | −1.98529e7 | −1.29434 | −0.647172 | − | 0.762344i | \(-0.724049\pi\) | ||||
−0.647172 | + | 0.762344i | \(0.724049\pi\) | |||||||
\(114\) | −1.01229e7 | −0.639936 | ||||||||
\(115\) | 552505. | 0.0338761 | ||||||||
\(116\) | −1.12514e7 | −0.669272 | ||||||||
\(117\) | −1.60161e6 | −0.0924500 | ||||||||
\(118\) | 4.27104e6 | 0.239302 | ||||||||
\(119\) | 8.16734e6 | 0.444290 | ||||||||
\(120\) | −103311. | −0.00545775 | ||||||||
\(121\) | 9.58375e6 | 0.491798 | ||||||||
\(122\) | −2.68186e7 | −1.33714 | ||||||||
\(123\) | −2.12563e6 | −0.102996 | ||||||||
\(124\) | 1.77585e7 | 0.836432 | ||||||||
\(125\) | −1.16729e6 | −0.0534557 | ||||||||
\(126\) | −2.00038e6 | −0.0890871 | ||||||||
\(127\) | −3.96590e7 | −1.71802 | −0.859010 | − | 0.511958i | \(-0.828920\pi\) | ||||
−0.859010 | + | 0.511958i | \(0.828920\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | −5.38759e6 | −0.220968 | ||||||||
\(130\) | 131351. | 0.00524363 | ||||||||
\(131\) | −3.36490e7 | −1.30774 | −0.653872 | − | 0.756605i | \(-0.726857\pi\) | ||||
−0.653872 | + | 0.756605i | \(0.726857\pi\) | |||||||
\(132\) | 9.31694e6 | 0.352585 | ||||||||
\(133\) | 1.60747e7 | 0.592466 | ||||||||
\(134\) | 3.30476e7 | 1.18652 | ||||||||
\(135\) | 147097. | 0.00514561 | ||||||||
\(136\) | −1.21915e7 | −0.415595 | ||||||||
\(137\) | 948259. | 0.0315069 | 0.0157534 | − | 0.999876i | \(-0.494985\pi\) | ||||
0.0157534 | + | 0.999876i | \(0.494985\pi\) | |||||||
\(138\) | −1.59689e7 | −0.517248 | ||||||||
\(139\) | −5.20308e7 | −1.64327 | −0.821634 | − | 0.570016i | \(-0.806937\pi\) | ||||
−0.821634 | + | 0.570016i | \(0.806937\pi\) | |||||||
\(140\) | 164054. | 0.00505289 | ||||||||
\(141\) | 3.83737e6 | 0.115283 | ||||||||
\(142\) | 2.26577e7 | 0.664060 | ||||||||
\(143\) | −1.18457e7 | −0.338753 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | −1.31383e6 | −0.0357892 | ||||||||
\(146\) | −2.57088e7 | −0.683671 | ||||||||
\(147\) | 3.17652e6 | 0.0824786 | ||||||||
\(148\) | 1.54271e7 | 0.391173 | ||||||||
\(149\) | 1.33560e7 | 0.330768 | 0.165384 | − | 0.986229i | \(-0.447114\pi\) | ||||
0.165384 | + | 0.986229i | \(0.447114\pi\) | |||||||
\(150\) | 1.68629e7 | 0.407956 | ||||||||
\(151\) | 5.22301e6 | 0.123453 | 0.0617265 | − | 0.998093i | \(-0.480339\pi\) | ||||
0.0617265 | + | 0.998093i | \(0.480339\pi\) | |||||||
\(152\) | −2.39949e7 | −0.554201 | ||||||||
\(153\) | 1.73586e7 | 0.391827 | ||||||||
\(154\) | −1.47949e7 | −0.326431 | ||||||||
\(155\) | 2.07367e6 | 0.0447280 | ||||||||
\(156\) | −3.79642e6 | −0.0800641 | ||||||||
\(157\) | −7.00155e7 | −1.44393 | −0.721964 | − | 0.691931i | \(-0.756760\pi\) | ||||
−0.721964 | + | 0.691931i | \(0.756760\pi\) | |||||||
\(158\) | 6.46916e7 | 1.30481 | ||||||||
\(159\) | −2.30787e7 | −0.455325 | ||||||||
\(160\) | −244886. | −0.00472655 | ||||||||
\(161\) | 2.53581e7 | 0.478879 | ||||||||
\(162\) | −4.25153e6 | −0.0785674 | ||||||||
\(163\) | −6.95049e7 | −1.25707 | −0.628534 | − | 0.777782i | \(-0.716345\pi\) | ||||
−0.628534 | + | 0.777782i | \(0.716345\pi\) | |||||||
\(164\) | −5.03854e6 | −0.0891972 | ||||||||
\(165\) | 1.08795e6 | 0.0188544 | ||||||||
\(166\) | −4.85716e7 | −0.824146 | ||||||||
\(167\) | 5.45990e7 | 0.907145 | 0.453572 | − | 0.891219i | \(-0.350149\pi\) | ||||
0.453572 | + | 0.891219i | \(0.350149\pi\) | |||||||
\(168\) | −4.74163e6 | −0.0771517 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −1.42361e6 | −0.0222238 | ||||||||
\(171\) | 3.41647e7 | 0.522506 | ||||||||
\(172\) | −1.27706e7 | −0.191364 | ||||||||
\(173\) | 2.84648e7 | 0.417971 | 0.208986 | − | 0.977919i | \(-0.432984\pi\) | ||||
0.208986 | + | 0.977919i | \(0.432984\pi\) | |||||||
\(174\) | 3.79734e7 | 0.546458 | ||||||||
\(175\) | −2.67777e7 | −0.377694 | ||||||||
\(176\) | 2.20846e7 | 0.305348 | ||||||||
\(177\) | −1.44148e7 | −0.195389 | ||||||||
\(178\) | −6.30273e7 | −0.837642 | ||||||||
\(179\) | 9.25538e7 | 1.20617 | 0.603085 | − | 0.797677i | \(-0.293938\pi\) | ||||
0.603085 | + | 0.797677i | \(0.293938\pi\) | |||||||
\(180\) | 348676. | 0.00445623 | ||||||||
\(181\) | 3.43985e7 | 0.431185 | 0.215593 | − | 0.976483i | \(-0.430832\pi\) | ||||
0.215593 | + | 0.976483i | \(0.430832\pi\) | |||||||
\(182\) | 6.02857e6 | 0.0741249 | ||||||||
\(183\) | 9.05127e7 | 1.09177 | ||||||||
\(184\) | −3.78523e7 | −0.447950 | ||||||||
\(185\) | 1.80143e6 | 0.0209179 | ||||||||
\(186\) | −5.99349e7 | −0.682944 | ||||||||
\(187\) | 1.28385e8 | 1.43572 | ||||||||
\(188\) | 9.09598e6 | 0.0998383 | ||||||||
\(189\) | 6.75127e6 | 0.0727393 | ||||||||
\(190\) | −2.80191e6 | −0.0296358 | ||||||||
\(191\) | 1.08204e7 | 0.112364 | 0.0561822 | − | 0.998421i | \(-0.482107\pi\) | ||||
0.0561822 | + | 0.998421i | \(0.482107\pi\) | |||||||
\(192\) | 7.07789e6 | 0.0721688 | ||||||||
\(193\) | −2.69909e7 | −0.270250 | −0.135125 | − | 0.990829i | \(-0.543144\pi\) | ||||
−0.135125 | + | 0.990829i | \(0.543144\pi\) | |||||||
\(194\) | −1.26508e7 | −0.124397 | ||||||||
\(195\) | −443310. | −0.00428141 | ||||||||
\(196\) | 7.52954e6 | 0.0714286 | ||||||||
\(197\) | −3.57337e7 | −0.333001 | −0.166501 | − | 0.986041i | \(-0.553247\pi\) | ||||
−0.166501 | + | 0.986041i | \(0.553247\pi\) | |||||||
\(198\) | −3.14447e7 | −0.287885 | ||||||||
\(199\) | 2.84954e7 | 0.256324 | 0.128162 | − | 0.991753i | \(-0.459092\pi\) | ||||
0.128162 | + | 0.991753i | \(0.459092\pi\) | |||||||
\(200\) | 3.99714e7 | 0.353301 | ||||||||
\(201\) | −1.11536e8 | −0.968787 | ||||||||
\(202\) | −7.37160e7 | −0.629263 | ||||||||
\(203\) | −6.03003e7 | −0.505922 | ||||||||
\(204\) | 4.11462e7 | 0.339332 | ||||||||
\(205\) | −588354. | −0.00476980 | ||||||||
\(206\) | −1.10650e8 | −0.881897 | ||||||||
\(207\) | 5.38952e7 | 0.422332 | ||||||||
\(208\) | −8.99891e6 | −0.0693375 | ||||||||
\(209\) | 2.52685e8 | 1.91455 | ||||||||
\(210\) | −553684. | −0.00412567 | ||||||||
\(211\) | 9.59044e7 | 0.702829 | 0.351415 | − | 0.936220i | \(-0.385701\pi\) | ||||
0.351415 | + | 0.936220i | \(0.385701\pi\) | |||||||
\(212\) | −5.47051e7 | −0.394323 | ||||||||
\(213\) | −7.64698e7 | −0.542203 | ||||||||
\(214\) | −1.17665e8 | −0.820729 | ||||||||
\(215\) | −1.49123e6 | −0.0102332 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | 9.51745e7 | 0.632283 | ||||||||
\(218\) | 4.89746e7 | 0.320164 | ||||||||
\(219\) | 8.67673e7 | 0.558215 | ||||||||
\(220\) | 2.57883e6 | 0.0163284 | ||||||||
\(221\) | −5.23138e7 | −0.326019 | ||||||||
\(222\) | −5.20665e7 | −0.319391 | ||||||||
\(223\) | 6.07312e7 | 0.366729 | 0.183364 | − | 0.983045i | \(-0.441301\pi\) | ||||
0.183364 | + | 0.983045i | \(0.441301\pi\) | |||||||
\(224\) | −1.12394e7 | −0.0668153 | ||||||||
\(225\) | −5.69124e7 | −0.333095 | ||||||||
\(226\) | 1.58823e8 | 0.915240 | ||||||||
\(227\) | −1.60653e8 | −0.911589 | −0.455794 | − | 0.890085i | \(-0.650645\pi\) | ||||
−0.455794 | + | 0.890085i | \(0.650645\pi\) | |||||||
\(228\) | 8.09829e7 | 0.452503 | ||||||||
\(229\) | −1.06088e8 | −0.583770 | −0.291885 | − | 0.956453i | \(-0.594282\pi\) | ||||
−0.291885 | + | 0.956453i | \(0.594282\pi\) | |||||||
\(230\) | −4.42004e6 | −0.0239540 | ||||||||
\(231\) | 4.99330e7 | 0.266530 | ||||||||
\(232\) | 9.00110e7 | 0.473247 | ||||||||
\(233\) | 2.39951e8 | 1.24273 | 0.621364 | − | 0.783522i | \(-0.286579\pi\) | ||||
0.621364 | + | 0.783522i | \(0.286579\pi\) | |||||||
\(234\) | 1.28129e7 | 0.0653720 | ||||||||
\(235\) | 1.06214e6 | 0.00533883 | ||||||||
\(236\) | −3.41683e7 | −0.169212 | ||||||||
\(237\) | −2.18334e8 | −1.06537 | ||||||||
\(238\) | −6.53387e7 | −0.314160 | ||||||||
\(239\) | −5.80559e7 | −0.275077 | −0.137538 | − | 0.990496i | \(-0.543919\pi\) | ||||
−0.137538 | + | 0.990496i | \(0.543919\pi\) | |||||||
\(240\) | 826490. | 0.00385921 | ||||||||
\(241\) | 1.29424e7 | 0.0595600 | 0.0297800 | − | 0.999556i | \(-0.490519\pi\) | ||||
0.0297800 | + | 0.999556i | \(0.490519\pi\) | |||||||
\(242\) | −7.66700e7 | −0.347754 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 2.14549e8 | 0.945499 | ||||||||
\(245\) | 879229. | 0.00381963 | ||||||||
\(246\) | 1.70051e7 | 0.0728292 | ||||||||
\(247\) | −1.02963e8 | −0.434751 | ||||||||
\(248\) | −1.42068e8 | −0.591447 | ||||||||
\(249\) | 1.63929e8 | 0.672913 | ||||||||
\(250\) | 9.33832e6 | 0.0377989 | ||||||||
\(251\) | −1.10147e8 | −0.439656 | −0.219828 | − | 0.975539i | \(-0.570550\pi\) | ||||
−0.219828 | + | 0.975539i | \(0.570550\pi\) | |||||||
\(252\) | 1.60030e7 | 0.0629941 | ||||||||
\(253\) | 3.98613e8 | 1.54750 | ||||||||
\(254\) | 3.17272e8 | 1.21482 | ||||||||
\(255\) | 4.80468e6 | 0.0181457 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 4.12507e8 | 1.51588 | 0.757940 | − | 0.652324i | \(-0.226206\pi\) | ||||
0.757940 | + | 0.652324i | \(0.226206\pi\) | |||||||
\(258\) | 4.31007e7 | 0.156248 | ||||||||
\(259\) | 8.26797e7 | 0.295699 | ||||||||
\(260\) | −1.05081e6 | −0.00370781 | ||||||||
\(261\) | −1.28160e8 | −0.446181 | ||||||||
\(262\) | 2.69192e8 | 0.924715 | ||||||||
\(263\) | 4.55717e8 | 1.54472 | 0.772360 | − | 0.635185i | \(-0.219076\pi\) | ||||
0.772360 | + | 0.635185i | \(0.219076\pi\) | |||||||
\(264\) | −7.45355e7 | −0.249316 | ||||||||
\(265\) | −6.38795e6 | −0.0210863 | ||||||||
\(266\) | −1.28598e8 | −0.418936 | ||||||||
\(267\) | 2.12717e8 | 0.683932 | ||||||||
\(268\) | −2.64381e8 | −0.838994 | ||||||||
\(269\) | 2.59372e8 | 0.812439 | 0.406219 | − | 0.913776i | \(-0.366847\pi\) | ||||
0.406219 | + | 0.913776i | \(0.366847\pi\) | |||||||
\(270\) | −1.17678e6 | −0.00363850 | ||||||||
\(271\) | 3.38421e8 | 1.03292 | 0.516458 | − | 0.856313i | \(-0.327250\pi\) | ||||
0.516458 | + | 0.856313i | \(0.327250\pi\) | |||||||
\(272\) | 9.75318e7 | 0.293870 | ||||||||
\(273\) | −2.03464e7 | −0.0605228 | ||||||||
\(274\) | −7.58607e6 | −0.0222787 | ||||||||
\(275\) | −4.20929e8 | −1.22052 | ||||||||
\(276\) | 1.27751e8 | 0.365750 | ||||||||
\(277\) | 3.61274e8 | 1.02131 | 0.510654 | − | 0.859786i | \(-0.329403\pi\) | ||||
0.510654 | + | 0.859786i | \(0.329403\pi\) | |||||||
\(278\) | 4.16246e8 | 1.16197 | ||||||||
\(279\) | 2.02280e8 | 0.557621 | ||||||||
\(280\) | −1.31244e6 | −0.00357293 | ||||||||
\(281\) | 4.75931e8 | 1.27959 | 0.639797 | − | 0.768544i | \(-0.279019\pi\) | ||||
0.639797 | + | 0.768544i | \(0.279019\pi\) | |||||||
\(282\) | −3.06989e7 | −0.0815176 | ||||||||
\(283\) | 4.36716e8 | 1.14537 | 0.572686 | − | 0.819775i | \(-0.305901\pi\) | ||||
0.572686 | + | 0.819775i | \(0.305901\pi\) | |||||||
\(284\) | −1.81262e8 | −0.469561 | ||||||||
\(285\) | 9.45644e6 | 0.0241975 | ||||||||
\(286\) | 9.47653e7 | 0.239535 | ||||||||
\(287\) | −2.70034e7 | −0.0674267 | ||||||||
\(288\) | −2.38879e7 | −0.0589256 | ||||||||
\(289\) | 1.56648e8 | 0.381753 | ||||||||
\(290\) | 1.05106e7 | 0.0253068 | ||||||||
\(291\) | 4.26964e7 | 0.101570 | ||||||||
\(292\) | 2.05671e8 | 0.483429 | ||||||||
\(293\) | 1.06844e8 | 0.248149 | 0.124075 | − | 0.992273i | \(-0.460404\pi\) | ||||
0.124075 | + | 0.992273i | \(0.460404\pi\) | |||||||
\(294\) | −2.54122e7 | −0.0583212 | ||||||||
\(295\) | −3.98986e6 | −0.00904858 | ||||||||
\(296\) | −1.23417e8 | −0.276601 | ||||||||
\(297\) | 1.06126e8 | 0.235057 | ||||||||
\(298\) | −1.06848e8 | −0.233889 | ||||||||
\(299\) | −1.62425e8 | −0.351401 | ||||||||
\(300\) | −1.34903e8 | −0.288469 | ||||||||
\(301\) | −6.84423e7 | −0.144658 | ||||||||
\(302\) | −4.17841e7 | −0.0872944 | ||||||||
\(303\) | 2.48791e8 | 0.513791 | ||||||||
\(304\) | 1.91960e8 | 0.391879 | ||||||||
\(305\) | 2.50530e7 | 0.0505604 | ||||||||
\(306\) | −1.38869e8 | −0.277063 | ||||||||
\(307\) | −7.83514e8 | −1.54548 | −0.772738 | − | 0.634725i | \(-0.781114\pi\) | ||||
−0.772738 | + | 0.634725i | \(0.781114\pi\) | |||||||
\(308\) | 1.18360e8 | 0.230821 | ||||||||
\(309\) | 3.73445e8 | 0.720066 | ||||||||
\(310\) | −1.65894e7 | −0.0316275 | ||||||||
\(311\) | −3.68900e8 | −0.695421 | −0.347711 | − | 0.937602i | \(-0.613041\pi\) | ||||
−0.347711 | + | 0.937602i | \(0.613041\pi\) | |||||||
\(312\) | 3.03713e7 | 0.0566139 | ||||||||
\(313\) | 7.75507e8 | 1.42949 | 0.714744 | − | 0.699387i | \(-0.246543\pi\) | ||||
0.714744 | + | 0.699387i | \(0.246543\pi\) | |||||||
\(314\) | 5.60124e8 | 1.02101 | ||||||||
\(315\) | 1.86868e6 | 0.00336859 | ||||||||
\(316\) | −5.17533e8 | −0.922641 | ||||||||
\(317\) | 8.70639e8 | 1.53508 | 0.767540 | − | 0.641001i | \(-0.221481\pi\) | ||||
0.767540 | + | 0.641001i | \(0.221481\pi\) | |||||||
\(318\) | 1.84630e8 | 0.321963 | ||||||||
\(319\) | −9.47883e8 | −1.63489 | ||||||||
\(320\) | 1.95909e6 | 0.00334217 | ||||||||
\(321\) | 3.97120e8 | 0.670123 | ||||||||
\(322\) | −2.02865e8 | −0.338619 | ||||||||
\(323\) | 1.11593e9 | 1.84258 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | 1.71518e8 | 0.277152 | ||||||||
\(326\) | 5.56039e8 | 0.888882 | ||||||||
\(327\) | −1.65289e8 | −0.261413 | ||||||||
\(328\) | 4.03083e7 | 0.0630719 | ||||||||
\(329\) | 4.87488e7 | 0.0754706 | ||||||||
\(330\) | −8.70356e6 | −0.0133321 | ||||||||
\(331\) | 8.64912e8 | 1.31091 | 0.655457 | − | 0.755233i | \(-0.272476\pi\) | ||||
0.655457 | + | 0.755233i | \(0.272476\pi\) | |||||||
\(332\) | 3.88573e8 | 0.582760 | ||||||||
\(333\) | 1.75724e8 | 0.260782 | ||||||||
\(334\) | −4.36792e8 | −0.641448 | ||||||||
\(335\) | −3.08720e7 | −0.0448650 | ||||||||
\(336\) | 3.79331e7 | 0.0545545 | ||||||||
\(337\) | −1.27542e9 | −1.81530 | −0.907651 | − | 0.419727i | \(-0.862126\pi\) | ||||
−0.907651 | + | 0.419727i | \(0.862126\pi\) | |||||||
\(338\) | −3.86145e7 | −0.0543928 | ||||||||
\(339\) | −5.36029e8 | −0.747290 | ||||||||
\(340\) | 1.13889e7 | 0.0157146 | ||||||||
\(341\) | 1.49608e9 | 2.04322 | ||||||||
\(342\) | −2.73317e8 | −0.369467 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 1.02165e8 | 0.135315 | ||||||||
\(345\) | 1.49176e7 | 0.0195584 | ||||||||
\(346\) | −2.27718e8 | −0.295550 | ||||||||
\(347\) | −5.04685e8 | −0.648436 | −0.324218 | − | 0.945982i | \(-0.605101\pi\) | ||||
−0.324218 | + | 0.945982i | \(0.605101\pi\) | |||||||
\(348\) | −3.03787e8 | −0.386404 | ||||||||
\(349\) | −4.12949e8 | −0.520005 | −0.260003 | − | 0.965608i | \(-0.583723\pi\) | ||||
−0.260003 | + | 0.965608i | \(0.583723\pi\) | |||||||
\(350\) | 2.14222e8 | 0.267070 | ||||||||
\(351\) | −4.32436e7 | −0.0533761 | ||||||||
\(352\) | −1.76677e8 | −0.215914 | ||||||||
\(353\) | −9.13045e8 | −1.10479 | −0.552396 | − | 0.833582i | \(-0.686287\pi\) | ||||
−0.552396 | + | 0.833582i | \(0.686287\pi\) | |||||||
\(354\) | 1.15318e8 | 0.138161 | ||||||||
\(355\) | −2.11661e7 | −0.0251097 | ||||||||
\(356\) | 5.04218e8 | 0.592302 | ||||||||
\(357\) | 2.20518e8 | 0.256511 | ||||||||
\(358\) | −7.40430e8 | −0.852891 | ||||||||
\(359\) | 1.03015e9 | 1.17508 | 0.587542 | − | 0.809193i | \(-0.300096\pi\) | ||||
0.587542 | + | 0.809193i | \(0.300096\pi\) | |||||||
\(360\) | −2.78940e6 | −0.00315103 | ||||||||
\(361\) | 1.30247e9 | 1.45711 | ||||||||
\(362\) | −2.75188e8 | −0.304894 | ||||||||
\(363\) | 2.58761e8 | 0.283940 | ||||||||
\(364\) | −4.82285e7 | −0.0524142 | ||||||||
\(365\) | 2.40163e7 | 0.0258512 | ||||||||
\(366\) | −7.24101e8 | −0.771997 | ||||||||
\(367\) | 1.00109e9 | 1.05716 | 0.528581 | − | 0.848883i | \(-0.322724\pi\) | ||||
0.528581 | + | 0.848883i | \(0.322724\pi\) | |||||||
\(368\) | 3.02818e8 | 0.316749 | ||||||||
\(369\) | −5.73921e7 | −0.0594648 | ||||||||
\(370\) | −1.44115e7 | −0.0147912 | ||||||||
\(371\) | −2.93185e8 | −0.298080 | ||||||||
\(372\) | 4.79480e8 | 0.482914 | ||||||||
\(373\) | 1.08945e9 | 1.08700 | 0.543498 | − | 0.839410i | \(-0.317099\pi\) | ||||
0.543498 | + | 0.839410i | \(0.317099\pi\) | |||||||
\(374\) | −1.02708e9 | −1.01521 | ||||||||
\(375\) | −3.15168e7 | −0.0308626 | ||||||||
\(376\) | −7.27678e7 | −0.0705963 | ||||||||
\(377\) | 3.86239e8 | 0.371245 | ||||||||
\(378\) | −5.40102e7 | −0.0514344 | ||||||||
\(379\) | 1.89668e8 | 0.178960 | 0.0894801 | − | 0.995989i | \(-0.471479\pi\) | ||||
0.0894801 | + | 0.995989i | \(0.471479\pi\) | |||||||
\(380\) | 2.24153e7 | 0.0209556 | ||||||||
\(381\) | −1.07079e9 | −0.991900 | ||||||||
\(382\) | −8.65636e7 | −0.0794536 | ||||||||
\(383\) | 7.33219e8 | 0.666865 | 0.333432 | − | 0.942774i | \(-0.391793\pi\) | ||||
0.333432 | + | 0.942774i | \(0.391793\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | 1.38209e7 | 0.0123431 | ||||||||
\(386\) | 2.15927e8 | 0.191096 | ||||||||
\(387\) | −1.45465e8 | −0.127576 | ||||||||
\(388\) | 1.01206e8 | 0.0879622 | ||||||||
\(389\) | −1.17464e9 | −1.01177 | −0.505885 | − | 0.862601i | \(-0.668834\pi\) | ||||
−0.505885 | + | 0.862601i | \(0.668834\pi\) | |||||||
\(390\) | 3.54648e6 | 0.00302741 | ||||||||
\(391\) | 1.76039e9 | 1.48933 | ||||||||
\(392\) | −6.02363e7 | −0.0505076 | ||||||||
\(393\) | −9.08524e8 | −0.755027 | ||||||||
\(394\) | 2.85869e8 | 0.235467 | ||||||||
\(395\) | −6.04327e7 | −0.0493380 | ||||||||
\(396\) | 2.51557e8 | 0.203565 | ||||||||
\(397\) | −1.96244e9 | −1.57409 | −0.787044 | − | 0.616897i | \(-0.788389\pi\) | ||||
−0.787044 | + | 0.616897i | \(0.788389\pi\) | |||||||
\(398\) | −2.27964e8 | −0.181249 | ||||||||
\(399\) | 4.34018e8 | 0.342060 | ||||||||
\(400\) | −3.19771e8 | −0.249821 | ||||||||
\(401\) | 1.98515e8 | 0.153741 | 0.0768703 | − | 0.997041i | \(-0.475507\pi\) | ||||
0.0768703 | + | 0.997041i | \(0.475507\pi\) | |||||||
\(402\) | 8.92286e8 | 0.685036 | ||||||||
\(403\) | −6.09616e8 | −0.463969 | ||||||||
\(404\) | 5.89728e8 | 0.444956 | ||||||||
\(405\) | 3.97163e6 | 0.00297082 | ||||||||
\(406\) | 4.82403e8 | 0.357741 | ||||||||
\(407\) | 1.29967e9 | 0.955550 | ||||||||
\(408\) | −3.29170e8 | −0.239944 | ||||||||
\(409\) | 1.84368e9 | 1.33246 | 0.666231 | − | 0.745745i | \(-0.267907\pi\) | ||||
0.666231 | + | 0.745745i | \(0.267907\pi\) | |||||||
\(410\) | 4.70683e6 | 0.00337276 | ||||||||
\(411\) | 2.56030e7 | 0.0181905 | ||||||||
\(412\) | 8.85204e8 | 0.623596 | ||||||||
\(413\) | −1.83121e8 | −0.127912 | ||||||||
\(414\) | −4.31161e8 | −0.298634 | ||||||||
\(415\) | 4.53740e7 | 0.0311629 | ||||||||
\(416\) | 7.19913e7 | 0.0490290 | ||||||||
\(417\) | −1.40483e9 | −0.948741 | ||||||||
\(418\) | −2.02148e9 | −1.35379 | ||||||||
\(419\) | 2.40877e9 | 1.59973 | 0.799863 | − | 0.600183i | \(-0.204906\pi\) | ||||
0.799863 | + | 0.600183i | \(0.204906\pi\) | |||||||
\(420\) | 4.42947e6 | 0.00291729 | ||||||||
\(421\) | −1.10193e9 | −0.719727 | −0.359864 | − | 0.933005i | \(-0.617177\pi\) | ||||
−0.359864 | + | 0.933005i | \(0.617177\pi\) | |||||||
\(422\) | −7.67235e8 | −0.496975 | ||||||||
\(423\) | 1.03609e8 | 0.0665588 | ||||||||
\(424\) | 4.37641e8 | 0.278828 | ||||||||
\(425\) | −1.85894e9 | −1.17464 | ||||||||
\(426\) | 6.11759e8 | 0.383395 | ||||||||
\(427\) | 1.14985e9 | 0.714730 | ||||||||
\(428\) | 9.41322e8 | 0.580343 | ||||||||
\(429\) | −3.19833e8 | −0.195579 | ||||||||
\(430\) | 1.19298e7 | 0.00723594 | ||||||||
\(431\) | −1.52987e8 | −0.0920414 | −0.0460207 | − | 0.998940i | \(-0.514654\pi\) | ||||
−0.0460207 | + | 0.998940i | \(0.514654\pi\) | |||||||
\(432\) | 8.06216e7 | 0.0481125 | ||||||||
\(433\) | −9.21111e8 | −0.545261 | −0.272630 | − | 0.962119i | \(-0.587894\pi\) | ||||
−0.272630 | + | 0.962119i | \(0.587894\pi\) | |||||||
\(434\) | −7.61396e8 | −0.447092 | ||||||||
\(435\) | −3.54734e7 | −0.0206629 | ||||||||
\(436\) | −3.91797e8 | −0.226390 | ||||||||
\(437\) | 3.46475e9 | 1.98604 | ||||||||
\(438\) | −6.94139e8 | −0.394718 | ||||||||
\(439\) | −1.42647e9 | −0.804708 | −0.402354 | − | 0.915484i | \(-0.631808\pi\) | ||||
−0.402354 | + | 0.915484i | \(0.631808\pi\) | |||||||
\(440\) | −2.06307e7 | −0.0115459 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | 4.18511e8 | 0.230531 | ||||||||
\(443\) | −1.42706e9 | −0.779884 | −0.389942 | − | 0.920840i | \(-0.627505\pi\) | ||||
−0.389942 | + | 0.920840i | \(0.627505\pi\) | |||||||
\(444\) | 4.16532e8 | 0.225844 | ||||||||
\(445\) | 5.88779e7 | 0.0316732 | ||||||||
\(446\) | −4.85850e8 | −0.259316 | ||||||||
\(447\) | 3.60612e8 | 0.190969 | ||||||||
\(448\) | 8.99154e7 | 0.0472456 | ||||||||
\(449\) | 2.50667e9 | 1.30688 | 0.653439 | − | 0.756979i | \(-0.273325\pi\) | ||||
0.653439 | + | 0.756979i | \(0.273325\pi\) | |||||||
\(450\) | 4.55299e8 | 0.235534 | ||||||||
\(451\) | −4.24477e8 | −0.217889 | ||||||||
\(452\) | −1.27059e9 | −0.647172 | ||||||||
\(453\) | 1.41021e8 | 0.0712756 | ||||||||
\(454\) | 1.28523e9 | 0.644591 | ||||||||
\(455\) | −5.63168e6 | −0.00280284 | ||||||||
\(456\) | −6.47863e8 | −0.319968 | ||||||||
\(457\) | −2.47735e9 | −1.21417 | −0.607087 | − | 0.794635i | \(-0.707662\pi\) | ||||
−0.607087 | + | 0.794635i | \(0.707662\pi\) | |||||||
\(458\) | 8.48703e8 | 0.412788 | ||||||||
\(459\) | 4.68681e8 | 0.226221 | ||||||||
\(460\) | 3.53603e7 | 0.0169381 | ||||||||
\(461\) | 3.93003e9 | 1.86828 | 0.934141 | − | 0.356904i | \(-0.116168\pi\) | ||||
0.934141 | + | 0.356904i | \(0.116168\pi\) | |||||||
\(462\) | −3.99464e8 | −0.188465 | ||||||||
\(463\) | −1.11168e9 | −0.520532 | −0.260266 | − | 0.965537i | \(-0.583810\pi\) | ||||
−0.260266 | + | 0.965537i | \(0.583810\pi\) | |||||||
\(464\) | −7.20088e8 | −0.334636 | ||||||||
\(465\) | 5.59892e7 | 0.0258237 | ||||||||
\(466\) | −1.91960e9 | −0.878741 | ||||||||
\(467\) | −1.34613e9 | −0.611616 | −0.305808 | − | 0.952093i | \(-0.598927\pi\) | ||||
−0.305808 | + | 0.952093i | \(0.598927\pi\) | |||||||
\(468\) | −1.02503e8 | −0.0462250 | ||||||||
\(469\) | −1.41692e9 | −0.634220 | ||||||||
\(470\) | −8.49715e6 | −0.00377512 | ||||||||
\(471\) | −1.89042e9 | −0.833652 | ||||||||
\(472\) | 2.73346e8 | 0.119651 | ||||||||
\(473\) | −1.07587e9 | −0.467462 | ||||||||
\(474\) | 1.74667e9 | 0.753333 | ||||||||
\(475\) | −3.65872e9 | −1.56640 | ||||||||
\(476\) | 5.22710e8 | 0.222145 | ||||||||
\(477\) | −6.23125e8 | −0.262882 | ||||||||
\(478\) | 4.64447e8 | 0.194509 | ||||||||
\(479\) | 4.82168e8 | 0.200458 | 0.100229 | − | 0.994964i | \(-0.468042\pi\) | ||||
0.100229 | + | 0.994964i | \(0.468042\pi\) | |||||||
\(480\) | −6.61192e6 | −0.00272887 | ||||||||
\(481\) | −5.29584e8 | −0.216984 | ||||||||
\(482\) | −1.03539e8 | −0.0421153 | ||||||||
\(483\) | 6.84668e8 | 0.276481 | ||||||||
\(484\) | 6.13360e8 | 0.245899 | ||||||||
\(485\) | 1.18179e7 | 0.00470376 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | −2.23691e9 | −0.877600 | −0.438800 | − | 0.898585i | \(-0.644596\pi\) | ||||
−0.438800 | + | 0.898585i | \(0.644596\pi\) | |||||||
\(488\) | −1.71639e9 | −0.668569 | ||||||||
\(489\) | −1.87663e9 | −0.725769 | ||||||||
\(490\) | −7.03384e6 | −0.00270088 | ||||||||
\(491\) | −1.00077e9 | −0.381549 | −0.190774 | − | 0.981634i | \(-0.561100\pi\) | ||||
−0.190774 | + | 0.981634i | \(0.561100\pi\) | |||||||
\(492\) | −1.36041e8 | −0.0514980 | ||||||||
\(493\) | −4.18612e9 | −1.57343 | ||||||||
\(494\) | 8.23701e8 | 0.307415 | ||||||||
\(495\) | 2.93745e7 | 0.0108856 | ||||||||
\(496\) | 1.13654e9 | 0.418216 | ||||||||
\(497\) | −9.71450e8 | −0.354955 | ||||||||
\(498\) | −1.31143e9 | −0.475821 | ||||||||
\(499\) | 1.35572e9 | 0.488447 | 0.244224 | − | 0.969719i | \(-0.421467\pi\) | ||||
0.244224 | + | 0.969719i | \(0.421467\pi\) | |||||||
\(500\) | −7.47066e7 | −0.0267278 | ||||||||
\(501\) | 1.47417e9 | 0.523740 | ||||||||
\(502\) | 8.81172e8 | 0.310884 | ||||||||
\(503\) | 5.92942e8 | 0.207742 | 0.103871 | − | 0.994591i | \(-0.466877\pi\) | ||||
0.103871 | + | 0.994591i | \(0.466877\pi\) | |||||||
\(504\) | −1.28024e8 | −0.0445435 | ||||||||
\(505\) | 6.88630e7 | 0.0237939 | ||||||||
\(506\) | −3.18891e9 | −1.09425 | ||||||||
\(507\) | 1.30324e8 | 0.0444116 | ||||||||
\(508\) | −2.53817e9 | −0.859010 | ||||||||
\(509\) | 7.46490e8 | 0.250906 | 0.125453 | − | 0.992100i | \(-0.459962\pi\) | ||||
0.125453 | + | 0.992100i | \(0.459962\pi\) | |||||||
\(510\) | −3.84374e7 | −0.0128309 | ||||||||
\(511\) | 1.10227e9 | 0.365438 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 9.22446e8 | 0.301669 | ||||||||
\(514\) | −3.30005e9 | −1.07189 | ||||||||
\(515\) | 1.03366e8 | 0.0333466 | ||||||||
\(516\) | −3.44806e8 | −0.110484 | ||||||||
\(517\) | 7.66300e8 | 0.243883 | ||||||||
\(518\) | −6.61437e8 | −0.209091 | ||||||||
\(519\) | 7.68549e8 | 0.241316 | ||||||||
\(520\) | 8.40648e6 | 0.00262182 | ||||||||
\(521\) | −1.06134e8 | −0.0328792 | −0.0164396 | − | 0.999865i | \(-0.505233\pi\) | ||||
−0.0164396 | + | 0.999865i | \(0.505233\pi\) | |||||||
\(522\) | 1.02528e9 | 0.315498 | ||||||||
\(523\) | −1.91251e9 | −0.584587 | −0.292293 | − | 0.956329i | \(-0.594418\pi\) | ||||
−0.292293 | + | 0.956329i | \(0.594418\pi\) | |||||||
\(524\) | −2.15354e9 | −0.653872 | ||||||||
\(525\) | −7.22998e8 | −0.218062 | ||||||||
\(526\) | −3.64573e9 | −1.09228 | ||||||||
\(527\) | 6.60713e9 | 1.96642 | ||||||||
\(528\) | 5.96284e8 | 0.176293 | ||||||||
\(529\) | 2.06086e9 | 0.605276 | ||||||||
\(530\) | 5.11036e7 | 0.0149103 | ||||||||
\(531\) | −3.89198e8 | −0.112808 | ||||||||
\(532\) | 1.02878e9 | 0.296233 | ||||||||
\(533\) | 1.72964e8 | 0.0494777 | ||||||||
\(534\) | −1.70174e9 | −0.483613 | ||||||||
\(535\) | 1.09919e8 | 0.0310337 | ||||||||
\(536\) | 2.11505e9 | 0.593258 | ||||||||
\(537\) | 2.49895e9 | 0.696382 | ||||||||
\(538\) | −2.07498e9 | −0.574481 | ||||||||
\(539\) | 6.34333e8 | 0.174485 | ||||||||
\(540\) | 9.41424e6 | 0.00257281 | ||||||||
\(541\) | −5.18332e9 | −1.40740 | −0.703700 | − | 0.710498i | \(-0.748470\pi\) | ||||
−0.703700 | + | 0.710498i | \(0.748470\pi\) | |||||||
\(542\) | −2.70737e9 | −0.730381 | ||||||||
\(543\) | 9.28758e8 | 0.248945 | ||||||||
\(544\) | −7.80255e8 | −0.207797 | ||||||||
\(545\) | −4.57504e7 | −0.0121062 | ||||||||
\(546\) | 1.62771e8 | 0.0427960 | ||||||||
\(547\) | 2.21651e9 | 0.579047 | 0.289523 | − | 0.957171i | \(-0.406503\pi\) | ||||
0.289523 | + | 0.957171i | \(0.406503\pi\) | |||||||
\(548\) | 6.06886e7 | 0.0157534 | ||||||||
\(549\) | 2.44384e9 | 0.630333 | ||||||||
\(550\) | 3.36743e9 | 0.863037 | ||||||||
\(551\) | −8.23902e9 | −2.09819 | ||||||||
\(552\) | −1.02201e9 | −0.258624 | ||||||||
\(553\) | −2.77365e9 | −0.697451 | ||||||||
\(554\) | −2.89019e9 | −0.722174 | ||||||||
\(555\) | 4.86387e7 | 0.0120769 | ||||||||
\(556\) | −3.32997e9 | −0.821634 | ||||||||
\(557\) | −2.37436e9 | −0.582175 | −0.291087 | − | 0.956697i | \(-0.594017\pi\) | ||||
−0.291087 | + | 0.956697i | \(0.594017\pi\) | |||||||
\(558\) | −1.61824e9 | −0.394298 | ||||||||
\(559\) | 4.38390e8 | 0.106150 | ||||||||
\(560\) | 1.04995e7 | 0.00252645 | ||||||||
\(561\) | 3.46641e9 | 0.828914 | ||||||||
\(562\) | −3.80745e9 | −0.904809 | ||||||||
\(563\) | −5.53237e9 | −1.30657 | −0.653283 | − | 0.757114i | \(-0.726609\pi\) | ||||
−0.653283 | + | 0.757114i | \(0.726609\pi\) | |||||||
\(564\) | 2.45591e8 | 0.0576416 | ||||||||
\(565\) | −1.48367e8 | −0.0346074 | ||||||||
\(566\) | −3.49373e9 | −0.809901 | ||||||||
\(567\) | 1.82284e8 | 0.0419961 | ||||||||
\(568\) | 1.45009e9 | 0.332030 | ||||||||
\(569\) | −8.34861e8 | −0.189986 | −0.0949930 | − | 0.995478i | \(-0.530283\pi\) | ||||
−0.0949930 | + | 0.995478i | \(0.530283\pi\) | |||||||
\(570\) | −7.56515e7 | −0.0171102 | ||||||||
\(571\) | 5.84940e9 | 1.31488 | 0.657438 | − | 0.753509i | \(-0.271640\pi\) | ||||
0.657438 | + | 0.753509i | \(0.271640\pi\) | |||||||
\(572\) | −7.58123e8 | −0.169377 | ||||||||
\(573\) | 2.92152e8 | 0.0648736 | ||||||||
\(574\) | 2.16027e8 | 0.0476779 | ||||||||
\(575\) | −5.77167e9 | −1.26609 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 2.46903e9 | 0.535071 | 0.267535 | − | 0.963548i | \(-0.413791\pi\) | ||||
0.267535 | + | 0.963548i | \(0.413791\pi\) | |||||||
\(578\) | −1.25318e9 | −0.269940 | ||||||||
\(579\) | −7.28754e8 | −0.156029 | ||||||||
\(580\) | −8.40852e7 | −0.0178946 | ||||||||
\(581\) | 2.08251e9 | 0.440525 | ||||||||
\(582\) | −3.41571e8 | −0.0718208 | ||||||||
\(583\) | −4.60868e9 | −0.963246 | ||||||||
\(584\) | −1.64537e9 | −0.341836 | ||||||||
\(585\) | −1.19694e7 | −0.00247187 | ||||||||
\(586\) | −8.54751e8 | −0.175468 | ||||||||
\(587\) | 5.50894e9 | 1.12418 | 0.562089 | − | 0.827077i | \(-0.309998\pi\) | ||||
0.562089 | + | 0.827077i | \(0.309998\pi\) | |||||||
\(588\) | 2.03297e8 | 0.0412393 | ||||||||
\(589\) | 1.30040e10 | 2.62224 | ||||||||
\(590\) | 3.19189e7 | 0.00639831 | ||||||||
\(591\) | −9.64809e8 | −0.192258 | ||||||||
\(592\) | 9.87335e8 | 0.195586 | ||||||||
\(593\) | −5.66367e9 | −1.11534 | −0.557669 | − | 0.830063i | \(-0.688304\pi\) | ||||
−0.557669 | + | 0.830063i | \(0.688304\pi\) | |||||||
\(594\) | −8.49006e8 | −0.166210 | ||||||||
\(595\) | 6.10372e7 | 0.0118791 | ||||||||
\(596\) | 8.54783e8 | 0.165384 | ||||||||
\(597\) | 7.69377e8 | 0.147989 | ||||||||
\(598\) | 1.29940e9 | 0.248478 | ||||||||
\(599\) | 4.65297e9 | 0.884578 | 0.442289 | − | 0.896872i | \(-0.354166\pi\) | ||||
0.442289 | + | 0.896872i | \(0.354166\pi\) | |||||||
\(600\) | 1.07923e9 | 0.203978 | ||||||||
\(601\) | −4.89509e9 | −0.919814 | −0.459907 | − | 0.887967i | \(-0.652117\pi\) | ||||
−0.459907 | + | 0.887967i | \(0.652117\pi\) | |||||||
\(602\) | 5.47538e8 | 0.102289 | ||||||||
\(603\) | −3.01147e9 | −0.559329 | ||||||||
\(604\) | 3.34273e8 | 0.0617265 | ||||||||
\(605\) | 7.16225e7 | 0.0131494 | ||||||||
\(606\) | −1.99033e9 | −0.363305 | ||||||||
\(607\) | 8.11357e8 | 0.147249 | 0.0736244 | − | 0.997286i | \(-0.476543\pi\) | ||||
0.0736244 | + | 0.997286i | \(0.476543\pi\) | |||||||
\(608\) | −1.53568e9 | −0.277100 | ||||||||
\(609\) | −1.62811e9 | −0.292094 | ||||||||
\(610\) | −2.00424e8 | −0.0357516 | ||||||||
\(611\) | −3.12248e8 | −0.0553803 | ||||||||
\(612\) | 1.11095e9 | 0.195913 | ||||||||
\(613\) | 2.27379e9 | 0.398693 | 0.199347 | − | 0.979929i | \(-0.436118\pi\) | ||||
0.199347 | + | 0.979929i | \(0.436118\pi\) | |||||||
\(614\) | 6.26811e9 | 1.09282 | ||||||||
\(615\) | −1.58856e7 | −0.00275384 | ||||||||
\(616\) | −9.46877e8 | −0.163215 | ||||||||
\(617\) | −8.69457e9 | −1.49022 | −0.745109 | − | 0.666943i | \(-0.767603\pi\) | ||||
−0.745109 | + | 0.666943i | \(0.767603\pi\) | |||||||
\(618\) | −2.98756e9 | −0.509164 | ||||||||
\(619\) | −9.22069e9 | −1.56259 | −0.781297 | − | 0.624160i | \(-0.785442\pi\) | ||||
−0.781297 | + | 0.624160i | \(0.785442\pi\) | |||||||
\(620\) | 1.32715e8 | 0.0223640 | ||||||||
\(621\) | 1.45517e9 | 0.243833 | ||||||||
\(622\) | 2.95120e9 | 0.491737 | ||||||||
\(623\) | 2.70229e9 | 0.447739 | ||||||||
\(624\) | −2.42971e8 | −0.0400320 | ||||||||
\(625\) | 6.09043e9 | 0.997856 | ||||||||
\(626\) | −6.20405e9 | −1.01080 | ||||||||
\(627\) | 6.82249e9 | 1.10537 | ||||||||
\(628\) | −4.48099e9 | −0.721964 | ||||||||
\(629\) | 5.73972e9 | 0.919631 | ||||||||
\(630\) | −1.49495e7 | −0.00238196 | ||||||||
\(631\) | −1.06468e9 | −0.168701 | −0.0843503 | − | 0.996436i | \(-0.526881\pi\) | ||||
−0.0843503 | + | 0.996436i | \(0.526881\pi\) | |||||||
\(632\) | 4.14026e9 | 0.652406 | ||||||||
\(633\) | 2.58942e9 | 0.405779 | ||||||||
\(634\) | −6.96511e9 | −1.08547 | ||||||||
\(635\) | −2.96384e8 | −0.0459354 | ||||||||
\(636\) | −1.47704e9 | −0.227662 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | 7.58307e9 | 1.15604 | ||||||||
\(639\) | −2.06469e9 | −0.313041 | ||||||||
\(640\) | −1.56727e7 | −0.00236327 | ||||||||
\(641\) | −3.49397e9 | −0.523981 | −0.261991 | − | 0.965070i | \(-0.584379\pi\) | ||||
−0.261991 | + | 0.965070i | \(0.584379\pi\) | |||||||
\(642\) | −3.17696e9 | −0.473848 | ||||||||
\(643\) | −1.19059e10 | −1.76613 | −0.883066 | − | 0.469249i | \(-0.844525\pi\) | ||||
−0.883066 | + | 0.469249i | \(0.844525\pi\) | |||||||
\(644\) | 1.62292e9 | 0.239439 | ||||||||
\(645\) | −4.02632e7 | −0.00590812 | ||||||||
\(646\) | −8.92742e9 | −1.30290 | ||||||||
\(647\) | 8.84544e9 | 1.28397 | 0.641984 | − | 0.766718i | \(-0.278111\pi\) | ||||
0.641984 | + | 0.766718i | \(0.278111\pi\) | |||||||
\(648\) | −2.72098e8 | −0.0392837 | ||||||||
\(649\) | −2.87854e9 | −0.413349 | ||||||||
\(650\) | −1.37214e9 | −0.195976 | ||||||||
\(651\) | 2.56971e9 | 0.365049 | ||||||||
\(652\) | −4.44831e9 | −0.628534 | ||||||||
\(653\) | 4.23921e9 | 0.595785 | 0.297892 | − | 0.954599i | \(-0.403716\pi\) | ||||
0.297892 | + | 0.954599i | \(0.403716\pi\) | |||||||
\(654\) | 1.32231e9 | 0.184847 | ||||||||
\(655\) | −2.51470e8 | −0.0349657 | ||||||||
\(656\) | −3.22466e8 | −0.0445986 | ||||||||
\(657\) | 2.34272e9 | 0.322286 | ||||||||
\(658\) | −3.89990e8 | −0.0533658 | ||||||||
\(659\) | −2.08660e9 | −0.284014 | −0.142007 | − | 0.989866i | \(-0.545356\pi\) | ||||
−0.142007 | + | 0.989866i | \(0.545356\pi\) | |||||||
\(660\) | 6.96285e7 | 0.00942721 | ||||||||
\(661\) | −5.01321e9 | −0.675167 | −0.337583 | − | 0.941296i | \(-0.609609\pi\) | ||||
−0.337583 | + | 0.941296i | \(0.609609\pi\) | |||||||
\(662\) | −6.91930e9 | −0.926956 | ||||||||
\(663\) | −1.41247e9 | −0.188227 | ||||||||
\(664\) | −3.10858e9 | −0.412073 | ||||||||
\(665\) | 1.20132e8 | 0.0158410 | ||||||||
\(666\) | −1.40580e9 | −0.184401 | ||||||||
\(667\) | −1.29971e10 | −1.69593 | ||||||||
\(668\) | 3.49433e9 | 0.453572 | ||||||||
\(669\) | 1.63974e9 | 0.211731 | ||||||||
\(670\) | 2.46976e8 | 0.0317243 | ||||||||
\(671\) | 1.80749e10 | 2.30965 | ||||||||
\(672\) | −3.03464e8 | −0.0385758 | ||||||||
\(673\) | −3.78775e9 | −0.478993 | −0.239496 | − | 0.970897i | \(-0.576982\pi\) | ||||
−0.239496 | + | 0.970897i | \(0.576982\pi\) | |||||||
\(674\) | 1.02034e10 | 1.28361 | ||||||||
\(675\) | −1.53664e9 | −0.192313 | ||||||||
\(676\) | 3.08916e8 | 0.0384615 | ||||||||
\(677\) | 1.42684e9 | 0.176732 | 0.0883662 | − | 0.996088i | \(-0.471835\pi\) | ||||
0.0883662 | + | 0.996088i | \(0.471835\pi\) | |||||||
\(678\) | 4.28823e9 | 0.528414 | ||||||||
\(679\) | 5.42402e8 | 0.0664932 | ||||||||
\(680\) | −9.11109e7 | −0.0111119 | ||||||||
\(681\) | −4.33764e9 | −0.526306 | ||||||||
\(682\) | −1.19687e10 | −1.44478 | ||||||||
\(683\) | −2.34845e9 | −0.282039 | −0.141020 | − | 0.990007i | \(-0.545038\pi\) | ||||
−0.141020 | + | 0.990007i | \(0.545038\pi\) | |||||||
\(684\) | 2.18654e9 | 0.261253 | ||||||||
\(685\) | 7.08665e6 | 0.000842411 0 | ||||||||
\(686\) | −3.22829e8 | −0.0381802 | ||||||||
\(687\) | −2.86437e9 | −0.337040 | ||||||||
\(688\) | −8.17317e8 | −0.0956821 | ||||||||
\(689\) | 1.87792e9 | 0.218731 | ||||||||
\(690\) | −1.19341e8 | −0.0138299 | ||||||||
\(691\) | 7.74789e8 | 0.0893327 | 0.0446663 | − | 0.999002i | \(-0.485778\pi\) | ||||
0.0446663 | + | 0.999002i | \(0.485778\pi\) | |||||||
\(692\) | 1.82175e9 | 0.208986 | ||||||||
\(693\) | 1.34819e9 | 0.153881 | ||||||||
\(694\) | 4.03748e9 | 0.458513 | ||||||||
\(695\) | −3.88843e8 | −0.0439367 | ||||||||
\(696\) | 2.43030e9 | 0.273229 | ||||||||
\(697\) | −1.87461e9 | −0.209699 | ||||||||
\(698\) | 3.30360e9 | 0.367699 | ||||||||
\(699\) | 6.47866e9 | 0.717489 | ||||||||
\(700\) | −1.71377e9 | −0.188847 | ||||||||
\(701\) | 1.22722e10 | 1.34558 | 0.672789 | − | 0.739834i | \(-0.265096\pi\) | ||||
0.672789 | + | 0.739834i | \(0.265096\pi\) | |||||||
\(702\) | 3.45948e8 | 0.0377426 | ||||||||
\(703\) | 1.12968e10 | 1.22634 | ||||||||
\(704\) | 1.41341e9 | 0.152674 | ||||||||
\(705\) | 2.86779e7 | 0.00308237 | ||||||||
\(706\) | 7.30436e9 | 0.781206 | ||||||||
\(707\) | 3.16057e9 | 0.336355 | ||||||||
\(708\) | −9.22544e8 | −0.0976946 | ||||||||
\(709\) | 4.42611e9 | 0.466402 | 0.233201 | − | 0.972428i | \(-0.425080\pi\) | ||||
0.233201 | + | 0.972428i | \(0.425080\pi\) | |||||||
\(710\) | 1.69329e8 | 0.0177552 | ||||||||
\(711\) | −5.89502e9 | −0.615094 | ||||||||
\(712\) | −4.03375e9 | −0.418821 | ||||||||
\(713\) | 2.05139e10 | 2.11951 | ||||||||
\(714\) | −1.76415e9 | −0.181380 | ||||||||
\(715\) | −8.85265e7 | −0.00905737 | ||||||||
\(716\) | 5.92344e9 | 0.603085 | ||||||||
\(717\) | −1.56751e9 | −0.158816 | ||||||||
\(718\) | −8.24119e9 | −0.830910 | ||||||||
\(719\) | −2.30699e9 | −0.231470 | −0.115735 | − | 0.993280i | \(-0.536922\pi\) | ||||
−0.115735 | + | 0.993280i | \(0.536922\pi\) | |||||||
\(720\) | 2.23152e7 | 0.00222812 | ||||||||
\(721\) | 4.74414e9 | 0.471394 | ||||||||
\(722\) | −1.04197e10 | −1.03033 | ||||||||
\(723\) | 3.49444e8 | 0.0343870 | ||||||||
\(724\) | 2.20150e9 | 0.215593 | ||||||||
\(725\) | 1.37248e10 | 1.33759 | ||||||||
\(726\) | −2.07009e9 | −0.200776 | ||||||||
\(727\) | 1.45573e10 | 1.40511 | 0.702555 | − | 0.711629i | \(-0.252042\pi\) | ||||
0.702555 | + | 0.711629i | \(0.252042\pi\) | |||||||
\(728\) | 3.85828e8 | 0.0370625 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.92131e8 | −0.0182796 | ||||||||
\(731\) | −4.75135e9 | −0.449890 | ||||||||
\(732\) | 5.79281e9 | 0.545884 | ||||||||
\(733\) | 1.18974e10 | 1.11580 | 0.557902 | − | 0.829907i | \(-0.311606\pi\) | ||||
0.557902 | + | 0.829907i | \(0.311606\pi\) | |||||||
\(734\) | −8.00872e9 | −0.747527 | ||||||||
\(735\) | 2.37392e7 | 0.00220526 | ||||||||
\(736\) | −2.42255e9 | −0.223975 | ||||||||
\(737\) | −2.22731e10 | −2.04948 | ||||||||
\(738\) | 4.59137e8 | 0.0420479 | ||||||||
\(739\) | −6.61920e8 | −0.0603324 | −0.0301662 | − | 0.999545i | \(-0.509604\pi\) | ||||
−0.0301662 | + | 0.999545i | \(0.509604\pi\) | |||||||
\(740\) | 1.15292e8 | 0.0104589 | ||||||||
\(741\) | −2.77999e9 | −0.251004 | ||||||||
\(742\) | 2.34548e9 | 0.210774 | ||||||||
\(743\) | −6.56840e9 | −0.587488 | −0.293744 | − | 0.955884i | \(-0.594901\pi\) | ||||
−0.293744 | + | 0.955884i | \(0.594901\pi\) | |||||||
\(744\) | −3.83584e9 | −0.341472 | ||||||||
\(745\) | 9.98136e7 | 0.00884388 | ||||||||
\(746\) | −8.71564e9 | −0.768623 | ||||||||
\(747\) | 4.42609e9 | 0.388506 | ||||||||
\(748\) | 8.21667e9 | 0.717861 | ||||||||
\(749\) | 5.04490e9 | 0.438698 | ||||||||
\(750\) | 2.52135e8 | 0.0218232 | ||||||||
\(751\) | −1.77094e10 | −1.52568 | −0.762840 | − | 0.646587i | \(-0.776196\pi\) | ||||
−0.762840 | + | 0.646587i | \(0.776196\pi\) | |||||||
\(752\) | 5.82143e8 | 0.0499191 | ||||||||
\(753\) | −2.97396e9 | −0.253835 | ||||||||
\(754\) | −3.08991e9 | −0.262510 | ||||||||
\(755\) | 3.90332e7 | 0.00330081 | ||||||||
\(756\) | 4.32081e8 | 0.0363696 | ||||||||
\(757\) | −1.73394e10 | −1.45277 | −0.726386 | − | 0.687286i | \(-0.758802\pi\) | ||||
−0.726386 | + | 0.687286i | \(0.758802\pi\) | |||||||
\(758\) | −1.51734e9 | −0.126544 | ||||||||
\(759\) | 1.07626e10 | 0.893448 | ||||||||
\(760\) | −1.79322e8 | −0.0148179 | ||||||||
\(761\) | −1.34566e10 | −1.10685 | −0.553424 | − | 0.832900i | \(-0.686679\pi\) | ||||
−0.553424 | + | 0.832900i | \(0.686679\pi\) | |||||||
\(762\) | 8.56634e9 | 0.701379 | ||||||||
\(763\) | −2.09978e9 | −0.171135 | ||||||||
\(764\) | 6.92509e8 | 0.0561822 | ||||||||
\(765\) | 1.29726e8 | 0.0104764 | ||||||||
\(766\) | −5.86575e9 | −0.471545 | ||||||||
\(767\) | 1.17293e9 | 0.0938620 | ||||||||
\(768\) | 4.52985e8 | 0.0360844 | ||||||||
\(769\) | 7.37377e9 | 0.584720 | 0.292360 | − | 0.956308i | \(-0.405560\pi\) | ||||
0.292360 | + | 0.956308i | \(0.405560\pi\) | |||||||
\(770\) | −1.10567e8 | −0.00872790 | ||||||||
\(771\) | 1.11377e10 | 0.875194 | ||||||||
\(772\) | −1.72742e9 | −0.135125 | ||||||||
\(773\) | 1.75212e10 | 1.36438 | 0.682189 | − | 0.731176i | \(-0.261028\pi\) | ||||
0.682189 | + | 0.731176i | \(0.261028\pi\) | |||||||
\(774\) | 1.16372e9 | 0.0902100 | ||||||||
\(775\) | −2.16624e10 | −1.67167 | ||||||||
\(776\) | −8.09649e8 | −0.0621986 | ||||||||
\(777\) | 2.23235e9 | 0.170722 | ||||||||
\(778\) | 9.39713e9 | 0.715429 | ||||||||
\(779\) | −3.68956e9 | −0.279636 | ||||||||
\(780\) | −2.83719e7 | −0.00214070 | ||||||||
\(781\) | −1.52706e10 | −1.14704 | ||||||||
\(782\) | −1.40831e10 | −1.05311 | ||||||||
\(783\) | −3.46032e9 | −0.257603 | ||||||||
\(784\) | 4.81890e8 | 0.0357143 | ||||||||
\(785\) | −5.23249e8 | −0.0386069 | ||||||||
\(786\) | 7.26819e9 | 0.533884 | ||||||||
\(787\) | −2.08015e10 | −1.52119 | −0.760594 | − | 0.649228i | \(-0.775092\pi\) | ||||
−0.760594 | + | 0.649228i | \(0.775092\pi\) | |||||||
\(788\) | −2.28695e9 | −0.166501 | ||||||||
\(789\) | 1.23044e10 | 0.891845 | ||||||||
\(790\) | 4.83461e8 | 0.0348873 | ||||||||
\(791\) | −6.80955e9 | −0.489216 | ||||||||
\(792\) | −2.01246e9 | −0.143942 | ||||||||
\(793\) | −7.36505e9 | −0.524469 | ||||||||
\(794\) | 1.56995e10 | 1.11305 | ||||||||
\(795\) | −1.72475e8 | −0.0121742 | ||||||||
\(796\) | 1.82371e9 | 0.128162 | ||||||||
\(797\) | 2.06060e10 | 1.44175 | 0.720874 | − | 0.693066i | \(-0.243741\pi\) | ||||
0.720874 | + | 0.693066i | \(0.243741\pi\) | |||||||
\(798\) | −3.47214e9 | −0.241873 | ||||||||
\(799\) | 3.38420e9 | 0.234716 | ||||||||
\(800\) | 2.55817e9 | 0.176650 | ||||||||
\(801\) | 5.74336e9 | 0.394868 | ||||||||
\(802\) | −1.58812e9 | −0.108711 | ||||||||
\(803\) | 1.73269e10 | 1.18091 | ||||||||
\(804\) | −7.13829e9 | −0.484393 | ||||||||
\(805\) | 1.89509e8 | 0.0128040 | ||||||||
\(806\) | 4.87693e9 | 0.328075 | ||||||||
\(807\) | 7.00305e9 | 0.469062 | ||||||||
\(808\) | −4.71782e9 | −0.314631 | ||||||||
\(809\) | −4.06471e9 | −0.269904 | −0.134952 | − | 0.990852i | \(-0.543088\pi\) | ||||
−0.134952 | + | 0.990852i | \(0.543088\pi\) | |||||||
\(810\) | −3.17731e7 | −0.00210069 | ||||||||
\(811\) | −6.91651e9 | −0.455317 | −0.227659 | − | 0.973741i | \(-0.573107\pi\) | ||||
−0.227659 | + | 0.973741i | \(0.573107\pi\) | |||||||
\(812\) | −3.85922e9 | −0.252961 | ||||||||
\(813\) | 9.13737e9 | 0.596354 | ||||||||
\(814\) | −1.03974e10 | −0.675676 | ||||||||
\(815\) | −5.19433e8 | −0.0336107 | ||||||||
\(816\) | 2.63336e9 | 0.169666 | ||||||||
\(817\) | −9.35148e9 | −0.599933 | ||||||||
\(818\) | −1.47495e10 | −0.942193 | ||||||||
\(819\) | −5.49353e8 | −0.0349428 | ||||||||
\(820\) | −3.76546e7 | −0.00238490 | ||||||||
\(821\) | −1.65831e10 | −1.04584 | −0.522920 | − | 0.852382i | \(-0.675157\pi\) | ||||
−0.522920 | + | 0.852382i | \(0.675157\pi\) | |||||||
\(822\) | −2.04824e8 | −0.0128626 | ||||||||
\(823\) | −3.10529e9 | −0.194179 | −0.0970896 | − | 0.995276i | \(-0.530953\pi\) | ||||
−0.0970896 | + | 0.995276i | \(0.530953\pi\) | |||||||
\(824\) | −7.08163e9 | −0.440949 | ||||||||
\(825\) | −1.13651e10 | −0.704667 | ||||||||
\(826\) | 1.46497e9 | 0.0904477 | ||||||||
\(827\) | −1.22275e10 | −0.751741 | −0.375871 | − | 0.926672i | \(-0.622656\pi\) | ||||
−0.375871 | + | 0.926672i | \(0.622656\pi\) | |||||||
\(828\) | 3.44929e9 | 0.211166 | ||||||||
\(829\) | 3.00252e10 | 1.83039 | 0.915197 | − | 0.403007i | \(-0.132035\pi\) | ||||
0.915197 | + | 0.403007i | \(0.132035\pi\) | |||||||
\(830\) | −3.62992e8 | −0.0220355 | ||||||||
\(831\) | 9.75439e9 | 0.589653 | ||||||||
\(832\) | −5.75930e8 | −0.0346688 | ||||||||
\(833\) | 2.80140e9 | 0.167926 | ||||||||
\(834\) | 1.12386e10 | 0.670861 | ||||||||
\(835\) | 4.08036e8 | 0.0242547 | ||||||||
\(836\) | 1.61718e10 | 0.957276 | ||||||||
\(837\) | 5.46157e9 | 0.321943 | ||||||||
\(838\) | −1.92701e10 | −1.13118 | ||||||||
\(839\) | −2.44073e10 | −1.42676 | −0.713382 | − | 0.700775i | \(-0.752838\pi\) | ||||
−0.713382 | + | 0.700775i | \(0.752838\pi\) | |||||||
\(840\) | −3.54358e7 | −0.00206283 | ||||||||
\(841\) | 1.36567e10 | 0.791699 | ||||||||
\(842\) | 8.81546e9 | 0.508924 | ||||||||
\(843\) | 1.28501e10 | 0.738774 | ||||||||
\(844\) | 6.13788e9 | 0.351415 | ||||||||
\(845\) | 3.60723e7 | 0.00205672 | ||||||||
\(846\) | −8.28871e8 | −0.0470642 | ||||||||
\(847\) | 3.28723e9 | 0.185882 | ||||||||
\(848\) | −3.50112e9 | −0.197161 | ||||||||
\(849\) | 1.17913e10 | 0.661281 | ||||||||
\(850\) | 1.48715e10 | 0.830596 | ||||||||
\(851\) | 1.78208e10 | 0.991227 | ||||||||
\(852\) | −4.89407e9 | −0.271101 | ||||||||
\(853\) | 2.26002e10 | 1.24678 | 0.623391 | − | 0.781911i | \(-0.285755\pi\) | ||||
0.623391 | + | 0.781911i | \(0.285755\pi\) | |||||||
\(854\) | −9.19877e9 | −0.505391 | ||||||||
\(855\) | 2.55324e8 | 0.0139704 | ||||||||
\(856\) | −7.53058e9 | −0.410365 | ||||||||
\(857\) | 8.14738e8 | 0.0442166 | 0.0221083 | − | 0.999756i | \(-0.492962\pi\) | ||||
0.0221083 | + | 0.999756i | \(0.492962\pi\) | |||||||
\(858\) | 2.55866e9 | 0.138295 | ||||||||
\(859\) | 2.14476e10 | 1.15452 | 0.577262 | − | 0.816559i | \(-0.304121\pi\) | ||||
0.577262 | + | 0.816559i | \(0.304121\pi\) | |||||||
\(860\) | −9.54387e7 | −0.00511658 | ||||||||
\(861\) | −7.29092e8 | −0.0389288 | ||||||||
\(862\) | 1.22389e9 | 0.0650831 | ||||||||
\(863\) | 2.51368e10 | 1.33129 | 0.665645 | − | 0.746269i | \(-0.268157\pi\) | ||||
0.665645 | + | 0.746269i | \(0.268157\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | 2.12727e8 | 0.0111755 | ||||||||
\(866\) | 7.36889e9 | 0.385558 | ||||||||
\(867\) | 4.22950e9 | 0.220405 | ||||||||
\(868\) | 6.09117e9 | 0.316141 | ||||||||
\(869\) | −4.36001e10 | −2.25381 | ||||||||
\(870\) | 2.83788e8 | 0.0146109 | ||||||||
\(871\) | 9.07571e9 | 0.465390 | ||||||||
\(872\) | 3.13437e9 | 0.160082 | ||||||||
\(873\) | 1.15280e9 | 0.0586414 | ||||||||
\(874\) | −2.77180e10 | −1.40434 | ||||||||
\(875\) | −4.00380e8 | −0.0202043 | ||||||||
\(876\) | 5.55311e9 | 0.279108 | ||||||||
\(877\) | −8.07486e9 | −0.404237 | −0.202119 | − | 0.979361i | \(-0.564783\pi\) | ||||
−0.202119 | + | 0.979361i | \(0.564783\pi\) | |||||||
\(878\) | 1.14118e10 | 0.569014 | ||||||||
\(879\) | 2.88479e9 | 0.143269 | ||||||||
\(880\) | 1.65045e8 | 0.00816421 | ||||||||
\(881\) | −2.80996e10 | −1.38447 | −0.692235 | − | 0.721672i | \(-0.743374\pi\) | ||||
−0.692235 | + | 0.721672i | \(0.743374\pi\) | |||||||
\(882\) | −6.86129e8 | −0.0336718 | ||||||||
\(883\) | −2.39587e10 | −1.17112 | −0.585559 | − | 0.810630i | \(-0.699125\pi\) | ||||
−0.585559 | + | 0.810630i | \(0.699125\pi\) | |||||||
\(884\) | −3.34809e9 | −0.163010 | ||||||||
\(885\) | −1.07726e8 | −0.00522420 | ||||||||
\(886\) | 1.14165e10 | 0.551461 | ||||||||
\(887\) | 1.33775e10 | 0.643637 | 0.321819 | − | 0.946801i | \(-0.395706\pi\) | ||||
0.321819 | + | 0.946801i | \(0.395706\pi\) | |||||||
\(888\) | −3.33226e9 | −0.159696 | ||||||||
\(889\) | −1.36030e10 | −0.649351 | ||||||||
\(890\) | −4.71023e8 | −0.0223964 | ||||||||
\(891\) | 2.86539e9 | 0.135710 | ||||||||
\(892\) | 3.88680e9 | 0.183364 | ||||||||
\(893\) | 6.66069e9 | 0.312996 | ||||||||
\(894\) | −2.88489e9 | −0.135036 | ||||||||
\(895\) | 6.91684e8 | 0.0322498 | ||||||||
\(896\) | −7.19323e8 | −0.0334077 | ||||||||
\(897\) | −4.38547e9 | −0.202882 | ||||||||
\(898\) | −2.00534e10 | −0.924103 | ||||||||
\(899\) | −4.87811e10 | −2.23920 | ||||||||
\(900\) | −3.64239e9 | −0.166548 | ||||||||
\(901\) | −2.03533e10 | −0.927038 | ||||||||
\(902\) | 3.39581e9 | 0.154071 | ||||||||
\(903\) | −1.84794e9 | −0.0835182 | ||||||||
\(904\) | 1.01647e10 | 0.457620 | ||||||||
\(905\) | 2.57071e8 | 0.0115288 | ||||||||
\(906\) | −1.12817e9 | −0.0503994 | ||||||||
\(907\) | −2.81472e10 | −1.25259 | −0.626296 | − | 0.779585i | \(-0.715430\pi\) | ||||
−0.626296 | + | 0.779585i | \(0.715430\pi\) | |||||||
\(908\) | −1.02818e10 | −0.455794 | ||||||||
\(909\) | 6.71737e9 | 0.296637 | ||||||||
\(910\) | 4.50535e7 | 0.00198191 | ||||||||
\(911\) | −1.72184e10 | −0.754534 | −0.377267 | − | 0.926105i | \(-0.623136\pi\) | ||||
−0.377267 | + | 0.926105i | \(0.623136\pi\) | |||||||
\(912\) | 5.18291e9 | 0.226252 | ||||||||
\(913\) | 3.27357e10 | 1.42356 | ||||||||
\(914\) | 1.98188e10 | 0.858551 | ||||||||
\(915\) | 6.76431e8 | 0.0291910 | ||||||||
\(916\) | −6.78962e9 | −0.291885 | ||||||||
\(917\) | −1.15416e10 | −0.494281 | ||||||||
\(918\) | −3.74945e9 | −0.159963 | ||||||||
\(919\) | 2.64594e10 | 1.12454 | 0.562272 | − | 0.826953i | \(-0.309928\pi\) | ||||
0.562272 | + | 0.826953i | \(0.309928\pi\) | |||||||
\(920\) | −2.82883e8 | −0.0119770 | ||||||||
\(921\) | −2.11549e10 | −0.892282 | ||||||||
\(922\) | −3.14402e10 | −1.32107 | ||||||||
\(923\) | 6.22238e9 | 0.260466 | ||||||||
\(924\) | 3.19571e9 | 0.133265 | ||||||||
\(925\) | −1.88185e10 | −0.781786 | ||||||||
\(926\) | 8.89346e9 | 0.368071 | ||||||||
\(927\) | 1.00830e10 | 0.415730 | ||||||||
\(928\) | 5.76070e9 | 0.236623 | ||||||||
\(929\) | 3.96644e8 | 0.0162310 | 0.00811551 | − | 0.999967i | \(-0.497417\pi\) | ||||
0.00811551 | + | 0.999967i | \(0.497417\pi\) | |||||||
\(930\) | −4.47913e8 | −0.0182601 | ||||||||
\(931\) | 5.51363e9 | 0.223931 | ||||||||
\(932\) | 1.53568e10 | 0.621364 | ||||||||
\(933\) | −9.96031e9 | −0.401502 | ||||||||
\(934\) | 1.07691e10 | 0.432478 | ||||||||
\(935\) | 9.59467e8 | 0.0383874 | ||||||||
\(936\) | 8.20026e8 | 0.0326860 | ||||||||
\(937\) | 1.37233e10 | 0.544967 | 0.272483 | − | 0.962160i | \(-0.412155\pi\) | ||||
0.272483 | + | 0.962160i | \(0.412155\pi\) | |||||||
\(938\) | 1.13353e10 | 0.448461 | ||||||||
\(939\) | 2.09387e10 | 0.825315 | ||||||||
\(940\) | 6.79772e7 | 0.00266941 | ||||||||
\(941\) | 9.81482e9 | 0.383989 | 0.191994 | − | 0.981396i | \(-0.438504\pi\) | ||||
0.191994 | + | 0.981396i | \(0.438504\pi\) | |||||||
\(942\) | 1.51234e10 | 0.589481 | ||||||||
\(943\) | −5.82032e9 | −0.226025 | ||||||||
\(944\) | −2.18677e9 | −0.0846060 | ||||||||
\(945\) | 5.04544e7 | 0.00194486 | ||||||||
\(946\) | 8.60696e9 | 0.330545 | ||||||||
\(947\) | 3.35417e10 | 1.28340 | 0.641698 | − | 0.766958i | \(-0.278230\pi\) | ||||
0.641698 | + | 0.766958i | \(0.278230\pi\) | |||||||
\(948\) | −1.39734e10 | −0.532687 | ||||||||
\(949\) | −7.06029e9 | −0.268158 | ||||||||
\(950\) | 2.92698e10 | 1.10761 | ||||||||
\(951\) | 2.35073e10 | 0.886279 | ||||||||
\(952\) | −4.18168e9 | −0.157080 | ||||||||
\(953\) | 2.09755e10 | 0.785032 | 0.392516 | − | 0.919745i | \(-0.371605\pi\) | ||||
0.392516 | + | 0.919745i | \(0.371605\pi\) | |||||||
\(954\) | 4.98500e9 | 0.185886 | ||||||||
\(955\) | 8.08647e7 | 0.00300433 | ||||||||
\(956\) | −3.71558e9 | −0.137538 | ||||||||
\(957\) | −2.55929e10 | −0.943902 | ||||||||
\(958\) | −3.85735e9 | −0.141746 | ||||||||
\(959\) | 3.25253e8 | 0.0119085 | ||||||||
\(960\) | 5.28954e7 | 0.00192960 | ||||||||
\(961\) | 4.94807e10 | 1.79847 | ||||||||
\(962\) | 4.23667e9 | 0.153431 | ||||||||
\(963\) | 1.07222e10 | 0.386896 | ||||||||
\(964\) | 8.28313e8 | 0.0297800 | ||||||||
\(965\) | −2.01712e8 | −0.00722579 | ||||||||
\(966\) | −5.47734e9 | −0.195502 | ||||||||
\(967\) | −3.47197e10 | −1.23476 | −0.617381 | − | 0.786664i | \(-0.711806\pi\) | ||||
−0.617381 | + | 0.786664i | \(0.711806\pi\) | |||||||
\(968\) | −4.90688e9 | −0.173877 | ||||||||
\(969\) | 3.01301e10 | 1.06382 | ||||||||
\(970\) | −9.45433e7 | −0.00332606 | ||||||||
\(971\) | 4.45891e9 | 0.156301 | 0.0781504 | − | 0.996942i | \(-0.475099\pi\) | ||||
0.0781504 | + | 0.996942i | \(0.475099\pi\) | |||||||
\(972\) | 9.18330e8 | 0.0320750 | ||||||||
\(973\) | −1.78465e10 | −0.621097 | ||||||||
\(974\) | 1.78953e10 | 0.620557 | ||||||||
\(975\) | 4.63098e9 | 0.160014 | ||||||||
\(976\) | 1.37311e10 | 0.472750 | ||||||||
\(977\) | 1.71692e10 | 0.589007 | 0.294503 | − | 0.955650i | \(-0.404846\pi\) | ||||
0.294503 | + | 0.955650i | \(0.404846\pi\) | |||||||
\(978\) | 1.50131e10 | 0.513196 | ||||||||
\(979\) | 4.24784e10 | 1.44687 | ||||||||
\(980\) | 5.62707e7 | 0.00190981 | ||||||||
\(981\) | −4.46281e9 | −0.150927 | ||||||||
\(982\) | 8.00618e9 | 0.269796 | ||||||||
\(983\) | 3.75095e10 | 1.25952 | 0.629758 | − | 0.776791i | \(-0.283154\pi\) | ||||
0.629758 | + | 0.776791i | \(0.283154\pi\) | |||||||
\(984\) | 1.08832e9 | 0.0364146 | ||||||||
\(985\) | −2.67049e8 | −0.00890358 | ||||||||
\(986\) | 3.34890e10 | 1.11258 | ||||||||
\(987\) | 1.31622e9 | 0.0435730 | ||||||||
\(988\) | −6.58961e9 | −0.217375 | ||||||||
\(989\) | −1.47521e10 | −0.484915 | ||||||||
\(990\) | −2.34996e8 | −0.00769729 | ||||||||
\(991\) | 1.97803e10 | 0.645616 | 0.322808 | − | 0.946464i | \(-0.395373\pi\) | ||||
0.322808 | + | 0.946464i | \(0.395373\pi\) | |||||||
\(992\) | −9.09235e9 | −0.295723 | ||||||||
\(993\) | 2.33526e10 | 0.756856 | ||||||||
\(994\) | 7.77160e9 | 0.250991 | ||||||||
\(995\) | 2.12956e8 | 0.00685344 | ||||||||
\(996\) | 1.04915e10 | 0.336456 | ||||||||
\(997\) | 1.83361e9 | 0.0585967 | 0.0292984 | − | 0.999571i | \(-0.490673\pi\) | ||||
0.0292984 | + | 0.999571i | \(0.490673\pi\) | |||||||
\(998\) | −1.08458e10 | −0.345384 | ||||||||
\(999\) | 4.74456e9 | 0.150562 |
(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 | 546.8.a.p.1.4 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.8.a.p.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial |