Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,6,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(154.930769939\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 28.0000 | 0.500879 | 0.250440 | − | 0.968132i | \(-0.419425\pi\) | ||||
0.250440 | + | 0.968132i | \(0.419425\pi\) | |||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 112.000 | 0.354175 | ||||||||
\(11\) | −15.0000 | −0.0373774 | −0.0186887 | − | 0.999825i | \(-0.505949\pi\) | ||||
−0.0186887 | + | 0.999825i | \(0.505949\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | −1066.00 | −1.74944 | −0.874720 | − | 0.484629i | \(-0.838954\pi\) | ||||
−0.874720 | + | 0.484629i | \(0.838954\pi\) | |||||||
\(14\) | 196.000 | 0.267261 | ||||||||
\(15\) | 252.000 | 0.289183 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −80.0000 | −0.0671379 | −0.0335689 | − | 0.999436i | \(-0.510687\pi\) | ||||
−0.0335689 | + | 0.999436i | \(0.510687\pi\) | |||||||
\(18\) | 324.000 | 0.235702 | ||||||||
\(19\) | −1319.00 | −0.838225 | −0.419113 | − | 0.907934i | \(-0.637659\pi\) | ||||
−0.419113 | + | 0.907934i | \(0.637659\pi\) | |||||||
\(20\) | 448.000 | 0.250440 | ||||||||
\(21\) | 441.000 | 0.218218 | ||||||||
\(22\) | −60.0000 | −0.0264298 | ||||||||
\(23\) | 529.000 | 0.208514 | ||||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | −2341.00 | −0.749120 | ||||||||
\(26\) | −4264.00 | −1.23704 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 784.000 | 0.188982 | ||||||||
\(29\) | −3586.00 | −0.791800 | −0.395900 | − | 0.918294i | \(-0.629567\pi\) | ||||
−0.395900 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(30\) | 1008.00 | 0.204483 | ||||||||
\(31\) | −7850.00 | −1.46712 | −0.733560 | − | 0.679625i | \(-0.762142\pi\) | ||||
−0.733560 | + | 0.679625i | \(0.762142\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −135.000 | −0.0215799 | ||||||||
\(34\) | −320.000 | −0.0474737 | ||||||||
\(35\) | 1372.00 | 0.189315 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 5074.00 | 0.609321 | 0.304661 | − | 0.952461i | \(-0.401457\pi\) | ||||
0.304661 | + | 0.952461i | \(0.401457\pi\) | |||||||
\(38\) | −5276.00 | −0.592715 | ||||||||
\(39\) | −9594.00 | −1.01004 | ||||||||
\(40\) | 1792.00 | 0.177088 | ||||||||
\(41\) | −17627.0 | −1.63764 | −0.818821 | − | 0.574049i | \(-0.805372\pi\) | ||||
−0.818821 | + | 0.574049i | \(0.805372\pi\) | |||||||
\(42\) | 1764.00 | 0.154303 | ||||||||
\(43\) | 10392.0 | 0.857093 | 0.428547 | − | 0.903520i | \(-0.359026\pi\) | ||||
0.428547 | + | 0.903520i | \(0.359026\pi\) | |||||||
\(44\) | −240.000 | −0.0186887 | ||||||||
\(45\) | 2268.00 | 0.166960 | ||||||||
\(46\) | 2116.00 | 0.147442 | ||||||||
\(47\) | −11805.0 | −0.779509 | −0.389755 | − | 0.920919i | \(-0.627440\pi\) | ||||
−0.389755 | + | 0.920919i | \(0.627440\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −9364.00 | −0.529708 | ||||||||
\(51\) | −720.000 | −0.0387621 | ||||||||
\(52\) | −17056.0 | −0.874720 | ||||||||
\(53\) | −345.000 | −0.0168706 | −0.00843528 | − | 0.999964i | \(-0.502685\pi\) | ||||
−0.00843528 | + | 0.999964i | \(0.502685\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | −420.000 | −0.0187216 | ||||||||
\(56\) | 3136.00 | 0.133631 | ||||||||
\(57\) | −11871.0 | −0.483950 | ||||||||
\(58\) | −14344.0 | −0.559887 | ||||||||
\(59\) | −31347.0 | −1.17237 | −0.586187 | − | 0.810176i | \(-0.699371\pi\) | ||||
−0.586187 | + | 0.810176i | \(0.699371\pi\) | |||||||
\(60\) | 4032.00 | 0.144591 | ||||||||
\(61\) | −5019.00 | −0.172700 | −0.0863501 | − | 0.996265i | \(-0.527520\pi\) | ||||
−0.0863501 | + | 0.996265i | \(0.527520\pi\) | |||||||
\(62\) | −31400.0 | −1.03741 | ||||||||
\(63\) | 3969.00 | 0.125988 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −29848.0 | −0.876258 | ||||||||
\(66\) | −540.000 | −0.0152593 | ||||||||
\(67\) | −26552.0 | −0.722620 | −0.361310 | − | 0.932446i | \(-0.617670\pi\) | ||||
−0.361310 | + | 0.932446i | \(0.617670\pi\) | |||||||
\(68\) | −1280.00 | −0.0335689 | ||||||||
\(69\) | 4761.00 | 0.120386 | ||||||||
\(70\) | 5488.00 | 0.133866 | ||||||||
\(71\) | −23492.0 | −0.553062 | −0.276531 | − | 0.961005i | \(-0.589185\pi\) | ||||
−0.276531 | + | 0.961005i | \(0.589185\pi\) | |||||||
\(72\) | 5184.00 | 0.117851 | ||||||||
\(73\) | −5356.00 | −0.117634 | −0.0588171 | − | 0.998269i | \(-0.518733\pi\) | ||||
−0.0588171 | + | 0.998269i | \(0.518733\pi\) | |||||||
\(74\) | 20296.0 | 0.430855 | ||||||||
\(75\) | −21069.0 | −0.432505 | ||||||||
\(76\) | −21104.0 | −0.419113 | ||||||||
\(77\) | −735.000 | −0.0141273 | ||||||||
\(78\) | −38376.0 | −0.714206 | ||||||||
\(79\) | 99870.0 | 1.80039 | 0.900197 | − | 0.435484i | \(-0.143423\pi\) | ||||
0.900197 | + | 0.435484i | \(0.143423\pi\) | |||||||
\(80\) | 7168.00 | 0.125220 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −70508.0 | −1.15799 | ||||||||
\(83\) | 47482.0 | 0.756543 | 0.378272 | − | 0.925695i | \(-0.376519\pi\) | ||||
0.378272 | + | 0.925695i | \(0.376519\pi\) | |||||||
\(84\) | 7056.00 | 0.109109 | ||||||||
\(85\) | −2240.00 | −0.0336280 | ||||||||
\(86\) | 41568.0 | 0.606056 | ||||||||
\(87\) | −32274.0 | −0.457146 | ||||||||
\(88\) | −960.000 | −0.0132149 | ||||||||
\(89\) | −58182.0 | −0.778599 | −0.389299 | − | 0.921111i | \(-0.627283\pi\) | ||||
−0.389299 | + | 0.921111i | \(0.627283\pi\) | |||||||
\(90\) | 9072.00 | 0.118058 | ||||||||
\(91\) | −52234.0 | −0.661226 | ||||||||
\(92\) | 8464.00 | 0.104257 | ||||||||
\(93\) | −70650.0 | −0.847042 | ||||||||
\(94\) | −47220.0 | −0.551196 | ||||||||
\(95\) | −36932.0 | −0.419850 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | 72722.0 | 0.784759 | 0.392380 | − | 0.919803i | \(-0.371652\pi\) | ||||
0.392380 | + | 0.919803i | \(0.371652\pi\) | |||||||
\(98\) | 9604.00 | 0.101015 | ||||||||
\(99\) | −1215.00 | −0.0124591 | ||||||||
\(100\) | −37456.0 | −0.374560 | ||||||||
\(101\) | −7315.00 | −0.0713528 | −0.0356764 | − | 0.999363i | \(-0.511359\pi\) | ||||
−0.0356764 | + | 0.999363i | \(0.511359\pi\) | |||||||
\(102\) | −2880.00 | −0.0274089 | ||||||||
\(103\) | 26791.0 | 0.248826 | 0.124413 | − | 0.992231i | \(-0.460295\pi\) | ||||
0.124413 | + | 0.992231i | \(0.460295\pi\) | |||||||
\(104\) | −68224.0 | −0.618520 | ||||||||
\(105\) | 12348.0 | 0.109301 | ||||||||
\(106\) | −1380.00 | −0.0119293 | ||||||||
\(107\) | 180228. | 1.52182 | 0.760909 | − | 0.648858i | \(-0.224753\pi\) | ||||
0.760909 | + | 0.648858i | \(0.224753\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | 170440. | 1.37406 | 0.687029 | − | 0.726630i | \(-0.258914\pi\) | ||||
0.687029 | + | 0.726630i | \(0.258914\pi\) | |||||||
\(110\) | −1680.00 | −0.0132382 | ||||||||
\(111\) | 45666.0 | 0.351792 | ||||||||
\(112\) | 12544.0 | 0.0944911 | ||||||||
\(113\) | 31666.0 | 0.233291 | 0.116645 | − | 0.993174i | \(-0.462786\pi\) | ||||
0.116645 | + | 0.993174i | \(0.462786\pi\) | |||||||
\(114\) | −47484.0 | −0.342204 | ||||||||
\(115\) | 14812.0 | 0.104441 | ||||||||
\(116\) | −57376.0 | −0.395900 | ||||||||
\(117\) | −86346.0 | −0.583146 | ||||||||
\(118\) | −125388. | −0.828993 | ||||||||
\(119\) | −3920.00 | −0.0253757 | ||||||||
\(120\) | 16128.0 | 0.102242 | ||||||||
\(121\) | −160826. | −0.998603 | ||||||||
\(122\) | −20076.0 | −0.122117 | ||||||||
\(123\) | −158643. | −0.945493 | ||||||||
\(124\) | −125600. | −0.733560 | ||||||||
\(125\) | −153048. | −0.876098 | ||||||||
\(126\) | 15876.0 | 0.0890871 | ||||||||
\(127\) | −58147.0 | −0.319903 | −0.159951 | − | 0.987125i | \(-0.551134\pi\) | ||||
−0.159951 | + | 0.987125i | \(0.551134\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 93528.0 | 0.494843 | ||||||||
\(130\) | −119392. | −0.619608 | ||||||||
\(131\) | −95801.0 | −0.487744 | −0.243872 | − | 0.969807i | \(-0.578418\pi\) | ||||
−0.243872 | + | 0.969807i | \(0.578418\pi\) | |||||||
\(132\) | −2160.00 | −0.0107899 | ||||||||
\(133\) | −64631.0 | −0.316819 | ||||||||
\(134\) | −106208. | −0.510970 | ||||||||
\(135\) | 20412.0 | 0.0963943 | ||||||||
\(136\) | −5120.00 | −0.0237368 | ||||||||
\(137\) | 153687. | 0.699577 | 0.349789 | − | 0.936829i | \(-0.386253\pi\) | ||||
0.349789 | + | 0.936829i | \(0.386253\pi\) | |||||||
\(138\) | 19044.0 | 0.0851257 | ||||||||
\(139\) | 316100. | 1.38767 | 0.693837 | − | 0.720132i | \(-0.255919\pi\) | ||||
0.693837 | + | 0.720132i | \(0.255919\pi\) | |||||||
\(140\) | 21952.0 | 0.0946573 | ||||||||
\(141\) | −106245. | −0.450050 | ||||||||
\(142\) | −93968.0 | −0.391074 | ||||||||
\(143\) | 15990.0 | 0.0653896 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −100408. | −0.396596 | ||||||||
\(146\) | −21424.0 | −0.0831799 | ||||||||
\(147\) | 21609.0 | 0.0824786 | ||||||||
\(148\) | 81184.0 | 0.304661 | ||||||||
\(149\) | −378667. | −1.39731 | −0.698653 | − | 0.715460i | \(-0.746217\pi\) | ||||
−0.698653 | + | 0.715460i | \(0.746217\pi\) | |||||||
\(150\) | −84276.0 | −0.305827 | ||||||||
\(151\) | −97703.0 | −0.348711 | −0.174355 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174355 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(152\) | −84416.0 | −0.296357 | ||||||||
\(153\) | −6480.00 | −0.0223793 | ||||||||
\(154\) | −2940.00 | −0.00998954 | ||||||||
\(155\) | −219800. | −0.734850 | ||||||||
\(156\) | −153504. | −0.505020 | ||||||||
\(157\) | −582567. | −1.88624 | −0.943120 | − | 0.332454i | \(-0.892123\pi\) | ||||
−0.943120 | + | 0.332454i | \(0.892123\pi\) | |||||||
\(158\) | 399480. | 1.27307 | ||||||||
\(159\) | −3105.00 | −0.00974022 | ||||||||
\(160\) | 28672.0 | 0.0885438 | ||||||||
\(161\) | 25921.0 | 0.0788110 | ||||||||
\(162\) | 26244.0 | 0.0785674 | ||||||||
\(163\) | −347407. | −1.02416 | −0.512082 | − | 0.858937i | \(-0.671126\pi\) | ||||
−0.512082 | + | 0.858937i | \(0.671126\pi\) | |||||||
\(164\) | −282032. | −0.818821 | ||||||||
\(165\) | −3780.00 | −0.0108089 | ||||||||
\(166\) | 189928. | 0.534957 | ||||||||
\(167\) | 170559. | 0.473242 | 0.236621 | − | 0.971602i | \(-0.423960\pi\) | ||||
0.236621 | + | 0.971602i | \(0.423960\pi\) | |||||||
\(168\) | 28224.0 | 0.0771517 | ||||||||
\(169\) | 765063. | 2.06054 | ||||||||
\(170\) | −8960.00 | −0.0237786 | ||||||||
\(171\) | −106839. | −0.279408 | ||||||||
\(172\) | 166272. | 0.428547 | ||||||||
\(173\) | 125346. | 0.318416 | 0.159208 | − | 0.987245i | \(-0.449106\pi\) | ||||
0.159208 | + | 0.987245i | \(0.449106\pi\) | |||||||
\(174\) | −129096. | −0.323251 | ||||||||
\(175\) | −114709. | −0.283141 | ||||||||
\(176\) | −3840.00 | −0.00934436 | ||||||||
\(177\) | −282123. | −0.676870 | ||||||||
\(178\) | −232728. | −0.550552 | ||||||||
\(179\) | 341736. | 0.797183 | 0.398592 | − | 0.917129i | \(-0.369499\pi\) | ||||
0.398592 | + | 0.917129i | \(0.369499\pi\) | |||||||
\(180\) | 36288.0 | 0.0834799 | ||||||||
\(181\) | −26378.0 | −0.0598474 | −0.0299237 | − | 0.999552i | \(-0.509526\pi\) | ||||
−0.0299237 | + | 0.999552i | \(0.509526\pi\) | |||||||
\(182\) | −208936. | −0.467557 | ||||||||
\(183\) | −45171.0 | −0.0997085 | ||||||||
\(184\) | 33856.0 | 0.0737210 | ||||||||
\(185\) | 142072. | 0.305196 | ||||||||
\(186\) | −282600. | −0.598949 | ||||||||
\(187\) | 1200.00 | 0.00250944 | ||||||||
\(188\) | −188880. | −0.389755 | ||||||||
\(189\) | 35721.0 | 0.0727393 | ||||||||
\(190\) | −147728. | −0.296879 | ||||||||
\(191\) | 509995. | 1.01154 | 0.505769 | − | 0.862669i | \(-0.331209\pi\) | ||||
0.505769 | + | 0.862669i | \(0.331209\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | −265715. | −0.513479 | −0.256740 | − | 0.966481i | \(-0.582648\pi\) | ||||
−0.256740 | + | 0.966481i | \(0.582648\pi\) | |||||||
\(194\) | 290888. | 0.554909 | ||||||||
\(195\) | −268632. | −0.505908 | ||||||||
\(196\) | 38416.0 | 0.0714286 | ||||||||
\(197\) | −384814. | −0.706456 | −0.353228 | − | 0.935537i | \(-0.614916\pi\) | ||||
−0.353228 | + | 0.935537i | \(0.614916\pi\) | |||||||
\(198\) | −4860.00 | −0.00880995 | ||||||||
\(199\) | −423655. | −0.758367 | −0.379184 | − | 0.925321i | \(-0.623795\pi\) | ||||
−0.379184 | + | 0.925321i | \(0.623795\pi\) | |||||||
\(200\) | −149824. | −0.264854 | ||||||||
\(201\) | −238968. | −0.417205 | ||||||||
\(202\) | −29260.0 | −0.0504540 | ||||||||
\(203\) | −175714. | −0.299272 | ||||||||
\(204\) | −11520.0 | −0.0193810 | ||||||||
\(205\) | −493556. | −0.820260 | ||||||||
\(206\) | 107164. | 0.175947 | ||||||||
\(207\) | 42849.0 | 0.0695048 | ||||||||
\(208\) | −272896. | −0.437360 | ||||||||
\(209\) | 19785.0 | 0.0313307 | ||||||||
\(210\) | 49392.0 | 0.0772873 | ||||||||
\(211\) | 387057. | 0.598506 | 0.299253 | − | 0.954174i | \(-0.403262\pi\) | ||||
0.299253 | + | 0.954174i | \(0.403262\pi\) | |||||||
\(212\) | −5520.00 | −0.00843528 | ||||||||
\(213\) | −211428. | −0.319311 | ||||||||
\(214\) | 720912. | 1.07609 | ||||||||
\(215\) | 290976. | 0.429300 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −384650. | −0.554519 | ||||||||
\(218\) | 681760. | 0.971606 | ||||||||
\(219\) | −48204.0 | −0.0679161 | ||||||||
\(220\) | −6720.00 | −0.00936079 | ||||||||
\(221\) | 85280.0 | 0.117454 | ||||||||
\(222\) | 182664. | 0.248754 | ||||||||
\(223\) | −299642. | −0.403497 | −0.201749 | − | 0.979437i | \(-0.564662\pi\) | ||||
−0.201749 | + | 0.979437i | \(0.564662\pi\) | |||||||
\(224\) | 50176.0 | 0.0668153 | ||||||||
\(225\) | −189621. | −0.249707 | ||||||||
\(226\) | 126664. | 0.164961 | ||||||||
\(227\) | −1.29649e6 | −1.66995 | −0.834974 | − | 0.550289i | \(-0.814518\pi\) | ||||
−0.834974 | + | 0.550289i | \(0.814518\pi\) | |||||||
\(228\) | −189936. | −0.241975 | ||||||||
\(229\) | 449749. | 0.566737 | 0.283368 | − | 0.959011i | \(-0.408548\pi\) | ||||
0.283368 | + | 0.959011i | \(0.408548\pi\) | |||||||
\(230\) | 59248.0 | 0.0738506 | ||||||||
\(231\) | −6615.00 | −0.00815643 | ||||||||
\(232\) | −229504. | −0.279943 | ||||||||
\(233\) | −529188. | −0.638587 | −0.319294 | − | 0.947656i | \(-0.603446\pi\) | ||||
−0.319294 | + | 0.947656i | \(0.603446\pi\) | |||||||
\(234\) | −345384. | −0.412347 | ||||||||
\(235\) | −330540. | −0.390440 | ||||||||
\(236\) | −501552. | −0.586187 | ||||||||
\(237\) | 898830. | 1.03946 | ||||||||
\(238\) | −15680.0 | −0.0179434 | ||||||||
\(239\) | 413400. | 0.468140 | 0.234070 | − | 0.972220i | \(-0.424796\pi\) | ||||
0.234070 | + | 0.972220i | \(0.424796\pi\) | |||||||
\(240\) | 64512.0 | 0.0722957 | ||||||||
\(241\) | 1.26352e6 | 1.40133 | 0.700663 | − | 0.713492i | \(-0.252888\pi\) | ||||
0.700663 | + | 0.713492i | \(0.252888\pi\) | |||||||
\(242\) | −643304. | −0.706119 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −80304.0 | −0.0863501 | ||||||||
\(245\) | 67228.0 | 0.0715542 | ||||||||
\(246\) | −634572. | −0.668564 | ||||||||
\(247\) | 1.40605e6 | 1.46642 | ||||||||
\(248\) | −502400. | −0.518705 | ||||||||
\(249\) | 427338. | 0.436790 | ||||||||
\(250\) | −612192. | −0.619495 | ||||||||
\(251\) | 1.16018e6 | 1.16236 | 0.581180 | − | 0.813775i | \(-0.302591\pi\) | ||||
0.581180 | + | 0.813775i | \(0.302591\pi\) | |||||||
\(252\) | 63504.0 | 0.0629941 | ||||||||
\(253\) | −7935.00 | −0.00779373 | ||||||||
\(254\) | −232588. | −0.226205 | ||||||||
\(255\) | −20160.0 | −0.0194151 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.27815e6 | −1.20712 | −0.603558 | − | 0.797319i | \(-0.706251\pi\) | ||||
−0.603558 | + | 0.797319i | \(0.706251\pi\) | |||||||
\(258\) | 374112. | 0.349907 | ||||||||
\(259\) | 248626. | 0.230302 | ||||||||
\(260\) | −477568. | −0.438129 | ||||||||
\(261\) | −290466. | −0.263933 | ||||||||
\(262\) | −383204. | −0.344887 | ||||||||
\(263\) | −622739. | −0.555158 | −0.277579 | − | 0.960703i | \(-0.589532\pi\) | ||||
−0.277579 | + | 0.960703i | \(0.589532\pi\) | |||||||
\(264\) | −8640.00 | −0.00762964 | ||||||||
\(265\) | −9660.00 | −0.00845011 | ||||||||
\(266\) | −258524. | −0.224025 | ||||||||
\(267\) | −523638. | −0.449524 | ||||||||
\(268\) | −424832. | −0.361310 | ||||||||
\(269\) | −1.54439e6 | −1.30130 | −0.650650 | − | 0.759378i | \(-0.725503\pi\) | ||||
−0.650650 | + | 0.759378i | \(0.725503\pi\) | |||||||
\(270\) | 81648.0 | 0.0681610 | ||||||||
\(271\) | 1.02695e6 | 0.849425 | 0.424713 | − | 0.905328i | \(-0.360375\pi\) | ||||
0.424713 | + | 0.905328i | \(0.360375\pi\) | |||||||
\(272\) | −20480.0 | −0.0167845 | ||||||||
\(273\) | −470106. | −0.381759 | ||||||||
\(274\) | 614748. | 0.494676 | ||||||||
\(275\) | 35115.0 | 0.0280002 | ||||||||
\(276\) | 76176.0 | 0.0601929 | ||||||||
\(277\) | −896465. | −0.701995 | −0.350997 | − | 0.936376i | \(-0.614157\pi\) | ||||
−0.350997 | + | 0.936376i | \(0.614157\pi\) | |||||||
\(278\) | 1.26440e6 | 0.981234 | ||||||||
\(279\) | −635850. | −0.489040 | ||||||||
\(280\) | 87808.0 | 0.0669328 | ||||||||
\(281\) | 793958. | 0.599835 | 0.299917 | − | 0.953965i | \(-0.403041\pi\) | ||||
0.299917 | + | 0.953965i | \(0.403041\pi\) | |||||||
\(282\) | −424980. | −0.318233 | ||||||||
\(283\) | −220788. | −0.163874 | −0.0819369 | − | 0.996638i | \(-0.526111\pi\) | ||||
−0.0819369 | + | 0.996638i | \(0.526111\pi\) | |||||||
\(284\) | −375872. | −0.276531 | ||||||||
\(285\) | −332388. | −0.242400 | ||||||||
\(286\) | 63960.0 | 0.0462374 | ||||||||
\(287\) | −863723. | −0.618970 | ||||||||
\(288\) | 82944.0 | 0.0589256 | ||||||||
\(289\) | −1.41346e6 | −0.995493 | ||||||||
\(290\) | −401632. | −0.280436 | ||||||||
\(291\) | 654498. | 0.453081 | ||||||||
\(292\) | −85696.0 | −0.0588171 | ||||||||
\(293\) | −541868. | −0.368744 | −0.184372 | − | 0.982857i | \(-0.559025\pi\) | ||||
−0.184372 | + | 0.982857i | \(0.559025\pi\) | |||||||
\(294\) | 86436.0 | 0.0583212 | ||||||||
\(295\) | −877716. | −0.587217 | ||||||||
\(296\) | 324736. | 0.215428 | ||||||||
\(297\) | −10935.0 | −0.00719329 | ||||||||
\(298\) | −1.51467e6 | −0.988045 | ||||||||
\(299\) | −563914. | −0.364783 | ||||||||
\(300\) | −337104. | −0.216252 | ||||||||
\(301\) | 509208. | 0.323951 | ||||||||
\(302\) | −390812. | −0.246576 | ||||||||
\(303\) | −65835.0 | −0.0411955 | ||||||||
\(304\) | −337664. | −0.209556 | ||||||||
\(305\) | −140532. | −0.0865019 | ||||||||
\(306\) | −25920.0 | −0.0158246 | ||||||||
\(307\) | −2.87122e6 | −1.73869 | −0.869343 | − | 0.494209i | \(-0.835458\pi\) | ||||
−0.869343 | + | 0.494209i | \(0.835458\pi\) | |||||||
\(308\) | −11760.0 | −0.00706367 | ||||||||
\(309\) | 241119. | 0.143660 | ||||||||
\(310\) | −879200. | −0.519617 | ||||||||
\(311\) | 2.38904e6 | 1.40063 | 0.700315 | − | 0.713834i | \(-0.253043\pi\) | ||||
0.700315 | + | 0.713834i | \(0.253043\pi\) | |||||||
\(312\) | −614016. | −0.357103 | ||||||||
\(313\) | 850937. | 0.490949 | 0.245475 | − | 0.969403i | \(-0.421056\pi\) | ||||
0.245475 | + | 0.969403i | \(0.421056\pi\) | |||||||
\(314\) | −2.33027e6 | −1.33377 | ||||||||
\(315\) | 111132. | 0.0631049 | ||||||||
\(316\) | 1.59792e6 | 0.900197 | ||||||||
\(317\) | −24742.0 | −0.0138289 | −0.00691443 | − | 0.999976i | \(-0.502201\pi\) | ||||
−0.00691443 | + | 0.999976i | \(0.502201\pi\) | |||||||
\(318\) | −12420.0 | −0.00688738 | ||||||||
\(319\) | 53790.0 | 0.0295954 | ||||||||
\(320\) | 114688. | 0.0626099 | ||||||||
\(321\) | 1.62205e6 | 0.878622 | ||||||||
\(322\) | 103684. | 0.0557278 | ||||||||
\(323\) | 105520. | 0.0562767 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 2.49551e6 | 1.31054 | ||||||||
\(326\) | −1.38963e6 | −0.724193 | ||||||||
\(327\) | 1.53396e6 | 0.793313 | ||||||||
\(328\) | −1.12813e6 | −0.578994 | ||||||||
\(329\) | −578445. | −0.294627 | ||||||||
\(330\) | −15120.0 | −0.00764305 | ||||||||
\(331\) | −2.49814e6 | −1.25327 | −0.626637 | − | 0.779311i | \(-0.715569\pi\) | ||||
−0.626637 | + | 0.779311i | \(0.715569\pi\) | |||||||
\(332\) | 759712. | 0.378272 | ||||||||
\(333\) | 410994. | 0.203107 | ||||||||
\(334\) | 682236. | 0.334633 | ||||||||
\(335\) | −743456. | −0.361946 | ||||||||
\(336\) | 112896. | 0.0545545 | ||||||||
\(337\) | −3.78265e6 | −1.81435 | −0.907175 | − | 0.420754i | \(-0.861766\pi\) | ||||
−0.907175 | + | 0.420754i | \(0.861766\pi\) | |||||||
\(338\) | 3.06025e6 | 1.45702 | ||||||||
\(339\) | 284994. | 0.134690 | ||||||||
\(340\) | −35840.0 | −0.0168140 | ||||||||
\(341\) | 117750. | 0.0548372 | ||||||||
\(342\) | −427356. | −0.197572 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 665088. | 0.303028 | ||||||||
\(345\) | 133308. | 0.0602988 | ||||||||
\(346\) | 501384. | 0.225154 | ||||||||
\(347\) | −1.25095e6 | −0.557718 | −0.278859 | − | 0.960332i | \(-0.589956\pi\) | ||||
−0.278859 | + | 0.960332i | \(0.589956\pi\) | |||||||
\(348\) | −516384. | −0.228573 | ||||||||
\(349\) | 4.06863e6 | 1.78807 | 0.894036 | − | 0.447995i | \(-0.147862\pi\) | ||||
0.894036 | + | 0.447995i | \(0.147862\pi\) | |||||||
\(350\) | −458836. | −0.200211 | ||||||||
\(351\) | −777114. | −0.336680 | ||||||||
\(352\) | −15360.0 | −0.00660746 | ||||||||
\(353\) | 2.47899e6 | 1.05886 | 0.529430 | − | 0.848353i | \(-0.322406\pi\) | ||||
0.529430 | + | 0.848353i | \(0.322406\pi\) | |||||||
\(354\) | −1.12849e6 | −0.478619 | ||||||||
\(355\) | −657776. | −0.277017 | ||||||||
\(356\) | −930912. | −0.389299 | ||||||||
\(357\) | −35280.0 | −0.0146507 | ||||||||
\(358\) | 1.36694e6 | 0.563694 | ||||||||
\(359\) | 4.14936e6 | 1.69920 | 0.849601 | − | 0.527426i | \(-0.176843\pi\) | ||||
0.849601 | + | 0.527426i | \(0.176843\pi\) | |||||||
\(360\) | 145152. | 0.0590292 | ||||||||
\(361\) | −736338. | −0.297378 | ||||||||
\(362\) | −105512. | −0.0423185 | ||||||||
\(363\) | −1.44743e6 | −0.576544 | ||||||||
\(364\) | −835744. | −0.330613 | ||||||||
\(365\) | −149968. | −0.0589205 | ||||||||
\(366\) | −180684. | −0.0705045 | ||||||||
\(367\) | 3.70454e6 | 1.43572 | 0.717860 | − | 0.696188i | \(-0.245122\pi\) | ||||
0.717860 | + | 0.696188i | \(0.245122\pi\) | |||||||
\(368\) | 135424. | 0.0521286 | ||||||||
\(369\) | −1.42779e6 | −0.545880 | ||||||||
\(370\) | 568288. | 0.215806 | ||||||||
\(371\) | −16905.0 | −0.00637647 | ||||||||
\(372\) | −1.13040e6 | −0.423521 | ||||||||
\(373\) | −57154.0 | −0.0212703 | −0.0106352 | − | 0.999943i | \(-0.503385\pi\) | ||||
−0.0106352 | + | 0.999943i | \(0.503385\pi\) | |||||||
\(374\) | 4800.00 | 0.00177444 | ||||||||
\(375\) | −1.37743e6 | −0.505815 | ||||||||
\(376\) | −755520. | −0.275598 | ||||||||
\(377\) | 3.82268e6 | 1.38521 | ||||||||
\(378\) | 142884. | 0.0514344 | ||||||||
\(379\) | −3.85427e6 | −1.37830 | −0.689150 | − | 0.724619i | \(-0.742016\pi\) | ||||
−0.689150 | + | 0.724619i | \(0.742016\pi\) | |||||||
\(380\) | −590912. | −0.209925 | ||||||||
\(381\) | −523323. | −0.184696 | ||||||||
\(382\) | 2.03998e6 | 0.715266 | ||||||||
\(383\) | −4.72959e6 | −1.64751 | −0.823753 | − | 0.566949i | \(-0.808124\pi\) | ||||
−0.823753 | + | 0.566949i | \(0.808124\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | −20580.0 | −0.00707609 | ||||||||
\(386\) | −1.06286e6 | −0.363085 | ||||||||
\(387\) | 841752. | 0.285698 | ||||||||
\(388\) | 1.16355e6 | 0.392380 | ||||||||
\(389\) | −3.23052e6 | −1.08243 | −0.541213 | − | 0.840886i | \(-0.682035\pi\) | ||||
−0.541213 | + | 0.840886i | \(0.682035\pi\) | |||||||
\(390\) | −1.07453e6 | −0.357731 | ||||||||
\(391\) | −42320.0 | −0.0139992 | ||||||||
\(392\) | 153664. | 0.0505076 | ||||||||
\(393\) | −862209. | −0.281599 | ||||||||
\(394\) | −1.53926e6 | −0.499540 | ||||||||
\(395\) | 2.79636e6 | 0.901779 | ||||||||
\(396\) | −19440.0 | −0.00622957 | ||||||||
\(397\) | 414238. | 0.131909 | 0.0659544 | − | 0.997823i | \(-0.478991\pi\) | ||||
0.0659544 | + | 0.997823i | \(0.478991\pi\) | |||||||
\(398\) | −1.69462e6 | −0.536247 | ||||||||
\(399\) | −581679. | −0.182916 | ||||||||
\(400\) | −599296. | −0.187280 | ||||||||
\(401\) | 1.52752e6 | 0.474379 | 0.237189 | − | 0.971463i | \(-0.423774\pi\) | ||||
0.237189 | + | 0.971463i | \(0.423774\pi\) | |||||||
\(402\) | −955872. | −0.295009 | ||||||||
\(403\) | 8.36810e6 | 2.56664 | ||||||||
\(404\) | −117040. | −0.0356764 | ||||||||
\(405\) | 183708. | 0.0556532 | ||||||||
\(406\) | −702856. | −0.211617 | ||||||||
\(407\) | −76110.0 | −0.0227749 | ||||||||
\(408\) | −46080.0 | −0.0137045 | ||||||||
\(409\) | −2.83674e6 | −0.838516 | −0.419258 | − | 0.907867i | \(-0.637710\pi\) | ||||
−0.419258 | + | 0.907867i | \(0.637710\pi\) | |||||||
\(410\) | −1.97422e6 | −0.580012 | ||||||||
\(411\) | 1.38318e6 | 0.403901 | ||||||||
\(412\) | 428656. | 0.124413 | ||||||||
\(413\) | −1.53600e6 | −0.443115 | ||||||||
\(414\) | 171396. | 0.0491473 | ||||||||
\(415\) | 1.32950e6 | 0.378937 | ||||||||
\(416\) | −1.09158e6 | −0.309260 | ||||||||
\(417\) | 2.84490e6 | 0.801174 | ||||||||
\(418\) | 79140.0 | 0.0221542 | ||||||||
\(419\) | −78114.0 | −0.0217367 | −0.0108684 | − | 0.999941i | \(-0.503460\pi\) | ||||
−0.0108684 | + | 0.999941i | \(0.503460\pi\) | |||||||
\(420\) | 197568. | 0.0546504 | ||||||||
\(421\) | −1.58554e6 | −0.435984 | −0.217992 | − | 0.975951i | \(-0.569951\pi\) | ||||
−0.217992 | + | 0.975951i | \(0.569951\pi\) | |||||||
\(422\) | 1.54823e6 | 0.423208 | ||||||||
\(423\) | −956205. | −0.259836 | ||||||||
\(424\) | −22080.0 | −0.00596464 | ||||||||
\(425\) | 187280. | 0.0502943 | ||||||||
\(426\) | −845712. | −0.225787 | ||||||||
\(427\) | −245931. | −0.0652745 | ||||||||
\(428\) | 2.88365e6 | 0.760909 | ||||||||
\(429\) | 143910. | 0.0377527 | ||||||||
\(430\) | 1.16390e6 | 0.303561 | ||||||||
\(431\) | −1.02160e6 | −0.264903 | −0.132452 | − | 0.991189i | \(-0.542285\pi\) | ||||
−0.132452 | + | 0.991189i | \(0.542285\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | 246539. | 0.0631926 | 0.0315963 | − | 0.999501i | \(-0.489941\pi\) | ||||
0.0315963 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(434\) | −1.53860e6 | −0.392104 | ||||||||
\(435\) | −903672. | −0.228975 | ||||||||
\(436\) | 2.72704e6 | 0.687029 | ||||||||
\(437\) | −697751. | −0.174782 | ||||||||
\(438\) | −192816. | −0.0480239 | ||||||||
\(439\) | −619792. | −0.153492 | −0.0767458 | − | 0.997051i | \(-0.524453\pi\) | ||||
−0.0767458 | + | 0.997051i | \(0.524453\pi\) | |||||||
\(440\) | −26880.0 | −0.00661908 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 341120. | 0.0830523 | ||||||||
\(443\) | −5.74450e6 | −1.39073 | −0.695366 | − | 0.718656i | \(-0.744758\pi\) | ||||
−0.695366 | + | 0.718656i | \(0.744758\pi\) | |||||||
\(444\) | 730656. | 0.175896 | ||||||||
\(445\) | −1.62910e6 | −0.389984 | ||||||||
\(446\) | −1.19857e6 | −0.285316 | ||||||||
\(447\) | −3.40800e6 | −0.806735 | ||||||||
\(448\) | 200704. | 0.0472456 | ||||||||
\(449\) | 4.80635e6 | 1.12512 | 0.562561 | − | 0.826756i | \(-0.309816\pi\) | ||||
0.562561 | + | 0.826756i | \(0.309816\pi\) | |||||||
\(450\) | −758484. | −0.176569 | ||||||||
\(451\) | 264405. | 0.0612108 | ||||||||
\(452\) | 506656. | 0.116645 | ||||||||
\(453\) | −879327. | −0.201328 | ||||||||
\(454\) | −5.18594e6 | −1.18083 | ||||||||
\(455\) | −1.46255e6 | −0.331194 | ||||||||
\(456\) | −759744. | −0.171102 | ||||||||
\(457\) | −2.65447e6 | −0.594549 | −0.297275 | − | 0.954792i | \(-0.596078\pi\) | ||||
−0.297275 | + | 0.954792i | \(0.596078\pi\) | |||||||
\(458\) | 1.79900e6 | 0.400744 | ||||||||
\(459\) | −58320.0 | −0.0129207 | ||||||||
\(460\) | 236992. | 0.0522203 | ||||||||
\(461\) | 6.45797e6 | 1.41528 | 0.707642 | − | 0.706571i | \(-0.249759\pi\) | ||||
0.707642 | + | 0.706571i | \(0.249759\pi\) | |||||||
\(462\) | −26460.0 | −0.00576746 | ||||||||
\(463\) | −3.39535e6 | −0.736092 | −0.368046 | − | 0.929808i | \(-0.619973\pi\) | ||||
−0.368046 | + | 0.929808i | \(0.619973\pi\) | |||||||
\(464\) | −918016. | −0.197950 | ||||||||
\(465\) | −1.97820e6 | −0.424266 | ||||||||
\(466\) | −2.11675e6 | −0.451549 | ||||||||
\(467\) | −3.62989e6 | −0.770197 | −0.385098 | − | 0.922876i | \(-0.625833\pi\) | ||||
−0.385098 | + | 0.922876i | \(0.625833\pi\) | |||||||
\(468\) | −1.38154e6 | −0.291573 | ||||||||
\(469\) | −1.30105e6 | −0.273125 | ||||||||
\(470\) | −1.32216e6 | −0.276083 | ||||||||
\(471\) | −5.24310e6 | −1.08902 | ||||||||
\(472\) | −2.00621e6 | −0.414497 | ||||||||
\(473\) | −155880. | −0.0320359 | ||||||||
\(474\) | 3.59532e6 | 0.735007 | ||||||||
\(475\) | 3.08778e6 | 0.627931 | ||||||||
\(476\) | −62720.0 | −0.0126879 | ||||||||
\(477\) | −27945.0 | −0.00562352 | ||||||||
\(478\) | 1.65360e6 | 0.331025 | ||||||||
\(479\) | −600524. | −0.119589 | −0.0597945 | − | 0.998211i | \(-0.519045\pi\) | ||||
−0.0597945 | + | 0.998211i | \(0.519045\pi\) | |||||||
\(480\) | 258048. | 0.0511208 | ||||||||
\(481\) | −5.40888e6 | −1.06597 | ||||||||
\(482\) | 5.05408e6 | 0.990887 | ||||||||
\(483\) | 233289. | 0.0455016 | ||||||||
\(484\) | −2.57322e6 | −0.499301 | ||||||||
\(485\) | 2.03622e6 | 0.393070 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | −2.40688e6 | −0.459866 | −0.229933 | − | 0.973206i | \(-0.573851\pi\) | ||||
−0.229933 | + | 0.973206i | \(0.573851\pi\) | |||||||
\(488\) | −321216. | −0.0610587 | ||||||||
\(489\) | −3.12666e6 | −0.591301 | ||||||||
\(490\) | 268912. | 0.0505964 | ||||||||
\(491\) | −2.77493e6 | −0.519455 | −0.259728 | − | 0.965682i | \(-0.583633\pi\) | ||||
−0.259728 | + | 0.965682i | \(0.583633\pi\) | |||||||
\(492\) | −2.53829e6 | −0.472746 | ||||||||
\(493\) | 286880. | 0.0531598 | ||||||||
\(494\) | 5.62422e6 | 1.03692 | ||||||||
\(495\) | −34020.0 | −0.00624053 | ||||||||
\(496\) | −2.00960e6 | −0.366780 | ||||||||
\(497\) | −1.15111e6 | −0.209038 | ||||||||
\(498\) | 1.70935e6 | 0.308857 | ||||||||
\(499\) | 3.68872e6 | 0.663168 | 0.331584 | − | 0.943426i | \(-0.392417\pi\) | ||||
0.331584 | + | 0.943426i | \(0.392417\pi\) | |||||||
\(500\) | −2.44877e6 | −0.438049 | ||||||||
\(501\) | 1.53503e6 | 0.273227 | ||||||||
\(502\) | 4.64071e6 | 0.821912 | ||||||||
\(503\) | 6.32946e6 | 1.11544 | 0.557720 | − | 0.830029i | \(-0.311676\pi\) | ||||
0.557720 | + | 0.830029i | \(0.311676\pi\) | |||||||
\(504\) | 254016. | 0.0445435 | ||||||||
\(505\) | −204820. | −0.0357391 | ||||||||
\(506\) | −31740.0 | −0.00551100 | ||||||||
\(507\) | 6.88557e6 | 1.18965 | ||||||||
\(508\) | −930352. | −0.159951 | ||||||||
\(509\) | 2.86719e6 | 0.490526 | 0.245263 | − | 0.969457i | \(-0.421126\pi\) | ||||
0.245263 | + | 0.969457i | \(0.421126\pi\) | |||||||
\(510\) | −80640.0 | −0.0137286 | ||||||||
\(511\) | −262444. | −0.0444615 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | −961551. | −0.161317 | ||||||||
\(514\) | −5.11260e6 | −0.853561 | ||||||||
\(515\) | 750148. | 0.124632 | ||||||||
\(516\) | 1.49645e6 | 0.247421 | ||||||||
\(517\) | 177075. | 0.0291361 | ||||||||
\(518\) | 994504. | 0.162848 | ||||||||
\(519\) | 1.12811e6 | 0.183838 | ||||||||
\(520\) | −1.91027e6 | −0.309804 | ||||||||
\(521\) | −7.27474e6 | −1.17415 | −0.587075 | − | 0.809533i | \(-0.699720\pi\) | ||||
−0.587075 | + | 0.809533i | \(0.699720\pi\) | |||||||
\(522\) | −1.16186e6 | −0.186629 | ||||||||
\(523\) | 1.17334e7 | 1.87573 | 0.937863 | − | 0.347006i | \(-0.112802\pi\) | ||||
0.937863 | + | 0.347006i | \(0.112802\pi\) | |||||||
\(524\) | −1.53282e6 | −0.243872 | ||||||||
\(525\) | −1.03238e6 | −0.163471 | ||||||||
\(526\) | −2.49096e6 | −0.392556 | ||||||||
\(527\) | 628000. | 0.0984993 | ||||||||
\(528\) | −34560.0 | −0.00539497 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −38640.0 | −0.00597513 | ||||||||
\(531\) | −2.53911e6 | −0.390791 | ||||||||
\(532\) | −1.03410e6 | −0.158410 | ||||||||
\(533\) | 1.87904e7 | 2.86495 | ||||||||
\(534\) | −2.09455e6 | −0.317862 | ||||||||
\(535\) | 5.04638e6 | 0.762247 | ||||||||
\(536\) | −1.69933e6 | −0.255485 | ||||||||
\(537\) | 3.07562e6 | 0.460254 | ||||||||
\(538\) | −6.17758e6 | −0.920158 | ||||||||
\(539\) | −36015.0 | −0.00533963 | ||||||||
\(540\) | 326592. | 0.0481971 | ||||||||
\(541\) | 3.98664e6 | 0.585617 | 0.292808 | − | 0.956171i | \(-0.405410\pi\) | ||||
0.292808 | + | 0.956171i | \(0.405410\pi\) | |||||||
\(542\) | 4.10779e6 | 0.600634 | ||||||||
\(543\) | −237402. | −0.0345529 | ||||||||
\(544\) | −81920.0 | −0.0118684 | ||||||||
\(545\) | 4.77232e6 | 0.688237 | ||||||||
\(546\) | −1.88042e6 | −0.269944 | ||||||||
\(547\) | 8.47845e6 | 1.21157 | 0.605784 | − | 0.795629i | \(-0.292859\pi\) | ||||
0.605784 | + | 0.795629i | \(0.292859\pi\) | |||||||
\(548\) | 2.45899e6 | 0.349789 | ||||||||
\(549\) | −406539. | −0.0575667 | ||||||||
\(550\) | 140460. | 0.0197991 | ||||||||
\(551\) | 4.72993e6 | 0.663707 | ||||||||
\(552\) | 304704. | 0.0425628 | ||||||||
\(553\) | 4.89363e6 | 0.680485 | ||||||||
\(554\) | −3.58586e6 | −0.496385 | ||||||||
\(555\) | 1.27865e6 | 0.176205 | ||||||||
\(556\) | 5.05760e6 | 0.693837 | ||||||||
\(557\) | 1.11666e7 | 1.52505 | 0.762524 | − | 0.646960i | \(-0.223960\pi\) | ||||
0.762524 | + | 0.646960i | \(0.223960\pi\) | |||||||
\(558\) | −2.54340e6 | −0.345803 | ||||||||
\(559\) | −1.10779e7 | −1.49943 | ||||||||
\(560\) | 351232. | 0.0473286 | ||||||||
\(561\) | 10800.0 | 0.00144883 | ||||||||
\(562\) | 3.17583e6 | 0.424147 | ||||||||
\(563\) | −3.61705e6 | −0.480932 | −0.240466 | − | 0.970658i | \(-0.577300\pi\) | ||||
−0.240466 | + | 0.970658i | \(0.577300\pi\) | |||||||
\(564\) | −1.69992e6 | −0.225025 | ||||||||
\(565\) | 886648. | 0.116850 | ||||||||
\(566\) | −883152. | −0.115876 | ||||||||
\(567\) | 321489. | 0.0419961 | ||||||||
\(568\) | −1.50349e6 | −0.195537 | ||||||||
\(569\) | −5.53948e6 | −0.717279 | −0.358640 | − | 0.933476i | \(-0.616759\pi\) | ||||
−0.358640 | + | 0.933476i | \(0.616759\pi\) | |||||||
\(570\) | −1.32955e6 | −0.171403 | ||||||||
\(571\) | 5.99194e6 | 0.769091 | 0.384545 | − | 0.923106i | \(-0.374358\pi\) | ||||
0.384545 | + | 0.923106i | \(0.374358\pi\) | |||||||
\(572\) | 255840. | 0.0326948 | ||||||||
\(573\) | 4.58996e6 | 0.584012 | ||||||||
\(574\) | −3.45489e6 | −0.437678 | ||||||||
\(575\) | −1.23839e6 | −0.156202 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −2.12121e6 | −0.265243 | −0.132622 | − | 0.991167i | \(-0.542339\pi\) | ||||
−0.132622 | + | 0.991167i | \(0.542339\pi\) | |||||||
\(578\) | −5.65383e6 | −0.703920 | ||||||||
\(579\) | −2.39144e6 | −0.296457 | ||||||||
\(580\) | −1.60653e6 | −0.198298 | ||||||||
\(581\) | 2.32662e6 | 0.285946 | ||||||||
\(582\) | 2.61799e6 | 0.320377 | ||||||||
\(583\) | 5175.00 | 0.000630578 0 | ||||||||
\(584\) | −342784. | −0.0415900 | ||||||||
\(585\) | −2.41769e6 | −0.292086 | ||||||||
\(586\) | −2.16747e6 | −0.260741 | ||||||||
\(587\) | −5.73403e6 | −0.686854 | −0.343427 | − | 0.939179i | \(-0.611588\pi\) | ||||
−0.343427 | + | 0.939179i | \(0.611588\pi\) | |||||||
\(588\) | 345744. | 0.0412393 | ||||||||
\(589\) | 1.03542e7 | 1.22978 | ||||||||
\(590\) | −3.51086e6 | −0.415225 | ||||||||
\(591\) | −3.46333e6 | −0.407873 | ||||||||
\(592\) | 1.29894e6 | 0.152330 | ||||||||
\(593\) | −1.19277e7 | −1.39290 | −0.696448 | − | 0.717608i | \(-0.745237\pi\) | ||||
−0.696448 | + | 0.717608i | \(0.745237\pi\) | |||||||
\(594\) | −43740.0 | −0.00508643 | ||||||||
\(595\) | −109760. | −0.0127102 | ||||||||
\(596\) | −6.05867e6 | −0.698653 | ||||||||
\(597\) | −3.81290e6 | −0.437844 | ||||||||
\(598\) | −2.25566e6 | −0.257941 | ||||||||
\(599\) | −1.08379e7 | −1.23418 | −0.617090 | − | 0.786892i | \(-0.711689\pi\) | ||||
−0.617090 | + | 0.786892i | \(0.711689\pi\) | |||||||
\(600\) | −1.34842e6 | −0.152913 | ||||||||
\(601\) | 6.61816e6 | 0.747397 | 0.373698 | − | 0.927550i | \(-0.378089\pi\) | ||||
0.373698 | + | 0.927550i | \(0.378089\pi\) | |||||||
\(602\) | 2.03683e6 | 0.229068 | ||||||||
\(603\) | −2.15071e6 | −0.240873 | ||||||||
\(604\) | −1.56325e6 | −0.174355 | ||||||||
\(605\) | −4.50313e6 | −0.500179 | ||||||||
\(606\) | −263340. | −0.0291297 | ||||||||
\(607\) | −5.31644e6 | −0.585665 | −0.292833 | − | 0.956164i | \(-0.594598\pi\) | ||||
−0.292833 | + | 0.956164i | \(0.594598\pi\) | |||||||
\(608\) | −1.35066e6 | −0.148179 | ||||||||
\(609\) | −1.58143e6 | −0.172785 | ||||||||
\(610\) | −562128. | −0.0611661 | ||||||||
\(611\) | 1.25841e7 | 1.36370 | ||||||||
\(612\) | −103680. | −0.0111896 | ||||||||
\(613\) | −4.59787e6 | −0.494203 | −0.247101 | − | 0.968990i | \(-0.579478\pi\) | ||||
−0.247101 | + | 0.968990i | \(0.579478\pi\) | |||||||
\(614\) | −1.14849e7 | −1.22944 | ||||||||
\(615\) | −4.44200e6 | −0.473578 | ||||||||
\(616\) | −47040.0 | −0.00499477 | ||||||||
\(617\) | 1.51913e7 | 1.60650 | 0.803250 | − | 0.595642i | \(-0.203102\pi\) | ||||
0.803250 | + | 0.595642i | \(0.203102\pi\) | |||||||
\(618\) | 964476. | 0.101583 | ||||||||
\(619\) | 7.60144e6 | 0.797388 | 0.398694 | − | 0.917084i | \(-0.369464\pi\) | ||||
0.398694 | + | 0.917084i | \(0.369464\pi\) | |||||||
\(620\) | −3.51680e6 | −0.367425 | ||||||||
\(621\) | 385641. | 0.0401286 | ||||||||
\(622\) | 9.55618e6 | 0.990395 | ||||||||
\(623\) | −2.85092e6 | −0.294283 | ||||||||
\(624\) | −2.45606e6 | −0.252510 | ||||||||
\(625\) | 3.03028e6 | 0.310301 | ||||||||
\(626\) | 3.40375e6 | 0.347154 | ||||||||
\(627\) | 178065. | 0.0180888 | ||||||||
\(628\) | −9.32107e6 | −0.943120 | ||||||||
\(629\) | −405920. | −0.0409085 | ||||||||
\(630\) | 444528. | 0.0446219 | ||||||||
\(631\) | 4.70843e6 | 0.470763 | 0.235382 | − | 0.971903i | \(-0.424366\pi\) | ||||
0.235382 | + | 0.971903i | \(0.424366\pi\) | |||||||
\(632\) | 6.39168e6 | 0.636535 | ||||||||
\(633\) | 3.48351e6 | 0.345548 | ||||||||
\(634\) | −98968.0 | −0.00977849 | ||||||||
\(635\) | −1.62812e6 | −0.160233 | ||||||||
\(636\) | −49680.0 | −0.00487011 | ||||||||
\(637\) | −2.55947e6 | −0.249920 | ||||||||
\(638\) | 215160. | 0.0209271 | ||||||||
\(639\) | −1.90285e6 | −0.184354 | ||||||||
\(640\) | 458752. | 0.0442719 | ||||||||
\(641\) | 345153. | 0.0331793 | 0.0165896 | − | 0.999862i | \(-0.494719\pi\) | ||||
0.0165896 | + | 0.999862i | \(0.494719\pi\) | |||||||
\(642\) | 6.48821e6 | 0.621280 | ||||||||
\(643\) | 1.05491e7 | 1.00621 | 0.503104 | − | 0.864226i | \(-0.332191\pi\) | ||||
0.503104 | + | 0.864226i | \(0.332191\pi\) | |||||||
\(644\) | 414736. | 0.0394055 | ||||||||
\(645\) | 2.61878e6 | 0.247857 | ||||||||
\(646\) | 422080. | 0.0397936 | ||||||||
\(647\) | −1.49902e7 | −1.40782 | −0.703910 | − | 0.710289i | \(-0.748564\pi\) | ||||
−0.703910 | + | 0.710289i | \(0.748564\pi\) | |||||||
\(648\) | 419904. | 0.0392837 | ||||||||
\(649\) | 470205. | 0.0438203 | ||||||||
\(650\) | 9.98202e6 | 0.926692 | ||||||||
\(651\) | −3.46185e6 | −0.320152 | ||||||||
\(652\) | −5.55851e6 | −0.512082 | ||||||||
\(653\) | 658304. | 0.0604148 | 0.0302074 | − | 0.999544i | \(-0.490383\pi\) | ||||
0.0302074 | + | 0.999544i | \(0.490383\pi\) | |||||||
\(654\) | 6.13584e6 | 0.560957 | ||||||||
\(655\) | −2.68243e6 | −0.244301 | ||||||||
\(656\) | −4.51251e6 | −0.409410 | ||||||||
\(657\) | −433836. | −0.0392114 | ||||||||
\(658\) | −2.31378e6 | −0.208333 | ||||||||
\(659\) | 2.09919e7 | 1.88295 | 0.941474 | − | 0.337086i | \(-0.109441\pi\) | ||||
0.941474 | + | 0.337086i | \(0.109441\pi\) | |||||||
\(660\) | −60480.0 | −0.00540446 | ||||||||
\(661\) | 668861. | 0.0595432 | 0.0297716 | − | 0.999557i | \(-0.490522\pi\) | ||||
0.0297716 | + | 0.999557i | \(0.490522\pi\) | |||||||
\(662\) | −9.99254e6 | −0.886198 | ||||||||
\(663\) | 767520. | 0.0678119 | ||||||||
\(664\) | 3.03885e6 | 0.267478 | ||||||||
\(665\) | −1.80967e6 | −0.158688 | ||||||||
\(666\) | 1.64398e6 | 0.143618 | ||||||||
\(667\) | −1.89699e6 | −0.165102 | ||||||||
\(668\) | 2.72894e6 | 0.236621 | ||||||||
\(669\) | −2.69678e6 | −0.232959 | ||||||||
\(670\) | −2.97382e6 | −0.255934 | ||||||||
\(671\) | 75285.0 | 0.00645509 | ||||||||
\(672\) | 451584. | 0.0385758 | ||||||||
\(673\) | 2.60177e6 | 0.221427 | 0.110714 | − | 0.993852i | \(-0.464686\pi\) | ||||
0.110714 | + | 0.993852i | \(0.464686\pi\) | |||||||
\(674\) | −1.51306e7 | −1.28294 | ||||||||
\(675\) | −1.70659e6 | −0.144168 | ||||||||
\(676\) | 1.22410e7 | 1.03027 | ||||||||
\(677\) | 8.72440e6 | 0.731583 | 0.365792 | − | 0.930697i | \(-0.380798\pi\) | ||||
0.365792 | + | 0.930697i | \(0.380798\pi\) | |||||||
\(678\) | 1.13998e6 | 0.0952405 | ||||||||
\(679\) | 3.56338e6 | 0.296611 | ||||||||
\(680\) | −143360. | −0.0118893 | ||||||||
\(681\) | −1.16684e7 | −0.964145 | ||||||||
\(682\) | 471000. | 0.0387757 | ||||||||
\(683\) | 2.08822e7 | 1.71287 | 0.856437 | − | 0.516251i | \(-0.172673\pi\) | ||||
0.856437 | + | 0.516251i | \(0.172673\pi\) | |||||||
\(684\) | −1.70942e6 | −0.139704 | ||||||||
\(685\) | 4.30324e6 | 0.350404 | ||||||||
\(686\) | 470596. | 0.0381802 | ||||||||
\(687\) | 4.04774e6 | 0.327206 | ||||||||
\(688\) | 2.66035e6 | 0.214273 | ||||||||
\(689\) | 367770. | 0.0295140 | ||||||||
\(690\) | 533232. | 0.0426377 | ||||||||
\(691\) | 8.86813e6 | 0.706540 | 0.353270 | − | 0.935521i | \(-0.385070\pi\) | ||||
0.353270 | + | 0.935521i | \(0.385070\pi\) | |||||||
\(692\) | 2.00554e6 | 0.159208 | ||||||||
\(693\) | −59535.0 | −0.00470911 | ||||||||
\(694\) | −5.00378e6 | −0.394366 | ||||||||
\(695\) | 8.85080e6 | 0.695057 | ||||||||
\(696\) | −2.06554e6 | −0.161625 | ||||||||
\(697\) | 1.41016e6 | 0.109948 | ||||||||
\(698\) | 1.62745e7 | 1.26436 | ||||||||
\(699\) | −4.76269e6 | −0.368688 | ||||||||
\(700\) | −1.83534e6 | −0.141570 | ||||||||
\(701\) | −1.03054e7 | −0.792084 | −0.396042 | − | 0.918232i | \(-0.629617\pi\) | ||||
−0.396042 | + | 0.918232i | \(0.629617\pi\) | |||||||
\(702\) | −3.10846e6 | −0.238069 | ||||||||
\(703\) | −6.69261e6 | −0.510748 | ||||||||
\(704\) | −61440.0 | −0.00467218 | ||||||||
\(705\) | −2.97486e6 | −0.225421 | ||||||||
\(706\) | 9.91598e6 | 0.748727 | ||||||||
\(707\) | −358435. | −0.0269688 | ||||||||
\(708\) | −4.51397e6 | −0.338435 | ||||||||
\(709\) | −6.85327e6 | −0.512014 | −0.256007 | − | 0.966675i | \(-0.582407\pi\) | ||||
−0.256007 | + | 0.966675i | \(0.582407\pi\) | |||||||
\(710\) | −2.63110e6 | −0.195881 | ||||||||
\(711\) | 8.08947e6 | 0.600131 | ||||||||
\(712\) | −3.72365e6 | −0.275276 | ||||||||
\(713\) | −4.15265e6 | −0.305916 | ||||||||
\(714\) | −141120. | −0.0103596 | ||||||||
\(715\) | 447720. | 0.0327523 | ||||||||
\(716\) | 5.46778e6 | 0.398592 | ||||||||
\(717\) | 3.72060e6 | 0.270281 | ||||||||
\(718\) | 1.65974e7 | 1.20152 | ||||||||
\(719\) | −1.25255e7 | −0.903595 | −0.451797 | − | 0.892121i | \(-0.649217\pi\) | ||||
−0.451797 | + | 0.892121i | \(0.649217\pi\) | |||||||
\(720\) | 580608. | 0.0417399 | ||||||||
\(721\) | 1.31276e6 | 0.0940474 | ||||||||
\(722\) | −2.94535e6 | −0.210278 | ||||||||
\(723\) | 1.13717e7 | 0.809056 | ||||||||
\(724\) | −422048. | −0.0299237 | ||||||||
\(725\) | 8.39483e6 | 0.593153 | ||||||||
\(726\) | −5.78974e6 | −0.407678 | ||||||||
\(727\) | 1.06505e7 | 0.747366 | 0.373683 | − | 0.927556i | \(-0.378095\pi\) | ||||
0.373683 | + | 0.927556i | \(0.378095\pi\) | |||||||
\(728\) | −3.34298e6 | −0.233779 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −599872. | −0.0416631 | ||||||||
\(731\) | −831360. | −0.0575434 | ||||||||
\(732\) | −722736. | −0.0498542 | ||||||||
\(733\) | −1.80782e7 | −1.24278 | −0.621390 | − | 0.783502i | \(-0.713432\pi\) | ||||
−0.621390 | + | 0.783502i | \(0.713432\pi\) | |||||||
\(734\) | 1.48182e7 | 1.01521 | ||||||||
\(735\) | 605052. | 0.0413118 | ||||||||
\(736\) | 541696. | 0.0368605 | ||||||||
\(737\) | 398280. | 0.0270097 | ||||||||
\(738\) | −5.71115e6 | −0.385996 | ||||||||
\(739\) | −6.39122e6 | −0.430500 | −0.215250 | − | 0.976559i | \(-0.569057\pi\) | ||||
−0.215250 | + | 0.976559i | \(0.569057\pi\) | |||||||
\(740\) | 2.27315e6 | 0.152598 | ||||||||
\(741\) | 1.26545e7 | 0.846640 | ||||||||
\(742\) | −67620.0 | −0.00450885 | ||||||||
\(743\) | 7.48524e6 | 0.497432 | 0.248716 | − | 0.968576i | \(-0.419991\pi\) | ||||
0.248716 | + | 0.968576i | \(0.419991\pi\) | |||||||
\(744\) | −4.52160e6 | −0.299474 | ||||||||
\(745\) | −1.06027e7 | −0.699882 | ||||||||
\(746\) | −228616. | −0.0150404 | ||||||||
\(747\) | 3.84604e6 | 0.252181 | ||||||||
\(748\) | 19200.0 | 0.00125472 | ||||||||
\(749\) | 8.83117e6 | 0.575193 | ||||||||
\(750\) | −5.50973e6 | −0.357665 | ||||||||
\(751\) | −9.45033e6 | −0.611430 | −0.305715 | − | 0.952123i | \(-0.598896\pi\) | ||||
−0.305715 | + | 0.952123i | \(0.598896\pi\) | |||||||
\(752\) | −3.02208e6 | −0.194877 | ||||||||
\(753\) | 1.04416e7 | 0.671088 | ||||||||
\(754\) | 1.52907e7 | 0.979488 | ||||||||
\(755\) | −2.73568e6 | −0.174662 | ||||||||
\(756\) | 571536. | 0.0363696 | ||||||||
\(757\) | −1.32568e7 | −0.840813 | −0.420406 | − | 0.907336i | \(-0.638113\pi\) | ||||
−0.420406 | + | 0.907336i | \(0.638113\pi\) | |||||||
\(758\) | −1.54171e7 | −0.974605 | ||||||||
\(759\) | −71415.0 | −0.00449971 | ||||||||
\(760\) | −2.36365e6 | −0.148439 | ||||||||
\(761\) | 1.45780e7 | 0.912509 | 0.456255 | − | 0.889849i | \(-0.349191\pi\) | ||||
0.456255 | + | 0.889849i | \(0.349191\pi\) | |||||||
\(762\) | −2.09329e6 | −0.130600 | ||||||||
\(763\) | 8.35156e6 | 0.519345 | ||||||||
\(764\) | 8.15992e6 | 0.505769 | ||||||||
\(765\) | −181440. | −0.0112093 | ||||||||
\(766\) | −1.89184e7 | −1.16496 | ||||||||
\(767\) | 3.34159e7 | 2.05100 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | −3.47693e6 | −0.212022 | −0.106011 | − | 0.994365i | \(-0.533808\pi\) | ||||
−0.106011 | + | 0.994365i | \(0.533808\pi\) | |||||||
\(770\) | −82320.0 | −0.00500355 | ||||||||
\(771\) | −1.15034e7 | −0.696929 | ||||||||
\(772\) | −4.25144e6 | −0.256740 | ||||||||
\(773\) | 1.20953e7 | 0.728064 | 0.364032 | − | 0.931386i | \(-0.381400\pi\) | ||||
0.364032 | + | 0.931386i | \(0.381400\pi\) | |||||||
\(774\) | 3.36701e6 | 0.202019 | ||||||||
\(775\) | 1.83768e7 | 1.09905 | ||||||||
\(776\) | 4.65421e6 | 0.277454 | ||||||||
\(777\) | 2.23763e6 | 0.132965 | ||||||||
\(778\) | −1.29221e7 | −0.765391 | ||||||||
\(779\) | 2.32500e7 | 1.37271 | ||||||||
\(780\) | −4.29811e6 | −0.252954 | ||||||||
\(781\) | 352380. | 0.0206721 | ||||||||
\(782\) | −169280. | −0.00989894 | ||||||||
\(783\) | −2.61419e6 | −0.152382 | ||||||||
\(784\) | 614656. | 0.0357143 | ||||||||
\(785\) | −1.63119e7 | −0.944778 | ||||||||
\(786\) | −3.44884e6 | −0.199121 | ||||||||
\(787\) | −5.54933e6 | −0.319377 | −0.159689 | − | 0.987167i | \(-0.551049\pi\) | ||||
−0.159689 | + | 0.987167i | \(0.551049\pi\) | |||||||
\(788\) | −6.15702e6 | −0.353228 | ||||||||
\(789\) | −5.60465e6 | −0.320521 | ||||||||
\(790\) | 1.11854e7 | 0.637654 | ||||||||
\(791\) | 1.55163e6 | 0.0881755 | ||||||||
\(792\) | −77760.0 | −0.00440497 | ||||||||
\(793\) | 5.35025e6 | 0.302128 | ||||||||
\(794\) | 1.65695e6 | 0.0932736 | ||||||||
\(795\) | −86940.0 | −0.00487867 | ||||||||
\(796\) | −6.77848e6 | −0.379184 | ||||||||
\(797\) | 3.29305e7 | 1.83634 | 0.918168 | − | 0.396191i | \(-0.129668\pi\) | ||||
0.918168 | + | 0.396191i | \(0.129668\pi\) | |||||||
\(798\) | −2.32672e6 | −0.129341 | ||||||||
\(799\) | 944400. | 0.0523346 | ||||||||
\(800\) | −2.39718e6 | −0.132427 | ||||||||
\(801\) | −4.71274e6 | −0.259533 | ||||||||
\(802\) | 6.11007e6 | 0.335436 | ||||||||
\(803\) | 80340.0 | 0.00439686 | ||||||||
\(804\) | −3.82349e6 | −0.208603 | ||||||||
\(805\) | 725788. | 0.0394748 | ||||||||
\(806\) | 3.34724e7 | 1.81489 | ||||||||
\(807\) | −1.38995e7 | −0.751306 | ||||||||
\(808\) | −468160. | −0.0252270 | ||||||||
\(809\) | 7.09564e6 | 0.381171 | 0.190586 | − | 0.981671i | \(-0.438961\pi\) | ||||
0.190586 | + | 0.981671i | \(0.438961\pi\) | |||||||
\(810\) | 734832. | 0.0393528 | ||||||||
\(811\) | 1.56211e7 | 0.833988 | 0.416994 | − | 0.908909i | \(-0.363084\pi\) | ||||
0.416994 | + | 0.908909i | \(0.363084\pi\) | |||||||
\(812\) | −2.81142e6 | −0.149636 | ||||||||
\(813\) | 9.24253e6 | 0.490416 | ||||||||
\(814\) | −304440. | −0.0161043 | ||||||||
\(815\) | −9.72740e6 | −0.512983 | ||||||||
\(816\) | −184320. | −0.00969052 | ||||||||
\(817\) | −1.37070e7 | −0.718437 | ||||||||
\(818\) | −1.13470e7 | −0.592921 | ||||||||
\(819\) | −4.23095e6 | −0.220409 | ||||||||
\(820\) | −7.89690e6 | −0.410130 | ||||||||
\(821\) | 2.26882e7 | 1.17474 | 0.587371 | − | 0.809318i | \(-0.300163\pi\) | ||||
0.587371 | + | 0.809318i | \(0.300163\pi\) | |||||||
\(822\) | 5.53273e6 | 0.285601 | ||||||||
\(823\) | 1.61712e7 | 0.832230 | 0.416115 | − | 0.909312i | \(-0.363391\pi\) | ||||
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(824\) | 1.71462e6 | 0.0879733 | ||||||||
\(825\) | 316035. | 0.0161659 | ||||||||
\(826\) | −6.14401e6 | −0.313330 | ||||||||
\(827\) | 2.97150e6 | 0.151082 | 0.0755410 | − | 0.997143i | \(-0.475932\pi\) | ||||
0.0755410 | + | 0.997143i | \(0.475932\pi\) | |||||||
\(828\) | 685584. | 0.0347524 | ||||||||
\(829\) | −3.42265e7 | −1.72972 | −0.864861 | − | 0.502011i | \(-0.832594\pi\) | ||||
−0.864861 | + | 0.502011i | \(0.832594\pi\) | |||||||
\(830\) | 5.31798e6 | 0.267949 | ||||||||
\(831\) | −8.06819e6 | −0.405297 | ||||||||
\(832\) | −4.36634e6 | −0.218680 | ||||||||
\(833\) | −192080. | −0.00959113 | ||||||||
\(834\) | 1.13796e7 | 0.566516 | ||||||||
\(835\) | 4.77565e6 | 0.237037 | ||||||||
\(836\) | 316560. | 0.0156654 | ||||||||
\(837\) | −5.72265e6 | −0.282347 | ||||||||
\(838\) | −312456. | −0.0153702 | ||||||||
\(839\) | 3.58526e7 | 1.75839 | 0.879197 | − | 0.476458i | \(-0.158080\pi\) | ||||
0.879197 | + | 0.476458i | \(0.158080\pi\) | |||||||
\(840\) | 790272. | 0.0386437 | ||||||||
\(841\) | −7.65175e6 | −0.373053 | ||||||||
\(842\) | −6.34214e6 | −0.308287 | ||||||||
\(843\) | 7.14562e6 | 0.346315 | ||||||||
\(844\) | 6.19291e6 | 0.299253 | ||||||||
\(845\) | 2.14218e7 | 1.03208 | ||||||||
\(846\) | −3.82482e6 | −0.183732 | ||||||||
\(847\) | −7.88047e6 | −0.377436 | ||||||||
\(848\) | −88320.0 | −0.00421764 | ||||||||
\(849\) | −1.98709e6 | −0.0946126 | ||||||||
\(850\) | 749120. | 0.0355635 | ||||||||
\(851\) | 2.68415e6 | 0.127052 | ||||||||
\(852\) | −3.38285e6 | −0.159655 | ||||||||
\(853\) | −2.14702e7 | −1.01033 | −0.505165 | − | 0.863023i | \(-0.668568\pi\) | ||||
−0.505165 | + | 0.863023i | \(0.668568\pi\) | |||||||
\(854\) | −983724. | −0.0461560 | ||||||||
\(855\) | −2.99149e6 | −0.139950 | ||||||||
\(856\) | 1.15346e7 | 0.538044 | ||||||||
\(857\) | −1.90679e7 | −0.886853 | −0.443426 | − | 0.896311i | \(-0.646237\pi\) | ||||
−0.443426 | + | 0.896311i | \(0.646237\pi\) | |||||||
\(858\) | 575640. | 0.0266952 | ||||||||
\(859\) | −3.81485e7 | −1.76398 | −0.881991 | − | 0.471266i | \(-0.843797\pi\) | ||||
−0.881991 | + | 0.471266i | \(0.843797\pi\) | |||||||
\(860\) | 4.65562e6 | 0.214650 | ||||||||
\(861\) | −7.77351e6 | −0.357363 | ||||||||
\(862\) | −4.08640e6 | −0.187315 | ||||||||
\(863\) | 3.78204e7 | 1.72862 | 0.864309 | − | 0.502961i | \(-0.167756\pi\) | ||||
0.864309 | + | 0.502961i | \(0.167756\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 3.50969e6 | 0.159488 | ||||||||
\(866\) | 986156. | 0.0446839 | ||||||||
\(867\) | −1.27211e7 | −0.574748 | ||||||||
\(868\) | −6.15440e6 | −0.277259 | ||||||||
\(869\) | −1.49805e6 | −0.0672941 | ||||||||
\(870\) | −3.61469e6 | −0.161910 | ||||||||
\(871\) | 2.83044e7 | 1.26418 | ||||||||
\(872\) | 1.09082e7 | 0.485803 | ||||||||
\(873\) | 5.89048e6 | 0.261586 | ||||||||
\(874\) | −2.79100e6 | −0.123590 | ||||||||
\(875\) | −7.49935e6 | −0.331134 | ||||||||
\(876\) | −771264. | −0.0339581 | ||||||||
\(877\) | 1.39887e7 | 0.614157 | 0.307079 | − | 0.951684i | \(-0.400649\pi\) | ||||
0.307079 | + | 0.951684i | \(0.400649\pi\) | |||||||
\(878\) | −2.47917e6 | −0.108535 | ||||||||
\(879\) | −4.87681e6 | −0.212894 | ||||||||
\(880\) | −107520. | −0.00468040 | ||||||||
\(881\) | 1.28587e7 | 0.558160 | 0.279080 | − | 0.960268i | \(-0.409971\pi\) | ||||
0.279080 | + | 0.960268i | \(0.409971\pi\) | |||||||
\(882\) | 777924. | 0.0336718 | ||||||||
\(883\) | 2.84134e7 | 1.22637 | 0.613184 | − | 0.789940i | \(-0.289888\pi\) | ||||
0.613184 | + | 0.789940i | \(0.289888\pi\) | |||||||
\(884\) | 1.36448e6 | 0.0587268 | ||||||||
\(885\) | −7.89944e6 | −0.339030 | ||||||||
\(886\) | −2.29780e7 | −0.983396 | ||||||||
\(887\) | −1.59646e7 | −0.681315 | −0.340657 | − | 0.940187i | \(-0.610650\pi\) | ||||
−0.340657 | + | 0.940187i | \(0.610650\pi\) | |||||||
\(888\) | 2.92262e6 | 0.124377 | ||||||||
\(889\) | −2.84920e6 | −0.120912 | ||||||||
\(890\) | −6.51638e6 | −0.275760 | ||||||||
\(891\) | −98415.0 | −0.00415305 | ||||||||
\(892\) | −4.79427e6 | −0.201749 | ||||||||
\(893\) | 1.55708e7 | 0.653405 | ||||||||
\(894\) | −1.36320e7 | −0.570448 | ||||||||
\(895\) | 9.56861e6 | 0.399293 | ||||||||
\(896\) | 802816. | 0.0334077 | ||||||||
\(897\) | −5.07523e6 | −0.210608 | ||||||||
\(898\) | 1.92254e7 | 0.795582 | ||||||||
\(899\) | 2.81501e7 | 1.16166 | ||||||||
\(900\) | −3.03394e6 | −0.124853 | ||||||||
\(901\) | 27600.0 | 0.00113265 | ||||||||
\(902\) | 1.05762e6 | 0.0432826 | ||||||||
\(903\) | 4.58287e6 | 0.187033 | ||||||||
\(904\) | 2.02662e6 | 0.0824807 | ||||||||
\(905\) | −738584. | −0.0299763 | ||||||||
\(906\) | −3.51731e6 | −0.142361 | ||||||||
\(907\) | −1.77405e7 | −0.716056 | −0.358028 | − | 0.933711i | \(-0.616551\pi\) | ||||
−0.358028 | + | 0.933711i | \(0.616551\pi\) | |||||||
\(908\) | −2.07438e7 | −0.834974 | ||||||||
\(909\) | −592515. | −0.0237843 | ||||||||
\(910\) | −5.85021e6 | −0.234190 | ||||||||
\(911\) | 771952. | 0.0308173 | 0.0154086 | − | 0.999881i | \(-0.495095\pi\) | ||||
0.0154086 | + | 0.999881i | \(0.495095\pi\) | |||||||
\(912\) | −3.03898e6 | −0.120987 | ||||||||
\(913\) | −712230. | −0.0282777 | ||||||||
\(914\) | −1.06179e7 | −0.420410 | ||||||||
\(915\) | −1.26479e6 | −0.0499419 | ||||||||
\(916\) | 7.19598e6 | 0.283368 | ||||||||
\(917\) | −4.69425e6 | −0.184350 | ||||||||
\(918\) | −233280. | −0.00913631 | ||||||||
\(919\) | −5.43187e6 | −0.212159 | −0.106079 | − | 0.994358i | \(-0.533830\pi\) | ||||
−0.106079 | + | 0.994358i | \(0.533830\pi\) | |||||||
\(920\) | 947968. | 0.0369253 | ||||||||
\(921\) | −2.58410e7 | −1.00383 | ||||||||
\(922\) | 2.58319e7 | 1.00076 | ||||||||
\(923\) | 2.50425e7 | 0.967549 | ||||||||
\(924\) | −105840. | −0.00407821 | ||||||||
\(925\) | −1.18782e7 | −0.456455 | ||||||||
\(926\) | −1.35814e7 | −0.520496 | ||||||||
\(927\) | 2.17007e6 | 0.0829420 | ||||||||
\(928\) | −3.67206e6 | −0.139972 | ||||||||
\(929\) | 8.30088e6 | 0.315562 | 0.157781 | − | 0.987474i | \(-0.449566\pi\) | ||||
0.157781 | + | 0.987474i | \(0.449566\pi\) | |||||||
\(930\) | −7.91280e6 | −0.300001 | ||||||||
\(931\) | −3.16692e6 | −0.119746 | ||||||||
\(932\) | −8.46701e6 | −0.319294 | ||||||||
\(933\) | 2.15014e7 | 0.808654 | ||||||||
\(934\) | −1.45196e7 | −0.544611 | ||||||||
\(935\) | 33600.0 | 0.00125693 | ||||||||
\(936\) | −5.52614e6 | −0.206173 | ||||||||
\(937\) | −8.19947e6 | −0.305096 | −0.152548 | − | 0.988296i | \(-0.548748\pi\) | ||||
−0.152548 | + | 0.988296i | \(0.548748\pi\) | |||||||
\(938\) | −5.20419e6 | −0.193128 | ||||||||
\(939\) | 7.65843e6 | 0.283450 | ||||||||
\(940\) | −5.28864e6 | −0.195220 | ||||||||
\(941\) | −1.01275e7 | −0.372847 | −0.186423 | − | 0.982470i | \(-0.559690\pi\) | ||||
−0.186423 | + | 0.982470i | \(0.559690\pi\) | |||||||
\(942\) | −2.09724e7 | −0.770054 | ||||||||
\(943\) | −9.32468e6 | −0.341472 | ||||||||
\(944\) | −8.02483e6 | −0.293093 | ||||||||
\(945\) | 1.00019e6 | 0.0364336 | ||||||||
\(946\) | −623520. | −0.0226528 | ||||||||
\(947\) | 1.46006e7 | 0.529050 | 0.264525 | − | 0.964379i | \(-0.414785\pi\) | ||||
0.264525 | + | 0.964379i | \(0.414785\pi\) | |||||||
\(948\) | 1.43813e7 | 0.519729 | ||||||||
\(949\) | 5.70950e6 | 0.205794 | ||||||||
\(950\) | 1.23511e7 | 0.444015 | ||||||||
\(951\) | −222678. | −0.00798410 | ||||||||
\(952\) | −250880. | −0.00897168 | ||||||||
\(953\) | −2.15955e7 | −0.770249 | −0.385124 | − | 0.922865i | \(-0.625841\pi\) | ||||
−0.385124 | + | 0.922865i | \(0.625841\pi\) | |||||||
\(954\) | −111780. | −0.00397643 | ||||||||
\(955\) | 1.42799e7 | 0.506659 | ||||||||
\(956\) | 6.61440e6 | 0.234070 | ||||||||
\(957\) | 484110. | 0.0170869 | ||||||||
\(958\) | −2.40210e6 | −0.0845623 | ||||||||
\(959\) | 7.53066e6 | 0.264415 | ||||||||
\(960\) | 1.03219e6 | 0.0361478 | ||||||||
\(961\) | 3.29933e7 | 1.15244 | ||||||||
\(962\) | −2.16355e7 | −0.753755 | ||||||||
\(963\) | 1.45985e7 | 0.507273 | ||||||||
\(964\) | 2.02163e7 | 0.700663 | ||||||||
\(965\) | −7.44002e6 | −0.257191 | ||||||||
\(966\) | 933156. | 0.0321745 | ||||||||
\(967\) | −1.45924e7 | −0.501835 | −0.250917 | − | 0.968008i | \(-0.580732\pi\) | ||||
−0.250917 | + | 0.968008i | \(0.580732\pi\) | |||||||
\(968\) | −1.02929e7 | −0.353059 | ||||||||
\(969\) | 949680. | 0.0324914 | ||||||||
\(970\) | 8.14486e6 | 0.277942 | ||||||||
\(971\) | 4.07609e7 | 1.38738 | 0.693690 | − | 0.720274i | \(-0.255984\pi\) | ||||
0.693690 | + | 0.720274i | \(0.255984\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 1.54889e7 | 0.524492 | ||||||||
\(974\) | −9.62750e6 | −0.325174 | ||||||||
\(975\) | 2.24596e7 | 0.756641 | ||||||||
\(976\) | −1.28486e6 | −0.0431750 | ||||||||
\(977\) | 3.40986e7 | 1.14288 | 0.571439 | − | 0.820645i | \(-0.306386\pi\) | ||||
0.571439 | + | 0.820645i | \(0.306386\pi\) | |||||||
\(978\) | −1.25067e7 | −0.418113 | ||||||||
\(979\) | 872730. | 0.0291020 | ||||||||
\(980\) | 1.07565e6 | 0.0357771 | ||||||||
\(981\) | 1.38056e7 | 0.458020 | ||||||||
\(982\) | −1.10997e7 | −0.367310 | ||||||||
\(983\) | 4.01373e7 | 1.32484 | 0.662421 | − | 0.749131i | \(-0.269529\pi\) | ||||
0.662421 | + | 0.749131i | \(0.269529\pi\) | |||||||
\(984\) | −1.01532e7 | −0.334282 | ||||||||
\(985\) | −1.07748e7 | −0.353849 | ||||||||
\(986\) | 1.14752e6 | 0.0375896 | ||||||||
\(987\) | −5.20600e6 | −0.170103 | ||||||||
\(988\) | 2.24969e7 | 0.733212 | ||||||||
\(989\) | 5.49737e6 | 0.178716 | ||||||||
\(990\) | −136080. | −0.00441272 | ||||||||
\(991\) | −2.97245e7 | −0.961458 | −0.480729 | − | 0.876869i | \(-0.659628\pi\) | ||||
−0.480729 | + | 0.876869i | \(0.659628\pi\) | |||||||
\(992\) | −8.03840e6 | −0.259352 | ||||||||
\(993\) | −2.24832e7 | −0.723578 | ||||||||
\(994\) | −4.60443e6 | −0.147812 | ||||||||
\(995\) | −1.18623e7 | −0.379850 | ||||||||
\(996\) | 6.83741e6 | 0.218395 | ||||||||
\(997\) | 486768. | 0.0155090 | 0.00775451 | − | 0.999970i | \(-0.497532\pi\) | ||||
0.00775451 | + | 0.999970i | \(0.497532\pi\) | |||||||
\(998\) | 1.47549e7 | 0.468931 | ||||||||
\(999\) | 3.69895e6 | 0.117264 |
(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 | 966.6.a.b.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.6.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial |