Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,6,Mod(1,387)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(387, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("387.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 387.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: | \(62.0685382676\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + \cdots - 22734604 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(9.86547\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 387.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.86547 | 1.56721 | 0.783604 | − | 0.621260i | \(-0.213379\pi\) | ||||
0.783604 | + | 0.621260i | \(0.213379\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 46.5966 | 1.45614 | ||||||||
\(5\) | 37.8251 | 0.676636 | 0.338318 | − | 0.941032i | \(-0.390142\pi\) | ||||
0.338318 | + | 0.941032i | \(0.390142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −124.747 | −0.962246 | −0.481123 | − | 0.876653i | \(-0.659771\pi\) | ||||
−0.481123 | + | 0.876653i | \(0.659771\pi\) | |||||||
\(8\) | 129.406 | 0.714872 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 335.337 | 1.06043 | ||||||||
\(11\) | −590.079 | −1.47038 | −0.735188 | − | 0.677863i | \(-0.762906\pi\) | ||||
−0.735188 | + | 0.677863i | \(0.762906\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 434.774 | 0.713518 | 0.356759 | − | 0.934196i | \(-0.383882\pi\) | ||||
0.356759 | + | 0.934196i | \(0.383882\pi\) | |||||||
\(14\) | −1105.94 | −1.50804 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −343.849 | −0.335790 | ||||||||
\(17\) | −1925.58 | −1.61599 | −0.807995 | − | 0.589189i | \(-0.799447\pi\) | ||||
−0.807995 | + | 0.589189i | \(0.799447\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 654.129 | 0.415700 | 0.207850 | − | 0.978161i | \(-0.433353\pi\) | ||||
0.207850 | + | 0.978161i | \(0.433353\pi\) | |||||||
\(20\) | 1762.52 | 0.985279 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5231.33 | −2.30439 | ||||||||
\(23\) | −2805.03 | −1.10565 | −0.552825 | − | 0.833297i | \(-0.686450\pi\) | ||||
−0.552825 | + | 0.833297i | \(0.686450\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1694.26 | −0.542163 | ||||||||
\(26\) | 3854.47 | 1.11823 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5812.80 | −1.40117 | ||||||||
\(29\) | 1456.23 | 0.321540 | 0.160770 | − | 0.986992i | \(-0.448602\pi\) | ||||
0.160770 | + | 0.986992i | \(0.448602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4419.85 | 0.826044 | 0.413022 | − | 0.910721i | \(-0.364473\pi\) | ||||
0.413022 | + | 0.910721i | \(0.364473\pi\) | |||||||
\(32\) | −7189.36 | −1.24112 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −17071.2 | −2.53259 | ||||||||
\(35\) | −4718.58 | −0.651090 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3753.09 | 0.450697 | 0.225348 | − | 0.974278i | \(-0.427648\pi\) | ||||
0.225348 | + | 0.974278i | \(0.427648\pi\) | |||||||
\(38\) | 5799.17 | 0.651488 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4894.78 | 0.483708 | ||||||||
\(41\) | −1972.85 | −0.183288 | −0.0916442 | − | 0.995792i | \(-0.529212\pi\) | ||||
−0.0916442 | + | 0.995792i | \(0.529212\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1849.00 | 0.152499 | ||||||||
\(44\) | −27495.7 | −2.14108 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −24867.9 | −1.73279 | ||||||||
\(47\) | −2204.84 | −0.145590 | −0.0727950 | − | 0.997347i | \(-0.523192\pi\) | ||||
−0.0727950 | + | 0.997347i | \(0.523192\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1245.12 | −0.0740834 | ||||||||
\(50\) | −15020.4 | −0.849683 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 20259.0 | 1.03898 | ||||||||
\(53\) | −24984.2 | −1.22173 | −0.610865 | − | 0.791735i | \(-0.709178\pi\) | ||||
−0.610865 | + | 0.791735i | \(0.709178\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −22319.8 | −0.994910 | ||||||||
\(56\) | −16143.0 | −0.687882 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12910.1 | 0.503920 | ||||||||
\(59\) | 42756.2 | 1.59907 | 0.799537 | − | 0.600616i | \(-0.205078\pi\) | ||||
0.799537 | + | 0.600616i | \(0.205078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −21022.8 | −0.723379 | −0.361689 | − | 0.932299i | \(-0.617800\pi\) | ||||
−0.361689 | + | 0.932299i | \(0.617800\pi\) | |||||||
\(62\) | 39184.0 | 1.29458 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −52733.9 | −1.60931 | ||||||||
\(65\) | 16445.4 | 0.482792 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −25272.1 | −0.687788 | −0.343894 | − | 0.939008i | \(-0.611746\pi\) | ||||
−0.343894 | + | 0.939008i | \(0.611746\pi\) | |||||||
\(68\) | −89725.4 | −2.35311 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −41832.4 | −1.02039 | ||||||||
\(71\) | −48082.8 | −1.13199 | −0.565997 | − | 0.824407i | \(-0.691509\pi\) | ||||
−0.565997 | + | 0.824407i | \(0.691509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58801.2 | 1.29145 | 0.645727 | − | 0.763568i | \(-0.276554\pi\) | ||||
0.645727 | + | 0.763568i | \(0.276554\pi\) | |||||||
\(74\) | 33272.9 | 0.706336 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 30480.2 | 0.605318 | ||||||||
\(77\) | 73610.8 | 1.41486 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 92704.7 | 1.67122 | 0.835611 | − | 0.549322i | \(-0.185114\pi\) | ||||
0.835611 | + | 0.549322i | \(0.185114\pi\) | |||||||
\(80\) | −13006.1 | −0.227208 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −17490.3 | −0.287251 | ||||||||
\(83\) | 1849.64 | 0.0294708 | 0.0147354 | − | 0.999891i | \(-0.495309\pi\) | ||||
0.0147354 | + | 0.999891i | \(0.495309\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −72835.2 | −1.09344 | ||||||||
\(86\) | 16392.3 | 0.238997 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −76359.5 | −1.05113 | ||||||||
\(89\) | 70380.3 | 0.941838 | 0.470919 | − | 0.882176i | \(-0.343922\pi\) | ||||
0.470919 | + | 0.882176i | \(0.343922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −54236.8 | −0.686579 | ||||||||
\(92\) | −130705. | −1.60999 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −19546.9 | −0.228170 | ||||||||
\(95\) | 24742.5 | 0.281277 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −88842.1 | −0.958714 | −0.479357 | − | 0.877620i | \(-0.659130\pi\) | ||||
−0.479357 | + | 0.877620i | \(0.659130\pi\) | |||||||
\(98\) | −11038.6 | −0.116104 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −78946.8 | −0.789468 | ||||||||
\(101\) | −179221. | −1.74818 | −0.874090 | − | 0.485763i | \(-0.838542\pi\) | ||||
−0.874090 | + | 0.485763i | \(0.838542\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 123443. | 1.14650 | 0.573248 | − | 0.819382i | \(-0.305683\pi\) | ||||
0.573248 | + | 0.819382i | \(0.305683\pi\) | |||||||
\(104\) | 56262.1 | 0.510074 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −221496. | −1.91471 | ||||||||
\(107\) | −98991.7 | −0.835871 | −0.417936 | − | 0.908477i | \(-0.637246\pi\) | ||||
−0.417936 | + | 0.908477i | \(0.637246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 46356.0 | 0.373715 | 0.186857 | − | 0.982387i | \(-0.440170\pi\) | ||||
0.186857 | + | 0.982387i | \(0.440170\pi\) | |||||||
\(110\) | −197876. | −1.55923 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 42894.2 | 0.323113 | ||||||||
\(113\) | −185076. | −1.36350 | −0.681750 | − | 0.731586i | \(-0.738781\pi\) | ||||
−0.681750 | + | 0.731586i | \(0.738781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −106101. | −0.748123 | ||||||||
\(116\) | 67855.3 | 0.468208 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 379054. | 2.50608 | ||||||||
\(119\) | 240211. | 1.55498 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 187142. | 1.16201 | ||||||||
\(122\) | −186377. | −1.13369 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 205950. | 1.20284 | ||||||||
\(125\) | −182289. | −1.04348 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −237332. | −1.30571 | −0.652856 | − | 0.757482i | \(-0.726429\pi\) | ||||
−0.652856 | + | 0.757482i | \(0.726429\pi\) | |||||||
\(128\) | −237451. | −1.28100 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 145796. | 0.756636 | ||||||||
\(131\) | 283496. | 1.44334 | 0.721671 | − | 0.692236i | \(-0.243374\pi\) | ||||
0.721671 | + | 0.692236i | \(0.243374\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −81600.9 | −0.400005 | ||||||||
\(134\) | −224049. | −1.07791 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −249181. | −1.15523 | ||||||||
\(137\) | −330992. | −1.50666 | −0.753331 | − | 0.657642i | \(-0.771554\pi\) | ||||
−0.753331 | + | 0.657642i | \(0.771554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 105975. | 0.465230 | 0.232615 | − | 0.972569i | \(-0.425272\pi\) | ||||
0.232615 | + | 0.972569i | \(0.425272\pi\) | |||||||
\(140\) | −219870. | −0.948081 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −426277. | −1.77407 | ||||||||
\(143\) | −256551. | −1.04914 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 55082.0 | 0.217565 | ||||||||
\(146\) | 521300. | 2.02398 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 174881. | 0.656279 | ||||||||
\(149\) | 196700. | 0.725836 | 0.362918 | − | 0.931821i | \(-0.381780\pi\) | ||||
0.362918 | + | 0.931821i | \(0.381780\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −412513. | −1.47230 | −0.736148 | − | 0.676820i | \(-0.763357\pi\) | ||||
−0.736148 | + | 0.676820i | \(0.763357\pi\) | |||||||
\(152\) | 84648.0 | 0.297172 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 652594. | 2.21739 | ||||||||
\(155\) | 167181. | 0.558931 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 410971. | 1.33064 | 0.665322 | − | 0.746557i | \(-0.268294\pi\) | ||||
0.665322 | + | 0.746557i | \(0.268294\pi\) | |||||||
\(158\) | 821871. | 2.61915 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −271938. | −0.839790 | ||||||||
\(161\) | 349920. | 1.06391 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −82488.7 | −0.243179 | −0.121589 | − | 0.992580i | \(-0.538799\pi\) | ||||
−0.121589 | + | 0.992580i | \(0.538799\pi\) | |||||||
\(164\) | −91928.2 | −0.266894 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16397.9 | 0.0461868 | ||||||||
\(167\) | 380336. | 1.05530 | 0.527650 | − | 0.849462i | \(-0.323073\pi\) | ||||
0.527650 | + | 0.849462i | \(0.323073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −182265. | −0.490892 | ||||||||
\(170\) | −645718. | −1.71365 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 86157.1 | 0.222060 | ||||||||
\(173\) | −91482.2 | −0.232392 | −0.116196 | − | 0.993226i | \(-0.537070\pi\) | ||||
−0.116196 | + | 0.993226i | \(0.537070\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 211354. | 0.521694 | ||||||||
\(176\) | 202898. | 0.493738 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 623955. | 1.47606 | ||||||||
\(179\) | 607572. | 1.41731 | 0.708656 | − | 0.705554i | \(-0.249302\pi\) | ||||
0.708656 | + | 0.705554i | \(0.249302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 351519. | 0.797540 | 0.398770 | − | 0.917051i | \(-0.369437\pi\) | ||||
0.398770 | + | 0.917051i | \(0.369437\pi\) | |||||||
\(182\) | −480835. | −1.07601 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −362987. | −0.790398 | ||||||||
\(185\) | 141961. | 0.304958 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.13624e6 | 2.37611 | ||||||||
\(188\) | −102738. | −0.212000 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 219354. | 0.440820 | ||||||||
\(191\) | 123308. | 0.244573 | 0.122286 | − | 0.992495i | \(-0.460977\pi\) | ||||
0.122286 | + | 0.992495i | \(0.460977\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −163481. | −0.315917 | −0.157959 | − | 0.987446i | \(-0.550491\pi\) | ||||
−0.157959 | + | 0.987446i | \(0.550491\pi\) | |||||||
\(194\) | −787627. | −1.50251 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −58018.3 | −0.107876 | ||||||||
\(197\) | −581124. | −1.06685 | −0.533425 | − | 0.845848i | \(-0.679095\pi\) | ||||
−0.533425 | + | 0.845848i | \(0.679095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 351526. | 0.629253 | 0.314627 | − | 0.949216i | \(-0.398121\pi\) | ||||
0.314627 | + | 0.949216i | \(0.398121\pi\) | |||||||
\(200\) | −219247. | −0.387577 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.58888e6 | −2.73976 | ||||||||
\(203\) | −181660. | −0.309400 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −74623.4 | −0.124020 | ||||||||
\(206\) | 1.09438e6 | 1.79680 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −149497. | −0.239592 | ||||||||
\(209\) | −385988. | −0.611235 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 327480. | 0.506383 | 0.253192 | − | 0.967416i | \(-0.418520\pi\) | ||||
0.253192 | + | 0.967416i | \(0.418520\pi\) | |||||||
\(212\) | −1.16418e6 | −1.77901 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −877608. | −1.30998 | ||||||||
\(215\) | 69938.6 | 0.103186 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −551364. | −0.794857 | ||||||||
\(218\) | 410968. | 0.585689 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.04003e6 | −1.44873 | ||||||||
\(221\) | −837191. | −1.15304 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 619602. | 0.834355 | 0.417177 | − | 0.908825i | \(-0.363019\pi\) | ||||
0.417177 | + | 0.908825i | \(0.363019\pi\) | |||||||
\(224\) | 896853. | 1.19427 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.64079e6 | −2.13689 | ||||||||
\(227\) | 757446. | 0.975635 | 0.487817 | − | 0.872946i | \(-0.337793\pi\) | ||||
0.487817 | + | 0.872946i | \(0.337793\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.21739e6 | 1.53405 | 0.767025 | − | 0.641617i | \(-0.221736\pi\) | ||||
0.767025 | + | 0.641617i | \(0.221736\pi\) | |||||||
\(230\) | −940632. | −1.17247 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 188444. | 0.229860 | ||||||||
\(233\) | −379715. | −0.458213 | −0.229107 | − | 0.973401i | \(-0.573580\pi\) | ||||
−0.229107 | + | 0.973401i | \(0.573580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −83398.2 | −0.0985115 | ||||||||
\(236\) | 1.99229e6 | 2.32848 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.12958e6 | 2.43698 | ||||||||
\(239\) | −281756. | −0.319064 | −0.159532 | − | 0.987193i | \(-0.550999\pi\) | ||||
−0.159532 | + | 0.987193i | \(0.550999\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.12524e6 | −1.24796 | −0.623981 | − | 0.781439i | \(-0.714486\pi\) | ||||
−0.623981 | + | 0.781439i | \(0.714486\pi\) | |||||||
\(242\) | 1.65911e6 | 1.82111 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −979590. | −1.05334 | ||||||||
\(245\) | −47096.8 | −0.0501275 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 284398. | 0.296609 | ||||||||
\(248\) | 571953. | 0.590515 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.61608e6 | −1.63536 | ||||||||
\(251\) | 675567. | 0.676837 | 0.338419 | − | 0.940996i | \(-0.390108\pi\) | ||||
0.338419 | + | 0.940996i | \(0.390108\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.65519e6 | 1.62572 | ||||||||
\(254\) | −2.10406e6 | −2.04632 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −417633. | −0.398286 | ||||||||
\(257\) | −1.85623e6 | −1.75306 | −0.876532 | − | 0.481343i | \(-0.840149\pi\) | ||||
−0.876532 | + | 0.481343i | \(0.840149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −468188. | −0.433681 | ||||||||
\(260\) | 766298. | 0.703014 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.51333e6 | 2.26202 | ||||||||
\(263\) | 1.54160e6 | 1.37430 | 0.687149 | − | 0.726516i | \(-0.258862\pi\) | ||||
0.687149 | + | 0.726516i | \(0.258862\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −945029. | −0.826667 | ||||||||
\(266\) | −723430. | −0.626892 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.17759e6 | −1.00152 | ||||||||
\(269\) | −1.16775e6 | −0.983945 | −0.491973 | − | 0.870611i | \(-0.663724\pi\) | ||||
−0.491973 | + | 0.870611i | \(0.663724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.20256e6 | −0.994684 | −0.497342 | − | 0.867555i | \(-0.665691\pi\) | ||||
−0.497342 | + | 0.867555i | \(0.665691\pi\) | |||||||
\(272\) | 662109. | 0.542634 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.93440e6 | −2.36125 | ||||||||
\(275\) | 999748. | 0.797184 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −504463. | −0.395030 | −0.197515 | − | 0.980300i | \(-0.563287\pi\) | ||||
−0.197515 | + | 0.980300i | \(0.563287\pi\) | |||||||
\(278\) | 939521. | 0.729112 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −610610. | −0.465446 | ||||||||
\(281\) | −1.52712e6 | −1.15374 | −0.576870 | − | 0.816836i | \(-0.695726\pi\) | ||||
−0.576870 | + | 0.816836i | \(0.695726\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.81916e6 | 1.35022 | 0.675110 | − | 0.737717i | \(-0.264096\pi\) | ||||
0.675110 | + | 0.737717i | \(0.264096\pi\) | |||||||
\(284\) | −2.24049e6 | −1.64834 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.27444e6 | −1.64422 | ||||||||
\(287\) | 246108. | 0.176369 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.28799e6 | 1.61143 | ||||||||
\(290\) | 488328. | 0.340970 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.73993e6 | 1.88054 | ||||||||
\(293\) | 2.35975e6 | 1.60582 | 0.802911 | − | 0.596099i | \(-0.203283\pi\) | ||||
0.802911 | + | 0.596099i | \(0.203283\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.61726e6 | 1.08199 | ||||||||
\(296\) | 485671. | 0.322190 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.74384e6 | 1.13754 | ||||||||
\(299\) | −1.21955e6 | −0.788901 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −230658. | −0.146741 | ||||||||
\(302\) | −3.65712e6 | −2.30740 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −224922. | −0.139588 | ||||||||
\(305\) | −795189. | −0.489464 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.59790e6 | −1.57317 | −0.786587 | − | 0.617480i | \(-0.788154\pi\) | ||||
−0.786587 | + | 0.617480i | \(0.788154\pi\) | |||||||
\(308\) | 3.43001e6 | 2.06024 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.48214e6 | 0.875962 | ||||||||
\(311\) | 2.21471e6 | 1.29842 | 0.649212 | − | 0.760607i | \(-0.275099\pi\) | ||||
0.649212 | + | 0.760607i | \(0.275099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.43630e6 | −1.40563 | −0.702813 | − | 0.711374i | \(-0.748073\pi\) | ||||
−0.702813 | + | 0.711374i | \(0.748073\pi\) | |||||||
\(314\) | 3.64345e6 | 2.08540 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.31972e6 | 2.43354 | ||||||||
\(317\) | 2.59108e6 | 1.44821 | 0.724106 | − | 0.689689i | \(-0.242253\pi\) | ||||
0.724106 | + | 0.689689i | \(0.242253\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −859290. | −0.472784 | ||||||||
\(320\) | −1.99467e6 | −1.08892 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.10220e6 | 1.66737 | ||||||||
\(323\) | −1.25958e6 | −0.671767 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −736620. | −0.386843 | ||||||||
\(326\) | −731301. | −0.381112 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −255298. | −0.131028 | ||||||||
\(329\) | 275047. | 0.140093 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.49362e6 | −1.25101 | −0.625503 | − | 0.780221i | \(-0.715106\pi\) | ||||
−0.625503 | + | 0.780221i | \(0.715106\pi\) | |||||||
\(332\) | 86186.7 | 0.0429136 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.37186e6 | 1.65388 | ||||||||
\(335\) | −955921. | −0.465383 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −159199. | −0.0763600 | −0.0381800 | − | 0.999271i | \(-0.512156\pi\) | ||||
−0.0381800 | + | 0.999271i | \(0.512156\pi\) | |||||||
\(338\) | −1.61586e6 | −0.769331 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.39387e6 | −1.59220 | ||||||||
\(341\) | −2.60806e6 | −1.21460 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.25195e6 | 1.03353 | ||||||||
\(344\) | 239271. | 0.109017 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −811033. | −0.364207 | ||||||||
\(347\) | −4.35264e6 | −1.94057 | −0.970285 | − | 0.241966i | \(-0.922208\pi\) | ||||
−0.970285 | + | 0.241966i | \(0.922208\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −502730. | −0.220938 | −0.110469 | − | 0.993880i | \(-0.535235\pi\) | ||||
−0.110469 | + | 0.993880i | \(0.535235\pi\) | |||||||
\(350\) | 1.87376e6 | 0.817604 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.24229e6 | 1.82492 | ||||||||
\(353\) | 990932. | 0.423260 | 0.211630 | − | 0.977350i | \(-0.432123\pi\) | ||||
0.211630 | + | 0.977350i | \(0.432123\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.81874e6 | −0.765948 | ||||||||
\(356\) | 3.27948e6 | 1.37145 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.38641e6 | 2.22122 | ||||||||
\(359\) | 1.78805e6 | 0.732223 | 0.366112 | − | 0.930571i | \(-0.380689\pi\) | ||||
0.366112 | + | 0.930571i | \(0.380689\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.04821e6 | −0.827194 | ||||||||
\(362\) | 3.11638e6 | 1.24991 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.52725e6 | −0.999758 | ||||||||
\(365\) | 2.22416e6 | 0.873844 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −68021.3 | −0.0263621 | −0.0131810 | − | 0.999913i | \(-0.504196\pi\) | ||||
−0.0131810 | + | 0.999913i | \(0.504196\pi\) | |||||||
\(368\) | 964507. | 0.371267 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.25855e6 | 0.477933 | ||||||||
\(371\) | 3.11671e6 | 1.17560 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −949477. | −0.353356 | −0.176678 | − | 0.984269i | \(-0.556535\pi\) | ||||
−0.176678 | + | 0.984269i | \(0.556535\pi\) | |||||||
\(374\) | 1.00733e7 | 3.72387 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −285318. | −0.104078 | ||||||||
\(377\) | 633130. | 0.229424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.53069e6 | 0.904982 | 0.452491 | − | 0.891769i | \(-0.350535\pi\) | ||||
0.452491 | + | 0.891769i | \(0.350535\pi\) | |||||||
\(380\) | 1.15292e6 | 0.409580 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.09318e6 | 0.383297 | ||||||||
\(383\) | −500631. | −0.174390 | −0.0871948 | − | 0.996191i | \(-0.527790\pi\) | ||||
−0.0871948 | + | 0.996191i | \(0.527790\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.78434e6 | 0.957348 | ||||||||
\(386\) | −1.44933e6 | −0.495108 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.13974e6 | −1.39603 | ||||||||
\(389\) | 4.08546e6 | 1.36889 | 0.684443 | − | 0.729066i | \(-0.260045\pi\) | ||||
0.684443 | + | 0.729066i | \(0.260045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.40130e6 | 1.78672 | ||||||||
\(392\) | −161125. | −0.0529601 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.15194e6 | −1.67198 | ||||||||
\(395\) | 3.50657e6 | 1.13081 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 953651. | 0.303678 | 0.151839 | − | 0.988405i | \(-0.451480\pi\) | ||||
0.151839 | + | 0.988405i | \(0.451480\pi\) | |||||||
\(398\) | 3.11645e6 | 0.986171 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 582570. | 0.182053 | ||||||||
\(401\) | −4.81115e6 | −1.49413 | −0.747064 | − | 0.664752i | \(-0.768537\pi\) | ||||
−0.747064 | + | 0.664752i | \(0.768537\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.92163e6 | 0.589397 | ||||||||
\(404\) | −8.35110e6 | −2.54560 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.61051e6 | −0.484894 | ||||||||
\(407\) | −2.21462e6 | −0.662694 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.42551e6 | −0.421370 | −0.210685 | − | 0.977554i | \(-0.567569\pi\) | ||||
−0.210685 | + | 0.977554i | \(0.567569\pi\) | |||||||
\(410\) | −661572. | −0.194365 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.75201e6 | 1.66946 | ||||||||
\(413\) | −5.33372e6 | −1.53870 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 69962.7 | 0.0199410 | ||||||||
\(416\) | −3.12575e6 | −0.885565 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.42197e6 | −0.957933 | ||||||||
\(419\) | −2.91631e6 | −0.811520 | −0.405760 | − | 0.913980i | \(-0.632993\pi\) | ||||
−0.405760 | + | 0.913980i | \(0.632993\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.91223e6 | 1.90070 | 0.950349 | − | 0.311186i | \(-0.100726\pi\) | ||||
0.950349 | + | 0.311186i | \(0.100726\pi\) | |||||||
\(422\) | 2.90327e6 | 0.793608 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.23309e6 | −0.873380 | ||||||||
\(425\) | 3.26243e6 | 0.876131 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.62254e6 | 0.696068 | ||||||||
\(428\) | −4.61268e6 | −1.21715 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 620039. | 0.161714 | ||||||||
\(431\) | −2.58575e6 | −0.670493 | −0.335246 | − | 0.942131i | \(-0.608820\pi\) | ||||
−0.335246 | + | 0.942131i | \(0.608820\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.71200e6 | −0.951455 | −0.475727 | − | 0.879593i | \(-0.657815\pi\) | ||||
−0.475727 | + | 0.879593i | \(0.657815\pi\) | |||||||
\(434\) | −4.88810e6 | −1.24571 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.16003e6 | 0.544182 | ||||||||
\(437\) | −1.83485e6 | −0.459619 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −415772. | −0.102966 | −0.0514830 | − | 0.998674i | \(-0.516395\pi\) | ||||
−0.0514830 | + | 0.998674i | \(0.516395\pi\) | |||||||
\(440\) | −2.88831e6 | −0.711233 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.42209e6 | −1.80705 | ||||||||
\(443\) | 602736. | 0.145921 | 0.0729605 | − | 0.997335i | \(-0.476755\pi\) | ||||
0.0729605 | + | 0.997335i | \(0.476755\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.66214e6 | 0.637282 | ||||||||
\(446\) | 5.49307e6 | 1.30761 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.57841e6 | 1.54855 | ||||||||
\(449\) | −1.84907e6 | −0.432849 | −0.216424 | − | 0.976299i | \(-0.569440\pi\) | ||||
−0.216424 | + | 0.976299i | \(0.569440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.16414e6 | 0.269503 | ||||||||
\(452\) | −8.62393e6 | −1.98545 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.71512e6 | 1.52902 | ||||||||
\(455\) | −2.05151e6 | −0.464564 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.35472e6 | −1.64731 | −0.823655 | − | 0.567091i | \(-0.808069\pi\) | ||||
−0.823655 | + | 0.567091i | \(0.808069\pi\) | |||||||
\(458\) | 1.07927e7 | 2.40418 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.94392e6 | −1.08937 | ||||||||
\(461\) | 3.51032e6 | 0.769298 | 0.384649 | − | 0.923063i | \(-0.374322\pi\) | ||||
0.384649 | + | 0.923063i | \(0.374322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.86607e6 | −1.48852 | −0.744262 | − | 0.667888i | \(-0.767199\pi\) | ||||
−0.744262 | + | 0.667888i | \(0.767199\pi\) | |||||||
\(464\) | −500723. | −0.107970 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.36635e6 | −0.718116 | ||||||||
\(467\) | −5.66490e6 | −1.20199 | −0.600993 | − | 0.799254i | \(-0.705228\pi\) | ||||
−0.600993 | + | 0.799254i | \(0.705228\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.15263e6 | 0.661821 | ||||||||
\(470\) | −739364. | −0.154388 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.53289e6 | 1.14313 | ||||||||
\(473\) | −1.09106e6 | −0.224230 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.10827e6 | −0.225377 | ||||||||
\(476\) | 1.11930e7 | 2.26427 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.49790e6 | −0.500041 | ||||||||
\(479\) | −4.55961e6 | −0.908006 | −0.454003 | − | 0.891000i | \(-0.650004\pi\) | ||||
−0.454003 | + | 0.891000i | \(0.650004\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.63174e6 | 0.321580 | ||||||||
\(482\) | −9.97576e6 | −1.95582 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.72019e6 | 1.69205 | ||||||||
\(485\) | −3.36046e6 | −0.648701 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.17550e6 | −1.75310 | −0.876552 | − | 0.481308i | \(-0.840162\pi\) | ||||
−0.876552 | + | 0.481308i | \(0.840162\pi\) | |||||||
\(488\) | −2.72047e6 | −0.517123 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −417535. | −0.0785603 | ||||||||
\(491\) | −3.41449e6 | −0.639179 | −0.319589 | − | 0.947556i | \(-0.603545\pi\) | ||||
−0.319589 | + | 0.947556i | \(0.603545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.80408e6 | −0.519605 | ||||||||
\(494\) | 2.52132e6 | 0.464848 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.51976e6 | −0.277377 | ||||||||
\(497\) | 5.99820e6 | 1.08926 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.99364e6 | −0.358423 | −0.179211 | − | 0.983811i | \(-0.557355\pi\) | ||||
−0.179211 | + | 0.983811i | \(0.557355\pi\) | |||||||
\(500\) | −8.49405e6 | −1.51946 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.98922e6 | 1.06074 | ||||||||
\(503\) | −9.15685e6 | −1.61371 | −0.806856 | − | 0.590748i | \(-0.798833\pi\) | ||||
−0.806856 | + | 0.590748i | \(0.798833\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.77907e6 | −1.18288 | ||||||||
\(506\) | 1.46740e7 | 2.54785 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.10589e7 | −1.90130 | ||||||||
\(509\) | −6.56697e6 | −1.12349 | −0.561746 | − | 0.827309i | \(-0.689870\pi\) | ||||
−0.561746 | + | 0.827309i | \(0.689870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.33529e6 | −1.24270 | ||||||||
\(512\) | 3.89593e6 | 0.656805 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.64563e7 | −2.74742 | ||||||||
\(515\) | 4.66924e6 | 0.775761 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.30103e6 | 0.214072 | ||||||||
\(518\) | −4.15070e6 | −0.679669 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.12812e6 | 0.345134 | ||||||||
\(521\) | −6.45805e6 | −1.04234 | −0.521168 | − | 0.853454i | \(-0.674503\pi\) | ||||
−0.521168 | + | 0.853454i | \(0.674503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 184405. | 0.0294794 | 0.0147397 | − | 0.999891i | \(-0.495308\pi\) | ||||
0.0147397 | + | 0.999891i | \(0.495308\pi\) | |||||||
\(524\) | 1.32100e7 | 2.10171 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.36670e7 | 2.15381 | ||||||||
\(527\) | −8.51076e6 | −1.33488 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.43185e6 | 0.222463 | ||||||||
\(530\) | −8.37813e6 | −1.29556 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.80232e6 | −0.582465 | ||||||||
\(533\) | −857745. | −0.130780 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.74437e6 | −0.565581 | ||||||||
\(536\) | −3.27035e6 | −0.491680 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.03527e7 | −1.54205 | ||||||||
\(539\) | 734719. | 0.108931 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.10369e6 | −1.04350 | −0.521748 | − | 0.853100i | \(-0.674720\pi\) | ||||
−0.521748 | + | 0.853100i | \(0.674720\pi\) | |||||||
\(542\) | −1.06613e7 | −1.55888 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.38437e7 | 2.00565 | ||||||||
\(545\) | 1.75342e6 | 0.252869 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.75210e6 | −1.39357 | −0.696787 | − | 0.717279i | \(-0.745388\pi\) | ||||
−0.696787 | + | 0.717279i | \(0.745388\pi\) | |||||||
\(548\) | −1.54231e7 | −2.19392 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.86324e6 | 1.24935 | ||||||||
\(551\) | 952562. | 0.133664 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.15647e7 | −1.60813 | ||||||||
\(554\) | −4.47230e6 | −0.619094 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.93809e6 | 0.677441 | ||||||||
\(557\) | 2.28586e6 | 0.312185 | 0.156092 | − | 0.987742i | \(-0.450110\pi\) | ||||
0.156092 | + | 0.987742i | \(0.450110\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 803896. | 0.108810 | ||||||||
\(560\) | 1.62248e6 | 0.218630 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.35386e7 | −1.80815 | ||||||||
\(563\) | −2.31099e6 | −0.307275 | −0.153638 | − | 0.988127i | \(-0.549099\pi\) | ||||
−0.153638 | + | 0.988127i | \(0.549099\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.00054e6 | −0.922593 | ||||||||
\(566\) | 1.61277e7 | 2.11608 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.22218e6 | −0.809230 | ||||||||
\(569\) | −1.17226e7 | −1.51790 | −0.758949 | − | 0.651151i | \(-0.774287\pi\) | ||||
−0.758949 | + | 0.651151i | \(0.774287\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.10057e6 | −0.654679 | −0.327340 | − | 0.944907i | \(-0.606152\pi\) | ||||
−0.327340 | + | 0.944907i | \(0.606152\pi\) | |||||||
\(572\) | −1.19544e7 | −1.52770 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.18186e6 | 0.276406 | ||||||||
\(575\) | 4.75245e6 | 0.599443 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 599429. | 0.0749546 | 0.0374773 | − | 0.999297i | \(-0.488068\pi\) | ||||
0.0374773 | + | 0.999297i | \(0.488068\pi\) | |||||||
\(578\) | 2.02841e7 | 2.52544 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.56663e6 | 0.316806 | ||||||||
\(581\) | −230737. | −0.0283581 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.47426e7 | 1.79640 | ||||||||
\(584\) | 7.60920e6 | 0.923224 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.09203e7 | 2.51666 | ||||||||
\(587\) | −4.32755e6 | −0.518379 | −0.259189 | − | 0.965826i | \(-0.583455\pi\) | ||||
−0.259189 | + | 0.965826i | \(0.583455\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.89115e6 | 0.343386 | ||||||||
\(590\) | 1.43377e7 | 1.69571 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.29050e6 | −0.151340 | ||||||||
\(593\) | 1.59099e7 | 1.85794 | 0.928968 | − | 0.370160i | \(-0.120697\pi\) | ||||
0.928968 | + | 0.370160i | \(0.120697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.08599e6 | 1.05216 | ||||||||
\(596\) | 9.16555e6 | 1.05692 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.08119e7 | −1.23637 | ||||||||
\(599\) | −73202.1 | −0.00833598 | −0.00416799 | − | 0.999991i | \(-0.501327\pi\) | ||||
−0.00416799 | + | 0.999991i | \(0.501327\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.77328e6 | −0.426121 | −0.213060 | − | 0.977039i | \(-0.568343\pi\) | ||||
−0.213060 | + | 0.977039i | \(0.568343\pi\) | |||||||
\(602\) | −2.04489e6 | −0.229974 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.92217e7 | −2.14387 | ||||||||
\(605\) | 7.07868e6 | 0.786256 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.39314e6 | 0.373792 | 0.186896 | − | 0.982380i | \(-0.440157\pi\) | ||||
0.186896 | + | 0.982380i | \(0.440157\pi\) | |||||||
\(608\) | −4.70277e6 | −0.515935 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.04973e6 | −0.767093 | ||||||||
\(611\) | −958605. | −0.103881 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.93491e6 | 0.637915 | 0.318957 | − | 0.947769i | \(-0.396667\pi\) | ||||
0.318957 | + | 0.947769i | \(0.396667\pi\) | |||||||
\(614\) | −2.30316e7 | −2.46549 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.52564e6 | 1.01145 | ||||||||
\(617\) | 1.07871e7 | 1.14076 | 0.570379 | − | 0.821382i | \(-0.306796\pi\) | ||||
0.570379 | + | 0.821382i | \(0.306796\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.97743e6 | 1.04663 | 0.523313 | − | 0.852140i | \(-0.324696\pi\) | ||||
0.523313 | + | 0.852140i | \(0.324696\pi\) | |||||||
\(620\) | 7.79008e6 | 0.813884 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.96345e7 | 2.03490 | ||||||||
\(623\) | −8.77976e6 | −0.906280 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.60054e6 | −0.163895 | ||||||||
\(626\) | −2.15990e7 | −2.20291 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.91498e7 | 1.93761 | ||||||||
\(629\) | −7.22687e6 | −0.728322 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.42994e6 | −0.342936 | −0.171468 | − | 0.985190i | \(-0.554851\pi\) | ||||
−0.171468 | + | 0.985190i | \(0.554851\pi\) | |||||||
\(632\) | 1.19965e7 | 1.19471 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.29711e7 | 2.26965 | ||||||||
\(635\) | −8.97711e6 | −0.883492 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −541345. | −0.0528598 | ||||||||
\(638\) | −7.61801e6 | −0.740952 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.98163e6 | −0.866772 | ||||||||
\(641\) | 1.41725e7 | 1.36239 | 0.681193 | − | 0.732104i | \(-0.261462\pi\) | ||||
0.681193 | + | 0.732104i | \(0.261462\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.26802e6 | 0.407098 | 0.203549 | − | 0.979065i | \(-0.434752\pi\) | ||||
0.203549 | + | 0.979065i | \(0.434752\pi\) | |||||||
\(644\) | 1.63051e7 | 1.54920 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.11667e7 | −1.05280 | ||||||||
\(647\) | −1.26038e7 | −1.18370 | −0.591849 | − | 0.806049i | \(-0.701602\pi\) | ||||
−0.591849 | + | 0.806049i | \(0.701602\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.52295e7 | −2.35124 | ||||||||
\(650\) | −6.53048e6 | −0.606264 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.84369e6 | −0.354103 | ||||||||
\(653\) | −1.67724e7 | −1.53926 | −0.769631 | − | 0.638489i | \(-0.779560\pi\) | ||||
−0.769631 | + | 0.638489i | \(0.779560\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.07233e7 | 0.976618 | ||||||||
\(656\) | 678364. | 0.0615465 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.43842e6 | 0.219556 | ||||||||
\(659\) | 1.72113e7 | 1.54383 | 0.771915 | − | 0.635725i | \(-0.219299\pi\) | ||||
0.771915 | + | 0.635725i | \(0.219299\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.67723e6 | 0.505397 | 0.252699 | − | 0.967545i | \(-0.418682\pi\) | ||||
0.252699 | + | 0.967545i | \(0.418682\pi\) | |||||||
\(662\) | −2.21071e7 | −1.96059 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 239353. | 0.0210678 | ||||||||
\(665\) | −3.08656e6 | −0.270658 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.08476e6 | −0.355510 | ||||||||
\(668\) | 1.77223e7 | 1.53667 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.47469e6 | −0.729352 | ||||||||
\(671\) | 1.24051e7 | 1.06364 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.92989e6 | 0.419565 | 0.209783 | − | 0.977748i | \(-0.432724\pi\) | ||||
0.209783 | + | 0.977748i | \(0.432724\pi\) | |||||||
\(674\) | −1.41137e6 | −0.119672 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.49292e6 | −0.714809 | ||||||||
\(677\) | 1.25498e7 | 1.05236 | 0.526180 | − | 0.850373i | \(-0.323624\pi\) | ||||
0.526180 | + | 0.850373i | \(0.323624\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.10828e7 | 0.922519 | ||||||||
\(680\) | −9.42528e6 | −0.781668 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.31217e7 | −1.90352 | ||||||||
\(683\) | 7.08503e6 | 0.581152 | 0.290576 | − | 0.956852i | \(-0.406153\pi\) | ||||
0.290576 | + | 0.956852i | \(0.406153\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.25198e7 | −1.01946 | ||||||||
\(686\) | 1.99646e7 | 1.61976 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −635777. | −0.0512075 | ||||||||
\(689\) | −1.08625e7 | −0.871726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.40053e6 | −0.748958 | −0.374479 | − | 0.927235i | \(-0.622178\pi\) | ||||
−0.374479 | + | 0.927235i | \(0.622178\pi\) | |||||||
\(692\) | −4.26276e6 | −0.338396 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.85882e7 | −3.04128 | ||||||||
\(695\) | 4.00853e6 | 0.314791 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.79888e6 | 0.296192 | ||||||||
\(698\) | −4.45694e6 | −0.346256 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.84839e6 | 0.759662 | ||||||||
\(701\) | −2.14131e7 | −1.64583 | −0.822914 | − | 0.568167i | \(-0.807653\pi\) | ||||
−0.822914 | + | 0.568167i | \(0.807653\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45501e6 | 0.187355 | ||||||||
\(704\) | 3.11172e7 | 2.36629 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.78508e6 | 0.663337 | ||||||||
\(707\) | 2.23574e7 | 1.68218 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.70494e7 | 1.27377 | 0.636887 | − | 0.770957i | \(-0.280222\pi\) | ||||
0.636887 | + | 0.770957i | \(0.280222\pi\) | |||||||
\(710\) | −1.61240e7 | −1.20040 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.10761e6 | 0.673293 | ||||||||
\(713\) | −1.23978e7 | −0.913316 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.70406e6 | −0.709886 | ||||||||
\(716\) | 2.83108e7 | 2.06381 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.58519e7 | 1.14755 | ||||||||
\(719\) | 1.59376e7 | 1.14974 | 0.574872 | − | 0.818243i | \(-0.305052\pi\) | ||||
0.574872 | + | 0.818243i | \(0.305052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.53991e7 | −1.10321 | ||||||||
\(722\) | −1.81584e7 | −1.29639 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.63796e7 | 1.16133 | ||||||||
\(725\) | −2.46723e6 | −0.174327 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.26202e6 | 0.579763 | 0.289881 | − | 0.957063i | \(-0.406384\pi\) | ||||
0.289881 | + | 0.957063i | \(0.406384\pi\) | |||||||
\(728\) | −7.01855e6 | −0.490816 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.97182e7 | 1.36950 | ||||||||
\(731\) | −3.56039e6 | −0.246436 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.20168e6 | 0.426334 | 0.213167 | − | 0.977016i | \(-0.431622\pi\) | ||||
0.213167 | + | 0.977016i | \(0.431622\pi\) | |||||||
\(734\) | −603041. | −0.0413149 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.01664e7 | 1.37225 | ||||||||
\(737\) | 1.49126e7 | 1.01131 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.19003e7 | −0.801578 | −0.400789 | − | 0.916170i | \(-0.631264\pi\) | ||||
−0.400789 | + | 0.916170i | \(0.631264\pi\) | |||||||
\(740\) | 6.61490e6 | 0.444062 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.76311e7 | 1.84242 | ||||||||
\(743\) | −7.41722e6 | −0.492912 | −0.246456 | − | 0.969154i | \(-0.579266\pi\) | ||||
−0.246456 | + | 0.969154i | \(0.579266\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.44020e6 | 0.491127 | ||||||||
\(746\) | −8.41756e6 | −0.553782 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.29451e7 | 3.45996 | ||||||||
\(749\) | 1.23489e7 | 0.804314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.46691e7 | 0.949084 | 0.474542 | − | 0.880233i | \(-0.342614\pi\) | ||||
0.474542 | + | 0.880233i | \(0.342614\pi\) | |||||||
\(752\) | 758131. | 0.0488877 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.61299e6 | 0.359556 | ||||||||
\(755\) | −1.56033e7 | −0.996209 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.41775e6 | 0.153346 | 0.0766729 | − | 0.997056i | \(-0.475570\pi\) | ||||
0.0766729 | + | 0.997056i | \(0.475570\pi\) | |||||||
\(758\) | 2.24357e7 | 1.41830 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.20182e6 | 0.201077 | ||||||||
\(761\) | −2.32422e7 | −1.45484 | −0.727422 | − | 0.686191i | \(-0.759282\pi\) | ||||
−0.727422 | + | 0.686191i | \(0.759282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.78279e6 | −0.359605 | ||||||||
\(764\) | 5.74574e6 | 0.356133 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.43833e6 | −0.273305 | ||||||||
\(767\) | 1.85893e7 | 1.14097 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.55432e7 | −1.55761 | −0.778806 | − | 0.627265i | \(-0.784174\pi\) | ||||
−0.778806 | + | 0.627265i | \(0.784174\pi\) | |||||||
\(770\) | 2.46844e7 | 1.50036 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.61765e6 | −0.460021 | ||||||||
\(773\) | −1.72159e7 | −1.03629 | −0.518146 | − | 0.855292i | \(-0.673378\pi\) | ||||
−0.518146 | + | 0.855292i | \(0.673378\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.48838e6 | −0.447851 | ||||||||
\(776\) | −1.14967e7 | −0.685358 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.62196e7 | 2.14533 | ||||||||
\(779\) | −1.29050e6 | −0.0761930 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.83727e7 | 1.66446 | ||||||||
\(782\) | 4.78851e7 | 2.80016 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 428134. | 0.0248765 | ||||||||
\(785\) | 1.55450e7 | 0.900362 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.48812e7 | −0.856449 | −0.428225 | − | 0.903672i | \(-0.640861\pi\) | ||||
−0.428225 | + | 0.903672i | \(0.640861\pi\) | |||||||
\(788\) | −2.70784e7 | −1.55349 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.10874e7 | 1.77221 | ||||||||
\(791\) | 2.30878e7 | 1.31202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.14016e6 | −0.516144 | ||||||||
\(794\) | 8.45456e6 | 0.475927 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.63799e7 | 0.916283 | ||||||||
\(797\) | −5.81135e6 | −0.324064 | −0.162032 | − | 0.986785i | \(-0.551805\pi\) | ||||
−0.162032 | + | 0.986785i | \(0.551805\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.24559e6 | 0.235272 | ||||||||
\(800\) | 1.21807e7 | 0.672893 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.26531e7 | −2.34161 | ||||||||
\(803\) | −3.46973e7 | −1.89892 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.32358e7 | 0.719878 | ||||||||
\(806\) | 1.70362e7 | 0.923708 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.31922e7 | −1.24972 | ||||||||
\(809\) | 2.41530e7 | 1.29748 | 0.648740 | − | 0.761010i | \(-0.275296\pi\) | ||||
0.648740 | + | 0.761010i | \(0.275296\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.14467e7 | 1.14501 | 0.572505 | − | 0.819901i | \(-0.305972\pi\) | ||||
0.572505 | + | 0.819901i | \(0.305972\pi\) | |||||||
\(812\) | −8.46476e6 | −0.450531 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.96336e7 | −1.03858 | ||||||||
\(815\) | −3.12014e6 | −0.164543 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.20949e6 | 0.0633936 | ||||||||
\(818\) | −1.26379e7 | −0.660375 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.47720e6 | −0.180590 | ||||||||
\(821\) | 1.06313e7 | 0.550465 | 0.275232 | − | 0.961378i | \(-0.411245\pi\) | ||||
0.275232 | + | 0.961378i | \(0.411245\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −871518. | −0.0448515 | −0.0224257 | − | 0.999749i | \(-0.507139\pi\) | ||||
−0.0224257 | + | 0.999749i | \(0.507139\pi\) | |||||||
\(824\) | 1.59742e7 | 0.819597 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.72859e7 | −2.41147 | ||||||||
\(827\) | 1.70354e7 | 0.866141 | 0.433071 | − | 0.901360i | \(-0.357430\pi\) | ||||
0.433071 | + | 0.901360i | \(0.357430\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.65731e6 | 0.285906 | 0.142953 | − | 0.989729i | \(-0.454340\pi\) | ||||
0.142953 | + | 0.989729i | \(0.454340\pi\) | |||||||
\(830\) | 620252. | 0.0312517 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.29273e7 | −1.14827 | ||||||||
\(833\) | 2.39758e6 | 0.119718 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.43862e7 | 0.714054 | ||||||||
\(836\) | −1.79857e7 | −0.890046 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.58545e7 | −1.27182 | ||||||||
\(839\) | −3.42452e7 | −1.67956 | −0.839779 | − | 0.542929i | \(-0.817315\pi\) | ||||
−0.839779 | + | 0.542929i | \(0.817315\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.83905e7 | −0.896612 | ||||||||
\(842\) | 6.12802e7 | 2.97879 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.52595e7 | 0.737366 | ||||||||
\(845\) | −6.89419e6 | −0.332155 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.33455e7 | −1.11814 | ||||||||
\(848\) | 8.59078e6 | 0.410245 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.89230e7 | 1.37308 | ||||||||
\(851\) | −1.05275e7 | −0.498313 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.21968e7 | −1.04452 | −0.522261 | − | 0.852785i | \(-0.674911\pi\) | ||||
−0.522261 | + | 0.852785i | \(0.674911\pi\) | |||||||
\(854\) | 2.32500e7 | 1.09088 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.28101e7 | −0.597541 | ||||||||
\(857\) | −3.15803e7 | −1.46881 | −0.734403 | − | 0.678714i | \(-0.762538\pi\) | ||||
−0.734403 | + | 0.678714i | \(0.762538\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.22037e6 | −0.0564297 | −0.0282148 | − | 0.999602i | \(-0.508982\pi\) | ||||
−0.0282148 | + | 0.999602i | \(0.508982\pi\) | |||||||
\(860\) | 3.25890e6 | 0.150254 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.29239e7 | −1.05080 | ||||||||
\(863\) | 2.43543e7 | 1.11314 | 0.556570 | − | 0.830801i | \(-0.312117\pi\) | ||||
0.556570 | + | 0.830801i | \(0.312117\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.46032e6 | −0.157245 | ||||||||
\(866\) | −3.29086e7 | −1.49113 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.56917e7 | −1.15743 | ||||||||
\(869\) | −5.47031e7 | −2.45732 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.09877e7 | −0.490749 | ||||||||
\(872\) | 5.99873e6 | 0.267158 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.62668e7 | −0.720318 | ||||||||
\(875\) | 2.27401e7 | 1.00409 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.52016e6 | 0.110644 | 0.0553222 | − | 0.998469i | \(-0.482381\pi\) | ||||
0.0553222 | + | 0.998469i | \(0.482381\pi\) | |||||||
\(878\) | −3.68601e6 | −0.161369 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.67465e6 | 0.334081 | ||||||||
\(881\) | −1.04311e6 | −0.0452785 | −0.0226393 | − | 0.999744i | \(-0.507207\pi\) | ||||
−0.0226393 | + | 0.999744i | \(0.507207\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.57753e7 | −1.54412 | −0.772061 | − | 0.635548i | \(-0.780774\pi\) | ||||
−0.772061 | + | 0.635548i | \(0.780774\pi\) | |||||||
\(884\) | −3.90102e7 | −1.67899 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.34354e6 | 0.228689 | ||||||||
\(887\) | 1.66616e7 | 0.711061 | 0.355531 | − | 0.934665i | \(-0.384300\pi\) | ||||
0.355531 | + | 0.934665i | \(0.384300\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.96065e7 | 1.25642 | ||||||||
\(890\) | 2.36012e7 | 0.998754 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.88713e7 | 1.21494 | ||||||||
\(893\) | −1.44225e6 | −0.0605218 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.29815e7 | 0.959004 | ||||||||
\(896\) | 2.96214e7 | 1.23264 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.63928e7 | −0.678365 | ||||||||
\(899\) | 6.43631e6 | 0.265606 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.81090e7 | 1.97430 | ||||||||
\(902\) | 1.03206e7 | 0.422368 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.39499e7 | −0.974727 | ||||||||
\(905\) | 1.32963e7 | 0.539645 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.59470e7 | 1.45092 | 0.725462 | − | 0.688262i | \(-0.241626\pi\) | ||||
0.725462 | + | 0.688262i | \(0.241626\pi\) | |||||||
\(908\) | 3.52944e7 | 1.42066 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.81876e7 | −0.728069 | ||||||||
\(911\) | −7.56404e6 | −0.301966 | −0.150983 | − | 0.988536i | \(-0.548244\pi\) | ||||
−0.150983 | + | 0.988536i | \(0.548244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.09143e6 | −0.0433331 | ||||||||
\(914\) | −6.52030e7 | −2.58168 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.67260e7 | 2.23380 | ||||||||
\(917\) | −3.53654e7 | −1.38885 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.22167e7 | −0.867741 | −0.433870 | − | 0.900975i | \(-0.642852\pi\) | ||||
−0.433870 | + | 0.900975i | \(0.642852\pi\) | |||||||
\(920\) | −1.37300e7 | −0.534812 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.11207e7 | 1.20565 | ||||||||
\(923\) | −2.09051e7 | −0.807698 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.35871e6 | −0.244351 | ||||||||
\(926\) | −6.08709e7 | −2.33283 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.04694e7 | −0.399071 | ||||||||
\(929\) | −9.18809e6 | −0.349290 | −0.174645 | − | 0.984631i | \(-0.555878\pi\) | ||||
−0.174645 | + | 0.984631i | \(0.555878\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −814470. | −0.0307965 | ||||||||
\(932\) | −1.76934e7 | −0.667224 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.02220e7 | −1.88376 | ||||||||
\(935\) | 4.29785e7 | 1.60777 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.06654e7 | 1.51313 | 0.756565 | − | 0.653919i | \(-0.226876\pi\) | ||||
0.756565 | + | 0.653919i | \(0.226876\pi\) | |||||||
\(938\) | 2.79495e7 | 1.03721 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.88607e6 | −0.143447 | ||||||||
\(941\) | 2.60105e7 | 0.957580 | 0.478790 | − | 0.877930i | \(-0.341076\pi\) | ||||
0.478790 | + | 0.877930i | \(0.341076\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.53391e6 | 0.202653 | ||||||||
\(944\) | −1.47017e7 | −0.536954 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.67273e6 | −0.351416 | ||||||||
\(947\) | 2.03967e7 | 0.739067 | 0.369534 | − | 0.929217i | \(-0.379517\pi\) | ||||
0.369534 | + | 0.929217i | \(0.379517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.55652e7 | 0.921475 | ||||||||
\(950\) | −9.82530e6 | −0.353213 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.10846e7 | 1.11161 | ||||||||
\(953\) | 4.87462e6 | 0.173864 | 0.0869318 | − | 0.996214i | \(-0.472294\pi\) | ||||
0.0869318 | + | 0.996214i | \(0.472294\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.66414e6 | 0.165487 | ||||||||
\(956\) | −1.31289e7 | −0.464603 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.04231e7 | −1.42304 | ||||||||
\(959\) | 4.12903e7 | 1.44978 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.09409e6 | −0.317651 | ||||||||
\(962\) | 1.44662e7 | 0.503984 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.24322e7 | −1.81721 | ||||||||
\(965\) | −6.18368e6 | −0.213761 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.26016e7 | −0.433371 | −0.216686 | − | 0.976241i | \(-0.569525\pi\) | ||||
−0.216686 | + | 0.976241i | \(0.569525\pi\) | |||||||
\(968\) | 2.42173e7 | 0.830686 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.97921e7 | −1.01665 | ||||||||
\(971\) | 1.39978e6 | 0.0476443 | 0.0238221 | − | 0.999716i | \(-0.492416\pi\) | ||||
0.0238221 | + | 0.999716i | \(0.492416\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.32201e7 | −0.447665 | ||||||||
\(974\) | −8.13452e7 | −2.74748 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.22867e6 | 0.242904 | ||||||||
\(977\) | −1.43010e6 | −0.0479325 | −0.0239662 | − | 0.999713i | \(-0.507629\pi\) | ||||
−0.0239662 | + | 0.999713i | \(0.507629\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.15300e7 | −1.38486 | ||||||||
\(980\) | −2.19455e6 | −0.0729928 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.02711e7 | −1.00173 | ||||||||
\(983\) | −4.26255e7 | −1.40697 | −0.703487 | − | 0.710708i | \(-0.748375\pi\) | ||||
−0.703487 | + | 0.710708i | \(0.748375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.19811e7 | −0.721869 | ||||||||
\(986\) | −2.48595e7 | −0.814329 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.32520e7 | 0.431905 | ||||||||
\(989\) | −5.18650e6 | −0.168610 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.88273e7 | 0.608980 | 0.304490 | − | 0.952516i | \(-0.401514\pi\) | ||||
0.304490 | + | 0.952516i | \(0.401514\pi\) | |||||||
\(992\) | −3.17759e7 | −1.02522 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.31769e7 | 1.70709 | ||||||||
\(995\) | 1.32965e7 | 0.425775 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.10574e7 | 0.670915 | 0.335458 | − | 0.942055i | \(-0.391109\pi\) | ||||
0.335458 | + | 0.942055i | \(0.391109\pi\) | |||||||
\(998\) | −1.76746e7 | −0.561724 | ||||||||
\(999\) | 0 | 0 |
(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 | 387.6.a.e.1.9 | 10 | ||
3.2 | odd | 2 | 43.6.a.b.1.2 | ✓ | 10 | ||
12.11 | even | 2 | 688.6.a.h.1.6 | 10 | |||
15.14 | odd | 2 | 1075.6.a.b.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.b.1.2 | ✓ | 10 | 3.2 | odd | 2 | ||
387.6.a.e.1.9 | 10 | 1.1 | even | 1 | trivial | ||
688.6.a.h.1.6 | 10 | 12.11 | even | 2 | |||
1075.6.a.b.1.9 | 10 | 15.14 | odd | 2 |