Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,10,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(46.8682610909\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 4752 x^{12} + 9346 x^{11} + 8576824 x^{10} - 26923636 x^{9} - 7450416552 x^{8} + 31594524240 x^{7} + 3232668379296 x^{6} + \cdots - 24\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(4.59170\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59170 | −0.114538 | −0.0572690 | − | 0.998359i | \(-0.518239\pi\) | ||||
−0.0572690 | + | 0.998359i | \(0.518239\pi\) | |||||||
\(3\) | 254.265 | 1.81235 | 0.906173 | − | 0.422907i | \(-0.138990\pi\) | ||||
0.906173 | + | 0.422907i | \(0.138990\pi\) | |||||||
\(4\) | −505.283 | −0.986881 | ||||||||
\(5\) | −1903.58 | −1.36209 | −0.681045 | − | 0.732241i | \(-0.738474\pi\) | ||||
−0.681045 | + | 0.732241i | \(0.738474\pi\) | |||||||
\(6\) | −658.979 | −0.207583 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | 2636.49 | 0.227573 | ||||||||
\(9\) | 44967.7 | 2.28460 | ||||||||
\(10\) | 4933.51 | 0.156011 | ||||||||
\(11\) | 18355.1 | 0.377999 | 0.188999 | − | 0.981977i | \(-0.439476\pi\) | ||||
0.188999 | + | 0.981977i | \(0.439476\pi\) | |||||||
\(12\) | −128476. | −1.78857 | ||||||||
\(13\) | −28561.0 | −0.277350 | ||||||||
\(14\) | −6222.67 | −0.0432913 | ||||||||
\(15\) | −484014. | −2.46858 | ||||||||
\(16\) | 251872. | 0.960815 | ||||||||
\(17\) | −373800. | −1.08547 | −0.542737 | − | 0.839903i | \(-0.682612\pi\) | ||||
−0.542737 | + | 0.839903i | \(0.682612\pi\) | |||||||
\(18\) | −116543. | −0.261673 | ||||||||
\(19\) | −246186. | −0.433384 | −0.216692 | − | 0.976240i | \(-0.569527\pi\) | ||||
−0.216692 | + | 0.976240i | \(0.569527\pi\) | |||||||
\(20\) | 961846. | 1.34422 | ||||||||
\(21\) | 610490. | 0.685002 | ||||||||
\(22\) | −47571.0 | −0.0432952 | ||||||||
\(23\) | 1.88050e6 | 1.40119 | 0.700595 | − | 0.713559i | \(-0.252918\pi\) | ||||
0.700595 | + | 0.713559i | \(0.252918\pi\) | |||||||
\(24\) | 670368. | 0.412442 | ||||||||
\(25\) | 1.67049e6 | 0.855290 | ||||||||
\(26\) | 74021.5 | 0.0317671 | ||||||||
\(27\) | 6.42903e6 | 2.32814 | ||||||||
\(28\) | −1.21318e6 | −0.373006 | ||||||||
\(29\) | −280114. | −0.0735435 | −0.0367718 | − | 0.999324i | \(-0.511707\pi\) | ||||
−0.0367718 | + | 0.999324i | \(0.511707\pi\) | |||||||
\(30\) | 1.25442e6 | 0.282746 | ||||||||
\(31\) | 4.45227e6 | 0.865873 | 0.432937 | − | 0.901424i | \(-0.357477\pi\) | ||||
0.432937 | + | 0.901424i | \(0.357477\pi\) | |||||||
\(32\) | −2.00266e6 | −0.337623 | ||||||||
\(33\) | 4.66707e6 | 0.685064 | ||||||||
\(34\) | 968777. | 0.124328 | ||||||||
\(35\) | −4.57049e6 | −0.514822 | ||||||||
\(36\) | −2.27214e7 | −2.25463 | ||||||||
\(37\) | 1.76160e7 | 1.54525 | 0.772624 | − | 0.634863i | \(-0.218944\pi\) | ||||
0.772624 | + | 0.634863i | \(0.218944\pi\) | |||||||
\(38\) | 638041. | 0.0496389 | ||||||||
\(39\) | −7.26207e6 | −0.502654 | ||||||||
\(40\) | −5.01877e6 | −0.309976 | ||||||||
\(41\) | 3.32158e7 | 1.83577 | 0.917883 | − | 0.396851i | \(-0.129897\pi\) | ||||
0.917883 | + | 0.396851i | \(0.129897\pi\) | |||||||
\(42\) | −1.58221e6 | −0.0784588 | ||||||||
\(43\) | −71574.6 | −0.00319265 | −0.00159632 | − | 0.999999i | \(-0.500508\pi\) | ||||
−0.00159632 | + | 0.999999i | \(0.500508\pi\) | |||||||
\(44\) | −9.27453e6 | −0.373040 | ||||||||
\(45\) | −8.55996e7 | −3.11183 | ||||||||
\(46\) | −4.87368e6 | −0.160490 | ||||||||
\(47\) | 2.72431e7 | 0.814360 | 0.407180 | − | 0.913348i | \(-0.366512\pi\) | ||||
0.407180 | + | 0.913348i | \(0.366512\pi\) | |||||||
\(48\) | 6.40422e7 | 1.74133 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | −4.32941e6 | −0.0979633 | ||||||||
\(51\) | −9.50443e7 | −1.96725 | ||||||||
\(52\) | 1.44314e7 | 0.273712 | ||||||||
\(53\) | −3.68347e7 | −0.641232 | −0.320616 | − | 0.947209i | \(-0.603890\pi\) | ||||
−0.320616 | + | 0.947209i | \(0.603890\pi\) | |||||||
\(54\) | −1.66621e7 | −0.266660 | ||||||||
\(55\) | −3.49404e7 | −0.514868 | ||||||||
\(56\) | 6.33022e6 | 0.0860147 | ||||||||
\(57\) | −6.25966e7 | −0.785441 | ||||||||
\(58\) | 725972. | 0.00842353 | ||||||||
\(59\) | 1.71700e8 | 1.84475 | 0.922375 | − | 0.386296i | \(-0.126246\pi\) | ||||
0.922375 | + | 0.386296i | \(0.126246\pi\) | |||||||
\(60\) | 2.44564e8 | 2.43619 | ||||||||
\(61\) | 7.90773e7 | 0.731253 | 0.365627 | − | 0.930762i | \(-0.380855\pi\) | ||||
0.365627 | + | 0.930762i | \(0.380855\pi\) | |||||||
\(62\) | −1.15390e7 | −0.0991754 | ||||||||
\(63\) | 1.07968e8 | 0.863497 | ||||||||
\(64\) | −1.23768e8 | −0.922145 | ||||||||
\(65\) | 5.43681e7 | 0.377776 | ||||||||
\(66\) | −1.20956e7 | −0.0784659 | ||||||||
\(67\) | 5.56151e7 | 0.337176 | 0.168588 | − | 0.985687i | \(-0.446079\pi\) | ||||
0.168588 | + | 0.985687i | \(0.446079\pi\) | |||||||
\(68\) | 1.88875e8 | 1.07123 | ||||||||
\(69\) | 4.78145e8 | 2.53944 | ||||||||
\(70\) | 1.18453e7 | 0.0589667 | ||||||||
\(71\) | 1.06698e7 | 0.0498304 | 0.0249152 | − | 0.999690i | \(-0.492068\pi\) | ||||
0.0249152 | + | 0.999690i | \(0.492068\pi\) | |||||||
\(72\) | 1.18557e8 | 0.519914 | ||||||||
\(73\) | 9.59021e7 | 0.395253 | 0.197627 | − | 0.980277i | \(-0.436677\pi\) | ||||
0.197627 | + | 0.980277i | \(0.436677\pi\) | |||||||
\(74\) | −4.56553e7 | −0.176990 | ||||||||
\(75\) | 4.24747e8 | 1.55008 | ||||||||
\(76\) | 1.24394e8 | 0.427698 | ||||||||
\(77\) | 4.40706e7 | 0.142870 | ||||||||
\(78\) | 1.88211e7 | 0.0575730 | ||||||||
\(79\) | −1.92106e8 | −0.554905 | −0.277453 | − | 0.960739i | \(-0.589490\pi\) | ||||
−0.277453 | + | 0.960739i | \(0.589490\pi\) | |||||||
\(80\) | −4.79458e8 | −1.30872 | ||||||||
\(81\) | 7.49577e8 | 1.93479 | ||||||||
\(82\) | −8.60854e7 | −0.210265 | ||||||||
\(83\) | −5.38923e8 | −1.24645 | −0.623226 | − | 0.782042i | \(-0.714178\pi\) | ||||
−0.623226 | + | 0.782042i | \(0.714178\pi\) | |||||||
\(84\) | −3.08471e8 | −0.676016 | ||||||||
\(85\) | 7.11558e8 | 1.47851 | ||||||||
\(86\) | 185500. | 0.000365679 0 | ||||||||
\(87\) | −7.12233e7 | −0.133286 | ||||||||
\(88\) | 4.83931e7 | 0.0860224 | ||||||||
\(89\) | 8.19043e7 | 0.138373 | 0.0691865 | − | 0.997604i | \(-0.477960\pi\) | ||||
0.0691865 | + | 0.997604i | \(0.477960\pi\) | |||||||
\(90\) | 2.21849e8 | 0.356423 | ||||||||
\(91\) | −6.85750e7 | −0.104828 | ||||||||
\(92\) | −9.50183e8 | −1.38281 | ||||||||
\(93\) | 1.13206e9 | 1.56926 | ||||||||
\(94\) | −7.06060e7 | −0.0932752 | ||||||||
\(95\) | 4.68635e8 | 0.590308 | ||||||||
\(96\) | −5.09207e8 | −0.611890 | ||||||||
\(97\) | −7.56732e8 | −0.867899 | −0.433949 | − | 0.900937i | \(-0.642880\pi\) | ||||
−0.433949 | + | 0.900937i | \(0.642880\pi\) | |||||||
\(98\) | −1.49406e7 | −0.0163626 | ||||||||
\(99\) | 8.25388e8 | 0.863575 | ||||||||
\(100\) | −8.44070e8 | −0.844070 | ||||||||
\(101\) | 1.68137e9 | 1.60774 | 0.803871 | − | 0.594803i | \(-0.202770\pi\) | ||||
0.803871 | + | 0.594803i | \(0.202770\pi\) | |||||||
\(102\) | 2.46326e8 | 0.225325 | ||||||||
\(103\) | −1.91743e9 | −1.67862 | −0.839310 | − | 0.543654i | \(-0.817040\pi\) | ||||
−0.839310 | + | 0.543654i | \(0.817040\pi\) | |||||||
\(104\) | −7.53009e7 | −0.0631175 | ||||||||
\(105\) | −1.16212e9 | −0.933035 | ||||||||
\(106\) | 9.54644e7 | 0.0734455 | ||||||||
\(107\) | −2.42552e9 | −1.78887 | −0.894435 | − | 0.447198i | \(-0.852422\pi\) | ||||
−0.894435 | + | 0.447198i | \(0.852422\pi\) | |||||||
\(108\) | −3.24848e9 | −2.29759 | ||||||||
\(109\) | 3.42217e8 | 0.232211 | 0.116105 | − | 0.993237i | \(-0.462959\pi\) | ||||
0.116105 | + | 0.993237i | \(0.462959\pi\) | |||||||
\(110\) | 9.05551e7 | 0.0589720 | ||||||||
\(111\) | 4.47912e9 | 2.80053 | ||||||||
\(112\) | 6.04745e8 | 0.363154 | ||||||||
\(113\) | 1.67651e9 | 0.967284 | 0.483642 | − | 0.875266i | \(-0.339314\pi\) | ||||
0.483642 | + | 0.875266i | \(0.339314\pi\) | |||||||
\(114\) | 1.62232e8 | 0.0899629 | ||||||||
\(115\) | −3.57967e9 | −1.90855 | ||||||||
\(116\) | 1.41537e8 | 0.0725787 | ||||||||
\(117\) | −1.28432e9 | −0.633633 | ||||||||
\(118\) | −4.44996e8 | −0.211294 | ||||||||
\(119\) | −8.97494e8 | −0.410270 | ||||||||
\(120\) | −1.27610e9 | −0.561783 | ||||||||
\(121\) | −2.02104e9 | −0.857117 | ||||||||
\(122\) | −2.04945e8 | −0.0837563 | ||||||||
\(123\) | 8.44562e9 | 3.32704 | ||||||||
\(124\) | −2.24966e9 | −0.854514 | ||||||||
\(125\) | 5.38020e8 | 0.197108 | ||||||||
\(126\) | −2.79819e8 | −0.0989032 | ||||||||
\(127\) | 2.63364e9 | 0.898337 | 0.449169 | − | 0.893447i | \(-0.351720\pi\) | ||||
0.449169 | + | 0.893447i | \(0.351720\pi\) | |||||||
\(128\) | 1.34613e9 | 0.443244 | ||||||||
\(129\) | −1.81989e7 | −0.00578618 | ||||||||
\(130\) | −1.40906e8 | −0.0432697 | ||||||||
\(131\) | 3.61555e9 | 1.07264 | 0.536319 | − | 0.844015i | \(-0.319814\pi\) | ||||
0.536319 | + | 0.844015i | \(0.319814\pi\) | |||||||
\(132\) | −2.35819e9 | −0.676077 | ||||||||
\(133\) | −5.91093e8 | −0.163804 | ||||||||
\(134\) | −1.44138e8 | −0.0386194 | ||||||||
\(135\) | −1.22382e10 | −3.17113 | ||||||||
\(136\) | −9.85521e8 | −0.247025 | ||||||||
\(137\) | −3.29030e9 | −0.797982 | −0.398991 | − | 0.916955i | \(-0.630640\pi\) | ||||
−0.398991 | + | 0.916955i | \(0.630640\pi\) | |||||||
\(138\) | −1.23921e9 | −0.290863 | ||||||||
\(139\) | 6.76805e9 | 1.53779 | 0.768895 | − | 0.639375i | \(-0.220807\pi\) | ||||
0.768895 | + | 0.639375i | \(0.220807\pi\) | |||||||
\(140\) | 2.30939e9 | 0.508068 | ||||||||
\(141\) | 6.92697e9 | 1.47590 | ||||||||
\(142\) | −2.76529e7 | −0.00570747 | ||||||||
\(143\) | −5.24241e8 | −0.104838 | ||||||||
\(144\) | 1.13261e10 | 2.19508 | ||||||||
\(145\) | 5.33220e8 | 0.100173 | ||||||||
\(146\) | −2.48549e8 | −0.0452715 | ||||||||
\(147\) | 1.46579e9 | 0.258907 | ||||||||
\(148\) | −8.90104e9 | −1.52498 | ||||||||
\(149\) | −1.16876e9 | −0.194261 | −0.0971305 | − | 0.995272i | \(-0.530966\pi\) | ||||
−0.0971305 | + | 0.995272i | \(0.530966\pi\) | |||||||
\(150\) | −1.10082e9 | −0.177543 | ||||||||
\(151\) | 9.70697e9 | 1.51945 | 0.759727 | − | 0.650242i | \(-0.225333\pi\) | ||||
0.759727 | + | 0.650242i | \(0.225333\pi\) | |||||||
\(152\) | −6.49068e8 | −0.0986266 | ||||||||
\(153\) | −1.68089e10 | −2.47987 | ||||||||
\(154\) | −1.14218e8 | −0.0163640 | ||||||||
\(155\) | −8.47526e9 | −1.17940 | ||||||||
\(156\) | 3.66940e9 | 0.496060 | ||||||||
\(157\) | −1.39697e10 | −1.83500 | −0.917502 | − | 0.397731i | \(-0.869798\pi\) | ||||
−0.917502 | + | 0.397731i | \(0.869798\pi\) | |||||||
\(158\) | 4.97881e8 | 0.0635577 | ||||||||
\(159\) | −9.36577e9 | −1.16213 | ||||||||
\(160\) | 3.81222e9 | 0.459873 | ||||||||
\(161\) | 4.51507e9 | 0.529600 | ||||||||
\(162\) | −1.94268e9 | −0.221607 | ||||||||
\(163\) | −1.12027e10 | −1.24302 | −0.621509 | − | 0.783407i | \(-0.713480\pi\) | ||||
−0.621509 | + | 0.783407i | \(0.713480\pi\) | |||||||
\(164\) | −1.67834e10 | −1.81168 | ||||||||
\(165\) | −8.88413e9 | −0.933119 | ||||||||
\(166\) | 1.39673e9 | 0.142766 | ||||||||
\(167\) | 1.66802e9 | 0.165950 | 0.0829751 | − | 0.996552i | \(-0.473558\pi\) | ||||
0.0829751 | + | 0.996552i | \(0.473558\pi\) | |||||||
\(168\) | 1.60955e9 | 0.155888 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | −1.84414e9 | −0.169346 | ||||||||
\(171\) | −1.10704e10 | −0.990108 | ||||||||
\(172\) | 3.61654e7 | 0.00315076 | ||||||||
\(173\) | −8.64313e9 | −0.733607 | −0.366804 | − | 0.930298i | \(-0.619548\pi\) | ||||
−0.366804 | + | 0.930298i | \(0.619548\pi\) | |||||||
\(174\) | 1.84589e8 | 0.0152663 | ||||||||
\(175\) | 4.01084e9 | 0.323269 | ||||||||
\(176\) | 4.62314e9 | 0.363187 | ||||||||
\(177\) | 4.36574e10 | 3.34332 | ||||||||
\(178\) | −2.12271e8 | −0.0158490 | ||||||||
\(179\) | −2.38067e10 | −1.73325 | −0.866623 | − | 0.498963i | \(-0.833714\pi\) | ||||
−0.866623 | + | 0.498963i | \(0.833714\pi\) | |||||||
\(180\) | 4.32521e10 | 3.07100 | ||||||||
\(181\) | 4.65133e9 | 0.322125 | 0.161062 | − | 0.986944i | \(-0.448508\pi\) | ||||
0.161062 | + | 0.986944i | \(0.448508\pi\) | |||||||
\(182\) | 1.77726e8 | 0.0120068 | ||||||||
\(183\) | 2.01066e10 | 1.32528 | ||||||||
\(184\) | 4.95791e9 | 0.318874 | ||||||||
\(185\) | −3.35334e10 | −2.10477 | ||||||||
\(186\) | −2.93395e9 | −0.179740 | ||||||||
\(187\) | −6.86114e9 | −0.410307 | ||||||||
\(188\) | −1.37655e10 | −0.803677 | ||||||||
\(189\) | 1.54361e10 | 0.879952 | ||||||||
\(190\) | −1.21456e9 | −0.0676127 | ||||||||
\(191\) | 2.48256e9 | 0.134974 | 0.0674870 | − | 0.997720i | \(-0.478502\pi\) | ||||
0.0674870 | + | 0.997720i | \(0.478502\pi\) | |||||||
\(192\) | −3.14699e10 | −1.67124 | ||||||||
\(193\) | −5.03343e9 | −0.261130 | −0.130565 | − | 0.991440i | \(-0.541679\pi\) | ||||
−0.130565 | + | 0.991440i | \(0.541679\pi\) | |||||||
\(194\) | 1.96122e9 | 0.0994074 | ||||||||
\(195\) | 1.38239e10 | 0.684661 | ||||||||
\(196\) | −2.91286e9 | −0.140983 | ||||||||
\(197\) | 1.06453e10 | 0.503570 | 0.251785 | − | 0.967783i | \(-0.418982\pi\) | ||||
0.251785 | + | 0.967783i | \(0.418982\pi\) | |||||||
\(198\) | −2.13916e9 | −0.0989121 | ||||||||
\(199\) | 2.20681e10 | 0.997530 | 0.498765 | − | 0.866737i | \(-0.333787\pi\) | ||||
0.498765 | + | 0.866737i | \(0.333787\pi\) | |||||||
\(200\) | 4.40423e9 | 0.194641 | ||||||||
\(201\) | 1.41410e10 | 0.611079 | ||||||||
\(202\) | −4.35760e9 | −0.184148 | ||||||||
\(203\) | −6.72554e8 | −0.0277968 | ||||||||
\(204\) | 4.80243e10 | 1.94144 | ||||||||
\(205\) | −6.32289e10 | −2.50048 | ||||||||
\(206\) | 4.96940e9 | 0.192266 | ||||||||
\(207\) | 8.45617e10 | 3.20116 | ||||||||
\(208\) | −7.19371e9 | −0.266482 | ||||||||
\(209\) | −4.51878e9 | −0.163818 | ||||||||
\(210\) | 3.01186e9 | 0.106868 | ||||||||
\(211\) | 3.56797e10 | 1.23923 | 0.619613 | − | 0.784908i | \(-0.287290\pi\) | ||||
0.619613 | + | 0.784908i | \(0.287290\pi\) | |||||||
\(212\) | 1.86119e10 | 0.632820 | ||||||||
\(213\) | 2.71296e9 | 0.0903099 | ||||||||
\(214\) | 6.28623e9 | 0.204894 | ||||||||
\(215\) | 1.36248e8 | 0.00434867 | ||||||||
\(216\) | 1.69501e10 | 0.529822 | ||||||||
\(217\) | 1.06899e10 | 0.327269 | ||||||||
\(218\) | −8.86923e8 | −0.0265969 | ||||||||
\(219\) | 2.43846e10 | 0.716335 | ||||||||
\(220\) | 1.76548e10 | 0.508114 | ||||||||
\(221\) | 1.06761e10 | 0.301056 | ||||||||
\(222\) | −1.16085e10 | −0.320767 | ||||||||
\(223\) | 7.94326e9 | 0.215093 | 0.107547 | − | 0.994200i | \(-0.465701\pi\) | ||||
0.107547 | + | 0.994200i | \(0.465701\pi\) | |||||||
\(224\) | −4.80839e9 | −0.127610 | ||||||||
\(225\) | 7.51181e10 | 1.95399 | ||||||||
\(226\) | −4.34502e9 | −0.110791 | ||||||||
\(227\) | 7.84841e10 | 1.96185 | 0.980923 | − | 0.194394i | \(-0.0622741\pi\) | ||||
0.980923 | + | 0.194394i | \(0.0622741\pi\) | |||||||
\(228\) | 3.16290e10 | 0.775137 | ||||||||
\(229\) | −7.05521e10 | −1.69532 | −0.847658 | − | 0.530544i | \(-0.821988\pi\) | ||||
−0.847658 | + | 0.530544i | \(0.821988\pi\) | |||||||
\(230\) | 9.27744e9 | 0.218601 | ||||||||
\(231\) | 1.12056e10 | 0.258930 | ||||||||
\(232\) | −7.38519e8 | −0.0167365 | ||||||||
\(233\) | −5.80112e10 | −1.28947 | −0.644733 | − | 0.764408i | \(-0.723031\pi\) | ||||
−0.644733 | + | 0.764408i | \(0.723031\pi\) | |||||||
\(234\) | 3.32858e9 | 0.0725751 | ||||||||
\(235\) | −5.18594e10 | −1.10923 | ||||||||
\(236\) | −8.67574e10 | −1.82055 | ||||||||
\(237\) | −4.88458e10 | −1.00568 | ||||||||
\(238\) | 2.32603e9 | 0.0469915 | ||||||||
\(239\) | −4.01270e10 | −0.795511 | −0.397756 | − | 0.917491i | \(-0.630211\pi\) | ||||
−0.397756 | + | 0.917491i | \(0.630211\pi\) | |||||||
\(240\) | −1.21909e11 | −2.37185 | ||||||||
\(241\) | −8.33869e9 | −0.159229 | −0.0796143 | − | 0.996826i | \(-0.525369\pi\) | ||||
−0.0796143 | + | 0.996826i | \(0.525369\pi\) | |||||||
\(242\) | 5.23792e9 | 0.0981725 | ||||||||
\(243\) | 6.40487e10 | 1.17837 | ||||||||
\(244\) | −3.99564e10 | −0.721660 | ||||||||
\(245\) | −1.09738e10 | −0.194584 | ||||||||
\(246\) | −2.18885e10 | −0.381073 | ||||||||
\(247\) | 7.03133e9 | 0.120199 | ||||||||
\(248\) | 1.17384e10 | 0.197050 | ||||||||
\(249\) | −1.37029e11 | −2.25900 | ||||||||
\(250\) | −1.39439e9 | −0.0225763 | ||||||||
\(251\) | 3.04136e10 | 0.483655 | 0.241827 | − | 0.970319i | \(-0.422253\pi\) | ||||
0.241827 | + | 0.970319i | \(0.422253\pi\) | |||||||
\(252\) | −5.45542e10 | −0.852169 | ||||||||
\(253\) | 3.45167e10 | 0.529648 | ||||||||
\(254\) | −6.82560e9 | −0.102894 | ||||||||
\(255\) | 1.80924e11 | 2.67958 | ||||||||
\(256\) | 5.98805e10 | 0.871376 | ||||||||
\(257\) | 2.81976e10 | 0.403192 | 0.201596 | − | 0.979469i | \(-0.435387\pi\) | ||||
0.201596 | + | 0.979469i | \(0.435387\pi\) | |||||||
\(258\) | 4.71661e7 | 0.000662738 0 | ||||||||
\(259\) | 4.22959e10 | 0.584049 | ||||||||
\(260\) | −2.74713e10 | −0.372820 | ||||||||
\(261\) | −1.25961e10 | −0.168017 | ||||||||
\(262\) | −9.37042e9 | −0.122858 | ||||||||
\(263\) | −1.07105e11 | −1.38042 | −0.690208 | − | 0.723611i | \(-0.742481\pi\) | ||||
−0.690208 | + | 0.723611i | \(0.742481\pi\) | |||||||
\(264\) | 1.23047e10 | 0.155902 | ||||||||
\(265\) | 7.01177e10 | 0.873416 | ||||||||
\(266\) | 1.53194e9 | 0.0187618 | ||||||||
\(267\) | 2.08254e10 | 0.250780 | ||||||||
\(268\) | −2.81014e10 | −0.332752 | ||||||||
\(269\) | 2.99847e10 | 0.349152 | 0.174576 | − | 0.984644i | \(-0.444145\pi\) | ||||
0.174576 | + | 0.984644i | \(0.444145\pi\) | |||||||
\(270\) | 3.17176e10 | 0.363215 | ||||||||
\(271\) | 7.25971e10 | 0.817631 | 0.408815 | − | 0.912617i | \(-0.365942\pi\) | ||||
0.408815 | + | 0.912617i | \(0.365942\pi\) | |||||||
\(272\) | −9.41497e10 | −1.04294 | ||||||||
\(273\) | −1.74362e10 | −0.189985 | ||||||||
\(274\) | 8.52747e9 | 0.0913993 | ||||||||
\(275\) | 3.06620e10 | 0.323299 | ||||||||
\(276\) | −2.41598e11 | −2.50613 | ||||||||
\(277\) | 4.16560e10 | 0.425127 | 0.212563 | − | 0.977147i | \(-0.431819\pi\) | ||||
0.212563 | + | 0.977147i | \(0.431819\pi\) | |||||||
\(278\) | −1.75408e10 | −0.176135 | ||||||||
\(279\) | 2.00209e11 | 1.97817 | ||||||||
\(280\) | −1.20501e10 | −0.117160 | ||||||||
\(281\) | 5.45536e10 | 0.521969 | 0.260985 | − | 0.965343i | \(-0.415953\pi\) | ||||
0.260985 | + | 0.965343i | \(0.415953\pi\) | |||||||
\(282\) | −1.79526e10 | −0.169047 | ||||||||
\(283\) | 6.14842e10 | 0.569802 | 0.284901 | − | 0.958557i | \(-0.408039\pi\) | ||||
0.284901 | + | 0.958557i | \(0.408039\pi\) | |||||||
\(284\) | −5.39128e9 | −0.0491767 | ||||||||
\(285\) | 1.19158e11 | 1.06984 | ||||||||
\(286\) | 1.35867e9 | 0.0120079 | ||||||||
\(287\) | 7.97511e10 | 0.693854 | ||||||||
\(288\) | −9.00551e10 | −0.771333 | ||||||||
\(289\) | 2.11385e10 | 0.178252 | ||||||||
\(290\) | −1.38195e9 | −0.0114736 | ||||||||
\(291\) | −1.92410e11 | −1.57293 | ||||||||
\(292\) | −4.84577e10 | −0.390068 | ||||||||
\(293\) | 2.80875e10 | 0.222643 | 0.111321 | − | 0.993784i | \(-0.464492\pi\) | ||||
0.111321 | + | 0.993784i | \(0.464492\pi\) | |||||||
\(294\) | −3.79888e9 | −0.0296546 | ||||||||
\(295\) | −3.26845e11 | −2.51272 | ||||||||
\(296\) | 4.64443e10 | 0.351658 | ||||||||
\(297\) | 1.18006e11 | 0.880032 | ||||||||
\(298\) | 3.02906e9 | 0.0222503 | ||||||||
\(299\) | −5.37089e10 | −0.388620 | ||||||||
\(300\) | −2.14617e11 | −1.52975 | ||||||||
\(301\) | −1.71851e8 | −0.00120671 | ||||||||
\(302\) | −2.51576e10 | −0.174035 | ||||||||
\(303\) | 4.27513e11 | 2.91379 | ||||||||
\(304\) | −6.20074e10 | −0.416402 | ||||||||
\(305\) | −1.50530e11 | −0.996033 | ||||||||
\(306\) | 4.35637e10 | 0.284039 | ||||||||
\(307\) | 2.54042e11 | 1.63224 | 0.816119 | − | 0.577884i | \(-0.196122\pi\) | ||||
0.816119 | + | 0.577884i | \(0.196122\pi\) | |||||||
\(308\) | −2.22681e10 | −0.140996 | ||||||||
\(309\) | −4.87536e11 | −3.04224 | ||||||||
\(310\) | 2.19653e10 | 0.135086 | ||||||||
\(311\) | 2.66154e11 | 1.61329 | 0.806643 | − | 0.591040i | \(-0.201282\pi\) | ||||
0.806643 | + | 0.591040i | \(0.201282\pi\) | |||||||
\(312\) | −1.91464e10 | −0.114391 | ||||||||
\(313\) | −3.34837e11 | −1.97190 | −0.985949 | − | 0.167047i | \(-0.946577\pi\) | ||||
−0.985949 | + | 0.167047i | \(0.946577\pi\) | |||||||
\(314\) | 3.62051e10 | 0.210178 | ||||||||
\(315\) | −2.05525e11 | −1.17616 | ||||||||
\(316\) | 9.70678e10 | 0.547625 | ||||||||
\(317\) | −8.40674e10 | −0.467586 | −0.233793 | − | 0.972286i | \(-0.575114\pi\) | ||||
−0.233793 | + | 0.972286i | \(0.575114\pi\) | |||||||
\(318\) | 2.42733e10 | 0.133109 | ||||||||
\(319\) | −5.14153e9 | −0.0277993 | ||||||||
\(320\) | 2.35602e11 | 1.25604 | ||||||||
\(321\) | −6.16726e11 | −3.24205 | ||||||||
\(322\) | −1.17017e10 | −0.0606594 | ||||||||
\(323\) | 9.20244e10 | 0.470427 | ||||||||
\(324\) | −3.78748e11 | −1.90941 | ||||||||
\(325\) | −4.77108e10 | −0.237215 | ||||||||
\(326\) | 2.90339e10 | 0.142373 | ||||||||
\(327\) | 8.70137e10 | 0.420846 | ||||||||
\(328\) | 8.75732e10 | 0.417772 | ||||||||
\(329\) | 6.54107e10 | 0.307799 | ||||||||
\(330\) | 2.30250e10 | 0.106878 | ||||||||
\(331\) | −9.02322e10 | −0.413177 | −0.206588 | − | 0.978428i | \(-0.566236\pi\) | ||||
−0.206588 | + | 0.978428i | \(0.566236\pi\) | |||||||
\(332\) | 2.72309e11 | 1.23010 | ||||||||
\(333\) | 7.92150e11 | 3.53027 | ||||||||
\(334\) | −4.32301e9 | −0.0190076 | ||||||||
\(335\) | −1.05868e11 | −0.459264 | ||||||||
\(336\) | 1.53765e11 | 0.658161 | ||||||||
\(337\) | −3.71614e11 | −1.56949 | −0.784743 | − | 0.619821i | \(-0.787205\pi\) | ||||
−0.784743 | + | 0.619821i | \(0.787205\pi\) | |||||||
\(338\) | −2.11413e9 | −0.00881062 | ||||||||
\(339\) | 4.26279e11 | 1.75305 | ||||||||
\(340\) | −3.59538e11 | −1.45912 | ||||||||
\(341\) | 8.17220e10 | 0.327299 | ||||||||
\(342\) | 2.86913e10 | 0.113405 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | −1.88706e8 | −0.000726562 0 | ||||||||
\(345\) | −9.10186e11 | −3.45895 | ||||||||
\(346\) | 2.24004e10 | 0.0840260 | ||||||||
\(347\) | 1.37583e11 | 0.509428 | 0.254714 | − | 0.967016i | \(-0.418019\pi\) | ||||
0.254714 | + | 0.967016i | \(0.418019\pi\) | |||||||
\(348\) | 3.59879e10 | 0.131538 | ||||||||
\(349\) | 1.26667e11 | 0.457034 | 0.228517 | − | 0.973540i | \(-0.426612\pi\) | ||||
0.228517 | + | 0.973540i | \(0.426612\pi\) | |||||||
\(350\) | −1.03949e10 | −0.0370266 | ||||||||
\(351\) | −1.83619e11 | −0.645708 | ||||||||
\(352\) | −3.67591e10 | −0.127621 | ||||||||
\(353\) | 4.56985e11 | 1.56645 | 0.783223 | − | 0.621741i | \(-0.213574\pi\) | ||||
0.783223 | + | 0.621741i | \(0.213574\pi\) | |||||||
\(354\) | −1.13147e11 | −0.382938 | ||||||||
\(355\) | −2.03108e10 | −0.0678735 | ||||||||
\(356\) | −4.13848e10 | −0.136558 | ||||||||
\(357\) | −2.28201e11 | −0.743552 | ||||||||
\(358\) | 6.16998e10 | 0.198523 | ||||||||
\(359\) | 9.39943e10 | 0.298660 | 0.149330 | − | 0.988787i | \(-0.452288\pi\) | ||||
0.149330 | + | 0.988787i | \(0.452288\pi\) | |||||||
\(360\) | −2.25683e11 | −0.708169 | ||||||||
\(361\) | −2.62080e11 | −0.812178 | ||||||||
\(362\) | −1.20549e10 | −0.0368955 | ||||||||
\(363\) | −5.13879e11 | −1.55339 | ||||||||
\(364\) | 3.46498e10 | 0.103453 | ||||||||
\(365\) | −1.82557e11 | −0.538371 | ||||||||
\(366\) | −5.21103e10 | −0.151795 | ||||||||
\(367\) | 3.48049e10 | 0.100148 | 0.0500741 | − | 0.998746i | \(-0.484054\pi\) | ||||
0.0500741 | + | 0.998746i | \(0.484054\pi\) | |||||||
\(368\) | 4.73644e11 | 1.34629 | ||||||||
\(369\) | 1.49364e12 | 4.19399 | ||||||||
\(370\) | 8.69084e10 | 0.241076 | ||||||||
\(371\) | −8.84400e10 | −0.242363 | ||||||||
\(372\) | −5.72010e11 | −1.54867 | ||||||||
\(373\) | 5.00571e11 | 1.33899 | 0.669493 | − | 0.742819i | \(-0.266512\pi\) | ||||
0.669493 | + | 0.742819i | \(0.266512\pi\) | |||||||
\(374\) | 1.77820e10 | 0.0469958 | ||||||||
\(375\) | 1.36800e11 | 0.357227 | ||||||||
\(376\) | 7.18263e10 | 0.185327 | ||||||||
\(377\) | 8.00034e9 | 0.0203973 | ||||||||
\(378\) | −4.00057e10 | −0.100788 | ||||||||
\(379\) | −1.07548e11 | −0.267749 | −0.133875 | − | 0.990998i | \(-0.542742\pi\) | ||||
−0.133875 | + | 0.990998i | \(0.542742\pi\) | |||||||
\(380\) | −2.36793e11 | −0.582564 | ||||||||
\(381\) | 6.69642e11 | 1.62810 | ||||||||
\(382\) | −6.43405e9 | −0.0154596 | ||||||||
\(383\) | 6.05542e11 | 1.43797 | 0.718985 | − | 0.695026i | \(-0.244607\pi\) | ||||
0.718985 | + | 0.695026i | \(0.244607\pi\) | |||||||
\(384\) | 3.42274e11 | 0.803311 | ||||||||
\(385\) | −8.38920e10 | −0.194602 | ||||||||
\(386\) | 1.30451e10 | 0.0299093 | ||||||||
\(387\) | −3.21855e9 | −0.00729391 | ||||||||
\(388\) | 3.82364e11 | 0.856513 | ||||||||
\(389\) | 1.31728e11 | 0.291678 | 0.145839 | − | 0.989308i | \(-0.453412\pi\) | ||||
0.145839 | + | 0.989308i | \(0.453412\pi\) | |||||||
\(390\) | −3.58274e10 | −0.0784197 | ||||||||
\(391\) | −7.02929e11 | −1.52095 | ||||||||
\(392\) | 1.51989e10 | 0.0325105 | ||||||||
\(393\) | 9.19308e11 | 1.94399 | ||||||||
\(394\) | −2.75894e10 | −0.0576779 | ||||||||
\(395\) | 3.65689e11 | 0.755831 | ||||||||
\(396\) | −4.17055e11 | −0.852245 | ||||||||
\(397\) | −6.44186e11 | −1.30153 | −0.650765 | − | 0.759279i | \(-0.725552\pi\) | ||||
−0.650765 | + | 0.759279i | \(0.725552\pi\) | |||||||
\(398\) | −5.71939e10 | −0.114255 | ||||||||
\(399\) | −1.50294e11 | −0.296869 | ||||||||
\(400\) | 4.20749e11 | 0.821776 | ||||||||
\(401\) | 4.16565e11 | 0.804513 | 0.402256 | − | 0.915527i | \(-0.368226\pi\) | ||||
0.402256 | + | 0.915527i | \(0.368226\pi\) | |||||||
\(402\) | −3.66492e10 | −0.0699918 | ||||||||
\(403\) | −1.27161e11 | −0.240150 | ||||||||
\(404\) | −8.49567e11 | −1.58665 | ||||||||
\(405\) | −1.42688e12 | −2.63536 | ||||||||
\(406\) | 1.74306e9 | 0.00318379 | ||||||||
\(407\) | 3.23343e11 | 0.584102 | ||||||||
\(408\) | −2.50583e11 | −0.447694 | ||||||||
\(409\) | −8.23424e11 | −1.45502 | −0.727510 | − | 0.686097i | \(-0.759322\pi\) | ||||
−0.727510 | + | 0.686097i | \(0.759322\pi\) | |||||||
\(410\) | 1.63870e11 | 0.286400 | ||||||||
\(411\) | −8.36609e11 | −1.44622 | ||||||||
\(412\) | 9.68845e11 | 1.65660 | ||||||||
\(413\) | 4.12253e11 | 0.697250 | ||||||||
\(414\) | −2.19158e11 | −0.366654 | ||||||||
\(415\) | 1.02588e12 | 1.69778 | ||||||||
\(416\) | 5.71980e10 | 0.0936399 | ||||||||
\(417\) | 1.72088e12 | 2.78701 | ||||||||
\(418\) | 1.17113e10 | 0.0187634 | ||||||||
\(419\) | −6.66183e11 | −1.05592 | −0.527959 | − | 0.849270i | \(-0.677043\pi\) | ||||
−0.527959 | + | 0.849270i | \(0.677043\pi\) | |||||||
\(420\) | 5.87198e11 | 0.920795 | ||||||||
\(421\) | 6.72240e11 | 1.04293 | 0.521465 | − | 0.853273i | \(-0.325386\pi\) | ||||
0.521465 | + | 0.853273i | \(0.325386\pi\) | |||||||
\(422\) | −9.24711e10 | −0.141938 | ||||||||
\(423\) | 1.22506e12 | 1.86049 | ||||||||
\(424\) | −9.71143e10 | −0.145927 | ||||||||
\(425\) | −6.24429e11 | −0.928395 | ||||||||
\(426\) | −7.03118e9 | −0.0103439 | ||||||||
\(427\) | 1.89865e11 | 0.276388 | ||||||||
\(428\) | 1.22558e12 | 1.76540 | ||||||||
\(429\) | −1.33296e11 | −0.190003 | ||||||||
\(430\) | −3.53114e8 | −0.000498089 0 | ||||||||
\(431\) | 1.06235e12 | 1.48293 | 0.741465 | − | 0.670991i | \(-0.234131\pi\) | ||||
0.741465 | + | 0.670991i | \(0.234131\pi\) | |||||||
\(432\) | 1.61929e12 | 2.23691 | ||||||||
\(433\) | −1.17404e12 | −1.60504 | −0.802521 | − | 0.596624i | \(-0.796508\pi\) | ||||
−0.802521 | + | 0.596624i | \(0.796508\pi\) | |||||||
\(434\) | −2.77050e10 | −0.0374848 | ||||||||
\(435\) | 1.35579e11 | 0.181548 | ||||||||
\(436\) | −1.72916e11 | −0.229164 | ||||||||
\(437\) | −4.62953e11 | −0.607253 | ||||||||
\(438\) | −6.31975e10 | −0.0820476 | ||||||||
\(439\) | 3.13450e11 | 0.402790 | 0.201395 | − | 0.979510i | \(-0.435453\pi\) | ||||
0.201395 | + | 0.979510i | \(0.435453\pi\) | |||||||
\(440\) | −9.21202e10 | −0.117170 | ||||||||
\(441\) | 2.59230e11 | 0.326371 | ||||||||
\(442\) | −2.76692e10 | −0.0344824 | ||||||||
\(443\) | 5.05500e10 | 0.0623597 | 0.0311799 | − | 0.999514i | \(-0.490074\pi\) | ||||
0.0311799 | + | 0.999514i | \(0.490074\pi\) | |||||||
\(444\) | −2.26322e12 | −2.76379 | ||||||||
\(445\) | −1.55911e11 | −0.188477 | ||||||||
\(446\) | −2.05865e10 | −0.0246364 | ||||||||
\(447\) | −2.97174e11 | −0.352068 | ||||||||
\(448\) | −2.97167e11 | −0.348538 | ||||||||
\(449\) | 8.38208e10 | 0.0973292 | 0.0486646 | − | 0.998815i | \(-0.484503\pi\) | ||||
0.0486646 | + | 0.998815i | \(0.484503\pi\) | |||||||
\(450\) | −1.94684e11 | −0.223807 | ||||||||
\(451\) | 6.09680e11 | 0.693917 | ||||||||
\(452\) | −8.47114e11 | −0.954594 | ||||||||
\(453\) | 2.46814e12 | 2.75378 | ||||||||
\(454\) | −2.03407e11 | −0.224706 | ||||||||
\(455\) | 1.30538e11 | 0.142786 | ||||||||
\(456\) | −1.65035e11 | −0.178746 | ||||||||
\(457\) | −1.47870e12 | −1.58583 | −0.792913 | − | 0.609334i | \(-0.791437\pi\) | ||||
−0.792913 | + | 0.609334i | \(0.791437\pi\) | |||||||
\(458\) | 1.82850e11 | 0.194178 | ||||||||
\(459\) | −2.40317e12 | −2.52713 | ||||||||
\(460\) | 1.80875e12 | 1.88351 | ||||||||
\(461\) | 1.45505e12 | 1.50046 | 0.750228 | − | 0.661179i | \(-0.229943\pi\) | ||||
0.750228 | + | 0.661179i | \(0.229943\pi\) | |||||||
\(462\) | −2.90416e10 | −0.0296573 | ||||||||
\(463\) | −1.20315e12 | −1.21676 | −0.608382 | − | 0.793644i | \(-0.708181\pi\) | ||||
−0.608382 | + | 0.793644i | \(0.708181\pi\) | |||||||
\(464\) | −7.05529e10 | −0.0706617 | ||||||||
\(465\) | −2.15496e12 | −2.13748 | ||||||||
\(466\) | 1.50348e11 | 0.147693 | ||||||||
\(467\) | −1.29013e12 | −1.25518 | −0.627592 | − | 0.778542i | \(-0.715959\pi\) | ||||
−0.627592 | + | 0.778542i | \(0.715959\pi\) | |||||||
\(468\) | 6.48947e11 | 0.625321 | ||||||||
\(469\) | 1.33532e11 | 0.127440 | ||||||||
\(470\) | 1.34404e11 | 0.127049 | ||||||||
\(471\) | −3.55199e12 | −3.32566 | ||||||||
\(472\) | 4.52687e11 | 0.419816 | ||||||||
\(473\) | −1.31376e9 | −0.00120682 | ||||||||
\(474\) | 1.26594e11 | 0.115189 | ||||||||
\(475\) | −4.11252e11 | −0.370669 | ||||||||
\(476\) | 4.53488e11 | 0.404888 | ||||||||
\(477\) | −1.65637e12 | −1.46496 | ||||||||
\(478\) | 1.03997e11 | 0.0911163 | ||||||||
\(479\) | −7.45278e11 | −0.646857 | −0.323429 | − | 0.946253i | \(-0.604836\pi\) | ||||
−0.323429 | + | 0.946253i | \(0.604836\pi\) | |||||||
\(480\) | 9.69315e11 | 0.833450 | ||||||||
\(481\) | −5.03129e11 | −0.428575 | ||||||||
\(482\) | 2.16114e10 | 0.0182377 | ||||||||
\(483\) | 1.14803e12 | 0.959819 | ||||||||
\(484\) | 1.02120e12 | 0.845873 | ||||||||
\(485\) | 1.44050e12 | 1.18216 | ||||||||
\(486\) | −1.65995e11 | −0.134968 | ||||||||
\(487\) | 5.96435e11 | 0.480488 | 0.240244 | − | 0.970712i | \(-0.422772\pi\) | ||||
0.240244 | + | 0.970712i | \(0.422772\pi\) | |||||||
\(488\) | 2.08487e11 | 0.166414 | ||||||||
\(489\) | −2.84845e12 | −2.25278 | ||||||||
\(490\) | 2.84407e10 | 0.0222873 | ||||||||
\(491\) | −5.32558e11 | −0.413523 | −0.206762 | − | 0.978391i | \(-0.566292\pi\) | ||||
−0.206762 | + | 0.978391i | \(0.566292\pi\) | |||||||
\(492\) | −4.26743e12 | −3.28340 | ||||||||
\(493\) | 1.04707e11 | 0.0798295 | ||||||||
\(494\) | −1.82231e10 | −0.0137674 | ||||||||
\(495\) | −1.57119e12 | −1.17627 | ||||||||
\(496\) | 1.12140e12 | 0.831944 | ||||||||
\(497\) | 2.56182e10 | 0.0188341 | ||||||||
\(498\) | 3.55139e11 | 0.258741 | ||||||||
\(499\) | −9.55707e11 | −0.690037 | −0.345019 | − | 0.938596i | \(-0.612127\pi\) | ||||
−0.345019 | + | 0.938596i | \(0.612127\pi\) | |||||||
\(500\) | −2.71852e11 | −0.194522 | ||||||||
\(501\) | 4.24120e11 | 0.300759 | ||||||||
\(502\) | −7.88228e10 | −0.0553969 | ||||||||
\(503\) | 1.79300e12 | 1.24889 | 0.624444 | − | 0.781070i | \(-0.285326\pi\) | ||||
0.624444 | + | 0.781070i | \(0.285326\pi\) | |||||||
\(504\) | 2.84656e11 | 0.196509 | ||||||||
\(505\) | −3.20062e12 | −2.18989 | ||||||||
\(506\) | −8.94570e10 | −0.0606648 | ||||||||
\(507\) | 2.07412e11 | 0.139411 | ||||||||
\(508\) | −1.33073e12 | −0.886552 | ||||||||
\(509\) | 2.18143e12 | 1.44050 | 0.720248 | − | 0.693717i | \(-0.244028\pi\) | ||||
0.720248 | + | 0.693717i | \(0.244028\pi\) | |||||||
\(510\) | −4.68901e11 | −0.306913 | ||||||||
\(511\) | 2.30261e11 | 0.149392 | ||||||||
\(512\) | −8.44412e11 | −0.543050 | ||||||||
\(513\) | −1.58274e12 | −1.00898 | ||||||||
\(514\) | −7.30796e10 | −0.0461809 | ||||||||
\(515\) | 3.64998e12 | 2.28643 | ||||||||
\(516\) | 9.19561e9 | 0.00571027 | ||||||||
\(517\) | 5.00051e11 | 0.307827 | ||||||||
\(518\) | −1.09618e11 | −0.0668958 | ||||||||
\(519\) | −2.19765e12 | −1.32955 | ||||||||
\(520\) | 1.43341e11 | 0.0859718 | ||||||||
\(521\) | 1.96104e11 | 0.116605 | 0.0583025 | − | 0.998299i | \(-0.481431\pi\) | ||||
0.0583025 | + | 0.998299i | \(0.481431\pi\) | |||||||
\(522\) | 3.26453e10 | 0.0192444 | ||||||||
\(523\) | 2.98958e12 | 1.74724 | 0.873620 | − | 0.486609i | \(-0.161766\pi\) | ||||
0.873620 | + | 0.486609i | \(0.161766\pi\) | |||||||
\(524\) | −1.82688e12 | −1.05857 | ||||||||
\(525\) | 1.01982e12 | 0.585876 | ||||||||
\(526\) | 2.77585e11 | 0.158110 | ||||||||
\(527\) | −1.66426e12 | −0.939882 | ||||||||
\(528\) | 1.17550e12 | 0.658220 | ||||||||
\(529\) | 1.73511e12 | 0.963336 | ||||||||
\(530\) | −1.81724e11 | −0.100039 | ||||||||
\(531\) | 7.72098e12 | 4.21451 | ||||||||
\(532\) | 2.98669e11 | 0.161655 | ||||||||
\(533\) | −9.48677e11 | −0.509150 | ||||||||
\(534\) | −5.39732e10 | −0.0287238 | ||||||||
\(535\) | 4.61718e12 | 2.43660 | ||||||||
\(536\) | 1.46629e11 | 0.0767322 | ||||||||
\(537\) | −6.05321e12 | −3.14124 | ||||||||
\(538\) | −7.77113e10 | −0.0399911 | ||||||||
\(539\) | 1.05814e11 | 0.0539998 | ||||||||
\(540\) | 6.18373e12 | 3.12953 | ||||||||
\(541\) | 2.82256e11 | 0.141663 | 0.0708314 | − | 0.997488i | \(-0.477435\pi\) | ||||
0.0708314 | + | 0.997488i | \(0.477435\pi\) | |||||||
\(542\) | −1.88150e11 | −0.0936498 | ||||||||
\(543\) | 1.18267e12 | 0.583801 | ||||||||
\(544\) | 7.48594e11 | 0.366481 | ||||||||
\(545\) | −6.51436e11 | −0.316292 | ||||||||
\(546\) | 4.51894e10 | 0.0217606 | ||||||||
\(547\) | 2.45530e12 | 1.17263 | 0.586315 | − | 0.810083i | \(-0.300578\pi\) | ||||
0.586315 | + | 0.810083i | \(0.300578\pi\) | |||||||
\(548\) | 1.66253e12 | 0.787513 | ||||||||
\(549\) | 3.55593e12 | 1.67062 | ||||||||
\(550\) | −7.94668e10 | −0.0370300 | ||||||||
\(551\) | 6.89603e10 | 0.0318726 | ||||||||
\(552\) | 1.26062e12 | 0.577910 | ||||||||
\(553\) | −4.61246e11 | −0.209734 | ||||||||
\(554\) | −1.07960e11 | −0.0486932 | ||||||||
\(555\) | −8.52636e12 | −3.81457 | ||||||||
\(556\) | −3.41978e12 | −1.51762 | ||||||||
\(557\) | −2.04361e11 | −0.0899602 | −0.0449801 | − | 0.998988i | \(-0.514322\pi\) | ||||
−0.0449801 | + | 0.998988i | \(0.514322\pi\) | |||||||
\(558\) | −5.18881e11 | −0.226576 | ||||||||
\(559\) | 2.04424e9 | 0.000885481 0 | ||||||||
\(560\) | −1.15118e12 | −0.494649 | ||||||||
\(561\) | −1.74455e12 | −0.743619 | ||||||||
\(562\) | −1.41386e11 | −0.0597853 | ||||||||
\(563\) | −3.84312e12 | −1.61212 | −0.806058 | − | 0.591837i | \(-0.798403\pi\) | ||||
−0.806058 | + | 0.591837i | \(0.798403\pi\) | |||||||
\(564\) | −3.50008e12 | −1.45654 | ||||||||
\(565\) | −3.19137e12 | −1.31753 | ||||||||
\(566\) | −1.59348e11 | −0.0652641 | ||||||||
\(567\) | 1.79973e12 | 0.731281 | ||||||||
\(568\) | 2.81309e10 | 0.0113401 | ||||||||
\(569\) | 2.72425e12 | 1.08954 | 0.544768 | − | 0.838587i | \(-0.316618\pi\) | ||||
0.544768 | + | 0.838587i | \(0.316618\pi\) | |||||||
\(570\) | −3.08821e11 | −0.122538 | ||||||||
\(571\) | −6.05815e11 | −0.238494 | −0.119247 | − | 0.992865i | \(-0.538048\pi\) | ||||
−0.119247 | + | 0.992865i | \(0.538048\pi\) | |||||||
\(572\) | 2.64890e11 | 0.103463 | ||||||||
\(573\) | 6.31229e11 | 0.244619 | ||||||||
\(574\) | −2.06691e11 | −0.0794727 | ||||||||
\(575\) | 3.14135e12 | 1.19843 | ||||||||
\(576\) | −5.56557e12 | −2.10673 | ||||||||
\(577\) | −4.47921e12 | −1.68233 | −0.841164 | − | 0.540781i | \(-0.818129\pi\) | ||||
−0.841164 | + | 0.540781i | \(0.818129\pi\) | |||||||
\(578\) | −5.47847e10 | −0.0204166 | ||||||||
\(579\) | −1.27983e12 | −0.473257 | ||||||||
\(580\) | −2.69427e11 | −0.0988587 | ||||||||
\(581\) | −1.29395e12 | −0.471114 | ||||||||
\(582\) | 4.98670e11 | 0.180161 | ||||||||
\(583\) | −6.76105e11 | −0.242385 | ||||||||
\(584\) | 2.52845e11 | 0.0899491 | ||||||||
\(585\) | 2.44481e12 | 0.863066 | ||||||||
\(586\) | −7.27942e10 | −0.0255010 | ||||||||
\(587\) | 5.14513e12 | 1.78865 | 0.894325 | − | 0.447418i | \(-0.147656\pi\) | ||||
0.894325 | + | 0.447418i | \(0.147656\pi\) | |||||||
\(588\) | −7.40638e11 | −0.255510 | ||||||||
\(589\) | −1.09609e12 | −0.375255 | ||||||||
\(590\) | 8.47085e11 | 0.287802 | ||||||||
\(591\) | 2.70673e12 | 0.912643 | ||||||||
\(592\) | 4.43696e12 | 1.48470 | ||||||||
\(593\) | −4.16705e12 | −1.38383 | −0.691915 | − | 0.721979i | \(-0.743233\pi\) | ||||
−0.691915 | + | 0.721979i | \(0.743233\pi\) | |||||||
\(594\) | −3.05835e11 | −0.100797 | ||||||||
\(595\) | 1.70845e12 | 0.558825 | ||||||||
\(596\) | 5.90552e11 | 0.191712 | ||||||||
\(597\) | 5.61115e12 | 1.80787 | ||||||||
\(598\) | 1.39197e11 | 0.0445118 | ||||||||
\(599\) | −1.65167e12 | −0.524207 | −0.262103 | − | 0.965040i | \(-0.584416\pi\) | ||||
−0.262103 | + | 0.965040i | \(0.584416\pi\) | |||||||
\(600\) | 1.11984e12 | 0.352757 | ||||||||
\(601\) | −5.18671e12 | −1.62165 | −0.810824 | − | 0.585289i | \(-0.800981\pi\) | ||||
−0.810824 | + | 0.585289i | \(0.800981\pi\) | |||||||
\(602\) | 4.45385e8 | 0.000138214 0 | ||||||||
\(603\) | 2.50089e12 | 0.770311 | ||||||||
\(604\) | −4.90477e12 | −1.49952 | ||||||||
\(605\) | 3.84720e12 | 1.16747 | ||||||||
\(606\) | −1.10799e12 | −0.333739 | ||||||||
\(607\) | −6.39931e11 | −0.191330 | −0.0956652 | − | 0.995414i | \(-0.530498\pi\) | ||||
−0.0956652 | + | 0.995414i | \(0.530498\pi\) | |||||||
\(608\) | 4.93028e11 | 0.146320 | ||||||||
\(609\) | −1.71007e11 | −0.0503775 | ||||||||
\(610\) | 3.90128e11 | 0.114084 | ||||||||
\(611\) | −7.78091e11 | −0.225863 | ||||||||
\(612\) | 8.49327e12 | 2.44734 | ||||||||
\(613\) | −4.23624e11 | −0.121174 | −0.0605868 | − | 0.998163i | \(-0.519297\pi\) | ||||
−0.0605868 | + | 0.998163i | \(0.519297\pi\) | |||||||
\(614\) | −6.58401e11 | −0.186953 | ||||||||
\(615\) | −1.60769e13 | −4.53173 | ||||||||
\(616\) | 1.16192e11 | 0.0325134 | ||||||||
\(617\) | −2.26957e12 | −0.630465 | −0.315233 | − | 0.949014i | \(-0.602083\pi\) | ||||
−0.315233 | + | 0.949014i | \(0.602083\pi\) | |||||||
\(618\) | 1.26355e12 | 0.348452 | ||||||||
\(619\) | −2.03001e12 | −0.555763 | −0.277882 | − | 0.960615i | \(-0.589632\pi\) | ||||
−0.277882 | + | 0.960615i | \(0.589632\pi\) | |||||||
\(620\) | 4.28240e12 | 1.16393 | ||||||||
\(621\) | 1.20898e13 | 3.26216 | ||||||||
\(622\) | −6.89791e11 | −0.184782 | ||||||||
\(623\) | 1.96652e11 | 0.0523001 | ||||||||
\(624\) | −1.82911e12 | −0.482958 | ||||||||
\(625\) | −4.28684e12 | −1.12377 | ||||||||
\(626\) | 8.67798e11 | 0.225857 | ||||||||
\(627\) | −1.14897e12 | −0.296896 | ||||||||
\(628\) | 7.05863e12 | 1.81093 | ||||||||
\(629\) | −6.58484e12 | −1.67733 | ||||||||
\(630\) | 5.32658e11 | 0.134715 | ||||||||
\(631\) | −1.89988e12 | −0.477083 | −0.238542 | − | 0.971132i | \(-0.576669\pi\) | ||||
−0.238542 | + | 0.971132i | \(0.576669\pi\) | |||||||
\(632\) | −5.06486e11 | −0.126282 | ||||||||
\(633\) | 9.07210e12 | 2.24590 | ||||||||
\(634\) | 2.17878e11 | 0.0535563 | ||||||||
\(635\) | −5.01334e12 | −1.22362 | ||||||||
\(636\) | 4.73236e12 | 1.14689 | ||||||||
\(637\) | −1.64648e11 | −0.0396214 | ||||||||
\(638\) | 1.33253e10 | 0.00318408 | ||||||||
\(639\) | 4.79797e11 | 0.113842 | ||||||||
\(640\) | −2.56247e12 | −0.603738 | ||||||||
\(641\) | 3.58899e12 | 0.839675 | 0.419837 | − | 0.907599i | \(-0.362087\pi\) | ||||
0.419837 | + | 0.907599i | \(0.362087\pi\) | |||||||
\(642\) | 1.59837e12 | 0.371338 | ||||||||
\(643\) | −1.24458e12 | −0.287127 | −0.143564 | − | 0.989641i | \(-0.545856\pi\) | ||||
−0.143564 | + | 0.989641i | \(0.545856\pi\) | |||||||
\(644\) | −2.28139e12 | −0.522653 | ||||||||
\(645\) | 3.46431e10 | 0.00788130 | ||||||||
\(646\) | −2.38500e11 | −0.0538817 | ||||||||
\(647\) | 6.58112e12 | 1.47649 | 0.738246 | − | 0.674532i | \(-0.235655\pi\) | ||||
0.738246 | + | 0.674532i | \(0.235655\pi\) | |||||||
\(648\) | 1.97625e12 | 0.440306 | ||||||||
\(649\) | 3.15158e12 | 0.697313 | ||||||||
\(650\) | 1.23652e11 | 0.0271701 | ||||||||
\(651\) | 2.71807e12 | 0.593125 | ||||||||
\(652\) | 5.66052e12 | 1.22671 | ||||||||
\(653\) | 2.73810e12 | 0.589304 | 0.294652 | − | 0.955605i | \(-0.404796\pi\) | ||||
0.294652 | + | 0.955605i | \(0.404796\pi\) | |||||||
\(654\) | −2.25513e11 | −0.0482028 | ||||||||
\(655\) | −6.88248e12 | −1.46103 | ||||||||
\(656\) | 8.36613e12 | 1.76383 | ||||||||
\(657\) | 4.31250e12 | 0.902994 | ||||||||
\(658\) | −1.69525e11 | −0.0352547 | ||||||||
\(659\) | −1.55865e12 | −0.321933 | −0.160966 | − | 0.986960i | \(-0.551461\pi\) | ||||
−0.160966 | + | 0.986960i | \(0.551461\pi\) | |||||||
\(660\) | 4.48900e12 | 0.920878 | ||||||||
\(661\) | −4.31825e12 | −0.879836 | −0.439918 | − | 0.898038i | \(-0.644992\pi\) | ||||
−0.439918 | + | 0.898038i | \(0.644992\pi\) | |||||||
\(662\) | 2.33855e11 | 0.0473244 | ||||||||
\(663\) | 2.71456e12 | 0.545618 | ||||||||
\(664\) | −1.42087e12 | −0.283659 | ||||||||
\(665\) | 1.12519e12 | 0.223115 | ||||||||
\(666\) | −2.05301e12 | −0.404350 | ||||||||
\(667\) | −5.26754e11 | −0.103048 | ||||||||
\(668\) | −8.42823e11 | −0.163773 | ||||||||
\(669\) | 2.01969e12 | 0.389823 | ||||||||
\(670\) | 2.74378e11 | 0.0526032 | ||||||||
\(671\) | 1.45147e12 | 0.276413 | ||||||||
\(672\) | −1.22261e12 | −0.231273 | ||||||||
\(673\) | −3.11290e12 | −0.584921 | −0.292461 | − | 0.956278i | \(-0.594474\pi\) | ||||
−0.292461 | + | 0.956278i | \(0.594474\pi\) | |||||||
\(674\) | 9.63112e11 | 0.179766 | ||||||||
\(675\) | 1.07396e13 | 1.99123 | ||||||||
\(676\) | −4.12175e11 | −0.0759139 | ||||||||
\(677\) | 5.23656e12 | 0.958071 | 0.479035 | − | 0.877796i | \(-0.340987\pi\) | ||||
0.479035 | + | 0.877796i | \(0.340987\pi\) | |||||||
\(678\) | −1.10479e12 | −0.200791 | ||||||||
\(679\) | −1.81691e12 | −0.328035 | ||||||||
\(680\) | 1.87602e12 | 0.336470 | ||||||||
\(681\) | 1.99558e13 | 3.55555 | ||||||||
\(682\) | −2.11799e11 | −0.0374882 | ||||||||
\(683\) | 1.03001e13 | 1.81112 | 0.905560 | − | 0.424218i | \(-0.139451\pi\) | ||||
0.905560 | + | 0.424218i | \(0.139451\pi\) | |||||||
\(684\) | 5.59371e12 | 0.977118 | ||||||||
\(685\) | 6.26335e12 | 1.08692 | ||||||||
\(686\) | −3.58725e10 | −0.00618447 | ||||||||
\(687\) | −1.79389e13 | −3.07250 | ||||||||
\(688\) | −1.80276e10 | −0.00306754 | ||||||||
\(689\) | 1.05203e12 | 0.177846 | ||||||||
\(690\) | 2.35893e12 | 0.396181 | ||||||||
\(691\) | −2.86194e12 | −0.477540 | −0.238770 | − | 0.971076i | \(-0.576744\pi\) | ||||
−0.238770 | + | 0.971076i | \(0.576744\pi\) | |||||||
\(692\) | 4.36723e12 | 0.723983 | ||||||||
\(693\) | 1.98176e12 | 0.326400 | ||||||||
\(694\) | −3.56575e11 | −0.0583489 | ||||||||
\(695\) | −1.28835e13 | −2.09461 | ||||||||
\(696\) | −1.87780e11 | −0.0303324 | ||||||||
\(697\) | −1.24161e13 | −1.99267 | ||||||||
\(698\) | −3.28282e11 | −0.0523478 | ||||||||
\(699\) | −1.47502e13 | −2.33696 | ||||||||
\(700\) | −2.02661e12 | −0.319028 | ||||||||
\(701\) | 4.39926e12 | 0.688095 | 0.344048 | − | 0.938952i | \(-0.388202\pi\) | ||||
0.344048 | + | 0.938952i | \(0.388202\pi\) | |||||||
\(702\) | 4.75886e11 | 0.0739582 | ||||||||
\(703\) | −4.33681e12 | −0.669686 | ||||||||
\(704\) | −2.27178e12 | −0.348569 | ||||||||
\(705\) | −1.31860e13 | −2.01031 | ||||||||
\(706\) | −1.18437e12 | −0.179418 | ||||||||
\(707\) | 4.03696e12 | 0.607670 | ||||||||
\(708\) | −2.20594e13 | −3.29946 | ||||||||
\(709\) | −5.62114e12 | −0.835442 | −0.417721 | − | 0.908575i | \(-0.637171\pi\) | ||||
−0.417721 | + | 0.908575i | \(0.637171\pi\) | |||||||
\(710\) | 5.26396e10 | 0.00777409 | ||||||||
\(711\) | −8.63857e12 | −1.26773 | ||||||||
\(712\) | 2.15940e11 | 0.0314900 | ||||||||
\(713\) | 8.37249e12 | 1.21325 | ||||||||
\(714\) | 5.91429e11 | 0.0851649 | ||||||||
\(715\) | 9.97933e11 | 0.142799 | ||||||||
\(716\) | 1.20291e13 | 1.71051 | ||||||||
\(717\) | −1.02029e13 | −1.44174 | ||||||||
\(718\) | −2.43605e11 | −0.0342079 | ||||||||
\(719\) | 4.66981e11 | 0.0651657 | 0.0325828 | − | 0.999469i | \(-0.489627\pi\) | ||||
0.0325828 | + | 0.999469i | \(0.489627\pi\) | |||||||
\(720\) | −2.15601e13 | −2.98989 | ||||||||
\(721\) | −4.60375e12 | −0.634458 | ||||||||
\(722\) | 6.79233e11 | 0.0930253 | ||||||||
\(723\) | −2.12024e12 | −0.288577 | ||||||||
\(724\) | −2.35024e12 | −0.317899 | ||||||||
\(725\) | −4.67928e11 | −0.0629011 | ||||||||
\(726\) | 1.33182e12 | 0.177923 | ||||||||
\(727\) | 3.43399e12 | 0.455926 | 0.227963 | − | 0.973670i | \(-0.426793\pi\) | ||||
0.227963 | + | 0.973670i | \(0.426793\pi\) | |||||||
\(728\) | −1.80797e11 | −0.0238562 | ||||||||
\(729\) | 1.53143e12 | 0.200827 | ||||||||
\(730\) | 4.73134e11 | 0.0616639 | ||||||||
\(731\) | 2.67546e10 | 0.00346553 | ||||||||
\(732\) | −1.01595e13 | −1.30790 | ||||||||
\(733\) | 1.03659e13 | 1.32630 | 0.663149 | − | 0.748488i | \(-0.269220\pi\) | ||||
0.663149 | + | 0.748488i | \(0.269220\pi\) | |||||||
\(734\) | −9.02038e10 | −0.0114708 | ||||||||
\(735\) | −2.79024e12 | −0.352654 | ||||||||
\(736\) | −3.76600e12 | −0.473075 | ||||||||
\(737\) | 1.02082e12 | 0.127452 | ||||||||
\(738\) | −3.87106e12 | −0.480371 | ||||||||
\(739\) | −1.30128e12 | −0.160499 | −0.0802495 | − | 0.996775i | \(-0.525572\pi\) | ||||
−0.0802495 | + | 0.996775i | \(0.525572\pi\) | |||||||
\(740\) | 1.69438e13 | 2.07716 | ||||||||
\(741\) | 1.78782e12 | 0.217842 | ||||||||
\(742\) | 2.29210e11 | 0.0277598 | ||||||||
\(743\) | −1.65678e12 | −0.199441 | −0.0997204 | − | 0.995015i | \(-0.531795\pi\) | ||||
−0.0997204 | + | 0.995015i | \(0.531795\pi\) | |||||||
\(744\) | 2.98466e12 | 0.357122 | ||||||||
\(745\) | 2.22482e12 | 0.264601 | ||||||||
\(746\) | −1.29733e12 | −0.153365 | ||||||||
\(747\) | −2.42341e13 | −2.84764 | ||||||||
\(748\) | 3.46682e12 | 0.404924 | ||||||||
\(749\) | −5.82369e12 | −0.676129 | ||||||||
\(750\) | −3.54544e11 | −0.0409161 | ||||||||
\(751\) | −1.21749e13 | −1.39664 | −0.698321 | − | 0.715785i | \(-0.746069\pi\) | ||||
−0.698321 | + | 0.715785i | \(0.746069\pi\) | |||||||
\(752\) | 6.86178e12 | 0.782450 | ||||||||
\(753\) | 7.73311e12 | 0.876550 | ||||||||
\(754\) | −2.07345e10 | −0.00233627 | ||||||||
\(755\) | −1.84780e13 | −2.06963 | ||||||||
\(756\) | −7.79959e12 | −0.868408 | ||||||||
\(757\) | −5.32413e12 | −0.589274 | −0.294637 | − | 0.955609i | \(-0.595199\pi\) | ||||
−0.294637 | + | 0.955609i | \(0.595199\pi\) | |||||||
\(758\) | 2.78733e11 | 0.0306674 | ||||||||
\(759\) | 8.77640e12 | 0.959905 | ||||||||
\(760\) | 1.23555e12 | 0.134338 | ||||||||
\(761\) | −1.33415e13 | −1.44202 | −0.721012 | − | 0.692923i | \(-0.756323\pi\) | ||||
−0.721012 | + | 0.692923i | \(0.756323\pi\) | |||||||
\(762\) | −1.73551e12 | −0.186479 | ||||||||
\(763\) | 8.21662e11 | 0.0877673 | ||||||||
\(764\) | −1.25440e12 | −0.133203 | ||||||||
\(765\) | 3.19971e13 | 3.37781 | ||||||||
\(766\) | −1.56938e12 | −0.164702 | ||||||||
\(767\) | −4.90394e12 | −0.511642 | ||||||||
\(768\) | 1.52255e13 | 1.57924 | ||||||||
\(769\) | 1.20587e13 | 1.24346 | 0.621729 | − | 0.783233i | \(-0.286431\pi\) | ||||
0.621729 | + | 0.783233i | \(0.286431\pi\) | |||||||
\(770\) | 2.17423e11 | 0.0222893 | ||||||||
\(771\) | 7.16965e12 | 0.730724 | ||||||||
\(772\) | 2.54331e12 | 0.257704 | ||||||||
\(773\) | −2.60650e12 | −0.262573 | −0.131286 | − | 0.991344i | \(-0.541911\pi\) | ||||
−0.131286 | + | 0.991344i | \(0.541911\pi\) | |||||||
\(774\) | 8.34151e9 | 0.000835430 0 | ||||||||
\(775\) | 7.43748e12 | 0.740573 | ||||||||
\(776\) | −1.99512e12 | −0.197511 | ||||||||
\(777\) | 1.07544e13 | 1.05850 | ||||||||
\(778\) | −3.41399e11 | −0.0334083 | ||||||||
\(779\) | −8.17728e12 | −0.795591 | ||||||||
\(780\) | −6.98499e12 | −0.675679 | ||||||||
\(781\) | 1.95846e11 | 0.0188358 | ||||||||
\(782\) | 1.82178e12 | 0.174207 | ||||||||
\(783\) | −1.80086e12 | −0.171219 | ||||||||
\(784\) | 1.45199e12 | 0.137259 | ||||||||
\(785\) | 2.65923e13 | 2.49944 | ||||||||
\(786\) | −2.38257e12 | −0.222661 | ||||||||
\(787\) | −3.98596e12 | −0.370379 | −0.185190 | − | 0.982703i | \(-0.559290\pi\) | ||||
−0.185190 | + | 0.982703i | \(0.559290\pi\) | |||||||
\(788\) | −5.37889e12 | −0.496964 | ||||||||
\(789\) | −2.72331e13 | −2.50179 | ||||||||
\(790\) | −9.47755e11 | −0.0865714 | ||||||||
\(791\) | 4.02531e12 | 0.365599 | ||||||||
\(792\) | 2.17613e12 | 0.196527 | ||||||||
\(793\) | −2.25853e12 | −0.202813 | ||||||||
\(794\) | 1.66954e12 | 0.149075 | ||||||||
\(795\) | 1.78285e13 | 1.58293 | ||||||||
\(796\) | −1.11506e13 | −0.984444 | ||||||||
\(797\) | −8.84099e12 | −0.776137 | −0.388069 | − | 0.921631i | \(-0.626858\pi\) | ||||
−0.388069 | + | 0.921631i | \(0.626858\pi\) | |||||||
\(798\) | 3.89518e11 | 0.0340028 | ||||||||
\(799\) | −1.01835e13 | −0.883966 | ||||||||
\(800\) | −3.34542e12 | −0.288766 | ||||||||
\(801\) | 3.68305e12 | 0.316127 | ||||||||
\(802\) | −1.07961e12 | −0.0921473 | ||||||||
\(803\) | 1.76029e12 | 0.149405 | ||||||||
\(804\) | −7.14520e12 | −0.603062 | ||||||||
\(805\) | −8.59480e12 | −0.721364 | ||||||||
\(806\) | 3.29564e11 | 0.0275063 | ||||||||
\(807\) | 7.62405e12 | 0.632783 | ||||||||
\(808\) | 4.43291e12 | 0.365880 | ||||||||
\(809\) | −3.43704e12 | −0.282109 | −0.141054 | − | 0.990002i | \(-0.545049\pi\) | ||||
−0.141054 | + | 0.990002i | \(0.545049\pi\) | |||||||
\(810\) | 3.69804e12 | 0.301849 | ||||||||
\(811\) | −1.68173e13 | −1.36509 | −0.682545 | − | 0.730843i | \(-0.739127\pi\) | ||||
−0.682545 | + | 0.730843i | \(0.739127\pi\) | |||||||
\(812\) | 3.39830e11 | 0.0274322 | ||||||||
\(813\) | 1.84589e13 | 1.48183 | ||||||||
\(814\) | −8.38008e11 | −0.0669019 | ||||||||
\(815\) | 2.13252e13 | 1.69310 | ||||||||
\(816\) | −2.39390e13 | −1.89017 | ||||||||
\(817\) | 1.76207e10 | 0.00138364 | ||||||||
\(818\) | 2.13407e12 | 0.166655 | ||||||||
\(819\) | −3.08366e12 | −0.239491 | ||||||||
\(820\) | 3.19485e13 | 2.46768 | ||||||||
\(821\) | −3.29338e12 | −0.252987 | −0.126494 | − | 0.991967i | \(-0.540372\pi\) | ||||
−0.126494 | + | 0.991967i | \(0.540372\pi\) | |||||||
\(822\) | 2.16824e12 | 0.165647 | ||||||||
\(823\) | −1.56498e13 | −1.18907 | −0.594536 | − | 0.804069i | \(-0.702664\pi\) | ||||
−0.594536 | + | 0.804069i | \(0.702664\pi\) | |||||||
\(824\) | −5.05529e12 | −0.382009 | ||||||||
\(825\) | 7.79628e12 | 0.585929 | ||||||||
\(826\) | −1.06844e12 | −0.0798616 | ||||||||
\(827\) | 1.49483e13 | 1.11126 | 0.555630 | − | 0.831430i | \(-0.312477\pi\) | ||||
0.555630 | + | 0.831430i | \(0.312477\pi\) | |||||||
\(828\) | −4.27276e13 | −3.15916 | ||||||||
\(829\) | 6.90186e12 | 0.507540 | 0.253770 | − | 0.967265i | \(-0.418329\pi\) | ||||
0.253770 | + | 0.967265i | \(0.418329\pi\) | |||||||
\(830\) | −2.65878e12 | −0.194460 | ||||||||
\(831\) | 1.05917e13 | 0.770477 | ||||||||
\(832\) | 3.53494e12 | 0.255757 | ||||||||
\(833\) | −2.15488e12 | −0.155068 | ||||||||
\(834\) | −4.46000e12 | −0.319218 | ||||||||
\(835\) | −3.17521e12 | −0.226039 | ||||||||
\(836\) | 2.28326e12 | 0.161669 | ||||||||
\(837\) | 2.86238e13 | 2.01587 | ||||||||
\(838\) | 1.72655e12 | 0.120943 | ||||||||
\(839\) | 1.53766e13 | 1.07135 | 0.535673 | − | 0.844425i | \(-0.320058\pi\) | ||||
0.535673 | + | 0.844425i | \(0.320058\pi\) | |||||||
\(840\) | −3.06391e12 | −0.212334 | ||||||||
\(841\) | −1.44287e13 | −0.994591 | ||||||||
\(842\) | −1.74225e12 | −0.119455 | ||||||||
\(843\) | 1.38711e13 | 0.945988 | ||||||||
\(844\) | −1.80284e13 | −1.22297 | ||||||||
\(845\) | −1.55281e12 | −0.104776 | ||||||||
\(846\) | −3.17499e12 | −0.213096 | ||||||||
\(847\) | −4.85251e12 | −0.323960 | ||||||||
\(848\) | −9.27762e12 | −0.616106 | ||||||||
\(849\) | 1.56333e13 | 1.03268 | ||||||||
\(850\) | 1.61833e12 | 0.106336 | ||||||||
\(851\) | 3.31267e13 | 2.16519 | ||||||||
\(852\) | −1.37081e12 | −0.0891251 | ||||||||
\(853\) | 2.50784e13 | 1.62192 | 0.810960 | − | 0.585102i | \(-0.198945\pi\) | ||||
0.810960 | + | 0.585102i | \(0.198945\pi\) | |||||||
\(854\) | −4.92072e11 | −0.0316569 | ||||||||
\(855\) | 2.10735e13 | 1.34862 | ||||||||
\(856\) | −6.39488e12 | −0.407099 | ||||||||
\(857\) | −1.08161e12 | −0.0684945 | −0.0342472 | − | 0.999413i | \(-0.510903\pi\) | ||||
−0.0342472 | + | 0.999413i | \(0.510903\pi\) | |||||||
\(858\) | 3.45463e11 | 0.0217625 | ||||||||
\(859\) | 6.50623e12 | 0.407718 | 0.203859 | − | 0.979000i | \(-0.434652\pi\) | ||||
0.203859 | + | 0.979000i | \(0.434652\pi\) | |||||||
\(860\) | −6.88438e10 | −0.00429162 | ||||||||
\(861\) | 2.02779e13 | 1.25750 | ||||||||
\(862\) | −2.75330e12 | −0.169852 | ||||||||
\(863\) | 1.96548e13 | 1.20620 | 0.603100 | − | 0.797666i | \(-0.293932\pi\) | ||||
0.603100 | + | 0.797666i | \(0.293932\pi\) | |||||||
\(864\) | −1.28752e13 | −0.786033 | ||||||||
\(865\) | 1.64529e13 | 0.999240 | ||||||||
\(866\) | 3.04275e12 | 0.183838 | ||||||||
\(867\) | 5.37479e12 | 0.323054 | ||||||||
\(868\) | −5.40143e12 | −0.322976 | ||||||||
\(869\) | −3.52613e12 | −0.209753 | ||||||||
\(870\) | −3.51381e11 | −0.0207941 | ||||||||
\(871\) | −1.58842e12 | −0.0935157 | ||||||||
\(872\) | 9.02251e11 | 0.0528449 | ||||||||
\(873\) | −3.40285e13 | −1.98280 | ||||||||
\(874\) | 1.19983e12 | 0.0695536 | ||||||||
\(875\) | 1.29179e12 | 0.0744997 | ||||||||
\(876\) | −1.23211e13 | −0.706938 | ||||||||
\(877\) | 6.41797e12 | 0.366353 | 0.183176 | − | 0.983080i | \(-0.441362\pi\) | ||||
0.183176 | + | 0.983080i | \(0.441362\pi\) | |||||||
\(878\) | −8.12369e11 | −0.0461348 | ||||||||
\(879\) | 7.14166e12 | 0.403505 | ||||||||
\(880\) | −8.80051e12 | −0.494693 | ||||||||
\(881\) | 6.78986e12 | 0.379725 | 0.189862 | − | 0.981811i | \(-0.439196\pi\) | ||||
0.189862 | + | 0.981811i | \(0.439196\pi\) | |||||||
\(882\) | −6.71846e11 | −0.0373819 | ||||||||
\(883\) | −3.84292e12 | −0.212734 | −0.106367 | − | 0.994327i | \(-0.533922\pi\) | ||||
−0.106367 | + | 0.994327i | \(0.533922\pi\) | |||||||
\(884\) | −5.39445e12 | −0.297107 | ||||||||
\(885\) | −8.31054e13 | −4.55391 | ||||||||
\(886\) | −1.31010e11 | −0.00714256 | ||||||||
\(887\) | −1.12350e13 | −0.609419 | −0.304710 | − | 0.952445i | \(-0.598559\pi\) | ||||
−0.304710 | + | 0.952445i | \(0.598559\pi\) | |||||||
\(888\) | 1.18092e13 | 0.637325 | ||||||||
\(889\) | 6.32336e12 | 0.339540 | ||||||||
\(890\) | 4.04075e11 | 0.0215877 | ||||||||
\(891\) | 1.37586e13 | 0.731347 | ||||||||
\(892\) | −4.01359e12 | −0.212271 | ||||||||
\(893\) | −6.70688e12 | −0.352931 | ||||||||
\(894\) | 7.70185e11 | 0.0403252 | ||||||||
\(895\) | 4.53179e13 | 2.36084 | ||||||||
\(896\) | 3.23206e12 | 0.167530 | ||||||||
\(897\) | −1.36563e13 | −0.704315 | ||||||||
\(898\) | −2.17238e11 | −0.0111479 | ||||||||
\(899\) | −1.24715e12 | −0.0636794 | ||||||||
\(900\) | −3.79559e13 | −1.92836 | ||||||||
\(901\) | 1.37688e13 | 0.696040 | ||||||||
\(902\) | −1.58011e12 | −0.0794799 | ||||||||
\(903\) | −4.36956e10 | −0.00218697 | ||||||||
\(904\) | 4.42011e12 | 0.220128 | ||||||||
\(905\) | −8.85418e12 | −0.438763 | ||||||||
\(906\) | −6.39669e12 | −0.315412 | ||||||||
\(907\) | −1.22450e13 | −0.600796 | −0.300398 | − | 0.953814i | \(-0.597119\pi\) | ||||
−0.300398 | + | 0.953814i | \(0.597119\pi\) | |||||||
\(908\) | −3.96567e13 | −1.93611 | ||||||||
\(909\) | 7.56073e13 | 3.67305 | ||||||||
\(910\) | −3.38315e11 | −0.0163544 | ||||||||
\(911\) | −2.30193e13 | −1.10728 | −0.553641 | − | 0.832755i | \(-0.686762\pi\) | ||||
−0.553641 | + | 0.832755i | \(0.686762\pi\) | |||||||
\(912\) | −1.57663e13 | −0.754664 | ||||||||
\(913\) | −9.89199e12 | −0.471157 | ||||||||
\(914\) | 3.83233e12 | 0.181637 | ||||||||
\(915\) | −3.82745e13 | −1.80516 | ||||||||
\(916\) | 3.56488e13 | 1.67307 | ||||||||
\(917\) | 8.68093e12 | 0.405419 | ||||||||
\(918\) | 6.22829e12 | 0.289452 | ||||||||
\(919\) | 2.26848e13 | 1.04909 | 0.524547 | − | 0.851381i | \(-0.324235\pi\) | ||||
0.524547 | + | 0.851381i | \(0.324235\pi\) | |||||||
\(920\) | −9.43778e12 | −0.434335 | ||||||||
\(921\) | 6.45941e13 | 2.95818 | ||||||||
\(922\) | −3.77105e12 | −0.171859 | ||||||||
\(923\) | −3.04740e11 | −0.0138205 | ||||||||
\(924\) | −5.66201e12 | −0.255533 | ||||||||
\(925\) | 2.94273e13 | 1.32164 | ||||||||
\(926\) | 3.11821e12 | 0.139366 | ||||||||
\(927\) | −8.62225e13 | −3.83497 | ||||||||
\(928\) | 5.60974e11 | 0.0248300 | ||||||||
\(929\) | −3.10075e13 | −1.36583 | −0.682915 | − | 0.730498i | \(-0.739288\pi\) | ||||
−0.682915 | + | 0.730498i | \(0.739288\pi\) | |||||||
\(930\) | 5.58501e12 | 0.244822 | ||||||||
\(931\) | −1.41922e12 | −0.0619120 | ||||||||
\(932\) | 2.93121e13 | 1.27255 | ||||||||
\(933\) | 6.76736e13 | 2.92383 | ||||||||
\(934\) | 3.34363e12 | 0.143766 | ||||||||
\(935\) | 1.30607e13 | 0.558876 | ||||||||
\(936\) | −3.38611e12 | −0.144198 | ||||||||
\(937\) | 5.09355e12 | 0.215870 | 0.107935 | − | 0.994158i | \(-0.465576\pi\) | ||||
0.107935 | + | 0.994158i | \(0.465576\pi\) | |||||||
\(938\) | −3.46075e11 | −0.0145968 | ||||||||
\(939\) | −8.51375e13 | −3.57376 | ||||||||
\(940\) | 2.62037e13 | 1.09468 | ||||||||
\(941\) | 4.47730e12 | 0.186150 | 0.0930749 | − | 0.995659i | \(-0.470330\pi\) | ||||
0.0930749 | + | 0.995659i | \(0.470330\pi\) | |||||||
\(942\) | 9.20570e12 | 0.380915 | ||||||||
\(943\) | 6.24622e13 | 2.57226 | ||||||||
\(944\) | 4.32465e13 | 1.77246 | ||||||||
\(945\) | −2.93838e13 | −1.19857 | ||||||||
\(946\) | 3.40487e9 | 0.000138226 0 | ||||||||
\(947\) | −3.14466e13 | −1.27057 | −0.635286 | − | 0.772277i | \(-0.719118\pi\) | ||||
−0.635286 | + | 0.772277i | \(0.719118\pi\) | |||||||
\(948\) | 2.46810e13 | 0.992487 | ||||||||
\(949\) | −2.73906e12 | −0.109624 | ||||||||
\(950\) | 1.06584e12 | 0.0424557 | ||||||||
\(951\) | −2.13754e13 | −0.847427 | ||||||||
\(952\) | −2.36624e12 | −0.0933666 | ||||||||
\(953\) | 4.14945e13 | 1.62957 | 0.814783 | − | 0.579765i | \(-0.196856\pi\) | ||||
0.814783 | + | 0.579765i | \(0.196856\pi\) | |||||||
\(954\) | 4.29282e12 | 0.167793 | ||||||||
\(955\) | −4.72575e12 | −0.183847 | ||||||||
\(956\) | 2.02755e13 | 0.785075 | ||||||||
\(957\) | −1.30731e12 | −0.0503820 | ||||||||
\(958\) | 1.93154e12 | 0.0740897 | ||||||||
\(959\) | −7.90001e12 | −0.301609 | ||||||||
\(960\) | 5.99055e13 | 2.27639 | ||||||||
\(961\) | −6.61687e12 | −0.250263 | ||||||||
\(962\) | 1.30396e12 | 0.0490881 | ||||||||
\(963\) | −1.09070e14 | −4.08685 | ||||||||
\(964\) | 4.21340e12 | 0.157140 | ||||||||
\(965\) | 9.58154e12 | 0.355682 | ||||||||
\(966\) | −2.97534e12 | −0.109936 | ||||||||
\(967\) | 4.47611e13 | 1.64620 | 0.823098 | − | 0.567900i | \(-0.192244\pi\) | ||||
0.823098 | + | 0.567900i | \(0.192244\pi\) | |||||||
\(968\) | −5.32845e12 | −0.195057 | ||||||||
\(969\) | 2.33986e13 | 0.852576 | ||||||||
\(970\) | −3.73334e12 | −0.135402 | ||||||||
\(971\) | 1.13104e13 | 0.408311 | 0.204155 | − | 0.978939i | \(-0.434555\pi\) | ||||
0.204155 | + | 0.978939i | \(0.434555\pi\) | |||||||
\(972\) | −3.23627e13 | −1.16291 | ||||||||
\(973\) | 1.62501e13 | 0.581230 | ||||||||
\(974\) | −1.54578e12 | −0.0550342 | ||||||||
\(975\) | −1.21312e13 | −0.429915 | ||||||||
\(976\) | 1.99174e13 | 0.702599 | ||||||||
\(977\) | −4.12140e13 | −1.44717 | −0.723585 | − | 0.690235i | \(-0.757507\pi\) | ||||
−0.723585 | + | 0.690235i | \(0.757507\pi\) | |||||||
\(978\) | 7.38232e12 | 0.258029 | ||||||||
\(979\) | 1.50336e12 | 0.0523048 | ||||||||
\(980\) | 5.54485e12 | 0.192032 | ||||||||
\(981\) | 1.53887e13 | 0.530508 | ||||||||
\(982\) | 1.38023e12 | 0.0473641 | ||||||||
\(983\) | 2.16993e12 | 0.0741233 | 0.0370617 | − | 0.999313i | \(-0.488200\pi\) | ||||
0.0370617 | + | 0.999313i | \(0.488200\pi\) | |||||||
\(984\) | 2.22668e13 | 0.757147 | ||||||||
\(985\) | −2.02642e13 | −0.685908 | ||||||||
\(986\) | −2.71368e11 | −0.00914351 | ||||||||
\(987\) | 1.66317e13 | 0.557839 | ||||||||
\(988\) | −3.55281e12 | −0.118622 | ||||||||
\(989\) | −1.34596e11 | −0.00447351 | ||||||||
\(990\) | 4.07206e12 | 0.134727 | ||||||||
\(991\) | 3.84824e13 | 1.26745 | 0.633725 | − | 0.773559i | \(-0.281525\pi\) | ||||
0.633725 | + | 0.773559i | \(0.281525\pi\) | |||||||
\(992\) | −8.91639e12 | −0.292339 | ||||||||
\(993\) | −2.29429e13 | −0.748819 | ||||||||
\(994\) | −6.63947e10 | −0.00215722 | ||||||||
\(995\) | −4.20084e13 | −1.35873 | ||||||||
\(996\) | 6.92386e13 | 2.22936 | ||||||||
\(997\) | −5.11699e13 | −1.64016 | −0.820080 | − | 0.572249i | \(-0.806071\pi\) | ||||
−0.820080 | + | 0.572249i | \(0.806071\pi\) | |||||||
\(998\) | 2.47691e12 | 0.0790355 | ||||||||
\(999\) | 1.13253e14 | 3.59755 |
(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 | 91.10.a.c.1.7 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.10.a.c.1.7 | ✓ | 14 | 1.1 | even | 1 | trivial |