Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [387,8,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, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("387.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 387 = 3^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
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: | \(120.893004862\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + \cdots + 238240894976 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{4}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(3.52766\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.52766 | 0.488581 | 0.244290 | − | 0.969702i | \(-0.421445\pi\) | ||||
0.244290 | + | 0.969702i | \(0.421445\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −97.4450 | −0.761289 | ||||||||
\(5\) | −304.619 | −1.08984 | −0.544919 | − | 0.838489i | \(-0.683439\pi\) | ||||
−0.544919 | + | 0.838489i | \(0.683439\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1421.71 | 1.56663 | 0.783317 | − | 0.621622i | \(-0.213526\pi\) | ||||
0.783317 | + | 0.621622i | \(0.213526\pi\) | |||||||
\(8\) | −1246.18 | −0.860532 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1683.83 | −0.532473 | ||||||||
\(11\) | 7143.27 | 1.61817 | 0.809083 | − | 0.587695i | \(-0.199964\pi\) | ||||
0.809083 | + | 0.587695i | \(0.199964\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1897.38 | −0.239525 | −0.119763 | − | 0.992803i | \(-0.538213\pi\) | ||||
−0.119763 | + | 0.992803i | \(0.538213\pi\) | |||||||
\(14\) | 7858.73 | 0.765427 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5584.49 | 0.340850 | ||||||||
\(17\) | −1140.96 | −0.0563249 | −0.0281624 | − | 0.999603i | \(-0.508966\pi\) | ||||
−0.0281624 | + | 0.999603i | \(0.508966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16176.5 | −0.541061 | −0.270531 | − | 0.962711i | \(-0.587199\pi\) | ||||
−0.270531 | + | 0.962711i | \(0.587199\pi\) | |||||||
\(20\) | 29683.6 | 0.829681 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 39485.6 | 0.790604 | ||||||||
\(23\) | −91608.2 | −1.56995 | −0.784977 | − | 0.619525i | \(-0.787325\pi\) | ||||
−0.784977 | + | 0.619525i | \(0.787325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14667.6 | 0.187745 | ||||||||
\(26\) | −10488.0 | −0.117027 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −138539. | −1.19266 | ||||||||
\(29\) | 229144. | 1.74468 | 0.872341 | − | 0.488898i | \(-0.162601\pi\) | ||||
0.872341 | + | 0.488898i | \(0.162601\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −212418. | −1.28064 | −0.640318 | − | 0.768110i | \(-0.721197\pi\) | ||||
−0.640318 | + | 0.768110i | \(0.721197\pi\) | |||||||
\(32\) | 190381. | 1.02706 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6306.85 | −0.0275192 | ||||||||
\(35\) | −433079. | −1.70738 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −482724. | −1.56672 | −0.783362 | − | 0.621566i | \(-0.786497\pi\) | ||||
−0.783362 | + | 0.621566i | \(0.786497\pi\) | |||||||
\(38\) | −89418.0 | −0.264352 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 379611. | 0.937839 | ||||||||
\(41\) | 384844. | 0.872049 | 0.436025 | − | 0.899935i | \(-0.356386\pi\) | ||||
0.436025 | + | 0.899935i | \(0.356386\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 79507.0 | 0.152499 | ||||||||
\(44\) | −696076. | −1.23189 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −506379. | −0.767049 | ||||||||
\(47\) | −380758. | −0.534941 | −0.267471 | − | 0.963566i | \(-0.586188\pi\) | ||||
−0.267471 | + | 0.963566i | \(0.586188\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.19772e6 | 1.45435 | ||||||||
\(50\) | 81077.5 | 0.0917287 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 184890. | 0.182348 | ||||||||
\(53\) | 361687. | 0.333709 | 0.166854 | − | 0.985982i | \(-0.446639\pi\) | ||||
0.166854 | + | 0.985982i | \(0.446639\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.17598e6 | −1.76354 | ||||||||
\(56\) | −1.77171e6 | −1.34814 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.26663e6 | 0.852418 | ||||||||
\(59\) | 1.95582e6 | 1.23979 | 0.619894 | − | 0.784685i | \(-0.287176\pi\) | ||||
0.619894 | + | 0.784685i | \(0.287176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −479312. | −0.270374 | −0.135187 | − | 0.990820i | \(-0.543163\pi\) | ||||
−0.135187 | + | 0.990820i | \(0.543163\pi\) | |||||||
\(62\) | −1.17417e6 | −0.625694 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 337544. | 0.160954 | ||||||||
\(65\) | 577976. | 0.261044 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.46363e6 | −1.00072 | −0.500362 | − | 0.865816i | \(-0.666800\pi\) | ||||
−0.500362 | + | 0.865816i | \(0.666800\pi\) | |||||||
\(68\) | 111181. | 0.0428795 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.39392e6 | −0.834191 | ||||||||
\(71\) | 1.56017e6 | 0.517332 | 0.258666 | − | 0.965967i | \(-0.416717\pi\) | ||||
0.258666 | + | 0.965967i | \(0.416717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.98243e6 | 0.897305 | 0.448652 | − | 0.893706i | \(-0.351904\pi\) | ||||
0.448652 | + | 0.893706i | \(0.351904\pi\) | |||||||
\(74\) | −2.66833e6 | −0.765471 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.57632e6 | 0.411904 | ||||||||
\(77\) | 1.01557e7 | 2.53507 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.64376e6 | 0.603292 | 0.301646 | − | 0.953420i | \(-0.402464\pi\) | ||||
0.301646 | + | 0.953420i | \(0.402464\pi\) | |||||||
\(80\) | −1.70114e6 | −0.371471 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.12728e6 | 0.426066 | ||||||||
\(83\) | −5.54958e6 | −1.06534 | −0.532668 | − | 0.846324i | \(-0.678810\pi\) | ||||
−0.532668 | + | 0.846324i | \(0.678810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 347559. | 0.0613850 | ||||||||
\(86\) | 439488. | 0.0745078 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.90183e6 | −1.39248 | ||||||||
\(89\) | 9.15035e6 | 1.37585 | 0.687927 | − | 0.725779i | \(-0.258521\pi\) | ||||
0.687927 | + | 0.725779i | \(0.258521\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.69752e6 | −0.375249 | ||||||||
\(92\) | 8.92676e6 | 1.19519 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.10470e6 | −0.261362 | ||||||||
\(95\) | 4.92766e6 | 0.589669 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.33147e6 | 0.481875 | 0.240937 | − | 0.970541i | \(-0.422545\pi\) | ||||
0.240937 | + | 0.970541i | \(0.422545\pi\) | |||||||
\(98\) | 6.62056e6 | 0.710565 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.42928e6 | −0.142928 | ||||||||
\(101\) | 5.03114e6 | 0.485894 | 0.242947 | − | 0.970040i | \(-0.421886\pi\) | ||||
0.242947 | + | 0.970040i | \(0.421886\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.58973e7 | 1.43348 | 0.716741 | − | 0.697339i | \(-0.245633\pi\) | ||||
0.716741 | + | 0.697339i | \(0.245633\pi\) | |||||||
\(104\) | 2.36448e6 | 0.206119 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.99928e6 | 0.163044 | ||||||||
\(107\) | 1.56322e7 | 1.23361 | 0.616805 | − | 0.787116i | \(-0.288427\pi\) | ||||
0.616805 | + | 0.787116i | \(0.288427\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.27583e7 | 0.943624 | 0.471812 | − | 0.881699i | \(-0.343600\pi\) | ||||
0.471812 | + | 0.881699i | \(0.343600\pi\) | |||||||
\(110\) | −1.20280e7 | −0.861630 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.93952e6 | 0.533987 | ||||||||
\(113\) | 1.58622e7 | 1.03416 | 0.517081 | − | 0.855937i | \(-0.327019\pi\) | ||||
0.517081 | + | 0.855937i | \(0.327019\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.79056e7 | 1.71099 | ||||||||
\(116\) | −2.23290e7 | −1.32821 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.08111e7 | 0.605737 | ||||||||
\(119\) | −1.62212e6 | −0.0882405 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.15392e7 | 1.61846 | ||||||||
\(122\) | −2.64948e6 | −0.132099 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.06991e7 | 0.974934 | ||||||||
\(125\) | 1.93303e7 | 0.885225 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.44940e7 | −1.06108 | −0.530539 | − | 0.847660i | \(-0.678011\pi\) | ||||
−0.530539 | + | 0.847660i | \(0.678011\pi\) | |||||||
\(128\) | −2.25029e7 | −0.948425 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.19486e6 | 0.127541 | ||||||||
\(131\) | −3.59703e7 | −1.39796 | −0.698979 | − | 0.715142i | \(-0.746362\pi\) | ||||
−0.698979 | + | 0.715142i | \(0.746362\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.29983e7 | −0.847645 | ||||||||
\(134\) | −1.36181e7 | −0.488934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.42185e6 | 0.0484693 | ||||||||
\(137\) | 1.88193e7 | 0.625289 | 0.312644 | − | 0.949870i | \(-0.398785\pi\) | ||||
0.312644 | + | 0.949870i | \(0.398785\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.72014e7 | −1.17492 | −0.587459 | − | 0.809254i | \(-0.699872\pi\) | ||||
−0.587459 | + | 0.809254i | \(0.699872\pi\) | |||||||
\(140\) | 4.22014e7 | 1.29981 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.62411e6 | 0.252758 | ||||||||
\(143\) | −1.35535e7 | −0.387592 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.98017e7 | −1.90142 | ||||||||
\(146\) | 1.64858e7 | 0.438406 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.70390e7 | 1.19273 | ||||||||
\(149\) | 4.39692e7 | 1.08892 | 0.544461 | − | 0.838786i | \(-0.316734\pi\) | ||||
0.544461 | + | 0.838786i | \(0.316734\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.09651e7 | −0.731902 | −0.365951 | − | 0.930634i | \(-0.619256\pi\) | ||||
−0.365951 | + | 0.930634i | \(0.619256\pi\) | |||||||
\(152\) | 2.01588e7 | 0.465600 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.61370e7 | 1.23859 | ||||||||
\(155\) | 6.47065e7 | 1.39568 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.67885e6 | −0.0346228 | −0.0173114 | − | 0.999850i | \(-0.505511\pi\) | ||||
−0.0173114 | + | 0.999850i | \(0.505511\pi\) | |||||||
\(158\) | 1.46138e7 | 0.294757 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.79935e7 | −1.11933 | ||||||||
\(161\) | −1.30240e8 | −2.45954 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.30485e6 | 0.150202 | 0.0751009 | − | 0.997176i | \(-0.476072\pi\) | ||||
0.0751009 | + | 0.997176i | \(0.476072\pi\) | |||||||
\(164\) | −3.75011e7 | −0.663881 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.06762e7 | −0.520502 | ||||||||
\(167\) | −4.62254e7 | −0.768021 | −0.384010 | − | 0.923329i | \(-0.625457\pi\) | ||||
−0.384010 | + | 0.923329i | \(0.625457\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.91485e7 | −0.942628 | ||||||||
\(170\) | 1.92119e6 | 0.0299915 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.74756e6 | −0.116095 | ||||||||
\(173\) | 4.56672e7 | 0.670568 | 0.335284 | − | 0.942117i | \(-0.391168\pi\) | ||||
0.335284 | + | 0.942117i | \(0.391168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.08531e7 | 0.294128 | ||||||||
\(176\) | 3.98915e7 | 0.551552 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.05800e7 | 0.672216 | ||||||||
\(179\) | −7.68660e7 | −1.00173 | −0.500863 | − | 0.865527i | \(-0.666984\pi\) | ||||
−0.500863 | + | 0.865527i | \(0.666984\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.38362e7 | 0.925538 | 0.462769 | − | 0.886479i | \(-0.346856\pi\) | ||||
0.462769 | + | 0.886479i | \(0.346856\pi\) | |||||||
\(182\) | −1.49110e7 | −0.183339 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.14161e8 | 1.35100 | ||||||||
\(185\) | 1.47047e8 | 1.70747 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.15021e6 | −0.0911430 | ||||||||
\(188\) | 3.71029e7 | 0.407245 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.72384e7 | 0.288101 | ||||||||
\(191\) | 4.61537e7 | 0.479280 | 0.239640 | − | 0.970862i | \(-0.422971\pi\) | ||||
0.239640 | + | 0.970862i | \(0.422971\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.04470e8 | 1.04603 | 0.523013 | − | 0.852325i | \(-0.324808\pi\) | ||||
0.523013 | + | 0.852325i | \(0.324808\pi\) | |||||||
\(194\) | 2.39429e7 | 0.235435 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.16711e8 | −1.10718 | ||||||||
\(197\) | −3.24556e7 | −0.302453 | −0.151226 | − | 0.988499i | \(-0.548322\pi\) | ||||
−0.151226 | + | 0.988499i | \(0.548322\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.90706e8 | 1.71545 | 0.857725 | − | 0.514109i | \(-0.171877\pi\) | ||||
0.857725 | + | 0.514109i | \(0.171877\pi\) | |||||||
\(200\) | −1.82785e7 | −0.161561 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.78104e7 | 0.237398 | ||||||||
\(203\) | 3.25777e8 | 2.73328 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.17231e8 | −0.950392 | ||||||||
\(206\) | 8.78747e7 | 0.700372 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.05959e7 | −0.0816422 | ||||||||
\(209\) | −1.15553e8 | −0.875526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.93604e6 | −0.0361735 | −0.0180867 | − | 0.999836i | \(-0.505758\pi\) | ||||
−0.0180867 | + | 0.999836i | \(0.505758\pi\) | |||||||
\(212\) | −3.52446e7 | −0.254049 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.64097e7 | 0.602718 | ||||||||
\(215\) | −2.42193e7 | −0.166199 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.01997e8 | −2.00629 | ||||||||
\(218\) | 7.05233e7 | 0.461036 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.12038e8 | 1.34256 | ||||||||
\(221\) | 2.16484e6 | 0.0134912 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.77562e8 | 1.67608 | 0.838038 | − | 0.545612i | \(-0.183703\pi\) | ||||
0.838038 | + | 0.545612i | \(0.183703\pi\) | |||||||
\(224\) | 2.70666e8 | 1.60903 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.76807e7 | 0.505271 | ||||||||
\(227\) | 1.27335e8 | 0.722535 | 0.361267 | − | 0.932462i | \(-0.382344\pi\) | ||||
0.361267 | + | 0.932462i | \(0.382344\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.66075e8 | 0.913861 | 0.456931 | − | 0.889502i | \(-0.348949\pi\) | ||||
0.456931 | + | 0.889502i | \(0.348949\pi\) | |||||||
\(230\) | 1.54252e8 | 0.835959 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.85556e8 | −1.50135 | ||||||||
\(233\) | 1.97183e8 | 1.02123 | 0.510616 | − | 0.859809i | \(-0.329417\pi\) | ||||
0.510616 | + | 0.859809i | \(0.329417\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.15986e8 | 0.582999 | ||||||||
\(236\) | −1.90585e8 | −0.943837 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.96652e6 | −0.0431126 | ||||||||
\(239\) | −7.22966e7 | −0.342551 | −0.171275 | − | 0.985223i | \(-0.554789\pi\) | ||||
−0.171275 | + | 0.985223i | \(0.554789\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.09906e8 | −1.42617 | −0.713084 | − | 0.701079i | \(-0.752702\pi\) | ||||
−0.713084 | + | 0.701079i | \(0.752702\pi\) | |||||||
\(242\) | 1.74338e8 | 0.790748 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.67066e7 | 0.205832 | ||||||||
\(245\) | −3.64847e8 | −1.58500 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.06929e7 | 0.129598 | ||||||||
\(248\) | 2.64712e8 | 1.10203 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.06851e8 | 0.432504 | ||||||||
\(251\) | −1.11482e8 | −0.444988 | −0.222494 | − | 0.974934i | \(-0.571420\pi\) | ||||
−0.222494 | + | 0.974934i | \(0.571420\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.54383e8 | −2.54045 | ||||||||
\(254\) | −1.35395e8 | −0.518422 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.67594e8 | −0.624336 | ||||||||
\(257\) | −8.26622e7 | −0.303767 | −0.151884 | − | 0.988398i | \(-0.548534\pi\) | ||||
−0.151884 | + | 0.988398i | \(0.548534\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.86293e8 | −2.45448 | ||||||||
\(260\) | −5.63209e7 | −0.198730 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.98831e8 | −0.683015 | ||||||||
\(263\) | 2.74508e8 | 0.930486 | 0.465243 | − | 0.885183i | \(-0.345967\pi\) | ||||
0.465243 | + | 0.885183i | \(0.345967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.10177e8 | −0.363688 | ||||||||
\(266\) | −1.27126e8 | −0.414143 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.40069e8 | 0.761840 | ||||||||
\(269\) | 9.06481e7 | 0.283940 | 0.141970 | − | 0.989871i | \(-0.454656\pi\) | ||||
0.141970 | + | 0.989871i | \(0.454656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.46059e8 | 0.751011 | 0.375505 | − | 0.926820i | \(-0.377469\pi\) | ||||
0.375505 | + | 0.926820i | \(0.377469\pi\) | |||||||
\(272\) | −6.37169e6 | −0.0191983 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.04026e8 | 0.305504 | ||||||||
\(275\) | 1.04775e8 | 0.303803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.60621e8 | 1.86755 | 0.933777 | − | 0.357857i | \(-0.116492\pi\) | ||||
0.933777 | + | 0.357857i | \(0.116492\pi\) | |||||||
\(278\) | −2.05637e8 | −0.574042 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.39696e8 | 1.46925 | ||||||||
\(281\) | −2.01108e7 | −0.0540700 | −0.0270350 | − | 0.999634i | \(-0.508607\pi\) | ||||
−0.0270350 | + | 0.999634i | \(0.508607\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.51117e8 | 0.658602 | 0.329301 | − | 0.944225i | \(-0.393187\pi\) | ||||
0.329301 | + | 0.944225i | \(0.393187\pi\) | |||||||
\(284\) | −1.52031e8 | −0.393839 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.49190e7 | −0.189370 | ||||||||
\(287\) | 5.47136e8 | 1.36618 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.09037e8 | −0.996828 | ||||||||
\(290\) | −3.85840e8 | −0.928997 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.90623e8 | −0.683108 | ||||||||
\(293\) | 3.74733e8 | 0.870333 | 0.435166 | − | 0.900350i | \(-0.356690\pi\) | ||||
0.435166 | + | 0.900350i | \(0.356690\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.95780e8 | −1.35117 | ||||||||
\(296\) | 6.01562e8 | 1.34822 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.43047e8 | 0.532027 | ||||||||
\(299\) | 1.73815e8 | 0.376044 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.13036e8 | 0.238910 | ||||||||
\(302\) | −1.71164e8 | −0.357593 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.03373e7 | −0.184421 | ||||||||
\(305\) | 1.46008e8 | 0.294663 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.69155e8 | 0.728156 | 0.364078 | − | 0.931369i | \(-0.381384\pi\) | ||||
0.364078 | + | 0.931369i | \(0.381384\pi\) | |||||||
\(308\) | −9.89619e8 | −1.92992 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.57676e8 | 0.681904 | ||||||||
\(311\) | 7.67471e8 | 1.44677 | 0.723387 | − | 0.690443i | \(-0.242584\pi\) | ||||
0.723387 | + | 0.690443i | \(0.242584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.94815e8 | 0.727761 | 0.363881 | − | 0.931446i | \(-0.381452\pi\) | ||||
0.363881 | + | 0.931446i | \(0.381452\pi\) | |||||||
\(314\) | −9.28008e6 | −0.0169160 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.57621e8 | −0.459279 | ||||||||
\(317\) | −5.25976e8 | −0.927381 | −0.463691 | − | 0.885997i | \(-0.653475\pi\) | ||||
−0.463691 | + | 0.885997i | \(0.653475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.63684e9 | 2.82318 | ||||||||
\(320\) | −1.02822e8 | −0.175413 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.19924e8 | −1.20169 | ||||||||
\(323\) | 1.84568e7 | 0.0304752 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.78299e7 | −0.0449698 | ||||||||
\(326\) | 4.59064e7 | 0.0733857 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.79586e8 | −0.750426 | ||||||||
\(329\) | −5.41327e8 | −0.838058 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.17755e9 | 1.78477 | 0.892386 | − | 0.451273i | \(-0.149030\pi\) | ||||
0.892386 | + | 0.451273i | \(0.149030\pi\) | |||||||
\(332\) | 5.40778e8 | 0.811028 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.55518e8 | −0.375240 | ||||||||
\(335\) | 7.50469e8 | 1.09063 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.76656e8 | −0.678423 | −0.339212 | − | 0.940710i | \(-0.610160\pi\) | ||||
−0.339212 | + | 0.940710i | \(0.610160\pi\) | |||||||
\(338\) | −3.26953e8 | −0.460550 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.38679e7 | −0.0467317 | ||||||||
\(341\) | −1.51736e9 | −2.07228 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.31965e8 | 0.711793 | ||||||||
\(344\) | −9.90803e7 | −0.131230 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.52433e8 | 0.327626 | ||||||||
\(347\) | −1.08505e8 | −0.139411 | −0.0697057 | − | 0.997568i | \(-0.522206\pi\) | ||||
−0.0697057 | + | 0.997568i | \(0.522206\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.46559e8 | −0.940102 | −0.470051 | − | 0.882639i | \(-0.655765\pi\) | ||||
−0.470051 | + | 0.882639i | \(0.655765\pi\) | |||||||
\(350\) | 1.15269e8 | 0.143705 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.35994e9 | 1.66196 | ||||||||
\(353\) | 4.13749e8 | 0.500640 | 0.250320 | − | 0.968163i | \(-0.419464\pi\) | ||||
0.250320 | + | 0.968163i | \(0.419464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.75259e8 | −0.563807 | ||||||||
\(356\) | −8.91656e8 | −1.04742 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.24889e8 | −0.489424 | ||||||||
\(359\) | 1.58431e8 | 0.180721 | 0.0903607 | − | 0.995909i | \(-0.471198\pi\) | ||||
0.0903607 | + | 0.995909i | \(0.471198\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.32193e8 | −0.707253 | ||||||||
\(362\) | 4.08141e8 | 0.452200 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.62860e8 | 0.285673 | ||||||||
\(365\) | −9.08504e8 | −0.977916 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.61609e7 | 0.0593065 | 0.0296533 | − | 0.999560i | \(-0.490560\pi\) | ||||
0.0296533 | + | 0.999560i | \(0.490560\pi\) | |||||||
\(368\) | −5.11585e8 | −0.535119 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.12824e8 | 0.834239 | ||||||||
\(371\) | 5.14214e8 | 0.522800 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.21691e9 | 1.21416 | 0.607080 | − | 0.794641i | \(-0.292341\pi\) | ||||
0.607080 | + | 0.794641i | \(0.292341\pi\) | |||||||
\(374\) | −4.50516e7 | −0.0445307 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.74494e8 | 0.460334 | ||||||||
\(377\) | −4.34773e8 | −0.417896 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.99936e9 | −1.88649 | −0.943245 | − | 0.332098i | \(-0.892244\pi\) | ||||
−0.943245 | + | 0.332098i | \(0.892244\pi\) | |||||||
\(380\) | −4.80176e8 | −0.448908 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.55122e8 | 0.234167 | ||||||||
\(383\) | 7.65586e8 | 0.696303 | 0.348151 | − | 0.937438i | \(-0.386809\pi\) | ||||
0.348151 | + | 0.937438i | \(0.386809\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.09361e9 | −2.76282 | ||||||||
\(386\) | 5.77476e8 | 0.511068 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.22080e8 | −0.366846 | ||||||||
\(389\) | 6.56361e8 | 0.565352 | 0.282676 | − | 0.959215i | \(-0.408778\pi\) | ||||
0.282676 | + | 0.959215i | \(0.408778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.04522e8 | 0.0884275 | ||||||||
\(392\) | −1.49257e9 | −1.25151 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.79403e8 | −0.147773 | ||||||||
\(395\) | −8.05339e8 | −0.657490 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.12150e8 | 0.731644 | 0.365822 | − | 0.930685i | \(-0.380788\pi\) | ||||
0.365822 | + | 0.930685i | \(0.380788\pi\) | |||||||
\(398\) | 1.05416e9 | 0.838136 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.19110e7 | 0.0639930 | ||||||||
\(401\) | 1.15178e8 | 0.0891997 | 0.0445999 | − | 0.999005i | \(-0.485799\pi\) | ||||
0.0445999 | + | 0.999005i | \(0.485799\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.03037e8 | 0.306745 | ||||||||
\(404\) | −4.90259e8 | −0.369906 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.80078e9 | 1.33543 | ||||||||
\(407\) | −3.44823e9 | −2.53522 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.39721e8 | −0.606881 | −0.303440 | − | 0.952850i | \(-0.598135\pi\) | ||||
−0.303440 | + | 0.952850i | \(0.598135\pi\) | |||||||
\(410\) | −6.48011e8 | −0.464343 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.54911e9 | −1.09129 | ||||||||
\(413\) | 2.78061e9 | 1.94230 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.69051e9 | 1.16104 | ||||||||
\(416\) | −3.61223e8 | −0.246008 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.38738e8 | −0.427765 | ||||||||
\(419\) | −9.18009e8 | −0.609674 | −0.304837 | − | 0.952404i | \(-0.598602\pi\) | ||||
−0.304837 | + | 0.952404i | \(0.598602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.86735e7 | 0.0644486 | 0.0322243 | − | 0.999481i | \(-0.489741\pi\) | ||||
0.0322243 | + | 0.999481i | \(0.489741\pi\) | |||||||
\(422\) | −2.72847e7 | −0.0176737 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.50728e8 | −0.287167 | ||||||||
\(425\) | −1.67352e7 | −0.0105747 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.81443e8 | −0.423577 | ||||||||
\(428\) | −1.52328e9 | −0.939134 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.33876e8 | −0.0812014 | ||||||||
\(431\) | −2.42488e9 | −1.45888 | −0.729440 | − | 0.684045i | \(-0.760219\pi\) | ||||
−0.729440 | + | 0.684045i | \(0.760219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.63675e9 | 0.968888 | 0.484444 | − | 0.874822i | \(-0.339022\pi\) | ||||
0.484444 | + | 0.874822i | \(0.339022\pi\) | |||||||
\(434\) | −1.66934e9 | −0.980233 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.24323e9 | −0.718370 | ||||||||
\(437\) | 1.48190e9 | 0.849441 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.40300e9 | −0.791465 | −0.395733 | − | 0.918366i | \(-0.629509\pi\) | ||||
−0.395733 | + | 0.918366i | \(0.629509\pi\) | |||||||
\(440\) | 2.71166e9 | 1.51758 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.19665e7 | 0.00659156 | ||||||||
\(443\) | −4.39909e8 | −0.240409 | −0.120204 | − | 0.992749i | \(-0.538355\pi\) | ||||
−0.120204 | + | 0.992749i | \(0.538355\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.78737e9 | −1.49946 | ||||||||
\(446\) | 1.53427e9 | 0.818898 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.79890e8 | 0.252156 | ||||||||
\(449\) | −2.11015e9 | −1.10015 | −0.550073 | − | 0.835116i | \(-0.685400\pi\) | ||||
−0.550073 | + | 0.835116i | \(0.685400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.74904e9 | 1.41112 | ||||||||
\(452\) | −1.54569e9 | −0.787295 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.03866e8 | 0.353016 | ||||||||
\(455\) | 8.21715e8 | 0.408960 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.13547e9 | −1.04661 | −0.523307 | − | 0.852144i | \(-0.675302\pi\) | ||||
−0.523307 | + | 0.852144i | \(0.675302\pi\) | |||||||
\(458\) | 9.18006e8 | 0.446495 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.71926e9 | −1.30256 | ||||||||
\(461\) | −7.44367e8 | −0.353862 | −0.176931 | − | 0.984223i | \(-0.556617\pi\) | ||||
−0.176931 | + | 0.984223i | \(0.556617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.70021e9 | 0.796105 | 0.398052 | − | 0.917363i | \(-0.369686\pi\) | ||||
0.398052 | + | 0.917363i | \(0.369686\pi\) | |||||||
\(464\) | 1.27965e9 | 0.594675 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.08996e9 | 0.498954 | ||||||||
\(467\) | 3.93170e9 | 1.78637 | 0.893185 | − | 0.449689i | \(-0.148465\pi\) | ||||
0.893185 | + | 0.449689i | \(0.148465\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.50257e9 | −1.56777 | ||||||||
\(470\) | 6.41131e8 | 0.284842 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.43731e9 | −1.06688 | ||||||||
\(473\) | 5.67940e8 | 0.246768 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.37270e8 | −0.101582 | ||||||||
\(476\) | 1.58067e8 | 0.0671766 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.99631e8 | −0.167364 | ||||||||
\(479\) | 1.45058e9 | 0.603071 | 0.301536 | − | 0.953455i | \(-0.402501\pi\) | ||||
0.301536 | + | 0.953455i | \(0.402501\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.15908e8 | 0.375270 | ||||||||
\(482\) | −1.71305e9 | −0.696798 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.07334e9 | −1.23212 | ||||||||
\(485\) | −1.31945e9 | −0.525165 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.29131e9 | 1.68360 | 0.841800 | − | 0.539790i | \(-0.181496\pi\) | ||||
0.841800 | + | 0.539790i | \(0.181496\pi\) | |||||||
\(488\) | 5.97311e8 | 0.232665 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.01675e9 | −0.774400 | ||||||||
\(491\) | 3.50889e8 | 0.133778 | 0.0668889 | − | 0.997760i | \(-0.478693\pi\) | ||||
0.0668889 | + | 0.997760i | \(0.478693\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.61445e8 | −0.0982690 | ||||||||
\(494\) | 1.69660e8 | 0.0633190 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.18625e9 | −0.436505 | ||||||||
\(497\) | 2.21812e9 | 0.810470 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.72276e9 | −1.34126 | −0.670630 | − | 0.741792i | \(-0.733976\pi\) | ||||
−0.670630 | + | 0.741792i | \(0.733976\pi\) | |||||||
\(500\) | −1.88364e9 | −0.673912 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.16236e8 | −0.217412 | ||||||||
\(503\) | −5.48803e9 | −1.92277 | −0.961387 | − | 0.275199i | \(-0.911256\pi\) | ||||
−0.961387 | + | 0.275199i | \(0.911256\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.53258e9 | −0.529545 | ||||||||
\(506\) | −3.61720e9 | −1.24121 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.38682e9 | 0.807788 | ||||||||
\(509\) | −3.85451e8 | −0.129556 | −0.0647778 | − | 0.997900i | \(-0.520634\pi\) | ||||
−0.0647778 | + | 0.997900i | \(0.520634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.24015e9 | 1.40575 | ||||||||
\(512\) | 1.95397e9 | 0.643387 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.56928e8 | −0.148415 | ||||||||
\(515\) | −4.84261e9 | −1.56226 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.71986e9 | −0.865623 | ||||||||
\(518\) | −3.79359e9 | −1.19921 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.20264e8 | −0.224636 | ||||||||
\(521\) | 3.74846e9 | 1.16124 | 0.580618 | − | 0.814176i | \(-0.302811\pi\) | ||||
0.580618 | + | 0.814176i | \(0.302811\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.64980e9 | 0.809949 | 0.404974 | − | 0.914328i | \(-0.367280\pi\) | ||||
0.404974 | + | 0.914328i | \(0.367280\pi\) | |||||||
\(524\) | 3.50512e9 | 1.06425 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.51739e9 | 0.454617 | ||||||||
\(527\) | 2.42361e8 | 0.0721316 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.98724e9 | 1.46476 | ||||||||
\(530\) | −6.09019e8 | −0.177691 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.24106e9 | 0.645303 | ||||||||
\(533\) | −7.30193e8 | −0.208878 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.76187e9 | −1.34443 | ||||||||
\(536\) | 3.07014e9 | 0.861155 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.01072e8 | 0.138727 | ||||||||
\(539\) | 8.55561e9 | 2.35337 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.07052e9 | −1.37677 | −0.688386 | − | 0.725344i | \(-0.741681\pi\) | ||||
−0.688386 | + | 0.725344i | \(0.741681\pi\) | |||||||
\(542\) | 1.36013e9 | 0.366929 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.17217e8 | −0.0578493 | ||||||||
\(545\) | −3.88641e9 | −1.02840 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.00582e9 | 0.785249 | 0.392624 | − | 0.919699i | \(-0.371567\pi\) | ||||
0.392624 | + | 0.919699i | \(0.371567\pi\) | |||||||
\(548\) | −1.83384e9 | −0.476026 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.79159e8 | 0.148432 | ||||||||
\(551\) | −3.70675e9 | −0.943980 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.75866e9 | 0.945138 | ||||||||
\(554\) | 3.65169e9 | 0.912450 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.62509e9 | 0.894452 | ||||||||
\(557\) | −5.43732e9 | −1.33319 | −0.666594 | − | 0.745421i | \(-0.732249\pi\) | ||||
−0.666594 | + | 0.745421i | \(0.732249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.50855e8 | −0.0365273 | ||||||||
\(560\) | −2.41853e9 | −0.581959 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.11166e8 | −0.0264176 | ||||||||
\(563\) | 4.80656e9 | 1.13516 | 0.567578 | − | 0.823320i | \(-0.307881\pi\) | ||||
0.567578 | + | 0.823320i | \(0.307881\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.83192e9 | −1.12707 | ||||||||
\(566\) | 1.38809e9 | 0.321780 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.94426e9 | −0.445180 | ||||||||
\(569\) | −7.07656e9 | −1.61038 | −0.805191 | − | 0.593015i | \(-0.797937\pi\) | ||||
−0.805191 | + | 0.593015i | \(0.797937\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.80378e9 | −0.855045 | −0.427523 | − | 0.904005i | \(-0.640614\pi\) | ||||
−0.427523 | + | 0.904005i | \(0.640614\pi\) | |||||||
\(572\) | 1.32072e9 | 0.295069 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.02438e9 | 0.667490 | ||||||||
\(575\) | −1.34367e9 | −0.294751 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.81170e8 | −0.0609332 | −0.0304666 | − | 0.999536i | \(-0.509699\pi\) | ||||
−0.0304666 | + | 0.999536i | \(0.509699\pi\) | |||||||
\(578\) | −2.26102e9 | −0.487031 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.80182e9 | 1.44753 | ||||||||
\(581\) | −7.88989e9 | −1.66899 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.58363e9 | 0.539996 | ||||||||
\(584\) | −3.71665e9 | −0.772159 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.07140e9 | 0.425228 | ||||||||
\(587\) | −8.79495e8 | −0.179473 | −0.0897367 | − | 0.995966i | \(-0.528603\pi\) | ||||
−0.0897367 | + | 0.995966i | \(0.528603\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.43618e9 | 0.692902 | ||||||||
\(590\) | −3.29327e9 | −0.660154 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.69576e9 | −0.534018 | ||||||||
\(593\) | 6.78081e8 | 0.133534 | 0.0667668 | − | 0.997769i | \(-0.478732\pi\) | ||||
0.0667668 | + | 0.997769i | \(0.478732\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.94128e8 | 0.0961678 | ||||||||
\(596\) | −4.28458e9 | −0.828985 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.60791e8 | 0.183728 | ||||||||
\(599\) | 6.13578e9 | 1.16648 | 0.583238 | − | 0.812301i | \(-0.301785\pi\) | ||||
0.583238 | + | 0.812301i | \(0.301785\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.78315e8 | −0.0898780 | −0.0449390 | − | 0.998990i | \(-0.514309\pi\) | ||||
−0.0449390 | + | 0.998990i | \(0.514309\pi\) | |||||||
\(602\) | 6.24824e8 | 0.116727 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.01739e9 | 0.557189 | ||||||||
\(605\) | −9.60743e9 | −1.76386 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.97283e9 | −1.62843 | −0.814215 | − | 0.580563i | \(-0.802832\pi\) | ||||
−0.814215 | + | 0.580563i | \(0.802832\pi\) | |||||||
\(608\) | −3.07969e9 | −0.555705 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.07080e8 | 0.143967 | ||||||||
\(611\) | 7.22440e8 | 0.128132 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.77928e9 | 1.36404 | 0.682021 | − | 0.731333i | \(-0.261101\pi\) | ||||
0.682021 | + | 0.731333i | \(0.261101\pi\) | |||||||
\(614\) | 2.04056e9 | 0.355763 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.26558e10 | −2.18151 | ||||||||
\(617\) | 8.81774e9 | 1.51133 | 0.755665 | − | 0.654958i | \(-0.227314\pi\) | ||||
0.755665 | + | 0.654958i | \(0.227314\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.50857e9 | −0.764050 | −0.382025 | − | 0.924152i | \(-0.624773\pi\) | ||||
−0.382025 | + | 0.924152i | \(0.624773\pi\) | |||||||
\(620\) | −6.30533e9 | −1.06252 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.24232e9 | 0.706865 | ||||||||
\(623\) | 1.30091e10 | 2.15546 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.03428e9 | −1.15250 | ||||||||
\(626\) | 2.18240e9 | 0.355570 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.63595e8 | 0.0263579 | ||||||||
\(629\) | 5.50770e8 | 0.0882456 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.47926e9 | −0.234391 | −0.117195 | − | 0.993109i | \(-0.537390\pi\) | ||||
−0.117195 | + | 0.993109i | \(0.537390\pi\) | |||||||
\(632\) | −3.29461e9 | −0.519152 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.90741e9 | −0.453101 | ||||||||
\(635\) | 7.46135e9 | 1.15640 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.27252e9 | −0.348353 | ||||||||
\(638\) | 9.04790e9 | 1.37935 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.85480e9 | 1.03363 | ||||||||
\(641\) | −6.56349e9 | −0.984309 | −0.492155 | − | 0.870508i | \(-0.663791\pi\) | ||||
−0.492155 | + | 0.870508i | \(0.663791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.43261e9 | 0.954221 | 0.477110 | − | 0.878843i | \(-0.341684\pi\) | ||||
0.477110 | + | 0.878843i | \(0.341684\pi\) | |||||||
\(644\) | 1.26913e10 | 1.87242 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.02023e8 | 0.0148896 | ||||||||
\(647\) | −1.74903e8 | −0.0253882 | −0.0126941 | − | 0.999919i | \(-0.504041\pi\) | ||||
−0.0126941 | + | 0.999919i | \(0.504041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.39710e10 | 2.00618 | ||||||||
\(650\) | −1.53834e8 | −0.0219714 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.09266e8 | −0.114347 | ||||||||
\(653\) | 1.10036e10 | 1.54646 | 0.773230 | − | 0.634126i | \(-0.218640\pi\) | ||||
0.773230 | + | 0.634126i | \(0.218640\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.09572e10 | 1.52355 | ||||||||
\(656\) | 2.14915e9 | 0.297238 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.99227e9 | −0.409459 | ||||||||
\(659\) | 1.09969e10 | 1.49683 | 0.748416 | − | 0.663230i | \(-0.230815\pi\) | ||||
0.748416 | + | 0.663230i | \(0.230815\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.20713e10 | 1.62574 | 0.812869 | − | 0.582447i | \(-0.197905\pi\) | ||||
0.812869 | + | 0.582447i | \(0.197905\pi\) | |||||||
\(662\) | 6.50911e9 | 0.872005 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.91579e9 | 0.916755 | ||||||||
\(665\) | 7.00570e9 | 0.923795 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.09915e10 | −2.73907 | ||||||||
\(668\) | 4.50443e9 | 0.584686 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.14834e9 | 0.532859 | ||||||||
\(671\) | −3.42386e9 | −0.437509 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.08129e9 | 0.516113 | 0.258057 | − | 0.966130i | \(-0.416918\pi\) | ||||
0.258057 | + | 0.966130i | \(0.416918\pi\) | |||||||
\(674\) | −2.63479e9 | −0.331464 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.76372e9 | 0.717612 | ||||||||
\(677\) | 7.05725e9 | 0.874128 | 0.437064 | − | 0.899430i | \(-0.356018\pi\) | ||||
0.437064 | + | 0.899430i | \(0.356018\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.15809e9 | 0.754922 | ||||||||
\(680\) | −4.33122e8 | −0.0528237 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.38745e9 | −1.01248 | ||||||||
\(683\) | −7.13819e9 | −0.857266 | −0.428633 | − | 0.903479i | \(-0.641005\pi\) | ||||
−0.428633 | + | 0.903479i | \(0.641005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.73270e9 | −0.681463 | ||||||||
\(686\) | 2.94052e9 | 0.347768 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.44006e8 | 0.0519791 | ||||||||
\(689\) | −6.86257e8 | −0.0799317 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.09452e10 | −1.26197 | −0.630987 | − | 0.775793i | \(-0.717350\pi\) | ||||
−0.630987 | + | 0.775793i | \(0.717350\pi\) | |||||||
\(692\) | −4.45004e9 | −0.510496 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.99781e8 | −0.0681137 | ||||||||
\(695\) | 1.13322e10 | 1.28047 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.39093e8 | −0.0491181 | ||||||||
\(698\) | −4.12672e9 | −0.459316 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.03203e9 | −0.223917 | ||||||||
\(701\) | −1.00558e10 | −1.10256 | −0.551282 | − | 0.834319i | \(-0.685861\pi\) | ||||
−0.551282 | + | 0.834319i | \(0.685861\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.80877e9 | 0.847694 | ||||||||
\(704\) | 2.41117e9 | 0.260450 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.28706e9 | 0.244603 | ||||||||
\(707\) | 7.15282e9 | 0.761218 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.17573e10 | 1.23892 | 0.619462 | − | 0.785027i | \(-0.287351\pi\) | ||||
0.619462 | + | 0.785027i | \(0.287351\pi\) | |||||||
\(710\) | −2.62707e9 | −0.275465 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.14030e10 | −1.18397 | ||||||||
\(713\) | 1.94592e10 | 2.01054 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.12864e9 | 0.422412 | ||||||||
\(716\) | 7.49021e9 | 0.762603 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.75753e8 | 0.0882970 | ||||||||
\(719\) | 1.29980e9 | 0.130414 | 0.0652072 | − | 0.997872i | \(-0.479229\pi\) | ||||
0.0652072 | + | 0.997872i | \(0.479229\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.26013e10 | 2.24574 | ||||||||
\(722\) | −3.49455e9 | −0.345550 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.19497e9 | −0.704602 | ||||||||
\(725\) | 3.36100e9 | 0.327556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.55479e10 | 1.50073 | 0.750363 | − | 0.661026i | \(-0.229879\pi\) | ||||
0.750363 | + | 0.661026i | \(0.229879\pi\) | |||||||
\(728\) | 3.36160e9 | 0.322914 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.02190e9 | −0.477791 | ||||||||
\(731\) | −9.07145e7 | −0.00858946 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.52604e9 | 0.236906 | 0.118453 | − | 0.992960i | \(-0.462206\pi\) | ||||
0.118453 | + | 0.992960i | \(0.462206\pi\) | |||||||
\(734\) | 3.10438e8 | 0.0289760 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.74404e10 | −1.61244 | ||||||||
\(737\) | −1.75984e10 | −1.61934 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.96231e9 | −0.816892 | −0.408446 | − | 0.912783i | \(-0.633929\pi\) | ||||
−0.408446 | + | 0.912783i | \(0.633929\pi\) | |||||||
\(740\) | −1.43290e10 | −1.29988 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.84240e9 | 0.255430 | ||||||||
\(743\) | −9.22267e9 | −0.824890 | −0.412445 | − | 0.910983i | \(-0.635325\pi\) | ||||
−0.412445 | + | 0.910983i | \(0.635325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.33939e10 | −1.18675 | ||||||||
\(746\) | 6.72664e9 | 0.593215 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.94197e8 | 0.0693862 | ||||||||
\(749\) | 2.22245e10 | 1.93262 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.49684e10 | 1.28954 | 0.644770 | − | 0.764377i | \(-0.276953\pi\) | ||||
0.644770 | + | 0.764377i | \(0.276953\pi\) | |||||||
\(752\) | −2.12634e9 | −0.182335 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.40328e9 | −0.204176 | ||||||||
\(755\) | 9.43255e9 | 0.797654 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.31799e10 | −1.10427 | −0.552136 | − | 0.833754i | \(-0.686187\pi\) | ||||
−0.552136 | + | 0.833754i | \(0.686187\pi\) | |||||||
\(758\) | −1.10518e10 | −0.921702 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.14076e9 | −0.507428 | ||||||||
\(761\) | 5.65319e9 | 0.464994 | 0.232497 | − | 0.972597i | \(-0.425310\pi\) | ||||
0.232497 | + | 0.972597i | \(0.425310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.81385e10 | 1.47831 | ||||||||
\(764\) | −4.49745e9 | −0.364871 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.23190e9 | 0.340200 | ||||||||
\(767\) | −3.71093e9 | −0.296961 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.55751e9 | 0.202803 | 0.101402 | − | 0.994846i | \(-0.467667\pi\) | ||||
0.101402 | + | 0.994846i | \(0.467667\pi\) | |||||||
\(770\) | −1.71004e10 | −1.34986 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.01801e10 | −0.796328 | ||||||||
\(773\) | −6.24612e9 | −0.486387 | −0.243194 | − | 0.969978i | \(-0.578195\pi\) | ||||
−0.243194 | + | 0.969978i | \(0.578195\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.11566e9 | −0.240433 | ||||||||
\(776\) | −5.39780e9 | −0.414668 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.62814e9 | 0.276220 | ||||||||
\(779\) | −6.22542e9 | −0.471832 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.11448e10 | 0.837128 | ||||||||
\(782\) | 5.77760e8 | 0.0432040 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.68863e9 | 0.495713 | ||||||||
\(785\) | 5.11408e8 | 0.0377332 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.24074e10 | −1.63863 | −0.819314 | − | 0.573345i | \(-0.805646\pi\) | ||||
−0.819314 | + | 0.573345i | \(0.805646\pi\) | |||||||
\(788\) | 3.16263e9 | 0.230254 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.45164e9 | −0.321237 | ||||||||
\(791\) | 2.25514e10 | 1.62015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.09436e8 | 0.0647613 | ||||||||
\(794\) | 5.04206e9 | 0.357467 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.85833e10 | −1.30595 | ||||||||
\(797\) | −7.81380e9 | −0.546712 | −0.273356 | − | 0.961913i | \(-0.588134\pi\) | ||||
−0.273356 | + | 0.961913i | \(0.588134\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.34430e8 | 0.0301305 | ||||||||
\(800\) | 2.79243e9 | 0.192826 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.36664e8 | 0.0435813 | ||||||||
\(803\) | 2.13043e10 | 1.45199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.96736e10 | 2.68050 | ||||||||
\(806\) | 2.22785e9 | 0.149870 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6.26972e9 | −0.418127 | ||||||||
\(809\) | −1.22193e9 | −0.0811386 | −0.0405693 | − | 0.999177i | \(-0.512917\pi\) | ||||
−0.0405693 | + | 0.999177i | \(0.512917\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.05088e10 | −0.691797 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(812\) | −3.17453e10 | −2.08082 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.90606e10 | −1.23866 | ||||||||
\(815\) | −2.52981e9 | −0.163695 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.28614e9 | −0.0825111 | ||||||||
\(818\) | −4.64169e9 | −0.296510 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.14235e10 | 0.723523 | ||||||||
\(821\) | 1.87258e10 | 1.18097 | 0.590486 | − | 0.807048i | \(-0.298936\pi\) | ||||
0.590486 | + | 0.807048i | \(0.298936\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.81070e9 | −0.238290 | −0.119145 | − | 0.992877i | \(-0.538015\pi\) | ||||
−0.119145 | + | 0.992877i | \(0.538015\pi\) | |||||||
\(824\) | −1.98109e10 | −1.23356 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.53703e10 | 0.948968 | ||||||||
\(827\) | −1.63714e10 | −1.00651 | −0.503254 | − | 0.864139i | \(-0.667864\pi\) | ||||
−0.503254 | + | 0.864139i | \(0.667864\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.71162e9 | −0.409153 | −0.204577 | − | 0.978851i | \(-0.565582\pi\) | ||||
−0.204577 | + | 0.978851i | \(0.565582\pi\) | |||||||
\(830\) | 9.34453e9 | 0.567263 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.40448e8 | −0.0385525 | ||||||||
\(833\) | −1.36655e9 | −0.0819158 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.40811e10 | 0.837018 | ||||||||
\(836\) | 1.12601e10 | 0.666529 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.07444e9 | −0.297875 | ||||||||
\(839\) | 1.35926e10 | 0.794577 | 0.397289 | − | 0.917694i | \(-0.369951\pi\) | ||||
0.397289 | + | 0.917694i | \(0.369951\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.52573e10 | 2.04391 | ||||||||
\(842\) | 5.45434e8 | 0.0314883 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.80993e8 | 0.0275385 | ||||||||
\(845\) | 1.80177e10 | 1.02731 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.48396e10 | 2.53554 | ||||||||
\(848\) | 2.01984e9 | 0.113745 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.25064e7 | −0.00516661 | ||||||||
\(851\) | 4.42214e10 | 2.45968 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.31755e9 | −0.458853 | −0.229427 | − | 0.973326i | \(-0.573685\pi\) | ||||
−0.229427 | + | 0.973326i | \(0.573685\pi\) | |||||||
\(854\) | −3.76679e9 | −0.206951 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.94806e10 | −1.06156 | ||||||||
\(857\) | 5.32901e8 | 0.0289210 | 0.0144605 | − | 0.999895i | \(-0.495397\pi\) | ||||
0.0144605 | + | 0.999895i | \(0.495397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.23176e10 | −1.73965 | −0.869827 | − | 0.493357i | \(-0.835770\pi\) | ||||
−0.869827 | + | 0.493357i | \(0.835770\pi\) | |||||||
\(860\) | 2.36005e9 | 0.126525 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.34039e10 | −0.712780 | ||||||||
\(863\) | −5.97266e9 | −0.316323 | −0.158161 | − | 0.987413i | \(-0.550557\pi\) | ||||
−0.158161 | + | 0.987413i | \(0.550557\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.39111e10 | −0.730810 | ||||||||
\(866\) | 9.04737e9 | 0.473380 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.94281e10 | 1.52737 | ||||||||
\(869\) | 1.88851e10 | 0.976226 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.67444e9 | 0.239699 | ||||||||
\(872\) | −1.58991e10 | −0.812018 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.19143e9 | 0.415020 | ||||||||
\(875\) | 2.74821e10 | 1.38683 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.05767e9 | −0.353315 | −0.176658 | − | 0.984272i | \(-0.556529\pi\) | ||||
−0.176658 | + | 0.984272i | \(0.556529\pi\) | |||||||
\(878\) | −7.75530e9 | −0.386695 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.21517e10 | −0.601102 | ||||||||
\(881\) | −2.62054e10 | −1.29114 | −0.645572 | − | 0.763700i | \(-0.723381\pi\) | ||||
−0.645572 | + | 0.763700i | \(0.723381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.36619e8 | −0.0262303 | −0.0131152 | − | 0.999914i | \(-0.504175\pi\) | ||||
−0.0131152 | + | 0.999914i | \(0.504175\pi\) | |||||||
\(884\) | −2.10952e8 | −0.0102707 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.43167e9 | −0.117459 | ||||||||
\(887\) | 2.81727e10 | 1.35549 | 0.677744 | − | 0.735298i | \(-0.262958\pi\) | ||||
0.677744 | + | 0.735298i | \(0.262958\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.48234e10 | −1.66232 | ||||||||
\(890\) | −1.54076e10 | −0.732606 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.70471e10 | −1.27598 | ||||||||
\(893\) | 6.15932e9 | 0.289436 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.34148e10 | 1.09172 | ||||||||
\(896\) | −3.19926e10 | −1.48584 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.16642e10 | −0.537510 | ||||||||
\(899\) | −4.86744e10 | −2.23430 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.12672e8 | −0.0187961 | ||||||||
\(902\) | 1.51958e10 | 0.689446 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.97672e10 | −0.889928 | ||||||||
\(905\) | −2.24919e10 | −1.00869 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.54442e9 | 0.157732 | 0.0788659 | − | 0.996885i | \(-0.474870\pi\) | ||||
0.0788659 | + | 0.996885i | \(0.474870\pi\) | |||||||
\(908\) | −1.24082e10 | −0.550058 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.54216e9 | 0.199810 | ||||||||
\(911\) | −9.71330e9 | −0.425650 | −0.212825 | − | 0.977090i | \(-0.568266\pi\) | ||||
−0.212825 | + | 0.977090i | \(0.568266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.96421e10 | −1.72389 | ||||||||
\(914\) | −1.18041e10 | −0.511355 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.61832e10 | −0.695713 | ||||||||
\(917\) | −5.11393e10 | −2.19009 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.30593e10 | 0.555029 | 0.277515 | − | 0.960721i | \(-0.410489\pi\) | ||||
0.277515 | + | 0.960721i | \(0.410489\pi\) | |||||||
\(920\) | −3.47755e10 | −1.47236 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.11461e9 | −0.172890 | ||||||||
\(923\) | −2.96024e9 | −0.123914 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.08040e9 | −0.294145 | ||||||||
\(926\) | 9.39820e9 | 0.388961 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.36246e10 | 1.79190 | ||||||||
\(929\) | 1.76183e10 | 0.720955 | 0.360478 | − | 0.932768i | \(-0.382614\pi\) | ||||
0.360478 | + | 0.932768i | \(0.382614\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.93748e10 | −0.786890 | ||||||||
\(932\) | −1.92145e10 | −0.777452 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.17331e10 | 0.872786 | ||||||||
\(935\) | 2.48271e9 | 0.0993310 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.93955e10 | 1.16733 | 0.583664 | − | 0.811996i | \(-0.301619\pi\) | ||||
0.583664 | + | 0.811996i | \(0.301619\pi\) | |||||||
\(938\) | −1.93610e10 | −0.765982 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.13022e10 | −0.443831 | ||||||||
\(941\) | −5.66655e9 | −0.221694 | −0.110847 | − | 0.993837i | \(-0.535356\pi\) | ||||
−0.110847 | + | 0.993837i | \(0.535356\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.52548e10 | −1.36908 | ||||||||
\(944\) | 1.09223e10 | 0.422582 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.13938e9 | 0.120566 | ||||||||
\(947\) | −2.82326e10 | −1.08025 | −0.540126 | − | 0.841584i | \(-0.681624\pi\) | ||||
−0.540126 | + | 0.841584i | \(0.681624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.65879e9 | −0.214927 | ||||||||
\(950\) | −1.31155e9 | −0.0496308 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.02146e9 | 0.0759338 | ||||||||
\(953\) | 2.48053e10 | 0.928366 | 0.464183 | − | 0.885739i | \(-0.346348\pi\) | ||||
0.464183 | + | 0.885739i | \(0.346348\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.40593e10 | −0.522338 | ||||||||
\(956\) | 7.04494e9 | 0.260780 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.01833e9 | 0.294649 | ||||||||
\(959\) | 2.67555e10 | 0.979599 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.76088e10 | 0.640027 | ||||||||
\(962\) | 5.06283e9 | 0.183350 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.01988e10 | 1.08573 | ||||||||
\(965\) | −3.18236e10 | −1.14000 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.08573e10 | −1.09740 | −0.548700 | − | 0.836019i | \(-0.684877\pi\) | ||||
−0.548700 | + | 0.836019i | \(0.684877\pi\) | |||||||
\(968\) | −3.93036e10 | −1.39274 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.29345e9 | −0.256585 | ||||||||
\(971\) | 3.26691e9 | 0.114517 | 0.0572585 | − | 0.998359i | \(-0.481764\pi\) | ||||
0.0572585 | + | 0.998359i | \(0.481764\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.28896e10 | −1.84067 | ||||||||
\(974\) | 2.37209e10 | 0.822574 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.67671e9 | −0.0921568 | ||||||||
\(977\) | −1.92954e10 | −0.661948 | −0.330974 | − | 0.943640i | \(-0.607377\pi\) | ||||
−0.330974 | + | 0.943640i | \(0.607377\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.53635e10 | 2.22636 | ||||||||
\(980\) | 3.55525e10 | 1.20664 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.93959e9 | 0.0653612 | ||||||||
\(983\) | −4.50199e10 | −1.51170 | −0.755852 | − | 0.654742i | \(-0.772777\pi\) | ||||
−0.755852 | + | 0.654742i | \(0.772777\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.88658e9 | 0.329624 | ||||||||
\(986\) | −1.44518e9 | −0.0480123 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.99087e9 | −0.0986615 | ||||||||
\(989\) | −7.28349e9 | −0.239416 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.47544e10 | −1.46076 | −0.730379 | − | 0.683042i | \(-0.760657\pi\) | ||||
−0.730379 | + | 0.683042i | \(0.760657\pi\) | |||||||
\(992\) | −4.04403e10 | −1.31529 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.22610e10 | 0.395980 | ||||||||
\(995\) | −5.80926e10 | −1.86956 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.11948e10 | 1.31647 | 0.658233 | − | 0.752815i | \(-0.271304\pi\) | ||||
0.658233 | + | 0.752815i | \(0.271304\pi\) | |||||||
\(998\) | −2.05781e10 | −0.655314 | ||||||||
\(999\) | 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 | 387.8.a.b.1.6 | 11 | ||
3.2 | odd | 2 | 43.8.a.a.1.6 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.8.a.a.1.6 | ✓ | 11 | 3.2 | odd | 2 | ||
387.8.a.b.1.6 | 11 | 1.1 | even | 1 | trivial |